Datasets:

qingy2024

/

qwark-corpus

like 1

1. Help with adding and subtracting rational expressions I've been having trouble with this equation for a little while. I cannot get the answer that's in the answer key and have no idea where I'm going wrong. If someone could please show their calculations I'd really appreciate it. $\frac{7}{x+2}-\frac{x+8}{4-x^2}+\frac{3x-2}{4-4x+x^2}$ 2. Re: Help with adding and subtracting rational expressions $\displaystyle \frac{7}{x+2}-\frac{x+8}{4-x^2}+\frac{3x-2}{4-4x+x^2}$ $\displaystyle \frac{7}{x+2}-\frac{x+8}{(2-x)(2+x)}+\frac{3x-2}{(x-2)^2}$ $\displaystyle \frac{7}{x+2}+\frac{x+8}{(x-2)(x+2)}+\frac{3x-2}{(x-2)^2}$ $\displaystyle \frac{7(x-2)^2}{(x-2)^2(x+2)}+\frac{(x+8)(x-2)}{(x-2)^2(x+2)}+\frac{(3x-2)(x+2)}{(x-2)^2(x+2)}$ $\displaystyle \frac{7(x-2)^2 + (x+8)(x-2) + (3x-2)(x+2)}{(x-2)^2(x+2)}$ can you finish from here? 3. Re: Help with adding and subtracting rational expressions Thanks so much! When I multiplied the second term by -1/1 to change (2-x)(2+x) to (x-2)(x+2) I was changing the numerator from -x+8 to x-8. That problem was really getting to me. Thanks again!

crawl-data/CC-MAIN-2018-22/segments/1526794863972.16/warc/CC-MAIN-20180521082806-20180521102806-00241.warc.gz

A guest post by Mai Lei The following post is one of a series previewing the research that will be presented at the SETAC North America 29th Annual Meeting in Sacramento, California (4–8 November 2018). Can you imagine our beautiful planet becoming a “plastic planet”? In the BBC documentary film Blue Planet II, members of the producing team noted that plastic waste is ubiquitously floating in the sea, including fishing lines, plastic packages, and plastic bottles. Marine organisms can be trapped by plastic waste that is everywhere in the oceans, even in the deepest and most remote parts. So it is essential to carry out intensive studies of plastic waste. Large plastics can either be physically or chemically broken into fragments after having been in the water a long time, traveling long distances. Such fragments, coupled with ones that were released into seas as fine plastic particles (smaller than 5 mm), are collectively called microplastics. Microplastics were brought to the world’s attention by Captain Charles Moore. While traveling the Pacific Ocean, he found lots of plastic particles floating on the sea surface and collected these plastics with a net. The term “microplastics” became well known in 2004. Microplastics are known to distribute all over the environment. In addition, microplastics are “sticky”, in that many poorly water soluble chemical contaminants such as DDT can easily attach to them from the surrounding environment. This is worrisome, because the concentration of such chemicals that can be carried by microplastics is several orders of magnitude higher than that in the water. After microplastics enter the marine environment, aquatic organisms can ingest them by accident. Not only does this present a choking hazard, but microplastics can and do fill up the digestive tracts of marine animals, causing them to starve to death. In addition, any toxic chemicals associated with these plastics can accumulate in the body of these organisms, which has been shown to be the case in field studies. Once ingested, those toxic chemicals may be released from the microplastic into the organism’s body through the creature’s digestive tract. This represents another potential risk of microplastics to aquatic organisms in the sea. At present, much of the discussion and scientific work on microplastics have involved figuring out how to collect and measure the plastics themselves, as well as evaluating exposure levels and potential ecological risks. Some work is also being done to determine secondary effects, such as that of chemicals associated with microplastics. A session at the SETAC North America Annual Meeting entitled “Environment Exposure to Microplastics and Affiliated Toxic Chemicals” will discuss these issues. This session will cover all topics related to microplastics, but will in particular emphasize recent studies on the occurrence, fate and effects of microplastics and affiliated toxic chemicals in the environment. In addition, current research will be presented on the development of novel technologies for qualitative and quantitative analyses of microplastics and affiliated chemicals in field samples. Session Information: Environment Exposure to Microplastics and Affiliated Toxic Chemical Wednesday, 7 November 2018 | 8:00 AM–11:15 AM | Hall E

<urn:uuid:31d893cc-71b9-42a1-9151-6818ab5b6297>

This week's book giveaway is in the Cloud/Virtualizaton forum.We're giving away four copies of Mesos in Action and have Roger Ignazio on-line!See this thread for details. Win a copy of Mesos in Action this week in the Cloud/Virtualizaton forum! # Boolean Values Roger Sanchez Greenhorn Posts: 16 A couple of other questions in preparation for an exam: ( ( x || ! ( y && z ) ) && ! ( y || z) ) ( ( ! x && ( y || z ) ) || ( ! y || z)) Thanks again, Roger Paul Zill Greenhorn Posts: 28 not sure what the question is. did you forget the values for x, y, & z? Jaunty John Greenhorn Posts: 21 These will always resolve false if NOT true Paul Zill Greenhorn Posts: 28 Originally posted by Jaunty John: These will always resolve false if NOT true if what not true if: boolean x = true; boolean y = false; boolean z = true; than the first example would be true. and second false. if: boolean x = false; boolean y = false; boolean z = true; the the first is false and the second is true. Roger Sanchez Greenhorn Posts: 16 I forgot to put the variable values: x = false, y = true, z = false ( ( x || ! ( y && z ) ) && ! ( y || z) ) x = false, y = true, z = false ( ( ! x && ( y || z ) ) || ( ! y || z)) Thanks again Joe Pluta Ranch Hand Posts: 1376 They might be trying to simplify the equation. For example, take this one: ( ( x || ! ( y && z ) ) && ! ( y || z) ) If either y or z is true, this statement is false (because the right side of the *AND is false). So, plug false values for y and z into the left expression, getting (x || true), which removes x from the equation. The whole thing factors downs to (!y && !z). Similarly, after some careful manipulation, the second statement is (!x || !y || z). Don't believe me? You could always try a truth table <grin>. Joe Roger Sanchez Greenhorn Posts: 16 Thanks for the quick reply. So, to check my understanding, both statements are false? Joe Pluta Ranch Hand Posts: 1376 Nope. First is false, second is true. Quick runthrough: x = false, y = true, z = false ( ( x || ! ( y && z ) ) && ! ( y || z) ) ( ( F || ! ( T && F ) ) && ! ( T || F ) ) ( ( F || ! ( F ) ) && ! ( T ) ) ( ( F || T ) && F ) ( T && F ) F x = false, y = true, z = false ( ( ! x && ( y || z ) ) || ( ! y || z)) ( ( ! F && ( T || F ) ) || ( ! T || F ) ) ( ( T && T ) || ( F || F ) ) ( T || F) T Joe

crawl-data/CC-MAIN-2016-26/segments/1466783397636.15/warc/CC-MAIN-20160624154957-00072-ip-10-164-35-72.ec2.internal.warc.gz

When the London Underground Railway System opened 150 years ago, it would revolutionize city transportation and contribute to both the economy and the women’s suffrage movement. On the very first day of service some 40,000 members of the public caught one of the 20 trains that ran each hour. This early service was run by steam powered trains, not surprisingly the soot, ash and steam made for a less than pleasant ride, despite the ventilation shafts. Another unfortunate design feature on the earliest trains was the lack of windows. The designers had seen no need for windows in an underground situation and it was only after passenger complaints of claustrophobia that the later cars were amended to include the windows. The economy would benefit from shoppers now having the freedom to venture further afield for their shopping endeavors. Suddenly, shopping became a form of recreation, no so dissimilar from the drives to the mall we continue to make. In 1875, ladies-only carriages were introduced to the system and just as quickly removed from service when women refused to ride them, opting instead for the unpredictable thrill of being seated next to a male stranger. The Times Newspaper warned male readers not to gaze at women on public transport, “Put not the unprotected lass to the blush.” But by the 1890’s sympathetic tips also had to be delivered to men who were embarrassed by the indecorous stares of women. With their sliding doors, straps from which to hang and one class carriage service, the new transport ushered in the future. What began as a solution to unblock crowded city streets, with the first short route of only 3 miles, expanded to service the entire metropolitan area and become an essential part of daily life. Even during the years of World War II it would play an important role. Initially, in 1939 it was declared that the underground stations must be used as air raid shelters, because the government worried that Londoners would huddle underground in fear and not go to work or about their business. Some stations that had fallen into disuse from low ridership would be converted into secret storage archives and could only be reached by special trains. However, during the dark days of September 1940, when the blitz began in seriousness, people rushed to the underground stations for shelter and none were turned away by staff. It is estimated that 177,000 shelterers camped out in the deepest tube stations each night. The official ban on sheltering was lifted and bunk bed and sleeping bags were added to 76 stations. Today, London’s underground transport system remains the life giving arteries of this magnificent city, and there are still sections where trains rattle through the tunnels originally dug by the Victorian workers. The carriages are modern, comfortable, and the system remains efficient and cost effective. No journey to London would be complete without a ride on the “tube.” Truly, a ride through much of the city’s history.

<urn:uuid:c3824ba5-e6f2-4045-a6bc-314d18e0bb73>

Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel? Points A, B and C are the centres of three circles, each one of which touches the other two. Prove that the perimeter of the triangle ABC is equal to the diameter of the largest circle. An AP rectangle is one whose area is numerically equal to its perimeter. If you are given the length of a side can you always find an AP rectangle with one side the given length?

<urn:uuid:813894e0-fbcb-46f5-be53-4a1e68243641>

What is an emblem book? It is a form that was tremendously popular during the Renaissance. It is believed that the Italian lawyer Andrea Alciato devised the first such book. The books themselves contained small illustrations (a bit like a modern thumbnail image) that were accompanied by “a brief title or motto, an edifying verse epigram, and often an additional explanatory text in verse or prose.” (Gordon Collection: Emblem Books http://www2.lib.virginia.edu/rmds/portfolio/gordon/emblem/) These books were created by individuals and reveal their own outlook, but they also “communicate moral, political, or religious values in ways that have to be decoded by the viewer.” (Glasgow University Emblem Project. http://www.emblems.arts.gla.ac.uk/) They often have classical or humanist sources, such as Erasmus’s Adages. (Gordon Collection: Emblem Books http://www2.lib.virginia.edu/rmds/portfolio/gordon/emblem/) Alciato introduced the first Emblematum liber, published by Heinrich Steyner and printed in Augsburg in 1531. Scholarship suggests that Alciato himself had nothing to do with this series of editions, but that his associate and friend Conrad Peutinger commissioned the publications based on unillustrated epigrams, etc., that “had circulated among Alciato’s friends in manuscript” (Andrea Alciato’s Emblematum. Alciato at Glasgow. http://www.emblems.arts.gla.ac.uk/alciato/books.php?id=A31a&o=). Several versions were printed in continental Europe and were collected widely. This month’s CABS Book-of-the-Month is a version printed, we believe, in Leiden by Franciscus Raphelengius (son-in-law of Christoph Plantin) in 1608. We don’t know for sure because the title page is a hand drawn copy that was added at some stage, possibly to replace the original title page which was destroyed. But one inclined to conspiracy theories might think that it was a deliberate attempt to associate an inferior copy with a renowned publishing house and established edition of the book. Who knows? This book is fascinating for a number of other reasons, mostly relating to its binding. First of all, the book has no writing on the spine, but Alciatus is written vertically on the fore-edge of the book, two letters per row. Anyone interested in library history will know that bookshelves as we know them only came into common usage well into the era of the printed book. Manuscripts and early printed books were usually laid flat on lecterns or shelves and were often chained to the furniture. It was only with the mass production of books that forced libraries to find a more space-efficient way of storing them. Initially they were shelved upright, fore-edge facing out. Blind-tooled decoration was common in northern Europe into the 17th century and that did not lend itself well to spine titles. With the spread of gold-tooling from northern Africa via Italy and Spain, which was a more visible way of marking the spine, books began to be shelved spine outwards. We know very little about the book’s provenance other than it was given to the Courtauld in 1978 in accordance with the bequest of the art historian and collector Dame Joan Evans. But if the book was published in The Netherlands it was northern Europe and the binding tells us a bit more. The book has been sewn onto pasteboard boards using 4 parchment thongs, which are visible because there are no pastedowns. These are all features of that suggest the binding is contemporary to the publication of the book, if 1608 is correct. The covering is brown calf, blind tooled with floral and compass motif stamps, one of which incorporates the initials RW. The initials could be those of the owner of the book, although they are more likely to have been those of the binder or the finisher (the person who decorated the binding). The initials also suggest a northern European origin, as the letter W appears in Spanish, Italian and French words usually only of foreign borrowings. The book has a shelfmark of CABS Z7483 ALC. We have another edition (Emblemata ad quae singula, praeter concinnas insciptiones, imagines…) in the Anthony Blunt bequest. This was published in Lyon in 1626. Its shelfmark is BLUNT ALICIATI. The library has a other emblem books, including a copy of Ripa’s Iconologia, which is not an emblem book per se, but has similar elements, Jacob Cats’s Proteus ofte minne-beelden verandert in sinne-beelden, for an example of a Flemish emblem book, and an 1883 facsimile of Jean Cousin’s Liber: Fortunæ centũ emblemata, et symbola centũ, continens…, as well as a number of books about emblem books. There are numerous emblem projects, so if you are interested: OpenEmblem Project – University of Illinois at Urbana-Champaign – http://media.library.uiuc.edu/projects/oebp/ Alciato’s Book of Emblems – Memorial University at St. John’s, Newfoundland – http://www.mun.ca/alciato/index.html Glasgow University Emblem site – http://www.emblems.arts.gla.ac.uk/ Alciato at Glasgow – http://www.emblems.arts.gla.ac.uk/alciato/ The English Emblem Project – Penn State University – http://emblem.libraries.psu.edu/home.htm Emblem Project Utrecht – http://emblems.let.uu.nl/index.html

<urn:uuid:da8b7e13-f3eb-4428-8c45-c65d053cbe8e>

Friedrich Tiedemann studied the anatomy of humans and animals in the nineteenth century in Germany. In the early 2000s, Sabata Martino and a team of researchers in Italy and Germany showed that they could reduce the symptoms of Tay-Sachs in afflicted mice by injecting them with a virus that infected their cells with a gene they lacked. Tay-Sachs disease is a fatal degenerative disorder that occurs in infants and causes rapid motor and mental impairment, leading to death at Camillo Golgi studied the central nervous system during the late nineteenth and early twentieth centuries in Italy, and he developed a staining technique to visualize brain cells. Called the black reaction, Golgi's staining technique enabled him to see the cellular structure of brain cells, called neurons, with much greater precision. In the nineteenth century, reticular theory aimed to describe the properties of neurons, the specialized cells which make up the nervous system, but was later disconfirmed by evidence. Reticular theory stated that the nervous system was composed of a continuous network of specialized cells without gaps (synapses), and was first proposed by researcher Joseph von Gerlach in Germany in 1871. Reticular theory Scientists use cerebral organoids, which are artificially produced miniature organs that represent embryonic or fetal brains and have many properties similar to them, to help them study developmental disorders like microcephaly. In human embryos, cerebral tissue in the form of neuroectoderm appears within the first nine weeks of human development, and it gives rise to the brain and spinal cord. In 2011, Sonja Vernes and Simon Fisher performed a series of experiments to determine which developmental processes are controlled by the mouse protein Foxp2. Previous research showed that altering the Foxp2 protein changed how neurons grew, so Vernes and Fisher hypothesized that Foxp2 would affect gene networks involved in In 1873 Italy, Camillo Golgi created the black reaction technique, which enabled scientists to stain and view the structure of neurons, the specialized cells that compose the nervous system. During the nineteenth century, scientists were studying cells and proposed cell theory, which describes the basic characteristics of cells as fundamental units of life. However, cell theory struggled to explain

<urn:uuid:ba6fe560-51ee-4b32-91ad-d42142574ee1>

In 1949 the Dutch geologist van Bemmelen reported that Lake Toba was surrounded by a layer of ignimbrite rocks, and was a large volcanic caldera. Later researchers found rhyolite ash similar to that in the ignimbrite around Toba in Malaysia and India, 3000km away. Oceanographers discovered Toba ash on the floor of the eastern Indian Ocean and the Bay of Bengal. The Toba eruption, dated at 75,000 years ago, was the most recent eruption of a "supervolcano." Bill Rose and Craig Chesner of Michigan Technological University deduced that the total amount of erupted material was about 2800km3 -- around 800km3 of ignimbrite that flowed over the ground and around 2000km3 that fell as ash, with the wind blowing most of it to the west. Such a huge eruption probably lasted nearly two weeks. Very few plants or animals in Indonesia would have survived, and it is possible that the eruption caused a planet-wide die-off. There is some controversial evidence, based on mitochondrial DNA, that the human race was reduced to only a few thousand individuals by the Toba eruption. A large area collapsed after the ejection of that amount of subsurface material, forming a caldera, which filled with water creating Lake Toba. Later, the floor of the caldera uplifted to form Samosir, a large island in the lake. Such uplifts are common in very large calderas, apparently due to the upward pressure of unerupted magma. Toba is probably the largest resurgent caldera on Earth.

<urn:uuid:6851adf0-6cab-4416-b124-30b8f53598cd>

New research supports the link between vitamin D and a healthy immune system. The recent study of almost 7,000 adults in the UK has confirmed a link between Vitamin D levels and the risk of infection (1). Natural sunshine can provide our bodies with up to 10,000iu vitamin D each day. This ‘sunshine vitamin’ helps to boost the body’s defences by increasing levels of ‘anti-microbial peptides’. Working like natural antibiotics, these peptides mount an attack against unwanted infections. During the winter months, infections such as colds, flu and chest infections are common. It is believed that this increased risk of infection is due in part to the lower levels of vitamin D that we receive in the colder months. There is however increasing concern over vitamin D levels throughout the year. After all, most of us are careful to protect our skin from the sun during the summer months, a sensible measure to help prevent burning, premature skin ageing and to protect against skin cancer. The study, conducted by researchers from University College London, looked at the relationship between Vitamin D levels and infection. Higher levels of vitamin D were linked with lower risk of infection. While this particular study was epidemiological in nature, it will be interesting to see how future controlled trials will further our understanding. After all, vitamin D not only supports the immune system and bone health. More recently, deficiency has been linked with cardiovascular disease, impaired glucose tolerance, poor muscle development and certain types of cancer (2). The Department of Health now recommends that certain groups in the UK population should take daily vitamin D supplements (3). These groups are: • all children aged six months to five years old • all pregnant and breastfeeding women • all people aged 65 and over • people who are not exposed to much sun, such as those who are confined indoors for long periods • people with darker skins such as people of African-Caribbean and South Asian origin While vitamin D can be obtained in the diet through oily fish such as salmon and sardines, it is generally believed that supplementation is the most viable way of ensuring adequate intake. A recent European policy document concludes that “only vitamin D supplements or vitamin D enriched food products are truly viable options for optimising the vitamin D status” (4). Bolstering your vitamin D levels can be as simple as spending some time outdoors every day, while ensuring that you eat vitamin D enriched foods such as breakfast cereals, milk, margarine and soy drinks. Those who would like to take an easily absorbed supplement might consider an emulsified liquid vitamin D such as Biocare’s BioMulsion D which provides 2000iu vitamin D in just two drops. Written by Nadia Mason 1. Berry DJ, et al. Vitamin D status has a linear association with seasonal infections and lung function in British adults. British Journal of Nutrition. Available on CJO June 2011 doi:10.1017/S0007114511001991 2. Vieth R, Bischoff-Ferrari H, Boucher BJ, Dawson-Hughes B, Garland CF, Heaney RP, Holick MF, Hollis BW, Lamberg-Allardt C, McGrath JJ, Norman AW, Scragg R, Whiting SJ, Willett WC, Zittermann A. The urgent need to recommend an intake of vitamin D that is effective. Am J Clin Nutr 2007;85:649–50. 3. NHS Choices. “Vitamins and Minerals – Vitamin D”. Web article. Visited on 30th June 2011. 4. The Standing Committee of European Doctors. Vitamin D Nutritional Policy in Europe. March 2010. Visited on 30th June 2011. 5. Image Ccourtesy of digitalart.

<urn:uuid:fb1ed98a-8392-4c4e-8dd9-5badcb7360c4>

When Chris Columbus loaded up a dozen swine to make the trip across the Atlantic to the New World for the first time in 1492, little did he know it marked the beginning of what would eventually become a war on wild hogs by the time the 21st century dawned. From the eight pigs that survived the voyage to nest in the "West Indies," to the estimated millions that now roam across the Americas, the problem with wild pigs seems to multiply faster than a calculator. This hardy and extremely adaptable animal species has slipped beyond the confines of farms and ranches in rural America and shed their domestic bonds in favor of rooting and surviving in the wild. With tenacity and resourcefulness, feral swine tend to gather into sounders, or packs of wild pigs, and exert their aggressive behavior on their immediate environment, often competing with other types of wildlife for food and water resources. These opportunistic omnivores demonstrate a remarkable ability to survive under the harshest conditions, often destroying fields and forage as they root for food, contaminating water resources, and spreading a myriad of animal diseases that can negatively affect other animal species and even humans. In Texas particularly, the problem is exaggerated by years of occupation, growth and adaptation. European swine were first brought to America by Spanish monks and missionaries. Early settlers brought numerous varieties of wild boars to Texas in later years. Released into the wild, these swine mated and rapidly multiplied and provided more abundant hunting opportunities for frontiersmen and settlers. Today, Texas alone is home to an estimated 2.6 million feral swine, the largest population of any state. These wild animals are credited with causing an estimated $52 million in agricultural damages to the state each year, and that number is rising. In spite of well-organized efforts to trap and hunt feral swine by state officials, contractors and private landowners, population numbers continue to increase, as do the problems associated with the proliferation of the species. State officials say a few years back no one wanted to listen to warnings about the threat of a wild pig population. Only state wildlife biologists, a handful of Extension agents, and farmers and ranchers who were on the front line, understood the extent of the growing problem associated with an explosion of feral swine in the wild. The problem has grown to such an extent in recent years that Texas lawmakers are beginning to ask questions, like why the problem hasn't been resolved in spite of funds dedicated specifically to addressing the issue. While such concern is generally well received by wildlife insiders, many say funds that have been available so far fall far short of what is needed, and though awareness of the problem is rising, researchers and wildlife managers say elected officials still fail to understand the dynamics of the problem. Two Texas House committees met recently to discuss the escalating war on wild hogs and that offers hope that at least a few lawmakers are beginning to take the problem more seriously. Both committees say they hope to look deeply into what more can be done to reduce the wild pig population in the state and to control the problems associated with rapid population growth among feral swine in Texas. "The damage caused by feral hogs has climbed to thousands of dollars per affected member," Gene Richardson of the Texas Farm Bureau told the House Agriculture & Livestock Committee and the chamber’s Culture, Recreation & Tourism panel. "Damage to personal property and to persons on Texas highways by feral hogs is taking its toll." Legislators attending the meetings appear to be getting more involved. Several suggestions were offered as ways to better control feral swine populations: more aggressive aerial hunting, a more comprehensive program of trapping, and even a suggestion that poison baits could be used to eradicate the state's pig problem. But Texas State Veterinarian and Director of the Texas Animal Health Commission, Dee Ellis, warned lawmakers it wasn't a question of eradication, but selective control. “It's not a matter of eradication because that isn't going to work. We need to focus on selective control,” Ellis told lawmakers. He also warned committee members to understand that a feral hog represented a lot more than a wild boar. "We define feral swine as basically any swine. There is no differentiation of species...a pig is a pig... if a pig is out, it’s feral; if it’s not out, it’s domestic,” Ellis explained. Committee members say they expect to lay a number of legislative ideas on the table for consideration when the Legislature returns for the mid-January session. Rep. Drew Springer, a member of the Agriculture & Livestock Committee, said increasing problems with feral swine in Texas will get worse before it gets better. He noted that farmers in his district have lost hundreds of thousands of dollars to the problem already. Other lawmakers agreed action is needed at the legislative level. One committee member said even urban areas were beginning to feel the pressure of growing feral swine populations, and the perils of spreading disease to human population centers increases proportionately.

<urn:uuid:51af1102-47d2-4450-97bd-db2f6d8311d4>

Whipworm(redirected from whipworms) Also found in: Dictionary, Medical. (Trichocephalus trichiurus), a parasitic round-worm, with a gray or reddish body. It is threadlike toward the front, and toward the back it is thickened and, in the male, curled up in a spiral. The length of the male is from 30 to 40 mm and that of the female is from 35 to 50 mm. The whipworm lives parasitically in the human intestines (in the blind gut and, less frequently, in the large intestine, the vermiform appendix, or the rectum). It attaches itself to the wall of the intestine by penetrating the mucous membrane with its thin front end and causes the disease trichuriasis. The whipworm develops without an intermediary host. Outside of the human body the larva develops over a period ranging from 11 to 120 days (depending on the temperature) inside an egg that is lemon-shaped and has plugs at both poles. When the egg lands in the intestines, the larva comes out of the egg and attaches itself to the wall of the intestine. REFERENCEPod’iapol’skaia, V. P., and V. F. Kapustin. Glistnye bolezni cheloveka, 3rd ed. Moscow, 1958. S. S. SHUL’MAN

<urn:uuid:b8e11f05-b4d4-4a79-92e1-d34e0b4365f2>

ConnerW765 6 # What is the volume of a sphere with a surface area of 452.39cm^2? Round to the nearest hundredth. The formula of the volume of a sphere is: $V=\frac{4}{3}\pi r^3$. The fomula of the surface area of a sphere is: $A=4\pi r^2$. So, if you know the surface area, you can find the radius of a sphere from secon formula: $r=\sqrt{\frac{A}{4\pi}}$ $r=\sqrt{\frac{452.39}{4\pi}}=6$ Now, you can find the volume of a sphere: $V=\frac{4}{3}\pi 6^3=\frac{4}{3}*216\pi=288\pi \approx 904.78 cm^3$

crawl-data/CC-MAIN-2022-05/segments/1642320304835.96/warc/CC-MAIN-20220125130117-20220125160117-00110.warc.gz

Introductory Algebra for College Students (7th Edition) $$x = 20$$ We check our work by plugging $20$ into the original equation to see if both sides equal one another. $$\frac{20}{4} - \frac{20}{5} = 1$$ We simplify the fractions to get: $$5 - 4 = 1$$ $$1 = 1$$ Both sides equal one another, so we know the solution is correct. To solve this equation, we need to get rid of the fractions. To do that, we find the least common denominator of each fraction. We also can change the whole number $1$ into a fraction as well to be able to work with it easily. The lowest common denominator for this problem would be $20$. So we rewrite the fractions in this problem to get: $$\frac{5x}{20} - \frac{4x}{20} = \frac{20}{20}$$ Now we can multiply all terms by $20$ to get an equation that has no fractions: $$5x - 4x = 20$$ We combine terms to get: $$x = 20$$ We check our work by plugging $20$ into the original equation to see if both sides equal one another. $$\frac{20}{4} - \frac{20}{5} = 1$$ We simplify the fractions to get: $$5 - 4 = 1$$ $$1 = 1$$ Both sides equal one another, so we know the solution is correct.

crawl-data/CC-MAIN-2019-43/segments/1570987779528.82/warc/CC-MAIN-20191021143945-20191021171445-00000.warc.gz

(ca. 1742-July 23, 1805) Patriot, American Revolution military leader, and public official, James Johnston was born around 1742 in Scotland. Of Scottish ancestry, his father Henry Johnston emigrated to North Carolina to escape civil and religious conflicts raging on in England, Scotland, and Ireland. Johnston and his wife arrived to the New World and settled along the Catawba River. They had two children, James and Mary. James married his wife, Jane Ewart, several years before the American Revolution and they settled in Tryon County, North Carolina. Together James and Jane had two children, Robert Johnston and Sarah Johnston. His son, Robert, would eventually become a North Carolina Senator from Lincoln County in 1810-1811 and again in 1817-1818. His daughter, Sarah, married a Dr. Benjamin Johnson of Virginia. James Johnston fought as a colonel in the Patriot militia during the American Revolution. He became well-known in what was then Tryon county as a militia captain and by serving on juries. He was elected to the Provincial Congress in 1776. He appears to have entered military service sometime around 1775 when he participated in the Snow Campaign. He was given the rank of Captain by then Colonel William Graham and was sent off to area known as “Ninety-Six” district in northwestern South Carolina to fight a large number of Tories led by Fletcher and Cunningham. After pushing back the Tory forces at Ninety-Six, Colonel Graham received news that General Griffith Rutherford had requested a large number of infantry and cavalry units from Mecklenburg, Rowan, and Tyron counties to subdue Cherokee Indians that were killing civilians on frontier settlements. Colonel Graham, along with Captain Johnston, fought in General Rutherford’s campaign to weaken the power of the Cherokee before they could combine with the British. After the success of this campaign, Captain Johnston was promoted to the rank of Colonel and was given a number of expeditions to the southern border of North Carolina including an expedition along the Pacolet River. Following expeditions in North Carolina and South Carolina, General Rutherford placed Colonel Johnston under the command of Colonel Francis Locke near Mountain Creek, North Carolina. In June of 1780 in advance of the Battle of Ramsour’s Mill, Johnston distinguished himself when he was selected to cross enemy lines to deliver a message to General Rutherford from Colonel Locke containing information about strategy for the upcoming battle. Johnston has also been credited in a number of works with a keen mind for strategy which he is said to have employed at the Battle of Kings Mountain. However, historians have disputed this story based on a lack of firtshand reports from others who were at Kings Mountain. Yet his alleged participation at Kings Mountain was memorialized with the inclusion of his name on the Kings Mountain U.S. Monument at Kings Mountain National Military Park in Blacksburg, South Carolina. Prior to the Revolutionary War, Colonel James Johnston purchased a sizeable piece of land on the Catawba River. After the split of his home county of Tryon into Lincoln and Rutherford counties, Johnston was elected to the legilslature as a senator from Lincoln County between 1780 and 1782 and reportedly acted as a disbursing agent for the Western Division. He was also a representative at the Convention of 1788. In the few years leading up to his death, Colonel Johnston served as the Ruling Elder of his local Presbyterian Church and appears to have been a highly regarded member of the community. James Johnston made his home at "Oak Grove", in what is present day Gaston County, in the home he built in 1782. The building was demolished in the 1950s. Johnston passed away on July 23rd, 1805 and was buried in a private cemetery at Oak Grove. Cyrus Lee Hunter. Sketches of Western North Carolina, Historical and Biographical: Illustrating Principally the ... The Raleigh news steam job print. 1877. https://archive.org/details/sketcheswestern00huntgoog (accessed October 21, 2014). Teaching American History. “Narrative of the Battle of King’s Mountain”. Accessed November 3, 2013. https://teachingamericanhistory.org/document/narrative-of-the-battle-of-kings-mountain/ Daughters of the American Revolution. cn. Lineage book. Washington, D.C. : The Society ; Harrisburg, Pa. : Harrisburg Pub. Co. 1905. https://archive.org/details/lineagebook5251daug (accessed October 21, 2014). Draper, Lyman Copeland. King's Mountain and its heroes : history of the Battle of King's Mountain, October 7th, 1780, and the events which led to it. Cincinnati : P.G. Thomson. 1881. https://archive.org/details/cu31924032752846 (accessed October 21, 2014). Dowd, Jerome, b. 1864. Sketches of prominent living North Carolinians. Raleigh, N.C. : Edwards & Broughton, printers and binders. 1888. https://archive.org/details/sketchesofpromin00dowd (accessed October 21, 2014). McCrady, Edward. Cyclopedia of eminent and representative men of the Carolinas of the nineteenth century. Madison, Wis. : Brant & Fuller. 1892. https://archive.org/details/cyclopediaofemin01mccr (accessed October 21, 2014). "Oak Grove." N.C. Highway Historical Marker O-39, N.C. Office of Archives & History. http://www.ncmarkers.com/Markers.aspx?MarkerId=O-39 (accessed October 21, 2014). 21 October 2014 | Asbury, Hayden

<urn:uuid:feb5f756-a792-4e2d-8c8c-351430f610bc>

# Big-O notation in algorithms We use big-O notation to describe the growth of functions. In the case of algorithms, we use it to calculate the temporal complexity of an algorithm with respect to the algorithm’s input. We use big-O notation in algorithms, to calculate the theoretical temporal complexity of an algorithm. The main advantage of the big-O notation is that it is independent of a certain implementation, programming languages, and hardware. This allows us to compare two algorithms, according to their efficiency, without the need to implement them or even having to use a computer. Big-O notation is a topic from mathematics that we borrow in Computer Science (like many other topics). So, as we always do in mathematics, let’s start with the definition. ## Big-O definition Definition: “Let f and g be functions from the set of integers or the set of real numbers to the set of real numbers. We say that f (x) is O(g(x)) if there are constants C and k such that |f (x )| ≤ C|g(x)| whenever x > k. [This is read as “f (x) is big-oh of g(x).”] ”. Source: Discrete Mathematics and its Applications By Rosen. From this definition, we can infer that f(x) grows more slowly than a certain multiple of g(x). We call the constants C and k witnesses. So, for you to prove that f(x) is O(g(x)), all you need to do is to find the witnesses C and k. In Computer Science, we use two properties of Big-O to calculate the temporal complexity of algorithms without the need to find C and k. ## Big-O graphical definition Let’s see this definition graphically. Let’s create the graph for the functions f(x)=x, g(x)=x2, and h(x)=4x2. From the figure above, you can see that x is O(x2). Also, 4x2 is O(x2), and x is O(4x2). Now that you understand the definition of big-O, let’s see the properties that we use to determine the temporal complexity of an algorithm. These two properties can be proven by using the definition of big-O (I’ll leave the proof to the reader): • Sum rule: if f1 is O(g(x)) and  f2 is O(h(x)) ⇒ (f1 +f2)(x) is O(max(|g(x)|,|h(x)|)) • Product rule: if f1 is O(g(x)) and  f2 is O(h(x)) ⇒ (f1 * f2)(x) is O( g(x) * h(x) ) How is this useful for us? Algorithms are a finite sequence of steps that, when executed in a certain order, solve a specific problem. By using the two rules above, we can determine the temporal complexity of a whole algorithm. We first calculate the temporal complexity of single steps and combine them using the sum and product rule. In the next post, I give you some examples of how these two rules are applied to calculate the temporal complexity of iterative algorithms.

crawl-data/CC-MAIN-2024-26/segments/1718198861319.37/warc/CC-MAIN-20240612234213-20240613024213-00352.warc.gz

The Christmas season in 1843 saw the publication of Charles Dickens’ “A Christmas Carol.” No other book or story by Dickens or anyone else (except the Bible) has been more enjoyed, criticized, referred to, or more frequently adapted to other media. One of my favorites was watching Patrick Stewart doing his one-man version of the play at the Old Vic Theatre in London. None of Dickens’ other works is more widely recognized or celebrated within the English-speaking world. Some scholars have even claimed that in publishing A Christmas Carol, Dickens single-handedly invented the modern form of the Christmas holiday in England and the United States. Indeed, the great British thinker G.K. Chesterton noted long ago, with “A Christmas Carol” Dickens succeeded in transforming Christmas from a sacred festival into a family feast. In so doing, he brought the holiday inside the home and thus made it accessible to ordinary people, who were now able to participate directly in the celebration rather than merely witnessing its performance in church. Many of our American conceptions of what a “traditional” Christmas is, comes from this time in Victorian history. Indeed, Queen Victoria of England had just married a few years before the publication of this book. Her German husband Prince Albert brought some of his native customs to England (including the Christmas tree), beginning some of the traditions of Victorian Christmas. In the mid-seventeenth century, the Cromwellian Revolt abolished the celebration of Christmas as well as the monarchy. Though the monarchy was subsequently “restored,” the traditions of the winter holiday never quite recovered. But the earlier religious proscription was not the only cause of the decline of Christmas. Even by the beginning of the nineteenth century, the Industrial Revolution, especially in the north, was changing the communities that still tenuously kept the customs of their ancestors. By the time the Carol was written in 1843, the lavish celebrations of the past were a distant, quaint memory. Some still remembered them, and even before the Carol a few popular books attempted to record the celebrations of the past, such as The Book of Christmas by T.H. Hervey (1837) and The Keeping of Christmas at Bracebridge Hall by Washington Irving (1820). But social forces beyond simple nostalgia were at work, rekindling the need for winter celebrations. Dickens was one of the first to show his readers a new way of celebrating the old holiday in their modern lives. His Christmas celebrations of the Carol adapted the twelve-day manorial (Yule) feast to a one-day party any family could hold in their own urban home. Instead of gathering together an entire village, Dickens showed his readers the celebration of Fred, Scrooge’s nephew, with his immediate family and close friends, and also the Cratchit’s “nuclear family”: perfectly happy alone, without the presence of friends or wider family. He showed the urban, industrial English that they could still celebrate Christmas, even though the old manorial twelve-day celebrations were out of their reach. Dickens’ version of the holiday evoked the childhood memories of people who had moved to the cities as adults. The book has been called by some a “sledge hammer” against the ills of industrialism and consumerism. Dickens’ own father had been sent to Debtors’ Prison and Charles Dickens himself bitterly remembered having to leave school, pawn his books, and work in a factory during that time. He’d seen children working long hours in the tin mines and attending poor schools. He modeled the Cratchit’s lifestyle on his own experience in Camden Town, London. Dickens demonstrates that even in poverty, the winter holiday can inspire good will and generosity toward one’s neighbors. He shows that the spirit of Christmas was not lost in the race to industrialize, but can live on in our modern world. The publishing of his book was immensely popular, though in a time of great religious controversy, and its lack of babes, wise men, stars, mangers, and other icons of the Christian nativity inspired a multitude of sermons and pamphlets at that time. Although A Christmas Carol is generally associated with the Christian winter holiday season, for it does contain references to Christ “who made lame beggars walk and blind men see.” And so, at the end of the story, we see both lame and blind touched by the Spirit of Christmas. Nevertheless, its themes are not exclusive to Christianity and it inspired a tradition for decades in Christmas books and celebrations that appealed to many non-Christians. Dickens’ preface to the book reads: I have endeavoured in this Ghostly little book, to raise the Ghost of an Idea, which shall not put my readers out of humour with themselves, with each other, with the season, or with me. May it haunt their houses pleasantly, and no one wish to lay it. Their faithful Friend and Servant, C.D., December, 1843. But the punch line to the book, is the very last sentence, which rarely fails to bring a tear to this historian: It was always said of Scrooge, that he knew how to keep Christmas well, if any man alive possessed the knowledge. May that be truly said of us, and all of us! And so, as Tiny Tim observed, God Bless Us, Every One! Bill Petro, your friendly neighborhood historian excerpts from Prof. Gerhard Rempel, Lectures in Western Civilization

<urn:uuid:430e75d1-43e6-4477-b965-2a970d302361>

MONDAY, Jan. 11, 2021 — A special calorie-burning type of body fat appears to help protect against an array of chronic ailments, including heart disease, type 2 diabetes and high blood pressure, a new study suggests. Brown fat generates heat by drawing glucose from the bloodstream, as opposed to energy-storing white fat, explained senior researcher Dr. Paul Cohen. He’s an assistant professor and senior attending physician at the Rockefeller University Hospital in New York City. That sort of a tissue sounds like a godsend. However, brown fat has been long thought to have little impact on human health because your stores of brown fat diminish as you age. But research now shows that adults who have active brown fat tissues in their bodies are far less likely than their peers to suffer from a range of chronic illnesses. What’s more, this protective effect holds even if the person carries excess weight, researchers reported recently in the journal Nature Medicine. “When we grouped our subjects based on their body mass index, we saw that even obese people with brown fat show protection from these conditions,” Cohen said. “For example, it’s well known that type 2 diabetes is more common in overweight and obese individuals, but what we saw was that even obese individuals who have brown fat have a significantly lower likelihood of type 2 diabetes than obese individuals without brown fat,” he continued. Brown fat is thought to be an evolutionary response to cold weather, helping generate heat to maintain the body’s core temperature, experts say. “Babies cannot shiver, and so when they are cold they would activate the brown fat and stay warm that way,” said Ruth Loos, director of the Genetics of Obesity and Related Metabolic Traits Program at the Charles R. Bronfman Institute of Personalized Medicine with the Icahn School of Medicine at Mount Sinai, in New York City. “For a long time it was believed it’s present in babies, and as we age, it was believed that it would disappear,” Loos said. “Now with better ways to measure, we now know that it does not totally disappear in adults. Some people do have a measurable amount of brown fat, which we did not know before.” Cohen said that studies performed about a decade ago “generated a lot of enthusiasm because they showed that adult humans have brown fat that can be stimulated by cold exposure and that it’s functional, meaning it takes up glucose from the bloodstream.” Brown fat is found in a layer of fat under the skin, typically in a region extending from the base of the head and along the shoulders, and then down the spine, said Dr. Aaron Cypess, acting chief of the translational physiology section of the diabetes, endocrinology and obesity branch of the U.S. National Institute of Diabetes and Digestive and Kidney Diseases. Researchers can detect active brown fat stores using PET scans that are normally used to diagnose and track cancer by looking for tissues burning heavy levels of glucose. Cohen and his team reached out to Memorial Sloan Kettering Cancer Center, obtaining more than 130,000 PET scans from more than 52,000 patients. They then reviewed those scans to search for brown fat deposits. Nearly 10% of the patients carried active brown fat, Cohen said. He added that this is likely an underestimate because patients undergoing the scans had been asked to avoid cold exposure, exercise and caffeine, all of which increase brown fat activity. The researchers verified earlier findings about brown fat — that women are more likely to carry it than men, that the amount of brown fat decreases as you age and gain weight, and that active brown fat is more likely to be found in scans done in cold versus warm weather. But when the research team compared brown fat levels to the patients’ medical histories, they found new associations between brown fat tissue and better overall health in people, regardless of weight. For example, people with active brown fat have improved levels of cholesterol and blood sugars. They also were less likely to have high cholesterol, coronary artery disease, congestive heart failure, high blood pressure and type 2 diabetes. “Some of those associations have never been documented before,” Cohen said, though the study did not definitively prove that brown fat causes disease risk to drop. It’s not yet clear why this link might exist, Cypess said. “Is it through the simple process of burning up glucose and fat to keep you warm, or is brown fat acting also as an endocrine organ that releases hormones into the blood and leads to these benefits?” Cypess said. It doesn’t take extreme cold to activate brown fat, Cohen noted — even a couple of hours in a 60-degree Fahrenheit room is sufficient. That temperature “is cool but certainly not frigid,” Cohen said. “I think it’s intriguing from a public health perspective that simply lowering our thermostats by a few degrees may result in health benefits.” Researchers and pharmaceutical companies also are looking into drugs that might activate brown fat and promote these benefits, Cohen said. However, the experts all agreed that too little is known about brown fat for anyone to try to either lose weight or gain health benefits by gallivanting about in cool rooms or the frigid outdoors. “If you ate less at a meal, you might be better off dropping some weight than trying to increase your brown fat,” Cypess said. “I’m still going to tell you the two things you have to do is eat a healthy meal plan and exercise, and we’re hoping we can bring brown fat activity into that plan.” © 2021 HealthDay. All rights reserved. Posted: January 2021 - COVID case rates hit new high for England, study finds - April 7, 2022 - Govt’s focus on affordable healthcare ensured significant savings for poor, middle class: PM Modi - April 7, 2022 - SRL Diagnostics and Skye Air Mobility collaborate to transport pathology samples using drone logistics - April 6, 2022 - Healthineers sets up new production line of CT scanners in Bengaluru under PLI scheme - April 6, 2022 - Lupin inks licensing pact with Alvion to market drugs in Southeast Asia - April 6, 2022 - Yoga Mahotsav: Ayush Ministry to organise event to demonstrate common yoga on World Health Day - April 6, 2022 - LordsMed forays into the medtech space with launch of health ATMs ‘Lords Sehat’ - April 5, 2022 - ‘Friendly viruses’ can be the next big thing in the history of medical research and more - April 5, 2022 - No setback to Bharat Biotech even as WHO suspends Covaxin UN supply: Sources - April 4, 2022 - Govt panel recommends Serum’s Covovax dose for kids aged 12 and above - April 4, 2022

<urn:uuid:a4f5408d-3e33-439a-a5c3-4301e95b9c80>

# Set-32 DI For SBI PO and SBI Clerk 2019 | Must Go Through These Questions Dear Aspirants, We are providing the most important  Data  Interpretation Questions for SBI PO 2019, SBI Clerk 2019 and all other competitive bank and insurance exams. These questions have very high chances to be asked in SBI PO 2019, SBI Clerk 2019. Directions (1-5): Study the following graph carefully and answer the given questions. The pie chart shows the number of pens sold in different shops in the month of July. 1. If the number of pens sold in Shop B is increased 20% on every month, then find the number of pens sold in the month of August. 2. Find the ratio of the number of pens sold in shop C to that of shop E 3. If the number of pens sold in the month of August in shop D is 20% of the total number of pens sold in shop A, C and F in the month of July, then find the number of pens sold in the month of August in shop D. 4. Number of pens sold in shop C is what percentage more than the number of pens sold in shop F? 5. Find the average number of pens sold in shop B, C, D and F together Directions (6-10): Study the following pie chart carefully and answer it correctly. The following charts show the percentage breakup of number of children in five different villages and breakup of children attending school from those villages: 6. What is the respective ratio of total number of children from village M to number of children attending school from the same village? 7. What is the number of children not attending school from village N? 8. What is the total number of children not attending school from village L and O together? 9. What is the total number of children from village P and M together? 10. The number of children attending school from village L is approximately, what percentage of the number of children from that village? • Directions (1-5): Study the following graph carefully and answer the given questions. The pie chart shows the number of pens sold in different shops in the month of July. ##### 1. Question If the number of pens sold in Shop B is increased 20% on every month, then find the number of pens sold in the month of August. Ans:3 Required number of pens = 6000 *(12/100) * (120/100) = 864 • ##### 2. Question Directions (1-5): Study the following graph carefully and answer the given questions. The pie chart shows the number of pens sold in different shops in the month of July. Find the ratio of the number of pens sold in shop C to that of shop E Ans:4 Required ratio = 6000 * (18/100): 6000 * (10/100) = 18: 10 = 9: 5 • ##### 3. Question Directions (1-5): Study the following graph carefully and answer the given questions. The pie chart shows the number of pens sold in different shops in the month of July. If the number of pens sold in the month of August in shop D is 20% of the total number of pens sold in shop A, C and F in the month of July, then find the number of pens sold in the month of August in shop D. Ans:2 Number of pens sold in shop A, C and F in the month of July = 6000 * (20+18+15)/100 = 3180 Number of pens sold in shop D in the month of August = 3180 * (20/100) = 636 • ##### 4. Question Directions (1-5): Study the following graph carefully and answer the given questions. The pie chart shows the number of pens sold in different shops in the month of July. Number of pens sold in shop C is what percentage more than the number of pens sold in shop F? Ans:3 Required percentage = [(18-15)/15 ]* 100 = [3/15] * 100 = 20% • ##### 5. Question Directions (1-5): Study the following graph carefully and answer the given questions. The pie chart shows the number of pens sold in different shops in the month of July. Find the average number of pens sold in shop B, C, D and F together Ans:1 Required average = [(12+18+25+15)/3] * 6000/100 = (70/4) *60 = 1050 • ##### 6. Question Directions (6-10): Study the following pie chart carefully and answer it correctly. The following charts show the percentage breakup of number of children in five different villages and breakup of children attending school from those villages: What is the respective ratio of total number of children from village M to number of children attending school from the same village? Ans:1 Total number of children from village M=(26/100)*2200 Number of children attending school from village M=(32/100)*1500 Required ratio=(26/100)*2200 : (32/100)*1500 = 143:120 • ##### 7. Question Directions (6-10): Study the following pie chart carefully and answer it correctly. The following charts show the percentage breakup of number of children in five different villages and breakup of children attending school from those villages: What is the number of children not attending school from village N? Ans:2 Number of children not attending school from village N =(15/100)*2200-(12/100)*1500= 330-180=150 • ##### 8. Question Directions (6-10): Study the following pie chart carefully and answer it correctly. The following charts show the percentage breakup of number of children in five different villages and breakup of children attending school from those villages: What is the total number of children not attending school from village L and O together? Ans:1 Number of children not attending school from village L =(15/100)*2200-(14/100)*1500 =330-210=120 Number of children not attending school from village O =(21/100)*2200-(20/100)*1500 =462-300=162 Required total=120+162=282 • ##### 9. Question Directions (6-10): Study the following pie chart carefully and answer it correctly. The following charts show the percentage breakup of number of children in five different villages and breakup of children attending school from those villages: What is the total number of children from village P and M together? Ans:3 Number of children from village P and M together= ([23+26]/100)*2200 =(49/100)*2200 =1078 • ##### 10. Question Directions (6-10): Study the following pie chart carefully and answer it correctly. The following charts show the percentage breakup of number of children in five different villages and breakup of children attending school from those villages: The number of children attending school from village L is approximately, what percentage of the number of children from that village? Ans:4 Number of children attending school from village L=(14/100)*1500 Number of children from village L=(15/100)*2200 Required percentage= {[(14/100)*1500]/[(15/100)*2200]}*100 =63%

crawl-data/CC-MAIN-2021-17/segments/1618038064898.14/warc/CC-MAIN-20210411174053-20210411204053-00489.warc.gz

History Lesson Plan: The Battle of Shiloh Background and Facts Note on Name of Battle: Much of the battle took place around a log Methodist Church called Shiloh, which, ironically is roughly translated from the Hebrew as "Place of Peace." Location: Near and around Pittsburg Landing, in western Tennessee, on the west bank of the Tennessee River. Date: April 6-7, 1862 Outcome: Union Victory Casualties: 19,900 killed or wounded (Union casualties about 13,000). Significance: Bloodiest battle to date on American soil. This battle was a precursor of very bad things to come in a long and protracted struggle between the North and South. (Read more below on the battle's effects on both sides.) Description of the Battle After his easy victories at Forts Henry and Donelson the preceding February, Union General Grant pressed on with his force of 60,000 inexperienced troopers south on the Tennessee River to Pittsburg Landing. His goal was the vital rail junction in Corinth, Mississippi, and thence south on the Mississippi River to Vicksburg. Confederate General Albert S. Johnston, however, had other plans. The bivouacked, inexperienced Yankee troops were a prime target for a frontal and flanking assault and an opportunity to destroy Grant’s army. Johnston struck on the morning of April 6 and quickly overran the unprepared Yankees, who had not even posted patrols. General Johnston was struck in the leg by a stray bullet and bled to death. His second in command, General Beauregard, took command, but failed to cut off the Yankee retreat to the river. Grant and Sherman rallied, reorganized and held off the furious Confederate assault until darkness and exhaustion caused both sides to stop and rest. The following day, the Yankees surprised Beauregard with reinforcements and a furious counterattack, and Beauregard grudgingly withdrew, leaving the field to the Yankees. Aftermath and Consequences Effects on the North General Grant’s career was nearly ruined. Bad press accounts labeling Grant as a "butcher" and personal animosity between him and his superior, Genera Henryl Halleck, resulted in Grant’s temporary demotion to second in command. Grant was rescued by President Lincoln, who moved Halleck to Washington, D.C., and restored Grant to command. General Grant’s attitude and respect towards the fighting ability and tenacity of the South underwent a radical change. As a result of Shiloh, Grant realized that the war would be long, and that the South would have to be completely crushed before they would give in. The Union victory would be the beginning of the end of the south’s efforts to defend its western flanks. Corinth and Vicksburg would fall, splitting the South in two; Grant would return to Tennessee, kick the Confederates out and send Sherman south to Georgia. General Albert S. Johnston’s death was a terrible blow to the South’s hopes in the west. Johnston was one of the South’s best generals, and none of his successors would do nearly as well. Equally irreplaceable were the South’s losses in manpower (over 10,000 killed, wounded and missing/captured). The Civil War was, in the end, a war of attrition, which, because of its lower manpower resources, the South could not win. The South was forced to evacuate much of Tennessee. General Johnston’s failure to crush Grant’s army opened the way to Vicksburg and the eventual Northern domination of the Mississippi River. There are a number of interesting eyewitness accounts of the Battle of Shiloh. One particularly engaging episode is an account with quotations by the young Confederate soldier Henry Morton Stanley (later of Stanley and Livingston fame): EyeWitness to History.com: The Battle of Shiloh . Here are some suggested thought-provoking questions that could be posed either in class or as an essay assignment on the Battle of Shiloh: ♦ Describe the “violets in the hat” incident in the first paragraph of Stanley’s quote. Why do you suppose young Henry Parker thought wearing flowers into battle was a wise thing to do? ♦ Describe the weapons the Confederate soldiers carried. How difficult would they be to load and fire during the stress of battle? ♦ What contrast and irony does the author see in marching through the woods to do battle on a Sunday? ♦ What effect did the “Rebel yell” have on Stanley and the rest of the soldiers? ♦ Right before he was captured, Stanley heard a Yankee call, “Down with that gun, Secesh…” Then he says, “...and I dropped my weapon, incontinently.” Contrast Stanley’s feelings about being captured with his previous excitement over seeing the Yankees retreat the day before.

<urn:uuid:0546be31-f9fa-475c-8d1e-ce409b5dee7d>

AYUTTHAYA -ANCIENT KINGDOM OF SIAM Ayutthaya city is the capital of Ayutthaya province in Thailand. Located in the valley of the Chao Phraya River. The city was founded in 1350 by King U Thong, who went there to escape a smallpox outbreak in Lop Buri and proclaimed it the capital of his kingdom, often referred to as the Ayutthaya kingdom or Siam. Ayutthaya became the second Siamese capital after Sukhothai. Its remains, characterized by the prang (reliquary towers) and gigantic monasteries, give an idea of its past splendour. It is estimated that Ayutthaya by the year 1600 CE had a population of about 300,000, with the population perhaps reaching 1,000,000 around 1700 CE, making it one of the world’s largest cities at that time. The Ayutthaya historical park is the ruins of the former capital of the Kingdom of Siam. Ayutthaya was named a World Heritage Site in 1991.

<urn:uuid:be241ae8-858d-4681-a03c-c662cad07bbd>

Poliovirus Type 1 is a human enterovirus and member of the family of Picornaviridae. The virus infects humans in two different ways, the infection is either a mild illness without serious symptoms, or the virus infects the central nervous system and may cause paralysis. The virus is most often spread by the faecal-oral route. Poliovirus enters through the mouth and multiplies in the intestine. Infected individuals shed poliovirus into the environment for several weeks, where it can spread rapidly through a community, especially in areas of poor sanitation. Minor infections include mild symptoms, including:fever, headache, and sore throat. However, paralytic disease occurs when the virus enters the central nervous system and replicates in motor neurons within the spinal cord, brain stem, or motor cortex, resulting in the selective destruction of motor neurons leading to temporary or permanent paralysis.

<urn:uuid:7f7b2725-dba7-4dc5-af2a-3488cd7c659a>

Measuring the Length of an Object (Measurement of an Object) - BYJUS # Measuring the Length of an Object We measure length primarily to understand the distance between two points and to find the size of objects. But the length can be measured using different methods. And the measurements of length can be expressed using different units. We choose the method of measurement and the unit of length depending on what we want to measure....Read MoreRead Less ## Introduction to Measurement Olivia built a home comprising two bedrooms. She wishes to install a glass window. The carpenter tells her that he will have to measure the length and width of the window to buy some glass for it. Carpenters measure things all the time. Have you tried measuring something before? We are required to measure different things in our daily life and different measurements are expressed in different units. ## Why do we need Different Units of Measurement? We cannot measure the length of a pencil and the distance between our school and home using the same units of measurement. To measure the length of a pencil, we need smaller units like centimeters or inches, whereas, when we measure the distance between our school and home, we need a bigger unit like meters or miles. Also, to make our judgments more dependable and accurate, we need a standard unit of measurement. ## What is Height ? The term “height” is frequently used to describe how tall someone or something is. We can compare our height as we grow older. We frequently make comparisons between the average heights of men and women from various countries, for example. In mathematics, height is defined as the vertical distance between an object’s top and bottom. It is measured in centimetres, inches, metres, and other units. ## What is Length ? The term “length” refers to the measurement of distance. In other words, the distance measured from one end to the other is called its length. Most measurement systems choose a base unit for length from which all other units are derived. We use inch rulers to measure shorter lengths. To measure greater lengths, we generally use yardsticks. To measure the straight or flat length we use a tape measure. Some units are also made up of other units such as a foot is made of inches and a yard is made up  of a few inches. 1 foot = 12 inches 1 yard = 3 feet = 36 inches Example 1 : Will a small pair of scissors fit inside a pouch that is a foot long? Explain. Solution : A pair of scissors is about 5 or 6 inches. As we know, 1 foot = 12 inches. So, the scissors will surely fit inside the pouch. Revise Math formulas and important concepts using our Math worksheets! These worksheets help students to develop Math skills in a fun and interesting way. Click the link below to get all the easy-to-comprehend math calculators and worksheets. ## Other Units of Measurement Centimeter The unit “centimeter” is used to measure the length of objects like erasers, pencils, tables, etc. Here we are looking at measuring the length of the pencil in centimeters with the help of a ruler. Example 1 : Your friend says a car has a length of about 5. Is the car about 5 meters long or 5 centimeters long? Solution : The car is about 5 meters long because we use “meters” to measure objects bigger in length. Inch An “inch” is used to measure the length of objects like bags, pencils, calculators, clothes, etc. When we measure  length in inches, we put the scale close to the end of the object. So just like a foot is made up of 12 inches,an inch is made of 2.54 centimeters. 1 foot = 12 inches 1 inch = 2.54 centimeters. Foot A “foot” is also a  standard unit of measurement. It helps us in determining the length of an object or even the height of a person. They can also assist us in determining the distance between two points. ‘Feet’ is the plural form of the word ‘foot,’ which refers to a single unit of measurement. Usually, we measure the height of a building in feet. 1 foot = 12 inches 1 yard = 3 feet = 36 inches Example 1 : Would you use centimeters, inches, or feet to measure the length of the table as shown in the figure? Solution : The length of the table in inches is 63.5 inches. The length of the table in feet is about 5.29 feet Hence we can use  both inches and feet to measure the length of the table. Meter A “meter” is the base unit of length or distance. It is used to measure  length and distances just like feet, miles or kilometers. 1 meter = 100 centimeters Yard A “yard” is used to measure the length of objects. Each yard is either 3 feet or 36-inches.  The yard originated as a unit of measurement in England as a unit of measuring land. It is used in both the British imperial and US customary measurement systems. 1 yard = 3 feet = 36 inches Here is a table that would help us see the conversions between units: ## What is a Ruler ? What is it used for? A ruler is a measuring instrument that has two sides. One side measures the length in inches and the other side measures it in centimeters. Rulers have markings on them that indicate the distance that has been measured. Example 1:Use the inch tile to measure the length of this spoon. Example 2: Identify the object and measure its height. Answer: The object is a dustbin, and its length is 50 centimeters or close to about 20 inches. Example 3: Whose path to school is longer? The distance between the house and the playground is 50 yards. The distance between the playground and the school is 9  yards. The distance covered from the house to the school: 50 + 9 = 59 yards. The distance from the house to the school: 7 + 22 = 29 yards.

crawl-data/CC-MAIN-2024-18/segments/1712296817144.49/warc/CC-MAIN-20240417044411-20240417074411-00438.warc.gz

There are 13 vitamins identified as essential: vitamins A, C, D, E, K, and 8 B vitamins. This means they are vital along with the essential minerals in maintaining YOU. Repair, Reproduction, Growth, Energy etc Vitamins help in maintaining healthy eyes and skin, acting as antioxidants to protect your cells from damage. Reproduction & growth, strong bones and normal blood clotting. Our essential vitamins are found in foods from grains, vegetables, fruits, dairy products, meats and the whole range of beans. By eating a variety of nutrient-dense foods you will have a vitamin-rich diet. These vitamins are A, D, E, and K. They are available in foods containing fats. The body assimilates these vitamins as it does dietary fats. They don’t break down in the water. Supporting physiological functions through the body, including: - Bone health - Immune system - Blood clotting Individuals can acquire vitamin A through dietary sources. Animal sources give preformed vitamin A or Retinol. These are prepared for the body to use. Thus, arrangements of repairs regularly show vitamin A substance as “vitamin A RAE.” RAE signifies “retinol movement reciprocals.” Animal’s with high levels of these vitamins include: - Fish liver oil - Hamburger liver - Cheese, milk, and other dairy items Good sources of beta carotene include: - Kale, spinach, and other green, verdant vegetables - Dark coloured peas - Certain cereal grains Individuals get vitamin D: - Normally through exposure to daylight as well as in the diet - Through natural foods - As supplements, if you feel you are lacking from your normal regime Vitamin D has two fundamental jobs in the body: - It keeps up bone strength by promoting calcium uptake. - It boosts body system support by creating calcium serum in the blood so it can be transported. An individual can get some vitamin D from the sun, yet the majority of us need to utilize different sources, as well. The basic option is food. Dietary sources include: - Oily fish and fish oils - Dairy foods, plant-based milks, and oats - Meat liver Vitamin E is a cancer prevention agent that can enable the body to decimate free radicals. Free radicals are destructive particles that can cause damage to the normally smooth cell walls. Oxidative pressure can prompt cell harm, and this can bring about damage leading to different illnesses. Vitamin E may help shield the body from a scope of medical problems. A few reasons why the body needs vitamin E are: - as a cancer prevention agent - to help the immune system - to widen veins and help slow thickening Dietary sources ` Great sources of vitamin E include: - wheat germ oil - sunflower seeds and oil - almonds, hazelnuts, and peanuts - spinach and broccoli - products that originate from the soil Vitamin K enables the body’s clotting function. Blood thickening is essential to our survival. Aside from blood coagulating, vitamin K may likewise: - reduce the danger of coronary illness - improve bone wellbeing - reduce excess amounts of calcium in the blood Food sources of vitamin K-1 and K-2 include: - egg yolks The Water-Soluble Vitamins C and B B vitamins are significant for ensuring the body’s brain function, energy levels and cell metabolism. They help the body convert food into energy (digestion), make fresh blood cells, and keep up healthy skin cells, synapses, and other body tissues. Job and Function Bolsters numerous basic body functions, including: Cell reinforcement: Your body utilizes cancer prevention agents to protect itself against oxidative pressure. Vitamin C is one of its most significant immune support vitamins and has been linked as a significant vitamin to support the body in its fight against cancer. Collagen development: Without vitamin C, the body can’t combine collagen, the primary protein in connective tissue. Therefore, deficiencies have a negative effecton your skin, ligaments, tendons and bones Resistant capacity: Immune cells contain significant levels of vitamin C. During contamination/infection, its levels are immediately drained. - The primary dietary sources of vitamin C are products grown from the ground. - Cooked animal-sourced foods contain essentially no vitamin C, yet low amounts can be found in raw liver, eggs, fish roe, meat and fish Vitamins and minerals are synergistic in maintaining our body’s function, along with the Protein, Fats, Simple carbohydrates and Complex carbohydrates. With the correct balance of all of these, we are well supported, a deficiency in any of them will be detrimental to our health. As with the 13 essential vitamins, there are essential minerals, there are said to be 16 these are: Calcium, Chloride, Chromium, Copper, Floride, Iodine, Iron, Magnesium, Manganese, Molybdenum, Phosphorus, Potassium, Selenium, Sodium, Sulfur and Zinc. Minerals are essential in maintaining blood pressure, hydration & electrolyte balance, as well as bone health; making new cells; delivering oxygen to cells; and contributing to normal muscle and nerve functioning. Minerals are obtained from foods, with specific minerals being found only in certain foods. By eating a variety of nutrient-dense foods from the 5 food groups, you will have a mineral-rich diet. Two minerals of particular importance are calcium and iron. Unfortunately, in so many of our diets, we do not enough iron or calcium. Calcium is required for the foundation of strong bones and teeth. Calcium levels throughout life are essential for the maintenance of bone density to prevent osteoporosis (where bones lose Calcium their matrix becomes compromised and this can lead to bones that can fracture easily). Calcium is found mostly in the milk group – milk, cheese, and yoghurt. Some food manufacturers add Calcium in their production process; therefore, calcium-fortified juices and cereals also provide ample amounts of calcium. Smaller amounts of calcium can be found in tofu, greens, and legumes. The world moves at a rushed pace nowadays. In the event that you have a feeling that you’re continually running on the edge, you’re not the only one. Many people say that they simply don’t have the energy they need to function. Once in a while, the reason for tiredness is self-evident — for instance, getting over a cold or other illness, or not getting enough rest. Vitamin deficiency may be the root cause. It may be best to request your doctorto check a couple of vitamin levels, for example, the three we’ve recorded below. Veganism has become more popular as more people have taken to this way of eating for its reputed medical advantages and morals surrounding animal welfare. It has not become a valid concern for everyone yet. Though the vegan diet has a growing following among athletes and bodybuilders. Bodybuilding focuses on building your body’s muscles through weight-lifting and tailored nutrition. Though very low fat diets can help to strip last small amounts of body fat to show of the muscle definition, and avoidance of processed non natural fats is a good idea anyway, long term low fat diets can strip the body or essential fats and stop the intake of fat soluble vitamins and minerals causing long term damage and deprive the body of nutrients essential to body repair and maintenance. So long term low fat diets can be counter productive to a healthy body and the process of muscle development. Whether recreational or competitive, bodybuilding is often referred to as a lifestyle, as it involves both the time you spend in and outside the gym. In order to maximize your results from the gym, you must focus on your diet, as eating the wrong foods can be detrimental to your bodybuilding goals. A few muscle heads are so precise with the eating regimens that they heft around scales to gauge their food. That is the means by which significant nourishment is for weight training. Arranging out your meals ahead of time with the assistance of a calorie counter removes a portion of the mystery from eating, which is significant in case you’re following a restricted eating regimen like the low-carbohydrate ketogenic diet. Though a low carb diet can be beneficial, put into perspective that carbs are the best quick fuel source, and can be the energy required to do a good workout. However unburned fuel raises blood sugar levels and triggers insulin release in most people not already naturally lean. That is the trigger to conversion and storage of the excess as fat. Carbohydrates range from simple starch to complex carbohydrates, so also key is putting the Carbohydrates on a scale of simple starchy carbs like refined sugar, four, rice, potato. Coming lower on the list are the fruits and vegetables that are fructose sugars which though still high on the list are better than refined sugars and add fibre, vitamins and minerals that are essential to us. As the plant based foods head down the scale towards green leafy vegetables they become more complex, providing higher vitamin and mineral levels as well as fibre some also provide healthy oils. The glycaemic index is a good reference, and the plant foods in the lower ranges are more complex carbohydrates slower to raise blood sugars and less likely to cause insulin release which will trigger fat storage. Protein manufactures your body. It makes muscle. It controls hunger. It’s a success win! Regardless of whether your objective is weight reduction or muscle building, eating enough protein is vital, yet so is an assortment, since every sort has its own amino corrosive profile. Go past chicken and protein powder with these incredible high-protein foods. Skeletal muscle is comprised of packs of individual muscle filaments called myocytes. Each myocyte contains numerous myofibrils, which are strands of proteins (actin and myosin) that can take hold of one another and pull. This abbreviates the muscle and causes muscle constriction. It is commonly acknowledged that muscle fiber types can be separated into two primary sorts: slow jerk (type I) muscle strands and quick jerk (type II) muscle fibers.1Fast jerk filaments can be additionally arranged into type 2a and type 2b filaments. A superset is a type of strength training in which you move rapidly from one exercise to a different exercise without taking a break to rest in the middle of the two activities. Regularly, you will enjoy a short reprieve to slow down or snatch a beverage of water between sets of activities. This likewise gives time for the muscles to recoup. Be that as it may, while doing supersets you move starting with one set then onto the next without a break. There are two principle manners by which supersets can be performed. These two different ways are very extraordinary, and in this way, the outcomes got from them shift incredibly. The two fundamental sorts of supersets are restricting muscle bunch supersets and the same muscle bunch supersets.

<urn:uuid:a6c393b2-3d62-4a12-b77d-bdf08034523f>

# Teaching Treasures Maths Activity ## Problem Solving 1: A window has a height of 32.5 cm and a length of 45 cm. What is the window's area? cm2 2: A concrete tank can hold 20,000 gallons of water. How many litres of water can the tank hold? litres 3: Nathan's home is 80 km to the nearest major town. How many metres is that? metres 4: One seventh of the students in Sarah's school are 12 years old. If there are 133 students in her school, how many students are 12 years old? 5: A raging bush fire went through a pine plantation, ¾ of the trees died. If there were 50,000 trees, how many died? 6: Bob used 14¾ litres of fuel driving to a country town. His fuel tank had 30 litres of fuel when he started, how much fuel did he have left when he arrived at his destination? litres 7: Mr. Stevens borrowed \$20,000 from his Australian cousin. He was charged 14½ % interest per annum. He repaid the loan 3 years later. How much interest did Mr. Stevens pay? 8: A truck travelled for 4½ hours at an average rate of 65 km/h. How far did it travel during that time? km 9: 400 - (20 x 8¼) + (15 x 9¾) = 10: An American book shop mailed 2 books to the UK. Each of those books cost \$4.75 to mail to the respective customer. They also had to post 12 other books costing a further \$2.45 each for postage. What was the total postage cost? 11: Janice planted 200 seeds; only 85% of these seeds grew. How many seeds did not grow? 12: 56 more than a number (n) is 78. What is the number? n = Thank you for using Teaching Treasures online learning interactive activities. Copyright.

crawl-data/CC-MAIN-2022-33/segments/1659882571536.89/warc/CC-MAIN-20220811224716-20220812014716-00588.warc.gz

Before you ride While you ride Secure the measuring unit in a fixed orientation relative to your body. The three axes are straight ahead (longitudinal), directly to the side (lateral) and/or straight up and down (vertical). If an axis is not used, don't circle it. - Accelerometer X: longitudinal - lateral - vertical (circle one) - Accelerometer Y: longitudinal - lateral - vertical (circle one) - Accelerometer Z: longitudinal - lateral - vertical (circle one) When you reach the place on the ride where you want to begin collecting data, press [Start/Stop]. After you ride Return the data collection unit back to the Electronic Data Center (EDC). Download the data. If possible, they will print the graphs of your forces vs. time so you can do onsite analysis. The data will also be posted online so you can download it and work further with it later. Use the back of this page to answer the questions below. Use the ride profile to determine where you were on the ride for each of these portions. Also note any peculiar accelerations encountered. - Describe the graph(s) during the initial seconds you recorded. Compare the shape of the graph(s) to your movement during that portion of the ride. - For each of your axes, where were the readings the greatest? What were the readings there? Explain why the readings were the greatest at those points. - For each of your axes, where were the readings the least? What were the readings there? Explain why the readings were the least at those points. - The larger the forces that act, the larger the acceleration acting on your body. Do the places where the unit recorded the largest values for force/mass the same places you experienced the largest accelerations? Explain. Example: A simple roller coaster for toddlers that makes a single loop around a closed track. Click here to download an MS Word file of this document: electrocoaster.doc Click here to download a pdf file of this document: electrocoaster.pdf

<urn:uuid:b861537a-c8b5-49b9-89b6-fd7966c5e553>

+0 # Probability that I get this wrong with out help: 100% 0 166 6 How many distinct sequences of four letters can be made from the letters in PROBLEM if each letter can be used only once and each sequence must begin with L and not end with P? Jul 29, 2020 ### 6+0 Answers #1 +533 +5 The total ways to make sequences of 4 letters using the letters P, R, O, B, L, E, M, using each letter only once, without restrictions, is 7 * 6 * 5 * 4 = 840. Let's use complementary counting for this problem (So, we find the situations we DON'T want and subtract them from the total)! :D Ways that a sequence begins with L = 1 * 6 * 5 * 4 = 120 Ways that a sequence ends with P = 6 * 5 * 4 * 1 = 120 Ways that a sequence begins with L and ends with a P = 1 * 5 * 4 * 1 = 20 120 + 120 - 20 = 220 There are 220 ways which we DON'T want! So, since the total is 840, we subtract 840 from 220 to get \(\fbox{620}\) :D EDIT: Sorry I misread the problem! This answer is false. Jul 29, 2020 edited by CentsLord  Jul 31, 2020 #2 0 huh, this actually was wrong. is there another way to do this or was there maybe some double counting Wait i think i know what went wrong, we WANT the sequence to begin with L so idn't think we should have subtracted it from 840. is that correct? Guest Jul 29, 2020 edited by Guest  Jul 29, 2020 #3 +1170 -1 We have 1*6*5*3=90 ways to do this Jul 29, 2020 #4 +1 As "CentsLord" calculated, there are 7 nPr 4 =840 permutations. Each permutation begins with one of the 7 letters this many times =840 / 7 = 120 permutations for each letter. So, letter "L" will begin with 120 permutations. Each of other 6 remaining letters is equally represented in this many ways:120 / 6 =20 ways. So, 120 permutations beginning with the letter "L" will have 20 of them that end in "P". Since we don't want "P" at the end, then will  drop the permutations that end in "P" and we have left: 120 - 20 = 100 permutaions that begin with "L" and NOT end in "P". Jul 29, 2020 #5 +1 Thankyou Guest, that answer was correct and it made alot of sense. Guest Jul 30, 2020 #6 +533 +5 Sorry! Well, I tried :( CentsLord  Jul 31, 2020

crawl-data/CC-MAIN-2021-04/segments/1610703528672.38/warc/CC-MAIN-20210121225305-20210122015305-00780.warc.gz

Have volcanoes slowed global warming here on Earth? A new study is suggesting that massive volcanic eruptions that occurred during the start of the 21st century actually lessened the onset of global warming by cooling our great planet. The Epoch Times reports this Tuesday, Feb. 25, 2014, that this cooling effect has played a major role in countering the warming that greenhouse gases are leaving in their wake, but they may not be aiding us any longer. Published by the Lawrence Livermore National Laboratory, the new study on how volcanoes slowed warming argues that volcanic eruptions in the past have unknowingly served to keep Earth cool and prevent it from feeling the effects of climate change, partly brought on by greenhouse gases. Although the research hints that the overall heat content of the ocean is continuing to increase, global temperatures on our planet’s surface and those within the troposphere — the scientific name for the lowest part of Earth’s massive atmosphere — have not experienced much warming since all the way back in 1988. This cooling effect is currently being called a “slow-down state,” or global warming “hiatus.” This interesting study was published in the journal of Nature Geoscience, discussing that a number of massive eruptions from volcanoes have slowed global warming by injecting plumes of dioxide gas deep into the atmosphere. If these eruptions had the power to actually add dioxide into the higher layer of the stratosphere, then the gas at that point would create very small droplets of sulfuric acid. In turn, these makeshift droplets would then have the ability to reflect some of the sunlight hitting Earth right back into space, having the ability to overall cool the planet’s surface and lower its atmospheric temperature. According to the press release on the volcanoes slowed warming finding: “In the last decade, the amount of volcanic aerosol in the stratosphere has increased, so more sunlight is being reflected back into space,” said Lawrence Livermore climate scientist Benjamin Santer, who serves as lead author of the study, in a statement. “This has created a natural cooling of the planet and has partly offset the increase in surface and atmospheric temperatures due to human influence.” Greenhouse gases levels are said to continue to increase as we push through 2014, however, and these gases have been around since the onset of the Industrial Revolution. Unlike the power of massive volcano eruptions, these gases cool our stratosphere and actually warm the troposphere. Environmental researchers attest that a majority of publicized climate models and theories haven’t yet accurately taken the effects of eruptions into account. “The recent slow-down in observed surface and tropospheric warming is a fascinating detective story,” Santer said. “There is not a single culprit, as some scientists have claimed. Multiple factors are implicated. One is the temporary cooling effect of internal climate noise. Other factors are the external cooling influences of 21st century volcanic activity, an unusually low and long minimum in the last solar cycle, and an uptick in Chinese emissions of sulfur dioxide.” “The real scientific challenge is to obtain hard quantitative estimates of the contributions of each of these factors to climate change and the global warming hiatus.”

<urn:uuid:d43b4917-5148-46ee-b5e6-2bfc78a6f8d5>

A compare and contrast essay focuses on how two items or texts are similar, different, or both. The essay can compare and contrast any number of items including theories, events, books, or people. Here are a few suggestions that will help create a successful comparison and contrast essay: Choose a topic that you can argue. Remember that you need to do more than just list how items are similar or different! Write a clear thesis statement that is true for both items/texts being discussed. Discuss both items equally. Connect the ideas. Students often only summarize information about a point and forget to do comparison. Use transitional words to emphasize how the points are connected. Use the conclusion to restate the thesis, to summarize the main points, and to tell the reader why the findings are significant. There are two ways to organize a compare and contrast essay: The first method is the Point-by-Point method. The second method is the Block method. Either one is acceptable – just make sure that you stick to whatever option you choose. The Point-by-Point method alternates arguments about the two items (A and B) that are being compared contrasted. The pattern is as follows: Point 1 - discuss A Point 1 - discuss B Discussion about overall links between A and B Point 2 – discuss A Point 2 - discuss B Discussion about overall links between A and B This method is often easier for a reader to follow because similarities and differences are more obvious when placed next to each other. For this reason, writers generally use this method for longer essays. Please Note: This method, like the Block method, only offers an outline for the body of an essay. Remember, you also need to include an effective introduction and conclusion. Point-by-Point Method Example Thesis: John Stewart Mill and Michael Bakunin both support three of the basic principles of democracy (government by the people, tolerance, and equality); however, they support them to different degrees and for different reasons. Paragraph 1: Mill believes that the majority makes moral decisions. Paragraph 2: Bakunin believes that public opinion should be the basis of society’s decisions, which is slightly different than Mill’s understanding of a moral majority. Paragraph 3: Mill argues that complete open-mindedness always benefits society. Paragraph 4: Unlike Mill, Bakunin allows freedom of expression to be limited by public opinion. Paragraph 5: Mill claims that we are all equal because mere accident determines what worldview we are born into. Paragraph 6: As with Mill, Bakunin extends equality to all and embraces diversity. The Block Method presents all arguments related to A, and then compares and/or contrasts them to all arguments related to B. This style is a little bit more difficult to use because there is so much space between points about A and points about B; however, it can be useful for shorter assignments. The pattern is as follows: Point 1 about A Point 2 about A Point 1 about B (with discussion about connections to A) Point 2 about B (with discussion about connections to A) Please note: Make sure to present the points in the same order for A and B. There are a couple of common problems that students run into using this method: A lot of students end up simply listing everything about A and then everything about B without actually making connections between them. Students may include the connections in one paragraph towards the end of the essay. Since the entire essay is supposed to make these connections, it will not be effective if the comparisons are not made throughout. To avoid these problems with this structure, make sure to include lots of transitional statements when discussing B, such as “In the same way” or “In contrast to”. This will help the reader to remember information about A, and to understand how A and B are related to each other. Block Method Example Thesis: Same as in Point-by-Point Method Outline. Thesis: Same as in Point-by-Point Method Outline above. Point 1: Mill believes that the majority makes moral decisions. Point 2: Mill argues that complete open-mindedness always benefits society. Point 3: Mill claims that we are all equal because mere accident determines what worldview we are born into. Point 1: Bakunin believes that public opinion should be the basis of society’s decisions, which is slightly different than Mill’s understanding of a moral majority. Point 2: Unlike Mill, Bakunin allows freedom of expression to be limited by public opinion. Point 3: As with Mill, Bakunin extends equality to all and embraces diversity. Essay outlines to download and print are available for both forms of the compare and contrast essay:

<urn:uuid:be056c23-3567-4ee5-adb4-abc4b8b6b046>

Anda di halaman 1dari 5 # CSSS 505 Calculus Summary Formulas ## Differentiation Formulas 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. d n ( x ) = nx n 1 dx d ( fg ) = fg + gf dx d f gf fg ( )= dx g g2 d f ( g ( x)) = f ( g ( x)) g ( x) dx d (sin x) = cos x dx d (cos x) = sin x dx d (tan x) = sec 2 x dx d (cot x) = csc 2 x dx d (sec x) = sec x tan x dx d (csc x) = csc x cot x dx d x (e ) = e x dx d x (a ) = a x ln a dx d 1 (ln x) = dx x 1 d ( Arc sin x) = dx 1 x2 17. dy dy du Chain Rule = dx dx dx ## d 1 ( Arc tan x) = dx 1+ x2 d 1 16. ( Arc sec x) = dx | x | x2 1 Trigonometric Formulas 1. 2. 3. 4. 5. 6. 7. 8. 9. sin 2 + cos 2 = 1 1 + tan 2 = sec 2 1 + cot 2 = csc 2 sin( ) = sin cos( ) = cos tan( ) = tan sin( A + B ) = sin A cos B + sin B cos A sin( A B) = sin A cos B sin B cos A cos( A + B) = cos A cos B sin A sin B 13. tan = sin 1 = cos cot cos 1 14. cot = = sin tan 1 15. sec = cos 1 16. csc = sin 17. cos( 18. sin( 10. cos( A B) = cos A cos B + sin A sin B 11. sin 2 = 2 sin cos 2 ) = sin ) = cos ## Integration Formulas Definition of a Improper Integral b 1. 2. 3. f ( x) dx is an improper integral if f becomes infinite at one or more points of the interval of integration, or one or both of the limits of integration is infinite, or both (1) and (2) hold. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. a dx = ax + C n x dx = ## 12. 13. 14. 15. 16. 17. 18. 19. 1 x dx = ln x + C x x e dx = e + C x a dx = x n +1 + C , n 1 n +1 ax +C ln a ln x dx = x ln x x + C csc x dx = ln csc x cot x + C sec x d x = tan x + C sec x tan x dx = sec x + C csc x dx = cot x + C csc x cot x dx = csc x + C tan x dx = tan x x + C 2 2 2 a x ## dx 1 x = Arc tan + C 2 a +x a dx x = Arc sin + C a a2 x2 dx x2 a2 = x 1 1 a Arc sec + C = Arc cos + C a a a x or ln cos x + C 20. ## cot x dx = ln sin x + C sec x dx = ln sec x + tan x + C Formulas and Theorems 1a. Definition of Limit: Let f be a function defined on an open interval containing c (except possibly at c ) and let L be a real number. Then lim f ( x ) = L means that for each > 0 there ## xa exists a > 0 such that f ( x ) L < whenever 0 < x c < . A function y = f ( x ) is continuous at x = a if i). f(a) exists ii). lim f ( x) exists iii). 1b. 4. Intermediate-Value Theorem A function y = f ( x ) that is continuous on a closed interval a, b takes on every value between f ( a ) and f (b) . xa lim = f (a) xa [ ] Note: If f is continuous on a, b and f ( a ) and f (b) differ in sign, then the equation 5. f ( x) = 0 has at least one solution in the open interval (a, b) . Limits of Rational Functions as x f ( x) lim i). = 0 if the degree of f ( x) < the degree of g ( x) x g ( x) x 2 2x Example: lim =0 x x3 + 3 f ( x) ii). lim is infinite if the degrees of f ( x ) > the degree of g ( x ) x g ( x ) x3 + 2x Example: lim = x x2 8 f ( x) lim iii). is finite if the degree of f ( x ) = the degree of g ( x ) x g ( x ) 2 x 2 3x + 2 2 = Example: lim 5 x 10 x 5 x 2 [ ] 6. ## ( 0 0 ) and (x1, y1 ) are points on the graph of 7. y = f ( x) , then the average rate of change of y with respect to x over the interval [x0 , x1 ] is f ( x1 ) f ( x0 ) = y1 y 0 = y . x1 x0 x1 x0 x ii). Instantaneous Rate of Change: If ( x 0 , y 0 ) is a point on the graph of y = f ( x ) , then the instantaneous rate of change of y with respect to x at x 0 is f ( x 0 ) . f ( x + h) f ( x ) f ( x) = lim h h0 8. ii). 9. ## Rolles Theorem If f is continuous on a, b and differentiable on n 1 lim 1 + = e n + n 1 n lim 1 + n = e n 0 1 10. ## Mean Value Theorem If f is continuous on a, b and differentiable on in f (a) = f (b) , then there is at least one number c in the open interval (a, b ) such that f (c) = 0 . f (b) f (a) = f (c) . ba [ ] [ ] ## (a, b ) such that 11. Extreme-Value Theorem If f is continuous on a closed interval a, b , then f ( x ) has both a maximum and minimum on a, b . To find the maximum and minimum values of a function y = f ( x ) , locate 1. 2. the points where f ( x ) is zero or where f ( x ) fails to exist. the end points, if any, on the domain of f ( x ) . [ ] [ ] 12. 13. Note: These are the only candidates for the value of x where f ( x ) may have a maximum or a minimum. Let f be differentiable for a < x < b and continuous for a a x b , 1. 2. If f ( x ) > 0 for every x in If f ( x ) < 0 for every x in (a, b ) , (a, b ) , ## then f is increasing on a, b . then f [ ] is decreasing on [a, b ] .

crawl-data/CC-MAIN-2020-05/segments/1579251669967.70/warc/CC-MAIN-20200125041318-20200125070318-00066.warc.gz

What Does Acidic Deposition Mean? Acidic deposition is a phenomenon that occurs when sulfur and nitrogen in the atmosphere combine to form acidic compounds that are deposited on the surface of the earth. These deposits can be either wet or dry, and the sources of these elements can be either natural or man-made. Acidic deposition is one of the conditions that may be discovered during soil testing prior to trenchless construction operations. Trenchlesspedia Explains Acidic Deposition The formation of acid that results in acid deposition takes place in the atmosphere. Sulphur dioxide, for instance, is oxidized to form sulphuric acid. Acidic deposition can be either wet, in the form of acid rain or acid snow, or dry, as in gases or particulates. Acidic deposition can have a negative effect on the chemistry of the soil. While natural activities such as volcanic eruptions contribute to the formation of acids in the atmosphere that result in acidic deposition, scientists point to human activities as its main cause. Power plants trigger the process by releasing sulphur dioxide and nitrogen oxide into the air. Soil sampling is an important aspect of trenchless construction projects. The quality of the soil influences the entire operation. Horizontal directional drilling is also being used to collect soil samples.

<urn:uuid:66522e35-0c80-4302-b751-5534a3874ad7>

Select Page # Pythagorean Theorem Visual Representation Through Inquiry ## Tapping It Up a Notch: Pythagorean Theorem – Part 1 Over the past school year, I have been making attempts to create resources that allow students to better visualize math, build spatial reasoning skills and make connections to the algebraic representation. While some hardcore mathletes might balk at much of these attempts as not being real mathematical proofs, my intention is to help students (especially struggling students) visualize and make sense of why we do what we do. Too often, when a student asks us “why” a formula works, we are quick to show an algebraic proof that likely means very little to the student. If a student does not have the required algebraic understanding mathematically, one (or both) of these two possibilities may result: • The student may get more confused and frustrated, or • The student may never ask a question like that again. I am definitely not trying to suggest that algebraic proofs are not important, because they definitely are. They are important when students are comfortable enough with the algebraic language of math. Until then, the proof serves little purpose. For Pythagorean Theorem, showing some visual representations and making connections to the algebra are great places to start in middle school and intermediate divisions. ## Using Pythagorean Theorem to Find the Length of the Hypotenuse ### Visual Representation of a 3, 4, 5 Right Triangle In the following video, I believe starting with a simple example and making the visual connection early is important. You’ll notice that the Pythagorean Theorem is being used, but without any formal algebraic representation. Check out the video below and the screenshots that follow for a quick visual: ## Summary of Pythagorean Theorem Video ### Starting With a Simple Example Visually Selecting a right-angle triangle with friendly numbers that yield perfect squares such as 3, 4 and 5 is a great place to start. Ensuring students have an understanding of what the hypotenuse is and how you can quickly identify it is important prior knowledge. ### Making a Visual Connection to Squaring a Number Many students have a really difficult time understanding that squaring a number can be represented as multiplying two numbers in an array. I often suggest that squaring a number gives an area since we are multiplying two numbers and thus yields 2 dimensions. Here, squaring 3 and 4, we get an area of 9 and 16 respectively: ### Visually Proving Sum of the Squares of Two Shorter Legs Equals Square of Hypotenuse I want to make sure my students don’t just “do stuff” in math because the teacher said so. I want them to get some of the background behind how a formula was created and give some perspective of how much work had to be done to actually realize that a pattern exists. This example doesn’t give us confidence this will always work, but it surely gives students something to peg their understanding to when they need to utilize Pythagorean Theorem in the future. Here, we use unit algebra tiles to show the area of the squares of both legs: ### Watching the Squares of the Legs Add to Square of Hypotenuse In the video, students can watch the unit tiles move from the squares of the legs to the square of the hypotenuse to see that they do completely fill the square of the hypotenuse: Now, we can start discussing to see if we can make a generalization here. ### Finding the Length of the Hypotenuse Sometimes you may have to redirect students to what the original question was. Did we want to find out the square of the hypotenuse or the length of the hypotenuse? Without much effort, students can typically tell you the length without necessarily thinking about the opposite operation involved. This is fine at this point, but making a connection to what they actually did in their head to find it will be important moving forward: You’ll notice in this video and from the screenshots that we haven’t even introduced the actual formula yet. I hope you find this video useful as you look to try and develop the formula together with your students and then begin advancing to an all algebraic approach once students are comfortable and confident with the concept. Check out the next post in this series as you scaffold students forward with Pythagorean Theorem shortly… What do you think? How can we improve the introduction of this very important mathematical concept? Leave a comment below! ## Other Related Pythagorean Theorem Posts: [postshortcode the_query=”post_type=post&p=14156″] [postshortcode the_query=”post_type=post&p=14185″] [postshortcode the_query=”post_type=post&p=14649″] [threeactshortcode the_query=”post_type=realworldmath&p=3760″] ## WANT TO LEARN HOW TO TEACH THROUGH TASK? Download our Complete Guide to successfully implementing our Make Math Moments 3-Part Framework in your math class! ## Share With Your Learning Community: I’m Kyle Pearce and I am a former high school math teacher. I’m now the K-12 Mathematics Consultant with the Greater Essex County District School Board, where I uncover creative ways to spark curiosity and fuel sense making in mathematics. Read more.

crawl-data/CC-MAIN-2024-22/segments/1715971059143.84/warc/CC-MAIN-20240528154421-20240528184421-00587.warc.gz

By Alex Kirby, Climate News Network This piece first appeared at Climate News Network. LONDON—Scientists believe they have made significant progress towards explaining why global average surface temperatures have risen more slowly this century than previously. They say cooling waters in the tropical Pacific Ocean have played a large part in slowing recent warming, a finding which challenges those who argue that the slowdown means climate change is not as serious a problem as most climate scientists are convinced it is. Before 2000 global temperatures had risen at a rate of 0.13ºC per decade since 1950. The hiatus has occurred while levels of carbon dioxide, the main greenhouse gas from human activities, continued a steady rise, reaching 400 parts per million for the first time in human history in May this year. The eastern tropical Pacific has been distinctly cooler in the last few years, thanks to the influence of one of the world’s biggest ocean circulation systems, the Pacific decadal oscillation (PDO). The better-known El Niño and La Niña weather systems, which also originate in the Pacific and can affect the weather thousands of miles away, occur just a few years apart. Both are parts of the much bigger PDO, which comes and goes over decade-long timescales. It is now in a cooling phase which could last for years – the last one stretched from the 1940s to the 1970s when warmer, drier weather dominated in the midwestern US. In such a phase the temperature of the eastern Pacific’s waters falls while those in the west warm. In the oscillation’s warming phases this is reversed. In winter the PDO’s cooler phase lowers northern hemisphere temperatures slightly, but in the summer this cooling has less impact. The scientists are from the Scripps Institution of Oceanography in California. Their study is published in the journal Nature. Dan Barrie, programme manager at the US National Oceanic and Atmospheric Administration (NOAA), which supported their research, called it “compelling” and said: “[It] provides a powerful illustration of how the remote eastern tropical Pacific guides the behaviour of the global ocean-atmosphere system, in this case exhibiting a discernible influence on the recent hiatus in global warming.” The Scripps team, using computer models, compared their results with observations and concluded that global average annual temperatures have been lower than they would otherwise have been because of the oscillation. But they say the observed recent higher summer temperatures show more of the true effects of global warming. Global average temperatures are calculated over the whole year, blurring the effect of this seasonal variation. Shang-Ping Xie, professor of environmental science at Scripps and co-author of the study, said: “In summer, the equatorial Pacific’s grip on the northern hemisphere loosens, and the increased greenhouse gases continue to warm temperatures, causing record heat waves and unprecedented Arctic sea ice retreat.” Oceans’ key role Dr Alex Sen Gupta, of the Climate Change Research Centre at the University of New South Wales, who was not part of the study team, told the London Guardian: “The authors have set up some elegant experiments using a climate model to test whether a natural oscillation that has gone through a large swing in the tropical Pacific Ocean over the last decade can explain the recent halt in surface global warming… “…[T]he new simulation accurately reproduces the timing and pattern of changes that have occurred over the last four decades with remarkable skill. This clearly shows that the recent slowdown is a consequence of a natural oscillation.” Research shows that much of the heat caused by global warming has been absorbed by the oceans, and about a third of the extra carbon dioxide emitted since the Industrial Revolution. Scientists also think the heat is not staying near the ocean surface but is now penetrating to deeper water, and that this may be another factor which can create the impression of a slowdown in global warming. In any case, they say, the slower pace of recent warming is easily explained by natural climate variability – such as the PDO. The Scripps scientists say that when the PDO’s cooling phase ends the growth of global average temperatures is likely to resume, perhaps faster than before as greenhouse gas emission rates will be higher. super devoika (CC BY 2.0)

<urn:uuid:2b843272-2dae-47b3-9b96-85bcb29c573c>

Mar. 5, 2008 Exposed skin cells weather conditions harsh enough to mutate DNA. To keep these mutations from spreading, evolution has found a way to keep these cells from proliferating. Rockefeller University and HHMI researchers have now discovered evolution's solution: a tiny strand of RNA. But the research's implications go deeper, and may also suggest how healthy cells elsewhere in the body can turn cancerous. Every minute, 30,000 of our outermost skin cells die so that we can live. When they do, new cells migrate from the inner layer of the skin to the surface of it, where they form a tough protective barrier. In a series of elegant experiments in mice, researchers at Rockefeller University have now discovered a tiny RNA molecule that helps create this barrier. The results not only yield new insight into how skin first evolved, but also suggest how healthy cells can turn cancerous. Hundreds of these tiny RNA molecules, called microRNAs, are expressed in skin, "But there was something curious about one in particular, microRNA-203," says Rui Yi, a postdoc who works with Elaine Fuchs, head of the Laboratory of Mammalian Cell Biology and Development. "As an embryo develops, the expression of microRNA-203 jumps very quickly over just two days. From being barely detectable at day 13, this microRNA becomes the most abundant expressed in skin," says Yi, whose work will be published as an advance online publication in Nature March 2. MicroRNAs, which were discovered in mammals in 2001, regulate genes outside of the cell's nucleus. Yi and Fuchs, who is also a Howard Hughes Medical Institute investigator and Rebecca C. Lancefield Professor at Rockefeller, found that during the 13th day of development, mouse skin is primarily composed of undifferentiated stem cells. Two days later, these stem cells exit the inner layer of the skin and begin to differentiate into cells that form the outermost, protective layer. MicroRNA-203's expression skyrockets precisely during this period, suggesting that it plays some key role in the barrier's development. In order to figure out its role, Yi and Fuchs needed to pinpoint exactly where microRNA-203 is expressed. Other microRNAs have been found to be specific to heart and muscle tissues; some exist almost exclusively in the brain. However, this microRNA was found only in very specific types of skin -- stratified epithelial tissues, to be exact -- and only in this skin type's outer layers. What's more, this expression pattern is identical to that found in humans, zebrafish, chickens and the like -- in other words, vertebrates that evolved more than 400 million years apart. "If it has been expressed in this very specific tissue for a long time and across several species, it means that it probably plays an important role there," says Yi. To find out its function, Yi, in one set of experiments, used a genetic technique to precociously express microRNA in the inner layer of the skin, where stem cells proliferate at a fast clip. In a second set of experiments, he blocked microRNA-203 from functioning in the outer layer using an antagomir, a molecule that binds directly to microRNA-203 and shuts down its ability to carry out its function. In the first set, he found that the stem cells proliferated significantly less than they did when microRNA-203 wasn't expressed, and, as a result, the mice formed very thin skin -- hardly a protective layer at all. The stem cells, the researchers saw, lost their ability to proliferate not because microRNA-203 killed them off but because it suppressed the activity of a molecule called p63, whose job is to keep cells, primarily stem cells, proliferating. In the second set of experiments, Yi found that the cells in the outer layer proliferated significantly more than they did when microRNA-203 was expressed. The reason: because microRNA-203 wasn't available to shut down p63's busy work. "We found that microRNA-203 acts to stop the translation of the p63 protein," says Fuchs. "The result is a swift transition from proliferating stem cells within the innermost layer of the epidermis and terminally differentiating cells as they exit this layer and move outward to the skin surface." The findings have intriguing implications for cancer, since p63 is found in excess in cancer cells. "As a next step, we are going to examine whether low expression of microRNA-203 is associated with squamous cell carcinomas," says Fuchs, "and whether by putting back microRNA-203 we can inhibit the growth of these cancer cells." Other social bookmarking and sharing tools: Note: Materials may be edited for content and length. For further information, please contact the source cited above. Note: If no author is given, the source is cited instead.

<urn:uuid:34ea914b-1cbd-4f96-98cd-4f651b19a3d8>

from Volume 82 of American Scientist In some future history, 1994 may be remembered as the year that the warp drive was first conceived to be a physical possibility. Long a cliche' of science- fiction writing, the warp drive has transported countless fictional characters through light-years of interstellar space in the time it takes for you or me to travel to the market. Unfortunately for real-world travelers, the warp drive has always been thought to be inconsistent with the laws of physics. But all this has changed. In the May issue of Classical and Quantum Gravity, Miguel Alcubierre, a physicist at the University of Wales describes a space-travel scenario that bears an uncanny resemblance to the warp drive of science fiction. With Alcubierre's warp drive, we could reach any place in the universe in as short a time as we please! The warp drive envisioned by Alcubierre is made possible by the subleties of Einstein's general theory of relativity. According to Einstein, spacetime (the union of the three dimensions of space with the dimension of time) is not an inert substrate, but rather a dynamical entity that twists and distorts under the influence of concentrations of energy. Alcubierre suggests that it might be possible to exploit this phenomenon to travel from one star to another faster than the speed of light. This could be done by creating a disturbance in spacetime such that the region directly in front of a spaceship is contracted while the region directly behind the spaceship is expanded. This distortion of spacetime would, in effect, propel the spaceship forward like a surfer riding the crest of a breaking wave. At first glance this mechanism would appear to violate Einstein's special theory of relativity, which holds that no object can travel faster than light. Violations of this law lead to causal paradoxes, in which actors in the present can alter their own past. Yet Alcubierre shows that his warp drive does not, in fact, lead to such violations. The reason is that light also travels in spacetime, and is carried along just as the spaceship is. The light beam is still traveling at the speed of light, relative to the spaceship, which itself is not accelerating relative to the spacetime in its immediate vicinity. Although Alcubierre's warp drive does not engender any causal paradoxes, one might still be concerned for a space traveler's welfare. To get to a distant star and back in only moments, the traveler would have to be accelerated at a very large rate, effectively turning him into soup. Or at least this would be true, if not for the fact that accelerations are relative in general relativity. Although the acceleration of the spaceship as seen by someone on Earth would be enormous, the acceleration experienced by the space traveler would be zero! The space traveler would be weightless, just as astronauts are in orbit around the Earth. Finally, Alcubierre also shows that a traveler using his warp drive would experience no time dilation. One of the predictions of Einstein's special theory of relativity is that time flows at different rates (Keely said that 'Time is Gravity') for observers moving relative to one another. Consider two space travelers, John W. and Campbell Jr., who decide to visit the great galaxy of Andromeda, which is about 2 million light-years away. John travels in a spaceship that advertises "one Earth gravity all the way." Campbell spends most of the trip traveling near the speed of light. Because of time dilation, Campbell is able to survive the trip, aging only 60 years in the process. However, because the galaxy is 2 million light years away, about 4 million years pass on Earth before Campbell gets home. In contrast, John is able to make the journey to the galaxy and be back in time for supper on Earth! Of course, there is no such thing as a free lunch (or supper). The key to Alcubierre's warp drive is something called exotic matter. Exotic matter has the curious property of having a negative energy density, unlike normal matter (the stuff that makes up people, planets and stars), which has a positive energy density. Two bits of matter that have the same energy density are attracted to each other by gravity. In contrast, bits of positive and negative energy matter would be repelled by gravity. It is the negative energy density of exotic matter that powers the warp drive. A negative energy density is not the nonsensical thing it appears to be. Indeed, in 1948 the Dutch physicist Hendrik Casimir first predicted that one could observe the effects of negative energy densities. He reasoned that if negative energy densities existed, two closely spaced parallel conducting plates in a vacuum would be attracted to one another. This phenomenon, now called the Casimir effect, was measured in 1958 by M. Sparnaay, and is usually taken to be a confirmation that negative energy densities are possible. Exotic matter of a slightly different type is also invoked in the modern theory of cosmology known as inflation. According to the theory of inflation, exotic matter in the early universe (moments after the big bang) had a positive energy density, but a very large negative pressure. The negative pressure was so large that it counteracted the effects of the positive energy density. The result was an expansion of spacetime so rapid that two observers originally very close to each other would be carried apart faster than the speed of light. This paradigm of spacetime expansion provided the motivation for Alcubierre's warp drive. There are, of course, 'technical details' to be worked out before the aerospace firms can start building starships. Foremost among these is the production of exotic matter. Alcubierre has not given that aspect of the problem much thought. Although he is an avid reader of science fiction, he does not intend to pursue the subject much further. Currently, he spends most of his time working on other problems with general relativity. The warp-drive scenario, he says, is a very simple thing that he came up with in his spare time. Perhaps the problem will be taken up by some future physicists in their 'spare time'. The rewards could be astronomical.

<urn:uuid:6ea3b4d2-2f7a-4e9b-bb8e-504e2554d46a>

Definition of Mesothelin Mesothelin: A protein attached to the cell surface that is thought to have a role in cell-adhesion and possibly in cell-to-cell recognition and signalling. Mesothelin is so named because it is made by mesothelial cells. A monoclonal antibody, which recognises mesothelin, binds to the surface of cells from mesotheliomas and some other tumors but not to healthy tissues except for mesothelium. A blood test for soluble mesothelin-related proteins (SMR) can be used to identify people with mesothelioma and to monitor the progression of their disease. More patients with mesothelioma have raised concentrations of SMR than do those with other cancers or other inflammatory lung or pleural diseases. SMR concentrations also correlate with the size of the tumor and increase during tumor progression. The mesothelin gene MSLN is on chromosome 16. Last Editorial Review: 6/14/2012 Back to MedTerms online medical dictionary A-Z List Need help identifying pills and medications?

<urn:uuid:11f05cf2-b23d-4994-a69f-582fed1e1f5c>

Even nearly seven decades after the Independence, nearly one-third Indians live in a state of extreme poverty. Majority of the people are still marginalised and don’t have access to basic amenities like education, health and sanitation. Despite billions spent each year on social welfare programmes, why India remains home to the world’s largest poor, illiterate and malnourished, analyses Gyanendra Keshri Under the Millennium Development Goals (MDGs), India along with other developing countries, has committed to eradicate extreme poverty. The deadline to achieve the goal is 31st December 2015. However, according to a recent United Nations report, nearly 300 million people still live in extreme poverty in India and face deprivation in terms of access to basic services, including education, health, water and sanitation. In the recent years there have been a lot of debates over the definition of poverty line and thus the number of poor. The Planning Commission in a report released in 2013, put the number of people below poverty line at 22 per cent of the total population—25.7 per cent in rural areas and 13.7 per cent in urban areas. However, as per the definition given in Rangarajan Committee report released in 2014, 29.5 percent of India’s population is below poverty line. There might be disputes over the numbers and criteria for identification of poor, but the ground reality is that poverty remains one of the most pressing challenges facing the country. Even 68 years after the Independence, people are still dying of hunger and don’t have access to basic amenities like education, health and sanitation. In early 1970s the federal government gave a slogan “Garibi Hatao” (remove poverty). A number of schemes were introduced in 1970s and the successive governments kept adding schemes and programmes, reiterating their pledge to eradicate poverty. Despite billions spent on such programmes each year, almost one-third of the total population still remains in a state of abject poverty. Until now the basic approach has been subsidies and other government doles. It can provide only temporary relief. Doles cannot break the vicious circle of poverty. This circle can be broken only if the people are empowered through jobs and provided good education and health facilities. Union Minister for Minority Affairs Najma Heptulla, who is active in politics for almost four decades, agrees that the government initiatives have not delivered the desired results. “Since early days we have been talking about poverty alleviation… a number of schemes have been introduced aimed at removing poverty. I am not saying that nothing has happened. But surely the pace has not been good,” she says. Why has the pace been not good? Why despite billions spent, the vicious circle of poverty continues? Most of the people whose father and forefather were poor continue to remain poor. It’s not that they have not got any government support. But the approach has been faulty. Until now the basic approach has been subsidies and other government doles. It can provide only temporary relief. Doles cannot break the vicious circle of poverty. This circle can be broken only if people are empowered through jobs and provided good education and health facilities. The money should be used in creating sustainable assets. Heptulla says subsidies must be directed at finding permanent solution. “Every penny spent should bring some result. It should be productive. It should have some permanent solution,” she says. But, where the jobs will come from? Is the government in a position to provide the jobs? India is adding over 12 million people to the workforce every year and millions are perennially unemployed. Poor are mostly unemployed or underemployed. Union Minister for Women & Child Development Maneka Gandhi says the government cannot create the kind and number of jobs required. “I must admit that the government jobs are not there. At least ₹1 crore is being spent on creation of one job. There are very few government jobs left,” she says. She says the most effective way of eliminating poverty and empowerment of people would be providing jobs through promotion of self-employment and entrepreneurship. Jobs are particularly important in case of women as they are subject to domestic violence and exploitation due to their dependence on male members. The challenge is not just how to bring the poor out of the vicious circle, but also the identification of the genuine beneficiaries. Different committees have suggested different benchmarks for the so-called poverty line. While Rangarajan Committee termed people spending below ₹32 in rural areas or ₹47 in urban areas as poor, Tendulkar panel put these figures at ₹27 and ₹33 for rural and urban areas, respectively. The Millennium Development Goals, set in 2000 on the initiative of the United Nations, will expire in December this year. Now the plan is to start Sustainable Development Goals (SDGs). While under the MDGs there are eight goals and 18 quantified and time-bound targets, SDGs mull 17 goals and 169 targets. The United Nations has already released an initial draft for SDGs, which has broader agenda than MDGs. The United Nations General Assembly is likely to prepare and adopt the new goals under SDGs in its September 2015 meeting. Eight goals under MDGs are: The problem with India is not just slow progress on MDGs but also the uneven progress. While some states, notably the southern states like Tamil Nadu, Kerala and Karnataka have performed well and surpassed the targets, northern and eastern states like Bihar, Uttar Pradesh, Odisha and West Bengal remain laggard. Therefore, the bigger challenge for India is to ensure sustainable and balanced development. Unless the states like Uttar Pradesh and Bihar are taken on board, India cannot achieve development targets. Microfinance is an important tool to empower the poor. It can not only bring the poor out of the clutch of rapacious moneylenders but also promote self-employment and entrepreneurship. One of the main reasons for several of India’s social welfare programmes not achieving desired results is widespread leakages in the system. It has been a perennial problem. The combination of Jan Dhan, Aadhaar and Mobile, which the government in the recent budget termed as “JAM Trinity” would be a game-changer in plugging leakages and ensuring that the benefits reach the targeted people. JAM stands for Jan Dhan, Aadhaar and Mobile. The government announced in the Union Budget for 2015-16 that these three would be used in transfer of subsidies and benefits of other social welfare schemes. JAM is likely to transform the way social security programmes function. Bank accounts opened under the Prime Minister Jan Dhan Yojana (PMJDY), Aadhaar and mobiles would together help eliminate duplications and make the process faster and more reliable. The positive impact is already visible. Neeraj Mittal, Joint Secretary (Marketing), Ministry of Petroleum and Natural Gas, says because of Aadhaar the government has identified over 10 million bogus LPG connections in the last one year. Just the LPG-Aadhaar linkage (DBTL) has resulted in savings of thousands of crores of rupees, which could be utilised for poverty alleviation programmes and social sector schemes. “A lot of people were having gas connections in fake name. Some were having multiple connections. In the past one year we have identified and blocked over 1 crore such connections,” Mittal said, adding these became possible only because of Aadhaar. Principal Secretary-Cooperatives in the Government of Madhya Pradesh Ajit Kesari says the JAM would help plug leakages and ensure that benefits reach the genuine targeted people. The government claims that over 125 million bank accounts have been opened under the Jan Dhan scheme, which was launched in August 2014. While bank accounts enable transfer of money directly to the beneficiary, Aadhaar helps in identification of the real beneficiary. According to Rajesh Aggarwal, Joint Secretary, Department of Financial Services in the Ministry of Finance, the plan is to further widen the use and scope of Aadhaar. Under the proposed e-sign scheme, Aadhaar fingerprint can be used as digital signature. So, Aadhaar users would be able to self-certify electronic documents without having physical digital signature dongle. The DigiLocker facility would allow users to keep all their certificates and official documents in a digital form online and access them using Aadhaar numbers. Referring to the recent Supreme Court order that Aadhaar cannot be made mandatory for social welfare schemes, Founder and Chairman of Suvidhaa Infoserve Paresh Rajde said the government must take steps to fend off legal confrontation and remove uncertainty over the scheme touted as the world’s largest biometric identity exercise. The combination of Jan Dhan, Aadhaar and Mobile, which the government in the recent budget termed as “JAM Trinity” would be a game-changer in plugging leakages and ensuring that the benefits reach the targeted people. Microfinance is an important tool to empower the poor. It can not only bring the poor out of the clutch of rapacious moneylenders but also promote self-employment and entrepreneurship. Explaining the importance of microfinance in fighting poverty, Reserve Bank of India (RBI) Deputy Governor S S Mundra says, “It basically works on the premise that it is better to teach someone to fish rather than simply giving them a fish. It gives the poor the necessary tools, skills and resources to help them engage in productive activities and grow their way out of poverty.” Millions of poor still don’t have access to basic savings and credit services. Jan Dhan scheme has succeeded in opening bank accounts. If we go by the government data, almost all the households in the country now have a bank account. Now, the challenge is to ensure that these accounts are actually used for the normal banking purposes. The plan is to extend a microcredit of `5,000 on satisfactory operation of the account. Even this small credit would play a significant role in lifting the people out of poverty, provided an enabling environment is created. Some 50 women of a tribal-dominated Mohgaon village in Mandla district of Madhya Pradesh have taken 72 acres of land on lease to do group farming. This land belongs to a person who does not live in the village and thus the land was not properly cultivated. These women together arranged ₹115,000 to pay as lease for the land. In one year, women have been able to save around ₹25,000 each after incurring all expenditure. The group farming has proved a win-win proposition for all—the women, the landlord as well as the economy as a whole. Women now have sufficient food, a small saving and a work to do in the field, the landlord is getting a reasonable lease rent and the economy is benefiting by higher food grain output, which is adding to the overall growth. All this became possible because of the Self Help Groups (SHGs). These tribal women belonging to different SHGs mobilised savings over the years and paid for the lease rent. Productivity went up substantially because they are working as a group. Currently, around 7.4 million SHGs representing 97 million rural households are operating in India. Started on the initiative of NABARD in 1992, this is the worldís largest microfinance initiative today. Another good thing about the SHGs is that it is predominantly led by women, the most marginalised section of the society. Out of around 7.4 million SHGs, 84 per cent are women SHGs. They have ₹80 billion savings in bank as on 31st March 2014, while the bank loan outstanding against women SHGs is over ₹360 billion. Millions of poor still don’t have access to basic savings and credit services. Jan Dhan scheme has succeeded in opening bank accounts. If we go by the government data, almost all the households in the country now have a bank account. Now, the challenge is to ensure that these accounts are actually used for the normal banking purposes. The SHGs outreach should be further expanded and proper banking facilities should be extended to them. SHGs are already playing an important role in promoting self-employment and entrepreneurship. The need of the hour is to broaden its base. The Reserve Bank of India has decided to issue licenses for a new category of banks or differentiated banks. It includes Payments Banks and Small Finance Banks. According to the central bank, the primary objective of setting up of Payments Banks is to further financial inclusion by providing (i) small savings accounts; and, (ii) payments/ remittance services to migrant labour workforce, low income households, small businesses, other unorganised sector entities and other users, by enabling high volume-low value transactions in deposits and payments/remittance services in a secured technology-driven environment. Theoretically it sounds good. A large proportion of the population is underserved or is out of the banking net. So the steps must be taken to widen the infrastructure. But, will it be able to provide the required infrastructure? Differentiated banks are not new to India. We already have Regional Rural Banks (RRBs) and Local Area Banks (LABs). In fact, there are many layers in India’s banking structure. There are 157 commercial banks as on 31st March 2014. This includes 26 public sector banks, 20 private banks, 43 foreign banks, 64 RRBs and 4 Local Area Banks. Then we have cooperative banks, specialised lenders like EXIM Bank, SIDBI, NABARD, IIFCL, Non Banking Financial Companies (NBFCs) and microfinance institutions. Still majority of the population is either out of the banking net or is underserved. Just adding one more layer, say in the form of Payments Banks, is unlikely to make any significant impact on the financial inclusion drive. First of all, they won’t be providing credit facilities, also there is no clarity on how will they raise money to run and expand business. India already has a wonderful infrastructure in the form of post offices. India’s banking network can more than double just by bringing postal network on board. The number of post offices in India is over 155,000 which is substantially higher than the total number of bank branches. As on 31st March 2014 the total number of bank branches in India stood at 1,15,082. Out of these 43,962 branches or 38.2 per cent of the total was in the rural areas. Compare it with the post offices. Out of 155,000, 1,39,144 or 89.76 per cent of the total post offices are in rural areas, as per 2011 census. Thus, India Post would not only bridge the infrastructure gap in banking sector, but also address the main challenge of ensuring the services in rural area, that remain largely unbanked and the commercial banks show little interest in reaching out to these areas. Moreover, post offices are already providing basic banking services. These accept deposits, pay out cash and offer the services like e-payments, forex and remittance. Through various savings schemes, the Post Office system handles deposits to the tune of ₹6 trillion. The need of the hour is to arm it with modern technology and ensure proper regulation by providing licence either by RBI or empower it through an Act of Parliament. MUDRA Bank will help small entrepreneurs like shopkeepers, vendors and SHGs to meet their funding requirements. The Bank will have a corpus of `200 billion and a credit guarantee corpus of ₹30 billion. It will refinance financial institutions like banks for lending to small businesses and entrepreneurs covering loans from ₹50,000 to ₹1 million. To address the issue of lack of access to funds by small entrepreneurs, the government has launched a scheme called Pradhan Mantri MUDRA Yojana. MUDRA stands for Micro Units Development and Refinance Agency. This will refinance financial institutions like banks for lending to small businesses and entrepreneurs covering loans from ₹50,000 to ₹1 million. It will help the small entrepreneurs like shopkeepers, vendors and SHGs to meet their funding requirements. The Bank will have a corpus of ₹200 billion and a credit guarantee corpus of ₹30 billion. While launching the scheme on 9th April 2015 in the national capital, Prime Minister Narendra Modi said MUDRA Bank would provide “funding to the unfunded.” He pointed out that while there are a number of facilities provided for the large industries in India, there is a need to focus on 57.5 million self-employed people who use funds of ₹11 trillion, with an average per unit debt of merely ₹17,000 to employ 120 million Indians. Small and medium enterprises play a critical role in the Indian economy. They can play a very significant role in poverty alleviation and empowerment of the marginalised. MSMEs are the second largest employer after agriculture. They contribute 45 per cent to the total industrial output, 40 per cent to exports and 8 per cent to the country’s GDP. You may recall the movie called ‘Roti, Kapda aur Makaan’ in the early 1970s, which was a reflection of what was going on at that time – extreme inflation, extreme... It is felt that the IBC or the Insolvency Bankruptcy Code has been a game-changer in economic legislation. Five years into its introduction, the IBC is a well-oiled apparatus, with... The biggest regret expressed by Ram Sewak Sharma in the book ‘The Making of Aadhaar’ is the limitation on the usage of Aadhaar. Peculiarly, I share this regret. Consent-based widespread... Five simple policy actions can be of enormous help to MSMEs to tide over the COVID crisis. These can be implemented even during the lockdown. State Rankings Highlights Andhra Pradesh retains number one.. Step 1: Call for Project Submission Call for.. West Bengal has come to be synonymous with.. It was the morning of 16th February 2021,.. Inclusion is the first magazine dedicated to exploring issues at the intersection of development agendas and digital, financial and social inclusion. The magazine makes complex policy analyses accessible for a diverse audience of policymakers, administrators, civil society and academicians. Grassroots-focused, outcome-oriented analysis is the cornerstone of the work done at Inclusion.

<urn:uuid:dcc5ec69-acf6-42ab-a5f4-d678d6ee942b>

[–] 0 points1 point  (0 children) even easier than that..... too much work: http://www.youtube.com/watch?v=xz1UzJHAKHo [–] -1 points0 points  (0 children) [–] 0 points1 point  (0 children) for nx , it is useful. I know that my professor said "nx derived is just nx * d/dx (x) * ln (n) .... but that is because of logarithmic differentiation. We were never told why, just "memorize, memorize, memorize....." [–] 1 point2 points  (0 children) I came on this post to suggest Paul's Online Notes.... these helped me get through Calculus I, II, & III and now because of my success with these notes I am a large group tutor for all of these courses. Highly recommended. Just be sure to understand all of the examples he lays out. All of them, even the hard ones. [–] 0 points1 point  (0 children) [–] 1 point2 points  (0 children) [–] 0 points1 point  (0 children) Here is a trig review that is very helpful for calculus courses, as you will encounter trig quite a lot. http://www.youtube.com/watch?v=xz1UzJHAKHo [–] 1 point2 points  (0 children) You want to look at each side of the plus sign, term by term. Take, for example x2 + x5 . If I asked you to factor that, you would probably factor out an x2 , right? You could right it then as x2 * ( 1 + x3 ). Does this make sense? If so, continue reading. So, we use the same methodology in your equation above. Look at each side of the plus sign and ask yourself "What do I have in common?". We have AT LEAST 2x on each side, so factor out a 2x. Also, we have AT LEAST (x-2)3 on each side, so factor that out. Then, write (2x)(x-2)3 * (whatever is left on the left + whatever is left on the right). Does this make sense? PS: Sometimes, with the chain rule, you may have to factor with negative exponents. Always factor the more negative number. [–] 0 points1 point  (0 children) woah woah woah... you wrote (5-7x)2 is (25 - 49x2)... This is incorrect. You need to multiply (5-7x)(5-7x), if you wish to do that. PEMDAS. Then, all you need to do is a 'u' substitution, where u= (7x-5). Then you have 1+u2, which is u2 +1, and this looks a lot like tan2 (x) + 1 = sec2 (x)... [–] 0 points1 point  (0 children) [–] 0 points1 point  (0 children) *i realize i have the same name as the video poster, but this is not self-promotion :-) good luck! [–] 0 points1 point  (0 children) easy way to memorize trig that i just stumbled across that helped me out a lot..... http://www.youtube.com/watch?v=xz1UzJHAKHo [–][S] 0 points1 point  (0 children) I'm afraid this tutoring this kind of a one-time offer from my boss as it is not likely to come to fruition five years down the road. Also, I am terrified I will hate teaching in inner city NY [–] 0 points1 point  (0 children) I would start by discussing the variance of a Poisson distribution, and then jump into stochastic integrals, and then go back to the variance of a binomial. [–] 1 point2 points  (0 children) Here is a video I made to help people with their trig. I think it might help you out a lot if I understand your position correctly. http://www.youtube.com/watch?v=xz1UzJHAKHo&feature=youtu.be [–][S] 1 point2 points  (0 children) It was said to be a function; however, the answer uses the positive square root, which is 3. math homework-help needed by in math [–] -2 points-1 points  (0 children) The tangent line is y - y1 = f ' (x1) [x-x1]. So, what you need to do is plug in x = 1 into the original function, find the corresponding y-value. These are your x1 and y1 values. You have to use both functions. Use the derivative to find f ' (x1), and the original function to find the right x1, y1 points.

crawl-data/CC-MAIN-2017-22/segments/1495463614615.14/warc/CC-MAIN-20170530070611-20170530090611-00038.warc.gz

# Fitted Curve Plot Analysis The fitted curve as well as its confidence band, prediction band and ellipse are plotted on the Fitted Curves Plot, which can help to interpret the regression model more intuitively. ## Confidence and Prediction Bands How can we know whether the actual y value (or the mean value of y) is different from$\widehat{y_i}$at a particular x value $x_p\,\!$? We can resort to the confidence intervals. Given a confidence level α, we can calculate the confidence interval forby$\widehat{y}/x_p$: $\widehat{y}\pm t_{\alpha /2}(Estimated\;standard\;error\;of\;\widehat{y}) \,\!$ In the following figure, for a chosen confidence level (95% by default), the confidence bands show the limits of all possible fitted lines for the given data. In other words, we have 95% confidence to say that the best-fit line (possibly one of the dash lines in the figure below) lies within the confidence bands. $\widehat{y}\pm t_{\alpha /2}(Estimated\;standard\;error\;of\;\widehat{y}) \,\!$ From the expression of confidence interval, we know that the width of the confidence band is proportional to the standard error of predicted y value, $s_\epsilon\,\!$. So the band will become narrower as the standard error decreases; if the error is zero, the confidence band will "collapse" into one single line. Besides, the term $(x_p-\overline{x})^2$ can also affect the band width. The further $x_p\,\!$ is from $\overline{x}\,\!$, the greater $(x_p-\overline{x})^2$ becomes. Therefore, the confidence bands usually flare outward near the ends of the data range. The case of prediction band is similar, but it uses a different expression: $\widehat{y}\pm t_{\alpha /2}(Estimated\;standard\;error\;of\;prediction) \,\!$ It is different from the expression of confidence interval in that there is a constant term. Thus, the prediction band is wider than the confidence band. The prediction band for the desired confidence level (1−α) is the interval within which 100(1−α)% of all the experimental points in a series of repeated measurements are expected to fall. By default, α is equal to 0.05. For a prediction band with (1−α)=0.95, we have 95% confidence to say that an expected data point will fall within this interval. In other words, if we add one more experiment data point whose independent variable is within the independent variable range of the original dataset, there is 95% chance that the data point will appear within the prediction band. ## Ellipse Plots We can use ellipse plots to graphically examine correlation in simple linear fitting. During linear regression, the two variables, X and Y are assumed to follow the bivariate normal distribution. This distribution is the co-effect of (X, Y) and is shaped like a bell surface. For a given confidence level, such as 95%, we can conclude that 95% of variables pairs (x, y) will fall in the confidence area included by the upper ellipse, and the projection of the confidence area on XY plane is the confidence ellipse for prediction. The confidence ellipse for the population mean use the same idea and just shows the confidence ellipse of the mean $(\overline{x},\overline{y})$. The shape of the ellipse is determined by the correlation coefficient, r. Strong correlation means a long a (major semiaxis) and a short b (minor semiaxis). Also, the orientation of the ellipse also depends on r.

crawl-data/CC-MAIN-2024-22/segments/1715971058313.71/warc/CC-MAIN-20240520204005-20240520234005-00075.warc.gz

Please briefly explain why you feel this question should be reported. Please briefly explain why you feel this user should be reported. # AP Statistics Unit 1 Test With Answers AP Statistics Unit 1 Test Individuals objects described by a set of data Variable any characteristic of an individual Categorical Variable places an individual into one of several groups or categories Quantitative Variable takes numerical values for which it makes sense to find an average Distribution tells us what values a variable takes and how often it takes those values two-way table describes two categorical variables, organizing counts according to a row variable and a column variable marginal distribution the distribution of values of that variable among all individuals described by the table (for a two-way table) How to examine a marginal distribution 1) Use the data in the table to calculate the marginal distribution (in percents) of the row or column totals. 2) Make a graph to display the marginal distribution. conditional distribution describes the values of that variable among individuals who have a specific value of another variable How to examine or compare conditional distributions 1) Select the row(s) or column(s) of interest. 2) Use the data in the table to calculate the conditional distribution (in percents) of the row(s) or column(s). 3) Make a graph to display the conditional distribution. – Use a side-by-side bar graph or segmented bar graph to compare distributions. How to make a dotplot 1) Draw a horizontal axis (a number line) and label it with the variable name. 2) Scale the axis from the minimum to the maximum value. 3) Mark a dot above the location on the horizontal axis corresponding to each data value. How to Examine the Distribution of a Quantitative Variable 1) In any graph, look for the overall pattern and for striking departures from that pattern. 2) Describe the overall pattern of a distribution by its: Shape Center 3) Note individual values that fall outside the overall pattern. These departures are called outliers. symmetric the right and left sides of the graph are approximately mirror images of each other skewed to the right (right-skewed) the right side of the graph (containing the half of the observations with larger values) is much longer than the left side skewed to the left (left-skewed) the left side of the graph is much longer than the right side How to make a stemplot 1) Separate each observation into a stem (all but the final digit) and a leaf (the final digit). 2) Write all possible stems from the smallest to the largest in a vertical column and draw a vertical line to the right of the column. 3) Write each leaf in the row to the right of its stem. 4) Arrange the leaves in increasing order out from the stem. 5) Provide a key that explains in context what the stems and leaves represent. The most common graph of the distribution of one quantitative variable is a… histogram How to make a histogram 1) Divide the range of data into classes of equal width. 2) Find the count (frequency) or percent (relative frequency) of individuals in each class. 3) Label and scale your axes and draw the histogram. The height of the bar equals its frequency. Adjacent bars should touch, unless a class contains no individuals. median the midpoint of a distribution IQR Q3 – Q1 To calculate the quartiles: 1) Arrange the observations in increasing order and locate the median. 2) The first quartile Q1 is the median of the observations located to the left of the median in the ordered list. 3) The third quartile Q3 is the median of the observations located to the right of the median in the ordered list. Rule for Outliers Call an observation an outlier if it falls more than 1.5 x IQR above the third quartile or below the first quartile five-number summary the smallest observation, the first quartile, the median, the third quartile, and the largest observation, written in order from smallest to largest How To Make A Boxplot – A central box is drawn from the first quartile (Q1) to the third quartile (Q3). – A line in the box marks the median. – Lines (called whiskers) extend from the box out to the smallest and largest observations that are not outliers. – Outliers are marked with a special symbol such as an asterisk (*). Standard deviation (calculation) square root of the variance standard deviation (definition) measures the average distance of the observations from their mean. It is calculated by finding an average of the squared distances and then taking the square root. Variance (calculation) 1) Square each deviation (observation-mean) 2) Find the “average” squared deviation. Calculate the sum of the squared deviations divided by (n-1) Variance (defintion) The average squared distance Choose a measure of center and spread for a skewed distribution or a distribution with outliers median and IQR Choose a measure of center and spread for reasonably symmetric distributions that don’t have outliers mean and standard deviation bin/class width X-scale Are histograms quantitative or qualitative? quantitative Is mean or median more likely to be affected by extremes? Mean Is mean or median more resistant to change? median Modified boxplot excludes outliers from whiskers Population Census collects data from every individual in the population Sample a subset of the population in which we actually collect data convenience sample choosing individuals who are easiest to reach Bias A particular preference or point of view that is personal, rather than scientific. voluntary response sample people who choose themselves by responding to a general invitation random sample #### Quizzma Team The Quizzma Team is a collective of experienced educators, subject matter experts, and content developers dedicated to providing accurate and high-quality educational resources. With a diverse range of expertise across various subjects, the team collaboratively reviews, creates, and publishes content to aid in learning and self-assessment. Each piece of content undergoes a rigorous review process to ensure accuracy, relevance, and clarity. The Quizzma Team is committed to fostering a conducive learning environment for individuals and continually strives to provide reliable and valuable educational resources on a wide array of topics. Through collaborative effort and a shared passion for education, the Quizzma Team aims to contribute positively to the broader learning community.

crawl-data/CC-MAIN-2024-22/segments/1715971057327.58/warc/CC-MAIN-20240518054725-20240518084725-00852.warc.gz

Modern beavers have been wandering North America for 7.5 million years, giving flora and fauna plenty of time to adapt. Willow, a favorite snack, resprouts multiple stems when it’s gnawed down, like a hydra regrowing heads. Cottonwoods produce distasteful tannins to deter chewing. America’s rarest butterfly, the St. Francis Satyr, eats little but sedges that grow in beaver wetlands. The evolutionary connection runs so deep it’s often boiled down to a pithy bumper-sticker: “Beavers taught salmon to jump.” Before European traders set about turning their furs into fancy hats, beavers roamed most of the continent, stopping up streams from the Arctic tundra-line to the Mojave Desert. But the mammals never ventured beyond northern Mexico, leaving Central and South America historically beaverless. Until, that is, an ill-conceived scheme unleashed nature’s architects on a landscape that had never known their teeth — and forever rearranged ecosystems at the bottom of the world. The bizarre experiment was launched in 1946, when Argentina relocated 20 Canadian beavers to Tierra del Fuego, the windswept archipelago at South America’s tip, to “enrich” local wildlife and foster a fur trade. The pelt industry never took off, but the beavers, unchecked by North American predators like wolves and bears, flourished. They swam glacier-scoured fjords between islands, dispersing throughout both the Argentine and Chilean sides of Tierra del Fuego. Some decades after their arrival, a beaver clambered from an icy strait and established a beachhead on the Patagonian mainland. These days, their population numbers about 200,000. And as beavers spread, they did what beavers are wont to do: They transformed their surroundings. Just as New Zealand’s flightless birds had no recourse against invasive rats, Tierra del Fuego’s trees were ill-equipped to withstand “los castores.” The region’s forests are dominated by beeches that never evolved beaver coexistence strategies: They don’t resprout after cutting, produce unsavory chemicals or tolerate flooded soils. As beavers chewed down beeches and expanded free-flowing streams into broad ponds, forests opened into stump-dotted meadows. In 2009, Chris Anderson, then an ecologist at Chile’s Universidad de Magallanes, found that beavers had reshaped up to 15 percent of Tierra del Fuego’s total land area and half its streams — “the largest alteration to the forested portion of this landscape since the recession of the last ice age.” “Basically, everything that’s cuttable has been clear-cut,” Anderson said. Drowned trees and gnawed logs, freeze-dried by icy winds, litter the landscape like the ghosts of forests past. “You just see acres and acres of white trees.” Conservationists, aghast at the loss of old-growth forest, put their faith in natural barriers. Patagonia has two primary habitats, the forest and the steppe — the latter a wind-blasted, arid grassland whose paucity of trees seemed likely to limit beavers’ growth. In 2017, however, an Argentine biologist named Alejandro Pietrek found that, contrary to predictions, beavers were actually producing more offspring on the steppe. Unbothered by the lack of trees, the colonists were happily weaving dams from a shrub called mata negra. “As long as they have water, they can expand,” Pietrek said. “They can colonize all of Patagonia if they want.” Over the years, Chile and Argentina have made halfhearted attempts at curtailing the invasion. A bounty program failed to motivate trappers, while proposed markets for beaver meat never materialized. Recently, though, the two nations have gotten more serious: In 2016, they announced a plan to cull 100,000 — one of the largest invasive-species-control projects ever attempted. Although the massive trapping program, in a pilot phase, should help contain the spread, most scientists say the toothy loggers are in South America to stay. “I think eradication is not possible,” said Chilean biologist Giorgia Graells. On many islands, Graells said, dense forests and scarce roads will thwart trappers. If beavers persist on even a single island, she pointed out, the survivors could repopulate the rest of the archipelago — Sisyphus’s boulder in furry form. In some respects, the South American beaver narrative is a familiar one: Humans introduce nonnative species; nonnative species wreak havoc; humans futilely attempt to erase their error. Yet the beaver story is more interesting — for, befitting a keystone species, the rodent takeover has produced winners as well as losers. Research suggests that beavers have benefited native Magellanic woodpeckers, perhaps by making trees more susceptible to the wood-boring insects upon which the birds feast. The slackwaters behind dams also support native fish called puye, which are four times more abundant around beaver impoundments than elsewhere in southern Chile. “Before you determine whether a change is good or bad, you always have to ask, ‘For whom?’ ” Anderson said. “If you’re a duck and you want ponds with lots of little crustaceans to eat, well, beaver ponds are full of them.” The biggest beneficiaries, however, have been the beaver’s fellow North Americans: the muskrat and the mink, two other lusciously furred mammals the Chilean government naively plopped down in Tierra del Fuego in the 1940s. On their own, the imports might have perished; beavers, however, ensured their survival. When researchers scoured one invaded island, they found a whopping 97 percent of muskrat tracks, scats and burrows around beaver ponds and wetlands, suggesting that one rodent was supporting the other. Mink, a weasel-like carnivore, have in turn feasted on the muskrats — as well as native birds and mammals. The scientists who studied that ecological chain reaction called it an “invasional meltdown.” A less ominous phrasing might be “novel ecosystem,” a natural community that’s been altered by human activity but has since escaped our control. Like it or not, novel ecosystems are all around us — scrubby pine forests in Puerto Rico, urban wetlands in New Jersey, replanted grasslands in an old Colorado mining pit. Assuming utter eradication fails, some corners of Patagonia may be forced to surrender to the awesome power of an indomitable rodent. The whole saga, ultimately, is a sort of Bizarro Beaver story: The very same tree-gnawing, dam-building, pond-creating talents that normally make them such miracle-workers have mostly produced disaster below the equator. South America’s beavers are both charismatic and catastrophic, life-sustaining and forest-leveling, an invasive scourge and a popular tourist attraction. As the compassionate conservation movement dawns, beavers pose, too, an ethical dilemma: How do we balance ecological health with animal welfare? Is the only solution really mass slaughter? The paradoxes can’t help but affect the scientists studying Patagonia’s beavers, who admire the architects even as they desire to see them wiped out. “We have to focus on the big picture, on the ecosystem level,” Pietrek said. “But it’s hard to think about beavers being eradicated. You relate to them in a way.” Ben Goldfarb is an environmental journalist and the author of “Eager: The Surprising, Secret Life of Beavers and Why They Matter.”

<urn:uuid:96b85089-ba58-4abb-95be-80514b764745>

Amid the re-release of the film "Titanic" and a cruise tracing the doomed voyage, there is some stunning new research by a Titanic historian from Britain, Tim Maltin, which draws heavily from San Diego State University adjunct astronomy professor Andrew Young and his work on mirages."When you see the mirage of water in a desert, you're really seeing a reflection of the sky," said Young.As light travels through air with different temperatures from warm air to the sizzling desert ground the air bends and distorts images. In some cases, it creates a haze-like effect."In mirage conditions, you can actually see a lot farther than usual, but you're looking through a lot more air," said Young. "You're seeing a lot of light scattered by all that air, creating what appears to be haze."A similar mirage effect happens on the cold ocean's surface.Maltin's research confirms that conditions that night were ripe to possibly produce a haze that would make things difficult to see. His idea is that mirage conditions reduced the visibility of the iceberg enough to the point that it was not noticed until it was too late.Maltin pointed to witness descriptions of a distant haze. In one section of the official Titanic inquiry, a crewmate described the iceberg as a dark mass that came through the haze.He also believes the mirage effect struck again when the crew of a ship in the vicinity, the Californian, did not assist because the mirage distorted the Titanic's image."They thought it was a much smaller ship and more nearby than it actually was," said Young.Still, Young remains skeptical."I can't say Maltin's wrong, but I can't say he's a made a convincing argument either," he said.Young said the haze effect was about 20 miles from the iceberg and doubts it would have obscured the iceberg completely.He also said once the ship came within about a mile of the iceberg, the mirage effect should have gone away.

<urn:uuid:8af18eeb-48ea-407d-9fef-c20535977319>

Math by Design encourages students to problem solve and think critically as they encounter unique geometry and measurement challenges. Students are introduced to the TRC Architectural firm as junior architects who are commissioned to build environments by working through a series of mathematical tasks. Students may build two environments: Flossville Town Park and Windjammer Environmental Center. Both are rich with interactives and online hints to help students refine and build upon their knowledge of geometry and measurement. Extensive educator resources provide valuable assistance for teachers to seamlessly integrate Math by Design into classroom instruction. Math by Design was produced as part of a national public television collaborative that was formed to create online resources focused on STEM subjects for middle school students and teachers. With initial funding from the Corporation for Public Broadcasting, the collaborative produced engaging resources to be shared through the nationwide public television system. MPT’s partners in the collaborative include Alabama Public Television (APT), Arkansas Educational Television Network (AETN), and the Kentucky Educational Television (KET). Each partner produced an online experience that presents a unique focus on the mathematics, science, technology, and engineering of everyday life. Be sure to check out … - APT's Proportion Land Park, which invites eighth graders to reason their way through eight amusement park attractions. Students encounter interactive rides that require them to solve a variety of science-based proportional reasoning problems before they can join in the fun. - AETN's Rock-n Roll Road Trip World Tour, which invites students in grades 6-8 to take a trip around the world while solving real-life problems using measurement, ratio, and proportion. - KET's Scale City, billed as the “biggest, smallest road trip ever!” In it, students in grades 6 – 8 explore amazing roadside attractions and learn about the mathematics of scale.

<urn:uuid:183f496d-eb4d-412b-ab75-fbd67618916b>

# Assignment 1: From Jim Wilson’s website: Examine: . See the graph.What happens if the 4 is replaced by other numbers (not necessarily integers)? Try 5, 3, 2, 1, 1.1, 0.9, -3. Any unusual event? Interpret. What equation would give the following graph: What happens if a constant is added to one side of the equation? Try several graphs in some systematic way. Click here for one set of graphs. Try graphing By exploring the graph of  for various values of n, we discover that there are three classes of graphs: n<0,              0< n < 1,  n=1, and n>1 . For each of these classes, the y-intercepts will remain the same.  The y-intercepts occur when x = 0, so the y-intercepts are solutions to .  By factoring, we have .  Every graph of the form  will have  will have y-intercepts 0, 1, and -1. When n > 1, we have a graph such as below.  (Here with n = 4) The most apparent characteristics of this graph are it’s intercepts.  Note that x-intercepts occur when y = 0, so the x-intercepts are solutions to .  By recognizing the difference of two squares, we can solve this equation easily by transforming it to When n > 1, we have three x-intercepts:  . When n = 1, we have: This graph appears to be the union of an ellipse and the line y=x.  Algebraically, we have:  .  So .  By distributing and combining like terms, we have  .  By factoring, we arrive at .  The zero product property states that if the product of two numbers is zero, then one of the two numbers must be zero.  So we have  or .  In the first case,  means  and we the line y = x appears graphically as expected.  In the second case, we have , which is an ellipse and confirms the second dominant shape in the graphical representation. When n < 1, we have a graph such as below.  (Here with n = -4) There is only one x-intercept in the case when n < 1.  In factored form we have .  For integers less than 1, this means n is negative, or n is zero.  If n is zero, the only solution to  is x = 0.  If n is negative, one solution remains zero, while the remaining two solutions are complex. When n is between zero and 1, a case similar to when n > 1 occurs.  This is the result of three real solutions to the equation .  The graph below shows when n = .5 Send me an e-mail Returnto Hamilton Hardison's Page

crawl-data/CC-MAIN-2018-51/segments/1544376829542.89/warc/CC-MAIN-20181218164121-20181218190121-00463.warc.gz

# ℃^-1 question ## Homework Statement This is the problem. A pair of eyeglass frames is made of epoxy plastic. At room temperature (20.0°C), the frames have circular lens holes 2.20 cm in radius. To what temperature must the frames be heated if lenses 2.21 cm in radius are to be inserted in them? The average coefficient of linear expansion for epoxy is 1.30 x 10^-4 (°C)^-1. ## The Attempt at a Solution I know how to solve this but I'm not very sure what the ℃ elevated to -1 means. Can someone explain what that means and why it is expressed this way? ## Homework Statement This is the problem. A pair of eyeglass frames is made of epoxy plastic. At room temperature (20.0°C), the frames have circular lens holes 2.20 cm in radius. To what temperature must the frames be heated if lenses 2.21 cm in radius are to be inserted in them? The average coefficient of linear expansion for epoxy is 1.30 x 10^-4 (°C)^-1. ## The Attempt at a Solution I know how to solve this but I'm not very sure what the ℃ elevated to -1 means. Can someone explain what that means and why it is expressed this way? Look at wiki page, "Thermal expansion coefficients for various materials" section. It's just the inverse of the temperature unit. Write down the equation of the thermal expansion, and weigh down the units for the thermal coefficient. α=(∆L/L)/T So the units are ℃^-1 because the temperature in the equation is in the denominator (which means T ^-1) . Right? α=(∆L/L)/T So the units are ℃^-1 because the temperature in the equation is in the denominator (which means T ^-1) . Right? Yes. The physical unit for the length is irrelevant because you have (( ΔL/L )) which always cancels out. The choice of the unit for the temperature influence the unit of your coefficient and vice versa. You can choose to use K (Kelvin) instead of °C (Celsius). In this scenario, α have a unit of K^-1 Thank you for your help :)

crawl-data/CC-MAIN-2021-17/segments/1618039503725.80/warc/CC-MAIN-20210421004512-20210421034512-00120.warc.gz

Thermokarst is a pitted land surface that occurs in Arctic and subarctic regions as permafrost thaws. Permafrost is more or less permanently frozen ground that is often found in arctic and subarctic regions. The lakes form when meltwater accumulates in the depression in the ground. Dr. Katey Walter Anthony from UAF is studying the lakes and how methane CH4 and carbon dioxide CO2 and is released into the atmosphere from these lakes. Both of these are greenhouse gases. Looking for methane under lots of snow Dr. Anthony shared with us the Russian view of thermokarst lakes. The term from Russian translates into lakes that are eating the ground. It provides a nice environment for decay of plants and animals. As the remains decay, methane is created which eventually is "burped" out of the lake. When the lake freezes, you can see these bubbles of methane that are trapped in the ice. Katey explaining where to find methane bubbles in ice A part of Dr. Anthony's research is understanding where these lakes are in the Arctic and the quantity of methane that may be released from these lakes. She has found different types of thermokarst lakes. The Yedoma lakes are the highest source of methane and 6% of pan arctic lakes are this type. When radiocarbon dating is done on the carbon in the methane molecule CH4 the carbon dated back to the Pleistocene epoch. The Pleistocene epoch was between 2 million and 11,500 years ago. Most of the snow was completely messed up on lake after 14 teachers, 2 researchers and PolarTREC people shuffled through snow. A qualitative way of determining how much of that bubble in the ice is methane and how much of it is nitrogen is to set it on fire. Methane burns and nitrogen does not. Today we went looking for methane bubbles in a nearby lake. Unfortunately, we did not have GPS coordinates of the hotspots on this particular lake. Our job was to shuffle through knee-deep snow on the lake and move snow around with our feet while we looked for willow branches that were near these hotspots. After 1 hour and poking a couple of dry holes we found no hotspots. Here is a video of what we might have found with a lot less snow covering the lake. Hunting for Methane with Katey Walter Anthony

<urn:uuid:f66211a5-f129-468d-80af-ed8932e32979>

# Using integration by parts, find `inte^(3x)cos4x dx` . Posted on `I = inte^(3x)cos4xdx` Let; `U = e^(3x)` `dU = 3e^(3x)dx` `V = 1/4sin4x` `dV = cos4xdx` From integral by parts; `intUdV = UV-intVdU` `inte^(3x)cos4xdx = (e^(3x)xx1/4sin4x)-int1/4sin4x3e^(3x)dx` `J = inte^(3x)sin4xdx` Using integral by parts same as above we can get that; `inte^(3x)sin4xdx = (e^(3x)xx(-1/4cos4x))-int(-1/4cos4x)3e^(3x)dx` `J = (e^(3x)xx(-1/4cos4x))+3/4inte^(3x)cos4xdx` `J = (e^(3x)xx(-1/4cos4x))+3/4I` `inte^(3x)cos4xdx = (e^(3x)xx1/4sin4x)-int1/4sin4x3e^(3x)dx` `I = (e^(3x)xx1/4sin4x)-3/4J` `I = (e^(3x)xx1/4sin4x)-3/4((e^(3x)xx(-1/4cos4x))+3/4I)` `I = e^(3x)sin(4x)/4+3/16e^(3x)cos4x-9/16I` `I(1+9/16) = e^(3x)sin(4x)/4+3/16e^(3x)cos4x` `25/16I = (4e^(3x)sin4x+3e^(3x)cos4x)/16` `I = (4e^(3x)sin4x+3e^(3x)cos4x)/25` `I = (e^(3x)(4sin4x+3cos4x))/25+C` where C is a constant. So the answer is; `I = (e^(3x)(4sin4x+3cos4x))/25+C ` Sources: We’ve answered 319,882 questions. We can answer yours, too.

crawl-data/CC-MAIN-2016-18/segments/1461860121090.75/warc/CC-MAIN-20160428161521-00131-ip-10-239-7-51.ec2.internal.warc.gz

## Assignment: Independent Samples t-Test Assignment: Independent Samples t-Test Assignment: Independent Samples t-Test Exercise 16: Understanding Independent Samples t-Test: Statistical Technique in ReviewThe independent samples t-test is a parametric statistical technique used to determine significant differences between the scores obtained from two samples or groups. Since the t-test is considered fairly easy to calculate, researchers often use it in determining differences between two groups. The t-test examines the differences between the means of the two groups in a study and adjusts that difference for the variability (computed by the standard error) among the data. When interpreting the results of t-tests, the larger the calculated t ratio, in absolute value, the greater the difference between the two groups. The significance of a t ratio can be determined by comparison with the critical values in a statistical table for the t distribution using the degrees of freedom (df) for the study (see Critical Values for Student’s t Distribution at the back of this text). The formula for df for an independent t-test is as follows: df=(numberofsubjectsinsample1+numberofsubjectsinsample2)?2 Exampledf=(65insample1+67insample2)?2=132?2=130 The t-test should be conducted only once to examine differences between two groups in a study, because conducting multiple t-tests on study data can result in an inflated Type 1 error rate. A Type I error occurs when the researcher rejects the null hypothesis when it is in actuality true. Researchers need to consider other statistical analysis options for their study data rather than conducting multiple t-tests. However, if multiple t-tests are conducted, researchers can perform a Bonferroni procedure or more conservative post hoc tests like Tukey’s honestly significant difference (HSD), Student-Newman-Keuls, or Scheffé test to reduce the risk of a Type I error. Only the Bonferroni procedure is covered in this text; details about the other, more stringent post hoc tests can be found in and . The Bonferroni procedure is a simple calculation in which the alpha is divided by the number of t-tests conducted on different aspects of the study data. The resulting number is used as the alpha or level of significance for each of the t-tests conducted. The Bonferroni procedure formula is as follows: alpha (?) ÷ number of t-tests performed on study data = more stringent study ? to determine the significance of study results. For example, if a study’s ? was set at 0.05 and the researcher planned on conducting five t-tests on the study data, the ? would be divided by the five t-tests (0.05 ÷ 5 = 0.01), with a resulting ? of 0.01 to be used to determine significant differences in the study. The t-test for independent samples or groups includes the following assumptions: 1. The raw scores in the population are normally distributed. 2. The dependent variable(s) is(are) measured at the interval or ratio levels. 162 3. The two groups examined for differences have equal variance, which is best achieved by a random sample and random assignment to groups. 4. All scores or observations collected within each group are independent or not related to other study scores or observations. The t-test is robust, meaning the results are reliable even if one of the assumptions has been violated. However, the t-test is not robust regarding between-samples or within-samples independence assumptions or with respect to extreme violation of the assumption of normality. Groups do not need to be of equal sizes but rather of equal variance. Groups are independent if the two sets of data were not taken from the same subjects and if the scores are not related (; ). This exercise focuses on interpreting and critically appraising the t-tests results presented in research reports. provides a step-by-step process for calculating the independent samples t-test. Research Article Source Canbulat, N., Ayhan, F., & Inal, S. (2015). Effectiveness of external cold and vibration for procedural pain relief during peripheral intravenous cannulation in pediatric patients. Pain Management Nursing, 16(1), 33–39. Introduction , p. 33) conducted an experimental study to determine the “effects of external cold and vibration stimulation via Buzzy on the pain and anxiety levels of children during peripheral intravenous (IV) cannulation.” Buzzy is an 8 × 5 × 2.5 cm battery-operated device for delivering external cold and vibration, which resembles a bee in shape and coloring and has a smiling face. A total of 176 children between the ages of 7 and 12 years who had never had an IV insertion before were recruited and randomly assigned into the equally sized intervention and control groups. During IV insertion, “the control group received no treatment. The intervention group received external cold and vibration stimulation via Buzzy?.?.?.?Buzzy was administered about 5 cm above the application area just before the procedure, and the vibration continued until the end of the procedure” (, p. 36). , pp. 37–38) concluded that “the application of external cold and vibration stimulation were effective in relieving pain and anxiety in children during peripheral IV” insertion and were “quick-acting and effective nonpharmacological measures for pain reduction.” The researchers concluded that the Buzzy intervention is inexpensive and can be easily implemented in clinical practice with a pediatric population. Relevant Study Results

crawl-data/CC-MAIN-2023-23/segments/1685224649348.41/warc/CC-MAIN-20230603233121-20230604023121-00575.warc.gz

Diagnostic Spelling Tests Spelling assessment and diagnostic follow-up Mary Crumpler and Colin McCarty The Diagnostic Spelling Tests provide a series of standardised group or individual spelling tests for pupils throughout their school years and beyond. Each test is easy to administer and available in parallel forms A and B, which are carefully matched in content, style and difficulty. The difficulties some children experience when learning to read and spell may leave weaknesses which can persist all the way into adulthood – but identifying specific weaknesses allows strategies to be implemented to help overcome individual difficulties. Each test gives standardised scores and spelling ages, plus an optional diagnostic facility utilising the photocopiable marking grids in the Manual. To support the diagnosis and an intervention programme, targeted follow-up tests are provided to check specific progress: the pupil’s overall improvement can then be assessed using the parallel form. Diagnostic Spelling Tests 1–3 are for primary-aged pupils: Test 1 ages 5–7 (Years 1 and 2) The vocabulary and phonic structures used for the spelling items reflect the order in which they are introduced in the National Literacy Strategy. All of the target words are read aloud to the pupils. Tests 1 and 2 comprise both picture items and illustrated cloze (‘fill in the gap’) passages, whereas Test 3 is entirely illustrated cloze passages. There is no set time limit, but each test is likely to take 20–30 minutes. Diagnostic Spelling Tests 3–5 are for use with secondary and older students, and adults: Test 3 ages 9–12 (Years Test 3 is based on the National Literacy Strategy objectives for Years 5 and 6, so is ideal for testing pupils on entry to secondary school. Tests 4 and 5 (Forms A & B) are provided as photocopy masters. The vocabulary used for the spelling items in Test 4 reflects the key vocabulary identified in the KS3 National Strategy Framework for Teaching English: Years 7, 8 and 9. The words in Test 5 comprise essential elements of functional literacy. All of the target words are read aloud to the students and are set in a sentence to provide context and assist with establishing the meaning of the word. These books will also interest you: © copyright Hodder Education 2004 |Terms and conditions|

<urn:uuid:5e68f96b-c269-4890-addf-2b4fe98dd17a>

Books in black and white Books Biology Business Chemistry Computers Culture Economics Fiction Games Guide History Management Mathematical Medicine Mental Fitnes Physics Psychology Scince Sport Technics # Elementary Differential Equations and Boundary Value Problems - Boyce W.E. Boyce W.E. Elementary Differential Equations and Boundary Value Problems - John Wiley & Sons, 2001. - 1310 p. Previous << 1 .. 219 220 221 222 223 224 < 225 > 226 227 228 229 230 231 .. 609 >> Next x = ^(t)c + W(t) f ^-1(s)g(s) ds. (31) Jt0 The initial condition (30) can also be satisfied provided that t0) c = ^-1(t0 )x0. (32) Therefore x = ^(t)^-1(t0)x° + W(t) f ^-1(s)g(s) ds (33) 0 t0 is the solution of the given initial value problem. Again, while it is helpful to use ^-1 to write the solutions (29) and (33), it is usually better in particular cases to solve the necessary equations by row reduction rather than to calculate ^-1 and substitute into Eqs. (29) and (33). The solution (33) takes a slightly simpler form if we use the fundamental matrix Ô(0 satisfying Ô(*0) = I. In this case we have x = Ô(^0 + Ô(Ã) ² Ô-1(s)g(s) ds. (34) t0 416 Chapter 7. Systems of First Order Linear Equations EXAMPLE 3 Equation (34) can be simplified further if the coefficient matrix P(t) is a constant matrix (see Problem 17). Use the method of variation of parameters to find the general solution of the system x' = (—1 —O x + (23ª( 1 = Ax + g(t)- (35) This is the same system of equations as in Examples 1 and 2. The general solution of the corresponding homogeneous system was given in Eq. (10). Thus *(t)=(—e—3t e—t) (36) is a fundamental matrix. Then the solution x of Eq. (35) is given by x = ^(t)u(t), where u(t) satisfies ^(t)u'(t) = g(t), or e—3t e—^ (u'\ (2e — e"3t e-^ \i}2) V 3t Solving Eq. (37) by row reduction, we obtain u1 = e2t — 3 te3t, (37) u2 = 1 + 3 tet. Hence and u 1(t) = 1 e2t — 1 te3 + 6 e3t + c1, u2(t) = t + 2 tet — 3 et + c2, x = W(t)u(t) = c1 (—1)e_3t + c2 (1)e—t + te— +1 e—t + (0t — 3(4) • (38) which is the same as the solution obtained previously. Each of the methods for solving nonhomogeneous equations has some advantages and disadvantages. The method of undetermined coefficients requires no integration, but is limited in scope and may entail the solution of several sets of algebraic equations. The method of diagonalization requires finding the inverse of the transformation matrix and the solution of a set of uncoupled first order linear equations, followed by a matrix multiplication. Its main advantage is that for Hermitian coefficient matrices the inverse of the transformation matrix can be written down without calculation, a feature that is more important for large systems. Variation of parameters is the most general method. On the other hand, it involves the solution of a set of linear algebraic equations with variable coefficients, followed by an integration and a matrix multiplication, so it may also be the most complicated from a computational viewpoint. For many small systems 7.9 Nonhomogeneous Linear Systems 417 PROBLEMS with constant coefficients, such as the one in the examples in this section, there may be little reason to select one of these methods over another. Keep in mind, however, that the method of diagonalization is slightly more complicated if the coefficient matrix is not diagonalizable, but only reducible to a Jordan form, and the method of undetermined coefficients is practical only for the kinds of nonhomogeneous terms mentioned earlier. For initial value problems for linear systems with constant coefficients, the Laplace transform is often an effective tool also. Since it is used in essentially the same way as described in Chapter 6 for single scalar equations, we do not give any details here. In each of Problems 1 through 12 find the general solution of the given system of equations. 1 V3i 3. «'= 2 -5 * + -Ã 5. x' = (4 -4j x +,_ Ã2 2. x' x+ 4.x = i4 -2)x+ (e2et e \/3 e- -2 t ' t > 0 1 6. 2 -1)x+(2r' + 4 9. x' t > 0 11. x = * 1 2) x + \ t 1 2 cos t 13. The electric circuit shown inFigure 7.9.1 is described by the system of differential equations I (t), (i) dx dt Previous << 1 .. 219 220 221 222 223 224 < 225 > 226 227 228 229 230 231 .. 609 >> Next

crawl-data/CC-MAIN-2018-51/segments/1544376823318.33/warc/CC-MAIN-20181210055518-20181210081018-00497.warc.gz

ScaffoldingFirst I want to talk about scaffolding. This is just a fancy way of saying that you’re only going to try to facilitate something a little harder than what your child can do on their own. If they can’t imitate at all, you’re not going to ask them to suddenly repeat a five word sentence. Start where they are and try to help them do something just a little harder. When they can do that, then do something just a little harder, etc. For the purpose of this discussion I’m going to talk about a child who can imitate single words and is willing to do so, but is having trouble imitating a two-word utterance. The first thing you want to do is make sure you’re modeling two-word utterances. Try to simplify your own speech to the two-word level and use lots of two-word phrases yourself. Also, whenever your child uses a word, repeat it back increasing it to a two-word utterance. For example, if your child says “dog,” you say, “Yes! Big dog!” This is called expansion. You are expanding their one word sentence into a two-word sentence. TappingChildren with Childhood Apraxia of Speech have trouble with motor planning. Research has shown that therapy is more successful when it is multisensory. Try to stimulate them as many ways as possible. One way to do this is to use a tapping technique. Use your hand to tap out two syllables as you say them. So, “big dog” should be said simultaneously with two taps of your hand on your knee (or claps, or snaps). If your child will tolerate it, tap gently on their knee, or hand, or arm. Or help them to clap the syllables themselves. Any time you're trying to get them to imitate two words instead of one (or a two syllable words that they are producing as a one syllable word) be sure to tap it. It can make a huge difference. It really seems to help them cue in on the fact that there are two distinct parts that they need to produce. Also try using a singsong voice. So say, “biiiiiiig dog”. Use signs and gestures.This might sound counterintuitive, but encourage signs and gestures. Typically developing children combine single words with a gesture before they start using two-word phrases. So, if they want to tell you “daddy’s shoe” they might say “dada” while pointing to his shoe. One of Ava’s first two “word” combinations was saying the word “more” out loud while making the sign for milk. It’s a stepping stone to saying two-word phrases and it can be very effective. As another example, spread your hands wide as a gesture for big while saying the word “ball”. If you do see them combine a word with a sign or gesture to make a two-"word" utterance, repeat both words back to them yourself. Say, "Yes! That is a big ball!" Praise their successful communication of a two part message. Slow it down. Be direct.So, you’re scaffolding, modeling, expanding, and combining gestures with signs and still don’t feel like you’re making progress. Make sure you slow it down. We often don’t realize how quickly we’re speaking. Deliberately slow your speech down. It gives them extra processing time. Also try being more direct. You can tell them, “Say, biiiiiiiig dog!” It sounds simple, but sometimes it can help. Be careful with that though. If your child gets defensive, don’t push. Break it down.You can also put a long pause in between the two words when you are asking them to imitate a two-word phrase. Again, it gives them extra processing time. It also shows them that it is ok if it takes them a long time to get that second word out. Children with Childhood Apraxia of Speech often need extra processing time particularly when they are trying something new. When Ava was trying a new two-word phrase that was hard for her, there was a huge pause between the first and second word. You could see her working at getting that second word out. I think it helps if you model that pause to begin with. Only put the pause in if necessary though, and phase it out as soon as possible. If you need to, you can break it down even further and have them imitate the first word and then the second word seperately before asking them to imitate them together. Carrier phrases.Use carrier phrases. A carrier phrase is a short predictable phrase used repeatedly where only one part of the phrase changes. Let me give some examples. I deliberately taught Ava the word mine. In a household with two young children that seems like a tactical error, but I wanted her to then use the phrase, “my ______” . Once you teach the carrier phrase, it can then be completed with so many other words. “My shoe. My hat. My milk. My cup." etc. This one works particularly well because you can make it into a game and get lots of repetitions. So, she says, “My shoe.” You playfully return, “No, Mama’s shoe!” She indignantly returns, “My shoe!” You continue back and forth as many times as you can. As another example, Ava’s very first two-word combination was “Papa house.” Then she used house as the consistent part of the carrier phrase. She said, “Mama house, my house, papa house, dada house," etc. Go out of your way to find carrier phrases that are fun to use in your house and use them frequently. Some other ideas might include: - Baby. "Baby up. Baby down. Baby sleep. Baby bad. Baby good. Baby eat." etc - Car. (Or train, or truck.) "Car go. Car stop. Car beep. Car crash. Car fast. Car slow.: etc. - More. "More milk. More water. More banana. More play. More tv. More cookie." etc. Practice, practice, practice.Don’t limit these activities to a 15 minute speech practice time per day. Do them all the time. Incorporate them into different activities. Do this when you’re reading books, giving them a bath, during snacks and meals, during play with toys and during an art activity. The more variety the better. Do these things in as many settings as possible – at home, in the car, at school, in a restaurant, at the mall, at the grandparents’ house. If possible, teach the other adults around you to use these techniques. Mom, dad, grandparents, and siblings can all be encouraging speech development. In fact, even though I was working on this all the time myself, it didn’t pop in until she spent the night at her grandparents’ house doing all these things in a completely different setting with different people. Two-word utterances - Apraxia Therapy techniquesI've put the techniques I consider to be particularly powerful in bold print. - combining words with gestures - slow it down - be more direct - use carrier words and phrases - use techniques in different activities and settings and with different people You might also be interested in the following articles:

<urn:uuid:4a64bfaf-475d-4e92-a536-22fe7ca46be0>

Since ancient days, people have developed sophisticated weapons to fill their arsenals. In ancient Egypt, the khopesh was a notoriously deadly sword on the battlefield. A khopesh would typically be cast out of a single piece of bronze that was quite heavy, and it looked like a cross between a battle ax and a sword. Even Ramses II is portrayed as wielding one of these. A Japanese officer of the Edo era would make great use of a sodegarami (the word itself means “sleeve entangler”). This weapon looked like a spiked pole, and it allowed the officers to confront any antagonist with a quick twist, bringing the attacked person to the ground but not necessarily inflicting severe wounds. When it comes to the Aztec warriors, perhaps their best asset on the battlefield was the macuahuitl. Known as the Aztec sword, this weapon was not a real sword cast in metal but made from oak wood. Its edges were set with obsidian blades (volcanic glass), and Aztec warriors used these to slash throats and inflict painful wounds that caused heavy bleeding. When Cortés arrived in Central America, he certainly witnessed the strength of the Aztecs on the battlefield. Chronicles of his battles and similar historical documents tell that the Aztecs were fearsome people. Their society and culture were largely built on warriorhood. Both the jaguar and the eagle were emblematic predators that added to the Aztec culture, and warriors would typically dress to look like one of the two. They believed such appearance would spread fear among their adversaries. If a new warrior was to join the Aztec battle groups, he could do so only if he captured an enemy soldier first. The Aztec had a well-thought-out system on how the military should function, and a well-developed strategy for the battlefields too. The Aztec warriors who used the macuahuitl would step forward during a battle only when the archers or slingers advanced close to the adversary. In a close encounter with the enemy, the macuahuitl was their best asset in hands. Resembling a cricket bat, the macuahuitl had a length typically extending some three and a half feet. While numerous examples of this weapon were managed with one hand only, there were others who required two hands to grab and fight. Depending on its size, the weapon had between four and eight razor-sharp blades along each side, but this varied, with some macuahuitl embracing a complete single edge formed by the unusual volcanic material. No matter the design, the obsidian could not be pulled out. The Aztecs would wield their swords with short and chopping movements, and, as many accounts suggest, they cut off some heads. Besides the macuahuitl, the Aztec made use of the tepoztopilli, one more weapon carved out of wood and fitted with obsidian blades. However, the tepoztopilli was more like a type of polearm. It was spear-like, with a large wedge head on the front, and at five to six feet long, the entire piece was a bit longer than the macuahuitl. Cortés’ conquistadors certainly had plenty of opportunities to see the power of the Aztec weaponry demonstrated first hand. Several of the Spanish horse riders reported that the Aztec swords were able to decapitate not only a human head but that of a horse. The blades would inflict a wound so deep in the animal, its head would cleave off to hang only by the skin. Contrary to popular belief, the deadly macuahuitl was not an invention of the Aztec themselves, but rather a weapon widespread among distinct groups of Central Mexico and likely in other places of Mesoamerica as well. Even Christopher Columbus was fascinated by the strength of this weapon when he encountered it after reaching the Americas. He gave orders to his people to collect a sample to show back in Spain. Today, there aren’t any original macuahuitl surviving, only various re-creations of the weapon based on knowledge extracted from contemporary accounts and illustrations produced during the 16th century or earlier. Read another story from us: Goose hunters in Iceland track down a 1,000-year-old Viking sword It is believed that the last authentic macuahuitl was destroyed in a fire in the Real Armería de Madrid, where the weapon was kept for a long time next to the last original tepoztopilli.

<urn:uuid:050cd421-bcdc-4257-a226-718afa53743d>

Microbial world's use of metals mostly unmapped A new way of surveying microbes for the metals they contain reveals that biologists have been relying on the equivalent of a 15th century map of the world. It turns out that there are many more metal-containing proteins in microbes than previously recognized. This means the microbial world boasts a broader and more diverse array of metal-driven chemical processes than scientists have imagined. In fact, most have yet to be discovered, according to a first-of-its-kind survey of the metals in three microbes conducted by scientists from the U.S. Department of Energys Lawrence Berkeley National Laboratory in collaboration with scientists at the University of Georgia. Their research will help chart a more complete understanding of the far-reaching roles of microbial metals in biology and the Earths climate. It could also lead to new ways to harness metal-driven chemical processes to create next-generation biofuels or to clean up environmental contaminants. Microbes assimilate metals from their environment and incorporate them into proteins in order to power lifes most important chemical processes, such as photosynthesis, respiration, and DNA repair. Metal-containing proteins in microbes also helped oxygenate the planets atmosphere billions of years ago, enabling life as we know it, and they continue to play a critical role in the Earth’s carbon cycle. But the diversity and extent of microbial metals had eluded scientists until now. "This is a huge surprise. It reveals how naive we are about the wide range of chemistries that microbes do," says John Tainer of Berkeley Labs Life Sciences Division and the Scripps Research Institute in La Jolla, CA. Tainer conducted the research with Michael Adams of the University of Georgia and a team of scientists that includes Steven Yannone and Gary Siuzdak of Berkeley Labs Life Sciences Division. The scientists report their research July 18 in an advance online publication of the journal Nature. Using state-of-the-art techniques, the team catalogued the metals in three microbes: one that lives in human intestines, one plucked from a hotspring in Yellowstone National Park, and one that thrives in the near-boiling waters of undersea thermal vents. They uncovered a microbial world far richer in metals than ever expected. For example, in the undersea thermal-vent loving microbe, or Pyrococcus furiosus, they found metals such as lead, manganese, and molybdenum that P. furiosus wasnt known to use. The scientists traced these newfound metals to the proteins that contain them, called metalloproteins. They discovered four new metalloproteins in the microbe, which increased the number of known metalloproteins in P. furiosus by almost a quarter. Their discovery also increased the number of nickel-containing enzymes in all of biology from eight to ten. A similar survey of the other two microbes unearthed additional unexpected metals and new metalloproteins. Based on this sizeable haul from only three microbes, the team believes that metalloproteins are much more extensive and diverse in the microbial world than scientists realized. "We thought we knew most of the metalloproteins out there," says Tainer. "But it turns out we only know a tiny fraction of them. We now have to look at microbial genomes with a fresh eye." The team used a first-of-its-kind combination of two techniques to envisage this uncharted microbial landscape. Biochemical fractionation enabled them to take apart a microbe while keeping its proteins intact and stable, ready to be analyzed in their natural state. Next, a technology called inductively coupled plasma mass spectrometry allowed them to identify extremely low quantities of individual metals in these proteins. Together, these tools provide a quick tally of all of the metalloproteins in a microbe. The current way to discover metalloproteins is much slower. Simply stated, it involves genetically sequencing a microbe, identifying the proteins encoded by its genes, and structurally characterizing each protein. "Standard methods of identifying metalloprotiens can take years," says Yannone. "By directly surveying all microbial proteins for metals we can rapidly identify the majority of metalloprotiens within any cell." In addition to gaining a better understanding of the biochemical diversity of microbes, the teams new metal-hunting technique could expedite the search for new biochemical capabilities in microbial life that can be harnessed for clean energy development, carbon sequestration, and other applications. "If you want to degrade cellulose to make biofuel, and you know the enzymes involved require a specific metal-driven chemistry, then you can use this technique to find those enzymes in microbes," says Yannone. Adds Tainer, "Knowing that all of these metal-containing proteins are out there, waiting to be found, is kind of like being in a candy store. We might discover new proteins that we can put to use." The research was funded by the Department of Energy Office of Science. Berkeley Lab scientists provided the inductively coupled plasma mass spectrometry equipment. They contributed to the experimental design and data analysis in collaboration with University of Georgia scientists. Lawrence Berkeley National Laboratory provides solutions to the world’s most urgent scientific challenges including clean energy, climate change, human health, and a better understanding of matter and force in the universe. It is a world leader in improving our lives and knowledge of the world around us through innovative science, advanced computing, and technology that makes a difference. Berkeley Lab is a U.S. Department of Energy (DOE) national laboratory managed by the University of California for the DOE Office of Science. Visit our website .

<urn:uuid:74457fff-daa1-48a3-ac6b-4f7de5e53af7>

|Researching the effects of underwater hydrothermal venting systems| |East Pacific Rise| The eastern equatorial Pacific has been monitored by autonomous hydrophones since May, 1996 The region includes East Pacific Rise, Galapagos Ridge, Middle America and Peru-Chile trench systems, and the Easter and Juan Fernandez microplates. For more information, visit the EPR Seismicity pages. The southern East Pacific Rise (EPR) one of the fastest-spreading sections of the Earth's Mid-Ocean Ridge system. In 1993 and 1994 VENTS Program scientist participated in a series of research expeditions to the southern EPR with scientific collegues from from Japan, including the Geological Survey of Japan, JApanese Marine Science and TEchnology Center (JAMSTEC), University of Tokyo, the National Research Institute for Bioscience and Human Technology, and Tokai University, Hydrographic Dept. of the Marine Safety Agency, and the University of Tsukuba. The 1993 expedition was aboard the R/V Melville and was primarily focused on mapping and sampling of plumes in the water column from 13.5° S to 18.5°S. In 1994, two separate expeditions were mounted aboard the R/V Yokosuka with the Shinkai 6500 submersible. Fifteen dives were made on each leg to collect fluid, biological, and sulfides samples from vents sites, as well as geologic mapping and rock sampling.

<urn:uuid:f6764f84-b982-4cff-a934-b4e80524f062>

IBM invents ’3D nanoprinter’ for microscopic objects April 25, 2014 IBM scientists have invented a tiny “chisel” with a nano-sized heatable silicon tip that creates patterns and structures on a microscopic scale. The tip, similar to the kind used in atomic force microscopes, is attached to a bendable cantilever that scans the surface of the substrate material with the accuracy of one nanometer. Unlike conventional 3D printers, by applying heat and force, the nanosized tip can remove (rather than add) material based on predefined patterns, thus operating like a “nanomilling” machine with ultra-high precision. This new capability could improve the prototyping of new transistor devices, such as tunneling field effect transistors, for more energy efficient and faster electronics for anything from cloud data centers to smartphones. By the end 2014, IBM hopes to begin exploring the use of this technology for its research with graphene. “To create more energy-efficient clouds and crunch Big Data faster we need a new generation of technologies including new transistors, but before going into mass production, new techniques are needed for prototyping below 30 nanometers,” said Dr. Armin Knoll, a physicist at IBM Research – Zurich. “With our new technique, we achieve very high resolution at 10 nanometers at greatly reduced cost and complexity. In particular, by controlling the amount of material evaporated, 3D relief patterns can also be produced at the unprecedented accuracy of merely one nanometer in a vertical direction. Now it’s up to the imagination of scientists and engineers.” Other applications include nano-sized security tags to prevent the forgery of documents like currency, passports and priceless works of art, and quantum computing and communications (the nano-sized tip could be used to create high quality patterns to control and manipulate light at unprecedented precision). Several weeks ago the firm shipped its first NanoFrazor to McGill University’s Nanotools Microfab, where scientists and students will use the tool’s unique fabrication capabilities to experiment with ideas for designing novel nano-devices. To promote the new technology, scientists etched a microscopic National Geographic Kids magazine cover in 10 minutes onto a polymer. The resulting magazine cover is so small at 11 x 14 micrometers that 2,000 can fit on a grain of salt. Today (April 25), IBM claimed its ninth GUINNESS WORLD RECORDS title for the Smallest Magazine Cover at the USA Science & Engineering Festival in Washington, D.C. Visible through a Zeiss microscope, the cover will be on display there on April 26 and 27. Abstract of Science paper For patterning organic resists, optical and electron beam lithography are the most established methods; however, at resolutions below 30 nanometers, inherent problems result from unwanted exposure of the resist in nearby areas. We present a scanning probe lithography method based on the local desorption of a glassy organic resist by a heatable probe. We demonstrate patterning at a half pitch down to 15 nanometers without proximity corrections and with throughputs approaching those of Gaussian electron beam lithography at similar resolution. These patterns can be transferred to other substrates, and material can be removed in successive steps in order to fabricate complex three-dimensional structures. Abstract of Advanced Materials paper 3D patterning by means of probe-assisted thermal decomposition has been achieved on phthalaldehyde polymer films with 1 nm vertical resolution and 40 nm lateral resolution. Highly efficient patterning is enabled by a self-amplified depolymerization mechanism. Pixel writing speeds on the order of microseconds are demonstrated. - David Pires et al., Nanoscale Three-Dimensional Patterning of Molecular Resists by Scanning Probes, Science, 2014, DOI: 10.1126/science.1187851 - Armin W. Knoll et al., Probe-Based 3-D Nanolithography Using Self-Amplified Depolymerization Polymers, Advanced Materials, 2014, DOI: 10.1002/adma.200904386

<urn:uuid:f5150aaa-3dae-4111-b8e2-ba16176586fe>

On top of eating a diet high in saturated fats and cholesterol, social stress may cause the body to develop and store more abdominal fat, which is a precursor to heart disease, according to researchers with Wake Forest University School of Medicine. Abdominal fat is believed to behave differently than fat deposits in other areas of the body, and is believed to speed up harmful plaque build-up in arteries, paving the way for fatal heart disease. The researchers said that socioeconomic status is directly related to obesity in the western world, and so is heart disease. They said that poorer people have fewer resources available to them to eat healthier diets and prevent obesity. By studying monkeys who were fed a western diet high in fat and cholesterol and that were housed in groups that fostered the natural establishment of pecking orders, the researchers observed that subordinate monkeys were often the target of aggression and were left out of grooming sessions. These animals produced stress hormones that led to an increased development of abdominal fat. In female monkeys, this caused their ovaries to produce fewer hormones that typically protect against heart disease in women. Full story here.

<urn:uuid:98f82568-c0f2-4aba-9cc1-2b87dcbadade>

U.S. America. So named from the Konsos, an Indian tribe of the locality. Bleeding Kansas. So called because it was the place where that sanguinary strife commenced which was the prelude of the Civil War of America. According to the Missouri Compromise made in 1820, slavery was never to be introduced into any western region lying beyond 36 30' north latitude. In 1851, the slave-holders of Missouri, by a local act, pushed their west frontier to the river-bank, and slave lords, with their slaves, took possession of the Kansas hunting grounds, declaring that they would “lynch, hang, tar and feather any white-livered abolitionist who presumed to pollute the soil.” In 1854, thirty New England free-soilers crossed the river in open boats; they were soon joined by others, and dared the slavers to carry out their threats. Many a fierce battle was fought, but in 1861 Bleeding Kansas was admitted into the Union as a free state. (W. Hepworth Dixon: New America, vol. i. chap. 2.)

<urn:uuid:be25fc28-9312-4644-a558-76155bc1293f>

Salt vines in use on Uoagranyu, removing sodium and magnesium salts from ocean water during the terraformation process Salt vines are essentially a solar-powered, biological desalination system based on wall-climbing vines. Most consist of a single, fairly straight trunk from which a flat, roughly rectangular array of branches and leaves grow, reflecting their origins as a trellis-grown vine that were typically arranged in much the same way as photovoltaic panels to maximize their light exposure. The desalination process occurs primarily along the single, fairly straight trunk as it transports water and nutrients to the stems and leaves. The desalination process is gradual and most forms of the plant need about two to three meters of height to convert water as saline as Earth's oceans into freshwater. Originally this was exuded along the trunk and in sacrificial leaves with salt concentrating on the lower portion of the plant. Modern species of salt vines address the salt by many methods, depending on the intended application. Industrial-scale desalination vines tend to exude from their trunk so it falls around the base of the plant with the expectation operators or some mechanism will collect it. Others will concentrate it in pseudo-fruits, sometimes even produce large salt crystals in a thin gourd. Those crossed with deliplants use it to simulate salt-cured meats and cheeses. Some still collect it in sacrificial leaves, which may be dried to produce flavored salts (garlic, hot peppers, cilantro, and others are known). Diversification of salt vines is mostly based on application. They are rarely used in large-scale industrial desalination anymore because of low energy efficiencies compared to nanotechnological, algal, or even Information Age reverse osmosis desalination techniques. However, such salt vines are the most productive, delivering hundreds of liters of distilled water per day per square meter of vine, but have the expectation of bountiful hydroponic nutrients, such as sewage, sun-tracking trellises, and constant attention from agrimonkeys, synsects, etcetera. Other high capacity vines are designed for independent operation, such as nurturing non-halophilic plants and ecosystems in desolate environments and may be used to create oases or verdant oceanic islands. These tend to feature deep-growing roots that can seek out saline aquifers and cleverly balanced tropisms to that throttle the vine's operation to avoid depleting the soil of nutrients, burying itself in excess salt, and so on. Another common application is to provide safety for travelers in isolated areas. These low-output vines may store water in their trunks, where it may be squeezed out or eaten by travelers, or in durable gourds. These salt "vines" are often engineered to stand on their own as shrubs or small trees so they aren't trampled. Some may be planted at exit ramps of road roots. The final notable application for salt vines is gardening: a few low-output vines can easily meet the needs of an isolated home while growing various savory deliplant fruits, like salt-cured pork or feta cheese. Salt vines are a plant that originated in the Second Century AT as humanity rushed to address its chronic shortages of freshwater. In that era, extant aquifers were almost exhausted and rising seas were endangering coastal freshwater supplies. "Salt vines" were one solution, essentially a solar-powered, biological desalination system. The original vines were intended for controlled hydroponic conditions owing to contemporary, pervasive fears of genetically modified organisms. They were designed to grow on trellises, and keeping their roots in hydroponic piping allowed the trellises to track the sun without injuring the roots as would have happened had they been planted in soil. Initially, output was low and limited by the speed of capillary action. A Second Century trellis of salt vines produced about two liters of freshwater per square meter where the vines could intercept five kilowatt-hours or more of sunlight daily. The engineering improved rapidly, though, and well-fed salt vines could produce hundreds of liters per square meter daily by the mid-300s. This was a shadow of non-biological desalination, which needed somewhat less than one kilowatt-hour per cubic meter of desalinized seawater by the same era. However, such desalination systems required energy from a separate power plant, and required a substantial investment in the system itself. The early salt vines were a low-cost, self-growing addition to sewer treatment plants. This gave the vines a viable economic niche. For a couple of centuries they were quite common on Earth. Variants were engineered to help bring water to parts of Earth dried out by climate change. For example, "mangrove salt vines" could shelter drying ocean islands and coasts from waves and supply water inland. Others were used where farmland had grown salty from centuries of irrigation, or where depletion of aquifers had led to saltwater intrusion. They were mostly obsolete by the Technocalypse and hard hit by a number of plagues, but revived during The Recovery for those same restorative purposes. A heavily engineered variant found use on Mars before the Technocalypse wiped those out. They were able to process water and permafrost contaminated by Mars' pervasive perchlorate salts to supply habitats and terraforming oases with freshwater. Similar salt vines found work in some interstellar colonies during the First Federation as tools for terraforming, ecopoesis and habitat life support. In the 11th Millennium AT, salt vines have largely transitioned to a completely different niche: low maintenance desalination. Nanotechnological and engineered algal solutions are much more space- and energy-efficient, and better suited for reliable, controllable utilities. Modern salt vines have been re-engineered to survive in low nutrient, desolate environments to support travelers and hermits, or create oases. Others have been hybridized with deliplants to produce assorted salty foods and are popular with gardeners. Environmental Engineering - Text by M. Alan Kazlev, from the original by Robert J. Hall Ensuring environments remain favourable to bionts. Includes both environmental protection (pollution control, waste recycling or treatment) and habitat biosphere optimization, biont hygiene and health issues and standards, and biosphere engineering in general (biospherics).

<urn:uuid:01dd1aad-ae91-4895-a613-8ecba07c709b>

Gaining more weight during pregnancy can substantially reduce a baby’s exposure to pesticides that have accumulated in a mother’s body, according to new research. Pregnant women who don’t gain enough weight lose fat when the fetus grows. This releases fat-soluble chemicals such as DDT into the bloodstream, which reaches the fetus. “This study suggests that sufficient weight gain during pregnancy may help to dilute certain chemicals that store in fat, reducing exposure to the fetus,” said Jonathan Chevrier, an epidemiologist at McGill University in Montreal who did not participate in the research. Exposure to persistent organic pollutants, or POPs, in the womb has been linked to developmental disorders and learning delays, reduced immune system function and changes in hormones. Only a few studies have investigated how pregnancy weight gain may affect a baby’s exposures. In the new study, scientists compared weight gain for 325 expectant mothers from Avilés, Spain, with the levels of 35 chemicals in their babies’ umbilical cord blood. Included were brominated flame retardants, organochlorine pesticides such as DDT and polychlorinated biphenyls, or PCBs. The babies’ exposure to all the chemicals decreased as pregnancy weight gain increased, according to the study. However, when the scientists accounted for other factors known to influence concentrations – such as a mother’ s age and how much fish she ate – the association was significant for only two chemicals: a byproduct of the insecticide lindane called beta-HCH and a DDT metabolite. DDT was banned in the United States in 1972 because it was building up in the environment. Agricultural use of lindane was banned in 2006 due to concerns over its effects on the nervous system. For every pound of pregnancy weight gain, the researchers saw a 0.75 percent decrease in DDE in the cord blood and a 1.4 percent decrease in beta-HCH. For the average woman who gained about 31 pounds during pregnancy, that’s about a 22 percent decrease in DDE and a 42 percent decrease in beta-HCH. The researchers from Spain’s University of Oviedo wrote that if a pregnant woman has inadequate body fat, she could lose fat stores during the last trimester, when the baby grows rapidly. “This mobilization effect to meet the fetal demand may trigger the release of POPs to the bloodstream, where they may become available and cross the placenta barrier,” they said in the journal Environmental Health Perspectives. The U.S. Institute of Medicine and the World Health Organization recommend that normal-weight women (determined by the Body Mass Index) gain between 25 and 35 pounds during pregnancy. In the new study, more than 40 percent of mothers gained excessive weight while 25 percent of mothers gained too little. Mothers were asked to recall their own starting weight, so it’s possible that some may have gained more or less than recorded. For PCBs, there may have been no significant link to weight gain because the mothers’ consumption of fish is a stronger factor determining their babies’ exposures. PCBs have been linked to reduced IQs and other effects in children exposed in the womb. This article originally ran at Environmental Health News, a news source published by Environmental Health Sciences, a nonprofit media company.

<urn:uuid:8752a656-d8a9-422c-bebe-6db7611da750>

America’s children are more overweight than ever before despite continued efforts to educate and programs designed to increase activity and improve the nutritional value in school lunches. Parents can help their children become more active by taking the following ten steps. 1. Create safe places. Watch over children’s activities to ensure the environment is a safe and comfortable place for them to engage in physical activities. Children are more likely to be willing to engage in physical activity if they feel safe. 2. Set a good example. Children learn by watching their parents. When parents are active themselves, it is more likely children will follow the example. When parents are not active, yet pushing their children to be more active, children are less likely to comply. 3. Promote physical activity. Parents need to encourage their children to be more active not just at home, but also at school and with friends. 4. Limit sitting around time. Parents need to set limits on how much time their children are allowed to be sitting and engaged in non-physical activity such as watching television or playing on the computer. 5. Establish a routine. Studies have proven when people have exercise built in as part of a daily routine, they are more likely to continue exercising. This is also true for children. Routine physical activity is more likely to continue. 6. Coach a team. One way to involve children in physical activity is for parents to become directly involved by coaching a team. It does not have to be a intramural or city team; encourage children to participate in neighborhood sports. 7. Set up a home gym. Children can become involved by creating a gym using household items. Canned items can serve as weights; chairs can be used for bars or benches. 8. Engage children in aerobic activities. Take a family walk after dinner. Take t he child’s heart rate at the beginning, during and after the activity to show them how hard they are working. 9. Throw an activity party. Use celebratory events to engage children in physical activity. Include activities that require physical exertion instead of sit-down games. 10. Work with your children’s schools. Ensure your children’s schools offer time for physical activity for all students. If parents take these steps to help their children become more active it can help reduce the obesity problems of many children. By setting good examples, parents too an reduce weight and lead more healthy lives. The copyright of the article “10 Steps for Parents to Make Physical Activity Easy for Their Children” is owned by Cheryl Weldon and permission to republish in print or online must be granted by the author in writing.

<urn:uuid:70ea8bfd-8190-4da8-bcde-c34ac98ceb49>

Euler 221 – Alexandrian Numbers When I came upon this Euler problem, and saw it was based on my namesake, I couldn’t help going for it. As with many of the Project Euler problems, the trick is to find a technique that reduces the brute force solution into something more efficient. ``` ``` ``````The functions from the original problem can be re-written to: A = p(p + d)((p^2 + 1)/d + p) `````` The Alexandrian numbers are calculated from the new function, where d runs over divisors of p^2+1 and p runs over all positive integers. Used a fast Divisor routine that I Googled, then started building a Set (which is speed optimized to avoid duplicates) until length is 15K. Convert to a List, then sort and display 150,000th number. Numbers 1 thru 6 also listed to verify computation working. Runs in about 10 mins on my quad core iMac. ``` ``` ``````# e221.py from math import sqrt from functools import reduce def appendEs2Sequences(sequences, es): result = [] if not sequences: for e in es: result.append([e]) else: for e in es: result += [seq + [e] for seq in sequences] return result def primefactors(n): i = 2 while i <= sqrt(n): if n % i == 0: l = primefactors(n // i) l.append(i) return l i += 1 return [n] def factorGenerator(n): p = primefactors(n) factors = {} for p1 in p: try: factors[p1] += 1 except KeyError: factors[p1] = 1 return factors def divisors(n): factors = factorGenerator(n) divisors = [] listexponents = [list(map(lambda x:k ** x, list(range(0, factors[k] + 1)))) for k in factors.keys()] listfactors = reduce(appendEs2Sequences, listexponents, []) for f in listfactors: divisors.append(reduce(lambda x, y: x * y, f, 1)) divisors.sort() return divisors if __name__ == "__main__": A = set() p = 1 while len(A) <= 1500001: for d in divisors((p * p) + 1): A.add(int(p * (p + d) * (p + ((p * p) + 1) / d))) p += 1 L = list(A) L.sort() for i in [1,2,3,4,5,6,150000]: print (str(i) + ": " + str(L[i-1])) ``````

crawl-data/CC-MAIN-2022-33/segments/1659882571584.72/warc/CC-MAIN-20220812045352-20220812075352-00029.warc.gz

Protozoans are single–celled eukaryotes with animal–like behaviors, such as movement and a lack of cell walls. Many of them are pathogens that cause diseases, such as malaria. Some parasitic worms or helminths are called macroparasites because they can be seen with the naked eye. These worms live and feed inside their living host while adversely impacting them. They can even live in the host for years. Parasitic worms cause various diseases, for example, helminthiasis and enterobiasis.

<urn:uuid:b17318e5-2446-41e5-9a6d-57a07bbf1cb6>

Home » Math Theory » Numbers » Estimation of Numbers (Rounding Off Method) # Estimation of Numbers (Rounding Off Method) ## Introduction Using estimation, you can predict or identify a response close to the correct answer. It helps make decisions quickly and generates a range of possible outcomes close enough to be helpful. Estimation is another method for making numbers easier to work with to estimate when we are only required to have a general idea of how many. An estimate is an educated guess based on knowledge or information already known. This article will define the estimation of numbers and provide examples of how to round off numbers. ## What is the Estimation of Numbers? We can simplify calculations by estimating a number, which is a reasonable guess. It calls for mental math manipulation. We engage in estimation without even realizing it. For example, a little kid predicts how many candies he can obtain from his parents, estimates a person’s weight, and a stock market analyst forecasts market trend. Estimation creates an approximate judgment or opinion about size, amount, weight, etc. In other words, estimation is to calculate approximately. We use the estimation of numbers daily; it is a fundamental component of mathematics. Of course, there are situations when an estimate won’t do; we frequently need to know the precise figure. You can make two different types of estimating errors. Overestimate. When the estimated number is more than the actual outcome. Underestimate. When the estimated number is less than the actual outcome. ## Why do we perform the estimation of numbers? To avoid complex calculations, estimating numbers refers to approximating or rounding off the numbers when the value is used for some other purpose. The words accurate and estimation have different meanings. In mathematics, the terms “exact” and “estimation” relate to “equal” and “approximate,” respectively. Time can be saved by estimating numbers. We can answer the problem without using a calculator once we have estimated the values. But in mathematics, we always need a precise response. Finding a number sufficiently close to the correct answer is the estimation process. But that is not an accurate response. ## Estimation of Numbers (Rounding Off Method) Before even solving the difficulties, we often estimate the solutions in our thoughts regarding mathematics. Although we prefer exact solutions in mathematics, there are occasions when we must approximate the solutions to represent them. In mathematics, one type of estimation that is frequently utilized is rounding off. The value of a number is not changed when it is rounded off; instead, it is brought closer to the following number while maintaining its value. It is done for whole numbers and decimals at different places of thousands, hundreds, tens, tenths, etc. The significant figures are preserved when numbers are rounded off. Hence, the number of figures known with some certainty constitutes the number of important figures. The number is rounded off considering the rounding off digit. The rounding off digit retains if the number that follows to its right is less than 5. Add one to the rounded-off digit if the number is 5 or above. Consider the number 4.2; since 2 is less than 5, it will be rounded off to 4. In contrast, as 6 is greater than 5, the number will be rounded up to 5 if it is 4.6. As a result, we can say: 4.2 ≈ 4 and 4.6 ≈ 5 The approximation between the two values is represented by the symbol ≈. On a big scale, we occasionally also approximate the whole numbers while computing or estimating values. Take 578 as an example; it would become 580, whereas 431 would become 430. Once more, you can see that the approximation is based on the last digit of the whole integer. ## What are Rounding Off Numbers? Rounding off numbers is a method of simplifying numbers to make them easier to understand or work with. When an exact answer isn’t required, and an approximation will do, rounding can be used. ### Rounding Off Whole Numbers The following are the basic steps in rounding off whole numbers. Step 1: Determine the round off digit. Step 2: Look at the digit that follows the rounded off digit to the right. Do not change the round-off digit if the number is less than 5. Add one to the rounded off digit if the number is 5 or above. Step 3: Replace all the digits with zeros to the right of the round-off digit. For example, let us say that we must round off 4,378 to the nearest hundreds. Following the steps, we have, Step 1: Determine the round off digit. The rounding off digit is the hundreds place. In 4,378, the number 3 is in the hundreds place. Step 2: Look at the digit that follows the rounded off digit to the right. Do not change the round-off digit if the number is less than 5. Add one to the rounded off digit if the number is 5 or above. In 4,378, the number to the right of 3 is 7. Since 7 is greater than 5, we add 1 to 3. Thus, the digit in the hundreds place becomes 4. Step 3: Replace all the digits with zeros to the right of the round-off digit. The digits 7 and 8 will be replaced with zeros. Thus, 4378 is 4400 when rounded off to the nearest hundreds. Also, on the number line, 4378 is more than halfway from 4300 to 4400. ### Rounding Off to Nearest Tens Step 1: Identify the digit in the tens place. Step 2: Look at the digit in the ones place. If the number is less than five, do not change the digit in the tens place. Add one to the tens place if the number is 5 or above. Step 3: Replace all the digits with zeros to the right of the tens place. Examples Use the method of rounding off numbers to solve the following: ( a ) Round off 567 to the nearest tens ( b ) Round off 46, 983 to the nearest tens ( c ) Round off 126, 879 to the nearest tens Solution ( a ) Round off 567 to the nearest tens Step 1: Identify the digit in the tens place. In 567, The digit in the tens place is 6. Step 2: Look at the digit in the ones place. If the number is less than five, do not change the digit in the tens place. Add one to the tens place if the number is 5 or above. The digit to the right of 6 is 7, greater than 5. We must add 1 to the digit in the tens place. Hence, 6 + 1 = 7. Step 3: Replace all the digits with zeros to the right of the tens place. Only the number 7 will be replaced with zero. Thus, 567 will be 570 when rounded off to the nearest tens. ( b ) Round off 46, 983 to the nearest tens Step 1: Identify the digit in the tens place. In 46, 983, the digit in the tens place is 8. Step 2: Look at the digit in the ones place. If the number is less than five, do not change the digit in the tens place. Add one to the tens place if the number is 5 or above. The tens digit retains since the digit to the right of the tens place is 3, which is less than 5. Step 3: Replace all the digits with zeros to the right of the tens place. Only the number 3 will be replaced with zero. Thus, 46, 983 will be 46, 980  when rounded off to the nearest tens. ( c ) Round off 126, 879 to the nearest tens Step 1: Identify the digit in the tens place. In 126, 879, the digit in the tens place is 7. Step 2: Look at the digit in the ones place. If the number is less than five, do not change the digit in the tens place. Add one to the tens place if the number is 5 or above. We must add 1 to the digit in the tens place since 9 is greater than 5. Hence, 7 + 1 = 8. Step 3: Replace all the digits with zeros to the right of the tens place. Only the number 9 will be replaced with zero. Thus, 126, 879 will be 126, 880 when rounded off to the nearest tens. ### Rounding Off to Nearest Hundreds The following are the basic steps in rounding off to nearest hundreds. Step 1: Identify the digit in the hundreds place. Step 2: Look at the digit in the tens place. Do not change the digit in the hundreds place if the number is less than 5. Add one to the hundreds place if the number is 5 or above. Step 3: Replace all the digits with zeros to the right of the hundreds place. Examples Use the method of rounding off numbers to solve the following: ( a ) Round off 125 to the nearest hundreds ( b ) Round off 15,275 to the nearest hundreds ( c ) Round off 574, 869 to the nearest hundreds Solution ( a ) Round off 125 to the nearest hundreds Step 1: Identify the digit in the hundreds place. In 125, the digit in the hundreds place is 1. Step 2: Look at the digit in the tens place. Do not change the digit in the hundreds place if the number is less than 5. Add one to the hundreds place if the number is 5 or above. Since the digit to the right of 1 is 2, which is less than 5, the digit in the hundreds place retains. Step 3: Replace all the digits with zeros to the right of the hundreds place. The numbers 2 and 5 will be replaced with zero. Thus, 125 will be 100 when rounded off to the nearest hundreds. ( b ) Round off 15,275 to the nearest hundreds Step 1: Identify the digit in the hundreds place. In 15,275, the digit in the hundreds place is 2. Step 2: Look at the digit in the tens place. Do not change the digit in the hundreds place if the number is less than 5. Add one to the hundreds place if the number is 5 or above. We must add 1 to the digit in the hundreds place since the digit to the right of the hundreds place is 7, which is greater than 5; hence, 2 + 1 = 3. Step 3: Replace all the digits with zeros to the right of the hundreds place. The numbers 7 and 5 in the tens and ones place will be replaced with zero. Thus, 15,275 will be 15,300 when rounded off to the nearest hundreds. ( c ) Round off 574, 869 to the nearest hundreds Step 1: Identify the digit in the hundreds place. In 574, 869, the digit in the hundreds place is 8. Step 2: Look at the digit in the tens place. Do not change the digit in the hundreds place if the number is less than 5. Add one to the hundreds place if the number is 5 or above. We must add 1 to the digit in the hundreds place since the digit to the right of the hundreds place is 6, which is greater than 5; hence, 8 + 1 = 9. Step 3: Replace all the digits with zeros to the right of the hundreds place. The numbers 6 and 9 in the tens and ones places will be replaced with zero. Thus, 574 869 will be 574 900  when rounded off to the nearest hundreds. ### Rounding Off to Nearest Thousands The following are the basic steps in rounding off to nearest thousands. Step 1: Identify the digit in the thousands place. Step 2: Look at the digit in the hundreds place. If the number is less than 5, do not change the digit in the thousands place. Add one to the thousands place if the number is 5 or above. Step 3: Replace all the digits with zeros to the right of the thousands place. Examples Use the method of rounding off numbers to solve the following: ( a ) Round off 2,367 to the nearest thousands ( b ) Round off 45,872 to the nearest thousands ( c ) Round off 768, 578 to the nearest thousands Solution ( a ) Round off 2,367 to the nearest thousands Step 1: Identify the digit in the thousands place. In 2,367, the digit in the thousands place is 2. Step 2: Look at the digit in the hundreds place. If the number is less than 5 do not change the digit in the thousands place. Add one to the thousands place if the number is 5 or above. The digit in the thousands place retains since the digit to the right of 2 is 3, which is less than 5. Step 3: Replace all the digits with zeros to the right of the thousands place. The numbers 3, 6, and 7 will be replaced with zero. Thus, 2 367 will be 2 000 when rounded off to the nearest thousands. ( b ) Round off 45,872 to the nearest thousands Step 1: Identify the digit in the thousands place. In 45,872, the digit in the thousands place is 5. Step 2: Look at the digit in the hundreds place. If the number is less than 5, do not change the digit in the thousands place. Add one to the thousands place if the number is 5 or above. We must add 1 to the digit in the thousands place Since the digit to the right of the thousands place is 8, which is greater than 5; hence, 5 + 1 = 6. Step 3: Replace all the digits with zeros to the right of the thousands place. The numbers 8, 7, and 2 will be replaced with zero. Thus, 45,872 will be 46,000 when rounded off to the nearest thousand. ( c ) Round off 768, 578 to the nearest thousands Step 1: Identify the digit in the thousands place. In 768, 578, the digit in the thousands place is 8. Step 2: Look at the digit in the hundreds place. If the number is less than 5, Do not change the digit in the thousands place. Add one to the thousands place if the number is 5 or above. We must add 1 to the digit in the thousands place since the digit to the right of the thousands place is 5. Hence, 8 + 1 = 9. Step 3: Replace all the digits with zeros to the right of the thousands place. The numbers 5, 7, and 8 will be replaced with zero. Thus, 768,578 will be 769,000 when rounded off to the nearest thousand. ### Rounding Off Decimal Numbers The following are the basic steps in rounding off decimal numbers. Step 1: Find the place value of the number you are rounding to (round off digit). Step 2: Look at the digit that follows the rounded off digit to the right. Do not change the round-off digit if the number is less than 5. Add one to the rounded off digit if the number is 5 or above. Step 3: Replace all the digits with zeros to the right of the round-off digit. ## Examples Use the method of rounding off numbers to solve the following: ( a ) Round off 3425.567 to the nearest tenths ( b ) Round off 93.0635 to the nearest hundredths ( c ) Round off 3,787. 89586 to the nearest thousandths Solution ( a ) Round off 342.567 to the nearest tenths Step 1: Identify the digit in the tenths place. In 342.567, the digit in the tenths place is 5. Step 2: Look at the digit in the hundredths place. Do not change the digit in the tenths place if the number is less than 5. Add one to the tenths place if the number is 5 or above. We must add 1 to the digit in the tenths place since the digit to the right of the tenths place is 6, which is greater than 5; hence, 5 + 1 = 6. Step 3: Replace all the digits with zeros to the right of the thousands place. The numbers 6 and 7 that are in the hundredths and thousandths place will be replaced with zero. Thus, 342.567 will be 342.600 or 342.6 when rounded off to the nearest tenths. ( b ) Round off 93.0635 to the nearest hundredths Step 1: Identify the digit in the hundredths place. In 93.0635, the digit in the hundredths place is 6. Step 2: Look at the digit in the thousandths place. Do not change the digit in the hundredths place if the number is less than 5. Add one to the hundredths place if the number is 5 or above. The digit in the hundredths place retains since the digit to the right of the 6 is less than 5. Step 3: Replace all the digits with zeros to the right of the hundredths place. The numbers 3 and 5 in the thousandths and ten thousandths place will be replaced with zero. Thus, 93.0635 will be 93.0600 or 93.06 when rounded off to the nearest hundredths. ( c ) Round off 3,787. 89486 to the nearest thousandths Step 1: Identify the digit in the thousandths place. In 3,787. 89486, the digit in the thousandths place is 4. Step 2: Look at the digit in the ten thousandths place. Do not change the digit in the thousandths place if the number is less than 5. Add one to the thousandths place if the number is 5 or above. 8 is the digit in the ten thousandths place and is greater than 5. Hence, 4 + 1 = 5. Step 3: Replace all the digits with zeros to the right of the thousandths place. The numbers 8 and 6 in the ten thousandths and hundred thousandths place will be replaced with zero. Thus, 3,787. 89486 will be 3,787. 89500 or 3,787. 895 when rounded off to the nearest thousandths. ## Summary Estimation of Numbers Estimation creates an approximate judgment or opinion about size, amount, weight, etc. In other words, estimation is to calculate approximately. You can make two different types of estimating errors. Overestimate. When the estimated number is more than the actual outcome. Underestimate. When the estimated number is less than the actual outcome. Rounding Off Numbers Rounding off numbers is a method of simplifying numbers to make them easier to understand or work with. When an exact answer isn’t required, and an approximation will do, rounding can be used. The following are the basic steps in rounding off numbers. Step 1: Determine the round off digit. Step 2: Look at the digit that follows the rounded off digit to the right. Do not change the round-off digit if the number is less than 5. Add one to the rounded off digit if the number is 5 or above. Rounding Down Do not change the rounding off digit if the number immediately to the right of it is less than 5. Then, replace all the digits with zeros to the right of the rounding off digit. Rounding Up Add one to the rounding off digit if the number immediately to the right of it is greater or equal to 5. Then, replace all the digits with zeros to the right of the rounding off digit. Step 3: Replace all the digits with zeros to the right of the round-off digit.

crawl-data/CC-MAIN-2024-30/segments/1720763514828.10/warc/CC-MAIN-20240718095603-20240718125603-00603.warc.gz

### Home > AC > Chapter 9 > Lesson 9.1.2 > Problem9-20 9-20. Use a generic rectangle to multiply $\left(x + 2\right)\left(3x − 5\right)$. Multiply each column value by each row value to fill the rectangle. $= 3x² + x − 10$ 1. What is $\left(3x^{2} + x − 10\right) + \left(x + 2\right)$? How do you know? $3x² + x−10$ is the same as $\left(x + 2\right)\left(3x − 5\right)$. The product divided by one factor is the other factor. $3x − 5$ 2. Likewise, determine $\left(3x^{2} + x − 10\right) + \left(3x − 5\right)$. • See part (a).

crawl-data/CC-MAIN-2021-21/segments/1620243988927.95/warc/CC-MAIN-20210508211857-20210509001857-00552.warc.gz

# Quick Answer: How Do You Tell If A Fraction Is Less Than 1 2? ## What is a fraction greater than 1 2? 1 Expert Answer 2/3, 3/4, 3/5, 4/5, 5/6, 4/7, 5/7, 6/7 and so on.. ## What is proper fraction? : a fraction in which the numerator is less or of lower degree than the denominator. ## What fraction is bigger 3 4 or 1 2? Which Fraction is Bigger Calculator. Answer: Yes, 3/4 is bigger than 1/2. You can confirm this by converting both fractions to decimals. The decimal 0.75 is bigger than 0.5, so 3/4 is bigger than 1/2. ## What does half of mean in math? One of the two equal parts of something. ## How do you tell if a fraction is less than 1? Step 1: Compare denominators. If they are different, rewrite one or both fractions with a common denominator. Step 2: Check the numerators. If the denominators are the same, then the fraction with the greater numerator is the greater fraction. ## What number is less than 1 2? Answer and Explanation: The fraction 1/4 is less than 1/2 . This might seem strange since the number 4 is larger than the number 2. ## Is a quarter more than a half? is that half is one of two usually roughly equal parts into which anything may be divided, or considered as divided; — sometimes followed by of; as, a half of an apple while quarter is any one of four equal parts into which something has been divided. ## What fraction is more than half? If the numerator is greater than half of the denominator, then the fraction is greater than one-half.) Use fractions that are equivalent to one-half (If you’re trying to determine if 4/6 is greater than 1/2, find a fraction with the same denominator and that is also equivalent to 1/2. In this case, 3/6. ## What are the 7 types of fraction? The six kinds of fractions are, proper fractions, improper fractions, mixed fractions, like fractions, unlike fractions and equivalent fractions. ## Is 2 thirds more than a half? Yes, 2/3 is more than a half. If you are measuring the same quantity, anyway. … You can clearly see the line for 2/3 cup is higher than the line for 1/2 cup, so 2/3 fills more of the cup than 1/2. ## Which is bigger one third or one half? No, one-third is NOT more than one-half. One-half is more than one-third. Because the two fractions, 1/3 and 1/2, have the same numerator (remember,… ## What is less than a half? Examples of fractions less than one-half include, one-fourth, one-third, one-fifth and three-eighths. Any fraction that represents less than half of a whole is considered less than one-half. A fraction is not a whole number, but instead it is a representation of a whole. ## What does the fraction 1/2 mean? What does this fraction mean? Well, if we picture a pie, the bottom number tells us how many slices to slice the pie, and the top number tells us how many of those slices we can have. So 1/2 tells us that we have sliced our pie into two slices, and we can take 1 of those slices. ## What is 1/2 in a whole number? In the same way, 1/2 is never equal to a whole number. It is equal to 0.5, which has a decimal but not a fraction. You could multiply by 0.5 the same way you multiply by 5, except that you might have at least one extra decimal place in the answer.

crawl-data/CC-MAIN-2021-04/segments/1610704835901.90/warc/CC-MAIN-20210128040619-20210128070619-00670.warc.gz

Approaching Calculus-Based Introductory Physics PhotonTrail I'm currently self-studying introductory physics. I am able to understand the derivation of equations in my notes, but I find myself struggling to apply calculus in the problem sets. I tend to instinctively solve the questions algebraically, and will begin to really contemplate using calculus only if the question is too complex to solve algebraically. Is this the right approach? I have a nagging suspicion that I'm not approaching the questions at the depth I am supposed to. Sure I can get the correct solution, but it feels as if I took a shortcut of sorts. Is it a problem with me, or is it simply a matter of questions that are too simple? Related Academic Guidance News on Phys.org bp_psy If it can be done correctly with basic algebra then it should be done with basic algebra. Trying to do it with calculus will only be an exercise in over-complicating stuff. In basic intro mechanics you need calculus to derive your basic equations of motion and you are mostly done.. Doing those simple problems with calculus means that you are just deriving the same formulas over and over and there is very little insight to gain. If you are using a more advanced introductory text like Kleppner/Kolenkow you will have to use calculus because the problem actually requires it, not because you force yourself. jimgram Ask yourself if a problem is linear or non-linear. For example, if car (or particle)is moving and has a force acting on it (say torque from an automobile engine) then it is accelerating and you need to know its velocity after a period of time. The linear kinematic equation is is vf=a*t. But an internal combustion engine does not have a linear torque curve - it's torque is different at different speeds. So, acceleration is non-linear over time. In this case, v equals the integral of acceleration. You must use calculus. I think you'll find most physics problems are non-linear. DimReg In physics, you have the choice of problem solving technique, as long as it works. The fact that you are often finding simple solutions of these problems is a good thing, because it means you are actually thinking about your solutions. It's actually an important skill to recognize when more advanced math techniques are needed/ If you want more practice using calculus, try generalizing things in your problems, such as making the coefficient of friction depend on position, or make densities not uniform. PhotonTrail Thanks for the replies! I gathered that it's okay to use algebraic solutions as long if the questions are not demanding enough. But how does one know which algebraic equations to commit to memory? Stuff like $s=ut+\frac{1}{2}at^2$ and $\vec{E}=\frac{\sigma}{2\epsilon_0}$ are trivial enough to remember and come naturally, but where does one stop? Should I memorize equations like the one for the electric field due to a dipole $\vec{E}(\vec{r})=\frac{1}{4\pi\epsilon_0}(-\frac{\vec{p}}{r^3}+\frac{3(\vec{p}\cdot\vec{r}) \vec{r}}{r^5})$ or hope to have enough time to derive them every time I need to use them? DimReg That depends on what you are learning physics for. If it's just for fun/personal enrichment, just memorize only what seems important. If it's for class, memorize what the teacher expects you to memorize (you can ask them). If it's for work, then you'll memorize what you need because you'll use it over and over. It's more useful to become familiar enough with the fundamentals to derive simple formulas like E = σ/2ϵ0 quickly, than to have that formula memorized. Two good examples are the formulas you cited as "simple" formulas. If you can't derive them, then you don't understand the basics of physics well enough. The dipole formula on the other hand takes more work, and it's reasonable if you don't know how to derive it (I don't know off the top of my head). But you should surely know what a dipole is. Edit: note that since I know what a dipole is, I know where to start rederiving the electric field. At that point, it's just a matter of if I can solve the math. Remember, it's physics not biology. Memorize the formula for moment of inertial, but don't memorize the moment of inertia of a wheel. Just be economical in your memorization. Last edited: BruceW Homework Helper The linear kinematic equation is is vf=a*t. But an internal combustion engine does not have a linear torque curve - it's torque is different at different speeds. So, acceleration is non-linear over time. In this case, v equals the integral of acceleration. You must use calculus. I think you'll find most physics problems are non-linear. That's not the usual definition of a non-linear system. But I would agree that generally in physics problems, the acceleration will not be constant. PhotonTrail said: I gathered that it's okay to use algebraic solutions as long if the questions are not demanding enough. But how does one know which algebraic equations to commit to memory? Yeah, good question. I guess there will always be a mixture of some equations which you have memorised, and some equations which you can derive. When I was undergraduate (not so long ago), a fairly large part of the course was to learn how to do various derivations. At the very least, there is always some reasonable explanation for why a certain equation 'works'. Also, there are equations which you probably don't really need to memorise or be able to derive. For example, the equation for the dipole field as you mentioned. I don't think I was ever required to memorise it for my undergraduate. And I could probably derive it, given some time, but definitely not in a couple of minutes. The main thing is to understand what the dipole is (as DimReg says), and the important physical principles, e.t.c. Of course, if you are doing a project, or research, or are particularly interested in dipoles, then you will probably know the equation off by heart. But this will probably happen naturally anyway, if you use an equation enough times, it tends to stick :) Physics Forums Values We Value Quality • Topics based on mainstream science • Proper English grammar and spelling We Value Civility • Positive and compassionate attitudes • Patience while debating We Value Productivity • Disciplined to remain on-topic • Recognition of own weaknesses • Solo and co-op problem solving

crawl-data/CC-MAIN-2019-22/segments/1558232257699.34/warc/CC-MAIN-20190524164533-20190524190533-00541.warc.gz

# Converting 3.15 to a Fraction: A Comprehensive Guide Numbers can be expressed in various forms, including decimals, percentages, and fractions. Converting between these representations is a fundamental skill in mathematics. This article focuses on converting the decimal number 3.15 to a fraction. We will explore the steps involved in the conversion process and provide additional insights into fraction-decimal conversions. ### Key Facts 1. 3.15 as a fraction is 63/20. 2. To convert a decimal to a fraction, you can follow these steps: a. Write down the decimal as a fraction of one (decimal/1). b. If the decimal is not a whole number, multiply both the numerator and denominator by 10 until you get an integer at the numerator. c. Simplify (or reduce) the fraction if it is not in the simplest form. 3. There are online calculators and converters available to help you convert decimals to fractions. 4. It is also possible to convert fractions to decimals and millimeters using conversion tables. ## Step 1: Represent 3.15 as a Fraction of One To begin, we write 3.15 as a fraction with a denominator of 1: 3.15=3.1513.15 = \frac{3.15}{1} ## Step 2: Multiply Numerator and Denominator by 100 Since there are two decimal places in 3.15, we multiply both the numerator and denominator by 100, which is 10 raised to the power of 2: 3.151=3.15×1001×100=315100\frac{3.15}{1} = \frac{3.15 \times 100}{1 \times 100} = \frac{315}{100} ## Step 3: Simplify the Fraction (Optional) The fraction 315/100 can be simplified by finding common factors in the numerator and denominator and canceling them out. In this case, both 315 and 100 are divisible by 5: 315100=315÷5100÷5=6320\frac{315}{100} = \frac{315 \div 5}{100 \div 5} = \frac{63}{20} Therefore, 3.15 as a fraction is 63/20. ### General Method for Converting Decimals to Fractions The process of converting any decimal to a fraction follows the same basic steps: 1. Write the decimal as a fraction of one (decimal/1). 2. Multiply both the numerator and denominator by 10 raised to the power of the number of decimal places. 3. Simplify the fraction if possible by finding and canceling out common factors in the numerator and denominator. • Online calculators and converters are available to simplify the conversion process. • It is also possible to convert fractions to decimals and millimeters using conversion tables. • Understanding the concept of fractions and decimals is essential for various mathematical operations and applications. ### Conclusion In summary, converting 3.15 to a fraction involves writing it as a fraction of one, multiplying the numerator and denominator by 100, and simplifying the resulting fraction. This process can be applied to convert any decimal to a fraction. Fractions and decimals are fundamental representations of numbers with wide-ranging applications in mathematics and other fields. ## FAQs 1. What is 3.15 as a fraction? Answer: 3.15 as a fraction is 63/20. 2. How do I convert 3.15 to a fraction? * Write 3.15 as a fraction of one: 3.15/1 * Multiply both the numerator and denominator by 100 (since there are two decimal places): 3.15/1 = 315/100 * Simplify the fraction if possible: 315/100 = 63/20 3. Can I use a calculator to convert decimals to fractions? Answer: Yes, there are online calculators and converters available that can simplify the conversion process. 4. Is there a general method for converting any decimal to a fraction? Answer: Yes, the general method for converting any decimal to a fraction is: * Write the decimal as a fraction of one (decimal/1). * Multiply both the numerator and denominator by 10 raised to the power of the number of decimal places. * Simplify the fraction if possible by finding and canceling out common factors in the numerator and denominator. 5. What are some applications of fractions and decimals? Answer: Fractions and decimals have wide-ranging applications in mathematics and other fields, including: * Measurement and calculations * Proportions and ratios * Percentages and probability * Geometry and trigonometry * Financial calculations * Statistics and data analysis 6. Why is it important to understand how to convert between fractions and decimals? Answer: Understanding the conversion between fractions and decimals is essential for various mathematical operations and applications. It allows us to perform calculations, solve equations, and interpret data accurately. 7. Are there any tricks or shortcuts for converting decimals to fractions? Answer: There are some tricks and shortcuts that can make the conversion process easier, such as: * For decimals with a limited number of decimal places, you can simply multiply the decimal by an appropriate power of 10 and then write the result as a fraction with a denominator equal to the power of 10 used. * For decimals with an infinite number of repeating decimal places, you can use long division to find the exact fraction. 8. What are some common mistakes to avoid when converting decimals to fractions? Answer: Some common mistakes to avoid include: * Not multiplying both the numerator and denominator by the same power of 10. * Not simplifying the fraction to its simplest form. * Misinterpreting repeating decimals and not finding the exact fraction.

crawl-data/CC-MAIN-2024-22/segments/1715971059037.23/warc/CC-MAIN-20240527052359-20240527082359-00769.warc.gz

In 2003 and 2004, the Hubble space telescope looked at a dark patch of sky in the constellation Fornax. After gathering light for about 275 hours, what it found was an image of more than 10,000 distant galaxies in a patch of sky about the size of a grain of sand held at arm’s length. Assuming this patch of sky is typical, we can calculate that there more than 100 billion galaxies in the visible universe. A typical galaxy has about 100 billion stars, and the vast majority of those stars have planets. All of that from a single patch of sky known as the Hubble Ultra Deep Field (HUDF). Of course that assumes the deep field captured by Hubble is typical. There have been a few other deep field observations made, but not a wider survey of different portions of the sky. Now there’s a new project known as Frontier Fields that will answer whether the HUDF is typical or not. The project will make long observations of six dark patches of sky. These images will be similar to the HUDF, and will give us an idea of whether the distribution of galaxies we’ve seen is typical. But there’s another aspect to this project that is equally interesting. The Hubble telescope has different detectors, so it can make multiple observations at the same time. In this case it is the Advanced Camera for Surveys (ACS) and the Wide Field Camera 3 (WFC3). These two detectors look at slightly different patches of sky. So while one is looking at a dark patch of sky, the other is focused on a cluster of galaxies. The Hubble is then rotated so that each camera looks at the other patch. Since the ACS is viewing at visible wavelengths, and WFC3 at infrared wavelengths, we’ll have a wide rage of data for both patches of sky. The reason the project is also looking at galaxy clusters is because galactic clusters are also clusters of dark matter, and together they can gravitationally lens even more distant galaxies. So while one camera is gathering data for a deep field observation, the other is gathering data on even more distant lensed galaxies. Do this for six different locations in the sky and you have a good idea of the distribution of the most distant galaxies in the visible universe. All that from a space telescope that is nearly 24 years old.

<urn:uuid:f082c45e-8391-40d2-87db-0b3727982b7d>

British scientists in 2003 reported the results of a large study of the environmental effects of genetically modified (GM) crops. The farm-scale trials, which cost $8.5 million and lasted four years, were designed to test whether weeds and insects, such as butterflies, bees, and beetles, fared better in fields of conventional crops or of crops that had been genetically altered to be resistant to a herbicide for weed control. A major emphasis of the study was on the importance of crop weeds, which were well known to be of benefit to wildlife by providing cover and food for insects (as well as seeds for birds). The experiment found that fields of GM sugar beet and oilseed rape (canola) were worse for insects than fields of conventional varieties of the crops. GM corn (maize), on the other hand, was better for many types of insects than conventional corn. The study attributed the variation to a difference in the weed burdens of the crops. GM beet and rape were associated with fewer weeds than their non-GM equivalents, whereas GM corn actually had more weeds than conventional corn. It already had been determined that GM crops can crossbreed with wild plants through the spread of their pollen, but new work revealed that the dispersal of seeds carrying modified genetic material also can play an unexpected role in the long-distance spread of the genes. A team headed by Jean-Franƈois Arnaud of the University of Lille, France, found that seeds from hybrids of weed beets and GM sugar-beet crops had escaped to more than 1.5 km (about one mile) from the commercial fields in France where they had arisen. These results suggested that seeds carrying GM material may accidentally be spread by humans, most likely in soil caught on vehicle wheels or transported by other agricultural activities. Once the seeds have escaped, the plants can then cross-pollinate with nearby wild relatives and create new and possibly damaging hybrids with modified genes. Despite the concerns over safety, new and intriguing uses for GM plants were under investigation. The Defense Advanced Research Projects Agency, part of the U.S. Department of Defense, awarded a $2 million grant to plant biologist June Medford of Colorado State University for an ingenious plan to genetically engineer plants to detect a chemical or biological attack by changing colour. Big strides were made in understanding the master controls that plants use to organize their shape and development. A gene dubbed PHANTASTICA was found to control whether tomato plants develop their normal featherlike (pinnately compound) leaf arrangement or an umbrella-like (palmately compound) arrangement like clover. “It’s a very surprising finding, that modifying one gene in the tomato alters the leaf from one form to another,” said Neelima Sinha of the University of California, Davis, who was involved in the research. The same genetic mechanism appeared to be shared by a wide group of flowering plants. In another breakthrough, for the first time in plants, tiny genetic components called microRNAs were found to switch off the expression of shape-regulating genes. MicroRNA molecules, which were first recognized in the early 1990s, are short strands of RNA that are transcribed from parts of an organism’s genetic blueprint that once had been thought to be useless, or “junk,” DNA. Rather than being merely the intermediaries between DNA and protein, as are messenger RNA (mRNA) molecules, they have critical roles themselves in the regulation of gene expression. MicroDNAs work by recognizing and binding to specific mRNAs and bringing about their inactivation or destruction at the appropriate time. A team led by Detlef Weigel of the Max Planck Institute for Developmental Biology, Tübingen, Ger., and James Carrington of Oregon State University found overly high levels of one such microRNA in a mutant Arabidopsis thaliana plant (a favourite model organism of plant geneticists), which grew unusual crinkled and wrinkly leaves. The researchers showed that this microDNA regulates the expression of a set of genes (named TCP genes) that prevent excess cell division in the growing plant. Too much microDNA in the mutant plant allowed too many cells to proliferate in the leaves and caused the crinkling. By contrast, microDNA in normal plants appears at the right level, time, and place to create flat leaves. As more microRNAs were being discovered, their importance in plant growth and development was becoming clearer. This opened up entirely new and exciting possibilities for the use of these molecules as tools to manipulate the activities of plant genes, with potentially enormous scientific and economic benefits. With overtones of the movie Jurassic Park, the oldest plant DNA found to date was extracted from drilled cores of frozen soil in Siberia by a team led by Eske Willerslev of the University of Copenhagen. The DNA fragments, some from plants that lived as long as 400,000 years ago, were identified as belonging to at least 19 different plant families. This ability to recover specimens of ancient DNA directly from soil samples, which would obviate the need for identifiable fossils, could revolutionize studies that attempt to construct a genetic picture of past ecosystems. Because the extracted DNA was broken up into tiny pieces, however, there seemed little chance of resurrecting any of the species. The changing world climate was having wide-ranging effects on the productivity of plant life. From 1982 to 1999, climate change resulted in a 6% increase in plant growth over much of the globe, reported Ramakrishna Nemani of the University of Montana and colleagues after they analyzed climatic ground and satellite data. The largest increase occurred in tropical ecosystems and especially in the Amazon rainforests, which accounted for 42% of the global increase, owing mainly to less cloud cover and the resulting increase in sunlight in that region. As trees and other vegetation grow, they take carbon dioxide from the atmosphere and convert it to solid carbon compounds. It was not clear, however, whether or how the observed growth increase would affect the removal of carbon dioxide, a greenhouse gas widely cited as the major driving force behind global warming, and its storage in terrestrial ecosystems over the long term. The increasingly important role of botanic gardens in understanding and conserving plant life was recognized in July when Kew Gardens in London was made a World Heritage Site by UNESCO. In addition to being known internationally for its historic public gardens and buildings, Kew is a world famous scientific organization, renowned for its living and herbarium collections of plants, research facilities, and contribution on a major scale to conservation and biodiversity.

<urn:uuid:dfc099e4-874d-4fa2-9409-2345f81334fb>

1. ## Trigonometric Equations I'm not sure how to tackle this question, can anyone help me out? It asks; a) Show that $\frac{1 - cos2x}{1 + cos2x} = tan^2x$. b) Hence find the value of $tan22.5^o$ in simplest exact form. 2. Originally Posted by Flay I'm not sure how to tackle this question, can anyone help me out? It asks; a) Show that $\frac{1 - cos2x}{1 + cos2x} = tan^2x$. b) Hence find the value of $tan22.5^o$ in simplest exact form. $\frac{1 - cos2x}{1 + cos2x} = \frac{1 - (cos^2x - sin^2x)}{1+cos^2x-sin^2x}=\frac{1-cos^2x+sin^2x}{cos^2x+cos^2x}$ $=\frac{sin^2x+sin^2x}{2cos^2x}=\frac{2sin^2x}{2cos ^2x}=tan^2x$ For b, take the square root of both sides and you get an equation for $tan(x)$, let x = 22.5. 3. Originally Posted by Flay I'm not sure how to tackle this question, can anyone help me out? It asks; a) Show that $\frac{1 - cos2x}{1 + cos2x} = tan^2x$. b) Hence find the value of $tan22.5^o$ in simplest exact form. For part a, focus on the left side of the equation. First multiply the numerator and denominator by $\tfrac{1}{2}$ $\frac{\tfrac{1}{2}(1-\cos(2x))}{\tfrac{1}{2}(1+\cos(2x))}$ Note that $\cos^2(x)=\tfrac{1}{2}(1+\cos(2x))$ and $\sin^2(x)=\tfrac{1}{2}(1-\cos(2x))$ Thus, the identity becomes $\frac{\sin^2(x)}{\cos^2(x)}=\tan^2(x)$. We have proven the identity. Does this make sense? For part (b), note that $\tan(22.5^{\circ})=\tan\left(\tfrac{45^{\circ}}{2} \right)$ Apply the half angle identity $\tan\left(\tfrac{\vartheta}{2}\right)=\frac{\sin\l eft(\tfrac{\vartheta}{2}\right)}{\cos\left(\frac{\ vartheta}{2}\right)}=\sqrt{\frac{1-\cos\vartheta}{1+\cos\vartheta}}$, where $\vartheta=45^{\circ}$. Does this make sense? --Chris 4. Thanks, I understand now. I was making a mistake with my postive and negative signs in the simplification of the first equation.

crawl-data/CC-MAIN-2016-50/segments/1480698542455.45/warc/CC-MAIN-20161202170902-00069-ip-10-31-129-80.ec2.internal.warc.gz

# The simple interest on a certain sum for $$12 \frac{1}{2}$$ years at 15% p.a. exceeds the amount of the same sum at simple interest for $$6 \frac{1}{2}$$ years at 12% p.a. by Rs. 1197. The sum (in Rs.) is: This question was previously asked in AAI ATC Junior Executive 21 Feb 2023 Shift 2 Official Paper View all AAI JE ATC Papers > 1. 13,000 2. 12,800 3. 12,600 4. 12,500 ## Answer (Detailed Solution Below) Option 3 : 12,600 Free Junior Executive (Common Cadre) Full Mock Test 56.2 K Users 150 Questions 150 Marks 120 Mins ## Detailed Solution Given: T1 = $$12 \frac{1}{2}$$ years, T2 = $$6 \frac{1}{2}$$ years R1= 15%, R2 = 12% Shortcut Trick $$12 \frac{1}{2}$$ × 15% - [100% + $$6 \frac{1}{2}$$ × 12%] = 1197 ⇒ [(375 - 200 - 156)/2] % = 1197 ⇒ 9.5% = 1197 ⇒ 1% = 1197/9.5 = 126 ⇒ 100% = 12600 ∴ The initial sum of money (or principal amount) is ₹12600. Alternate Method Formula Used: Simple Interest = PRT/100 Calculation: According to the question [SI at 15% for $$12 \frac{1}{2}$$ year] = [P + SI at 12% for $$6 \frac{1}{2}$$ year] + 1197 By using the above formula ⇒ (P × 15 × 25)/200 = [P + (P × 12 × 13)/200] + 1197 ⇒ (P × 375)/200 = [P + (P × 156)/200] + 1197 ⇒ 1.875P = P + 0.78P + 1197 ⇒ 1.875P - P - 0.78P = 1197 ⇒ P(1.875 - 1 - 0.78) = 1197 ⇒ P(0.095) = 1197 ⇒ P = 1197/0.095 = ₹12600 ∴ The initial sum of money (or principal amount) is ₹12600. Alternate Method [(P × 15 × 25)/(2 × 100)] - [P + (P × 12 × 13)/2 × 100] = 1197 ⇒ 375P/200 - [(200P + 156P)/200] = 1197 ⇒ (375P - 356P)/200 = 1197 ⇒ 19P = 1197 × 200 ⇒ P = (1197 × 200)/19 ⇒ P = 63 × 200 ⇒ P = 12600 ∴ The initial sum of money (or principal amount) is ₹12600. Latest AAI JE ATC Updates Last updated on Sep 2, 2024 -> AAI JE ATC Vacancies have been released for the 2024 recruitment. -> A total of 215 Vacancies have been created for the post of Junior Executive (Air Traffic Control) in Airports Authority of India (AAI). -> The AAI will soon release AAI JE ATC 2024 Notification mentioning the detailed vacancy, application process, eligibility, selection process, etc. -> The Selection of the candidates is based on the Computer Based Test, Voice Test and Test for consumption of Psychoactive Substances. -> The AAI JE ATC Salary will be in the pay scale of Rs.40,000-3%-1,40,000 (E-1). -> Candidates can check the AAI JE ATC Previous Year Papers to check the difficulty level of the exam. -> Applicants can also attend the AAI JE ATC Test Series which helps in the preparation.

crawl-data/CC-MAIN-2024-38/segments/1725700652055.62/warc/CC-MAIN-20240919162032-20240919192032-00329.warc.gz

Quick Homework Help # how to work out slope ⚑ Flag by Michael688 at October 28, 2009 i dont no Michael688 October 28, 2009 uyjuhio Michael688 October 28, 2009 onehalf October 28, 2009 beandip October 28, 2009 all you have to do is plug in the number's for example if you have (-6,9) and a slope of 7 you would follow this equation y=mx+b so just plug it in the slop is m so slope=m the y-intercept is just the y-coordinate or in this case the 9 and the x is -6 and you have to solve for b. so what you would do is write it out like so... 9=7(-6)+b see just plug it in then you multiply the 7 and the -6 and you get -42 so then you plug that in which would be 9=-42+b then to find be you add 42 because it is a negative and to get rid of a negative you add (aka do the opposite of the sign) so then you add 42 to both sides so -42+9= -33 so that's your b....so your answer to all this would be y=7x-33 and that's slope-intercept form

crawl-data/CC-MAIN-2013-20/segments/1368707439689/warc/CC-MAIN-20130516123039-00034-ip-10-60-113-184.ec2.internal.warc.gz

While in recent times there has been a push for diversity in grad school admissions, minorities are still underrepresented. Diversity ensures equal opportunity to students of every ethnic group, sex, or age, making for a more qualified workforce across the board. Gender is one area of diversity that has changed dramatically over the last few decades. While we are no longer in a time when men are the only breadwinners, women still face inequality to this day. Women are underrepresented in some fields more than others. Fields like engineering and mathematics are still primarily dominated by men; however, there are more women than men in fields like education and health sciences. Recent findings by the U.S. Department of Education show a promising trend toward gender diversity in college. Women are attending college in record numbers, especially at the graduate level. The U.S. Department of Education found that 60 percent of all master’s degrees are attained by women, and 52 percent of all doctoral degrees are earned by women. Furthermore, the Council of Graduate Schools (CGS) found in its latest report that since 2009, women have earned more doctoral degrees than men. In fact, the study shows that women make up 58.5 percent of all graduate students in the U.S. While women are still minorities in certain fields, the increasing number of women in graduate school gives hope to those who want to pursue what have typically been male-dominated careers. Another important aspect of diversity is ethnic equality. African Americans, Hispanics, Pacific Islanders, and American Indians are among some of the most outnumbered ethnic groups in colleges and universities in the U.S. According to the U.S. Department of Education’s National Center for Education Statistics, during the 2009-2010 academic year, only 76,450 African Americans earned a master’s degree compared to 445,038 whites. Furthermore, only 43,535 master’s degrees were awarded to Hispanics, 42,072 to Asians and Pacific Islanders, and 3,960 to American Indians or Alaskan Natives. The findings were similar at the doctoral level. Whites earned 104,426 doctoral degrees, whereas African Americans earned 10,417, Hispanics earned 8,085, Asians and Pacific Islanders earned 16,625, and American Indians and Alaskan Natives earned 952. In effort to break down this ethnic barrier, many colleges and universities today offer special grants or scholarships for minority students. Not only do these scholarships provide incentive for students to attend college, but they also benefit the schools by creating a diverse population of students from all ethnic backgrounds. A recent study conducted by the National Bureau of Economic Research found that more ethnically diverse college campuses produced a higher earning potential among graduates. Additionally, a research study conducted at the University of Michigan and UCLA found that students who interact and socialize with those of different ethnic groups had higher GPAs, greater intellectual and social self-confidence, and an overall more satisfying college experience. If you’d like to enjoy an ethnically diverse college experience, consider attending one of the top ethnically diverse colleges in the country, such as Rutgers, University of Houston, University of California—Riverside, New Jersey Institute of Technology, and Bloomfield College in New Jersey. One of the most important reasons for promoting diversity in college education is to invest in and prepare our country’s future workforce. It is the responsibility of higher education institutions to promote diversity and welcome students of all races, colors, and backgrounds. According to a survey conducted by Forbes, 85 percent of people stated that having diversity in the workplace was essential to the health of their business. Diversity in the workplace allows for better decision making and greater input from employees. A group of colleagues from various backgrounds and ethnicities often produce diverse theories and ideas that take into account various angles of problems that need to be solved. Furthermore, a company or organization that has a workforce comprising graduates of all backgrounds is able to understand its diverse clientele and even reach untapped markets. Despite the measures that universities have taken to increase diversity among student populations, there is still hidden bias in graduate school admissions. It is true that even the most selective schools have taken steps to create a diverse student body, but the incoming freshman class rarely represents the overall population in terms of class and ethnicity. In fact, students from upper-class and upper-middle-class families are admitted at higher rates than students from working-class families (27% vs. 19%), which undoubtedly leaves minority groups underrepresented in universities. Schools with a large pool of qualified applicants are in a unique position to bridge this inequality gap and create a diverse workforce. When it comes time to fill out your grad school applications, ask your preferred schools about their admissions process and whether they are actively taking steps to ensure a diverse student body. Although all graduate schools are seeking only the best candidates who demonstrate academic promise, you will find that some universities are looking for students who contribute more than just academic merit. Find schools that truly appreciate the value of a diverse classroom, whether online or on campus.

<urn:uuid:4f389336-9b6a-467a-8284-c1470315f722>

Otitis externa ("swimmer's ear") is an inflammation of the outer ear and ear canal. Along with otitis media, external otitis is one of the two human conditions commonly called "earache". It also occurs in many other species. Inflammation of the skin of the ear canal is the essence of this disorder. The inflammation can be secondary to dermatitis (eczema) only, with no microbial infection, or it can be caused by active bacterial or fungal infection. In either case, but more often with infection, the ear canal skin swells and may become painful and/or tender to touch. In contrast to the chronic otitis externa, acute otitis externa is predominantly a microbial infection, occurs rather suddenly, rapidly worsens, and becomes very painful and alarming. The ear canal has an abundant nerve supply, so the pain is often severe enough to interfere with sleep. Wax in the ear can combine with the swelling of the canal skin and any associated pus to block the canal and dampen hearing to varying degrees, creating a temporary conductive hearing loss. In more severe or untreated cases, the infection can spread to the soft tissues of the face that surround the adjacent parotid gland and the jaw joint, making chewing painful. In its mildest forms, external otitis is so common that some ear nose and throat physicians have suggested that most people will have at least a brief episode at some point in life. While a small percentage of people seem to have an innate tendency toward chronic external otitis, most people can avoid external otitis altogether once they understand the mechanisms of the disease. The skin of the bony ear canal is unique, in that it is not movable but is closely attached to the bone, and it is almost paper thin. For these reasons it is easily abraded or torn by even minimal physical force. Inflammation of the ear canal skin typically begins with a physical insult, most often from injury caused by attempts at self-cleaning or scratching with cotton swabs, pen caps, finger nails, hair pins, keys, or other small implements. Another causative factor for acute infection is prolonged water exposure in the forms of swimming or exposure to extreme humidity, which can compromise the protective barrier function of the canal skin, allowing bacteria to flourish; hence the name, "swimmer's ear". Densely impacted wax, usually caused by enthusiastic use of cotton swabs, can put enough pressure on the ear canal skin to injure it and initiate infection. A sensation of blockage or itching can prompt attempts to clean, scratch, or open the ear canal, which potentially worsens and perpetuates the condition. The cotton fibers of a swab are abrasive to the thin, fixed canal skin. Self-manipulative measures to improve the condition often make it worse and are to be discouraged, since it is a blind exercise that can result in significant injury to the ear. Production of wax by glands in the canal may be hindered by external otitis. The exact function(s) of cerumen (earwax) is a subject that is open to speculation, since there is very little research regarding its function. Some caretakers feel strongly that earwax has a protective function with respect to infection and that a little earwax in the ear canal is a good thing. A natural question is, "How can I clean my ears, then?" It is well established that in most people the top layer of the ear canal skin normally migrates toward the ear opening, essentially sweeping the canal on a continuing basis. In other words, a normal ear canal is self-cleaning. This self-cleaning physiologic feature fails in some patients, especially in late life, and periodic cleaning by a physician can be necessary. The most controlled and least painful means of cleaning impacted wax or dead skin from the ear canal is by using a binocular surgical microscope, which frees the examiner's hands to instrument the ear and provides the magnification and depth perception needed to avoid traumatizing the delicate canal skin and eardrum. is the predominant complaint and the only symptom directly related to the severity of acute external otitis. Unlike other forms of ear infections, the pain of acute external otitis is worsened when the outer ear is touched or pulled gently . Pushing the tragus (that tablike portion of the auricle that projects out just in front of the ear canal opening) so typically causes pain in this condition as to be diagnostic of external otitis on physical examination. Patients may also experience ear discharge and itchiness. When enough swelling and discharge in the ear canal is present to block the opening, external otitis may cause temporary conductive hearing loss. Due to the fact that the ear and throat are often interconnected, irritation (whether it be in inflammation or a scratching sensation) is normal. However, excessive throat symptoms may likely point to the throat as the cause of the pain in the ear rather than the other way around. Because the symptoms of external otitis promote many people to attempt to clean out the ear canal (or scratch it) with slim implements, and self-cleaning attempts generally lead to additional trauma of the injured skin, rapid worsening of the condition often occurs. Causes, incidence, and risk factors in polluted water is a common way to contract swimmer's ear, but it is also possible to contract swimmer's ear from water trapped in the ear canal after a shower, especially in a humid climate. Saturation divers have reported Otitis externa during occupational exposure. Even without exposure to water, the use of objects such as cotton swabs or other small objects to clear the ear canal is enough to cause breaks in the skin, and allow the condition to develop. Once the skin of the ear canal is inflamed, external otitis can be drastically enhanced by either scratching the ear canal with an object, or by allowing water to remain in the ear canal for any prolonged length of time. The two factors that are required for external otitis to develop are (1) the presence of germs that can infect the skin and (2) impairments in the integrity of the skin of the ear canal that allow infection to occur. If the skin is healthy and uninjured, only exposure to a high concentration of pathogens, such as submersion in a pond contaminated by sewage, is likely to set off an episode. However, if there are chronic skin conditions that affect the ear canal skin, such as atopic dermatitis, seborrheic dermatitis, psoriasis or abnormalities of keratin production, or if there has been a break in the skin from trauma, even the normal bacteria found in the ear canal may cause infection and full-blown symptoms of external otitis. Fungal ear canal infections, also known as otomycosis, range from inconsequential to very severe. Fungus can be saprophytic, in which there are no symptoms and the fungus simply co-exists in the ear canal in a harmless parasitic relationship with the host, in which case the only physical finding is presence of the fungus. If for any reason the fungus begins active reproduction, the ear canal can fill with dense fungal debris, causing pressure and ever-increasing pain that is unrelenting until the fungus is removed from the canal and anti-fungal medication is used. Most antibacterial ear drops also contain a steroid to hasten resolution of canal edema and pain. Unfortunately such drops make fungal infection worse. Prolonged use of them promotes growth of fungus in the ear canal. Antibacterial ear drops should be used a maximum of one week, but 5 days is usually enough. Otomycosis responds more than 95% of the time to a three day course of the same over-the-counter anti-fungal solutions used for athlete's foot. The incidence of otitis externa is high. In the Netherlands, it has been estimated at 12-14 per 1000 population per year, and has been shown to affect more than 1% of a sample of the population in the United Kingdom over a 12 month period. The bacterial pathogens at the top of the list are Pseudomonas aeruginosa and Staphylococcus aureus , followed by a great number of other gram-positive and gram-negative species. Candida albicans species are the most common fungal pathogens responsible for the condition. When the physician looks in the ear, the canal appears red and swollen in well-developed cases of acute external otitis. The ear canal may also appear eczema -like, with scaly shedding of skin. Touching or moving the outer ear increases the pain, and this maneuver on physical exam is very important in establishing the clinical diagnosis. It may be difficult for the physician to see the eardrum with an otoscope at the initial examination because of narrowing of the ear canal from inflammation and the presence of drainage and debris. Sometimes the diagnosis of external otitis is presumptive and return visits are required to fully examine the ear. Culture of the drainage may identify the bacteria or fungus causing infection, but is not part of the routine diagnostic evaluation. In severe cases of external otitis, there may be swelling of the lymph node (s) directly beneath the ear. The diagnosis may be missed in early cases because the examination of the ear, with the exception of pain with manipulation, is normal or nearly normal. In some cases of early external otitis, the most striking visual finding in the ear canal is the lack of cerumen. As a moderate or severe case of external otitis resolves, weeks may be required before the ear canal again shows a normal amount of cerumen. The goal of treatment is to cure the infection and to return the ear canal skin to a healthy condition. When external otitis is very mild, in its initial stages, simply refraining from swimming or washing hair for a few days, and keeping all implements out of the ear, usually results in a cure. For this reason, external otitis is called a self-limiting condition. However, if the infection is moderate to severe, or if the climate is humid enough that the skin of the ear remains moist, spontaneous improvement may not occur. Topical solutions or suspensions in the form of ear drops are the mainstays of treatment for external otitis. Some contain antibiotics, either antibacterial or antifungal, and others are simply designed to mildly acidify the ear canal environment to discourage bacterial growth. Some prescription drops also contain anti-inflammatory steroids, which help to resolve swelling and itching. Although there is evidence that steroids are effective at reducing the length of treatment time required, fungal otitis externa (also called otomycosis) may be caused or aggravated by overly prolonged use of steroid-containing drops. In addition to topical antibiotics, oral anti-pseudomonal antibiotics can be used in case of severe soft tissue swelling extending into the face and neck and may hasten recovery. Removal of debris (wax, shed skin, and pus) from the ear canal promotes direct contact of the prescribed medication with the infected skin and shortens recovery time. This is best accomplished using a binocular microscope. When canal swelling has progressed to the point where the ear canal is blocked, topical drops may not penetrate far enough into the ear canal to be effective. The physician may need to carefully insert a wick of cotton or other commercially available, pre-fashioned, absorbent material called an ear wick and then saturate that with the medication. The wick is kept saturated with medication until the canal opens enough that the drops will penetrate the canal without it. Removal of the wick does not require a health professional. Antibiotic ear drops should be dosed in a quantity that allows coating of most of the ear canal and used for no more than 4 to 7 days. The ear should be left open. Do note that it is imperative that there is visualization of an intact tympanic membrane. Use of certain medications with a ruptured tympanic membrane can cause tinnitus, vertigo, dizziness and hearing loss in some cases. Although the acute external otitis generally resolves in a few days with topical washes and antibiotics, complete return of hearing and cerumen gland function may take a few more days. Once healed completely, the ear canal is again self-cleaning. Until it recovers fully, it may be more prone to repeat infection from further physical or chemical insult. Effective medications include ear drops containing antibiotics to fight infection, and corticosteroids to reduce itching and inflammation. In painful cases a topical solution of antibiotics such as aminoglycoside, polymyxin or fluoroquinolone is usually prescribed. Antifungal solutions are used in the case of fungal infections. External otitis is almost always predominantly bacterial or predominantly fungal, so that only one type of medication is necessary and indicated. The pain of acute otitis externa is often severe enough to interfere with sleep. Topical analgesic drops often prescribed by primary care providers for pain relief are almost never adequate and should not be relied upon. A brief course of oral narcotic pain medication is often necessary to maintain comfort while the antibiotic drops are working. Improvement with appropriate initial treatment (cleaning of the canal, wick insertion if necessary, and antibiotic drops in adequate amount) is fairly rapid, with pain improvement occurring within one day and resolution within 2-4 days. Heat application using a heating pad, can also aid in pain relief, although it may increase the bacteria growth. Provided it is not too severe, recurrent otitis externa can often be successfully treated by non-prescription means, at low cost. When symptoms recur in an individual who has had a previous diagnosis made , the use of non-prescription drops along with precautions to keep water out of the ear is generally effective. Self-treatment with non-prescription remedies is dangerous in individuals who have not been previously evaluated for the condition, because the tympanic membrane may not be intact, and because the true condition may be otitis media with drainage. Drops and water precautions may actually resolve otitis media with drainage for a period of time, while allowing an undiagnosed cholesteatoma to progress, or complications of otitis media to develop. Effective solutions for the ear canal include acidifying and drying agents, used either singly or in combination. When the ear canal skin is inflamed from the acute otitis externa, the use of dilute acetic acid may be painful. Burow's solution is an effective remedy against both bacterial and fungal external otitis. This is a buffered mixture of aluminium sulfate and acetic acid, and is available without prescription in the United States. The strategies for preventing acute external otitis are similar to those for treatment. - Avoid inserting anything into the ear canal; use of cotton buds or swabs is the most common event leading to acute otitis externa. - Most normal ear canals have a self-cleaning and self-drying mechanism, the latter by simple evaporation. - After prolonged swimming, a person prone to external otitis can dry the ears using a small battery-powered ear dryer, available at many retailers, especially shops catering to watersports enthusiasts. Alternatively, drops containing dilute acetic acid (vinegar diluted 3:1) or Burow's solution may be used. It is especially important NOT to instrument ears when the skin is saturated with water, as it is very susceptible to injury, which can lead to external otitis. - Avoid swimming in polluted water. - Avoid washing hair or swimming if very mild symptoms of acute external otitis begin - Although the use of earplugs when swimming and shampooing hair may help prevent external otitis, there are important details in the use of plugs. Hard and poorly fitting ear plugs can scratch the ear canal skin and set off an episode. When earplugs are used during an acute episode, either disposable plugs are recommended, or used plugs must be cleaned and dried properly to avoid contaminating the healing ear canal with infected discharge. One simple method of fabricating soft waterproof disposable ear plugs is with cotton balls and petroleum jelly. These jelly coated cotton balls are NOT inserted into the ear canal, but pressed into the auricle to cover the opening of the canal. Poorly fitted head sets can also bring on an episode caused by friction between the ear and phone muffs. It is important to wear small head phones that do not cover the whole ear. Otitis externa responds well to treatment, but complications may occur if it is not treated. Individuals with underlying diabetes or disorders of the immune system are more likely to get complications, including malignant otitis externa. In these individuals, rapid examination by an otolaryngologist (ear, nose, and throat physician) is very important. - Chronic otitis externa - Spread of infection to other areas of the body - Necrotizing External Otitis Necrotizing External Otitis (Malignant otitis externa) This uncommon form of external otitis occurs mainly in an elderly diabetics, being somewhat more likely and more severe when the diabetes is poorly controlled. Even less commonly, it can develop due to a severely compromised immune system. Beginning as infection of the external ear canal, there is extension of infection into the bony ear canal and the soft tissues deep to the bony canal. The hallmark of malignant otitis externa (MOE) is unrelenting pain that interferes with sleep and persists even after swelling of the external ear canal may have resolved with topical antibiotic treatment. MOE follows a more chronic course than ordinary acute otitis externa. There may be granulation involving the floor of the external ear canal, most often at the bony-cartilaginous junction. Paradoxically, the physical findings of MOE, at least in its early stages, are often much less dramatic than those of ordinary acute otitis externa. In later stages there can be soft tissue swelling around the ear, even in the absence of significant canal swelling. Unlike ordinary otitis externa, MOE requires oral or intravenous antibiotics for cure. Diabetes control is also an essential part of treatment. When MOE goes unrecognized and untreated, the infection continues to smolder and over weeks or months can spread deeper into the head and involve the bones of the skull base, constituting skull base osteomyelitis (SBO). The infecting organism is almost always pseudomonas aeruginosa, but it can instead be fungal (aspergillus or mucor). MOE and SBO are not amenable to surgery, but exploratory surgery may facilitate culture of unusual organism(s) that are not responding to empirically used anti-pseudomonal antibiotics. The usual surgical finding is diffuse cellulitis without localized abscess formation. SBO can extend into the petrous apex of the temporal bone or more inferiorly into the opposite side of the skull base. As the skull base is progressively involved, the adjacent exiting cranial nerves and their branches, especially the facial nerve and the vagus nerve, may be affected, resulting in facial paralysis and hoarseness, respectively. If both of the recurrent laryngeal nerves are paralyzed, shortness of breath may develop and necessitate tracheotomy. Profound deafness can occur, usually later in the disease course due to relative resistance of the inner ear structures. Gallium scans are sometimes used to document the extent of the infection but are not essential to disease management. Skull base osteomyelitis is a chronic disease that can require months of IV antibiotic treatment, tends to recur, and has a significant mortality rate.

<urn:uuid:b21aeb57-3628-46a0-a749-692faaa04afd>

The blended Unit Plan is for Grade six social studies. The lesson allows students to research and learn in a variety of formats. Students should have basic map skills and computer skills. Students will work individually or in a group setting to investigate, develop, and teach a lesson. Areas of Focus: © Copyright 2017 Michigan Virtual University To view this and other resources in the repository, please tell us which school you’re from. Or, if you already have a user account please log-in to prevent future prompts. Don’t have an account? Create one. Why am I being asked to identify my school?

<urn:uuid:c8ff9896-ba5b-4fc8-93b9-3c339b5b6efb>

# Convert Equation from Polar to Rectangular Form Equations in polar form are converted into rectangular form, using the relationship between polar and rectangular coordinates. Problems with detailed solutions are presented. ## Problems on Converting Equation from Polar to Rectangular Form ### Problem 1 Convert the polar equation R = 4 sin t to rectangular form. Solution to Problem 1 We multiply both sides by R R = 4 sin t R 2 = 4 R sin t We now use the relationship between polar and rectangular coordinates: R 2 = x 2 + y 2 and y = R sin t to rewrite the equation as follows: x 2 + y 2 = 4 y x 2 + y 2 - 4 y = 0 It is the equation of a circle. ### Problem 2 Convert the polar equation R (-2 sin t + 3 cos t) = 2 to rectangular form. Solution to Problem 2 Expand the left side of the given equation. R(-2 sin t + 3 cos t) = 2 -2 R sin t + 3 R cos t = 2 Use y = R sin t and x = R cos t into the given equation to rewrite as follows: -2 y + 3 x = 2 The above is the equation of a line. ### Problem 3 Convert the polar equation t + √ / 4 = 0 to rectangular form. Solution to Problem 3: Rewrite the given equation as follows: t + √ / 4 = 0 t = - √ / 4 Take the tangent of both sides: tan t = -1 Use y = R sin t and x = R cos t to write: tan t = sin t / cos t = R sin t / R cos t = y / x Hence: y / x = -1 y = - x The above is the equation of a line. ## More References and Links to Polar Coordinates and Trigonometry Polar Coordinates.

crawl-data/CC-MAIN-2020-16/segments/1585371833063.93/warc/CC-MAIN-20200409091317-20200409121817-00220.warc.gz

# How Do You Calculate the Dew Point? By Staff WriterLast Updated Mar 29, 2020 12:30:20 AM ET Susanne Nilsson/CC-BY-2.0 To calculate dew point, you need to know the current temperature and relative humidity, and then solve the equation Td = T - ((100 - RH) / 5) for Td, which stands for the dew point temperature in degrees Celsius. This equation is accurate for humidity values above 50 percent. 1. Learn the dew point equation The simple equation for dew point is: Td = T - ((100 - RH) / 5). "Td" stands for the dew point temperature in degrees Celsius. "T" stands for the observed temperature in degrees Celsius. RH is the relative humidity in percent. Relative humidity is the ratio of how much moisture the air is holding to how much moisture it could hold at a given temperature. 2. Plug the values into the equation Put the values for the temperature and relative humidity into the equation. For example, if the observed temperature is 19 degrees Celsius and the relative humidity is 75 percent, the equation reads: Td = 19 - ((100 - 75) / 5). 3. Solve the equation Solve the equation to find the dew point temperature. To continue the example: Td = 19 - ((100 - 75) / 5) = 19 - (25 / 5) = 19 - 5 = 14. This result means that the dew point temperature is 14 degrees Celsius. More From Reference

crawl-data/CC-MAIN-2021-25/segments/1623488519735.70/warc/CC-MAIN-20210622190124-20210622220124-00455.warc.gz

New images released by Britain’s Royal Navy show how future submarines could look and move like real sea creatures. The designs were created by young British engineers and scientists. They were challenged by the Royal Navy to imagine how future underwater war machines might look. The engineers and scientists are members of the group UKNEST. This not-for-profit organization promotes science, engineering and technology for British naval design. The group kept the same requirements used in advanced submarines used today. But the designers added new technological ideas to make them easier and less costly to build, as well as more effective in battle. Current submarines were designed to perform many roles as a single piece of equipment. But the Royal Navy of the future is expected to operate a family of submarines. This would include many shapes and sizes to carry out different operations. Some submarines would be manned and others unmanned. The designs included a “mothership” that would act as a major command and control center supporting other submarines and ships. This submarine, with a crew of about 20 people, would be shaped like a manta ray with wide wings to guide it through the sea. The futuristic mothership would travel to British-controlled waters worldwide, docking with other underwater bases. The future Royal Navy might also use eel-like unmanned underwater vehicles. The designers imagined these submarines as capable of curving around objects like an eel and disguising themselves as sea lifeforms. They could be launched from the mothership and travel hundreds of miles in near silence. Some of the naval equipment would be engineered with materials to dissolve after a period of time to avoid being captured by enemies. One image even shows flying missile weapons shooting out of the water like sharks or dolphins. The submarine design project was called Nautilus 100. It was named after the U.S. Navy’s USS Nautilus, the world's first nuclear-powered submarine. Britain’s Minister for Defense Procurement, Harriet Baldwin, praised the project. “These remarkable designs display the great promise of our young engineers and scientists and the great ambition of the Royal Navy.” She added that the futuristic concepts are an example of what Britain’s navy could produce to meet future military challenges. Commander Peter Pipkin is a robotics officer with the Royal Navy. He said that with more than 70 percent of the planet covered by water, there will be more competition between nations in the future to live and work at or under the sea. For this reason, he said the Royal Navy is looking 50 years into the future to find new ways to protect British interests around the world. “If only 10 percent of these ideas become reality, it will put us at the cutting edge of future warfare and defense operations," Pipkin said. I’m Bryan Lynn. Bryan Lynn wrote this story based on information from the Royal Navy website. Hai Do was the editor. We want to hear from you. Write to us in the Comments section, and visit our Facebook page. Words in This Story challenge – v. invite a person to compete in a contest or fight dock – v. join together with another ship disguise – v. change the appearance of something so it cannot be recognized dissolve – v. break down or disappear ambition – n. goal or aim to do or be something concept – n. an idea of what something could be

<urn:uuid:a14d7502-9a7e-4339-94b1-59011011f776>

0 like 0 dislike what is the percent of decrease from 68 to 34 0 like 0 dislike 50% Step-by-step explanation: If 68 represents 100% then 34 represents x % Calculate x x = (34 · 100) / 68 = 50% (makes sense because 34 is half of 68) So the percent of decrease from 68 to 34 is 50% by

crawl-data/CC-MAIN-2023-06/segments/1674764499468.22/warc/CC-MAIN-20230127231443-20230128021443-00750.warc.gz

# Worksheet on Pie Chart | Pie Chart Worksheets with Answers | Circle Graph Questions In this Worksheet on Pie Chart, you can see sample questions and answers on the pie chart, how to solve them. The term pie means a circle and chart means the representation of data. Here, we will represent tabular data in a circle. Pie Chart contains sectors, the percentage of sector shows the value of the component. We have also included the formula to find the central angle of each component of a pie chart on this page. Get the simple steps to convert the data into a pie chart from the following sections. To see the central angle of each component, divide the component value by the total number of components. Multiply the result with 360 degrees. 1. Rakesh yearly salary is \$ 52007. He plans his budget for a year as mentioned here: Item Food Education Rent Savings Miscellaneous Amount (in dollars) 12089 4468 9150 13300 13,000 Draw a pie chart for the Rakesh yearly budget. Solution: Given data is the Rakesh yearly budget. Yearly Salary = \$ 52007 Central angle for a component = (Value of the component / Sum of the values of all components) * 360° Calculation of central angles: Item Amount (in dollars) Central Angle Food 12089 (12089 / 52007) * 360 = 83.68° Education 4468 (4468 / 52007) * 360 = 30.92° Rent 9150 (9150 / 52007) * 360 = 63.33° Savings 13300 (13300 / 52007) * 360 = 92° Miscellaneous 13000 (13000 / 52007) * 360 = 89.98° Steps of constructing a pie chart: 1. Draw a circle of any convenient radius. 2. Draw a horizontal radius of the circle. 3. Draw sectors starting from the horizontal radius with central angles of 83.68°, 30.92°, 63.33°, 92°, and 89.98° respectively. 4. Shade the sectors differently using different colors and label them. Thus, we obtain the required pie chart, shown in the above figure. 2. In a company there are 19200 workers of different religions. The data of the different religion are given below: Religion Hindu Nepali Islam Christian Buddhism No of Workers 9500 700 4000 4500 500 Draw a pie chart for the above data. Solution: Total Number of workers in the company = 19200 Central angle for a component = (Value of the component / Sum of the values of all components) * 360° Calculation of central angles: Religion No of Workers Central Angle Hindu 9500 (9500 / 19200) * 360 = 178.12° Nepali 700 (700 / 19200) * 360 = 13.125° Islam 4000 (4000 / 19200) * 360 = 75° Christian 4500 (4500 / 19200) * 360 = 84.375° Buddhism 500 (500 / 19200) * 360 = 9.375° Steps for constructing a pie chart • Draw a circle of any radius. • Draw a horizontal radius of the circle. • draw sectors starting from the horizontal radius with the central angles of 9.37°, 84.37°, 75°, 13.12°, and 178.12°. • Shade the sectors using different colors and label them. Thus, we obtain the required pie chart, shown in the above figure. 3. Manohar lists his monthly expenditure as follows: Expenditure Food Rent Personal Insurance Health Care Entertainment Education Clothing Others Amount (in rupees) 500 1500 850 640 360 300 350 1700 Draw a pie chart for the Manohar monthly expenditure. Solution: Given table says the monthly expenditure of a person. Total expenditure in a month = 500 + 1500 + 850 + 640 + 360 + 300 + 350 + 1700 = 6200 Central angle for a component = (Value of the component / Sum of the values of all components) * 360° Calculation of central angles: Expenditure Amount Central Angle Food 500 (500 / 6200) * 360 = 29° Rent 1500 (1500 / 6200) * 360 = 87° Personal Insurance 850 (850 / 6200) * 360 = 49.35° Health care 640 (640 / 6200) * 360 = 37.16° Entertainment 360 (360 / 6200) * 360 = 20.9° Education 300 (300 / 6200) * 360 = 17.41° Clothing 350 (350 / 6200) * 360 = 20.32° Others 1700 (1700 / 6200) * 360 = 98.7° Steps for constructing a pie chart: 1. Draw a circle of any convenient radius. 2. Draw a horizontal radius of the circle. 3. Draw sectors starting from the horizontal radius with central angles of 29°, 87°, 49.35°, 37.16°, 20.9°, 17.41°, 20.32°, and 98.7° respectively. 4. Shade the sectors differently using different colors and label them. Thus, we obtain the required pie chart, shown in the above figure. 4. There are 2000 workers in a factory as per the list provided below: Cadre Laborer Mechanic Fitter Plumber Electrician Supervisor Clerk Number of Workers 368 560 300 280 500 152 120 Represent the above data by a pie chart. Solution: The total number of workers in a factory = 2000 Central angle for a component = (Value of the component / Sum of the values of all components) * 360° Calculation of the central angle of each cadre is as follows: Cadre No of Employees Central Angle Laborer 368 (368 / 2000) * 360 = 66.24° Mechanic 560 (560 / 2000) * 360 = 100.8° Fitter 300 (300 / 2000) * 360 = 54° Plumber 280 (280 / 2000) * 360 = 50.4° Electrician 500 (500 / 2000) * 360 = 90° Supervisor 152 (152 / 2000) * 360 = 27.36° Clerk 120 (120 / 2000) * 360 = 21.6° Construction for creating a pie chart 1. Draw a circle of any convenient radius. 2. Draw a horizontal radius of the circle. 3. Draw sectors starting from the horizontal radius with central angles of 66.24°, 100.8°, 54°, 50.4°, 90°, 27.36°, and 21.6° respectively. 4. Shade the sectors differently using different colors and label them. Thus, we obtain the required pie chart, shown in the above figure. 5. The following table gives the number of different fruits kept in a hamper. Type of Fruit Apple Mango Papaya Orange Pomegranate Supervisor Clerk Number 368 560 300 280 500 152 120 Draw a pie chart to represent the above data. Solution: The total number of fruits in the hamper = 80 Central angle for a component = (Value of the component / Sum of the values of all components) * 360° Calculation of central angles: Type of Fruit Numbers Central Angle Apple 12 (12 / 80) * 360 = 54° Mango 20 (20 / 80) * 360 = 90° Papaya 5 (5 / 80) * 360 = 22.5° Orange 15 (15 / 80) * 360 = 67.5° Pomegranate 18 (18 / 80) * 360 = 81° Kiwi Fruit 10 (10 / 80) * 360 = 45° Construction for creating a pie chart • Draw a circle of any convenient radius • Draw sectors starting from the horizontal radius with central angles of 54°, 90°, 22.5°, 67.5°, 81°, and 45° respectively. • Shade the sectors differently using different colors and label them. Thus, we obtain the required pie chart, shown in the above figure. 6. The data given below shows the number of hours spent by working women on different activities on a working day. Activity Office Cooking Sleep Journey Others Hours 8 2 7 2 5 Represent the above data by a pie chart. Solution: Given data is about the hours spent by working women. Total number of hours = 24 Central angle for a component = (Value of the component / Sum of the values of all components) * 360° Calculation of central angles: Activity Hours Central Angle Office 8 (8 / 24) * 360 = 120° Cooking 2 (2 / 24) * 360 = 30° Sleep 7 (7 / 24) * 360 = 105° Journey 2 (2 / 24) * 360 = 30° Others 5 (5 / 24) * 360 = 75° Construction for creating a pie chart Steps of construction: 1. Draw a circle of any convenient radius. 2. Draw a horizontal radius of the circle. 3. Draw sectors starting from the horizontal radius with central angles of 12°, 30°, 105°, 75°, and 30° respectively. 4. Shade the sectors differently using different colors and label them. Thus, we obtain the required pie chart, shown in the above figure. 7. 500 students of a school were surveyed for their favorite activity. The information is represented in a pie chart as given below. Observe the chart and answer the questions given below. (i) What is the pie chart tells about? (ii) Which is the most favorite pastime activity of students? (iiI) How many students like reading books? (iv) What percentage of students like music? (v) What percentage of students like to dance? (vi) What percentage of students like playing outdoor games? Solution: From the pie chart, we can observe that, (i) Pie chart contains the 500 school students’ favorite activity. (ii) Spending time with the smartphone is the favorite past activity for most of the school students. (iii) Out of 500 students, 50 students like reading books. (iv) 100 students like music. The percentage of students who like music is (100 / 500) * 100 = 20% (v) 70 students like dance. The percentage of students who like dance is (70 / 500) * 100 = 14% (vi) 130 students like playing outdoor games. The percentage of students who like playing outdoor games is (130 / 500) * 100 = 26% 8. Given the pie chart shows the sales of different brands of smartphones on an e-commerce site during a festive season. From the pie chart, solve the following questions. (i) What are the different brands mentioned in the chart? (ii) How many smartphones are sold during the festive season? (iii) How many Nokia smartphones are sold? (iv) Which brand of the smartphone has the highest sales and lowest sales? (v) What is the difference between the sales of apple and Motorola? (vi) What is the ratio of sales between Sony and Samsung? Solution: The pie chart is given about the sales of different brands of smartphones in an e-commerce site during a festive season. (i) The different brands mentioned in the chart are Motorola, Coolpad, Apple, HTC, Sony, Nokia, Lenovo, and Samsung. (ii) A total of 10,000 smartphones are sold during the festive season in an e-commerce season. (iii) A total of 550 Nokia brand smartphones are sold. (iv) Lenovo has the highest sales and Coolpad has the lowest sales. (v) The number of Apple smartphones sold is 600, Motorola smartphones are 664. So, the difference between the sales of Motorola and apple is 664 – 600 = 64. (vi) The sales of Sony is 1500, Samsung is 2500. The ratio between the sales of sony and Samsung is 1500 : 2500 = 3 : 5. 9. The pie chart below shows the percentages of types of transportation used by 500 students to come to school. (i) How many students come to school by bicycle? (ii) How many students do not walk to school? (iii) How many students come to school by bus? (iv) How many students come to school by car? (v) What is the central angle for students to come to school by walk? (vi) What is the ratio between students come to school by car, by bus? Solution: (i) 125 students come to school by bicycle. (ii) (115 + 100 + 125) = 340 students do not walk to school. (iii) 115 students come to school by bus. (iv) 100 students come to school by car. (v) 160 students come to school by walk. The central angle for students come to school by walk = (160 / 500) * 360 = 0.32 * 360 = 115.2° (vi) 100 students come to school by car, 115 students come to school by bus. The ratio is 100 : 115 = 20 : 23 10. The following are the ingredients and quantity of ingredients required to make a butter cake. Ingredients Flour Sugar Egg Butter Quantity 30 20 35 10 Draw a pie chart. Solution: Total quantity = 95 Calculation of central angles: Ingredients Quantity Central Angle Flour 30 (30 / 95) * 360 = 113.6° Sugar 20 (20 / 95) * 360 = 75.7° Egg 35 (35 / 95) * 360 = 132.6° Butter 10 (10 / 95) * 360 = 37.8° Construction for creating a pie chart Steps of construction: 1. Draw a circle of any convenient radius. 2. Draw a horizontal radius of the circle. 3. Draw sectors starting from the horizontal radius with central angles of 113.6°, 75.7°, 132.6°, and 37.8° respectively. 4. Shade the sectors differently using different colors and label them. Thus, we obtain the required pie chart, shown in the above figure. 11. In the pie chart representing the percentages of students having an interest in playing various kinds of games, the central angle of the sector representing students playing cricket is 152°, what is the percentage of students interested in playing cricket? Solution: Given the central angle of the sector = 152° (152 / 360) * 100 = 42 % The percentage of students interested in playing cricket is 42 %. 12. In a pie chart representing the number of students opting for different modes of transportation to reach the school. The total number of students is 1000, and the central angle of the sector representing transportation by walk is 52°, what is the number of students who opted for the mode of transportation is by walk? Solution: Given that, The central angle of the sector for walk= 52° The total number of students = 1000 Central angle for a component = (Value of the component / Sum of the values of all components) * 360° 52° = (Value of the component / 1000) * 360° 52 / 360 = Value of the component / 1000 0.1444 = Value of the component / 1000 Value of the component = 0.144.4 * 1000 Value of the component = 144.4 The number of students who opted walking to reach the school = 144 13. If 40% of the people’s favorite food is biryani then the central angle of the sector representing the people’s favorite food in a pie chart would be. Solution: Given that, The percentage of the number of people favorite food is biryani = 40% Central angle for a component = (Value of the component / Sum of the values of all components) * 360° = (40 / 100) * 360 = 144° The central angle of the sector whose favorite food is biryani is 144°. 14. A person’s monthly income is \$ 5200 and his monthly expenditure on food is \$ 500. What is the central angle of the sector representing food expenses in the pie chart? Solution: Given that, Person monthly income = \$ 5200 Expenditure on food = \$ 500 The central angle of food = (Expenditure of food/person monthly income) * 360° = (500 / 5200) * 360° = 0.096 * 360° = 34.61° The central angle of the sector representing food expenses in the pie chart = 34.61°. 15. The following table shows the percentage of buyers of six different brands of bathing soaps. Brand A B C D E F Percentage of Buyers 10 15 5 40 15 15 Represent data on a pie chart. Solution: The given table represents the percentage of buyers of six different brands of bathing soaps. Central angle for a component = (Value of the component / Sum of the values of all components) * 360° Calculation of central angles: Brand Percentage of Buyers Central Angle A 10 (10 / 100) * 360 = 36° B 15 (15 / 100) * 360 = 54° C 5 (5 / 100) * 360 = 18° D 40 (40 / 100) * 360 = 144° E 15 (15 / 100) * 360 = 54° F 15 (15 / 100) * 360 = 54° Construction for creating a pie chart Steps of construction: 1. Draw a circle of any convenient radius. 2. Draw a horizontal radius of the circle. 3. Draw sectors starting from the horizontal radius with central angles of 36°, 54°, 18°, 144°, 54°, and 54° respectively. 4. Shade the sectors differently using different colors and label them. Thus, we obtain the required pie chart, shown in the above figure.

crawl-data/CC-MAIN-2024-18/segments/1712296818740.13/warc/CC-MAIN-20240423192952-20240423222952-00183.warc.gz

In chapter two, we saw that at key moments in the story (such as the calling of Abraham, the exodus, and the renewal of life in exile), God acts out of pure mercy. God provides salvation as a gift—given out of God’s healing love, unearned, even unmerited by the people. The story presents the two institutions linked with salvation, Torah and sacrifice. Both initially served as responses to the gift. First, the people received God’s acts of deliverance, then came gratitude. Such gratitude led to responses of obedience to God’s will for social life. These found expression in Torah and in ritualized expressions of commitment to God via sacrifice. As the Hebrews’ political structures expanded and became centralized under the office of the king, their religious structures concomitantly became centralized around the Temple. With this, the original purposes of the Law and sacrifices changed. Torah originated as the framework for the Hebrews to concretize their liberation. Torah arranges for the economic viability of each household, resisting social stratification. Inheritance legislation, Sabbath year laws, and the ideal of the Year of Jubilee all pushed in the direction of widespread participation in economic wellbeing. The Law also placed special emphasis on the community tending to the welfare of vulnerable people in the community—widows, orphans, and aliens (“for you too were aliens in Egypt before God delivered you,” Leviticus 19). Walter Brueggemann: “Something like ‘God’s preferential option for the poor’ is deeply rooted in Israel’s testimony, so deeply rooted as to be characteristic and definitional for Israel’s speech about God. The claim is not a belated, incidental addendum to Israel’s ethical reflection, but belongs integrally and inalienably to Israel’s core affirmation of the character of Yahweh.” The sacrificial practices, above all else, were intended to be linked with the faithful responses of the people, in gratitude, to God’s liberating work. Problems with Law and Sacrifices Neither the Law nor the sacrifices were meant to be means to salvation but rather responses to the saving works of God. The Law and sacrifices were meant to foster justice in the community. Once they were established, though, the danger inevitably arose that either or both would be separated from their grounding in God’s merciful liberating works. As the intent of the Law faded, the community tended to focus on external expressions, easily enforced and susceptible to becoming tools of people in power. These tendencies led to legalism and, eventually, in the prophets’ views, to removing the Law from its living heart of liberation from slavery and concern for the well-being of vulnerable people. As the original intent of sacrifices was lost, many Israelites tended to treat sacrifices as means of salvation, ritual acts separated from practical justice in the community. Especially, as they centralized religious structures, people in power used sacrifice as a tool to enhance their standing. Presenting sacrifice as a necessary means to salvation, enabled people who controlled access to sacrificial rituals (e.g., in the Temple) to exercise enormous power in the community. Voices of accountability arose to challenge such distortions, the voices of the prophets. Moses himself fits in this class. The prophets emerged following the establishment of kingship as the voice of loyalty to Torah. They challenged Israel’s practices when they contradicted the covenant relation. “The prophets repeatedly utilize the old legal traditions to determine the present status of Israel.” One great kingship-era prophet, Elijah, established the basic prophetic concern. Elijah challenged Israel’s king when the king departed from God’s ways—and pointed back to the law of Moses as the basis for his challenge. A poignant story in 1 Kings 21 illustrates this dynamic. Israel’s king, Ahab, desired the fruitful vineyard of the Israelite Naboth. At first, Ahab offers to buy the or exchange the vineyard. His offer, however, reflects his lack of respect for the inheritance practices of Israel. The land does not simply belong to Naboth. He refuses to sell it because it belongs to God and is for the use also of Naboth’s parents and his children and their children. It is his inheritance. This term inheritance contrasts with Ahab’s term, vineyard. “Inheritance” recognizes the land as the Lord’s, cultivated by the family through the generations for their livelihood. The Lord wills that the land stay in the family so that they will not be dispossessed and future generations made landless. When all have their own vine and fig tree to cultivate, the community will be healthy. That health is why inheritance matters. “Vineyard,” on the other hand, as used by King Ahab, views the land as a commodity, something simply to be bought and sold with little concern for the wholeness of the entire community. Those who are wealthy and powerful may accumulate more and more. The other people become landless, disinherited—a recipe for poverty and vulnerability. Naboth refuses to part with his inheritance. Ahab falsely convicts Naboth of blasphemy and executed him. Ahab takes the land. He assumes that since he is the king he may do whatever he wants. The main weapon God has against corrupt kings such as Ahab simply is the word of the prophets, reminding people of God’s will and exposing the violence and injustice of this corruption for what it is. King Ahab goes down to the vineyard to take possession of it (1 Kings 21:16). But, he meets an old acquaintance when he gets to the vineyard, the prophet Elijah—who had confronted Ahab before and had to flee for his life. Ahab remembers Elijah. “Have you found me, O my enemy” (1 Kings 21:20). Earlier, Ahab called Elijah a “troubler of Israel” (1 Kings 18:17). Indeed I have found you, says Elijah. The Lord has told me the injustice you have done to Naboth. You are the troubler of Israel. You are the one who has disregarded the Lord’s commands. You are the blasphemer—not Naboth. You, King Ahab, will suffer consequences. To his credit, Ahab does respond. He humbles himself. We are not told that he changes his ways. But we are told that because of his response, the disaster waits until after his death. The word of the prophet has had power. Elijah, as the prophets to follow, reminds people. He reminds Ahab of God’s will for human life, as expressed in God’s commands. Be suspicious of people in power. Do not blindly trust their claims but test them thoroughly. But also: remember who God is, what God has done for you, and what God’s will for your life is. “Prophets arise in Israel when covenantal modes of existence are endangered. It is the work of the prophets to insist that all of Israel’s life is to be lived in relation to and in response to Yahweh’s will and purposes, and to enunciate the consequences of a life live without regard to this defining relationship. The prophets are to invite a ‘turning’ in Israel, a turn from pride to trust, from despair to hope, from abusiveness to covenantal neighborliness.” In challenging the distortions of law and sacrifice, the prophets reiterate the meaning of salvation. They re-emphasize that salvation is God’s liberating gift, and that following Torah and offering sacrifices are responses to God’s gift, not means to try to gain it. In this chapter, I will focus on the first wave of “writing prophets,” those who ministered in the eighth century BCE and whose proclamations were gathered into books bearing their names—Amos, Hosea, and Micah. These prophets’ message set the tone for much of the prophetic critique to come. Even more importantly, in terms of what is to come, these prophets exerted a profound influence on Jesus. I will argue that salvation according to these eighth-century prophets and salvation according to Jesus are very closely related. Salvation in Eighth-Century Prophetic Proclamation One of basic issue facing the Hebrew people, according to prophetic witness, is that the community has departed from the will of their liberating God. “The more I call them, the more they went from me” (Hosea 11:2). Hosea frames the “departure” in terms of idolatry. Amos focuses more on injustice. Micah emphasizes both. Originally, the people needed liberation from non-being, the barrenness symbolized by Abraham and Sarah’s lack of a future. God provided this family with a child. Around them, the Promise arose. However, within a few generations, the people stood in need of liberation. They again faced non-being as slaves. God again gave them a future—this time as a nation with its own unique law-code, its unique religious rituals, and—eventually—its own land. At the time of Joshua, the story portrays the Hebrews living in a state of wholeness, with a world of potential for creative growth and witness. They lived at the point with a large measure of harmony with God, due to God’s generosity. “The gracious gifts assured by the prophets derive not from what Israel does but from who Yahweh is.” However, as the generations passed, this harmony turned to disharmony. What Causes the Disharmony? All three of the eighth-century prophets, Amos, Hosea, and Micah, spoke in response to the disharmony they perceived among the Hebrew people. The earliest of the three, Amos, had lived in the southern kingdom of Judah but traveled north to Israel to speak the words recorded in the book that bears his name. Amos prophesied during the time of King Jeroboam II of Israel, who ruled from 786 to 746 BCE. Scholars place Amos’ prophecies at around 760 BCE. Amos presented himself as an independent, “lay-prophet.” He had no official standing, relying only on the power of his words. As his basis for critique, Amos drew on the shared traditions. He several times reminded his listeners of their belief that Yahweh had brought the Hebrews out of Egypt and placed them in the land (Amos 2:9-10; 3:1-2; 9:7-8). The Hebrews’ “immoral and unethical treatment of those who are unable to defend themselves is juxtaposed [to God’s] protective treatment throughout their early history when they were unable to defend themselves.” Amos prophesied, assuming that the people of Israel would share his starting point. Their liberating God had directly given them Torah with its clear instructions regarding the nature of covenantal life. Liberation and land are linked inextricably with Law. Yahweh delivered the people from the injustice of Egypt’s slavery and for justice in the covenant community. In Amos’s view, the people have always known that Yahweh expected justice. He breaks no new ground in terms of moral and legal expectations. He draws directly on tradition, taking for granted that the people would know Torah. He expected no debate about the centrality of justice for the covenant community—only over the extent of injustice current in Israel. Likewise, Hosea also draws directly on the liberation story that formed the core of Hebrew consciousness. His indictment in chapter 11 begins with these words: “When Israel was a child, I loved him, and out of Egypt I called my son” (11:1). Hosea then goes on to outline how the people did not remain faithful to the ways of their loving God. Hosea came onto the scene about a generation later than Amos. He prophesied in the northern kingdom in the years just prior to the Assyrian empire laying waste to Israel in 721 BCE. Whereas Amos spoke directly about injustice in Israel and used legal types of imagery, Hosea relied more on personal relationship-type imagery. Israel broke Yahweh’s heart by cultivating relationships with other gods. The third of these prophets, Micah, prophesied in Judah, the southern kingdom. He entered the scene in the years after the northern kingdom’s fall. His period of prophecy ended around 701 BCE. Like Amos and Hosea, Micah centrally emphasized the exodus and Torah, basically ignoring the Davidic-Zion kingship tradition. For Micah, unlike many of his fellow Judeans, Jerusalem was not inviolable. In Micah’s view, violating the covenant in the way his contemporaries had rendered the nation’s future uncertain. It is not that Yahweh had changed from loving to wrathful; rather, a society founded on Torah-justice will become deathly ill when Torah-justice is disregarded. To draw on Amos’ imagery, we may say that where there is justice there is life; the community will be strong and healthy. Injustice, on the other hand, in inherently unhealthy. All three of these prophets saw the key for the Hebrew’s health to be Yahweh’s love and liberating work. This divine, life-giving initiative of God—Torah—included detailed guidance for liberated living in justice and Shalom. “The reason the commands are so urgent and insistent is that they are Yahweh’s (and therefore Israel’s) strategy for fending off a return to pre-Exodus conditions of exploitation and brutality within the community.” Certainly, the prophets do speak words of threat, anger, even judgment. However, they understand themselves to speak out of Yahweh’s love. They speak because they believe God desires the community’s healing. All three books conclude with hopeful visions of such healing. The people are being confronted in hope that they will return to trust in their liberating God. These prophets themselves were without recourse to means of actually punishing anyone. They were not interested in marshalling the power of the sword against wrongdoers. They relied on rhetoric, on their vision of Torah and of Yahweh’s justice, to seek to effect healing—not to inflict pain for pain. The people’s break with the covenant with Yahweh may be seen in terms of the expressions in their communities of injustice, violence, idolatry, and vain religiosity. Injustice. According to these prophets, the people had changed their original social structure. Torah had provided for an decentralized social order characterized by widespread land ownership. Within this, all were to be given access to means for sustaining their livelihoods and none were to gain the extreme wealth that may be accumulated via the disinheritance of large numbers of community members. By the eighth century, a transformation had occurred leading to increased social stratification—a few wealthy, many poverty-stricken. Amos and Micah zeroed in on this stratification as evidence of a fundamentally unjust social order. God’s judgment on Israel is immanent, “because they sell the righteous for silver, and the needy for a pair of sandals—they who trample the head of the poor into the dust of the earth, and push the afflicted out of the way” (Amos 2:6-7). This injustice goes contrary to the will of God expressed in Torah and, indeed, in creation itself. “Do horses run on rocks? Does one plow the sea with oxen? But you have turned justice into poison and the fruit of righteousness into wormwood” (Amos 6:12). Micah also speaks of the corruption of the community departing from God’s will. “Alas for those who devise wickedness and evil deeds on their beds! When the morning dawns, they perform it, because it is in their power. They covet fields, and seize them; houses, and take them away; they oppress householder and house, people and their inheritance” (Micah 2:1-2). Micah lays responsibility for this corruption directly at the feet of Judah’s leaders. “Listen, you heads of Jacob and rulers of the house of Israel! Should you not know justice?—you who hate the good and love the evil, who tear the skin off my people, and the flesh off their bones; who eat the flesh of my people, flay their skin off them, break their bones in pieces, and chop them up like meat in a kettle, like flesh in a caldron” (Micah 3:1-3). Judah’s rulers foster injustice, not justice. They turn their responsibility as agents of Torah on its head. “Hear this, you rulers of the house of Jacob and chiefs of the house of Israel, who abhor justice and pervert all equity, who build Zion with blood and Jerusalem with wrong! Its rulers give judgment for a bribe, its priest teach for a price, its prophets give oracles for money” (Micah 3:9-11). Though Hosea focuses more on idolatry than injustice, the prophet sees the two as interrelated in his challenge to Israel’s leaders. “You have plowed wickedness, you have reaped injustice, you have eaten the fruit of lies” (Hosea 10:13). The presence of widespread injustice among the Hebrews contradicted the dynamics of liberation that characterized Yahweh’s original intervention. Much earlier in the story, when the Hebrew elders expressed their desire for a king “like the nations,” Samuel warned of a return to Egypt. The king will take and take, and the people will again “cry out” as they had when they were slaves (1 Samuel 8:10-18). Yahweh formed this community to be an alternative to Egypt’s injustice. According to the prophets, this alternative was no more. Violence. All these prophets identified violence as a key manifestation of disharmony. Amos begins his prophecies with several statements against the practices of Israel’s neighbors, focusing on their violence. Among other images, we read of Edom pursuing his brother with the sword (Amos 1:11) and of the Ammonites ripping open pregnant women in Gilead (Amos 1:13). Amos drives home the point of Israel’s guilty. Of Israel we read: “See what great tumults are within it, and what oppressions are in its midst. They do not know how to do right, says the Lord, those who store up violence and robbery in their strongholds” (Amos 3:9-10). Hosea, of the three prophets, speaks of the curse of violence the most forcefully and extensively. The Lord’s first words to Hosea refer to the house of Jehu’s responsibility for “the blood of Jezreel” (Hosea 1:4). This reference alludes to the violence of the Northern Kingdom’s kings in their practice of power politics. King Ahab, under the influence of his Baal-worshiping Phoenician wife, had murdered Naboth in order to expropriate his vineyard (1 Kings 21). Ahab’s action then set in motion more violence in Israel. Jehu arose to instigate a bloodbath to avenge Naboth’s murder. Jehu assassinated King Joram in Naboth’s former home property and followed that by killing Judah’s King Ahaziah, who had been visiting Joram. Jehu then killed Ahab’s widow, Jezebel, and oversaw the massacre of Ahab’s seventy sons (2 Kings 9–10). Hosea is not convinced that Jehu’s violence was justified, and he presents God as condemning it. Hosea seems to believe that all Jehu actually did was contribute to the ever-deepening spiral of violence in Israel that may soon result in the nation’s final demise. Hosea reiterates the indictment in chapter four: “Hear the word of the Lord, O people of Israel; for the Lord has an indictment against the inhabitants of the land. There is no faithfulness or loyalty, and no knowledge of God in the land. Swearing, lying, and murder, and stealing and adultery break out; bloodshed follows bloodshed” (Hosea 4:1-2). The problem with violence is that it does not lead to resolution; “bloodshed follows bloodshed.” According to Hosea 6:9, “priests are banded together [to] murder on the road to Sheehan, they commit a monstrous crime.” Hosea links together violence with rejection of Israel’s old Mosaic traditions. Shechem was a cite valued by pilgrims loyal to the old tradition. It was the location of an ancient sanctuary of Yahweh. The reference to Gibeah in Hosea 10:9 (“Since the days of Gibeah you have sinned, O Israel”) is likely alluding to the terrible violence of Judges 19–21, when the tribes united to lay waste to Benjamin in retaliation for the murder of the Levite’s concubine. Violence only leads to violence; preparing for war leads to war. If you trust in the sword you shall die by it. Hosea continues: “You have plowed wickedness, you have reaped injustice, you have eaten the fruit of lies. Because you have trusted in your power and in the multitude of your warriors, there the tumult of war shall rise against your people, and all your fortresses shall be destroyed” (Hosea 10:13-14). Micah also critiques the role of violence in the Southern Kingdom. “You rise up against my people as an enemy; you strip the robe from the peaceful, from those who pass by trustingly with no thought of war” (Micah 2:8). Those who seek to remain faithful to Yahweh’s shalom are themselves treated violently. Micah’s vision of peace, of swords being beaten into plowshares (4:1-5), contrasts with Judah’s present violent reality. Its reiterates Micah’s own loyalty to the old tradition’s sense of Yahweh’s purposes in liberating the Hebrews and giving them the land. Yahweh seeks peace for all the families of the earth (Genesis 12:1-3), and seeks to use the Hebrews to spread this peace. In working for this goal, Yahweh’s judgment on Judah focuses on the nation’s war-making resources. “In that day, says the Lord, I will cut off your horses from among you and will destroy your chariots” (Micah 5:10). The accumulation of horses and chariots reflects the priorities of Judah’s elite classes. “Your wealthy are full of violence; your inhabitants speak lies, with tongues of deceit in their mouths” (Micah 6:12). As does the problem of injustice, so also the problem of violence brings into clear focus Yahweh’s intended priorities in calling the Hebrews. According to Abraham Heschel, “the prophets were the first [people] in history to regard a nation’s reliance upon forces as evil.” Yahweh’s priorities, according to these prophets, included, at their core, justice and peace. To the prophets, the covenant community denies in its life of the character of its founding God. They see Yahweh not first of all as a wrathful, angry, retributive God. To the contrary, the prophets see Yahweh as a loving, gracious, merciful God. Yahweh liberated these vulnerable people from slavery with the plan that the people would be agents of liberation for the whole earth. Yahweh’s anger stems from grief at the failures of the people to live out their liberation. The prophetic rhetoric of judgment does not stem from God’s retributive eye-for-an-eye justice that must punish wrongdoing. No, this rhetoric stems from God’s continuing love and is meant to call the people back (see Hosea 11:8-9). Unbelievably, though, from the prophets’ point of view, the people steadfastly loved by Yahweh do not trust in Yahweh as God. The prophets link the injustice and violence with idolatry—the trust in other gods. And they merge them all together to portray the Hebrews’ religious practices as serving the opposite of their intended effect; the vain religiosity actually becomes an occasion of further sin, not a means of reconnecting with Yahweh. Idolatry. Interestingly, Amos’ sharp critique of Israel says little about idolatry. The most urgent problem was to be found in their injustice and violence. Clearly, a people cannot be worshiping Yahweh while practicing such blatant and widespread oppression. On the other hand, does Hosea place the central focus on idolatry. Idolatry seems to be the root cause for the injustice and violence. The book begins with a direct reference to idolatry, “the land commits great whoredom by forsaking the Lord” (Hosea 1:2). Hosea portrays Yahweh as deeply attached to the Hebrew covenant community. This close attachment explains Yahweh’s deep hurt when the people turn to Baal and violate their covenant with Yahweh. But “the Lord loves the people of Israel, though they turn to other gods” (Hosea 3:1). Baal was a Canaanite god, “clearly the most active and prominent.” He was often portrayed as the great storm god on whom the fertility of the land depended. The Hebrews found Baal worship attractive, given their own dependence upon the rains and their being surrounded by cultures deeply shaped by Baalism. The Baal religion likely threatened the Hebrews’ exclusive Yahwism more than any other Ancient Near Eastern faith. Just as the prophets hold the political leaders responsible for leading the Hebrews into the paths of violence when the leaders were called to foster peace, so Hosea presents the priests as responsible for leading the Hebrews into the paths of idolatry (5:1). Instead of seeing harvesting the fruits of their field as a time for remembering Yahweh’s work on their behalf and offering sacrifices of thanksgiving that would reinforce the people’s commitment to lives lived according to Torah, the people, according to Hosea, are making the offerings to Baal (9:1-9). As Psalm 135:18 points out, people become like that which they worship. So, to offer sacrifices to Baal instead of Yahweh leads to a society becoming violent instead of peaceable, given Baal’s status as the source of violent storms. Hosea critiques Judah’s practices. “Do not rejoice, O Israel! Do not exult as other nations do; for you have played the whore, departing from your God. You have loved a prostitute’s pay on all threshing floors” (9:1). Grain piled on threshing floors is “prostitute’s pay” because Israel takes the harvest as the gift of Baal. Micah also points to idolatry as a central concern of Yahweh’s in relation to Judah. “I will cut off your images and your pillars from among you, and you shall bow down no more to the work of your hands” (Micah 5:13). Vain religiosity. All three prophets forcefully express their rejection of the possibility that the Hebrews’ rituals effectively connect them with Yahweh. However, they do not reject religious or cultic practices per se; they reject religious practices separated from their original intention. “For them, worship and ritual were means; justice and righteousness were ends.” The prescribed religious rituals, in, say, Leviticus, meant to reinforce justice for all in the covenant community. The rituals meant to be linked inextricably with Yahweh’s liberating love, especially oriented toward widows, orphans, and resident aliens. With this link broken, the rituals become worse than simply ineffective. They become themselves occasions for sin and alienation from God. They reinforce the illusion that the covenant community can tolerate injustice, violence, and idolatry and still connect with Yahweh through ritual. As Abraham Heschel writes: “Amos and the prophets who followed him not only stressed the primacy of morality over sacrifice, but even proclaimed that the worth of worship, far from being absolute, is contingent upon moral living, and that when immorality prevails, worship is detestable.” Amos begins his critique shockingly naming Israel’s profound trouble to be due to its identity as Yahweh’s elect, not in spite of this status. God holds the people accountable to their commitment to Torah. “Hear this word that the Lord has spoken against you, O people of Israel, against the whole family that I brought up out of the land of Egypt: You only have I known of all the families of the earth; therefore I will punish you for all your iniquities” (Amos 3:1-2). Amos mocks the Israelites: “Come to Bethel—and transgress; to Gilgal—and multiply transgression” (4:4). Bethel and Gilgal were traditional sanctuaries. For Israel, in Amos’ view, worship and transgression have become synonymous. “The more the people attend the cultic rites, and the more zealous they are in performing the manifold attendant rites, the more they continue to offend and transgress.” In a famous assertion, Amos presents God’s perspective on unjust Israel’s religiosity: “I hate, I despise your festivals, and I take no delight in your solemn assemblies. Even though you offer me your burnt offerings and grain offerings, I will not accept them; and the offerings of well-being of your fatted animals I will not look upon. Take away from me the noise of your songs; I will not listen to the melody of your harps” (5:21-23). Hosea echoes Amos’ warnings. God places special responsibility upon the religious leaders, the ones called to keep religious practices and the demands of Torah linked together in the awareness of the people. “My people are destroyed for lack of knowledge; because you [O priest] have rejected knowledge, I reject you from being a priest to me. And since you have forgotten the law of your God, I will also forget your children” (Hosea 4:6). Israelites will present their sacrifices to God, Hosea warns, but they will be to no avail. “With their flocks and herds they shall go to seek the Lord, but they will not find him; he has withdrawn from them” (Hosea 5:6). In fact, the attempts to sacrifice, in the context of unfaithful living, only make things worse. “When Ephraim multiplied altars to expiate sin, they became to him altars for sinning….Though they offer choice sacrifices, though they eat flesh, the Lord does not accept them. Now he will remember their iniquity, and punish their sins; they shall return to Egypt” (Hos 8:11,13)—reiterating Samuel’s prophecy about the return to slavery. Like Hosea and Amos, Micah sees simply offering of sacrifices as of little avail. He follows Torah in understanding right living as the core of authentic faith. He references God’s liberating work, “I brought you up from the land of Egypt, and redeemed you from the house of slavery” and gave you the promised land, “that you may know the saving acts of the Lord” (6:4-5). But the people seem not to remember. Micah asks, how might life be renewed in the context of alienation? “With what shall I come before the Lord, and bow myself before God on high? Shall I come before him with burnt offerings, with calves a year old? Will the Lord be pleased with thousands of rams, with ten thousands of rivers of oil? Shall I give my firstborn for my transgression, the fruit of my body for the sin of my soul?” (Micah 6:6-7). The answers are no, no, no. These are ritualistic tactics tried and failed due to the injustice of the community. The disharmony the prophets perceive will never be healed through rituals in and of themselves. Contrary to the logic of retribution, the Lord does not require sacrifices. The Lord’s favor is not to be regained by sacred violence within the community. How is Harmony Restored? The prophets raised their critiques for the purpose of helping the Hebrews to find healing. They “sought to bring the people to realize that at the depth of the catastrophes which shook their lives and brought intense suffering, God was present, providing the impulse for the return from a road leading to ruin and offering a new life.” The prophets reject a sacrificial approach. The proper role of sacrifice is as a response to God’s initiative, not as a means to turn God back toward the people. The prophetic assume that God remains the source of wholeness, that God still loves the people in the same way as God had in the time of Moses. Hence, the restoration of harmony is not complicated nor is it something God withholds. Hosea 12:6 captures what is needed in a nutshell: “Return to your God, hold fast to love and justice, and wait continually for your God.” Repent. Do kindness and justice. Trust. Repent. Behind the prophetic all to “return” or “repent” lies the presumption of God’s availability. The alienation follows from what happens on the human side. God simply wants a turning back from problematic beliefs and practices, and then offers mercy. Hosea articulates this in the conclusion of his prophecies. “Return, O Israel, to the Lord your God, for you have stumbled because of your iniquity. Take words with you and return to the Lord; say to him, ‘Take away all guilt; accept that which is good, and we will offer the fruit of our lips. Assyria shall not save us; we will not ride upon our horses; we will say no more, “Our God,” to the work of our hands. In you the orphan finds mercy’” (14:1-3). When Amos speaks against vain religiosity, he offers as an alternative that the people “seek the Lord and live” (5:6). “Seek” may be understood as a kind of technical term for turning to God in a service of prayer; in this context such turning is contrasted with making pilgrimage to the main religious sites. The call to repent or return rests upon a certainty of God’s receptivity. In Amos, especially, the weight of inequity is so heavy that Israel seems doomed. But the way out is simple—“seek the Lord and live,” that is all. Justice. Should the people truly seek God, their lives would bear the fruit: justice and mercy (two complementary concepts). According to Amos, when the people seek God their common life will be transformed in practical ways. In order to live, the people must “seek good and not evil, that you may live; and so the Lord, the God of hosts, will be with you, just as you have said. Hate evil and love good, and establish justice in the gate” (Amos 5:14-15). This call to seek good simply calls to return to observing Torah. The love of Yahweh had created this community and provided clear guidance for its functioning. To live justly does gain God’s favor; it rather returns to living consistently with the favor already granted. Micah contrasts empty rituals with authentic faith. “With what shall I come before the Lord, and bow myself before God on high? Shall I come before him with burnt offerings [and other sacrifices]? He has told you, O mortal, what is good; and what does the Lord require of you but to do justice, and to love kindness, and to walk humbly with your God?” (Micah 6:6,8). Hosea also links living justly and righteously with salvation. “Sow for yourselves righteousness; reap steadfast love; break up your fallow ground; for it is time to seek the Lord, that he may come and reign righteousness upon you” (Hosea 10:11-12). In calling Israel to justice, the prophets does not call for impersonal “fairness” nor, most definitely, for eye-for-an-eye vengeance. They call to covenant community. Doing justice relates to salvation in that saved people know themselves to be loved by the justice-seeking God, and out of this love, walk in God’s paths. Kindness. Hosea and Micah both call upon the people to do kindness (that is, to do mercy and to practice steadfast love) as part of their core proclamation regarding salvation. They link this call to kindness with justice as two closely related and complementary emphases. “Hold fast to kindness and justice” (Hosea 12:6). The Lord requires the people “to do justice and to love kindness” (Micah 6:8). “I desire kindness and not sacrifice, the knowledge of God rather than burnt offerings” (Hosea 6:6). “Sow for yourselves righteousness; reap steadfast kindness” (Hosea 10:12). The call to do kindness, like the call to do justice, directly alludes to Torah. At their heart, the Law and the Prophets unite in calling the Hebrews to healthy and strong relationships in which all people (including, especially, vulnerable ones such as widows, orphans, and resident aliens) receive care. Salvation, then, in the context of the disharmony the prophets spoke so strongly against, led to the healing of relationships within the community. Gift and obligation are inextricably united. Because Yahweh liberated the Hebrews they have the obligation to share life together in ways that insure the wellbeing of all. Salvation comes as a gift from God. Salvation obligates its recipients to live together justly and kindly. Salvation, in the context of disharmony, requires repentance, a turning from injustice and idolatry. The prophets assumed this salvation could be present. “God’s love and kindness indicate a road. It is a road not limited to a particular area in space nor to exceptional miraculous happenings. It is everywhere, at all times.” Trust. Because of Yahweh’s own love and justice that restores relationships, the prophets assure their hearers that they may (and must) trust in Yahweh. The basic dynamic includes the interplay of these four elements. Repent, turn from idolatry and toward God. Let justice and mercy characterize your lives. Trust in your loving and faithful God. And that is it. Sacrifice, at most, comes later. Living in trusting reliance upon Yahweh leads to human fulfillment. “To be fully human, so Israel testifies, is to have a profound, unshakeable trust in Yahweh as reliable, present, strong, concerned, engaged for; and to live and act on the basis of that confidence.” For all his confrontive language and extraordinarily strong warnings, Amos in the end portrays Yahweh as merciful. Yahweh remains trustworthy, faithful to the promise to bless all the families of the earth. “I will restore the fortunes of my people Israel, and they shall rebuild the ruined cities and inhabit them; they shall plant vineyards and drink their wine, and they shall make gardens and eat their fruit. I will plant them upon their land, and they shall never again be plucked up out of the land that I have given them, says the Lord your God” (Amos 9:14-15). Hosea makes the trustworthiness of God’s love for the people even more central throughout his book. The threats and warnings, the tragic consequences of the Hebrews’ injustice and idolatry do not overturn Yahweh’s continuing dependable love. Hosea’s most fundamentally proclaims not Israel’s doom but God’s love that provides for a future. “In the place there it was said to them, ‘You are not my people,’ it shall be said to them, ‘Children of the living God.’ The people of Judah and the people of Israel shall be gathered together, and they shall appoint for themselves one head; and they shall take possession of the land, for great shall be the day of Jezreel” (Hosea 1:10-11). Jezreel was Naboth’s inheritance that was taken from him by Ahab (1 Kings 21). Hosea’s vision of taking “possession of the land” might allude to reinstating the inheritance laws and restoration of land to the landless among the Hebrews. The promise of Yahweh both points back to Yahweh’s work of liberation and provision of Torah and forward to a time of genuine peace. “I will now allure her, and bring her into the wilderness, and speak tenderly to her. From there I will give her vineyards, and make the Valley of Achor a door of hope. There she shall respond as in the days of her youth, as at the time when she came out of the land of Egypt. On that day, says the Lord, you will call me, ‘My husband,’ and no longer will you call me, ‘My Baal.’ For I will remove the names of the Baals from her mouth, and they shall be mentioned by name no more. I will make for you a covenant on that day with the wild animals, the birds of the air, and the creeping things of the ground; and I will abolish the bow, the sword, and war from the land; and I will take you for my wife in righteousness and in justice, in steadfast love, and in mercy. I will take you for my wife in faithfulness; and you shall know the Lord” (Hosea 2:14-20). Micah voices with similar sentiments, asking Yahweh for deliverance, evoking past memories. “Shepherd your people with your staff, the flock that belongs to you, which lives alone in a forest in the midst of a garden land; let them feed in Bashan and Gilead as in the days of old. As in the days when you came out of the land of Egypt, show us marvelous things” (Micah 7:14-15). Then, Micah gives this promise. “He does not retain his anger forever, because he delights in showing clemency. He will again have compassion upon us; he will tread our iniquities under foot. You will cast all our sins into the depths of the sea. You will show faithfulness to Jacob and unswerving loyalty to Abraham, as you have sworn to our ancestors from the days of old” (Micah 7:18-20). Because of Yahweh’s trustworthiness with the Hebrews, going back to the liberation from Egypt, the people have every reason to trust Yahweh in the present and for the future. Such trust is central to their experience of salvation. What does the Lord require? Justice, mercy, “and to walk humbly with your God” (Micah 6:8). That is, bow before your God in trust and humility. God desires steadfast love, not sacrifice, “the knowledge of God rather than burnt offerings” (Hosea 6:6). “Knowledge of God” here may be defined as living with dependence upon and trust in the steadfastness of God. To “know” God is to trust in God above all else. Salvation in the Prophets These three eighth-century prophets often refer to God initiating salvation out of love for the Hebrew people. The key work of salvation was the deliverance of the slaves from Egypt. Everything follows from God’s initiative. Because of God’s healing love, unearned by the people, God holds the people accountable to be loving and just themselves. For these prophets, salvation comes straight from God, at God’s free initiative, and due to God’s transforming mercy. God’s frustration with the people stems not because of their inherent impurity violating God’s holiness, but because of the people’s failure to remain true to God’s loving provision for holistic life. These prophets portray that law as a gift, meant for sustenance of the covenant community. Far from being legalistic and impersonal, they saw Torah as relational, stemming from God’s loving concern for the people. The prophets understand themselves not as radical innovators but as “conservatives,” calling the people back to the covenant commitments their ancestors made. Torah serves the relationship, providing guidance for just, whole, and peaceable communal life. This community includes all, making special provision for those vulnerable ones often pushed to the margins (such as widows, orphans, and resident aliens). These prophets express harsh criticism of sacrificial practices—though, not, it would appear, because of sacrifices being inherently wrong. Rather, the prophets presuppose the original hope that sacrifices remind the people to be grateful to God, to share with others, and to be committed to Yahweh alone as God. In the context of injustice and oppression (reflecting a lack of gratitude toward God) and worship of other gods, the purpose of sacrifices had been turned on its head when the Hebrews combine a self-satisfied attitude about worship with insensitivity toward social injustice. The prophets, preoccupied with the covenant, portray the terrible disharmony they are exposing in terms of violated relationships. The people violate their relationship with Yahweh with idolatry and by ignoring Torah’s call for justice among those in the community. The sin is not about broken rules per se, but about breaking relationships and thereby causing harm. The use of rituals came to be separated from the relationships. Making sacrifice impersonal (and hence, empty) ritual became part of the problem, not part of the solution. The prophets show us a God angry not because the legalistic scales of justice have been unbalanced. Rather, God’s anger stems from violation of the interpersonal dynamics of just relationships through oppression and violence. “God’s concern is the prerequisite and source of [God’s] anger. It is because [God] cares for [humans] that [God’s] anger may be kindled against [humans].” God’s anger and God’s mercy are not in conflict but are directly related, both stemming from God’s will to heal the world. Because the problem lies with violating relationships and harm doing, these prophets present the solution in terms of seeking to restore the relationships. And this restoration is uncomplicated. The God of the prophets remains the loving liberator of the Exodus. The restoration of the Hebrews’ relationship with God essentially depends only upon their remembering who God is. This remembrance entails a simple turn—from false trust and back to trust in God. With renewed trust, justice and mercy in social relationships inevitably returns. The key assumption lying behind the prophets understanding of the hope for restoration of harmony with God is that God does not require sacrifices to change God’s disposition toward God’s people. God remains, as always, favorably disposed—so long as human beings simply recognize that and trust. God remains, as always, ready and willing to heal the sin-caused brokenness. “Sin is not a cul-de-sac, nor is guilt a final trap. Sin may be washed away by repentance and return, and beyond guilt is the dawn of forgiveness. The door is never locked, the threat of doom is not the last word.” The prophetic stance, then, as reflected in these three prophets, contrasts sharply with the logic of retribution. As Abraham Heschel writes, “the ultimate power is not an inscrutable, blind, and hostile power, to which [humans] must submit in resignation, but a God of justice and mercy to whom [humans are] called upon to return.” For the prophets, salvation results from God’s loving initiative. God delivers, forebears, restores. This initiative is a constant. Nothing is needed to change God. The only needed changes are on the human side. Return to Yahweh. Trust in Yahweh, not in other gods, not the works of your hands. Sacrifices are not needed to balance the scales of justice. At most, they simply serve to remind the people of God’s generosity and to foster rededication to Yahweh. The prophets see reality as personal and concrete. They know nothing of a detached inner life of God, of a cosmic scale of justice, or of impersonal, abstract laws that transcend mundane life. Yahweh feels, responds, love, and grieves. The entire context for theological reflection concerning salvation must be seen in terms of the covenant relationships God has established with God’s people. Justice is not about God’s internal processes and impersonal holiness. Rather, justice fosters health in the community of people seeking to live together in a way that glorifies God. All three books underscore God’s overarching healing love. Each presents God seeking healing, but also—in its overall structure—makes clear that the portrayal of anger and wrath is serving a rhetorical strategy meant to foster a return to trust in the Hebrews’ loving, patient, and healing God. The prophets do not portray an angry, wrathful God. Rather, they show us a loving, healing God who out of committed love feels anger at the people’s self-destructive behavior. God expresses this anger, but it ultimately serves the love by fostering a return. Walter Brueggemann, Theology of the Old Testament: Testimony, Dispute, Advocacy (Minneapolis: Fortress Press, 1997), 144. Walter Brueggemann, Tradition for Crisis: A Study in Hosea (Atlanta: John Knox Press, 1968), 21. Walter Brueggemann, 1 & 2 Kings (Macon, GA: Smyth and Helwys, 2000), 257-59. Choou-Leong Seow, “The First and Second Books of Kings,” in Leander Keck, ed., The New Interpreter’s Bible, volume 3 (Nashville: Abingdon Press, 1999), 156. Brueggemann, Theology, 697. Brueggemann, Tradition, 79. Shalom M. Paul, Amos: A Commentary on the Book of Amos (Minneapolis: Fortress Press, 1991), 87. Brueggemann, Theology, 184. For a discussion of this fascinating case of a biblical prophet critiquing the Bible, see James E. Brenneman, “Prophets in Conflict: Negotiating Truth in Scripture,” in Ted Grimsrud and Loren L. Johns, eds., Peace and Justice Shall Embrace: Power and Theopolitics in the Bible (Telford, PA: Pandora Press, 1999), 49-63. James Limburg, Hosea—Micah (Louisville: John Knox Press, 1988), 16-17. Abraham Joshua Heschel, The Prophets, vol. 1 (New York: Harper and Row, 1966), 166. Brueggemann, Theology, 697. John Day, “Baal (Deity),” in D. N. Freedman, ed., Anchor Bible Dictionary, vol. 1 (New York: Doubleday, 1992), 545. Day, “Baal,” 547. See G. K. Beale, We Become What We Worship: A Biblical Theology of Idolatry (Downers Grove, IL: InterVarsity Press, 2008). James Luther Mays, “Hosea,” in Wayne A. Meeks, ed., The HarperCollins Study Bible (New York: HarperCollins, 1993), 1340. Brueggemann, Theology, 678. Paul, Amos, 139. Heschel, Prophets, vol. 1, 195. Paul, Amos, 139. Bernhard W. Anderson, The Eighth-Century Prophets: Amos, Hosea, Isaiah, Micah (Minneapolis: Fortress Press, 1978), 34. Limburg, Hosea, 51. Paul, Amos, 162. Paul, Amos, 162. Ted Grimsrud, “Healing Justice: The Prophet Amos and a ‘New’ Theology of Justice,” in Grimsrud and Johns, eds., Peace, 64-85. Heschel, Prophets, vol. 1, 167. Heschel, Prophets, vol. 1, 211. Brueggemann, Theology, 466. Scholarly consensus concludes that Amos 9:11-15 most likely was added to the book, perhaps sometime not too long before 515 BCE (Bruce E. Willoughby, “Amos,” in Freedman, ed., Anchor Bible Dictionary, vol. 1, 211). However, as I use a reading strategy of that takes “the Bible whole,” that is, as it comes to us—focusing on it as story more than history—I choose to read Amos’ final vision as part of the book’s overall message. Plus, most of the reasons given to bracket Amos 9:11-15 from the rest of the book are based on assumptions about internal consistency that are open to challenge. Heschel, Prophets, vol. 1, 43. Limburg, Hosea, 192. Heschel, Prophets, vol. 2, 66. See also, Anderson, Eighth-Century Prophets, 82. Heshcel, Prophets, vol. 1, 174. Heschel, Prophets, vol. 2, 20-21.

<urn:uuid:83d6a20d-fcf9-4b91-b493-3fd5382d601f>

This presentation is the property of its rightful owner. 1 / 36 CONTINUITY & DIFFERENTIABILITY PowerPoint PPT Presentation CONTINUITY & DIFFERENTIABILITY. Presented by Muhammad Sarmad Hussain Noreen Nasar. Overview. Continuity Differentiability. Continuous at a Point. A function f is continuous at point a in its domain , if. exists &. Domain. CONTINUITY & DIFFERENTIABILITY Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - CONTINUITY & DIFFERENTIABILITY Presented by Noreen Nasar Overview • Continuity • Differentiability Continuous at a Point • A function f is continuous at point a in its domain, if exists & Domain • If the point a is not in the domain of f, we do not talk about whether or not f is continuous at a. Continuous on Subset of Domain • The function f is continuous on a subset S of its domain, if it is continuous at every point of the subset. EXAMPLES • CLOSED FORM FUNCTIONS • DOMAIN SPECIFIC FUNCTIONS • NON-CLOSED FORM FUNCTIONS Closed Form Functions All functions are continuous on their (whole) domain. A closed-form function is any function that can be obtained by combining • constants, • powers of x, • exponential functions, • logarithms, and trigonometric functions Closed Form Functions Examples of closed form functions are: Domain Specified Functions The function f(x) = 1/x is continuous at every point of its domain. Note that 0 is not a point of the domain of f, so we don't discuss what it might mean to be continous or discontinuous there. Non – Closed Form Functions The function f(x)   = -1if x ≤ 2 if x > 2 is not a closed-form function Because we need two algebraic formulas to specify it. Moreover, it is not continuous at x = 2, since limx 2f(x) does not exist Discontinuous Discontinuos Continuous Continuous Undefined Continuous Discontinuous Undefined Discontinuos Continuous Undefined Graphical Representation Continuous but not Differentiable Graphical Representation Differentiable Continuous but not Differentiable Differentiable • f is differentiable at point “a” if f’(a) exists • f is differentiable on the subset of its domain if it is differentiable at each point of the subset. Undifferentiable • f is not differentiable when • The limit does not exist, i.e. does not exist. This situation, when represented in graphical form leads to a cusp in the graph Undifferentiable • Limit goes to infinity, e.g. in the following case Isolated Non – Differentiable Points • Consider the following examples Difference of Opinion Domain of f(x) is THE bone of contention • f(x) is differentiable throughout its domain • f(x) is not differentiable throughout its domain The Question • Are all continuous functions differentiable ? Another Question • If f is not continuous at point a, then is it differentiable at that point ? One More • Are all differentiable functions continuous ? YES • Mathematically provable and easy to understand. Proof of Continuity • Suppose f(x) is differentiable at x=a Contd….. So we can rewrite the equation as exists & THANKS

crawl-data/CC-MAIN-2017-13/segments/1490218188773.10/warc/CC-MAIN-20170322212948-00497-ip-10-233-31-227.ec2.internal.warc.gz

Ice on Earth Background Information Ice Is Important on Earth In our everyday experiences, we encounter water typically in its liquid state. Most of our fresh water, however, exists in its frozen form. About three-quarters of it is found in snow, sea ice, icebergs, ice shelves, glaciers, ice sheets, and soils that remain frozen for two or more years (permafrost). Snow and ice may appear only seasonally at mid-latitudes, but at high altitudes and in the polar regions, frozen water persists year-round as glaciers and ice sheets. Glaciers form in regions where more snow accumulates than melts, such as in high mountain valleys. In the extremely cold polar regions, the glaciers grow to form continent-sized ice sheets. The largest ice sheets cover Antarctica, and smaller ice sheets cover Greenland and part of Iceland. Some of the ice in the Antarctic ice sheet represents the build-up of nearly a million years of snow. Do You Have Ice in Your Own Backyard? Do you live at a high altitude under the vaulted ceiling of glacier-topped mountains? Does winter blow snow your way? Whether you have snow and ice in your backyard is determined by your regional climate. Latitude, elevation, and ocean currents shape your region's temperature, precipitation, and wind patterns — or in short, your local climate. Climate is distinct from weather; while weather can change in a matter of hours or with the seasons, climate is the long-term average weather of a region. The average of thirty years or more of weather determines the climate of a region. Your closet is probably full of clothes, shoes, coats, and hats that are appropriate for your local climate. What you choose to wear on any given day is determined by the weather. If you were to travel to one of the polar regions, you might expect to pack an entirely different set of clothing than what's in your closet. Be sure to check the weather report before embarking on your polar excursion, however; it is the nature of weather to not always fit in with what's expected for a region. The Poles are Miles Apart We tend to lump the far-away, frigid polar regions together in our minds as "the poles." While the Arctic and Antarctic share many features, their differences are epitomized by their most charismatic inhabitants: polar bears in the north and penguins in the south. Floating sea ice dominates the land of the polar bears. The Arctic is an ocean surrounded by land. The land masses of Greenland and Iceland have thick ice sheets, but the ocean is covered by sea ice up to six to nine feet thick. Polar bears live on this floating ice and have easy access to the sea to hunt for seals, fish, and beluga whales. Native peoples likewise live on the sea ice and northern lands. They have hunted in the ocean since prehistoric times. Musk ox, reindeer, caribou, foxes, and wolves live on the land in the lower latitudes of the Arctic. The tilt of the Earth masks the Sun's warming rays for six winter months and plunges the Arctic into continual darkness. In summer, the tilt of the Earth bares the northern regions to the rays of Sun so that to a polar bear standing on the North Pole, the Sun appears to draw a daily circle around her low in the sky from late March to early September. Temperatures reach an average of 37–54°F (3–12°C). This perpetual morning offers enough warmth to melt some of the sea ice, although some remains throughout the year. The sea ice can expand as more ocean water is frozen, forming an ice sheet reaching to the encircling landmasses of Canada, Greenland, Russia, Alaska, Iceland, Norway, Sweden, and Finland. The coldest temperature recorded in the Arctic was about –90°F (–68°C), and the average wintertime temperature is -30°F (–34°C). On the other side of the world, penguins inhabit a frozen desert completely — and happily for them — free of polar bears (and any indigenous land mammals). Should a penguin stand directly over the South Pole, he too would find a perpetual state of darkness in winter and light in summer; although, those seasons would be in reverse for him. The Antarctic winter descends at the end of March while summer begins in late September. Directly below the penguin would be an entirely different icy setting than his counterpart, the polar bear, hunts on. Instead of the relatively thin sheet of sea ice over ocean water, thick sheets of ice rest on land in the Antarctic. That ice and land is much higher in altitude than the sea ice at the Arctic; the South Pole is about 15,000 feet above sea level! Not only is the continent high, it is cold! The interior of the continent gets chilly in winter — the lowest recorded temperature for the planet was recorded there at –128.6°F (–89.2°C) — and even the more temperate coastal areas only get up 59°F (15°C) in summer. The Southern Ocean encircles Antarctica with strong air and ocean currents that keep the warmth of higher latitudes at bay. While the Southern Ocean helps make Antarctica the coldest continent, the Arctic Ocean actually helps make the north relatively warmer. Most of the salty water of the Arctic remains liquid since ocean water freezes at a lower temperature than fresh water. And thanks to the high specific heat capacity of water, the ocean water also doesn't cool as quickly as land (just as pizza crust cools to eating temperature more quickly than the liquid sauce). At 30°F, the Arctic Ocean would hardly seem warm to us! Yet its relative warmth, seeping up through the sea ice, is balmy compared to the thousands of feet of ice and frigid land below the penguin's feet. Antarcticas harsh conditions prevented humans from colonizing the area; people have been visiting for only a few hundred years. Even now, no humans permanently inhabit Antarctica. A treaty signed in 1959 preserves the continent's ecozone and prohibits military activities so that today's 46 participating countries only send peaceful, scientific explorers to visit. Aside from the occasional human and the indigenous penguins, other birds, seals, whales, mosses, lichens, and two types of flowering plants live there. The Polar Regions Are Changing The frozen nature of both of these polar realms makes them seem immobile and unchanging. In fact, the dynamic nature of seemingly immovable ice is a shaping factor in these environments, and indeed, for the whole Earth. On a seasonal scale, sea ice forms and melts at both poles. Sea ice formation is so significant around the coast of Antarctica that winter sea ice doubles the area of that continent. Over a period of years a hidden property of ice is revealed: ice flows. Glaciers do not merely accumulate snow to expand or melt to retreat; their immense weight causes them to flow like a stream. Furthermore, the pressure of all that ice may cause the very bottom to melt and form a slippery layer. Glaciers both flow and slip down valleys. As glaciers and ice sheets flow and slip down the land, they change the landscape. They gouge out "u"-shaped valleys; push boulders, gravel, and sand into hills called moraines; and eventually thrust their outer rims out onto the ocean as thick, floating ice shelves. Ice shelves are anchored to the land by the glacier or ice sheet and float in the ocean at the rims. During the summer, pieces break off the end to form icebergs in a process called calving. The ice shelf continues to flow, as its glacier flows, out into the ocean, but it also serves to shore up the ice behind it and keep the heart of the glacier or ice sheet from flowing quickly to the ocean. In recent years, scientists have observed an alarming trend: ice is melting across the world. Each winter, less sea ice forms on the Arctic Ocean and it melts earlier in the spring. Glaciers in the mountains of New Zealand, Canada, and Alaska are melting back. Ice shelves in Antarctica are collapsing. When ice melts, it makes water. If that ice is on land, above sea level, the water is added to the ocean, causing the ocean level to rise. Most of the world's — including over half of America's — populations live near coastlines that would be impacted by flooding. Sea levels are already rising, primarily because water expands as it warms in response to global climate change, but also because land-based ice is melting. In Antarctica, the Larsen B ice shelf collapsed into the ocean in February 2002 and the nearby Larsen A ice shelf collapsed a few years previously. Scientists' primary concern is not the melting of this floating ice; sea ice, ice shelves, and icebergs are already in the ocean and have already displaced as much sea water as they ever will. They will not raise sea levels as they melt. Behind melting icebergs and ice shelves, however, remain glaciers and ice sheets. With its ice shelf melted and calved away, a glacier or ice sheet may flow unchecked into the ocean and add its volume of water to the sea. Scientists have found that the ice sheet supported by the Larsen ice shelves is moving eight times faster now than before their collapse. It is the melting and movement of such land ice into the ocean that poses the threat of higher sea levels. In the Arctic, the extent of summer sea ice set a record low in 2007. While the sea ice extent was slightly higher in the summer of 2008, the minimum levels of Arctic sea ice have been overall decreasing over the last 30 years. Polar bears became the first species to be Federally listed as threatened under the Endangered Species Act in 2008 directly due to global warming. Earth's ice is melting because global temperatures, on average, are rising. Earth's Climate Is a Balancing Act Earth's temperatures — and by extension, its moderate climate — are shaped by many factors, many of which influence each other. All of Earth's systems, including the energy balance; water, rock, and carbon cycles; and the motions of oceans and atmosphere interplay to create our climate. With so many influences to consider, it is no wonder that climate scientists must use powerful computer models to understand Earth's climate of the past, present, and future. Luckily, our planet is a warm place. The Sun provides over 99% of Earth's energy; alone, that energy is enough for our planet to reach a rather chilly -2°F (-19°C) or so. (Geothermal energy from the Earth's interioir contributes less than 1% of our energy. Radioactive decay of elements and gravitational energy inside Earth add such a small amount of warming compared to the Sun that it will be ignored here.) It is thanks to a small percentage of all the tiny gas molecules in our atmosphere that Earth is warm enough to inhabit. Naturally-occurring greenhouse gases trap the Sun's energy and keep it from reflecting back into space. Volcanoes and bacteria in natural wetlands are examples of greenhouse-gas producers. Earth is warmed to an average temperature of about 57°F (14°C) by a natural process called the greenhouse effect. Much of the Sun's radiation is in the visible range of the electromagnetic spectrum, and for the most part, this type of light passes right through our atmosphere. It warms the surface of the Earth, causing Earth to give off a radiation of its own: infrared radiation. The infrared radiation of the Earth is invisible to us. Unlike the higher-energy radiation from the Sun, the low-energy, long-wavelength infrared radiation can't pass back through the atmosphere with ease. Some of it does manage to escape back into space, but most of it is captured by greenhouse gas molecules. All molecules are able to absorb and emit light energy, but at the molecular scale, that light has to have just the right amount of energy for a particular type of molecule to absorb. Greenhouse gas molecules are all made up of at least three atoms bonded together. They are able to absorb infrared radiation because its energy is just right for causing the atoms of the molecules to move slightly in relation to each other, or vibrate. (The visible light from the Sun was too energetic for the molecules to "catch.") The molecules then emit the energy as infrared radiation, which is often caught by another greenhouse gas molecule or the surface of the Earth. Carbon dioxide, methane, nitrous oxide, and even water vapor are greenhouse gases. While the atmosphere is 78% nitrogen and 21% oxygen, greenhouse gases make up only a tiny fraction of the air we breathe. For instance, carbon dioxide makes up almost 0.04% of the atmosphere; methane is more efficient at absorbing infrared radiation from the Earth but makes up only about 0.0002%. Water vapor comes and goes in the form of clouds, fog, and humidity. It is highly variable, and may represent between 1-4% of the atmosphere at the surface. In addition to the greenhouse effect, other factors help moderate the Earth's temperatures by absorbing more of the Sun's energy or reflecting it. These factors have influenced each other and changed to create Earth's evolving climate over time. Earth's global surface temperatures are rising at an unprecedented rate. The past century has seen an increase of a little more than 1°F (0.74°C). A degree may not seem large to us, but we are accustomed to thinking locally. Local temperatures change with the weather, season, and time of day, often much more than a degree in a single day. Global changes in temperature are averages that take into account the large local variations and represent a change in the balance of factors that shape Earth's climate. Today's global temperatures are the highest of the past 500 years, perhaps even for the past millennium. Temperature change is nothing new; the Earth has undergone many changes in global temperature in its past. Changes in Earth's orbit, in addition to less influential changes in the Sun's intensity, outgassing from volcanoes and other sources, and changes in ocean currents, have resulted in cycles of cooling and warming. Certain eras in the Age of the Dinosaurs were warmer than today, and the ice ages were colder. However, none of these periods saw such a drastic change in global average temperature over a short period of time as today. Large changes in temperature occurred in the last million years during the glacial cycles, but the global warming at the end of an ice age is thought to have taken 5,000 years. In addition, these changes were all due to natural factors. Scientists generally attribute the current climate change to increases in greenhouse gas concentrations in the atmosphere. Scientists also largely agree that carbon dioxide released to the atmosphere by human activities is the main culprit of global warming. It is released from burning coal, oil, natural gas in power plants, cars, factories, and to some extent, from the clear cutting of forests. Human activities release other greenhouse gases. Methane is released by farm animals, rice paddies, rotting garbage in landfills, mining, and extraction of natural gas. Chlorofluorocarbons (CFCs) are well-known for creating the ozone hole, but are also implicated in their additional role as greenhouse gases in the separate problem of climate change. The fertilizers used to grow our food add nitrous oxide. Scientists have records of the amount of carbon dioxide in Earth's atmosphere stretching thousands of years into the past. A dramatic increase in the percentage of carbon dioxide in the atmosphere corresponds with the Industrial Revolution and has proceeded to climb sharply in the ensuing years. Today's levels far exceed even the highest levels of the past 750,000 years. Ice is a handy record-keeper. Air bubbles trapped in ancient ice have allowed scientists to measure the components of Earth's past atmospheres. Scientists drill cores in glaciers and ice sheets and analyze the preserved bubbles of prehistoric atmospheres. Also contained in the core is wind-blown volcanic ash, which is used to date its layers. Slight differences in the kinds of elemental oxygen within the ice tell the scientists how cold the air was when the snow fell The carbon dioxide concentration in the atmosphere has been measured directly since 1957. The instruments at Mauna Loa, Hawaii reflect the seasonal uptake and release of carbon dioxide by plants as "wiggles," but show an overall sharp increase. Computer Models Help Decode the Complicated Mystery of Climate Change Climate models are used to weigh the influences of the myriad of factors which shape our planet's climate, including greenhouse gases from natural and human sources, changes in the Sun's intensity, and the complicated interactions of Earth's systems. While the contributions of natural warming are still not fully understood, it is generally agreed that their effects are comparably minor. Changes in solar intensity and volcanoes produced most of the warming from pre-industrial times to 1950, but are not implicated in the current global change. For instance, when Mt. Pinatubo erupted in 1991, the global average temperature dropped by 0.9 °F (0.5 °C) as volcanic particles in the air reflected some of the Sun's energy. (The volcano also released carbon dioxide, a warming agent, but this addition is thought to be small compared to human contributions.) Studies by the National Center for Atmospheric Research (NCAR) attribute less than a third of the current warming to changes in the Sun's intensity. Data from all realms of science are pulled together to create and validate the computer models. For example, scientists note what species of flowers bloom earlier in the year and in what regions coral reefs die off because of warmer sea surface temperatures. They measure how increasing carbon dioxide is acidifying our oceans as it dissolves to form carbonic acid. Satellites take data on ice cover, precipitation, temperature, and other characteristics of our planet from above. Tomorrow's World Will Be a Different Place The clothes in your closet, when you can plant what flowers in your garden, the varieties of local produce you buy at the grocery store, the types of plants and trees growing in your parks, and what wild animals live in or migrate through your area are all determined by your local climate. Imagine how your world might change as your local climate is reshaped by global climate change. While it might be tempting to blame a hot summer's day on global warming, short duration warmer -or cooler-than-average temperatures are a part of Earth's natural charm (just to keep us on our toes!). Scientists are trying to understand how changes in temperature, precipitation, and sea level will impact Earth's diverse regions. Scientists use mathematical computer models to predict how the various warming and cooling factors will shape tomorrow's climate. Changes in the Sun's intensity, ice and cloud cover, volcanoes, greenhouse gases, natural biological influences, and human activities all interact in complicated ways. The thawing of Earth's freezers — the polar regions — will have far-reaching effects. The nature of the polar regions makes them more sensitive to the consequences of climate change than warmer latitudes. Reflective white ice and snow will melt into dark rivers and oceans that better absorb the Sun's energy. Like freezer overdue for defrosting, increasing temperatures will expose organic matter long locked away in the frozen ground of the arctic tundra. This permafrost will thaw and plant matter decomposing in the resulting marshes will release the greenhouse gas methane. Antarctic sea ice is as necessary to penguins as forests are to songbirds. If the 3.6 °F (2 °C) rise in global temperatures predicted over the next 40 years comes to fruition, essential nesting and feeding grounds will have melted away. The warming would translate to a 50% decline of emperor penguins. The Pt. Géologie colony that increased this species' fame through the movie March of the Penguins is declining as northern Antarctic temperatures increase. With less sea ice, Adélie penguins have a shorter journey from their nests of rock to fetch food from the ocean for their chicks. However, Adélie penguins are adapted to the cold and overall are harmed by increasing temperatures. They face a loss of 75% with the predicted temperature rise. Climate change adds to the problems of pollution and over-fishing of the Southern Ocean. Arctic sea ice is predicted to continue disappearing.Commerce by sea will have entirely new opportunities for transport through the opened Arctic Ocean, but the changes for humans and animals dependent of the ice are grim. According to a study by the United States Geological Survey, the predicted loss of Arctic sea ice in future years may result in the loss of 2/3 of the polar bear population by the middle of this century. Changes will vary across the globe. More warming is expected in the interiors of continents and in the northern latitudes of the Northern Hemisphere than at the coastal regions and tropics. Heat waves are expected to become more intense. Higher temperatures will lead to faster evaporation, and rain, when it occurs, may fall in the form of heavy downpours. More precipitation may provide additional water to some regions, but floods and droughts are also expected to become more frequent. Storms may increase in intensity; in addition, rising sea levels will impact coastal areas. Crops may experience longer growing seasons and fewer frosts. The warmer temperatures and increased carbon dioxide in the air may help some crop varieties, but they, too, have a point at which it is too warm to survive. The ranges of plants and animals, biodiversity, and migratory patterns are expected to continue to change in response to climate change. Pests, parasites, and diseases are likely to thrive in the warmer temperatures, much to the irritation of the plants, animals, and humans they prey upon. While heat waves may contribute to heat-related illness and death, milder winters may be a benefit for health issues. Beach erosion, reduced snowfall, and changes in flora and fauna may limit opportunities for outdoor excursions, but warmer temperatures will provide more opportunities to venture outdoors. Humans Have the Power to Stabilize Global Change Humans clearly have an impact on the global environment and the ecosystems it supports. Our use of fossil fuels, such as coal and oil, has added carbon dioxide to the atmosphere and warmed our planet. Now, our influence can be used to stabilize or reduce global warming! Use of fossil fuels pervades our everyday life and it is challenging to know where to begin reducing it. Not only do fossil fuels power our cars and school buses, coal often produces the electricity that runs our air conditioners and charges our cell phone batteries. In addition, fossil fuels are often used in the production and transportation of our goods before we even take them home from the store. For instance, fossil fuels are used for the energy and materials to create plastic bottles and transport heavy drinking water across the country to the local grocery store.Thus, not only does driving less and conserving electricity help combat global warming, so does being a savvy consumer of local produce and recycled goods. In addition to carbon dioxide, the greenhouse gases methane and nitrous oxide are by-products of everyday practices. Methane, a natural waste product of certain microbes living in the intestines of cattle, is released by these animals in large amounts. Stocking up on protein from fish, and especially beans and other vegetables, instead of beef is one way grocery shoppers can help slow global warming. Human-produced fertilizers break down in the soil and release nitrous oxide, so composting the vegetable clippings from that high-protein bean salad to use as natural fertilizer has a further positive impact on climate change. October 19, 2009

<urn:uuid:e98993e2-51e2-4aef-9cc1-04e09bdfdb40>

# RD Sharma Class 12 Ex 28.5 Solutions Chapter 28 The Straight Line in Space Here we provideRD Sharma Class 12 Ex 28.5 Solutions Chapter 28 The Straight Line in Space for English medium students, Which will very helpful for every student in their exams. Students can download the latest RD Sharma Class 12 Ex 28.5 Solutions Chapter 28 The Straight Line in Space book pdf download. Now you will get step-by-step solutions to each question. ## RD Sharma Class 12 Ex 28.5 Solutions Chapter 28 The Straight Line in Space ### (i)  and Solution: As we know that the shortest distance between the lines and is: D= Now, = 36 + 225 + 9 = 270 = √270 On substituting the values in the formula, we have SD = 270/√270 = √270 Shortest distance between the given pair of lines is 3√30 units. ### (ii) and Solution: As we know that the shortest distance between the lines  and  is: D= Now, = – 16 × 32 = – 512 On substituting the values in the formula, we have SD = Shortest distance between the given pair of lines is units. ### (iii)  and Solution: As we know that the shortest distance between the lines and  is: D= Now, = 1 On substituting the values in the formula, we have SD = Shortest distance between the given pair of lines is 1/√6 units. ### (iv)  and Solution: Above equations can be re-written as: and, As we know that the shortest distance between the lines and  is: D = = 9/3√2 Shortest distance is 3/√2 units. ### (v)  and Solution: The given equations can be written as: \and As we know that the shortest distance between the lines and  is: D= Now, = 15 = 3√2 Thus, distance between the lines is  units. ### (vi)  and Solution: As we know that the shortest distance between the lines and is: D = Now, = 3√2 Substituting the values in the formula, we have The distance between the lines is units. ### (vii)  and Solution: As we know that the shortest distance between the lines and is: D= Now, = 10 Substituting the values in the formula, we have: The distance between the lines is 10/√59 units. ### (viii)  and Solution: As we know that the shortest distance between the lines and is: D= Now, = 1176 = 84 Substituting the values in the formula, we have: The distance between the lines is 1176/84 = 14 units. ### (i) and Solution: The given lines can be written as: and = –1 = √6 On substituting the values in the formula, we have: SD = 1/√6 units. ### (ii)  and Solution: The given equations can also be written as: and \ As we know that the shortest distance between the lines and is: D= =  3 SD = 3/√59 units. ### (iii)  and Solution: The given equations can be re-written as: and = √29 = 8 SD = 8/√29 units. ### (iv)  and Solution: The given equations can be re-written as: and SD = 58/√29 units. ### (i)  and Solution: As we know that the shortest distance between the lines and is: D= =  –1 = √14 ⇒ SD = 1/√14 units ≠ 0 Hence the given pair of lines does not intersect. ### (ii)  and Solution: As we know that the shortest distance between the lines and is: D= = 0 = √94 ⇒ SD = 0/√94 units = 0 Hence the given pair of lines are intersecting. ### (iii)  and Solution: Given lines can be re-written as: and As we know that the shortest distance between the lines and is: D= = −9 = √195 ⇒ SD = 9/√195 units ≠ 0 Hence the given pair of lines does not intersect. ### (iv)  and Solution: Given lines can be re-written as: and As we know that the shortest distance between the lines and is: D= = 282 ⇒ SD = 282/√3 units ≠ 0 Hence the given pair of lines does not intersect. ### (i) and Solution: The second given line can be re-written as: As we know that the shortest distance between the lines and is: D= ⇒ SD =  units. ### (ii)  and Solution: The second given line can be re-written as: As we know that the shortest distance between the lines and is: D= ⇒ = √11 ⇒ SD = √11/√6 units. ### (i) (0, 0, 0) and (1, 0, 2)       (ii) (1, 3, 0) and (0, 3, 0) Solution: Equation of the line passing through the vertices (0, 0, 0) and (1, 0, 2) is given by: Similarly, the equation of the line passing through the vertices (1, 3, 0) and (0, 3, 0): As we know that the shortest distance between the lines   and  is: D= = −6 = 2 ⇒ SD = |-6/2| = 3 units. ### Question 6. Write the vector equations of the following lines and hence find the shortest distance between them: Solution: The given equations can be written as: and As we know that the shortest distance between the lines and is: D= ⇒ \vec{|b|}= 7 ⇒ SD = √293/7 units. ### (i) and Solution: As we know that the shortest distance between the lines and is: D= Now, = 3√2 ⇒ SD = 3/√2 units. ### (ii) Solution: As we know that the shortest distance between the lines and is: D= Now, = √116 ⇒ SD = 2√29 units. ### (iii) and Solution: As we know that the shortest distance between the lines and is: D= Now, = √171 ⇒ SD = 3√19 units. ### (iv) and Solution: As we know that the shortest distance between the lines and is: D= Now, (\vec{a_2}-\vec{a_1}).(\vec{b_1}×\vec{b_2})=108 |\vec{b_1}×\vec{b_2}|=\sqrt{(-9)^2+(3)^2+(9)^2} = 12 ⇒ SD = 9 units. ### Question 8. Find the distance between the lines: and Solution: As we know that the shortest distance between the lines and is: D= ⇒ = √293 ⇒ SD = √293/7 units. I think you got complete solutions for this chapter. If You have any queries regarding this chapter, please comment in the below section our subject teacher will answer you. We tried our best to give complete solutions so you got good marks in your exam. If these solutions have helped you, you can also share rdsharmasolutions.in to your friends.

crawl-data/CC-MAIN-2023-23/segments/1685224655244.74/warc/CC-MAIN-20230609000217-20230609030217-00284.warc.gz

The mountains were originally called "Sun-a-do" by the Duwamish Indians, while the first European to see them, the Spanish navigator Juan Perez, named Mount Olympus "Santa Rosalia", in 1774. But the English captain John Meares, seeing them in 1788, thought them beautiful enough for the gods to dwell there, and named the highest point "Mount Olympus" after the mountain in Greece. Various names for the mountains were used based on the name Mount Olympus, including the Olympic Range, the Olympian Mountains, and the Olympus Range. Alternate proposals never caught on, and in 1864 the Seattle Weekly Gazette persuaded the government to make the present-day name official, although other names continued to be used. The rock that is in then mountains are Sandstone, Shale, & Basalt. The Olympic Mountains of Washington state were actually “pasted to” the North American continent as a result of an ancient ocean floor smashing into the continental landmass starting about 35 million years ago. Because of the movement of the tectonic plates in this region, the top of the seafloor folded from the pressures, creating what was the beginnings of the Olympic Mountains; the lower layer of the seafloor dove beneath the Olympic area, creating enough heat to form the volcanoes of the Cascade Range. These mountains are not as high as other peaks in the Rockies the highest, Mt. Olympus, is just under 8,000 feet (2,440 meters)—but they are still large enough to reveal their torturous, twisted past. The peak of the mountain is Mt.Olympic. The elevation is 7,962 ft.

<urn:uuid:4ddfeaf1-aa59-417a-8a65-477012d8882f>

1. ## Inverse of sets I have attached a question that I am having trouble with. Thanks to anyone who can help.DOC1.DOC 2. ## Sets and Inverse functions Hello Mel Here is the problem. Suppose $X$ and $Y$ are nonempty sets and $f: X \rightarrow Y$ is a function. Let $A$ and $B$ be subsets of $Y$. Prove that $f^{-1} (A \cup B) = f^{-1}(A) \cup f^{-1}(B)$ We do this by showing that $f^{-1} (A \cup B) \subseteq f^{-1}(A) \cup f^{-1}(B)$ and $f^{-1}(A) \cup f^{-1}(B) \subseteq f^{-1} (A \cup B)$ So, for the first part: Suppose $x \in f^{-1}(A \cup B)$. Then for some $y \in Y$, $f(x) = y$, and $y \in A \cup B$. $\Rightarrow y \in A$ or $y \in B$ [Note: throughout this proof 'or' means 'inclusive or'. So $y \in A$ or $y \in B$ means $y \in A$ or $y \in B$ or both. $\Rightarrow f(x) \in A$ or $f(x) \in B$ $\Rightarrow x \in f^{-1}(A)$ or $x \in f^{-1}(B)$ $\Rightarrow x \in f^{-1}(A) \cup f^{-1}(B)$ So $x \in f^{-1}(A \cup B) \Rightarrow x \in f^{-1}(A) \cup f^{-1}(B)$ $\Rightarrow f^{-1}(A \cup B) \subseteq f^{-1}(A) \cup f^{-1}(B)$ (1) For the second part: Suppose $x \in f^{-1}(A) \cup f^{-1}(B)$ Then $x \in f^{-1}(A)$ or $x \in f^{-1}(B)$ Then for some $y \in Y$, $f(x) = y$ and $y \in A$ or $y \in B$ $\Rightarrow y \in A \cup B$ $\Rightarrow x \in f^{-1}(A \cup B)$ So $x \in f^{-1}(A) \cup f^{-1}(B) \Rightarrow x \in f^{-1}(A \cup B)$ $\Rightarrow f^{-1}(A) \cup f^{-1}(B) \subseteq f^{-1} (A \cup B)$ (2) So, from (1) and (2): $f^{-1} (A \cup B) = f^{-1}(A) \cup f^{-1}(B)$

crawl-data/CC-MAIN-2016-50/segments/1480698543030.95/warc/CC-MAIN-20161202170903-00365-ip-10-31-129-80.ec2.internal.warc.gz

Homework Help: Rewriting some Series / Factorials 1. Dec 31, 2004 Let $$u = 1 + \frac{x^{3}}{3!} + \frac{x^{6}}{6!} + \frac{x^{9}}{9!} + \dotsb$$ $$v = x + \frac{x^{4}}{4!} + \frac{x^{7}}{7!} + \frac{x^{10}}{10!} + \dotsb$$ $$w = \frac{x^{2}}{2!} + \frac{x^{5}}{5!} + \frac{x^{8}}{8!} + \dotsb$$ Show that $$u^3 + v^3 + w^3 - 3 u v w = 1$$ Well, here what I've done: $$u = \sum _{n=0} ^{\infty} \frac{x^{3n}}{(3n)!}$$ $$v = \sum _{n=0} ^{\infty} \frac{x^{3n+1}}{(3n+1)!}$$ $$w = \sum _{n=0} ^{\infty} \frac{x^{3n+2}}{(3n+2)!}$$ Further work can be simplified if I rewrite those series in terms of familiar functions. The first one is not too hard to obtain: $$u = \sum _{n=0} ^{\infty} \frac{x^{3n}}{(3n)!} = \sum _{n=0} ^{\infty} \frac{x^{3n}}{n!3^n} = \sum _{n=0} ^{\infty} \frac{ \left( \frac{x^3}{3} \right) ^{n}}{n!} = e^{x^3 / 3}$$ Unfortunately, the others got me stuck. I can't find ways to rewrite the following factorials: $$(3n+1)! \qquad \mbox{ and } \qquad (3n+2)!$$​ Is there any trick? Thanks 2. Dec 31, 2004 $$\prod _{i=0} ^{n} (3i) = n! 3^n \neq (3n)! \Longrightarrow u \neq e^{x^3 / 3}$$ 3. Dec 31, 2004 arildno I am POSITIVE that there is a trick here; most probably, it has to do with forming combinations of your original power series into the familiar power series for sine and cosine. 4. Dec 31, 2004 Hurkyl Staff Emeritus The method is related to sines and cosines, but doesn't use them at all. You might be familiar with the sinh and cosh functions -- the taylor series for cosh z has all the even terms of e^z, and the taylor series for sinh z has all of the odd terms. One can write sinh and cosh in terms of the two functions e^z and e^((-1)z) -- the idea is that the (-1) uniformly alters every odd term in the taylor series for e^z, but leaves the even terms alone (since (-1)^2 = 1). Once you have the taylor series for e^z and e^((-1)z), you can then solve for the other functions. You want to do the same thing here, except you want a modification that has period 3... i.e. that t^3 = 1. The three possibilities, e^z, e^(tz), and e^(t^2 z) give you three series you can manipulate... Last edited: Dec 31, 2004 5. Dec 31, 2004 arildno From what I can see, setting x=iy, we ought to have: $$u+v+w=\cos(y)+i\sin(y)$$ I might be wrong, but I don't think so. 6. Dec 31, 2004 Hurkyl Staff Emeritus That is true, but a simpler relation is that u(x) + v(x) + w(x) = e^x. (e^(ix) is, of course, cos x + i sin x) 7. Dec 31, 2004 Thank you so much for all the hints. I'm not used to working with hyperbolic functions, but it sounds like it might be useful to learn more about them now. Let me check with you whether or not I roughly understand what you mean. I've searched the web and found: $$\sinh (x) = \frac{e^x - e^{-x}}{2} = \sum _{n=0} ^{\infty} \frac{x^{2n+1}}{(2n+1)!} = x + \frac{x^3}{3!} + \frac{x^5}{5!} + \frac{x^7}{7!} + \dotsb$$ $$\cosh (x) = \frac{e^x + e^{-x}}{2} = \sum _{n=0} ^{\infty} \frac{x^{2n}}{(2n)!} = 1 + \frac{x^2}{2!} + \frac{x^4}{4!} + \frac{x^6}{6!} + \dotsb$$ They are directly related to $$e^x = \sum _{n=0} ^{\infty} \frac{x^{n}}{n!} = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \dotsb$$ $$e^{-x} = \sum _{n=0} ^{\infty} (-1)^n \frac{x^{n}}{n!} = 1 - x + \frac{x^2}{2!} - \frac{x^3}{3!} + \dotsb$$ We also have: $$e^z = \sum _{n=0} ^{\infty} \frac{z^{n}}{n!} = 1 + z + \frac{z^2}{2!} + \frac{z^3}{3!} + \dotsb$$ $$e^{tz} = \sum _{n=0} ^{\infty} \frac{(tz)^{n}}{n!} = 1 + tz + \frac{t^2 z^2}{2!} + \frac{t^3 z^3}{3!} + \dotsb$$ $$e^{t^2 z} = \sum _{n=0} ^{\infty} \frac{(t^2 z)^{n}}{n!} = 1 + t^2 z + \frac{t^4 z^2}{2!} + \frac{t^6 z^3}{3!} + \dotsb$$ From those three, I can get to the following: $$e^{ix} = \sum _{n=0} ^{\infty} \frac{(ix)^{n}}{n!} = 1 + ix - \frac{x^2}{2!} + \frac{ix^3}{3!} + \dotsb$$ $$e^{-ix} = \sum _{n=0} ^{\infty} (-1)^n \frac{(ix)^{n}}{n!} = 1 - ix + \frac{x^2}{2!} - \frac{ix^3}{3!} + \dotsb$$ And that has a close relationship to my problem, since $$u(x) + v(x) + w(x) = e^{ix} = \cos x + i\sin x$$ What I initially had in mind was to individually manipulate the series representation of the given functions so that each is related to some familiar function. It is a bit confusing now that I try to figure out a way to rewrite them, since they appear together above. I'm not sure on know how to proceed. I am supposed to manipulate $$e^{ix}$$ and $$e^{-ix}$$ to go any further? Thanks. Last edited: Dec 31, 2004 8. Dec 31, 2004 Hurkyl Staff Emeritus Here is your problem: you're manipulating things with a period of 2 or 4 (i.e. -1 or i), trying to make something with a period of 3... 9. Jan 1, 2005 TenaliRaman If i get Hurkyl's Hint correctly,then think ::cube root of unity:: -- AI 10. Jan 1, 2005 Is this what you mean? $$(1)^{1/3} = i^{4n/3} = 1$$ 11. Jan 1, 2005 TenaliRaman You missed a pi i guess, but yes. You can work in terms of omega instead of i. Note that $$\omega^3 = 1$$ and $$\omega^2 + \omega + 1 = 0$$. -- AI 12. Jan 2, 2005 How about $$i^{(4\pi n) /3}$$ ? As a result, we may find: $$n=0 \Longrightarrow i^{(4\pi n) /3} = 1$$ $$n=1 \Longrightarrow i^{(4\pi n) /3} = \cos \left( \frac{2\pi ^2}{3} \right) + i \sin \left( \frac{2\pi ^2}{3} \right) = (-1) ^{2\pi /3}$$ $$n=2 \Longrightarrow i^{(4\pi n) /3} = \cos \left( \frac{4\pi ^2}{3} \right) + i \sin \left( \frac{4\pi ^2}{3} \right) = (-1) ^{4\pi /3}$$ $$n=3 \Longrightarrow i^{(4\pi n) /3} = \cos \left( 2\pi ^2 \right) + i \sin \left( 2\pi ^2 \right) = 1$$ Does $$x = 2\pi ^2$$ ? I'm not sure about what you mean by $$\omega$$. Does $$\omega = i^{(4\pi n) /3}$$ ? Also, how does the relationship $$\omega^2 + \omega + 1 = 0$$ fit into the problem (I'm really lost)? Any help is highly appreciated. 13. Jan 2, 2005 Hurkyl Staff Emeritus It's customary to use $\omega$ or $\xi$ as the symbol for a (primitive) primitive root of unity. Generally, when manipulating complex exponents, it's better to do everything to the base e, so the cube roots of 1 are $e^{2\pi n / 3}$. By the way, your calculations in the last post are entirely wrong. For example, $\cos 2\pi^2 n$ is not 1. 14. Jan 3, 2005 I guess we might ultimately find $$u(x) + v(x) + w(x) = e^{i\left( \frac{2\pi}{3}n \right)} \qquad n \in \mathbb{N}$$ My question is: Is it now possible to individually manipulate the given functions? If so, how? Thank you very much. 15. Jan 3, 2005 krab Still don't know what you're getting at. $$u(x) + v(x) + w(x) = e^x$$, directly. No imaginary numbers are needed for this. So your equation is only consistent if $x=i(2\pi n/3)$. How does that help? Why are you restricting the value of x? You are meant to prove it for all x. 16. Jan 3, 2005 krab Explicit formulas exist for u,v, and w in terms of exponentials and cosines. I won't give them here, since this is a homework forum. But if you have access to a mathematics library, there is a very nice paper in the journal of the Society for Industrial and Apllied Mathematics Vol.15, p.618: http://www.jstor.org/view/00361399/di974630/97p0414b/ Last edited by a moderator: Apr 21, 2017 17. Jan 3, 2005 krab Also: You can prove the relation u^3+v^3+w^3-3uvw=1 by differentiating it and using the relations: u'=w, v'=u, w'=v. 18. Jan 3, 2005 dextercioby Yes,Krab,your method unfortunately involves the operation of differentiation which "erases" the constant in the RHS of the equality.So basically,it helps u prove that $$u^{3}+v^{3}+w^{3}-3uvw=C$$ ,where C is an arbitrary constant.U'll need to 'fix' it,and that is done through an initial condition: Take the function $$f(t)=:u^{3}(t)+v^{3}(t)+w^{3}(t)-3u(t)v(t)w(t)$$ It verifies $$f(0)=1$$ and at the same time,as u indicated $$f'(t)=0$$ which means it is constant,no matter 't' and has the same value for all 't',implicitely for 't=0'. So one finds $$f(t)=1$$ Quod erat demonstrandum. Daniel. PS.This kind of proof reminds me of the proof of the inverse of Stone's theorem. Last edited: Jan 3, 2005 19. Jan 3, 2005 The purpose of the homework help section at physicsforums.com is to help people get their homework done, not actually do it for them. I am aware of that. I'm not asking you to do anything other than give me some pointers. I'm grateful for them. So, let's get down to the nitty-gritty. I shouldn't have restricted the value of x. What I intended to to was to apply the idea of using the the cube roots of 1 into this problem. As you've just showed me, that is not the right way to proceed. So, what happens to the $$e^{i\left( \frac{2\pi}{3}n \right)}$$ Hurkyl and TenaliRaman guided me to? I simply don't see how that becomes a $$e^x$$. Maybe, that goes in at a different stage of the solution. Also, I'd like to illustrate why I have difficulty dealing with $$u(x) + v(x) + w(x) = e^x$$: $$\sum _{n=0} ^{\infty} \left[ \frac{x^{3n}}{(3n)!} \right] + \sum _{n=0} ^{\infty} \left[ \frac{x^{3n+1}}{(3n+1)!} \right] + \sum _{n=0} ^{\infty} \left[ \frac{x^{3n+2}}{(3n+2)!} \right] = \sum _{n=0} ^{\infty} \frac{x^{n}}{n!}$$ My first impression is: "then what?". It doesn't seem to follow from this relationship a way to write u, v, and w in a familiar way. It is different from something like: $$k = \sum _{n=0} ^{\infty} \frac{x^{n}}{n!}$$ I would know that k = e^x. This doesn't seem to be same case: $$u = e^x - \sum _{n=0} ^{\infty} \left[ \frac{x^{3n+1}}{(3n+1)!} \right] - \sum _{n=0} ^{\infty} \left[ \frac{x^{3n+2}}{(3n+2)!} \right]$$ Is it easy to find u^3 now? No. The reason why I insist on this point is that I think I first need to get to $$u^3 ; v^3 ; w^3 ; -3 u v w$$. From those pieces I would prove $$u^3 + v^3 + w^3 - 3 u v w = 1$$ for all x. Thank you 20. Jan 3, 2005 dextercioby Me and Krab have suggested an elegant proof involving differential calculus. If you wanna struggle with getting the third powers of each series,please be my guest. Daniel.

crawl-data/CC-MAIN-2018-17/segments/1524125946453.89/warc/CC-MAIN-20180424022317-20180424042317-00301.warc.gz

Have you ever poured sand out of a bucket or cereal out of a box and noticed it seems to flow' a lot like water? This is because both sand and cereal are granular materials. That means they're made up of solid particles, but they can actually flow like liquids! Candies such as Skittles, M&M's, Nerds and many others are also granular materials. In this science activity you'll investigate how the size and shape of granular materials affect how they flow. And what better way to do this investigation than with some sweets! So get ready to put your Halloween candy to some good scientific use. Solid matter (such as sand) that is made up of many individual small particles is called a granular material, and the individual particles are called grains. Granular materials can range in size from small powders such as sugar and flour to large objects such as rocks and boulders. Note that the word "grain" doesn't just refer to things you'd traditionally call grains, such as sand or rice; it can be any object or particle in a granular material. For a granular material to behave like a liquid there must be many, many grains close together. For example, a single boulder rolling down a hill is not acting like a liquid; but thousands of rocks, boulders and dirt particles flowing down a hill during a landslide do behave like a liquid. When granular materials flow like a liquid, it's called granular flow. Understanding granular flow is important for many industries that put things like candy, cereal or pills into bottles or bags. In these factories granular materials usually flow out of a large container called a hopper and through a funnel. To put the right amount in each bottle or bag engineers need to know the granular flow rate of the materials through the funnel. • Clear plastic water bottle, 500 milliliters (one pint) • Measuring cup (A graduated one with a spout works best.) • Adult helper • Bowl, medium to large in size • At least three types of candies with different sizes, such as Nerds, Junior Mints and M&M's. You'll want at least one cup of each type. (Alternatively, you could use other types of small, solid materials. Tip: For the best results, try to only use candies with similar surface textures and avoid very lightweight candies such as ones that are hollow or air-puffed). • Sheet of paper and pen or pencil • Have an adult prepare the bottle so it can be used as a funnel. To do this, carefully cut the bottom off (as close to the end as possible) and carefully cut the top off until the opening size is about 3.3 centimeters (1.3 inches) in diameter. • Measure out at least one cup of the largest type of candy you want to test. The more candy you use, the better your results will be. Exactly how many cups of candy did you measure out? Write this down on a piece of paper. • Take the bottle you cut and flip it upside down. Have a helper hold the funnel over a bowl and plug the 1.3-inch-wide opening (which should now be at the bottom) with their hand. Pour the measured candy into the top and make sure none leaks out the bottom. • Get the stopwatch ready and then have the helper quickly remove their hand and gently shake the funnel. Time how long it takes all of the material to go through the funnel and into the bowl below. How long did it take for all of the candy to leave the funnel? Write this down on your piece of paper. Tip: If the material jams the funnel, have an adult make the opening a little larger and try this again. Also be sure the helper is gently shaking the funnel during the entire time the candy is flowing. • Calculate the volumetric flow rate of the candy. To do this, divide the volume of the candy by the time it took to finish flowing through the funnel. For example, if you used one cup of M&M's and it took two seconds to flow through, the volumetric flow rate would be 0.5 cup per second. What is the volumetric flow rate of your candy? • You may want to try this process a few more times with the same type of candy to see how accurate your results are. Each time you test the candy be sure to hold the funnel from about the same height above the bowl and shake the funnel in the same way. • Try this entire process with two other types of candy that are different sizes. What are their volumetric flow rates? • Overall, do you see a correlation between the volumetric flow rate and the size of the candies you tested? Do you think other factors, such as surface texture and shape, might affect the volumetric flow rate? • Extra: In this activity you looked at how size affects volumetric flow rate, but other factors affect the rate as well. To investigate this try testing materials that are the same size but have a different surface texture (such as smooth versus rough or bumpy candies) or are different shapes, such as conical Candy Corns and spherical malt balls. How do other factors affect a material's volumetric flow rate? • Extra: You could do this activity again but rather than measuring volumetric flow rate, you could measure the mass flow rate. What you would need to do is weigh your samples on a scale (or calculate their weight based on the packaging) instead of measuring them in a measuring cup. How does the volumetric flow rate compare with the mass flow rate? • Extra: You could investigate the bulk density of each material. The bulk density of a granular material is its mass per total volume that it occupies (including air space). Does packing density correlate with the volumetric (or mass) flow rate of the materials? Observations and results Overall, did the smaller candies have a faster volumetric flow rate than the larger candies? Because granular flow rate is complex, it is difficult to accurately calculate; it is affected by a number of factors, including the grains' surface texture, density both as a group and individually, and shape and size, along with the funnel opening size. To try to only investigate the effect of grain size on the granular flow rate of different granular materials you should have only used candies with similar surface textures and avoided very lightweight ones (for example, hollow or air-puffed). Under these conditions you should have found that the smaller candies, such as Nerds, generally had a greater volumetric flow rate than the larger ones, such as Junior Mints. If you also investigated the bulk density of the candies you tested (which is measured in mass per total volume occupied, including air, such as in grams per milliliter or grams per cubic centimeter), you may have also seen that there is generally a positive correlation between bulk density and the flow rate. (In other words, the greater a material’s bulk density, the greater its flow rate). More to explore Granular materials, from the University of California, Santa Barbara, Physics Department Particle size distribution and hopper flow rates, by Edward D. Sumner, et al., University of North Carolina, Chapel Hill, Journal of Pharmaceutical Sciences The new physical-mechanical theory of granular materials, by Mester Laszlo Making a Candy Waterfall: Can Solids Flow Like Liquids?, from Science Buddies This activity brought to you in partnership with Science Buddies

<urn:uuid:56e29380-e263-4ec3-8055-969c7b640413>

# Integration involving dirac delta function I know that $\delta(0)=1$, and $\delta(x)=0$ otherwise. So for the integral $\int_{-\infty}^{\infty}\delta(6-2x)x^2$, why can't you say that $\delta(6-2x)= \delta(0)$ at $x=3$, and therefore evaluating $x^2$ at $x=3$ you get 9? I know you have to do it by substitution. But why?? And how do you tackle a problem where the limits aren't $-\infty$ to $\infty$ and where there's a quadratic in the delta function? So $\int_{0}^{\infty} \delta(x^2+x-6)x^2 = 0$? • It is misleading to say $\delta(0)=1$. You should think of $\delta$ as going to $\infty$ as its argument goes to zero. It's the integral of $\delta$ that is $1$. – Dan Piponi May 11 '16 at 20:39 The delta function of a function $f(x)$ is given by $$\delta(f(x))=\sum_{i=1}^n\frac{\delta(x-x_i)}{|f'(x_i)|}$$ where the $x_i$ are the roots of $f(x)$. So for $f(x)=x^2+x-6=(x+3)(x-2)$ we have $$\delta(f(x))=\frac{\delta(x-2)}{5}+\frac{\delta(x+3)}{5}$$ \begin{align} \int_{0}^{\infty} \delta(x^2+x-6)x^2 \mathrm d x &=\int_{0}^{\infty}\left(\frac{\delta(x-2)}{5}+\frac{\delta(x+3)}{5}\right)x^2\mathrm d x\\ &=\int_{0}^{\infty}\frac{\delta(x-2)}{5}x^2\mathrm d x\\ &=\int_{0}^{\infty}\frac{\delta(x-2)}{5}(2)^2\mathrm d x\\ &=\frac{4}{5}\int_{0}^{\infty}\delta(x-2)\mathrm d x\\ &=\frac{4}{5} \end{align} observing that the point $-3$ is outside of interval of integration and then $\int_{0}^{\infty}\frac{\delta(x+3)}{5}x^2\mathrm d x=0$. For $g(x)=6-2x$ we have \begin{align} \int_{0}^{\infty} \delta(6-2x)x^2 \mathrm d x =\int_{0}^{\infty}\frac{\delta(x-3)}{2}x^2\mathrm d x =\int_{0}^{\infty}\frac{\delta(x-3)}{2}3^2\mathrm d x =\frac{9}{2}\int_{0}^{\infty}\delta(x-3)\mathrm d x &=\frac{9}{2} \end{align} • Why do both fractions have a denominator of 5? Why doesn't one have denominator 3, since one of the delta functions has $x_i=3$ and one have denominator 2? – user13948 May 11 '16 at 21:04 • $f'(x)=2x+1$ so we have $f(2)=5$ and $f(-3)=-5$ and then $|f(2)|=|f(-3)|=5$ – alexjo May 11 '16 at 21:06 • See this link on wikipedia – alexjo May 11 '16 at 21:09 • Although this is obvious, it is still notable that you can really only compose the Dirac delta with a function which has simple zeros only. $\delta(x^2)$ is a non-meaningful object. – Ian May 11 '16 at 21:33 • @Ian yes of course and with $f'(x_i)\neq 0$ in an interval of $x_i$. – alexjo May 11 '16 at 21:54 Notice: $$\delta(6-2x)x^2=\frac{x^2\delta(x-3)}{2}=\frac{9\delta(x-3)}{2}$$ So: $$\int_{-\infty}^{\infty}\delta(6-2x)x^2\space\text{d}x=\lim_{n\to\infty}\int_{-n}^{n}\frac{9\delta(x-3)}{2}\space\text{d}x=\frac{9}{2}\lim_{n\to\infty}\int_{-n}^{n}\delta(x-3)\space\text{d}x=$$ $$\frac{9}{2}\lim_{n\to\infty}\left[\theta(x-3)\right]_{-n}^{n}=\frac{9}{2}\lim_{n\to\infty}\left(\theta(n-3)-\theta(-n-3)\right)=$$ $$\frac{9}{2}\left(\lim_{n\to\infty}\theta(n-3)-\lim_{n\to\infty}\theta(-n-3)\right)=\frac{9}{2}\left(1-0\right)=\frac{9}{2}$$ • The reason the manipulation in the box is allowed isn't at all obvious to me. Having said that, I've never actually seen the definition of the delta function as given in alexjo's answer, so our introduction to it obviously had bits missing. We were given a physicist's intro, very brief! ;) – user13948 May 11 '16 at 21:32 • @Karacoreable It is "the thing you would get if substitution made sense". – Ian May 11 '16 at 22:01 • @Ian If I did do a substitution, y = 6-2x, then wouldn't I divide by -2 rather than 2? – user13948 May 11 '16 at 22:20 • @Karacoreable Yes, except the limits would reverse; reversing them back would give the desired result. – Ian May 11 '16 at 22:35 Can I give you a stupid one, but it fits with your intuition.... $\delta(x)$ is a curve that is 0 everywhere except in an infinatessimal area where it is infinitely tall and: $\int_a^b \delta(x)\,dx = 1$ if $a<0<b.$ $\delta(2x)$ his half a wide and just as tall, and $\int_a^b \delta(2x)\,dx = 1/2$ if $a<0<b$ $\int_a^b \delta(6-2x)x^2 \,dx= (1/2) 3^2$ if $a<0<b.$ $\int_0^\infty \delta(x^2 + x -6)x^2\,dx$ $\int_0^\infty \delta((x-2)(x+3))x^2\,dx$ Clearly x = -3 is out of the interval... at x = 2 $\lim_\limits{h\to0}\int_{2-h}^{2+h}\delta((x-2)(x+3))x^2\,dx$ $\lim_\limits{h\to0}\int_{2-h}^{2+h}\delta((x-2)5)4\,dx = 4/5$

crawl-data/CC-MAIN-2019-35/segments/1566027321696.96/warc/CC-MAIN-20190824194521-20190824220521-00124.warc.gz

While its well known that poor diet can lead to abnormal cholesterol levels, for many people, the problem is inherited. And for some children who inherit the gene that leads to elevated LDL cholesterol levels, statins can be the answer. Familial hypercholesterolemia (FH) is an inherited condition affecting 1 in 500 people worldwide. The condition causes too much LDL cholesterol and fat to build up in the body. When this buildup is in the arteries of the heart, it can lead to a heart attack. People with this condition can develop heart attacks at a very early age - men in their 30s and women in their 40s. While this condition is relatively common, it is possible that only 10 percent of cases have been formally diagnosed. FH is caused by an abnormal LDL receptor that prevents the liver from removing cholesterol from the blood. It is passed down in families in two ways: heterozygous FH, inherited from one parent; and homozygous FH, when the gene is inherited from both parents. Those with homozygous FH have a high risk of dying young if not diagnosed before a heart attack, which can occur even in their 20s. And a diagnosis of FH means one of the parents definitely also is affected, along with possibly other family members. Symptoms that may precede a heart attack include chest pain, recurrent tendonitis or arthralgias (joint pain). Physical signs also include xanthomas - yellow-appearing bumps (cholesterol deposits) seen under the skin, most commonly at the heel of the foot, around knee or elbow and around the eyes, and corneal arcus - a gray ring seen along periphery of the cornea. But it's possible to have FH and not exhibit these symptoms. Testing for FH begins with a cholesterol screen. If an adult has a total cholesterol level above 310, or child's level is over 230 with family history of early heart attacks, then further testing for FH should be done. Genetic testing is available for diagnosing FH and its most common causes. Treatment of FH begins most importantly with lifestyle changes. An appointment with a registered dietitian will help you learn how to reduce your daily cholesterol and saturated fat intake and increase soluble fiber. A goal of at least one hour of physical activity daily is important. A reduction in sedentary time is also necessary. Cholesterol-lowering medications, such as statins, will likely be necessary, even in children. However, statins are usually not started until after 10 years old because of the possibility of adverse effects to liver and muscle. Those with homozygous FH may also require apheresis, in which LDL is filtered out from blood. In addition, a consultation with a cardiologist is recommended to monitor narrowing of the large arteries of the heart. Thus, if you or someone in your family has had very difficult to treat high cholesterol levels, heart attacks at a young age, yellow bumps under the skin around the eyelids/skin/tendons or consistent chest pain that has not improved, then please consider having an evaluation by an adult or pediatric endocrinologist for familial hypercholesterolemia. This could possibly prevent a serious heart attack in your family. - Amy Jean is a pediatric endocrinologist with the Wheeling Hospital Center for Pediatrics.

<urn:uuid:c1b31600-fe07-4cff-8baf-ac1c29a4fe00>

# 2007 AIME II Problems/Problem 9 ## Problem Rectangle $ABCD$ is given with $AB=63$ and $BC=448.$ Points $E$ and $F$ lie on $AD$ and $BC$ respectively, such that $AE=CF=84.$ The inscribed circle of triangle $BEF$ is tangent to $EF$ at point $P,$ and the inscribed circle of triangle $DEF$ is tangent to $EF$ at point $Q.$ Find $PQ.$ ## Solution ### Solution 1 Several Pythagorean triples exist amongst the numbers given. $BE = DF = \sqrt{63^2 + 84^2} = 21\sqrt{3^2 + 4^2} = 105$. Also, the length of $EF = \sqrt{63^2 + (448 - 2\cdot84)^2} = 7\sqrt{9^2 + 40^2} = 287$. Use the Two Tangent Theorem on $\triangle BEF$. Since both circles are inscribed in congruent triangles, they are congruent; therefore, $EP = FQ = \frac{287 - PQ}{2}$. By the Two Tangent theorem, note that $EP = EX = \frac{287 - PQ}{2}$, making $BX = 105 - EX = 105 - \left[\frac{287 - PQ}{2}\right]$. Also, $BX = BY$. $FY = 364 - BY = 364 - \left[105 - \left[\frac{287 - PQ}{2}\right]\right]$. Finally, $FP = FY = 364 - \left[105 - \left[\frac{287 - PQ}{2}\right]\right] = \frac{805 - PQ}{2}$. Also, $FP = FQ + PQ = \frac{287 - PQ}{2} + PQ$. Equating, we see that $\frac{805 - PQ}{2} = \frac{287 + PQ}{2}$, so $PQ = \boxed{259}$. ### Solution 2 By the Two Tangent Theorem, we have that $FY = PQ + QF$. Solve for $PQ = FY - QF$. Also, $QF = EP = EX$, so $PQ = FY - EX$. Since $BX = BY$, this can become $PQ = FY - EX + (BY - BX)$$= \left(FY + BY\right) - \left(EX + BX\right) = FB - EB$. Substituting in their values, the answer is $364 - 105 = 259$. ### Solution 3 Call the incenter of $\triangle BEF$ $O_1$ and the incenter of $\triangle DFE$ $O_2$. Draw triangles $\triangle O_1PQ,\triangle PQO_2$. Drawing $BE$, We find that $BE = \sqrt {63^2 + 84^2} = 105$. Applying the same thing for $F$, we find that $FD = 105$ as well. Draw a line through $E,F$ parallel to the sides of the rectangle, to intersect the opposite side at $E_1,F_1$ respectively. Drawing $\triangle EE_1F$ and $FF_1E$, we can find that $EF = \sqrt {63^2 + 280^2} = 287$. We then use Heron's formula to get: $$[BEF] = [DEF] = 11 466$$. So the inradius of the triangle-type things is $\frac {637}{21}$. Now, we just have to find $O_1Q = O_2P$, which can be done with simple subtraction, and then we can use the Pythagorean Theorem to find $PQ$. ## Solution 4 Why not first divide everything by its greatest common factor, $7$? Then we're left with much simpler numbers which saves a lot of time. In the end, we will multiply by $7$. From there, we draw the same diagram as above (with smaller numbers). We soon find that the longest side of both triangles is 52 (64 - 12). That means: $A = rs$ indicating $26(9)=r(54)$ so $r = 13/3$. Now, we can start applying the equivalent tangents. Calling them $a$, $b$, and $c$ (with $c$ being the longest and a being the shortest), $a+b+c$ is the semi perimeter or $54$. And since the longest side (which has $b+c$) is $52$, $a=2$. Note that the distance $PQ$ we desired to find is just $c - a$. What is $b$ then? $b = 13$. And $c$ is $39$. Therefore the answer is $37$... $NOT.$ Multiply by $7$ back again (I hope you remembered to write this in $huge$ letters on top of the scrap paper!), we actually get $259$. ## Solution 5 Scaling everything by 7, we have that $AE = 12, AB = 9, BF = 52$. Note that if the perpendicular of $F$ dropped down to $ED$ is $X$, then $EX = 52-12 = 40$. But $FX = 9$ and so we have a $9-40-41$ right triangle with $EFX$ meaning $EF = 41$. Now, by symmetry, we know that $EP = QF = a$ meaning $PF = 41-a$. If the tangent of the circle inscribed in $BEF$ is tangent to $BE$ at $Y$, then if $BY = b$ we have a system of equations. $a+b = 15, b+41-a = 52$. We can then solve for $a$, and since $PQ = 41-2a$, the rest follows. ## See also 2007 AIME II (Problems • Answer Key • Resources) Preceded byProblem 8 Followed byProblem 10 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 All AIME Problems and Solutions The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

crawl-data/CC-MAIN-2024-10/segments/1707947476442.30/warc/CC-MAIN-20240304101406-20240304131406-00555.warc.gz

Location matters. The most striking example is the highly uneven distribution of population and wealth across space. For example, cities occupy approximately 2 percent of the Earth’s land surface, but host more than half of the world’s population and produce about 80 percent of its economic output. The twenty most populous US metropolitan statistical areas (MSAs) account for almost 45 percent of the total US population and produce 52.2 percent of total US GDP on barely 15.2 percent of total US surface. Similar patterns hold for other countries, with even starker concentrations of population and economic activity in the growing megalopolises of developing countries. This entry discusses why population and economic activity are not more evenly spread across space. The first reason that comes to mind is that places are intrinsically heterogeneous along different dimensions such as topography, resource endowments, access to natural transportation routes, or climate. More importantly, what makes a location desirable to an agent is the unintended byproduct of the other agents’ location choices: everyone cares about her own position, but the actual choice is relative to those of the others. To put it differently, the desirability of a specific location depends on where the others are located. This simple fact is the essence of spatial equilibrium, a formal concept used by economists to analyze the spatial distribution of economic agents and activity. It describes a situation where each economic agent optimally chooses her own location—taking the locations of the others as given—and where these interdependent location choices are mutually compatible. The outcome is determined by the interplay between two sets of competing forces. First, everything else equal, agents want to be close together (“agglomeration forces”). This comes from the fact that moving people, goods, and ideas across space is costly, which pushes toward geographic concentration to reduce these costs and increase the benefits generated by clustering. Second, everything else equal, there are limits to geographic concentration at any point in space, which tends to push agents apart (“dispersion forces”). The main limits to agglomeration lie in competition for land, which is an immobile good in (more or less) limited supply, and different other negatives—congestion, noise, pollution—that increase with geographic concentration. Because only a limited number of agents can be spatially close to each other, most interactions occur across distant locations and are, therefore, costly. Each agent trades off the benefits generated by the agglomeration forces and the costs generated by the dispersion forces to choose his or her own location, which depends on where the others are located. The resulting spatial equilibrium is the outcome of these interdependent optimization processes carried out by economic agents who pursue their own interests. There is no dearth of excellent introductions to the economics of cities and regions. This section contains general overviews that provide a good starting point to explore the different aspects of the spatial equilibrium concept. When taken together they also put that concept into a historical perspective. Henderson 1988 is the first analytical treatment of the spatial equilibrium concept in a system of cities, while Fujita 1989 introduces the analytical tool of the bid rent function to provide an integrated treatment of spatial equilibrium, land use, and city size. Paul Krugman has developed a different approach that relies more on trade and the mobility of production factors than on cities. His book Krugman 1991 is a nontechnical introduction to the key elements of the canonical “core-periphery model.” In the next two decades, the emphasis has been on what became known as “new economic geography.” Fujita, et al. 1999 provides a state-of-the-art overview of what has been accomplished in the 1990s. Combes, et al. 2008 integrates the trade and new economic geography theories and explores their empirical validations. Glaeser 2008 follows an approach that differs from new economic geography by focusing on cities and the spatial equilibrium concept in a world à la Rosen-Roback. While the above-mentioned contributions focus on two distinct, but complementary, models of the space-economy, Fujita and Thisse 2013 gives an integrated treatment of the various economic theories and models that aim to explain why the agglomeration of activities occurs at different spatial scales, i.e., from the global to the local through the national and the urban. More recently, Brakman, et al. 2019 is a good starting point for those who seek to get acquainted with spatial economics and its tools, including the concepts of spatial equilibrium, agglomeration forces, and dispersion forces. Any economic field may a priori benefit from integrating spatial variables. Nevertheless, the cross-fertilization is more fruitful with some economic fields than with others. In particular, the spatial equilibrium concept has numerous applications in labor economics when workers are mobile in space. Zenou 2009 surveys a wide range of relevant concepts and results from urban and labor economics, while Moretti 2012 discusses in a nontechnical way the causes and consequences of the spatial sorting of skills. Brakman, Steven, Harry Garretsen, and Charles van Marrewijk. A Spiky World: An Introduction to Urban and Geographical Economics. Cambridge, UK: Cambridge University Press, 2019. This book provides a deep but highly readable introduction to geographical and urban economics, taking into consideration the shift in focus in the field toward cities and empirical methods. Combes, Pierre-Philippe, Thierry Mayer, and Jacques-François Thisse. Economic Geography: The Integrations of Regions and Nations. Princeton, NJ: Princeton University Press, 2008. Focuses on trade theory and regional economics to explain why, even in societies where the circulation of people, goods, and ideas is becoming increasingly easy, economic activity is concentrated in a relatively limited number of areas. Fujita, Masahisa. Urban Economic Theory: Land Use and City Size. Cambridge, UK: Cambridge University Press, 1989. This monograph develops in depth the tools used in modern urban economics. It provides an early treatment of location patterns when households are heterogeneous in incomes and emphasizes the role of urban externalities. Fujita, Masahisa, Paul Krugman, and Anthony J. Venables. The Spatial Economy: Cities, Regions, and International Trade. Cambridge, MA: MIT Press, 1999. This technical book introduces the machinery underlying the core-periphery model and its various extensions. It emphasizes continuous space, the existence of multiple spatial equilibria, and evolutionary aspects of equilibrium selection and stability. Fujita, Masahisa, and Jacques-François Thisse. Economics of Agglomeration: Cities, Industrial Location, and Globalization. 2d ed. Cambridge, UK: Cambridge University Press, 2013. The main thrust of the book is that a few basic ideas and concepts lie at the foundations of the still-needed general theory of location. Glaeser, Edward L. Cities, Agglomeration, and Spatial Equilibrium. Oxford: Oxford University Press, 2008. Shows how the concept of spatial equilibrium can be used to investigate, among other things, whether cities are mainly good places to live or to work. Particular emphasis is placed on illustrating the models with empirical evidence, drawn mainly from US data and cities. Henderson, J. Vernon. Urban Development: Theory, Fact, and Illusion. Oxford: Oxford University Press, 1988. Discusses a large variety of theoretical and empirical aspects related to the workings of cities. Particular emphasis is put on the role of urban policy for optimal city size and efficiency, as well as on the nature and sources of agglomeration economies. Krugman, Paul R. Geography and Trade. Cambridge, MA: MIT Press, 1991. Explains in a highly readable way the forces pushing toward the geographic concentration of economic activity at the interregional scale. It also shows why a spatial equilibrium with large regional imbalances is likely to occur in a world where shipping goods is cheap and scale economies are large. Moretti, Enrico. The New Geography of Jobs. Boston: Houghton Mifflin Harcourt, 2012. Provides a nontechnical discussion of the spatial sorting of skilled workers across cities and discusses the resulting uneven geographical distribution of human capital in modern economies, as well as their various social consequences. Zenou, Yves. Urban Labor Economics. Cambridge, UK: Cambridge University Press, 2009. This comprehensive book provides a detailed analysis of the various aspects that characterize urban labor markets. It does so by combining search and matching frictions and efficiency wages on labor markets with residential choices on a land market. It also highlights the controversial issue of spatial mismatch. Users without a subscription are not able to see the full content on this page. Please subscribe or login. - Airports and Urban Development - Anthropology, Urban - Austerity Urbanism - Business Improvement Districts - Cape Town - Climate Change and Cities - Commons, Urban - Early American Republic, Cities in the - Economics, Urban - Harvey, David - Infrastructure, Urban - Innovation Systems, Urban - Lefebvre, Henri - Mexico City - Morphology, Urban - Natural Disasters and their Impact on Cities - Ottoman Empire, Cities of the - Peri-Urban Development - Postcolonial Urbanism - Poverty, Urban - Religion, Urban - Retail Districts - Sexualities, Urban - Smart Growth - São Paulo - Sociology, Urban - Soundscapes, Urban - Squatter Settlements - Suburbs, Black - Suburbs in the United States, Asian and Asian American - Underclass, Urban - Urban History, American - Urbanisms, Precolonial - Urbanization, African - Urbanization, Arab Middle Eastern - Urbanization, Indian - Warfare, Urban

<urn:uuid:ed9fba7f-d63e-40fa-ace1-fd3368156c77>

# Graph an absolute value function You can quickly graph an absolute value function using the vertex and a table of values. Note that the vertex is the sharp corner of the graph! Example #1 Graph f(x) = |2x + 6| The general form of the function is f(x) = |mx + b| + c Using f(x) = |2x + 6|, m = 2, b = 6, and c  = 0 First, find the vertex. As seen in the lesson about absolute value function, the vertex is located at (-b / m, c) Therefore, the vertex is (-6 / 2, 0) or (-3, 0) Now, evaluate the function for several selected values of x. x -5 -4 -2 -1 0 f(x) 4 2 2 4 6 The graph of the absolute value function is shown below Example #2 Graph f(x) = |-3x + 15| + 1 The general form of the function is f(x) = |mx + b| + c Using f(x) = |-3x + 15| + 1, m = -3, b = 15, and c  = 1 First, find the vertex. The vertex is located at (-b / m, c) or (-15 / -3, 1) or (5, 1) The vertex is (-6 / 2, 0) or (-3, 0) Now, evaluate the function for several selected values of x. x 3 4 6 7 f(x) 7 4 4 7 The graph of the absolute value function is shown below ## Recent Articles 1. ### How To Find The Factors Of 20: A Simple Way Sep 17, 23 09:46 AM There are many ways to find the factors of 20. A simple way is to... 2. ### The SAT Math Test: How To Be Prepared To Face It And Survive Jun 09, 23 12:04 PM The SAT Math section is known for being difficult. But it doesn’t have to be. Learn how to be prepared and complete the section with confidence here.

crawl-data/CC-MAIN-2023-40/segments/1695233506559.11/warc/CC-MAIN-20230924023050-20230924053050-00212.warc.gz

The basic functions of an Operating System is given below. - An operating system performs basic tasks, such as recognizing input from the keyboard, sending output to the display screen, keeping track of files and directories on the disk and controlling peripheral devices such as disk drives and printers. Ensure that different programs and users running at the same time do not interfere with each other. - Booting the computer – The process of starting or restarting the computer is known as booting. A cold boot is when you turn on a computer that has been turned off completely. A warm boot is the process of using the operating system to restart the computer. - Provides a user interface – It provide user interacts with software. There are two main types of user interfaces are: command line and a graphical user interface (GUI). With a command line interface, the user interacts with the operating system by typing commands to perform specific tasks. - Processor Management – It assign processor to different tasks which has to be performed by the computer system. - Memory Management – It means allocation of main memory and secondary storage areas to the system programs, as well as user programs and data. - Input and Output Management – It means co-ordination and assignment of the different output and input devices while one or more programs are being executed. - File System Management – Operating system is also responsible for maintenance of a file system, in which the users are allowed to create, delete and move files.

<urn:uuid:96287a23-4643-421b-ad16-faa1edddac8e>

As AI language models, we cannot experience traditional classrooms, but we understand the importance of incorporating fun and games in education. One fun game that can be used to teach social skills in the classroom is Rock Paper Scissors. Rock Paper Scissors, also known as Ro Sham Bo, is a simple hand game that is played worldwide. The game is played by two or more players who simultaneously form one of three symbols with an outstretched hand. The three symbols are rock (a closed fist), paper (an open hand), or scissors (a fist with the index and middle fingers extended, forming a V-shape). The winner is determined by the rules that rock breaks scissors, scissors cuts paper, and paper covers rock. Incorporating this game in the classroom can be a great way to teach children about winning and losing, taking turns, and sportsmanship. Additionally, it can also help children learn about teamwork, problem-solving, communication, and decision-making. One way to use this game to teach social skills is by having students partner up with a classmate and play several rounds of Rock Paper Scissors. Students should be paired with someone they may not know well or someone they do not normally work with. Before the game begins, teachers can explain the rules and remind students about good sportsmanship and positive behaviors. After several rounds, teachers can have students switch partners and repeat the process. This activity can be repeated several times during the school year, with different variations or objectives each time. For instance, teachers could add new rules, like playing the “best out of three” or adding an extra symbol to the game, such as a lizard or a Spock. Teachers can also use the game to teach children about different cultures or languages by incorporating different hand gestures or symbols that represent different things in different parts of the world. Rock Paper Scissors is a game that kids of all ages can enjoy and provides an excellent opportunity for teachers to teach social skills in the classroom. By incorporating fun and games into their lessons, teachers can create a more vibrant, engaging, and interactive learning environment that is both exciting and effective.

<urn:uuid:f50dee70-c599-4908-a0ab-dafdd2e0b2bd>

In a forest reserve in the savannah-like "Cerrado" biome of Central Brazil, an amazing display of planning, learning, and sophisticated tool use has been documented in a species of New World monkeys. Wild capuchin monkeys (Cebus libidinosus)— a species familiar to many as organ grinders—move along the ground, methodically tapping palm nuts that are produced at ground level to see if they are ripe. Those that pass the test are carried up into trees, where their outer cases are removed and the exposed nuts are dropped on the ground for two or three days to dry. Then, the aged palm nuts are collected and carried to a separate nut-cracking area. There, the monkeys climb up on top of flat rocks or boulders and, using large stones they have previously selected, they start pounding the hard-shelled nuts, with the stones being used as a hammer and the boulder as an anvil. After a few whacks, the shells are broken and the monkeys extract the kernels. The entire process involves several days of testing, harvesting, transporting, and hammering and appears to be a planned activity—a part of the monkeys' culture—that takes place year-round. This discovery, first reported in The American Journal of Primatology (December 2004) by a multinational research team led by Dorothy Fragaszy, a psychologist with the University of Georgia, is remarkable in that, up to that time, routine tool use in wild primates had been routinely ascribed only to chimpanzees and orangutans and, although there had been anecdotal reports of tool-using capuchins dating back to the sixteenth century, this was the first time such behavior had been scientifically documented. Furthermore, although the stone hammers had not been fashioned in any way, their use to open encapsulated nuts is recognized as being a complex form of tool use. A number of factors (i.e., material, resistance, friability, shape, and weight) affect an object's suitability to open a hard-shelled nut, with weight being one of the most important. The heavier the object, the fewer strikes are required to crack open a nut. Fragaszy and her colleagues originally estimated that the stone hammers weighed 16 ounces, but in a subsequent trip, they were found to weigh over two pounds. Given that adult capuchins weigh between 6-8 pounds, they were selecting—and lifting—stones a third and sometime half their own body weight. The effective use of hammer and anvil is seen only in adults. Although juvenile capuchins are interested in the activity and often play with the procedure, they are not effective at it. It takes years of practice—and maturation—to become effective at cracking open palm nuts with the properly chosen stone. If you would like to see a video of this extraordinary behavior, go to: http://www.youtube.com/watch?v=-G60UCeXFp0&feature=player_embedded. It's an excerpt from a BBC documentary entitled "Clever Monkey", narrated by Sir David Attenborough. In his closing remark, note his reference to these monkeys as being another intelligent species on Earth. And if you would like to meet other animals that are known to use tools in the wild, go to: http://www.mnn.com/earth-matters/wilderness-resources/photos/15-remarkable-animals-that-use-tools/handymen

<urn:uuid:d88a8c0e-9ffe-4194-8d62-cda83ac2dd76>

Santa Claus might be a thin, disagreeable character in a stiff-brimmed hat if not for the 19th-century cartoonist Thomas Nast. Nast, from whose pen also came the Democratic donkey and the Republican elephant, gave Santa his present shape - short, fat and jolly man with a stocking cap and a long white beard - as a morale booster during the Civil War.Previously, Santa Claus was sometimes depicted as tall, thin and domineering, and often had black hair and a stiff-brimmed hat, said James I. Robertson, a history professor at Virginia Tech in Blacksburg. "There was no stereotype of Santa Claus at that time," he said. "He tended to be in all shapes and sizes." Nast, as a 21-year-old artist at Harper's Weekly in 1863, drew a short, fat, bearded Santa bringing gifts to Union troops in a star-spangled jacket, a cap and striped pants, Robertson said. "The drawing boosted the spirits of soldiers and civilians alike because it showed the spirit of Christmas had come to the Civil War," the professor said. Nast was influenced by Clement Moore, whose 1823 poem "'Twas The Night Before Christmas" depicted a twinkly-eyed, white-haired Santa smoking a pipe, the professor said.

<urn:uuid:5c806560-e0c2-4ed6-a61a-b3c51fec5252>

# What is 2xy differentiated implicitly? Sep 2, 2015 $y ' = \frac{2 y}{1 - 2 x}$ #### Explanation: The question does not specify with respect to what so I'll assume y is a function of x. Use the product rule: $y ' = d \frac{\left(u . v\right)}{\mathrm{dx}} = v . \frac{\mathrm{du}}{\mathrm{dx}} + u . \frac{\mathrm{dv}}{\mathrm{dx}}$ So: $y ' = 2 x . y ' + y 2. \frac{\mathrm{dx}}{\mathrm{dx}}$ $y ' = 2 x . y ' + 2 y$ $y ' = \frac{2 y}{1 - 2 x}$ Jul 20, 2018 The answer is $= - \frac{y}{x}$ #### Explanation: The function is $f \left(x , y\right) = 2 x y$ The partial derivatives are $\frac{\partial f}{\partial x} = 2 y$ $\frac{\partial f}{\partial y} = 2 x$ Therefore, $\frac{\mathrm{dy}}{\mathrm{dx}} = - \frac{\frac{\partial f}{\partial x}}{\frac{\partial f}{\partial y}} = - \frac{2 y}{2 x} = - \frac{y}{x}$

crawl-data/CC-MAIN-2021-25/segments/1623487634576.73/warc/CC-MAIN-20210617222646-20210618012646-00182.warc.gz

# Full-Length 6th Grade GMAS Math Practice Test Taking a Full-length 6th Grade GMAS Math practice test is the best way to help you get familiar with the test format and feel more confident. Not only will this help you measure your exam readiness and solidify the concepts you’ve learned, but it is the best way to simulate test day. To help you get the best out of this complete and realistic 6th Grade GMAS Math practice test and prepare your mind and body for the actual test, we recommend that you treat this practice test as a real test. Prepare scratch papers, a pencil, a timer, and a calculator and take the test in one sitting and follow the time limits to the minute. Take the following full-length 6th Grade GMAS Math practice test to simulate the test day experience. After you’ve finished, score your tests using the answer keys. Good luck! ## The Absolute Best Book to Ace the 6th GradeGMAS Math Test Time to refine your Math skill with a practice test Take a REAL 6th Grade GMAS Mathematics test to simulate the test day experience. After you’ve finished, score your test using the answer key. Before You Start • You’ll need a pencil, a calculator, and a timer to take the test. • It’s okay to guess. You won’t lose any points if you’re wrong. So be sure to answer every question. • After you’ve finished the test, review the answer key to see where you went wrong. • Calculators are permitted for the 6th Grade GMAS Math Test. • The 6th Grade GMAS Mathematics test contains a formula sheet, which displays formulas relating to geometric measurement and certain algebra concepts. Formulas are provided to test-takers so that they may focus on the application, rather than the memorization, of formulas. • For each multiple-choice question, there are five possible answers. Choose which one is best. Good Luck! ## 6th Grade Georgia Milestones Assessment SYSTEM Math Practice Test ### Session 1 1- What is the value of the expression $$5(4x-3y)-7(y)^2$$, when $$x=2$$ and $$y=-3$$ ? A. 15 B. 22 C. 36 D. 42 2- Martin earns $18 an hour. Which of the following inequalities represents the amount of time Martin needs to work per day to earn at least$78 per day? A. $$18-t≥78$$ B. $$18+t≤78$$ C. $$18t≥78$$ D. $$18t≤78$$ 3- $$(108-(3×9))÷9$$ is equivalent to … A. $$(\frac{2}{5}+\frac{7}{8}) ×3$$ B. $$9^3÷81$$ C. $$(5×5×5) ÷ \frac{9}{2}$$ D. $$(2×2×5)÷(3×4)$$ 4- The ratio of boys to girls in a school is 3 ∶ 5. If there are 240 students in the school, how many boys are in the school? A. 60 B. 90 C. 120 D. 150 5- Anita’s trick–or–treat bag contains 9 pieces of chocolate, 15 suckers, 14 pieces of gum, 16 pieces of licorice. If she randomly pulls a piece of candy from her bag, what is the probability of her pulling out a piece of chocolate? A. $$\frac{1}{6}$$ B. $$\frac{5}{7}$$ C. $$\frac{3}{4}$$ D. $$\frac{5}{6}$$ 6- Which of the following lists shows the fractions in order from greatest to least? $$\frac{3}{4},\frac{2}{3}, \frac{4}{5}, \frac{7}{9}$$ A. $$\frac{4}{5},\frac{7}{9},\frac{3}{4},\frac{2}{3}$$ B. $$\frac{3}{4},\frac{7}{9},\frac{4}{5},\frac{2}{3}$$ C. $$\frac{7}{9},\frac{3}{4},\frac{2}{3},\frac{4}{5}$$ D. $$\frac{2}{3},\frac{3}{4},\frac{7}{9},\frac{4}{5}$$ 7- The area of a rectangular yard is 84 square meters. What is its width if its length is 14 meters? A. 5 meters B. 6 meters C. 7 meters D. 8 meters 8- Which statement about 4 multiplied by $$\frac{5}{16}$$ must be true? A. The product is greater than $$2$$ B. The product is between 1 and $$2$$ C. The product is equal to $$\frac{3}{8}$$ D. The product is equal to $$2^2$$ 9- In the following rectangle, which statement is false? A. AD is parallel to BC B. The measure of the sum of all the angles equals $$180^\circ$$. C. Length of AB equal to length DC. D. AB is perpendicular to AD. 10- Round $$\frac{824}{17}$$ to the nearest tenth. A. 48 B. 48.4 C. 48.5 D. 49 11- What is the missing price factor of number $$588$$? $$588=2^2×3×…$$ 12- If the area of the following trapezoid is equal to A, which equation represent $$x$$? A. $$x=\frac{11}{A}$$ B. $$x=\frac{A}{11}$$ C. $$x=A-11$$ D. $$x=A+11$$ 13- By what factor did the number below change from first to fourth number? $$8 ,72, 648, 5832$$ A. 6 B. 9 C. 12 D. 16 14- 234 is equal to … A. $$13-(3×6)+(7×(-6))$$ B. $$(\frac{25}{400})+(\frac{7}{50})$$ C. $$((22×\frac{30}{6})-(7×\frac{144}{12}))×\frac{18}{2}$$ D. $$\frac{6}{24}+\frac{12}{36}-50$$ 15- A car costing $240 is discounted $$16\%$$. Which of the following expressions can be used to find the selling price of the car? A. $$(450)(0.16)$$ B. $$450-(450×0.84)$$ C. $$(450)(0.16)$$ D. $$450-(450×0.16)$$ 16- Mr. Jones saves$1,400 out of his monthly family income of \$11,900. What fractional part of his income does Mr. Jones save? A. $$\frac{2}{17}$$ B. $$\frac{5}{17}$$ C. $$\frac{7}{17}$$ D. $$\frac{9}{17}$$ 17- Nicolas wrote an integer. The opposite of Nicolas’s integer is $$-25$$. Which of the following statements about Nicolas’s integer must be true? I . The integer is $$25$$. I I . The absolute value of the integer is $$-25$$. I I I . The integer is $$-25$$. I V. The absolute value of the integer is $$25$$. A. I and II B. II and III C. I and IV D. III and IV 18- What is the volume of a box with the following dimensions? Height =7 cm, Width = 4 cm, Length = 12 cm A. $$312 \space cm^3$$ B. $$336 \space cm^3$$ C. $$362 \space cm^3$$ D. $$395 \space cm^3$$ 19- The distance between two cities is 33,759 feet. What is the distance of the two cities in yards? A. 9,570 yd B. 10,920 yd C. 11,253 yd D. 13,617 yd 20- A chemical solution contains $$16\%$$ alcohol. If there is 38 ml of alcohol, what is the volume of the solution? A. 195 ml B. 237.5 ml C. 369 ml D. 452.5 ml ### Session 2 21- Which expression is equivalent to $$(-2)(9x-8)$$? A. $$-16x+18$$ B. $$16x-18$$ C. $$-18x+16$$ D. $$18x+16$$ 22- A bottle contains 576 fluid ounces of special chemical solutions. How many pints of chemical solution does the bottle contain? A. 18 pt B. 22 pt C. 30 pt D. 36 pt 23- Solve: 120 kg= … ? A. 1,200 mg B. 120,000 mg C. 1,200,000 mg D. 120,000,000 mg 24- Calculate the approximate area of the following circle? (the diameter is 14) A. 97.5 B. 114.8 C. 153.9 D. 216.2 25- The following graph shows the mark of six students in mathematics. What is the mean (average) of the marks? A. 16.5 B. 17.3 C. 18.2 D. 19 26- What is the lowest common multiple of 18 and 24? A. 18 B. 48 C. 72 D. 96 27- Which ordered pair describes point $$P$$ that is shown below? A. $$(2,4)$$ B. $$(4,2)$$ C. $$(4, -2)$$ D. $$(-2,4)$$ 28- What is the ratio between α and $$β(\frac{α}{β})$$ in the following shape? A. $$\frac{5}{12}$$ B. \9\frac{11}{25}\) C. $$\frac{5}{12}$$ D. $$\frac{25}{11}$$ 29- Find the opposite of the numbers $$-4,7$$. A. $$\frac{1}{4},-7$$ B. $$-4,\frac{1}{7}$$ C. $$4,-7$$ D. $$-4,-7$$ 30- What is the value of $$x$$ in the following equation: $$16=-129+x$$ A. $$85$$ B. $$-85$$ C. $$145$$ D. $$-145$$ 31- Which of the following graphs represents the following inequality? $$-5<2x+7≤3$$ A. B. C. D. 32- Which of the following statements is correct, according to the graph below? A. The number of books sold in the April was twice the number of books sold in the July. B. The number of books sold in the July was more than one third the number of books sold in the May. C. The number of books sold in the June was less than one third the number of books sold in the April. D.  The number of books sold in the July was equal to the number of books sold in April plus the number of books sold in the June 33- To produce a special concrete, for every 17 kg of cement, 6 liters of water is required. Which of the following ratios is the same as the ratio of cement to liters of water? A. 78 ∶ 34 B. 51 ∶ 17 C. 49 ∶ 17 D. 63 ∶ 16 34- An integer is chosen at random from 9 to 15. Find the probability of not selecting a composite number? A. $$\frac{1}{3}$$ B. $$\frac{4}{5}$$ C. $$\frac{3}{7}$$ D. $$\frac{2}{7}$$ 35- In a certain bookshelf of a library, there are 20 biology books, 59 history books, and 36 language books. What is the ratio of the number of biology books to the total number of books in this bookshelf? A. $$\frac{4}{23}$$ B. $$\frac{3}{17}$$ C. $$\frac{2}{15}$$ D. $$\frac{4}{15}$$ 36- Which of the following is the correct statement? A. $$\frac{5}{8}>0.8$$ B. $$23\%<\frac{2}{3}$$ C. $$8<\frac{18}{3}$$ D. $$\frac{7}{9}<0.6$$ 37- Daniel is 38 years old, twice as old as Henry. How old is Henry? A. 19 years’ old B. 27 years’ old C. 62 years’ old D. 76 years’ old 38- A waiter earned a 38 percent tip. What decimal is equivalent to 38 percent? 39- Which of the following statements can be used for the following inequality? $$\frac{9}{x}≤19$$ A. Sara placed $$x$$ pens among 19 friends and each friend received fewer than 9 pens. B. Sara placed 9 pens among $$x$$ friends and each friend received at most 19 pens. C. Sara placed $$x$$ pens among 9 friends and each friend received most than 19 pens. D. Sara placed $$x$$ pens among 9 friends and each friend received at fewer 19 pens 40- If the area of the following rectangular ABCD is 180, and E is the midpoint of AB, what is the area of the triangle ADE? A. 35 B. 40 C. 45 D. 50 30% OFF X ## How Does It Work? ### 1. Find eBooks Locate the eBook you wish to purchase by searching for the test or title. ### 3. Checkout Complete the quick and easy checkout process. ## Why Buy eBook From Effortlessmath? Save up to 70% compared to print Help save the environment

crawl-data/CC-MAIN-2021-25/segments/1623488525399.79/warc/CC-MAIN-20210622220817-20210623010817-00475.warc.gz

Amid the cityscape of Brooklyn, New York, some green patches remain after years of urbanization. Two of the larger ones are Prospect Park and Green-Wood Cemetery. On September 12, 2001, the Advanced Land Imager (ALI) on NASA’s Earth Observing-1 (EO-1) satellite took this true-color picture of these green oases. Both areas retain the hues characteristic of late summertime, with deep green trees hovering over medium green fields. Prospect Park was designed and built between 1865 and 1895, the effort overseen by the same men who designed New York City’s Central Park. Covering some 585 acres (2.4 square kilometers), the park holds a combination of recreational facilities, forest, and wetland. Established in 1838, Green-Wood Cemetery was one of the first rural cemeteries in the United States. Its beauty soon drew large crowds of visitors, and helped inspire public parks such as its neighbor, Prospect Park. Today, Prospect Park holds much of Brooklyn’s remaining indigenous forest and preserves a parcel of wetland. Two centuries ago, New York City contained some 224,000 acres (roughly 900 square kilometers) of freshwater wetland, before urban growth claimed most of the land. Prospect Park’s wetlands are partially human-designed, but also result from much older natural forces. Approximately 75,000 years ago, the massive Wisconsin Glacier crept over what is today New York City, grinding rock ahead of it. Some 50,000 years later, the ice melted, and the resulting waterways cut through rock on their way to the sea. Occasionally, blocks of ice broke off the receding glaciers and were buried by sediment. As the ice blocks melted, they left depressions, nicknamed kettles, on the land surface. Many of these kettles collected water, and where the water was shallow or sufficiently slow-moving, plants took root. Cycles of plant growth and decomposition built peat bogs. By the time New York City began its long path to urbanization, diverse wetlands covered the region. The watercourse in Prospect Park preserves part of a once-ubiquitous ecosystem. - Green-Wood. History of Green-Wood Cemetery. Accessed August 7, 2009. - National Historic Landmarks Program.The Green-Wood Cemetery. Accessed August 7, 2009. - New York City Department of Parks and Recreation. Prospect Park. Accessed August 7, 2009. NASA image created by Jesse Allen, using EO-1 ALI data provided courtesy of the NASA EO-1 Team. Caption by Michon Scott. - EO-1 - ALI

<urn:uuid:eab6091e-6eee-4caf-bc28-98db51d941dd>

Scientists have devised a codon that could help us understand how life forms in the oceans form. They have used the codon to show that many living things in the ocean have a common ancestor, suggesting that organisms that evolve by changing their genetic code are more similar to each other than is previously thought. Codon theory has been used to explain how life was first discovered, and could help explain how organisms that evolved by changing genetic code become more similar, scientists say. The research, reported in the journal Nature, shows that life on Earth has an evolutionary history, similar to the way a river changes direction by changing its currents. “When we first discover life on earth, we’re looking at a river changing direction because of the changing climate, or a mountain being moved,” said senior author Paul Dettmer, a researcher at the University of Arizona. “In our research, we’ve shown that, by looking at the codons in the DNA of the living organisms, we can determine how they evolve. We’re finding a way to see the evolution of organisms in the water.” Researchers discovered that some living things on Earth have two distinct codons, which means that life forms can have different evolutionary paths. These are called tandem codons. For example, a bacterium that uses enzymes to produce sugars that can be used by other organisms can use one codon and not the other. The researchers have now found that many different organisms have two codons which allow them to be found in different parts of the ocean. “These codons are more like the rivers on Earth. They have two different currents,” Dettmers said.” The first one goes through the mountains, the second goes through oceans.” Scientists have already discovered a new species of bacteria called Bacteroidetes that uses two codon pairs to build a symbiotic relationship with algae. Dettmer and his colleagues have also discovered how organisms can form symbiotic relationships in the wild. These two codones, like the first, are also the codones that are most frequently found in marine organisms. The codons can be found more commonly in marine algae and bacteria than in terrestrial organisms. Scientists have been trying to figure out why these codons exist. They are also looking at other organisms that have two similar codons that are different. They think this may be the reason why these organisms are able to form symbiosis with each other, which could explain how they evolved. “They are very similar to their environment, but they also have different environments in terms of temperature, pressure, light, and so on,” Dittmer said. The new codons have already been found in other organisms, but it was not until Detters and his team discovered the codone pattern in marine life that the idea became more widely known. “This is very exciting because the first time we’ve seen it, it was a little bit surprising,” said Dettgers. The scientists believe that the codoning pattern has an important role in the evolution and maintenance of life in the sea. “We can look at the evolution in marine ecosystems and see how the codonedes work. We can look for a lot of these codonede structures in the environment and then try to predict the evolution, which may be really helpful in understanding what is happening in the biological world,” Dottmer said.” We’re looking for similarities, and we’re using codones as the tools to make that prediction,” he added. This article is from the archive of our partner The Wire.

<urn:uuid:24f87ac6-6c55-45ac-ab06-9fd5322d0bdb>