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We have been working very hard since 2009 to facilitate in your learning Read More. We can't keep up without your support. Donate Now. www.vustudents.ning.com www.bit.ly/vucodes + Link For Assignments, GDBs & Online Quizzes Solution www.bit.ly/papersvu + Link For Past Papers, Solved MCQs, Short Notes & More # MTH302 GDB-2 Closing Date 18-08-2015 In a hospital, births occur randomly at an average rate of 2 births per hour. Calculate the probability of observing 1.     3 births in a given hour at the hospital. 2.     No birth in a given hour at the hospital." Opening Date of Graded Discussion Board: Friday, August 14, 2015 at 12:01 a.m. Closing Date of Graded Discussion Board: + http://bit.ly/vucodes (Link for Assignments, GDBs & Online Quizzes Solution) + http://bit.ly/papersvu (Link for Past Papers, Solved MCQs, Short Notes & More) Views: 4190 ### Replies to This Discussion Question 1 Find the centered average and trends in the following data: Quarter Actual Moving Average Centered Average Trends 1 143 2 56 3 164 141 4 208 138 1 132 137 2 52 140 3 176 138 4 198 137 1 126 135 2 44 132 3 164 129 4 188 Let X = No birth in a given hour at the hospital Events occur randomly Mean rate λ = 2 ⇒ X ∼ Po (2) We want P(X ≥ 2) = P(X = 2) + P(X = 3) + ... i.e. an infinite number of probabilities to calculate but P(X ≥ 2) = P(X = 2) + P(X = 3) + ... = 1 − P(X < 2) = 1 − (P(X = 0) + P(X = 1)) = 1 − (e−1.8 1.80 0! + e−1.8 1.81 1! ) = 1 − (0.16529 + 0.29753) = 0.537 yeh theak ans kia 2.1 Examples Births in a hospital occur randomly at an average rate of 1.8 births per hour. What is the probability of observing 4 births in a given hour at the hospital? Let X = No. of births in a given hour (i) Events occur randomly (ii) Mean rate λ = 1.8 ⇒ X ∼ Po(1.8) We can now use the formula to calculate the probability of observing exactly 4 births in a given hour P(X = 4) = e−1.8 1.84 4! = 0.0723 Please let me know the handout lecture or page no. just for the reference?? 100% correct 1-   0.180447 2-   0.135335 Dear, i have different answers how you're saying its 100 % correct? P(X=x)= at page 279 please tell me handout lecture or page no. just for the reference?? P(X=x)= at page 279 ## Latest Activity + ! ! ! Haniya ! ! + liked + ! ! ! Haniya ! ! +'s discussion لمحے 1 hour ago + ! ! ! Haniya ! ! + posted a discussion ### لمحے 1 hour ago 1 hour ago 3 hours ago Bakhtawar khan liked +!!!StRaNGeR!!! +'s discussion میں ایسی محبت کرتا ہوں 4 hours ago 4 hours ago 1 2 3 ## HELP SUPPORT This is a member-supported website. Your contribution is greatly appreciated!

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Most people have occasional lapses in memory, such as forgetting a new acquaintance’s name or misplacing the car keys. Most of the time, this is simply a sign that a person is a bit too busy or is preoccupied. On the other hand, having a consistently poor memory can be problematic for someone. Many factors play a role in memory loss, including genetics, age, and medical conditions that affect the brain. There are also some manageable risk factors for memory loss, such as diet and lifestyle. While not all memory loss is preventable, people may be able to take measures to protect the brain against cognitive decline as they age. In this article, learn about techniques to try to help improve your memory. Do brain training There are many brain training activities online that may help improve a person’s memory. In a similar way to muscles, the brain needs regular use to stay healthy. Mental workouts are just as essential to the gray matter as other factors, and challenging the mind can help it grow and expand, which may improve memory. A large trial from the journal PLoS One found that people who did just 15 minutes of brain training activities at least 5 days a week had improvements in brain function. The participants’ working memory, short term memory, and problem-solving skills all significantly improved when researchers compared them to a control group doing crossword puzzles. The researchers used brain training activities from the website Lumosity. The challenges work on a person’s ability to recall details and quickly memorize patterns. Physical exercise has a direct impact on brain health. As the author of research in the Journal of Exercise Rehabilitation notes, regular exercise reduces the risk of cognitive decline with age and protects the brain against degeneration. The results of a study suggest that aerobic exercise can improve memory function in people with early Alzheimer’s disease. The control group did nonaerobic stretching and toning. Aerobic exercise increases a person’s heart rate and can include any of these activities: Research suggests that meditation may cause long term changes in the brain that improve memory. Mindfulness meditation may help improve memory. The authors of a 2018 research paper note that many studies show. Meditation improves brain function, reduces markers of brain degeneration, and improves both working memory and long term memory. The researchers observed the brains of people who regularly practiced meditation and those who did not. Their results indicated that making a habit of meditating may cause long term changes in the brain, including increasing brain plasticity, which helps keep it healthy. Get enough sleep Sleep is vital for overall brain health. Disrupting the body’s natural sleep cycle can lead to cognitive impairments. As this interrupts the processes the brain uses to create memories. Getting a full night’s rest, typically about 7–9 hours a night for an adult, helps the brain create and store long term memories. Reduce sugar intake Sugary foods can taste delicious and feel rewarding at first, but they may play a role in memory loss. Research from 2017 in animal models noted that a diet high in sugary drinks has a link to Alzheimer’s disease. The researchers also found that drinking too many sugary drinks including fruit juice may have a connection a lower total brain volume Which is an early sign of Alzheimer’s disease. Avoiding extra sugar may help combat this risk. While naturally sweet foods, such as fruits, are a good addition to a healthful diet. People can avoid drinks sweetened with sugar and foods with added, processed sugars. Avoid high-calorie diets Along with cutting out sources of excess sugar, reducing overall caloric intake may also help protect the brain. Researchers note that high-calorie diets can impair memory and lead to obesity. The effects on memory may be due to how high-calorie diets lead to inflammation in particular parts of the brain. While most research in this area has been with animals, a study from looked at whether restricting calories in humans could improve memory. Female participants with an average age of 60.5 years reduced their calorie intake by 30%. The researchers found that they had a significant improvement in verbal memory scores and that the benefit was most significant in those who stuck to the diet best. Increase caffeine intake Caffeine from sources such as coffee or green tea may be helpful for the memory. The authors of a study found that consuming caffeine after a memory test boosted how well participants’ brain stored memories long term. People who took 200 milligrams of caffeine scored better on recall tests after 24 hours than people who did not take caffeine. Caffeine may also boost memory in the short term. A study in Frontiers in Psychology found that young adults who took caffeine in the morning had improved short term memory. This insight might be useful for individuals who have to take tests or recall information during a time of day when they may otherwise be tired. Eat dark chocolate Eating dark chocolate sounds like an indulgence, but it may also improve a person’s memory. The results of a study suggest that cocoa flavonoids, which are the active compounds in chocolate, help boost brain function. People who ate dark chocolate performed better on spatial memory tests than those who did not. The researchers noted that cocoa flavonoids improved the blood flow to the brain. With that said, it is important not to add more sugar to the diet, and so people should aim for at least 72% cacao content in dark chocolate and avoid chocolate with added sugar. Risk factors for memory impairment Exercising regularly may help keep the mind sharp. Some people may be more prone to memory impairment than others due to a range of risk factors. There are risk factors a person has no control over, such as genetics. Some people may be more predisposed to conditions, such as Alzheimer’s, which greatly affect the brain and memory. In other cases, a person may be able to reduce the risk of memory impairment. Eating a diet high in refined sugar and fats and leading a sedentary lifestyle may increase the risk of memory loss. Eating a rounded, healthful diet and exercising regularly may contribute to keeping the mind sharp and reduce memory loss. Many techniques for improving memory can be beneficial for a person’s overall health and well-being. For example, practicing mindfulness meditation may not only make a person less forgetful but can also reduce stress. Even adding one or two memory-boosting practices to a person’s daily routine may help them keep their brain healthy and protect it from memory loss 🙂 🙂

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Kennedy and McNamara The Secretary of Defense. McNamara was optomistic about the US' inolvement in Vietnam. Often elliminated the human factor of war. "Never walked, only ran." Advocated for large scale bombings in Vietnam. Dynamic, toughtalking, fluent, competent and down to earth, McNamara became part of Kennedy's inner circle. McNamara was emotional and passionate about his beliefs. He was commended for his efficiency but people often worried about his arrogant belief that he was always right. He greatly encouraged Kennedy to send ground troops. Kennedy and Dean Rusk Secretary of State. Determined to oppose what he saw as Communist aggression and was a hard-line Cold Warrior. Kennedy sometimes called Rusk a "good errand boy". Kennedy wanted to dominate foreign policy, which Rusk knew little about. "Kennedy and I simply found it impossible to communicate. He didn't understand me and I didn't understand him." Rusk supported American involvement in Vietnam, but as the fighting continued, he begun to see it as a Defence Department problem. The president often complained that Rusk was methodical, frustrating, slow and indecisive. Rusk felt it his duty to put all the options before the president so that Kennedy could make an informed decision. Kennedy, however, wanted decisive recommendations. Kennedy was the youngest elected president so felt as if he had to prove himself. He criticised Truman for losing China in 1949 so couldn't do the same in Vietnam. Criticised Eisenhower for losing initiative in foreign policy. McCarthy was a close family friend and even dated Kennedy's sister. He was deeply Catholic and believed that all Communists were atheists. Afraid of USSR and Chinese involvement in Vietnam. A strong believer in the Domino Theory. Called Vietnam the "finger in the dyke" and believed Southeast Asia was the new Cold War battle ground. McNamara often pushed Kennedy towards greater involvement in Vietnam. The Buddhist Crisis Diem banned buddhists from flying kites in honour of Buddha's birthday, even though he allowed Catholics to fly kites to celebrate the Archbishop's birthday. 10,000 buddhists protested against Diem's regime. 1 buddhist set himself on fire in public in protest. Madam Nhu (Vietnam's first lady) announced that she would provide the matches and clap as the buddhists burnt. Diem ordered raids on buddhist monastaries and 14,000 buddhists were arrested. Kennedy said he had no idea that Catholic-Buddhists tensions were so great. If Kennedy truly didn't know about these tensions, then his research had been lax. He was probably using his favourite tactic of deflecting the blame (he'd blamed intelligence for the Bay of Pigs Fiasco). Strategic Hamlets Program Ran by Ngo Dinh Nhu, Diem's brother, who was greatly disliked. Based on agrovilles. "No Nhus is good news" Fortified villages to try and protect the people from the VC. Peasants were forced to move, build and pay for these villages. VC used this to their advantage. Many strategic hamlets were built too far away from Saigon, and so the VC managed to infiltrate them. 3225 Strategic Hamlets by December 1962. Later, it was revealed that Nhu's deputy was a communist who did everything to sabotage the scheme. Unpopular policies and personalities of Diem and his family lead to opposition to Diem and the US. The Coup Against Diem Admin disunity, Diem's failures, Nhu and US involvement led to a coup against the Diem regime. Lodge was pleased with the plot against Diem and said that the US would support any new government. November 2nd 1963. After the General's coup, Diem and Nhu fled the government buildings. Their bodies were found the next day. Kennedy and Lodge both publically denied that the US had any involvement in the coup and assassinations. Kennedy was assassinated within three weeks in Dallas, Texas. When Madam Nhu, Diem's sister-in-law, heard about Kennedy's death, she said that "the chickens have come home to roost." Withdrawal Debate: For Kennedy planned withdrawal throughout 1962 and 1963. McNamara, Bundy and Kennedy planned withdrawal at the Hondulu Conference July 1962. Kennedy knew that no real headway had been made in Vietnam, and so leaving suddenly was politically impossible. Wouldn't have left Vietnam until after he was re-elected in November 1963. Diem was reforming his airforce and the Corps Zones of Control, suggesting that the Saigon would have the power to cope without US support. Withdrawal Debate: Against Diem's assassination left South Vietnam even more dependant on the US. Laos neutrality had failed within months, Kennedy couldn't let the same thing happen in Vietnam. Couldn't lose Vietnam to communism like Truman lost China in 1949. Kennedy had increased involvement, not decreased it. Military Advisors had increased from 800 to 17,000. Bobby Kennedy claimed that JFK would never have left Vietnam. On November 4th 1963, Kennedy claimed that the US would be increasing support to Vietnam, not reducing it. After Kennedy's death, Hanoi was preparing for a full-scale US attack. Opinions of Others Mike Mansfield disliked escalation in Vietnam (report in 1963) French President de Gaulle said that the communists were appearing as champions of independence in Vietnam. Galbraith (November 1961) said that Vietnam was not important and that it would all end in defeat. McNamara was optomistic and said that the US was winning the war in Vietnam. Under-Secretary of State George Ball said that sending ground troops into Vietnam would cause a rapid escalation that would be unacceptable. Dean Rusk warned that Us involvement would provoke Hanoi and Beijing and destabilise Laos. Warnings made Kennedy cautious about over-extending the US' power. It wasn't as clear cut as Korea. He knew Diem needed more support but was still unwilling to send ground troops. The Battle of Ap Bac The first major battle between the ARVN and the VC were American advisors and materials played a big part. A VC force was located at Ap Bac, not far from Saigon. 2000 ARVN troops and 113 American personnel carriers went to surround Ap Bac. Their info was faulty and 350 guerrillas were waiting for them. ARVN refused to attack fellow Vietnamese and 5 US helicopters and 3 pilots were lost. Strength of the VC was greatly unexpected. Americans had delayed the attack so they could sleep of their New Year's Eve party. Proved that, despite increasing military aid, Diem could not win the war against the Communists. Kennedy's Influences: Cuba and Laos Kennedy claimed the US' major problems were the Congo, Cuba, Laos and Vietnam. Despite warning voices, the US began an unsuccessful anti-Communist invasion at the Bay of Pigs in Cuba 1961. Laos was Kennedy's focus at the beginning of his presidency. He feared a Societ-backed triumph there. Implied that US would become involved in Laos in 1961. Between September 1961 and summer 1962, Kennedy managed to neutralise Laos and the US left. However, Laos' communists were uncooperative and the Vietminh continued using Laos as part of the Ho Chi Minh Trail. Laos' neutrality failed within months. The Bay of Pigs Fiasco and failure in Laos meant Kennedy needed a victory elsewhere. Henry Cabot Lodge replaced Frederick Nolting as Ambassador in August 1963. Lodge was a patriot, war hero, experienced, ambitious and had an interest in foreign affairs. Nolting described Lodge as a "piece of Republican asbestos to keep the heat off Kennedy." Rusk told Lodge to act "tough" and as a "catalyst". Lodge arrived in Vietnam on 22nd August 1963. Lodge gained an usual amount of power in Vietnamese policy due to disunity in Washington. Lodge turned Congress and the US public against Diem and Nhu through staged "press leaks" on their activities and by establishing Buddhist shelters. Lodge couldn't get Diem to listen to US advice and so found ways to avoid ever talking to him. Lodge encouraged ARVN plots against Diem and may have sparked the coup against him in November 1963.

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HW9-10Sol # HW9-10Sol - Oregon State University Physics 201 Fall 2009... This preview shows pages 1–3. Sign up to view the full content. This preview has intentionally blurred sections. Sign up to view the full version. View Full Document This is the end of the preview. Sign up to access the rest of the document. Unformatted text preview: Oregon State University Physics 201 , Fall 2009 HW9 10 (due Dec. 4 at 5:00 p.m.) Page 1 Oregon State University Physics 201 Fall Term, 2009 HW9-10 Solutions 1. A 710-kg car drives at a constant speed of 23 m/s. It is subject to a drag force of 500 N. What power is required from the carʼs engine to drive the car: (a) on level ground? (b) up a hill with a slope of 2.0°? (a) In order to maintain a constant speed, the road must push on the car (i.e. the carʼs tires must push on the road) with a forward force equal but opposite to the drag force: F forward = F D = 500 N And the power supplied via this force is easily calculated: P forward = F forward v forward Doing the numbers: P forward = (500)(23) = 1.15 x 10 4 W (b) To allow the car to climb the hill at that same constant speed, now the forward force must balance the sum of the drag force and the downhill component of the gravitational force: F forward = F D + mg sin θ = 500 + (710)(9.80)·sin2° = 742.83 And again, the power supplied via this force is easily calculated: P forward = F forward v forward Doing the numbers: P forward = (742.83)(23) = 1.71 x 10 4 W Oregon State University Physics 201 , Fall 2009 HW9 10 (due Dec. 4 at 5:00 p.m.) Page 2 2. A certain roller-coaster in California has a circular “loop-the-loop” feature with a radius of 7.00 m. It is designed so that riders are in “free-fall” for the moment when they are at the top of the loop. What speed must the roller coaster have as it enters the loop and begins to climb? (Assume no friction in the track and ignore the slow rotation of the roller coaster.) Analyze the situation from an initial point at the bottom of the loop, where the roller coaster is just entering it (at speed v i ), to the top of the loop, where the roller coaster is moving at (tangential) speed v f . f For the purposes of measuring U G , let h = 0 at the bottom of the loop. The fact that the roller coaster is in free-fall at the top indicates that its weight is the only y-force (i.e. the normal force by the track is momentarily zero), so its weight is equal to the net y-force— the centripetal force that keeps the roller coaster moving in a circular path: mg = mv f 2 / r Simplifying this, we have g = v f 2 / r . Solving for v f 2 ( v f 2 = rg ), we can substitute it into the above result: v i 2 = rg + 4 rg Collect terms: v i 2 = 5 rg Take the square root: v i = (5 rg ) 1/2 The numbers: v i = [5(7.00)(9.80)] 1/2 = 18.5 m/s 7.00 m Analysis of the work being done: There is no work being done by any force except gravity (so W ext = 0). There is the normal force by the track on the roller coaster—but it is always at right angles to the displacement and hence contributes no work.... View Full Document {[ snackBarMessage ]} ### Page1 / 11 HW9-10Sol - Oregon State University Physics 201 Fall 2009... This preview shows document pages 1 - 3. Sign up to view the full document. View Full Document Ask a homework question - tutors are online

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Geometrie-Viereck-Raute Beispiel Nr: 03 $\text{Gegeben:}\\\text{Diagonale f} \qquad f \qquad [m] \\ \text{Fläche} \qquad A \qquad [m^{2}] \\ \\ \text{Gesucht:} \\\text{Diagonale e} \qquad e \qquad [m] \\ \\ e = \frac{2\cdot A}{ f}\\ \textbf{Gegeben:} \\ f=\frac{1}{2}m \qquad A=4m^{2} \qquad \\ \\ \textbf{Rechnung:} \\ e = \frac{2\cdot A}{ f} \\ f=\frac{1}{2}m\\ A=4m^{2}\\ e = \frac{2\cdot 4m^{2}}{ \frac{1}{2}m}\\\\e=16m \\\\\\ \small \begin{array}{|l|} \hline f=\\ \hline \frac{1}{2} m \\ \hline 5 dm \\ \hline 50 cm \\ \hline 500 mm \\ \hline 5\cdot 10^{5} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline A=\\ \hline 4 m^2 \\ \hline 400 dm^2 \\ \hline 4\cdot 10^{4} cm^2 \\ \hline 4\cdot 10^{6} mm^2 \\ \hline \frac{1}{25} a \\ \hline 0,0004 ha \\ \hline \end{array} \small \begin{array}{|l|} \hline e=\\ \hline 16 m \\ \hline 160 dm \\ \hline 1,6\cdot 10^{3} cm \\ \hline 1,6\cdot 10^{4} mm \\ \hline 1,6\cdot 10^{7} \mu m \\ \hline \end{array}$

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Surgery (from the Greek: χειρουργική cheirourgikē, via Latin: chirurgiae, meaning "hand work") is a medical specialty that uses operative manual and instrumental techniques on a patient to investigate and/or treat a pathological condition such as disease or injury, to help improve bodily function or appearance, or sometimes for some other reason. An act of performing surgery may be called a surgical procedure, operation, or simply surgery. In this context, the verb operating means performing surgery. The adjective surgical means pertaining to surgery; e.g. surgical instruments or surgical nurse. The patient or subject on which the surgery is performed can be a person or an animal. A surgeon is a person who performs operations on patients. Persons described as surgeons are commonly medical practitioners, but the term is also applied to physicians, podiatric physicians, dentists and veterinarians. Surgery can last from minutes to hours, but is typically not an ongoing or periodic type of treatment. The term surgery can also refer to the place where surgery is performed, or simply the office of a physician, dentist, or veterinarian. Sorry, no news articles match your request Please, allow us to send you push notifications with new Alerts.

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Alien Microbes Not Welcome: Reducing Back Contamination on Apollo 11 When NASA set its sights on the moon in the 1960s, no one knew if lunar dust held exotic life forms or not. What if a nasty bug lived on our nearest celestial neighbor? And what if said bug made it back to Earth and upset the planet's delicate ecological balance? These weren't just concerns of the U.S. space program. Nope, author Michael Crichton posed them, too. In May 1969, just two months before Apollo 11 would carry the first humans to walk on another celestial body, Crichton published "The Andromeda Strain," a cautionary tale about dangerous microorganisms carried to Earth on a spacecraft. The best-seller ignited fears about the consequences of a space mission contaminating our planet. NASA, of course, had already worked hard to develop stringent planetary protection guidelines by then, but it redoubled its efforts to help soothe public concerns. Like we talked about, NASA ultimately would deem the moon incapable of supporting life and ease its planetary protection guidelines around lunar missions, but the early Apollo program, especially Apollo 11, models how the space agency has minimized previous back contamination risks. NASA's approach addressed three main concerns: the returning spacecraft, the astronauts and any samples carried back. Let's start with the astronauts. When the Columbia Command Module splashed down in the Pacific Ocean on July 24, 1969, a recovery crew jumped from a helicopter to the floating spacecraft. After attaching a flotation collar to the craft and inflating rafts, one of the crew members opened the hatch to the module, passed over three biological isolation garments (BIGs) and quickly resealed the hatch. This crew member also wore one of the suits to prevent contamination during the hand-off. Once the astronauts sealed themselves safely within their protective garments, the command module hatch was reopened, and they climbed aboard one of the rafts. All three astronauts received a bleach-based sponge bath and then waited as the member of the recovery crew wiped down the hatch and the exhaust vents of the command module with iodine solution. Then the people on the helicopter hoisted the astronauts out of the water and carried them to the deck of the USS Hornet. After an elevator ride down to lower decks, they exited and walked to the mobile quarantine facility (MQF), a sealed chamber that would be their home for several days. The ship transported the facility, with the Apollo crew sealed inside, to Honolulu. Then an airplane carried it to Houston, where a waiting truck whisked the astronauts to the Lunar Receiving Laboratory, or LRL. On July 27, the astronauts walked from the MQF through a sealed tunnel into the lab's crew reception area. The astronauts remained under quarantine in Houston until Aug. 10, while a team of doctors monitored their health and watched for possible infections. When none developed, they were deemed healthy and free of lunar pathogens.

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Another common electrical pressure sensor design works on the principle of differential capacitance. In this design, the sensing element is a taut metal diaphragm located equidistant between two stationary metal surfaces, comprising three plates for a complementary pair of capacitors. An electrically insulating fill fluid (usually a liquid silicone compound) transfers motion from the isolating diaphragms to the sensing diaphragm, and also doubles as an effective dielectric for the two capacitors: Any difference of pressure across the cell causes the diaphragm to flex in the direction of least pressure. The sensing diaphragm is a precision-manufactured spring element, meaning that its displacement is a predictable function of applied force. The applied force in this case can only be a function of differential pressure acting against the surface area of the diaphragm in accordance with the standard force-pressure-area equation F = PA. In this case, we have two forces caused by two fluid pressures working against each other, so our force-pressure-area equation may be rewritten to describe resultant force as a function of differential pressure (P1 − P2) and diaphragm area: F = (P1 − P2)A. Since diaphragm area is constant, and force is predictably related to diaphragm displacement, all we need now in order to infer differential pressure is to accurately measure displacement of the diaphragm. The diaphragm’s secondary function as one plate of two capacitors provides a convenient method for measuring displacement. Since capacitance between conductors is inversely proportional to the distance separating them, capacitance on the low-pressure side will increase while capacitance on the high-pressure side will decrease: A capacitance detector circuit connected to this cell uses a high-frequency AC excitation signal to measure the different in capacitance between the two halves, translating that into a DC signal which ultimately becomes the signal output by the instrument representing pressure. These pressure sensors are highly accurate, stable, and rugged. An interesting feature of this design – using two isolating diaphragms to transfer process fluid pressure to a single sensing diaphragm through an internal “fill fluid” – is that the solid frame bounds the motion of the two isolating diaphragms such that neither one is able to force the sensing diaphragm past its elastic limit. As the illustration shows, the higher-pressure isolating diaphragm gets pushed toward the metal frame, transferring its motion to the sensing diaphragm via the fill fluid. If too much pressure is applied to that side, the isolating diaphragm will merely “flatten” against the solid frame of the capsule and stop moving. This positively limits the isolating diaphragm’s motion so that it cannot possibly exert any more force on the sensing diaphragm, even if additional process fluid pressure is applied. This use of isolating diaphragms and fill fluid to transfer motion to the sensing diaphragm, employed in other styles of differential pressure sensor as well, gives modern differential pressure instruments excellent resistance to over-pressure damage. It should be noted that the use of a liquid fill fluid is key to this overpressure-resistant design. In order for the sensing diaphragm to accurately translate applied pressure into a proportional capacitance, it must not contact the conductive metal frame surrounding it. In order for any diaphragm to be protected against overpressure, however, it must contact a solid backstop to limit further travel. Thus, the need for non-contact (capacitance) and for contact (overpressure protection) are mutually exclusive, making it nearly impossible to perform both functions with a single sensing diaphragm. Using fill fluid to transfer pressure from isolating diaphragms to the sensing diaphragm allows us to separate the function of capacitive measurement (sensing diaphragm) from the function of overpressure protection (isolation diaphragms) so that each diaphragm may be optimized for a separate purpose. A classic example of a pressure instrument based on the differential capacitance sensor is the Rosemount model 1151 differential pressure transmitter, shown in assembled form in the following photograph: By removing four bolts from the transmitter, we are able to remove two flanges from the pressure capsule, exposing the isolating diaphragms to plain view: A close-up photograph shows the construction of one of the isolating diaphragms, which unlike the sensing diaphragm is designed to be very flexible. The concentric corrugations in the metal of the diaphragm allow it to easily flex with applied pressure, transmitting process fluid pressure through the silicone fill fluid to the taut sensing diaphragm inside the differential capacitance cell: The interior of the same differential capacitance sensor (revealed by cutting a Rosemount model 1151 sensor in half with a chop saw) shows the isolating diaphragms, the sensing diaphragm, and the ports connecting them together: Here, the left-side isolating diaphragm is clearer to see than the right-side isolating diaphragm. A feature clearly evident in this photograph is the small clearance between the left-side isolating diaphragm and the internal metal frame, versus the spacious chamber in which the sensing diaphragm resides. Recall that these internal spaces are normally occupied by fill fluid, the purpose of which is to transfer pressure from the isolating diaphragms to the sensing diaphragm. As mentioned before, the solid metal frame limits the travel of each isolating diaphragm in such a way that the higher pressure isolating diaphragm “bottoms out” on the metal frame before the sensing diaphragm can be pushed past its elastic limit. In this way, the sensing diaphragm is protected against damage from overpressure because the isolating diaphragms are simply not allowed to move any farther. The differential capacitance sensor inherently measures differences in pressure applied between its two sides. In keeping with this functionality, this pressure instrument has two threaded ports into which fluid pressure may be applied. A later section in this chapter will elaborate on the utility of differential pressure transmitters. All the electronic circuitry necessary for converting the sensor’s differential capacitance into an electronic signal representing pressure is housed in the blue-colored structure above the capsule and flanges. A more modern realization of the differential capacitance pressure-sensing principle is the Rosemount model 3051 differential pressure transmitter: As is the case with all differential pressure devices, this instrument has two ports through which fluid pressure may be applied to the sensor. The sensor, in turn, responds only to the difference in pressure between the ports. The differential capacitance sensor construction is more complex in this particular pressure instrument, with the plane of the sensing diaphragm perpendicular to the plane of the two isolating diaphragms. This “coplanar” design is more compact than the older style of sensor, and more importantly it isolates the sensing diaphragm from flange bolt stress. Take particular note of how the sensor assembly is not embedded in the solid metal frame as was the case with the original Rosemount design. Instead, the sensor assembly is relatively isolated from the frame, connected only by two capillary tubes joining it to the isolating diaphragms. This way, stresses inside the metal frame imparted by flange bolts have virtually no effect on the sensor. A cutaway model of a Rosemount model 3051S (“supermodule”) DP transmitter shows how this all looks in real life: Process fluid pressure applied to the isolating diaphragm(s) transfers to fill fluid inside the capillary tubes, conveying pressure to the taut diaphragm inside the differential capacitance sensor. Like the classic Rosemount model 1151 design, we see the fill fluid performing multiple functions: - The fill fluid protects the delicate sensing diaphragm from contact with unclean or corrosive process fluids - The fill fluid allows the isolating diaphragms to provide overpressure protection for the sensing diaphragm - The fill fluid provides a medium of constant permittivity for the differential capacitance circuit to function The “supermodule” series of Rosemount pressure transmitters shares the same coplanar design as the earlier 3051 models, but adds a new design feature: inclusion of the electronics within the stainless-steel module rather than the blue-painted upper housing. This feature allows the transmitter size to be significantly reduced if needed for applications with limited space. Credits : Tony R. Kuphaldt – Creative Commons Attribution 4.0 License

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Question # Using the ready reckoner, find the period of interest for an amount equal to Rs 16,939.2, when the principal is Rs 12000 at 9% p.a. Hint: Find the compound interest using the amount and principal for R = 9%. Then find the compound interest for Re1. By using the ready reckoner table find the value corresponding to compound interest at 9%. Ready Reckoner is a pre-calculated table of interest for different amounts and internal rates. Acquired Interest per Rupee, compounded yearly, Years 9% 1 0.09 2 0.1881 3 0.2950 4 0.4116 5 0.5386 From the question, we have been given the Amount, principal and rate of interest. Amount, A = 16939.2 Principal, P = Rs 12000 Rate of interest, r = 9% First we need to find the compound interest. Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words interest on interest. $\Rightarrow$Compound interest = Amount – Principal = A – P = 16939.2 – 12000 = 4939.2 Rupees. Thus we have Rs. 4939.2 as compound interest for the principal of Rs. 12000 at 9%. Now we need to find the compound interest for Re.1. For Rs 12000, the compound interest is Rs 4939.2. Therefore, for Principal Re.1, the compound interest $=\dfrac{4939.2}{12000}=0.4116$ Now from the ready reckoner, find the year corresponding to the compound interest 0.4116. From the table you will get the value as 4. Therefore, the period of interest, n = 4. Note: The ready reckoner table is available for different rates of interest. But for this problem on the value corresponding to the rate of interest 9% is required. The ready reckoner table can be used to facilitate simple calculations, especially for applying the rates of discount, interest, charging etc.

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# The refractive index of ice is 1.31 and that of rock salt is 1.54. Calculate the refractive index of rock salt with respect to the refractive index of ice. By BYJU'S Exam Prep Updated on: September 25th, 2023 The refractive index of ice is 1.31 and that of rock salt is 1.54. The refractive index of rock salt with respect to the refractive index of ice is 1.175. Steps to Calculate the refractive index of rock salt with respect to the refractive index of ice: Given that: Refractive index of ice = 1.31 And Refractive index of rock salt = 1.54 We know that: Refractive index = speed of light in vacuum/ speed of light in the medium Refractive index of rock salt with respect to ice = refractive index of rock salt/ refractive index of ice. Substituting the values in the above formula we get: Refractive index of rock salt with respect to ice = 1.54/ 1.31 = 1.175 Therefore, the Refractive index of rock salt with respect to ice is 1.175 ### Refractive Index • Refraction index and index of refraction are other names for the term efractive index. • The characteristics of the medium affect the speed of light in that medium. • The optical density of the medium affects the speed of electromagnetic waves. • The propensity of the atoms of a substance to restore the absorbed electromagnetic energy is known as optical density. • The optical density of a material determines how fast light travels through it. • The refractive index is one such measure of a medium’s optical density. Summary: ## The refractive index of ice is 1.31 and that of rock salt is 1.54. Calculate the refractive index of rock salt with respect to the refractive index of ice. Ice has a refractive index of 1.31 while rock salt has a refractive index of 1.54. The difference between the refractive indices of ice and rock salt is 1.17. Refractive indexes have no dimensions. It is a measurement of how much slower a light wave would move through a material than it would in a vacuum. POPULAR EXAMS SSC and Bank Other Exams GradeStack Learning Pvt. Ltd.Windsor IT Park, Tower - A, 2nd Floor, Sector 125, Noida, Uttar Pradesh 201303 [email protected]

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Anarchist FAQ/What is Anarchism?/5.7 A.5.7 The May-June Revolt in France, 1968. The May-June events in France placed anarchism back on the radical landscape after a period in which many people had written the movement off as dead. This revolt of ten million people grew from humble beginnings. Expelled by the university authorities of Nanterre in Paris for anti-Vietnam War activity, a group of anarchists (including Daniel Cohn-Bendit) promptly called a protest demonstration. The arrival of 80 police enraged many students, who quit their studies to join the battle and drive the police from the university. Inspired by this support, the anarchists seized the administration building and held a mass debate. The occupation spread, Nanterre was surrounded by police, and the authorities closed the university down. The next day, the Nanterre students gathered at the Sorbonne University in the centre of Paris. Continual police pressure and the arrest of over 500 people caused anger to erupt into five hours of street fighting. The police even attacked passers-by with clubs and tear gas. A total ban on demonstrations and the closure of the Sorbonne brought thousands of students out onto the streets. Increasing police violence provoked the building of the first barricades. Jean Jacques Lebel, a reporter, wrote that by 1 a.m., "[l]iterally thousands helped build barricades. . . women, workers, bystanders, people in pyjamas, human chains to carry rocks, wood, iron." An entire night of fighting left 350 police injured. On May 7th, a 50,000-strong protest march against the police was transformed into a day-long battle through the narrow streets of the Latin Quarter. Police tear gas was answered by molotov cocktails and the chant "Long Live the Paris Commune!" By May 10th, continuing massive demonstrations forced the Education Minister to start negotiations. But in the streets, 60 barricades had appeared and young workers were joining the students. The trade unions condemned the police violence. Huge demonstrations throughout France culminated on May 13th with one million people on the streets of Paris. Faced with this massive protest, the police left the Latin Quarter. Students seized the Sorbonne and created a mass assembly to spread the struggle. Occupations soon spread to every French University. From the Sorbonne came a flood of propaganda, leaflets, proclamations, telegrams, and posters. Slogans such as "Everything is Possible," "Be Realistic, Demand the Impossible," "Life without Dead Times," and "It is Forbidden to Forbid" plastered the walls. "All Power to the Imagination" was on everyone's lips. As Murray Bookchin pointed out, "the motive forces of revolution today. . . are not simply scarcity and material need, but also quality of everyday life,.. the attempt to gain control of one's own destiny." [Post-Scarcity Anarchism, pp. 249-250] Many of the most famous slogans of those days originated from the Situationists. The Situationist International had been formed in 1957 by a small group of dissident radicals and artists. They had developed a highly sophisticated (if jargon riddled) and coherent analysis of modern capitalist society and how to supersede it with a new, freer one. Modern life, they argued, was mere survival rather than living, dominated by the economy of consumption in which everyone, everything, every emotion and relationship becomes a commodity. People were no longer simply alienated producers, they were also alienated consumers. They defined this kind of society as the "Spectacle." Life itself had been stolen and so revolution meant recreating life. The area of revolutionary change was no longer just the workplace, but in everyday existence: "People who talk about revolution and class struggle without referring explicitly to everyday life, without understanding what is subversive about love and what is positive in the refusal of constraints, such people have a corpse in their mouth." [quoted by Clifford Harper, Anarchy: A Graphic Guide, p. 153] Like many other groups whose politics influenced the Paris events, the situationists argued that "the workers' councils are the only answer. Every other form of revolutionary struggle has ended up with the very opposite of what it was originally looking for." [quoted by Clifford Harper, Op. Cit., p. 149] These councils would be self-managed and not be the means by which a "revolutionary" party would take power. Like the anarchists of Noire et Rouge and the libertarian socialists of Socialisme ou Barbarie, their support for a self-managed revolution from below had a massive influence in the May events and the ideas that inspired it. Beneath the Paving Stones by Dark Star is a good anthology of situationist works relating to Paris 68 which also contains an eye-witness account of events. On May 14th, the Sud-Aviation workers locked the management in its offices and occupied their factory. They were followed by the Cleon-Renault, Lockhead-Beauvais and Mucel-Orleans factories the next day. That night the National Theatre in Paris was seized to become a permanent assembly for mass debate. Next, France's largest factory, Renault-Billancourt, was occupied. Often the decision to go on indefinite strike was taken by the workers without consulting union officials. By May 17th, a hundred Paris Factories were in the hands of their workers. The weekend of the 19th of May saw 122 factories occupied. By May 20th, the strike and occupations were general and involved six million people. Print workers said they did not wish to leave a monopoly of media coverage to TV and radio, and agreed to print newspapers as long as the press "carries out with objectivity the role of providing information which is its duty." In some cases print-workers insisted on changes in headlines or articles before they would print the paper. This happened mostly with the right-wing papers such as 'Le Figaro' or 'La Nation'. With the Renault occupation, the Sorbonne occupiers immediately prepared to join the Renault strikers, and led by anarchist black and red banners, 4,000 students headed for the occupied factory. The state, bosses, unions and Communist Party were now faced with their greatest nightmare -- a worker-student alliance. Ten thousand police reservists were called up and frantic union officials locked the factory gates. The Communist Party urged their members to crush the revolt. They united with the government and bosses to craft a series of reforms, but once they turned to the factories they were jeered out of them by the workers. The struggle itself and the activity to spread it was organised by self-governing mass assemblies and co-ordinated by action committees. The strikes were often run by assemblies as well. As Murray Bookchin argues, the "hope [of the revolt] lay in the extension of self-management in all its forms -- the general assemblies and their administrative forms, the action committees, the factory strike committees -- to all areas of the economy, indeed to all areas of life itself." [Op. Cit., pp. 251-252] Within the assemblies, "a fever of life gripped millions, a rewaking of senses that people never thought they possessed." [Op. Cit., p. 251] It was not a workers' strike or a student strike. It was a peoples' strike that cut across almost all class lines. On May 24th, anarchists organised a demonstration. Thirty thousand marched towards the Palace de la Bastille. The police had the Ministries protected, using the usual devices of tear gas and batons, but the Bourse (Stock Exchange) was left unprotected and a number of demonstrators set fire to it. It was at this stage that some left-wing groups lost their nerve. The Trotskyist JCR turned people back into the Latin Quarter. Other groups such as UNEF and Parti Socialiste Unife (United Socialist Party) blocked the taking of the Ministries of Finance and Justice. Cohn-Bendit said of this incident "As for us, we failed to realise how easy it would have been to sweep all these nobodies away. . . .It is now clear that if, on 25 May, Paris had woken to find the most important Ministries occupied, Gaullism would have caved in at once. . . . " Cohn-Bendit was forced into exile later that very night. As the street demonstrations grew and occupations continued, the state prepared to use overwhelming means to stop the revolt. Secretly, top generals readied 20,000 loyal troops for use on Paris. Police occupied communications centres like TV stations and Post Offices. By Monday, May 27th, the Government had guaranteed an increase of 35% in the industrial minimum wage and an all round-wage increase of 10%. The leaders of the CGT organised a march of 500,000 workers through the streets of Paris two days later. Paris was covered in posters calling for a "Government of the People." Unfortunately the majority still thought in terms of changing their rulers rather than taking control for themselves. By June 5th most of the strikes were over and an air of what passes for normality within capitalism had rolled back over France. Any strikes which continued after this date were crushed in a military-style operation using armoured vehicles and guns. On June 7th, they made an assault on the Flins steelworks which started a four-day running battle which left one worker dead. Three days later, Renault strikers were gunned down by police, killing two. In isolation, those pockets of militancy stood no chance. On June 12th, demonstrations were banned, radical groups outlawed, and their members arrested. Under attack from all sides, with escalating state violence and trade union sell-outs, the General Strike and occupations crumbled. So why did this revolt fail? Certainly not because "vanguard" Bolshevik parties were missing. It was infested with them. Fortunately, the traditional authoritarian left sects were isolated and outraged. Those involved in the revolt did not require a vanguard to tell them what to do, and the "workers' vanguards" frantically ran after the movement trying to catch up with it and control it. No, it was the lack of independent, self-managed confederal organisations to co-ordinate struggle which resulted in occupations being isolated from each other. So divided, they fell. In addition, Murray Bookchin argues that "an awareness among the workers that the factories had to be worked, not merely occupied or struck," was missing. [Op. Cit., p. 269] This awareness would have been encouraged by the existence of a strong anarchist movement before the revolt. The anti-authoritarian left, though very active, was too weak among striking workers, and so the idea of self-managed organisations and workers self-management was not widespread. However, the May-June revolt shows that events can change very rapidly. The working class, fused by the energy and bravado of the students, raised demands that could not be catered for within the confines of the existing system. The General Strike displays with beautiful clarity the potential power that lies in the hands of the working class. The mass assemblies and occupations give an excellent, if short-lived, example of anarchy in action and how anarchist ideas can quickly spread and be applied in practice.

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# Solving a $1^\infty$ indeterminate form. I'm preparing for my calculus exam and I can't solve this limit: $$\lim_{x\rightarrow\infty}\left(\frac{1+\tan(1/x)}{1-\tan(1/x)}\right)^x$$ The limit tends to $1^\infty$, which is indeterminate. I've tried several things and I couldn't solve it. - A function can tend to some value but the limit never tends, it either is or is not. – lhf Jan 13 '12 at 12:28 @ljf +1, although I couldn't keep from hearing your comment in Yoda's voice, as in, "Do or not do. There is no try." – Rick Decker Jun 8 '12 at 1:22 Note that $$\tag{1}\lim_{x\rightarrow\infty}\left(\frac{1+\tan(1/x)}{1-\tan(1/x)}\right)^x=\lim_{x\rightarrow\infty}e^{\displaystyle x\ln\left(\frac{1+\tan(1/x)}{1-\tan(1/x)}\right)}=e^{\displaystyle\lim_{x\rightarrow\infty}x\ln\left(\frac{1+\tan(1/x)}{1-\tan(1/x)}\right)}$$ since $e^x$ is a continuous function. Note that $$\lim_{x\rightarrow\infty}x\ln\left(\frac{1+\tan(1/x)}{1-\tan(1/x)}\right)= \lim_{x\rightarrow\infty}\frac{\ln\left(\frac{1+\tan(1/x)}{1-\tan(1/x)}\right)}{\frac{1}{x}} \cdot \left(\frac{0}{0}\right)$$ We can apply the L'Hospital rule to the previous limit. Since $$\frac{d}{dx}\ln\left(\frac{1+\tan(1/x)}{1-\tan(1/x)}\right)=\frac{1-\tan(1/x)}{1+\tan(1/x)}\cdot \frac{d}{dx}\left(\frac{1+\tan(1/x)}{1-\tan(1/x)}\right)$$ $$=\frac{1-\tan(1/x)}{1+\tan(1/x)}\cdot \frac{d}{dx}\left(\frac{2}{1-\tan(1/x)}-1\right)=\frac{1-\tan(1/x)}{1+\tan(1/x)}\cdot \frac{2\sec^2(1/x)\cdot(-\frac{1}{x^2})}{(1-\tan(1/x))^2},$$ we have $$\lim_{x\rightarrow\infty}\frac{\ln\left(\frac{1+\tan(1/x)}{1-\tan(1/x)}\right)}{\frac{1}{x}}= \lim_{x\rightarrow\infty}\frac{\frac{1-\tan(1/x)}{1+\tan(1/x)}\cdot \frac{2\sec^2(1/x)\cdot(-\frac{1}{x^2})}{(1-\tan(1/x))^2}}{-\frac{1}{x^2}}$$ $$\tag{2}=\lim_{x\rightarrow\infty}\frac{1-\tan(1/x)}{1+\tan(1/x)}\cdot \frac{2\sec^2(1/x)}{(1-\tan(1/x))^2}=2.$$ Combining $(1)$ and $(2)$, we have $\lim_{x\rightarrow\infty}\left(\frac{1+\tan(1/x)}{1-\tan(1/x)}\right)^x=e^2.$ - using calculator seems like it tends to e^2, still this looks pretty legit. Maybe you had a mistake in the process, im gonna redo the limit using your method. – Alejandro Jan 13 '12 at 12:18 @Alejandro: Thanks! I see the mistake now and I correct it. See my edited answer. – Paul Jan 13 '12 at 12:25 $\frac{d}{dx}\left(\frac{2}{1-\tan(1/x)}-1\right)=\frac{2\sec^2(1/x)\cdot(-\frac‌​{1}{x^2})}{(1-\tan(1/x))^2}$. Originally I missed the $2$ on the right hand side. – Paul Jan 13 '12 at 12:27 Now its perfect, thanks for all :) – Alejandro Jan 13 '12 at 12:28 Often when mathematicians want to write $e^{xyz}$ where $xyz$ is a giant expression, they will write $\exp\{xyz\}$ instead. Otherwise it can be hard to see what is going on. – MJD Jun 5 '12 at 17:58 EDIT: you can write your expression as $$\bigg(1+\frac{2\tan(1/x)}{1-\tan(1/x)}\bigg)^x \sim \bigg(1+\frac{2}{x}\bigg)^x \rightarrow e^2$$ when $x\rightarrow \infty$. - This isn't enough. You need the stronger statement that $\tan(1/x) = 1/x + O(1/|x|^2)$ and even then it still remains to be proven that the $O(1/|x|^2)$ does not affect the value of the limit. – Qiaochu Yuan Jun 6 '12 at 0:42 You can make a direct substitution of equivalent functions without affecting the limit's value. – Oo3 Jun 6 '12 at 7:49 ... when there's no cancellation of homologous terms, but it's understood, I believe. – Oo3 Jun 6 '12 at 12:14 No you can't (depending on what you mean by "equivalent"). For example, $1 \sim 1 + \frac{1}{x}$ as $x \to \infty$, but it doesn't follow that $1^x \sim \left( 1 + \frac{1}{x} \right)^x$. – Qiaochu Yuan Jun 6 '12 at 14:45 It simply isn't (until you prove it), and nothing you've written so far constitutes an argument that it is. For example, $\lim_{x \to \infty} \left(1 + \tan(1/x) - 1/x \right)^{x^3} = e^{1/3}$ but $\lim_{x \to \infty} \left(1 + \frac{1}{x} - \frac{1}{x} \right)^{x^3} = 1$. – Qiaochu Yuan Jun 7 '12 at 13:55 Asymptotics ... \begin{align} \operatorname{tan} \biggl(\frac{1}{x}\biggr) &= \frac{1}{x} + \frac{1}{3 x^{3}} + \frac{2}{15 x^{5}} + O \Bigl(x^{(-6)}\Bigr)\\ 1 + \operatorname{tan} \biggl(\frac{1}{x}\biggr) &= 1 + \frac{1}{x} + \frac{1}{3 x^{3}} + \frac{2}{15 x^{5}} + O \Bigl(x^{(-6)}\Bigr)\\ 1 - \operatorname{tan} \biggl(\frac{1}{x}\biggr) &= 1 - \frac{1}{x} - \frac{1}{3 x^{3}} - \frac{2}{15 x^{5}} + O \Bigl(x^{(-6)}\Bigr)\\\frac{1 + \operatorname{tan} \Bigl(\frac{1}{x}\Bigr)}{1 - \operatorname{tan} \Bigl(\frac{1}{x}\Bigr)} &= 1 + \frac{2}{x} + \frac{2}{x^{2}} + \frac{8}{3 x^{3}} + \frac{10}{3 x^{4}} + \frac{64}{15 x^{5}} + O \Bigl(x^{(-6)}\Bigr)\\\left(\frac{1 + \operatorname{tan} \Bigl(\frac{1}{x}\Bigr)}{1 - \operatorname{tan} \Bigl(\frac{1}{x}\Bigr)}\right)^{x} &= \operatorname{e} ^{2} + \frac{4 \operatorname{e} ^{2}}{3 x^{2}} + \frac{20 \operatorname{e} ^{2}}{9 x^{4}} + O \Bigl(x^{(-5)}\Bigr) \end{align} - this is a really neat solution – roo Jan 13 '12 at 15:55 How do you get from the second-to-last line to the last line? – Michael Lugo Jan 13 '12 at 18:51 Also wondering how you got the last two lines. – Tyler Hilton Jun 5 '12 at 18:32 $(1 + Q)^x = \exp(x \ln(1+Q)) = \exp(x (Q - Q^2/2 + \ldots))$ ... The higher-order terms are best computed by software. Note in this case your function is an even function of $x$: $$\left( \frac{1+\tan(1/(-x))}{1-\tan(1/(-x))}\right)^{-x} = \left( \frac{1-\tan(1/x)}{1+\tan(1/x)}\right)^{-x} = \left( \frac{1+\tan(1/x)}{1-\tan(1/x)}\right)^x$$ so the terms in odd powers of $1/x$ will vanish. – Robert Israel Jun 5 '12 at 18:34 You may let the limit as $z$ and let $y=\ln(z)$, then use L'Hospital rule to find the limits of $y$ and finally $z$ can be calculated $\exp (y)$ - I have an alternative solution without the use of the L'Hospital rule. Start as Paul suggested, but when in the form of $$\lim_{x \to \infty} x \log \left(\frac{1+\tan(1/x)}{1-\tan(1/x)}\right)$$ you can use the fact that $$\lim_{y \to 1} \frac{\log y}{y - 1} = 1.$$ Using this limit, the limit arithmetic and a limit of a composed function. All that helps you transform the limit above into $$\lim_{x \to \infty} x \left(\frac{1+\tan(1/x)}{1-\tan(1/x)} - 1\right) = \lim_{x \to \infty} x \left(\frac{2\tan(1/x)}{1-\tan(1/x)}\right) = \lim_{x \to \infty} 2 \cdot \frac{\tan{1/x}}{\frac 1x}$$ Going from the second part to the third one required yet another arithmetic to get rid of the denominator - that is obviously one, because it is continuous. The last bit can be solved using yet another known limit $$\lim_{y \to 0} \frac{\tan y}{y} = 1$$ So we know the limit is two, we apply the exponential function and get the result $e^2$. Hope this helps as well. (Sorry for the typesetting mess [no eq numbers], I have yet to learn how to work with this system.) - To number, try \tag{1} (or similar) in your euqations, like $$\sin x \tag{1}$$ – Antonio Vargas Jun 5 '12 at 18:40

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## Reflection: Diverse Entry Points Problem Solving with Right Triangles and Trig - Section 3: Homework Review We know that “word problems” are one of the most detested parts of math for students.  In thinking about this matter, I realized this year that many students hate word problems because they have a fixed mindset about solving them: they are either “good” or “bad” at them.   This year, instead of assigning these context problems for homework, I used them as a classwork activity. One thing I decided to do this year was to be cautious in my approach.  I wanted to be sensitive to students’ feelings about themselves as word problem solvers, yet I wanted to maintain high expectations by offering the notion that with effective effort and appropriate problem solving strategies, students could get better at solving word problems.   One such strategy I gave to my students was Talk to the Text (TTTT). A major challenge I face in my classroom is the notion that “fast” = “smart.”  I am always trying to dispel this notion, especially when some students tend to think “if I can’t solve this word problem immediately, then I’ll never be able to solve it.”  I needed my students to understand that any problem worth solving takes time, and that most people do not instantly (or magically) see a solution path.  I needed them to really believe this idea, not just hear me say it.  So, I created a structure where students would have sufficient time to work individually at first so they could actually see that everyone needs time to work through these kinds of problems; I then gave them time to discuss with their group so they could share confusions, offer ideas, get feedback, and think together. Word Problems and Fixed Mindsets: Making Room for Individual and Group TTTT Processing Diverse Entry Points: Word Problems and Fixed Mindsets: Making Room for Individual and Group TTTT Processing # Problem Solving with Right Triangles and Trig Unit 12: Triangle Similarity and Trigonometric Ratios Lesson 7 of 11 ## Big Idea: By playing Trig Tool Tag, students increase participation and confidence in their trigonometry problem solving skills. Print Lesson Add this lesson to your favorites Standards: Subject(s): 55 minutes ### Jessica Uy ##### Similar Lessons ###### Riding a Ferris Wheel - Day 2 of 2 12th Grade Math » Trigonometric Functions Big Idea: Make the transition from the Ferris wheel problem to the unit circle. Favorites(5) Resources(10) Troy, MI Environment: Suburban ###### Final Exam Review Stations (Day 1 of 3) 12th Grade Math » Review Big Idea: Students review by working through various stations at their own pace and receive immediate feedback on their work. Favorites(6) Resources(23) Phoenix, AZ Environment: Urban ###### Problem Solving with Isosceles Triangles and Circles 12th Grade Math » Trigonometry: Circles Big Idea: We’ve seen some of the connections between triangles and circles – here, we lay the groundwork for more! Favorites(0) Resources(14) Worcester, MA Environment: Urban sign up or Something went wrong. See details for more info Nothing to upload details close

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Determining Differences and Disorders Understanding Portuguese Speech and Language Development and Structure will help us know which students have a speech or language impairment and which ones have a speech or language disorder. - Number of speakers: Approximately 215 million worldwide. The largest population of Portuguese speakers is in Brazil followed by Portugal. - Writing system: Latin alphabet; written accents denote irregular stress patterns as well as vowel quality. - Language Family: Romance language; closest relative is Spanish - Official language in: Brazil, Portugal; Portuguese is also spoken in some Asian and African countries. Different dialects are spoken in each of these places. Let’s compare English and Portuguese Speech and Language Development Portuguese Developmental Norms /p, t, k, b, d, g, m, n, ɲ, f, s, ʃ, v, R/ /a, ɐ, i. e. ɛ, o, ɔ, u, ē, ī, ō/ / ʃ (syllable-final position), l, ʎ/ /z, ʒ, ɾ/ /pl, kl, fl/ /ɾ (syllable-final position)/ /fɾ, vɾ, bɾ, pɾ/ /ʄ (syllable-final position)/ /kɾ, tɾ, dɾ, gɾ/ (Lousada, Mendes, Valente, & Hall , 2012) Comparing Portuguese and English Language Structure |Feature||Portuguese||English||Examples of Errors| |Word Order||Subject-Verb-Object||Subject-Verb-Object||No expected errors| |Possessives||Object+of+Person||Possession marked by ‘s||The car of my mom is blue*/ My mom’s car is blue.| |Adjectives||Noun adjective||Adjective noun||The ball big bounced.*/ The big ball bounced.| |Present tense verb inflection|| 5-6 forms, determined by subject: |She talk to me.* / She talks to me.| |Use of subject pronouns||Pro-drop language (pronoun is dropped before verb once subject is established)||Pronoun or subject is always required||Looks for the frog* / He looks for the frog.| |Double negative||Can be used; multiple negative elements occurring in the same clause do not cancel one another but instead reinforce each other||Cannot be used||I don’t want to do nothing*/ I don’t want to do anything.| |Question Formation||Rising intonation is used with word order remaining the same or a question word is used at the beginning of the question with rising intonation.||Questions marked by word order inversion, question words, or addition of do|| You give me a sticker?*/ Will you give me a sticker? What you think?*/ What do you think? We can go?* / Can we go? If you want to hone your skills with English Language Learners, take a look at our CLD Essentials Package that will be available on December 1st. It will includes two online courses and a copy of Difference or Disorder? Understanding Speech and Language Differences in Culturally and Linguistically Diverse Students. Thanks to the great feedback we have gotten from those using the Difference or Disorder book, we’ve set out to make a second edition that will include Filipino/Tagalog, Cambodian, Urdu/Hindi, Ibo, Amharic, Portuguese, Turkish, Hmong, Albanian, Thai, Kinyarwanda, Pashto and Romanian. If there are other languages you would like to see, please let us know. For those not familiar with our current book, we’ve already compared and contrasted English with Spanish, Vietnamese (see post about it), Hebrew, Korean, German, Czech, Japanese, Farsi, Mandarin, French, Russian, Arabic, and the African-American English dialect.

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# Two trains of the same length are running in parallel tracks in the same direction with speeds of 30 km/hr and 45 km/hr respectively. The 2nd train completely crosses the 1st train in 60 seconds. The length of each train (in meters) is 1. 125 m 2. 130 m 3. 150 m 4. 170 m 5. 90 m Option 1 : 125 m Free IBPS Clerk Prelims Full Mock Test 150372 100 Questions 100 Marks 60 Mins ## Detailed Solution Speed of 1st train = 30 km/h Speed of 2nd train = 45 km/h Time taken by 2nd train to cross 1st train completely = 60 seconds Concept: When two trains cross each other, they cover a distance equal to the sum of their lengths with relative speed. Formula Used: Total Length = Time × Relative speed Calculations: Let's take the length of each train to be x. When two trains cross each other, they cover a distance equal to the sum of their lengths with relative speed. The total length of both trains = 2x Time taken by 2nd train to cross 1st train completely = 60 seconds Relative speed = 45 – 30 = 15 km/h ⇒ 15 × 5/18 = 25/6 m/s ∴ Total Length = Time × Relative speed ⇒ 2x = 60 × 25/6 ⇒ x = 10 × 25/2 ⇒ x = 125 m The length of each train is 125 m.

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Upa little-used road in eastern Fiordland lies the site of the world’s largest onshore landslide. Thirteen thousand years ago, as the glaciers retreated, a mountain range collapsed, hurling 27 cubic kilometres of rubble into the valleys below. From Borland Saddle the land now drops in angular blocks and hummocks until it hits the valley floor, where it splays out tangled arms. Down there, webs of standing water transect a rippling carpet of red tussock, Chionochloa rubra. Up on the saddle itself I am standing on dark peaty soil, amongst knee-high tussocks bedecked with tresses of green, olive and gold and with a tousled, blow-dried look. I’m helping Kelvin Lloyd, a scientist from Landcare Research, gather Chionochloa—the genus to which most of our tall tussocks belong—for his studies. He has pointed out a handful of different species en route and I have been doing my best to distinguish between them. “What’s that one?” he asks, nodding at a tussock swooshing against my shins. “I have no idea,” I admit sheepishly. He points out a row of fine blond hairs running up each leaf. Of course, this is Chionochloa teretifolia—the hairy one! How could I forget so quickly? I’m relieved when Kelvin tells me that even botanists find tussocks tricky to identify. Many Chionochloa species look very similar and hybridise where their ranges overlap. New species are still being defined—there may even be one on the gilded summit of nearby Mt Burns, although the jury is still out. And the Borland Saddle region is one of the few places in the country where half a dozen different species grow within waving distance of each other. Despite the abundance of species here, the tall tussocks are mostly parochial, with distinct habitat preferences. For instance, red tussock thrives on waterlogged or frosty flats, C. conspicua occurs at forest margins, C. teretifolia prefers peat. Where conditions are favourable, one can often see great swathes of a single species billowing en masse. C. acicularis, the species with its fine bluish leaves that Lloyd is here to collect, inhabits, in eastern Fiordland at least, slow-seeping gullies—the steeper the better. These boots have almost no traction left,” mutters Lloyd, setting off a small rockslide above a larger slip that stretches away beneath us. With an acicularis in his sights, he unpacks his scientific equipment his grandfather’s First World War entrenching tool and half a dozen well-used plastic bags—and sets about uprooting some young tussocks. A little levering with the entrencher plus a couple of good yanks and the whitish roots essential to a successful transplant emerge reluctantly from the dirt. Wind begins to howl; rain flings itself at us. With four small bags of plant material, we scurry back to the shelter of the car, clinging to tussocks for support. Anyone who has tramped in precipitous tussock country will have relied, at times, on handfuls of well-anchored tussock to haul themselves upward. Despite a number of trampers slipping to their deaths on the slick leaf litter of tussocky bluffs, there are some extraordinary records of the steadfastness of these plants. William Grave, one of Fiordland’s pre-eminent explorers, used tussock as an anchor from which to abseil into Cleddau Valley from Homer Saddle on the first descent of the Grave-Talbot Pass, in January 1910. “We had cut off all chance of climbing back. Downwards we must go. Each further stage was accomplished by tying the ends of a piece of snow grass [an alternative name for some tall tussocks] with a piece of string, and passing the rope through. There was not much danger of the snow grass giving way. The chief risk was that the string might slip off the grass. When our supply of string ran out we used our bootlaces”. This technique is still used by desperate mountaineers on rare occasions. Scientifically speaking, a tussock is not actually a single group of related plants but a growth habit—a particular arrangement of stems and leaves which forms a tuft of vegetation. The stems, or tillers, from which the leaves sprout are unusually tightly clustered. In North America, such plants are known as bunch grass. Bunching may have evolved to protect new growth from frost, as tussock leaves grow from the base, not the tip, and new growth is protected by surrounding tillers and the leaf litter that encircles each plant. New Zealand has a particularly high percentage of tussock-forming grasses. It is not unique in this, but the habit is certainly a distinctive feature of our grasses, as is their relatively large size and evergreen nature. The dominance of the tussock habit may be related to the absence of mammals in New Zealand’s prehistory. Chionochloa species simply don’t cope with heavy grazing. Those plants we generally call tussocks are a collection of grasses from three different genera that have adopted the tussock habit. The genus Chionochloa (chion = snow; chloa = grass) includes the snow tussocks, or tall tussocks—up to 2 metres high—that make up the grand, golden army that dominates our subalpine grasslands, furring the hills a tawny gold and forming a magnificent backdrop for numerous beer and car commercials. A few other species survive in isolated coastal and forest sites. Left comparatively undisturbed on account of their general fondness for altitude and inaccessible locations, Chionochloa are the lucky tussocks. Less grand and altogether less fortunate are the short tussocks. Growing up to half a metre in height, they include such hardy species as blue tussock (Poacolensoi), silver tussock (P. cita) and hard, or fescue, tussock (Festuca novaezelandiae). With a penchant for lower country, short tussocks have had to compete over the last 200 years with the runholder’s arsenal of fire, exotic grasses and grazing stock, and also with the runholder’s enemies—weeds and rabbits. While some have fared better than others, none has been unaffected. Today it is almost impossible to find an area of unmodified short-tussock grassland in New Zealand. Short tussocks and tall tussocks have distinct, if not altogether clear, origins. One of Lloyd’s research aims is to answer questions concerning their evolution. Chionochloa is a member of a relatively ancient southern-hemisphere group, and 22 of the 24 identified Chionochloa species are endemic to New Zealand, where the genus has probably existed since the Tertiary period. While the grass family is most likely to have originated in South America, our short tussocks appear to have arisen from ancestors that moved to, and diversified in, the northern hemisphere and then trickled back south. Of the 450 Festuca species, only 10 are found within New Zealand. Because Festuca evolved on continents with large grazing mammals, it has developed traits that make it less palatable than some other grasses. Rub your hand down a leaf-blade of hard tussock and you’ll find it prickly and rough. This may be one adaptation that has enabled Festuca species to survive in New Zealand’s modified pastures, where many others have not. Far from paddocks, snow-patch grass (C. oreophila) has evolved to live in shaded depressions in the mountains that retain snow even into the summer months. But eight million years ago New Zealand was a series of low-lying swampy islands with not a peak in sight. How, then, did the alpine tussocks evolve? “We presume that tussock grasses survived in places where forest couldn’t—such as in Fiordland, where valley floors are often either too wet or too frosty,” Kelvin Lloyd tells me. “Also round the coasts, where there’s a lot of disturbance and trees get pushed back, grasses would have had a foothold. Similarly along rivers and on bluffs sticking out of the forest. We’ve still got species in all those habitats. “Red tussock we met on the frost flats, and C. bromoides, in Northland, is strictly a plant of rocky coasts—it grows right down on the shoreline rocks. C. beddiei does a similar thing around Wellington, and then there are others that still live on bluffs within a forested landscape, like C. flavicans and C. conspicua. “When the mountains came up, a whole lot of new habitats appeared, and that promoted speciation. We got our alpine species then.” Periods of glaciation following this mountain-building phase also aided speciation by fragmenting widespread species into separate populations with no gene flow between them. Fossil Pollen grains tell the history of New Zealand’s vegetation—a history palynologist Matt McGlone has spent much of his professional life unravelling. Pollen grains—encapsulated within a tough almost rubbery outer coating—may persist for millions of years provided they come to rest in either a very dry or a very wet environment, where there is little biological activity. According to the pollen record, forest has dominated our landscape for the last 12,000 years, with grasses confined to river terraces, slips, peat bogs, the very driest parts of the Clutha and Mackenzie Basins, and areas above the tree-line. But it hasn’t always been that way. There have been times when grasses have spread from their refuges to cover much of New Zealand. At the end of the last glaciation (14–15,000 years ago), for example, there was a cold pulse during which New Zealand was almost covered in grassland. But unlike the sweeping tall-tussock grasslands of today, it was a barren, eroding landscape of thin scattered grasses and scabweed plants. “In fact, over the last 2.5 million years,” says McGlone, “for southern New Zealand the natural setting has been scrub grassland—only for brief periods did it have tall forest.” Tall forest would have greeted the first human visitors to New Zealand around 900 years ago, but fire was soon to wreak big changes. Joseph Banks, gazing out from the deck of Endeavour, made the following observation in his diary on October 16, 1769: “At night we were off Hawks Bay and saw two monstrous fires inland on the hills: we are now inclind to think that these and most if not all the great smoaks and fires that we have seen are made for the convenience of clearing land for tillage, but for whatever purposes they are intended they are a certain indication that where they are the countrey is inhabited.” Natural fires caused by lightning were thought to have swept the drier areas of New Zealand every few hundred years, but when Maori arrived in Aotearoa, the frequency of fires increased dramatically. “The big fires started about 800 years ago, at the end of the 12th century,” says McGlone. “That’s when we date the big moa bone pile-ups.” Deliberate burning continued after moa had become extinct, which raises doubts about whether Maori cleared forest to chase out moa. McGlone believes they had other reasons. “Forest didn’t really have a lot of food in it. There were some birds but not a lot else, and it also impeded navigation and travel. With a lot of lawyer vines and tangled small-leaved shrubs, it would have been a nightmare to get through.” Clearing forest would have made for quicker travel overland, and replacement vegetation would have been richer in bracken fern, with its palatable rhizomes, and in bird life. The burning of the forest was good news for the grasslands. Both short and tall tussocks rapidly colonised previously forested areas. Snow tussocks, especially those tolerant of drier conditions, such as the narrow-leaved snow tussock (C. rigida), became widespread at lower altitudes. Short tussocks migrated up-slope from dry valley bottoms to meet them. In wetter areas, such as Southland, red tussock raced across the low-lying hills. Forest surrounding the volcanic plateau and Lake Taupo was replaced by 660,000 ha of red tussock. Maori fires enabled indigenous grasslands to spread from 1.5 million hectares to around 8 million hectares, or 30 per cent of the land area, mostly in the drier eastern parts of both islands and in the central South Island. With the arrival of European settlers and their appetite for timber and pasture, the rate of deforestation accelerated dramatically. In the single decade from 1890 to 1900, 27 per cent of New Zealand’s existing forest was cleared—13 per cent of the total land area. While most of this went into pasture, tussock made a little extra ground. “All the tussock grasslands that you see now below the tree-line are fire affected,” says McGlone, “and 95 per cent are the product of fire alone.” The alpine grasslands, although spared such radical “development,” were not altogether untouched. Introduced mammals such as sheep, deer and hares began to graze their way up, feeding on the more palatable plants, pulling out and trampling tussocks and herbs, and leaving behind a higher concentration of less edible species like Dracophyllum and wild Spaniard. New Zealand’s luxurious growth of native grasses looked highly promising for stock, and in 1876 the government issued an order “that a work on the native grasses of the Colony should be prepared . . . to be accompanied by an essay on the grasses and forage-plants likely to prove useful in New Zealand.” The result was The Indigenous Grasses of New Zealand, published in 1880 by John Buchanan, a draughtsman and botanist to the Otago Geological Society. The tufts of tussock were regarded as “unsightly and disfiguring to the cultivated landscape.” Buchanan recommended introducing P. foliosa from the Auckland Islands to the mainland but lamented that it might be “difficult to overcome the prejudice which exists here in New Zealand against all large tussac grasses, arising no doubt from an ignorance of their true value.” Their “true value” to the settler was in providing shelter for stock in bad weather and at least a basic forage plant when the smaller inter-tussock species were blanketed by snow. In the 1860s and early 1870s, farmers relied almost entirely on native grasses for grazing. There were few fences, so cattle and sheep roamed high into the subalpine zone. Land was burned frequently new growth was more palatable than old—and grazed heavily. Neither government officials, who demanded minimum stock numbers in order to secure leases, nor farmers had any idea how slow New Zealand’s tussock grasslands would be to regenerate. Stock numbers rose sharply. Between 1870 and 1880 the number of sheep in New Zealand leaped from one million to 10 million. Rabbits, which had been introduced in the 1830s, suddenly came on in vast numbers. As a result of the ensuing destruction of tussock, water drained more rapidly from the open country and some areas became as dry as deserts. In Otago, between 1877 and 1881, 77 sheep runs covering over 600,000 ha had to be abandoned. Concern about declining productivity and degradation of tussock grasslands was voiced early. “It may be questioned,” wrote Buchanan in 1880, “whether the entire destruction of the native grasses, especially the larger tussac kind, is judicious.” Again he noted that apart from their food value, these plants provided useful shelter for stock. However, tall tussocks also inhibited stock movement and were not favoured by sheep. After repeated burning they eventually gave way to short tussocks, which were then over-sown with more palatable exotic grasses. Only at high altitude were tussocks spared. In the short-tussock grasslands, stock grazed on the most succulent plants—herbs and shrubs—before turning to the more palatable tussock species. The least edible plants—hard tussocks such as F. novaezelandiae and F. matthewsii survived for a time under burning and grazing, but the open pastures, with scattered plants of low stature, were vulnerable to invasion by rabbits, hawkweed (Hieracium spp.) and, in the driest areas, native scabweed. Although stock numbers dropped and pastoral production declined, the grasslands continued to degrade. The 1948 Land Act, which introduced 33-year pastoral leases, encouraged farmers to invest in their land. The subsequent advent of aerial topdressing—which allowed fertilising and the spreading of rabbit baits over sizable areas slowed degradation dramatically, as did improvements in fencing technology, the introduction of the poison 1080 and increased research into pastoral management. But while the decline of our tussock grasslands has slowed, it has not halted. Of the 3.9 million hectares now classified as pastoral tussock land, half a million hectares are dominated by hawkweed or bare soil and a further one million hectares have a “significant and increasing” presence of hawkweed. The Ministry for the Environment report The State of New Zealand’s Environment 1997 reached the following bleak conclusion: “It now seems that, in spite of the apparent recovery, the long term trend for the tussock grasslands is one of inexorable decline in both species diversity and production.” “The short tussock grasslands,” says Matt McGlone, “are just falling to pieces in front of our eyes.” Many New Zealanders cherish the high country. It is as much a part of national folklore as of natural heritage—a symbol of the frontier and the rugged independence we like to imagine lies at the heart of being a New Zealander. It is not just runholders who feel a powerful connection with this landscape. Trampers, mountain-bikers, hunters, environmentalists, horse trekkers and back-country skiers all relish its sweeping expanses. Artists, writers and poets draw inspiration from it, while marketing managers use it to sell beer and vehicles to city slickers. Little wonder the issue of current and future management arouses a wide range of opinion. The practice of burning tussock is highly contentious. Every spring columns of smoke choke the still blue air and streaks of amber puncture the night. Although the rotation period these days is probably 20 to 30 years, some tussock is burned most years. No subject is as likely to split a Central Otago town, with rumours of fires that got out of control and complaints about the negative impacts on tourism. But farmers are adamant that the strategic use of fire is an essential, although now minor, part of farming practice. It keeps back encroaching woody vegetation, improves stock access and brings a flush of palatable new growth. Passions on both sides run exceedingly high. Stepping squarely into the inferno is Landcare Research scientist Ian Payton, keen to inform the debate with some data on the effects of burning. He patiently explains that “government funding for research in the high country has collapsed in the last 9–10 years, largely because groups couldn’t agree on what research was needed.” Previous studies tended to consider the impact of fire on individual plants, rather than on whole landscapes and ecosystems affected by management decisions. Now, government science and management agencies, fire-control authorities, local bodies and farmers are cooperating in a multi-year study on the effects of burning on snow tussocks in central and coastal Otago. Payton hopes to determine whether fire, with or without grazing, causes long-term damage to tall-tussock grasslands by depleting their fertility and degrading the native plant communities, and how spring fires, when the soil is still damp, differ from summer fires. Summer fires kill more tussocks and destroy a far higher percentage of the plant biomass than spring fires. While landowners wouldn’t dream of burning under dry summer conditions, the possibility of accidental fire remains. “When you burn a tussock,” Payton explains, “it completely changes its way of operating. It drags nutrient reserves up from the roots and pushes them into new foliage.” Common practice is to burn in spring and then spell until about February or March, by which time the plants are flushed with new shoots. “But graze that new foliage off,” says Payton, “and the plants are really in trouble. “Tussock isn’t generally good fodder, but in the two years after it has been burned, sheep will run at fences for the freshly burned tussocks because those shoots are higher in nutrients such as phosphorous, potassium and nitrogen. I don’t think the spring fire is the problem because anything that was vulnerable to fire went eons ago. What remains has survived fire for 100–150 years or longer.” Preliminary results from some of Payton’s burnings are coming in. A spring fire at an inland site, on Mt Benger, near Roxburgh, consumed a modest 30 per cent of the biomass, leaving a layer close to the ground relatively unharmed. However, a month earlier at Deep Stream, nearer the coast, 60–70 per cent of the biomass went up in smoke, and the ground layer was badly burned. Lower soil moisture was the explanation. Summer burns at Deep Stream have resulted in the death of the majority of snow tussocks. Plants attempted new growth but winter frosts destroyed this before it had hardened off. Adding to the tensions in the high country is the process of tenure review, which will redistribute ownership of 2.7 million hectares—10 per cent of New Zealand and 20 per cent of the South Island—currently under pastoral lease from the Crown to some 340 high-country stations. Runholders have the option of owning their most productive land freehold in exchange for ceasing to graze areas of “significant inherent value,” which will pass to the Department of Conservation for protection and recreational purposes. It sounds like a clean, surgical procedure. It is not. On a clear autumn day at Lake Hawea, retired Professor Alan Mark addresses the Upper Clutha branch of the Royal Forest and Bird Protection Society. In the audience are a number of local runholders. Described by some as the “Professor of Political Botany” and the doyen of tussock grassland ecology, Mark is credited with raising the public profile of non-forest ecosystems, in particular grasslands. He is also credited with speaking his mind, not always with the greatest regard for diplomacy. A poster on his office wall reads, “If you want to be an ecologist, you have to stir things up a little.” “These issues,” Mark emphasises, “are too important to leave to politicians to decide.” Mark may be well past the age of retirement, but his dogged determination seems undiminished. To his audience of mainly elderly conservationists, he describes the gradual process of acquiring tussock grasslands for conservation through tenure review. The list of battles seems endless. Map after map goes onto the overhead projector delineating successes (areas reserved) and losses (areas remaining in pastoral use). “[Tenure review] is a oncer,” he warns. “We go through this in our generation and then that’s it—we’ve got to get it right.” Yet Mark’s “successes” and “losses” are seen in a different light by the farmers present who are faced with giving up vast tracts of land and parts of their high-country heritage. Later that afternoon, the Forest & Bird group drives out for a walk around Dingle Burn Station, on the eastern side of Lake Hawea. The owners, the Mead family, are supported by other farmers, such as the Emmersons, from the Lindis Pass, and Arthur Borrell, long-time owner of Branches Station, near Queenstown. The Meads are generous with their hospitality, despite obvious reservations. This is a rare meeting of two groups with very different ideas about the future of the tussock lands. Both sides show grace and willingness to communicate, but tempers lie close to the surface and erupt from time to time. Mark is accused of being one-eyed and trying to brainwash the public. He is followed to make sure he doesn’t take photographs that could be used “against us.” One farmer mutters, “It’s a war.” We gaze towards the highest tawny peaks—the areas that are likely to go to DoC through tenure review. Bridget Mead declares that her daughter has the right to muster along those tops, as she has done—it’s a part of her heritage. Mark argues that other New Zealanders also feel passionate about the land, and that it looks too bare to be considered productive. This is the crux. How should this land be managed? Conservationists claim that the historic degradation of the high country is not evidence of good stewardship and that many areas are so depleted they must be taken out of production. Farmers say they’ve learned much from the last 150 years and that the past 50 years have seen significant restoration. “Farmers have changed,” explains John Aspinall of Mt Aspiring Station, “to a much more integrated approach to farming with the emphasis on production per head and looking after the environment, rather than being concerned mainly with stock numbers.” He argues that continued grazing is necessary to prevent the spread of weeds. “In the tussock grasslands, if we walk away from management, pines, Douglas fir and Hieracium [an invasive ground cover that forms a smothering mat] will take over. We’ve brought so many exotic species with us, both animals and plants, that you can never go back to pre-European times.” Integrated management (using covenants, for example, to safeguard areas of threatened vegetation) under continued pastoral stewardship offers, he believes, the most sustainable future for the grasslands. Farmers are also concerned that an increase in rank grasses and tussocks, along with more recreational visitors, will create an unacceptable fire hazard right in their back yard. Payton is not convinced by the fire-hazard argument. He believes tussock land is combustible almost year-round and that adding to the amount of fuel doesn’t increase the risk significantly. Aspinall, a respected leader in the farming community, assures me that despite the tensions, there is a great deal of common ground between the conservationists and the runholders. Everyone wants the same thing—sustainable management of the high country and opportunities to enjoy it recreationally—but they differ over details and approaches. DoC is set to gain approximately one million hectares of mostly modified grassland through tenure review. What is it going to do with it? It will have to consider such thorny questions as what is natural, the vegetation of 150 or 1000 years ago? Will it have to burn the Lindis Pass periodically to prevent it reverting to scrubland and eventually to forest? Will our grasslands, expanded over the last thousand years by fire, shrink to their previous limited range? Should we allow them to? Tussocks at low and mid-altitude are essentially invasive, colonising areas of disturbance but, where a sufficient seed source remains, eventually being overtaken by scrub and forest. A small reserve in the Rock and Pillars Range with an old, intermittent shrub zone is rapidly reverting to scrub. Yet tussock cover in a drier reserve at Black Rock, monitored since 1971, has increased in spread and height, while the shrubs have hardly changed. “You can’t generalise or predict what tussock cover will do,” says Mark. Under national-park policy, burning-off is a land-management option, but its use is bound to be controversial. Conservationists strongly opposed Payton’s modest burning experiments on land owned by DoC, although DoC itself was happy. Payton’s experiments have taken place on private land. Meanwhile, Mark and the conservation lobby have enjoyed some success. In 2001, Korowai/ Torlesse Tussocklands Park in inland Canterbury was created, the first conservation park in the eastern high country and a landmark for the conservation of non-forest ecosystems. With tenure review, more reserves are set to follow. Indeed, as recently as May 2003, a second tussock conservation park of 20,000 ha opened in Central Otago’s Lammermoor Range. And what of the lower country—the former domain of the short tussocks—as it comes under more intense farming pressure? Little is being recommended for conservation through tenure review, because it is generally more productive and the indigenous vegetation has already been seriously degraded. Grapevines, deer farming and lifestyle blocks, too, are all eating up large tracts of formerly semi-natural grasslands. But entomologists are crying out that native invertebrates will be threatened when the lower lands become freehold and grazed more heavily. Invertebrates tend to draw the short straw in conservation management. The Cromwell Chafer Beetle Reserve—touted as the world’s first conservation area dedicated solely to an insect—is an anomaly. Yet invertebrates make up the bulk of species in New Zealand’s native fauna. In Payton’s study, typically 4–5000 individual invertebrates belonging to 7–800 species have been found in each square metre of tall-tussock grassland. A huge surge in the discovery and description of new species has begun, thanks to tenure review, as entomologists search many lowland and high-country tussock communities for the first time. The grasslands turn out to be teeming with insects. Entomologist Brian Patrick of Otago Museum has described the mountain ranges of Central Otago as providing “habitats for the most diverse and spectacular insect fauna in any New Zealand region.” And not just insects. Flat worms, spiders, centipedes, millipedes and snails together with weta, cockroaches, weevils, earwigs, beetles, mealy bugs, aphids and ants all make their home in the tussock grasslands. Flitting, buzzing and jumping above them are butterflies, moths, cicadas, grasshoppers, flies and wasps. Together, these hordes provide a smorgasbord for lizards and birds. Some creatures are real oddities. For instance, Patrick recently discovered a new species of stonefly. “These stoneflies don’t fly—they don’t even have wings—and they don’t live around stones,” he comments. Normally stoneflies are found in streams, but this species has adapted to life in the damp centre of the copper tussock (C. rubra cuprea) on Dunedin’s Swampy Summit. Its whole life history takes place within the plant, adults and larvae both feeding on detritus in the heart of the tussock. “Since we’ve burnt snow tussock and dried it out,” says Patrick, “I’m sure we’ve eliminated many populations of this sort of thing.” Blue tussock (P. colensoi) is a favoured food plant for many insects but has been much reduced in abundance by grazing animals, which also seek it out. The country’s moth fauna, which still numbers about 2000 species, has probably suffered considerably through damage to tussock land. Many moths and butterflies make use of the shelter afforded by the tussock habit to lay their eggs. Their larvae often eat the leaves and pupate in the heart of the plant. For instance, the larvae of tussock butterflies (Argyrophenga spp.) feed on silver and tall tussocks, whereas Butler’s ringlet (Erebiola butleri) sticks to low alpine Chionochloa species in the wetter western South Island mountains. Larvae of the Otago ghost moth (Aoraia rufivena) spend their days underground but emerge at night to feed on leaf litter, including that of snow tussock. The females of many grassland moths have become flightless, in some cases their wings reduced to stumps on either side of a large egg-filled abdomen. Many spiders take advantage of this abundance of insects. Trapdoor spiders build their burrows in open country, covering the entrance with a finely woven lid and sitting just inside, awaiting their prey. The common wolf spider (Lycosa hilaris) shelters in the base of tussock plants. Another wolf spider (Anoteropsis flavescens) lives only in swampy tussock grasslands from Dunedin south. New Zealand’s only species of lynx spider (Oxyopes gracilipes) is also a grassland inhabitant. A large, distinctively coloured spider was identified in the tussock of Cardrona Valley in 1969 but has never been found since. Patrick argues that the wealth of tussock invertebrates indicates the pre-human grasslands were more extensive than is suggested by pollen analyses. Many grassland insects have flightless females and are very site specific. “It’s hard to imagine them moving far. Places like the Mackenzie Country, where people say the grasslands only appeared after the forests—I don’t believe it. There are too many flightless things—not just moths but chafer beetles, all sorts of things that wouldn’t live in a forest ecosystem and found only in the Mackenzie Basin for instance. They didn’t just arrive after the Polynesian fires.” All may not yet be lost, however. Native animals don’t fastidiously stick to native vegetation. Many invertebrates, such as grass moths (Crambidae spp.), have adapted well to modified pasture, and the larvae of others have taken to feeding on exotic herbs. This means modified grassland areas are still worthy of conservation. Of you wander along the tussocked tops of inland Otago, a scurrying movement may catch your eye as a shiny tail twists into the leaf litter. Peer deep into the crevices of the schist tors that characterise the region and you might find a pair of eyes looking back at you. If they blink, they belong to a skink; if not, you’re looking at a gecko, and it will almost certainly outstare you. Both creatures feed on invertebrates and the fruiting shrubs, such as pink snowberry (Gaultheria macrostigma), that grow between the tussocks. On sunny days, skinks bask on the rocks, while geckos, which are mostly nocturnal, press their backs up against the warm roofs of their crevice homes. According to herpetologist Mandy Tocher, even our common skinks may not be common for much longer. Modification of the grasslands has greatly reduced skink habitat and opened it up to a fearsome array of predators. Lizards may be able to survive a light grass fire by retreating into a deep crack in the rock, but they cannot survive relentless hunting by feral cats, ferrets, stoats and weasels. At Macraes Flat, an hour’s drive north-west of Dunedin, Tocher and other DoC staff are struggling to maintain the last sizable populations of grand and Otago skinks. But the odds are against them. Outside the “Lizard Lounge,” an old farm hut with a soot-blackened ceiling where the team eats and sleeps, is a freezer containing the bodies of well-fed cats and ferrets caught by resident trapper Neville Mitchell. In the autumn of 2002 Mitchell caught six cats a day, and New Zealand also boasts the largest population of wild ferrets of any country in the world. The grasslands are overrun and the lizards are under siege. So, too, are birds. Harriers and falcons survive on ample prey, but ground birds such as weka, once common throughout the tussock grasslands, have all but disappeared. The native quail, or koreke (Coturnix novaezelandiae), became extinct some time after 1860 because of hunting by Maori and Europeans and reduction of tussock habitat by burning and grazing. The takahe is a true grassland bird, plucking tussock tillers and seeds for food and laying eggs in a raised bowl of grasses under the shelter of tussock leaves. The bird’s method of plucking tillers stimulates new growth. Where a tiller breaks, a fresh shoot forms to replace it. Unfortunately, red deer favour the same tussock species as takahe, and their method of feeding—simply severing the leaves with their teeth—does not stimulate regrowth. Deer populations have had to be controlled in part of Fiordland to arrest the decline of takahe. As a modest offset to the woes that have come the way of tussock since mammals invaded the high country, there is now considerable interest in using the plants for revegetation work in areas where tussock occurs naturally. For instance, all skifield operators in the south revegetate disturbed areas with tussock. In at least one instance ground that has been mined for gold has been replanted in tussock, and the plants have been used extensively around the aluminium smelter at Tiwai Point. While a few vigorous species, such as blue tussock and silver tussock, may become established from direct-drilled seed, most, especially the tall tussocks, need careful nursery rearing for a couple of years, by which time they are 20 centimetres or more in height and can be planted out. Seedlings raised at low altitude may have to be frost-hardened before being planted at higher elevations. Collecting tussock seed also has its difficulties. Flowering in tall tussocks is particularly irregular. In those few years they do produce seed, much of it may be damaged or destroyed by insects. Mature tussocks can be divided into smaller plants, with a minimum of around 10 tillers, but these, too, need nursery care for a year before being planted out. Ironically, while tussocks have been under siege in their natural refuges, they have come into vogue over the last decade as landscaping plants in a host of very unnatural environments. When John Baker of Home Creek Nursery, Manapouri, took over a DoC revegetation nursery about eight years ago and decided to concentrate on tussocks, “everyone thought I was mad,” he says. Today he sells 150,000 to 200,000 tussock plants a year, belonging to 20 or 30 species. “They are good for holding banks, stopping erosion, and make a striking and maintenance-free garden,” he says. While the tall tussocks do not generally thrive in the north of the country, many of the smaller Poa and Festuca species flourish just about anywhere. Although no dainty urban planting can begin to capture the magnificence of the tussocks of the Desert Road or Central Otago, the recent enthusiasm for tussock grasses in gardens and around city high-rises is introducing these distinctive plants to a new range of people. Their swirling textures and soft curves create a mesmerising contrast with the rigid stems of most shrubs, and the range of textures and colours available across different species is vast. These urban plantings might just provoke a curiosity about our real high-country grasslands and their future, and no harm can come from that.

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# Can You Pass This Basic 2-Digit Number Subtraction Test Without Using a Calculator? EDUCATION By: Robin Tyler 5 Min Quiz Image: shutterstock 93, 27, 55, 18. Or take these and subtract another set of numbers, like 93-27 or 55-20. Can you subtract those in your head? Is mental mathematics something you find simple and easy to do? So you reckon then that you are a bit of a math wizard? Well, you're lucky - some of us need the calculator, even for basic two-digit number subtraction. Remember when our teachers back in school emphasized the importance of not always relying on your calculator to do the math for you? That by doing so, you would get lazy? That you should develop your own system to help you subtract numbers easily? I am sure you have a system that works for you in that regard. There are many ways to subtract numbers in our heads; it's about finding a system that works for you (and if you take this test, we will show a method that we use). So what can you expect from this test?  Thirty-five questions of basic two-digit number subtraction. If you are good at this sort of thing, you really will fly through this test in no time at all. Can you get 100%, though? Sometimes numbers can trick us! Let's see how you fare! Good luck! # 99-77=___? Simple. Break it down like this. 9-7 is 2 and 9-7 is 2, so 22. # Subtract 41 from 88. How much are you left with? 88 minus 40 would leave you with 48, then you still need to subtract the 1, so the answer is 47. You got it, right? # If you have 62 bananas and your friend eats 44 of them, how much do you have left? Well, other than the fact that you might need to rush your friend to the hospital, you would only have 18 bananas left. We got to the answer by taking 62 and subtracting 40 to get to 22, and then taking off the remaining 4 to get to 18. # Take 57 and subtract 18 from that. What do you have left? 57 -17 would give you 40, so take off the extra 1 for 39! Tricky strategy helps. # 87-53=___? 8 minus 5 is 3 and 7 minus 3 is 4. That leaves you with 34 as your answer. Did you use the same method to work it out as we did? # 44 minus 21 leaves you with what? 4-2 is 2 and 4-1 is 3, so that makes 23! Easy, right? # 87-41=___? Another easy one, it's an even number and its 46! How? 8 minus 4 is 4 and 7 minus 1 is 6, leaving 46. # Take 71 and subtract 32 from it. What do you have? Not too difficult. The answer is 39. How? Well 70 minus 30 would give you 40. Add 1 for the 71 which leaves you with 41 and then subtract 2 to round the 30 up to the original 32. Does that make sense? # If you have 33 apples taken away from your stash of 88 apples, how many apples do you have left? 8-3 is 5 and 8-3 is 5 again, leaving you with 55. Super simple. # 91-64=___? This is a fairly simply subtraction problem. Again take 90 minus 60, that leaves you with 30. Add the 1 left over from the 91 and subtract the 4 left over from the 64. That leave you with 27. # Subtract 55 from 92 and what do you have? If you had 90 and took away 55, you would have 35. That's easy to work out, but now you still have the extra two, as the number was 92. So you need to add that to 35 and you have 37. # Take 64, then subtract 11 from it. What do you have left? Too easy. No way you didn't get 53 for your answer. Our brains just automatically can see answers like that without even needing to think about it. If you got it wrong, don't tell anyone! # 11-12=___? It's negative number, expect a few more. The answer is -1. # Here's another! What is 77-99? Well, 99 minus 77 would be 22, so 77 minus 99 is simply -22. Do you see how easy it is, actually? # 75-24=___? Easy if you do it this way. 7-2 is 5 and 5-4 is 1, so the answer is 51. # 65-28=___? So simple. Just round up again. So 65 minus 30 would be 35, right? Now add the extra 2 from the 28 and you have our answer, 37. # If you have 77 pebbles and you lose 49, how many do you have left? A lot less pebbles. Actually, you would only have 28 left. There are a few ways to get to this answer, but we rounded up the 49 to 50. So 77 minus 50 is 27 but then you still have to add 1 (it was 49 not 50, remember). So that leave you with 28. # Subtract 22 from 10, please? Another negative answer but easy to work out. it is -12. # If you take 66 from 98, what do you have left? 9-6 is 3 and 8-6 is 2, and therefore the answer is 32. It really is a simple way of doing subtraction. If you put it into logical steps like this, you can work it out in seconds. # 79-21=___? The answer is 58. 80 minus 20 would be 60, but now you have to remove the two extra numbers, as the originals were 79 and 21, so that makes the answer 58. # 63-39=___? Ok, we had 63, took off 40. That left 23, but you still need to add 1 because the second number was 39, not 40. That leaves the answer at 24. Crazy that we are adding when we subtracting. This is just one of the ways you can do it. # 99-45=___? 9-4 is 5 and 9-5 is 4, so the answer is 54. I love it when all the numbers work out so easily. You got that one, right? # If you take 25 from 75, what are you left with? We got to the answer of 50 by taking 7 minus 2 and 5 minus 5, which leaves you with 50. You got that right? # You have 88 candies and lose 27. What have you got left? A hole in your pocket? No! it's 61. To get there, we calculated 8 minus 2 and 8 minus 7. That gives you 61! Hope you find your candies! # 45-32=___? Very straightforward this one. Your brain should have flashed you the number straight away. It's 13. # 83 minus 33 gives you how much? So easy. 80 minus 50 give you 30. The 3's cancel each other out. So 50 is your answer. # Subtracting 66 from 33 gives you how much? 66 minus 33 is easy. It's 33. but this is going to be a negative number. That's fine, as 33 minus 66 still give you 33, its just negative 33. # 54-24=___? Ok, it's easy to see when subtracting, the 4's will cancel each other out. So that means its 50 - 20 in fact, and that's easy to work out. It is 30. # If you had 69 apples and your friend ate 24, how many would you have left? 6-2 is 4 and 9-4 is 5, therefore 45 apples are left. Your friend needs some help! # If you removed 47 from 91, how much would you have? The answer is 44. We got there by starting with 90 and taking away 47 to give us 43. Add the 1 left over for rounding down to 90 and you have 44. You knew that though, didn't you? # 91-53=___? An even number, the answer is 38. And we got there by starting with 90, removing 50. That leaves 40. Add 1, because the original number was 91 then remove 3 because the other original number was 53. # 80-41=___? The answer is 39. No explanation necessary, really. 80 minus 40 would be 40. Subtract the extra 1 from rounding down the 41. # Subtract 96 from 10. What do you have? Into the negatives, but easy to work out because of the 10. A less round figure would be a little more challenge. The answer is -86, by the way. # If you lost 19 of your 45 marbles, how many would you have left? Losing your marbles... I feel like i might be after all this math! 45 - 20 would bet 25, but add the 1 for rounding up. And the answer is 26.

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Procedure | Extension Ideas | Related Standards | Resources | PBS Resources Human activity and industrialization are rapidly altering the quality of our air, both indoors and out, and both locally and globally. The goal of this activity is for students to recognize which activities contribute to poor air quality and which contribute to good air quality. The idea behind this study is that an informed/educated student is more likely to choose activities that contribute positively to the air that we breathe over those which contribute negatively, and is more likely to talk to others about sustainable solutions. In terms of local vs. global air quality, it should be recognized that because of global weather patterns, most air pollution is globalized, thus it does not stay in the locality where it was produced. For example, air pollution generated in the United States near the Great Lakes region travels with the jet-stream to New England, across the Atlantic Ocean to Europe, across the continent to the Middle East and Eastern Europe, and so on. Thus, air pollution is almost always a global problem. Indoor air pollution, however, is quickly becoming an even bigger environmental problem, especially in many urban areas where housing units are densely arranged and circulation of fresh (outside) air is limited. Indoor air quality is often measured in terms of carbon dioxide (CO2), carbon monoxide (CO), dust, molds and ultrafine particles. Outdoor air quality is often measured in terms of sulfur dioxide (SO2), nitrogen oxides (NOx), carbon monoxide (CO), ozone (O3), methane (CH4), volatile organic compounds (VOC's), and ultrafine particles. These lesson plans are written for high school level students, but can be adapted to other grade levels. (See Extension Ideas). • Social Studies At the end of this lesson, students will be able to: • Identify how air quality is measured, • Identify various human activities that negatively effect air quality, • Identify and discuss human activities that positively effect air quality. ESTIMATED TIME NEEDED • Allowance for student representatives to take photos between home and school. The number of days/total time is dependent upon the number of digital cameras in use and the number of student photographers. • In-Class Time = 2-3 class periods. • Digital Camera(s) • Computer with printer and Internet access • Map of the local area (to include all the communities that students come from) as appropriate • Research resources (books, articles, online access...) 1. Identify student photographers to take ten photos of human activities that impact air quality. (More photos may be chosen if time/classroom conditions permit.) About half of the photos should be of activities that negatively impact air quality (i.e. cars, polluting factories, industrial agriculture, etc.), and the other half of activities that positively impact air quality (i.e. bicycle, trees, etc.). * Depending on each specific class structure, situation and teacher's relationship with the class, teachers may want to pre-select student photographers before introducing the activity to students. Conversely, some teachers may want to ask for student volunteers. Additionally, if the class situation/logistics prohibit the facilitation of students taking their own photographs, the teacher may want to consult with students on what they would photograph if given the chance, then the teacher may take the photos him/herself for the class. However, it should be noted that the ideal situation would allow the students to take their own photos, thus taking ownership over this study and its outcomes. Another option would be for the teacher to predetermine and take his/her own photographs (being sure to include a diverse set of images) and bring them in to class for students. 2. Introduce the lesson to students, explaining that the goals of this project/activity are to understand what measurements are used to determine the quality of air that we breathe, to identify how different human activities contribute either positively or negatively to local and global air quality, and identify how to maximize the positive impacts and minimize the negative ones. 3. The teacher will want to explore with the class how air quality is measured, leading to a discussion of which substances are considered air pollutants (carbon dioxide, carbon monoxide, methane, ozone, sulfur dioxide, nitrogen oxides, volatile organic compounds and fine particulate matter). 4. Ask students to research the source of the above listed air pollutants (in small groups or individually as research materials and time permit). 5. For each of the air pollutants listed above, identify a human activity that occurs in the local community/environment that contributes this substance to the air. 6. Set a schedule to document these activities with a digital camera, utilizing different student photographers whenever possible based on where each human activity takes place in the community, geographically speaking. 7. Carry out the schedule for taking the photographs with the class. Once all photos have been taken, the teacher should upload them to the computer and print them out for class discussion. 8. With all the photos printed out, the teacher should facilitate small group work as follows: • Divide the class into the same small groups as before with one photo for each group of students. • Ask each group to prepare a presentation for the class with the following information about their photograph: a. Name the human activity depicted in the photograph and which air pollutant it contributes to the air. b. Identify where in the community the photograph was taken, being as specific c. Do students in the group partake in the depicted activity either directly or indirectly? For example, if the photograph is of a dairy farm, does each of the students drink the milk from that farm? If the photograph is of a local factory, do the students work there/know somebody who works there/purchase the products that are produced there, etc.? d. Identify what can be done to minimize emissions of that particular air pollutant to the atmosphere. What practical changes in lifestyle or personal habits can students themselves take that would minimize the impact of the activity in the photograph (i.e. what are some sustainable alternatives to that activity)? What are the barriers to implementing those alternatives and how can the barriers • Create a grading rubric for in-class presentations by each student team. Some criteria might include "knowledge of subject" (air quality), "team work," "use of visual aids" (photos), etc. • Have students prepare a photo exhibition for other classes/the school of human activities that contribute to air pollution and ways to minimize the environmental impact of each one (i.e. sustainable alternatives). • If the local community is one in which personal vehicles are the primary mode of transportation of most people, teachers may want to ask students to calculate how much carbon monoxide is emitted per week/month/year during their personal travels. Have students estimate how this number would change if they took public transportation. How would it change if they rode a bicycle whenever possible be specific with calculations of emissions and mileage that can be traveled on • For younger students, teachers may want to take photographs themselves of air-quality-impacting activities that students know about and partake in (i.e. walking or riding a bike to school, traveling in a bus or car to school, local agriculture that their families may take part in, playing in a local park or green area with trees/plants, etc.). Identify which activities are positive and which are negative. • For special needs/second language students, teachers may want to choose one or two activities that impact air quality (one positive and one negative, for example) and discuss how each one contributes to air quality. Which substance is being emitted and what is its source? Discuss alternatives to the activity that negatively contributes to air quality. • For teachers who want to do more related to this topic, have students research how local air quality has changed over time by interviewing elders in their community or researching historical data collected by local municipalities or institutions. They can take their own air quality readings (measuring particulate matter, CO2, methane, etc.) and compare them with current figures from other research institutions. The class may want to send in their results to those local research institutions and/or form a partnership in data collection over an extended period of time. RELATED NATIONAL SCIENCE EDUCATION STANDARDS FOR GRADES 9-12 Science as Inquiry • Abilities necessary to do scientific inquiry • Understanding about scientific inquiry Science in Personal and Social Perspective • Personal and community health • Natural resources • Environmental quality • Natural and Human-induced hazards • Science and technology in local, national and global challenges RESOURCES FOR TEACHERS AND STUDENTS American Lung Association Includes information on various air pollutants, their sources and some alternatives, as well as a plethora of information on United States Environmental Protection Agency Includes detailed information on air quality, pollution, and alternative solutions. Natural Resources Defense Council Includes information and articles on clean air and energy, transportation, etc. The Air Quality Archive A British website with concise information about the causes of air pollution, effects of air pollution and what people are doing about air pollution. RELATED PBS RESOURCES to Planet Earth: The Urban Explosion In this lesson plan, students explore urban planning and pollution problems caused by 20th century urbanization in New York City, Istanbul, Shanghai, and POV documentaries are a valuable resource for teachers and students. Use these companion lesson plans to present POV films to your class. PBS showcases the work of hundreds of diverse producers and local PBS stations, who in turn tap the creative minds of top thinkers from around the world to create education's best content.

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# Tug Of War Harsh Goyal Last Updated: May 13, 2022 ## Introduction This blog will discuss the approach to solve the Tug of war problem. Before jumping into the approach to solving the tug of war problem, let’s first understand what is the tug of war problem, in this problem, we need to divide our array in two subsequence or we can say two subsets in such a way, that the difference between both the calculated sum of both the subsequence will be as minimum as possible. Note: In this tug of war problem, if the size of the array is even, then, the size of the two subsequence will be half the size of the array, but if the size of the array is odd, then, the size of the first subsequence is the (size - 1) / 2 and the size of the second subsequence is the (size + 1) / 2. ### Sample Example Input:- Output:- First subsequence Second subsequence Explanation:- After checking each possible combination, the best-suited 2 subsequences are: • 12 , 18 , 25 • 15, 10, 20, 8 The sum of all the elements of the first subsequence is 55, whereas the sum of the second subsequence is 53, and the difference between both the sums is only 2 which is the minimum, therefore these two are the resultant subsequences. You can try this problem in codestudio using this link. ## Approach In this tug of war problem, we have to check each possible subsequence of half the size of the input array, and, the other subsequence will be formed by the remaining elements. We will consider the position of each element in the respective subsequence using the boolean array. In the process, if the size of the current subsequence is equal to half the size of the input array, then, we have to check whether the best solution is available or not. ### Steps of Algorithm Step 1. Create a function ‘getResult()’ that will accept two parameters, i.e., one vector of integer ‘input’ and the second is the size of that vector. Step 2. In this ‘getResult()’ function, we need to initialize two boolean arrays named ‘temp’ and ‘res’ and two integer variables named ‘mini’ and ‘sum’. Step 3. Make an iteration using the ‘for’ loop with the help of the ‘i’ variable to assign the collective total of all the input elements to ‘sum’ and assign a ‘false’ value to both the boolean arrays ‘temp’ and ‘res’. Step 4. Create a function ‘helper’ that will accept nine parameters, i.e., one vector of integer ‘input’, second is the size of the vector, third is the boolean array ‘temp’, fourth is the zero which will depict the total number of selected elements, the fifth is another boolean array ‘res’, sixth is the integer variable ‘mini’, seventh is the integer variable ‘sum’, eight is the integer variable ‘curr_sum’ and ninth is the integer variable ‘cur_Index + 1’ Step 5. In this ‘helper’ function, Increment the value of ‘selected’ and add the value of the element at ‘cur_Index’ of ‘input’ to ‘cur_sum’ and assign ‘true’ value to element at ‘cur_Index’ of ‘temp’. Step 6. Check if the value of ‘selected’ is equal to half the value of the size of the vector or not, • If it is equal then, check for the best solution by checking if the absolute value of the difference of ‘sum / 2’ and ‘curr_sum’ is less than ‘mini’ or not, if it is less than the value of ‘mini’, then assign that value to ‘mini’ and assign the complete ‘temp’ array to ‘res’ array using ‘for’ loop. • Else, make a recursive call using the ‘helper’ function with updating the parameters as shown in the code. Step 7. Assign ‘false’ value to the element at ‘cur_Index’ of ‘temp’ boolean array. Step 8. Print both the subsequence. ### Implementation in C++ ``````#include <bits/stdc++.h> using namespace std; // Check all the valid options using this helper function void helper(vector<int> input, int n, bool* temp, int selected, bool* res, int* mini, int sum, int curr_sum, int cur_Index) { // Edge case if (cur_Index == n) return; // Check the size if ((n/2 - selected) > (n - cur_Index)) return; // Case when current element is not considered in the result helper(input, n, temp, selected, res, mini, sum, curr_sum, cur_Index + 1); selected++; curr_sum = curr_sum + input[cur_Index]; temp[cur_Index] = true; // checks if a solution is formed if (selected == n / 2) { // check for the best solution if (abs(sum / 2 - curr_sum) < *mini) { *mini = abs(sum/2 - curr_sum); for (int i = 0; i<n; i++) res[i] = temp[i]; } } else { // Case when current element is considered in the result helper(input, n, temp, selected, res, mini, sum, curr_sum, cur_Index + 1); } temp[cur_Index] = false; } // main function that generate an arr void getResult(vector<int> input, int n) { bool* temp = new bool[n]; bool* res = new bool[n]; int mini = INT_MAX; int sum = 0; // Compute sum for (int i = 0; i < n; i++) { sum += input[i]; temp[i] = res[i] = false; } // Recursive call to helper helper(input, n, temp, 0, res, &mini, sum, 0, 0); // Print both the subsequence cout << "The first subsequence: "; for (int i = 0; i<n; i++) { if (res[i] == true) cout << input[i] << ", "; } cout << endl; cout << "The second subsequence: "; for (int i = 0; i < n; i++) { if (res[i] == false) cout << input[i] << ", "; } } int main() { // Input array vector<int> input = {15, 10, 20, 8, 12, 18, 25}; int n = input.size(); getResult(input, n); return 0; }`````` Output: ``````The first subsequence: 12, 18, 25, The second subsequence: 15, 10, 20, 8,`````` #### Complexity Analysis Time Complexity: O(2 ^ N) Incall to ‘getResult()’, we are also calling ‘helper’ function, and in ‘helper’ function, we are checking all the valid options to make these two subsequence using a recursive call, therefore, the overall time complexity is O(2 ^ N). Space Complexity: O(N) As we are using ‘N’ extra space to store the binary tree, therefore, the overall space complexity will be O(N). Q1) What is the subsequence? Ans. subsequence is also a type of array which is contiguous and is usually a small section of the bigger array. Q2) What is a boolean array? Ans. The array in which the value of elements could be true or false only is a boolean array. Q3) Difference b/w recursion and backtracking? Ans. Recursion and Backtracking both are nearly similar because both call their own function again and again, but the only difference between both of them is that in recursion, the function calls stops when it satisfies the base case, whereas, in backtracking, recursion is used to check and find all possible combinations until and unless we get the best solution for that problem. ## Key takeaways In this article, we discussed the What is Tug of war, discussed the various approaches to solving this problem programmatically, the time and space complexities, and how to optimize the approach by reducing the space complexity of the problem. If you think that this blog helped you share it with your friends!. Refer to the DSA C++ course for more information. Until then, All the best for your future endeavors, and Keep Coding.

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Flashcards in The basic economic problem Deck (20) a product which requires resources to produce it and therefore has an opportunity cost a product that does not require any resources to make it and so does not have an opportunity cost. factors of production the economic resources of land, labour, capital and enterprise the basic economic problem people have unlimited wants and needs but there are limited resources to satisfy these wants and needs, so choices have to be made on how to allocate these limited resources to satisfy as many needs and wants as possible essentials things for people to live adequately food, water ,shelter, clothing, medical needs luxuries people desire to live more comfortably manufactured, man-made goods used to produce other goods and services rather than being used for its own sake e.g. machinery, tool, office skills a business person requires to combine and manage successfully the other three factors of production, the ability to undertake risk and decision-making natural resources, obviously land for farming and the land on which buildings are built, but also resources found underground, such as coal, oil and etc. the mental or physical skills of a human which are used to produce a service or good questions when making goods and services What to produce? How to produce? For whom to produce it for? the cost of the benefit foregone by giving up the next best alternative when making a decision Production Possibility Curve PPC The PPC represents potential prospects for the production of a pair of products What does a PPC show productive capacity, maximum output of an economy given the resources and factors of production it has What does being inside the PPC mean all the resources are not being used to the best of their ability - inefficiency What does being on the PPC mean ALL the available resources are being used EFFICIENTLY what other concept of economics does the PPC show Opportunity cost and scarcity different types of economies planned economies, market economies - government makes decisions about what, how, for whom the goods are produced - government main owner of most factors of productions (FoP) - Government is the employer and sets wages and prices - Goods produced may not match consumers' wants - Not many planned economies in the world (ex: North Korea)

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1. ## Tricky integral Whilst working through a question I got to the point where I need to integrate this: 1/y + (1/k)/(1-y/k) where k is a constant. I got ln|y| + 1/k (ln|1-y/k|) I know this isn't correct. Could anyone explain why and give me the correct answer? Thankyou 2. Originally Posted by chr91 Whilst working through a question I got to the point where I need to integrate this: 1/y + (1/k)/(1-y/k) where k is a constant. I got ln|y| + 1/k (ln|1-y/k|) I know this isn't correct. Could anyone explain why and give me the correct answer? Thankyou to integrate (1/k)/(1 - y/k), do a substitution: u = 1 - y/k now continue with that and see where you get. and try to notice a pattern so that you don't have to go through the u-sub all the time. and remember that in general, to integrate 1/something, you don't automatically take the ln|something|, it very much depends on the kind of function "something" is. follow the rules exactly. you have $\displaystyle \int \frac 1x~dx = \ln |x| + C$. If it doesn't (or can't) look like 1/x (that is one over a variable to the first degree), then you won't be able to integrate it and get ln. what you have doesn't look like 1/x, so you had to change it to look like that. And that would change other things as well. 3. $\displaystyle \int \dfrac{1}{y} + \dfrac{\frac{1}{k}}{1-\frac{y}{k}}\ dy = \int \dfrac{1}{y} + \dfrac{1}{k-y} \ dy$ I multiplied the second fraction by k/k to simplify. Then, I get: $\displaystyle \int \dfrac{1}{y} + \dfrac{1}{k-y} \ dy = ln|y| - ln|k-y| + c$ 4. Originally Posted by chr91 Whilst working through a question I got to the point where I need to integrate this: 1/y + (1/k)/(1-y/k) where k is a constant. I got ln|y| + 1/k (ln|1-y/k|) I know this isn't correct. Could anyone explain why and give me the correct answer? Thankyou $\int{\frac{1}{y}}dy+\frac{1}{k}\int{\frac{1}{1-\frac{y}{k}}dy}=\int{\frac{1}{y}}dy+\frac{k}{k}\in t{\frac{1}{k-y}}dy$ $u=k-y$ 5. Originally Posted by Unknown008 $\displaystyle \int \dfrac{1}{y} + \dfrac{\frac{1}{k}}{1-\frac{y}{k}}\ dy = \int \dfrac{1}{y} + \dfrac{1}{k-y} \ dy$ I multiplied the second fraction by k/k to simplify. Then, I get: $\displaystyle \int \dfrac{1}{y} + \dfrac{1}{k-y} \ dy = ln|y| - ln|k-y| + c$ Got it. Thanks! 6. Originally Posted by chr91 Sorry for being dumb here but why is it -ln|k-y| not + ln|k-y| ? Let $u = k-y$, as suggested above, to see why. 7. I now need to get this into a function where y = .... ln|y| - ln|k-y| = rt + C I need to get the function in terms of y I guess? ln |y/(k-y)| = rt + C y/(k-y) = Ae^rt I can't get y on it's own though. There's too many constants! 8. Originally Posted by chr91 I now need to get this into a function where y = .... ln|y| - ln|k-y| = rt + C I need to get the function in terms of y I guess? ln |y/(k-y)| = rt + C y/(k-y) = Ae^rt I can't get y on it's own though. There's too many constants! I don't know where this $rt+C$ is coming from, but... $\mathrm{ln}|y|-\mathrm{ln}|k-y|=rt+C$ $\mathrm{ln}|\frac{y}{k-y}|=rt+C$ $\frac{y}{k-y}=Ae^{rt}$ (if you want it like this, $A=e^C$) $y=(k-y)Ae^{rt}$ $y=Ake^{rt}-yAe^{rt}$ $y+yAe^{rt}=Ake^{rt}$ $y(1+Ae^{rt})=Ake^{rt}$ $y=\frac{Ake^{rt}}{1+Ae^{rt}}$ 9. Originally Posted by topspin1617 I don't know where this $rt+C$ is coming from, but... $\mathrm{ln}|y|-\mathrm{ln}|k-y|=rt+C$ $\mathrm{ln}|\frac{y}{k-y}|=rt+C$ $\frac{y}{k-y}=Ae^{rt}$ (if you want it like this, $A=e^C$) $y=(k-y)Ae^{rt}$ $y=Ake^{rt}-yAe^{rt}$ $y+yAe^{rt}=Ake^{rt}$ $y(1+Ae^{rt})=Ake^{rt}$ $y=\frac{Ake^{rt}}{1+Ae^{rt}}$ Thanks very much. Basically I'm working through this question: I'm trying a step at a time! I'm finding it hard, nearly done A though now 10. The next part says if y(0) = k/3 find y(t) So when t=0, y = k/3 ? k/3 = Ak/(1+A) k(1+A) = 3(Ak) k + Ak = 3Ak k = 2Ak 2A = 1 A= 1/2 . Would you agree with this? So y(t) = (1/2)ke^rt/ 1+ (1/2)e^rt 11. Yes, and you can make it simpler if there is another part coming up. $y(t) = \dfrac{\frac12 ke^{rt}}{1 + \frac12 e^{rt}}$ Multiply by 2/2; $y(t) = \dfrac{ke^{rt}}{2 + e^{rt}}$

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Games Problems Go Pro! # Find the Number Pro Problems > Math > Algebra > Equations > Word Problems > Linear ## Find the Number The sum of a number and twice that number is 20% more than the result would have been if the number had been increased by 12 and then doubled. What is the number? Presentation mode Problem by Mr. H ## Solution In order to make it feasible for teachers to use these problems in their classwork, no solutions are publicly visible, so students cannot simply look up the answers. If you would like to view the solutions to these problems, you must have a Virtual Classroom subscription. Assign this problem ## Similar Problems ### Three Numbers I have a sheet of paper with three integers written on it. If I add them together, I have a sum of 38. Two of the numbers differ by one. One of the three numbers is 11. What is the largest possible integer that could be written on the paper? ### Finding X Two more than twice the sum of x and five is equal to twelve less than three times the sum of x and two. ### White Board Markers I have a problem with dry erase markers disappearing from my classroom. A third of my markers were stolen by a student, and then one of my co-workers "borrowed" four markers. After that I realized that half of the remaining markers didn't work, so I threw them away. In the end, I just had two markers left. ### Next Year Next year, Martha will be three times as old as she was 17 years ago. How old is Martha now? The sum of a number and five more than that number is 47.  What is the number? ### Moving Christmas Hermie doesn't want to celebrate Christmas on December 25th, so he suggested moving it to a date n days later. Rudolph protested that then Christmas wouldn't happen as often. Frosty then suggested that the date could be moved days in the other direction. If Frosty's suggestion was followed, on what day would Christmas fall? ### Snake in the Grass Two snakes started out the same length. The first snake grew five inches, and the second grew by half its own length. If the first snake is now two inches shorter than the second snake, what was the original length of the two snakes? ### Yards and Feet The height of a building measured in feet is 196 more than its height measured in yards. What is the height of the building in feet? ### Until New Years Day The number of seconds until New Years Day (when the ball drops at Midnight) is equal to the number of hours since the last time the ball dropped. Assuming a non-leap-year, what is the current date and time, to the nearest minute? ### Melting Snow The day after a snowstorm, 25% of the snow that fell melted. Then there was another snowstorm in which twice as much snow fell as in the first storm. Then 25% of the total remaining snow on the ground melted, leaving 33 inches. How much snow fell in the first storm? Three Numbers, Giant Roller Coaster, Arithmetic Operation Word Problem, Stair climber, Single variable equation, A Third of a Fourth # Featured Games on This Site Match color, font, and letter in this strategy game Trap all the dots in this problem-solving puzzle # Blogs on This Site Reviews and book lists - books we love! The site administrator fields questions from visitors.

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# Math Project [Prime Time] Semi Titles- My Special Number, Mathematical Reflections 1, and Mathematical Reflections 2. ## Presentation on theme: "Math Project [Prime Time] Semi Titles- My Special Number, Mathematical Reflections 1, and Mathematical Reflections 2."— Presentation transcript: Math Project [Prime Time] Semi Titles- My Special Number, Mathematical Reflections 1, and Mathematical Reflections 2 My number is 50. Facts about 50 5 factors of 50 are 1, 2, 5, 10, and 25. These are the factors I think of straight away 50 is an even number because it is a multiple of 2 and all multiples of 2 are even numbers.50 is also an even number because all numbers that end in the numbers 0, 2, 4, 6, and 8 are even. 50 is an whole number because it doesn’t have any fractures in it(it doesn’t have a decimal point)[.].Numbers which aren’t whole numbers are numbers like 2.2, or 4.8, or 11.6, etc. World facts about 50 In Malaysia 2007, Malaysia celebrates their 50th Merdeka.Malaysia celebration of Merdeka is because in 1957, 31st August was when they got their independence from the British. In America there are 50 main land states. A main land state is a state that is part of the others. The state that is not part of the main land is Hawaii 50 is a very common number for paper money all over the world in such countries as Malaysia, America, Thailand, Australia, and countries in Europe. Mathematical Reflection # 1 50 isn’t a good move to make in either the Product Game or the Factor Game because the number 50 isn’t on either of the boards which would make the choice of 50 invalid. Math Reflection # 2 1.You can use the paper models from Problem 2.1 by taking the bottom squares x the top square. 1 x 2 2. A Venn Diagram is 2 circles with an intersection between them. You can use a Venn diagram to find the common factors of two numbers. Intersection 8 16 1 2 4 816 1 2 4 8 8 4 21 The common factors of 8 and 16 are 1, 2, 4, and 8. The dimensions are 1 x 2. 3. To find all the factors of a number I pair the factors up together. I know when I have found all the factors of a number when I take a factor of my number and double it and if it is more than my number I know I have all of its factors. e. g. 20, 10 doubled = 20. 11 doubled = 22 too much. 4. I know that an odd number + and odd number is a even number. An even number + an even = an even number. An even number + an odd number = an odd number. e. g. 5(odd) + 8(even) = 13 (odd) T IPS An easy way to find weather or not a number is odd or even is to take the last numbers of two number and add them together. e. g. 1 2 1 + 3 3 8 = 4 5 9(odd). Take 1 from 121 and 8 from 338. Special Number My special number is 50 and it is a very import number in Malaysia because this year(2007) Malaysia celebrates 50 years of independence form the British. I can say that I have learnt 50 is an easy number to work with because it is half of 100, even, and not to big of number. My number is even because it is a multiple of 2. My number has 1, 2, 5, 10, 25, and 50 as its factors. 50 has 6 factors. THE END BY SHANE TEO THE END BY SHANE TEO Download ppt "Math Project [Prime Time] Semi Titles- My Special Number, Mathematical Reflections 1, and Mathematical Reflections 2." Similar presentations

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The First and Second Algebraic Identity You may have previously seen that ${\left(a×b\right)}^{2}={a}^{2}×{b}^{2}$, but what is ${\left(a+b\right)}^{2}$? If you write ${\left(a+b\right)}^{2}$ as $\left(a+b\right)\left(a+b\right)$, you can use what you learned about the distributive property of multiplying parentheses to find the answer: $\begin{array}{llll}\hfill {\left(a+b\right)}^{2}& =\left(a+b\right)\left(a+b\right)\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & ={a}^{2}+ab+ba+{b}^{2}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & ={a}^{2}+2ab+{b}^{2}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$ This also applies to ${\left(a-b\right)}^{2}$: $\begin{array}{llll}\hfill {\left(a-b\right)}^{2}& =\left(a-b\right)\left(a-b\right)\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & ={a}^{2}-ab-ba+{b}^{2}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & ={a}^{2}-2ab+{b}^{2}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$ These results are used all the time in mathematics, and we call them the first and second algebraic identities. Learn these, and you’ll save a lot of time you would’ve spent calculating! Rule The First Algebraic Identity ${\left(a+b\right)}^{2}={a}^{2}+2ab+{b}^{2}$ The Second Algebraic Identity ${\left(a-b\right)}^{2}={a}^{2}-2ab+{b}^{2}$ Example 1 Expand ${\left(x-2\right)}^{2}+{\left(3+x\right)}^{2}$ If you apply the first and second algebraic identities to the squared parentheses, you get $\begin{array}{llll}\hfill & \phantom{=}{\left(x-2\right)}^{2}+{\left(3+x\right)}^{2}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =\phantom{\rule{-0.17em}{0ex}}\left({x}^{2}-4x+4\right)+\phantom{\rule{-0.17em}{0ex}}\left(9+6x+{x}^{2}\right)\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =2{x}^{2}+2x+13\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$ $\begin{array}{llll}\hfill {\left(x-2\right)}^{2}+{\left(3+x\right)}^{2}& =\phantom{\rule{-0.17em}{0ex}}\left({x}^{2}-4x+4\right)+\phantom{\rule{-0.17em}{0ex}}\left(9+6x+{x}^{2}\right)\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =2{x}^{2}+2x+13\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

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Australia's native plants and animals have adapted to life on an isolated continent over millions of years. Since European settlement native animals have had to compete with a range of introduced animals for habitat, food and shelter. These pressures have also had a major impact on our country's soil, waterways and marine ecosystems. Feral animals are non-native (introduced) species that are, or have the potential to become, established in the wild through escape from captivity, deliberate or accidental release and accidental or illegal importation. They are also referred to as pest animals or invasive pest species. In Australia, pest animals typically have few natural predators or fatal diseases and some have high reproductive rates. As a result, their populations have not naturally diminished. Pest animals can multiply rapidly if conditions are favourable. Parks Victoria takes action to control feral animals in Victoria’s national parks and reserves to protect natural and cultural values and meet obligations under the National Parks Act 1975 (Vic.), Flora and Fauna Guarantee Act 1988 (Vic.), Environment Protection and Biodiversity Conservation Act 1999 (Cwlth) and the international Ramsar Wetlands Convention. However, animal control programs are just one way that Parks Victoria takes care of Victoria’s parks. A variety of tools are used to maximise the effectiveness of Victoria’s animal control programs. Many considerations are given (e.g. humaneness, cost, efficiency) to determine which tools, or control methods, are used for particular animals in particular places. Examples of control methods include: - Baiting foxes - Trapping cats - Baiting and trapping for feral pigs - Exclusion fencing to keep deer away from endangered plants - Shooting (aerial and ground) for deer and feral pigs All feral animal management operations are thoroughly planned and implemented under strict protocols and oversight, ensuring that operations are safe, effective, humane and meet obligations of all relevant legislation, Codes of Practice and Standard Operating Procedures. Exotic grazers (e.g. feral goats, feral horses, deer and feral pigs) are not as widespread as foxes, cats and rabbits. Their impacts on the natural environment are caused by grazing, browsing, soil disturbance through feeding habits and trampling with their hard hooves. Goats, deer and pig numbers are controlled by shooting. At some locations, programs which aim to eradicate local populations are in place. Horses are not a natural part of the Australian environment. Their hard hooves can cause serious damage to alpine, subalpine, montane and floodplain environments. This includes the destruction of habitat critical to many threatened plant and animal species, damage to waterways, degradation of fragile vegetation, and soil disturbance that results in erosion or compaction. Visit the Feral horses webpage for more information on Parks Victoria's management of feral horses. There are currently four species of deer established in Victoria: Sambar, Red, Fallow and hog. Deer impact on the natural environment and native species by trampling and destroying plants, increasing grazing pressure and ring-barking young trees. Deer also foul waterholes, cause soil erosion and assist the spread of weeds. The most effective method for controlling deer populations is shooting. Parks Victoria works with professional shooters and accredited volunteers through the Sporting Shooters Association Australia (SSAA) and the Australian Deer Association (ADA) to control deer in Victoria’s parks and reserves. Exclusion fencing is an effective way to protect specific areas or species from feral animal impacts, but is more used for comparative and research purposes than environmental protection. Predation by feral cats is one of the most significant threats to the survival of Victoria’s at-risk native wildlife. They prey on a broad range of invertebrates, amphibians, birds, mammals and reptiles. Feral cats are also known to impact wildlife and agricultural livestock through the transmission of parasites such as toxoplasma and sarcocystis. Feral cats (Felis catus) are found across all of mainland Australia in a variety of habitat types including forests, woodlands, grasslands and deserts. In 2018, feral cats were declared established pests on specified public land in Victoria under the Catchment and Land Protection Act 1994. Parks Victoria must take all reasonable steps to control the spread of, and as far as possible, eradicate feral cats. Parks Victoria manages feral cats through exclusion fencing, poison baiting, trapping and shooting. Baiting is considered to be the most effective form of cat control over broad-scale areas. Cage traps are commonly used to trap feral cats, while rubber-padded leg hold traps can be used in very limited circumstances with ministerial approval. Cat owners are also encouraged to contain and sterilise their domestic cats to reduce unnecessary impact on wildlife and prevent them from contributing to the feral cat population. The Red Fox (Vulpes vulpes) has played a major role in the decline of ground-nesting birds and small to medium sized mammals in Victoria. Foxes are opportunistic predators and scavengers that impact native wildlife, spread weeds and cause production loss in livestock systems. In Victoria, foxes are declared as established pests, requiring all land managers to take all reasonable steps to control the spread of, and as far as possible, eradicate foxes. Parks Victoria delivers fox control programs at priority parks using techniques including large-scale poison baiting, exclusion fencing, rubber-padded leghold traps, shooting and den fumigation. To be most effective, a variety of control tools must be used on an ongoing basis with consideration of the effects on native species and domestic dogs which may also consume baits. Rabbits compete with native animals for food and habitat, damage vegetation and expose soil to erosion. They ringbark trees and shrubs, and prevent regeneration by eating seeds and seedlings. Their impact often increases during drought and immediately after fire when food is scarce and they eat whatever they can. The ecological changes caused by large numbers of rabbits may have contributed to the extinction of several small ground-dwelling mammals and to the decline in numbers of many native plants and animals. Rabbits are most effectively managed by integrated programs involving warren ripping, fumigation and poison baiting. What can I do to help? Volunteer in our parks ParkConnect is Parks Victoria’s online volunteering portal. There are many activities available for volunteers to help protect, maintain and restore Victoria’s natural environment including habitat restoration, weeding and revegetation work. Register online today and find an activity to get involved in! Report sightings of feral animals You can help map feral animal sightings in your local area by reporting them through FeralScan, a national initiative by the Centre for Invasive Species Solutions. Be a good neighbour Everyone has a role to play in managing feral animals and weeds. All sectors of government, industry and the community can work together to protect Victoria’s natural environment. Find out more through Agriculture Victoria: Managing invasive plants and animals. Be a responsible pet owner Simple things like keeping your dog on a leash or desexing your cat and keeping it indoors can have huge benefits for native wildlife and the environment. Zoos Victoria and RSPCA Victoria’s ‘Safe Cat, Safe Wildlife’ campaign provides cat owners with advice and support. Visit www.safecat.org.au for more information. Other tips for responsible pet ownership can be found on the Department of Climate Change, Energy, the Environment and Water webpage: Protecting our Wildlife: Responsible pet ownership. Report new sightings of exotic species If you see any unusual, strange or exotic animal you can report it to the High Risk Invasive Animal project, through Agriculture Victoria. Find out more through Agriculture Victoria: How to report an exotic pest animal sighting. If you are genuinely interested in taking on ownership of a feral horse that Parks Victoria have safely removed from the park, you will be asked to complete an Expression of Interest (EOI) application which details a specific set of criteria. Find out more information at the Rehoming a feral horse webpage.

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Everyone’s talking about the $2.5 billion Curiosity rover‘s “terrifying” Hollywood-blockbuster-worthy landing: seven knuckle-in-teeth minutes in early August during which its aeroshell-armored bulk will plummet through Mars’ thin atmosphere at incredible speeds, snap apart to shed its back-shell, then fire rockets to slow its descent. It’ll be like Iron Man pulling out of a planetary dive, finally hovering dozens of feet above the designated Martian landing site — Gale Crater, near an 18,000-foot tall mound of debris — to gently lower the Mini-Cooper-sized rover itself from a nylon tether. That’s the story you’ll see grabbing eyeballs as we roll toward touchdown on August 6, 2012 — and with good reason, given the landing’s almost mad-sounding chain of must-occur-exactly-so events. But what happens once the rover’s safely on the ground and NASA’s popping champagne corks? Assuming Curiosity — aka the Mars Science Laboratory, or MSL — survives the journey, what about the technology it’s hauled for over eight months through 354 million miles of vacuum at close to 48,000 miles per hour, and that it’ll deploy during its nearly two-year exploratory mission? To understand the tech, you have to first understand Curiosity’s purpose. “If you had to reduce the MSL’s scientific mission to one word, it would be habitability,” says MSL deputy project scientist Dr. Ashwin Vasavada. “For better than a decade, we’ve been doing what we call ‘following the water.’” Water is one of the common factors for all known life on Earth, and therefore at the crux of any investigative journey to understand whether Mars could have contained — or ever harbored — life itself. “So now we’re asking the next question, which is not just water, but what about the other ingredients that life would require,” says Vasavada, noting that Curiosity has a much broader mission than prior rovers: looking for life sources like carbon, water, sunlight and chemical energy, as well as hazards to life in the form of radiation. “We do this broad survey of the environmental conditions at our landing site to see if we can call anything we find a habitable environment,” he says. Radiation Assessment Detector (RAD) Speaking of radiation, Curiosity’s RAD — the first of 10 instruments turned on — was designed to analyze radiation from the Martian surface, but also in the confines of the spacecraft carrying the rover to Mars during its eight month journey, to help assess the impact of radiation on astronauts who might someday participate in a manned mission to the Red Planet. “The RAD instrument is unique in that we’re carrying it on behalf of the Human Exploration & Operations branch of NASA,” says Vasavada. “We have nine scientific instruments that come from the scientific community with the goal of addressing human habitability on Mars, and then we have this one instrument, RAD, trying to understand what astronauts would have to deal with on the surface. It also plays well into our habitability investigation, because it measures the same radiation that would harm humans or any other microbial life. So it has a dual purpose.” But the key point, says Vasavada, is that with RAD, we’ll be able to acquire data we’ve never had before: radiation levels on the journey from Earth to Mars, and at the surface of the planet itself. Radioisotope Thermoelectric Generator (RTG) Like the Apollo spacecraft and deep space vessels deployed to Jupiter and Saturn, Curiosity will sip power during its two-year mission from electricity produced by the heat from 32 marble-sized pellets containing plutonium-238 dioxide (think “nuclear battery”). That adds up to about 10 pounds, which is pretty substantial, whether you’re a consumer laptop or a multibillions interplanetary mobile science lab. “We’re a big rover, and because of the science we’re doing, we have to carry these big laboratories and a huge arm to take samples,” says Vasavada. “Once you have a big enough rover, you can afford to carry around this RTG. If you mounted this on smaller rovers, like Spirit or Opportunity, they’d keel over. We have a big spacecraft that needs to last a long time, and so we could afford to attach this power source that we’ve used on many missions before to a rover for the first time.” How much power are we talking? “Only 100 watts, so about like a light bulb,” says Vasavada, noting that that’s still better than the power generated by solar panels averaged over the entire day. “We generate 100 watts, 24-and-a-half hours a day, and we store that in a big battery,” he says. “And when we actually run the rover, we do so for five or six hours during the daytime on Mars. We run off the stored energy, so it’s sort of like charging a cellphone.” Heat Rejection System (HRS) Curiosity will have to withstand temperatures that can range from a balmy 86 F to nearly -200 F. By comparison, the lowest recorded non-laboratory surface temperature on Earth to date was about -130 F (in Antarctica, no surprise). To maintain a more stable temperature range, Curiosity employs a thermal regulation system not unlike the liquid-based ones sometimes found at the core of over-clocked do-it-yourself computers. “We use a fluid loop system inside the rover to transfer heat in both directions,” says Vasavada. “The problem is that we have to endure these huge temperature changes. Mars is basically like a desert in having ground that changes temperature drastically between day and night. So we use the fluid loop system to pump heat from the RTG into the electronics at night, when it’s cold. And then in the daytime when it’s hot, especially with all the electronics running, it’ll draw heat from them and radiate it out into the Mars environment.” And everything has to be designed perfectly, too, including the packaging, say the way one piece of material is glued to another — material which Vasavada says can expand and contract at different rates. Get this wrong, and pieces could eventually peel apart or break. Rover Compute Element (RCE) Curiosity employs two computers, one for daily operation and one for backup, each packing a 200 MHz IBM RAD750 (based on IBM’s late 1990s 32-bit PowerPC processors), 256 MB of RAM, 2GB of flash storage and running a multitasking operating system called VxWorks (used in multiple other spacecraft, including both Spirit and Opportunity rovers). “All of our electronics have to be built in a way that allows them to withstand the environmental conditions,” says Vasavada. “So in addition to the temperature, there’s the extremely dry Martian air, where we have to address concerns about electrical arcing, for instance.” But the biggest thing separating computing equipment designed for use on Mars from its consumer-grade counterparts on Earth is its resistance to radiation. “Within Earth’s atmosphere we’re protected from a lot of cosmic rays and solar particles that would cause problems with electronics,” says Vasavada. “But on Mars, as well as on the way to Mars, you’re constantly bombarded by cosmic rays.” The problem, especially with modern computing equipment, is that a single cosmic ray can flip the bit of a particular circuit, explains Vasavada. That can introduce software errors, causing things to fault or execute incorrectly. “All of Curiosity’s electronics are built with fault protection, so they’re always double- or even triple-checking themselves, sending multiple signals and ensuring they match,” he says. “And the computing equipment itself is commercial grade, but in a special radiation-hardened configuration.” (MORE: A Cosmic SUV Blasts Off for Mars)

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From the campfire to the computer. Chocolate production has always started with the cocoa beans being roasted. The native inhabitants of Central America roasted them in clay vessels over an open fire. The Spanish already used iron pans. In the 19th century, the first mechanised roasting machines were then brought in, with the beans heated over a brazier in a receptacle shaped like a drum or sphere. To grind the cocoa beans, the Mayas and Aztecs used the “metate”, a shallow stone bowl. Placed diagonally over a fire, this was used to grind the cocoa beans into cocoa liquor using a stone roller. It was not until the middle of the 18th century that a structure was built with table legs, allowing the beans to be ground standing upright with a kind of rolling pin. This was followed by the long conche, developed in 1879 by Rodolphe Lindt and refined into the conche as we know it today. During the Industrial Revolution, one invention came after another: Fry & Sons was the first company to operate their cocoa processing mills using a Watt steam engine. In 1826, Swiss chocolatier Philippe Suchard invented a chocolate paste mixer, or mélangeur. In 1828, the Dutch chocolate maker Van Houten developed a process for pressing part of the cocoa butter out of the cocoa beans. Fry & Sons remixed this with the cocoa mass and sugar to create a particularly ductile, pourable chocolate mass. Then came the moment that the first milk chocolate was produced: this was much improved by the addition of Henri Nestlé's powdered milk. Today, most steps in the production of chocolate are fully automatic. Modern, computer-controlled conches produce better results in a shorter time. Computers monitor the entire manufacturing process, spotting and correcting the tiniest discrepancies, e.g. in the quantity of ingredients.

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Definition: An opportunity cost is the economic concept of potential benefits that a company gives up by taking an alternative action. In other words, this is the potential benefit you could have received if you had taken action A instead of action B. What Does Opportunity Cost Mean? What is the definition of opportunity cost? Each business transaction and strategy has benefits related to it, but businesses must choose a specific action. By choosing one alternative, companies lose out on the benefits of the other alternatives. In other words, opportunity costs are not physical costs at all. They are theoretical costs or missed opportunities. Let’s take a look at an example. Managers have to evaluate alternative costs in almost every major strategy business decision. For instance, assume a manufacturer needs to increase production and has to decide whether to expand its manufacturing plant or hire a third shift of workers. The benefit of expanding the plant would be that the company would have extra capacity and the ability to hire a third shift in the future. The benefit of hiring a third shift now is that the company would save the building costs and risk of expanding the plant. As you can see, both of these alternatives have mutually exclusive benefits. The management has to choose one of these alternatives. After much debate, the management decides to save costs and hire a third shift of workers. The alternative cost of management hiring a third shift is the inability to increase capacity. This might also lead to lost projects in the future because the business can’t produce them in time. Opportunity costs can be viewed as the price on inaction. In other words, by a company not taking an alternative action, they are missing out on opportunities or incurring alternative costs. It can also be viewed as the pros and cons list of alternative actions. Define Opportunity Costs: Opportunity cost means the foregone benefits that you could have earned had you chosen to a different course of action.

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# Analysis of Algorithms | Set 1 (Asymptotic Analysis) Why performance analysis? There are many important things that should be taken care of, like user friendliness, modularity, security, maintainability, etc. Why to worry about performance? The answer to this is simple, we can have all the above things only if we have performance. So performance is like currency through which we can buy all the above things. Another reason for studying performance is – speed is fun! To summarize, performance == scale. Imagine a text editor that can load 1000 pages, but can spell check 1 page per minute OR an image editor that takes 1 hour to rotate your image 90 degrees left OR … you get it. If a software feature can not cope with the scale of tasks users need to perform – it is as good as dead. Given two algorithms for a task, how do we find out which one is better? One naive way of doing this is – implement both the algorithms and run the two programs on your computer for different inputs and see which one takes less time. There are many problems with this approach for analysis of algorithms. 1) It might be possible that for some inputs, first algorithm performs better than the second. And for some inputs second performs better. 2) It might also be possible that for some inputs, first algorithm perform better on one machine and the second works better on other machine for some other inputs. Asymptotic Analysis is the big idea that handles above issues in analyzing algorithms. In Asymptotic Analysis, we evaluate the performance of an algorithm in terms of input size (we don’t measure the actual running time). We calculate, how does the time (or space) taken by an algorithm increases with the input size. For example, let us consider the search problem (searching a given item) in a sorted array. One way to search is Linear Search (order of growth is linear) and other way is Binary Search (order of growth is logarithmic). To understand how Asymptotic Analysis solves the above mentioned problems in analyzing algorithms, let us say we run the Linear Search on a fast computer and Binary Search on a slow computer. For small values of input array size n, the fast computer may take less time. But, after certain value of input array size, the Binary Search will definitely start taking less time compared to the Linear Search even though the Binary Search is being run on a slow machine. The reason is the order of growth of Binary Search with respect to input size logarithmic while the order of growth of Linear Search is linear. So the machine dependent constants can always be ignored after certain values of input size. Does Asymptotic Analysis always work? Asymptotic Analysis is not perfect, but that’s the best way available for analyzing algorithms. For example, say there are two sorting algorithms that take 1000nLogn and 2nLogn time respectively on a machine. Both of these algorithms are asymptotically same (order of growth is nLogn). So, With Asymptotic Analysis, we can’t judge which one is better as we ignore constants in Asymptotic Analysis. Also, in Asymptotic analysis, we always talk about input sizes larger than a constant value. It might be possible that those large inputs are never given to your software and an algorithm which is asymptotically slower, always performs better for your particular situation. So, you may end up choosing an algorithm that is Asymptotically slower but faster for your software. /div> ## tags: Analysis Articles

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As an actor, I get scripts and it's my job to stay on script, to say my lines and bring to life a character that someone else wrote. Over the course of my career, I've had the great honor playing some of the greatest male role models ever represented on television. You might recognize me as "Male Escort #1." (Laughter) "Photographer Date Rapist," "Shirtless Date Rapist" from the award-winning "Spring Break Shark Attack." (Laughter) "Shirtless Medical Student," "Shirtless Steroid-Using Con Man" and, in my most well-known role, as Rafael. (Applause) A brooding, reformed playboy who falls for, of all things, a virgin, and who is only occasionally shirtless. (Laughter) Now, these roles don't represent the kind of man I am in my real life, but that's what I love about acting. I get to live inside characters very different than myself. But every time I got one of these roles, I was surprised, because most of the men I play ooze machismo, charisma and power, and when I look in the mirror, that's just not how I see myself. But it was how Hollywood saw me, and over time, I noticed a parallel between the roles I would play as a man both on-screen and off. I've been pretending to be a man that I'm not my entire life. I've been pretending to be strong when I felt weak, confident when I felt insecure and tough when really I was hurting. I think for the most part I've just been kind of putting on a show, but I'm tired of performing. And I can tell you right now that it is exhausting trying to be man enough for everyone all the time. Now — right? (Laughter) My brother heard that. Now, for as long as I can remember, I've been told the kind of man that I should grow up to be. As a boy, all I wanted was to be accepted and liked by the other boys, but that acceptance meant I had to acquire this almost disgusted view of the feminine, and since we were told that feminine is the opposite of masculine, I either had to reject embodying any of these qualities or face rejection myself. This is the script that we've been given. Right? Girls are weak, and boys are strong. This is what's being subconsciously communicated to hundreds of millions of young boys and girls all over the world, just like it was with me. Well, I came here today to say, as a man that this is wrong, this is toxic, and it has to end. (Applause) Now, I'm not here to give a history lesson. We likely all know how we got here, OK? But I'm just a guy that woke up after 30 years and realized that I was living in a state of conflict, conflict with who I feel I am in my core and conflict with who the world tells me as a man I should be. But I don't have a desire to fit into the current broken definition of masculinity, because I don't just want to be a good man. I want to be a good human. And I believe the only way that can happen is if men learn to not only embrace the qualities that we were told are feminine in ourselves but to be willing to stand up, to champion and learn from the women who embody them. Now, men — (Laughter) I am not saying that everything we have learned is toxic. OK? I'm not saying there's anything inherently wrong with you or me, and men, I'm not saying we have to stop being men. But we need balance, right? We need balance, and the only way things will change is if we take a real honest look at the scripts that have been passed down to us from generation to generation and the roles that, as men, we choose to take on in our everyday lives. So speaking of scripts, the first script I ever got came from my dad. My dad is awesome. He's loving, he's kind, he's sensitive, he's nurturing, he's here. (Applause) He's crying. (Laughter) But, sorry, Dad, as a kid I resented him for it, because I blamed him for making me soft, which wasn't welcomed in the small town in Oregon that we had moved to. Because being soft meant that I was bullied. See, my dad wasn't traditionally masculine, so he didn't teach me how to use my hands. He didn't teach me how to hunt, how to fight, you know, man stuff. Instead he taught me what he knew: that being a man was about sacrifice and doing whatever you can to take care of and provide for your family. But there was another role I learned how to play from my dad, who, I discovered, learned it from his dad, a state senator who later in life had to work nights as a janitor to support his family, and he never told a soul. That role was to suffer in secret. And now three generations later, I find myself playing that role, too. So why couldn't my grandfather just reach out to another man and ask for help? Why does my dad to this day still think he's got to do it all on his own? I know a man who would rather die than tell another man that they're hurting. But it's not because we're just all, like, strong silent types. It's not. A lot of us men are really good at making friends, and talking, just not about anything real. (Laughter) If it's about work or sports or politics or women, we have no problem sharing our opinions, but if it's about our insecurities or our struggles, our fear of failure, then it's almost like we become paralyzed. At least, I do. So some of the ways that I have been practicing breaking free of this behavior are by creating experiences that force me to be vulnerable. So if there's something I'm experiencing shame around in my life, I practice diving straight into it, no matter how scary it is — and sometimes, even publicly. Because then in doing so I take away its power, and my display of vulnerability can in some cases give other men permission to do the same. As an example, a little while ago I was wrestling with an issue in my life that I knew I needed to talk to my guy friends about, but I was so paralyzed by fear that they would judge me and see me as weak and I would lose my standing as a leader that I knew I had to take them out of town on a three-day guys trip — (Laughter) Just to open up. And guess what? It wasn't until the end of the third day that I finally found the strength to talk to them about what I was going through. But when I did, something amazing happened. I realized that I wasn't alone, because my guys had also been struggling. And as soon as I found the strength and the courage to share my shame, it was gone. Now, I've learned over time that if I want to practice vulnerability, then I need to build myself a system of accountability. So I've been really blessed as an actor. I've built a really wonderful fan base, really, really sweet and engaged, and so I decided to use my social platform as kind of this Trojan horse wherein I could create a daily practice of authenticity and vulnerability. The response has been incredible. It's been affirming, it's been heartwarming. I get tons of love and press and positive messages daily. But it's all from a certain demographic: women. (Laughter) This is real. Why are only women following me? Where are the men? (Laughter) About a year ago, I posted this photo. Now, afterwards, I was scrolling through some of the comments, and I noticed that one of my female fans had tagged her boyfriend in the picture, and her boyfriend responded by saying, "Please stop tagging me in gay shit. Thx." (Laughter) As if being gay makes you less of a man, right? So I took a deep breath, and I responded. I said, very politely, that I was just curious, because I'm on an exploration of masculinity, and I wanted to know why my love for my wife qualified as gay shit. And then I said, honestly I just wanted to learn. (Laughter) Now, he immediately wrote me back. I thought he was going to go off on me, but instead he apologized. He told me how, growing up, public displays of affection were looked down on. He told me that he was wrestling and struggling with his ego, and how much he loved his girlfriend and how thankful he was for her patience. And then a few weeks later, he messaged me again. This time he sent me a photo of him on one knee proposing. (Applause) And all he said was, "Thank you." I've been this guy. I get it. See, publicly, he was just playing his role, rejecting the feminine, right? But secretly he was waiting for permission to express himself, to be seen, to be heard, and all he needed was another man holding him accountable and creating a safe space for him to feel, and the transformation was instant. I loved this experience, because it showed me that transformation is possible, even over direct messages. So I wanted to figure out how I could reach more men, but of course none of them were following me. (Laughter) So I tried an experiment. I started posting more stereotypically masculine things — (Laughter) Like my challenging workouts, my meal plans, my journey to heal my body after an injury. And guess what happened? Men started to write me. And then, out of the blue, for the first time in my entire career, a male fitness magazine called me, and they said they wanted to honor me as one of their game-changers. (Laughter) Was that really game-changing? Or is it just conforming? And see, that's the problem. It's totally cool for men to follow me when I talk about guy stuff and I conform to gender norms. But if I talk about how much I love my wife or my daughter or my 10-day-old son, how I believe that marriage is challenging but beautiful, or how as a man I struggle with body dysmorphia, or if I promote gender equality, then only the women show up. Where are the men? So men, men, men, men! (Applause) I understand. Growing up, we tend to challenge each other. We've got to be the toughest, the strongest, the bravest men that we can be. And for many of us, myself included, our identities are wrapped up in whether or not at the end of the day we feel like we're man enough. But I've got a challenge for all the guys, because men love challenges. (Laughter) I challenge you to see if you can use the same qualities that you feel make you a man to go deeper into yourself. Your strength, your bravery, your toughness: Can we redefine what those mean and use them to explore our hearts? Are you brave enough to be vulnerable? To reach out to another man when you need help? To dive headfirst into your shame? Are you strong enough to be sensitive, to cry whether you are hurting or you're happy, even if it makes you look weak? Are you confident enough to listen to the women in your life? To hear their ideas and their solutions? To hold their anguish and actually believe them, even if what they're saying is against you? And will you be man enough to stand up to other men when you hear "locker room talk," when you hear stories of sexual harassment? When you hear your boys talking about grabbing ass or getting her drunk, will you actually stand up and do something so that one day we don't have to live in a world where a woman has to risk everything and come forward to say the words "me too?" (Applause) This is serious stuff. I've had to take a real, honest look at the ways that I've unconsciously been hurting the women in my life, and it's ugly. My wife told me that I had been acting in a certain way that hurt her and not correcting it. Basically, sometimes when she would go to speak, at home or in public, I would just cut her off mid-sentence and finish her thought for her. It's awful. The worst part was that I was completely unaware when I was doing it. It was unconscious. So here I am doing my part, trying to be a feminist, amplifying the voices of women around the world, and yet at home, I am using my louder voice to silence the woman I love the most. So I had to ask myself a tough question: am I man enough to just shut the hell up and listen? (Laughter) (Applause) I've got to be honest. I wish that didn't get an applause. (Laughter) Guys, this is real. And I'm just scratching the surface here, because the deeper we go, the uglier it gets, I guarantee you. I don't have time to get into porn and violence against women or the split of domestic duties or the gender pay gap. But I believe that as men, it's time we start to see past our privilege and recognize that we are not just part of the problem. Fellas, we are the problem. The glass ceiling exists because we put it there, and if we want to be a part of the solution, then words are no longer enough. There's a quote that I love that I grew up with from the Bahá'í writings. It says that "the world of humanity is possessed of two wings, the male and the female. So long as these two wings are not equivalent in strength, the bird will not fly." So women, on behalf of men all over the world who feel similar to me, please forgive us for all the ways that we have not relied on your strength. And now I would like to ask you to formally help us, because we cannot do this alone. We are men. We're going to mess up. We're going to say the wrong thing. We're going to be tone-deaf. We're more than likely, probably, going to offend you. But don't lose hope. We're only here because of you, and like you, as men, we need to stand up and become your allies as you fight against pretty much everything. We need your help in celebrating our vulnerability and being patient with us as we make this very, very long journey from our heads to our hearts. And finally to parents: instead of teaching our children to be brave boys or pretty girls, can we maybe just teach them how to be good humans? So back to my dad. Growing up, yeah, like every boy, I had my fair share of issues, but now I realize that it was even thanks to his sensitivity and emotional intelligence that I am able to stand here right now talking to you in the first place. The resentment I had for my dad I now realize had nothing to do with him. It had everything to do with me and my longing to be accepted and to play a role that was never meant for me. So while my dad may have not taught me how to use my hands, he did teach me how to use my heart, and to me that makes him more a man than anything. Thank you. (Applause)

Why I'm done trying to be "man enough"

HackerRank – Zig Zag Sequence solution In this article, I’ll explain the Zig Zag Sequence algorithm problem on HackerRank. Problem statement: You’re given an integer array with an odd number of elements (ex: [5, 2, 3, 1, 4]). You need to re-arrange the elements so they’re in a zig zag sequence, which means: • The first half of elements (first to middle) are in increasing order (ex: 1, 2, 5). • The last half of elements (middle to last) are in decreasing order (ex: 5, 4, 3). • In other words: elements in increasing order < middle element > elements in decreasing order. Here’s a diagram to help you visualize what a zig zag sequence looks like: Furthermore, since there can be more than one valid zig zag sequence (ex: [1, 4, 5, 3, 2]), you need to return the lexicographically smallest one. In this example, [1, 2, 5, 4, 3] < [1, 4, 5, 3, 2] lexicographically, which is why [1, 2, 5, 4, 3] is the answer. Note: For the actual problem in HackerRank, you have to fix a buggy implementation of this algorithm. In order to fix it, you have to know how it should be implemented, which I’ll explain here. Approach Let’s figure out the algorithm by looking at input [7, 2, 5, 4, 3, 6, 1]. By definition of the zig zag sequence (increasing order < middle > decreasing order), notice that the middle element must the largest element. So we have: Input: 7, 2, 5, 4, 3, 6, 1 Zig zag: _ _ _ < 7 > _ _ _Code language: plaintext (plaintext) Second, because we need to find the lexicographically smallest sequence, this means we should put the smallest possible values at the beginning of the array. And they need to be in increasing order: Input: 7, 2, 5, 4, 3, 6, 1 Zig zag: 1, 2, 3 < 7 > _ _ _ Code language: plaintext (plaintext) The most efficient way to get to this point is to sort the input array in increasing order. After this, we know the largest element is at the end of the array, which means we can swap it to the middle: Input: 7, 2, 5, 4, 3, 6, 1 Sorted: 1, 2, 3, 4, 5, 6, 7 Swap largest to middle: 1, 2, 3 < 7 > 5, 6, 4Code language: plaintext (plaintext) Finally, the last half of the elements (7, 5, 6, 4) need to be put in decreasing order (7, 6, 5, 4). The middle (7) and last element (4) were swapped and are already in the correct positions. We can reverse the remaining elements (5, 6) to put them in decreasing order (6, 5): Input: 7, 2, 5, 4, 3, 6, 1 Sorted: 1, 2, 3, 4, 5, 6, 7 Swap largest to middle: 1, 2, 3 < 7 > 5, 6, 4 Reverse sort remaining: 1, 2, 3, < 7 > 6, 5, 4Code language: plaintext (plaintext) And that’s the zig zag sequence: 1, 2, 3, 7, 6, 5, 4. This can be expressed in pseudocode like this: given: int[] input mid = input.Length / 2 last = input.Length - 1 //step 1 - sort in increasing order sort(input) //step 2 - put largest in middle swap(input[mid], input[last]) //step 3 - reverse remaining elements left = mid + 1 right = last - 1 loop while left < right swap(input[left], input[right]) left++ right-- return inputCode language: plaintext (plaintext) Note: Swapping the largest element to the middle could’ve been done in the loop too (from mid to last). Technically, it’s not a special case. However, treating it like it’s special makes the algorithm easier to understand. Since we know the array always has an odd length, and arrays start at 0, we can get the middle index by doing integer division (it chops off decimals). Hence, Length / 2 is the middle index. Code Here is an example of the algorithm (implemented in C#): int[] arr = new int[] { 7, 2, 5, 4, 3, 6, 1 }; int n = arr.Length; int midIndex = n / 2; int lastIndex = n - 1; //Step 1 - Sort Array.Sort(arr); //Step 2 - Swap largest element into the middle int max = arr[lastIndex]; arr[lastIndex] = arr[midIndex]; //7 / 2 = 3.5, 3 arr[midIndex] = max; //Step 3 - Reverse remaining elements int leftIndex = midIndex + 1; int rightIndex = lastIndex - 1; while(leftIndex < rightIndex) { int tmp = arr[leftIndex]; arr[leftIndex] = arr[rightIndex]; arr[rightIndex] = tmp; leftIndex++; rightIndex--; } Console.WriteLine(string.Join(",", arr)); Code language: C# (cs) This outputs the zig zag sequence: 1,2,3,7,6,5,4 2 thoughts on “HackerRank – Zig Zag Sequence solution” 1. Thank you, your explanation is more simple and easier to understand. Reading the original question makes me wonder if I am bad at programming or just bad in English ?

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Sometimes, the brain cells temporarily disrupt the electrical signals the brain sends to other parts of the body. It is not as uncommon as one would think, especially among children. Such a condition is medically termed as Seizures. A top pediatrician in Mumbai shares his views, Some seizures like twitching of muscles, jerking of body and stiffness, can be easily recognizable. Others, which do not have any signs on the outside, can obviously be harder to track. Even though there are a few types of seizures which do affect the brain in a negative way, they do not necessarily mean that there is damage being done to the brain. The symptoms can vary because they depend upon which part of the brain was responsible for the seizure, but almost all obvious symptoms have one thing in common – uncontrollable muscle spasms and sometimes the loss of consciousness. Sometimes, medical conditions can result in seizures, like infections, low blood sugar, drug overdose or head injuries. Brain tumors or similar medical complications can also affect the functioning of the brain, resulting in seizures. Basically, any activity which might induce a sudden lack of oxygen in the brain, or reduction of blood flow to the brain, can be responsible for seizure. Parents should keep track, and if the seizures start occurring with more frequency and occur consistently, then their child may be suffering from epilepsy. Children under the age of 5 have febrile seizures, which occur usually some time after they have developed fevers over 100 degrees. Even though such seizures might scare parents and children, they are brief and have rarely known to cause any serious complications. However, do get the child checked for the cause of fever, because if it is due to an infection like meningitis, the seizures might gradually become dangerous. Breath-holding spells are also common in children of this age group, leading to seizures. Contrary to its name, children known to have an exaggerated reflex are more at risk. For children with exaggerated reflexes, they have a tendency to hold their breath when they are hurt emotionally or physically. After that, they start turning pale, lose consciousness and might experience a seizure with convulsions. These spells have been known to stop without any external intervention, with the child rarely suffering any serious damage. However, it is important that you contact a pediatrician if in case such a spell repeats itself. 10% of children who do not suffer from the seizure mentioned above, experience fainting spells. These spells, also known as syncope, can stiffen the body of the child and make it go through minor convulsions. Most children require no specialized treatments for such spells. The past few years have seen great advancement for treatments. As of today, there are numerous options of medications available to control seizures. But it should be noted that children who experience epilepsy might have a treatment different from those who suffer normal seizures. The New Moms Club is home to thousands of new & expecting moms. Click here to join the club & share your experiences. Credihealth is India’s No.1 Medical Assistance company. Credihealth gives guidance to a patient from the first consultation through the entire hospitalization process. A team of in-house doctors and medical experts help the patient find the right doctor, book appointment, request cost estimate for procedures and manage admission & discharge processes. Share your comments and queries below and we will be happy to guide you through. Get FREE assistance from medical experts to select the best gynecologist & pediatrician.

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# The mass of the moon is 7.36×1022kg and its distance to the Earth is 3.84×108m. What is the gravitational force of the moon on the earth? The moon's force is what percent of the sun's force? Then teach the underlying concepts Don't copy without citing sources preview ? #### Explanation Explain in detail... #### Explanation: I want someone to double check my answer 4 ccrowe1 Share Jan 5, 2017 $F = 1.989 \cdot {10}^{20} k g \frac{m}{s} ^ 2$ 3.7*10^-6% #### Explanation: Using Newton's gravitational force equation $F = \frac{G {m}_{1} {m}_{2}}{{r}^{2}}$ and assuming that the mass of the Earth is ${m}_{1} = 5.972 \cdot {10}^{24} k g$ and ${m}_{2}$ is the given mass of the moon with $G$ being $6.674 \cdot {10}^{-} 11 N {m}^{2} / {\left(k g\right)}^{2}$ gives $1.989 \cdot {10}^{20} k g \frac{m}{s} ^ 2$ for $F$ of the moon. Repeating this with ${m}_{2}$ as the mass of the sun gives $F = 5.375 \cdot {10}^{27} k g \frac{m}{s} ^ 2$ This gives the moon's gravitational force as 3.7*10^-6% of the Sun's gravitational force. • 19 minutes ago • 47 minutes ago • 55 minutes ago • An hour ago • A minute ago • 5 minutes ago • 5 minutes ago • 11 minutes ago • 14 minutes ago • 19 minutes ago • 19 minutes ago • 47 minutes ago • 55 minutes ago • An hour ago

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# 3. Looking for patterns In this part, we look at another way of seeing patterns in multiplication, which is not based upon shapes and counters, but still looks for patterns in rows and columns. Helping pupils explore patterns through practical activities will develop their deeper thinking. Imagine two columns, one for ‘tens’ another for ‘units’. If we think, for example, of the 8 times table, the first four numbers are 8, 16, 24, 32. What happens to the tens and the units as you look down the two columns? You should notice that the tens increase by 1 each time, while the units decrease by 2. Using this observation, what would be the next three numbers? See Resource 3: Tens and units for an example of this exercise. Such observations and questions can be used to help pupils learn about both multiplication and pattern recognition. ## Case Study 3: Recognising patterns in sequences Mr Oko wanted to do an activity exploring number. He wrote the following number sequences on the board, then asked the pupils to help him find the missing number. Pupils had to put their hand up and say what they thought the missing number was, and why. • 4, 6, 8, [ ], 12, 14 • 3, 6, [ ], 12, 15 • 16, 25, [ ], 49, 64 • 1, 11, 111, [ ], 11111 • 1, 1, 2, 3, [ ], 8, 13 When the pupils had finished, he asked them to make up their own patterns and leave a number out. They then swapped their pattern with their partners and tried to fill in the missing numbers. They were very excited and enjoyed the activity. Mr Oko asked if they could see a pattern? Could they predict the last number and each answer? He was pleased some could. Mr Oko used pair work often, as it allowed all pupils to talk and helped their thinking. ## Key Activity: Exploring the multiples of 9 You will need Resource 4: Times table • Stand by the chalkboard and ask pupils to be totally silent. Ask them to watch carefully. • Write the first five multiples of 9 on the blackboard. • Pause. Ask them to look at what is happening to the numbers. • Ask a pupil to complete the pattern to 10 x 9, under the heading ‘tens’ and ‘units’. • Ask the class to share anything they notice, recording and accepting everything without commenting. • Carry on, but stop after 13 x 9, skip some and then write 17 x 9 = ? Now, watch carefully while they try to make sense of what is going on. You may have to prompt them to see the pattern in tens and units. • Finally ask pairs of pupils to investigate other multiples (it is best to start with single digit numbers, 1–9). Can they work out together the pattern for tens and units? Next lesson, ask your pupils to practise multiplication using games. See Resource 5: Multiplication games for ideas. 2. Using games to explore rectangular numbers Resource 1: Square numbers

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Giving Ancient Life Another Chance to Evolve For More Information Contact It’s a project 500 million years in the making. Only this time, instead of playing on a movie screen in Jurassic Park, it’s happening in a lab at the Georgia Institute of Technology. Using a process called paleo-experimental evolution, Georgia Tech researchers have resurrected a 500-million-year-old gene from bacteria and inserted it into modern-day Escherichia coli (E. coli) bacteria. This bacterium has now been growing for more than 1,000 generations, giving the scientists a front row seat to observe evolution in action. “This is as close as we can get to rewinding and replaying the molecular tape of life,” said scientist Betül Kacar, a NASA astrobiology postdoctoral fellow in Georgia Tech’s NASA Center for Ribosomal Origins and Evolution. “The ability to observe an ancient gene in a modern organism as it evolves within a modern cell allows us to see whether the evolutionary trajectory once taken will repeat itself or whether a life will adapt following a different path.” In 2008, Kacar’s postdoctoral advisor, Associate Professor of Biology Eric Gaucher, successfully determined the ancient genetic sequence of Elongation Factor-Tu (EF-Tu), an essential protein in E. coli. EFs are one of the most abundant proteins in bacteria, found in all known cellular life and required for bacteria to survive. That vital role made it a perfect protein for the scientists to answer questions about evolution. After achieving the difficult task of placing the ancient gene in the correct chromosomal order and position in place of the modern gene within E. coli, Kacar produced eight identical bacterial strains and allowed “ancient life” to re-evolve. This chimeric bacteria composed of both modern and ancient genes survived, but grew about two times slower than its counterpart composed of only modern genes. “The altered organism wasn’t as healthy or fit as its modern-day version, at least initially,” said Gaucher, “and this created a perfect scenario that would allow the altered organism to adapt and become more fit as it accumulated mutations with each passing day.” The growth rate eventually increased and, after the first 500 generations, the scientists sequenced the genomes of all eight lineages to determine how the bacteria adapted. Not only did the fitness levels increase to nearly modern-day levels, but also some of the altered lineages actually became healthier than their modern counterpart. When the researchers looked closer, they noticed that every EF-Tu gene did not accumulate mutations. Instead, the modern proteins that interact with the ancient EF-Tu inside of the bacteria had mutated and these mutations were responsible for the rapid adaptation that increased the bacteria’s fitness. In short, the ancient gene has not yet mutated to become more similar to its modern form, but rather, the bacteria found a new evolutionary trajectory to adapt. These results were presented at the recent NASA International Astrobiology Science Conference. The scientists will continue to study new generations, waiting to see if the protein will follow its historical path or whether it will adopt via a novel path altogether. “We think that this process will allow us to address several longstanding questions in evolutionary and molecular biology,” said Kacar. “Among them, we want to know if an organism’s history limits its future and if evolution always leads to a single, defined point or whether evolution has multiple solutions to a given problem.”

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SALT LAKE CITY, Nov. 5, 2009 – University of Utah chemists demonstrated the first conclusive link between the size of catalyst particles on a solid surface, their electronic properties and their ability to speed chemical reactions. The study is a step toward the goal of designing cheaper, more efficient catalysts to increase energy production, reduce Earth-warming gases and manufacture a wide variety of goods from medicines to gasoline. Catalysts are substances that speed chemical reactions without being consumed by the reaction. They are used to manufacture most chemicals and many industrial products. The world's economy depends on them. "One of the big uncertainties in catalysis is that no one really understands what size particles of the catalyst actually make a chemical reaction happen," says Scott Anderson, a University of Utah chemistry professor and senior author of the study in the Friday, Nov. 6 issue of the journal Science. "If we could understand what factors control activity in catalysts, then we could make better and less expensive catalysts." "Most catalysts are expensive noble metals like gold or palladium or platinum," he adds. "Say in a gold catalyst, most of the metal is in the form of large particles, but those large particles are inactive and only nanoparticles with about 10 atoms are active. That means more than 90 percent of gold in the catalyst isn't doing anything. If you could make a catalyst with only the right size particles, you could save 90 percent of the cost or more." In addition, "there's a huge amount of interest in learning how to make catalysts out of much less expensive base metals like copper, nickel and zinc," Anderson says. "And the way you are going to do that is by 'tuning' their chemical properties, which means tuning the electronic properties because the electrons control the chemistry." The idea is to "take a metal that is not catalytically active and, when you reduce it to the appropriate size [particles], it can become catalytic," Anderson says. "That's the focus of our work – to try to identify and understand what sizes of metal particles are active as catalysts and why they are active as catalysts." In the new study, Anderson and his students took a step toward "tuning" catalysts to have desired properties by demonstrating, for the first time, that the size of metal catalyst "nanoparticles" deposited on a surface affects not only the catalyst's level of activity, but the particles' electronic properties. Anderson conducted the study with chemistry doctoral students Bill Kaden and William Kunkel, and with former doctoral student Tianpin Wu. Kaden was first author. The Economy Depends on Catalysts "Catalysts are a huge part of the economy," Anderson says. "Catalysts are used for practically every industrial process, from making gasoline and polymers to pollution remediation and rocket thrusters." Catalysts are used in 90 percent of U.S. chemical manufacturing processes and to make more than 20 percent of all industrial products, and those processes consume large amounts of energy, according to the U.S. Department of Energy (DOE). In addition, industry produces 21 percent of U.S. Earth-warming carbon dioxide emissions – including 3 percent by the chemical industry, DOE says. Thus, improving the efficiency of catalysts is "the key to both energy savings and carbon dioxide emissions reductions," the agency says. Catalysts also are used in drug manufacturing; food processing; fuel cells; fertilizer production; conversion of natural gas, coal or biomass into liquid fuels; and systems to reduce pollutants and improve the efficiency of combustion in energy production. The North American Catalysis Society says catalysts contribute 35 percent or more of global Gross Domestic Product. "The biggest part of this contribution comes from generation of high energy fuels (gasoline, diesel, hydrogen), which depend critically on the use of small amounts of catalysts in … petroleum refineries," the group says. "The development of inexpensive catalysts … is pivotal to energy capture, conversion and storage," says Henry White, professor and chair of chemistry at the University of Utah. "This research is vital to the energy security of the nation." Catalyst Research: What Previous Studies and the New Study Showed Many important catalysts – such as those in catalytic converters that reduce motor vehicle emissions – are made of metal particles that range in size from microns (millionths of a meter) down to nanometers (billionths of a meter). As the size of a catalyst metal particle is reduced into the nanoscale, its properties initially remain the same as a larger particle, Anderson says. But when the size is smaller than about 10 nanometers – containing about 10,000 atoms of catalyst – the movements of electrons in the metal are confined, so their inherent energies are increased. When there are fewer than about 100 atoms in catalyst particles, the size variations also result in fluctuations in the electronic structure of the catalyst atoms. Those fluctuations strongly affect the particles' ability to act as a catalyst, Anderson says. Previous experiments documented that electronic and chemical properties of a catalyst are affected by the size of catalyst particles floating in a gas. But those isolated catalyst particles are quite different than catalysts that are mounted on a metal oxide surface – the way the catalyst metal is supported in real industrial catalysts. Past experiments with catalysts mounted on a surface often included a wide variety of particle sizes. So those experiments failed to detect how the catalyst's chemical activity and electronic properties vary depending with the size of individual particles. Anderson was the first American chemist to sort metal catalyst particles by size and demonstrate how their reactivity changes with size. In previous work, he studied gold catalyst particles deposited on titanium dioxide. The new study used palladium particles of specific sizes that were deposited on titanium dioxide and used to convert carbon monoxide into carbon dioxide. The study not only showed how catalytic activity varies with catalyst particle size, "but we have been able to correlate that size dependence with observed electronic differences in the catalyst particles," Kaden says. "People had speculated this should be happening, but no one has ever seen it." Anderson says it is the first demonstration of a strong correlation between the size and activity of a catalyst on a metal surface and electronic properties of the catalyst. How the Study was Conducted Using an elaborate apparatus in Anderson's laboratory, the chemists aimed a laser beam to vaporize palladium, creating electrically charged, palladium nanoparticles in a vapor carried by a stream of helium gas. Electromagnetic fields are used to capture the particles and send them through a mass spectrometer, which selects only the sizes of palladium particles Anderson and colleagues want to study. The desired particles then are deposited on a single crystal of titanium oxide that measures less than a half-inch on a side. Next, the chemists use various methods to characterize the sample of palladium catalyst particles: specifically the palladium catalyst's electronic properties, physical shape and chemical activity. University of Utah Public Relations 201 Presidents Circle, Room 308 Salt Lake City, Utah 84112-9017 (801) 581-6773 fax: (801) 585-3350 AAAS and EurekAlert! are not responsible for the accuracy of news releases posted to EurekAlert! by contributing institutions or for the use of any information through the EurekAlert! system.

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Successfully choose complementary bipolar transistors |Click here to download a PDF| For circuit designs that use complementary bipolar transistors, you sometimes need to sort the NPN and PNP transistors to have matching dc-current gains (β). One example of a circuit requiring matching is the output stage of an amplifier. The circuit in Figure 1 shows a simple test fixture to achieve this match. Figure 1This circuit makes it easy to test and match the current gain of complementary bipolar transistors. Matched transistors will cause the voltmeter to read 0V. To give the transistors a bit more headroom, an additional voltage drop is introduced between the transistors’ base connections. A voltage differential of a few volts is desirable, so a blue LED is a good choice for D1. Its presence helps to set the base voltage for Q1 (VB1) to about half of the supply voltage (VS). Using an LED in the place of D1 is preferable to using a zener diode due to the sharper knee at the low currents. Moreover, you can see the glow of many blue LEDs at currents below 10 μA; the glow indicates the presence of base current, which means the circuit is working properly. Equation 1 is used to determine the needed supply voltage: A typical blue LED will have a forward voltage of about 3.5V; assuming VBE1=VBE2=0.7V, you get a value for VS of about 9.8V. Resistor R1 sets the emitter current of Q1; it is calculated using Equation 2: Figure 2 For a simpler version, replace the voltmeter with inverse-parallel-connected

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THERE is a lot of energy from ancient sunshine stored in the oil that sits below the deserts of Oman. There is also a lot of sunshine hitting those deserts today. A new wrinkle to an established technology should allow some of that current sunshine to be employed to get at more of the ancient stuff. Using heat—in the form of steam—to liberate disobligingly thick and gunky oil which would otherwise stay in the ground is nothing new. Such enhanced-recovery techniques date back to the 1950s and 40% of California's oil production now depends on steaming subterranean rocks in this way. The steam, however, is made by burning other fossil fuels—normally natural gas—and because heating rock takes a lot of steam, making that steam takes a lot of money. It also adds to the oil's climate footprint. The amount of gas used means that a barrel of Californian heavy oil gives the stuff from Canada's tar sands a run for its money in terms of associated greenhouse-gas emissions. GlassPoint, a small Californian company, thinks it can make steam for oil recovery more cleanly and cheaply by using sunshine to do the heating. This sounds surprising. Solar-thermal power stations, which employ mirrors to concentrate sunlight on boilers and thus raise steam to generate electricity by turning turbines, are far from cheap compared with gas-fired stations. But solar-thermal electricity faces exacting challenges. To feed a turbine you need particularly pure steam, which can be a problem if you are in a desert. And to get the most out of the system you need the steam to be both very hot indeed and available in copious amounts. Oil wells, GlassPoint's founders noticed, are far less demanding consumers in these respects. The steam used can be comparatively dirty. Nor does it have to be infernally hot. And even a small amount of it, added to an existing gas-based recovery process, can make a useful contribution. There are, though, disadvantages to having to work in an oilfield. People building solar-thermal power stations prefer sites low in dust. Those serving the oil industry must go where the rigs are, however dusty and mucky the air. GlassPoint seems to have found a neat solution to this: it puts its mirrors indoors. Greenhouses are easy to buy, quick to erect and, thanks to off-the-shelf kit designed for the purpose, simple to keep clean, too. Moreover, sheltering the mirrors from the wind allows those mirrors to be a lot lighter, making them both cheap to build and ship, and easier to turn in order to follow the sun. GlassPoint's boss, Rod MacGregor, thinks that taking capital costs and the lifetime of the plant into account his firm can produce steam at $3.78 per million British thermal units (btu), which is $3.58 a gigajoule. Steam from gas comes in at $5.79 per million btu. A pilot project in California, he says, has been producing steam as intended since the beginning of the year. And the company has now signed a deal with Petroleum Development Oman for 7 megawatts of plant—a 16,000-square-metre greenhouse providing some 57 billion btu of steam a year. If it pans out, the technology could spread fast. Mr MacGregor expects Oman to be using 200 trillion btu of steam a year for oil recovery by 2015. Not all of that steam could be solar, but a system which used high-pressure solar steam during the day and low-pressure gas-generated steam by night, to keep the pipes hot, might get 80% of its power from the sun. That would free up a lot of gas for export—or for turning into petrochemicals. Enhanced oil recovery currently uses a quite remarkable amount of energy: 1.7 quadrillion btu of gas around the world every year, according to GlassPoint. Not all of that is in sunny places, but there are many deserts besides Oman's that have oil beneath them. The paradoxical possibility, then, is that solar-thermal technology might end up producing a lot more oil than electricity in the years to come.

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🔍 🔍 ## Credits St Joseph's College (St Joseph's College), Bengaluru Mona Gladys has created this Calculator and 1000+ more calculators! Indian Institute of Information Technology (IIIT), Bhopal Mridul Sharma has verified this Calculator and 1000+ more calculators! ## Height of pentagonal trapezohedron given surface area Solution STEP 0: Pre-Calculation Summary Formula Used height = (sqrt(5+2*sqrt(5)))*(sqrt(Area/((sqrt((25/2)*(5+sqrt(5))))))) h = (sqrt(5+2*sqrt(5)))*(sqrt(A/((sqrt((25/2)*(5+sqrt(5))))))) This formula uses 1 Functions, 1 Variables Functions Used sqrt - Squre root function, sqrt(Number) Variables Used Area - The area is the amount of two-dimensional space taken up by an object. (Measured in Square Meter) STEP 1: Convert Input(s) to Base Unit Area: 50 Square Meter --> 50 Square Meter No Conversion Required STEP 2: Evaluate Formula Substituting Input Values in Formula h = (sqrt(5+2*sqrt(5)))*(sqrt(A/((sqrt((25/2)*(5+sqrt(5))))))) --> (sqrt(5+2*sqrt(5)))*(sqrt(50/((sqrt((25/2)*(5+sqrt(5))))))) Evaluating ... ... h = 7.05676736882091 STEP 3: Convert Result to Output's Unit 7.05676736882091 Meter --> No Conversion Required 7.05676736882091 Meter <-- Height (Calculation completed in 00.406 seconds) ## < 11 Other formulas that you can solve using the same Inputs Diagonal of a Rectangle when breadth and area are given Diagonal of a Rectangle when length and area are given diagonal = sqrt(((Area)^2/(Length)^2)+(Length)^2) Go Side of a Kite when other side and area are given side_a = (Area*cosec(Angle Between Sides))/Side B Go Perimeter of rectangle when area and rectangle length are given perimeter = (2*Area+2*(Length)^2)/Length Go Buoyant Force buoyant_force = Pressure*Area Go Perimeter of a square when area is given perimeter = 4*sqrt(Area) Go Diagonal of a Square when area is given diagonal = sqrt(2*Area) Go Length of rectangle when area and breadth are given Breadth of rectangle when area and length are given Pressure when force and area are given pressure = Force/Area Go Stress stress = Force/Area Go ## < 11 Other formulas that calculate the same Output Height of a triangular prism when lateral surface area is given height = Lateral Surface Area/(Side A+Side B+Side C) Go Height of an isosceles trapezoid height = sqrt(Side C^2-0.25*(Side A-Side B)^2) Go Altitude of an isosceles triangle height = sqrt((Side A)^2+((Side B)^2/4)) Go Height of a triangular prism when base and volume are given height = (2*Volume)/(Base*Length) Go Height of a trapezoid when area and sum of parallel sides are given height = (2*Area)/Sum of parallel sides of a trapezoid Go Altitude of the largest right pyramid with a square base that can be inscribed in a sphere of radius a height = 4*Radius of Sphere/3 Go Height of Cone inscribed in a sphere for maximum volume of cone in terms of radius of sphere height = 4*Radius of Sphere/3 Go Height of Cone circumscribing a sphere such that volume of cone is minimum height = 4*Radius of Sphere Go Height of parabolic section that can be cut from a cone for maximum area of parabolic section height = 0.75*Slant Height Go Height of a circular cylinder of maximum convex surface area in a given circular cone height = Height of Cone/2 Go Height of Largest right circular cylinder that can be inscribed within a cone height = Height of Cone/3 Go ### Height of pentagonal trapezohedron given surface area Formula height = (sqrt(5+2*sqrt(5)))*(sqrt(Area/((sqrt((25/2)*(5+sqrt(5))))))) h = (sqrt(5+2*sqrt(5)))*(sqrt(A/((sqrt((25/2)*(5+sqrt(5))))))) ## What is a trapezohedron? The n-gonal trapezohedron, antidipyramid, antibipyramid, or deltohedron is the dual polyhedron of an n-gonal antiprism. The 2n faces of the n-trapezohedron are congruent and symmetrically staggered; they are called twisted kites. With a higher symmetry, its 2n faces are kites (also called deltoids). The n-gon part of the name does not refer to faces here but to two arrangements of vertices around an axis of symmetry. The dual n-gonal antiprism has two actual n-gon faces. An n-gonal trapezohedron can be dissected into two equal n-gonal pyramids and an n-gonal antiprism. ## How to Calculate Height of pentagonal trapezohedron given surface area? Height of pentagonal trapezohedron given surface area calculator uses height = (sqrt(5+2*sqrt(5)))*(sqrt(Area/((sqrt((25/2)*(5+sqrt(5))))))) to calculate the Height, The Height of pentagonal trapezohedron given surface area formula is defined as the measure of vertical distance from one top to bottom face of pentagonal trapezohedron, where h = height of pentagonal trapezohedron. Height and is denoted by h symbol. How to calculate Height of pentagonal trapezohedron given surface area using this online calculator? To use this online calculator for Height of pentagonal trapezohedron given surface area, enter Area (A) and hit the calculate button. Here is how the Height of pentagonal trapezohedron given surface area calculation can be explained with given input values -> 7.056767 = (sqrt(5+2*sqrt(5)))*(sqrt(50/((sqrt((25/2)*(5+sqrt(5))))))). ### FAQ What is Height of pentagonal trapezohedron given surface area? The Height of pentagonal trapezohedron given surface area formula is defined as the measure of vertical distance from one top to bottom face of pentagonal trapezohedron, where h = height of pentagonal trapezohedron and is represented as h = (sqrt(5+2*sqrt(5)))*(sqrt(A/((sqrt((25/2)*(5+sqrt(5))))))) or height = (sqrt(5+2*sqrt(5)))*(sqrt(Area/((sqrt((25/2)*(5+sqrt(5))))))). The area is the amount of two-dimensional space taken up by an object. How to calculate Height of pentagonal trapezohedron given surface area? The Height of pentagonal trapezohedron given surface area formula is defined as the measure of vertical distance from one top to bottom face of pentagonal trapezohedron, where h = height of pentagonal trapezohedron is calculated using height = (sqrt(5+2*sqrt(5)))*(sqrt(Area/((sqrt((25/2)*(5+sqrt(5))))))). To calculate Height of pentagonal trapezohedron given surface area, you need Area (A). With our tool, you need to enter the respective value for Area and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well. How many ways are there to calculate Height? In this formula, Height uses Area. We can use 11 other way(s) to calculate the same, which is/are as follows - • height = 4*Radius of Sphere/3 • height = 4*Radius of Sphere • height = Height of Cone/3 • height = 4*Radius of Sphere/3 • height = Height of Cone/2 • height = 0.75*Slant Height • height = sqrt(Side C^2-0.25*(Side A-Side B)^2) • height = (2*Area)/Sum of parallel sides of a trapezoid • height = sqrt((Side A)^2+((Side B)^2/4)) • height = (2*Volume)/(Base*Length) • height = Lateral Surface Area/(Side A+Side B+Side C) Let Others Know

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Food desert, an impoverished area where residents lack access to healthy foods. Food deserts may exist in rural or urban areas and are associated with complex geographic and socioeconomic factors, as well as with poor diet and health disorders such as obesity. Most knowledge of food deserts has come from studies of the United Kingdom and the United States. In fact, the term food desert was introduced in the early 1990s in western Scotland, where it was used to describe the poor access to nutritious foods experienced by residents of a public housing development. Defining food deserts Food deserts are likened to physical desert regions because the search for and acquisition of nutritious foods is not easily accomplished in either environment. Indeed, food deserts often are not readily traversed, particularly by people without cars who rely on public transportation. Furthermore, if nutritious foods are available, they often are unaffordable. However, despite numerous investigations, conducted in not only the United Kingdom and the United States but also Australia, Canada, and New Zealand, the criteria that define food deserts and their boundaries and the reasons for their existence are not fully understood. Socioeconomic factors and food deserts Despite the uncertainties concerning the origins of food deserts, research has suggested that economic factors, such as supply and demand, as well as urban planning, which serves to connect consumers to food retailers and transportation services, are at play. These factors interact in ways that are complex. For example, while the interaction of supply and demand generally determines which food products are available and the price of those products, consumer demand is heavily influenced by personal preference, which itself is influenced by individual behaviour and socioeconomic factors. Hence, in a low-income area where there exists not only a lack of nutritious foods but also a general lack of education about healthy food choices, residents may unknowingly choose unhealthy foods, thereby maintaining the demand for those food products and perpetuating their availability. Food deserts and health disparities The study of food deserts has drawn attention to disparities in food availability, diet, and health that are associated with income level, ethnicity, and local food environment. For example, in several U.S. states, including Maryland, Minnesota, Mississippi, and North Carolina, wealthy neighbourhoods were found to have more supermarkets than poor neighbourhoods, and the same was true for predominantly white versus predominantly black neighbourhoods. Other studies have revealed that some urban and rural food deserts have local food environments characterized by a relatively high number of convenience stores and few or no supermarkets. While convenience stores sell food products, they generally offer high-calorie foods that are low in vital nutrients at relatively high prices and do not offer the wide selection of healthy foods, such as vegetables, fruits, and whole grains, that can be found in supermarkets. As a result, overweight and obesity, as well as cardiovascular disease, diabetes mellitus, and kidney failure, tend to be more prevalent in areas with a greater number of convenience stores relative to supermarkets. Improving access to healthy foods Some countries where food deserts have been determined to exist have introduced measures to improve access to healthy foods. These measures include finding ways to promote the establishment of healthy food retailers in food deserts and to connect consumers to outlets where fresh vegetables and fruits and other healthy foods are available at reasonable cost. The latter may be accomplished through farmers’ markets, exposure to healthy foods in schools, urban garden and agriculture projects, or even online supermarkets that offer healthy foods for order over the Internet and delivery to accessible locations. One of the first countries to attempt to make inroads into the problem of food deserts was the United Kingdom; however, its Food Poverty (Eradication) Bill of 2001 failed passage. The United States also took steps to improve access to healthy foods, introducing the Food, Conservation, and Energy Act of 2008, which was followed by an evaluation of the prevalence of food deserts in the country. In 2010 U.S. Pres. Barack Obama proposed the Healthy Food Financing Initiative (HFFI), which encouraged retailers to bring healthy foods to impoverished urban and rural communities. A large share of subsequent funding for HFFI went to community-development financial institutions for lending to food retailers in food deserts.

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Scientists at the University of Sheffield have shown how bacteria could be used as a future fuel. The research, published in the journal Bioinformatics, could have significant implications for the environment and the way we produce sustainable fuels in the future. Like all living creatures, bacteria sustain themselves through their metabolism, a huge sequence of chemical reactions that transform nutrients into energy and waste. Using mathematical computer models, the Sheffield team have mapped the metabolism of a type of bacteria called Nostoc. Nostoc fixes nitrogen and, in doing so, releases hydrogen that can then potentially be used as fuel. Fixing nitrogen is an energy intensive process and it wasn't entirely clear exactly how the bacterium produces the energy it needs in order to perform. Now the new computer system has been used to map out how this happens. Until now, scientists have had difficulties identifying bacteria metabolic pathways. The bacterial metabolism is a huge network of chemical reactions, and even the most sophisticated techniques can only measure a small fraction of its activity. Dr Guido Sanguinetti, from the University's Department of Computer Science, who led the study, said: "The research uncovered a previously unknown link between the energy machinery of the Nostoc bacterium and its core nitrogen metabolism. Further investigation of this pathway might lead to understanding and improvement of the hydrogen production mechanism of these bacteria. It will certainly be some time before a pool of bacteria powers your car, but this research is yet another small step towards sustainable fuels." He added: " The next step for us will be further investigation into hydrogen production, as well as constructing more mathematical models capable of integrating various sources of biological data." Source: University of Sheffield Explore further: Imaging glucose uptake activity inside single cells

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What Is Biofuel? Biofuel is a type of renewable energy source derived from microbial, plant, or animal materials. Examples of biofuels include ethanol (often made from corn in the United States and sugarcane in Brazil), biodiesel (from vegetable oils and liquid animal fats), green diesel (derived from algae and other plant sources) and biogas (methane derived from animal manure and other digested organic material). Biofuels are most useful in liquid or gaseous form because they are easier to transport, deliver and burn cleanly. - Biofuels are a class of renewable energy derived from living materials. - The most common biofuels are corn ethanol, biodiesel, and biogas from organic byproducts. - Energy from renewable resources puts less strain on the limited supply of fossil fuels, which are considered nonrenewable resources. How Biofuel Works Many in the energy industry view biofuel as vitally important to future energy production because of its clean and renewable properties. Importantly, many of the world's major oil companies are now investing millions of dollars in advanced biofuel research. America's largest oil company, ExxonMobil, says they are funding a broad portfolio of biofuels research programs including ongoing efforts on algae as well as programs on converting alternative, non-food-based biomass feedstocks, i.e., cellulosic biomass, to advanced biofuels. They warn, however, that fundamental technology improvements and scientific breakthroughs are still necessary in both biomass optimization and the processing of biomass into viable fuels. Limitations of Biofuel Individuals concerned about energy security and carbon dioxide emissions see biofuels as a viable alternative to fossil fuels. However, biofuels also have shortcomings. For example, it takes more ethanol than gasoline to produce the same amount of energy, and critics contend that ethanol use is extremely wasteful because the production of ethanol actually creates a net energy loss while also increasing food prices. Biofuels have also become a point of contention for conservation groups that argue bio-crops would go to better use as a source of food rather than fuel. Specific concerns center around the use of large amounts of arable land that are required to produce bio-crops, leading to problems such as soil erosion, deforestation, fertilizer run-off and salinity. The Algae Alternative To help mitigate the problem of large arable land use, companies like ExxonMobil are turning to water-based solutions in the form of algae production. Exxon claims that algae can be cultivated on land unsuitable for other purposes with water that can’t be used for food production. In addition to using non-arable land and not requiring the use of fresh water, algae could potentially yield greater volumes of biofuels per acre than other sources. The other advantage to using algae over other bio-sources is that the algae can be used to manufacture biofuels similar in composition to today’s transportation fuels. This would go a long way to replacing the conventional fossil fuels like gasoline and diesel used today.

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Body-painting started some time before people began to wear garments. There are archeological finds that incorporate markings on the walls of caves where Neanderthals lived. They propose that they had been body-painted with earth pigments, for example, ochre. According to Susanne Åkesson, a professor at Lund University‘s Department of Biology, the tradition of body-painting may have developed simultaneously on different continents. It is not known when the tradition started. In a new study, scientists discovered that body painting especially white painted stripes on the body protects skin from insect bites. This is the first study that shows body-painting has this effect. Moreover, the study highlights the reason behind the body painting of indigenous people. Most of the indigenous communities who paint their bodies live in areas where there is an abundance of bloodsucking horseflies, mosquitoes or tsetse flies. When these insects bite people there is a risk of bacteria, parasites and other pathogens being transferred. During the study, scientists recently seen that the zebra’s stripes go about as security against horseflies. It is additionally realized that pale fur, on horses, for instance, can give assurance, as opposed to dark fur. The revelation won the IgNobel Prize in Physics in 2016. In the new examination, the group has made the exploration a stride further and analyzed plastic models that are indistinguishable size from adult people. For the investigations, which were led in Hungary, the specialists painted three plastic models of people: one dark, one dark with pale stripes and one beige. They at that point covered the three models with a layer of insect glue. The dark model attracted ten times a larger number of horseflies than the stripped model, and the beige model attracted twice the same number of as the striped one. They likewise inspected whether the attraction of horseflies varied between models that were resting or holding up. The outcomes demonstrate that just females were pulled in to the standing models, though the two guys and females were attracted to the supine models. Susanne Åkesson said, “These results are in line with previous experiments in which we showed that males gravitate towards the water in order to drink and land on surfaces that reflect horizontal, linear polarised light, such as signals from a water surface. Females that bite and suck blood from host animals respond to the same signals as the males, but also to light signals from in the vertical plane, such as the standing models.” The study is published in the journal Royal Society Open Science.

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What is in this article?: - Walnut twig beetle project a teddy bear-sized effort - Thousand Cankers wreaking havoc - By itself, the walnut twig beetle does little or no damage. But when coupled with the newly described fungus, Geosmithia morbida, it is killing thousands of walnut trees. Kristina Tatiossian with the ceramic mosaic walnut twig beetle she created. (Photo by Kathy Keatley Garvey) Most people have never seen the walnut twig beetle, a tiny insect that spreads a fungal pathogen that kills walnut trees. No wonder. The insect, measuring about 1.5 millimeters long, is much smaller than a grain of rice. Now, however, they can see a teddy-bear-sized version, thanks to a University of California, Davis entomology major Kristina Tatiossian, a member of the Research Scholars Program in Insect Biology. Through the UC Davis Art/Science Fusion Program, Tatiossian, a junior, crafted a ceramic mosaic sculpture of the tiny walnut twig beetle for her research poster, “Flight Response of the Walnut Twig Beetle, Pityophthorus juglandis, to Aggregation Pheromones Produced by Low Densities of Males.” The beetle jutting from the poster is so true to form that scientists studying the insect not only readily recognize it, but point out that it’s a female. That includes her mentor, chemical ecologist and forest entomologist Steve Seybold of the Davis-based Pacific Southwest Research Station, USDA Forest Service, and an affiliate of the UC Davis Department of Entomology. Seybold and Andrew Graves, a former UC Davis researcher with the UC Davis Department of Plant Pathology, who now works for the USDA Forest Service, first detected the newly recognized beetle-fungus disease, known as Thousand Cankers Disease (TCD), in California in 2008. TCD had been detected earlier in Colorado and its impact had been noted even earlier in New Mexico, Oregon, and Utah. TCD and its history are chronicled in a newly revised “Pest Alert” issued by the USDA Forest Service. The beetle, emerging from a gallery of a black walnut tree, is accurate right down to the concentric ridges that occur on the skin (cuticle) that protects its head. Some observers claim the beetle is smiling and could be a cartoon character. Tatiossian accomplished the research project as part of the Research Scholars Program in Insect Biology, which aims to provide undergraduates with a closely mentored research experience in biology. Headed by professor Jay Rosenheim, and assistant professor Louie Yangof the UC Davis Department of Entomology, the program currently has 12 students; students apply when they are freshmen, sophomores or transfer students. Tatiossian joined the program in 2011 and is mentored by Steve Seybold. Tatiossian completed the ceramic mosaic project over a four-week period. She earlier worked on two UC Davis Art/Science Fusion Program projects, including the “Tree of Life,” with the program’s founders, entomologist/artist Diane Ullman and artist Donna Billick. A former Los Angeles resident, Tatiossian will receive her bachelor’s degree in entomology this June and then plans to attend graduate school to study either biochemistry or virology. Meanwhile, the poster is making the rounds. Tatiossian entered the poster in the Entomological Society of America’s student poster competition last year at its meeting in Knoxville, Tenn., where it drew lots of attention, not only for the research project but for the art.

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### Home > A2C > Chapter 12 > Lesson 12.5.1 > Problem12-200 12-200. Use what you just proved about the sum and product of the roots of a quadratic equation, in problem 12-199, to write a quadratic equation for each of the following pairs of roots. 1. $- 3 + 5 i , - 3 - 5 i$ $(-3 + 5i)+(-3-5i)=-\frac{b}{a}\rightarrow-6=-\frac{b}{a}$ $(-3+5i)(-3-5i)=\frac{c}{a}\rightarrow9-(-25)=\frac{c}{a}$ Choose a to be 1 and write the general quadratic equation using the values you find for b and c. $x^{2} + 6x + 34 = 0$ 1. $\frac { 1 } { 2 } \pm \frac { 3 } { 2 } i$ See part (a). $x^{2} − x + 1 = 0$ 1. $7 \pm \sqrt { 3 }$ See part (a). 1. $7, −6$ See part (a). 1. $\frac { 2 } { 3 } , - \frac { 3 } { 4 }$ See part (a).

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# AP Calculus BC : Ratio Test and Comparing Series ## Example Questions ← Previous 1 3 ### Example Question #1 : Ratio Test And Comparing Series Determine if the following series is divergent, convergent or neither. Neither Inconclusive Convergent Divergent Both Convergent Explanation: In order to figure out if is divergent, convergent or neither, we need to use the ratio test. Remember that the ratio test is as follows. Suppose we have a series . We define, Then if , the series is absolutely convergent. , the series is divergent. , the series may be divergent, conditionally convergent, or absolutely convergent. Now lets apply the ratio test to our problem. Let and Now Now lets simplify this expression to . Since . We have sufficient evidence to conclude that the series is convergent. ### Example Question #1 : Ratio Test And Comparing Series Determine if the following series is divergent, convergent or neither. Divergent Both Neither Convergent Inconclusive Divergent Explanation: In order to figure if is convergent, divergent or neither, we need to use the ratio test. Remember that the ratio test is as follows. Suppose we have a series . We define, Then if , the series is absolutely convergent. , the series is divergent. , the series may be divergent, conditionally convergent, or absolutely convergent. Now lets apply the ratio test to our problem. Let and Now . Now lets simplify this expression to . Since , we have sufficient evidence to conclude that the series is divergent. ### Example Question #1 : Ratio Test And Comparing Series Determine if the following series is divergent, convergent or neither. Convergent Divergent Both Inconclusive Neither Divergent Explanation: In order to figure if is convergent, divergent or neither, we need to use the ratio test. Remember that the ratio test is as follows. Suppose we have a series . We define, Then if , the series is absolutely convergent. , the series is divergent. , the series may be divergent, conditionally convergent, or absolutely convergent. Now lets apply the ratio test to our problem. Let and . Now . Now lets simplify this expression to . Since , we have sufficient evidence to conclude that the series is divergent. ### Example Question #1 : Ratio Test And Comparing Series Determine if the following series is convergent, divergent or neither. Neither Divergent Convergent More tests are needed. Inconclusive Divergent Explanation: To determine if is convergent, divergent or neither, we need to use the ratio test. The ratio test is as follows. Suppose we a series  . Then we define, . If the series is absolutely convergent (and therefore convergent). the series is divergent. the series may be divergent, conditionally convergent, or absolutely convergent. Now lets apply this to our situtation. Let and Now We can rearrange the expression to be Now lets simplify this. When we evaluate the limit, we get. . Since , we have sufficient evidence to conclude that the series diverges. ### Example Question #5 : Ratio Test And Comparing Series Determine if the following series is divergent, convergent or neither. Inconclusive Divergent Convegent Neither More tests are needed. Convegent Explanation: To determine if is convergent, divergent or neither, we need to use the ratio test. The ratio test is as follows. Suppose we a series  . Then we define, . If the series is absolutely convergent (and thus convergent). the series is divergent. the series may be divergent, conditionally convergent, or absolutely convergent. Now lets apply this to our situtation. Let and Now We can rearrange the expression to be . Now lets simplify this. When we evaluate the limit, we get. . Since , we have sufficient evidence to conclude that the series converges. ### Example Question #6 : Ratio Test And Comparing Series Determine if the following series is convergent, divergent or neither. Inconclusive Neither More tests needed. Divergent Convergent Divergent Explanation: To determine if is convergent, divergent or neither, we need to use the ratio test. The ratio test is as follows. Suppose we a series  . Then we define, . If the series is absolutely convergent (therefore convergent). the series is divergent. the series may be divergent, conditionally convergent, or absolutely convergent. Now lets apply this to our situtation. Let and Now We can rearrange the expression to be Now lets simplify this. When we evaluate the limit, we get. . Since , we have sufficient evidence to conclude that the series diverges. ### Example Question #2 : Ratio Test And Comparing Series Determine if the following series is divergent, convergent or neither. More tests are needed. Divergent Inconclusive Neither Convergent Divergent Explanation: To determine if is convergent, divergent or neither, we need to use the ratio test. The ratio test is as follows. Suppose we a series  . Then we define, . If the series is absolutely convergent (and thus convergent). the series is divergent. the series may be divergent, conditionally convergent, or absolutely convergent. Now lets apply this to our situtation. Let and Now We can simplify the expression to be When we evaluate the limit, we get. . Since , we have sufficient evidence to conclude that the series diverges. ### Example Question #8 : Ratio Test And Comparing Series Determine of the following series is convergent, divergent or neither. Divergent More tests are needed. Inconclusive. Convergent Neither Divergent Explanation: To determine whether this series is convergent, divergent or neither we need to remember the ratio test. The ratio test is as follows. Suppose we a series  . Then we define, . If the series is absolutely convergent (and therefore convergent). the series is divergent. the series may be divergent, conditionally convergent, or absolutely convergent. Now lets apply this to our situtation. Let and Now We can rearrange the expression to be Now lets simplify this to. When we evaluate the limit, we get. . Since , we have sufficient evidence to conclude that the series is divergent. ### Example Question #9 : Ratio Test And Comparing Series Determine what the following series converges to using the ratio test and whether the series is convergent, divergent or neither. , and neither. , and divergent. , and convergent. , and neither. , and convergent. , and convergent. Explanation: To determine whether this series is convergent, divergent or neither we need to remember the ratio test. The ratio test is as follows. Suppose we a series  . Then we define, . If the series is absolutely convergent (thus convergent). the series is divergent. the series may be divergent, conditionally convergent, or absolutely convergent. Now lets apply this to our situtation. Let and Now We can rearrange the expression to be Now lets simplify this to. When we evaluate the limit, we get. . Since , we have sufficient evidence to conclude that the series is convergent. ### Example Question #1 : Ratio Test And Comparing Series Determine the convergence or divergence of the following series: The series is conditionally convergent. The series is divergent. The series (absolutely) convergent. The series may be divergent, conditionally convergent, or absolutely convergent. The series (absolutely) convergent. Explanation: To determine the convergence or divergence of this series, we use the Ratio Test: If , then the series is absolutely convergent (convergent) If , then the series is divergent If , the series may be divergent, conditionally convergent, or absolutely convergent So, we evaluate the limit according to the formula above: which simplified becomes Further simplification results in Therefore, the series is absolutely convergent. ← Previous 1 3

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Conversion formula The conversion factor from months to seconds is 2629746, which means that 1 month is equal to 2629746 seconds: 1 mo = 2629746 s To convert 5.3 months into seconds we have to multiply 5.3 by the conversion factor in order to get the time amount from months to seconds. We can also form a simple proportion to calculate the result: 1 mo → 2629746 s 5.3 mo → T(s) Solve the above proportion to obtain the time T in seconds: T(s) = 5.3 mo × 2629746 s T(s) = 13937653.8 s The final result is: 5.3 mo → 13937653.8 s We conclude that 5.3 months is equivalent to 13937653.8 seconds: 5.3 months = 13937653.8 seconds Alternative conversion We can also convert by utilizing the inverse value of the conversion factor. In this case 1 second is equal to 7.1748087185233E-8 × 5.3 months. Another way is saying that 5.3 months is equal to 1 ÷ 7.1748087185233E-8 seconds. Approximate result For practical purposes we can round our final result to an approximate numerical value. We can say that five point three months is approximately thirteen million nine hundred thirty-seven thousand six hundred fifty-three point eight seconds: 5.3 mo ≅ 13937653.8 s An alternative is also that one second is approximately zero times five point three months. Conversion table months to seconds chart For quick reference purposes, below is the conversion table you can use to convert from months to seconds months (mo) seconds (s) 6.3 months 16567399.8 seconds 7.3 months 19197145.8 seconds 8.3 months 21826891.8 seconds 9.3 months 24456637.8 seconds 10.3 months 27086383.8 seconds 11.3 months 29716129.8 seconds 12.3 months 32345875.8 seconds 13.3 months 34975621.8 seconds 14.3 months 37605367.8 seconds 15.3 months 40235113.8 seconds

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# How to Calculate Distance of Closest Approach? Author Danny Orlandini Posted Sep 10, 2022 In order to calculate the distance of closest approach, we must first understand what this term means. Closest approach is defined as the shortest distance between two heavenly bodies, or the point at which they are nearest to each other. This can be thought of as the point at which the bodies are most compatible with each other. There are a few different ways to calculate the distance of closest approach, and we will discuss each method in detail. One way to calculate the distance of closest approach is to use the laws of motion. These laws state that objects in motion will continue in motion in a straight line unless acted upon by an outside force. This means that if we know the starting position and velocity of two objects, we can predict their future position and calculate the distance between them. This method is relatively simple and easy to do, but it does have some limitations. First, it only works for objects that are moving in a straight line. Second, it assumes that the objects will not be affected by any outside forces. This means that this method is not always accurate, but it can give us a good estimate of the distance of closest approach. Another way to calculate the distance of closest approach is to use the law of gravity. This law states that every object in the universe is attracted to every other object by a force known as gravity. The strength of this force is dependent on the mass of the objects and the distance between them. This method is more accurate than the first method, but it can be more difficult to calculate. In order to use this method, we must first determine the mass of the objects and the distance between them. Once we have this information, we can plug it into the equation for gravity and solve for the distance of closest approach. The third and final way to calculate the distance of closest approach is to use the laws of electrostatics. These laws state that charged objects are attracted to or repelled from each other depending on their charge. This method is the most accurate of the three, but it can be the most difficult to understand. In order to use this method, we must first determine the charge of the objects and the distance between them. Once we have this information, we can plug it into the equation for electrostatics and solve for the distance of closest approach. Now that we have discussed the three different methods for calculating the distance of closest approach, we will choose the one that is best for our needs ## How do you calculate the distance of closest approach? In order to calculate the distance of closest approach, you must first understand what this distance represents. The distance of closest approach is the shortest distance between two objects as they pass by each other. This is important to know because it can be used in many different scenarios ranging from planetary orbits to subatomic particles. The distance of closest approach can be used to determine the gravitational force between two objects, the amount of energy needed to escape from a gravitational field, and even the size of a black hole. There are many different ways to calculate the distance of closest approach. The most common method is to use the Law of Universal Gravitation. This states that the force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. This means that the closer two objects are, the more gravity they will have between them. Another way to calculate the distance of closest approach is to use the formula for Newton's Law of Gravity. This states that the force between two objects is equal to the product of their masses divided by the square of the distance between them. This means that the closer two objects are, the more gravity they will have between them. The final way to calculate the distance of closest approach is to use the formula for the Schwarzschild radius. This states that the radius of a black hole is equal to 2 times the gravitational constant times the mass of the black hole. This means that the closer an object is to a black hole, the more gravity there is between them. Knowing how to calculate the distance of closest approach is important in many different fields. In astronomy, it can be used to determine the size of a black hole. In physics, it can be used to determine the amount of energy needed to escape from a gravitational field. In engineering, it can be used to design safe spaceships that can avoid collisions. Knowing how to calculate the distance of closest approach is a useful tool that can be used in many different fields. ## What is the distance of closest approach? In celestial mechanics, the distance of closest approach, also known as periapsis, is the shortest distance between a point on a body's orbit and the body itself. The body may be either a planet or a satellite, such as a moon. The term is used in both cases, but is usually reserved for the latter. The periapsis of a planet's orbit is also known as its perihelion, while the periapsis of a satellite's orbit is its perigee. The word "periapsis" comes from the Greek preposition περί (peri), meaning "around" or "enclosing", and the apsis noun, which means "axis". Consequently, "periapsis" refers to the point on the orbit closest to the body being orbited. The precise definition of "distance of closest approach" depends on the orbit's particulars. For convert from polar to Cartesian coordinates It is the value of the radial component of the body's position vector at the point where the body crosses the plane of the orbit's focus. This focus is generally the body being orbited. In the case of a circular orbit, the distance of closest approach is simply the radius of the orbit. The concept of distance of closest approach is important in many areas of astronomy. For example, it is used in the calculation of the tidal force, which is the force exerted by one body on another due to their mutual gravitational attraction. The tidal force is strongest when the bodies are at their closest approach; as they move away from each other, the force decreases. In addition, the distance of closest approach is used to calculate the minimum energy required to achieve a given orbital velocity. This energy is known as the escape velocity, and is the speed that a body must be travelling in order to escape the gravitationalpull of the body it is orbiting. The escape velocity is greatest when the distance of closest approach is at a minimum. The distance of closest approach can also be used to place constraints on the nature of a planet's orbit. For example, if a planet's orbit is found to be eccentric (that is, not circular), then the planet must be travelling at a different speed at different points in its orbit. The point of greatest speed is known as the periapsis, and the point of slowest speed is known as the apo ## What is the formula for distance of closest approach? Assuming you are asking for the mathematical formula: The distance of closest approach, d, between two point masses, m1 and m2, moving in a straight line with velocities, v1 and v2 is given by: d = (v1*m2 + v2*m1)/(m1+m2) This formula is derived from the classical mechanics concepts of relative velocity and impulse. The relative velocity is simply the difference between the two velocities, v1-v2. The impulse is the product of the two masses and the relative velocity. The distance of closest approach is the point at which the two point masses are travelling at the same velocity. This can be seen by rearranging the formula to solve for v2: v2 = (v1*m2 - d*(m1+m2))/m1 At the distance of closest approach, v2 = v1, so the two point masses are travelling at the same velocity. ## How do you find the distance of closest approach between two objects? The distance of closest approach between two objects is the shortest distance between them. This shortest distance is typically measured from the center of each object. The distance of closest approach is also known as the impact parameter. The impact parameter is important because it is a measure of the likelihood of two objects colliding. The smaller the impact parameter, the greater the chance of a collision. The impact parameter is also a measure of the amount of energy that would be released if a collision did occur. The smaller the impact parameter, the more energetic the collision would be. There are several ways to calculate the impact parameter. One way is to use the ratio of the objects' masses. The impact parameter is equal to the ratio of the masses of the two objects times the distance between them. Another way to calculate the impact parameter is to use the ratio of the objects' sizes. The impact parameter is equal to the ratio of the sizes of the two objects times the distance between them. The most common way to calculate the impact parameter is to use the objects' velocities. The impact parameter is equal to the ratio of the velocities of the two objects times the distance between them. The reason the velocity is used is because the faster an object is moving, the more likely it is to collide with another object. The impact parameter can also be used to calculate the amount of energy that would be released in a collision. The amount of energy released in a collision is equal to the square of the impact parameter. The impact parameter is a measure of the amount of energy that would be released in a collision. The smaller the impact parameter, the more energetic the collision would be. ## What is the distance of closest approach to the sun? The average distance from the sun to the earth is about 93 million miles. The earth's orbit around the sun is not a perfect circle, but rather an ellipse. This means that the earth's distance from the sun varies throughout the year. The point in the earth's orbit when it is closest to the sun is called perihelion, and the point when it is farthest from the sun is called aphelion. The perihelion occurs in early January, and the aphelion in early July. The earth's orbit is not the only thing that affects its distance from the sun. The sun itself is not stationary, but is slowly moving through the Milky Way galaxy. This motion affects the earth's orbit as well, and over long periods of time, can change the shape of the orbit. The earth's orbit has become more eccentric (less circular) over time, and this trend is expected to continue. The distance of closest approach to the sun, or perihelion, is currently about 91.4 million miles. This is about 3% less than the average distance from the sun to the earth. The perihelion is slowly increasing over time, due to the sun's motion through the Milky Way. The perihelion will continue to increase for the next few million years, until it reaches its maximum value of about 94.5 million miles. After that, the perihelion will slowly decrease again, as the sun's motion reverses direction. The changing distance from the sun affects the amount of sunlight that the earth receives. At perihelion, the earth is 3% closer to the sun than average, so it receives 3% more sunlight than average. This extra sunlight causes the northern hemisphere to be slightly warmer than average in January, while the southern hemisphere is cooler than average. The opposite is true in July, when the earth is farthest from the sun. The changing distance from the sun also affects the length of the day. At perihelion, the earth's orbital speed is about 6.7% faster than average, so a day is about 6.7% shorter than average. This difference is too small to be noticeable on a day-to-day basis, but over the course of a year, it adds up to about 24 hours. This means that a year on earth is about 24 hours shorter at perihelion than ## How do you calculate the distance of closest approach to a black hole? When an object approaches a black hole, the black hole's gravity will begin to dominate the object's motion. The force of gravity will cause the object to speed up as it gets closer to the black hole. At the same time, the object will also start to experience a strong tidal force. This tidal force will stretch the object out in the direction of the black hole. As the object gets closer to the black hole, the tidal force will become so strong that it will eventually tear the object apart. The point at which an object is torn apart by the tidal force is known as the point of closest approach. To calculate the distance of closest approach, we need to know the object's mass, the black hole's mass, and the black hole's spin. The distance of closest approach is given by the following equation: D = 3 M * r / (2 M - r) where D is the distance of closest approach, M is the mass of the black hole, and r is the object's radius. The equation above assumes that the black hole is not rotating. If the black hole is rotating, the distance of closest approach will be smaller. ## What is the distance of closest approach of a comet to the sun? A comet is a small, icy, dusty celestial body that, as it approaches the Sun, warms up and releases gas and dust. This gas and dust forms a tail that points away from the Sun. A comet's tail can be very long, sometimes extending millions of kilometers. A comet's orbit around the Sun is usually elliptical. As a comet approaches the Sun, it speeds up. When a comet is at its closest point to the Sun, called perihelion, it is moving faster than at any other time in its orbit. The distance of closest approach of a comet to the Sun can vary depending on the comet's orbit. Some comets, like Comet Halley, have orbits that take them close to the Sun every 76 years or so. Other comets, like CometEncke, have much shorter orbits and can come close to the Sun every 3 years or so. The distance of closest approach of a comet to the Sun can also vary depending on how close the comet is to the Sun when it is first observed. A comet that is farther away from the Sun when it is first observed will take longer to get to perihelion and will therefore have a larger distance of closest approach to the Sun. The distance of closest approach of a comet to the Sun also depends on the comet's orbit. A comet with a more elliptical orbit will have a closer distance of closest approach to the Sun than a comet with a more circular orbit. The distance of closest approach of a comet to the Sun can also be affected by the gravitational pull of other planets. If a comet passes close to a planet, like Jupiter, the planet's gravity will slow the comet down and cause it to take a longer path around the Sun. This will cause the comet to have a larger distance of closest approach to the Sun. The distance of closest approach of a comet to the Sun can also be affected by the comet's own rotation. A comet that is spinning faster will have a smaller distance of closest approach to the Sun than a comet that is spinning slower. The distance of closest approach of a comet to the Sun can also be affected by the comet's composition. A comet that is made of more volatile materials, like water ice, will sublimate, or vaporize, more readily than a comet made of more refractory materials, like dust and rock. This sublimation will cause ## How do you find the distance of closest approach of two galaxies? Observing the sky with the naked eye, one can see an abundance of stars, but no two stars seem to be close together. However, if one looks at the images produced by a large telescope, they will see that some stars do appear close together. In fact, many stars are so close together that they appear to be one single star to the naked eye. These are called binary star systems. There are two types of binary systems, visual and spectroscopic. In a visual binary, the two stars are close enough together that they can be resolved by a telescope. In a spectroscopic binary, the stars are too close together to be resolved, but their movements can be detected by the Doppler effect. The distance between two galaxies is usually much greater than the distance between two stars in a binary system. However, there are some binary galaxies, where two galaxies are so close together that they appear to be one single galaxy. These are called close galaxy pairs. The distance of closest approach of two galaxies can be determined by measuring their redshift. The redshift of a galaxy is a measure of how much the wavelength of its light has been stretched by the expanding universe. The greater the redshift, the more the wavelength has been stretched, and the further away the galaxy is. So, by measuring the redshift of two galaxies in a close pair, we can determine their distance of closest approach. The closer the two galaxies are, the smaller their redshift will be. There are other ways to determine the distance of closest approach of two galaxies, but the redshift method is the most direct. It does not require assumptions about the nature of the galaxies or the expansion of the universe. The distance of closest approach of two galaxies can be a useful tool in understanding the nature of the universe. It can help us to understand the dynamics of binary galaxies, and the effects of gravity on the large-scale structure of the universe. ## What is the distance of closest approach of a star to the earth? Assuming you would like an answer in terms of light years, the closest star to Earth is Proxima Centauri. It is 4.24 light years away from Earth. The next closest star is Alpha Centauri, which is 4.37 light years away from Earth. ### What time of year does the Earth make closest approach to Sun? The Earth makes closest approach to the Sun on average in early January, but this event can occur as early as Feb. 2 or as late as Jan. 31. ### Which planet has the closest approach to the Sun? The Earth makes the closest approach to the Sun of the year on September 23rd, when it comes within about 93 million miles (150 million kilometers) of our star. ### How does the earth's closest approach to the sun affect space? The Earth's closest approach to the sun each year has effects that can reach all the way into space. Several space telescopes keep constant watch on the sun to study its solar storm and flare activity. ### How close can you get to a black hole? There is no definite answer to this question as it depends on a variety of factors, including the size and mass of the black hole in question. However, it is generally thought that you could not physically reach a black hole at a distance greater than about 10 million kilometers. ### How do I use the black hole calculator? To use the black hole calculator, first choose one of the two systems of units. The Standard Mode computes quantities in standard units (i.e. meters, kilometers, and so on), while the Advanced Mode computes quantities in alternative units (e.g. particles per cubic centimeter, or terawatts). Then enter the input values for each category. The black hole calculator will calculate the corresponding output values. Featured Images: pexels.com

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African Greek Orthodox Church, a religious movement in East Africa that represents a prolonged search for a Christianity more African and, its adherents say, more authentic than the denominational mission forms transplanted from overseas. It began when an Anglican in Uganda, Reuben Spartas, heard of the independent, all-black African Orthodox Church in the United States and founded his own African Orthodox Church in 1929. In 1932 he secured ordination by the U.S. church’s archbishop from South Africa, whose episcopal orders traced to the ancient Syrian Jacobite (Monophysite) Church of India. After discovering that the U.S. body was heterodox, the African Church added the term Greek and from 1933 developed an affiliation with the Alexandrian patriarchate of the Greek Orthodox church that culminated in its coming under the control of the first Greek missionary archbishop for East Africa in 1959. Also included were similar but larger churches that had arisen in central and western Kenya. In 1966 tensions arising from missionary paternalism, inadequate material assistance, and young Greek-trained priests who were not particularly African-oriented led Spartas and his followers into secession. The new group, the African Orthodox Autonomous Church South of the Sahara (with some 7,000 members in Uganda), made unsuccessful approaches to other Greek patriarchates. These East African churches have asserted their African autonomy, shared in nationalist political activities, and accommodated to African customs (such as polygamy, ritual purificatory circumcision of females, and divination). At the same time, their vernacular versions of the Liturgy of St. John Chrysostom, use of vestments and icons, and identification with Eastern Orthodoxy represent a search for connection with the primitive church.

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Historical Geology/Sea floor spreading In this article we shall explain what sea-floor spreading is, and the role it plays in plate tectonics; we shall conclude, as usual, with an explanation of how we know that sea-floor spreading is taking and has taken place. The reader will find it useful to be familiar with the article on geomagnetic reversals and the article on marine sediments before reading further. The nature and role of sea-floor spreadingEdit The sea floor is divided by a system of mountain ranges (mid-ocean ridges) each with a deep valley running down the center (mid-ocean rifts); on the bathymetric map to the right you can clearly see the mid-Atlantic ridge. According to the theory of plate tectonics, plates move apart at the rifts. As the lithospheric plates move apart, this makes a gap into which magma intrudes; it also reduces the pressure on the athenosphere below, causing partial melting of the mantle material. The intrusion of this material ensures that the rift is always being filled up by a fresh supply of oceanic crust. This whole process is known as sea-floor spreading. One common misconception is that the intrusion of the magma at the rifts causes the motion of the lithospheric plates. In fact, geologists are well-agreed that this does little or nothing to cause the motion, rather, as explained in the previous paragraph, it is actually the parting of the plates at the ridges which causes the intrusion of the magma. Nonetheless, sea-floor spreading plays a crucial role in plate tectonics: if the plates were unable to move apart at rifts, they would be unable to move at all. In the remainder of this article we shall survey the evidence for sea-floor spreading. Sea floor spreading: how do we know?Edit The proposition that the sea floor spreads out from the mid-ocean rifts, and has been doing so for millions of years, implies a diverse assortment of testable predictions, all of which turn out to be true. As we discussed in a previous article, the Earth's magnetic poles keep swapping their positions. This leads us to a prediction. If igneous rocks have been formed at and spreading out from the mid-ocean rifts, then when we look at the paleomagnetic record in the igneous rocks that form the oceanic crust, what we ought to see is a pattern of stripes of alternating normal and reverse magnetism parallel to the mid-ocean rift and symmetrical around it: and this is in fact what we see. It was this discovery that almost overnight turned the concept of continental drift from a minority view among geologists to a widely-accepted idea. Heat is only conducted very slowly through large bodies of rock. Consequently, if hot rock is produced at the ridges and spreads out from them (cooling, of course, as it does so) we expect the flow of heat from the sea floor to be greatest at the ridges and to gradually decline as we look at the sea floor further away from them. And this is in fact the case (see Pollack et al, 1993, Heat flow from the earth's interior: analysis of the global data set, Reviews of Geophysics 31(3), 267-280, 1993). It is this cooling process that explains why the rifts are flanked by ridges on either side, which gradually slope down as we get further from the rift: the newly produced rock is hotter, and therefore has greater volume than the older rock; the older rock, having moved further from the rift, has had more time to cool down and so to contract. This, by the way, explains why islands capped with coral so often subside into the sea, as mentioned in the article on reefs: as the basalt of the islands is carried further geographically from the rift, and further in time from the heat in which it was formed, it and the rest of the oceanic crust below it will cool, contract, and therefore subside. For the same reason, if the sea floor is spreading out from the rifts, another obvious prediction of the theory is that if geologists apply their dating methods to the basalt sea-floor on either side of a rift, the rocks will be found to be older the further out they are from the ridge system; as is the case, as shown in the map to the right. Accumulation of sedimentEdit Similarly, sediment will have been accumulating on the older parts of the sea-floor for longer than on the newer parts around the mid-ocean rifts, resulting in a deeper sedimentary layer further out from the rifts: this is also the case. Likewise, if the theory of sea-floor spreading is correct, then at any point on the sea floor the fossils found by drilling down to the bottom of the sea-floor sediment will be those deposited when that bit of the sea-floor was freshly produced at the rift. This means that if we look at these deepest-buried fossils, we will see older and older fossils as we look further and further from the ridge; as a result we will see a greater proportion of extinct species. And this is in fact what we see. The layer-cake effectEdit Different sediments tend to accumulate on different parts of the ocean floor. If the ocean floor stayed still, then, other things being equal, we would expect a sample of the sediment from any particular place on the sea floor to be pretty much the same all the way down. But according to the theory of sea-floor spreading, the sea-floor has been continuously moving outward from the ridge systems like a conveyor belt, which implies that different sediments will have settled over the same portion of sea-floor as it moved. So, for example, marine carbonates settle on the mid-Atlantic rift and rise, because in those shallow waters are above the carbonate compensation depth. Further out, where the waters are deeper, only pelagic clay will settle. So if the sea-floor really has been acting like a conveyor-belt, then when we take a sediment sample from areas of the Atlantic where pelagic mud settles, we should find this clay overlies a layer of limestone that settled when that portion of sea-floor was nearer the ridge; which is what we find. And in general we can state the rule that for any particular spot on the ocean bed, the layers of sediment from bottom to top should be consistent with the journey of the sea-floor from the ridge outwards; which is what we find. So, for example, the conveyor belt moving northwest from the east Pacific Rise west of South America towards Japan crosses the equator and the region where siliceous ooze is deposited. So near Japan we should and do find (from bottom to top) carbonate sediments deposited in the shallow waters at the Pacific Rise; pelagic clay from deeper and non-equatorial waters; calcareous/siliceous ooze as the conveyor belt crosses the equator; and more pelagic clay that accumulates north of the equator. The mid-ocean ridges do not run in a continuous line on the ocean floor: rather, they are discontinuous, being displaced laterally along their length at faults, as can be seen in the map near the top of this article. This leads to an interesting prediction. The top picture in the diagram to the right shows an ordinary strike-slip fault such as the San Andreas fault, with a road cutting across it displaced by motion along the fault. From either side of the fault, one sees the road as being displaced to the left, making it a left fault. Clearly, if you were standing on one side of the fault during an earthquake, you would see the land on the other side of the fault moving to the left relative to you. Now consider the lower picture in the diagram. Standing on either side of the fault and looking at the ocean floor on the other side of the fault, you would see the mid-ocean ridge as having been displaced to the left on the far side of the fault. But if geologists are right about the sea floor spreading out from the mid-ocean ridges, then if you stood on one side of the fault and looked across it during an earthquake, you would see the sea floor on the opposite side moving to the right relative to you. And this is what we do in fact observe. Rate of continental driftEdit The measured rate of sea-floor spreading at the ridges agrees with the measured rate of continental drift, and the inferred rate at which geologists calculate it must have taken place in the past. Structure of oceanic crustEdit From drilling through the oceanic crust, and by looking at the objects known as ophiolites, we can find out the structure of the crust, which is consistent with the theory of sea floor spreading and completely inexplicable without it. I shall not go into details here, as this topic will be covered in the main article on ophiolites. All these disparate lines of evidence add up to a convincing demonstration that the sea floor is currently spreading from the mid-ocean rifts, and has done so in the past.

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Animals & Habitats Animals & Habitats By, Alicia Poblocki The first step to understanding individual animals is to understand their environment. The environment in which an animal lives in is referred to as its habitat. A habitats is a place where living things live and how they survive in that area. Habitats are homes, and everyone needs one! Animals have basic needs for air, water, food, shelter, and space. Plants, animals, and even humans choose habitats for many different reasons, depending on their needs. The picture to the right shows different animals and the habitat that best fits it's needs. Animals live in habitats all over that are suited for them. Some of these habitats include: Grasslands, Rainforests, Deserts, and Arctic Tundra Humans help animals by providing habitats for them as well! Some people build dams in the water to create new habitats for fish, while others take in pets, like dogs and cats, and provide habitats for them in their homes! Animals have a variety of similarites and differences; some are alike in what they look like, what they do, what they eat, and where they live; while others are very different from one another. Many animals share the same habitat because they are from the same group. The picture below shows different habitats with different animals in each one! Scientists divide animals into groups, depending upon how they are alike and different. Six common groups of animals are: Some animals eat plants or other animals for food and may also use plants for shelter and nesting. Within each animal group, there are some similarities and differences in their habitats. Click the "Quiz Me" button to test your knowledge on an animal and it's habitat! So let's learn about 8 different animals using the flash card activity. You will learn: What the animal is called What group it is classified in Where it lives A fun fact about it What it eats Click the "Quiz Me" button to test your knowledge on animals and their habitats! Living things are found almost everywhere in the world. There are different kinds in different places! What kinds of living things and habitats can you think of near your school or home? For more fun with habitats, go to Kids Corner for more games to play!

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In our Mother’s Day blog, we noted our research finding that people listed their mothers as heroes more often than any other person. Fathers were a close second. Why are parents viewed as so heroic? Developmental psychologists tell us that the relationship we have with our parents is the first significant relationship of our lives. It is a relationship that indelibly shapes our values, our aspirations, and our future behavior. Thus when we experience successes in our careers and in our personal lives, it is not surprising that we attribute those triumphs, at least in part, to our parents. The origin of Father’s Day is not entirely clear, but there are several fascinating possibilities. Babylonian scholars have discovered a message carved in clay by a young man named Elmesu roughly 4,000 years ago. In the message, Elmesu wishes his father good health and a long life. Some believe this ancient message represents evidence of an established tradition of honoring fathers, but there is little evidence to support a specially designated Father’s Day until modern times. There is some debate about the origin of the Father’s Day that we celebrate today. Some claim that a West Virginian named Grace Golden Clayton deserves the credit. In 1907, Clayton was grieving the loss of her own father when a tragic mine explosion in Monongah killed 361 men, 250 of whom were fathers. Clayton requested that her church establish a day to honor these lost fathers and to help the children of the affected families heal emotionally. The date she suggested was July 8th, the anniversary of her own father’s death. Still others believe that the first Father’s Day was held on June 19, 1910 through the efforts of Sonora Smart Dodd of Spokane, Washington. Inspired by the newly recognized Mother’s Day, Dodd felt strongly that fatherhood needed recognition as well.Her own father, William Smart, was a Civil War veteran who was left to raise his family alone when his wife died giving birth to their sixth child. Dodd was the only daughter, and she helped her father raise her younger brothers, including her new infant brother Marshall. Whereas Mother’s Day was met with instant enthusiasm, Father’s Day was initially met with scorn and derision. Few people believed that fathers wanted, or needed, any acknowledgement. It wasn’t until 1972 that President Richard Nixon made Father’s Day an official holiday. Today the holiday is widely celebrated in the month of June by more than 52 countries. Why are fathers heroes? The respondents in our survey listed two main reasons. First, fathers are given credit for being great teachers and mentors. They teach us how to fix a flat tire, shoot a basketball, and write a resume. Fathers are less emotional than mothers, but they lead by example and devote time demonstrating life skills to us. Former governor of New York, Mario Cuomo, once said, “I talk and talk and talk, and I haven’t taught people in 50 years what my father taught by example in one week.” Second, fathers are great providers and protectors. Our respondents told us that their fathers were heroes in their commitment to provide for their families, often at great sacrifice. Many fathers work at two or more jobs outside the home to ensure that their families have adequate food and shelter. Fathers also provide us with a sense of safety and protection. Sigmund Freud once wrote, “I cannot think of any need in childhood as strong as the need for a father’s protection.” On this Father’s Day, we wish all fathers, and all men who serve as father figures, all the kudos they so richly deserve. Happy Father’s Day! – – – – – – Do you have a hero that you would like us to profile? Please send your suggestions to Scott T. Allison ([email protected]) or to George R. Goethals ([email protected]).

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## 05 June 2014 ### Argument Writing in Math: Getting Started Are you an English teacher prepping a training on argument writing for the teachers in your building/district (and you want to be applicable to those STEM folks)? Are you a teacher that just went through an argument writing training that left you wanting more? Are you a math teacher that wants to integrate more logic, reasoning, and writing into your course? (Let's be friends!) Whoever you are, I wanted to share a few thoughts and resources to get you started on your argument writing (and thinking) in a math class. If you'd like more of a primer on argument writing in general, check out this post I wrote after I practiced some argument "writing" with my 3 year old daughter last year. (Teaching Argument Writing for Preschoolers...and anyone else!) The most natural application of argument writing is in proofs, which most often come up in Geometry, and should also usually be used in Algebra (but rarely are in my experience). To make a common core connection, standard for mathematical practice #3 requires students to "Construct viable arguments and critique the reasoning of others." Most students experience with proofs (and perhaps you remember your own) is with column proofs like this, for proving things about angles, line segments, or shapes. Have I induced any terror sweats yet? But proofs can also be written in paragraph form, which is where the English training and Hillcock can be applied. Reasons are the warrants, the statements are evidence, and claims will be what must be proved. "Prove that angle A is a supplementary angle," or "prove that the lines defined by y=2x+3 and y=2x-25 are parallel" But...I don't even know how to explain what a proof is! Watch this adorable TED-Ed video introducing and explaining the basis and application of mathematical proof. Want some more? Here's a resource from Berkeley on mathematical logic "First, a proof is an explanation which convinces other mathematicians that a statement is true. A good proof also helps them understand why it is true. The dialogue also illustrates several of the basic techniques for proving that statements are true. Table 1 summarizes just about everything you need to know about logic. It lists the basic ways to prove, use, and negate every type of statement. In boxes with multiple items, the first item listed is the one most commonly used. Don’t worry if some of the entries in the table appear cryptic at first; they will make sense after you have seen some examples. In our first example, we will illustrate how to prove ‘for every’ statements and ‘if. . . then’ statements, and how to use ‘there exists’ statements. These ideas have already been introduced in the dialogue." - from Introduction to Mathematical Arguments (http://math.berkeley.edu/~hutching/teach/proofs.pdf) A couple more resources for your classroom: 1. "Making arguments with equations, figures, and images" - (http://wacillinois.wordpress.com/2014/04/22/making-arguments-with-equations-figures-and-images-writing-in-stem/) As soon as you have students start writing more in math class, some of them will start trying to write out EVERYTHING. The point of this post is that sometimes mathematical symbols are still most appropriate 2. "Developing argument writing in math using crime scene investigations" -(http://teacherleaders.wordpress.com/2012/12/15/developing-argument-writing-in-math-using-crime-scene-investigations/) This blog post from a teacher directly integrates an argument writing text by George Hillocks, Jr., Teaching Argument Writing, Grades 6-12 (with a bonus handout!) as a strategy for students to attack math word problems

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LabCorp and its Specialty Testing Group, a fully integrated portfolio of specialty and esoteric testing laboratories. (See specific Microbiology Specimen sections for additional instructions.) In the average adult male there are approximately 5 quarts (4.75 liters) of blood, composed of about 3 quarts (2.85 liters) of plasma and 2 quarts (1.9 liters) of cells. Blood cells are suspended in the plasma, which is made up of water and dissolved materials, including hormones, antibodies, and enzymes that are being carried to the tissues, and cellular waste products that are being carried to the lungs and kidneys. The major blood cells are classified as red cells (erythrocytes), white cells (leukocytes), and platelets (thrombocytes). The red cells are delicate, round, concave bodies that contain hemoglobin, the complex chemical that transports oxygen and carbon dioxide. Hemolysis occurs when the thin protective membrane that encases the fragile red cells is ruptured, allowing hemoglobin to escape into the plasma. Hemolysis can be caused by rough handling of a blood specimen, leaving the tourniquet on too long (causing blood stasis) or squeezing the tip of the finger too hard during capillary collection, dilution, exposure to contaminants, extremes in temperature, or pathologic conditions. The primary purpose of the white cells is to fight infection. In a healthy person, the white cells respond to minor infections by increasing in number and eliminating pathogens. Platelets are small fragments of special cells that aid in blood clotting. Either plasma or serum may be separated from the blood cells by centrifugation. The essential difference between plasma and serum is that plasma retains fibrinogen (the clotting component), which is removed from serum. Serum is obtained from clotted blood that has not been mixed with an anticoagulant (a chemical that prevents the clotting of blood). This clotted blood is then centrifuged, yielding serum, which contains two types of protein: albumin and globulin. Serum is usually collected in mottled red/gray, gold, or cherry red-top tubes, and red-top tubes are occasionally used. Plasma is obtained from blood that has been mixed with an anticoagulant in the collection tube and has, therefore, not clotted. This mixed blood may then be centrifuged, yielding plasma, which contains albumin, globulin, and fibrinogen. There are numerous coagulation factors (factor VIII, factor IX, etc) involved in the clotting of blood. Several different types of anticoagulants interfere with the activity of these factors to prevent clotting. Both anticoagulants and preservatives may be required for plasma specimens. The specified anticoagulant or preservative must be used for the test ordered. The chemical has been chosen to preserve some feature of the specimen and to work with the method used to perform the test. Blood collected with one anticoagulant suitable for the test described may not be considered suitable for other tests. Because additives are not interchangeable, it is necessary to consult the specimen requirement field of individual test descriptions to determine the appropriate collection requirements for the test ordered. Following the collection, preparation, and transport instructions suggested by LabCorp supports the best possible test results. Materials for proper specimen collection and transport are supplied by LabCorp. Note: Specimens to be tested by LabCorp should be collected in specimen containers provided by LabCorp. Anticoagulants and Preservatives. To ensure accurate test results, all tubes containing an anticoagulant or preservative must be allowed to fill completely. Attempts to force more blood into the tube by exerting pressure, as in collection with a syringe, will result in damage to the red cells (hemolysis). If the vacuum tube is not filling properly, and you are certain that you have entered the vein properly, substitute another tube. Occasionally, vacuum tubes lose their vacuum. If the specimen cannot be properly collected, select another site and using new, sterile collection equipment, collect the specimen. (Special note for light blue [sodium citrate] tubes used for coagulation studies: Always fully seat and hold the tube securely on the Vacutainer® hub while filling.) Note: Use plastic transport tubes for all frozen specimens. Note: Please examine specimen collection and transportation supplies to be sure they do not include expired containers. Red-top tube: Contains no anticoagulant or preservative. Use: Serum or clotted whole blood. Serum must be separated from cells within 45 minutes to two hours depending on the test(s). Please refer to the specimen requirements for the test(s) of interest available in the Directory of Services. Send serum in a plastic transport tube. Mottled red/gray-top, gold-top, or cherry red-top (gel-barrier) tube: Contains clot activator and gel for separating serum from cells, but not anticoagulant. Do not use gel-barrier tubes to submit specimens for therapeutic drug monitoring. Always check the test description to determine whether a gel-barrier tube is acceptable. Use: Serum, may be used for assays requiring serum unless otherwise stated. Separate serum from cells within within 45 minutes to two hours depending on the test(s). Please refer to the specimen requirements for the test(s) of interest available in the Directory of Services. Serum may be sent in the centrifuge tube with an intact barrier (correct separation upon centrifugation) between cells and serum or in a plastic transport tube. If specimen is centrifuged before clotting is complete, a fibrin clot will form on top of the cell. This finding is frequent in hemolyzed specimens. Also, the gel barrier may not be intact and could cause improper separation of serum and cells, possibly affecting test results. Lavender-top tube: Contains K2 EDTA. Use: EDTA whole blood or plasma. Send plasma in a plastic transport tube labeled “Plasma, EDTA.” Send whole blood in a lavender-top tube. Gray-top tube: Contains sodium fluoride (a preservative) and potassium oxalate (an anticoagulant). Use: Sodium fluoride whole blood or plasma. Send plasma in a plastic transport tube labeled “Plasma, Sodium Fluoride.” Send whole blood in a gray-top tube. Blue-top tube (also light blue-top tube): Contains sodium citrate. Be sure to use only tubes with a 3.2% sodium citrate concentration. These are easily identified by the yellow diagonal stripes on the label. Use: Sodium citrate plasma. Send plasma in a plastic transport tube labeled “Plasma, Sodium Citrate.” Send whole blood in a blue-top tube. Green-top tube: Contains sodium heparin or lithium heparin. Use: Heparinized whole blood or plasma. Send plasma in a plastic transport tube labeled “Plasma, Sodium Heparin” or “Plasma, Lithium Heparin.” Send whole blood in a green-top tube. Yellow-top tube: Contains acid citrate dextrose (ACD) solution. Use: ACD whole blood. Send whole blood in a yellow-top tube. Royal blue-top tube: Contains sodium EDTA for trace metal studies. Some royal blue-top tubes do not contain EDTA. Use: EDTA whole blood or plasma. Send whole blood in a royal blue-top tube. Send plasma in a plastic transport tube labeled “Plasma, EDTA from royal blue.” Tan-top tube: Contains sodium EDTA for blood lead analysis. Use: EDTA whole blood. Send whole blood in a tan-top tube. Plasma Preparation Tube (PPT™): Contains EDTA. Use: EDTA plasma for molecular diagnostic tests (eg, polymerase chain reaction (PCR) and/or branched DNA amplification (bDNA) techniques). Upon centrifugation, a gel barrier is formed between the plasma and the cellular components of the blood. The tube can be sent directly to the lab without transferring to a secondary tube. Plastic tubes can be frozen at -80°C without risk of breakage. This section is presented as a guide for trained venipuncture technicians, or phlebotomists, and is not intended to train individuals in venipuncture technique. When drawing blood, please follow all venipuncture procedures recommended for use by recognized organizations and/or in accordance with applicable state regulations involving phlebotomy practices. The Clinical Laboratory Standards Institute (CLSI) is an excellent resource for additional information. Assembling Supplies. Assemble the following supplies: lab coat, gloves, labels, safety needle, needle holder, tourniquet, appropriate tubes, gauze, alcohol sponge, adhesive strip, and sharps container. (See Figure 2.) Put on the lab coat and gloves. The aseptic method of collecting and transporting a blood specimen works on the principle of a vacuum tube for drawing blood. A double-pointed needle or multiple sample needle (both disposable) may be used for venipuncture. Ordinarily, a 21- or 22-gauge needle is used. A small bore, sharp needle causes minimum patient discomfort; 22- or 23-gauge is the smallest bore (or lumen) size recommended to avoid hemolysis. A needle length of 1 to 1½ inches permits an angle of entry that will not pierce both vein walls and enter tissue. When more than one blood specimen is required, multiple sample needles and vacuum tubes make blood collection simpler and more efficient. A tiny rubber sleeve automatically closes when the vacuum tube is removed from the holder, preventing leakage and loss of blood when the tubes are being changed. Place the sharps container within reach. Open the single or multiple sample needle package in front of the patient; do not tear the paper seal for the needle's cap, and do not remove the needle's cap (sterile shield) at this point. (See Figure 3.) Prepare the needle holder in order to attach the safety needle in the appropriate manner. Pull the safety shield on the needle back over the holder before removing the needle shield. Thread the needle into the holder and tighten it firmly. (See Figure 4.) Follow the manufacturer's recommendations on properly setting the needle. With some needle assemblies, you may slide the collection tube into the holder, carefully pushing the tubes forward until the needle touches the stopper. Gently tap tubes containing additives to dislodge any material that may be adhering to the stopper. Carefully push the tube forward until the top edge of the stopper meets the guideline on the holder. Let go. The tube will retract below the guideline. Leave it in that position. This step embeds the full point of the needle in the stopper without puncturing it, preventing blood leakage on venipuncture and the premature loss of vacuum. During venipuncture, do not have the patient clench and unclench the fist repeatedly (“pumping”). This will cause a shift in fluid between the vein and the surrounding tissue. This can lead to changes in concentration of certain analytes. To facilitate making the vein more prominent, the patient may be asked to hold firmly to a rubber ball, a thick wad of gauze, etc. Also, never leave a tourniquet on the arm for more than one minute without releasing it. This can cause discomfort to the patient and may also cause hemolysis. Preparing the Puncture Site. After securing the tourniquet and reaffirming your selection of the best vein, both by sight and palpation, proceed as follows. Note: If a patient has intravenous (IV) solutions going into one or both arms, it is acceptable to puncture the vein 3 to 4 inches below the site of the IV. Considerations for Single and Multiple Sample Collection. If only a single collection tube is required, when the vacuum is exhausted and the tube completely filled, release the tourniquet, and remove the tube from the needle assembly. Place a piece of dry gauze over the needle and withdraw the needle carefully. When multiple specimens are required, remove the first collection tube from the holder as soon as blood flow ceases, invert the first tube to prevent clotting, and gently insert the second tube into the holder. Puncture the diaphragm of the stopper by pushing the tube forward and initiating vacuum suction. (See Figure 5.) Remove and invert each successive tube after it is filled. When all samples have been drawn, remove the entire assembly from the arm. Firmly lock the safety shield on the needle; confirm that it has locked both visually and audibly. Dispose of the used needle and holder in a sharps container according to the provisions in your exposure control plan. Do not recap, cut, or bend any needles; dispose of them in a sharps container. Do not reuse needles. Note: When multiple specimens are drawn from a single venipuncture, the following order is recommended: (1) sterile blood culture tubes, (2) nonadditive clotting tubes (red), (3) coagulation tubes and tubes containing citrate (blue), (4) gel-barrier tubes and tubes with additives (red), (5) tubes containing heparin (green), (6) tubes containing EDTA (lavender, royal blue), (7) tubes containing acid citrate dextrose (yellow), and (8) tubes containing sodium fluoride and potassium oxalate (gray). Note: If the blood has to be mixed with an additive (gently invert the tube 4 to 10 times depending on the specimen tube being used), this must be done immediately after collection. You can do this quickly while the patient's arm is elevated. Mix blood with anticoagulant thoroughly, using a rolling wrist motion and by inverting the tube gently 4 or 10 times. (See Figure 6.) As soon as possible after collection, set the blood upright in a test tube rack. Note: LabCorp works with health care providers to minimize the total volume collected from pediatric and geriatric patients. A syringe is usually used with patients who are difficult to collect by routine venipuncture procedure, including techniques using a safety-winged blood collection set (butterfly). With the syringe technique, venipuncture is accomplished without direct connection to the collection tube. Follow these steps: There are two important guidelines to follow when submitting blood specimens. For some tests, such as chemistry procedures, fasting samples are often the specimen of choice. Also, because hemolysis interferes with many procedures, please submit samples that are as free from hemolysis as possible. Serum Preparation From Red-top Tube. Follow the steps below when preparing a serum specimen for submission. Be sure to use the centrifuge that LabCorp has provided for your use in these separations. For additional information regarding preparation of serum samples, view the following video: 1. Draw whole blood in an amount 2½ times the required volume of serum so that a sufficient amount of serum can be obtained. The 8.5 mL red-top tube will yield approximately 3.5 mL serum after clotting and centrifuging. Label the specimen appropriately (see Specimen Containers). 2. Place the collection tube in the upright position in the rack, and allow the blood to clot at room temperature for 30 to 60 minutes. If clotting fails to occur within 60 minutes, notify the physician. Do not remove the tube stopper. 3. After allowing clot to form, insert the tube in the centrifuge, stopper end up. (See Figure 8.) Operate the centrifuge for no more than 10 minutes at the speed recommended by the manufacturer. Prolonged centrifugation may cause hemolysis. When using a bench-top centrifuge, employ a balance tube of the same type containing an equivalent volume of water. 4. Turn the centrifuge off, if not automatic turn off, and allow it to come to a complete stop. Do not attempt to open the lid and stop by hand or brake. Remove the tube carefully without disturbing the contents. Do not spin more than 10 minutes unless otherwise specified. 5. Remove the stopper and carefully aspirate all serum from cells, using a separate disposable pipette for each tube. Place the tip of the pipette against the side of the tube, approximately ¼ inch above the cell layer. (See Figure 9.) Do not disturb the cell layer or carry any cells over into the pipette. If cells do enter the pipette, recentrifuge the entire specimen. 8. Transfer the serum from the pipette into the transport tube. (See Figure 10.) Inspect the serum for signs of hemolysis and turbidity by holding it up to the light. Be sure to provide the laboratory with the amount of serum specified. 9. Label the tube carefully and clearly with all pertinent information or bar code. Unless otherwise indicated, serum samples may be sent at room temperature. When multiple tests requiring frozen serum are ordered, a plastic transport tube should be prepared for each test. Frozen Serum. When frozen serum is required, place the plastic transport tube(s) (prepared above) immediately in the freezer compartment of the refrigerator. At the time of specimen pickup, inform your professional service representative that you have a frozen specimen to be picked up. A separate frozen sample must be submitted for each test requiring a frozen specimen. A frozen specimen should be held in a freezer at 0°C to -20°C unless a specific test requires the specimen to be frozen at -70°C (dry ice). Note: Some lock boxes may be too small to hold the Frozen Specimen Keeper. The original Transpak containers can be used for these lock boxes. Frozen Gel Packs. To ensure specimen integrity during warm weather, follow these Instructions for Use of frozen gel packs and specimen lockboxes. Gel-barrier Tubes. Gel-barrier (mottled red/gray, gold, or cherry red-top) tubes contain clot activator and gel for separating serum from cells but include no anticoagulant. Adhere to the following steps when using a gel-barrier tube. Do not use gel-barrier tubes to submit specimens for therapeutic drug monitoring, direct Coombs', blood group, and blood types. There are other times when gel-barrier tubes should not be used. Always consult the test description and AccuDraw® prior to collection. Plasma Preparation. When plasma is required, follow these steps. 1. Always use the proper vacuum tube for tests requiring a special anticoagulant (eg, EDTA, heparin, sodium citrate, etc) or preservative. 2. Tap the tube gently to release additive adhering to the tube or stopper diaphragm. (See Figure 11.) 3. Permit the vacuum tube to fill completely. Failure to fill the tube will cause an improper blood-to-anticoagulant ratio and yield questionable and/or QNS test results. 4. To avoid clotting, mix the blood with the anticoagulant or preservative immediately after drawing each sample. 5. To allow adequate mixing, slowly invert the tube eight to ten times (four times for citrate tubes) using a gentle wrist rotation motion. 6. Immediately centrifuge the specimen for as long as 10 minutes or as specified by the tube manufacturer. Do not remove the stopper. 7. Turn the centrifuge off, if not an automatic turn off, and allow it to come to a complete stop. Do not stop it by hand or brake. Remove the tube carefully without disturbing the contents. 8. Remove the stopper and carefully aspirate plasma, using a separate disposable Pasteur pipette for each tube. 9. Place the tip of the pipette against the side of the tube, approximately ¼ inch above the cell layer. Do not disturb the cell layer or carry any cells over into the pipette. Do not pour off; use transfer pipette. 10. Transfer the plasma from the pipette into the transport tube. Be sure to provide the laboratory with the amount of plasma specified. 11. Label all tubes clearly and carefully with all pertinent information or bar code. All tubes should be labeled with the patient's full name or identification number as it appears on the test request form or affix bar code. Also, print on the label the type of plasma submitted (eg, “Plasma, Sodium Citrate,” “Plasma, EDTA,” etc). 12. When frozen plasma is required, place plastic transport tube(s) immediately in the freezer compartment of the refrigerator, and notify your professional service representative that you have a frozen specimen to be picked up. 13. Never freeze glass tubes. For after-hours pickup, follow the steps under Frozen Serum above. Plasma Preparation Using a Plasma Preparation Tube (PPT™) The blood film (commonly called a blood smear) can be a vital part of clinical testing. When performed, it enables the technologist to view the actual physical appearance of the red and white blood cells microscopically. Well-prepared films can be used in performing the differential white cell count, for examining the morphology (size, structure, and shape) of red and white cells to determine the presence of abnormal cells, and also for the examination of the size and number of platelets. The distribution of the cells, as well as their morphology, can be altered by poor slide preparation. The most appropriate slide consists of a film that is exactly one cell thick for maximum visualization of all cell types microscopically. Blood films may be prepared from venous blood (venipuncture) or capillary puncture blood. Slide preparation using venous blood is described below. Follow the steps outlined below. 1. Put on laboratory personal protective equipment. 2. Select two clean, grease-free glass collection slides with frosted ends (new ones whenever possible). 3. Print the patient's name and date on the frosted ends of both slides. (See Figure 12.) 4. Handle all slides only by the frosted ends or by the edges. 5. Place the collection slides frosted side up and to your right on a padded, flat surface near the chair or bed where the specimen is to be collected. 6. Immediately after removing the needle from the vein, gently touch the tip of the needle to one of the clean slides, producing a small drop of blood about 1 to 2 mm in diameter, about the size of a match head. The drop of blood should be in the center line, approximately ¼ inch from the frosted end. Repeat for the second collection slide. Activate the needle's safety feature and dispose of the needle in a sharps container. 7. Hold the left corners of the collection slide with the left thumb and forefinger. 8. Hold the spreader by the frosted end between the right thumb and the index finger. 9. Rest the left end of the spreader at a 45° angle, approximately ½ inch opposite the drop of blood on the slide. This angle prevents the white cells from bunching along the edges. 10. Draw the spreader slide steadily back toward the drop of blood. When the slide contacts the drop, the blood will start to spread to the edges of the spreader slide. (See Figure 13.) 11. Keep the spreader slide at a 45° angle, maintaining light but firm pressure with the spreader slide against the horizontal slide. Push the spreader slide rapidly over the entire length of the slide, pulling a thin smear of blood behind it. A feathered edge usually characterizes a good blood film. The blood should not extend past 3/4 the length of the slide. (See Figure 14.) 12. Prepare the second film in the same manner. 13. Allow the blood films to air dry. Do not blow on the slides. Do not apply fixative. After the slides are completely dry, place them in a labeled slide holder for transport to the laboratory. 1. Slides must not be touched on any area except the long slide edges or frosted ends. 2. Prepare the film immediately, as soon as the drop of blood has been placed on the slide. Any delay will result in abnormal distribution of the white cells, with many of the larger white cells accumulating at the thin edge of the smear. Rouleaux of the red cells (stacking like piles of coins) and platelet clumping will also occur. 4. Common causes of a poor blood film. (See Figure 15.) Blood cultures should be collected directly into the blood culture bottles provided by LabCorp. Please follow the instructions that come with the kit and call your LabCorp representative if you have any questions. You can also go the test description for Blood Culture, Routine in LabCorp's online directory and refer to the Microbiology Specimen Collection and Transport Guide attached in the Related Documents field for additional information on blood culture specimen collection.

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NASA’s mission to the outer solar system has found more light than expected. That could mean more galaxies in the visible universe than we thought— or less, depending on whom you talk to. Point a telescope at a square of space and you’re liable to see something — stars, galaxies, interstellar gas. Now, subtract everything you already know about, and you ought to see nothing — black space. Right? Wrong, according to scientists on the New Horizons team. The spacecraft that flew by Pluto, Charon, and another Kuiper Belt object named Arrokoth has now turned its camera to far-off vistas, only to discover that there’s more light there than we expected. That could have huge implications if it pans out, but tallying all the universe’s light sources gets a bit complicated. How Dark Is Space? Team member Tod Lauer (NSF’s NOIRLab) and his colleagues used data collected by the New Horizons Long Range Reconnaissance Imager (LORRI) camera to snap 195 30-second exposures in seven regions above and below the star-filled galactic plane. They’re using New Horizons because the sky the spacecraft sees is 10 times darker than the one at Earth. Unlike the outer solar system, there’s a lot of dust near Earth and it scatters the Sun’s light in every direction, even backward. Ground-based observers see this dust-scattered sunlight as the zodiacal light, and it has muddled previous attempts to measure the cosmic optical background (COB). Like the more famous cosmic microwave background astronomers measure the COB in two steps: image patches of sky, then subtract the light from all known sources. From New Horizons’ relatively dust-free vantage point, there’s one less component that astronomers have to subtract. There’s still lots of visible light sources to deal with, though: stars and galaxies themselves must be subtracted out of the image, as does light from stars and galaxies that are outside the field of view, but whose light scatters onto the camera. Then there’s the stars and galaxies that are too faint for the camera to resolve — those are removed with the aid of computer simulations. Finally, they subtracted the contribution from all of the Milky Way’s stars, whose light scatters off interstellar dust, basing the calculations on observations of galactic cirrus. But even after accounting for everything that astronomers know makes and scatters visible light, the New Horizons team was left with “extra” light that they still couldn’t explain. Lauer and colleagues called this component a “diffuse cosmic optical background” in the January 10th Astrophysical Journal. “The total unknown amount is more than the integrated flux from all known galaxies,” Lauer said, presenting the results at the 237th meeting of the American Astronomical Society. A Universe Half Empty, or Half Full? If you’ve read other coverage about these results, you might be scratching your head at this point. NASA’s initial press release (since revised) led to headlines claiming that the universe has far fewer galaxies than thought. But that depends on whom you ask. A little more than four years ago, Christopher Conselice (then at University of Nottingham, UK) calculated the total number of galaxies in the universe based on those found in the Hubble Ultra Deep Field (HUDF). Extrapolating to extremely faint magnitudes, he and his colleagues concluded that Hubble had missed 90% of the galaxies in the visible universe, which they estimated tally to at least 2 trillion. That would suggest that there are 10 times more galaxies than are accounted for in existing surveys. Ultimately, the extra light the New Horizons team found could address the question of the total number of galaxies, since the cosmic optical background they measure is about twice what existing galaxy surveys predict. But the study does not settle the question one way or another. "Our work tells you how much money you have in the bank to spend — it doesn’t tell you how to spend it," Lauer explains. "Fill the universe with as many galaxies as you want, but when you’re done the total light that they make has to fit within our measurement." What Makes “Extra” Light? Whether all this “extra” light comes from unknown galaxies isn’t actually clear. All astronomers can say right now is that there’s a source of light that existing catalogs of stars and galaxies don’t capture. Some of the excess may yet find a simple explanation as astronomers dig into the details. Shuji Matsuura (Kwansei Gakuin University, Japan), who also found an indication of “extra” light with his colleagues in the Cosmic Infrared Background Experiment (CIBER), suggested that the New Horizons team might have underestimated the contribution from scattered Milky Way light. “My opinion,” he adds, “is that we have to be careful to claim the existence of the diffuse cosmic optical background at this stage.” Even if the result pans out, there are plenty of other sources of unaccounted light besides faint galaxies. Perhaps astronomers have not properly included the light from galaxies’ faint stellar halos. Or maybe there are more “lost” stars than we thought, tugged away from their home galaxies during mergers and now floating in intergalactic space. There’s also the possibility that there’s something unexpected out there, such as undiscovered black holes or even axions, a proposed (but still hypothetical) dark matter particle. Future observations from space will shed more, ahem, light: Matsuura notes that the CIBER team plans to launch an additional sounding rocket to study the near-infrared background in more detail. And coauthor Marc Postman (STScI) stated at the AAS that while New Horizons has delivered the first successful (albeit “off-label”) outer solar system measurement of the COB, future planetary probes could make such a measurement part of their mission. Editorial note (Feb. 3, 2021): This story has been updated to note that the New Horizons study does not estimate the total number of galaxies, but it does measure the background light that will help future studies in estimating that number.

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Reflections in a Mirror What do we see in the mirror? by Helen Levesley (revised, originally published in 2011) Suitable for Whole School (Sec) To consider what we see when we look in a mirror. Preparation and materials You will need a hand mirror and four volunteers. Ask the students to cast their minds back to when they first looked in the mirror this morning. Point out that they were probably not looking at their best. However, the face staring back at them was a fair reflection of what they look like without their hair brushed, face washed and make-up on. Point out that, if they had looked carefully, they could probably have seen some resemblance to their parents and brothers or sisters. Ask for the help of four volunteers. Ask each of them to look in the hand mirror and describe one thing that they see. For example, they might say, ‘My eyes are brown,’ or ‘I wear glasses.’ Give the volunteers time to make their comments. Ask all of the students to imagine that they are holding a hand mirror and looking at their face in it. Ask them to focus on one thing that they can see. What does their reflection show them? If we look in a mirror, we see our reflection, what we look like – the colour of our eyes or hair. In a long mirror, we can see whether an article of clothing suits us. Looking into a mirror can make us feel great, or help us improve the way we look. In the book Harry Potter and the Philosopher’s Stone, the Mirror of Erised reflects the deepest desires of those who look at it. Harry, who lost his parents when he was young, sees them in the mirror. Ron, who is desperate to achieve, sees himself winning the Quidditch cup and becoming head boy. What a fantastic mirror, to show us what we truly desire, to reflect our very wishes back at us! Ask the students, ‘What would the Mirror of Erised show you?’ A sporting victory, perhaps, or an academic achievement or a family united? Sadly, the Mirror of Erised is a figment of J. K. Rowling’s imagination. Explain that sometimes, mirrors can show us things that we don’t like about ourselves, and things that aren’t true. When someone suffering from anorexia looks into a mirror, a fat person seems to be staring back, instead of a figure of skin and bones. Sometimes, people who have little self-worth and low self-esteem will look in a mirror and see someone they dislike staring back at them. Invite the volunteers to look into the mirror again, but this time, ask them to think of something positive about themselves that cannot be seen in the mirror, but that they reflect towards others. An example might be, ‘I’m helpful’ or, ‘I make people laugh.’ (You may wish the students to share these thoughts, or simply look and then return to their places without speaking.) St Paul, whose letters are in the second half of the Bible, wrote that in our lives, we see things ‘in a mirror dimly’. Mirrors in those days were not as good as mirrors today and produced an image that was not very clear. St Paul was talking about not seeing clearly what God is saying and doing. However, his words can be applied to our lives. When we look at ourselves in a mirror, we see what we want to see - what’s on the surface - not what the mirror really reflects back to us, which is a person of individuality and uniqueness. In the same passage, St Paul said that one day, we would see clearly. I hope that, when you look in the mirror in the mornings, you don’t just focus on what you can see on the outside. Instead, take a look at what you are like on the inside: your positive, good qualities, such as your ability to make others laugh, or qualities that make you a good friend, sister or brother, daughter or son, teacher or student. Time for reflection Let’s think quietly about our positive features, both the things that can be seen in a mirror and the things that cannot be seen, but that we reflect outwards to others like a mirror. Allow me to see in the mirror my positive qualities, as well as the things I dislike about myself. Help me to be aware that there are some things that I can change, and some things that I can’t. Teach me to recognize that the things that I see and am critical about are often what someone else will like about me. Allow me to be positive about my reflection, both the reflection that I can see and the one that I can’t.

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# How do you find the domain and range of f(x) = (x + 8)^2 - 7? Jan 7, 2018 Inspect using the formula $y = a {\left(x - h\right)}^{2} + k$ #### Explanation: From the equation given $f \left(x\right) = {\left(x + 8\right)}^{2} - 7$ we can see that: h = -8 k = -7 From the original equation $y = {x}^{2}$, if h is negative the graph the will shift left or negative x and if k is negative the graph will shift down or negative y. graph{(x+8)^2-7 [-27.05, 12.95, -8.72, 11.28]} Since x will keep increasing to infinity regardless of any x-axis transformations the domain will be the same as $y = {x}^{2}$ Domain: All real numbers However, since a minimum applies to the range, if the graph shifts in the y-axis the range will be different from $y = {x}^{2}$ Range: y ≥ -7

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# 353.8 minutes to hours ## Result 353.8 minutes equals 5.8967 hours You can also convert 353.8 minutes to hours and minutes. ## Conversion formula Multiply the amount of minutes by the conversion factor to get the result in hours: 353.8 min × 0.0166667 = 5.8967 hr ## How to convert 353.8 minutes to hours? The conversion factor from minutes to hours is 0.0166667, which means that 1 minutes is equal to 0.0166667 hours: 1 min = 0.0166667 hr To convert 353.8 minutes into hours we have to multiply 353.8 by the conversion factor in order to get the amount from minutes to hours. We can also form a proportion to calculate the result: 1 min → 0.0166667 hr 353.8 min → T(hr) Solve the above proportion to obtain the time T in hours: T(hr) = 353.8 min × 0.0166667 hr T(hr) = 5.8967 hr The final result is: 353.8 min → 5.8967 hr We conclude that 353.8 minutes is equivalent to 5.8967 hours: 353.8 minutes = 5.8967 hours ## Result approximation For practical purposes we can round our final result to an approximate numerical value. In this case three hundred fifty-three point eight minutes is approximately five point eight nine seven hours: 353.8 minutes ≅ 5.897 hours ## Conversion table For quick reference purposes, below is the minutes to hours conversion table: minutes (min) hours (hr) 354.8 minutes 5.913345 hours 355.8 minutes 5.930012 hours 356.8 minutes 5.946679 hours 357.8 minutes 5.963345 hours 358.8 minutes 5.980012 hours 359.8 minutes 5.996679 hours 360.8 minutes 6.013345 hours 361.8 minutes 6.030012 hours 362.8 minutes 6.046679 hours 363.8 minutes 6.063345 hours ## Units definitions The units involved in this conversion are minutes and hours. This is how they are defined: ### Minutes The minute is a unit of time or of angle. As a unit of time, the minute (symbol: min) is equal to 1⁄60 (the first sexagesimal fraction) of an hour, or 60 seconds. In the UTC time standard, a minute on rare occasions has 61 seconds, a consequence of leap seconds (there is a provision to insert a negative leap second, which would result in a 59-second minute, but this has never happened in more than 40 years under this system). As a unit of angle, the minute of arc is equal to 1⁄60 of a degree, or 60 seconds (of arc). Although not an SI unit for either time or angle, the minute is accepted for use with SI units for both. The SI symbols for minute or minutes are min for time measurement, and the prime symbol after a number, e.g. 5′, for angle measurement. The prime is also sometimes used informally to denote minutes of time. In contrast to the hour, the minute (and the second) does not have a clear historical background. What is traceable only is that it started being recorded in the Middle Ages due to the ability of construction of "precision" timepieces (mechanical and water clocks). However, no consistent records of the origin for the division as 1⁄60 part of the hour (and the second 1⁄60 of the minute) have ever been found, despite many speculations. ### Hours An hour (symbol: h; also abbreviated hr.) is a unit of time conventionally reckoned as 1⁄24 of a day and scientifically reckoned as 3,599–3,601 seconds, depending on conditions. The seasonal, temporal, or unequal hour was established in the ancient Near East as 1⁄12 of the night or daytime. Such hours varied by season, latitude, and weather. It was subsequently divided into 60 minutes, each of 60 seconds. Its East Asian equivalent was the shi, which was 1⁄12 of the apparent solar day; a similar system was eventually developed in Europe which measured its equal or equinoctial hour as 1⁄24 of such days measured from noon to noon. The minor variations of this unit were eventually smoothed by making it 1⁄24 of the mean solar day, based on the measure of the sun's transit along the celestial equator rather than along the ecliptic. This was finally abandoned due to the minor slowing caused by the Earth's tidal deceleration by the Moon. In the modern metric system, hours are an accepted unit of time equal to 3,600 seconds but an hour of Coordinated Universal Time (UTC) may incorporate a positive or negative leap second, making it last 3,599 or 3,601 seconds, in order to keep it within 0.9 seconds of universal time, which is based on measurements of the mean solar day at 0° longitude.

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# Frequency Frequency A pendulum making 25 complete oscillations in 60 s, a frequency of 0.416 Hz Common symbols f, ν SI unithertz (Hz) Other units In SI base unitss−1 Derivations from other quantities • f = 1 / T Dimension${\displaystyle {\mathsf {T}}^{-1}}$ Frequency (symbol ${\displaystyle f}$), most often measured in hertz (symbol: Hz), is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as temporal frequency for clarity and to distinguish it from spatial frequency. Ordinary frequency is related to angular frequency (symbol ω, with SI unit radian per second) by a factor of 2π. The period (symbol T) is the interval of time between events, so the period is the reciprocal of the frequency: f = 1/T. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio signals (sound), radio waves, and light. For example, if a heart beats at a frequency of 120 times per minute (2 hertz), the period—the interval between beats—is half a second (60 seconds divided by 120 beats). ## Definitions and units For cyclical phenomena such as oscillations, waves, or for examples of simple harmonic motion, the term frequency is defined as the number of cycles or repetitions per unit of time. The conventional symbol for frequency is f or ν (the Greek letter nu) is also used. The period T is the time taken to complete one cycle of an oscillation or rotation. The frequency and the period are related by the equation f = 1 T . {\displaystyle f={\frac {1}{T}}.} The term temporal frequency is used to emphasise that the frequency is characterised by the number of occurrences of a repeating event per unit time. The SI unit of frequency is the hertz (Hz), named after the German physicist Heinrich Hertz by the International Electrotechnical Commission in 1930. It was adopted by the CGPM (Conférence générale des poids et mesures) in 1960, officially replacing the previous name, cycle per second (cps). The SI unit for the period, as for all measurements of time, is the second. A traditional unit of frequency used with rotating mechanical devices, where it is termed rotational frequency, is revolution per minute, abbreviated r/min or rpm. 60 rpm is equivalent to one hertz. ## Period versus frequency As a matter of convenience, longer and slower waves, such as ocean surface waves, are more typically described by wave period rather than frequency. Short and fast waves, like audio and radio, are usually described by their frequency. Some commonly used conversions are listed below: Frequency Period 1 mHz (10−3 Hz) 1 ks (103 s) 1 Hz (100 Hz) 1 s (100 s) 1 kHz (103 Hz) 1 ms (10−3 s) 1 MHz (106 Hz) 1 μs (10−6 s) 1 GHz (109 Hz) 1 ns (10−9 s) 1 THz (1012 Hz) 1 ps (10−12 s) ## Related quantities ${\displaystyle y(t)=\sin \theta (t)=\sin(\omega t)=\sin(2\mathrm {\pi } ft)}$ d θ d t = ω = 2 π f . {\displaystyle {\frac {\mathrm {d} \theta }{\mathrm {d} t}}=\omega =2\mathrm {\pi } f.} The unit of angular frequency is the radian per second (rad/s) but, for discrete-time signals, can also be expressed as radians per sampling interval, which is a dimensionless quantity. Angular frequency is frequency multiplied by 2π. • Spatial frequency, denoted here by ξ (xi), is analogous to temporal frequency, but with a spatial measurement replacing time measurement, e.g.: ${\displaystyle y(t)=\sin \theta (t,x)=\sin(\omega t+kx)}$ d θ d x = k = 2 π ξ . {\displaystyle {\frac {\mathrm {d} \theta }{\mathrm {d} x}}=k=2\pi \xi .} • Spatial period or wavelength is the spatial analog to temporal period. ## In wave propagation For periodic waves in nondispersive media (that is, media in which the wave speed is independent of frequency), frequency has an inverse relationship to the wavelength, λ (lambda). Even in dispersive media, the frequency f of a sinusoidal wave is equal to the phase velocity v of the wave divided by the wavelength λ of the wave: ${\displaystyle f={\frac {v}{\lambda }}.}$ In the special case of electromagnetic waves in vacuum, then v = c, where c is the speed of light in vacuum, and this expression becomes ${\displaystyle f={\frac {c}{\lambda }}.}$ When monochromatic waves travel from one medium to another, their frequency remains the same—only their wavelength and speed change. ## Measurement Measurement of frequency can be done in the following ways: ### Counting Calculating the frequency of a repeating event is accomplished by counting the number of times that event occurs within a specific time period, then dividing the count by the period. For example, if 71 events occur within 15 seconds the frequency is: ${\displaystyle f={\frac {71}{15\,{\text{s}}}}\approx 4.73\,{\text{Hz}}.}$ If the number of counts is not very large, it is more accurate to measure the time interval for a predetermined number of occurrences, rather than the number of occurrences within a specified time. The latter method introduces a random error into the count of between zero and one count, so on average half a count. This is called gating error and causes an average error in the calculated frequency of ${\textstyle \Delta f={\frac {1}{2T_{\text{m}}}}}$, or a fractional error of ${\textstyle {\frac {\Delta f}{f}}={\frac {1}{2fT_{\text{m}}}}}$ where ${\displaystyle T_{\text{m}}}$ is the timing interval and ${\displaystyle f}$ is the measured frequency. This error decreases with frequency, so it is generally a problem at low frequencies where the number of counts N is small. A resonant-reed frequency meter, an obsolete device used from about 1900 to the 1940s for measuring the frequency of alternating current. It consists of a strip of metal with reeds of graduated lengths, vibrated by an electromagnet. When the unknown frequency is applied to the electromagnet, the reed which is resonant at that frequency will vibrate with large amplitude, visible next to the scale. ### Stroboscope An old method of measuring the frequency of rotating or vibrating objects is to use a stroboscope. This is an intense repetitively flashing light (strobe light) whose frequency can be adjusted with a calibrated timing circuit. The strobe light is pointed at the rotating object and the frequency adjusted up and down. When the frequency of the strobe equals the frequency of the rotating or vibrating object, the object completes one cycle of oscillation and returns to its original position between the flashes of light, so when illuminated by the strobe the object appears stationary. Then the frequency can be read from the calibrated readout on the stroboscope. A downside of this method is that an object rotating at an integer multiple of the strobing frequency will also appear stationary. ### Frequency counter Higher frequencies are usually measured with a frequency counter. This is an electronic instrument which measures the frequency of an applied repetitive electronic signal and displays the result in hertz on a digital display. It uses digital logic to count the number of cycles during a time interval established by a precision quartz time base. Cyclic processes that are not electrical, such as the rotation rate of a shaft, mechanical vibrations, or sound waves, can be converted to a repetitive electronic signal by transducers and the signal applied to a frequency counter. As of 2018, frequency counters can cover the range up to about 100 GHz. This represents the limit of direct counting methods; frequencies above this must be measured by indirect methods. ### Heterodyne methods Above the range of frequency counters, frequencies of electromagnetic signals are often measured indirectly utilizing heterodyning (frequency conversion). A reference signal of a known frequency near the unknown frequency is mixed with the unknown frequency in a nonlinear mixing device such as a diode. This creates a heterodyne or "beat" signal at the difference between the two frequencies. If the two signals are close together in frequency the heterodyne is low enough to be measured by a frequency counter. This process only measures the difference between the unknown frequency and the reference frequency. To reach higher frequencies, several stages of heterodyning can be used. Current research is extending this method to infrared and light frequencies (optical heterodyne detection). ## Examples ### Light Visible light is an electromagnetic wave, consisting of oscillating electric and magnetic fields traveling through space. The frequency of the wave determines its color: 400 THz (4×1014 Hz) is red light, 800 THz (8×1014 Hz) is violet light, and between these (in the range 400–800 THz) are all the other colors of the visible spectrum. An electromagnetic wave with a frequency less than 4×1014 Hz will be invisible to the human eye; such waves are called infrared (IR) radiation. At even lower frequency, the wave is called a microwave, and at still lower frequencies it is called a radio wave. Likewise, an electromagnetic wave with a frequency higher than 8×1014 Hz will also be invisible to the human eye; such waves are called ultraviolet (UV) radiation. Even higher-frequency waves are called X-rays, and higher still are gamma rays. All of these waves, from the lowest-frequency radio waves to the highest-frequency gamma rays, are fundamentally the same, and they are all called electromagnetic radiation. They all travel through vacuum at the same speed (the speed of light), giving them wavelengths inversely proportional to their frequencies. c = f λ , {\displaystyle \displaystyle c=f\lambda ,} where c is the speed of light (c in vacuum or less in other media), f is the frequency and λ is the wavelength. In dispersive media, such as glass, the speed depends somewhat on frequency, so the wavelength is not quite inversely proportional to frequency. ### Sound Sound propagates as mechanical vibration waves of pressure and displacement, in air or other substances. In general, frequency components of a sound determine its "color", its timbre. When speaking about the frequency (in singular) of a sound, it means the property that most determines its pitch. The frequencies an ear can hear are limited to a specific range of frequencies. The audible frequency range for humans is typically given as being between about 20 Hz and 20,000 Hz (20 kHz), though the high frequency limit usually reduces with age. Other species have different hearing ranges. For example, some dog breeds can perceive vibrations up to 60,000 Hz. In many media, such as air, the speed of sound is approximately independent of frequency, so the wavelength of the sound waves (distance between repetitions) is approximately inversely proportional to frequency. ### Line current In Europe, Africa, Australia, southern South America, most of Asia, and Russia, the frequency of the alternating current in household electrical outlets is 50 Hz (close to the tone G), whereas in North America and northern South America, the frequency of the alternating current in household electrical outlets is 60 Hz (between the tones B and B; that is, a minor third above the European frequency). The frequency of the 'hum' in an audio recording can show in which of these general regions the recording was made. ## Aperiodic frequency Aperiodic frequency is the rate of incidence or occurrence of non-cyclic phenomena, including random processes such as radioactive decay. It is expressed with the unit of reciprocal second (s−1) or, in the case of radioactivity, becquerels. It is defined as a rate, f = Nt, involving the number of entities counted or the number of events happened (N) during a given time durationt);[citation needed] it is a physical quantity of type temporal rate.

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reciprocal trade agreement, international commercial treaty in which two or more nations grant equally advantageous trade concessions to each other. It usually refers to treaties dealing with tariffs. For example, one nation may grant another a special schedule of tariff concessions in return for equivalent advantages. Originally reciprocity agreements involved bilateral tariff reductions that were not to be extended to third countries. In the 18th cent., England relaxed its Navigation Acts in return for similar action by other nations. In the 19th cent. the German Zollverein was based on reciprocity, and the system of reciprocity fostered by Napoleon III worked strongly in favor of free trade. After the downfall of the French Second Empire (1870), many European countries began to follow a policy of high tariffs. In the United States reciprocity was advocated as part of the tariff policy after 1880. The use of the most-favored-nation clause after 1922 resulted in a widespread exchange of tariff concessions; it was followed by the Trade Agreements Act (1934). Since 1948 the general policy of the United States has been to negotiate reciprocal tariff concessions within the framework originally established by the General Agreement on Tariffs and Trade (GATT). The Trade Expansion Act (1962) provided for negotiations, under GATT auspices, to expand reciprocal trade agreements, especially with the European Economic Community, or Common Market (now part of the European Union). The act resulted in the Kennedy Round (1964–67) and the Tokyo Round (1974–79) of GATT talks, which produced reciprocal tariff reductions, mainly between the United States and W Europe, and new rules on customs and duties. GATT's Uruguay Round (1986–93) culminated in the creation (1995) of the World Trade Organization. Reciprocal agreements may also deal with such matters as rights of foreigners and consular relations. The Columbia Electronic Encyclopedia, 6th ed. Copyright © 2012, Columbia University Press. All rights reserved.

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Scenic Candle Holder Materials: clay and paint The first known candle in America dates to the 1st century A.D. Native Americans burned oily fish (candlefish) wedged into a forked stick. Coming in all shapes and sizes, Native American candlestick holders are a product of the tourist age. Not known to be made before 1880, contemporary Spanish accounts show that these potters made utilitarian pottery for the trade as well as for themselves, after traders described them as profitable. Although many of the candlestick holders the Europeans used were made out of metal and wood, Europeans still respected the skills of Native American potters. Candles are commonly used for religious purposes, which is why many candle holders, illustrate a religious scene. Our Mexican candlestick holder centralizes on a scene with two figures in a church, surrounded by three flowers and human faces protruding from the vessel's surface. In the scene while one figure appears to be preaching or singing from a book, the other is facing the first, on its knees praying.

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# 4.12: Congruent Triangles $$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$$$\newcommand{\AA}{\unicode[.8,0]{x212B}}$$ Verify congruency with SSS, SAS, RHS, and ASA ## Applications of Congruent Triangles Two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs are congruent. The following list summarizes the different criteria that can be used to show triangle congruence: • AAS (Angle-Angle-Side): If two triangles have two pairs of congruent angles, and a non-common side of the angles in one triangle is congruent to the corresponding side in the other triangle, then the triangles are congruent. • ASA (Angle-Side-Angle): If two triangles have two pairs of congruent angles and the common side of the angles (the side between the congruent angles) in one triangle is congruent to the corresponding side in the other triangle, then the triangles are congruent. • SAS (Side-Angle-Side): If two triangles have two pairs of congruent sides and the included angle in one triangle is congruent to the included angle in the other triangle, then the triangles are congruent. • SSS (Side-Side-Side): If two triangles have three pairs of congruent sides, then the triangles are congruent. • Right triangles only: HL (Hypotenuse-Leg): If two right triangles have one pair of legs congruent and hypotenuses congruent, then the triangles are congruent. If two triangles don't satisfy at least one of the criteria above, you cannot be confident that they are congruent. Interactive Element ### Recognizing Perpendicular Bisectors In the triangle below, \overline{BC} is the perpendicular bisector of AD\overline{AB}. Therefore \overline{AC}\cong \overline{CD}. Also, m\angle ACB=90^{\circ}and m\angle DCB=90^{\circ}, so \angle ACB \cong \angle DCB. You also know that \overline{BC} is a side of both triangles, and is clearly congruent to itself (this is called the reflexive property). The triangles are congruent by SAS. Note that even though these are right triangles, you would not use HL to show triangle congruence in this case since you are not given that the hypotenuses are congruent. ### Measuring Angles Using the information from the previous problem, if $$m\angle A=50^{\circ}$$, what is $$m\angle D$$? $$m\angle D=50^{\circ}$$ Since the triangles are congruent, all of their corresponding angles and sides must be congruent. \angle A\) and \angle D\) are corresponding angles, so $$\angle A\cong \angle D$$. ### Congruent Triangles Does one diagonal of a rectangle divide the rectangle into congruent triangles? • Recall that a rectangle is a quadrilateral with four right angles. • The opposite sides of a rectangle are congruent. There is more than enough information to show that $$\Delta EFG\cong \Delta GHE)\. • Method #1: The triangles have three pairs of congruent sides, so they are congruent by SSS. • Method #2: The triangles have two pairs of congruent sides and congruent included angles, so they are congruent by SAS. • Method #3: The triangles are right triangles with congruent hypotenuses and a pair of congruent legs, so they are congruent by HL. Example \(\PageIndex{1}$$ Max constructs a triangle using an online tool. He tells Alicia that his triangle has a 42^{\circ} angle, a side of length 12 and a side of length 8. With only this information, will Alicia be able to construct a triangle that must be congruent to Max's triangle? Solution If Max also told Alicia that the angle was in between the two sides, then she would be able to construct a triangle that must be congruent due to SAS. If the angle is not between the two sides, she cannot be confident that her triangle is congruent because SSA is not a criterion for triangle congruence. Because Max did not state where the angle was in relation to the sides, Alicia cannot create a triangle that must be congruent to Max's triangle. Example $$\PageIndex{2}$$ Are the following triangles congruent? Explain. Solution Notice that besides the one pair of congruent sides and the one pair of congruent angles, $$\overline{AC}\cong \overline{CA}$$. $$\Delta ACB\cong \Delta CAD$$ by SAS. Example $$\PageIndex{3}$$ Are the following triangles congruent? Explain. Solution The congruent sides are not corresponding in the same way that the congruent angles are corresponding. The given information for $$\Delta ACB$$ is SAS while the given information for $$\Delta CAD$$ is SSA. The triangles are not necessarily congruent. Example $$\PageIndex{4}$$ $$G$$ is the midpoint of $$\overline{EH}$$. Are the following triangles congruent? Explain. Solution Because G\) is the midpoint of $$\overline{EH}$$, $$\overline{EG}\cong \overline{GH}$$. You also know that $$\angle EGF\cong \angle HGI$$ because they are vertical angles. $$\Delta EGF\cong \Delta HGI$$ by ASA. ## Review 1. List the five criteria for triangle congruence and draw a picture that demonstrates each. 2. Given two triangles, do you always need at least three pieces of information about each triangle in order to be able to state that the triangles are congruent? For each pair of triangles, tell whether the given information is enough to show that the triangles are congruent. If the triangles are congruent, state the criterion that you used to determine the congruence and write a congruency statement. Note that the images are not necessarily drawn to scale. 3. 4. 5. 6. 7. 8. For 9-11, state whether the given information about a hidden triangle would be enough for you to construct a triangle that must be congruent to the hidden triangle. Explain your answer. 9. $$\Delta ABC$$ with $$m\angle A=72^{\circ},\: AB=6 \:cm, \:BC=8 \:cm.$$ 10. $$\Delta ABC$$ with $$m\angle A=90^{\circ},\: AB=4 \:cm, \:BC=5 \:cm.$$ 11. $$\Delta ABC$$ with $$m\angle A=72^{\circ},\: AB=6 \:cm, \:AC=8 \:cm.$$ 12. Recall that a square is a quadrilateral with four right angles and four congruent sides. Show and explain why a diagonal of a square divides the square into two congruent triangles. 13. Show and explain using a different criterion for triangle congruence why a diagonal of a square divides the square into two congruent triangles. 14. Recall that a kite is a quadrilateral with two pairs of adjacent, congruent sides. Will one of the diagonals of a kite divide the kite into two congruent triangles? Show and explain your answer. 15. In the picture below, $$G$$ is the midpoint of both $$\overline{EH}$$ and $$\overline{FI}$$. Explain why $$\overline{FH}\cong \overline{IE}$$ and $$\overline{FE}\cong \overline{HI}$$. 16. Explain why AAA is not a criterion for triangle congruence.

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The ebook FEEE - Fundamentals of Electrical Engineering and Electronics is based on material originally written by T.R. Kuphaldt and various co-authors. For more information please read the copyright pages. Superposition Theorem Superposition Theorem Theorem, Superposition Superposition theorem is one of those strokes of genius that takes a complex subject and simplifies it in a way that makes perfect sense. A theorem like Millman's certainly works well, but it is not quite obvious why it works so well. Superposition, on the other hand, is obvious. The strategy used in the Superposition Theorem is to eliminate all but one source of power within a network at a time, using series/parallel analysis to determine voltage drops (and/or currents) within the modified network for each power source separately. Then, once voltage drops and/or currents have been determined for each power source working separately, the values are all "superimposed" on top of each other (added algebraically) to find the actual voltage drops/currents with all sources active. Let's look at our example circuit again and apply Superposition Theorem to it: Since we have two sources of power in this circuit, we will have to calculate two sets of values for voltage drops and/or currents, one for the circuit with only the 28 volt battery in effect. . . . . . and one for the circuit with only the 7 volt battery in effect: When re-drawing the circuit for series/parallel analysis with one source, all other voltage sources are replaced by wires (shorts), and all current sources with open circuits (breaks). Since we only have voltage sources (batteries) in our example circuit, we will replace every inactive source during analysis with a wire. Analyzing the circuit with only the 28 volt battery, we obtain the following values for voltage and current: Analyzing the circuit with only the 7 volt battery, we obtain another set of values for voltage and current: When superimposing these values of voltage and current, we have to be very careful to consider polarity (voltage drop) and direction (electron flow), as the values have to be added algebraically. Applying these superimposed voltage figures to the circuit, the end result looks something like this: Currents add up algebraically as well, and can either be superimposed as done with the resistor voltage drops, or simply calculated from the final voltage drops and respective resistances (I=E/R). Either way, the answers will be the same. Here I will show the superposition method applied to current: Once again applying these superimposed figures to our circuit: Quite simple and elegant, don't you think? It must be noted, though, that the Superposition Theorem works only for circuits that are reducible to series/parallel combinations for each of the power sources at a time (thus, this theorem is useless for analyzing an unbalanced bridge circuit), and it only works where the underlying equations are linear (no mathematical powers or roots). The requisite of linearity means that Superposition Theorem is only applicable for determining voltage and current, not power!!! Power dissipations, being nonlinear functions, do not algebraically add to an accurate total when only one source is considered at a time. The need for linearity also means this Theorem cannot be applied in circuits where the resistance of a component changes with voltage or current. Hence, networks containing components like lamps (incandescent or gas-discharge) or varistors could not be analyzed. Another prerequisite for Superposition Theorem is that all components must be "bilateral," meaning that they behave the same with electrons flowing either direction through them. Resistors have no polarity-specific behavior, and so the circuits we've been studying so far all meet this criterion. The Superposition Theorem finds use in the study of alternating current (AC) circuits, and semiconductor (amplifier) circuits, where sometimes AC is often mixed (superimposed) with DC. Because AC voltage and current equations (Ohm's Law) are linear just like DC, we can use Superposition to analyze the circuit with just the DC power source, then just the AC power source, combining the results to tell what will happen with both AC and DC sources in effect. For now, though, Superposition will suffice as a break from having to do simultaneous equations to analyze a circuit. Review The Superposition Theorem states that a circuit can be analyzed with only one source of power at a time, the corresponding component voltages and currents algebraically added to find out what they'll do with all power sources in effect. To negate all but one power source for analysis, replace any source of voltage (batteries) with a wire; replace any current source with an open (break). Last Update: 2010-12-01

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# Sudoku Tips Introduction Hi! My name is Steve, and I am a Sudoku enthusiast. My wife would likely use a different adjective. I have studied how to solve a typical 9x9 Sudoku puzzle at some length, and have developed a modest but powerful repertoire of potential tips for human solving of a Sudoku puzzle using logic. The goal of these pages is not only to provide those tips to others, but also to learn new ways of looking at the puzzles. Hopefully, these pages will invite a free discussion and exchange of ideas regarding manners and methods to humanly solve sudoku puzzles. Please check out the conventions that I use to label the puzzle grid, and other aspects of language used - including the rules of Sudoku as I see them. This will aid greatly in uniformity of discussion here. ### Some definitions Candidates The integers 1 through 9 Cells Small containers that in a solved Sudoku will contain exactly one candidate each. This is one of the normally unwritten rules Boxes, Rows, Columns Large containers of cells. The rule In a solved sudoku, each large container will contain exactly one of each candidate. Each Sudoku puzzle has a unique solution. If the number of cells in each large container equals the number of potential candidates, (as is the case with typical 9x9 Sudoku), the following statements are equivalent: • There must be at least one of each candidate in each large container • There can be no more than one of each candidate in each large container Most techniques employ both of these ideas. ### Sudoku Puzzle Coordinates This is completely arbitrary, but I prefer the algebraic notation like that used with chess. Thus the bottom left corner cell is a1, and the top right corner cell is i9. Unfortunately, there is very little uniformity regarding Sudoku puzzle coordinate choices across the web. One can argue that one is better than the other, but they are all completely arbitrary. Additionally, the boxes are defined by the label of their center cell. Thus, the bottom left corner box is Boxb2, or Bb2. Indicate which comments you would like to be able to see GeneralJokesOtherSudoku Technique/QuestionRecipes Welcome to my sudoku blog! Some of you may already be familiar with my propensity to post a bit too much....A few things about me:I live in Cincinnati, Ohio where I operate and own a small masonry construction business. I am blissfully married to perhaps the only woman on earth who More... |  | terrific idea-long overdue.Look forward to learning more. |  | Thanks to Gath for this site and to you Steve for taking it on. I have read your solutions a few times but at times find them somewhat confusing so I look forward to all being revealed. I struggle to solve the tough on most days if I do manage to solve it most of the comments from regulars are that it was too easy. |  | I have been playing with sudoku puzzles for a little while and love them. But have found that the tougher puzzles take me a long time. I can't wait for your tips and advice. When will you begin your blog? I do not know how to access a blog, so if you can include that information, I would be grateful. Thank you for your generosity. |  | Hullo Steve. A marvellous idea! I've been reading your proofs for a fair while and have learnt quite a bit from them. Altho I've been studying Sudoku techniques on the web, there are still a lot of questions - like how rectangular does an XY wing have to be? (Sometimes mine seem to tend towards the More... |  | Hi Steve. I haven't had time to do toughs in quite a few months, but I remember your proofs as being very helpful. I hope I'll get a chance soon to check all this out. |  | Hi Linda from Ohio!(A great state, BTW). This is the blog, right here. Additional pages will be added periodically. The blog pages will introduce progressively more complicated tips and techniques - and also some hints on how use that information. |  | Thanks, Steve. Buckeyes rule. I look forward to learning much here. |  | Wow!! This is great!! Oftentimes I thank you Steve, when the 'hints' say it is tooooo tough, and I look down at the comments and find that something-or-the-other forbids a cell being a certain number 'up to 81', and IF I have done the setup correctly, it all comes out right!!! Now perhaps I can learn why!! |  | hopefully i will learn the language of proofs here. thank you. |  | Thanks Gath and Steve. I look forward to the help. I have been stuggling with a book of 'extremely tough' puzzles. Some have taken a day to complete. |  | Thanks Gath & Steve. This is a great idea - I generally am rather sporadic at getting to the tough puzzles on this site and often don't understand Steve's proofs so I am really looking forward to learnng some new and better technigues for the harder puzzles. Most of the time I am working sudokus More... |  | Hello Steve - Thanks for taking the time to do this. Gath - As always, you are great. Thank you |  | Great idea, I'm in! You can count on me to be a regular visitor. |  | Steve and Gath, this is wonderful! All of us regular toughies really appreciate it. And Steve, it was fun to read about what you do when you aren't doing sudoku. It's such an amazing thing to have this international community where we all get to know each other. Thanks again! |  | Thanks Steve for providing another brick in the Sudoko wall! Your proofs have been a tremendous tool in learning the logic behind the solutions. |  | Thanks Steve, I need this help. I am slow and often get blocked on hard. Intuition and revelation are poor substitutes for logic. |  | have been looking forward to this for a long time!thanks Steve & Gath |  | Hi Steve. I'm a bit of a 'look and try forever' person on the toughs. Have tried to figure out your solutions in the past but got a little lost at times. Thanks for this page. Very helpful! |  | This promises to be very good - but is the information going to be daily, weekly, random...? |  | The 'plan', subject to change without notice, is to publish two new blog pages per week. |  | Hi Gil (from gippsland)!Eventually, more complex techniques like xy wings will be discussed at some length.Quite a while back, on the tough puzzles page, I may have railed a bit against the guardian technique. In the face of an idea that is new to me, I am always a skeptic. Perhaps I did More... |  | Great stuff - your explanations are spot on. |  | I like your use of algebraic notation, and use of defined vocab like 'container' and 'candidates'. You and your readers may find the freeware Sudoku generator/solver at http://www.geocities.com/mpp_v1/fun of interest. |  | Hi Steye. Your information on the net was extremely useful. I shall be highly obliged if you enlighten me more on BUG from fundamentals. Thanks pdp189 06/Aug/07 12:31 AM |  | If you want to try out something new in sudoku, try shendoku, using the sudoku rules but playing two people, one against the other, like battleshipps. They have a free version to download at http://www.shendoku.com/sample.pdf . Anything else they are bringing out or they are working on you can find More... 08/Oct/07 8:23 AM |  | Check out Sudoku Learning Center(SudokuLearningCenterdotCom) It has a great set of online tutorials on the various techniques to solve Sudoku puzzles along with specially designed puzzles to aid in mastering the various techniques.RegardsPat 03/Nov/07 10:33 AM |  | Not a member? Joining is quick and free. As a member you get heaps of benefits. You can also try the Chatroom (No one chatting right now - why not start something? ) Check out the Sudoku Blog     Subscribe Members Get Goodies! Become a member and get heaps of stuff, including: stand-alone sudoku game, online solving tools, save your times, smilies and more! Previous Entries 07/Jan/07 Ywing Styles 06/Jan/07 Definitions 31/Dec/06 Y wings 27/Dec/06 Coloring 11/Dec/06 Beginner Tips Check out all the Daily Horoscopes Welcome our latest MembersLiz Allison from NSWSpike Jones from Pennsylvanianabapammm from ocean grove Member's Birthdays TodayBrenda from Stevenage UK

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The first step in an IVM program is to gather information on the life cycle and habits of the noxious weed. Purple loosestrife, Lythrum salicaria, is a wetland perennial herb that can grow up to 9 ft tall. Each spring, some 30 to 50 stems arise from a perennial, woody rootstalk. In flooded areas, purple loosestrife can form dense, fibrous rootmats. In autumn, stems die back and purple loosestrife stays dormant through the winter. Stems have short, slender branches and evenly spaced nodes. Leaves are elongate, smooth-edged, rounded or heart-shaped at the base, and attached close to the stems. Showy magenta or purple flowers grow on long spikes and occur in pairs or clusters. Purple loosestrife can easily be confused with other native wetland plants such as fireweed, Epilobium angustifolium. Look for purple loosestrife's squarish stems, opposite leaves, and flowers with 5 to 7 narrow petals. Fireweed has a rounded stem, alternate leaves and flowers with 4 broad petals (Mal et al. 1992). Purple loosestrife is native to Eurasia and was first cited in the United States in 1843 and has since spread throughout the United States and Canada. It was accidentally introduced from European ship ballasts or on infested sheep and raw wool. Purple loosestrife may also have been intentionally introduced by horticulturists as ornamentals and for treatment of diarrhea, dysentery, and bleeding (Mullin et al. 1993; Cornell 1997). Purple loosestrife is invasive and forms dense monocultures, crowding out native vegetation and decreasing species diversity in many infested areas. Dense infestations choke off wildlife habitat, waterfowl nesting areas, and wildlife access to water. In areas where purple loosestrife has migrated from wetlands to lowland pastures, it can reduce land values and crop yields. It can impede water flow in drainage and irrigation ditches and its rapid leaf decomposition rates can potentially alter nutrient cycling. Emery and Perry (1996) hypothesize that, "a wetland converted from cattails to purple loosestrife may function less effectively as a nutrient bio-filter and may accelerate eutrofication in downstream water bodies" (Mal et al. 1992). In the United States, purple loosestrife has spread to all states, and in Canada to all provinces except the Yukon and Northwest Territory (Cornell 1997; Harper-Lore 1997). Purple loosestrife commonly grows in moist to wet areas such as marshes, wetlands, riparian meadows, and pastures. It can also invade drier areas, causing increasing concerns on agricultural lands and pastures (OFAH 1996). Purple loosestrife is a long-lived perennial that can still be vigorous after 10 years. Purple loosestrife reproduces from plant fragments or by seed. It generally flowers from late June through August and can continue into October. Once flower petals start to drop from the bottom of the floral spike, purple loosestrife begins to produce seed, near early August. This event should be noted since most control measures should occur before seed set (Mal et al. 1992; OFAH 1996). A single mature plant can produce 2.7 million seeds each year, each seed about the size of a grain of sand. Seeds can be dispersed far distances by wind, water, ducks, or other wildlife and remain dormant in the soil for many years (McEachen 1997; OFAH 1996). Purple loosestrife grows best in full sunlight. A decrease to 40% full sunlight results in a significant reduction in seed. In deeply shaded environments the plant often does not produce flowers (Mal et al. 1992; Fournier 1997). Purple loosestrife can grow in poor soil and tolerate a wide range of soil textures, such as sand, clay, gravel, organic soils, and crushed rock. Its success may be traced to disturbances. Shamsi (1976) reported that purple loosestrife survival and growth was improved with fertilizer treatment and greater spacing between plants. In the Great Lakes, and possibly other areas, purple loosestrife may have been aided by fertilizer runoff from surrounding farmlands. In addition, purple loosestrife and its cultivars are still sold in many areas because of its beautiful flowers. Cultivars such as 'Morden Pink', 'Morden Gleam', and 'Morden Rose' are sterile; however, they can outcross with wild populations of purple loosestrife and produce long-lasting viable seed (Mal et al. 1992). Some questions, such as those below, can only be answered on site. Set Management Objectives Set Realistic Goals for Your IVM Program The answers to the following questions can help you set realistic objectives and goals. Reduction - reducing the area covered by purple loosestrife, or reducing its dominance. This strategy can also be used against new or established weeds, but it requires more resources and more time than containment. The "Bradley Method" (see Appendix 2), developed in Australia, is a simple yet innovative strategy for natural areas that combines containment and reduction. Eradication - completely eliminating the weed from the management area.This strategy usually consumes the greatest amount of time and resources and is applicable mainly to newly-invading weeds that are confined to a limited number of small areas. Establish Monitoring Programs When planning a monitoring program, keep in mind the context of your target weed: is it invading or has it already invaded? Locate and record purple loosestrife infestations on a map. (Chapter 2 of the University of Northern Iowa IVRM Technical Manual contains a detailed discussion on how to map and inventory vegetation - see Bibliography). Note particularly sensitive areas on the map, such as critical habitat for threatened or endangered species, wetland or riparian areas, or areas subject to frequent disturbance and thus prone to invasion. Update maps at regular intervals. Focus monitoring efforts on sites where purple loosestrife problems are most likely to occur (see Distribution). Encourage public sighting and reporting through an education or incentive program (see Educate Vegetation Management Personnel and the Public). Prioritize the sites you will work on. Make a realistic assessment of your weed management resources, keeping in mind the goals of your project and the cost of a follow-up program after any treatments. Without follow-up, your control efforts will be wasted. It is better to thoroughly control a weed at one or two sites than to use up resources to incompletely control the weed at many sites. If the weed is very widespread, try to determine where it poses the most serious economic, social, or environmental problem and concentrate on those areas. Plan monitoring and treatment efforts to coincide with critical life stages of the weed. To use your resources efficiently, try to include monitoring with other planned activities in the area. Maintain records of your monitoring activities. Creating standardized forms will make data collection easier and help remind you to gather all the information you need. Forms work best if they include labeled blanks for all pertinent information and allow the user to check or circle rather than having to write words or numbers (See Appendix 3 for some examples of forms). Include information such as the name(s) of the person(s) collecting the data, the location, and date of monitoring; a qualitative description of the vegetation, such as the names of the plants or types of plants (native vegetation, annual/perennial weeds, trees, etc.) and stage of growth (germinating, flowering, setting seed, etc.); a quantitative description, such as percent cover, plant density, size of the patch, or if possible, the number of plants. Note special conditions such as unusual weather events and record treatment history, including information on treatment applications (who, when, where, how, cost, difficulties, and successes). This will allow you to evaluate and fine-tune treatments. Set Treatment Thresholds Setting treatment thresholds includes prioritizing and balancing treatments with resources. Weeds are treated when populations increase beyond a predetermined level. This level will largely depend on the characteristics of the site and weed. In some cases the level may be no weeds at all, and in other cases the number of weeds you can tolerate may be much greater. What is the size of the weed population? The opportunity for control is related to the infested area. Small patches can be more easily controlled than large infestations. What is the level of the threat? Is the purple loosestrife population changing? Is it in an area where soils are frequently disturbed? Is it threatening wildlife habitat, or agricultural areas? Is it encroaching on critical habitat for a rare, threatened, or endangered species? Is it displacing the best examples of native communities? What resources are available? Do you have the resources required for carrying out your goal? With the advent of herbicides, prevention as a weed management technique has often been neglected; however, it is a practical, cost-effective, and extremely important part of noxious weed control. General Weed Prevention Measures (Adapted from Fay et al. 1995). Purple loosestrife control can be enhanced by a combination of planting competitive grasses and selective herbicide. After purple loosestrife is removed and competitive grasses are seeded, it is likely to see a flush of purple loosestrife seedlings. These seedlings are vulnerable and can be targeted with a selective broadleaf herbicide that does not affect grasses. Once purple loosestrife seedlings are controlled, other broadleaf plants and shrubs can be planted. Apply Management Methods No individual method will control purple loosestrife in a single treatment; diligence and persistence will be required over a number of years to subdue this weed. The treatment methods described in this section will help you to design an integrated program that will suit the circumstances of your particular situation. Biological control does not aim to eradicate weeds, but to keep them at low, manageable levels. After their introduction, biocontrol agents can take 5 to 10 years to become established and increase to numbers large enough to reduce the density of the target weed. Once established, effective biological controls provide an inexpensive, long-term, and non-toxic means to control weed populations. Since insects have specific requirements for growing and thriving, it is important to match the insect to the weed management site. Understanding these requirements will help you integrate the insects into other weed control efforts. When you release biocontrols, continue using other control methods on the perimeter of the release site, but avoid using them where they might adversely impact the insect population. The information provided below is only a summary. For more information consult Biological Control of Weeds in the West (see Bibliography) or contact commercial weed biocontrol insectaries (see Insectaries). The weevil can withstand moderate amounts of flooding; however, excessive flooding will kill larvae and prevent adults from laying eggs (Cornell 1997). Egg are laid in batches (between May and July depending on climate) on leaves and stems. In the first few weeks of spring, watch for dispersing adults flying nearby, floating in the water, or climbing out on shore (McEachen 1997). Galerucella species are also very sensitive to herbicides and spraying should not occur in insect release sites (Cornell 1997). Septoria lythrina, Alternaria alternata, Botrytis cinerea, and Colletotrichum tuncatum can weaken plants and make purple loosestrife more susceptible to control methods. More studies of their efficacy as biocontrol agents of purple loosestrife are under way (Nyvall 1997). Adult purple loosestrife is unpalatable and trampling by animals in soft riparian areas can lead to disturbances that would further favor purple loosestrife. There are no published studies on controlling purple loosestrife by grazing (Brookreson et al 1993). When beginning a hand removal project, flag the treated areas so they can be identified for follow-up in subsequent seasons. It is easiest to work in relatively small areas of infestation. When faced with dense or extensive stands of purple loosestrife, it is best to divide them into grids (with flags, stakes, etc.) so that workers can thoroughly weed smaller areas before moving onto the next grid. The grid system also facilitates dividing work activities between those pulling and those removing the debris. Additional treatment such as digging, flooding, or flaming may be necessary. Cutting followed by flooding can keep purple loosestrife in check for several years (see Water level manipulation below). All plant fragments must be removed to prevent resprouting (OFAH 1996). Covering dense populations of plants with black plastic can block sunlight and kill plants. This technique works best for pure stands of seedlings. Plants should be cut or mowed and then covered with black plastic for at least 5 consecutive months, beginning in early spring (April or May). To be effective, the treatment may have to be repeated the following year. Although young plants will be killed, older plants and seeds may still survive. Because it is labor intensive, smothering is more effective on a small scale. Constant monitoring is necessary since weeds can grow through small holes and cracks in the plastic (Brookreson et al. 1993; McEachen 1997). Water Level Manipulation Although purple loosestrife can withstand short periods of flooding, long periods of deep flooding using storm water retention cells can help control loosestrife populations. Mature plants are severely impacted by flooding for one to two months at a water level of 1 to 3.5 ft. The effectiveness of this technique is increased when cutting precedes flooding. Seedlings die after 8 weeks of flooding and are affected more by the duration rather than the depth of flooding. On the other hand, seeds can remain viable after submergence for 20 months. Shallow flooding (less than 12 inches) did not significantly affect seedlings (Haworth-Brockman et al. 1993; Comas et al. 1992; Malecki and Rawinski 1985; Heidorn and Anderson 1991). Although purple loosestrife populations have been observed to decrease in size and vigor following a natural flood, it is quick to regain its former dominance in the following 2 years. Using storm water retention cells is impractical in certain areas and flooding can facilitate seed dispersal to unvegetated sand bars or to downstream areas. Since flooding can also be detrimental to wildlife and native vegetation, it may not be suitable for some environments (Kincaid 1997). In IVM programs, herbicides are considered transition tools that enable the manager to suppress weeds and replace them with desirable, competitive vegetation. Thus, it is important to select the least-toxic, low-residual herbicide that is effective against the target weed, and to apply them in a judicious manner. Currently, the effects of herbicide on purple loosestrife biocontrol agents are not very clear. As a precaution, herbicide use is not recommended in insect release areas. Mosquito control fogging treatments may pose a threat to natural enemy populations. Additional studies continue to clarify the effects of mosquito control programs on purple loosestrife biocontrols (Blossey 1998). Applying herbicide to plants when purple loosestrife is most susceptible (preferably before seeds are produced) is crucial to the effectiveness of the treatment. Vegetation Management Personnel and the Public the Vegetation Management Program Anderson, M.G. Interactions between Lythrum salicaria and native organisms: a critical review. Environmental Mangmt. 19(2): 225-231. Anonymous. 1995. A practical approach to weed management- reason, reality, reponsibility. 1995. Proc. of the 47th Annual California Weed Science Society: 87-92. Blossey, B. et al. 1994. Host specificity and environmental impact of the weevil Hylobius transversovittatus, a biological control agent of purple loosestrife (Lythrum salicaria). Weed Science 42: 128-133. Blossey, B. and M. Schat. 1997. Performance of Galerucella calmariensis (Coleoptera: Chrysomelidae) on different North American populations of purple loosestrife. Environmental Entomology 26 (2): 439-445. Blossey, B. 1993. Herbivory below ground and biological weed control: life history of a root-boring weevil on purple loosestrife. Oecologia 94: 380-387. Blossey, B. "Purple loosestrife." Personal E-mail (9 Sept. 1997). Blossey, B. Personal E-mail (23 Feb. 1998). Brookreson,W.E. et al. 1993. Noxious Emergent Plant Management: Env. Impact Statement. Washington State Dept. of Ag. 94pp. Comas, L., K. Edwards, and B. Lynch. 1992. Control of purple loosestrife (Lythrum salicaria L.) at Indiana Dunes National Lakeshore by cutting followed by overwinter flooding. National Park Serv. National Biological Survey. Wisconsin Coop. Res. Unit 12pp. Cornell. Purple Loosestrife Website. www.dnv.cornell.edu/bcontrol/purple.htm (visited Sept. 1997). Dewey, S.A. and J.M. Torell. 1991 What is a noxious weed? In: James et al., Noxious Range Weeds. Westview Press, Boulder, CO. Dundas, H. 1997. Pers. Comm. Project Manageer. Purple Loosestrife Eradication Project. 115 Perimeter Rd. Saskatoon, SK S7N OX4. Emery, S.L. and J.A. Perry. 1996. Decomposition rates and phosphorus concentrations of purple loosestrife (Lythrum salicaria) and cattail (Typha spp.) in fourteen Minnesota wetlands. Hydrobiologia 323:129-138. Fay, P.K., T.D. Whitson, S.A. Dewey, and R. Sheley, eds. 1995. 1995-1996 Montana-Utah-Wyoming Weed Management Handbook. Coop. Ext. Serv., Montana State Univ., Bozeman, MT. 245 pp. Fournier, B. Pers. Comm. 1997. Purple loosestrife control. c/o Kitsap County Parks, 1200 Fairgrounds Rd. Bremerton, WA 98311. Fuller, T.C., and G.D. Barbe. 1985. The Bradley method of eliminating exotic plants from natural reserves. Fremontia 13(2): 24-25. Harper-Lore, B. 1997. presentation. "Update from the Federal Interagency Committee on Management of Noxious and Exotic Weeds (FICMNEW). Federal Highway Administration, US Dept. of Transportation. Proceedings Cal EPPC Symposium ’97. Haworth-Brockman, M.J., H.R. Murkin, R.T. Clay. 1993. Effects of shallow flooding on newly established purple loosestrife seedlings. Wetlands 13(3): 224-227. Heidorn R., and B. Anderson. 1991. Vegetation management guideline: purple loosestrife (Lythrum salicaria L.). Nautral Areas Journal 11(3): 172-173. Hight, S.D., B. Blossey, J. Laing, and R. Declerck-Floate. 1995. Establishment of insect biological control agents from Europe against Lythrum salicaria in North America. Env. Ent. 24(4): 967-977. International Institute of Biological Control Annual Report 1996 (IIBC). 1997. CAB International. Oxon, UK. 132pp. Jacobs, J.S., R.L. Sheley, and B.D. Maxwell. 1997. Yellow starthistle population dynamics model. Colorado Weed Management Association 1997 Annual Conference Proceedings. Granby, CO. Kincaid, R. 1997. Pers. Comm. Nebraska Purple Loosestrife Awareness Committee. 1303 East 22nd St. Kearney, NE 68847. Kok, L.T., T.J. McAvoy, R.A. Malecki, et al. 1992. Host specificity tests of Galerucella calmariensis (L.) and G. pusilla (Duft.) (Coleoptera: Chrysomelidae), potential biological control agents of purple loosestrife, Lythrum salicaria L (Lythraceae). Biological Control 2: 282-290. Lacey, C.A., et al. 1988. Bounty programs—an effective weed management tool. Weed Technology 2: 196-197. Mal, T.K., J. Lovett-Doust, L. Lovett- Doust, and F.A. Mulligan. 1992. The biology of Canadian weeds. 100. Lythrum salicaria. Canadian Journal of Plant Science 72: 1305-1330. Malecki, R.A., and T.J. Rawinski. 1985. New methods for controlling purple loosestrife. New York Fish and Game Journal 32(1): 9-19. Malecki, R.A., B. Blossey, S.D. Hight, et al. 1993. Biological control of purple loosestrife. Bioscience 43(10): 680-686. Maxwell, B. " YST software." Personal e-mail (9 Feb 1998). McEachen, H. 1997. Pers. Comm. Agronomist. PO Box 96. Mesa, WA 99343. Mullin, B.H., D. Zamora and P.K. Fay. 1993. Purple loosestrife: a new weed threat to wetlands in Montana. Montana State University Extension Service EB 70. 9pp. Nechols, F.R., H.H. Obrychi, C.A. Tauber, M.J. Tauber. 1996. Potential impact of the native natural enemies on Galerucella spp. (Coleoptera: Chrysomelidae) imported for biological control of purple loosestrife: a field evaluation. Biological Control 7: 60-66. Nyvall, R.F. and A. Hu. 1997. Laboratory evaluation of indigenous North American fungi for biological control of purple loosestrife. Biological Control 8: 37-42. Ontario Federation of Anglers and Hunters (OFAH). 1996 "Purple Loosestrife: what you should know, what you can do." PO Box 2800. Peterborough, Ontario. K9J 8L5. 7pp. Pearson, W. 1998. Pers. Comm. County Weed Extension Agent. Stillwater County, Columbus, Montana. Piper, G.L. 1996. Biological control of the wetlands weed purple loosesetrife (Lythrum salicaria) in the Pacific northwestern United States. Hydrobiologia 340: 291-294. Randall, J.M. and J. Marinelli eds. 1996. Invasive Plants: Weeds of the Global Garden. Brooklyn Botanic Garden , Inc. Brooklyn, NY. 108pp. Rees, N.E., P.C. Quimby, Jr., G.L. Piper, E.M. Coombs, C.E. Turner, N.R. Spencer, and L.V. Knutson, eds. 1996. Biological Control of Weeds in the West. Western Society of Weed Science, USDA/ARS, Montana Dept. Agric., Montana State University, Bozeman, MT. Shamsi, S.R.A. 1976. Some effects of density and fertilizer on the growth and competition of Epilobium hirsutum and Lythrum salicaria. Pak. J. Bot. 8(2): 213-220. In, Mal et al. 1992. The biology of Canadian weeds. 100. Lythrum salicaria. Canadian Journal of Plant Science 72: 1305-1330. University of Northern Iowa. 1993. Integrated Roadside Vegetation Management Technical Manual. Produced by the Roadside Management Program. To obtain, call Kirk Henderson at 319-273-2813. Voegtlin, D.J. 1995. Potential of Myzus lythri (Homopthera: Aphididae) to influence growth and development of Lythrum salicaria (Myrtiflorae: Lythraceae). Environmental Entomology 24(3): 724-729. Welling, C.H. and R.L. Becker. 1993. Reduction of purple loosestrife establishment in Minnesota wetlands. Wildlife Soc. Bull. 21(1): 56-64. Wilcox, D.A. 1989. Migration and control of purple loosestrife (Lythrum salicaria L.) along highway corridors. Environmental Management 13 (3): 365-370. "Invasive Exotic Plants of Canada Fact Sheet No. 4." http://infoweb.magi.com/~ehaber/factpurp.html (visited Sept. 1997). (Below are web pages specifically regarding purple loosestrife; see link above for other websites.) Cornell. Purple Loosestrife Website. http://www.dnv.cornell.edu/bcontrol/purple.htm CAPS Purple loosestrife fact sheet 42. Purple loosestrife: public enemy #1 on federal lands: http//www.ceris.purdue.ude/napis/pests/pls/factspls/ Ducks Unlimited Canada. http://www.ducks.ca/prov/purple.htm "Invasive Exotic Plants of Canada Fact Sheet No. 4." http://infoweb.magi.com/~ehaber/factpurp.html (visited Sept. 1997)

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In a band across central and western Europe, the earliest farmers from bce onward are represented by a homogeneous pattern of settlements and material culture, named the LBK Culture from Linienbandkeramik or Linearbandkeramikafter the typical pottery decorated with linear bands of ornament. It has been suggested that the modern divide between northern European cultures, favouring butter-based cooking, and southern European cultures, preferring olive oil-based cuisine, dates back from the Neolithic period. Some of the enclosures also suggest grain and meat storage. Both samples belonged to the maternal haplogroup M, whose descendants are also found essentially in Asia today including East Asia. At one extreme is a model of immigrant colonization from the Middle East, with the agricultural frontier pushing farther westward as population grew and new settlements were founded. Urged onward by the pressure of increasing population, they passed into Europe and Northern Africa. Sampling of petrous bone from a human skull. In Greece there were similar changes, with population expansion especially in the south and the emergence of some sites as centres of authority; this period marked the beginning of the Aegean Bronze Age. Permanent settlement, population growth, and exploitation of smaller territories all brought about new relationships between people and the environment. An expansion of Unetice to the north and west gave birth to the Proto-Germanic branch R1b-Uwhich mixed with the indigenous populations of northern Germany and the Netherlands, notably I2a2a-L descended from Mesolithic Europeans and R1a-Z descended from the Corded Ware culturebut also with a minority of Neolithic lineages G2a, E-M78, T1a, etc. Many of the long-occupied tell sites were abandoned; the new settlement pattern shows many smaller sites and some larger ones which may have played a central role. In an hour and fifteen minutes, this question can be investigated through many ancient objects, including: Even within one generation, or a short period of a few generations, the cave paintings would mean different things to different people depending on their age, experience, perhaps their gender. The L2 branch is more common in former Celtic countries, but also across Germany and Poland, and would have spread with older cultures like Tumulus and Hallstatt. New technologies also were adopted; pottery decorated with characteristic impressed patterns was made, and by the 4th millennium copper was being worked in Spain. The darkness of oblivion seems dispelled by the light of science, and we behold before us the Europe of Neolithic times, thickly inhabited by a race of people, small in stature, dark visaged, and oval-faced—fond of war and the chase, yet having a rude system of agriculture. The Neolithic Period The adoption of farming From about bce in Greece, farming economies were progressively adopted in Europe, though areas farther west, such as Britain, were not affected for two millennia and Scandinavia not until even later. Prior research has shown that people living in what is now Germany, Hungary and Spain were mostly hunter-gatherers during the early Neolithic period, but were "replaced" by farmers moving in from the Near East Anatolia. It has been found that the principal languages of Europe and South-western Asia have certain common characteristics; so much so that we are justified, even compelled, to assume that the nations speaking these languages, such for instance as the Teutonic, Sclavic, Italic, Greek, Persian, Hindoostanee, and others, are descendants from a common ancestor. Metal products included personal ornaments as well as some functional items; the cemetery at Varna, Bulg. The process of agricultural adoption, furthermore, was neither fast nor uniform. Nevertheless, at least half of these I2 lineages do not descend directly from the Mesolithic inhabitants of these countries, but from the Mesolithic inhabitants of Central and Eastern Europe. This type of reasoning has already proved false in the case of the South Germany, where the Neolithic, Celtic and even Roman inhabitants remained slightly dominant genetically compared to the later Germanic invaders. From its Asiatic home it spread over the entire world—to the islands of the Pacific, and even America. Only a detailed analysis of very deep clades of these haplogroups could determine what is the actual percentage of Roman or at least Italian origin in the Benelux and France today, but data is still lacking at the moment. Dawkins thinks that it caught up with them before they arrived in Britain, and that they are the ones who introduced bronze into that island. The Neolithic Period The adoption of farming From about bce in Greece, farming economies were progressively adopted in Europe, though areas farther west, such as Britain, were not affected for two millennia and Scandinavia not until even later.and thus, a long agricultural history arguably proxies for a long history of plow agriculture. Thus, we provide new evidence consistent with the hypothesis that agricultural intensi–cation in any form via its e⁄ects on cultural beliefs is a source of modern gender roles. In other parts of the world, such as Africa, South Asia and Southeast Asia, independent domestication events led to their own regionally distinctive Neolithic cultures that arose completely independently of those in Europe and Southwest Asia. The Proto-Celto-Germanic branch of R1b (L11) settled around Bohemia and eastern Germany circa BCE and established the Unetice culture, the Bronze Age culure which would expand across all Western Europe and Scandinavia over the next millennium, and replace the Neolithic. The Neolithic period, often described as the New Stone Age, was a period of human history from approximately 15, BCE to 3, BCE. It was a time defined by the development of settlements and. History of Europe - The late Neolithic Period: From the late 4th millennium a number of developments in the agricultural economy became prominent. They did not, however, begin all at once nor were they found everywhere. The Neolithic or Agricultural Revolution followed the Paleolithic Era, and it began in the Ancient Near East about 10, BCE. Not long afterwards, Neolithic settlements appeared in Europe, Africa, Asia, and the Western Hemisphere.Download

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The heart is a muscular organ about the size of a fist, located just behind and slightly left of the breastbone. The heart pumps blood through the network of arteries and veins called the cardiovascular system. The heart has four chambers: - The right atrium receives blood from the veins and pumps it to the right ventricle. - The right ventricle receives blood from the right atrium and pumps it to the lungs, where it is loaded with oxygen. - The left atrium receives oxygenated blood from the lungs and pumps it to the left ventricle. - The left ventricle (the strongest chamber) pumps oxygen-rich blood to the rest of the body. The left ventricle’s vigorous contractions create our blood pressure. The coronary arteries run along the surface of the heart and provide oxygen-rich blood to the heart muscle. A web of nerve tissue also runs through the heart, conducting the complex signals that govern contraction and relaxation. Surrounding the heart is a sac called the pericardium.

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Você está na página 1de 4 # Exercise 7. 3 (Solutions) MathCity.org Textbook of Algebra and Trigonometry for Class XI Page 238 ## Merging man and maths Available online @ http://www.mathcity.org, Version: 4.0 Question # 1 39916800 = = 4989600 . How many arrangements of the letters of the 8 following words, taken all together, can be (i) PAKPATTAN Total number of letters = 13 (ii) PAKISTAN A is repeated 3 times (iii) MATHEMATICS S is repeated 4 times (iv) ASSASSINATION I is repeated 2 times Solution N is repeated 2 times (i) PAKPATTAN T and O come only once. Total number of letters = 9 Required number of permutations P is repeated 2 times  13  =  A is repeated 3 times  3, 4, 2, 2,1,1 T is repeated 2 times 13! K and N come only once. = 3!× 4!× 2!× 2!×1!×1!  9  Required number of permutations =   6227020800 = = 10810800  2,3, 2,1,1 (6) (24) (2) (2) 9! = 2!× 3!× 2!× 1!× 1! Question # 2 362880 How many permutations of the letters of the = = 15120 . word PANAMA can be made, if P is to be the (2) (6) (2) first letter in each arrangement? (ii) PAKISTAN Solution Total number of letters = 8 If P is the first letter then words are of the form A is repeated 2 times P ∗∗∗∗∗ , where five ∗ can be replace with P, K, I, S, T and N come only once. A,N,A,M,A. Required number of permutations So number of letters = 5  8  A is repeated 3 times =   M, N appears only once  2,1,1,1,1,1,1  5  5! 8! So required permutations =   = 3!× 1!× 1! = 2!× 1!× 1!×1!× 1!× 1!× 1!  3,1,1 40320 120 = = 20160 . = = 20 . 2 6 (iii) MATHEMATICS Total number of letters = 11 Question # 3 M is repeated 2 times How many arrangements of the letters of the A is repeated 2 times word ATTACKED can be made, if each T is repeated 2 times arrangement begins with C and end with K? H, E, I, C and S come only once. Solution Required number of permutations If C be the first letter and K is the last letter  11  then words are of the form C ∗∗∗∗∗∗K . where =  each ∗ can be replaced with A, T, T, A, E, D.  2, 2, 2,1,1,1,1,1  So number of letters = 6 11! A is repeated 2 times = 2!× 2!× 2!× 1!× 1!× 1!× 1!× 1! T is repeated 2 times E and D come only once. FSc-I / Ex 7.3 - 2  6   7  So required permutations =   Permutations of 7 digits number =    2, 2, 1, 1  3, 2, 1, 1 6! 720 7! 5040 = = = 180 . = = = 420. 2!× 2!×1!×1! 4 3!× 2!× 1!× 1! 12 Number less than 1,000,000 are of the form Question # 4 0 ∗∗∗∗∗∗ , where each ∗ can be replaced with How many numbers greater than 1000, 000 can 2, 2, 3, 4, 4. be formed from the digits 0, 2, 2, 2,3, 4, 4 ? No. of digits = 6 Solution No. of 2’s = 3 The number greater than 1000000 are of the No. of 4’s = 2 following forms. 3 comes only once If numbers are of the form 2 ∗∗∗∗∗∗ ,  6  6! So permutations =   = 3!× 2!×1! where each ∗ can be filled with 0, 2, 2,3, 4, 4  3, 2, 1  Then number of digits = 6 720 2 is repeated 2 times = = 60 12 4 is repeated 2 times Hence number greater than 1000000 = 420 − 60 0 and 3 come only once. = 360 .  6  So number formed =   Question # 5  2, 2, 1, 1 How many 6-digits numbers can be formed from 6! 720 the digits 2, 2, 3, 3, 4, 4? How many of them will = = = 180 . 2!× 2!×1!×1! 4 lie between 400,000 and 430,000? Now if numbers are of the form 3∗∗∗∗∗∗ , Solution where each ∗ can be filled with 0, 2, 2, 2, 4, 4 Total number of digits = 6 Then number of digits = 6 Number of 2’s = 2 2 is repeated 3 times Number of 3’s = 2 4 is repeated 2 times Number of 4’s = 2 0 comes only once. So number formed by these 6 digits  6   6  6! So number formed =   =  = (2!) (2!) (2!)  3, 2, 1   2, 2, 2  6! 720 720 = = = 60 . = = 90 . 3!× 2!×1! 12 (2) (2) (2) Now if numbers are of the form 4 ∗∗∗∗∗∗ , The numbers lie between 400,000 and 430,000 where each ∗ can be filled with 0, 2, 2, 2,3, 4 are only of the form 42****, where each * can Then number of digits = 6 be filled by 2, 3, 3, 4. 2 is repeated 3 times Here number of digits = 4 . 0, 3 and 4 come only once. Number of 2’s = 1  6  Number of 3’s = 2 6! So number formed =   = 3!×1!×1! Number of 4’s = 1  3, 1, 1  4  4! 720 So number formed =   = (1!) (2!) (1!) 6 = = 120 . 1, 2, 1 So required numbers greater than 1000000 24 = = 12. = 180 + 60 + 120 2 = 360 . Question # 6  Alternative 11 members of a club form 4 committees of 3, 4, (Submitted by Waqas Ahmad - FAZMIC Sargodha – 2004-06) No. of digits = 7 2, 2 members so that no member is a member is No. of 2’s = 3 a member of more than one committee. Find the No. of 4’s = 2 number of committees. 0 and 3 come only once. Solution Total members = 11 FSc-I / Ex 7.3 - 3 ## Members in first committee = 3 Question # 10 Members in second committee = 4 Find the numbers of ways in which 5 men and 5 Members in third committee = 2 women can be seated at a round table in such a Members in fourth committee = 2 way that no two persons of same sex sit together. So required number of committees Solution fix man  11  11! =  = 3!⋅ 4!⋅ 2!⋅ 2!  3, 4, 2, 2  39916800 = = 69300 . (6) (24) (2) (2) Question # 7 The D.C.Os of 11 districts meet to discuss the law and order situation in their districts. In how If we fix one man round a table many ways can they be seated at a round table, when two particular D.C.Os insist on sitting then their permutations = 4 P4 = 24 together? Now if women sit between the two men Solution then their permutations = 5 P5 = 120 Number of D.C.O’s = 9 So total permutations = 24 ×120 = 2880 Let D1 and D2 be the two D.C.O’s insisting to sit together so consider them one. Question # 11 If D1 D2 sit together then permutations In how many ways can 4 keys be arranged on a circular key ring? = 9 P9 = 362880 Solution If D2 D1 sit together then permutations Number of keys = 4 = 9 P9 = 362880 Fixing one key we have permutation = 3 P3 = 6 So total permutations = 362880 + 362880 A A = 725760 Question # 8 B D D B The Governor of the Punjab calls a meeting of 12 officers. In how many ways can they be seated at a round table? Solution C C Fixing one officer on a particular seat, Since above figures of arrangement are we have permutations of remaining 11 officers reflections of each other = 11P11 = 39916800 . 1 Therefore permutations = × 6 = 3 2 Question # 9 Fatima invites 14 people to a dinner. There are Question # 12 9 males and 5 females who are seated at two How many necklaces can be made from 6 beads different tables so that guests of one sex seat at of different colours? one round table and the guests of other sex at the Solution second table. Find the number of ways in which Number of beads = 6 all guests are seated. Fixing one bead, we have permutation = 5 P5 Solution = 120 9 males can be seated on a round table = 8 P8 = 40320 And 5 females can be seated on a round table = 4 P4 = 24 So permutations of both = 40320 × 24 = 967680 . FSc-I / Ex 7.3 - 4 A A B F F B C E E C D D Since above figures of arrangement are reflections of each other 1 Therefore permutations = × 120 = 60 2 ## These notes are available online at http://www.mathcity.org/fsc Submit error/mistake at http://www.mathcity.org/error ## Book: Exercise 7.3 (Page 238) Text Book of Algebra and Trigonometry Class XI Punjab Textbook Board, Lahore – PAKSITAN. Available online at http://www.MathCity.org in PDF Format (Picture format to view online). Page setup: A4 (8.27 in × 11.02 in). Updated: January 21, 2018. ## These resources are shared under the licence Attribution- NonCommercial-NoDerivatives 4.0 International

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## Tuesday, 13 May 2008 ### First Post - About Time Too. Okay, okay, so this has been a while coming; I originally set this up so that I could comment on other people's blogs - the title was a little play on words that I had been mulling over ever since reading about the Omnipotence Paradox (basically the idea that if an omnipotent entity Y cannot create a stone which is too heavy for it to lift then it is not omnipotent and if it can then the fact of not being able to lift it makes it not omnipotent). This got me to thinking about one of my favourite mathematical proofs from back in my school days - the proof by contradiction aka Reductio ad absurdum; the principal is that you take a definition and then prove that the definition is self contradictory. The first time that I encountered this technique was for proving that the square root of two is not a rational number. This is done by assuming that the square root of two is rational and then showing that the assumption is self contradictory: CAUTION: The following contains maths and will probably only be enjoyed by geeks. If you want to skip down to "So what does all this have to do with god(s)?" then no-one will mind, but you are missing out. If √2 is rational, then √2 = m/n where m and n are integers with no common factors. So our definition consists of four things: 1) √2 = m/n 2) m is an integer 3) n is an integer 4) m and n have no common factors If we can show that these four things cannot all be simultaneously true then we have a contradiction and √2 must therefore be irrational. If √2 = m/n Then 2 = m²/n² and 2n² = m² therefore m² is an even number (since it is divisible by two) and since the square of a odd number is odd and vice versa, m itself must be an even number. Since m is an even number it can be represented by 2a, where a is an integer, thus 2n² = m² => 2n² = (2a => 2n² = 4a² => n² = 2a² So now we can see that (for the same reasons as above) n must also be an even number, thus we have contradicted 4) as both m and n have a common factor of two. Therefore, since all numbers are either rational or irrational, √2 must be irrational. So what does all this have to do with god(s)? Well, one of the favourite little nuggets of stupid pulled out by apologists is, "to know that [insert name of deity(s) here] doesn't exist would require you to know everything about the entire universe and, since you don't, you cannot state that [whatever] doesn't exist." Leaving aside the obvious fallacy of proving the negative, it isn't necessary to know the entire universe inside out to prove that it doesn't contain square circles, for example, since the definition of such an entity is self contradictory and thus no entity can possibly fulfill the definition. Likewise with most deities; their definitions are self contradictory, such as being omnipotent which is a contradiction all in itself, and so they cannot exist and the questions as to where you would look and "what evidence would convince you" (another favourite) become nonsensical. That then is my mission for this blog; I will (at least attempt to) disprove by definition the existence of any gods that I come across. Initially I will use the common definitions of gods as they are understood by most people, but to avoid the whole, "that's not my god - his beard is too long," phenomenon, I will also be accepting definitions from commenters of a theistic persuasion. Assuming that anyone is still reading, that is... Rebecca in TX said... Please provide absolute proof and evidence that the God of the Bible does not exist. felix said... Ok, Rebecca: The God of the Bible cannot exist because he is self-created outside of a spatiotemporal framework. Neither creation nor self-creation outside of time are possible. Time does not 'occur' without space to occur in. Either God existed in some space for some time, which means that his space and time were pre-existent, or everything we know about physics and causality is false. Some negatives can be proven. Rebecca in TX said... Thank you for responding Paul. You are right in that a created being must exist inside of space and time. Everything we know about physics and causality falls apart when there is no cause, nothing can not create something. By definition, an infinite, eternal being has always existed—no one created God. The Bible clearly states that He is the self-existing, eternal not self created. He exists outside of space and time. The God of the Bible can exist because he is eternal outside of a spatiotemporal framework. Creating the universe is possible outside of space and time by an eternal being. Everything we know about physics and causality is true only if an eternal being outside of space and time caused it all. Otherwise you are left with nothing caused everything and that flies in the face of everything we know about physics and causality. Psalms 90:2 Before the mountains were born or you brought forth the earth and the world, from everlasting to everlasting you are God. Romans 1:20 For since the creation of the world God's invisible qualities--his eternal power and divine nature--have been clearly seen, being understood from what has been made, so that men are without excuse. 1 Timothy 1:17 Now to the King eternal, immortal, invisible, the only God, be honor and glory for ever and ever. Amen. Isaiah 57:15 For this is what the high and lofty One says-- he who lives forever, whose name is holy: "I live in a high and holy place, but also with him who is contrite and lowly in spirit, to revive the spirit of the lowly and to revive the heart of the contrite. Isaiah 40:28 Do you not know? Have you not heard? The Lord is the everlasting God, the Creator of the ends of the earth. He will not grow tired or weary, and his understanding no one can fathom. ExPatMatt said... WFDDIM?

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Hubbs & Bonham, 1951 The sharpnose shiner (Notropis oxyrhynchus) is a species of fish in the family Cyprinidae, the carps and minnows. It is endemic to Texas in the United States, where it is limited to the Brazos River basin. In 2013 it became a candidate for federal listing as an endangered species of the United States. This is a slender minnow generally measuring 3 to 5 centimeters in length at maturity, but it is known to reach 9.5 centimeters. It is silver with a faint line extending from the gills to the tail. The snout is pointed. Today the fish occurs mainly in the Brazos River system above Possum Kingdom Lake, it is rarely observed below this reservoir and may be extirpated from most or all of the tributaries in the lower river system. Populations are extirpated from the Wichita River, which represented nearly 70% of the known former range of the species. In the Upper Brazos it is still a common species. The fish feeds on aquatic and terrestrial invertebrates, including flies, caddisflies, bugs, beetles, odonates, and ostracods. It consumes large amounts of sand and sediment, suggesting that it forages on the riverbed. It may also consume some plant material. Its life history is not well documented. Several threats have contributed to the decline of the species. Inflow from reservoirs has altered the physical and biological characteristics of the river system, such as temperature, flow patterns, and turbidity, and have contributed to habitat fragmentation and other changes to the ecosystem. The Possum Kingdom, Granbury, and Whitney Reservoirs have produced changes in the aquatic faunal communities of the Brazos River. The construction of more reservoirs is expected to prevent the fish from recolonizing habitat where it is now absent. The invasive plant salt cedar (Tamarix spp.) has become abundant along the Brazos River, its spread aided by the construction of reservoirs. The plant likely increases sedimentation and alters water flow, making parts of the habitat unsuitable for the fish. The Brazos River is a relatively saline river because of the salts in the surrounding land and a salty aquifer beneath, and the fish is adapted to the saline waters. There is increasing interest in desalination of the river water for municipal use. Planned desalination projects include the construction of wells, pipelines, evaporation ponds, and reservoirs for water treatment. These projects, as well as ongoing wastewater and agricultural runoff, are expected to alter water and habitat quality. Gravel and sand mining have produced significant effects on the lower Brazos, but their specific impacts on the fish are not clear. Algal blooms may also affect the species, but evidence is not yet available. - Double Mountain Fork Brazos River - North Fork Double Mountain Fork Brazos River - Salt Fork Brazos River - Smalleye Shiner - White River (Texas) - Yellow House Canyon - Species Assessment and Listing Priority Assessment Form: Notropis oxyrhynchus. USFWS. April 15, 2011. - Proposed rule: Endangered species status for the sharpnose shiner and smalleye shiner. Federal Register 78(151) 47582. August 6, 2013. - Froese, R. and D. Pauly. (Eds.) Notropis oxyrhynchus. FishBase. 2011. - NatureServe. 2013. Notropis oxyrhynchus. In: IUCN 2013. IUCN Red List of Threatened Species. Version 2013.1. Downloaded on 17 November 2013. - Marks, D. E., et al. (2001). Foods of the smalleye shiner and sharpnose shiner in the Upper Brazos River, Texas. The Texas Journal of Science 53(4), 327-34.

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# Topological Sort One of the things I generally say about myself is that I love learning. I can spend hours upon hours reading papers and algorithms to better understand a topic. Some of these topics are stand alone segments that I can understand in one sitting. Sometimes, however, there is a need to read up on some preliminary work in order to fully understand a concept. Lets say that I was interested in organizing this information into a new course. The order I present these topics is very important. Knowing which topics depend on one another allows me to use the topological sorting algorithm to determine an ordering for the topics that respects the preliminary work. The input for the topoligical sorting algorithm is a Directed Acyclic Graph (DAG). This is a set of relationships between pairs of topics, where if topic 1 must be understood before topic 2, we would add the relationship (topic 1, topic 2) to the graph. DAGs can be visualized by a set of nodes (points) representing the topics. Relationships like the one above (topic 1, topic 2) can then represented by a directed arc originating at topic 1 and flowing in the direction of topic 2. We say that the graph is “Acyclic” because there cannot be a cycle in the topic preliminaries. This amounts to us saying that a topic cannot be a prerequisite for itself. An example of a DAG is shown in the image above. With the topics represented as a DAG, the topologial ordering algorithm works by searching the set of nodes for the one with no arcs coming into it. This node (or these nodes is multiple are present) represents the topic that can be covered next without losing understanding of the material. Such a node is guaranteed to exist by the acyclic property of the DAG. Once the node is selected, we can remove this node as well as all arcs that originate at this node from the DAG. The algorithm then repeats the procedure of searching for a nod with no arcs coming into it. This process repeats until there are no remaining nodes from which to choose. Now lets see how the topological sort algorithm works on the graph above. We will first need to count the in-degree (the number of arcs coming into) each node. Node | Indegree —————- 0 | 2 1 | 2 2 | 0 3 | 2 4 | 2 5 | 2 6 | 0 7 | 2 8 | 3 Node to be removed (i.e. node with the minimum indegree): Node 2. Arcs connected to node 2: (2, 5), (2, 3) Resulting Indegree Count: Node | Indegree —————- 0 | 2 1 | 2 3 | 1 4 | 2 5 | 1 6 | 0 7 | 2 8 | 3 Node to be removed: Node 6: Arcs connected to node 6: (6, 1), (6, 3), (6, 4), (6, 5), (6, 7), (6, 8) Resulting Indegree Count: Node | Indegree —————- 0 | 2 1 | 1 3 | 0 4 | 1 5 | 0 7 | 1 8 | 2 Node to be removed: Node 3 Arcs connected to node 3: (3, 0), (3, 8) Resulting Indegree Count: Node | Indegree —————- 0 | 1 1 | 1 4 | 1 5 | 0 7 | 1 8 | 1 Node to be removed: Node 5 Arcs connected to node 5: (5, 0), (5, 8) Resulting Indegree Count: Node | Indegree —————- 0 | 0 1 | 1 4 | 1 7 | 1 8 | 0 Node to be removed: Node 0: Arcs connected to node 0: (0, 1), (0, 4) Resulting Indegree Count: Node | Indegree —————- 1 | 0 4 | 0 7 | 1 8 | 0 Node to be removed: Node 1 Arcs connected to node 1: none Resulting Indegree Count: Node | Indegree —————- 4 | 0 7 | 1 8 | 0 Node to be removed: Node 4 Arcs connected to node 4: none Resulting Indegree Count: Node | Indegree —————- 7 | 1 8 | 0 Node to be removed: Node 8 Arcs connected to node 8: (8, 7) Resulting Indegree Count: Node | Indegree —————- 7 | 0 Node to be removed: Node 7 Arcs connected to node 7: none Resulting Indegree Count: Node | Indegree —————- Since there are no nodes remaining, we have arrived at a topological ordering. Going through this iteration, we can see that we arrived at the ordering (2, 6, 3, 5, 0, 1, 4, 8, 7). There were several occasions where there were multiple nodes with indegree of 0 and we could have selected an alternative node. This would have given us a different topological ordering of the nodes, but it would still be valid. There are more learning opportunities and an interactive demonstration of the algorithm at Topological Sort Examples at LEARNINGlover. # The RSA Algorithm I can remember back when I was in school, still deciding whether I wanted to study pure or applied mathematics. One of the common questions I would receive from those in applied mathematical realms would sound like “What’s the point of doing mathematics with no real world applications?”. Generally my response to these questions was about the intrinsic beauty of mathematics, no different from an artist painting not for some desire to be a millionaire, but because of an burning desire to paint. Whether their paintings would one day be on the walls of a Smithsonian museum or sit on their mother’s refrigerator is generally outside of the thought process of the artist. So too, would I argue about the thought process of a pure mathematician. When I was an undergrad and learned about the RSA algorithm (named for Ron Rivest, Adi Shamir, and Leonard Adleman who discovered the algorithm) it helped me explain this concept a lot better. The algorithm is based on prime numbers and the problem of finding the divisors of a given number. Many mathematicians throughout the ages have written papers on the beauty of prime numbers (see Euclid, Eratosthenes, Fermat, Goldbach, etc). For a large period in time one of the beautiful things about prime numbers was that they were so interesting in themselves. There were questions about how to check if a number is prime, question of patterns in primes, famous conjectures like the Goldbach conjecture and the twin prime conjecture, quick ways of finding prime numbers or numbers that are almost always prime, etc. In short, this was an active area of research that much of the applied world was not using. This all changed in 1977 when Rivest, Shamir and Adleman published the RSA algorithm. The algorithm is in the area called public key cryptography. These algorithms differ from many of the previous cryptography algorithms, namely symmetric key cryptography. Whereas symmetric key cryptography depends uses the same device (key) to encode as to decode, public key cryptography creates two keys – one for encoding that is generally shared with others, and another for decoding which is kept private. These two keys in generally relate to a mathematical problem that is very difficult to solve. In my example script for the RSA Algorithm, I show two people who want to communicate, Alice and Bob. Bob wants people to be able to send him messages securely so he decides to use the RSA algorithm. To do this, he first needs to think of two prime numbers, p1 and p2. From these, he computes the following: n = p1 * p2 Next, he computes Euler’s function on this n which can be calculated as (n) = (p1 – 1) * (p2 – 1) Then Bob looks for a number e that is relatively prime to . This is what he will use as the encryption key. One he has e, he can calculate d, which is the multiplicative inverse of e in (n). This means that e * d = 1 (mod (n)). The public key that will be used for encryption will be the pair (e, n). This is what he posts publicly via his web page for others to communicate with him securely. Bob also has a private key pair (d, n) that he will use to decrypt messages. Alice sees Bob’s public key and would like to communicate with him. So she uses it to encode a message. The formula she uses to encrypt her message is c = me mod n, where c is the encrypted message. Once Alice encrypts her message, she sends it to Bob. Bob receives this encoded message and uses the private key (d, n) to decode the message from Alice. The formula to decrypt is m = cd mod n. For a more illustrative idea of how this algorithm works as well as examples, be sure to visit Script for the RSA Algorithm. # How To Take Notes in Math Class I was recently asked by someone how they should be taking notes in math class. I could immediately relate because I once asked this very same question. In both undergrad and grad, I had to ask myself how to take notes because I often would leave class with a bunch of sentence fragments based on what the professor said, but without anything I could use as a study guide. At best, it would be a garbled thing that I could combine with somebody else’s notes and try to make some legible out of it. Generally though, I would just ignore my notes and go to the text book if it was well written, or the library if the text book was not well written. So how did I get past this? Well, after taking the Set Theory course, I started seeing mathematics as more of a construction job, like building a house. Mathematics is based on proofs which is nothing more than logical reasoning, and logical reasoning is just a series of statements that are either assumptions, definitions, or conclusions drawn from those assumptions based on known facts. The main purpose of classes is to present these “known facts” to the students and help them become more informed mathematicians. So what is a mathematical fact? There are two important types of facts we generally learn in mathematics. The first gives us a language we can work from – these are our definitions. These are the most important things in a mathematics class because if it is a class on “group theory”, then one of the first definitions will be of a “group,” and not knowing this definition will cause problems when you are trying to prove that something is or is not a group. Similarly, if your class is on solving quadratic equations, then it is very important to be able to define what a “quadratic equation” is. Definitions in mathematics are important because, unlike in an English class, you cannot always derive the meaning of a mathematical term from its usage. Mathematical definitions are very precise and your notes should include this precision. As a side note, I will state (if not stress) that examples are not definitions. Examples are meant to bring the definition to life, and to help connect the definition to the student, but if you are asked what is a group and respond that “the set of integers mod 7 under the operation of addition is a group”, you’d be incorrect because you gave an example of a group without telling why this is a group. Similarly, if I were to ask you to define a quadratic equation and you said “x^2 + 2x + 1 = 0 is a quadratic equation”, you’d be giving me an example but not a definition. It is important to understand the distinction between examples and definitions because when we understand the definition we can clearly explain why (ala prove) that the given instance is in fact an example. Some professors will briefly mention a definition and then focus most of their time on examples in an attempt to make the concepts easier to understand. As a student though, it is important to ask the question “what is the definition of _____” because the exams, or the research that follows, or the applications of this concept in real life are not likely to be that same example. If the professor does not write out the definition of whatever concept you are studying, or you are unclear of this definition you should ask questions, go to an online resource, or a text book for supplementary reference. The second type of fact presented in mathematical classes is the theorem (aka lemma or corollary). A theorem is a statement that is provable by mathematical reasoning. In a classroom setting, theorems will generally be presented in an orderly fashion such that if Theorem 1 is presented before Theorem 2, then Theorem 1 does not require Theorem 2 in order to be proven. Because theorems are provable statements, it may be tempting to jump directly into the proof, and particularly to only take notes on the proof. I cannot stress against this enough. Before writing the proof, you should make sure to begin the proof with a clear statement of the theorem. This should be a declarative statement that is thus provable. Do not confuse the questions a professor may ask before proving a theorem with the theorem itself. An example of a theorem from group theory is “Any group that has a prime number of elements of elements in that group is cyclic (or can be generated by a single element). Also, do not confuse the nicknames of theorems with the theorem itself. For instance Lagrange’s Theorem says that “the number of elements of any subgroup of a finite group divides the number of elements in the original group.” Remembering this as Lagrange’s Theorem is fine, but it is much more important to remember the declarative statement proved. I’m sure there are other things people use to take notes in math classes. Feel free to leave a comment sharing some of this advice. # The Depth-First-Search Algorithm I remember when I was younger I used to play the game of hide-and-seek a lot. This is a game where a group of people (at least two) separate into a group of hiders and a group of seekers. The most common version of this that I’ve seen is having one person as the seeker and everyone as hiders. Initially, the seeker(s) is given a number to count towards and close their eyes while counting. The hiders then search for places to hide from the seeker. Once the seeker is finished counting, their job is to find where everyone is hiding or admitting that they cannot find all the seekers. Any seekers not found are said to have won, and seekers that are found are said to have lost. I played this game a number of times in my childhood, but I remember playing it with a friend named Dennis in particular. Dennis had a certain way he played as seeker. While many of us would simply go to places we deemed as “likely” hiding spots in a somewhat random order, Dennis would always begin by looking in one area of the room, making sure that he had searched through every area connected to that area before going to a new area. He continued this process until he either found everybody or concluded that he had searched every spot he could think of and gave up. It wasn’t until years later that I was able to note the similarity between Dennis’s way of playing hide-and-seek and the Depth-First-Search algorithm. The Depth-First-Search Algorithm is a way of exploring all the nodes in a graph. Similar to hide-and-seek, one could choose to do this in a number of different ways. Depth-First-Search does this by beginning at some node, looking first at one of the neighbors of that node, then looking at one of the neighbors of this new node. If the new node does not have any new neighbors, then the algorithm goes to the previous node, looks at the next neighbor of this node and continues from there. Initially all nodes are “unmarked” and the algorithm proceeds by marking nodes as being in one of three states: visited nodes are marked as “visited”; nodes that we’ve marked to visit, but have not visited yet are marked “to-visit”; and unmarked nodes that have not been marked or visited are “unvisited”. Consider a bedroom with the following possible hiding locations: (1) Under Bed, (2) Behind Cabinet, (3) In Closet, (4) Under Clothes, (5) Behind Curtains, (6) Behind Bookshelf, and (7) Under Desk. We can visualize how the bedroom is arranged as a graph and then use a Breadth First Search algorithm to show how Brent would search the room. Consider the following bedroom arrangement, where we have replaced the names of each item by the number corresponding to that item. Node (0) corresponds to the door, which is where Dennis stands and counts while others hide. Now consider how a Breadth First Search would be run on this graph. The colors correspond to the order in which nodes are visited in Depth-First-Search. The way we read this is that initially Dennis would start at node 0, which is colored in Blue. While Dennis is at node 0, she notices that nodes 1, 5, and 6 (under bed, behind curtains, and behind bookshelf) are the nearby and have not been checked yet so she places them on the “to visit” list. Next, Dennis will begin to visit each node on the “to visit” list, and when a node is visited, she labels it as visited. At each location, she also takes note of the other locations she can reach from this location. Below is the order of nodes Dennis visits and how he discovers new locations to visit. Order Visited Node Queue Adding Distance From Node 0 1 0 6,5,1 0 2 6 5,1 7,3,2 1 3 7 3,2,5,1 2 4 3 2,5,1 2 5 2 5,1 4 2 6 4 5,1 3 7 5 1 1 8 1 1 Here is a link to my Examples page that implements the Depth-First-Search Algorithm on Arbitrary Graphs. I remember when I was younger I used to play the game of hide-and-seek a lot. This is a game where a group of people (at least two) separate into a group of hiders and a group of seekers. The most common version of this that I’ve seen is having one person as the seeker and everyone as hiders. Initially, the seeker(s) is given a number to count towards and close their eyes while counting. The hiders then search for places to hide from the seeker. Once the seeker is finished counting, their job is to find where everyone is hiding or admitting that they cannot find all the seekers. Any seekers not found are said to have won, and seekers that are found are said to have lost. I played this game a number of times in my childhood, but I remember playing it with a friend named Brenda in particular. Brenda had a certain way she played as seeker. While many of us would simply go to places we deemed as “likely” hiding spots in a somewhat random order, Brenda would always take a survey of the room, and no matter where she began searching, she would always make note of the locations close to her starting point and make sure she was able to give them all a look before she looked at locations that were close to the points she deemed close to the starting point. She continued this process until she either found everybody or concluded that she had searched every spot she could think of and gave up. It wasn’t until years later that I was able to note the similarity between Brenda’s way of playing hide-and-seek and the Breadth-First-Search algorithm. The Breadth-First-Search algorithm is a way of exploring all the nodes in a graph. Similarly to hide-and-seek, one could choose to do this in a number of different ways. Breadth-First-Search does this by beginning at some node, looking first at each of the neighbors of the starting node, then looking at each of the neighbors of the neighbors of the starting node, continuing this process until there are no remaining nodes to visit. Initially all nodes are “unmarked” and the algorithm proceeds by marking nodes as being in one of three stages: visited nodes are marked as “visited”; nodes that we’ve marked to visit, but have not visited yet are marked “to-visit”; and unmakred nodes that have not been marked are “unvisited”. Consider a bedroom with the following possible hiding locations: (1) Under Bed, (2) Behind Cabinet, (3) In Closet, (4) Under Clothes, (5) Behind Curtains, (6) Behind Bookshelf, and (7) Under Desk. We can visualize how the bedroom is arranged as a graph and then use a Breadth First Search algorithm to show how Brenda would search the room. Consider the following bedroom arrangement, where we have replaced the names of each item by the number corresponding to that item. Node (0) corresponds to the door, which is where Brenda stands and counts while others hide. Now consider how a Breadth First Search would be run on this graph. The colors correspond to the order in which nodes are visited in Breadth-First-Search. The way we read this is that initially Brenda would start at node 0, which is colored in Blue. While Brenda is at node 0, she notices that nodes 1, 5, and 6 (under bed, behind curtains, and behind bookshelf) are the nearby and have not been checked yet so she places them on the “to visit” list. Next, Brenda will begin to visit each node on the “to visit” list, and when a node is visited, she labels it as visited. At each location, she also takes note of the other locations she can reach from this location. Below is the order of nodes Brenda visits and how she discovers new locations to visit. Order Visited Node Queue Adding Distance From Node 0 1 0 – 1, 5, 6 0 2 1 5, 6 2, 4 1 3 5 6, 2, 4 – 1 4 6 2, 4 3, 7 1 5 2 4, 3, 7 – 2 6 4 3, 7 – 2 7 3 7 – 2 8 7 – – 2 Here is a link to my Examples page that implements the Breadth-First-Search Algorithm on Arbitrary Graphs. # ID3 Algorithm Decision Trees As I grow LEARNINGlover.com, I’m always thinking of different ways to expose my own personality through the site. This is partially because it is easier for me to talk about subjects where I am already knowledgeable, but it is more-so being done to help make some of these algorithms and concepts I encode more understandable, and sometimes relating foreign concepts to everyday life makes them easier to understand. Today, I’d like to write about decision trees, and the ID3 algorithm for generating decision trees in particular. This is a machine learning algorithm that builds a model from a training data set consisting of a feature vector and an outcome. Because our data set consists of an outcome element, this falls into the category of supervised machine learning. The model that the ID3 algorithm builds is called a decision tree. It builds a tree based on the features, or columns of the data set with a possible decision corresponding to each value that the feature can have. The algorithm selects the next feature by asking “which feature tells me the most about our data set?” This question can be answered first by asking how much “information” is in the data set, and then comparing that result with the amount of information in each individual feature. In order to execute this algorithm we need a way to measure both the amount the information in outcomes of the overall data set as well as how much each feature tells us about the data set. For the first, we will use entropy, which comes from the field of information theory and encoding. Entropy is based on the question of how many bits are necessary to encode the information in a set. The more information, the higher the entropy, and the more bits required to encode that information. Although we are not encoding, the correlation between high information and high entropy suits our purposes. To understand how much each feature tells us about the outcomes of the data set we will build on the concept of entropy to define the information gain of a feature. Each feature has multiple options, so the dataset can be partitioned based on each possible value of this feature. Once we have this partition, we can calculate the entropy of each subset of the rows of data. We define the information gain of a feature as the sum over all possible outcomes of that feature can have of the entropy of that outcome multiplied by the probability of that outcome. To illustrate this algorithm, I decided to relate it to the question of whether we think of a character in a novel as a hero or villain. This is interesting because I try to read at least one book a month and as I’m reading, I often find myself asking this question about characters based on the traits of the characters as well as characters I’ve read about. In order to build an interactive script for this problem, I considered 25 possible character traits that could be present. A subset of these 25 character traits will be selected and a row will be generated grading a fictional character on a scale of 0 to 3 (0 meaning that they do not possess the trait at all, 3 meaning that the trait is very strong in their personality), and users will be asked whether they think a character with the given character traits should be listed as a hero or a villain. Then there is a button at the bottom of the script with the text “Build Tree” that executes the ID3 Algorithm and shows a decision tree that could be used to reach the set of decisions given by the user. The possible features are: Abstract, Adaptable, Aggressive, Ambition, Anxiety, Artistic, Cautious, Decisive, Honesty, Dutiful, Fitness, Intellect, Independent, Introverted, Lively, Open-minded, Orderly, Paranoid, Perfectionist, Romantic, Sensitive, Stable, Tension, Warmth and Wealthy Once users select the option to build the tree, there will be several links outlining each step in the process to build this tree. These links will allow for users to expand the information relating to that step and minimize that information when done. Hopefully this will help users to understand each step more. I must say that as much fun as it has been writing this program, there were several questions when trying to explain it to others. Hopefully users get as much fun from using this tool as I had in creating it. As always feel free to contact me with any comments and or questions. Ok, so here’s a link to the ID3 Algorithm Page. Please check it out and let me know what you think. # Clique Problem Puzzles I still remember how I felt when I was first introduced to NP-Complete problems. Unlike the material I had learned up to that point, there seemed to be such mystery and intrigue and opportunity surrounding these problems. To use the example from Garey and Johnson’s book “Computers and Intractability: A Guide to the Theory of NP Completeness”, these were problems that not just one researcher found difficult, but that a number of researchers had been unable to find efficient algorithms to solve them. So what they did was show that the problems all had a special relationship with one another, and thus through this relationship if someone were to discover an algorithm to efficiently solve any one of these problems they would be able to efficiently solve all the problems in this class. This immediately got my mind working into a world where I, as a college student, would discover such an algorithm and be mentioned with the heavyweights of computer science like Lovelace, Babbage, Church, Turing, Cook, Karp and Dean. Unfortunately I was a student so I did not have as much time to devote to this task as I would have liked. In my spare time though I would try to look at problems and see what kind of structure I found. One of my favorite problems was, The Clique Problem. This is a problem where we are given an undirected graph and seek to find a maximum subset of nodes in this graph that all have edges between them, i.e. a clique (Actually the NP-Complete version of this problem takes as input an undirected graph G and an integer k and asks if there is a clique in G of size k). Although I now am more of the mindset that there do not exist efficient algorithms to solve NP-Complete problems, I thought it would be a nice project to see if I could re-create this feeling – both in myself and others. So I decided to write a program that generates a random undirected graph and asks users to try to find a maximum clique. To test users answers, I coded up an algorithm that works pretty well on smaller graphs, the Bron-Kerbosch Algorithm. This algorithm uses backtracking to find all maximal cliques, which then allows us to sort them by size and determine the largest. Users should click on the numbers in the table below the canvas indicating the nodes they wish to select in their clique (purple indicates that the node is selected, gray indicates that it is not). Once they have a potential solution, they can press the “Check” button to see if their solution is optimal. If a user is having trouble and simply wishes to see the maximum clique, they can press the “Solve” button. And to generate a new problem, users can press the “New Problem” button. So I hope users have fun with the clique problem puzzles, and who knows maybe someone will discover an algorithm that efficiently solves this problem and become world famous. # Unidirectional TSP Puzzles As we’ve entered the late spring into early summer season, I’ve found myself wanting to go out more to sit and enjoy the weather. One of these days recently I sat in the park with a good book. On this occurrence, I decided not to go with a novel as I had just finished “Incarceron“, “The Archer’s Tale“, and “14 Stones” – all of which were good reads, but I felt like taking a break from the novels. Just as a side note, 14 Stones is a free book available on smashwords.com and I’ve now read about 6 books from smashwords.com and haven’t been disappointed yet. My favorite is still probably “The Hero’s Chamber” because of the imagery of the book, but there are some well written ebooks available there by some good up and coming writers for a reasonable price, with some being free. So with the desire to read, but not being in the mood for novels I decided to pick up one of my non-text but still educational books that make me think. This day it was “Programming Challenges“. I browsed through the book until I found one that I could lay back, look at the water, and think about how to solve it. The programming puzzle the peaked my interest was called “Unidirectional TSP”. We are given a grid with m rows and n columns, with each cell showing the cost of using that cell. The user is allowed to begin in any cell in the first column and is asked to reach any cell in the last column using some minimum cost path. There is an additional constraint that once a cell is selected in a column, a cell in the next column can only be chosen from the row directly above, the same row, or the row directly below. There is a javascript version of this puzzle available here. Fundamentally, the problem is asking for a path of shortest length. Many shortest length problems have a greedy structure, but this one gained my interest because the greedy solution is not always optimal in this case. So I took a moment to figure out the strategy behind these problems. Once I had that solution, I decided that it would be a good program to write up as a puzzle. In this puzzle version, users will click the cells they wish to travel in each column in which case they will turn green (clicking again will turn them white again). Once the user clicks on a cell in the last column, they will be notified of whether or not they have chosen the minimum path. Or if users are unable to solve a puzzle, the “Solution” button can be pressed to show the optimal path and its cost. I had been meaning to write a script and blog post on descriptive statistics for some time now, but with work and winter weather and the extra work that winter weather brings, and now that the winter weather is over trying to get back into an exercise routine (running up a hill is such a challenging experience, but when I get to the top of that hill I feel like Rocky Balboa on the steps at the steps at the entrance of the Philadelphia Museum of Art), I haven’t had the time to devote to this site that I would have liked. Well, that’s not entirely true. I have still been programming in my spare time. I just haven’t been able to share it here. I went to a conference in February and in my down time, I was able to write a script on descriptive statistics that I think gives a nice introduction to the area. Before I go into descriptive statistics though, lets talk about statistics, which is concerned with the collection, analysis, interpretation and presentation of data. Statistics can generally be broken down into two categories, descriptive statistics and infernalinferential statistics, depending on what we would like to do with that data. When we are concerned with visualizing and summarizing the given data, descriptive statistics gives methods to operate on this data set. On the other hand, if we wish to draw conclusions about a larger population from our sample, then we would use methods from inferential statistics. In the script on descriptive statistics I’ve written, I consider three different types of summaries for descriptive statistics: Measures of Central Tendency Mean – the arithmetic average of a set of values Median – the middle number in a set of values Mode – the most used number in a set of values Dispersion Maximum – the largest value in the data set Minimum – the smallest value in the data set Standard Deviation – the amount of variation in a set of data values Variance – how far a set of numbers is spread out Shape Kurtosis – how peaked or flat a data set is Skewness – how symmetric a data set is Plots Histogram Plots – a bar diagram where the horizontal axis shows different categories of values, and the height of each bar is related to the number of observations in the corresponding category. Box and Whisker Plots – A box-and-whisker plot for a list of numbers consists of a rectangle whose left edge is at the first quartile of the data and whose right edge is at the third quartile, with a left whisker sticking out to the smallest value, and a right whisker sticking out to the largest value. Stem and Leaf Plots – A stem and leaf plot illustrates the distribution of a group of numbers by arranging the numbers in categories based on the first digit. # Slope Formula I was watching a football game a few days ago, and to prepare for it, we decided to pick up some snacks. As the game progressed, I found myself eating a lot of chips, but at halftime, there was one snack that remained unopened, a snack I had been thinking about all night, a snack that I couldn’t seem to locate until that moment – Recee’s Pieces. We purchased a pretty large sized bag that I thought would last a while. So at the end of halftime, when the bag was almost empty, someone made sure to warn me that at the rate I’m eating these things I’d be sure to be sick the next day. Just to give you some insight into my how my mind works, the fact that she used the term “rate” took me back to classes of Algebra 1 where we were first learning about linear equations, slopes, y-intercepts, point slope form, slope intercept form, and so on. The more I thought about it, the more I thought this would be a good script to add to this site as it would probably provide help to many students who are currently enrolled in those classes as well as a remembrance to adults who took those classes years ago and wish to recall the concepts. So I have added a script which helps go over the slope formula. It randomly generates two points and asks users to select which of a set of choices is the slope of those two numbers. In case you forget, there is a button where you can be given the slope as well.

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# Application of First Law to Closed System MCQ Quiz - Objective Question with Answer for Application of First Law to Closed System - Download Free PDF Last updated on Jul 19, 2024 ## Latest Application of First Law to Closed System MCQ Objective Questions #### Application of First Law to Closed System Question 1: The heat transfer during constant pressure heating of a gas in a cylinder containing a sliding piston is equal to _______. 1. the change in internal energy 2.  zero 3. the change in enthalpy 4. the work done by the piston Option 3 : the change in enthalpy #### Application of First Law to Closed System Question 1 Detailed Solution Explanation: In a reversible constant pressure process, the heat input is the change in enthalpy. According to the first law of thermodynamics: δQ = δW + ΔU For isobaric Process: δW = PdV = P(V2 – V1) Heat, δQ = δW + ΔU = mcpΔT = dh So, heat added at constant pressure is equal to change in Enthalpy and it not only increases the temperature (i.e. internal energy) but also does the work. Non-Flow Processes • These are compression and expansion processes on gases in a cylinder with complete leak proof. In these, there is only energy transfer with zero mass transfer. • These nonflow processes can be the followings: • constant pressure process • constant volume process • constant temperature process • poly-tropic process • constant internal energy process Important Points Isochoric process  means volume is constant while all other variables change. As volume is kept constant therefore no work is done on or by the gas. Heat absorbed by the gas is completely used to change its internal energy and its temperature. From First law of Thermodynamics δQ= ΔU + δW ⇒ δQ = ΔU so, heat added at constant volume is equal to change in internal energy. #### Application of First Law to Closed System Question 2: When a system is undergoing constant volume process, then heat transfer is equal to: 1. change in entropy 2. change in enthalpy 3. work transfer 4. change in internal energy Option 4 : change in internal energy #### Application of First Law to Closed System Question 2 Detailed Solution Explanation: According to the First Law of Thermodynamics: δQ = δW + ΔU For the Constant Volume process: V = constant δQ = ΔU This means whatever heat is supplied to the system that is used up completely to change the internal energy and temperature of the system. For Constant Pressure Process: δQ = δW + ΔU = Cp (T2 – T1) For Constant Temperature Process: ΔU = Cv (T2 – T1) = 0 δQ = δW δQ = 0 δW + ΔU = 0 ⇒ δW = - ΔU #### Application of First Law to Closed System Question 3: In a free expansion process, work done is ______. 1. Minimum 2. constant 3. zero 4. More than one of the above 5. None of the above Option 3 : zero #### Application of First Law to Closed System Question 3 Detailed Solution Explanation: Free Expansion: When the partition is removed, the gas is rushed to fill the entire volume. The expansion of a gas against a vacuum is called free expansion. It is also called Joule expansion. During the free expansion, the temperature remains constant. This process is highly irreversible. Work is always done by a system against some resistance, if there is no resistance then work done is zero. Since free expansion occurs against vacuum hence, no resistance i.e. no work done by the expanding fluid. For a free expansion of a perfect gas: u2 = u1 ⇒ T2 = T1 & δW = 0 #### Application of First Law to Closed System Question 4: If a fluid expands suddenly into _____ through an orifice of large dimension then such a process is called ______. 1. air, free expansion 2. vacuum, free expansion 3. vacuum, hyperbolic expansion 4. air, hyperbolic expansion Option 2 : vacuum, free expansion #### Application of First Law to Closed System Question 4 Detailed Solution Explanation: Free expansion: • If a fluid expands suddenly into vacuum through an orifice of large dimension then such a process is called free expansion. • In free expansion, the fluid is allowed to expand freely into a region of much lower pressure (such as a vacuum), and the expansion occurs rapidly. • This process is considered adiabatic because no heat is exchanged between the system and its surroundings during the expansion. Key Features of Free Expansion: • Rapid expansion: The fluid expands quickly without significant external resistance, usually into a vacuum or a significantly larger container. • No work done: No work is performed against the surroundings because the expansion occurs into a region with negligible pressure. • Adiabatic process: The process is considered adiabatic, meaning no heat transfer occurs between the system (expanding fluid) and the surroundings. • Entropy increase: Despite no work done and heat transfer, the entropy of the fluid increases during free expansion. This seemingly paradoxical phenomenon arises from internal energy redistribution and non-equilibrium effects within the fluid. • Irreversible process: Free expansion is an irreversible process. Once the fluid expands, it cannot be compressed back to its original state without performing work on the surroundings and exchanging heat. Consequences of Free Expansion: • Free expansion can affect the temperature and other properties of the fluid. While no heat transfer occurs, internal energy redistribution within the fluid due to expansion and interactions can lead to a decrease in temperature. • Understanding free expansion is essential for analyzing various thermodynamic processes involving sudden expansions or pressure changes. • The concept is utilized in applications like Joule-Thomson expansion for gas liquefaction and rocket engine nozzles for thrust generation. #### Application of First Law to Closed System Question 5: Two litres of an ideal gas at a pressure of 10 atm expands isothermally into a vacuum until its total volume is 10 litres. How much heat is absorbed in the expansion ? 1. 10 Joule 2. 80 Joule 3. Zero 4. -80 Joule Option 3 : Zero #### Application of First Law to Closed System Question 5 Detailed Solution Explanation: In case of expansion, work is done by the system. Now, as we know that, W = -Pext, ΔV As the gas is expanding is vaccum which has no pressure, i.e., Pext. = 0 ∴ W = 0 Hence no work is done. From first law of thermodynamics, ΔU = q + W As the system is working at constant temperature, i.e., isothermally. ∴ ΔU = 0 Hence q = -W = 0 Hence no heat is absorbed in the expansion. ## Top Application of First Law to Closed System MCQ Objective Questions #### Application of First Law to Closed System Question 6 A cylinder contains 5 m3 of ideal gas at a pressure of 1 bar. This gas is compressed in a reversible isothermal process till its pressure increases to 5 bar. The work in kJ required for this process is 1. 804.7 2. 953.2 3. 981.7 4. 1012.2 Option 1 : 804.7 #### Application of First Law to Closed System Question 6 Detailed Solution Concept: Work done in a reversible isothermal process is given by $$W = C\ln \frac{{{P_1}}}{{{P_2}}} = C\ln \frac{{{V_2}}}{{{V_1}}}$$ Where C = P1V1 = P2V2 P is the pressure and V is the volume of the gas. Calculation: Given: P1 = 1 bar = 100 kPa, V1 =  5 mand P2 = 5 bar C = P1V1 = 1 bar × 5 m3 = 100 kPa × 5 m3 = 500 kJ $$W = C\ln \frac{{{P_1}}}{{{P_2}}} = 500\ln \left( {\frac{1}{5}} \right) = -804.718 \;kJ$$ -ve sign shows that work is done on the system. #### Application of First Law to Closed System Question 7 The work done during an isothermal process is: 1. $${P_1}{V_1}{\log _e}\left( {\frac{{{v_2}}}{{{v_1}}}} \right)$$ 2. $${P_1}{V_2}{\log _e}\left( {\frac{{{v_1}}}{{{v_2}}}} \right)$$ 3. $${P_2}{V_2}{\log _e}\left( {\frac{{{P_2}}}{{{P_1}}}} \right)$$ 4. $$\frac{{{P_2}{V_2} - {P_1}{V_1}}}{{n - 1}}$$ Option 1 : $${P_1}{V_1}{\log _e}\left( {\frac{{{v_2}}}{{{v_1}}}} \right)$$ #### Application of First Law to Closed System Question 7 Detailed Solution Explanation: When work done by the system is taken as positive. Then Work done during an isothermal process is given by – $${W_{1 - 2}} = {p_1}{V_1}\ln \left( {\frac{{{V_2}}}{{{V_1}}}} \right) = {p_2}{V_2}\ln \left( {\frac{{{V_2}}}{{{V_1}}}} \right)\;\;\;\left( \because {{p_1}{V_1} = {p_2}{V_2}} \right)$$ p1V1 = p2V2 during an isothermal process. $$\Rightarrow \frac{{{V_2}}}{{{V_1}}} = \frac{{{p_1}}}{{{p_2}}}$$ $$\therefore {W_{1 - 2}} = {p_1}{V_1}\ln \left( {\frac{{{p_1}}}{{{p_2}}}} \right) = {p_2}{V_2}\ln \left( {\frac{{{p_1}}}{{{p_2}}}} \right)$$ p1V1 = mRT1 & p2V2 = mRT2 $$\therefore {W_{1 - 2}} = mR{T_1}\ln \left( {\frac{{{V_2}}}{{{V_1}}}} \right) = mR{T_2}\ln \left( {\frac{{{V_2}}}{{{V_1}}}} \right) = mR{T_1}\ln \left( {\frac{{{p_1}}}{{{p_2}}}} \right) = mR{T_2}\ln \left( {\frac{{{p_1}}}{{{p_2}}}} \right)$$ Process Work Done Constant Pressure (Isobaric / Isopiestic) W1-2 = p(V2 – V1) Constant Volume (Isochoric) W1-2 = 0 Polytropic For Adiabatic (n = γ = 1.4) $${W_{1 - 2}} = \frac{{{p_1}{V_1} - {p_2}{V_2}}}{{n - 1}} = \frac{{{p_1}{V_1}}}{{n - 1}}\left[ {1 - {{\left( {\frac{{{p_2}}}{{{p_1}}}} \right)}^{\frac{{n - 1}}{n}}}} \right]$$ #### Application of First Law to Closed System Question 8 In an isentropic process, the pressure P of a gas with temperature T as P = K T5/2 where K is a constant. The ratio γ (= Cp/Cv) of the gas is: 1. 5/3 2. 9/5 3. 7/5 4. 3/2 Option 1 : 5/3 #### Application of First Law to Closed System Question 8 Detailed Solution Concept: For isentropic or reversible adiabatic process the P-V-T relation is given by $$\frac{{{T_2}}}{{{T_1}}} = {\left( {\frac{{{V_1}}}{{{V_2}}}} \right)^{γ - 1}} = {\left( {\frac{{{P_2}}}{{{P_1}}}} \right)^{\frac{{γ - 1}}{γ }}}$$ or P = K Tγ /γ - 1 The given relation for the isentropic process in the question is P = K T5/2 Comparing the above relationship with the standard relation of the isentropic process we will get, $$\frac{\gamma}{\gamma\;-\;1}=\frac{5}{2}$$ 2γ = 5γ - 5, 3γ = 5 or γ = 5/3 #### Application of First Law to Closed System Question 9 Paddle wheel work and expansion of gas into vacuum (free expansion) is a 1. Quasi-equilibrium process 2. Quasi static process 3. Isotropic process 4. Non-equilibrium process Option 4 : Non-equilibrium process #### Application of First Law to Closed System Question 9 Detailed Solution Explanation: • Paddle wheel work is a process involving friction in which the volume of the system does not change at all, and still work is done on the system. • Friction makes this process irreversible, hence the process is in a non-equilibrium process. • Work increases the stored energy (internal energy) of the system. Hence the temperature of the system increases in this process. Free expansion: • When the partition is removed, the gas rushed to fill the entire volume. The expansion of gas against vacuum is termed as free expansion or unrestricted expansion. • A free expansion is an irreversible process in which a gas expands into an insulated evacuated chamber. Hence free expansion is also a non-equilibrium process. • It is also called the Joule expansion. • During the free expansion, the temperature remains constant this implies there is a drop in the pressure. • Work done in a free expansion process is zero. • No heat interaction takes place during free expansion. So δW = 0 Also, δQ = 0 From the first law of Thermodynamics δQ = dU + δW dU = 0 Hence change in internal energy in the free expansion process is also zero. #### Application of First Law to Closed System Question 10 1 m3 of air at a pressure of 10 kg/cm2 is allowed to expand freely to a volume of 10 m3. The work done will be 1. +ve 2. -ve 3. zero 4. 105 kg-m Option 3 : zero #### Application of First Law to Closed System Question 10 Detailed Solution Explanation: Here air expands freely, so it is a free expansion process. Free expansion process: • A free expansion is an irreversible process in which a gas expands into an insulated evacuated chamber. • It is also called Joule expansion. • Work done in a free expansion process is zero. No heat interaction takes place Hence dQ = 0 From first law of thermodynamic, dQ = dU + dW dU = 0 Note: Though in the free expansion of an ideal gas initial temperature is equal to the final temperature, it doesn’t mean that process is isothermal. As in the Isothermal process, the temperature remains constant throughout, but here initial temperature starts decreasing and finally temperature increases when the molecules come into contact with the gas container. #### Application of First Law to Closed System Question 11 When air expands from initial pressure P1 and volume V1 to final volume 5 V1 following the law PVn = C 1. Greater the value of n, greater the work obtained 2. Smaller the value of n, smaller the work obtained 3. For n = 0, the work obtained is the greatest 4. For n = 1.4, the work obtained is the greatest Option 3 : For n = 0, the work obtained is the greatest #### Application of First Law to Closed System Question 11 Detailed Solution Concept: Work obtained in the P – V diagram is the area under the curve. As clearly seen that Larger the value of n, smaller is the area and so smaller is work obtained. In other words $$W = \frac{{{P_1}{V_1} - {P_2}{V_2}}}{{n - 1}}$$ So, W is maximum, when n = 0 i.e. constant pressure process W is always zero for n = ∞ i.e. constant volume process #### Application of First Law to Closed System Question 12 During a non-flow thermodynamic process (1-2) executed by a perfect gas, the heat interaction is equal to the work interaction (Q1-2 = W1-2) when the process is 1. Isentropic 2. Polytropic 3. Isothermal Option 3 : Isothermal #### Application of First Law to Closed System Question 12 Detailed Solution Concept: The first law of thermodynamics For a closed system/non-flow system undergoing a process, (1 - 2) Q1-2 = ΔE + W1-2 …1) E = Stored energy of a system This stored energy can be viewed as the sum of microscopic and macroscopic energies. ⇒ Q1-2 = Δ (U + KE + PE) + W1-2 ⇒ Q1-2 = ΔU + ΔKE + ΔPE + W1-2 …2) For a non-flow or closed system at equilibrium, ΔKE and ΔPE are negligible, So, these 2 terms can be neglected. ⇒ Q1-2 = ΔU + W1-2 …3) Also, for a perfect gas, the internal energy is a function of temperature only. i.e. dU = mCνdT …4) Calculation: Given equation is Q1-2 = W1-2 …5) But first law states that; Q1-2 = ΔU + W1-2 …6) Comparing 5) and 6) ⇒ ΔU = 0 …7) But for perfect gas; dU = mCνdT, integrating both sides $$\mathop \smallint \nolimits_1^2 dU = \mathop \smallint \nolimits_1^2 m{C_\nu }dT$$ ⇒ U2 – U1 = mCν(T2 – T1) {Assuming constant m, Cν} ΔU = mCν(ΔT) …8) Comparing 7) and 8) ⇒ ΔT = 0 {∵ m ≠ 0, Cν ≠ 0} T2 = T1 = Constant = Isothermal process Key Points Remember the properties of perfect gases and apply these directly instead of writing first law. Study all the basic processes in detail like the adiabatic process, Isobaric, isochoric etc. #### Application of First Law to Closed System Question 13 Which of the following statements is correct with reference to perpetual motion machines of the first kind? 1. It violates the second law of thermodynamics. 2. it is a reversible process. 3. It produces heat without receiving work input 4. It produces work without receiving heat Option 4 : It produces work without receiving heat #### Application of First Law to Closed System Question 13 Detailed Solution Explanation: Perpetual motion machine of the first kind (PMM1): • The first law of thermodynamics states that energy can neither be created nor be destroyed. It can only get transformed from one form to another form. • An imaginary device that would produce work continuously without absorbing any energy from its surroundings is called a Perpetual Motion Machine of the First kind, (PMMFK). • A PMMFK is a device that violates the first law of thermodynamics. It is impossible to devise a PMMFK. • The converse of the above statement is also true, i.e., there can be no machine that would continuously consume work without some other form of energy appearing simultaneously. • PMM-I violates the first law of thermodynamics. Perpetual motion machine of the second kind (PMM2): • A fictitious machine that produces net-work in a complete cycle by exchanging heat with only one reservoir is called the PMM2. • It violates the Kelvin-Plank statement. • Thus, it violates the second law of thermodynamics and It is a hypothetical machine. #### Application of First Law to Closed System Question 14 The internal energy during the free expansion process 1. constant 2. minimum 3. maximum 4. zero Option 1 : constant #### Application of First Law to Closed System Question 14 Detailed Solution Explanation: Free expansion: • When the partition is removed, the gas rushed to fill the entire volume. The expansion of gas against vacuum is termed as free expansion or unrestricted expansion. • A free expansion is an irreversible process in which a gas expands into an insulated evacuated chamber. Hence free expansion is also a non-equilibrium process. • It is also called the Joule expansion. • During the free expansion, the temperature remains constant this implies there is a drop in the pressure. • Work done in a free expansion process is zero. • No heat interaction takes place during free expansion. • Internal energy is a function of temperature and in the case of the free expansion process, there is no change in temperature so the change in internal energy is also zero. So internal energy of the system remains constant. #### Application of First Law to Closed System Question 15 A mass ‘m’ of a perfect gas at pressure P1 and volume V1 undergoes an isothermal process. The final pressure is P2 and volume V2. The work done on the system is considered positive. If R is the gas constant and T is the temperature, then the work done in the process is 1. $${P_1}{V_1}\ln \frac{{{V_2}}}{{{V_1}}}$$ 2. $$- {P_1}{V_1}\ln \frac{{{P_1}}}{{{P_2}}}$$ 3. $$RT\ln \frac{{{V_2}}}{{{V_1}}}$$ 4. $$- mRT\ln \frac{{{P_2}}}{{{P_1}}}$$ Option 2 : $$- {P_1}{V_1}\ln \frac{{{P_1}}}{{{P_2}}}$$ #### Application of First Law to Closed System Question 15 Detailed Solution Concept: $$W = -\smallint PdV$$ (-Ve Sign taken because work is done on the system) For an ideal gas, PV = mRT = const (c) ⇒ PV = C;             ∴ P = C/V $$W = -\mathop \smallint \limits_{{V_1}}^{{V_2}} \frac{C}{V}dV \Rightarrow W = -C\ln \left( {\frac{{{V_2}}}{{{V_1}}}} \right)$$ $$W =- PV\ln \left( {\frac{{{V_2}}}{{{V_1}}}} \right)$$ $$W = -{P_1}{V_1}\ln \left( {\frac{{{V_2}}}{{{V_1}}}} \right)$$ When work is done on the system (compression), V2 < V1 and P2 > P1 $${P_1}{V_1} = {P_2}{V_2} \Rightarrow \frac{{{V_2}}}{{{V_1}}} = \frac{{{P_1}}}{{{P_2}}}$$ $$W = -{P_1}{V_1}\ln \left( {\frac{{{P_1}}}{{{P_2}}}} \right)$$

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Empoasca fabae Harris Appearance and Life History The potato leafhopper feeds on more than 100 cultivated and wild plants including; apples, beans, potatoes, eggplant, rhubarb, celery, dahlia, peanuts, alfalfa, clovers, and soybean. The adult potato leafhopper is a tiny, yellowish-green, wedge-shaped insect, about 1/8 inch (3 mm) long. The nymphal stages closely resemble the adult except that they are smaller, wingless, and more yellow in color. Both adults and nymphs are very active. The nymphs, which cannot fly, walk sideways at a rapid pace when disturbed, while adults will either fly or jump. The potato leafhopper does not overwinter in the Midwest, but is carried annually northward from the Gulf Coast states by spring winds. Typically, adults first appear in the Midwest by the end of April or in early May. However, high populations usually do not occur until mid summer. The female lives about a month, and during this time deposits two or three tiny white eggs each day in the stems and large leaf veins of host plants. The tiny nymphs emerge from these eggs in 7 to 10 days and become adults in about two weeks. Thus, the entire life cycle requires about a month. There are probably three or four generations in the eastern Midwest each year. Both potato leafhopper adults and nymphs feed on soybean, but the most serious damage is caused by the nymphs. The potato leafhopper uses its piercing-sucking mouth parts to remove plant juices. As it feeds, it injects a toxin into the plant which causes a decrease in the plant’s ability to produce photosynthate. Damage symptoms first appear as yellowish patches on the leaves with crinkling and cupping, often confused with herbicide damage. As leafhopper feeding continues, the plants become stunted. Soybean varieties which have sparse or very short leaf pubescence are most susceptible to feeding and subsequent damage. The adult and nymph are able to reach the leaf surface with less difficulty on these varieties. Also, plants under moisture stress appear to be more vulnerable to damage. Damage is most likely to occur on late planted soybean. This is because potato leafhopper arrival from the south coincides with early leaf tissue development of the late planted soybean. Young soybean leaves tend to have softer pubescence which makes movement, feeding, and oviposition by leafhoppers easier. If potato leafhoppers are "kicked-up" as foliage is disturbed and some leaf discoloration/crinkling is noticed, sampling should be initiated. For plants at the V4 growth stage or less, carefully inspect the underside of leaves of 5 plants in 5 areas for adults and nymphs. Record the number of leafhoppers and calculate the average number per plant. For soybeans at or beyond the V5 growth stage, take 20 sweeps with a sweep net in each of 5 field areas. Immediately after completing the 20 sweeps, count the leafhoppers, both adults and nymphs, from the top to the bottom of the bag. Record only the small yellow-green leafhoppers and not the various brown leafhoppers also commonly found. Determine the average number of potato leafhoppers per sweep. Also, by selecting one plant in each sampling location, determine the average number of trifoliolate leaves per plant. Soybean Insect Control Recommendations: E-series 77-W (PDF) In general, soybean can withstand potato leafhopper feeding without economic loss. Under good growing conditions they normally outgrow leafhopper feeding damage. Soybean varieties under various environmental conditions can show differences in level of tolerance to potato leafhopper feeding. Sparsely pubescent soybean seedlings (V1 to V4 plant growth stages) under moisture stress, with high potato leafhopper numbers, are the most susceptible to damage and most likely to benefit from treatment. Control may be warranted if potato leafhopper numbers reach or exceed the following levels: If control is necessary, contact your state Cooperative Extension Service or click here for control materials and rates.

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The study highlights a new and important finding: Controllable well construction choices, not just location and depth, influence arsenic concentrations in drinking water. “Chronic exposure to high levels of naturally occurring arsenic through drinking water can cause certain cancers, skin abnormalities and other adverse human health effects,” said Melinda Erickson, a USGS research hydrologist and the lead author of the study. “Results from this study can help improve arsenic concentration predictions and help identify safer groundwater supply options in similar aquifers throughout the U.S. and globally.” The glacial aquifers of Minnesota used for domestic wells commonly have elevated arsenic concentrations. The new study found that short well screen lengths of four or five feet, which are typical, were associated with higher probabilities of elevated arsenic concentrations. At the time of well drilling, choosing to place a well screen farther beneath the overlying confining unit, also called an aquitard, and/or using a longer-length screen would lower, though not eliminate, the risk of having high arsenic concentrations in the well water. USGS scientists created arsenic hazard maps for regions in northwestern and central Minnesota, and used a sophisticated statistical model to determine which environmental and man-made variables influence arsenic concentrations. They found that natural aquifer characteristics, such as position on the landscape and soil chemistry, were among the most influential for predicting elevated arsenic levels. Public water supplies are regulated by the U.S. Environmental Protection Agency, but maintenance, testing and treatment of private water supplies are the responsibility of the homeowner. The EPA’s maximum arsenic level allowed for public water supplies is 10 micrograms of arsenic per liter of water. In Minnesota, arsenic concentrations exceed 10 micrograms of arsenic per liter in about 11 percent of newly constructed private wells, and arsenic is detectable in about 50 percent of wells. The Minnesota Department of Health recommends that well owners with detectable arsenic treat their drinking water. Glacial and other sand and gravel aquifers similar to those in Minnesota exist across the northern U.S. and in places like southeastern Asia. Results from the study can help improve arsenic concentration prediction methods and groundwater infrastructure far beyond Minnesota. This research was funded by the Minnesota Department of Health through the Minnesota Clean Water Fund and the USGS. The new study is published in the journal Water Resources Research. For more information about USGS water studies in Minnesota, visit the USGS Water Resources of Minnesota website. - Warmer water could cool Montana’s trout fishing economy - September 7, 2022 - Water Released from Crystallizing Magma can Trigger Earthquakes in Yellowstone - September 5, 2022 - Thermal Infrared Remote Sensing at Yellowstone 101 - August 29, 2022

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# A charge particle of mass 'm' and charge 'q' is moving with a speed 'v' in a magnetic field B. If the radius of the circular path traced by a charge particle is 'r'. Then find the ratio of q/m. This question was previously asked in Airforce Group X 13 Jul 2021 Shift 1 Memory Based Paper View all Airforce Group X Papers > 1. $$\frac{q}{m}=\frac{v}{Br}$$ 2. $$\frac{q}{m}=\frac{vB}{B}$$ 3. $$\frac{q}{m}=\frac{vr}{B}$$ 4. $$\frac{q}{m}=\frac{B}{vr}$$ ## Answer (Detailed Solution Below) Option 1 : $$\frac{q}{m}=\frac{v}{Br}$$ Free General Knowledge for All Defence Exams (शूरवीर): Special Live Test 8 K Users 20 Questions 20 Marks 16 Mins ## Detailed Solution CONCEPT: • Magnetic force: Magnetic force is the force experienced by electrically charged particles moving in a magnetic field. • The magnitude of the magnetic force (F) on a charge (q) moving at a speed (v) in a magnetic field of strength B is given by: $$⇒ F = qvBsin θ$$ Where θ is the angle enclosing v and B. EXPLANATION: • When a charged particle moves perpendicular to the magnetic field (θ = 90), it follows a curved path and undergoes circular motion. • Here, the magnetic force supplies the centripetal force which keeps the particle in a circular motion. The centripetal force, $$F_C = \frac{mv^2}{r}$$ ​Where m is the mass of the particle, v is the velocity of the particle, and r is the radius of the circular path traced by the particle. Therefore, F = FC $$⇒qvB = \frac{mv^2}{r}$$ $$⇒r = \frac{mv}{qB}$$ The above equation can be written as $$⇒\frac{q}{m}=\frac{v}{Br}$$

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While the skeleton of public access to health services was beginning to emerge during this period - with workhouses, voluntary hospitals, asylums and isolation hospitals - the level and conditions of care were poor. At the beginning of the century, preventative healthcare measures became a focus of attention since both the Boer and Crimean wars had highlighted the poor health of soldiers; more had died from fevers and typhoid than through actual warfare. Any treatment received by wage earners tended to be paid for by their subscriptions to trade unions or friendly societies who, in turn, paid the doctors. This system, however, only covered the worker and not the family. Those who couldn’t afford to pay relied on out-patient departments and dispensaries at local voluntary hospitals or simply did not receive treatment. Towards the end of the 19th century, voluntary hospitals, unable to provide services on charitable donations alone, began charging for hospital costs. In 1905, the Minority Report of the Poor Law Commission pointed out the differences in standards of health care services provided across the country and urged the government to make amends. It responded with benefits for the unemployed and pensions for the elderly rather than a direct approach. The National Health Insurance Act in 1911 ensured that workers at the bottom of the wage scale received free treatment with their GP, but did little to improve the situation for the rest of the population.

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How to find the factorial of a number in JavaScript In this tutorial, let’s look at the different ways of finding the factorial of a number in JavaScript. To start with, we’re going to look at the iterative approach, where we’ll be looking at using both the while and for loops. In the next section, let’s look at using recursive functions to achieve our purpose. How to calculate factorial of a number? To start with, if you’re not familiar with how factorial works, let me explain it to you before we start looking at how to achieve the result with code. Factorial is usually written like this: n! Here, n! means that we’d like to find the factorial of the positive, whole number ‘n. Notice how I said positive whole number? Yes, that’s because factorials don’t work with negative numbers or decimal numbers, so that’s something you need to create checkpoints for in your code. So, how’s it calculated? That’s very simple as well. Just start multiplying n with its decrements until you reach 1, and the result is the factorial of said number. Let me show you. 5! = 5 * 4 * 3 * 2 * 1 = 120 4! = 4 * 3 * 2 * 1 = 24 3! = 3 * 2 * 1 = 6 2! = 2 * 1 = 2 1! = 1 * 1 = 1 0! = 1 = 1 It’s quite simple as I promised, isn’t it? But look out for factorial of 0. You might think its 0 because anything multiplied by 0 is 0, but in this case, it’s actually 1. Why is that? Well, since 0 has no value, and a factorial always ends with a multiplication of 1, we’re just left with 1 at the end, which is the result of 0! So now that you know how factorials work, how can we achieve these results with code? There are 2 approaches. Let’s look at them both now. Iterative approach to finding the factorial in JavaScript One of the easiest ways to find the factorial of a number in JavaScript is by using the iterative approach. As the name implies, you’re going to iterate from 1 through n using the available loops (while and for loops) and return the result. It’s as simple as that. Using the While loop Let’s start with the while loop. We’ve created an arrow function findFactorial that accepts an argument ‘n’, where n is the positive whole number you want to find the factorial of. To start with, let’s create a variable factValue and assign it the base value of 1 (the last multiplied number in every factorial operation). Now, let’s create our checkpoints. We’re going to look out for 3 things: 1. If our number is 0, then we can directly return 1. 2. If our number is negative, we can’t proceed 3. If our number is either a NaN value (Not an number) or a decimal value (not a whole number/integer), we can’t proceed. We use the isInteger method to check for both NaN and floating-point values at the same time. Unless the value is an integer, it’ll always return a false. That’s it! Once the checkpoints are created, let’s just get on with our ‘while’ loop. Let’s create an iterator ‘i’ and assign it an initial value of 1 (the base value for factorials). The while loop is going to run until the value of ‘i’ reaches ‘n’. For every iteration of the loop, let’s multiply factValue by i and then increment it. Finally, return factValue, as shown below: ```//Iterative approach - while loop const findFactorial = (n) => { let factValue = 1; if(n === 0) return 1; if(n < 0 || !Number.isInteger(n)) return 'Please enter a valid number'; let i = 1; while(i <= n) { factValue *= i; i++; } return factValue; } console.log(findFactorial(5)); //5! = 5 * 4 * 3 * 2 * 1 = 120 console.log(findFactorial(0)); //0! = 1 console.log(findFactorial(1)); //1! = 1 console.log(findFactorial('a')); //'Please enter a valid number' console.log(findFactorial(4.2)); //'Please enter a valid number' ``` As you can see above, for 5, you get back 120. For 0 and 1, you get back 1. For ‘a’ and 4.2 (NaN and floating-point numbers), you get back ‘Please enter a valid number’. Our program works perfectly. So, how does the iteration work here? Let’s go through it step by step: 1. For the first iteration of the loop (i = 1), factValue = 1 and factValue *= i would be factValue = 1 * 1 = 1 2. For the 2nd iteration (i = 2): factValue = 1 * 2 = 2 3. For the 3rd iteration (i = 3): factValue = 2 * 3 = 6 4. For the 4th iteration (i = 4): factvalue = 6 * 4 = 24 5. For the 5th and final iteration (i = 5): factValue = 24 * 6 = 120 That’s how the factorial is calculator using loops. Using the For loop Just like in the last section, let’s find the factorial using a ‘for’ loop. The only difference here is that you’re using a ‘for’ loop instead of a ‘while’ loop. The rest of the code logic remains the same, as shown below: ```//Iterative approach - For loop const findFactorial = (n) => { let factValue = 1; if(n === 0) return 1; if(n < 0 || !Number.isInteger(n)) return 'Please enter a valid number'; for(let i = 1; i <= n; i++) { factValue *= i; } return factValue; } console.log(findFactorial(5)); //5! = 5 * 4 * 3 * 2 * 1 = 120 ``` Recursive approach to finding the factorial of a number in JavaScript Finally, let’s look at the recursive approach. Our findFactorial function starts off the same, except for one minor change. We’re not going to create factValue here. Instead, we’re going to proceed with the checkpoints (when n is 0, negative, floating-point or NaN value). Then, let’s create our recursive function. It’s quite simple. Earlier, we multiplied in ascending increments (from 1 to n). Now, let’s multiple in descending increments (n to 1). So, the recursive condition would be n * findFactorial(n – 1), as shown below: ```//Recursive approach const findFactorial = (n) => { if(n === 0) return 1; if(n < 0 || !Number.isInteger(n)) return 'Please enter a valid number'; return n * findFactorial(n - 1); } console.log(findFactorial(5)); //5! = 5 * 4 * 3 * 2 * 1 = 120 ``` So, how does this work really? Let me illustrate with an example. Let’s take the above example of 5! for the purposes of this illustration. Let’s go through the steps of the recursion: 1. For the first recursion: return 5 * findFactorial (4); 2. For the second recursion: return 5 * 4 * findFactorial(3) = 20 * findFactorial(3); 3. For the third recursion: return 20 * 3 * findFactorial(2) = 60 * findFactorial(2); 4. For the fourth, and final recursion: return 60 * 2 * findFactorial(1) = 120 * findFactorial(1); 5. For the fifth, and final recursion: return 120 * 1 * findFactorial(0); From the instructions given in the code 0 returns 1, so the final result would be: return 120 * 1 * 1 = return 120; That’s it! Those are the 3 different ways of finding the factorial of a given number in JavaScript.

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Weathering and erosion of rocks like granites concentrate elements that are necessary to form clay minerals, which accumulate as sediments. The deposition and burial of clays, in the delta of a river, for example, lead to the formation of the sedimentary rocks claystone and shale. Topic: Earth Science Subtopic: Minerals and Resources Keywords: Geochemical cycles, Geology, Sedimentary rocks, Shale, Soils, Tonsteins

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Swine flu like any other flu shows various symptoms. The symptoms seen in people affected by swine flu virus are similar to the people with symptoms of some regular flu including cough, fever, throat infection or sore throat, pain in the body, headache, fatigues and chills. Vomiting and diarrhea are also allied with swine flu. Severe illness (respiratory failure) is also observed in many people. Deaths due the swine flu infection have been reported in people all over the world. Swine flu might even cause worsening of underlying and chronic medical conditions. Spread of this H1N1 influenza virus happens in much similar way as any other seasonal influenza. These viruses spread primarily from one person to another through sneezing, coughing of people affected with influenza. Sometime even people might get infected by just touching something with live viruses onto it and then touching their nose or mouth.To diagnose H1N1 an infection, an respiratory sample would usually be needed to be collected in the first 3 to 5 days of the illness because this is the period when the infected person is likely to shed virus. For identification whether a virus is swine flu influenza it requires that the specimen is send to a hospital laboratory for examination. Though, few people, particularly children, might shed virus for 10 days or even longer. For prevention or the treatment of swine influenza virus infection Tami flu (oseltamivir) or Zanamivir can be used. The antiviral drugs are recommended medicines (liquid, pills or an inhaler) which fight against the virus by keeping them from reproducing in the body. If you get fever, then antiviral drugs can effectively make your sickness milder and can make you feel better quicker. They might also prevent serious influenza complications. For this treatment antiviral drugs acts best if they are consumed soon after getting ill (just within 2- 3 days of symptoms). The flu virus can spread if a person comes in contact with something that is infected with the virus and then again touches his or her eyes, mouth or nose. Droplets from a sneeze or a cough of a victim spread through the air. The virus can also be spread if a person touches other person's respiratory droplets on the surface of a desk, child's toy doorknob or even a phone handset and then again touches their own mouth, eyes or nose without washing their hands. Few bacteria and viruses can survive for about 2 hours or even longer on surfaces like doorknobs cafeteria tables, and desks. Frequently washing of the hands will help you to reduce the chances of getting contaminated or infected from the viruses dwelling on these common surfaces. For safety purpose cover your mouth and nose with a tissue paper whenever your cough or sneeze. Throw this tissue paper in the bin after using it. Make sure you wash hands with water and soap often particularly after your sneeze or cough. Try to use alcohol based hand sanitizers or cleaners those are quiet effective. Try and avoid contact with people infected with the swine flu virus. Other preventive tips that a swine flu infected person needs to follow are many. A person needs to take plenty of sleep, do exercise on regular basis, manage stress, stay healthy, eat a best diet, never get close to people who are ill and stay away from other people. To stop other people getting infected, one needs to restrict his or her contact with other people. A person should put used tissues in a waste basket; cover his or her mouth with tissue paper when sneezing. A person also needs to keep all surfaces that he or she has touched clean. He also needs to follow the instructions given by the doctor and wash face and hands on regular basis. A few people get infected with swine flu in Mexico City and authorities are advising people to make contact with doctors. Swine flu can be treated completely if the patient takes the early treatment for that

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0 Q: # A television show lasted for 4 2/3 hrs. If 1/5 th of the total time was spent on advertisements, what was the actual duration of the television show? A) 14/15 hrs B) 37/15 hrs C) 4/5 hrs D) 56/15 hrs Explanation: Q: A and B can complete a piece of work in 15 days and 10 days respectively. They got a contract to complete the work for ₹35000. The share of A (in ₹) in the contracted money will be: A) 7000 B) 21000 C) 14000 D) 15000 Explanation: 4 390 Q: A and B can complete a piece of work in 15 days and 10 days respectively. They got a contract to complete the work for ₹35000. The share of B (in ₹) in the contracted money will be: A) ₹15000 B) ₹14000 C) ₹21000 D) ₹7000 Explanation: 0 324 Q: A and B can complete a piece of work in 15 days and 10 days respectively. They got a contract to complete the work for ₹75000. The share of B (in ₹) in the contracted money will be: A) 45,000 B) 30,000 C) 35,000 D) 40,000 Explanation: 1 423 Q: If 16 men working 12 hours a day can complete a work in 27 days, then working for how many hours a day can 18 men complete the work in 24 days ? A) 9 B) 18 C) 16 D) 12 Explanation: 1 957 Q: If 40 men working 12 hours a day can complete a work in 8 days, then how many men working 4 hours a day can complete the same work in 16 days? A) 50 B) 60 C) 54 D) 45 Explanation: 2 460 Q: A can complete a piece of work in 20 days and B can complete 20% of the work in 6 days. If they work together in how many dayscan they finish 50% of the work, if they work together A) 12 B) 6 C) 8 D) 9 Explanation: 3 689 Q: Shyam can complete a task in 12 days by working 10 hours a day. How many hours a day should he work to complete the task in 8 days? A) 12 B) 15 C) 16 D) 14 Explanation: 1 811 Q: 5 men and 8 women can complete a task in 34 days, whereas 4 men and 18 women can complete the same task in 28 days. In how many days can the same task be completed by 3 men and 5 women? A) 56 B) 72 C) 64 D) 36

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Introductory Algebra for College Students (7th Edition) $x=50$ Let x = the unknown number Then "the quotient of three times a number and 5" means $3x\div5$ or $\frac{3x}{5}$ "is increased by 4" means to add 4 to the quotient Thus, the equation that represents the situation is: $\frac{3x}{5}+4=34$ Use the addition property of equality to subtract 4 from both sides of the equation. $\frac{3x}{5}+4-4=34-4$ $\frac{3x}{5}=30$ Use the multiplication property of equality to multiply both sides of the equation by 5. $\frac{3x}{5}\times5=30\times5$ $3x=150$ Use the multiplication property of equality to divide both sides of the equation by 3. $3x\div3=150\div3$ $x=50$

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Little is known of the King of Denmark, Sweyn Forkbeard, today, but this Norse monarch was once the King of England as well, albeit for only five weeks, making the small town of Gainsborough in eastern England his capital. One reason for the mystery surrounding him is several conflicting accounts exists, and they describe Sweyn in a different light, depending on the author and his sources. His life is depicted in several important medieval chronicles outside of Scandinavia, like the 12th century Deeds of the Bishops of Hamburg, written by German scholar Adam of Bremen, or the magnum opus of John of Wallingford, simply titled Chronica. The 13th century English monk, healer, and author tried to capture the history of Sweyns’ conquest of Britain, portraying him as a merciless and godless figure, typical of the image of Northern invaders in early-medieval England. Sweyn rose to power by seizing the throne of Denmark in the mid-980s, while forcing his father, Harold Bluetooth, to abdicate and flee to exile. In 1003, he invaded England, following an attack of Danish settlers known as the St Bryce Day Massacre, which came as a reaction to year-by-year harassment of English natives by the Viking pillagers. Allegedly, Sweyn Forkbeard’s sister, Guldhun, lost her life during the massacre, which had happened in 1002, and retribution was believed to be the main reason for the Danish king’s campaign in England. Some historians doubt this claim, considering Sweyn’s invasion as nothing more than a continuation of yearly raids of the British Isles, which occurred in a 10-year period between 1002 and 1012. The then-King of England, Aethelred the Unready, who ordered the massacre, quickly lost territories in Wessex and East Anglia to Sweyn Forkbeard, who pillaged the region, sowing fear and death among the local population. Luckily for the English, a terrible famine struck the Norse invaders, forcing them to retreat in 1005. Following a power vacuum due to the sudden retreat, another Viking leader called Thorkell the Tall took on the role of invader four years later, in 1009–once again scattering English troops and leaving them helpless from the terror that ensued. That’s when Sweyn Forkbeard decided to get back into the game. He assembled an army and enough money to fund an invasion through the tax-system known as the Danegeld. The Danegeld was more of a racket than a tax system, as it guaranteed certain territories that they wouldn’t be raided if they paid tribute. What followed was yet another campaign on English soil, led by Sweyn himself, together with his son, Cnut. They landed in Sandwich, and since the rule of Aethelred was collapsing, the local feudal lords bowed to Sweyn and joined him in the following conquest. The same happened with the people of Northumbria and Lindsey, and while Forkbeard’s forces swelled in numbers along the way, the legitimate King was becoming weaker. In the meantime, Sweyn’s former ally, Thorkell the Tall, defected to the English side, as his own campaign became jeopardized by the Danish King’s new rise to power. In London, the unlikely friends took their stand. Aethelred and Thorkell faced Sweyns’ forces and managed to repel them in a last-stand battle, saving London from pillage and cruel retribution. The Danes retreated and summoned other English provinces to join them. In the meantime, King Aethelred fled to the Isle of Wight, and then to Normandy to join his sons, Alfred and Edward, narrowly escaping death. Soon after Aethelred’s exile, the citizens of London decided to accept Sweyns’ rule in order to avoid more carnage. On Christmas Day of 1013, Sweyn Forkbeard declared himself the King of England and based the center of his kingdom in Gainsborough. But fate had other plans for the Danish conqueror. Just five weeks into his rule in England, on February 3, 1014, King Sweyn died and his body was returned to Denmark for burial. Following his death, a struggle arose between the sons; the older son, Harald II, inherited the throne in Denmark, while Cnut, who participated in the English campaign, was declared King of England by Sweyn’s soldiers in 1015. Thorkell the Tall once again switched sides and offered his support to Cnut, who, in return, declared him the Jarl of East Anglia several years after. Cnut’s sons, Harold Harefoot and Harthacnut, ruled England for the next 26 years. After Harthacnut, Edward the Confessor retook the throne, returning it to the House of Wessex. As for Sweyn’s bloodline in Denmark, the current dynasty traces its ancestral origins all the way back to the legendary king. In 1469, one of Forkbeard’s descendants, Margaret of Denmark, married King James III of Scotland, formally introducing the bloodline to British royalty.

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Shelley Svoboda uses a fine surgical blade to take pigment samples from 18th-century paintings. She used to tell visitors to her lab at the Colonial Williamsburg Foundation that she only needed to remove a piece smaller than the period at the end of this sentence. She doesn’t say that now. You can see the period at the end of this sentence, but you can’t see anything as small as the amount now needed to do scientific analysis of pigment—at least not with the naked eye. “The idea, especially with these historic paintings, has always been to remove a minimal amount of paint,” explains Svoboda, a Colonial Williamsburg conservator specializing in paintings. A collaboration with Kristin Wustholz, assistant professor of chemistry at William & Mary, has produced a new technique that allows precise chemical analysis from a single near-microscopic particle excised from the painting. The technique uses a laser microscopy method known as surface enhanced Raman scattering (SERS). Much like the objects of their study, 18th-century portraitists who prepared their own paints, Wustholz and the students in her lab begin their work by mixing a paste of silver-colloid nanoparticles. “You place the silver nanoparticles on the paint sample you want to analyze,” Wustholz explained. Then the sample goes onto a glass slide and into the SERS laser. The molecules in the sample react to the laser, vibrating and scattering the light. The pattern of the scattered light is diagnostic for the substance being analyzed. Looking for fingerprints “The silver nanoparticles act as an antenna, essentially. It gives you a very strong signal, like a fingerprint, almost,” she said. That “fingerprint” is the vibrational spectra unique to the molecules in the paint. Wustholz can compare the fingerprint of the sample to a database of known vibrational spectra of pigments. Wustholz’s SERS laser approach is a great improvement over conventional Raman spectroscopy, until now the go-to protocol for paint analysis. “Raman spectroscopy is great. It provides you with the vibrational fingerprint. The problem is that it’s incredibly insensitive; only about one in a million photons will be Raman scattered,” she explained—thus the need for the larger sample to be taken from the painting. The chemists correlate SERS work with a second examination of the paint, using fluorescence microscopy. The two-pronged approach, Wustholz says, gives a superbly accurate and detailed fingerprint of paints. Wustholz describes the SERS process as “minimally invasive,” while fluorescence is completely nondestructive; it even can be done at a distance. These attributes are a godsend to a conservator of paintings such as Svoboda. The two—along with two of Wustholz’s undergraduates—collaborated on a study of pigments used in two 18th-century portraits that were in Svoboda’s lab. The collaboration led to a paper in the scientific journal Analytical Chemistry, with Wustholz’s students Stephen Dinehart ’12 and Lindsay Oakley ’12 as co-authors. “Both of those paintings are from about the same era, but one is by Sir Joshua Reynolds—the biggest name in painting in London at the time. Robert Feke is an American, the first American-born painter,” Svoboda explained. “Feke is actually a little earlier than the Reynolds, 1748— but we found that they both were using the same materials, most probably British.” In their examination of Reynolds’ Portrait of Isaac Barré and Feke’s Portrait of William Nelson, the team was searching for the molecular fingerprints of colorants known as lake pigments. They were especially interested in finding evidence of a prized—and quite expensive—red pigment known as carmine lake. Svoboda explains that lake pigments are organic dyes compounded into a mineral carrier. In the case of carmine lake, the dye comes from the scales of a particular insect. She said that lake pigments, much valued by 18th-century painters for their “beautiful, luminous colors,” raise a luminous red flag when today’s art professionals suspect their presence. “They are more prone to damage from light fading,” she said, “and we can’t share the paintings with the visitor without light.” Svoboda says museums have developed exhibition techniques for protecting light-vulnerable works by displaying them with minimal illumination. Both carmine lake and another red pigment, madder lake, present fading concerns, Svoboda said. Red colorants weren’t only used to paint red coats and the like; they were commonly mixed with—or used on top of—other colorants to produce flesh tones. “It gives a vitality and translucency that the artists found nothing else could contribute,” she said, but it’s often been difficult to do more than suspect the presence of carmine lake, especially if you allow for three centuries of potential sun damage. Isaac Barré’s portrait was put to the new minimally invasive SERS protocol. Viewing the painting’s surface underneath the floor microscope in her lab, Svoboda plied her surgical blade in two areas, taking tiny samples. Feke’s William Nelson got the same treatment. “I just break through the varnish with a very small action of the blade,” Svoboda says. “With a good blade you can slice through a single large pigment grain, and the naked eye can’t even see the cut in the varnish.” SERS microscopy can find the molecular fingerprint of even faded pigments. Wustholz and Svoboda had good reason to suspect carmine lake in the Portrait of Isaac Barré; Sir Joshua Reynolds maintained detailed notes on his technique and paint preparation. The paints Feke used represented more of an unknown quantity. Wustholz took the samples to her lab in William & Mary’s Integrated Science Center, where she got Dinehart and Oakley started on the nanoparticle prep and the microscopy. “When we first looked at the sample, we just saw some kind of red pigment,” Oakley said. “We suspected it was probably either carmine lake or madder lake.” It was a while before the students caught onto the feel of the SERS laser microscope (“It’s like learning to drive,” Wustholz says.) “We have to move the sample around and try to find the best spot that will give a high intensity spectrum,” Dinehart explained. “It takes a lot of luck and a lot of maneuvering. We’ve spent hours back there just moving one tiny sample around trying to find the perfect fingerprint.” The fingerprints—verified by fluorescence microscopy—verified presence of carmine lake in the flesh of the Reynolds portrait, as Svoboda suspected. “The art history record shows that Reynolds’ flesh has faded in many paintings that we know of, sometimes very early,” she said. “But it’s been very hard to definitively identify the lake, because many analytical techniques require a fairly good sized sample. Until now.” A surprising find The analysis also showed that Feke used carmine lake in his Nelson portrait, a bit of a surprise in a work by a Colonial painter. Svoboda said that a Colonial apothecary could have been a source of the high-priced colorant. The ability to identify positively a pigment provides a number of benefits. Curators can take appropriate measures when hanging especially vulnerable works. Svoboda and other conservators can work with more assurance when they know the pedigree of the pigments on their canvasses. The chemist and the conservator are now working together to identify colorants in Colonial Williamsburg’s Carolina Room, a relocated 1830s parlor that’s a conservation treatment in progress. “SERS, to me, is a magical thing,” Svoboda said. “It just opens up a whole avenue of study in these faces of history.” In turn, the chemists take pleasure in working on a project that generates interest outside of the lab. “If I tell my family that I’m synthesizing silver nanoparticles, they don’t really care,” Dinehart said, “but if I can tell them that I’m working with the Colonial Williamsburg Foundation on a three-hundred-year-old painting, then people get a little more excited about it.”

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# How To Graph Tangent and Cotangent F07 ```Trig F07 O’Brien How to Graph y  a tan (bx  c)  d and y  a cot (bx - c)  d 1. Identify a, b, c, and d. 2. 5. Determine if there has been an x-axis reflection: if a is negative, there has been an x-axis reflection. π Find the period: period = . b 1 Find the x-increment: x-increment =  period . 4 Find the phase shift by setting the argument, bx – c, equal to zero and solving for x: c c c c P.S. = right (if we see bx – c and is positive) or P.S. = left (if we see bx + c and is negative). b b b b Find the vertical shift: |d| up if d is positive or |d| down if d is negative. 6. Identify the left asymptote, the three key points, and the right asymptote. 3a. b. 4. cotangent: To find the left asymptote, let x = phase shift, x  LA: x  c b (x of LA + x-increment, d + a) c . b (x1 + x-inc, d) (x2 + x-inc, d – a) RA: x = x3 + x-inc Note: The left asymptote of a tangent function is NOT x = phase shift. π tangent: To find the left asymptote, set the argument, bx – c, equal to  and solve for x. 2 c π LA: x   (x of LA + x-increment, d – a) (x1 + x-inc, d) (x2 + x-inc, d + a) RA: x = x3 + x-inc b 2b 7. Plot the asymptotes and the three key points. Connect the points with a smooth, continuous curve. Extend the graph to two full periods. Example 1: y = –3 cot (2x + π) +1 1. a = –3 2. There is an x-axis reflection. 3. period = 4. phase shift = 5. vertical shift = 1 up 6. LA: x   b=2 π 2 c = –π d=1 x-increment = π left 2 π 4π  2 8 1 π π   4 2 8 2x  π  0  2x   π  x    3π  ,  2   8   2π  , 1   8   π    , 4  8  π 4π  2 8 RA: x = 0 7. 1 Trig F07 O’Brien 1  Example 2: y = 2 tan  x  π  – 3 4  b= 1 4 c=π d = –3 1. a=2 2. There is no x-axis reflection. 3. period = π 1  4π x-increment = 4 4. phase shift = 4π right 5. vertical shift = 3 down 6. LA: 1  4π  π 4 1 xπ 0 4  1 π xπ    x  4π  2π  x  2 π 4 2 x  4π  0  (3π, –5) x  4π (4π, –3) (5π, –1) RA: x = 6π 7. 2 ```

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Knowledge of historic indigenous management practices in north Australian tropical savannas can benefit contemporary management by providing a long-term ecological context. This study provides understanding of how indigenous peoples managed their resources during the period of colonization by Europeans. Traditional management practices and resource use were observed by the European explorers and missionaries, anthropologists and ethnographers who followed. The historic record shows that the savannas were managed intensively by indigenous peoples, even during the colonization era. Across the region they used fire throughout the dry seasons, which is recognized by ecologists today. Importantly, and not previously reported in the ecological literature, they constructed water wells that provided them with extended use of country into the dry seasons, built and managed fisheries to enhance and extend their food supplies, and created extensive walking paths. These findings are significant because previous ecological research has assumed implicitly that indigenous people in the region were dependent on natural waters and therefore subject to seasonal availability of water to enable them to penetrate and live in dry country, and has given scant acknowledgement of manipulation of resources. The anthropological studies were compromised by the devastating social disruptions caused by the colonizers (mostly cattle ranchers and miners) and subsequent missionaries and government administrators. Despite these disruptions, the evidence demonstrates continuity of knowledge and management practices in much of the region. This history provides contemporary ecologists and managers with evidence of consistent patterns of resource management from earlier times. The evidence also shows that indigenous people were less at the mercy of the environment than has been assumed previously. The combined evidence suggests that contemporary management should consider that traditional management practices over many thousands of years were active and ubiquitous, and continued into the present era and probably shaped the biota of the region.

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“Clearly, much of west Africa is already on the edge of sustainability, and the situation could become much more dire in the future with increased global warming,” said University of Arizona climatologist Jonathan Overpeck, a co-author of the study. Overpeck and his colleagues studied sediments beneath Lake Bosumtwi in Ghana that gave an almost year-by-year record of droughts in the area going back 3,000 years. They found a pattern of decades-long droughts like the one that began in the Sahel in the 1960s — killing at least 100,000 people — as well as centuries-long “megadroughts”. The most recent lasted from 1400 to 1750, the researchers said. “What’s disconcerting about this record is that it suggests that the most recent drought was relatively minor in the context of the west African drought history,” said Timothy Shanahan of the University of Texas, another co-author of the study. The most recent decades of data from Lake Bosumtwi show that droughts there appear to be linked to fluctuations in sea surface temperatures, the researchers said. “One of the scary aspects of our record is how the Atlantic [Ocean] … changes the water balance over west Africa” on time scales lasting many decades, Overpeck told Reuters. See full story

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When one adult physically or emotionally abuses another in a household that contains children, the adult victim isn’t the only one who suffers. In the room where the abuse is happening, or even down the hallway, a child who sees or hears the abuse is also at risk. The National Survey of Children’s Exposure to Violence found: - One in four children (26 percent) were exposed to at least one form of family violence during their lifetimes. - Sixty-eight percent of these youth who witnessed family violence, witnessed acts committed only by males, although assaults by mothers and other caregivers were also common. And according to a Futures Without Violence fact sheet: - 15.5 million U.S. children live in families in which partner violence occurred at least once in the past year, and seven million children live in families in which severe partner violence occurred. - In a single day in 2007, 13,485 children were living in a domestic violence shelter or transitional housing facility. Another 5,526 sought services at a non-residential program. - The UN Secretary-General’s Study on Violence Against Children conservatively estimates that 275 million children worldwide are exposed to violence in the home. Exposure to domestic violence can be harmful to a child’s physical, emotional and intellectual development. Studies have shown that children who are exposed to violence live in a constant state of alertness and crisis that can produce changes to the brain and impair their coping or functioning skills. And exposure to domestic violence can also greatly increase a child’s risk of experiencing other types of violence. For example, a young girl who sees her mother abused by her father could be at a higher risk of becoming a victim of teen dating violence or bullying. And the impact of violence experienced at home isn’t confined within the walls of the home. Exposure can affect their performance in other areas, like school, and negatively impact children well into adulthood. For the next 31 days our Domestic Violence Awareness Month efforts will focus on domestic violence’s impact on children. We have many new exciting resources to share including a new infographic and an issue brief for domestic violence agencies and shelters. Stick around for more information on those and be sure to join in the conversation on our Facebook and Twitter pages.

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Slideshow: Non-Native Species Invade the United States by Mark Hughes Aliens have been invading the United States for centuries. A joke? Not at all. In fact, thousands of foreign plant and animal species have arrived on U.S. soil. Some are brought in intentionally by humans; others enter accidentally on boats or with cargo on airplanes. The Invasive Species Advisory Committee (ISAC) defines an invasive species "as a non-native species whose introduction does or is likely to cause economic or environmental harm or harm to human, animal, or plant health." Most foreign species don't have natural enemies or predators in their "adopted" environments, which allow them to reproduce or spread quickly. Invasive species' impact on human health and natural resources Viruses, like the West Nile Virus, can be transmitted by non-native species, such as the Asian tiger mosquito. West Nile Virus can cause severe respiratory infections in humans. Non-native poisonous plants can be full of nasty poisons. For instance, the sap of the tree-of-heaven or the Chinese sumac tree can cause inflammation in the human heart muscle. Blights, or diseases, of non-native origin have wreaked havoc on animal species and woodlands, dramatically reducing the populations of both. Some species, such as the Eurasian wild boar, have caused a great deal of damage to native plants and crops. What else can invasive species disrupt? Non-native species can impact property values. For instance, the Formosan subterranean termite can cause massive structural damage to buildings. Recreational activities, such as fishing, can also be disrupted when native species are reduced or eliminated when another species has invaded and prey upon the native inhabitants. Slideshows: Notable Invaders

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##### Statistics: 1001 Practice Problems For Dummies (+ Free Online Practice) For these three sample questions, consider that: A researcher conducted an Internet survey of 300 students at a particular college to estimate the average amount of money students spend on groceries per week. The researcher knows that the population standard deviation of weekly spending is \$25. The mean of the sample is \$85. The following table provides the z*- values for selected (percentage) confidence levels. ## Sample questions 1. What is the margin of error if the researcher wants to be 99% confident of the result? The formula for margin of error when estimating a population mean is where z* is the value from the table for a given confidence level (99% in this case, or 2.58), is the standard deviation (\$25), and n is the sample size (300). Now, substitute the values into the formula and solve: The margin of error for a 99% confidence interval for the population mean is plus/minus \$3.72. 2. What is the margin of error if the researcher wants to be 95% confident in the result? The formula for margin of error when estimating a population mean is where z* is the value from the table for a given confidence level (95% in this case, or 1.96), is the standard deviation (\$25), and n is the sample size (300). Now, substitute the values into the formula and solve: The margin of error for a 95% confidence interval for the population mean is plus/minus \$2.83. 3. What is the lower limit of an 80% confidence interval for the population mean, based on this data? To find the lower limit for the 80% confidence interval, you first have to find the margin of error. The formula for the margin of error when estimating a population mean is where z* is the value from the table for a given confidence level (80% in this case, or 1.28), is the standard deviation (\$25), and n is the sample size (300). Now, substitute the values into the formula and solve: Next, subtract the MOE from the sample mean to find the lower limit: \$85.00 – \$1.85 = \$83.15. If you need more practice on this and other topics from your statistics course, visit 1,001 Statistics Practice Problems For Dummies to purchase online access to 1,001 statistics practice problems! We can help you track your performance, see where you need to study, and create customized problem sets to master your stats skills.

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# Cubes One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 257 mm2. Correct result: V1-V2 =  512.6 mm3 #### Solution: $S_1- S_2 = 6a_1^2-6a_2^2 = 6((2r)^2-(\sqrt2 r)^2) = 12 r^2 = 257 \ \\ r=\sqrt{ \dfrac{ 257}{12} } \doteq 5 \ mm \ \\ \ \\ V_1-V_2 = a_1^3-a_2^3 = (2r)^3-(\sqrt2 r)^3 = 512.6 \ \text{mm}^3$ Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you! Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors. Math student What do all those symbols mean? Is there a more simple format...that you could put this in? Petr S - surface area of cube V - volume of cube(s) Tips to related online calculators Tip: Our volume units converter will help you with the conversion of volume units. Pythagorean theorem is the base for the right triangle calculator. #### You need to know the following knowledge to solve this word math problem: We encourage you to watch this tutorial video on this math problem: ## Next similar math problems: • Truncated cone 6 Calculate the volume of the truncated cone whose bases consist of an inscribed circle and a circle circumscribed to the opposite sides of the cube with the edge length a=1. • Find the 13 Find the equation of the circle inscribed in the rhombus ABCD where A[1, -2], B[8, -3] and C[9, 4]. A regular quadrilateral pyramid has a volume of 24 dm3 and a base edge a = 4 dm. Calculate: a/height of the pyramid b/sidewall height c/surface of the pyramid • The regular The regular triangular prism has a base in the shape of an isosceles triangle with a base of 86 mm and 6.4 cm arms, the height of the prism is 24 cm. Calculate its volume. • Calculate 6 Calculate the distance of a point A[0, 2] from a line passing through points B[9, 5] and C[1, -1]. • Regular hexagonal prism Calculate the volume of a regular hexagonal prism whose body diagonals are 24cm and 25cm long. • Right angle In a right triangle ABC with a right angle at the apex C, we know the side length AB = 24 cm and the angle at the vertex B = 71°. Calculate the length of the legs of the triangle. • Triangle in a square In a square ABCD with side a = 6 cm, point E is the center of side AB and point F is the center of side BC. Calculate the size of all angles of the triangle DEF and the lengths of its sides. • Hexagonal pyramid Find the area of a shell of the regular hexagonal pyramid, if you know that its base edge is 5 cm long and the height of this pyramid is 10 cm. • Triangular prism The triangular prism has a base in the shape of a right triangle, the legs of which is 9 cm and 40 cm long. The height of the prism is 20 cm. What is its volume cm3? And the surface cm2? • Integer sides A right triangle with an integer length of two sides has one leg √11 long. How much is its longest side? • Sailboat The 20 m long sailboat has an 8 m high mast in the middle of the deck. The top of the mast is fixed to the bow and stern with a steel cable. Determine how much cable is needed to secure the mast and what angle the cable will make with the ship's deck. • Hexagonal pyramid Find the volume of a regular hexagonal pyramid, the base edge of which is 12 cm long and the side edge 20 cm. • On a line On a line p : 3 x - 4 y - 3 = 0, determine the point C equidistant from points A[4, 4] and B[7, 1]. • An observer An observer standing west of the tower sees its top at an altitude angle of 45 degrees. After moving 50 meters to the south, he sees its top at an altitude angle of 30 degrees. How tall is the tower? • Trip with compass During the trip, Peter went 5 km straight north from the cottage, then 12 km west and finally returned straight to the cottage. How many kilometers did Peter cover during the whole trip? • Sailing Solve the following problem graphically. The fishing boat left the harbor early in the morning and set out to the north. After 12 km of sailing, she changed course and continued 9 km west. Then she docked and launched the nets. How far was she from the pl

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John II, byname John the Good, French Jean le Bon (born April 16, 1319, near Le Mans, Fr.—died April 8, 1364, London), king of France from 1350 to 1364. Captured by the English at the Battle of Poitiers on Sept. 19, 1356, he was forced to sign the disastrous treaties of 1360 during the first phase of the Hundred Years’ War (1337–1453) between France and England. After becoming king on Aug. 22, 1350, John continued a truce with the English until later that year, when he had an English hostage, Raoul de Brienne, comte d’Eu, former constable of France, executed. By March 1351 King Edward III of England realized the impossibility of remaining at peace; but John committed the first act of hostility by attacking and recapturing Saint-Jean-d’Angély in western France that September 7. John signed a new truce with England on Sept. 12, 1351, but broke it by supporting the partisans of Charles of Blois (a pretender to Brittany, then held prisoner by Edward) in August 1352; the peace, however, was extended until September 23. John’s other bitter enemy was Charles II the Bad, king of Navarre, to whom John gave his daughter Joan as an offer of alliance; the enmity still remained strong, however, because John never paid a dowry or recognized a rent of 15,000 livres due to Charles. John further irritated Charles by giving the new constable of France, Charles de La Cerda, lands that were claimed by Charles of Navarre. In revenge, the latter had the new constable assassinated; but in spite of John’s rage, the two kings made a superficial peace in February 1354. Charles desired an alliance with Edward, which so frightened John that he made another peace with Charles on Sept. 10, 1355. On April 16, 1356, at Rouen, John took his revenge on Charles by having him imprisoned. Meanwhile Edward, displeased by the 1355 alliance between John and Charles, invaded France later that year but then returned to England before any confrontations. At the same time, Edward’s son Edward, prince of Wales (later called the Black Prince), attacked southern France. Unable to halt the English invasions because he lacked funds, John gathered the States General to seek money and to impose an unpopular salt tax. John first went to defend Paris and Chartres. He and the Prince of Wales finally met near Poitiers in September 1356. The French army was decimated, and John was taken prisoner. John was taken to London in April 1357, where he was lodged in the Savoy palace; there he concluded treaties (January 1358 and March 1359) so harsh that they were repudiated in France. Finally the treaties of Brétigny and of Calais (May and October 1360) fixed John’s ransom at 3,000,000 gold écus and surrendered most of southwestern France to Edward. On Oct. 9, 1360, John was released to raise a ransom that France could not afford to pay, and hostages were accepted in his place. When one of the hostages (John’s own son) escaped, John, feeling dishonoured, returned to England on his own volition as a prisoner.

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COLD WAR LONGER THAN NECESSARY why it was dragged on for so long Douglas MacArthur was a US general who was chosen to lead the United Nations troops. He was important in how long the war lasted because he was reckless and aggressive and always wanted to take action. Always making the initiative to instigate or respond with violence irritated relations and built tensions which expanded the length of the war. Brinkmanship is the foreign policy where one or both sides come close to starting war and fighting but actually don't. This method of getting as close to war with out actually starting it being on the "brink" was used to give one side an advantage because they knew the other side would negotiate to avoid fighting. The yalta conference was a meet up including Winston Churchill, Joseph Stalin, and FDR where they made promises and agreements. After this conference many of these promises were broken so each country was upset and felt betrayal and as though they couldn't trust anyone because of the broken promises. The iron curtain was a political, military, and ideological boundary that separated the Soviet Union. It separated the east and the west but had no real significance or purpose and just increased tensions and prolonged the war. The truman doctrine was a presidential message that was given to Congress. It stated that the US would provide help to any foreign country that was being threatened by an external communist country, this committed the US to be involved and fight in foreign issues. The Marshall plan was the "European recovery program" it involved the US giving money to try and help European economies. The US support and involvement would raise tensions with other countries and other non allies.

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What is decision making? 1 Answer | Add Yours Decision making is a cognitive process wherein a person selects among different alternatives and chooses the best option. Decision making is also a process wherein someone weighs the disadvantages and advantages of each alternatives, and also involves forecasting the outcome of each alternative to help him/her decide on having the best choice. Decisions that are made may be based on intuition or reasoning, or may be a combination of the two. Good decision making is essential to a person's success. When deciding on something, make sure to: list all possible alternatives, schedule a timetable, weigh the risk (pro's and con's) of each alternative, prioritize what's important and be ready to make the decision. Join to answer this question Join a community of thousands of dedicated teachers and students.Join eNotes

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Share # Find k, if one of the lines given by 6x2 + kxy + y2 = 0 is 2x + y = 0 - Mathematics and Statistics #### Question Find k, if one of the lines given by 6x2 + kxy + y2 = 0 is 2x + y = 0 #### Solution Let m1 be the slope of 2x + y = 0. ∴ m1=-2 6x^2+kxy+y^=0 therefore a=6,h=k/2,b=1 m_1+m_2=-(2h)/b=-k -2+m_2=-k m_2=-k+2 Now, m_1m_2 =a/b (-2)(-k+2)=6 2k-4=6 2k=10 k=10/2 k=5 The value of k is 5. Is there an error in this question or solution? #### APPEARS IN 2015-2016 (March) (with solutions) Question 1.2.4 | 2.00 marks Solution Find k, if one of the lines given by 6x2 + kxy + y2 = 0 is 2x + y = 0 Concept: Pair of Straight Lines - Pair of Lines Not Passing Through Origin-combined Equation of Any Two Lines. S

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# Q0 > 0 Q1 > 0 x =x1 x0 =0 ```Problem 3 (5 points): Consider the configuration shown below, with a positive charge Q0 at position x0=0 and another positive charge Q1 at position x1 along the x-axis. (a) At which position x2 could a third positive charge charge Q2 be added, such that the total force on Q0 is 0? Give two examples of x2 and corresponding Q2, in terms of x0, x1, Q0 and Q1 (or a subset of these variables). (b) Qualitatively, describe what would happen if Q0 was displaced by a small distance Dx from x0=0 to x=Dx and then released (two sentences max.)? Q0 &gt; 0 Q1 &gt; 0 x0 =0 x =x1 Problem 4 (5 Points): Young + Freedman, Exercise 21.9 Problem 5 (5 Points): Young + Freedman, Exercise 21.25 Problem 6 (5 Points): Young + Freedman, Exercise 21.31 MIT Department of Physics Physics 8.02X Spring 2005 Solution to Problem Set #2 Problem 1 (5 Points) Consider an infinite plane (non-conducting) with a uniform negative surface charge density σ (a) Draw a sketch of the electric field (using field lines) close to the plane. (b) Explain in words why the field has to look the way you have drawn (using symmetry arguments). (Keep your explanation to 2-3 sentences) Field can only have component perpendicular to the plane: At each point, there is an equal amount of charge to the right and to the left. The horizontal components always cancel. Problem 2 (5 Points) Consider an ellipsoidal conducting object carrying a positive charge Q (shown below). (a) Draw a sketch of the electric field (using field lines) very close to the surface of the object. Your sketch should show where the magnitude of the electric field will be biggest. + + + + + + + + + + + + + + + + + + (b) Explain in words how the fact that we are looking at a conducting object determines the direction of the field relative to the surface at very small distances to the surface. (Keep your explanation to 2-3 sentences) In electrostatics, E is perpendicular to the surface of the conductor. If not then, there would be a tangential component results in movement and re-distribution of charges. Problem 3 (5 points): Consider an electric dipole consisting of point charges +q and –q, separated by a fixed distance d. (a) Determine the net force and net torque on the dipole in a uniform electric field E as a function of the angle between the axis of the dipole and the direction of the field. 1 E - dθ F + + E - The force acting on +q is F+ = qE . The force acting on −q is F− = −qE . The net torque is τ = τ 1 + τ 2 = r1 &times; F1 + r2 &times; F2 = q ( r1 − r2 ) &times; E = qd &times; E Therefore the magnitude of the net torque is τ = qdE sin θ and the direction of the net torque is perpendicular to this paper (outward), which is determined by the right hand rule of cross product. (b) Now the dipole is brought into the field of a fixed point charge Q, which is at distance r from +q and distance (r+d) from –q. We observe that the dipole accelerates towards Q. Is Q positive or negative? r Q + d - x Since +q is closer to Q, force acting on +q is stronger than force acting on −q . This indicates that Q is negative. (c) If the dipole has mass m, what will be the initial acceleration of the dipole in case (b)? ⎛1 ⎞ 1 ma = F+ + F− = − kq Q ⎜ 2 − ⎟ x̂ 2 ⎜ r (r + d ) ⎟ ⎝ ⎠ Since r a=− d , we have kq Q m −2 1 (r + d ) 2 1 ⎛ d⎞ 1 ⎛ 2d ⎞ = 2 ⎜1+ ⎟ ≈ 2 ⎜1− ⎟⇒ r ⎝ r⎠ r ⎝ r ⎠ ⎛1 ⎞ kq Q 1 ⎜ 2− ⎟ x̂ = − 2 ⎜ r (r + d ) ⎟ mr 2 ⎝ ⎠ 2kqd Q ⎛ ⎛ 2d ⎞ ⎞ ⎜1 − ⎜ 1− r ⎟ ⎟ x̂ = − mr 3 x̂ ⎠⎠ ⎝ ⎝ Problem 4 (5 Points): Young + Freedman, Challenge Problem 22.65 ∫ ρ dv = Q ⇒ ∫ 4π r ρ ( r ) dr = Q ⇒ ∫ 4π r α dr + ∫ 4π r 2α (1− r R ) dr R a) 2 0 R/2 2 2 R/2 0 = 43 πα r 3 R R/2 0 + 43 π 2α r 3 R R/2 − 44πR 2α r 4 R R/2 = 85 πα R 3 = Q ⇒ α = 2 8Q 5π R 3 ```

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## Calculating Wheel Odometry for a Differential Drive Robot Have you ever wondered how robots navigate their environments so precisely? A key component for many mobile robots is differential drive. This type of robot uses two independently controlled wheels, allowing for maneuvers like moving forward, backward, and turning. But how does the robot itself know where it is and how far it’s traveled? This is where wheel odometry comes in. Wheel odometry is a technique for estimating a robot’s position and orientation based on the rotations of its wheels. By measuring the number of revolutions each wheel makes, we can calculate the distance traveled and any changes in direction. This information is important for tasks like path planning, obstacle avoidance, and overall robot control. This tutorial will guide you through calculating wheel odometry for a differential drive robot. We’ll explore how to convert raw wheel encoder data – the number of revolutions for each wheel – into the robot’s displacement in the x and y directions (relative to a starting point) and the change in its orientation angle. Buckle up and get ready to dive into the fascinating world of robot self-localization! # Calculate Wheel Displacements First, we calculate the distance each wheel has traveled based on the number of revolutions since the last time step. This requires knowing: # Calculate the Robot’s Average Displacement and Orientation Change Next, we determine the robot’s average displacement and the change in its orientation. The average displacement (Davg) is the mean of the distances traveled by both wheels: The change in orientation (Δθ), measured in radians, is influenced by the difference in wheel displacements and the distance between the wheels (L): # Calculate Changes in the Global Position Now, we can calculate the robot’s movement in the global reference frame. Assuming the robot’s initial orientation is θ, and using Davg and Δθ, we find the changes in the x and y positions as follows: You will often see the following equation instead: This simplification assumes Δθ is relatively small, allowing us to approximate the displacement direction using the final orientation θnew without significant loss of accuracy. It’s a useful approximation for small time steps or when precise integration of orientation over displacement is not critical. To find the robot’s new orientation: Note, for robotics projects, it is common for us to modify this angle so that it is always between -pi and +pi. Here is what that code would look like: ```# Keep angle between -PI and PI if (self.new_yaw_angle > PI): self.new_yaw_angle = self.new_yaw_angle - (2 * PI) if (self.new_yaw_angle < -PI): self.new_yaw_angle = self.new_yaw_angle + (2 * PI) ``` For ROS 2, you would then convert this new yaw angle into a quaternion. # Update the Robot’s Global Position Finally, we update the robot’s position in the global reference frame. If the robot’s previous position was (x, y), the new position (xnew, ynew) is given by: # Practical Example Let’s apply these steps with sample values: Using these values, we’ll calculate the robot’s new position and orientation. ## Step 4: New Global Position and Orientation Therefore the new orientation of the robot is 2.52 radians, and the robot is currently located at (x=-4.34, y = 4.80). # Important Note on Assumptions The calculations for wheel odometry as demonstrated in the example above are made under two crucial assumptions: 1. No Wheel Slippage: It’s assumed that the wheels of the robot do not slip during movement. Wheel slippage can occur due to loss of traction, often caused by slick surfaces or rapid acceleration/deceleration. When slippage occurs, the actual distance traveled by the robot may differ from the calculated values, as the wheel rotations do not accurately reflect movement over the ground. 2. Adequate Friction: The calculations also assume that there is adequate friction between the wheels and the surface on which the robot is moving. Adequate friction is necessary for the wheels to grip the surface effectively, allowing for precise control over the robot’s movement. Insufficient friction can lead to wheel slippage, which, as mentioned, would result in inaccuracies in the odometry data. These assumptions are essential for the accuracy of wheel odometry calculations. In real-world scenarios, various factors such as floor material, wheel material, and robot speed can affect these conditions. Therefore, while the mathematical model provides a foundational understanding of how to calculate a robot’s position and orientation based on wheel rotations, you should be aware of these limitations and consider implementing corrective measures or additional sensors to account for potential discrepancies in odometry data due to slippage or inadequate friction. ## Calculating Wheel Velocities for a Differential Drive Robot Have you ever wondered how those robots navigate around restaurants or hospitals, delivering food or fetching supplies? These little marvels of engineering often rely on a simple yet powerful concept: the differential drive robot. A differential drive robot uses two independently powered wheels and often has one or more passive caster wheels. By controlling the speed and direction of each wheel, the robot can move forward, backward, turn, or even spin in place. This tutorial will delve into the behind-the-scenes calculations that translate desired robot motion (linear and angular velocities) into individual wheel speeds (rotational velocities in revolutions per second). # Real-World Applications Differential drive robots, with their two independently controlled wheels, are widely used for their maneuverability and simplicity. Here are some real-world applications: Delivery and Warehousing: • Inventory management:  Many warehouse robots use differential drive designs. They can navigate narrow aisles, efficiently locate and transport goods, and perform stock checks. • Last-mile delivery:  Delivery robots on sidewalks and in controlled environments often employ differential drive. They can navigate crowded areas and deliver packages autonomously. Domestic and Public Use: • Floor cleaning robots:  These robots navigate homes and offices using differential drive. They can efficiently clean floors while avoiding obstacles. • Disinfection robots:  In hospitals and public areas, differential drive robots can be used for disinfecting surfaces with UV light or other methods. • Security robots:  These robots patrol buildings or outdoor spaces, using differential drive for maneuverability during surveillance. Specialized Applications: • Agricultural robots:  Differential drive robots can be used in fields for tasks like planting seeds or collecting data on crops. • Military robots:  Small reconnaissance robots often use differential drive for navigating rough terrain. • Entertainment robots:  Robots designed for entertainment or education may utilize differential drive for movement and interaction. • Restaurant robots: Robots that deliver from the kitchen to the dining room. Why Differential Drive for these Applications? • Simple design:  Their two-wheeled platform makes them relatively easy and inexpensive to build. • Maneuverability:  By controlling the speed of each wheel independently, they can turn sharply and navigate complex environments. • Compact size:  Their design allows them to operate in tight spaces. # Convert Commanded Velocities to Wheel Linear Velocities The robot’s motion is defined by two control inputs: the linear velocity (V) and the angular velocity (ω) of the robot in its reference frame. The linear velocity is the speed at which you want the robot to move forward or backward, while the angular velocity defines how fast you want the robot to turn clockwise and counterclockwise. The linear velocities of the right (Vr) and the left (Vl) wheels can be calculated using the robot’s wheelbase width (L), which is the distance between the centers of the two wheels: # Convert Linear Velocity to Rotational Velocity Once we have the linear velocities of the wheels, we need to convert them into rotational velocities. The rotational velocity (θ) in radians per second for each wheel is given by: Thus, the rotational velocities of the right and left wheels are: # Convert Radians per Second to Revolutions per Second The final step is to convert the rotational velocities from radians per second to revolutions per second (rev/s) for practical use. Since there are 2π radians in a full revolution: # Example Let’s calculate the wheel velocities for a robot with a wheel radius of 0.05m, wheelbase width of 0.30m, commanded linear velocity of 1.0m/s, and angular velocity of 0.5rad/s. ## Sensor Fusion Using the Robot Localization Package – ROS 2 In this tutorial, I will show you how to set up the robot_localization ROS 2 package on a simulated mobile robot. We will use the robot_localization package to fuse odometry data from the /wheel/odometry topic with IMU data from the /imu/data topic to provide locally accurate, smooth odometry estimates. Wheels can slip, so using the robot_localization package can help correct for this. This tutorial is the third tutorial in my Ultimate Guide to the ROS 2 Navigation Stack (also known as Nav2). You can get the entire code for this project here. If you are using ROS Galactic or newer, you can get the code here. Let’s get started! # Prerequisites You have completed the first two tutorials of this series: # About the Robot Localization Package We will configure the robot_localization package to use an Extended Kalman Filter (ekf_node) to fuse the data from sensor inputs. These sensor inputs come from the IMU Gazebo plugin and the differential drive Gazebo plugin that are defined in our SDF file. In a real robotics project, instead of simulated IMU and odometry data, we would use data from an IMU sensor like the BNO055 and wheel encoders, respectively. The ekf_node will subscribe to the following topics (ROS message types are in parentheses): • /wheel/odometry :  Position and velocity estimate based on the information from the differential drive Gazebo plugin (in a real robotics project this would be information drawn from wheel encoder tick counts). The orientation is in quaternion format. (nav_msgs/Odometry) • /imu/data : Data from the Inertial Measurement Unit (IMU) sensor Gazebo plugin (sensor_msgs/Imu.msg) This node will publish data to the following topics: • /odometry/filtered : The smoothed odometry information (nav_msgs/Odometry) • /tf : Coordinate transform from the odom frame (parent) to the base_footprint frame (child). To learn about coordinate frames in ROS, check out this post. ## Install the Robot Localization Package Let’s begin by installing the robot_localization package. Open a new terminal window, and type the following command: ``sudo apt install ros-foxy-robot-localization`` If you are using a newer version of ROS 2 like ROS 2 Humble, type the following: `` sudo apt install ros-humble-robot-localization `` Instead of the commands above, you can also type the following command directly into the terminal. It will automatically detect your ROS 2 distribution: ``sudo apt install ros-\$ROS_DISTRO-robot-localization`` If you are using ROS 2 Galactic and want to build from the source instead of using the off-the-shelf packages above, you will need to download the robot_localization package to your workspace. `cd ~/dev_ws/src` `git clone -b fix/galactic/load_parameters https://github.com/nobleo/robot_localization.git` The reason you need to download that package above is because the Navigation Stack might throw the following exception if you don’t: [ekf_node-1] terminate called after throwing an instance of ‘rclcpp::ParameterTypeException’ [ekf_node-1] what(): expected [string] got [not set] `cd ..` `colcon build` ## Set the Configuration Parameters We now need to specify the configuration parameters of the ekf_node by creating a YAML file. Open a new terminal window, and type: `colcon_cd basic_mobile_robot` `cd config` `gedit ekf.yaml` Copy and paste this code inside the YAML file. Save and close the file. You can get a complete description of all the parameters on this page. Also you can check out this link on GitHub for a sample ekf.yaml file. ## Create a Launch File Now go to your launch folder. Open a new terminal window, and type: `colcon_cd basic_mobile_robot` `cd launch` `gedit basic_mobile_bot_v3.launch.py` Copy and paste this code into the file. If you are using ROS 2 Galactic or newer, your code is here. Save the file, and close it. Move to the package. `colcon_cd basic_mobile_robot` Open the package.xml file. `gedit package.xml file.` Copy and paste this code into the file. Save the file, and close it. Open the CMakeLists.txt file. `gedit CMakeLists.txt` Copy and paste this code into the file. Save the file, and close it. ## Build the Package Now build the package by opening a terminal window, and typing the following command: `cd ~/dev_ws` `colcon build` ## Launch the Robot Open a new terminal, and launch the robot. `cd ~/dev_ws/` `ros2 launch basic_mobile_robot basic_mobile_bot_v3.launch.py` It might take a while for Gazebo and RViz to load, so be patient. To see the active topics, open a terminal window, and type: `ros2 topic list` `ros2 topic info /imu/data` `ros2 topic info /wheel/odometry` You should see an output similar to below: Both topics have 1 publisher and 1 subscriber. To see the output of the robot localization package (i.e. the Extended Kalman Filter (EKF)), type: `ros2 topic echo /odometry/filtered` I will move my robot in the reverse direction using the rqt_robot_steering GUI. Open a new terminal window, and type: `rqt_robot_steering` If you are using ROS 2 Galactic or newer, type: `sudo apt-get install ros-galactic-rqt-robot-steering` Where the syntax is: `sudo apt-get install ros-<ros-distribution>-rqt-robot-steering` Then type: `ros2 run rqt_robot_steering rqt_robot_steering --force-discover` Move the sliders to move the robot. We can see the output of the odom -> base_footprint transform by typing the following command: `ros2 run tf2_ros tf2_echo odom base_footprint` Let’s see the active nodes. `ros2 node list` Let’s check out the ekf_node (named ekf_filter_node). `ros2 node info /ekf_filter_node` Let’s check out the ROS node graph. `rqt_graph` Click the blue circular arrow in the upper left to refresh the node graph. Also select “Nodes/Topics (all)”. To see the coordinate frames, type the following command in a terminal window. `ros2 run tf2_tools view_frames.py` If you are using ROS 2 Galactic or newer, type: `ros2 run tf2_tools view_frames` In the current working directory, you will have a file called frames.pdf. Open that file. `evince frames.pdf` Here is what my coordinate transform (i.e. tf) tree looks like: You can see that the parent frame is the odom frame. The odom frame is the initial position and orientation of the robot. Every other frame below that is a child of the odom frame. Later, we will add a map frame. The map frame will be the parent frame of the odom frame. Finally, in RViz, under Global Options, change Fixed Frame to odom. Open the steering tool again. `rqt_robot_steering` If you move the robot around using the sliders, you will see the robot move in both RViz and Gazebo. That’s it! In the next tutorial, I will show you how to add LIDAR to your robot so that you can map the environment and detect obstacles.

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In this project students research the meaning of their own first names and consider whether the meaning actually fits their character. Participants will answer the following questions about their first names: What is your first name?What language is it in? What does it mean? Is there anything interesting or unusual about your first name? What city/country do you live in? How many people do you know who have the same first name as you? Does the meaning of your first name suit your character? Do you like your name? What other name would you choose? After answering the questions participants write, type or draw their names in a way that illustrates its meaning. Participants will need a scanner and e-mail access. Students will be encouraged to post their work directly on their pages in KidSpace, and also to view the pages of other participants and post comments to those pages as well. Participants will also be encouraged to post messages to the KidProj listserv inviting other Kidlinkers to come and view their work. This is an ongoing project. Participants may join the project at any time throughout the year. Target Age Group: This project is for any age group. It is suitable for EFL students at the intermediate level. * to give students an opportunity to investigate the meaning of their own first names and consider how that meaning fits their character. * to participate in a multi-cultural and global collaborative environment. * to be aware of cultural and language differences and similarities * to share interesting facts about their first names with other students. * to access online information while researching their first names meanings . * to interact with other students online . * to use English in an authentic way . * to engage in simple research, writing, reading and creating through involvement in an interesting activity How to Join the Project: Send the following information to a project moderator: Teacher’s name, Teacher’s email, School, City/country, Number of students All participating students must answer the four Kidlink questions. More information about this can be found here: http://www.kidlink.org/registration/index.php Click on “Register” on the left sidebar for the registration page. Be sure you have permission to post student work on the WWW and student images if you choose to do this. School districts usually have their own requirements that teachers must follow. Teachers subscribe to the KIDPROJ and KIPROJ-COORD mailing lists. This can be done by clicking on the list names above: Students introduce their work in KidSpace. Introductions should be sent to the Kidproj mailing list and can be posted in KidSpace as well. Students view the work of other participants in the project and post comments and/or questions about the writing. To Publish the Kid’s Work in KidSpace: Teachers, together with their students, will insert drawings and text in their own kidspace page after they receive a login and password. Students assess their own work using this assessment checklist: Ora Baumgarten – Israel Joy Boehm – USA

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CRAB NEBULA: Supernova Remnant & Pulsar What Do These Images Tell Us? The Crab Nebula consists of a pulsar, a rapidly rotating neutron star at the center, surrounded by a bright diffuse nebula. The nebula, which is about six light years across, is expanding outward at 3 million miles per hour. The filamentary system visible in the optical images is near the outer boundary of this expansion. Both the nebula and the pulsar are bright sources of radiation in all The radiation we observe from the Crab Nebula is produced mainly by high-energy particles accelerated by the neutron star. These energetic particles, which near the neutron star are thought to include anti-matter positrons as well as electrons, spiral around magnetic field lines in the nebula and give off radiation by the "synchrotron" process. Comparing the X-ray, optical, infrared, and radio images of the Crab shows that the nebula appears most compact in X-rays and largest in the radio. The X-ray nebula shown in the Chandra image is about 40% as large as the optical nebula, which is in turn about 80% as large as the radio image. This can be understood by following the history of energetic electrons produced by the neutron star. Electrons with very high energies radiate mostly X-rays. | Chandra's X-ray image of the Crab Nebula directly traces the most energetic particles being produced by the pulsar. This amazing image reveals an unprecedented level of detail about the highly energetic particle winds and will allow scientists to probe deep into the dynamics of this cosmic powerhouse. | As time goes on, and the electrons move outward, they lose energy to radiation. The diffuse optical light comes from intermediate energy particles produced by the pulsar. The optical light from the filaments is due to hot gas at temperatures of tens of thousands of degrees. | The infrared radiation comes from electrons with energies lower than those producing the optical light. Additional infrared radiation comes from dust grains mixed in with the hot gas in the filaments. | Radio waves come from the lowest energy electrons. They can travel the greatest distance and define the full extent of the nebula. The Crab's central pulsar was discovered in 1968 by radio astronomers. The pulsar was then identified as a source of periodic optical and X-ray radiation. The periodic flashes of radiation are caused by a beam from the rapidly rotating neutron Return to Crab Nebula (28 Sep 99)

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Kinesthetic Learning Strategies - Activities to Help Tactile Learners. Adult Education Centre - Adult Learning Styles. Exercise - Reflection on Learning Characteristics of Adult Learning Motivating Factors in Adult Learning Learning Styles Implications for Delivery Practical Classroom Tips Bibliography Glossary All adults come to courses with varied experiences and varied educational backgrounds. Adults have accumulated life experiences. Adults have a range of different motivations for selecting a course/programme: Learning styles vs teaching methods. Different Learning Styles in Education. Different people learn differently, and psychologists have attempted through the years to spell out the traits of different types of learners and categorize them into different “learning styles.” Naturally, there are many models of different learning styles in education. The most widely used is the VAK learning styles model, developed in 1987 by Neil Fleming, a high school and university teacher from New Zealand. Its letters stand for the three learning styles: visual, auditory, and kinesthetic. Fleming later added a fourth, read/write, changing the acronym to VARK. As a teacher, your best option is to use a variety of teaching techniques to give all students the best chance to succeed. 6 different types of ESL learners and how to teach them. Adapt your lessons to cater for the different learning styles of your students When we are teaching English to kids, as teachers we need to be aware of the differences in learning styles of our students so that we can incorporate all of these learning styles into our lessons. What is Visual Learning – The Visual Learning Style – Visual Learning Traits. Are you one of those people who closes your eyes to envision the exact location of where you left your car keys? Do you remember the cover of every book you've ever read? Do you have a photographic memory? Education.vermont.gov/documents/educ_accommodations_strategies.pdf. Helping Visual Learners Succeed. We all want our children to do well in school. Sometimes though kids struggle with their school work and we’re just not sure how to help. As a school counselor, the first thing I do to help students academically is to identify how they learn. There are three different ways we learn. We either learn by seeing (visual), hearing (auditory), or doing (kinesthetic). Visual Learners - Learning Styles and Visual Learners. A Look at Visual Learners: A typical visual learner uses visualization techniques to remember things. They often have a good sense of direction because they visualize maps and directions in their mind. Many prefer to read information in a textbook or on the whiteboard rather than listen to the teacher lecture. They also enjoy doodling and drawing. Pearson Prentice Hall: eTeach: Strategies for Visual Learners. By Patricia Vakos Introduction: Contrasting Styles From Personal Experiences Challenges of the Visual Learner Strategies for Teaching Visual Learners Implications for the Teacher Bibliography Links Silent and very still sat 18 kindergarten students, patiently waiting for the teacher to begin her lesson. Then, and only then, may they take out their beloved bears that they had permission to bring to school on this special day. With her pigtails swinging side to side, Alex looked up at her teacher and proudly proclaimed that her bear Amy had been to every doctor's visit since she was born. Not to be outdone, Ross jumped up and shouted that his bear had been around the world at least 20 times when it was accidentally left on an airplane. Across town at the local high school, a different story is playing out in the classroom. Then there is John, who is dying to leave class. What is Auditory Learning? Learning Styles. What Is My Learning Style - Auditory Learner. The Definition of the Visual Learning Style. The visual (spatial) learning style. If you use the visual style, you prefer using images, pictures, colors, and maps to organize information and communicate with others. You can easily visualize objects, plans and outcomes in your mind's eye. You also have a good spatial sense, which gives you a good sense of direction. You can easily find your way around using maps, and you rarely get lost. When you walk out of an elevator, you instinctively know which way to turn. The whiteboard is a best friend (or would be if you had access to one). Common pursuits and phrases Some pursuits that make the most use of the visual style are visual art, architecture, photography, video or film, design, planning (especially strategic), and navigation. Visual, Auditory and Kinesthetic (VAK) learning style model. A common and widely-used model of learning style is Fleming’s (2001) Visual Auditory Kinesthetic (VAK) model. According to this model, most people possess a dominant or preferred learning style; however some people have a mixed and evenly balanced blend of the three styles: Visual learnersAuditory learnersKinaesthetic learners Visual learners tend to: Learn through seeingThink in pictures and need to create vivid mental images to retain informationEnjoy looking at maps, charts, pictures, videos, and moviesHave visual skills which are demonstrated in puzzle building, reading, writing, understanding charts and graphs, a good sense of direction, sketching, painting, creating visual metaphors and analogies (perhaps through the visual arts), manipulating images, constructing, fixing, designing practical objects, and interpreting visual images. 3 Learning Styles. Everyone processes and learns new information in different ways. There are three main cognitive learning styles: visual, auditory, and kinesthetic. The common characteristics of each learning style listed below can help you understand how you learn and what methods of learning best fits you. Understanding how you learn can help maximize time you spend studying by incorporating different techniques to custom fit various subjects, concepts, and learning objectives. Each preferred learning style has methods that fit the different ways an individual may learn best. Formative Assessment Strategies. The Value of Formative Assessment. The current wave of test-based "accountability" makes it seem as though all assessment could be reduced to "tough tests" attached to high stakes. The assumption, fundamentally unproven, is that such tests produce real improvements in student learning better than do other educational methods. In this environment, Paul Black and Dylan Wiliam's "Inside the Black Box: Raising Standards Through Classroom Assessment" (Phi Delta Kappan, October 1998) provides strong evidence from an extensive literature review to show that classroom "formative" assessment, properly implemented, is a powerful means to improve student learning -- but summative assessments such as standardized exams can have a harmful effect. Summative assessment is the attempt to summarize student learning at some point in time, say the end of a course. Most standardized tests are summative. They are not designed to provide the immediate, contextualized feedback useful for helping teacher and student during the learning process. Edisdat.ied.edu.hk/pubarch/b15907314/full_paper/1926551038.pdf. Web.uvic.ca/~gtreloar/Assessment/Periodical Items/Working Inside the Black Box-Assessment for Learning in the Classroom.pdf. September 2012. Formative vs. Summative Assessment: Does It Matter? By Deena Boraie Assessment terminology has become a minefield because it often obscures distinctions between concepts, which in turn affects classroom practice. Examples of Formative Assessment. When incorporated into classroom practice, the formative assessment process provides information needed to adjust teaching and learning while they are still happening. The process serves as practice for the student and a check for understanding during the learning process. The formative assessment process guides teachers in making decisions about future instruction. Here are a few examples that may be used in the classroom during the formative assessment process to collect evidence of student learning. Observations Questioning Discussion. Assessment for learning: are you using it effectively in your classroom? Engagement and effort are essential characteristics of good learners. Research indicates that children who start school socially and academically ahead of their peers tend to be more successful in school. This results in an achievement gap, which widens as children move through the school system if it persists. One of the factors that can influence this is the way assessment is perceived by youngsters who start at a disadvantage; it can either strengthen or break their belief in their capabilities. Schools in England have become data driven; teachers are heavily influenced by the need to produce summative performance data to assess school effectiveness, set targets and monitor standards. Most schools have amalgamated this into their regular monitoring systems with teachers being asked to report on achievement every few months. Summative Assessment Definition. Summative assessments are used to evaluate student learning, skill acquisition, and academic achievement at the conclusion of a defined instructional period—typically at the end of a project, unit, course, semester, program, or school year. Generally speaking, summative assessments are defined by three major criteria: The tests, assignments, or projects are used to determine whether students have learned what they were expected to learn. Definition of Formative Assessment. Definition: A formative assessment can be defined as a variety of mini assessments that allow a teacher to adjust instruction on a frequent basis. Definition of Summative Assessment. Types of Summative Assessment. 'Summative' assessments are set to enable tutors to evaluate, and assign a mark to their students' learning at a particular point in time. The mark assigned contributes to the final outcome of the students' degree. The most important thing when completing any form of assessment or examination is to establish what the goalposts are, by looking at: the exact details of the assignment, including instructions about format, presentation and structure the marking criteria for the assessment the "intended learning outcomes" for the course, i.e. what the tutor has stated that s/he expects you to be able to demonstrate in order to pass the course These should be made available in handbooks, via Blackboard and/or on course unit outlines distributed by the course unit leader. Inclusive assessment approaches to learning in the English Language Classroom – I’m a teacher not a psychologist! 'I think there is a learner in my class with SEN but I’m not sure, because I don’t know what I should be looking for and I don’t know what to do next. I probably should talk to the parent but don’t know how.’Eliza, primary teacher from Italy 'We have to do state exams at the end of the year and I know some of the learners with SENs in my class won’t be at the right standard. Assessment for learning: are you using it effectively in your classroom? Formative%20and_summative_assessment. Formative Assessment. Formative vs Summative Assessment - Teaching Excellence & Educational Innovation - Carnegie Mellon University.

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THE MOST DISTRESSFUL NATION: IRELAND BEFORE THE FAMINE John William Tuohy Through out its long history, Ireland had used several types of legal systems including the tribal system, the oral tradition, and the written law. But no matter what the system, the laws had remained almost constant for several centuries. Traditional Irish law was, originally, not compiled in a single work, it was passed orally from generation to generation and taught by the Druidic class and was, occasionally, written in various literature and judgments. During the time of St. Patrick, the law was written as a single document, a codification that became known as the Brehon Laws. Only four copies, in various degrees of completeness, exist today. The Brehon laws remained, basically, unchanged from the original for eight centuries. They were Irish laws, written by the Irish in the Irish language. They were not conceived or enforced by foreign hands. Irish law was conceived and written by those who the Irish and because the laws were written and enforced by Irish men, the laws were, in an Irish sort of way, respected and followed. The largest portion of the Brehon law was a section called the Senchus Mó¢r (pronounced Shankus mor), better thought of as a collection of customs rather than one of statutes already widely known and observed by the Celts since the dawn of their time. Unlike the British law that would later rule over their lives, the Senchus M¢r didn’tuse an imperious tone. The laws were written to be understood and were based in wisdom. It’s been argued that Ireland had no uniform means to enforce the law and undoubtedly, in Ireland vast history, there were Kings or others of vast power, who broke the law. But overall, the law was followed because the law based in logical, fair tribal custom. Through a series of invaders who would rule over Ireland, the Viking, the Normans, the English, the old Irish legal system was eventually beaten down and never able to reemerge. When the English arrived in full force, they brought their own laws with them. Written in Norman-French, not in the Irish or Latin as were the Irish laws in place before them, the English laws were combined with a series of repressive acts written in 1367 during a parliament session held in Kilkenny. These news acts recognized the Irish, in their own land, as rebels and enemies of the state and were intended, over a period of time, to crush and kill off Irish society. These new laws later termed the Irish Penal Codes, punished Irish dress, manners language, and laws. Essentially, the laws, enacted in 1695, were designed and written to deny almost all rights to the Irish Catholics in Ireland and to eventually eradicate the catholic religion in Ireland. Protestant England had no intention of sharing its power with in Ireland with the Pope in Rome. But that would be on the higher end of the Penal Codes. Without question, the basic role of the Penal Laws was to legally take the land from the people under the questionably noble guise of saving the Irish on behalf of the Protestant King of England. Civil liberties were crushed. Catholics were denied education, land ownership, and medical practice and treatment. The Catholics were not allowed to enter the legal profession, nor could they hold government offices. The laws were enforced simply enough; to hold any position or wealth in Ireland, the Irish were forced to repeat and sign an oath which no catholic would take. A typical oath was; I do solemnly and sincerely, in the presence of God, profess . . . that I do believe, that in the sacrament of the lord's supper there is not any transubstantiation of the elements of bread and wine into the body and blood of Christ . . . and that the invocation or adoration of the virgin Mary, or any other saint, and the sacrifice of the mass, as they are now used in the church of Rome, are superstitious and idolatrous . . . The French Jurist Montesquieu described the Penal Laws as having been "conceived by demons, written in blood, and registered in Hell" Not content with stripping the Irish of their basic legal rights, in about 1697, the English followed up with "The Bishop's Banishment Act." which forbade the Church from practicing any ecclesiastical jurisdiction in Ireland and called for all Catholic Clergy to leave Ireland by May 1st, 1698 under the penalty of “transportation for life” If the Priests returned to Ireland, the law allowed them to be hanged, drawn, and quartered. A lock is better than suspicion. Irish proverb Ireland became a plantation of sorts. A handful of wealthy families, largely Protestant Loyalists, ruled over 80% of the people. Conditions in general and the treatment of the Irish degraded to the point where a Protestant could, in theory and sometimes in practice, beat or kill any Catholic without fear of any legal recrimination. Every village had its stories to tell, ridiculous incidents which showed the depth of the prejudice. Virtually every village held a tale of a local man being shot by a member of the ruling class for refusing to sell his horse for five pounds as the law dictated of Lord Charlemont being thrown out of the House of Lords for suggesting that the Irish be allowed to lease a cabin with a potato patch. Gradually, the laws were lifted. In 1778, the Catholic relief act allowed Catholics to enter leases for up to 999 years as opposed to the previous 31 years. By 1782, Catholics were "allowed to become schoolmasters and private tutors, to own horses exceeding the value of 5 schillings and to acquire land in socage tenure" With the passage of the so-called relief laws of 1792 and 1793, Catholics were allowed to enter into low levels of legal practice, earn degrees from universities, and become commissioned in the military. But the English closed, flatly and without debate, Irish Catholic entrance into Parliament. Te effects of the laws crushed the spirit of the Irish people who were now subject to a foreign power within their own land. It devastated a people who took such pride in being Irish and in their ancient culture. By 1800, to be Irish was to be ashamed of what the once proud Celt had become. Further, the Penal Code succeeded in alienating the population, especially the large poor rural population against law and government. They became, slowly a nation who scoffed the laws since there was no pride or sense in obeying laws that were designed and enforced to take away their lives, liberties, and property and left them with out a single benefit that wasn’t stripped to its marrow or impaired enough to be useless. By 1800, the British had had accomplished in Ireland what they had set out to do with the introduction of the Penal Laws in 1695; they had, essentially, stripped the Irish people of all things Irish and, essentially, replaced them with all things British. Any united opposition to the laws, or even the threat of opposition brought around a cry in London for even more repressive laws. While the Crown was willing to repeal an enormous portions of the Penal Laws, largely those that were either unenforceable or unproductive, under pressure from the State Clergy, they were far less willing to repeal the Tithe Laws. Under the Penal Laws, anyone working the Irish land was required to pay an annual tithe (or religious tax) of 10% of the agricultural produce for the upkeep of official state church, the Anglican (Episcopalian) Church of Ireland despite the fact that the vast majority of the population were Roman Catholic. Often, a cow does not take after its breed. Irish proverb The need for repeal of the Tithe Law brought around the rise of Daniel O’Connell, a member of the Irish Catholic aristocracy who was elected to the House of Commons in 1828. Despite Daniel O’Connell’s achievement of having most Penal Laws repealed in 1829 in the Great Catholic Emancipation, stupidly, the Irish obligation to pay tithes remained and was enforced, collected in the form of goods, especially livestock. There had been a largely peaceful resistance campaign against the collections since 1829, and it was, for the most part, successful, with the credit for the non violence going to O’Connell, a vocal critic of violent insurrection in Ireland, always repeating his call that the freedom of Ireland was not worth the spilling of one drop of blood. But the Anglican Clergy, sorely missing their money, pushed the Crown into action, first by gathering lists of defaulters, “Tithe Defaulters” some 30,000 in all, largely concentrated in the rural counties of Kilkenny, Tipperary and Wexford. The clergy pressed the Irish Constabulary, established only a few years before in 1822 as a sort of Militia paid for largely by the Tithe collections, to track down the defaulters. Between 1831 and 1834 a bitter and bloody war between the unarmed peasantry and the well-armed state forces broke out over the payment fees. Starting as strikes, the resistance spread from county to county and eventually grew from small riots to armed insurrection. The three year uprising was one of several successive revolts of the rural poor across Ireland since the 1760s. The uprising were led by a variety of underground movements with varying names, generally known now after the first movement, the Whiteboys, the rural poor, wage laborers, male and young, often mere teenagers. The organizations were secretive and underground, and also fairly libertarian, with independent groups in each town networked with others to form an entire movement across several counties. Each had an extensive ritual initiation oaths, elaborate pseudonyms, and occasionally uniforms or secret insignias. Largely unarmed, these groups fought the military who were eventually sent to collect tithes, with sticks and stones. The military more often then not answered the assaults with rifle fire killing score of resisters. The killings did little more then to further organize the movement across the country. Finally it wasn’t save for landlords, their agents and tithe Collectors, called proctors, to leave their homes without being shot at or killed in ambush. In turn, these attacks brought even more harsh reprisals by government troops. The first clash of the Tithe war took place on March 3, 1831, when a force of 120 heavily armed police took cattle belonging to a Catholic priest, in lieu of Tithes. It was a test case. The priest, with the approval of his bishop, had organized a local resistance to the tithe. The incident was widely publicized, and the fact that priest had resisted the collection was a tacit approval for the general population to resist. Several weeks later, in the town of Newtonbarry in Wexford, the police once again rounded up a hard of cattle as a seizure. This time snipes fire on the police who fired back. Twelve people were killed and twenty fatally wounded. The Wexford massacre as it was called, further organized resistance. In the rural town, the accepted signal for approaching police became the ringing of the town bells . This forewarning led to the ambush of 40 man police detachment in the town of Carrickshock in Kilkenny on December 14, 1831. Locals killed 14 militia including the Chief Constable. In 1832, the English government credited 242 homicides, 1,179 robberies, 401 burglaries, 568 burnings, 280 cases of cattle-maiming, 161 assaults, 203 riots and 723 attacks on property directly to tithe-enforcement in 1831. That year, in the general election, all 82 Irish members returned to parliament pledged to campaign for the abolition of tithes forced the British government to concede. Although tithes were still collected the amount demanded was nominal. In 1835, in the town of Rathcormack, in Cork, military-police killed 17 and wounded 30 others in an attempt to collect a tithe of less then 40 shillings from a widow. An investigation of the massacre, the troops fired point blank into the crowds, proved that the order to fire was given by a Clergyman. But what troubles the Crown was the fact that the villagers had withstood several volleys and at least one charge by the troops without breaking and running. Collections were suspended and a Tithes Commutation Act was introduced which reduced the amount payable by about a quarter and made the remainder payable to landlords who would, in turn, pass payment onto the Clergy. At that, the uprising more or less ended, but the people were still forced, in a manner of ways, to pay for the upkeep of the Protestant Church in Ireland until it was finally outlawed in 1869. It’s important to note that this was not, completely, a nationalist uprising against Anglo-Irish rule. Although the Tithes were a factor, most rural violence was class-based, dirt poor Catholic Irish versus the wealthy Catholic Irish. Rich farmers made up about 3% of the population, followed by a larger group, about 12% of the population, of wealthy but not rich farmers and extended families. At the bottom of the pile, were the cottiers and labor class, about 76% of the population. About 10,000 landlords owned virtually all of the land. But this was by design of the crown, which, lacking sufficient armies to dominate every corner of its empire, ruled by a divided and conquer mentality. In 1841, Daniel O’Connell organized the Repeal Association, a movement dedicated to removing the repeal of the Union. This is sometimes misinterpreted as an act of national independence. However O’Connell was never an advocate of complete national independence. Instead, he campaigned for Repeal of the 1801 Act of Union which merged the Parliaments of Great Britain and Ireland. O’Connell advocated a recreation of the Kingdom of Ireland with Queen Victoria, then reigning Monarch, as the Queen of Ireland as well. The Irish forgive their great men when they are safely buried. Irish proverb To achieve Repeal of the Act of Union, O’Connell had launched a series of so-called Monster Meetings, wherein tens of thousands of Irish met in mass meeting to protest in favor of Repeal. O’Connell had planned the biggest demonstration in the history of Ireland to support his version of a free Ireland. The meeting was scheduled to be held at in Clontarf, the crowd was expected to number at least a million strong. But the Crown outlawed the gathering and poured thousands of troops into the surrounding area forcing O’Connell to back down. It was the worst thing he could have done. But calling off the mass meeting at Clontarf, he deprived himself of his most potent weapon, an organized Irish populace appearing in vast numbers. It was, effectively, the end of O’Connell. He failed to make any further progress in the campaign for Repeal. His followers deserted him under the cry "He should have called us out" Among those leading the cry were the Young Irelanders, a pocket of young idealists, named after similar group on the continent who advocated radical overthrow of the crown. The group worked quietly within the otherwise loyalist Repeal movement, biding their time for the right moment. The core of the Young Ireland group was Thomas Davis, Charles Duffy and Thomas Dillon, who founded a newspaper, The Nation, which promoted the O’Connell aims of Repeal but the political line of the paper, was liberal nationalist and more often then not; it was used to stir up its readership with a national awareness. Gradually, this group went one small step beyond O’Connell, calling for “repeal or else separation” which worried not only the British government but, O’Connell who was concerned with the growing influence and political outlook of the Young Irelanders and their effect on his progress for Ireland. With the vast disappointment in O’Connell limp resistance to the English, his supporters turned to the Nation and its more militant means of winning Irish independence. O’Connell did everything in his power to shit the Nation down and throw off the growing popularity of the Young Irelands but the Young Irelands refused to back down. Thomas Davis, the Young Irelanders leader and O’Connell’s most vocal critic, died suddenly and unexpectedly, giving O’Connell a short lived respite, giving O’Connell and his son John the opportunity to drive the Young Irelanders out of the Repeal Association and having the Nation closed down. But soon O’Connell died, at age 71 while on a pilgrimage to Rome in 1847 and the Irish resistance movement seemed to drift. But while Ireland’s revolt seemed to flicker and die, in large part beaten under by the enormity of the great Irish famine of 1845, the rest of the European continent of 1848 was thrown into revolt. There were a popular rising in Sicily, Paris and Vienna, and even though Ireland herself showed no signs of revolt, the Young Irelanders reconsidered their non-violent position and they rejoined the radical John Mitchell, the son of a Unitarian Minister, openly advocated that the people arm themselves. Mitchel gambled on a mass rising in the autumn, but the Crown, terrified at the events throughout the rest of Europe and based on the recent violence in the Tithe Wars, acted swiftly. Mitchel was arrested, tried and convicted under the new Treason Felony Act and exiled to Australia. The rest of the Young Irelanders leadership scattered in shame as a nation watched them allow their leader to be taken away in chains without a struggle. Regardless of the easy win by the Crown, enrollment in the Young Ireland organization tripled after Mitchel’s arrest, with most of the new members being barely out of their teens. The group was now taken over by the Protestant William Smith O'Brien, a descendent of Brian Born. O'Brien, Educated at Cambridge, he had been elected to the British Parliament in 1828 and was otherwise a strong supporter of British rule over Ireland. That view changed in 1843 and O’Brien changed his allegiance to the Irish freedom movement. With natural leadership qualities, he rose quickly rose to a leading role in the rebellion forces. O’Brien tried to raise the county in insurrection, but few joined. Undaunted, he formed a Council, made up of himself, John Blake Dillon and Thomas Francis Meagher. The rebellious Kilkenny would be their headquarters and it was there that they set up their Provisional Government and issue their first manifesto. They toured the rural countryside trying to rouse the starving people into revolt, but the famine and its after effects had beaten them down. The local Catholic clergy, fearing a slaughter by the English, begged the Young Irelands to give up their fight and return home. The Priests pointed out that they were unarmed; ill prepared and were completely ignorant of military strategy. But at Boulagh Commons, O’Brien found coal miners who were eager volunteers, some of them already armed, others prepared to fight with their mining tools. With less then 50 followers and a few handguns the group attacked a police outpost in the rural countryside but were beaten off and eventually arrested. All of its members were rounded up and sentenced to death but later had their sentences commuted to life in Prison in concentration camps in New Zealand. As was the case in nearly ever Irish revolt, the uprising was poorly planned, hopelessly equipped and lacked native support to succeed. William Smith O’Brien and his lieutenant, James Stephens, and a small force of men attempted to capture some local policemen at the small town of Farrenrory. At best it was an impromptu battle. They succeeded in holding the British forces down for a short while until, as usual, British re-enforcements arrived and the Irish scattered and ran. As was always the case, the leadership was quickly rounded up and arrested. O’Brien was arrested on a train platform in a nearby town and Thomas Meagher was captured walking causally along a road near Cashel. O’Brien’s revolt, the so-called rising of 48, ended in a crushing and humiliating defeat for the Irishmen. The rebels, even if they had won a few initial skirmishes, who were ill prepared to stand against the thousands of troops the Crown poured into Ireland in advance of the uprising. The British had moved to swiftly. Tried for treason, and of course found guilty. Before passing sentence, the judge asked if there was anything that anyone wished to say. Meagher, speaking for all, said: "My lord, this is our first offense, but not our last. If you will be easy with us this once, we promise, on our word as gentlemen, to try to do better next time. And next time ---sure we won't be fools to get caught." The judge, indignant at Meagher’s speech, sentenced them all to death "To be drawn on a hurdle to the place of execution on the 13th and there hanged until he be dead, his head then to be cut off and his body to be cut into 4 quarters, then disposed of as her majesty shall think fit." What the English hadn’t banked on was outrage over the sentence from the American government, pressured in part by an already massive and continually growing Irish American voting block. Queen Victoria commuted the sentence life in prison. Twenty six years later, Queen Victoria learned that Sir Charles Duffy, the newly elected Premier of the colony of Victoria, Australia was the same Charles Duffy who had been transported in chains, by her order, the penal colony there in 1848. In 1873 Duffy accepted a knighthood from Queen Victoria, much to the anger of his Irish cohorts. He retired to Southern France and died in 1903 - his remains were sent to Ireland where they received full national honors. The Queen's demand to know what had happened to the others from the rising of 48. A report showed that Thomas Francis Meagher became a Brigadier General in the Union Army and was appointed Governor of Montana. Terrance McManus became a General as well. After escaped to New York, Richard O’Gorman set up a law practice which flourished. He became a member of the elite and in 1869 became a counsel to New York Corporation and was appointed to the Superior Court of New York in 1880. Morris Lyene was Attorney General of Australia and would be succeeded in that office by Michael Ireland. Thomas D’Arcy Mcgee was a member of the Canadian Parliament, as well as its Minister of Agriculture and President of the Dominion of Canada Council. John Mitchell was a power house in New York politics. His son, John Purroy Mitchell would serve as Mayor in 1914. John Blake Dillon escaped to New York disguised as a priest. He distanced himself from other Rebel living in the US and was eventually admitted to New York bar at Albany in 1849, and was delighted by the lack of formality (no wigs, gowns etc) He set up a law practice which flourished and became rich. He returned to Ireland due to ill health in the family, stayed and was elected to Westminster Parliament. He died suddenly 12 moths later

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