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The evolution of Greek vase painting
A comparison of earlier pieces (from the Neolithic and early bronze age [2nd millennium BC]) show the improvements that the potters wheel brought to the fineness and shapes of the vessels. Bronze age examples (all dating before 1100 BC) from Cyprus, Crete (so-called 'Minoan' wares) and the Greek mainland (so-called 'Mycenaean') show a variety of coarse as well as fine wares, some made by hand and others made on the potter's wheel.
The interaction of Greeks and near easterners is suggested by similarities in these wares to those that their eastern neighbours used, and in the inclusion of 'Oriental' motifs such a lions, sphinxes, and lotuses, especially on Archaic vases (those made in the period from 700-480). 'Naucratite' wares (from Naucratis, a Greek trading post in Egypt) show the infusion of Greek styles in Egypt.
In the high Archaic period (7th-6th c. BCE) the Corinthians were the biggest producers of Greek decorated wares, and they pioneered in the development of the so-called black-figure style (black figures on a red background). The Athenians took over this style and with it became the preeminent producers of decorative wares in the 6th century BCE. They also experimented with more techniques, of which the most important became the red-figure style (red figures on a black background), which began to be produced in 530 BC.
After Athens lost its fortunes through the Peloponnesian War (431-404 BC) many of its artists sought markets abroad (e.g. the Kerch style was used for Athenian exports to the region of the Black Sea in the 4th c. BC). Some of these artists moved abroad and set up successful businesses in southern Italy - in the regions of Sicily, Apulia, Lucania, and Campania, and towns such as Gnathia (Egnazia) and Paestum - where they adapted the red figure style to local fabrics, shapes, and decorations. These and later Hellenistic styles took particular advantage of the use of added colour. | <urn:uuid:2a8417af-a9c9-47e6-9c67-708bc939cfd6> | {
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Christopher Columbus is credited with the discovery of the island of Jamaica. The year was 1494 and it was his second voyage to the New
World. He is said to have exclaimed that Jamaica was the “fairest island eyes have beheld”. Later, on his fourth voyage, Columbus was given the opportunity to become better acquainted with the island when his ships were damaged by storms and he was stranded there for an entire year.
The Spanish soon settled in and began their usual business of importing African slaves. At the same time, the peaceful native Arawak Indian population dwindled due to diseases brought to the island, extermination or transport as slaves to the neighboring island of Hispaniola.
In spite of Columbus’ rave reviews of the island, the Spanish population of the island numbered only about 1500 when the British arrived in 1655. The attackers, sent by Oliver Cromwell, Lord Protector of England and under the command of Admiral William Penn – father of William Penn of Pennsylvania – and General Robert Venables, succeeded in their conquest and the Spanish surrendered. Jamaica was the second choice of the British attackers, having failed at taking the island of Hispaniola.
Some of the Spanish fled to the mountainous interior of the island and it was not until five years later in 1660, that the last Spaniard, Don Arnaldo de Ysassi left from what is now called Runaway Bay in 1660.
This same year, a governor was appointed and ten years later, in 1670, British control was formalized with the Treaty of Madrid.
$1,500 Trip GiveAway Each Week when you Book your Hotel through Instant Book on TripAdvisor! (10/20-11/20)
Port Royal – The Wicked City
Around this time, the city of Port Royal became one of the largest European cities in the New World. At one time, it was second only to Boston. Port Royal thrived largely due to the activity of Pirates and buccaneers who had made it their headquarters due to it’s strategic location and large harbor. Soon it gained the reputation of being ‘the wealthiest and wickedest city on the face of the earth’ due to the loose morals and ill-gotten wealth of its residents which was comprised in large part of pirates, prostitutes, cutthroats and drunkards. It is said that there was one drinking house for every 10 residents and pirates congregated in Port Royal from all parts of the world.
Originally privateers or buccaneers were charged with defense of the city and the island. There were several attempts of the Spanish to
reclaim the island, all of which were unsuccessful. A privateer, or corsair generally was a pirate with a letter of marque, an endorsement from a higher authority charging them with defending or avenging on behalf of the issuing authority or government. Oftentimes these letters of marque were invalid or those in their possession failed to observe the terms of the letter.
Buccaneers were more specifically pirates who had been suppliers of provisions such as water and meat to non-Spaniards. They were generally outcasts such as Indians, mulattos or other displaced individuals. The term buccaneer is of somewhat unclear derivation, but possibly referred to the makeshift gridiron used to cook the meat that they sold to the English and French. ‘Boucaner’ is also a French term associated with ‘lowlives’. They became useful not only for their willingness to trade with the non-Spaniard settlers of the area, but because they were known as good navigators and sharpshooters. They would also typically have a letter of marque.
Pirates, on the other hand, were those who plundered and acted on their own behalf, with no attempt to follow any rules. Pirate is generally used as a broad term to include all of the above.
In 1675, the notorious pirate Henry Morgan became Lieutenant Governor after he was knighted by the crown, and actually started trying to clean the place up which resulted in numerous hangings.
On June 7, 1692, Port Royal was nearly completely destroyed by a massive 7.5 magnitude earthquake. Around 2000 people were killed and 33 acres including four of the five forts were submerged. Unsurprisingly, many saw this as punishment for the wickedness of the city’s inhabitants.
Those remaining, however, continued their wicked ways and there was rampant looting after the earthquake. For another 50 years pirates would continue to attack Spanish ships. Besides Henry Morgan, many of the most famous pirates of the days were somehow associated with Port Royal, including Blackbeard, Black Bart and Calico Jack, who was famous for his skull and crossbone flag, the “Jolly Roger” and who was hanged at the gallows in Port Royal.
The earthquake of 1692 was not the end of Port Royal’s calamities either. Fires, earthquakes and hurricanes followed, including Hurricane Charlie in 1951 which left only a few buildings standing.
Today, most of Port Royal remains under 40 feet of water. Compared to Pompeii in Italy, it is remarkably well preserved and divers have explored and catalogued the city since the 1950s. It is a national heritage site and many of the artifacts that have been found are on display in museums in Kingston, including a pocket watch dated 1686 that stopped at 11.43. It is said that you can still hear the bells toll from this lost underwater city.
The Maroons were former slaves who banded together and established communities in the interior parts of the island. Of the former slaves of the Spanish, who were, for the most part driven out in 1655, there were three groups that formed. The first group allied themselves with the Spanish who had remained and fled to the ‘Cockpit Country’. The second group allied with the English, and the third remained without European alliances, but joined with the remaining Arawak Indian population.
Each group formed communities in the island’s interior. It should not come as a surprise that skirmishes and conflicts occurred, usually set off by events such as the theft of a pig. This led to two major conflicts known as the Maroon Wars.
The first Maroon War of the 1730’s led to somewhat favorable results for the Maroons, with the agreement that the Maroons would remain in 5 main towns under their own rule, but subject to a British supervisor.
The outcome of the second Maroon War, which took place in the 1790’s, was less favorable and resulted in deportations to places as far away as Nova Scotia and Sierra Leone in West Africa.
In the 18th century, sugar replaced piracy as the principal source of income and the establishment of large plantations in the interior was likely a contributing factor to the conflicts with the Maroons.
In 1834 slavery was abolished and by the late 1800’s, Jamaica was suffering from a sever economic decline with many of the sugar plantations forced into bankruptcy.
Morant Bay Rebellion
Although the freed slaves were permitted to vote, there was a hefty poll tax in force that was prohibitive for the majority of the non British population. In 1864, less than 2,000 black Jamaican men were eligible to vote. The population at the time was over 436,000 and blacks outnumbered the whites by 32:1. This, plus several events led to a bloody rebellion in the year 1865.
The attempts of the former slaves to sustain themselves through planting crops and cultivating the land were thwarted by droughts, then floods as well as outbreaks of cholera and smallpox. A petition to Queen Victoria herself was sent asking for help, but the reply that came back was only that they should try harder.
In October, 1865, a man was convicted of trespassing on an abandoned sugar plantation. During his trial there was a disturbance caused by one of the spectators and a fight broke out. More arrest warrants were issued for rioting and assaulting policemen, including a warrant for a Baptist preacher named Paul Bogle.
On October 11, Bogle led a group of several hundred protestors to Morant Bay. In the conflict that resulted, more than 25 lives were lost as the rebels took over the parish of St. Thomas-in-the-East. Governor John Eyre sent troops to round up the rebels and capture Bogle. As many as 439 rebels were killed and 354 more were later executed, including Bogle. This rebellion is considered to be the most extreme act of suppression against former slaves in the history of the British West Indies.
In 1866, Jamaica was made a crown colony under direct British rule, which was requested as a result of the bloodshed that had occurred. Some progress occurred in the economy and by 1890, bananas had replaced sugar as the main export.
In 1872, the capitol was moved from Spanish Town to Kingston, which had been founded as a refuge for the survivors of nearby Port Royal. In 1907, it was also largely destroyed by a 6.5 magnitude earthquake, at the time, considered among the deadliest in history. Nearly every structure in the city was damaged or destroyed. Fires broke out and it is estimated that 800-1,000 lives were lost, with thousands more being left homeless.
After a referendum in September, 1961, Jamaica opted for independence, which it officially received on August 6, 1962, though it remains a member of the British Commonwealth of Nations.
Today, Jamaica is famous as a tourist destination. It’s spectacular beaches and resorts draw over a 1 million foreign visitors every year and tourism accounts for at least half of the country’s economy. | <urn:uuid:bd3dd4a8-a970-4c15-a3a4-e2bc47e9a8e2> | {
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# CBSE Class 6 Maths Chapter 7 Notes Fractions
## CBSE Class 6 Maths Chapter 7 Notes Fractions
### Fractions Class 6 Notes Conceptual Facts
1. A fraction is a part of a whole number having numerator and denominator.
For example: $$\frac{5}{7}$$ where 5 is numerator and 7 is the denominator.
2. Representation of a fraction on a number line.
For example: $$\frac{2}{3}$$
3. Proper fractions: Numerator is less than the denominator.
For example: $$\frac{2}{3}, \frac{5}{8} \text { and } \frac{1}{5}$$
4. Improper fractions: Numerator is bigger than the denominator.
For example: $$\frac{5}{2}, \frac{7}{5}, \frac{10}{3} \text { and } \frac{6}{5}$$
5. Mixed fractions: It is represented by Quotient $$\frac{\text { Remainder }}{\text { Divisor }}$$
For example: $$5 \frac{1}{7}, 3 \frac{2}{3} \text { and } 4 \frac{5}{7}$$
6. Equivalent fractions: Two or more fractions are said to be equivalent fractions, if they represent the same quantity.
For example: $$\frac{2}{5}, \frac{6}{15}, \frac{4}{10} \text { and } \frac{8}{20}$$
7. Simplest form of a fraction: A fraction is said to be simple if numerator and the denominator have no common factor except 1.
For example: Simplest form of $$\frac{15}{20} \text { is } \frac{3}{4}$$
8. Like fractions: Two or more fractions having same denominators are called like fractions.
For example: $$\frac{2}{5}, \frac{3}{5}, \frac{4}{5}, \frac{6}{5}$$
9. Unlike fractions: Two or more fractions having different denominators are called unlike fractions.
For example: $$\frac{8}{9}, \frac{5}{7}, \frac{6}{5}, \frac{7}{10}$$
+ | crawl-data/CC-MAIN-2024-38/segments/1725700651697.32/warc/CC-MAIN-20240916112213-20240916142213-00421.warc.gz | null |
# Gmat Math Ques
of 7
## Content
All Units Questions
14. X, y and z are three digits numbers, and x=y+z. Is the hundreds’ digit of x equal to the sum of hundreds’ digits of y and z? 1). the tens’ digit of x equal to the sum of tens’ digits of y and z 2). the units’ digit of x equal to the sum of units’ digits of y and z yes only A satifies. Statement 1: 321 + 221 = 542, 952 = 521 + 432 -->satifies Statement 2: 952 = 521 + 432 but 364 + 240 = 604 ---> does nt satisfy
62. n=? 1). The tens¡¯ digit of 11^n is 4 2). The hundreds¡¯ digit of 5^n is 6 E it is. From 1, n = 10k + 4 (k>=0, this is the series n lies in) From 2, n = 2m+3 (where, m>=0) Thus, there's no value of m and k that can satisfy n, thus the answer is E. Or wouldnt the series repeat after 10 numbers? from A: n can be 4,14,24... from B: cannot determine.. Both together also insufficient.. Answer E 77. What is the remainder when n is divided by 10? 1). The tens?digit of 11^n is 4
2). The hundreds?digit of 5^n is 6 stem 1>> 11^0=01 | 11^1=11 | 11^2=121 | 11^3=1331 | 11^4=14641 | 11^5=161051 | the units digit start from 0,1,2,3,4,5 etc... take n with units digit =4, 14641...sufficient.....and this applicable for all n values of 14,24,34,etc.. stem 2>> 5^0=1 | 5^1=5 | 5^2=25 | 5^3=125 | 5^4=525 | 5^5=2625 | 5^6=13125 it doent follow a pattern, so - insufficient.. A it is.... Or 11^4 = 14641 11^14 = xxxxxxxxxxxx241. (it will be 15 digit number u can check using calc.) similarly 11 ^ 24 = ....841 (a 25 digit number) we get n = 4 , 14,24,34,44..... every time dividing by 10 leaves 4.. so stem(1) alone sufficient. stem(2) after n>2 and n even we get 6 in hundreds place and n odd we get 1 in hundreds place .. it can be better understood by values. 5 ^ 3 = 125 5^4 = 625 5^5 = 3125 5^6 = 15625 so for every n >2 and n is even we get 6 in hundreds place so n can have 4, 6, 8,10,12... when divided by 10 leaves diffirent values so not sufficient..
clearly answer is (A) ie stem(1) alone sufficient and stem(2) not sufficient.
111. Is number 3 the tens?digit of x? 1). When x is divided by 100, the remainder is 30 2). When x is divided by 110, the remainder is 30 Statement (1). When x is divided by 100, the remainder is 30 This will be true only for 130 ,230,330 ..etc Ten's digit always 3 SUFF Statement 2). When x is divided by 110, the remainder is 30 x = 140,250,360 --> ten's digit other than 3 x = 1130 --> ten's digit 3 INSUFF Answer (A
125. Integers x and y have three digits and z is the sum of x and y. Is the tens?digit of z equal to the sum of the tens?digits of x and y? 1). Both x and y have units?digits greater than 6 2). The sum of tens?digit of x and y is 7 A. X = ABC Y = DEF, Z = (X+Y) i) Given than C and F are greater than 6, that implies, the tens' digit of Z will NEVER be sum of B and E. And, hence SUFF. There will always be carry from sum of units digit of X and Y. ii) INSUFF, as we do not know about the units' digit.
I fell for that GMAT trap.... was looking at B for a moment....... Without the tenths digit we cant really support claims of stmt 2 so it is insufficient. and as gere79 said stmt is really sufficient if you take a closer look at it. 130. X=10^n*25^2, what is the unit's digit of x? 1). Forget...useless 2). n^2=1 n can be +/-1, so x can be 6250 or 62.5. Discarding A it is E Agree, E. But is given X is an integer, then B. 133. If b is an integer and b<10, x=1+ b/100. b=? 1). 1<=b<=3 2). The thousandth's digit of 10X^2 is equal to the tens's digit of x^2 Ones....... tenths........hund..............thousand...........ten-thous andths 0. 1 ; ; 2 3 4 .1234 =1/10 + 2/100 +3/1000 + 4/10000 (thousandths’ digit of 10X^2 ) is equal to the tens’ digit of x^2 1000 of 10x^2 = 10 of x^2 take b=1 so x^2 = 1.201 and 10x^2 = 12.01 which is only possible when b=9 so the x^2 value is = 1.09^2 = 1.1881 so the value of b=9....
IMO B 134. Of the 24 positive integers, all have the units's digit of 5, 1/3 have tens?digit of 0, 1/3 have tens' digit of 1, 1/3 of tens' digit of 2. What is the tens' digit of sum of 24 numbers? Pretty straight forward 6 it is (24 * 5 ) = 120 for the units 8 * 0 = 0 for the 1st 1/3 8 * 1 = 8 for the 2nd 1/3 8 * 2 = 16 for the 3rd 1/3 so the sum of tenths of the 24 numbers = 12(carry over from the units) + 8 + 16 = 36 we are looking for the tenths so answer is 6 .....we carry over 3 to the hundreds side.
140. Is the tens?digit of x greater than that of y? 1). x-y=37 2). The units' digit of x is ... greater than that of y E it is. But to be sure there must be the indication in the question stem that x and y are positive. 1). x-y=37 INSUFF For example: x = 64 and y = 27 (6>4) or x = 114 and y = 77 (1<7). 2). The units’ digit of x is … greater than that of y INSUFF 146. If 300<X<400, is the tens?digit of x greater than 5? 1). The units' digit of x is greater than 4 2). When x is added with 237, the hundreds?digit will be equal to 6 IMO B
hundered's digit cannot be 4; hence the ten's digit got be 7,8,9 in X to get 600, min 363 must be added.. since 300<X<400, x has to be greater than or equal to 363 or tens digit has to be greater than 5. so B 159. What is the unit's digit of X? 1). x/(10^n)=25^2 2). n^2=1 Let the unit digit be u. Now1>> x/(10^n) = 625.. Now n can take any value ranging from -ve to +ve. So u can have 6,2,5,0. Insuff 2>> n^2=1. ; n^2=1; n can be +1,-1. So u can be 2 or 0. E is the answer
161. x and y are 2-digt integers. What is the difference between two tens' digit? 1). x-y=27 2). Units' digit of x minus the units' digit of y is greater than 3 C From 1, x-y = 27 (consider 2 representative cases x = 97 & y = 70 or x = 86, y=59) .. so the diff of tens digits can be either 2 or 3 From 1 & 2, The diff between Units' digit of x minus the units' digit of y will be greater than 3 only for cases where the diff between tens digits is 2 (and not for the cases where the diff is 3)
## Recommended
#### tele ques
Or use your account on DocShare.tips
Hide | crawl-data/CC-MAIN-2024-30/segments/1720763517915.15/warc/CC-MAIN-20240722190551-20240722220551-00081.warc.gz | null |
The mystery behind lunar swirls, one of the solar system’s most beautiful optical anomalies, may finally be solved thanks to a joint Rutgers University and University of California Berkeley study.
The solution hints at the dynamism of the moon’s ancient past as a place with volcanic activity and an internally generated magnetic field. It also challenges our picture of the moon’s existing geology.
Lunar swirls resemble bright, snaky clouds painted on the moon’s dark surface. The most famous, called Reiner Gamma, is about 40 miles long and popular with backyard astronomers. Most lunar swirls share their locations with powerful, localized magnetic fields. The bright-and-dark patterns may result when those magnetic fields deflect particles from the solar wind and cause some parts of the lunar surface to weather more slowly.
“But the cause of those magnetic fields, and thus of the swirls themselves, had long been a mystery,” said Sonia Tikoo, coauthor of the study recently published in the Journal of Geophysical Research — Planets and an assistant professor in Rutgers University-New Brunswick’s Department of Earth and Planetary Sciences. “To solve it, we had to find out what kind of geological feature could produce these magnetic fields — and why their magnetism is so powerful.”
Working with what is known about the intricate geometry of lunar swirls, and the strengths of the magnetic fields associated with them, the researchers developed mathematical models for the geological “magnets.” They found that each swirl must stand above a magnetic object that is narrow and buried close to the moon’s surface.
The picture is consistent with lava tubes, long, narrow structures formed by flowing lava during volcanic eruptions; or with lava dikes, vertical sheets of magma injected into the lunar crust.
But this raised another question: How could lava tubes and dikes be so strongly magnetic? The answer lies in a reaction that may be unique to the moon’s environment at the time of those ancient eruptions, over 3 billion years ago.
Past experiments have found that many moon rocks become highly magnetic when heated more than 600 degrees Celsius in an oxygen-free environment. That’s because certain minerals break down at high temperatures and release metallic iron. If there happens to be a strong enough magnetic field nearby, the newly formed iron will become magnetized along the direction of that field.
This doesn’t normally happen on earth, where free-floating oxygen binds with the iron. And it wouldn’t happen today on the moon, where there is no global magnetic field to magnetize the iron.
But in a study published last year, Tikoo found that the moon’s ancient magnetic field lasted 1 billion to 2.5 billion years longer than had previously been thought — perhaps concurrent with the creation of lava tubes or dikes whose high iron content would have become strongly magnetic as they cooled.
“No one had thought about this reaction in terms of explaining these unusually strong magnetic features on the moon. This was the final piece in the puzzle of understanding the magnetism that underlies these lunar swirls,” Tikoo said.
The next step would be to actually visit a lunar swirl and study it directly. Tikoo serves on a committee that is proposing a rover mission to do just that.
Materials provided by Rutgers University. Note: Content may be edited for style and length. | <urn:uuid:be8f6cfc-ad7a-452a-8091-99e42c098709> | {
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Updated: Jul 27
Find out about what makes bees so incredible!
As you walk throughout the patch you will likely see many Bees at work. Around the fields of our farm we plant wildflowers to provide food to the bees - and here at the patch there's a lot of delicious nectar to support local bees too. That's why you are likely to spot lots of them!
How many bees can you spot on one Sunflower head?
You might be surprised to learn there are more than 250 species of bee in the UK. Bumblebees, mason bees, mining bees - these are just one small part of a big, beautiful family. Bumblebees nest in colonies, while solitary bees (like Mason and Mining bees) live and nest alone.
One species of honey bee – the European or Western honey bee – lives in the UK. These are farmed bees that have been introduced by beekeepers, rather than being native to our shores. Sadly it's now incredibly rare to find a truly wild honey bee colony.
What makes Bees so Important?
Bees have cultural and environmental importance as pollinators and producers of honey and medicinal products. The movement of pollen between plants is necessary for plants to fertilize and reproduce. Both farmed and wild bees control the growth and quality of vegetation — when they thrive, so do crops.
While there are other methods of pollination, including by other animals and the wind, wild bees can pollinate on a much bigger and more efficient scale.
Estimates suggest it would cost UK farmers an incredible £1.8 billion a year to manually pollinate their crops.
Did you know? Broccoli, carrots, fennel, parsnips, turnips, kale, apples, raspberries and tomatoes are among more than 60 British crops that rely on pollination by bees. | <urn:uuid:8391b41a-2658-46ef-b273-4575b2207933> | {
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# linear equations
A shopkeeper buys a number of books for Rs.1200. If he had bought 5 less books for the same amount, each book would have cost him Rs.20 more. How many books did he buy?
I have this question found in my brother's tenth class book and unable to understand it.
Update:
I could not give a suitable title and since the problem is of Quadratic Equation, so the current title is obviously wrong. I shall appreciate if someone can give a suitable title and edit the same.
-
## 3 Answers
Doing this step by step: Let $x$ be the amount of books and $p$ the price. We have $$xp=1200$$ If he bought 5 less books at the price $p+20$ then $$(x-5)(p+20)=1200$$ Working this out we have $$x=5+\frac{p}{4}$$ Substituting this in the first equation and working it out gives $$p^2+20p-4800=0$$ which only positive solution is $p=60$, and we can conclude that $x=20$.
Number of books = 20
-
I think you should have $x=20=\frac{1200}{60}$. ($x=-15$ is the other solution.) – copper.hat Feb 24 '13 at 16:11
It was a typo, sorry. – Marra Feb 24 '13 at 16:12
If $n$ is the initial number of books, and $P$ is the initial price, then we have: $n P = 1200$, $(n-5)(P+20)=1200$.
Equating the two equations (since they both equal $1200$) gives $4n-P=20$, which gives $P=4n-20$. Substituting this into the equation $n P =1200$ gives $n^2-5n-300=0$ which has solutions $\{-15,20\}$. Since we are looking for positive solutions, this gives $n=20$.
-
Let $x$ be the number of books.
Each Book costs : $\frac{1200}{x}$
Solving the equation: $\frac{1200}{x-5} = \frac{1200}{x}+20$ gives the solution the solution as $x=20$.
- | crawl-data/CC-MAIN-2016-30/segments/1469257824201.28/warc/CC-MAIN-20160723071024-00032-ip-10-185-27-174.ec2.internal.warc.gz | null |
# Carol spends 17 hours in a 2-week period practicing her culinary skills. How many hours does she practice in 5 weeks?
May 11, 2018
42 hours and 30 minutes
#### Explanation:
To get the time she practices in one week, divide 17 by 2 ; $\frac{17}{2}$
This equals 8.5
If you want to find out how many hours she practices in five weeks, then you multiply 8.5 by 5.
$8.5 \times 5$
This equals 42.5 | crawl-data/CC-MAIN-2020-40/segments/1600400274441.60/warc/CC-MAIN-20200927085848-20200927115848-00106.warc.gz | null |
The force that causes water to move through a plant is caused by transpiration - the loss of water from the leaves by evaporation and diffusion.
Water is transported form the roots to the leaves by specialised vessels called xylem.
Water is absorbed from the soil by specialised cells called root-hair cells.
- xylem vessels are made form cells joined end-to-end as they specialise the cells gradually:
- lose their… | <urn:uuid:b6587482-f1a7-44f1-b26b-3e9202e6ab7a> | {
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In compound interest, the interest for each period is added to the principle before interest is calculated for the next period. With this method the principle grows as the interest is added to it. This method is mostly used in investments such as savings account and bonds.
To understand compound interest clearly, let’s take an example.
1000 is borrowed for three years at 10% compound interest. What is the total amount after three years?
You can understand the process of compound interest by image shown below.
Year Principle Interest (10%) Amount 1st 1000 100 1100 2nd 1100 110 1210 3rd 1210 121 1331
## Difference between Simple Interest and compound interest
After three years,
In simple interest, the total amount would be 1300
And in compound interest, the total amount would be 1331.
## Basic Formulas of Compound Interest
If A = Amount
P = Principle
C.I. = Compound Interest
T = Time in years
R = Interest Rate Per Year
## Shortcut Formulas for Compound Interest
Rule 1: If rate of interest is R1% for first year, R2% for second year and R3% for third year, then
Example
Find the total amount after three years on Rs 1000 if the compound interest rate for first year is 4%, for second year is 5% and for third year is 10%
Sol:
P = 1000
R1 = 4%, R2 = 5% and R3 = 10%
(From the table given at the bottom of the page)
A = 1201.2
Rule 2:
If principle = P, Rate = R% and Time = T years then
1. If the interest is compounded annually:
2. If the interest is compounded half yearly (two times in year):
3. If the interest is compounded quarterly (four times in year):
Example
Find the total amount on 1000 after 2 years at the rate of 4% if
1. The interest is compounded annually
2. The interest is compounded half yearly
3. The interest is compounded quarterly.
Sol:
Here P = 1000
R = 4%
T = 2 years
If the interest is compounded annually
(From the table given at the bottom of the page)
A = 1081.6
If the interest is compounded half yearly
A = 1082.4
If the interest is compounded quarterly
A = 1082.9
Rule 3: If difference between Simple Interest and Compound Interest is given.
• If the difference between Simple Interest and Compound Interest on a certain sum of money for 2 years at R% rate is given then
Example
If the difference between simple interest and compound interest on a certain sum of money at 10% per annum for 2 years is Rs 2 then find the sum.
Sum:
• If the difference between Simple Interest and Compound Interest on a certain sum of money for 3 years at R% is given then
Example
If the difference between simple interest and compound interest on a certain sum of money at 10% per annum for 3 years is Rs 2 then find the sum.
Sol:
Rule 4: If sum A becomes B in T1 years at compound interest, then after T2 years
Example
Rs 1000 becomes 1100 after 4 years at certain compound interest rate. What will be the sum after 8 years?
Sum:
Here A = 1000, B = 1100
T1 = 4, T2 = 8
Look up Table
Simple Interest | crawl-data/CC-MAIN-2019-18/segments/1555578586680.51/warc/CC-MAIN-20190423035013-20190423061013-00533.warc.gz | null |
Deposition of sediment, usually sand, which is evident by the seaward advance of a shoreline indicator, such as the high water line, berm crest, or vegetation line. Accretion causes
the beach to become wider. Opposite of erosion.
Transport and deposition of sand by wind; the principal means by which sand dunes are formed.
See LONGSHORE CURRENT.
Placement of fixed engineering structures, typically rock, wood timbers, or concrete, on or along the shoreline to reduce coastal erosion. Armoring structures include seawalls, revetments, bulkheads, and rip rap.
Generally dry portion of the beach between the berm crest and the vegetation line that is submerged only during high water levels and eroded during storm events.
The seaward return flow of swash on the beach face due to gravity.
Submerged mound of sand that generally runs parallel to the shore and causes waves to break before reaching the beach.
A low-lying, sandy island or spit that lies offshore and generally parallel to the mainland.
Accumulation of wave-deposited, loose sediment, usually sand, that extends from the outermost breakers to the landward limit of wave and swash action.
Volumetric loss of sand, usually measured by a loss of dry beach width.
Periodic collection of data, such as dry beach width, to study changes over time.
Decrease in usable (dry) beach width caused by episodic storm impact or long-term erosion.
Sand artificially placed on the beach, usually by pumping sea bottom sediments onshore, to replace that being lost alongshore or offshore. Beach nourishment projects are usually large scale, spanning many miles of shoreline to rebuild eroded beaches.
Measurement of the elevation or height of the beach surface taken along a line that runs from the dune to the water across the beach. Profiles taken at different dates can
be compared to illustrate and quantify storm, seasonal, and longer-term changes in beach width, height, volume, and shape.
Feature usually located at mid-beach and characterized by a sharp break in slope, separating the flatter backshore from the seaward-sloping foreshore.
Small, often circular or oval depression in sand dunes, caused by wind scouring where protective vegetation has been disturbed.
High, steep bank or cliff along the mainland of non-coastal origin. Steepened bluffs are caused by wave undercutting of the cliff toe.
Structure built parallel to the shoreline and seaward of the beach designed to protect the beach and upland areas by causing waves to break and dissipate their energy before reaching the shore.
State or locally required seaward limit of beachfront construction, usually for a house.
Rigid structures with vertical walls built parallel to the shoreline to serve as barriers to wave attack and prevent storm surge flooding of upland areas; constructed out of treated wood, corrugated steel, PVC, or other materials.
Stretch of shore that is connected by a common longshore sediment transport system, such as the south shore of Long Island, New York.
Crenulated beach surface, characterized by an evenly spaced series of rounded, small headlands (projections) and bays (or embayments). The along-shore spacing of cusps ranges from a few feet to 100’s of feet and their relief varies from a few inches to several feet.
Lowering of the beach profile.
In the direction of net longshore sediment transport.
Mound or ridge of sand deposited by the wind, capable of movement when unvegetated. Dune building can be augmented by sand fencing or planting beach grass.
Technique of rebuilding an eroded or degraded dune through one or more methods (sand fill, fencing, revegetation, etc.).
Light construction that provides pedestrian access across a dune without trampling the vegetation.
Tidal current moving away from the coast during a falling (ebbing) tide, often with high velocity flows through tidal inlets.
EBB TIDAL DELTA
Sandy shoals formed by ebbing currents found on the seaward side of tidal inlets.
Physical removal of sand from the beach which is transported offshore, alongshore, or into bays and lagoons via inlets. Erosion results in shoreline recession—landward retreat of a shoreline indicator such as the high water line, vegetation line or dune line. Opposite of accretion.
EROSION HOT SPOTS
Areas where erosion is occurring at a much higher rate than adjacent beach areas, which can threaten beachfront development or infrastructure. Typically the dry beach has narrowed considerably.
Areas where the coastal environment (natural or built) will soon be threatened if shore erosion trends continue.
EUSTATIC SEA-LEVEL RISE
World-wide changes of sea level over decades to centuries caused by addition of water from the melting of glacial ice and/or thermal expansion of sea water due to global warming.
Distance of open water over which the wind blows in the development of waves. The fetch length can restrict wave development so that only relatively small waves occur in narrow bays
Tidal current moving toward the shore, through a tidal inlet, or up a tidal river, estuary, or lagoon.
FLOOD TIDAL DELTA
Sandy shoals formed on a rising (flooding) tide and found on the estuarine or lagoonward side of a tidal inlet.
Seaward sloping portion of the beach within the normal range of tides.
Elongated cloth bags or tubes made out of plastic material that can be stacked or arranged as a form of semi-hard coastal engineering.
Shore protection structures which extend from the beach backshore into the surf zone, perpendicular to the shoreline. A groin is intended to build up an eroded beach by trapping littoral drift or to retard the erosion of a stretch of beach. Often mis-identified as jetties.
Emplacement of treated wood, rocks, concrete, PVC, and/or steel in the form of breakwaters, bulkheads, groins, jetties, seawalls, etc.
HIGH WATER LINE
The line or “wetted bound” separating wet from dry sand and formed by swash uprush on the beach face.
Tropical cyclones with winds 75 mph or greater which spiral inward toward a core of low pressure and rotate in a counterclockwise direction in the Northern Hemisphere.
Local or regional changes in the ground surface elevation, resulting in land subsidence or uplift.
Shore-perpendicular structures built at the sides of an inlet to maintain navigable waterways. They stabilize an inlet by intercepting the longshore transport of sand that would otherwise fill it in or cause the channel to shift position. Jetties are often confused with groins, but are much longer and more substantial structures, usually built in pairs.
Sediment budget of the beach consisting of sources and sinks.
Sand and coarser material moved in the breaker and swash zones by waves and longshore currents along the shoreline.
Area from the landward edge of the coastal upland (usually the dune) to the seaward edge of the nearshore zone.
Current moving along (parallel to) the shore, generated by waves breaking at an angle to the shoreline.
LONGSHORE SEDIMENT TRANSPORT
Sediment transport along the beach (parallel to the shoreline) caused by longshore currents and/or waves approaching obliquely to the shoreline. See
MEAN SEA LEVEL
The average elevation of the sea surface determined from tide gauges.
Small tide range, occurring at the first and third quarters of the moon, when the gravitational pull of
the sun opposes that of the moon.
Underwater area close to the beach, often characterized by sand bars, where sediment is actively being moved by waves and currents. This zone typically extends to a depth of 25 to 30 feet along the Atlantic coast.
Location of longshore sediment transport divergence, where the littoral drift moves away in opposite directions along the coast. Normally areas of higher erosion rates.
Extratropical storms with winds that commonly blow from the northeast, occur during the winter, and can generate large waves and elevated tides, resulting in considerable beach and dune erosion.
OBLIQUE WAVE APPROACH
Waves that approach the beach at an angle (e.g., not straight-on) and generate longshore currents.
Area seaward of the nearshore zone where sediment transport is only initiated by large swell waves or coastal storms.
Wave uprush overtopping the beach and dunes during storms; water and entrained sand that are moved landward of the dune. Also called an overwash surge during major events. See
Dark-brown to black, fibrous material produced by plants which grow in marshes or bogs. When exposed on the beach face, it indicates long-term erosion and landward barrier migration.
Period of time (twice a year) when the moon is at its closest approach to the Earth, and the tidal range is larger than normal.
PERIGEAN SPRING TIDES
Coincidence of perigean and spring tidal conditions resulting in the highest high and the lowest low tides, Nor’easters, such as Ash Wednesday Storm of 1962, become even more damaging when they occur during perigean spring high tides.
Landward movement of the shoreline due to the loss of beach material and/or direct inundation of the land.
The bending of waves by bars and shoals that can cause the concentration of wave energy on a portion of the shoreline, resulting in accelerated beach erosion.
RELATIVE SEA LEVEL RISE
The gradual rise in the water level relative to the land surface due to worldwide changes in the volume of seawater and/or local vertical movement of the land.
Facing of stone, concrete or rubble built to protect an embankment or upland against erosion by wave action or currents.
A longshore feature that may become exposed at low tide; often formed by a bar moving onshore as a form of post-storm beach recovery.
Strong, localized current flowing seaward from the shore; visible as an agitated band of water, which is the return movement of water piled up on the shore by incoming waves. Rip currents are by far the biggest killers of ocean swimmers.
Layer, facing or protective mound of stones randomly placed to prevent erosion of upland areas. Also the name of the stone so used.
Part of the swash action caused by breaking waves.
Sand-filled cloth or geo-textile bags that can be stacked to provide semi-hard coastal protection and are designed to retain sand while allowing water to flow through.
Much larger features than cusps that may migrate along the shoreline. Sand waves can locally cause accelerated erosion known as erosion “hot spots.” Also called shoreline meanders, sand humps, or giant beach cusps.
Vertical drop-off of the dry beach caused by oblique wave attack during stormy conditions; beach scarps can be several inches to over six feet high and disappear by the return of sand onshore during berm accretion. Dunes can also be scarped, forming vertical, wave-cut faces.
Removal of beach material by waves and currents such as at the base of a dune or toe of a shore structure.
Erosion of a dune or berm, usually by oblique wave attack during a storm.
Short period, steep waves generated during a storm that cause beach erosion.
Vertical or near vertical shore-parallel structures designed to prevent upland erosion and storm surge flooding. Seawalls are generally massive concrete structures emplaced along
a considerable stretch of shoreline at urban beaches.
Stretch of sand-starved, eroded beach that is downdrift of a structure such as a jetty or groin and hence in the littoral drift “shadow” of that structure.
A large deposit of sand, generally created by currents near inlets, that can be an obstruction to boats and can cause wave refraction.
Boundary between the land and the sea, which is often defined as the mean high water line for mapping purposes.
Artificial emplacement of sand via beach nourishment or through building and enhancement of sand dunes with sand fencing or vegetative plantings. Sand scraping of the beach to build up sand dunes is another means of “soft stabilization”.
Separation of particles into various size categories by moving water or wind.
Dredged sediment, usually from inlets or lagoons, that can be clean or polluted.
Larger than average tidal range that occurs twice monthly during new and full moon times.
Sudden, temporary rise of sea level primarily due to winds but also caused by atmospheric pressure reduction, resulting in piled-up water against the coast, which is the primary cause of coastal flooding during a storm.
Sheet of water that flows up and down the beach foreshore caused by waves breaking and gravity, respectively. See
Long period waves that tend to widen the dry beach, usually in summer months or during fairweather.
Channel through a barrier beach, which is characterized by swift currents that interrupt the littoral drift of sand.
Amount of water that flows in and out of a semi-enclosed bay or estuary between high and low tide.
Difference in height between high and low tide.
General layman’s term used to describe coastal currents which may “suck” swimmers underwater. A more accurate description is backwash from large breaking waves or seaward-flowing rip currents.
Use of sand bags and/or geotextile tubes that can be stacked or arranged to provide protection to beachfront properties.
Direction opposite that of the predominant movement of the littoral drift. Opposite of downdrift.
Mainland or land behind the dunes; high ground that is above normal tidal flooding.
The movement of water (swash) up the beach face when a wave breaks on the foreshore.
Sand deposited during storms landward of the dune line, sometimes extending to the marshes or into the bay waters.
Vertical difference between a wave’s crest and trough; higher waves are more energetic and can cause rapid beach changes.
Distance between successive wave crests.
Time in seconds between successive wave crests. Swell are long period, while sea are short period waves. | <urn:uuid:6a0b419f-9e56-473d-aea0-4074b05e633d> | {
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Cereal leaf beetle
Editor’s note: This article is from the archives of the MSU Crop Advisory Team Alerts. Check the label of any pesticide referenced to ensure your use is included.
The cereal leaf beetle is a small grain pest that is native to Europe and Asia. In 1962, it was found near Galien, Michigan in Berrien County. It has since spread across the Midwest and to the East Coast, and also found in some wheat-producing states in the western United States. Cereal leaf beetle was initially an important defoliator in wheat and oats, but as a pest it is now relatively uncommon in Michigan. The US government and universities such as MSU released several beneficial parasitoids in the 1960s and 1970s, and these natural enemies effectively control cereal leaf beetle in many parts of the Midwest.
Cereal leaf beetle adults overwinter along edges of field. They have pretty dark-blue wing covers, a distinctive red thorax (a red neck), and red legs. They emerge in the spring and lay eggs on the upper surface of small grain leaves. Larvae are white, fat, and hump-backed with a black head and six small legs. However, larvae won’t appear white in the field because they have a unique defense mechanism to avoid being eaten – they smear a covering of excrement over their body, as in the photograph.
Larvae feed for two to three weeks on grain leaves, scraping the leaf surface. Hot-spots in fields appear white or frosted (similar to heavy alfalfa weevil feeding), but damage to an entire field is rare in Michigan. Infestations may be greater along field edges, and greater in oats than in wheat.
Larvae pupate underground in late-May or early June (although the life cycle seems delayed in 2009). There is only one generation per year. New adults emerge and may feed on small grains or corn briefly, but then they spend the rest of the summer in an inactive state along field edges. Thus the only damage occurs in May and early June as larvae feed.
Early in the season, the threshold is three or more eggs or larvae per plant. On larger plants, the threshold is one or more larvae per flag leaf. I have never seen a field over threshold in Michigan, but cereal leaf beetle is still a problem on the East Coast. Avoid unnecessary insecticide applications to small grains for cereal leaf beetle, aphids, and other insects because broad-spectrum insecticides kill the parasitoids that are responsible for most of the control of cereal leaf beetle in Michigan.
USDA bulletin from 1965 warns farmers
of the then recently-discovered cereal
Close-up of a cereal leaf beetle larva. Note
its shiny, wet covering of fecal pellets. This
covering provides a defense against
predatory insects. (If you were a
ladybug, would you want to eat this?)
Cereal leaf beetle larvae feed by scraping
the leaf surface. Feeding gives leaves a
Typical cereal leaf beetle feeding in
Michigan is light and involves a few plants
or a small hot spot in a field.
Cereal leaf beetle damage. Photo credit: J. Tooker,
Penn State University.
Exceptional cereal leaf beetle damage is rare,
but can occur, particularly in the eastern
United States where parasitoids are not as
well-established. This wheat field in Bucks
County, Pennsylvania is heavily damaged and
has multiple larvae per flag leaf.
Photo credit: J. Tooker, Penn State University.
Dr. DiFonzo’s work is funded in part by MSU‘s AgBioResearch. | <urn:uuid:6c51f9f1-2f52-4ae1-b537-932e95f4ea82> | {
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| Island Gray Foxes are thought to have arrived on three of the six California Channel Islands they now inhabit some 16,000 years ago, either by swimming or by rafting on floating debris. Humans, who first colonized the islands about 6,000 or so years after the foxes arrived, took them to three other islands. Island foxes are only one-half or two-thirds the size of mainland gray foxes. They eat everything from fruits and berries to mice, insects, and occasionally lizards and birds. They face few predators—golden eagles and red-tailed hawks occasionally prey on them—so the animals are less skittish and often active during the day. However, they face special challenges: inbreeding is high, competition with feral cats and exposure to canine diseases are hazards, and development on the islands threatens to limit their habitat and food supply.
Also known as:
Island Fox, Channel Island Fox
716 mm males; 689 mm females
625-716 mm males; 590-787 mm females
2 kg males; 1.9 kg females
1.6-2.5 kg males; 1.5-2.3 kg females
Baird, S.F., 1857 . Mammals. In Reports of explorations and surveys for a railroad route from the Mississippi River to the Pacific Ocean, Beverly Tucker, Printer, Washington, D.C., 8 (part1):143, 757 pp.
Mammal Species of the World
Mammalian Species, American Society of Mammalogists' species account
Click to enlarge. | <urn:uuid:f714f143-b8da-484f-83b9-30da7a36d611> | {
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# How to Answer Multiple Choice Maths Questions
Math is many people’s big nightmare. A lot of people freeze when it comes to math exams, and even multiple choice ones. But fear not, as there are effective ways to combat this, and how to answer multiple choice math questions will put you on a pathway to success. By careful applications of the following methods, you can stroll through multiple choice tests while being confident that your answers are correct.
The first step in any multiple choice math question is to read the question, and to read it well. You really need to understand what it is the examiner is after, translate the questions with your own words. Once you have understood this, you are half way there.
Next, try and use the process of elimination to seek your answer. Often, you don’t even need to make the calculation in order to find the correct answer.
Conside this example:
334 x 412 =
1. 54,559
2. 137,608
3. 22,528
4. 229,766
You only need to perform two very quick calculations to solve this problem. The first one is to multiply the 2 from 412, by the 4 in 334. The answer is of course 8. This is the final digit in the answer, so instantly, you can take answers a and d out of your thoughts. Secondly, multiply 334 x 100. You can do this in your head, and you will get a six figure number. As 412 is greater than 100, you should be able to see that it is impossible for answer c to be correct, because that only has five digits.
Therefore, answer b has to be the correct one. And you have discovered this by not even having to multiply the main question out. This is much easier.
Sometimes, you can look at a question, and are able to estimate the answer before you have even attempted the calculation. This too is very useful, and will speed up the process. Often, one or two of the answers are way out anyway, so you can even use logic, especially if the math is being applied to a real life situation.
Of course, not all questions are going to be that easy, but you can still apply other principles depending on what the question is to perform process of elimination. In such questions, using the process of elimination will give you so much extra time that you can apply to harder questions later in the test.
In more complex questions, you will need to perform the calculation to find the correct solution. For these, you will need a piece of scrap paper to make these calculations. When doing so, it is important to be as neat as you can, and to do every single step, even if you normally don’t. Try to visualize the problem, draw them out, sketch the diagram or something, and write the numbers beside. Often you will find alternative methods which come out with the same solutions too.
This will help you to double check, and hopefully make it easier to spot any errors you may have made during the process. If you have skipped steps or are messy, then you will waste time finding your mistake and perhaps run out of time. You can also work backwards from solution to question to see if your answer is correct.
How to answer multiple choice math questions quickly and effectively can save you so much time and stress, and enable you to be able to give more time and focus to the tougher questions on the test. Use these tips and methods, and you will be successful in your math tests. | crawl-data/CC-MAIN-2019-09/segments/1550249578748.86/warc/CC-MAIN-20190224023850-20190224045850-00031.warc.gz | null |
Table of Contents
- List of illustrations
- Chapter I - WHAT ARE "SPECIES" AND WHAT IS MEANT BY THEIR "ORIGIN"
- Chapter II - THE STRUGGLE FOR EXISTENCE
- Chapter III - THE VARIABILITY OF SPECIES IN A STATE OF NATURE
- Chapter IV - VARIATION OF DOMESTICATED ANIMALS AND CULTIVATED PLANTS
- Chapter V - NATURAL SELECTION BY VARIATION AND SURVIVAL OF THE FITTEST
- Chapter VI - DIFFICULTIES AND OBJECTIONS
- Chapter VII - ON THE INFERTILITY OF CROSSES BETWEEN DISTINCT SPECIES AND THE USUAL STERILITY OF THEIR HYBRID OFFSPRING
- Chapter VIII - THE ORIGIN AND USES OF COLOUR IN ANIMALS
- Chapter IX - WARNING COLOURATION AND MIMICRY
- Chapter X - COLOURS AND ORNAMENTS CHARACTERISTIC OF SEX
- Chapter XI - THE SPECIAL COLOURS OF PLANTS: THEIR ORIGIN AND PURPOSE
- Chapter XII - THE GEOGRAPHICAL DISTRIBUTION OF ORGANISMS
- Chapter XIII - THE GEOLOGICAL EVIDENCES OF EVOLUTION
- Chapter XIV - FUNDAMENTAL PROBLEMS IN RELATION TO VARIATION AND HEREDITY
- Chapter XV - DARWINISM APPLIED TO MAN
- View Copyright
AN EXPOSITION OF THE
THEORY OF NATURAL SELECTION
WITH SOME OF ITS APPLICATIONS
ALFRED RUSSEL WALLACE
LL.D., F.L.S., ETC.
WITH MAP AND ILLUSTRATIONS
MACMILLAN AND CO.
AND NEW YORK
All rights reserved
PRESSWORK BY JOHN WILSON AND SON,
The present work treats the problem of the Origin of Species on the same general lines as were adopted by Darwin; but from the standpoint reached after nearly thirty years of discussion, with an abundance of new facts and the advocacy of many new or old theories.
While not attempting to deal, even in outline, with the vast subject of evolution in general, an endeavour has been made to give such an account of the theory of Natural Selection as may enable any intelligent reader to obtain a clear conception of Darwin's work, and to understand something of the power and range of his great principle.
Darwin wrote for a generation which had not accepted evolution, and which poured contempt on those who upheld the derivation of species from species by any natural law of descent. He did his work so well that "descent with modification" is now universally accepted as the order of nature in the organic world; and the rising generation of naturalists can hardly realise the novelty of this idea, or that their fathers considered it a scientific heresy to be condemned rather than seriously discussed.
The objections now made to Darwin's theory apply, solely, to the particular means by which the change of species has been brought about, not to the fact of that change. The objectors seek to minimise the agency of natural selection and to subordinate it to laws of variation, of use and disuse, of intelligence, and of heredity. These views and objections are urged with much force and more confidence, and for the most part by the modern school of laboratory naturalists, to whom the peculiarities and distinctions of species, as such, their distribution and their affinities, have little interest as compared with the problems of histology and embryology, of physiology and morphology. Their work in these departments is of the greatest interest and of the highest importance, but it is not the kind of work which, by itself, enables one to form a sound on the questions involved in the action of the law of natural selection. These rest mainly on the external and vital relations of species to species in a state of nature—on what has been well termed by Semper the "physiology of organisms," rather than on the anatomy or physiology of organs.
It has always been considered a weakness in Darwin's work that he based his theory, primarily, on the evidence of variation in domesticated animals and cultivated plants. I have endeavoured to secure a firm foundation for the theory in the variations of organisms in a state of nature; and as the exact amount and precise character of these variations is of paramount importance in the numerous problems that arise when we apply the theory to explain the facts of nature, I have endeavoured, by means of a series of diagrams, to exhibit to the eye the actual variations as they are found to exist in a sufficient number of species. By doing this, not only does the reader obtain a better and more precise idea of variation than can be given by any number of tabular statements or cases of extreme individual variation, but we obtain a basis of fact by which to test the statements and objections usually put forth on the subject of specific variability; and it will be found that, throughout the work, I have frequently to appeal to these diagrams and the facts they illustrate, just as Darwin was accustomed to appeal to the facts of variation among dogs and pigeons.
I have also made what appears to me an important change in the arrangement of the subject. Instead of treating first the comparatively difficult and unfamiliar details of variation, I commence with the Struggle for Existence, which is really the fundamental phenomenon on which natural selection depends, while the particular facts which illustrate it are comparatively familiar and very interesting. It has the further advantage that, after discussing variation and the effects of artificial selection, we proceed at once to explain how natural selection acts.
Among the subjects of novelty or interest discussed in this volume, and which have important bearings on the theory of natural selection, are: (1) A proof that all specific characters are (or once have been) either useful in themselves or correlated with useful characters (Chap. VI); (2) a proof that natural selection can, in certain cases, increase the sterility of crosses (Chap. VII); (3) a fuller discussion of the colour relations of animals, with additional facts and arguments on the origin of sexual differences of colour (Chaps. VIII-X); (4) an attempted solution of the difficulty presented by the occurrence of both very simple and very complex modes of securing the cross-fertilisation of plants (Chap. XI); (5) some fresh facts and arguments on the wind-carriage of seeds, and its bearing on the wide dispersal of many arctic and alpine plants (Chap. XII); (6) some new illustrations of the non-heredity of acquired characters, and a proof that the effects of use and disuse, even if inherited, must be overpowered by natural selection (Chap. XIV); and (7) a new argument as to the nature and origin of the moral and intellectual faculties of man (Chap. XV).
Although I maintain, and even enforce, my differences from some of Darwin's views, my whole work tends forcibly to illustrate the overwhelming importance of Natural Selection over all other agencies in the production of new species. I thus take up Darwin's earlier position, from which he somewhat receded in the later editions of his works, on account of criticisms and objections which I have endeavoured to show are unsound. Even in rejecting that phase of sexual selection depending on female choice, I insist on the greater efficacy of natural selection. This is pre-eminently the Darwinian doctrine, and I therefore claim for my book the position of being the advocate of pure Darwinism.
I wish to express my obligation to Mr. Francis Darwin for lending me some of his father's unused notes, and to many other friends for facts or information, which have, I believe, been acknowledged either in the text or footnotes. Mr. James Sime has kindly read over the proofs and given me many useful suggestions; and I have to thank Professor Meldola, Mr. Hemsley, and Mr. E. B. Poulton for valuable notes or corrections in the later chapters in which their special subjects are touched upon.
Godalming, March 1889.
WHAT ARE "SPECIES" AND WHAT IS MEANT BY THEIR "ORIGIN"
Definition of species—Special creation—The early transmutationists—Scientific opinion before Darwin—The problem before Darwin—The change of opinion effected by Darwin—The Darwinian theory—Proposed mode of treatment of the subject
THE STRUGGLE FOR EXISTENCE
Its importance—The struggle among plants—Among animals—Illustrative cases—Succession of trees in forests of Denmark—The struggle for existence on the Pampas—Increase of organisms in a geometrical ratio—Examples of rapid increase of animals—Rapid increase and wide spread of plants—Great fertility not essential to rapid increase—Struggle between closely allied species most severe—The ethical aspect of the struggle for existence
THE VARIABILITY OF SPECIES IN A STATE OF NATURE
Importance of variability—Popular ideas regarding it—Variability of the lower animals—The variability of insects—Variation among lizards– Variation among birds—Diagrams of bird-variation—Number of varying individuals—Variation in the mammalia—Variation in internal organs—Variations in the skull—Variations in the habits of animals—The variability of plants—Species which vary little—Concluding remarks
VARIATION OF DOMESTICATED ANIMALS AND CULTIVATED PLANTS
The facts of variation and artificial selection—Proofs of the generality of variation—Variations of apples and melons—Variations of flowers—Variations of domestic animals—Domestic pigeons—Acclimatisation—Circumstances favourable to selection by man—Conditions favourable to variation—Concluding remarks
NATURAL SELECTION BY VARIATION AND SURVIVAL OF THE FITTEST
Effect of struggle for existence under unchanged conditions—The effect under change of conditions—Divergence of character—In insects—In birds—In mammalia—Divergence leads to a maximum of life in each area—Closely allied species inhabit distinct areas—Adaptation to conditions at various periods of life—The continued existence of low forms of life—Extinction of low types among the higher animals—Circumstances favourable to the origin of new species—Probable origin of the dippers—The importance of isolation—On the advance of organisation by natural selection—Summary of the first five chapters
DIFFICULTIES AND OBJECTIONS
Difficulty as to smallness of variations—As to the right variations occurring when required—The beginnings of important organs—The mammary glands—The eyes of flatfish—Origin of the eye—Useless or non-adaptive characters—Recent extension of the region of utility in plants—The same in animals—Uses of tails—Of the horns of deer—Of the scale-ornamentation of reptiles—Instability of non-adaptive characters—Delbœuf's law—No "specific" character proved to be useless—The swamping effects of intercrossing—Isolation as preventing intercrossing—Gulick on the effects of isolation—Cases in which isolation is ineffective
ON THE INFERTILITY OF CROSSES BETWEEN DISTINCT SPECIES AND THE USUAL STERILITY OF THEIR HYBRID OFFSPRING
Statement of the problem—Extreme susceptibility of the reproductive functions—Reciprocal crosses—Individual differences in respect to cross-fertilisation—Dimorphism and trimorphism among plants—Cases of the fertility of hybrids and of the infertility of mongrels—The effects of close interbreeding—Mr. Huth's objections—Fertile hybrids among animals—Fertility of hybrids among plants—Cases of sterility of mongrels—Parallelism between crossing and change of conditions—Remarks on the facts of hybridity—Sterility due to changed conditions and usually correlated with other characters—Correlation of colour with constitutional peculiarities—The isolation of varieties by selective association—The influence of natural selection upon sterility and fertility—Physiological selection—Summary and concluding remarks
THE ORIGIN AND USES OF COLOUR IN ANIMALS
The Darwinian theory threw new light on organic colour—The problem to be solved—The constancy of animal colour indicates utility—Colour and environment—Arctic animals white—Exceptions prove the rule—Desert, forest, nocturnal, and oceanic animals—General theories of animal colour—Variable protective colouring—Mr. Poulton's experiments—Special or local colour adaptations—Imitation of particular objects—How they have been produced—Special protective colouring of butterflies—Protective resemblance among marine animals—Protection by terrifying enemies—Alluring coloration—The coloration of birds' eggs—Colour as a means of recognition—Summary of the preceding exposition—Influence of locality or of climate on colour—Concluding remarks
WARNING COLORATION AND MIMICRY
The skunk as an example of warning coloration—Warning colours among insects—Butterflies—Caterpillars—Mimicry—How mimicry has been produced—Heliconidæ—Perfection of the imitation—Other cases of mimicry among Lepidoptera—Mimicry among protected groups—Its explanation—Extension of the principle—Mimicry in other orders of insects—Mimicry among the vertebrata—Snakes—The rattlesnake and the cobra—Mimicry among birds—Objections to the theory of mimicry—Concluding remarks on warning colours and mimicry
COLOURS AND ORNAMENTS CHARACTERISTIC OF SEX
Sex colours in the mollusca and crustacea—In insects—In butterflies and moths—Probable causes of these colours—Sexual selection as a supposed cause—Sexual coloration of birds—Cause of dull colours of female birds—Relation of sex colour to nesting habits—Sexual colours of other vertebrates—Sexual selection by the struggles of males—Sexual characters due to natural selection—Decorative plumage of males and its effect on the females—Display of decorative plumage by the males—A theory of animal coloration—The origin of accessory plumes—Development of accessory plumes and their display—The effect of female preference will be neutralised by natural selection—General laws of animal coloration—Concluding remarks
THE SPECIAL COLOURS OF PLANTS: THEIR ORIGIN AND PURPOSE
The general colour relations of plants—Colours of fruits—The meaning of nuts—Edible or attractive fruits—The colours of flowers—Modes of securing cross-fertilisation—The interpretation of the facts—Summary of additional facts bearing on insect fertilisation—Fertilisation of flowers by birds—Self-fertilisation of flowers—Difficulties and contradictions—Intercrossing not necessarily advantageous—Supposed evil results of close interbreeding—How the struggle for existence acts among flowers—Flowers the product of insect agency—Concluding remarks on colour in nature
THE GEOGRAPHICAL DISTRIBUTION OF ORGANISMS
The facts to be explained—The conditions which have determined distribution—The permanence of oceans—Oceanic and continental areas—Madagascar and New Zealand—The teachings of the thousand-fathom line—The distribution of marsupials—The distribution of tapirs—Powers of dispersal as illustrated by insular organisms—Birds and insects at sea—Insects at great altitudes—The dispersal of plants—Dispersal of seeds by the wind—Mineral matter carried by the wind—Objections to the theory of wind-dispersal answered—Explanation of north temperate plants in the southern hemisphere—No proof of glaciation in the tropics—Lower temperature not needed to explain the facts—Concluding remarks
THE GEOLOGICAL EVIDENCES OF EVOLUTION
What we may expect—The number of known species of extinct animals—Causes of the imperfection of the geological record—Geological evidences of evolution—Shells—Crocodiles—The rhinoceros tribe—The pedigree of the horse tribe—Development of deer's horns—Brain development—Local relations of fossil and living animals—Cause of extinction of large animals—Indications of general progress in plants and animals—The progressive development of plants—Possible cause of sudden late appearance of exogens—Geological distribution of insects—Geological succession of vertebrata—Concluding remarks
FUNDAMENTAL PROBLEMS IN RELATION TO VARIATION AND HEREDITY
Fundamental difficulties and objections—Mr. Herbert Spencer's factors of organic evolution—Disuse and effects of withdrawal of natural selection—Supposed effects of disuse among wild animals—Difficulty as to co-adaptation of parts by variation and selection—Direct action of the environment—The American school of evolutionists—Origin of the feet of the ungulates—Supposed action of animal intelligence—Semper on the direct influence of the environment—Professor Geddes's theory of variation in plants—Objections to the theory—On the origin of spines—Variation and selection overpower the effects of use and disuse—Supposed action of the environment in imitating variations—Weismann's theory of heredity—The cause of variation—The non-heredity of acquired characters—The theory of instinct—Concluding remarks
DARWINISM APPLIED TO MAN
General identity of human and animal structure—Rudiments and variations showing relation of man to other mammals—The embryonic development of man and other mammalia—Diseases common to man and the lower animals—The animals most nearly allied to man—The brains of man and apes—External differences of man and apes—Summary of the animal characteristics of man—The geological antiquity of man—The probable birthplace of man—The origin of the moral and intellectual nature of man—The argument from continuity—The origin of the mathematical faculty—The origin of the musical and artistic faculties—Independent proof that these faculties have not been developed by natural selection—The interpretation of the facts—Concluding remarks
LIST OF ILLUSTRATIONS
Portrait of Author
Map showing the 1000-fathom line
|To face page 349|
Diagram of Variations of Lacerta muralis
Diag”am of Variation of Lizards
Diag”am of Variation of wings and tail of Birds
Diag”am of Variation of Dolichonyx oryzivorus
Diag”am of Variation of Agelæus phœniceus
Diag”am of Variation of Cardinalis virginianus
Diag”am of Variation of tarsus and toes
Diag”am of Variation of Birds in Leyden Museum
Diag”am of Variation of Icterus Baltimore
Diag”am of Variation of Agelæus phœniceus
Diag”am of Curves of Variation
Diag”am of Variation of Cardinalis virginianus
Diag”am of Variation of Sciurus carolinensis
Diag”am of Variation of skulls of Wolf
Diag”am of Variation of skulls of Ursus labiatus
Diag”am of Variation of skulls of Sus cristatus
Primula veris (Cowslip). From Darwin's Forms of Flowers
Gazella sœmmerringi (to show recognition marks)
Recognition marks of African Plovers (from Seebohm's Charadriadæ)
Recognition of Œdicnemus vermiculatus and Œ. senegalensis (from Seebohm's Charadriadæ)
Recognition of Cursorius chalcopterus and C. gallicus (from Seebohm's Charadriadæ)
Recognition of Scolopax megala and S. stenura (from Seebohm's Charadriadæ)
Methoa psidii and Leptalis orise
Opthalmis licea and Artaxa simulans (from the Official Narrative of the Voyage of the Challenger)
Wings of Ituna Ilione and Thyridia megisto (from Proceedings of the Entomological Society)
Mygnimia aviculus and Coloborhombus fasciatipennis
Mimicking Insects from the Philippines (from Semper's Animal Life)
Malva sylvestris and M. rotundifolia (from Lubbock's British Wild Flowers in Relation to Insects)
Lythrum salicaria, three forms of (from Lubbock's British Wild Flowers in Relation to Insects)
Orchis pyramidalis (from Darwin's Fertilisation of Orchids)
Humming-bird fertilising Marcgravia nepenthoides
Diagram of mean height of Land and depth of Oceans
Geological development of the Horse tribe (from Huxley's American Addresses)
Diagram illustrating the Geological Distribution of Plants (from Ward's Sketch of Palæobotany)
Transformation of Artemia salina to A. Milhausenii (from Semper's Animal Life)
Branchipus stagnalis and Artemia salina (from Semper's Animal Life)
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# Ch 17: NES Middle Grades Math: Money & Consumer Math
Revisit the fundamentals of money and consumer math when you explore the informative lessons in this chapter. Strengthening your knowledge of these concepts could get you ready for the NES Middle Grades Math examination for teacher certification.
## NES Middle Grades Math - Money and Consumer Math - Chapter Summary
Use this chapter's lessons as a study resource when you're preparing to take the NES Middle Grades Math examination. As you begin your review, you'll find steps and examples related to topics such as number value, sales commissions, interest formulas, and shipping and handling. Item unit price, sales tax and discounts are also covered. Further examining these subjects could help you with:
• Teaching the value of nickels, dimes, quarters and pennies
• Explaining how to identify a missing coin
• Adding, subtracting and dividing money amounts
• Solving word problems that involve multiplying money by decimals and whole numbers
• Describing the process of making change
• Understanding sales commissions and sales mark-up
• Calculating discounts and taxes as well as tips and shipping and handling
• Outlining the steps for compounding interest formulas and solving interest problems
• Describing item unit price
The lessons are fairly short, self-paced, informational and fun to explore. They include written transcripts, pop quizzes and worksheets. Experienced instructors present the above concepts on money and consumer math. Prepare to pass the NES Middle Grades Math examination by going over the information and building your expertise in each topic.
### NES Middle Grades Math - Money and Consumer Math Objectives
There are four content domains on the NES Middle Grades Math examination. Number Sense and Operations, Algebra and Functions, Measurement and Geometry and Statistics, Probability and Discrete Mathematics are each respectively worth 17%, 33%, 25% and 25% of the assessment score. Display what you picked up during your review of this chapter as well as your ability to teach other math subjects during this examination, which consists of 150 multiple-choice questions. The assessment is computer-based, and it must be finished within a four-hour, 15-minute time frame.
14 Lessons in Chapter 17: NES Middle Grades Math: Money & Consumer Math
Test your knowledge with a 30-question chapter practice test
Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken
### Earning College Credit
Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level. | crawl-data/CC-MAIN-2019-39/segments/1568514573264.27/warc/CC-MAIN-20190918085827-20190918111827-00172.warc.gz | null |
The term "learning styles" refers to the way people take in and process information. Learning styles Inventories are not personality tests. Their purpose is to show people how they see the world. And we all see the world differently.
According to Anthony Gregorc, creator of the Gregorc Learning Styles Inventory, there are four "mind qualities". People fall, on a continuum, between being concrete (using their senses, being hands-on, enjoying the physical world) or being abstract (prefer doing things in their heads). He identifies a second continuum as well. Sequential people like doing activities step-by-step. They believe there's a place for everything, and everything should be in its place. On the other extreme, random people like change. They like to move things around. They have a high tolerance for ambiguity.
In his Inventory, Gregorc combines these two continuums to create four possible learning styles:
Each of the four types has natural abilities, characteristics that define them as learners and characteristics that define them as teachers.
Knowing their learning styles can help students better understand each other. If students are not communicating well with each other, it could be that they have very different learning styles.
Once students have identified their learning styles and recognize that people process information differently, they may become more tolerant of these differences. For example, when they're in a group situation and they're struggling with someone who has a different learning style — especially one that's quite different than theirs — they're going to need to "bend and stretch" in order for the outcome to be successful. If this "bending and stretching" doesn't occur, they could end up being upset with the interaction.
For some specific suggestions on how to incorporate learning styles into your classes, click on the "Words of Wisdom" link.
- Dunn, R. & Dunn, K. (1978). Teaching Students Through Their Individual Learning Styles. Reston, VA: Reston Publishing Company, Inc.
- Gregorc, A. (1985). Inside Styles: Beyond the Basics. Columbia, CT: Gregorc Associates.
- Honey, P. & Mumbord, A. (1982). Manual of Learning Styles. London: P. Honey
- Peng, Lim Lum. Learning Styles. Oct (2002). Vol. 5 No. 7. Applying Learning Styles in Instructional Strategies.
No Links are available at this time.
Words of Wisdom
As instructors, it's helpful to know that your students have different learning styles. For instance, when you're teaching:
- Some students will always raise their hands. Others will need more time to reflect before they answer.
- In order to get abstract random students to answer questions, it helps if you ask them "feeling" questions. (e.g., "How do you feel about this?")
- Some students will work well in groups, others will hate working in groups.
- Some students will follow you around and drive you crazy wanting to know "is this right?" They need external validation. Other students never check with you, and they should!
- Some students like authoritarian personalities — others bristle.
- Some students don't mind showing their work to others, others are much more private.
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Art is a natural component of literacy activities; encourage children to illustrate their stories, as well as to make up stories for their illustrations! Through different art media, the activities in this section encourage the development of children's language. Children explore their feelings, ideas, even their capacity for role-playing --------- all through art.
This Is Me - ages 4 and up
Materials: markers, crayons, 1 unbreakable hand mirror, white drawing paper (heavyweight), magazines, glue, scissors
Invite children to make a collage about themselves on the white paper. Heavyweight paper will work best, as children will be drawing on the other side. They may choose to cut out magazine pictures of their favorite foods, toys or animals. Children can also use crayons or markers to represent their favorite colors or to draw pictures. Some children may want to label the items in the collage, using phrases such as "favorite food," "favorite color" or "my dog." Invite children to write or dictate their labels. When children finish--allow collages to dry. Later, ask children to illustrate the other side of their papers with a self-portrait. Set out an unbreakable mirror along with crayons and markers in different colors. Suggest that children look carefully in the mirrors and really notice the shape and color of their hair, eyes, mouth and so on. When children are finished allow them to share what they have done. Encourage them to explain what the items in their collages represent. Ask children where they would like their pictures to be hung.
Mother Goose Puppets - ages 5 and up
Materials - a few mittens or socks, poster-board, plastic-foam balls, scissors, stapler, collage materials(yarn, fabric scraps, paper scraps, buttons, sequins, and feathers), markers, crayons, paper plates, Popsicle sticks, glue, tape
Recite several nursery rhymes together, and ask children to choose a nursery rhyme character they would like to make into a puppet. For stick puppets, children can glue a Popsicle stick to a poster-board shape, or to a paper plate. To make a ball puppet, help them poke a hole big enough for their finger in a plastic-foam ball. Or children can use a sock or mitten to make their puppets. Allow children to create a face, hair and if they like clothes and props. Encourage them to think about what their character might look like, and help them problem-solve to represent those features with art materials. When children finish, they can use their puppets to recite their nursery rhyme.
Tips - Model language by describing colors, shapes and the process you see in children's work. Your comments will help prompt children to express their own ideas. | <urn:uuid:60ea2cef-4089-46ab-91fa-960ebd5b7f74> | {
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The Battle That Inspired The Marathon
The Battle of Marathon was a pivotal battle in the Graeco-Persian Wars. This battle took place in August or September 490 BC. During the battle, the Athenians and their Plataean allies successfully repelled the invading Persians, despite being outnumbered. The victory of the Athenians at the Battle of Marathon was significant as it brought an end to the first Persian invasion of Greece.
Additionally, the Persians did not return to Greece until a decade later. It is also thanks to this ancient battle that we have the marathon today. This sporting event is a modern invention that was inspired by an amazing feat performed by one of the Athenian soldiers who participated in the battle.
Preamble to the Battle of Marathon
The Graeco-Persian Wars broke out in 492 BC and the first Persian invasion of Greece was launched that year by Darius I. A year before that, the Ionian Revolt , which began in 499 BC, was finally crushed by the Persians. This was a revolt by the Greek colonies in Asia Minor that were under Persian rule .
The Greek rebels sought aid from mainland Greece and Athens, and Eretria responded by sending them a small fleet of ships. Thus, the involvement of these two city states in the Ionian Revolt was used by the Persians to justify their invasion of Greece once the revolt was put down. According to Herodotus, “These places [Athens and Eretria] were the ostensible targets of the expedition, but in fact the Persians intended to conquer as many Greek towns and cities as they could”.
The Persian expedition against the Greeks involved a combined land and sea force and overall command was given to Mardonius, the son of Gobryas, “a young man who had recently married Darius’ daughter Artozostra”. Using their fleet, the Persians conquered the island of Thasos, while the land army subdued the Macedonians. After this, however, the Persians experienced some setbacks.
Persian warriors, possibly ‘Immortals’, a frieze in Darius's palace at Susa. (Jastrow / Public Domain )
From Thasos, the Persian fleet sailed westwards to the mainland where it hugged the coast and sailed up to Acanthus. As the ships set out to round the headland at Athos they were caught in a storm and many were destroyed. Herodotus reported that about 300 ships were destroyed and over 20,000 men lost their lives.
The ancient historian even spares a few lines to report the ways in which the shipwrecked men lost their lives, “The men died in various ways: some were seized by the sharks that infest the sea around Mont Athos , others were dashed onto the rocks, others drowned because they did not know how to swim, and others died of cold”. The Persian land army did not fare so well either.
According to Herodotus, while the Persians were encamped in Macedonia the Brygi, a Thracian tribe, launched a night attack against them. Many men were killed and Mardonius himself was wounded. The Persians responded by subduing the Brygi. Once this was accomplished, however, Mardonius pulled his forces back to Asia thus bringing the Persian expedition of 492 BC to an end.
In the following year, Darius sent heralds throughout Greece with orders to “demand earth and water for the king”. This was meant to see if the Greeks would submit to the Persians or resist them. At the same time, instructions were sent to the coastal states which were already part of the Achaemenid Empire to build long ships and transport ships for horses, so as to prepare for another invasion.
Many of the Greeks submitted to Darius’ demands, including one of Athens’ rivals, Aegina. The Athenians accused the Aeginetans of being traitors of Greece and used it as a pretext to start a war with them. While this war was being fought, Darius’ forces were ready.
- What Went Wrong? The Real Story of the Battle of Thermopylae
- The Magnificent Helmet of Greek Warrior Miltiades
- Where Did It Begin? Gathering Place for the Battle of Salamis is Found
Answer of the Athenian Aristides to the ambassadors of Mardonius: "As long as the sun holds to its present course, we shall never come to terms with Xerxes”. ( पाटलिपुत्र / Public Domain )
Mardonius was relieved of his command and two new commanders, “a Mede called Datis and Artaphrenes, the son of Artaphrenes, who was Darius’ nephew” were appointed. Their mission, according to Herodotus, was to “reduce Athens and Eretria to slavery and to bring the captives before him [Darius]”.
Unlike the previous expedition, the land and sea forces were not separated. Instead, it was an amphibious operation and the land forces boarded the ships at Cilicia. Herodotus reported that a fleet of 600 triremes was sent against the Greeks.
This fleet first sailed to the island of Samos, off the Ionian coast, and thence across the Aegean Sea by sailing from island to island. This was different from the route taken by Mardonius whose fleet sailed along the Ionian coast to the Hellespont, so as to join up with the land army at Thrace.
The first place that Datis and Artaphrenes planned to attack was the island of Naxos. Instead of staying to fight the islanders fled into the hills. The Persians razed the sanctuaries and the town to the ground and enslaved anyone they caught. The next stop for the Persians was the neighboring island of Delos.
The Delians, having heard of the Persian approach, fled to another island, Tenos. Herodotus reported that Datis had no intention of destroying the island. Instead, after finding out where the Delians were hiding the commander sent a herald to inform them that he would harm neither the island nor its inhabitants and urged them to return to their homes. Before leaving the island, Datis “heaped up 300 talents of frankincense on the altar and burnt it as an offering. Datis then sailed away with his army”.
The next target of the Persian invaders was Eretria. When the Eretrians received news of the Persian fleet they requested for assistance from Athens and received it. Unfortunately, the Eretrians were divided into two factions, those who wanted to abandon the city, and to flee to the Euboean hills on the one hand, and those who wanted to surrender the city to the Persians on the other.
One of the Eretrian leaders, Aeschines the son of Nothon, saw that there was no way to save the city, explained the situation to the Athenians who arrived and begged them to leave. The Athenians heeded Aeschines’ advice and left Eretria, thus saving themselves. In the meantime, the Eretrians resolved not to abandon their city and prepared to be besieged.
After several days of intense fighting, the city fell to the Persians through treachery. The city was plundered, burnt to the ground, and the population reduced to slavery. A few days after the destruction of Eretria, the Persians left for Attica, and were confident that they would be able to deal with the Athenians easily too.
The Persians Head for Marathon
Following the advice of Hippias, the son of Pisistratus (the former tyrant of Athens), the Persians chose to land at Marathon, as it had “terrain that was admirably suited to cavalry maneuvers” and was close to Eretria. Herodotus’ claim of the former, however, has been contradicted by a scholium (a marginal comment made by an ancient commentator) found in Plato’s Menexenus, which states that the terrain of Marathon was “rugged, unsuitable for horses, full of mud, swamps and lakes”.
A picture reconstructing the beached Persian ships at Marathon before the battle. (Dorieo / Public Domain )
Instead, it is speculated that the site, being a relatively poorer region of Attica, was more sympathetic towards Hippias, hence the former tyrant’s choice for the Persian landing. When they heard of the Persians’ arrival the Athenians marched to Marathon as well.
Before leaving for Marathon, however, the Athenian commanders dispatched a professional courier by the name of Philippides to Sparta in order to request their aid during the upcoming battle with the Persians. Although the Spartans agreed to provide assistance to the Athenians, they “could not do so straight away, because there was a law they were reluctant to break. It was the ninth day of the month, and they said that they would not send an army into the field then or until the moon was full”.
From this passage, scholars were able to determine the date of the Battle of Marathon, i.e. on the 12th either of August or September 490 BC in the Julian calendar. In any case, the Spartans did not make it to the Battle of Marathon and the only Greeks who came to Athens’ aid were the Plataeans.
Meanwhile, the Athenian commanders were divided as to how to proceed. On the one hand, there were those who wished to avoid fighting, arguing that they were outnumbered by the Persians. On the other, there were those in favor of engaging the enemy. Both sides were supported by five commanders and it was up to the War Archon, Callimachus of Aphidnae, to cast the deciding vote.
In Herodotus’ account, a rousing speech was made, at the mouth of Miltiades, by one of the commanders who favored engaging the Persians, which won Callimachus over. The Athenians, however, did not engage the Persians immediately.
Herodotus reported that “when each of the commanders who had inclined towards engaging the enemy held the presidency of the board of commanders for the day, he stood down in favor of Miltiades. While accepting the post each time, Miltiades waited until the presidency was properly his before giving battle.” Although not reported by Herodotus, other ancient historians wrote that on the day of battle, the Athenians learned that the Persian cavalry was away and therefore seized the opportunity to attack the invaders.
The Day of the Battle of Marathon
Herodotus reported that the right wing of the army was under the command of the War Archon, which was in accordance with Athenian customs at that time, while the Plataeans were placed on the left. Between the two, the Athenian tribes were arranged one after another in their usual order. Herodotus also tells his readers that the Athenian army was extended over the same length as the Persian army.
Although the center was only a few ranks deep and therefore the weakest, the two wings were at full strength. After the battle lines were drawn and favorable omens obtained from the sacrifices, the Athenians attacked by charging the Persians at a run. This was a remarkable feat and Herodotus asserted that “They were the first Greeks known to charge enemy forces at a run, and the first to endure the sight of Persian dress and the men wearing it”.
Initial disposition of forces at Battle of Marathon. (Master Thief Garrett~commonswiki / GNU FDL )
During the battle, the Athenian center was broken by the Persians, who pursued them inland. The left and right wings of the Athenians, however, were victorious in their battle against their respective opponents. Therefore, they combined into a single fighting unit and attacked the Persians who had broken through the center.
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Map showing the armies' main movements during the Battle of Marathon. (Warden / GNU FDL )
The Persians were defeated and retreated back to their ships anchored along the coast. The Athenians gave chase and killed any Persian they were able to overtake. In addition, seven Persian ships were captured by the Athenians. Herodotus does not give the strength of the Athenian and Persian armies that fought at the Battle of Marathon, but reports that 6,400 Persian soldiers were killed, while the Athenians lost 192 men.
The Soros, a burial mound to the fallen of the Battle of Marathon. (Jacopo Werther / CC BY-SA 2.0 )
Although the Athenians won the Battle of Marathon, the Persian army had not been completely defeated and their fleet was still a threat to Athens. In fact, following the defeat at Marathon the Persian fleet began to sail around Cape Sounion, hoping to arrive at Athens before the army returned.
According to Herodotus, “The Athenians raced back as quickly as possible to defend the city, which they managed to reach before the Persians got there…. The invaders hove to off Phalerum, which was Athens’ naval harbor in those days, but then after riding at anchor there for a while they sailed back to Asia.” The Persians didn’t returned to Greece until 10 years later.
The First Marathon Runner
Finally, a popular legend that has survived till this day is that it was a messenger, Pheidippides, who ran from Marathon back to Athens to announce the victory over the Persians. Right after he delivered his message, Pheidippides died of exhaustion. Although the story is commonly attributed to Herodotus, it is not actually found in his writings.
Painting of Pheidippides as he gave word of the Greek victory over Persia at the Battle of Marathon to the people of Athens. (Themadchopper / Public Domain )
Herodotus does report that a herald by the name of Philippides was sent by the Athenians to seek aid from the Spartans and the two stories might have been conflated. In any case, the story inspired the creation of the marathon. In 1896, the first modern Olympics was held in Athens and the founder of the International Olympic Committee, Pierre de Coubertin, organized the first official marathon.
This race started from the Marathon Bridge to the Olympic Stadium in Athens, a distance of about 24.85 miles (40 kilometers) and was won by Spiridon Louis, a Greek postal worker, who finished the race in 2 hours 58 minutes. During the 1908 Olympics, which was held in London, the marathon began at the lawn of Windsor Castle and finished in front of the royal box at White City Stadium. The total distance between the two points was 26.2 miles (42.195 kilometers). Although this would become the standard distance for future marathons it was only formally adopted in 1921.
Top image: Greek troops rushing forward at the Battle of Marathon. Source: पाटलिपुत्र / Public Domain .
By Wu Mingren
Clark, M. 2003. The Real Story Of The Marathon . [Online] Available at: https://www.runnersworld.com/uk/events/a760877/the-real-story-of-the-mar...
Current World Archaeology. 2010. Greece: The battle of Marathon . [Online] Available at: https://www.world-archaeology.com/features/greece-the-battle-of-marathon/
EyeWitness to History. 2006. The Battle of Marathon, 490 BC . [Online] Available at: http://www.eyewitnesstohistory.com/marathon.htm
Herodotus, The Histories - Waterfield, R. (trans.). 1998. Herodotus’ The Histories . Oxford University Press.
History.com Editors. 2009. Battle of Marathon . [Online] Available at: https://www.history.com/topics/ancient-history/battle-of-marathon
Lendering, J. 2019. Marathon (490 BCE) . [Online] Available at: https://www.livius.org/articles/battle/marathon-490-bce/
New World Encyclopedia. 2019. Battle of Marathon . [Online] Available at: https://www.newworldencyclopedia.org/entry/Battle_of_Marathon
Nix, E. 2014. Why is a marathon 26.2 miles? . [Online] Available at: https://www.history.com/news/why-is-a-marathon-26-2-miles
Peterson, D. 2010. Why Are Marathons 26.2 Miles Long? . [Online] Available at: https://www.livescience.com/11011-marathons-26-2-miles-long.html
Rickard, J. 2015. Battle of Marathon, 12 September 490 BC . [Online] Available at: http://www.historyofwar.org/articles/battles_marathon.html
The Editors of Encyclopaedia Britannica. 2018. Battle of Marathon . [Online] Available at: https://www.britannica.com/event/Battle-of-Marathon
The Editors of Encyclopaedia Britannica. 2019. Greco-Persian Wars . [Online] Available at: https://www.britannica.com/event/Greco-Persian-Wars
The Editors of Encyclopaedia Britannica. 2019. Marathon. [Online] Available at: https://www.britannica.com/sports/marathon-race
www.nationalgeographic.org. 2019. Sep 12, 490 BCE: Battle of Marathon . [Online] Available at: https://www.nationalgeographic.org/thisday/sep12/battle-marathon/ | <urn:uuid:105ae7f0-724a-4952-a083-b2b8cf751b9e> | {
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The game's true origins, however, go unmentioned in the official literature. Three decades before Darrow's patent, in 1903, a Maryland actress named Lizzie Magie created a proto-Monopoly as a tool for teaching the philosophy of Henry George, a nineteenth-century writer who had popularized the notion that no single person could claim to "own" land. In his book Progress and Poverty (1879), George called private land ownership an "erroneous and destructive principle" and argued that land should be held in common, with members of society acting collectively as "the general landlord."
Magie called her invention The Landlord's Game, and when it was released in 1906 it looked remarkably similar to what we know today as Monopoly.
But it was Monopoly with a significant twist:
The game's most expensive properties to buy, and those most remunerative to own, were New York City's Broadway, Fifth Avenue, and Wall Street. In place of Monopoly's "Go!" was a box marked "Labor Upon Mother Earth Produces Wages." The Landlord Game's chief entertainment was the same as in Monopoly: competitors were to be saddled with debt and ultimately reduced to financial ruin, and only one person, the supermonopolist, would stand tall in the end. The players could, however, vote to do something not officially allowed in Monopoly: cooperate. Under this alternative rule set, they would pay land rent not to a property's title holder but into a common pot-the rent effectively socialized so that, as Magie later wrote, "Prosperity is achieved."
With a lengthy section on the philosophy underpinning the original version of the game, this is more interesting than an article about a board game has the right to be. | <urn:uuid:67c60bb6-785d-416b-bba5-7cbc58ac5ddb> | {
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Learn to Read and Spell with Miss Letterly is an informational book that teaches reading and spelling concepts in a sequential format while set in a warm and friendly fictional environment. This book steps well beyond the letters and sounds of the alphabet. Miss Letterly, a caring kindergarten teacher, helps her twenty-six students (the letters of the alphabet) learn how to work together to make words. Through her daily playground adventures, Miss Letterly explains consonants, vowels, digraphs, consonant blends, syllable types, odd spelling patterns, and how to blend syllables into two-syllable words. Written and illustrated in a simple manner, this book can be enjoyed at home or used as a resource in professional educational environments.
- 9″x12″ Spiral Bound: 48 pages full color. | <urn:uuid:496f8d03-682b-4a59-8dc7-d2d77a8abb93> | {
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Discovered in 1858 by famed English entomologist, Alfred Russel Wallace, the Wallace giant bee, scientifically known as Megachile pluto, lives up to its reputation as the largest bee in the world. It boasts a wingspan of two-and-a-half inches and a length of an inch-and-a-half, about the size of a large egg.
After its initial finding by Wallace, the bee proved so elusive that it was declared extinct until 1981 when American researcher Adam Catton Messer observed several males and females on three different islands located in the Moluccas, otherwise known as Malukus, an archipelago in eastern Indonesia.
Now, 38 years later, a team of researchers from the Search for Lost Species Program at Global Wildlife Conservation (GWC) has reported finding a female Wallace giant bee. And, believe it or not, they have the photos to prove it.
A Bee of a Tale
GWC researchers scoured the Bacan Islands in the Moluccas- one of the last-known areas of habitat for the enormous bee. The research team tasked with finding the “holy grail” of bees included entomologist, Eli Wyman, ornithologist, Glenn Chilton, behavioral ecologist, Simon Robson, and natural history photographer, Clay Bolt. Their successful find has not only proven an internet sensation but has sparked hopes of preserving what remains of this remarkable species.
The bee itself is about the size of a human thumb. Females of the species sport massive stag-beetle-like mandibles. These make the flying giants look like the work of nightmares. Despite their vicious appearance, the arthropods serve a wholly, peaceful purpose. Females use their jaws to scratch resin off trees, which they then use to build their nests.
Finding an Elusive Creature
How did the team find such a shy creature? They started by pouring over Messer’s notes from his encounter with the large insect. According to Messer, the bees liked to build their nests in the lowland forest inside the homes of tree-dwelling termites. Using satellite imagery, the GWC team identified the best areas to search and familiarized themselves with the island’s terrain.
But once they arrived, they only had five days to find the creature. While interviewing locals, they felt disheartened to learn that no one had ever heard of, let alone seen, the behemoth they were looking for. The insect seemed to have virtually disappeared.
Scoping Out Termite Nests
Disappointed by the lack of local eyewitnesses, the team started scoping out termite nests. They spent hours observing what entered and left each burrow. In a few instances, the team thought they’d found a specimen, only to realize a wasp had duped them. The work proved hot, muggy, and grueling, but they weren’t about to give up.
Finally, on the last day of their five-day excursion, they spotted a termite nest with serious giant bee potential. Suspended eight feet above the ground, the only way to access the termite home was by climbing, and that’s exactly what Bolt did. What he saw inside proved both humbling and breathtaking — the first sighting of a Wallace giant bee in nearly forty years.
The Discovery of a Lifetime
Just four years prior, the GWC team had dreamed of seeing a giant bee in the wild, and now they couldn’t believe their eyes. Capturing photos to confirm their discovery proved of the highest order; they patiently waited for the shy bee to emerge from her termite nest.
After a couple of hours, she poked her head out and proved otherwise camera shy. The researchers finally resorted to tickling her with a piece of grass in the hopes of getting her to emerge. Soon enough she crawled into a large tube that the team provided. The researchers captured photos before and during her flight as she was released from the tube.
A Future for the Wallace Giant Bee
The researchers hope that by sharing the news of this discovery, they’ll raise public awareness and support for the plight of the Wallace giant bee. They also hope that the rediscovery will spark future research. If scientists can learn more about the life history of the bee, perhaps they can better protect it from extinction.
Deforestation continues to ramp up in Indonesia making it more important than ever to educate the public of the high stakes involved in preserving this incredibly rare species. What’s more, the international trade of this species remains unrestricted– another factor impacting the bee’s fight for survival.
If the Wallace giant bee can become an iconic symbol of the conservation movement, perhaps they’ll stand a fighting chance. And, perhaps, more than a handful of researchers will have the opportunity to observe them in the wild.
“It was absolutely breathtaking to see this ‘flying bulldog’ of an insect that we weren’t sure existed anymore, to have real proof right there in front of us in the wild,” said Clay Bolt.
By Engrid Barnett, contributor for Ripleys.com | <urn:uuid:d03babc9-afb3-4e9b-9277-b1dcc772d1a1> | {
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Learn about Radon in the home and workplace, the risks to health, how to protect new buildings and reduce radon in existing buildings, and where to get help.
What is radon?
Radon is a colourless, odourless radioactive gas. It is formed by the radioactive decay of the small amounts of uranium that occur naturally in all rocks and soils.
Why is it a risk to our health?
Radioactive elements decay and emit radiation. Any exposure to radiation is thought to be a risk to health - radiation is a form of energy and can cause damage in living tissues increasing the risk of cancer.
Where is radon found?
Radon is everywhere; formed from the uranium in all rocks and soils. Outdoors everywhere and indoors in many areas the radon levels are low and the risk to health is small. Public Health England have prepared maps indicating the chance of a building having a high radon level. These maps cover England, Wales, Scotland and Northern Ireland. But even in the areas with the highest chance of a building having a high radon level not all buildings will have high levels. The maps can be viewed at www.UKradon.org.
What is a low level?
The amount of radon is measured in becquerels per cubic metre of air (Bq m-3). The average level in UK homes is 20 Bq m-3. For levels below 100 Bq m-3, your individual risk remains relatively low and not a cause for concern, However, the risk increases as the radon level increases.
How does radon enter a building?
The floors and walls of dwellings contain many small cracks and gaps formed during and after construction. Radon from the ground is drawn into the building through these cracks and gaps because the atmospheric pressure inside the building is usually slightly lower than the pressure in the underlying soil. This small pressure difference is caused by the stack (or chimney) effect of heat in the building and by the effects of wind.
What is radioactivity and radiation?
Radioactivity is where unstable elements, such as naturally occurring uranium, thorium and radon, break down; energy is released and different elements formed. The new elements may also be unstable so the process is repeated until a stable element is formed. The energy given off is called radiation and can be alpha or beta particles or gamma rays. Alpha particles are more harmful than beta particles or gamma rays. This is because alpha particles contain more energy and are absorbed over a smaller area.
What is our exposure to radiation?
We are all exposed to radiation from natural and man-made sources. Just 20 Bq m-3 (the average radon level in UK homes) gives us half our exposure to radiation from all sources. Higher radon levels give higher exposures: that is why it is important to find out the levels in your home and in your school or workplace.
Why is radiation harmful to us?
The radioactive elements formed by the decay of radon can be inhaled and enter our lungs. Inside the lungs, these elements continue to decay and emit radiation, most importantly alpha particles. These are absorbed by the nearby lung tissues and cause localised damage. This damage can lead to lung cancer.
What evidence is there that radon is harmful?
Studies in many countries have shown that increased exposure to radon increases your risk of lung cancer.
What is the Radon Action level?
Public Health England recommends that radon levels should be reduced in homes where the average is more than 200 becquerels per metre cubed (200 Bq m-3). This recommendation has been endorsed by the Government. This Action Level refers to the annual average concentration in a home, so radon measurements are carried out with two detectors (in a bedroom and living room) over three months, to average out short-term fluctuations.
What is the Target Level?
The Target Level of 100 Bq m-3 is the ideal outcome for remediation works in existing buildings and protective measures in new buildings. If the result of a radon assessment is between the Target and Action Levels, action to reduce the level should be seriously considered, especially if there is a smoker or ex-smoker in the home. top
How can you protect against radon?
A range of practical and cost effective solutions have been developed by BRE to help reduce radon levels in existing buildings and to prevent radon entry into new buildings. | <urn:uuid:e6491825-05af-4e5f-ac80-3ccb4d92afba> | {
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One of the main monotheistic religions, Islam was founded approximately 14 centuries ago (610 AD) in the Arabian town of Mecca by the Prophet Mohammed. In contrast to the widespread polytheistic beliefs existent at the time, Mohammed preached belief in one God, a day of Judgement and an afterlife composed of both heaven and hell. The religion also teaches, among other principles, charity and kindness for the poor and needy, personal redemption, equal rights for men and women and the right of divorce for women.
The Beliefs of Islam
The central beliefs of Islam are expressed in the Five Pillars of Islam:
Creed (Shahadah) - 'La Ilaha Illallah Muhammadur Rasoolullah' - 'There is no God but Allah, and Mohammed is the Messenger of Allah'. Central to Islam, it is said that anyone who sincerely believes this is a Muslim.
Prayer (Salat) - Muslims pray five times a day - just after dawn (but before sunrise), just after noon, in the afternoon, just after sunset, and at night-time. Prayers are obligatory and serve to maintain a lasting connection to Allah and a person's consciousness of God, Taqwa.
Fasting (Ramadan) - This takes place in the ninth month of the Islamic calendar, just before the first festival of Eid. Apart from being allowed to eat from dusk until dawn, nothing is taken into the body during the 30 days of the month - there is no smoking, medicine or sex. Every day, the fast is broken just after the Maghrib prayer, just after sunset. Ill people, children, the elderly, pregnant women or people who would suffer serious hardship due to fasting are exempt from the fast. The purpose of fasting is to remember the poor in society, to instil a sense of devotion and self-discipline and to remove distractions to allow one to focus more clearly on one's actions, and on God.
Charity (Zakat1) - A certain portion of the income of every Muslim is given to help the poor and needy. The money is given directly; through a mosque or charity or an equivalent amount of voluntary work is done. It usually benefits the homeless, the poorest families, the hospitals, or anyone else in great need. Although different schools of law provide differing definitions, there are common rules to which all Muslims adhere.
Pilgrimage (Hajj) - At least once in a Muslim's life, if possible, a Muslim goes on a sacred pilgrimage to Mecca - the Hajj. This lasts for several days and is thought to wash away all the sins in the person's life.
Further Information About Islam
The universal Islamic greeting is: As-salaamu alaikum - 'May peace be with you'. 'Islam' itself means 'peace' or 'submission', reflecting its ego-dissolving nature. Modesty is a characteristic of Islam, as each person realises that they are completely dependent upon Allah.
The religion is monotheistic and, as such, doesn't believe in multiple gods or the division of one God. People are born innocent and then make mistakes during their lives that might lead them to evil acts. A person is thus responsible for his or her own actions, but is capable of personal redemption - forgiveness for sins committed, if sincerely prayed for, is believed to be granted. Muslims believe in the prophets of Christianity and Judaism, angels and the devil (although he is known as Iblis). Muslims believe religion pervades and defines every aspect of life and, as such, see the goal of governments and social institutions as to provide a just society within which a person may find peace and fulfilment and experience the freedom to pursue a spiritual life.
The Holy Book of Islam is known as the Qur'an, and is seen as the sacred and eternal word of God. Allah, as God is called in Arabic, is believed to be the same God as in Judaism and Christianity. He is eternal, absolute, omnipotent, omniscient and the Creator and Destroyer of the universe and all the worlds.
Muslims believe that Jesus was the Messiah, and that He, like Moses, was sent to guide humanity and bring humanity closer to God. They do not, however, believe that either Jesus or Moses were God incarnate. Islam accepts that those outside of their faith may also go to heaven if they are good, kind and believe in God.
About 80% of Muslims are non-Arabs and live outside the Arabian world. Islam does not believe in races, or 'chosen people' - it is open to all. Indeed, most of the converts to Islam are from the West - mainly Europe and America - the majority being educated women aged 16 to 35.
The word Jihad is often translated in the West as 'holy war' but in fact means only 'struggle': it is often applied to the study of mathematics, history and the Qur'an, not just to resisting invasions of one's homeland. Muslims have their own Islamic calendar which is based upon the Moon (like the Chinese and Jewish calendars) rather than the Sun. Its starting date is that of the Hijra (622 AD) and each year is 11 days shorter than the Gregorian calendar, meaning that Muslim dates move by 11 days each year. Ramadan, therefore, starts and ends on different days.
Islam has its own economic system, different to that of the rest of the world. With the notion of welfare, interest on loans is strictly forbidden. Investment, however, is both allowed and encouraged.
Intoxication is forbidden in Islam, and so drugs (including cigarettes) and alcohol are not allowed. The taking of poison and suicide are also forbidden. Like Jews, Muslims have dietary laws. Food must be Halal, which means 'pure' or 'allowed'. Most food is allowed, but there are special rules for animals and meat - animals must be free-range, have lived a good life (free from pain and disease), be killed quickly and painlessly and a prayer said before it is killed as a reminder that this has only been allowed by God's permission. Blood must be drained from the animal before it is fit to eat to prevent it becoming carrion (decomposing meat). Muslims don't eat carnivores or diseased animals, nor do they eat battery animals. Fish are allowed if they are caught in the open water; a prayer is said for them once they are caught. Muslims do not hunt for sport - this is Haram in Islam, and is utterly forbidden. Muslims regard Kosher food as Halal.
Muslim scholars were among the first to use and to spread the base ten number system, now commonly used in mathematics. With this system, it was possible to develop algebra, named after the Muslim book of maths, Al-Jibr, and new algorithms, named after the Muslim scholar Al-Khwarizmi who first defined them and set out their systematic use. Islam encourages enquiry into the workings of the world and there is no artificial distinction between 'science' and 'religion'.
In Islam, women and men are intended to be treated as equal and families are very important - old people, for example, are almost never put into homes, instead living with the family until they pass away.
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Seventeenth-century Londoners were used to exotic animals. As a port London had its fair share of sailors and traders bringing in animals from abroad, like parrots, monkeys and lions. Even so, you can imagine the wonder it must have caused when in 1675 Lord George Berkeley imported an elephant to London.
The illustrations above are taken from two pamphlets describing the elephant. They are part of a long tradition of cheap books describing wondrous beasts: 77 years earlier, for example, Londoners had been able to read about A Most Strange and Wonderfull Herring (1598), with pictures on its sides of men fighting and of strange runic letters. The difference with Berkeley’s elephant and the Dutch herring is the the latter was written about in a heavily didactic way. Readers were meant to see the herring as a portent to be linked to contemporary events. By 1675 the elephant could be presented as a curiosity of the natural world rather than something linked to the supernatural.
Both authors are at pains to describe the elephant’s physical details, its age, and the likely size it will grow to. The woodcuts would also have given a (not too inaccurate) sense of what the animal looked like. In other respects, though, readers still would have taken away a perception of the elephant filtered through very old-fashioned lenses.
Like many early modern descriptions of elephants, A Full and True Relation is taken almost entirely from Pliny the Elder’s account of elephants:
- The closest of all the animals to man in intelligence.
- They understand the language of the country they were bred in.
- They excel in goodness and honesty.
- They fight to the death with dragons/snakes.
- They carry castles full of men on their back.
- They have 2 year pregnancies and live for 200 to 300 years.
The author also adds a detail from Isidore of Seville that they are afraid of mice, and another from Bartholomaeus Anglicus that they go down to the river at new moon to wash themselves.
A True and Perfect Description sneers at Pliny and other classical and medieval authors, saying that it will not repeat lies that the reader can look up in those texts. The author corrects Pliny’s assertion that the elephant does not have joints. Certainly it seems that there are more first and second-hand accounts of elephants within the text. This anecdote was particularly nice:
They are said to be very amourous of handsome women, (whence it appears that he is worse than a Beast that hates them), and to be very Kind and Grateful to their Keepers, insomuch as one upon a time (as the story has it) one of them seeing in his Masters absence a Man lying with his Mistris, as soon as he came from her, fell upon him and Killed him, I wish every Citizen had one of them for that trick.
But other details are still taken from standard bestiaries: the story that elephants bury their teeth to hide them from men, and that they are chaste animals.
Apart from the pamphlets, and a mock-speech by the elephant to celebrate it being shown at Bartholomew Fair, the only contemporary reactions to the elephant that I can find are one by Robert Hooke, and one in a newspaper. In Hooke’s diary he recorded the following:
12 August. Elephant sold for £1600.
2 September. Walkd to see elephant.
1 October. Saw elephant 3sh.
Meanwhile the City Mercury‘s edition of November 2 described how Berkeley had been sold the elephant for £2,000, and that the elephant:
was now to be seen at the White Horse Inn over against Salisbury Court in Fleet Street, at which place there is provided accommodation for the Nobility, Gentry and Commonalty for that purpose.
It’s also possible that it inspired Francis Barlow’s picture of a fight between an elephant and a rhinoceros (1684). Barlow’s print-shop, as Aubrey Noakes has pointed out, was just round the corner from Salisbury Court. On 25 August 1684 a rhinoceros was imported into London, and it seems possible that Barlow matched the pair in the death-match to end all death-matches…
1. Anonymous, A full and true relation of the elephant that is brought over into England from the Indies, and landed at London, August 3d. 1675. Giving likewise a true account of the wonderful nature, understanding, breeding, taking and taming of elephants (London, 1675).
2. Anonymous, A True and perfect description of the strange and wonderful elephant sent from the East-Indies and brought to London on Tuesday the third of August, 1675 : with a discourse of the nature and qualitites of elephants in general (London, 1675).
3. Anonymous, A description of the rhinoceros, lately brought from the East-Indies, and sold the 25th. of this instant August, to Mr. L. for 2320£ (London, 1684). | <urn:uuid:0568668b-d705-4955-837a-b0388651cc69> | {
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In English, many things are named after a particular country – but have you ever wondered what those things are called in those countries?
- And of course, today we have such adept flyers as the swallows, hummingbirds, falcons, and the soaring albatrosses which demonstrate the great diversity of flight adaptations in birds.
- It features free-flying displays and an opportunity for people to see at close hand some 30 different birds of prey, including eagles, buzzards and falcons.
- Unlike most hawks, falcons do not build nests (though caracaras do).
- American kestrels, smallest of North America's falcons, migrate at about the same time as the jays and flickers.
- Pete takes us inside the lives and minds of all thirty-four species of diurnal raptors found in North America - hawks, falcons, eagles, vultures, the osprey and the harrier.
- The new facility boasts more than 50 birds of prey, ranging from large eagles and incredibly fast falcons to hawks and owls.
- Adult pipits and wagtails have a number of avian predators among the falcons and hawks and owls (Strigiformes).
- These rugged plants make ideal cover for mice, rabbits, and other creatures that are, in turn, prey for the region's raptors - owls, hawks, falcons, and eagles.
- The Royal Society for the Protection of Birds estimates that around 100 birds of prey, including eagles, falcons and hen harriers, are either poisoned, shot, trapped or have their nests destroyed every year on the Scottish moors.
- The Gyrfalcon is the largest falcon in the world.
- Tens of thousands of hawks, kites, falcons, eagles, osprey, vultures, and harriers appear in the skies over the Golden Gate from August through December.
- Hawks, harriers, falcons, eagles, and vultures are diurnal migrants.
- They're subject to a lot of pressures from predators, aerial predators such as falcons, sea eagles, and they need to have a clear line of sight to an area of escape for them, and also so they can see predators in advance.
- These conditions resulted in many migrants (including red footed falcons, red throated pipits and grey-headed wagtails) all travelling far to the west of normal routes from Africa to northern breeding grounds.
- Accipiters have rounded wings, whereas falcons have pointed ones.
- The enemies are not only humans but many other predators that consider rodent meat very tasty, snakes, large lizards, small and large mammals and birds of prey especially owls, kestrels, and falcons.
English has borrowed many of the following foreign expressions of parting, so you’ve probably encountered some of these ways to say goodbye in other languages.
Many words formed by the addition of the suffix –ster are now obsolete - which ones are due a resurgence?
As their breed names often attest, dogs are a truly international bunch. Let’s take a look at 12 different dog breed names and their backstories. | <urn:uuid:7c2c2d31-186f-48db-9e00-649b077672ae> | {
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# Point (geometry)
In modern mathematics, a point refers usually to an element of some set called a space.
More specifically, in Euclidean geometry, a point is a primitive notion upon which the geometry is built. Being a primitive notion means that a point cannot be defined in terms of previously defined objects. That is, a point is defined only by some properties, called axioms, that it must satisfy. In particular, the geometric points do not have any length, area, volume, or any other dimensional attribute. A common interpretation is that the concept of a point is meant to capture the notion of a unique location in Euclidean space.
## Points in Euclidean geometry
A finite set of points (blue) in two-dimensional Euclidean space.
Points, considered within the framework of Euclidean geometry, are one of the most fundamental objects. Euclid originally defined the point as "that which has no part". In two-dimensional Euclidean space, a point is represented by an ordered pair (x, y) of numbers, where the first number conventionally represents the horizontal and is often denoted by x, and the second number conventionally represents the vertical and is often denoted by y. This idea is easily generalized to three-dimensional Euclidean space, where a point is represented by an ordered triplet (x, y, z) with the additional third number representing depth and often denoted by z. Further generalizations are represented by an ordered tuplet of n terms, (a1, a2, … , an) where n is the dimension of the space in which the point is located.
Many constructs within Euclidean geometry consist of an infinite collection of points that conform to certain axioms. This is usually represented by a set of points; As an example, a line is an infinite set of points of the form $\scriptstyle {L = \lbrace (a_1,a_2,...a_n)|a_1c_1 + a_2c_2 + ... a_nc_n = d \rbrace}$, where c1 through cn and d are constants and n is the dimension of the space. Similar constructions exist that define the plane, line segment and other related concepts. By the way, a degenerate line segment consists of only one point.
In addition to defining points and constructs related to points, Euclid also postulated a key idea about points; he claimed that any two points can be connected by a straight line. This is easily confirmed under modern expansions of Euclidean geometry, and had lasting consequences at its introduction, allowing the construction of almost all the geometric concepts of the time. However, Euclid's postulation of points was neither complete nor definitive, as he occasionally assumed facts about points that did not follow directly from his axioms, such as the ordering of points on the line or the existence of specific points. In spite of this, modern expansions of the system serve to remove these assumptions.
## Dimension of a point
There are several inequivalent definitions of dimension in mathematics. In all of the common definitions, a point is 0-dimensional.
### Vector space dimension
The dimension of a vector space is the maximum size of a linearly independent subset. In a vector space consisting of a single point (which must be the zero vector 0), there is no linearly independent subset. The zero vector is not itself linearly independent, because there is a non trivial linear combination making it zero: $1 \cdot \mathbf{0}=\mathbf{0}$.
### Topological dimension
The topological dimension of a topological space X is defined to be the minimum value of n, such that every finite open cover $\mathcal{A}$ of X admits a finite open cover $\mathcal{B}$ of X which refines $\mathcal{A}$ in which no point is included in more than n+1 elements. If no such minimal n exists, the space is said to be of infinite covering dimension.
A point is zero-dimensional with respect to the covering dimension because every open cover of the space has a refinement consisting of a single open set.
### Hausdorff dimension
Let X be a metric space. If SX and d ∈ [0, ∞), the d-dimensional Hausdorff content of S is the infimum of the set of numbers δ ≥ 0 such that there is some (indexed) collection of balls $\{B(x_i,r_i):i\in I\}$ covering S with ri > 0 for each iI that satisfies $\sum_{i\in I} r_i^d<\delta$.
The Hausdorff dimension of X is defined by
$\operatorname{dim}_{\operatorname{H}}(X):=\inf\{d\ge 0: C_H^d(X)=0\}.$
A point has Hausdorff dimension 0 because it can be covered by a single ball of arbitrarily small radius.
## Geometry without points
Although the notion of a point is generally considered fundamental in mainstream geometry and topology, there are some systems that forgo it, e.g. noncommutative geometry and pointless topology. A "pointless" or "pointfree" space is defined not as a set, but via some structure (algebraic or logical respectively) which looks like a well-known function space on the set: an algebra of continuous functions or an algebra of sets respectively. More precisely, such structures generalize well-known spaces of functions in a way that the operation "take a value at this point" may not be defined. A further tradition starts from some books of A. N. Whitehead in which the notion of region is assumed as a primitive together with the one of inclusion or connection.
## Point masses and the Dirac delta function
Main article: Dirac delta function
Often in physics and mathematics, it is useful to think of a point as having non-zero mass or charge (this is especially common in classical electromagnetism, where electrons are idealized as points with non-zero charge). The Dirac delta function, or δ function, is (informally) a generalized function on the real number line that is zero everywhere except at zero, with an integral of one over the entire real line.[1][2][3] The delta function is sometimes thought of as an infinitely high, infinitely thin spike at the origin, with total area one under the spike, and physically represents an idealized point mass or point charge.[4] It was introduced by theoretical physicist Paul Dirac. In the context of signal processing it is often referred to as the unit impulse symbol (or function).[5] Its discrete analog is the Kronecker delta function which is usually defined on a finite domain and takes values 0 and 1.
## References
1. ^ Dirac 1958, §15 The δ function, p. 58
2. ^ Gel'fand & Shilov 1968, Volume I, §§1.1, 1.3
3. ^ Schwartz 1950, p. 3
4. ^ Arfken & Weber 2000, p. 84
5. ^ Bracewell 1986, Chapter 5
• Clarke, Bowman, 1985, "Individuals and Points," Notre Dame Journal of Formal Logic 26: 61–75.
• De Laguna, T., 1922, "Point, line and surface as sets of solids," The Journal of Philosophy 19: 449–61.
• Gerla, G., 1995, "Pointless Geometries" in Buekenhout, F., Kantor, W. eds., Handbook of incidence geometry: buildings and foundations. North-Holland: 1015–31.
• Whitehead A. N., 1919. An Enquiry Concerning the Principles of Natural Knowledge. Cambridge Univ. Press. 2nd ed., 1925.
• --------, 1920. The Concept of Nature. Cambridge Univ. Press. 2004 paperback, Prometheus Books. Being the 1919 Tarner Lectures delivered at Trinity College.
• --------, 1979 (1929). Process and Reality. Free Press. | crawl-data/CC-MAIN-2015-22/segments/1432207930259.97/warc/CC-MAIN-20150521113210-00248-ip-10-180-206-219.ec2.internal.warc.gz | null |
# How the Mathematical Pirate works out the high times tables
"Arr!" said the Mathematical Pirate.
"Pieces of eight!" said the Mathematical Pirate's parrot.
"How many pieces of eight?"
"Seven!"
"That'll be... seventy and ten minus twenty and four, making fifty and six!"
"Who's a clever boy?" asked the parrot. "Awk!"
---
The Mathematical Pirate is, indeed, a clever boy. He's using a combination of number bonds and the small times tables he knows by h-arrrr-t.
The way it works is this:
• He knows that $3 + 7 = 10$, so $7\times$ something is the same as $10\times$ the thing minus $3 \times$ the thing.
• He knows that $8 \times 10$ is 80 and $8 \times 3$ is 24.
• Now the clever bit: he thinks of 80 as seventy-and-ten before trying to take 24 away -- saving himself from the terrors of borrowing and carrying1
• Then he takes twenty from the seventy (leaving 50) and four from the ten (leaving 6), so his answer is 56
Alternatively, he could have worked the same thing the other way: since $2 + 8 = 10$, $8\times$ something is $10\times$ the thing minus $2\times$ the thing. Seven tens are 70, which he thinks of as sixty-ten; seven twos are 14; taking the ten from the 60 leaves 50, and taking the 4 from the 10 leave 6. 56 again!
This is a really powerful trick -- the Mathematical Pirate claims he learnt it from a Ninja, but nobody saw it.
In a more general form, if you need to work out (big times table number) × (something else) -- for instance, $7\times4$ you'll need:
• What you add to (big times table number) to make 10 -- here, it's 3 -- and call that (little number)
• $10\times$ (the something else) -- which would be 40, which you think of as "next ten down and ten" -- here, that's 30 and 10.
• (little number) × (the something else) -- $3 \times 4 = 12$
• Take the tens in this away from the tens above (giving 20); do the same with the units to get 8
• Add these up to get the answer, 28.
## Colin
Colin is a Weymouth maths tutor, author of several Maths For Dummies books and A-level maths guides. He started Flying Colours Maths in 2008. He lives with an espresso pot and nothing to prove.
1. Yeah, yeah, I know, that's exactly what he's doing. []
#### Share
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##### Where do you teach?
I teach in my home in Abbotsbury Road, Weymouth.
It's a 15-minute walk from Weymouth station, and it's on bus routes 3, 8 and X53. On-road parking is available nearby. | crawl-data/CC-MAIN-2019-18/segments/1555578732961.78/warc/CC-MAIN-20190425173951-20190425195951-00464.warc.gz | null |
Early life[change | change source]
Aemilianus was born around 207 or around 214. The Epitome de Caesaribus (a Latin history) and Zonaras (a Greek historian) say that Aemilianus was born at this time and at Djerba, an island in the Mediterranean Sea near Africa, part of the Roman Empire.
Emperor[change | change source]
After defeating the Goths (a barbarian tribe) in modern-day Bulgaria, his soldiers proclaimed him as an emperor instead of Trebonianus Gallus, the emperor at the time. After defeating Gallus in battle at Interamna (Northern Italy), he captured the capital city of the empire, Rome.[source?]
When the governor of Roman Germany, Valerianus, arrived in Italy bringing troops to help Trebonianus Gallus, Aemilianus's own troops killed Aemilianus. They did not want a civil war and Valerian had a bigger army than Aemilianus.[source?]
Death[change | change source]
Family[change | change source]
References[change | change source]
- Kienast, Dietmar; Eck, Werner; Heil, Matthäus (2017) . "Aeimilius Aemilianus (Juli/Aug. 268–Sept./Okt. 253)". Römische Kaisertabelle: Grundzüge einer römischen Kaiserchronologie (in German) (6th ed.). Darmstadt: Wissenschaftliche Buchgesellschaft (WBG). pp. 203–204. ISBN 978-3-534-26724-8. | <urn:uuid:388a87ac-854d-4707-9126-592114ecacbf> | {
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## What is the result of subtracting the second equation from the first? -2x + y = 0 -7x + 3y = 2
Question
What is the result of subtracting the second equation from the first?
-2x + y = 0
-7x + 3y = 2
in progress 0
1 week 2021-09-12T22:49:47+00:00 2 Answers 0
5x – 2y = -2
Step-by-step explanation:
-2x – (-7x) = -2x + 7x = 5x
y – 3y = -2y
0 – 2 = -2
5x -2y = -2
Step-by-step explanation:
-2x + y = 0
-7x + 3y = 2
Subtract the second equation from the first
-2x + y = 0
-(-7x + 3y = 2)
————————–
Distribute the minus sign
-2x + y = 0
+7x – 3y = -2
————————–
5x -2y = -2 | crawl-data/CC-MAIN-2021-39/segments/1631780057421.82/warc/CC-MAIN-20210923104706-20210923134706-00546.warc.gz | null |
In observance of this year's Presidents' Day, we reprise this essay from 1996. Though Presidents' Day officially honors George Washington and Abraham Lincoln, it also offers a timely opportunity to remember other presidents who served as models worth honoring and remembering, especially as this year is filled with presidential politics.
When historians are asked to grade the men who have served as America's presidents, they usually give high marks to the "activist" ones – those who expanded the frontiers of the federal government, pushed taxes and spending higher, and left a mark on the country by foisting vast new bureaucracies on future generations.
That's why historians rarely mention Grover Cleveland except to note that he remains the only man ever to serve two nonconsecutive terms (he was elected first in 1884, then again in 1892). A Democrat, Cleveland was an "activist" in a sense that makes him unpopular with most of today's historians. He worked tirelessly to limit government and expand the scope of individual liberty. He was also known in his day as one of the most honest men in American public life, a trait that catapulted him from mayor of Buffalo, New York, to president of the United States in the space of four years, with a two-year term as governor of New York along the way. As Americans prepare for another presidential election, they would do well to recount the reasons why their ancestors chose Grover Cleveland twice before.
Cleveland said what he meant and meant what he said. He did not lust for political office and never felt he had to cut corners, equivocate, or flip-flop on the issues in order to get elected. A man who knew where he stood, he was so forthright and plain-spoken that he makes Harry Truman seem like an indecisive waffler by comparison. Biographer Allan Nevins summed him up this way: "His honesty was of the undeviating type which never compromised an inch; his courage was immense, rugged, unconquerable; his independence was elemental and self-assertive. . . . Under storms that would have bent any man of lesser strength he ploughed straight forward, never flinching, always following the path that his conscience approved to the end."
Frequent warnings of the redistributive nature of government were a trademark of Cleveland, the son of a poor Protestant minister. He regarded as a "serious danger" the notion that government should dispense favors and advantages to individuals or their businesses. In vetoing a bill in 1887 that would have appropriated a mere $10,000 to aid drought-stricken farmers in Texas, Cleveland stated that "though the people support the Government, the Government should not support the people." For relief of citizens in misfortune, he felt it was important to rely upon "the friendliness and charity of our countrymen."
That veto was one of many. In fact, Cleveland in his first term vetoed twice as many bills as all previous 21 presidents combined. Most of those bills were little more than cynical attempts by somebody to get something from somebody else by the force of the government's gun. Disdainful of pork barrel politics, he felt that those who would use and benefit from government projects should pay for them. Compare that attitude with the pandering to special interests that seems so common today!
Cleveland broke with the old practice of bloating the federal bureaucracy with political cronies. He maintained the highest standards in choosing the people who served around him, making appointments only when necessary and then, only of people whose character and qualifications were beyond reproach. The White House during his tenure was scandal-free, a model of propriety for the rest of the country. He had no enemies list.
On the major issues of his day, Cleveland let honesty be the source of his convictions. It was dishonest, he felt, for the government to spend more than it had and send its bills to future generations. So he always worked to produce a surplus budget. It was dishonest, he believed, for government to steal from people by inflating the currency. So he made sure the dollar was "as good as gold." It was dishonest, he said, for government to think it could spend money better than the people who first earned it. So he cut taxes whenever he could. It was dishonest, he argued, to stifle competition and consumer choice by restricting imports. So he fought to reduce tariffs.
Grover Cleveland ran for president as the Democratic Party's nominee three times. He won twice and lost once. He carried Michigan in none of those elections. In 1996, the one hundredth anniversary of his last year in office, it is doubtful that a candidate of his views could win Michigan or any other state. The question is, does that reflect poorly on Cleveland or on the voters of today? | <urn:uuid:b29c9e39-a270-40d2-97a5-7954e9148c70> | {
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Amount
From
To
# 4 dekameters to meters
How many meters in 4 dekameters? 4 dekameters is equal to 40 meters.
This page provides you how to convert between dekameters and meters with conversion factor.
# How to convert 4 dam to m?
To convert 4 dam into m, follow these steps:
We know that, 1 dam = 10 m
Hence, to convert the value of 4 dekameters into meters, multiply both sides by 4 and we get:
1 dam = 10 m
(1 * 4) dam = (10 * 4) m
4 dam = 40 m
### Thus, 4 dam equals to 40 m
Dekameters Conversion of Dekameters to Meters
3.99 dam 3.99 dam = 39.9 m
3.9 dam 3.9 dam = 39 m
4 dam 4 dam = 40 m
5 dam 5 dam = 50 m | crawl-data/CC-MAIN-2023-06/segments/1674764499819.32/warc/CC-MAIN-20230130133622-20230130163622-00461.warc.gz | null |
Dictionary.com Word FAQs
When do you use lie and lay?
To lay is to place something; to lie is to recline (though there are other meanings). Lay is followed by an object, the thing being placed. For example: He lays the book down to eat. To lie is to recline, as in: She lies quietly on the chaise lounge. The best way to explain it is that lie in the sense of 'to recline' or 'be situated' is intransitive and cannot take a direct object. But lay meaning 'to place something' or 'put down' or 'arrange' is always transitive and requires a direct object. Because lie is intransitive, it has only an active voice, while lay can be active or passive because it is transitive. Part of the source of the confusion is the past tense of lie, which is lay: She lay on the chaise all day. The past participle of lie is lain, as in: She has lain there since yesterday, as a matter of fact. The past tense of lay is laid, as is the past participle. | <urn:uuid:50e789e7-43b7-41db-8671-9a7f4e42c072> | {
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What are the communication challenges for individuals with ASD?
Communication is a process where we assign and express meaning in an attempt to create shared understanding. This process requires the coordination of many skills (ex. listening, observing, questioning, analyzing, and evaluating). During typical speech and language development, children learn to transfer these skills to all areas of life: home, school, community, work, and beyond. It is through communication that children express their thoughts and ideas, learn new things and build relationships with others.
For many children with autism, communication can be challenging. Possible signs and symptoms may include:
- Limited or lack of verbal speech
- Difficulty expressing needs and wants
- Echolalia (repeating a word or phrase that has been previously heard)
- Loss of words that the child was previously able to say
- Inability to identify objects (poor vocabulary development)
- Difficulty answering questions
- Limited attention to people and objects in environment
- Poor response to verbal instructions
- Disruptive behaviors to gain access to or avoid items, activities, people or places
Communicating during social situations may also be a challenge for individuals with ASD. They may have a difficult time interacting with others, appear to have little or no interest in making friends, or not know how to interact with others in a social manner. In addition, individuals with ASD may have difficulty understanding the emotions of others and may respond inappropriately. This may lead to misunderstandings in the communication exchange.
Sensory issues can also effect communication. There may be certain sounds, tastes or sights that cause anxiety or provoke an unusual response. The response may not make sense to others because the individual with autism does not have the tools or ability to appropriately communicate the reasons for his or her response.
What can be done to better support communication?
The first step in supporting the communication development of someone with autism is to have a complete evaluation by a Speech-Language Pathologist. This evaluation would determine both communication and social needs of the child. Once the evaluation is completed, an appropriate treatment plan that meets the needs of the child and their family will be developed. The overall objective of Speech-Language Pathology services is to optimize the individual ability to communicate in all environments, thereby improving quality of life.
Speech and language treatment may include a combination of traditional speech and language approaches, behavior modification strategies and augmentative and alternative communication (AAC) interventions. | <urn:uuid:6560fc46-3e1e-4fe7-a5fe-91a0882cb83b> | {
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When modeling real world situations, we often use what's called inverse variation to describe a relation between two variables. Inverse variation is a relation in which the absolute value of one variable gets smaller while the other gets larger. Inverse variation and direct variation are important concepts to understand when learning equations and interpreting graphs.
Sample Problems (6)
Need help with "Inverse Variation" problems? Watch expert teachers solve similar problems to develop your skills.
Tell whether each relationship is an inverse variation:
Tell whether the relationship 3xy = -10 is an inverse variation.
If the points (½,4) and (x,1⁄10) are solutions to an inverse variation, find x. | <urn:uuid:a8074abf-f0b0-40f3-be26-cdde658a5864> | {
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Sands of Time
Samples from Arctic Sea Floor May Rock Global Climate Theories
By Eric Gorton
In her microscope, Kristen St. John is discovering a fascinating climate history for the Arctic. Sand grains dug from a previously untouched area of the Arctic are indicating the region froze much earlier than previously thought.
Sitting there in glass vials on a laboratory shelf, the specimens look rather ordinary—no different, in fact, than the sand that takes you six months to clean out of your car after a trip to the beach.
The vials' content is certainly more interesting under a microscope, where every grain has its own color, its own texture, its own size. Yes, sand really is a bunch of tiny rocks.
Ah, but there's so much more to sand than that, especially the sand sitting on the shelves in the lab of JMU geology Associate Professor Kristen St. John. These samples came from the Arctic sea floor, where they'd been for up to 46 million years.
"That's like a time capsule of what's been happening in the Arctic, and no one had recovered it before," said St. John, who is part of an international team of scientists studying sediment recovered during an Integrated Ocean Drilling Program expedition in August 2004.
One goal of the expedition, which dug deeper into time in sampling the Arctic than any before it, was to confirm or debunk a theory that the central Arctic's Lomonosov Ridge was once part of Russia. To find the answer, core samples had to be taken from the harder bedrock buried beneath millions of years of sediment buildup, then compared to rock on land. More than 400 meters of sediment was recovered from four holes, St. John said, revealing a geologic time line from the present—the mud and sand at the top—to more than 56 million years ago—the sand at the bottom of the deepest holes.
St. John, who could not participate in the coring expedition due to the birth of her youngest child just months before, got her first look at the samples in Bremen, Germany, in November 2004 when the cores were opened for the first time. One of four sedimentologists on the international team, her job was to describe in writing her observations of the sediment: its composition, its texture, any color changes and any anomalies, such as larger pebbles occasionally embedded in finer sand.
While describing the cores centimeter by centimeter can be a bit tedious, the task was highly important. "It's like being a scribe to the rest of the scientific community that didn't get to see it with their own eyes," she said.
The close inspection also turned out to be very rewarding. So far, St. John says, there's evidence that the Arctic may have froze over about 40 million years ago, nearly the same time, geologically speaking, as the Antarctic, which generally is thought to have frozen tens of millions of years ahead of the Arctic as the earth's climate shifted from the "greenhouse world" of the dinosaur age to the "ice house world" that exists today.
"We've got lots of records for the Cenozoic (era) for pretty much every other latitude, but nothing spanning that for the Arctic. So that's just a big—what's the story? So we're still trying to figure out what some of that story is, but, even just from what we did in Bremen, we could see some things right away that have major climatic implications," St. John said.
The Proof Is In The Pebbles
Under the microscope, the sand grains take on their own characteristics and reveal a history of the Arctic.
The pebbles found amidst the sediment offer the most compelling evidence that the Arctic froze much earlier than previously thought, St. John said. The pebbles are consistent with rock found in Russia hundreds of miles away and the only way they could have reached the central Arctic was to be brought there by ice.
"Every now and then, we would see another pebble in the core. And it wasn't just going back to seven million years ago (the time most commonly associated with the freezing of the Arctic). We were seeing pebbles all the way into the middle Eocene (40 million years ago), all the way to the time that the long-term record for Antarctica showed that there was ice there.
"What's the significance of one pebble? Well, the significance is that those pebbles, to get to the central arctic, to get to a ridge, a high spot on the sea floor in the central arctic, there's only so many ways it can get there. ... You can't say, ‘Well, it was just brought there from a big storm and rivers were churned up and it was flowing out there. That will make it into the deep basin, at the base of the continental slope perhaps. ... It can't be wind blown. These are pebbles that are, oh, I don't know, a couple centimeters in diameter, they're not going to be windblown that far from land.
"You start eliminating all of the possibilities that you can think of and it pretty much comes down to: It was brought by ice. Because when ice forms on land, it freezes whatever it's touching into it, like a fly in an ice cube. So it's freezing pebbles, big ones, all different sizes of sediment and it's bringing it out there."
And as the floating ice melted, it dropped its catch to the sea floor.
"The fact that we were seeing pebbles back this far, that was really neat, that was just so exciting," St. John said. "There's always going to be naysayers and they're going to say, ‘well, maybe it was just some log or something, or a bird or whatever. But when you see enough of them, there's too many, and you start to see a pattern."
Even if the findings prove the Arctic froze much sooner than previously believed, St. John says the research will not fuel current debates on the effects of global warming. Long before human existence, climate cycles occurred, she said. Humans, however, have affected the earth's climate by burning fossil fuels, cutting forests, farming and in other ways.
"I don't think any credible scientist would argue that we haven't had an influence on climate," she said.
How much of an effect, however, is up for debate. Have humans significantly changed existing climate cycles? That's what climate modelers are trying to determine, she said.
As for St. John, her main goal is satisfying her own curiosity about the earth's mysteries and sharing what she learns with others.
"The earth is just this big puzzle and trying to contribute another piece to the puzzle, to try to understand how the earth works, how it worked in the past is very satisfying and very interesting," she said. "The fun part is making a contribution that other people can then build upon.
"What I do in a laboratory is pretty straightforward—sitting at a microscope, looking at sand grains—but, it opens up this whole world that people don't even really ever think about. You know, you walk on the beach on grains of sand and it's just where you put your towel. But those are clues to something that happened before. You just need to learn how to read what the clues are."
St. John and her students are busy now studying the layers of Arctic sand and verifying the time line it appears to have created.
A grain of sand viewed through a scanning electron microscope.
Seniors Brendan Quirk, Kirsten Mullen and Michelle Summa have been involved with a variety of tasks, such as sorting the sand by grain size, weighing it, photographing it through microscopes and logging their findings. They present their research at the annual Geology and Environmental Sciences Senior Symposium April 28 in Memorial Hall, the former Harrisonburg High School.
In May, St. John travels to Sicily to report on what she and her students have learned and also to hear from others on the international team who are researching other aspects of the cores and bedrock samples, which did prove to be the same type of rock as that found in Russia.
The results of the initial finding from the work in Bremen have been submitted to the journal "Nature" for review. | <urn:uuid:99f2886d-0640-48ea-86c0-02df3d695ca1> | {
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Isn't radiation dangerous?
There are different types of radiation, including ultraviolet rays from the sun, microwaves, radio waves, and ionizing radiation (like from x-rays and other imaging tests). While too much radiation can harm or kill living tissue, the amount of radiation in most imaging tests is generally very safe. In fact, no harm has been shown from the levels of radiation used in the imaging tests described here. Imaging machines have improved over the years, decreasing the amount of radiation used. Most people are exposed to more radiation from the environment than from these tests.
Radiologists take special steps to reduce radiation exposure during a test. For example, they only x-ray the body parts that need to be x-rayed and use lead aprons to cover other parts of the body not being studied. If you're still concerned, keep in mind that the benefits of imaging tests are greater than the risk of radiation.
What types of imaging tests are there?
X-rays can help diagnose many illnesses. During an x-ray, electromagnetic waves (a form of light) pass through the body and create an image on film. This image is called an x-ray or radiograph. X-rays are usually used to see bones, muscles or organs (like the heart or liver), and air inside the body. Metal objects also can be seen.
X-rays can be done on most parts of the body. For example, chest x-rays can reveal pneumonia or a collapsed lung, an enlarged heart, or rib fractures. Arm or leg x-rays can show broken bones or other bone problems.
Time: Each x-ray takes only a few seconds, like a picture taken with a camera. Results may be ready during your visit or may take several days.
Radiation: X-rays expose the body to very small amounts of radiation, but only to the areas of the body being studied.
Cost/availability: Low cost; widely available.
Before the test: Nothing special needs to be done before the test.
During the test: The body part to be examined is placed between the x-ray machine and the x-ray film. Other parts of the body may be covered with a lead-lined apron to reduce radiation exposure. The machine is turned on, and a picture is taken. Patients must keep very still for the image to be clear. Young children may need special straps to keep them still during the test. If you can stay with your child, you will be given a lead-lined apron to wear.
Fluoroscopy is a type of x-ray that creates a real-time “x-ray movie” of the inside of the body. An x-ray beam placed on a specific area of the body creates images that are shown on a TV-like monitor.
Fluoroscopy is mainly used to diagnose illness of the stomach and intestines, lungs and airway, or bladder. Fluoroscopy is also used to help guide instruments or devices into the body, such as a catheter for feeding tubes.
Time: About 5 to 20 minutes.
Radiation: Higher than x-rays, but it depends on how long the test lasts. For most studies, the fluoroscopy camera is only on when needed to keep radiation doses as low as possible.
Pain: None, but preparing before the test may be unpleasant.
Cost/availability: More expensive than x-rays; widely available.
Before the test: For some types of fluoroscopy tests patients may need to fast, drink only liquids, or have an enema. Sometimes a contrast material (a fluid that shows things in the body that are hard to see without it) is injected or given by mouth. If the child cannot drink it, a tube may need to be placed through the mouth to the stomach. (Placement of the feeding tube is very safe and is only uncomfortable for a short time. The use of the feeding tube can shorten the time it takes to do the test. Less time can reduce your child's exposure to radiation.)
During the test: The room is darkened, and the area of the body being examined is placed between the x-ray and fluoroscopy screen. Images of the body are then sent to a monitor where they can be seen in motion.
Computed tomography or CT scan
A CT scan is a special type of x-ray that uses computers to create detailed images of the body. A rotating x-ray tube that surrounds the patient takes pictures of organs and tissues from many angles. Hundreds of images can be created in a short time.
A CT scan is very useful because it can create more detailed pictures than an ordinary x-ray. It is often used to find tumors, infections, or evidence of injury in different parts of the body.
Time: A CT scan only takes a few seconds. Results can take a few hours to 24 hours, depending on where it's done.
Radiation: Higher than x-rays but lower than the dose from fluoroscopy.
Pain: None, unless the child will need an injection of a contrast material. This must be done through a vein (IV) in the arm.
Cost/availability: High cost; widely available.
Before the test: A contrast material may need to be injected or taken by mouth.
During the test: The patient lies on a narrow table that slides in and out of the CT scanner. The x-ray tube rotates around the patient, sending information to a computer that forms the images. Young patients may need to be sedated for a CT scan.
Magnetic resonance imaging (MR imaging or MRI)
An MRI uses a large and powerful magnet, radio waves, and a computer to create very detailed images of the inside of the body.
An MRI is very helpful in studying the brain and spinal cord, the soft tissues of the body, and the joints. An MRI is often used to detect birth defects, inflammation, infection, tumors, and injury.
Time: About 30 to 60 minutes. Results are usually ready within 24 hours.
Pain: None, but patients may need an injection of a contrast material and an IV. Also, some patients may feel cramped in the machine (open MRI machines are available in some areas). During scanning, loud humming and knocking will be heard. Small children may be frightened by these noises.
Cost/availability: High cost; not available everywhere.
Before the test: Younger children may need to be sedated before the test. All metal objects need to be removed before the test. Internal items like pacemakers, hearing aids, or insulin pumps may not be allowed in the MRI scanner room and may mean your child can't have an MRI.
During the test: The patient lies on a table that slides into the scanner (a narrow tunnel that holds the magnet). It's important that the patient stay very still. Inside the scanner, the patient will hear a fan and feel air blowing. Because the machine can be noisy, patients are given earphones. Some centers have headphones that your child can use to listen to music during the exam.
Ultrasound uses sound waves to create images of the body. The sound waves enter the body, and the returning echoes are captured as images. These images are called sonograms, echocardiograms (heart echo), or ultrasound scans.
Ultrasound tests can help diagnose illnesses of the kidneys, bladder, and uterus; the heart (called an echocardiography); as well as the liver, spleen, gallbladder, and pancreas. Ultrasound is also used to look at the brains of young infants, especially premature babies. It is best used for looking at parts of the body that are either solid (like the liver) or fluid-filled (like the gallbladder). Ultrasound doesn't produce clear images of organs filled with gas or air (such as lungs) or with hard surfaces, such as the inside of bones.
Time: 15 minutes to 1 hour.
Cost/availability: Moderate cost; widely available.
Before the test: In some cases, patients may need to fast or drink more water before the test.
During the test: First, a special jelly or oil is put on the skin. Next, a hand-held device called a transducer is moved back and forth over the area being examined. The transducer creates sound waves (that can't be heard or felt) that are reflected back to the machine. A computer creates images from the sound waves.
A nuclear imaging scan (sometimes called radionuclide scanning) shows the structure of a body part as well as how it works. Before the scan, a radioactive substance called a tracer is injected or given by mouth. A machine called a gamma camera used outside the body then detects the rays of energy given off by the tracer, and an image is created and shown on a computer screen.
Organs including the kidneys, liver, heart, lungs, and brain are often studied using this test. Bone imaging may show trauma, infection, or a tumor even before any problems are seen with x-rays.
Time: Between 15 minutes and 1 hour. Most results take 1 to 3 days.
Radiation: Less radiation than from fluoroscopy or CT. The tracer loses its radioactivity within 24 hours, leaving the body in the urine or stool. For most nuclear medicine studies, the amount of radiation in the urine or stool is not harmful for the child or those exposed to the urine or stool.
Pain: None, but patients may need the tracer injected and an IV. With some exams, a catheter may need to be placed into the bladder.
Cost/availability: Moderate cost; often available wherever CT or MRI is available.
Before the test: The tracer is usually given by mouth or through an injection. Patients may need to fast or drink a lot of water before some nuclear imaging scans. Young children may need to be sedated.
During the test: After the tracer is in place, the patient lies on a scanning table. The camera is then moved slowly over the body. Images are created and displayed on a computer. | <urn:uuid:596f8cc5-85dd-49f1-ad62-cd845fc1a0d7> | {
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Scientists have used a supercomputer to shed new light on one of the most important theories of physics, the Standard Model, which encapsulates understanding of all the material that makes up the universe. This 30-year-old theory explains all the known elementary particles and three of the four forces acting upon them - however, it excludes the force of gravity, which is its shortcoming.
Physicists have been trying to find the missing pieces in the jigsaw that would extend the Standard Model into a complete theory of all the forces of nature. However, the landmark findings by researchers at the Universities of Edinburgh and Southampton, and their partners in Japan and the US, confirm the Standard Model to even greater precision than before, deepening the puzzle.
The project's enormously complex calculations relate to the behaviour of tiny particles found in the nuclei of atoms, known as quarks. In order to carry out these calculations, the researchers first designed and built a supercomputer that was among the fastest in the world, capable of tens of trillions of calculations per second. The computations themselves have taken a further three years to complete.
Their result shows that the Standard Model's claim to be the best theory invented holds firm. It raises the stakes for the riddle to be solved by experiments at the Large Hadron Collider at CERN, which will switch on later this year. Physicists’ efforts to confront Standard Model predictions using the most powerful computers available with the most precise experiments offer no clues about what to expect.
Professor Chris Sachrajda of the University of Southampton’s School of Physics and Astronomy said: ‘Modern supercomputers and improved theoretical techniques are allowing us to explore the limits of the Standard Model to an unprecedented precision. The next stage will be to combine such computations with new experimental results expected from the Large Hadron Collider to unravel the next level of fundamental physics.’
Professor Richard Kenway of the University of Edinburgh's School of Physics added: ‘Although the Standard Model has been a fantastic success, there were one or two dark corners where experimental tests had been inconclusive, because vital calculations were not accurate enough. We shone a light on one of these, but to our enormous frustration, nothing was lurking there.’
The research, published in Physical Review Letters, was supported by the Science and Technology Facilities Council.
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Vocal Matching in Animals
Imitating the calls of group members and mates is a reliable signal of social bonds in some animal species
We can often tell the country or region someone is from simply by hearing them speak. We do this, usually unconsciously, using cues such as speech pattern and vocabulary, which characterize regional dialects. We can also frequently discover clues about someone’s social identity based on hearing them speak: People from different socioeconomic classes or age groups may use different inflections or intonations, even if they have the same regional dialect. In the movie Good Will Hunting, for example, characters from universities in Boston use different accents than do working-class characters from South Boston. The entire cast had to adopt a regional accent, but the actors imitated subtly different versions of that accent that were appropriate for the group their characters represented.
The phenomenon in which individuals from the same geographic area or social group share vocal characteristics is not unique to humans. Such shared vocal characteristics also occur in animal species that are capable of vocal learning. Vocal learning is defined as the production of a vocalization based on auditory input. It is a uncommon trait in the animal world, documented only in birds, cetaceans, bats, elephants and some species of primates. Although most animals probably do not need social experience to produce vocalizations that are species-typical, a handful of species are believed to learn to produce the vocal signals they make. Many of the species that are capable of learned vocal production also engage in vocal matching—imitating companions to generate vocalizations with similar acoustic structures. The occurrence of vocal matching across diverse species suggests that this relatively rare trait may play an important social function in the animal world. Like the aspects of human speech that point to social class and region of origin, shared features of animal communication signals have the potential to reflect aspects of individuals’ social background, because matched vocalizations in animals can be specific to different species, subspecies, populations, social groups, bonded pairs or families.
Orca whales (Orcinus orca) are one species capable of learning matched vocalizations. These whales hunt in stable groups, called pods. Research by Volker Deecke of the University of St. Andrews in Scotland and John Ford and colleagues at the University of British Columbia demonstrated that all of the pods in a given geographic region, which are genetically related to one another and are termed clans, produce a set of matched vocalizations. The shared features of these vocalizations result in a vocal dialect that is analogous to a human accent, reflecting the animals’ lineage and group membership. However, the vocalizations of pod mates share even more characteristics than do the dialects of clan members, making it possible for researchers to determine which particular social group a whale belongs to as well as its region of origin.
This example illustrates that shared vocalizations in animals clearly have the potential to reflect an individual’s social identity. However, we don’t expect animals to pay attention or respond to matched vocalizations unless doing so improves their survival and reproduction (which evolutionary biologists refer to as fitness). That is, in contrast to considering the complex social factors that influence patterns of language similarity in humans, studying vocal matching in animals first requires evaluating how the behavior affects measures related to individuals’ fitness, because traits in animals are shaped by natural and sexual selection. | <urn:uuid:7f51347f-4356-4fc3-b4cd-4c60d9bce3c1> | {
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American Burying Beetle
A bright, shiny beetle with a distinctive orange-and-black pattern on its wing covers. To tell this species from other members of its genus, look for a reddish-orange mark on the shieldlike plate (pronotum) just behind the head. There are orange marks on the face and antennae tips, as well. Like other burying beetles, the wing covers are wider in back than toward the front, and they aren't long enough to cover the tip of the abdomen. In flight, they seem like bumblebees.
Similar species: Because reintroduction efforts are under way, you may hopefully start to see this species in the wild. Meanwhile, other burying beetles, such as the tomentose burying beetle (Nicrophorus tomentosus), are much more likely to be seen. There are about 15 species in the genus Nicrophorus in North America. | <urn:uuid:540718e0-e23b-4499-8e2b-512b4b9940d9> | {
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## Understanding Poker Math
I am surprised, by how many people don’t understand poker math. This is why I’m going to write. About the basics of poker math. For those of you, who would like to know how it works. Of course, remember poker is not all math. It’s just nice to know and more interesting. When your playing a game.
The Bases of Probabilities as We Know It.
Poker math formula consists, of knowing just one easy mathematical procedure. Which is permutations and combinations. It might sound like two procedures. However, they are just about the same, but work together masterfully. For example, You have a 52 card deck. And, want to figure out, how many possible 5 card poker hands there are. Before, you take the first card. You realize, there is 52 cards you can choose from. So, take your first card. Then, there is 51 cards to choose from. Etc., Etc. After, you drawn your 5 cards. Then what? Well, every time you took a card from the deck. There were a certain number of cards left in the deck. Right? So, every time you drew a card. Take the numbers that was left in the deck. And, times them by each other. Such as, 52 X 51 X 50 X 49 X 48 = 311,875,200. The formulation that was just done. Is called a permutation. This is not what we are after. This formulation gives us hands with the exact same cards. Just in different orders.
This formula needs to be memorized in the initial stages because poker math involves having as many cards under your sleeve as in your hand for that is the mark of an expert player which is why one should gain knowledge of dominoqq for understanding the deck of cards in poker.
Now, that we have our permutation. We need one more permutation. To turn our poker math into a combination. It’s simple, How many cards did you draw from the deck? You drew your 1st card from the deck, Then the 2nd,3rd,4,th, and 5th. Take each time you drew a card. Then, times it by the other times you drew a card. Such as, 1 X 2 X 3 X 4 X 5 = 120. This would be your final permutation that is needed.
So, how do I create a combination with my two permutations? All you have to do is divide the totals, of your two permutations together. Just as this, 311,875,200 / 220 = 2,598,960. Which is 2,598,960 possible 5 card poker hands. Now, you know how many possible 5 card hands there are. This can be applied to any poker game. By just switching up the variables.
It’s Really That Simple.
Well, I hope it was simple enough. Remember, poker math is not everything. But, nice to know. So, you can realize how unlucky you were. | crawl-data/CC-MAIN-2021-21/segments/1620243991413.30/warc/CC-MAIN-20210512224016-20210513014016-00578.warc.gz | null |
Unfortunately, drowning is one of the most common reasons for deaths abroad. Safety in the water is extremely important no matter if you are in the lake, ocean, or river. Even some of the most proficient swimmers have experienced an unpleasant water-related incident.
- Wear water shoes to protect your feet from being cut on rocks and sediments. Infections can occur if coastal waters enter a wound.
- Inexperienced and experienced swimmers in areas known for unpredictable water patterns or rough waters should wear a life jacket.
- Don’t dive headfirst—protect your neck. Check for depth and obstructions before entering the water, and go in feet first.
- At the beach, even in shallow water, wave action can cause a loss of footing.
- Keep a lookout for aquatic life. Water plants and animals may be dangerous. Avoid patches of plants and leave animals alone.
- Use the buddy system. Many drownings involve single swimmers. When you swim with a buddy, if one of you has a problem, the other may be able to help, including signaling for assistance from others. Swimmers should have someone onshore watching them.
- Obey the signs and posted flags – really learn and understand what they mean.
- Talking to a local can be important, especially if you notice few people in the water. They are the most knowledgeable about their town and/or country.
- Riptides/currents pose an extreme threat to any swimmer.
- If you are caught in a riptide, stay calm and don’t fight the current.
- Swim parallel to the shore until you are out of the current. Once you are free, turn and swim toward shore.
- If you can't swim to the shore, float or tread water until you are free of the riptide, then head toward shore.
- If you feel you can’t make it to the shore, draw attention to yourself by waving and calling for help.
- Stay at least 100 feet away from piers and jetties. Permanent riptides often exist near these structures.
- If someone is in trouble in the water, get help from a lifeguard. If a lifeguard is not available, have someone call emergency responders. Provide the victim with something that floats – a life jacket, cooler, inflatable ball, etc. and yell instructions on how to escape the current.
- When at the beach, check conditions before entering the water. Check to see if any warning flags are up or ask a lifeguard about water conditions, beach conditions, or any potential hazards.
- Do not leave your personal effects unattended while in the water. Keep a close eye on your personal belongings!
- For more information, you can visit the following: | <urn:uuid:54f19294-a580-4c6f-b5e6-4a18fe8772c0> | {
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## Conversion formula
The conversion factor from inches to kilometers is 2.54E-5, which means that 1 inch is equal to 2.54E-5 kilometers:
1 in = 2.54E-5 km
To convert 23.3 inches into kilometers we have to multiply 23.3 by the conversion factor in order to get the length amount from inches to kilometers. We can also form a simple proportion to calculate the result:
1 in → 2.54E-5 km
23.3 in → L(km)
Solve the above proportion to obtain the length L in kilometers:
L(km) = 23.3 in × 2.54E-5 km
L(km) = 0.00059182 km
The final result is:
23.3 in → 0.00059182 km
We conclude that 23.3 inches is equivalent to 0.00059182 kilometers:
23.3 inches = 0.00059182 kilometers
## Alternative conversion
We can also convert by utilizing the inverse value of the conversion factor. In this case 1 kilometer is equal to 1689.7029502214 × 23.3 inches.
Another way is saying that 23.3 inches is equal to 1 ÷ 1689.7029502214 kilometers.
## Approximate result
For practical purposes we can round our final result to an approximate numerical value. We can say that twenty-three point three inches is approximately zero point zero zero one kilometers:
23.3 in ≅ 0.001 km
An alternative is also that one kilometer is approximately one thousand six hundred eighty-nine point seven zero three times twenty-three point three inches.
## Conversion table
### inches to kilometers chart
For quick reference purposes, below is the conversion table you can use to convert from inches to kilometers
inches (in) kilometers (km)
24.3 inches 0.001 kilometers
25.3 inches 0.001 kilometers
26.3 inches 0.001 kilometers
27.3 inches 0.001 kilometers
28.3 inches 0.001 kilometers
29.3 inches 0.001 kilometers
30.3 inches 0.001 kilometers
31.3 inches 0.001 kilometers
32.3 inches 0.001 kilometers
33.3 inches 0.001 kilometers | crawl-data/CC-MAIN-2020-40/segments/1600400206763.24/warc/CC-MAIN-20200922192512-20200922222512-00430.warc.gz | null |
What if, during every unit of inquiry, learners had opportunities to develop their thinking and understanding by expressing themselves in ‘100 languages’?
What if we made that into an explicit ongoing unit of inquiry, for teachers as much as learners, interwoven through all the other units?
What if every unit had these two additional lines of inquiry?
- How we might express our learning through ‘100 languages’.
- How expressing ourselves in different ways deepens our understanding.
What if learners asked themselves…
What theories and ideas do I have?
What might I make to show my understanding?
How might I communicate my ideas?
How is my thinking changing?
Which questions and ideas would I like to explore further?
How might I learn from my failures?
What if teacher research questions included…
How might the ‘100 languages’ inspire curiosity and inquiry?
How might we select intelligent materials that help develop ideas?
How will we observe and listen to what is revealed by the children?
How might we make the ideas and wonderings visible?
How might we decide which student examples will drive the inquiry?
How will we encourage and honour children’s theories?
How will we ensure there is time for conversation that helps move the inquiry along?
Might this support us in slowing down to make time and space for deeper learning?
Might this encourage planning and teaching that responds to emerging inquiries?
Might this foster learner agency and enhance opportunities for learners to drive the learning?
Might this create opportunities for every learner to shine?
Might this support our current focus on cultivating action, both in students and teachers?
Might this be an expression of every single one of our learning principles?
- We learn in different ways, depending on abilities, preferences and interests.
- Learning takes place through inquiry: questioning, exploring, experimenting and problem solving.
- Learning occurs by acquiring skills and knowledge, constructing meaning and transfer to other contexts.
- Learning is active and social and can be enhanced by collaboration and interaction.
- Learning takes place when we feel secure, valued and are able to take risks.
- Learning needs to be challenging, meaningful, purposeful and engaging.
- Learning includes metacognition and reflection, and requires learners to take ownership of their learning.
Let’s see how it goes! | <urn:uuid:03e031dd-cb32-454a-8284-f0091bec655a> | {
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This class examined English writers’ ability to create textual worlds of all sorts by exploring works written in the sixteenth and seventeenth centuries, periods marked by religious controversy, exploration and scientific discovery, foreign and civil war, and the flourishing of literary culture. English writers in the period were deeply invested in writing about the virtues of their own country. The period’s literature often extols the qualities that made England different from (and, in their minds, superior to) other places. Creating their own versions of this nation in literary texts, they fashioned grand utopias and peopled their rich landscapes with beautiful fairy queens, fierce dragons, and brave knights. But they were not simply content to think about England and earth; they were also fascinated by the prospect of other worlds––and different forms of government––outside of both. In addition to glorifying the English nation, then, they constructed what The Tempest’s Miranda terms “brave new worlds” in Heaven, Hell, and even America. The literary works in which these worlds appear demonstrate the beauty and richness of the human imagination as well as its capacity for fear and cruelty.
Our readings covered a wide variety of works from the 16th including Thomas More’s Utopia (1516), Book I (and in one section, some of Book III) of Edmund Spenser’s The Faerie Queene (1596), and Sir Walter Raleigh’s The Discovery of the Large, Rich, and Beautiful Empire of Guiana (1595). Shifting into the 17th century, we read poems by Andrew Marvell, Katherine Phillips and John Donne, as well as Book 1 and Book 9 of John Milton’s Paradise Lost (1667) and Margaret Cavendish’s The Description of New World Called The Blazing World (1666). We also read accounts by English travelers in Europe and the Mediterranean, and by English colonists in the Americas and Ireland. Students wrote short, weekly close reading assignments called “5-on-2s” (five sentences on two elements or units of analysis–two words, two lines, two metaphors) as well as several longer responses to the course material in class meetings. In order to fulfill am HCLAS objective assigned to the course, they also gave oral presentations and developed, in collaboration, a rubric for assessing the strength of their oral communication skills. In addition to three major exams, students completed a take-home final exam, two essay questions that required them to incorporate at least ten works from the class into analyses on broad and narrow topics. | <urn:uuid:960fb60c-7b69-4621-bee2-b53a66f63679> | {
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We love teaching kindergarten to all of our new Parkwood Panthers! There are many goals we work toward achieving in kindergarten. Among the most important of those goals is for each of our students to become an independent thinker and to develop a lifelong love of school.
In kindergarten we follow the Common Core State Standards, however we have specifically targeted some skills that are more critical for math success for this year and the years beyond.
Essential Standards in Math
- I can read and write and match objects for all numbers 0-20.
- I can make and take apart teen numbers (like 13 is one ten and 3 more).
- I can show and explain addition and subtraction sentences with tools, numbers, and symbols.
- When I am given one number between 1 and 10, I can find the other number to make ten.
- I can count to 100 by 1s and 10s.
Kindergarten uses the Superkids Curriculum to teach reading. Students learn their letters and sounds. They learn to blend and produce sounds reading the phonics readers. The curriculum also emphasizes vocabulary to increase understanding and learning. Superkids is a fun, motivational program that students love. It is also rigorous and phonics-based.
Kindergarteners have English Language Arts expectations that are essential to the foundation of their learning. For instance, students will recognize and name all upper and lower case letters of the alphabet, as well as know their sounds, Students will also demonstrate the ability to make rhymes and identify all of the sounds in words.
Essential Standards in Reading
- I can read and write all my upper-case and lower-case letters and tell the sounds they make.
- I can blend 3-4 consonants and vowels together to read a word (read a consonant-vowel-consonant (CVC) or a consonant-consonant-vowel-consonant (CCVC) combination to blend/read the word – can be real or nonsense:
real CVC word can be /s/-/u/-/n/ or sun or nonsense CVC word can be /g/-/o/-/f/ or gof
- I can recognize and make rhyming words (do bat and cat rhyme? - yes, do bat and ball rhyme? – no) and (make three more words that rhyme with bat and cat…sat, hat, mat, rat,etc.)
- I can take apart and put together word parts by their sounds.
I can read memory words (such as the, a, I, is, was, with, of, to, you, she, see, my, are, he, do, does, like)
Essential Standards in Writing
- I know that words are separated by spaces in print.
- I can use pictures and words to tell about the events in a story (journaling).
- I can write sentences—I know how to use a capital and ending punctuation.
- I use pictures and words to tell what I think about a topic or a book (response to a question or an opinion about a book or movie).
A note about spelling: kindergarteners learn more about letters and sounds when they are doing best guess/inventive spelling rather than copying words provided by adults.
In kindergarten, we have three hands-on science kits. Our kits are:
- Discovering Animals
- Push, Pull, Go
We also teach science content in literacy time, using nonfiction texts to learn more about various science topics.
For kindergarten students, social studies is primarily about learning about themselves, their families, and their communities.
We use a variety of resources to teach these concepts, including the Scholastic Let’s Find Out Magazines.
Second Step teaches kindergarteners how to be successful learners; how to understand and recognize their feelings, and how to make friends. Students also learn positive and effective ways to solve problems. Our students learn to reach out and ask for help, as well as gain a host of strategies in resolving conflict, thus empowering them to solve their own problems. | <urn:uuid:5d529377-74a3-4da4-9945-38bf5ad36bb7> | {
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Hydraulic cylinders draw power from a pressurised hydraulic fluid, which is typically some type of oil. The hydraulic cylinder basically consists of two parts: a barrel cylinder and a movable piston or plunger connected to a piston rod. The barrel cylinder is closed at both ends, with the bottom at one end and the head at the other end, through which the piston is inserted and which has a bore through which the piston rod exits. The piston divides the inside of the cylinder into two chambers: the lower chamber and the piston rod chamber. Hydraulic pressure acts on the piston to produce the linear movement.
The maximum force is a function of the active surface area of the piston and the maximum allowable pressure, where: F = P * A
This force is constant from the beginning to the end of the stroke. The speed depends on the fluid flow and the piston surface. Depending on the version, the cylinder can apply tensile and/or compressive forces. | <urn:uuid:ff3ff082-5e07-4bf0-b931-4ac5b75ac33a> | {
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Yulia
2021-01-22
To determine:To Find:the measure of side BB
Bertha Stark
Calculation:
Since, plane of $\mathrm{△}{A}^{\prime }{B}^{\prime }{C}^{\prime }$ is similar to the plane of $\mathrm{△}ABC$
Since, ABCD is a parallelogram.
$\mathrm{\angle }V=\mathrm{\angle }V\therefore$(Common)
$\mathrm{\angle }VAB=\mathrm{\angle }V{A}^{\prime }{B}^{\prime }\therefore$(Corresponding angle in two similar plane)
Therefore by AA similarity, $\mathrm{△}VAB\sim \mathrm{△}V{A}^{\prime }{B}^{\prime }$
Ratio of corresponding sides in two similar triangles is equal.
$\frac{VA}{V{A}^{\prime }}=\frac{VC}{V{C}^{\prime }}$
$\frac{V{A}^{\prime }+{\mathrm{\forall }}^{\prime }}{V{A}^{\prime }}=\frac{VB}{V{B}^{\prime }}$
$\frac{15+20}{15}=\frac{49}{V{B}^{\prime }}$
$V{B}^{\prime }=\frac{15×49}{35}$
VB'=21
VB=BB'+VB'
49=BB+21
BB'=28 | crawl-data/CC-MAIN-2023-40/segments/1695233510528.86/warc/CC-MAIN-20230929190403-20230929220403-00791.warc.gz | null |
# How do you solve abs(5-2x)=13?
Mar 2, 2018
$x = - 4 \text{ or } x = 9$
#### Explanation:
$\text{the value inside the "color(blue)"absolute value bars "" can be}$
$\text{positive or negative }$
$\Rightarrow \text{there are 2 possible solutions}$
$5 - 2 x = 13 \leftarrow \textcolor{red}{\text{positive inside bars}}$
$\text{subtract 5 from both sides}$
$\cancel{5} \cancel{- 5} - 2 x = 13 - 5$
$\Rightarrow - 2 x = 8$
$\text{divide both sides by } - 2$
$\frac{\cancel{- 2} x}{\cancel{- 2}} = \frac{8}{- 2}$
$\Rightarrow x = - 4 \leftarrow \textcolor{b l u e}{\text{first solution}}$
$- \left(5 - 2 x\right) = 13 \leftarrow \textcolor{red}{\text{negative inside bars}}$
$\Rightarrow - 5 + 2 x = 13$
$\text{add 5 to both sides}$
$\cancel{- 5} \cancel{+ 5} + 2 x = 13 + 5$
$\Rightarrow 2 x = 18$
$\text{divide both sides by 2}$
$\frac{\cancel{2} x}{\cancel{2}} = \frac{18}{2}$
$\Rightarrow x = 9 \leftarrow \textcolor{b l u e}{\text{second solution}}$
$\textcolor{b l u e}{\text{As a check}}$
$\text{Substitute these 2 possible solutions into the left side}$
$\text{of the equation and if equal to right side then they are}$
$\text{the solutions}$
$x = - 4 \Rightarrow | 5 + 8 | = | 13 | = 13 \leftarrow \text{ True}$
$x = 9 \Rightarrow | 5 - 18 | = | = 13 | = 13 \leftarrow \text{ True}$
$\Rightarrow x = - 4 \text{ or "x=9" are the solutions}$ | crawl-data/CC-MAIN-2020-16/segments/1585371620338.63/warc/CC-MAIN-20200406070848-20200406101348-00472.warc.gz | null |
Home Contact KS2 Maths GCSE EFL Advice Parents Games Other
GCSE Maths > Shape and Space - Transformations
A translation occurs when a shape is moved from one place to another. It is equivalent of picking up the shape and putting it down somewhere else. Vectors are used to describe translations.
A reflection is like placing a mirror on the page. When describing a reflection, you need to state the line which the shape has been reflected in.
When describing a rotation, the centre and angle of rotation are given. If you wish to use tracing paper to help with rotations: draw the shape you wish to rotate onto the tracing paper and put this over shape. Push the end of your pencil down onto the tracing paper, where the centre of rotation is and turn the tracing paper through the appropriate angle. The resultant position of the shape on the tracing paper is where the shape is rotated to.
### Enlargements
Enlargements have a centre of enlargement and a scale factor.
1) Draw a line from the centre of enlargement to each vertex ('corner') of the shape you wish to enlarge. Measure the lengths of each of these lines.
2) If the scale factor is 2, draw a line from the centre of enlargement, through each vertex, which is twice as long as the length you measured. If the scale factor is 3, draw lines which are three times as long. If the scale factor is 1/2, draw lines which are 1/2 as long, etc.
#### Example
The centre of enlargement is marked. Enlarge the triangle by a scale factor of 2. | crawl-data/CC-MAIN-2013-48/segments/1386164013918/warc/CC-MAIN-20131204133333-00037-ip-10-33-133-15.ec2.internal.warc.gz | null |
# Secondary Math II Outline of NROC Resources
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Below is an outline of the NROC resources that can be used as interventions when teaching the Secondary Mathematics II course. Note: Some of the resources below are from the HippoCampus collection and are subject to these Terms of Use.
Quarter 1
Unit 1: Extending the Number System
Lesson 1: Properties of Exponents
Standard: N.RN.1
Lesson 2: Rational Exponents
Standard: N.RN.2
Lesson 3: Properties of Number Sets
Standard: N.RN.3
Lesson 4: Complex Numbers
Standard: N.CN.1, N.CN.2
Lesson 5: Operations on Polynomials
Standard: A.APR.1
Unit 2: Quadratic Functions and Modeling
Lesson 1: Key Features of Functions
Standard: F.IF.4
Lesson 2: Applications of Domain
Standard: F.IF.5
Lesson 3: Average Rate of Change
Standard: F.IF.6
Lesson 4: Graph Linear and Quadratic Functions
Standard: F.IF.7
Lesson 5: Graph Square Root, Cube Root, and Piecewise Functions
Standard: F.IF.7
Lesson 6: Writing Quadratic Functions By Factoring
Standard: F.IF.8, A.SSE.3
Lesson 7: Writing Quadratic Functions by Completing the Square
Standard: F.IF.8, A.SSE.3
Unit 3: Using Functions
Lesson 1: Interpreting Exponential Functions
Standard: F.IF.8
Lesson 2: Comparing Properties of Functions
Standard: F.IF.9, F.LE.3
Lesson 3: Write Functions that Model a Relationship
Standard: F.BF.1
Lesson 4: Transformations of Functions
Standard: F.BF.3
Lesson 5: Inverse Functions
Standard: F.BF.4
Quarter 2
Unit 4: Expressions and Equations
Lesson 1: Interpreting Expressions By Examining Polynomials
Standard: A.SSE.1, A.SSE.2
Lesson 2: Writing Equivalent Expressions
Standard: A.SSE.3
Lesson 3: Using Equations and Inequalities
Standard: A.CED.1, A.CED.2
Lesson 4: Rearranging Formulas
Standard: A.CED.4
Lesson 5: Deriving the Quadratic Formula
Standard: A.REI.4
Standard: A.REI.4, N.CN.7
Lesson 7: Extending Polynomial Identities to Complex Numbers
Standard: N.CN.8
• Resource: None
Lesson 8: The Fundamental Theorem of Algebra
Standard: N.CN.9
• Resource: None
Lesson 9: Moduli and Quotients of Complex Numbers (Honors)
Standard: N.CN.3
Lesson 10: Complex Numbers on the Coordinate Plane (Honors)
Standard: N.CN.4, N.CN.5, N.CN.6
• Resource: None
Lesson 11: Solve Systems of Equations
Standard: A.REI.7
Lesson 12: Systems of Equations and Matrices (Honors)
Standard: A.REI.8, A.REI.9
• Resource: None
Unit 5: Proof
Lesson 1: Introduction to Formal Proof
Standard: G.CO.9, G.CO.10, G.CO.11
Lesson 2: Theorems About Lines and Angles
Standard: G.CO.9
Standard: G.CO.10
Standard: G.CO.11
Lesson 5: Proof Using Coordinates
Standard: G.GPE.6, G.GPE.4
Unit 6: Similarity and Right Triangle Trigonometry (Extends into Q3)
Lesson 1: Dilations
Standard: G.SRT.1
• Resource: None
Lesson 2: Triangle Similarity
Standard: G.SRT.2, G.SRT.3
Lesson 3: Using Similarity and Congruence
Standard: G.SRT.4, G.SRT.5
Lesson 4: Trigonometric Ratios
Standard: G.SRT.6, G.SRT.7
Lesson 5: Solving Right Triangles
Standard: G.SRT.8
Lesson 6: Trigonometric Identities
Standard: F.TF.8
Lesson 7: Addition and Subtraction Formulas In Trigonometry (Honors)
Standard: F.TF.9
• Resource: None
Quarter 3
Unit 7: Circles Without Coordinates
Lesson 1: Similarity of Circles
Standard: G.C.1
• Resource: None
Lesson 2: Circle Relationships
Standard: G.C.2
Lesson 3: Circle Constructions
Standard: G.C.3, G.C.4
Lesson 4: Arc Length and Area of a Sector
Standard: G.C.5
• Resource: None
Standard: G.C.5
Lesson 6: Circumference and Area of Circles
Standard: G.GMD.1
Lesson 7: Volume
Standard: G.GMD.1, G.GMD.3
Lesson 8: Cavalieri’s Principle (Honors)
Standard: G.GMD.2
• Resource: None
Unit 8: Circles With Coordinates
Lesson 1: Equations of Circles
Standard: G.GPE.1
Lesson 2: Equations of Parabolas
Standard: G.GPE.2
Lesson 3: Equations of Ellipses (Honors)
Standard: G.GPE.3
Lesson 4: Equations of Hyperbolas (Honors)
Standard: G.GPE.3
Quarter 4
Unit 9: Applications of Probability
Lesson 1: Introduction to Probability
Standard: S.CP.1
Lesson 2: Independence
Standard: S.CP.2, S.CP.5
Lesson 3: Conditional Probability
Standard: S.CP.3, S.CP.5
Lesson 4: Constructing and Using Two-Way Tables
Standard: S.CP.4
• Resource: None
Lesson 5: Rules of Probability
Standard: S.CP.6, S.CP.7, S.CP.8
• Resource: None
Lesson 6: Permutations and Combinations
Standard: S.CP.9
Lesson 7: Making Decisions from Probability
Standard: S.MD.1, S.MD.2
• Resource: None
*Created by Annie Swinton, Mountain Heights Academy | crawl-data/CC-MAIN-2017-47/segments/1510934809746.91/warc/CC-MAIN-20171125090503-20171125110503-00411.warc.gz | null |
## Calculating the occupancy problem
The occupancy problem refers to the experiment of randomly throwing $k$ balls into $n$ cells. Out of this experiment, there are many problems that can be asked. In this post we focus on question: what is the probability that exactly $j$ of the cells are empty after randomly throwing $k$ balls into $n$ cells, where $0 \le j \le n-1$?
For a better perspective, there are many other ways to describe the experiment of throwing $k$ balls into $n$ cells. For example, throwing $k$ balls into 6 cells can be interpreted as rolling $k$ dice (or rolling a die $k$ times). Throwing $k$ balls into 365 cells can be interpreted as randomly selecting $k$ people and classifying them according to their dates of birth (assuming 365 days in a year). Another context is coupon collecting – the different types of coupons represent the $n$ cells and the coupons being collected represent the $k$ balls.
_____________________________________________________________________________________
Practice Problems
Let $X_{k,n}$ be the number of cells that are empty (i.e. not occupied) when throwing $k$ balls into $n$ cells. As noted above, the problem discussed in this post is to find the probability function $P(X_{k,n}=j)$ where $j=0,1,2,\cdots,n-1$. There are two elementary ways to do this problem. One is the approach of using double multinomial coefficient (see this post) and the other is to use a formula developed in this post. In addition to $X_{k,n}$, let $Y_{k,n}$ be the number of cells that are occupied, i.e. $Y_{k,n}=n-X_{k,n}$.
Practice Problems
Compute $P(X_{k,n}=j)$ where $j=0,1,2,\cdots,n-1$ for the following pairs of $k$ and $n$.
1. $k=5$ and $n=5$
2. $k=6$ and $n=5$
3. $k=7$ and $n=5$
4. $k=6$ and $n=6$
5. $k=7$ and $n=6$
6. $k=8$ and $n=6$
We work the problem for $k=7$ and $n=5$. We show both the double multinomial coefficient approach and the formula approach. Recall the $k$ here is the number of balls and $n$ is the number of cells.
_____________________________________________________________________________________
Example – Double Multinomial Coefficient
Note that the double multinomial coefficient approach calculate the probabilities $P(Y_{7,5}=j)$ where $Y_{7,5}$ is the number of occupied cells when throwing 7 balls into 5 cells. In throwing 7 balls into 5 cells, there is a total of $5^7=$ 78125 many ordered samples. To calculate $P(Y_{7,5}=j)$, first write down the representative occupancy sets for the event $Y_{7,5}=j$. For each occupancy set, calculate the number of ordered samples (out of 78125) that belong to that occupancy set. Then we add up all the counts for all the occupancy sets for $Y_{7,5}=j$. This is best illustrated with an example. To see the development of this idea, see this post.
Fist, consider the event of $Y_{7,5}=1$ (only one cell is occupied, i.e. all the balls going into one cell). A representative occupancy set is (0, 0, 0, 0, 7), all the balls going into the 5th cell. The first multinomial coefficient is on the 5 cells and the second multinomial coefficient is on the 7 balls.
(0, 0, 0, 0, 7)
$\displaystyle \frac{5!}{4! 1!} \times \frac{7!}{7!}=5 \times 1 =5$
Total = 5
So there are 5 ordered samples out of 16807 that belong to the event $Y_{7,5}=1$. Note that the first multinomial coefficient is the number of to order the 5 cells where 4 of the cells are empty and one of the cells has 7 balls. The second multinomial coefficient is the number of ways to order the 7 balls where all 7 balls go into the 5th cell.
Now consider the event $Y_{7,5}=2$ (all 7 balls go into 2 cells). There are three representative occupancy sets. The following shows the calculation for each set.
(0, 0, 0, 1, 6)
$\displaystyle \frac{5!}{3! 1! 1!} \times \frac{7!}{1! 6!}=20 \times 7 =140$
(0, 0, 0, 2, 5)
$\displaystyle \frac{5!}{3! 1! 1!} \times \frac{7!}{2! 5!}=20 \times 21 =420$
(0, 0, 0, 3, 4)
$\displaystyle \frac{5!}{3! 1! 1!} \times \frac{7!}{3! 4!}=20 \times 35 =700$
Total = 140 + 420 + 700 = 1260
Here’s an explanation for the occupancy set (0, 0, 0, 3, 4). The occupancy set refers to the scenario that 3 of the 7 balls go into the 4th cell and 4 of the 7 balls go into the 5th cell. But we want to count all the possibilities such that 3 of the 7 balls go into one cell and 4 of the 7 balls go into another cell. Thus the first multinomial coefficient count the number of ways to order 5 cells where three of the cells are empty and one cell has 3 balls and the remaining cell has 4 balls (20 ways) The second multinomial coefficient is the number of ways to order the 7 balls where 3 of the 7 balls go into the 4th cell and 4 of the 7 balls go into the 5th cell (35 ways). So the total number of possibilities for the occupancy set (0, 0, 0, 3, 4) is 20 times 35 = 700. The sum total for three occupancy sets is 1260.
We now show the remaining calculation without further elaboration.
Now consider the event $Y_{7,5}=3$ (all 7 balls go into 3 cells). There are four representative occupancy sets. The following shows the calculation for each set.
(0, 0, 1, 1, 5)
$\displaystyle \frac{5!}{2! 2! 1!} \times \frac{7!}{1! 1! 5!}=30 \times 42 =1260$
(0, 0, 1, 2, 4)
$\displaystyle \frac{5!}{2! 1! 1! 1!} \times \frac{7!}{1! 2! 4!}=60 \times 105 =6300$
(0, 0, 1, 3, 3)
$\displaystyle \frac{5!}{2! 1! 2!} \times \frac{7!}{1! 3! 3!}=30 \times 140 =4200$
(0, 0, 2, 2, 3)
$\displaystyle \frac{5!}{2! 2! 1!} \times \frac{7!}{2! 2! 3!}=30 \times 210 =6300$
Total = 1260 + 6300 + 4200 + 6300 = 18060
Now consider the event $Y_{7,5}=4$ (all 7 balls go into 4 cells, i.e. one empty cell). There are three representative occupancy sets. The following shows the calculation for each set.
(0, 1, 1, 1, 4)
$\displaystyle \frac{5!}{1! 3! 1!} \times \frac{7!}{1! 1! 1! 4!}=20 \times 210 =4200$
(0, 1, 1, 2, 3)
$\displaystyle \frac{5!}{1! 2! 1! 1!} \times \frac{7!}{1! 1! 2! 3!}=60 \times 420 =25200$
(0, 1, 2, 2, 2)
$\displaystyle \frac{5!}{1! 1! 3!} \times \frac{7!}{1! 2! 2! 2!}=20 \times 630 =12600$
Total = 4200 + 25200 + 12600 = 42000
Now consider the event $Y_{7,5}=4$ (all 7 balls go into 5 cells, i.e. no empty cell). There are two representative occupancy sets. The following shows the calculation for each set.
(1, 1, 1, 1, 3)
$\displaystyle \frac{5!}{4! 1!} \times \frac{7!}{1! 1! 1! 1! 3!}=5 \times 840 =4200$
(1, 1, 1, 2, 2)
$\displaystyle \frac{5!}{3! 2!} \times \frac{7!}{1! 1! 1! 2! 2!}=10 \times 1260 =12600$
Total = 4200 + 12600 = 16800
The following is the distribution for the random variable $Y_{7,5}$.
$\displaystyle P(Y_{7,5}=1)=\frac{5}{78125}=0.000064$
$\displaystyle P(Y_{7,5}=2)=\frac{1260}{78125}=0.016128$
$\displaystyle P(Y_{7,5}=3)=\frac{18060}{78125}=0.231168$
$\displaystyle P(Y_{7,5}=4)=\frac{42000}{78125}=0.5376$
$\displaystyle P(Y_{7,5}=5)=\frac{16800}{78125}=0.21504$
3.951424
Remarks
In throwing 7 balls at random into 5 cells, it is not like that the balls are in only one or two cells (about 1.6% chance). The mean number of occupied cells is about 3.95. More than 50% of the times, 4 cells are occupied.
The above example has small numbers of balls and cells and is an excellent example for practicing the calculation. Working such problems can help build the intuition for the occupancy problem. However, when the numbers are larger, the calculation using double multinomial coefficient can be lengthy and tedious. Next we show how to use a formula for occupancy problem using the same example.
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Example – Formula Approach
The formula we use is developed in this post. Recall that $X_{k,n}$ is the number of empty cells when throwing $k$ balls into $n$ cells. The formula calculates the probabilities $P(X_{7,5}=j)$ where
$0 \le j \le 5$. The first step is to compute the probabilities $P(X_{7,m}=0)$ for $m=5,4,3,2,1$. Each of these is the probability that all m cells are occupied (when throwing 7 balls into $m$ cells). These 5 probabilities will be used to calculate $P(X_{7,5}=j)$. This is a less direct implementation of the formula but gives a more intuitive explanation.
\displaystyle \begin{aligned} P(X_{7,5}=0)&=1-P(X_{7,5} \ge 1) \\&=1-\sum \limits_{j=1}^5 (-1)^{j+1} \binom{5}{j} \biggl[ 1-\frac{j}{5} \biggr]^7 \\&=1-\biggl[5 \biggl(\frac{4}{5}\biggr)^7-10 \biggl(\frac{3}{5}\biggr)^7+10 \biggl(\frac{2}{5}\biggr)^7 -5 \biggl(\frac{1}{5}\biggr)^7 + 0 \biggr] \\&=1-\frac{81920-21870+1280-5}{78125} \\&=\frac{16800}{78125} \end{aligned}
\displaystyle \begin{aligned} P(X_{7,4}=0)&=1-P(X_{7,4} \ge 1) \\&=1-\sum \limits_{j=1}^4 (-1)^{j+1} \binom{4}{j} \biggl[ 1-\frac{j}{4} \biggr]^7 \\&=1-\biggl[4 \biggl(\frac{3}{4}\biggr)^7-6 \biggl(\frac{2}{4}\biggr)^7+4 \biggl(\frac{1}{4}\biggr)^7 - 0 \biggr] \\&=1-\frac{8748-768+4}{16384} \\&=\frac{8400}{16384} \end{aligned}
\displaystyle \begin{aligned} P(X_{7,3}=0)&=1-P(X_{7,3} \ge 1) \\&=1-\sum \limits_{j=1}^3 (-1)^{j+1} \binom{3}{j} \biggl[ 1-\frac{j}{3} \biggr]^7 \\&=1-\biggl[3 \biggl(\frac{2}{3}\biggr)^7-3 \biggl(\frac{1}{3}\biggr)^7+0 \biggr] \\&=1-\frac{384-3}{2187} \\&=\frac{1806}{2187} \end{aligned}
\displaystyle \begin{aligned} P(X_{7,2}=0)&=1-P(X_{7,2} \ge 1) \\&=1-\sum \limits_{j=1}^2 (-1)^{j+1} \binom{2}{j} \biggl[ 1-\frac{j}{2} \biggr]^7 \\&=1-\biggl[2 \biggl(\frac{1}{2}\biggr)^7-0 \biggr] \\&=1-\frac{2}{128} \\&=\frac{126}{128} \end{aligned}
$P(X_{7,1}=0)=1$
Each of the above 5 probabilities (except the last one) is based on the probability $P(X_{7,m} \ge 1)$, which is the probability that there is at least one cell that is empty when throwing 7 balls into $m$ cells. The inclusion-exclusion principle is used to derive $P(X_{7,m} \ge 1)$. The last of the five does not need calculation. When throwing 7 balls into one cell, there will be no empty cells.
Now the rest of the calculation:
$\displaystyle P(X_{7,5}=0)=\frac{16800}{78125}$
\displaystyle \begin{aligned} P(X_{7,5}=1)&=P(\text{1 empty cell}) \times P(\text{none of the other 4 cells is empty}) \\&=\binom{5}{1} \biggl(1-\frac{1}{5} \biggr)^7 \times P(X_{7,4}=0) \\&=5 \ \frac{16384}{78125} \times \frac{8400}{16384} \\&=\frac{42000}{78125} \end{aligned}
\displaystyle \begin{aligned} P(X_{7,5}=2)&=P(\text{2 empty cells}) \times P(\text{none of the other 3 cells is empty}) \\&=\binom{5}{2} \biggl(1-\frac{2}{5} \biggr)^7 \times P(X_{7,3}=0) \\&=10 \ \frac{2187}{78125} \times \frac{1806}{2187} \\&=\frac{18060}{78125} \end{aligned}
\displaystyle \begin{aligned} P(X_{7,5}=3)&=P(\text{3 empty cells}) \times P(\text{none of the other 2 cells is empty}) \\&=\binom{5}{3} \biggl(1-\frac{3}{5} \biggr)^7 \times P(X_{7,2}=0) \\&=10 \ \frac{128}{78125} \times \frac{126}{128} \\&=\frac{1260}{78125} \end{aligned}
\displaystyle \begin{aligned} P(X_{7,5}=4)&=P(\text{4 empty cells}) \times P(\text{the other 1 cell is not empty}) \\&=\binom{5}{4} \biggl(1-\frac{4}{5} \biggr)^7 \times P(X_{7,1}=0) \\&=5 \ \frac{1}{78125} \times 1 \\&=\frac{5}{78125} \end{aligned}
Note that these answers agree with the ones from the double multinomial coefficient approach after making the adjustment $Y_{7,5}=5-X_{7,5}$.
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Problem 1
5 balls into 5 cells
$\displaystyle P(X_{5,5}=0)=P(Y_{5,5}=5)=\frac{120}{3125}$
$\displaystyle P(X_{5,5}=1)=P(Y_{5,5}=4)=\frac{1200}{3125}$
$\displaystyle P(X_{5,5}=2)=P(Y_{5,5}=3)=\frac{1500}{3125}$
$\displaystyle P(X_{5,5}=3)=P(Y_{5,5}=2)=\frac{300}{3125}$
$\displaystyle P(X_{5,5}=4)=P(Y_{5,5}=1)=\frac{5}{3125}$
Problem 2
6 balls into 5 cells
$\displaystyle P(X_{6,5}=0)=P(Y_{6,5}=5)=\frac{1800}{15625}$
$\displaystyle P(X_{6,5}=1)=P(Y_{6,5}=4)=\frac{7800}{15625}$
$\displaystyle P(X_{6,5}=2)=P(Y_{6,5}=3)=\frac{5400}{15625}$
$\displaystyle P(X_{6,5}=3)=P(Y_{6,5}=2)=\frac{620}{15625}$
$\displaystyle P(X_{6,5}=4)=P(Y_{6,5}=1)=\frac{5}{15625}$
Problem 3
7 balls into 5 cells. See above.
Problem 4
6 balls into 6 cells
$\displaystyle P(X_{6,6}=0)=P(Y_{6,6}=6)=\frac{720}{46656}$
$\displaystyle P(X_{6,6}=1)=P(Y_{6,6}=5)=\frac{10800}{46656}$
$\displaystyle P(X_{6,6}=2)=P(Y_{6,6}=4)=\frac{23400}{46656}$
$\displaystyle P(X_{6,6}=3)=P(Y_{6,6}=3)=\frac{10800}{46656}$
$\displaystyle P(X_{6,6}=4)=P(Y_{6,6}=2)=\frac{930}{46656}$
$\displaystyle P(X_{6,6}=5)=P(Y_{6,6}=1)=\frac{6}{46656}$
Problem 5
7 balls into 6 cells
$\displaystyle P(X_{7,6}=0)=P(Y_{7,6}=6)=\frac{15120}{279936}$
$\displaystyle P(X_{7,6}=1)=P(Y_{7,6}=5)=\frac{100800}{279936}$
$\displaystyle P(X_{7,6}=2)=P(Y_{7,6}=4)=\frac{126000}{279936}$
$\displaystyle P(X_{7,6}=3)=P(Y_{7,6}=3)=\frac{36120}{279936}$
$\displaystyle P(X_{7,6}=4)=P(Y_{7,6}=2)=\frac{1890}{279936}$
$\displaystyle P(X_{7,6}=5)=P(Y_{7,6}=1)=\frac{6}{279936}$
Problem 6
8 balls into 6 cells
$\displaystyle P(X_{8,6}=0)=P(Y_{8,6}=6)=\frac{191520}{1679616}$
$\displaystyle P(X_{8,6}=1)=P(Y_{8,6}=5)=\frac{756000}{1679616}$
$\displaystyle P(X_{8,6}=2)=P(Y_{8,6}=4)=\frac{612360}{1679616}$
$\displaystyle P(X_{8,6}=3)=P(Y_{8,6}=3)=\frac{115920}{1679616}$
$\displaystyle P(X_{8,6}=4)=P(Y_{8,6}=2)=\frac{3810}{1679616}$
$\displaystyle P(X_{8,6}=5)=P(Y_{8,6}=1)=\frac{6}{1679616}$
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$\copyright \ 2015 \text{ by Dan Ma}$
## A Problem of Rolling Six Dice
Problem
Suppose that we roll 6 fair dice (or equivalently, roll a fair die 6 times). Let $X$ be the number of distinct faces that appear. Find the probability function $P(X=k)$ where $k=1,2,3,4,5,6$.
Equivalent Problem
Suppose that we randomly assign 6 candies to 6 children (imagine that each candy is to be thrown at random to the children and is received by one of the children). What is the probability that exactly $k$ children have been given candies, where $k=1,2,3,4,5,6$?
___________________________________________________________________________
Discussion
Note that both descriptions are equivalent and are refered to as occupancy problem in [1]. The essential fact here is that $n$ objects are randomly assigned to $m$ cells. The problem then asks: what is the probability that $k$ of the cells are occupied? See the following posts for more detailed discussions of the occupancy problem.
Each of these posts presents different different ways of solving the occupancy problem. The first post uses a counting approach based on the multinomial coefficients. The second post developed a formula for finding the probability that exactly $k$ of the cells are empty.
The first approach of using mulltinomial coefficients is preferred when the number of objects $n$ and the number of cells $m$ are relatively small (such as the problem indicated here). Otherwise, use the formula approach.
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Using the approach of multinomial coefficients as shown in this post (the first post indicated above), we have the following answers:
$\displaystyle P(X=1)=\frac{6}{6^6}=\frac{6}{46656}$
$\displaystyle P(X=2)=\frac{930}{6^6}=\frac{930}{46656}$
$\displaystyle P(X=3)=\frac{10800}{6^6}=\frac{10800}{46656}$
$\displaystyle P(X=4)=\frac{23400}{6^6}=\frac{23400}{46656}$
$\displaystyle P(X=5)=\frac{10800}{6^6}=\frac{10800}{46656}$
$\displaystyle P(X=6)=\frac{720}{6^6}=\frac{720}{46656}$
For more practice problems on calculating the occupancy problem, see this post.
___________________________________________________________________________
Reference
1. Feller, W., An Introduction to Probability Theory and its Applications, Vol. I, 3rd ed., John Wiley & Sons, Inc., New York, 1968 | crawl-data/CC-MAIN-2019-18/segments/1555578530253.25/warc/CC-MAIN-20190421060341-20190421082341-00145.warc.gz | null |
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Develop drought information tools and guides to monitor drought, and integrate those tools and guides to support collaborative drought planning by ranchers and Forest Service staff. | <urn:uuid:90693ea8-ccd2-46b6-8360-218ed460f003> | {
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## M2 - Row operations as matrix multiplication
#### Example 1 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$C$$ that may be used to perform the row operation $$R_1 \to R_1 + -4R_2$$.
2. Give a $$4 \times 4$$ matrix $$N$$ that may be used to perform the row operation $$R_1 \to -5R_1$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_1 \to R_1 + -4R_2$$ and then $$R_1 \to -5R_1$$ to $$A$$ (note the order).
1. $$C= \left[\begin{array}{cccc} 1 & -4 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
2. $$N= \left[\begin{array}{cccc} -5 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
3. $$NCA$$
#### Example 2 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$M$$ that may be used to perform the row operation $$R_3 \to R_3 + 4R_2$$.
2. Give a $$4 \times 4$$ matrix $$C$$ that may be used to perform the row operation $$R_1 \to -4R_1$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_1 \to -4R_1$$ and then $$R_3 \to R_3 + 4R_2$$ to $$A$$ (note the order).
1. $$M= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 4 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
2. $$C= \left[\begin{array}{cccc} -4 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
3. $$MCA$$
#### Example 3 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$P$$ that may be used to perform the row operation $$R_2 \to R_2 + -4R_4$$.
2. Give a $$4 \times 4$$ matrix $$Q$$ that may be used to perform the row operation $$R_4 \leftrightarrow R_2$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_2 \to R_2 + -4R_4$$ and then $$R_4 \leftrightarrow R_2$$ to $$A$$ (note the order).
1. $$P= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & -4 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
2. $$Q= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \end{array}\right]$$
3. $$QPA$$
#### Example 4 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$P$$ that may be used to perform the row operation $$R_1 \to R_1 + 5R_4$$.
2. Give a $$4 \times 4$$ matrix $$B$$ that may be used to perform the row operation $$R_2 \to -5R_2$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_2 \to -5R_2$$ and then $$R_1 \to R_1 + 5R_4$$ to $$A$$ (note the order).
1. $$P= \left[\begin{array}{cccc} 1 & 0 & 0 & 5 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
2. $$B= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & -5 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
3. $$PBA$$
#### Example 5 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$C$$ that may be used to perform the row operation $$R_3 \to R_3 + 4R_1$$.
2. Give a $$4 \times 4$$ matrix $$Q$$ that may be used to perform the row operation $$R_1 \to 5R_1$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_3 \to R_3 + 4R_1$$ and then $$R_1 \to 5R_1$$ to $$A$$ (note the order).
1. $$C= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 4 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
2. $$Q= \left[\begin{array}{cccc} 5 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
3. $$QCA$$
#### Example 6 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$N$$ that may be used to perform the row operation $$R_3 \to R_3 + -4R_2$$.
2. Give a $$4 \times 4$$ matrix $$C$$ that may be used to perform the row operation $$R_1 \to 5R_1$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_1 \to 5R_1$$ and then $$R_3 \to R_3 + -4R_2$$ to $$A$$ (note the order).
1. $$N= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & -4 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
2. $$C= \left[\begin{array}{cccc} 5 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
3. $$NCA$$
#### Example 7 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$C$$ that may be used to perform the row operation $$R_4 \leftrightarrow R_1$$.
2. Give a $$4 \times 4$$ matrix $$Q$$ that may be used to perform the row operation $$R_2 \to 5R_2$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_4 \leftrightarrow R_1$$ and then $$R_2 \to 5R_2$$ to $$A$$ (note the order).
1. $$C= \left[\begin{array}{cccc} 0 & 0 & 0 & 1 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0 \end{array}\right]$$
2. $$Q= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 5 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
3. $$QCA$$
#### Example 8 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$Q$$ that may be used to perform the row operation $$R_4 \leftrightarrow R_1$$.
2. Give a $$4 \times 4$$ matrix $$C$$ that may be used to perform the row operation $$R_4 \to 2R_4$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_4 \leftrightarrow R_1$$ and then $$R_4 \to 2R_4$$ to $$A$$ (note the order).
1. $$Q= \left[\begin{array}{cccc} 0 & 0 & 0 & 1 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0 \end{array}\right]$$
2. $$C= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 2 \end{array}\right]$$
3. $$CQA$$
#### Example 9 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$Q$$ that may be used to perform the row operation $$R_2 \to R_2 + 4R_4$$.
2. Give a $$4 \times 4$$ matrix $$C$$ that may be used to perform the row operation $$R_4 \to -5R_4$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_4 \to -5R_4$$ and then $$R_2 \to R_2 + 4R_4$$ to $$A$$ (note the order).
1. $$Q= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 4 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
2. $$C= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & -5 \end{array}\right]$$
3. $$QCA$$
#### Example 10 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$P$$ that may be used to perform the row operation $$R_1 \to R_1 + 3R_2$$.
2. Give a $$4 \times 4$$ matrix $$B$$ that may be used to perform the row operation $$R_3 \to 3R_3$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_3 \to 3R_3$$ and then $$R_1 \to R_1 + 3R_2$$ to $$A$$ (note the order).
1. $$P= \left[\begin{array}{cccc} 1 & 3 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
2. $$B= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 3 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
3. $$PBA$$
#### Example 11 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$B$$ that may be used to perform the row operation $$R_1 \to 4R_1$$.
2. Give a $$4 \times 4$$ matrix $$C$$ that may be used to perform the row operation $$R_2 \leftrightarrow R_1$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_1 \to 4R_1$$ and then $$R_2 \leftrightarrow R_1$$ to $$A$$ (note the order).
1. $$B= \left[\begin{array}{cccc} 4 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
2. $$C= \left[\begin{array}{cccc} 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
3. $$CBA$$
#### Example 12 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$B$$ that may be used to perform the row operation $$R_4 \to R_4 + -3R_2$$.
2. Give a $$4 \times 4$$ matrix $$P$$ that may be used to perform the row operation $$R_4 \to 4R_4$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_4 \to R_4 + -3R_2$$ and then $$R_4 \to 4R_4$$ to $$A$$ (note the order).
1. $$B= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & -3 & 0 & 1 \end{array}\right]$$
2. $$P= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 4 \end{array}\right]$$
3. $$PBA$$
#### Example 13 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$B$$ that may be used to perform the row operation $$R_1 \to R_1 + -5R_3$$.
2. Give a $$4 \times 4$$ matrix $$M$$ that may be used to perform the row operation $$R_1 \to -3R_1$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_1 \to -3R_1$$ and then $$R_1 \to R_1 + -5R_3$$ to $$A$$ (note the order).
1. $$B= \left[\begin{array}{cccc} 1 & 0 & -5 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
2. $$M= \left[\begin{array}{cccc} -3 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
3. $$BMA$$
#### Example 14 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$Q$$ that may be used to perform the row operation $$R_3 \leftrightarrow R_4$$.
2. Give a $$4 \times 4$$ matrix $$C$$ that may be used to perform the row operation $$R_3 \to 4R_3$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_3 \leftrightarrow R_4$$ and then $$R_3 \to 4R_3$$ to $$A$$ (note the order).
1. $$Q= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \end{array}\right]$$
2. $$C= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 4 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
3. $$CQA$$
#### Example 15 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$M$$ that may be used to perform the row operation $$R_3 \to R_3 + -4R_2$$.
2. Give a $$4 \times 4$$ matrix $$P$$ that may be used to perform the row operation $$R_3 \to 5R_3$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_3 \to 5R_3$$ and then $$R_3 \to R_3 + -4R_2$$ to $$A$$ (note the order).
1. $$M= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & -4 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
2. $$P= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 5 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
3. $$MPA$$
#### Example 16 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$Q$$ that may be used to perform the row operation $$R_4 \leftrightarrow R_3$$.
2. Give a $$4 \times 4$$ matrix $$N$$ that may be used to perform the row operation $$R_2 \to R_2 + -4R_1$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_2 \to R_2 + -4R_1$$ and then $$R_4 \leftrightarrow R_3$$ to $$A$$ (note the order).
1. $$Q= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \end{array}\right]$$
2. $$N= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ -4 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
3. $$QNA$$
#### Example 17 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$P$$ that may be used to perform the row operation $$R_4 \leftrightarrow R_3$$.
2. Give a $$4 \times 4$$ matrix $$B$$ that may be used to perform the row operation $$R_4 \to R_4 + -2R_3$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_4 \leftrightarrow R_3$$ and then $$R_4 \to R_4 + -2R_3$$ to $$A$$ (note the order).
1. $$P= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \end{array}\right]$$
2. $$B= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & -2 & 1 \end{array}\right]$$
3. $$BPA$$
#### Example 18 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$Q$$ that may be used to perform the row operation $$R_4 \to R_4 + 2R_3$$.
2. Give a $$4 \times 4$$ matrix $$N$$ that may be used to perform the row operation $$R_2 \leftrightarrow R_4$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_4 \to R_4 + 2R_3$$ and then $$R_2 \leftrightarrow R_4$$ to $$A$$ (note the order).
1. $$Q= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 2 & 1 \end{array}\right]$$
2. $$N= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \end{array}\right]$$
3. $$NQA$$
#### Example 19 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$M$$ that may be used to perform the row operation $$R_2 \to R_2 + 4R_3$$.
2. Give a $$4 \times 4$$ matrix $$Q$$ that may be used to perform the row operation $$R_3 \to 5R_3$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_2 \to R_2 + 4R_3$$ and then $$R_3 \to 5R_3$$ to $$A$$ (note the order).
1. $$M= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 4 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
2. $$Q= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 5 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
3. $$QMA$$
#### Example 20 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$P$$ that may be used to perform the row operation $$R_4 \to R_4 + 4R_1$$.
2. Give a $$4 \times 4$$ matrix $$Q$$ that may be used to perform the row operation $$R_4 \leftrightarrow R_1$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_4 \to R_4 + 4R_1$$ and then $$R_4 \leftrightarrow R_1$$ to $$A$$ (note the order).
1. $$P= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 4 & 0 & 0 & 1 \end{array}\right]$$
2. $$Q= \left[\begin{array}{cccc} 0 & 0 & 0 & 1 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0 \end{array}\right]$$
3. $$QPA$$
#### Example 21 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$M$$ that may be used to perform the row operation $$R_1 \to R_1 + 5R_2$$.
2. Give a $$4 \times 4$$ matrix $$Q$$ that may be used to perform the row operation $$R_2 \leftrightarrow R_1$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_2 \leftrightarrow R_1$$ and then $$R_1 \to R_1 + 5R_2$$ to $$A$$ (note the order).
1. $$M= \left[\begin{array}{cccc} 1 & 5 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
2. $$Q= \left[\begin{array}{cccc} 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
3. $$MQA$$
#### Example 22 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$Q$$ that may be used to perform the row operation $$R_1 \to 2R_1$$.
2. Give a $$4 \times 4$$ matrix $$P$$ that may be used to perform the row operation $$R_3 \leftrightarrow R_2$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_1 \to 2R_1$$ and then $$R_3 \leftrightarrow R_2$$ to $$A$$ (note the order).
1. $$Q= \left[\begin{array}{cccc} 2 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
2. $$P= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
3. $$PQA$$
#### Example 23 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$Q$$ that may be used to perform the row operation $$R_4 \to 2R_4$$.
2. Give a $$4 \times 4$$ matrix $$N$$ that may be used to perform the row operation $$R_4 \leftrightarrow R_1$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_4 \to 2R_4$$ and then $$R_4 \leftrightarrow R_1$$ to $$A$$ (note the order).
1. $$Q= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 2 \end{array}\right]$$
2. $$N= \left[\begin{array}{cccc} 0 & 0 & 0 & 1 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0 \end{array}\right]$$
3. $$NQA$$
#### Example 24 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$N$$ that may be used to perform the row operation $$R_2 \to R_2 + 3R_3$$.
2. Give a $$4 \times 4$$ matrix $$B$$ that may be used to perform the row operation $$R_2 \leftrightarrow R_1$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_2 \to R_2 + 3R_3$$ and then $$R_2 \leftrightarrow R_1$$ to $$A$$ (note the order).
1. $$N= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 3 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
2. $$B= \left[\begin{array}{cccc} 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
3. $$BNA$$
#### Example 25 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$P$$ that may be used to perform the row operation $$R_3 \to R_3 + 4R_2$$.
2. Give a $$4 \times 4$$ matrix $$Q$$ that may be used to perform the row operation $$R_4 \to 4R_4$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_4 \to 4R_4$$ and then $$R_3 \to R_3 + 4R_2$$ to $$A$$ (note the order).
1. $$P= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 4 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
2. $$Q= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 4 \end{array}\right]$$
3. $$PQA$$
#### Example 26 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$C$$ that may be used to perform the row operation $$R_3 \to -3R_3$$.
2. Give a $$4 \times 4$$ matrix $$N$$ that may be used to perform the row operation $$R_4 \leftrightarrow R_2$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_3 \to -3R_3$$ and then $$R_4 \leftrightarrow R_2$$ to $$A$$ (note the order).
1. $$C= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & -3 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
2. $$N= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \end{array}\right]$$
3. $$NCA$$
#### Example 27 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$M$$ that may be used to perform the row operation $$R_2 \leftrightarrow R_1$$.
2. Give a $$4 \times 4$$ matrix $$C$$ that may be used to perform the row operation $$R_2 \to R_2 + -4R_4$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_2 \to R_2 + -4R_4$$ and then $$R_2 \leftrightarrow R_1$$ to $$A$$ (note the order).
1. $$M= \left[\begin{array}{cccc} 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
2. $$C= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & -4 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
3. $$MCA$$
#### Example 28 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$N$$ that may be used to perform the row operation $$R_4 \to R_4 + -3R_3$$.
2. Give a $$4 \times 4$$ matrix $$M$$ that may be used to perform the row operation $$R_1 \to 4R_1$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_1 \to 4R_1$$ and then $$R_4 \to R_4 + -3R_3$$ to $$A$$ (note the order).
1. $$N= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & -3 & 1 \end{array}\right]$$
2. $$M= \left[\begin{array}{cccc} 4 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
3. $$NMA$$
#### Example 29 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$B$$ that may be used to perform the row operation $$R_1 \to 5R_1$$.
2. Give a $$4 \times 4$$ matrix $$C$$ that may be used to perform the row operation $$R_4 \to R_4 + -5R_2$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_4 \to R_4 + -5R_2$$ and then $$R_1 \to 5R_1$$ to $$A$$ (note the order).
1. $$B= \left[\begin{array}{cccc} 5 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
2. $$C= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & -5 & 0 & 1 \end{array}\right]$$
3. $$BCA$$
#### Example 30 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$Q$$ that may be used to perform the row operation $$R_4 \to R_4 + -2R_3$$.
2. Give a $$4 \times 4$$ matrix $$M$$ that may be used to perform the row operation $$R_2 \to 3R_2$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_4 \to R_4 + -2R_3$$ and then $$R_2 \to 3R_2$$ to $$A$$ (note the order).
1. $$Q= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & -2 & 1 \end{array}\right]$$
2. $$M= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 3 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
3. $$MQA$$
#### Example 31 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$C$$ that may be used to perform the row operation $$R_3 \leftrightarrow R_1$$.
2. Give a $$4 \times 4$$ matrix $$M$$ that may be used to perform the row operation $$R_1 \to -3R_1$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_3 \leftrightarrow R_1$$ and then $$R_1 \to -3R_1$$ to $$A$$ (note the order).
1. $$C= \left[\begin{array}{cccc} 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
2. $$M= \left[\begin{array}{cccc} -3 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
3. $$MCA$$
#### Example 32 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$P$$ that may be used to perform the row operation $$R_4 \to R_4 + -3R_1$$.
2. Give a $$4 \times 4$$ matrix $$C$$ that may be used to perform the row operation $$R_3 \to 5R_3$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_3 \to 5R_3$$ and then $$R_4 \to R_4 + -3R_1$$ to $$A$$ (note the order).
1. $$P= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ -3 & 0 & 0 & 1 \end{array}\right]$$
2. $$C= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 5 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
3. $$PCA$$
#### Example 33 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$Q$$ that may be used to perform the row operation $$R_3 \leftrightarrow R_1$$.
2. Give a $$4 \times 4$$ matrix $$B$$ that may be used to perform the row operation $$R_4 \to 5R_4$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_4 \to 5R_4$$ and then $$R_3 \leftrightarrow R_1$$ to $$A$$ (note the order).
1. $$Q= \left[\begin{array}{cccc} 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
2. $$B= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 5 \end{array}\right]$$
3. $$QBA$$
#### Example 34 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$Q$$ that may be used to perform the row operation $$R_1 \to 5R_1$$.
2. Give a $$4 \times 4$$ matrix $$P$$ that may be used to perform the row operation $$R_2 \to R_2 + -5R_3$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_1 \to 5R_1$$ and then $$R_2 \to R_2 + -5R_3$$ to $$A$$ (note the order).
1. $$Q= \left[\begin{array}{cccc} 5 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
2. $$P= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & -5 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
3. $$PQA$$
#### Example 35 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$B$$ that may be used to perform the row operation $$R_2 \to R_2 + 5R_3$$.
2. Give a $$4 \times 4$$ matrix $$N$$ that may be used to perform the row operation $$R_4 \leftrightarrow R_1$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_2 \to R_2 + 5R_3$$ and then $$R_4 \leftrightarrow R_1$$ to $$A$$ (note the order).
1. $$B= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 5 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
2. $$N= \left[\begin{array}{cccc} 0 & 0 & 0 & 1 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0 \end{array}\right]$$
3. $$NBA$$
#### Example 36 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$C$$ that may be used to perform the row operation $$R_4 \leftrightarrow R_1$$.
2. Give a $$4 \times 4$$ matrix $$Q$$ that may be used to perform the row operation $$R_3 \to 4R_3$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_4 \leftrightarrow R_1$$ and then $$R_3 \to 4R_3$$ to $$A$$ (note the order).
1. $$C= \left[\begin{array}{cccc} 0 & 0 & 0 & 1 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0 \end{array}\right]$$
2. $$Q= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 4 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
3. $$QCA$$
#### Example 37 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$C$$ that may be used to perform the row operation $$R_1 \leftrightarrow R_4$$.
2. Give a $$4 \times 4$$ matrix $$P$$ that may be used to perform the row operation $$R_4 \to -3R_4$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_4 \to -3R_4$$ and then $$R_1 \leftrightarrow R_4$$ to $$A$$ (note the order).
1. $$C= \left[\begin{array}{cccc} 0 & 0 & 0 & 1 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0 \end{array}\right]$$
2. $$P= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & -3 \end{array}\right]$$
3. $$CPA$$
#### Example 38 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$B$$ that may be used to perform the row operation $$R_1 \to -2R_1$$.
2. Give a $$4 \times 4$$ matrix $$C$$ that may be used to perform the row operation $$R_4 \leftrightarrow R_3$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_1 \to -2R_1$$ and then $$R_4 \leftrightarrow R_3$$ to $$A$$ (note the order).
1. $$B= \left[\begin{array}{cccc} -2 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
2. $$C= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \end{array}\right]$$
3. $$CBA$$
#### Example 39 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$C$$ that may be used to perform the row operation $$R_4 \to R_4 + -2R_3$$.
2. Give a $$4 \times 4$$ matrix $$Q$$ that may be used to perform the row operation $$R_1 \to 2R_1$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_1 \to 2R_1$$ and then $$R_4 \to R_4 + -2R_3$$ to $$A$$ (note the order).
1. $$C= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & -2 & 1 \end{array}\right]$$
2. $$Q= \left[\begin{array}{cccc} 2 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
3. $$CQA$$
#### Example 40 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$Q$$ that may be used to perform the row operation $$R_1 \to R_1 + 3R_2$$.
2. Give a $$4 \times 4$$ matrix $$P$$ that may be used to perform the row operation $$R_3 \to 5R_3$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_1 \to R_1 + 3R_2$$ and then $$R_3 \to 5R_3$$ to $$A$$ (note the order).
1. $$Q= \left[\begin{array}{cccc} 1 & 3 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
2. $$P= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 5 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
3. $$PQA$$
#### Example 41 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$Q$$ that may be used to perform the row operation $$R_3 \to R_3 + -4R_4$$.
2. Give a $$4 \times 4$$ matrix $$M$$ that may be used to perform the row operation $$R_2 \leftrightarrow R_3$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_3 \to R_3 + -4R_4$$ and then $$R_2 \leftrightarrow R_3$$ to $$A$$ (note the order).
1. $$Q= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & -4 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
2. $$M= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
3. $$MQA$$
#### Example 42 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$M$$ that may be used to perform the row operation $$R_2 \leftrightarrow R_3$$.
2. Give a $$4 \times 4$$ matrix $$N$$ that may be used to perform the row operation $$R_2 \to 3R_2$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_2 \to 3R_2$$ and then $$R_2 \leftrightarrow R_3$$ to $$A$$ (note the order).
1. $$M= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
2. $$N= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 3 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
3. $$MNA$$
#### Example 43 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$C$$ that may be used to perform the row operation $$R_3 \leftrightarrow R_1$$.
2. Give a $$4 \times 4$$ matrix $$Q$$ that may be used to perform the row operation $$R_4 \to R_4 + -3R_3$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_3 \leftrightarrow R_1$$ and then $$R_4 \to R_4 + -3R_3$$ to $$A$$ (note the order).
1. $$C= \left[\begin{array}{cccc} 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
2. $$Q= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & -3 & 1 \end{array}\right]$$
3. $$QCA$$
#### Example 44 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$B$$ that may be used to perform the row operation $$R_3 \to -4R_3$$.
2. Give a $$4 \times 4$$ matrix $$M$$ that may be used to perform the row operation $$R_2 \leftrightarrow R_3$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_3 \to -4R_3$$ and then $$R_2 \leftrightarrow R_3$$ to $$A$$ (note the order).
1. $$B= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & -4 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
2. $$M= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
3. $$MBA$$
#### Example 45 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$M$$ that may be used to perform the row operation $$R_2 \to R_2 + -2R_4$$.
2. Give a $$4 \times 4$$ matrix $$P$$ that may be used to perform the row operation $$R_3 \leftrightarrow R_1$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_2 \to R_2 + -2R_4$$ and then $$R_3 \leftrightarrow R_1$$ to $$A$$ (note the order).
1. $$M= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & -2 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
2. $$P= \left[\begin{array}{cccc} 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
3. $$PMA$$
#### Example 46 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$B$$ that may be used to perform the row operation $$R_4 \to R_4 + 3R_3$$.
2. Give a $$4 \times 4$$ matrix $$Q$$ that may be used to perform the row operation $$R_4 \to 3R_4$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_4 \to 3R_4$$ and then $$R_4 \to R_4 + 3R_3$$ to $$A$$ (note the order).
1. $$B= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 3 & 1 \end{array}\right]$$
2. $$Q= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 3 \end{array}\right]$$
3. $$BQA$$
#### Example 47 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$P$$ that may be used to perform the row operation $$R_2 \to R_2 + -4R_4$$.
2. Give a $$4 \times 4$$ matrix $$B$$ that may be used to perform the row operation $$R_2 \leftrightarrow R_3$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_2 \leftrightarrow R_3$$ and then $$R_2 \to R_2 + -4R_4$$ to $$A$$ (note the order).
1. $$P= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & -4 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
2. $$B= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
3. $$PBA$$
#### Example 48 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$N$$ that may be used to perform the row operation $$R_4 \leftrightarrow R_1$$.
2. Give a $$4 \times 4$$ matrix $$B$$ that may be used to perform the row operation $$R_2 \to R_2 + -2R_3$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_2 \to R_2 + -2R_3$$ and then $$R_4 \leftrightarrow R_1$$ to $$A$$ (note the order).
1. $$N= \left[\begin{array}{cccc} 0 & 0 & 0 & 1 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0 \end{array}\right]$$
2. $$B= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & -2 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
3. $$NBA$$
#### Example 49 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$Q$$ that may be used to perform the row operation $$R_1 \to R_1 + 4R_4$$.
2. Give a $$4 \times 4$$ matrix $$N$$ that may be used to perform the row operation $$R_2 \leftrightarrow R_1$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_1 \to R_1 + 4R_4$$ and then $$R_2 \leftrightarrow R_1$$ to $$A$$ (note the order).
1. $$Q= \left[\begin{array}{cccc} 1 & 0 & 0 & 4 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
2. $$N= \left[\begin{array}{cccc} 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
3. $$NQA$$
#### Example 50 π
Let $$A$$ be a $$4 \times 4$$ matrix.
1. Give a $$4 \times 4$$ matrix $$P$$ that may be used to perform the row operation $$R_3 \leftrightarrow R_1$$.
2. Give a $$4 \times 4$$ matrix $$M$$ that may be used to perform the row operation $$R_3 \to 3R_3$$.
3. Use matrix multiplication to describe the matrix obtained by applying $$R_3 \leftrightarrow R_1$$ and then $$R_3 \to 3R_3$$ to $$A$$ (note the order).
1. $$P= \left[\begin{array}{cccc} 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
2. $$M= \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 3 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$
3. $$MPA$$ | crawl-data/CC-MAIN-2020-40/segments/1600401600771.78/warc/CC-MAIN-20200928104328-20200928134328-00660.warc.gz | null |
From "SONAR Technology for Fish Finders" compiled by Nolan Laxamana
It is clear to anyone who has immersed himself or herself in a lake or ocean that sounds can be heard underwater. The sounds of waves, power boats, and other bathers can be heard with remarkable clarity, even at considerable distances. In fact, sounds move quite efficiently through water, far more easily than they do through air. As an example, whales use sound to communicate over distances of tens or even hundreds of kilometers. The ability of sound to travel over such great distances allows remote sensing in a water environment. Devices that use sounds in such an application fall under the family of instruments known as sonars. To understand sonars, you must first understand sound. In particular, you must understand how sound moves in water.
Sound travels in water in a moving series of pressure fronts known as a compressional wave. These pressure fronts move (or propagate) at a specific speed in water, the local speed of sound. The local speed of sound can change depending on the conditions of the water such as its salinity, pressure, and temperature, but it is independent of the SONAR Technology for Fish Finders characteristics of the sound itself all sound waves travel at the local speed of sound. In a typical ocean environment, the speed of sound is in the neighborhood of 1500 meters per second (m/s).
The physical distance between pressure fronts in a traveling sound wave is its wavelength. The number of pressure fronts that pass a stationary point in the water per unit time is the frequency of the wave. Wavelength, if measured in meters (m), and frequency, if measured in cycles per second (Hz), are related to each other through the speed of sound, which is measured in meters per second (m/s):
speed of sound = frequency ´ wavelength
When a sound wave encounters a change in the local speed of sound, its wavelength changes, but its frequency remains constant. For this reason, sound waves are generally described in terms of their frequency. As a sound wave propagates, it loses some of its acoustic energy. This happens because the transfer of pressure differences between molecules of water is not 100% efficient some energy is lost as generated heat. The energy lost by propagating waves is called attenuation. As a sound wave is attenuated, its amplitude is reduced.
Sound waves are useful for remote sensing in a water environment because some of them can travel for hundreds of kilometers without significant attenuation. Light and radio waves (which are used in radar), on the other hand, penetrate only a few meters into water before they lose virtually all of their energy. The level of attenuation of a sound wave is dependent on its frequency high frequency sound is attenuated rapidly, while extremely low frequency sound can travel virtually unimpeded throughout the ocean. A sound wave from a typical sonar operating at 12 kHz loses about half of its energy to attenuation traveling 3000 meters through water.
While acoustic energy travels well in water, it gets interrupted by a sudden change in medium, such as rock or sand. When a moving sound pulse encounters such a medium, some fraction of its energy propagates [absorbed] into the new material. The energy that is not transmitted [absorbed] into the new material must go back into the original medium the water as sound. Some amount of it is reflected off the surface of the material essentially it bounces off in a direction that depends on the angle of incidence (surface). The remainder is scattered
SONAR Technology for Fish Finders in all directions. How much energy goes into reflection and how much goes into scattering depends on the characteristics of the material and the angle of incidence. The energy returned to the water (in other words, the energy that is not transmitted into the new medium) is called an echo. The echo maintains the frequency characteristics of the source wave. | <urn:uuid:c982e2d9-8ce8-42a5-8d3d-fe5d3a3f9776> | {
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Japanese Gifts / Traditional Arts & Crafts - Online Shop Saiga > Japanese Learning > Japanese Language
There was no peculiar character in Japan originally. Based on the Kanji
imported from China, predecessors took pains and adapted the Chinese character
to Japanese in the Nara period(710-794). The Chinese character used thus
is called "Manyogana". ("Manyogana" were used for old
books, such as "Manyoshu", "Kojiki", and "Nihonshoki".
However, it is too difficult for general people to read "Manyogana"
now.) The Japanese notation of the Kana character (Hiragana, Katakana)
was produced based on this "Manyogana." Then, the character culture
peculiar to Japan different from China progressed.
Japanese consists of three different character sets. Many persons say, "Japanese language is difficult". One of the reason might be the kanji. However, the Kanji can be written in Kana characters. And, the Kanji is unnecessary when talking. "Japanese language education" of Japan starts from the study of Kana characters. All Kanji are not mastered even if it is a Japanese. In short, if you mastered the "Kana character" which is the alphabet of the Japanese language and know the words, you can do communication to some extent.
Kanamoji is a generic name for the character of Hiragana and Katakana.
It is equivalent to the English alphabet and the kana character has the
46 standard phonetic characters. Kanamoji is the first step of Japanese
Hiragana was devised as what is replaced with difficult "Manyogana" at the Heian period (794-1192). Hiragana was formed into the simple style from Chinese character. That is, Hiragana is Ultimate Sosho (fully cursive style). Their shape is rounded and rather simple. For example, the character "" was changed as follows.
*If you want to learn about "Kaisho, Gyosho, and Sosho", please see about the style of handwriting.
Katakana was devised to write characters easily at the Heian period (794-1192). Katakana was formed using a part of Chinese character. Their shape is angular and simple. For example, the character "" was formed from the left part of the following Kanji.
Kanamoji has 46 standard phonetic characters. These are called "Seion".
There are "Dakuon", "Handakuon", "Yoon",
"Sokuon" and "Chouon" besides Seion. And, "Tokushuon"
was added in order to write borrowed words. If you want to listen to the
basic pronunciation of kana characters with a sound, please see page of
Listen to Basic Pronunciation Voice.
It is possible to write a sentence by only Kanamoji. However, the sentence of only Kana characters will have pauses of words difficult to understand, and will turn into a sentence which is very hard to read. Therefore, Japanese is usually written by using both Kanamoji and Kanji. Each Kana character does not have a meaning. The use of Kanamoji is as follows.
Japan is a country with many borrowed words. Katakana is used when writing
borrowed words, foreign names and place-names. The borrowed word is the
word established with the original meaning. "Japanized English"
was constructed by combining English words. Although they sound like English,
they are the words of expression which is not in original English. As a
matter of course, only Japanese people can understand "Japanized English".
And, in order that they have flooded too much, we are confused to the difference
with original English.
|The word borrowed from German "Arbeit". A meaning is "work". In Japan, it means short-term labor contracts, such as a side job and temporary employment.|
|The word borrowed from Portuguese "Castella". This is the baked confectionery imported from Portugal to Nagasaki at the Muromachi period (1338-1573).|
|The word borrowed from French "Croissant". The word about cooking and dress has much borrowing from French.|
|The word borrowed from English "Radio".|
|The word borrowed from Spanish "Medias" or Portuguese "Meias". A meaning is stretchy cloth.|
|"Salary" and "man" were combined. People who are working for a company by getting salary. It is used in the same meaning as "Office worker" of English.|
|"Personal computer" was abridged.|
|"Back" and "mirror" were combined. It is used in the same meaning as "Rear-view mirror" of English.|
|"Pair" and "look" were combined. It is used in the same meaning as "same outfit, matching outfits" of English.|
|"Paper" and "driver" were combined. It is used in the same meaning as "Sunday driver" of English.|
<Note>The symbol of " " is used when lengthening a vowel sound.
The Chinese character was imported from China. However, the Chinese character
of Japan has improved so that a Chinese character can be written briefly.
For example, the basis of the Kanji "" was "". There are many kanjis which Japanese character culture produced.
(The kanji of 10,000 or more are in the "Chinese-Japanese dictionary"
of Japan. There is a kanji of 6000 or more which can be used with a personal
computer. There are about 2000 also with the "Chinese characters in
common use" used usually now.) Please see Japanese Kanji Dictionary with Pronunciation and Japanese Kanji Dictionary help page, if you want to learn in detail about each Kanji.
The Kanji can be written using Kana characters. If so, why does we use the Kanji purposely? The Kanji has the advantage that we can understand a meaning on the shape. For example, it is "" when Kanji is written in Hiragana. There are some words pronounced "" as follows. (Chinese character), (organizer), (inspector), (feeling), a name of a person called Kanji. If it is written as "" in hiragana, we have to interpret the meaning in the context. However, if it has written with the Chinese character, we can understand the meaning only by seeing the word. Of course, if we do not know the Kanji, it is not meaningful. So, it is significant to study the kanji.
Kanji has two kinds of readings "On-yomi" and "Kun-yomi".
"On-yomi" is Chinese pronunciation. "Kun-yomi" is the
original pronunciation of Japan. At the time of "Kun-yomi", "Okurigana(a
declensional kana ending)" is added to a Kanji in almost cases. The
inside of the parenthesis of the following example is "Okurigana".
Kanji has a meaning in each and is equivalent to a word. They can combine
and can make idioms indicating various meanings. The number of idioms has
tens of thousands.
Apart from the usual idioms, there are 1000 or more "Four character
Kanji compound words" used as a proverb. These features are that there
is much amount of information compared with the number of characters.
|A partner's thought is understood without using words. To have a tacit understanding.|
|Clouds are drifting in the sky, and water is flowing. That is, the free heart without tenacity of purpose is expressed.|
*If you want to learn more about "Yoji-jyukugo", please see Four character Kanji compound word list.
A radical is one of the component which compose a Chinese character. They
were defined as a standard for classifying Chinese characters. The dictionary
of the Chinese character is arranged for each radical. When looking for
Kanji which pronunciation does not understand in a dictionary, you can
search by the radical. There are many radicals which are one of Kanji originally.
The Kanji with the same radical often has a common point in a meaning.
The punctuation marks used in Japanese are Kuten "" and Touten "". As for the Touten in lateral writing, "" or "" is used. Kuten is equivalent to an English period. It is always used in the end of a sentence. Touten is used in order to make a sentence easy to read and to understand. However, there is no regular rule in this.
Japanese does not have a grammatical plural form per se like English. However,
some Kanji can indicate plurality by iterating. The iteration mark of Kanji | <urn:uuid:bbc4d86f-2a45-4b1e-b2e6-762349fd009b> | {
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# Math Magic Tricks
Math magic tricks are a fun way for kids to amaze their friends and also help them build some math skills along the way!
## Magic Square Math Trick
In this magic math trick, the math magician performs an instant calculation by quickly giving the sum of any four numbers a volunteer covers up!
Are you ready? Great, Let's go.........
PreparationPrint the magic square. Ok, you printed the magic square, right. The first thing you need to know before I show you the trick is the square that you see on this page is special. It’s actually called a magic square. No kidding......Do you know why it’s called a magic square? Notice what happens if you add up all the numbers in the top row.
24 + 11 + 3 + 20 + 7 = 65
Now take a look at the second row.
5 + 17 + 9 + 21 + 13 = 65
Can you guess what the numbers in the third row add up to? If you guessed 65, you’re right. But there’s more……. The numbers in the first column add up to 65 also.
24 + 5 + 6 + 12 + 18 = 65
And the other two columns also add up to 65. And the two diagonals also add up to 65. So that’s why it’s called a magic square65 is the magic number. Now back to our math magic trick.
Performing The Trick:
• First you need to know what the magic number is for the square you are using. For the square shown on this page, I already explained to you that the magic number is 65.
• Next, you figure out what number to subtract from 65 after the volunteer covers up any four numbers.
I'll show you how to find the number to subtract from 65 with a few examples. Look at the first example below. Here you can see someone covered up four numbers at random with the green square.
As soon as they cover up four numbers with a square, in your mind you will extend a diagonal line, two numbers past the outside corner of the covered square. In order to go over two numbers past the outside corner of the covered square, you can only go in one direction.
If you try to go diagonally in any other direction, you will not be able to go two numbers over. Take a look at the picture below. Notice that you can only extend the line two numbers in one direction. The number you arrive at is 8.
This is the number that you subtract from 65.
65 - 8 = 57
So the numbers that are covered add up to 57.
Look back at the top picture and check for yourself to see that the numbers that are covered up, when added together are:
24 +11 + 5 + 17 = 57!
And there you have it.....
Have Fun With It!
By the way, I'll be adding some other magic squares for this magic trick so you can mix it up a bit.
Here's another cool math trick that uses a square with 16 numbers. You can also check out lots of other magic tricks on the main Math Tricks page.
In case you want your students to learn more about magic square puzzles, check out magic square puzzles here.
Go to main Math Tricks page
Return from Math Magic Tricks to Learn With Math Games Home
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# KVL, KCL and Ohm’s Law
## Working principle
According to Kirchoff’s Voltage Law (KVL), the sum of all voltages around a loop is equal to zero. When going around the loop, intuitively, you can treat the voltage source as a positive value, and the resistors as negative, voltage-consuming, values. In this simulation, the input voltage equals the sum of the voltage drops across R1 and R2: Vin - VR1 - VR2 = 0. In other words, Vin = VR1 + VR2.
You can find the voltage across R2 by using the voltage divider rule. First, use the equation for determining Req for two unequal resistors from the resistor network model (this also applied for equal valued resistors, though those can be solved without this equation):
Next, use the voltage divider equation to find VR2:
Additionally, the voltage across R2 and R3 is equal because these resistors are connected in parallel: VR2 = VR3.
According to Kirchoff’s Current Law (KCL), the sum of all currents entering a node equals to the sum of all currents leaving it. The current IR1 in this simulation divides into two - IR2 and IR3 – and is, thus, equal to their sum: IR1 - IR2 - IR3 = 0. In other words, IR1 = IR2 + IR3.
By Ohm's Law, current through each resistor will be equal to the voltage across the resistor divided by its resistance. This simulation shows that current flows through the path of least resistance (there is more current flowing through R2 than R3): V = IR1 = I2R2 = I3R3.
This model also lists the amount of power dissipated by each resistor. You can verify that the power dissipated equals to the current running through a resistor times the voltage across it.
### Experiments
• Equate R2 and R3 values. What is the current through these resistors in relation to the current through R1 now?
• Change the R2 or R3 value to zero ohms. What is the current through the remaining two non-zero resistors now? | crawl-data/CC-MAIN-2023-50/segments/1700679100674.56/warc/CC-MAIN-20231207121942-20231207151942-00348.warc.gz | null |
The substance can be used to solve the two most highly discussed issues in the field of renewable energy- hydrogen production and solar energy storage.
Production of pure hydrogen is a widely spread practice, which benefits quite a number of industries from agriculture all the way to petroleum refining. Currently, the process involves the use of a catalysts, most commonly platinum, to extract the gas from water through electrolysis. But platinum is the most expensive metal on the market right now, meaning that any attempt to scale up the generation of hydrogen via this process to an industrial level is quite a luxury.
In a parallel universe, not so far from hydrogen production, engineers are struggling with another major problem, this time related to solar energy. As great as all advances in solar cells development can be, energy storage still remains a major set back, resulting in a huge amount of electricity being wasted.
A team of chemical engineers at Stanford University decided to search for a common solution to both problems. Inspired by petrochemical plants, they conducted an experiment which involved splitting of the water molecule through electrolysis in a cost-effective manner, while at the same time use this process to store solar.
In the study published in the latest issue of the journal Angewandte Chemie, the lead authors Professor Thomas Jaramillo and research associate Jakob Kibsgaard, describe how a modification of molybdenum phosphide can replace platinum as a catalysts, making the process of hydrogen production much cheaper and more efficient. Their new catalysts was produced by adding sulfur atoms to make the very effective and stable molybdenum phosphosulfide.
In addition, the scientists describe how the system that produces hydrogen through electrolysis can also function as energy storage. To be more precise, solar power can break the water molecule into atoms of hydrogen and oxygen at day time, while at night, the two elements can be combined and generate power.
The new catalysts definitely sets the base for exciting new research and development of eco-friendly energy strategies.
Image (c) Stanford University | <urn:uuid:4f721415-ae34-4812-b6be-cba9b15fff63> | {
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Saturday , July 22 2017
Home / Geometry / Circle| Part – 2
# Circle| Part – 2
Exercise : Two chords AB and AC of a circle make circle make equal angles with the radius through A. Prove that AB=AC.
Particular enunciation: Let O is the centre of the circle ABC. The two chords AB and AC has made equal angles ∠BAO and ∠CAO with the radius OA through A.
It is required to prove that AB=AC.
Construction: from the centre O we draw the perpendicular OM and ON respectively to AB and AC.
Proof: O is the centre and OM⊥AB
The perpendicular from the centre of a circle to a chord bisects the chord.
∴AM= ½ AB Again ON⊥AC
∴AN= ½ AC —————————– (1)
In ∆AOM and ∆AON
∠AMO=∠ANO [1 right angle]
∠MAO=∠NAO [supposition]
And AO=AO [common side]
So, ∆AOM≌∆AON [ASA theorem]
∴AM=AN
Or, ½ AB= ½ AC [from 1]
Or, AB=AC [proved]
Exercise: In the figure , O is the centre of circle and the chord AB = chord AC . Prove that ∠BAO=∠CAO.
Particular enunciation: Given that O is the centre of the circle and the chord AB=AC. We join O and A.
We have to prove that ∠BAO=∠CAO
Construction: We join O, B and O, C
Proof: In ∆AOB and ∆AOC
AB=AC [given]
OA=OA [common side]
So ∆AOB≌∆AOC [SSS theorem]
∴∠BAO=∠CAO. [proved]
Ex: A circle passes through the vertices of a right – angled triangle. Show that the centre lies on the midpoint of the hypotenuse.
General enunciation: A circle passes through the vertices of a right-angled triangle. It is required to show the centre lies on the midpoint of the hypotenuse.
Particular enunciation: Let ABC is a right – angled triangle. Its ∠ABC= 1 right angle and AC is the hypotenuse, The circle passes through the vertices A,B and C.
Construction: From O we draw the perpendicular OD to AB and the perpendicular OE to BC. Again we join O, B.
Proof: O is the centre of the circle and OD⊥AB
The perpendicular from the centre of a circle to a chord bisects the chord]
In ∆AOD and ∆BOD
OD=OD [common side]
And ∠ADO=∠BDO= 1 right angle [OD⊥AB]
So ∆AOD≌∆BOD [SAS theorem]
∴AO=BO
Similarly from ∆BOE and ∆COE it is proved that CO=BO
So AO=BO=CO ——————————-(2)
Therefore O is the centre of the circle.
Hypotenuse AC=AO+CO
=CO+CO [from 2]
=2CO
Or, 2CO=AC
Or, CO= ½ AC
Therefore O lies on the midpoint of the hypotenuse AC. (proved)
Exercise: A chord AB of one of two concentric circles intersect the other at C and D. Prove that AC=BD.
General enunciation: A chord AB of one of two concentric circles intersects the other at C and D. We have to prove that AC=BD.
Particular enunciation: Let O be the two circles ABE and CDF. The chord AB of the circle ABE intersects the circle CDF at C and D.
It is required to prove that AC=BD.
Construction: From O we draw the perpendicular OP on AB or CD.
Proof: O is the centre and OP⊥CD, OP⊥AB.
The perpendicular from the centre of a circle to a chord bisects the chord.
∴CP=PD and AP=BP ————————- (1)
Again, AP=AC+CP
And BP=PD+BD
Since AP=BP [from 1]
So AC+CP=PD+BD
Or, AC+CP=CP+BD [CP=PD]
Or, AC+CP=BD+CP
Or, AC=BD. (proved)
## If two triangles have the three sides of the one equal to the three sides of the other, each to each, then they are equal in all respects.
If two triangles have the three sides of the one equal to the three sides ... | crawl-data/CC-MAIN-2017-30/segments/1500549424079.84/warc/CC-MAIN-20170722142728-20170722162728-00120.warc.gz | null |
## Precalculus (6th Edition) Blitzer
Published by Pearson
# Chapter 2 - Section 2.6 - Rational Functions and Their Graphs - Exercise Set - Page 402: 118
#### Answer
If the degree of the numerator term is one more than that of the denominator term, then the graph of the rational function has a slant asymptote. The slant asymptote is given by the quotient function obtained after the simplification of the rational function.
#### Work Step by Step
The graph of a rational function $f\left( x \right)=\frac{p\left( x \right)}{g\left( x \right)}$ (where $p\left( x \right)\text{ and }q\left( x \right)$ are the functions of variable $x$ , and $q\left( x \right)\ne 0$ ) has the slant asymptote when the degree of the function of the numerator is 1 more than the degree of the function of the denominator. It can be determined by doing the division. When the numerator is divided by the denominator, then the quotient function obtained is the equation of the slant asymptote of the rational function. Thus, the rational function, after division, can be written as $f\left( x \right)=q\left( x \right)+\frac{r\left( x \right)}{g\left( x \right)}$ And then the slant asymptote of the function $f\left( x \right)$ is given by $y=q\left( x \right)$.
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback. | crawl-data/CC-MAIN-2019-51/segments/1575540518337.65/warc/CC-MAIN-20191209065626-20191209093626-00031.warc.gz | null |
The sea otter is one of few species of mammals, on land or in the sea, that uses tools
-- an ability that at one time was thought to be possessed only by humans.
Among the items in the sea otter's tool kit are rocks, driftwood, empty clam shells, and even glass bottles, all of which may be used to crack open the shells of prey such as clams and abalone (marine snails). While it seems fairly unsophisticated to us, the act of prying open a clam shell with something other than one's teeth or hands (or paws, as the case may be) requires relatively advanced cognitive ability. The task involves forethought, problem solving, and learning, skills made possible by complex structures
and integrated neural networks in the brain. To extract a clam or snail from its shell, for instance, a sea otter must identify the type of object that will help it to pry open the shell.
Sea otters seem to be specially equipped in other ways for tool use as well. For example, the dexterity of their forefeet enables them to manipulate tools with decent precision and to pick snails out of kelp beds and dig clams from beneath the mud on the bottom of the sea floor. They also have loose flaps of skin under their forelegs that serve as pouches to hold both prey and tools as they forage underwater. They then carry the objects with them to the ocean's surface, where they eat (rolled over on their backs, in their characteristic belly-up fashion).
In addition to rocks and other hard objects for opening shells, sea otters have been known to employ other kinds of tools, including kelp fronds. An observation described
in the 1980s indicated that sea otters may wrap crabs in kelp fronds to immobilize them, holding them captive until the sea otters get around to eating them. Sea otters also use kelp fronds as security blankets -- in a snug kelp wrap, a sea otter is safe from drifting off in currents as it rests.
It is thought that all sea otters -- there are two subspecies, the California, or southern, sea otter (Enhydra lutris nereis
) and the northern sea otter (Enhydra lutris kenyoni) -- can
learn to use tools. Pups appear to learn to use objects by watching their mothers
, and adults presumably can learn new foraging and tool-use techniques
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Go to the following website
The Basis of the American Republic
1 How does the US Constitution compare to others around the world ?
2 What document governed the colonies before the Constitution ?
3 How was government power divided before the Constitution ?
4 What was the original intent of the federal convention in May, 1787 ?
5 What was the primary purpose of the constitution ?
6 Describe the differences between the Articles of Confederation and the Constitution | <urn:uuid:cda133e0-d518-483f-a9d4-f7d6fc6d35eb> | {
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Defining the word 'law' is an extremely complex and almost impossible task to accomplish. Therefore, it's very important to try to determine the relevant factors that in essence shape the law in order to make the law more plausible and abided by all. An automatic and general definition of law is described as a set of rules enforced by the government. Chiba combined this definition with Ehrlich (1936: 486-506) who established the concept of "living law" to determine that law is enforced and made by society and with Weber (1967: 233) who outlined that law is outlined by religious ethics.
Thus, Chiba concluded 'the three-level structure of law' or otherwise known as the tripartite, to emphasise that the whole structure of law is pluralistic, consisting of different systems of law interacting with one another whether in harmony or in conflicts. The three levels include official law, unofficial law and legal postulates. Chiba defined official law as the "legal system sanctioned by the legitimate authority of a country". This is typically understood to be state law.
This implies that official law carries the overall jurisdiction over the whole country. It is still important to remember that even official law may be influenced by the norms of the country as a whole including principles that are supported by religious law, family law, local law, ethnic law and so forth so long as they are officially sanctioned by the state. Unofficial law is law that is not sanctioned by the state but rather by a circle of people "whether of a country or within or beyond it".
Basically, all types of law other than state law are classified under unofficial law. Unofficial law can also have an influence on official law but this can produce negative or positive results such as the conflicting role of Hindu law within the state law of a Western country. Finally, Chiba defines a legal postulate as "a value principle or value system specifically connected with a particular official or unofficial law". A legal postulate may include legal ideas of justice, equity and natural law.
Overall, it's clear to see that Chiba believed that the law consisted of many aspects under the legocentricism of state, religion and society (Menski 2000: 35). Chiba's theory is relevant for our understanding of the legal systems of Asia and Africa as we can then distinguish that the legal systems are made up from official law, which are influenced from unofficial law and are connected through legal postulates. This enforces our understanding that it is not only the state, which makes the law, but the people of the country, their traditions and religions also make the law without them realising it.
There's an underlying principle of morality that is connected to upbringing and religion which consequently builds the law to make the law what it is today within every legal system even though some factors may override others. b) Analyse Chiba (1989) and his 'new' theory of legal pluralism. What actually is new here? How does it relate to your discussion in part a)? Griffiths (1986a: 38) highlights that "legal pluralism is a concomitant of social pluralism: the legal organisation of society is congruent with its social organisation".
Legal pluralism has been a concept that has been around for a considerable length of time. It involves social and cultural diversity that are entailed in the figuring of law. Chiba's 1989 theory is referred to the 'three dichotomies of law', which includes what Chiba calls the 'identity postulate of indigenous law'. Each of his dichotomies are concerned with contrasting terms of law in order to identify the relationship between them. The first dichotomy is official law vs. unofficial law, which are defined above.
This dichotomy relates to the different manners of legal authorisation. The distinguishing relationship between official law and unofficial law is that the different types of unofficial law function automatically in a systematic arrangement but may cause conflicts and this is where the different types of official law are needed to resolve the conflicts in order to establish a balanced society and to regulate a system where the state law provides the legal principles that are influences by unofficial law.
The second dichotomy is the contrast of legal rules vs. legal postulates. Legal rules are the "formalised verbal expressions of particular legal regulations" in order to be able to assign specific patterns of behaviour or the required patterns of behaviour, such as the Dharma in Hindu law. Legal postulates are values and ideas that are specifically related to a particular law, which are used to modify the existing legal rules. The relationship within this dichotomy is that both legal rules and legal postulates interact to coexist as a rule.
The third dichotomy is the contrast between indigenous law and transplanted law. Indigenous law is law that originated in the local culture of people. Transplanted law is defined as state law that is transferred by people from a foreign culture. This relates to the different origins of law in human society, for example, between the people of Western countries and non- Western countries. This third dichotomy is what is actually new in Chiba's legal pluralism theory.
This third dichotomy is an important extension to what was discussed in section a) above as it informs us that law is not necessarily something that is just made through the state and religion etc but it is also something that can be transferred to other countries whether it be state law or local law. This model further reinstates the point I made at the beginning of this assignment, that law is such a complex mechanism so it can be virtually impossible to define into a simple sentence. Chiba's theory thus helps us in understanding the foundation and body of law as a whole, that law is composed of official law vs.
unofficial law, legal rules vs. legal postulates, and indigenous law vs. transplanted law. The combination of these three dichotomies into a legal culture becomes a useful analytical tool for observing the structure of the law belonging to a group of people, to individuals or to the universe as a whole. Surely, if we were to disentangle the web of law, we might or could end up with laws that universally belong to us all. In essence, Chiba's new theory ultimately boils down to the most important three principles of the structure of law: state, religion and society, which influence one another and interact in the shaping of the law.
c) In the light of a) and b) above, and your reading of comparative jurisprudence, what sense do you make of the term 'ethno-jurisprudence' in relation to Hindu law? In your view, can Chiba's new theory be applied anywhere in the world? Literature is the true reflection of the culture of any religion. It treasures all the knowledge and history and delivers it from generation to generation. This great heritage cannot be reserved without reserving the language. Therefore, the learning of ethno-jurisprudence is very important for people so that they understand and enjoy the great literature we have. | <urn:uuid:89da7695-892f-4b19-8f7e-e3731f7f30c9> | {
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NASA's Hubble Space Telescope snapped this shot of Mars on Aug. 26, 2003, when the Red Planet was 34.7 million miles from Earth. The picture was taken just 11 hours before Mars made its closest approach to us in 60,000 years.
NASA's overarching goal of sending astronauts to Mars may not be worth the time, money and trouble, a prominent researcher says.
NASA's human spaceflight efforts have long been geared toward eventually putting boots on the Red Planet. But the agency should think seriously about ditching this plan, for the benefits of a manned Mars mission may not justify its enormous costs, said space architect Brent Sherwood of NASA's Jet Propulsion Laboratory in Pasadena, Calif.
"Our rationale for exploring Mars, I think, is perhaps fatally weak," Sherwood said during a presentation with NASA's Future In-Space Operations working group Wednesday (Aug. 1).
Sherwood's presentation during a weekly FISO group meeting occurred just days ahead of the huge NASA Mars rover Curiosity's landing on the Red Planet. Curiosity, a 1-ton robot built to explore Mars for two years to determine if microbial life could have ever survived on the planet, will land today (Aug. 5) at 10:31 p.m. PDT (1:31 a.m. EDT, 0531 GMT on Aug. 6).
"I would suggest that maybe instead of whining about not getting enough money, we ought to quit that and redesign our human spaceflight product for success," he added. [Giant Leaps: Top Milestones of Human Spaceflight]
Red Planet dreams
The urge to explore is part of human nature, and Mars has been an inviting target for the better part of a century.
Indeed, researchers began thinking up ways to get our species to the Red Planet before the Space Age even dawned. The famed rocket scientist Wernher von Braun published his seminal book "The Mars Project" in 1948, for example, nine years before humanity launched its first satellite to Earth orbit.
So it's perhaps no surprise that NASA is seeking to get astronauts to Mars. But the space agency isn't legally required to work toward this goal, Sherwood said, citing the NASA Authorization Act of 2010.
According to the Act, "The long-term goal of the human spaceflight and exploration efforts of NASA shall be to expand permanent human presence beyond low-Earth orbit and to do so, where practical, in a manner involving international partners."
The Act doesn't stipulate that sending people to Mars must be part of this process, so NASA has some flexibility. Sherwood thinks the agency should re-examine its human spaceflight program, because pushing for the Red Planet in the next three decades or so may not constitute the best use of NASA's limited resources. [Future Visions of Human Spaceflight]
$100 billion for six astronauts?
A manned Mars mission would be incredibly expensive. NASA estimates peg the overall expenditures at about $100 billion over 30 or 40 years, Sherwood said, but those numbers may be too low.
The International Space Station (ISS), after all, was initially anticipated to cost $10 billion over 10 years. But it ended up costing 10 times that, and took nearly three decades to assemble.
NASA officials have said the agency will work with international partners on any potential manned Mars mission, so the agency wouldn't have to fork out the entire $100 billion (or however much such an effort ends up costing). But the returns to the agency and the nation could still up being comparatively meager, Sherwood said.
"After all of that investment, and all this commitment sustained over these decades, you get six civil servants on another planet, and probably only two of them are U.S. civil servants, because it's got to be an international project," Sherwood said.
"So maybe that's worth it; I don't know," he added. "I think it may be judged in the grand arc of modern history to be seen as not worth it, and I think that's the risk. But that's the conversation to have."
While reaching Mars would be a triumphant moment for our species, there's unlikely to be much scientific rationale for putting humans on the Red Planet three decades from now, Sherwood said. NASA's robotic explorers have become more and more capable and durable over the last 15 years or so, and there's no reason to think such improvements won't continue.
"The humans are not going to be doing anything close to the kind of science that we're already doing robotically or that we can do on ISS in low-Earth orbit right now," Sherwood said.
And robotic missions — like NASA's Mars Science Laboratory, which is due to drop the car-size Curiosity rover on the Red Planet Sunday night — are cheap by comparison. MSL, the biggest and most ambitious rover ever launched, costs $2.5 billion.
Human spaceflight alternatives
If NASA did decide to turn its human spaceflight efforts away from Mars, where could it direct them? Sherwood gave three alternatives, all of which he said are worth a look.
One is colonizing the moon, which would extend humanity's footprint beyond Earth and teach us how to utilize space-based resources. Sherwood said a focus on lunar settlement could conceivably result in 100 or so people living on Earth's nearest neighbor by 2050.
Another option is to help accelerate the pace of passenger space travel, an effort that NASA is already encouraging via its Commercial Crew Development program. Going more fully down this path could help extend spaceflight to the masses, with potentially thousands of people visiting orbiting hotels and resorts by mid-century, Sherwood said.
Finally, NASA could focus on making space-based solar power — a long-held dream of futurists and science-fiction writers — a reality. Building power-beaming stations in space could help secure a clean-energy future for the planet and give our species a foothold in Earth orbit, with perhaps 100 skilled workers living offworld by 2050, Sherwood said.
These three options could all stimulate economic expansion here on Earth and bring more private money into spaceflight, something a manned Mars mission would be unlikely to accomplish, Sherwood said.
Sherwood stressed that he's not against sending astronauts to Mars. He just thinks NASA needs to take a long look at whether or not that should be the ultimate goal of its human spaceflight efforts.
"I love human exploration, and I love the idea of humans to Mars," he said. "But I think there's a problem that we have. And the purpose of this conversation is to try to expose that problem in the terms I've been thinking about it, share that with you and stimulate discussion."
NASA Television will broadcast live coverage of Curiosity's landing on Aug. 5 beginning at 8 p.m. EDT (11 p.m. EDT; 0300 GMT Aug. 6). You can watch the webcast on SPACE.com here.
Visit SPACE.com for complete coverage of NASA's Mars rover landing Sunday. Follow SPACE.com senior writer Mike Wall on Twitter @michaeldwall or SPACE.com @Spacedotcom. We're also on Facebook and Google+. | <urn:uuid:9d26a669-25e8-4f5f-8141-6d329fcdd395> | {
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The host, the vector, and the parasite
Malaria is caused by a single-celled eukaryotic (that is, not a virus or a bacteria, but a cellular organism whose nucleus is enclosed in a membrane) parasite in the genus Plasmodium. While five species in this genus are known to cause the disease, P. falciparum is most often responsible. The parasite’s life cycle requires both human and mosquito hosts to complete its life cycle.
The Plasmodium is in its motile stage when it first encounters a human, when the parasite is injected along with the mosquito’s salivary secretions into the human’s skin. They travel to the liver, where they enter a liver cell (hepatocyte) and undergo several divisions, producing thousands of cellular descendants. These descendants are then released into the human’s bloodstream where they enter red blood cells (Figure 1). It is at this stage in the parasite’s life cycle, about a week after the original mosquito bite, that the human host is most likely to start experiencing symptoms of malaria, which can include a severe fever, chills, and digestive issues. Some of the parasite cells now within the human’s red blood cells will then mature into male and female forms, which can then be ingested by another mosquito when it bites an infected human.
At this point, the male and female forms of the parasite fuse, replicate, and move to the salivary glands of the mosquito, where it can then be injected into a new human host when the mosquito bites. The parasite can also be transmitted from a pregnant human host to their unborn child but is not transmitted from an infected female mosquito to her offspring. Thus preventing mosquito bites is not only key to preventing infections of the primary, human hosts, it’s also critical to stopping the spread from human to human, by way of the mosquito vector.
Between 2016 and 2018, McCann and colleagues[i] conducted a randomized trial covering 65 villages in the Majete region of southern Malawi to test two additional interventions: housing improvements and larval source management. Housing improvements focused on closing gaps through which mosquitoes can enter a house; open eaves were closed with mud and bricks and screens were added to windows (Figure 2). Larval source management involved draining or filling pools of standing water that weren’t needed; pools of water that served some function (such as providing water for livestock) were sprayed with the insecticide Bti (Bacillus thuringiensis serotype israelensis, a bacteria that is known to be toxic to mosquitoes and a few other Dipteran families; Figure 3). Villages were assigned to either intervention, both, or neither, but all villages continued to receive malaria prevention support from the National Malaria Control Program (NMCP) of Malawi, which involved distribution of bed nets and access to treatment. To assess the effects of these interventions, the research team then set up traps for host-seeking mosquitoes inside and outside people’s homes to monitor the mosquito population, sampled for larvae in bodies of water to track the prevalence of larvae, and used rapid malaria diagnostic tests and interviews to track infections in the local population. In the end, the researchers failed to see a statistically significant effect of these interventions. McCann suspects this could be attributed to overall improvements made in the control areas which did not receive either housing improvements of larval source management, but did receive interventions from the NMCP, which relies on bed net distribution as its primary intervention.
Importantly, at all stages of this project, the members of the 65 villages that the researchers engaged with were in charge of implementing the interventions in their communities. Community members trained under the title of health animators led the effort to implement these interventions and were trained about the biology of the parasite and the vector, information that they relayed to the rest of their community through workshops held every other week. Since community members were trained to carry out the interventions themselves, even now that the study period is over, many continue to work on improving houses to limit mosquito entry.
Katie Reding is a PhD student in the Pick lab at the University of Maryland, studying the regulatory interactions underlying segmentation of the milkweed bug embryo.
[i] Importantly, this project was carried out by a vast network of collaborators, including the College of Medicine at the University of Malawi in Blantyre, Malawi; the Academic Medical Centre at the University of Amsterdam in Amsterdam, The Netherlands; the Liverpool School of Tropical Medicine in Liverpool, United Kingdom, Lancaster University in Lancaster, United Kingdom, The Hunger Project-Malawi, African Parks in Majete, Malawi, and the Ministry of Health of Malawi | <urn:uuid:9dec2217-6e32-466d-974f-f7be69f88fb2> | {
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Simplifying Exponential Expressions
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1 Simplifying Eponential Epressions
2 Eponential Notation Base Eponent Base raised to an eponent Eample: What is the base and eponent of the following epression? 7 is the base 7 is the eponent
3 Goal To write simplified statements that contain distinct bases, one whole number in the numerator and one in the denominator, and no negative eponents. E: ab 9bc 6a b c 4a
4 Multiplying Terms When we are multiplying terms, it is easiest to break the problem down into steps. First multiply the number parts of all the terms together. Then multiply the variable parts together. Eamples: a. ( 4 )( -5 ) = ( )(. ) = -0 Only the z is squared b. (5z)(z)(4y) = (5... 4)(y. z. z) = 0yz
5 Eploration Evaluate the following without a calculator: 4 = = = = Describe a pattern and find the answer for: 0 = 8 7 9
6 Zero Power a 0 = Anything to the zero power is one Can a equal zero? No. You can t divide by 0.
7 Eploration Simplify: 4 Use the definition of eponents to epand 4 There are 7 variables Notice (from the initial epression) +4 is 7! 7
8 Product of a Power If you multiply powers having the same base, add the eponents. a m n
9 Simplify: Add the eponents since the bases are the same Eample 9 y 0 9 Anything raised to the 0 power is
10 Practice Simplify the following epressions: ) ) z y 5 y 4 ) y
11 Eploration Simplify: 5 The Product of a Power Rule says to add all the s Adding five times is equivalent to multiplying by 5. The same eponents from the initial epression! 5 5 Use the definition of eponents to epand
12 Power of a Power a mn To find a power of a power, multiply the eponents.
13 Eample 6 Simplify: Multiply the powers of a eponent raised to another power Any base without a power, is assumed to have an eponent of s s t 4t s s 6 t 9 ss t 4t 4 8s t 4t s t 9 Multiply numbers without eponents and add the eponents when the bases are the same
14 Practice Simplify the following epressions: ) y 4 8 y ) 5 a 4 a a ) y y 7 y
15 Eploration Simplify: z 5 z z z z z Adding five times is equivalent to multiplying by 5 Notice: Both the z and were raised to the 5 th power! z z The Product of a Power Rule says to add the eponents with the same bases Use the definition of eponents to epand
16 Power of a Product a m b m If a base has a product, raise each factor to the power
17 Eample Simplify: 4 5 Everything inside the parentheses is raised to the eponent outside the parentheses y y 5 y 0 0 y Multiply the powers of a eponent raised to another power y 45 Multiply numbers without eponents and add the eponents when the bases are the same
18 Practice Simplify the following epressions: ) pqr ab a pqr 4 5 ) 4 ) - yz 54 y z 9 8 5a b 7
19 First Four a 5 b d 6 0. r 8 s a 7 b 7 c. 6z 8. 9a m 6 n z y r 5 s 5 t 5 4. a 4 b 4 c 6. 08a 7. 7b y
20 Eploration Complete the tables (with fractions) by finding the pattern /5 /5 /5 / / /6 /8 ¼ ½ 4 8 6
21 Negative Powers A simplified epression has no negative eponents. a m a m Negative Eponents flip and become positive a m
22 Eample Simplify: 0 4 All of the old rules still apply for negative eponents Flip ONLY the thing with the negative eponent to the bottom and the eponent becomes positive 4a b 5a 45 a 0 4 0a b 0b a 6 b 6 This is not simplified since there is a negative eponent
23 Simplify: Everything with a positive eponent stays where it is. Eample 8y 8 y y y Everything with a negative eponent is flipped and eponent becomes positive. Since all of the negative eponents are gone, apply all of the old rules to simplify.
24 Practice Simplify the following epressions: ) 8 ) ) y y 8 4 4) a b 5 7 y y 7 8 a 4b 6
25 Eploration Simplify: 0 Use the definition of eponents to epand The 6 s in the denominator cancel 6 out of the 0 s in the numerator. This is the same as subtracting the eponents from the initial epression! Since everything is multiplied, you can cancel common factors Only 4 s remain in the numerator
26 Quotient of a Power a m n To find a quotient of a power, subtract the denominator s eponent from the numerator s eponent if the bases are the same. a 0
27 Eample Simplify: Divide the base numbers first 6 6 y 6y 6 y Subtract the eponents of the similar bases since there is division Not simplified since there is a negative eponents 4 y 4 y Flip any negative eponents
28 Practice Simplify the following epressions: 6 0 ab ) 5 a a 5 ) 4 y 6 y 5 ) 9 4y 4y 7 6 y
29 Eploration Simplify: Use the definition of eponents to epand Use the definition of eponents to rewrite. Notice: Both the numerator and denominator were raised to the 6 th power! a b a a a a a a b b b b b b aaaaaa bbbbbb 6 a 6 b 6 Multiply the fractions
30 Power of a Quotient a m b To find a power of a quotient, raise the denominator and numerator to the same power. m
31 Eample Simplify: Everything in the fraction is raised to the power out side the parentheses. Subtract the eponents when there is division, and add when there is multiplication 7 y y 5 y 6 8 y 5 y 7 y 5 y 8 y y y 9 9 Multiply the fractions
32 Practice Simplify the following epressions: ) ) ) a bc y s f zr 4 8 a b y f r s z
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Ages: 3-0 through 8-11
Testing Time: 40 minutes
The TEMA-3 measures the mathematics performance of children between the ages of 3-0 and 8-11 and is also useful with older children who have learning problems in mathematics. It can be used as a norm-referenced measure or as a diagnostic instrument to determine specific strengths and weaknesses. Thus, the test can be used to measure progress, evaluate programs, screen for readiness, discover the bases for poor school performance in mathematics, identify gifted students, and guide instruction and remediation. The test measures informal and formal (school-taught) concepts and skills in the following domains: numbering skills, number-comparison facility, numeral literacy, mastery of number facts, calculation skills, and understanding of concepts. It has two parallel forms, each containing 72 items.
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Also provided is a book of remedial techniques (Assessment Probes and Instructional Activities) for improving skills in the areas assessed by the test. Numerous teaching tasks for skills covered by each TEMA-3 item are included. After giving the test, the examiner decides which items need additional assessment information and uses the book to help the student improve his or her mathematical skills.
Several important improvements were made in the TEMA-3. First, a linear equating procedure is used to adjust scores on the two test forms to allow the examiner to use scores on Form A and B interchangeably. Second, bias studies are now included that show the absence of bias based on gender and ethnicity. Finally, the pictures of animals and money in the Picture Book are now in color to make them more appealing and more realistic in appearance.
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COMPLETE TEMA-3 KIT INCLUDES: Examiner's Manual, Picture Book Form A, Picture Book Form B, 25 Examiner Record Booklets Form A, 25 Examiner Record Booklets Form B, 25 Worksheets Form A, 25 Worksheets Form B, Assessment Probes, 5" x 8" cards, 25 blocks, 25 tokens, and a mesh bag, all in a sturdy storage box.
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LynnM Posts: 34, Reputation: 2 Junior Member #1 Oct 5, 2010, 03:13 PM
Exponential Equation
Can anyone help me with this question:
( [(9^{2x-1}) (3^{3x})^2] / [(27^{x+2})^4] ) = 81^3
I know that x=-19 but I keep getting -1.5 and 8. Step by step would be really appreciated. Thank you.
Unknown008 Posts: 8,076, Reputation: 723 Uber Member #2 Oct 6, 2010, 01:59 AM
$\frac{(9^{2x-1}) (3^{3x})^2}{(27^{x+2})^4} = 81^3$
Okay, put everything to base 3.
$\frac{((3^2)^{2x-1}) (3^{3x})^2}{((3^3)^{x+2})^4} = (3^4)^3$
Now, work out the powers:
$\frac{(3^{4x-2}) (3^{6x})}{(3^{12x+24})} = (3^{12})$
Now, you know that $(a^x)(a^y) = a^{x+y}$ and $\frac{a^x}{a^y} = a^{x-y}$
Apply this:
$3^{4x-2 + 6x - 12x - 24} = 3^{12}$
Now, simplify:
$3^{-2x-26} = 3^{12}$
Equate the powers:
$-2x - 26 = 12$
This gives you:
$x = \frac{12 + 26}{-2} = -19$
LynnM Posts: 34, Reputation: 2 Junior Member #3 Oct 6, 2010, 07:03 AM
Thanks once again! I now see where I was going wrong. After I worked out the powers, instead of adding the top powers, I was trying to multiply them. (Actually, I think I did try to add them at one point but still ended up with the wrong answer!) Oye! Lol!
Question Tools Search this Question Search this Question: Advanced Search | crawl-data/CC-MAIN-2024-18/segments/1712296818468.34/warc/CC-MAIN-20240423064231-20240423094231-00173.warc.gz | null |
Reduction of Federal Budget Deficit
Reductionof Federal Budget Deficit
Reductionof Federal Budget Deficit
United Statesfederal government has run deficit budgets in 36 out of the last 40years. A deficit budget occurs when government spending exceeds thetotal taxes collected. The government of the day has to borrow eitherinternally or externally to fund the debt. Budget deficits are notnecessarily bad because they accelerate economic growth. However,debt increases beyond certain levels impact the economy negatively.For instance, high government debt implies that the savings generatedin the economy will be used to repay the debt instead of beinginvested in development projects. High interest costs created by hugedebts discourage work and savings are reduced. US annual debtcurrently stands at 7 percent of gross domestic product compared tothe general average of 3 percent of GDP. This paper suggestsdifferent policy options that should be undertaken to reduce thebudget deficit by 2.5 trillion US dollars over the next 10 years.Some of the policies relate to reducing spending while others relateto increasing taxes. By applying the following measures, thefederal government will be able to reduce spending by 940 billiondollars, increase revenue by 1561 billion dollars and eliminate 2.501trillion dollars from the federal budget deficit. By increasing taxeson alcoholic beverages by 40 cents on a fifth of liquor and 50 centson a pack of beer or a bottle of wine, the federal government willincrease revenues by 63.8 billion dollars. Eligible business ownersshould pay Medicare/social security taxes based on both their shareof firm’s profit and their personal income. This action will helpthe government increase revenue by 129 billion dollars. An increaseof corporate tax rate by one percent will lead to 113 billion dollarsincrease in national revenue. A repeal of certain tax preferences forgas, oil and mining industries would increase tax revenue by 33.8billion dollars. Special deduction offered to some productionactivities should be repealed to reduce spending by 192 billiondollars (Bartel & Davenport, 2014). The federal governmentshould impose an annual fee on large financial institutions, and thiswould help raise 64.4 billion dollars. The terms for federal gas andoil leasing, including expansion of offshore drilling should bechanged, and this act would reduce the deficit by 5.9 billiondollars. Federal insurance premiums that are paid by employers shouldbe increased to cut the deficit by 5.3 billion dollars. An increasein excise tax on cigarettes to 1.51 dollars a packet would increaserevenue by 37.4 billion dollars. Ford class aircraft carriers used bydefense should stop being build to cut on spending by 10.2 billiondollars. Development of a new long-range bomber should also bedeferred. Pell grants should be limited to the neediest students tocut on spending. Retirees who had higher earnings should have theirsocial security reduced. Highway funding should be limited torevenues from fuel taxes and other roads related taxes. If this weredone, spending would reduce by 64.5 billion dollars (Roubini &Sachs, 2009).
The different policies described above have economic benefits andtradeoffs. Limiting funding of highways to user fees has manyeconomic benefits. Some of these benefits include reduction ingovernment spending, reduction in air pollution, reduction ofcongestion on major highways and promotion of wider infrastructureinvestments. The limitation associated with such a policy is thatless fuel would be consumed. Individuals who own cars would preferusing public means and thus leaving their cars at home. An increasein corporate taxes by one percent will lead to various economicbenefits. The national government will raise more finances and thusreduce the debt. However, the result of an increase in corporatetaxes will mostly depend on the timing. During the recession,spending would decrease significantly but during the boom, spendingwould not be affected much. The tradeoff of increasing corporatetaxes is that the investment spending can reduce significantly.Investors would cut their investments and this will reduce theirearnings. The economy can also be affected if the reduction ininvestment spending is significant. Increase of excise tax oncigarettes and alcoholic drinks have the economic benefit ofincreasing revenue and thus lowering budget deficit. The expectationwould be that consumption of these products would not be affected bythe increase. In reality, however, increase in these taxes will causea reduction in consumption thus lowering the level of spending in theeconomy. This policy will affect both the users of these products andthe producers. The consumers of alcohol and cigarettes will be forcedto take less of the products due to the high prices. The companiesthat produce these products would also be affected because demand fortheir products would be affected negatively. If the impact issignificant, it may affect economic growth in the end. There are manyeconomic reasons why budget deficit should be decreased. The increasein public debt beyond certain levels implies that most of thecountries savings will be used to pay interest costs. When debtlevels are high, the country’s savings are used to pay the debtinstead of developing the economy. The result of this is sloweconomic growth (Feldstein, 2011).
Bartel, B. & Davenport, J. (2014). Interactive game: You fix thefederal budget. Retrieved on 1st April 2014 from:
Feldstein, M. S. (2011). The budget deficit and the dollar.Macroeconomics Annual 1(3).
Roubini, N., & Sachs, J. D. (2009). Government spending andbudget deficits in the industrial economies. New York: Wiley. | <urn:uuid:bca74170-1ec6-415c-98a7-847b91e896fe> | {
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Question
# Factorise the following:$$a^2-12ab+36b^2-25$$.
A
(a+3b+5)(a+6b5)
B
(a3b+5)(a6b5)
C
(a+2b5)(a6b+5)
D
(a6b+5)(a6b5)
Solution
## The correct option is D $$(a - 6b + 5)(a- 6b -5)$$$$a^2-12ab+36b^2-25$$$$=a^2-2\times a\times 6b+(6b)^2-5^2$$$$=(a-6b)^2-5^2$$$$=(a-6b+5)(a-6b-5)$$Mathematics
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0
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We’re all familiar with the hypothesis of panspermia – that life can be “seeded” from the contents of asteroids, comets and planetoids vis-a-vis meteorite impacts – but so far no direct evidence has been found. So why should we even consider meteorites to be potential parents? The truth is out there – they contain the essentials – right down to amino acids. Up until now, what we’ve recovered has been considered structured. Then along came Tagish Lake…
In January, 2000, a large meteoroid exploded in Earth’s atmosphere over northern British Columbia, Canada, resulting in a debris fall over frozen Tagish Lake. It was a rare observed fall, and the meteorites were meticulously gathered, documented and preserved in their frozen state. The reason was twofold: to preserve the integrity of the space stones and to ensure no contamination could occur either to Earth or to the specimens.
“The Tagish Lake meteorite fell on a frozen lake in the middle of winter and was collected in a way to make it the best preserved meteorite in the world,” said Dr. Christopher Herd of the University of Alberta, Edmonton, Canada, lead author of a paper about the analysis of the meteorite fragments published June 10 in the journal Science.
For meteorite collectors, we’re well aware of the value of an observed fall and equally aware of the documentation needed to make a meteorite valuable both to market and scientific study. It’s more than just writing down the date and time of the observation and where the fragments were collected. To be done properly, the field needs to be measured. Each fragment needs to be photographed in the position in which it was found. The depth measured and more. Nothing is left to speculation.
“The first Tagish Lake samples – the ones we used in our study that were collected within days of the fall – are the closest we have to an asteroid sample return mission in terms of cleanliness,” adds Dr. Michael Callahan of NASA’s Goddard Space Flight Center in Greenbelt, Md., a co-author on the paper.
What the scientists found was the Tagish Lake meteorites are rich in carbon – and contain an assortment of organic matter including amino acids. While these “building blocks of life” aren’t new to meteoritic structure, what was out of the ordinary was different pieces had greatly differing amounts of amino acids. This varies way off the beaten path.
“We see that some pieces have 10 to 100 times the amount of specific amino acids than other pieces,” said Dr. Daniel Glavin of NASA Goddard, also a co-author on the Science paper. “We’ve never seen this kind of variability from a single parent asteroid before. Only one other meteorite fall, called Almahata Sitta, matches Tagish Lake in terms of diversity, but it came from an asteroid that appears to be a mash-up of many different asteroids.”
The team set to work on the recovered fragments – identifying different minerals present in each meteorite. What they were looking for was to see how much each had been changed by the presence of water. What they found was the different fragments each had a different water signature not accounted for from their landing on Earth. Some had more interaction and others less. This alteration may explain the diversity in amino acid production.
“Our research provides new insights into the role that water plays in the modification of pre-biotic molecules on asteroids,” said Herd. “Our results provide perhaps the first clear evidence that water percolating through the asteroid parent body caused some molecules to be formed and others destroyed. The Tagish Lake meteorite provides a unique window into what was happening to organic molecules on asteroids four-and-a-half billion years ago, and the pre-biotic chemistry involved.”
How does this change the way we look at the panspermia theory? If future falls continue to show this widespread variability, scientists are going to have to be a bit more reserved in their judgements about whether or not meteorites could deliver enough bio-molecules to make the hypothesis viable.
“Biochemical reactions are concentration dependent,” says Callahan. “If you’re below the limit, you’re toast, but if you’re above it, you’re OK. One meteorite might have levels below the limit, but the diversity in Tagish Lake shows that collecting just one fragment might not be enough to get the whole story.”
While the Tagish Lake samples are undoubtedly some of the most carefully preserved specimens collected so far, there is still a possibility of contamination from both Earth atmosphere and their lake landing. But don’t simply write off these new findings just yet. In one fragment, the amino acid abundances were high enough to show they were made in space by analyzing their isotopes. These versions of elements with different masses can tell us a lot more about the story. For example, the carbon 13 found in the Tagish Lake samples is a much heavier, and less common, variety of carbon. Because amino acids prefer lighter forms of carbon, the enriched and heavier carbon 13 deposits were most likely created in space.
“We found that the amino acids in a fragment of Tagish Lake were enriched in carbon 13, indicating they were probably created by non-biological processes in the parent asteroid,” said Dr. Jamie Elsila of NASA Goddard, a co-author on the paper who performed the isotopic analysis.
The team compared their results with researchers at the Goddard Astrobiology Analytical Lab for their expertise with the difficult analysis. “We specialize in extraterrestrial amino acid and organic matter analysis,” said Dr. Jason Dworkin, a co-author on the paper who leads the Goddard laboratory. “We have top-flight, extremely sensitive equipment and the meticulous techniques necessary to make such precise measurements. We plan to refine our techniques with additional challenging assignments so we can apply them to the OSIRIS-REx asteroid sample return mission.”
We look forward to their findings!
Original Story Source: NASA / Goddard Spaceflight News. | <urn:uuid:882c3c25-b80e-4ef6-9bf8-7a1654b66549> | {
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21st November 2019
14
# What numbers make 12?
The sum of two numbers is 12. One number is x. The other number is ______.
1st number2nd numbersum
21012
6612
4812
x12 - x12
Herein, what is the common denominator of 12 and 15?
Consider the numbers 12 and 15 again: The multiples of 12 are : 12, 24, 36, 48, 60, 72, 84, . The multiples of 15 are : 15, 30, 45, 60, 75, 90, . 60 is a common multiple (a multiple of both 12 and 15), and there are no lower common multiples.
What is the least common denominator of 12 and 8?
Step 1: List the Multiples of Each Number
Multiples of 8Multiples of 12
8 x 3 = 2412 x 3 = 36
8 x 4 = 3212 x 4 = 48
8 x 5 = 4012 x 5 = 60
8 x 6 = 4812 x 6 = 72
What is the lowest common multiple of 12 and 15?
The multiples of 15 are : 15, 30, 45, 60, 75, 90, . 60 is a common multiple (a multiple of both 12 and 15), and there are no lower common multiples. Therefore, the lowest common multiple of 12 and 15 is 60. | crawl-data/CC-MAIN-2022-05/segments/1642320300574.19/warc/CC-MAIN-20220117151834-20220117181834-00495.warc.gz | null |
difference of b to base 2010 and b to base 2009
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• Dec 18th 2010, 04:17 PM
rcs
difference of b to base 2010 and b to base 2009
Attachment 20139
thanks a lot
• Dec 18th 2010, 04:25 PM
dwsmith
$\displaystyle \displaystyle b_{2010}=\frac{1-b_{2009}}{1+b_{2009}}, \ b_{2009}=\frac{1-b_{2008}}{1+b_{2008}}$
$\displaystyle \displaystyle \frac{1-b_{2009}}{1+b_{2009}}-\frac{1-b_{2008}}{1+b_{2008}}=\frac{(1-b_{2009})(1+b_{2008})-(1-b_{2008})(1+b_{2009})}{(1+b_{2009})(1+b_{2008})}=\ frac{2b_{2008}-2b_{2009}}{(1+b_{2009})(1+b_{2008})}$
• Dec 18th 2010, 11:46 PM
HallsofIvy
The first thing I would do is calculate a few values:
$\displaystyle b_1= \frac{1}{3}$
$\displaystyle b_2= \frac{1- \frac{1}{3}}{1+ \frac{1}{3}}= \frac{2}{3}\frac{3}{4}= \frac{1}{2}$
$\displaystyle b_3= \frac{1- \frac{1}{2}}{1+ \frac{1}{2}}= \frac{1}{2}\frac{2}{3}= \frac{1}{3}$
Of course then
$\displaystyle b_4= \frac{1- \frac{1}{3}}{1+ \frac{1}{3}}= \frac{2}{3}\frac{3}{4}= \frac{1}{2}$
and
$\displaystyle b_5= \frac{1- \frac{1}{2}}{1+ \frac{1}{2}}= \frac{1}{2}\frac{2}{3}= \frac{1}{3}$
Get the point?
• Dec 18th 2010, 11:50 PM
dwsmith
I wasn't obtaining a pattern when I did it. I guess addition and subtraction have gotten tougher.
• Dec 19th 2010, 01:29 AM
rcs
thanks for giving me hits guys! Long Live! God Bless.
• Dec 19th 2010, 06:16 AM
HallsofIvy
Of course you really need to prove that $\displaystyle b_n= \frac{1}{3}$ for n odd and $\displaystyle \frac{1}{2}$ for n even, but that is easy using induction. | crawl-data/CC-MAIN-2018-26/segments/1529267864110.40/warc/CC-MAIN-20180621075105-20180621095105-00600.warc.gz | null |
## Math 6A, Lesson 16, Spring 2017, 6/18/2017
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Math 6A, Lesson 16, Spring 2017, 6/18/2017
Final class of the year. Handed out final exam and report card for each student.
Congratulations to all my student a successful school year! Have a safe and wonderful summer!
Picture 1 of 1
## Math 6A, Lesson 15, Spring 2017, 6/11/2017
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Math 6A, Lesson 15, Spring 2017, 6/11/2017
Final Exam covers all the materials we have learned this semester: algebraic expression, solve equations, solve word problems using equations; rate and ratio; percentage and its applications; geometry.
## Math 6A, Lesson 14, Spring 2017, 6/4/2017
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Math 6A, Lesson 14, Spring 2017, 6/4/2017
1. Classification of Triangles
• The number of equal sides in the triangle: scalene triangle – no equal sides; isosceles triangle – to equal sides; equilateral triangles – three equal sides
• The type of angles of the triangle: acute-angled triangle – all angles are acute; right-angled triangle – one of the angles is a right angle; obtuse-angled triangle – one of the angles is an obtuse angle
• Is an equilateral triangle also an isosceles triangle?
• Is it Possible to draw a triangle with more than one obtuse angle?
• Can a scalene triangle be an acute-angled, right-angled or obtuse-angled triangle?
• All the three angles in a scalene triangle are different size
• The angles opposite the equal sides of an isosceles triangle are equal
• All the three angles in an equilateral triangle are equal in size
• A closed plane figure with four straight sides joined by four vertices is called a quadrilateral
• Vertices, diagonals
• Parallelogram: 2 pairs of parallel and equal opposite sides
• Rectangle: all angles are right angles
• Rhombus: all sides are equal, diagonals are perpendicular to each other
• Square: all sides are equal, all angles are right angles
• Trapezoid: 1 pair of parallel sides
3. Review for final exam
• Redo all quiz problems
• Review geometry materials we have learned so far
4. Home Work:
• Page 52-53: 24, 25, 26, 27
• Redo all quiz problems
• Final Exam next week on 6/11/2017. Ms. Lija Li will be monitoring the exam.
• Final class on 6/18/2017: review final exam, report card, and party. Please bring food/snacks to share. | crawl-data/CC-MAIN-2024-33/segments/1722641299002.97/warc/CC-MAIN-20240815141847-20240815171847-00359.warc.gz | null |
Fine Arts at GSIS focuses student learning on an aesthetic understanding and arts practice developed through the art forms of drama, music and visual arts, experienced individually or in combinations with others. Although these three forms may be used in interrelated ways, each has unique language, techniques and conventions. Students develop creative ways of expressing themselves and develop a critical appreciation of their own works and those of others. They use their senses, perceptions, feelings, values and knowledge to communicate through the arts.
Aesthetic understanding helps students to appreciate and critically respond to various arts experiences with enjoyment. Through their arts experiences, students come to understand broader questions about the values and attitudes held by individuals and communities. Arts practice involves the exploration and development of ideas and feelings through the use of a range of skills and knowledge of art techniques and processes. The arts provide a powerful means of expression and communication of life experiences and imagination. The arts contribute to the development of an understanding of the physical, emotional, intellectual, aesthetic, social, moral and spiritual dimensions of human experience. They also assist the expression and identity of individuals and groups through the recording and sharing of experiences and imagination.
In linking all units of study with the principles of IB Educational expectations Fine Arts at GSIS encompasses five key areas:
The arts play an important role in the life of the community. While some works of the arts are presented in formal settings, such as galleries and theatres, the arts also permeate everyday life. Their influence is evident, for example, in the design of the clothes we wear, the buildings in which we live and work, and many of the objects we use every day. The arts are important for the expression of the life and culture of communities, and contribute to the transmission of values and ideas from generation to generation.
The arts are a major form of human communication and expression. Individuals and groups use them to explore, express and communicate ideas, feelings and experiences. Each arts form is a language in its own right, being a major way of symbolically knowing and communicating experience. Through the arts individuals and groups express, convey and invoke meaning. Like other language forms, arts languages have their own conventions, codes, practices and meaning structures. They also communicate cultural contexts. Students benefit from understanding and using these ways of knowing and expressing feelings and experiences.
Artistic works can inform, teach, persuade and provoke thought. They can reproduce and reinforce existing ideas and values, challenge them, or offer new ways of thinking and feeling. They can confirm existing values and practices, and they can bring about change. As a result, the arts play an important role in shaping our understanding of ourselves as individuals and members of society and our understanding of the world in which we live.
The arts provide a major means of personal creativity, satisfaction and pleasure. They allow the opportunity for creative problem solving, self-expression and the use of the imagination in a range of different forms. The study of the arts can provide students with immediate satisfaction as well as providing the basis for lifelong enjoyment.
The Arts involves the development of students' skills across a wide range of human activities. Learning in the arts promotes the integration of skills from different areas of human potential, promoting 'multi-sensory; learning and the development of 'multiple intelligences'. The arts develop verbal and physical skills, logical and intuitive thinking, interpersonal skills and spatial, rhythmic, visual and kinesthetic awareness. They promote emotional intelligence, a way of understanding, using and making responses through the emotions and students' intrapersonal qualities and experiences. Through the arts, students learn to use and experiment with a range of traditional and emerging technologies. | <urn:uuid:6b77058f-9d51-40bd-98a3-b1bb41465635> | {
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Basque fishermen were the earliest European settlers at Port aux Choix, arriving in the sixteenth century. They named their settlement Portuchoa, meaning “the little port,” which has been altered to Port au Choix. The French controlled the Great Northern Peninsula from the start of the eighteenth century up until 1904.
The harbours at Port aux Choix are protected by Riche Point Peninsula that is connected to the main island of Newfoundland by an isthmus. Port aux Choix Habour is situated south of the isthmus, and the larger Old Port aux Choix Harbour, known locally as Back Arm, is located north of the isthmus. Point Riche Lighthouse was constructed on the westernmost point of the peninsula in 1871, and in 1913, a lighthouse was built on Querré Island (Grassy Island) to mark the entrance to Back Arm.
Known as Port aux Choix, the lighthouse consisted of a small, square building, painted white, with a hexagonal, wooden lantern, painted red, on its roof. The lighthouse displayed a fixed white dioptric light at a height of twenty-six feet.
The square, wooden lighthouse was still in use on Querré Island as late as 1960. In 2021, a square, skeletal tower, with a red-and-white rectangular daymark, was displaying a flashing white light with a period of six seconds at Port aux Choix. A pair of range lights on the isthmus also serve to guide mariners into Back Arm.
Keepers: William H. Beliard (at least 1921). | <urn:uuid:f443cc66-2d70-48b2-99e9-d2fe0f07ecc5> | {
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## Reflection: Developing a Conceptual Understanding Visually representing percent word problems (Day 2) - Section 2: Finding the missing part
I've created several videos to show how to use the various tools to solve percent problems.
Videos: How to use the tools for ratios and proportions.
This will help you develop an understanding of how to use the tools. I also used these videos to help educate the parents. This has been a big struggle in my classroom. The students were going home and asking for help. The parents were not able to use the tools so they would show them the way they learned. I explained to the students that the way their parents learned is not a wrong way, however, the way we are being asked to learn is different.
How to videos...
Developing a Conceptual Understanding: How to videos...
# Visually representing percent word problems (Day 2)
Unit 3: Ratios and Proportions
Lesson 22 of 25
## Big Idea: Using a variety of visual representations to solve real world percent problems.
Print Lesson
Standards:
Subject(s):
85 minutes
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|Creating 2D, 3D, and animated math models is an integral|
part of teaching and learning math today.
Jo Boaler, author of Mathematical Mindsets, is not a big fan of homework, however she recommends that reflective homework assignments can be very helpful and positive. To begin the year, I may include lessons related to social development, work habits, and math effort during each lesson. I also may ask students to reflect on these elements as part of their nightly homework to build capacity as well as practice and knowledge of reflective practice--a skill that's a valuable element of any learner's toolbox.
As a new or existing math teacher, take some time this summer to review and analyze your school's report card or progress report. Think about the standards students will be scored on. In systems like the one I work in scores are simply progress notes such as "progressing towards expectations, meets expectations, or exceeds expectations" and in other systems students are still scored with old-time traditional grades. I am a fan of standards-based reports as they foster a progressive, learner's mindset. The kind of mindset that demonstrates to learners that we're all on the continuum and our good efforts help us to move closer to our goals (standards).
Below I analyze each element of the report card that I have to grade in the year ahead. The analysis demonstrates to me a good order and process for teaching each concept. Not all required standards are included on our reports, but the standards with greatest priority are included.
Perseveres when faced with challenges:
What does this look like? How does one persevere? When have you persevered in the past? To introduce this topic, I may present an open task and have students work on it with a focus on their needed perseverance. We'll reflect later on what that felt like, and how they motivated themselves and each other to keep going.
Uses positive strategies to resolve conflict:
We'll review the "Take the first step" process of conflict resolution which is to talk to the person you're having the conflict with. The second step is to get help. We'll brainstorm the types of conflicts that happen at school and the many ways one can resolve those conflicts.
Accepts responsibility for own actions:
What do you do when you make a mistake or do something wrong? How do you deal with that?
Follows school and classroom rules:
First we'll create a class constitution with our rules and protocols. Then we'll talk about ways one can work to follow those rules.
Plays cooperatively with peers:
What does it mean to play cooperatively? What does this look like?
What is initiative? How does one demonstrate that in school?
Seeks help as needed:
Don't stay stuck! When you need help, seek it out. How can one do this?
Manages time well:
What does it mean to manage time? What strategies do you use to do this.
Works independently and productively:
What id independent work? When might a student be asked to work independently? What does "working productively" mean? What does that look like?
Transitions in a timely and appropriate manner:
What does transition mean? When do we transition? What is appropriate behavior for transition?
Follows directions, routines, and procedures:
First we need to establish routines and procedures and make those routines and procedures explicit. Similarly all directions need to be clear and explicit. So to follow directions, routines, and procedures, first students need to understand what they are. Next students need to brainstorm together the strategies they use to follow directions, routines, and procedures well.
What does optimal participation look like in the math classroom? How can we encourage one another to participate? What hinders student participation?
Asks for Clarification:
What does the word "clarification" mean? What are the ways that you might ask for clarification during class or after class? What happens if you ask, and you're still not clear?
Attends to Work:
What's expected with regard to "attending to work" and what does that look like in a classroom? Will this look different during different kinds of learning experiences?
Perseveres when Challenged:
What does perseverance look like in the math classroom? What behaviors are exhibited when you are persevering, and what activities are not exhibited in this regard?
Attends to precision while applying mathematical concepts:
Why is precision important in mathematics? What strategies can one use to be precise?
Math Concept, Knowledge, and Skill
Communicate mathematical thinking orally and in writing using math vocabulary:
Math vocabulary study is integral to math understanding. Every unit should begin with a review of the vocabulary. Vocabulary should be clearly visible in the classroom and accessible for at-home study too. Students should regularly express their mathematically thinking with written or spoken words. Creation of math scripts and videos support this work which ties in nicely with the Standards of Mathematical Practice.
Represent and interpret data using graphing skills:
Initially this is a great standard to meet when making early year infographics to help a class get to know one another. The line plot is the featured graph for fifth grade at this time. Later in the year this standard can be reviewed as you solve fraction problems and chart fraction/decimal data related to real-world problem solving.
Automatically recalls multiplication and division facts through 12:
What do we know about the numbers one through twelve? What factors and multiples can we identify related to these numbers? Which of these numbers are square numbers, composite numbers, prime numbers, or perfect numbers? Where are these numbers present in our culture, and what other names do we have for these numbers? How can we gain automaticity with facts? Why is this important? How do we do with this now, and how can we develop this skill?
Coordinate Grid Knowledge and Use: Able to graph points on the coordinate plane to solve problems.
Understand how to graph points, and then how to use graphing to determine numerical relationships. Student enjoy learning this and practicing it. This study can be embedded throughout the year as students analyze numerical relationships and solve problems.
Classifies two-dimensional figures based on their properties with particular attention to parallel, intersecting, and perpendicular lines:
Students enjoy this study which can be taught well using drawing, tangrams, geoblocks, and online games/venues.
Understand the concepts of volume and applies formulas to solve problems:
Since volume problems essentially include simple numbers, this is a great unit to introduce as you review basic facts. It's also good to review area and perimeter at this time before you get to area models of multiplication and division with larger numbers. Further this unit comes nicely after an initial review of two-dimension geometry since understanding those shapes and how to talk about them informs the volume, area, and perimeter unit.
Use positive and negative numbers to describe quantities:
This concept fits nicely into initial number talk at the start of the year when we look carefully at the numbers 1-12 and where those numbers fit on the number line. Again this can be reviewed during money-related word problems.
Writes and interprets numerical expressions using parentheses:
This is a great skill to teach as you teach students to use calculators effectively. This is also a great teaching goal to master when you are working with "easy numbers" and warming up math year skills. Though it is scheduled on our reports for Term Two, most teach this early in the year as it can be useful and practiced throughout the year as number concepts, knowledge, and skill become more sophisticated.
Generates, extends, and compares patterns and relationships:
Again this is scheduled for term two, but should be a focus of every math lesson with the following questions: What patterns do you see? How do the patterns compare? How might you extend the pattern? What relationships do you see? How would you define the relationship? Can you represent the pattern and/or relationship using a numerical or algebraic expression? Can you graph the relationship or pattern?
Understands the base ten place value system from millions to thousandths?
What are the parts of the place value system? How do these parts work together? Why was the base ten place value system invented? What value does it have in our culture? How do the values of numbers change as you move up and down the place value system? How do the values of numbers change when you add, subtract, multiply, or divide by base ten numbers?
Perform addition, subtraction, multiplication operations with multi-digit whole numbers?
Why do we use the word "operation" when we talk about addition, subtraction, and multiplication? Why do we add, subtract, and multiply? How can we perform those operations effectively and efficiently? Is there one way to do this? Is there a best way or does this depend on when and why we are performing the operation? What 2D, 3D, and animated models can we make to demonstrate these operations?
Perform division operation with multi-digit whole numbers?
What does it mean to divide? When would we use this operation? How can you divide one number by another? What words do we use to describe the numbers associated with division? What models can we make to depict division?
Performs operations with decimals to the hundredths:
When do we need or want to add, subtract, multiply, or divide decimal numbers? Why is this important? How can we perform these operations? Working with money and problem solving is an important art of this study.
Convert standard measurement units within a given measurement system:
This study fits nicely with new science standards that included working with matter. Many experiments can be done that find students converting measurements while exploring matter. This also alines well with base ten system study as students look at models of the base ten system and match those models to metric models.
1/2 = 1 divided by 2 which equals .5, both 1/2 and .5 are equivalent to half of the whole. Proper fractions like decimals demonstrate part of a whole. We can easily turn a fraction into a decimal by dividing the numerator by the denominator. Sometimes it's easier to work with fractions and sometimes it's easier to work with decimals. A good way to practice this skill is to begin by making a fraction, decimal, percent, and ratio equivalency chart. Later it's good to look at how this skill relates to meaningful fraction numbers with real-time problem solving and project work.
Add and subtract fractions with unlike denominators and solve word problems with addition and subtraction of fractions:
Use a signature story to describe and discuss this skill: "Amy and Paul were making cookies. They each had a table of ingredients. The cookies called for 3/4 cup of sugar. In the end, Paul had 1/8 cup of sugar let and Amy had 2/6 cups of sugar left. Together do they have enough sugar left to make one more batch of cookies?" How would we figure this out? What can we do to figure out if they have enough sugar left? Later students can make up their own stories and demonstrate this skill conceptually. Lots of fraction model wok supports this effort as well.
Applies and extends previous understandings of multiplication to multiply a fraction or whole number by a fraction and solves related real-world problems.
This work also benefits from signature stories. Begin with multiplying a whole number by a fraction: "Emily wanted to give every child 1/2 a piece of paper for the art project. There were twelve children. How many whole pieces of paper did Emily need? What if Emily wanted to give each child 1/3 piece of paper, then how many sheets of paper would she need?" Draw a model of this story. Solve the problem with a model and mathematically. Make up your own problem, solve with model and numbers. Present your problem to the class.
Next, work with multiplying a fraction by a fraction using the area model. Again use a signature story: "I bought a big rectangular cake for my dad's birthday. After the party I had 1/2 of the cake left. I wanted to give my brother 1/4 of the half cake. What portion of the original cake did I give to my brother?" Show how this problem looks with a model, then solve the problem mathematically. Have students make up their own problems to solve with the area model (similar to the cake), picture model, and using the fraction multiplication algorithm.
Applies and extends previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions:
Introduce with a story: "I was going to the fireworks with my family. I had three pieces of licorice, but there were eight people in the car. I decided to split the licorice into 1/4 pieces. If I did that, would I have enough licorice pieces for all people in the car?" How can we write this problem as an expression? What would this problem look like as a model? Do I have enough pieces if I divide 3 by 1/4? Or "I had 1/4 of a pizza left. I want to split it into 3 equal pieces. What size pieces will I end up with?" What does this problem look like as an expression and model? Students can make up their own fraction division problems to solve with friends and present to the class.
Understand what a mixed number is and solve related world problems:
Discuss mixed numbers. Brainstorm when we use mixed numbers in real-time. Look at the many ways we can write and/or model a mixed number. Add, subtract, multiply, and divide mixed numbers. Solve and create real-world mixed number problems. | <urn:uuid:1f11ab6a-8328-4561-9e8b-6d34d040ace5> | {
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An International Group of Researchers verified the discovery of an entirely new bird specie. The bird was first spotted nearly 15 years ago in the island of Indonesia.
It is pretty rare to find such kind of bird even in the island of Indonesia. Hence, researchers took such a long time to identify the new species of bird.
Two years ago, scientists got hold of two specimen from the Central Sulawesi. The team spent nearly 3-4 weeks in the forests of Indonesia to catch the bird. Afterwards, scientists closely examined each and every aspect of the specie.
Later on, experts realized that the bird is pretty similar to another specie known as Gray Streaked Flycatcher. Therefore, researchers gave it a name similar to Gray Streaked Flycatcher. They called the new specie Sulawesi Streaked Flycatcher.
The body structure, genetics of the bird makes it distinct from the rest of the bird. It has a mottled throat and short wings that are quite difficult to find in other birds. Generally, the bird survive in an area that is full of cocoa plantation. Fortunately, the specie is safe from the dangers of annihilation.
J.Berton, a postdoctoral fellow of Princeton University expressed that scientists believe that they have identified nearly 98 percent birds of the world. Therefore, the new discovery is pretty astonishing for the researchers. Generally, the avian hotspot is considered pretty significant in terms of researcher. Thus Far, ornithologists merely studied a small part of that region.
The experts from Princeton University collaborated with researchers of Michigan State University for this particular study. They printed the report in the latest edition of Journal PLOS One. | <urn:uuid:3b64315e-c0b9-40bb-96dd-f51946ebe562> | {
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The Levellers were a loose political group that formed in England in 1647 around demands for a widening of voting rights, the toleration of religious difference and for due judicial process. The group were popularly named after the practice of 'levelling' hedges and fences, erected by landowners to keep peasants out of what used to be common land available for all to gather firewood and graze livestock. The Levellers however did not support such action and tried to distance themselves from it.
A more radical group formed in 1649 who named themselves the 'True Levellers'. Led by Gerard Winstanley they advocated an end to all property rights, a return to the state of affairs before the Norman invasion of 1066, when land was not owned by the state or the monarchy, but instead small plots of land were owned by peasants according to folk-laws or customs, which usually followed kinship principles and where each cultivated their own small holding. Over and above this the True Levellers also advocated the collective cultivation of land. In 1649, the group took over St George's Hill in Surrey and began digging the land for cultivation, living and working in the same place. This was to be the start of a series of collective communities across England, established mostly in the south, including Wellingborough in Northamptonshire, Cox Hall in Kent, Iver in Buckinghamshire, Barnet in Hertfordshire, Enfield in Middlesex, Dunstable in Bedfordshire, Bosworth in Leicestershire, as well as a few other sites across Gloucestershire and Nottinghamshire. The activities of these groups, of digging the land for cultivation as well the removal of hedges and fences, earnt them their popular name of The Diggers. At the same time the group also published a manifesto, The True Leveller's Standard Advance. At its peak the movement consisted of some 100-200 people across southern and central England, but the communities were heavily persecuted by the government. They were eventually driven out by angry landowners supported by the clergy. The movement finally came to an end around 1652, the same year that Winstanley published his treatise on social reform, The Law of Freedom in a Platform.
Whilst the Digger movement only lasted for a few years in the C17, their vision of a society based on common ownership of the land has inspired many, including the San Francisco Diggers of the 1960s whose mixture of direct action and street theatre advocated a free lifestyle, handing out free food, setting up free shops and establishing a free medical centre. The Land is Ours which has been campaigning in the UK since the mid-1990s references the Diggers in their call for access to land, the saving of common spaces and the participation of ordinary people in decisions about land-use and its resources. The Diggers and Dreamers website and publications for communal living in Britain are another offshoot from this short period of history.
Gerard Winstanley, 'The True Levellers Standard Advanced' (London, 1649), http://www.marxists.org/reference/archive/winstanley/1649/levellers-standard.htm
---, 'The Law of Freedom in a Platform' (London, 1652), http://www.bilderberg.org/land/lawofree.htm
Lewis Henry Berens, 'The Digger Movement in the Days of the Commonwealth' (London: Simpkin, Marshall & Co., 1906) www.gutenberg.org/etext/17480
Christopher Hill, The English Revolution 1640 (London: Lawrence and Wishart, 1940) http://www.marxists.org/archive/hill-christopher/english-revolution/index.htm
---, 'Levellers and True Levellers', in The World Turned Upside Down: Radical Ideas During the English Revolution (London: Temple Smith, 1972).
Steve Wyler, A History of Community Asset Ownership (London: Development Trusts Association, 2009).
"The earth (which was made to be a Common Treasury of relief for
all, both Beasts and Men) was hedged in to In-closures by the
teachers and rulers, and the others were made Servants and Slaves:
And that Earth that is within this Creation made a Common
Store-house for all, is bought and sold, and kept in the hands of a
few, whereby the great Creator is mightily dishonoured, as if he
were a respector of persons, delighting in the comfortable
Livelihoods of some, and rejoicing in the miserable povertie and
straits of others. From the beginning it was not so."
Gerard Winstanley, The True Levellers Standard Advanced (London, 1649), http://www.marxists.org/reference/archive/winstanley/index.htm
"The Work we are going about is this, To dig up
Georges-Hill and the waste Ground thereabouts, and to Sow
Corn, and to eat our bread together by the sweat of our brows."
- Gerard Winstanley, The True Levellers Standard Advanced (London, 1649), http://www.marxists.org/reference/archive/winstanley/index.htm
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Elsmere Canyon, like the rest of the coast range, was created a million years ago through a series of stupendous earthquakes that literally lifted the rugged mountains out of a warm shallow sea. Indeed, numerous marine fossils can still be found there, including some that are known from nowhere else.
Still an active rift zone, the Whitney Fault slices up the east escarpment of its junction with the Santa Clara Fault, while to the north, under present Sierra Highway, lies the Placerita Fault. It is dotted with asphaltum seepages, artesian wells, and even a couple of cascading waterfalls. These, along with stands of oaks and an abundance of animals, were a powerful attraction to the first settlers, the Native Americans.
No one knows when humans began exploring the canyon, for there has never been a full scale archaeological investigation of it. Certainly mammoth hunters were in the Santa Clara River Valley more than 12,000 years ago. About 450 A.D., a group of Shoshones migrated down from the high plains pushing aside the previous occupants to settle the San Gabriel Mountains, Antelope, and Santa Clara valleys. Those who came to be know as Tataviam (residents of the Sunny Slopes) set up some 25 semi-permanent village sites scattered from Crown Valley to Piru Creek. One of these Rancherias was near the mouth of Elsmere, called Santa Rosa by Fr. Crespi in 1769. An 1849 Mexican grant map, however, refers to it as Tochonanga, while the Van Valkenbert map of Old Indian Villages pegs it as Nuhubit.
The Tataviam made exquisite arrowheads, used for hunting small game, nearly microscopic beads, and intricate baskets. They painted and etched strange symbols upon stone, some of which may be astronomical notations. Their summer homes were constructed of sycamore poles thatched with grass resembling an upside down basket, while in winter they moved into domed adobe structures partly underground. The staple of their diet was acorns supplemented by a variety of plants and animals. Oil was valued for medicinal purposes while water sources were considered sacred. They were also great traders, items from as far away as Arizona and Catalina Island having been found locally. One of their trails, Grapevine, wound from present day Newhall to Sylmar by way of Elsmere. Captain Gaspar de Portola, Governor of All the Californias, led an expedition north from San Diego seeking the Bay of Monterey. On August 8, 1769, they followed the Indian trail over the mountains and into a draw which Fr. Juan Crespi recorded as Arroyo de Santa Clara. A couple of days later, while camped at modern Castaic Junction, Fr. Crespi named the river and the whole valley for St. Clare.
Other Spaniards followed the Grapevine-Elsmere trail, including Fr. Garces in 1776 and Fr. Vicente de Santa Maria in 1795. With the founding of the Mission San Fernando two years later, traffic increased over the mountains, especially with the founding of Rancho San Francisco and the establishment of a submission in the Santa Clara Valley in 1804. Generally called The High Road by the Spanish, its major feature was a spine, a rock that nearly closed off the canyon, Puerta, meaning door. By placing a few branches across La Puerta, Franciscan padres kept half wild cattle from roaming over the mountain tops.
After California became part of the Mexican Republic, mission lands were cut up and given to leading citizens, including Lt. Antonio de Valle, who was granted the Rancho San Francisco in the Santa Clara River Valley on January 22, 1839. The southern boundary ran through the hills until it reaches The Door (La Puerta) and bar which is in the high road from San Fernando to San Francisco. Also, a plat of Rancho San Francisco filed June 7, 1880, plainly shows the road up Elsmere past a false Puerta and Oak Tree Puerta.
During the Mexican-American War, Col. John C. Fremont camped at the junction of Whitney and Elsmere with his Buckskin Battalion on January 10, 1847. Dividing his command in half, Fremont crossed The Pass of San Bernardo guided by a local, Juan Cordova, to accept the surrender of California three days later. For years afterward The High Road up Elsmere was know as Fremont Pass. Fremont Peak on the south slope looms over his march down Grapevine Canyon to Sylmar.
John Woodhouse Audubon led a map-making and scientific party over the pass in November 1849 commenting the hills are of a friable whitish clay and sandstone. Four years later, Lt. Richard S. Williamson with the Pacific Railroad surveys actually dragged his wagons up Elsmere and lowered them down the far side with ropes and pulleys. A Los Angeles businessman, Henry Clay Wiley installed a windlass atop the Santa Clara Divide and a tavern-hotel-stable at the location of Eternal Valley Cemetery. Within a year (1854), Wiley sold out to Sanford and Cyrus Lyon just as Phineas Banning got the supply business to Ft. Tejon and the Kern River gold miners. Banning made a few adjustments to the old road, carving a small cut through the Santa Clara Divide then running eastward before plunging down Elsmere to Lyon Station. By the way, Ft. Tejon was connected to the other southwestern posts by a U.S. Army Camel Corps led by Lt. Edward F. Beale. Frequently Beale led his camels down to Los Angeles by way of Fremont Pass, making a colorful spectacle as they paraded through the dusty streets.
On October 21, 1858, the Butterfield Overland State rolled into Los Angeles, then headed north to follow the new Banning route over the mountains to Lyon Station, Butterfield set a speed record of just 21 days from St. Louis to San Francisco.
The transcontinental camels and coaches came to an end with the outbreak of the Civil War in 1861. Soledad Canyon gold and silver, Pico oil, San Francisco, and Rancho Tejon cattle were needed for the war effort, Elsmere becoming more and more of a hindrance to transportation than any sort of help. So, in 1863, E. F. Beale made a 90-foot-deep slash through the mountains a half mile to the west, bypassing the old road. Beale’s cut would be the new road until 1910 when the Newhall tunnel was carved along Sierra Highway.
After the railroad was completed in 1876, a number of Orientals squatted in Elsmere, working the Placenta gold fields. For a time, it was marked China Gulch on maps.
Acting as agent for the Governor of Kansas, Henry C. Needham arrived in 1887 to set up the St. John Tract, a dry colony. Needham was a well known leader of the Prohibition Party who came within seconds of becoming nominated for president in 1920. The Needham Ranch extended from Lyon Station down into Elsmere.
A fellow Kansan, Don L. Clampett, obtained a lease from Needham and brought in an oil well, Elsmere No. 1 in 1889. A company that would become Chevron, USA moved in the following year sinking 22 wells with only moderate success. Most of them filled with water or the sandy soil caved in.
After the turn of the century, a Black resort community started in the canyon, quickly fading away. The Los Angeles Aqueduct came in 1910, Tunnel Station being established to construct a siphon under Elsmere up to the famed Cascades tumbling down to the Van Norman Reservoir.
Elsmere, with its rich cavalcade of history, should be preserved as a National Historic Trail. | <urn:uuid:627a7218-e6d8-41ef-b0b8-16dbb30622c5> | {
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Confused by weather forecasts? Here are some of the more common and basic meteorological terms, concepts, and phenomena. We hope this helps clear the clouds!
Anomaly: The deviation of (usually) temperature or precipitation in a given region over a specified period from the normal value for the same region.
Atmosphere: The mass of air surrounding the Earth and bound to it more or less permanently by the Earth's gravitational attraction.
Atmospheric Pressure (also called air pressure or barometric pressure): The pressure asserted by the mass of the column of air directly above any specific point.
Aurora Borealis (also known as the northern lights): The luminous, radiant emission from the upper atmosphere over middle and high latitudes, and centered around the Earth's magnetic poles. These silent fireworks are often seen on clear winter nights in a variety of shapes and colors.
Barometer: A device for measuring atmospheric pressure.
Blizzard: Includes winter storm conditions of sustained winds or frequent gusts of 35 mph or more that cause major blowing or drifting of snow, reducing visibility to less than one-quarter mile for 3 or more hours OR a typical Tuesday in New England during the wintertime.
Circulation: The pattern of the movement of air. General circulation is the flow of air of large, semi-permanent weather systems, while secondary circulation is the flow of air of more temporary weather systems.
Climate: The prevalent long term weather conditions in a particular area. Climatic elements include precipitation, temperature, humidity, sunshine and wind velocity and phenomena such as fog, frost, and hail storms. Climate cannot be considered a satisfactory indicator of actual conditions since it is based upon a vast number of elements taken as an average.
Cold Front: A narrow transition zone separating advancing colder air from retreating warmer air. The air behind a cold front is cooler and typically drier than the air it is replacing.
Cyclone: An area of low pressure around which winds blow counterclockwise in the Northern Hemisphere. Also the term used for a hurricane in the Indian Ocean and in the Western Pacific Ocean.
Drought: Abnormally dry weather in a region over an extended period sufficient to cause a serious hydrological (water cycle) imbalance in the affected area. This can cause such problems as crop damage and water-supply shortage.
Flurries: Light snow falling for short durations. No accumulation or just a light dusting is all that is expected.
Fog: Water that has condensed close to ground level, producing a cloud of very small droplets that reduces visibility to less than one km (three thousand and three hundred feet).
Humidity: The amount of water vapor in the atmosphere.
Indian Summer: An unseasonably warm period near the middle of autumn, usually following a substantial period of cool weather. Learn more about Indian Summers here.
Jet Stream: Strong winds concentrated within a narrow band in the upper atmosphere. It normally refers to horizontal, high-altitude winds. The jet stream often "steers" surface features such as front and low pressure systems.
Tornado: A violent rotating column of air, in contact with the ground, pendant from a cumulonimbus cloud. A tornado does not require the visible presence of a funnel cloud. It has a typical width of tens to hundreds of meters and a lifespan of minutes to hours.
Warm Front: A narrow transitions zone separating advancing warmer air from retreating cooler air. The air behind a warm front is warmer and typically more humid than the air it is replacing.
Wind: Air in motion relative to the surface of the earth.
If you have questions about any other meteorological terms, please post below! | <urn:uuid:77fdd873-6635-4156-b949-e0cc11308900> | {
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That Ain't No Chicken
A Red Jungle Fowl (Galla galla), an ancestor of domestic chickens
Why It Matters
There's More Than One Way To Make A Dinosaur
The movie and novel Jurassic Park set people's mind a flutter with possibilities. Dinosaurs! Cloned dinosaurs from ancient DNA! How cool is that! Unfortunately, science has poured some cold water on this cool idea. It seems DNA doesn't stick around for millions of years, even under the best conditions it seems to be readable for only around 1.5 million years. Not much use in trying to bring back animals that disappeared over 65 million years ago. Read this article to find out more. *http://www.nature.com/news/dna-has-a-521-year-half-life-1.11555
But all is not lost for those hoping for the dinosaurs return. Actually, as some of you know, they never really went away. Oh, the Age of the Dinosaurs ended and with it their world dominance, and most of them certainly disappeared. But some survived...we call them birds, and scientists like Jack Horner think they may be key to some very interesting science.
Use the resources below to answer the following questions:
- What appears to be the main culprit in the degradation of DNA? Given this situation, if you were looking for an area with maximum preservation potential, where would you look?
- What does half-life mean? Where else have you heard this term used?
- How do the behaviors of dinosaurs that Jack Horner and his colleagues have figured out compare to the behavior of birds we know today? Do you see any evidence that could be used to argue birds are not dinosaurs?
- What are osteocytes? What do they do in vertebrates?
- What is transgenesis? Do you think it could be used to bring back dinosaurs? Explain your reasoning as fully as possible. | <urn:uuid:933ff3dc-c22a-483a-b6b0-a306d3b03ef9> | {
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Suppose one has a bounded sequence ${(a_n)_{n=1}^\infty = (a_1, a_2, \dots)}$ of real numbers. What kinds of limits can one form from this sequence?
Of course, we have the usual notion of limit ${\lim_{n \rightarrow \infty} a_n}$, which in this post I will refer to as the classical limit to distinguish from the other limits discussed in this post. The classical limit, if it exists, is the unique real number ${L}$ such that for every ${\varepsilon>0}$, one has ${|a_n-L| \leq \varepsilon}$ for all sufficiently large ${n}$. We say that a sequence is (classically) convergent if its classical limit exists. The classical limit obeys many useful limit laws when applied to classically convergent sequences. Firstly, it is linear: if ${(a_n)_{n=1}^\infty}$ and ${(b_n)_{n=1}^\infty}$ are classically convergent sequences, then ${(a_n+b_n)_{n=1}^\infty}$ is also classically convergent with
$\displaystyle \lim_{n \rightarrow \infty} (a_n + b_n) = (\lim_{n \rightarrow \infty} a_n) + (\lim_{n \rightarrow \infty} b_n) \ \ \ \ \ (1)$
and similarly for any scalar ${c}$, ${(ca_n)_{n=1}^\infty}$ is classically convergent with
$\displaystyle \lim_{n \rightarrow \infty} (ca_n) = c \lim_{n \rightarrow \infty} a_n. \ \ \ \ \ (2)$
It is also an algebra homomorphism: ${(a_n b_n)_{n=1}^\infty}$ is also classically convergent with
$\displaystyle \lim_{n \rightarrow \infty} (a_n b_n) = (\lim_{n \rightarrow \infty} a_n) (\lim_{n \rightarrow \infty} b_n). \ \ \ \ \ (3)$
We also have shift invariance: if ${(a_n)_{n=1}^\infty}$ is classically convergent, then so is ${(a_{n+1})_{n=1}^\infty}$ with
$\displaystyle \lim_{n \rightarrow \infty} a_{n+1} = \lim_{n \rightarrow \infty} a_n \ \ \ \ \ (4)$
and more generally in fact for any injection ${\phi: {\bf N} \rightarrow {\bf N}}$, ${(a_{\phi(n)})_{n=1}^\infty}$ is classically convergent with
$\displaystyle \lim_{n \rightarrow \infty} a_{\phi(n)} = \lim_{n \rightarrow \infty} a_n. \ \ \ \ \ (5)$
The classical limit of a sequence is unchanged if one modifies any finite number of elements of the sequence. Finally, we have boundedness: for any classically convergent sequence ${(a_n)_{n=1}^\infty}$, one has
$\displaystyle \inf_n a_n \leq \lim_{n \rightarrow \infty} a_n \leq \sup_n a_n. \ \ \ \ \ (6)$
One can in fact show without much difficulty that these laws uniquely determine the classical limit functional on convergent sequences.
One would like to extend the classical limit notion to more general bounded sequences; however, when doing so one must give up one or more of the desirable limit laws that were listed above. Consider for instance the sequence ${a_n = (-1)^n}$. On the one hand, one has ${a_n^2 = 1}$ for all ${n}$, so if one wishes to retain the homomorphism property (3), any “limit” of this sequence ${a_n}$ would have to necessarily square to ${1}$, that is to say it must equal ${+1}$ or ${-1}$. On the other hand, if one wished to retain the shift invariance property (4) as well as the homogeneity property (2), any “limit” of this sequence would have to equal its own negation and thus be zero.
Nevertheless there are a number of useful generalisations and variants of the classical limit concept for non-convergent sequences that obey a significant portion of the above limit laws. For instance, we have the limit superior
$\displaystyle \limsup_{n \rightarrow \infty} a_n := \inf_N \sup_{n \geq N} a_n$
$\displaystyle \liminf_{n \rightarrow \infty} a_n := \sup_N \inf_{n \geq N} a_n$
which are well-defined real numbers for any bounded sequence ${(a_n)_{n=1}^\infty}$; they agree with the classical limit when the sequence is convergent, but disagree otherwise. They enjoy the shift-invariance property (4), and the boundedness property (6), but do not in general obey the homomorphism property (3) or the linearity property (1); indeed, we only have the subadditivity property
$\displaystyle \limsup_{n \rightarrow \infty} (a_n + b_n) \leq (\limsup_{n \rightarrow \infty} a_n) + (\limsup_{n \rightarrow \infty} b_n)$
for the limit superior, and the superadditivity property
$\displaystyle \liminf_{n \rightarrow \infty} (a_n + b_n) \geq (\liminf_{n \rightarrow \infty} a_n) + (\liminf_{n \rightarrow \infty} b_n)$
for the limit inferior. The homogeneity property (2) is only obeyed by the limits superior and inferior for non-negative ${c}$; for negative ${c}$, one must have the limit inferior on one side of (2) and the limit superior on the other, thus for instance
$\displaystyle \limsup_{n \rightarrow \infty} (-a_n) = - \liminf_{n \rightarrow \infty} a_n.$
The limit superior and limit inferior are examples of limit points of the sequence, which can for instance be defined as points that are limits of at least one subsequence of the original sequence. Indeed, the limit superior is always the largest limit point of the sequence, and the limit inferior is always the smallest limit point. However, limit points can be highly non-unique (indeed they are unique if and only if the sequence is classically convergent), and so it is difficult to sensibly interpret most of the usual limit laws in this setting, with the exception of the homogeneity property (2) and the boundedness property (6) that are easy to state for limit points.
Another notion of limit are the Césaro limits
$\displaystyle \mathrm{C}\!\!-\!\!\lim_{n \rightarrow \infty} a_n := \lim_{N \rightarrow \infty} \frac{1}{N} \sum_{n=1}^N a_n;$
if this limit exists, we say that the sequence is Césaro convergent. If the sequence ${(a_n)_{n=1}^\infty}$ already has a classical limit, then it also has a Césaro limit that agrees with the classical limit; but there are additional sequences that have a Césaro limit but not a classical one. For instance, the non-classically convergent sequence ${a_n= (-1)^n}$ discussed above is Césaro convergent, with a Césaro limit of ${0}$. However, there are still bounded sequences that do not have Césaro limit, such as ${a_n := \sin( \log n )}$ (exercise!), basically because such sequences oscillate too slowly for the Césaro averaging to be of much use in accelerating the convergence. The Césaro limit is linear, bounded, and shift invariant, but not an algebra homomorphism and also does not obey the rearrangement property (5).
Using the Hahn-Banach theorem, one can extend the classical limit functional to generalised limit functionals ${\mathop{\widetilde \lim}_{n \rightarrow \infty} a_n}$, defined to be bounded linear functionals from the space ${\ell^\infty({\bf N})}$ of bounded real sequences to the real numbers ${{\bf R}}$ that extend the classical limit functional (defined on the space ${c_0({\bf N}) + {\bf R}}$ of convergent sequences) without any increase in the operator norm. (In some of my past writings I made the slight error of referring to these generalised limit functionals as Banach limits, though as discussed below, the latter actually refers to a subclass of generalised limit functionals.) It is not difficult to see that such generalised limit functionals will range between the limit inferior and limit superior. In fact, for any specific sequence ${(a_n)_{n=1}^\infty}$ and any number ${L}$ lying in the closed interval ${[\liminf_{n \rightarrow \infty} a_n, \limsup_{n \rightarrow \infty} a_n]}$, there exists at least one generalised limit functional ${\mathop{\widetilde \lim}_{n \rightarrow \infty}}$ that takes the value ${L}$ when applied to ${a_n}$; for instance, for any number ${\theta}$ in ${[-1,1]}$, there exists a generalised limit functional that assigns that number ${\theta}$ as the “limit” of the sequence ${a_n = (-1)^n}$. This claim can be seen by first designing such a limit functional on the vector space spanned by the convergent sequences and by ${(a_n)_{n=1}^\infty}$, and then appealing to the Hahn-Banach theorem to extend to all sequences. This observation also gives a necessary and sufficient criterion for a bounded sequence ${(a_n)_{n=1}^\infty}$ to classically converge to a limit ${L}$, namely that all generalised limits of this sequence must equal ${L}$.
Because of the reliance on the Hahn-Banach theorem, the existence of generalised limits requires the axiom of choice (or some weakened version thereof); there are models of set theory without the axiom of choice in which no generalised limits exist. For instance, consider a Solovay model in which all subsets of the real numbers are measurable. If one lets ${e_n: {\bf R} \rightarrow \{0,1,2\}}$ denote the function that extracts the ${n^{th}}$ ternary digit past the decimal point (thus ${e_n(x) = \lfloor 3^n x \rfloor \hbox{ mod } 3}$, and lets ${\mathop{\widetilde \lim}}$ be a generalised limit functional, then the function ${f(x) := \mathop{\widetilde \lim}_{n \rightarrow \infty} e_n(x)}$ is non-constant (e.g. ${f(0)=0}$ and ${f(1/2)=1}$), but also invariant almost everywhere with respect to translation by ternary rationals ${a/3^n}$, and hence cannot be measurable (due to the continuity of translation in the strong operator topology, or the Steinhaus lemma), and so generalised limit functionals cannot exist.
Generalised limits can obey the shift-invariance property (4) or the algebra homomorphism property (3), but as the above analysis of the sequence ${a_n = (-1)^n}$ shows, they cannot do both. Generalised limits that obey the shift-invariance property (4) are known as Banach limits; one can for instance construct them by applying the Hahn-Banach theorem to the Césaro limit functional; alternatively, if ${\mathop{\widetilde \lim}}$ is any generalised limit, then the Césaro-type functional ${(a_n)_{n=1}^\infty \mapsto \mathop{\widetilde \lim}_{N \rightarrow \infty} \frac{1}{N} \sum_{n=1}^N a_n}$ will be a Banach limit. The existence of Banach limits can be viewed as a demonstration of the amenability of the natural numbers (or integers); see this previous blog post for further discussion.
Generalised limits that obey the algebra homomorphism property (3) are known as ultrafilter limits. If one is given a generalised limit functional ${p\!\!-\!\!\lim_{n \rightarrow \infty}}$ that obeys (3), then for any subset ${A}$ of the natural numbers ${{\bf N}}$, the generalised limit ${p\!\!-\!\!\lim_{n \rightarrow \infty} 1_A(n)}$ must equal its own square (since ${1_A(n)^2 = 1_A(n)}$) and is thus either ${0}$ or ${1}$. If one defines ${p \subset 2^{2^{\bf N}}}$ to be the collection of all subsets ${A}$ of ${{\bf N}}$ for which ${p\!\!-\!\!\lim_{n \rightarrow \infty} 1_A(n) = 1}$, one can verify that ${p}$ obeys the axioms of a non-principal ultrafilter. Conversely, if ${p}$ is a non-principal ultrafilter, one can define the associated generalised limit ${p\!\!-\!\!\lim_{n \rightarrow \infty} a_n}$ of any bounded sequence ${(a_n)_{n=1}^\infty}$ to be the unique real number ${L}$ such that the sets ${\{ n \in {\bf N}: |a_n - L| \leq \varepsilon \}}$ lie in ${p}$ for all ${\varepsilon>0}$; one can check that this does indeed give a well-defined generalised limit that obeys (3). Non-principal ultrafilters can be constructed using Zorn’s lemma. In fact, they do not quite need the full strength of the axiom of choice; see the Wikipedia article on the ultrafilter lemma for examples.
We have previously noted that generalised limits of a sequence can converge to any point between the limit inferior and limit superior. The same is not true if one restricts to Banach limits or ultrafilter limits. For instance, by the arguments already given, the only possible Banach limit for the sequence ${a_n = (-1)^n}$ is zero. Meanwhile, an ultrafilter limit must converge to a limit point of the original sequence, but conversely every limit point can be attained by at least one ultrafilter limit; we leave these assertions as an exercise to the interested reader. In particular, a bounded sequence converges classically to a limit ${L}$ if and only if all ultrafilter limits converge to ${L}$.
There is no generalisation of the classical limit functional to any space that includes non-classically convergent sequences that obeys the subsequence property (5), since any non-classically-convergent sequence will have one subsequence that converges to the limit superior, and another subsequence that converges to the limit inferior, and one of these will have to violate (5) since the limit superior and limit inferior are distinct. So the above limit notions come close to the best generalisations of limit that one can use in practice.
(Added after comments) If ${\beta {\bf N}}$ denotes the Stone-Cech compactification of the natural numbers, then ${\ell^\infty({\bf N})}$ can be canonically identified with the continuous functions on ${\beta {\bf N}}$, and hence by the Riesz representation theorem, bounded linear functionals on ${\ell^\infty({\bf N})}$ can be identified with finite measures on this space. From this it is not difficult to show that generalised limit functionals can be canonically identified with probability measures on the compact Hausdorff space ${\beta {\bf N} \backslash {\bf N}}$, that ultrafilter limits correspond to those probability measures that are Dirac measures (i.e. they can be canonically identified with points in ${\beta {\bf N} \backslash {\bf N}}$), and Banach limits correspond to those probability measures that are invariant with respect to the translation action of the integers ${{\bf Z}}$ on ${\beta {\bf N} \backslash {\bf N}}$.
We summarise (some of) the above discussion in the following table:
Limit Always defined Linear Shift-invariant Homomorphism Constructive Classical No Yes Yes Yes Yes Superior Yes No Yes No Yes Inferior Yes No Yes No Yes Césaro No Yes Yes No Yes Generalised Yes Yes Depends Depends No Banach Yes Yes Yes No No Ultrafilter Yes Yes No Yes No | crawl-data/CC-MAIN-2021-39/segments/1631780056974.30/warc/CC-MAIN-20210920010331-20210920040331-00542.warc.gz | null |
This page was enrolled in the International Ophthalmologists contest.
- 1 Definition
- 2 Clinical presentation
- 3 Systemic Associations
- 4 Investigations
- 5 Treatment
- 6 References
Panuveitis, also known as Diffuse uveitis, is the inflammation of all uveal components of the eye with no particular site of predominant inflammation.
The uvea is a highly vascular layer that lines the sclera, and its principal function is to provide nutrition to the eye. The iris is responsible for the metabolism of the anterior segment by diffusion of metabolites through the aqueous. The ciliary body secretes aqueous which bathes the avascular structures of the anterior segment. The choroid provides nourishment for the outer layers of the retina. Although topographically separate, the iris, ciliary body, and choroid are closely related forming a continuous whole and diseases affecting one portion often affect the other regions as seen in panuveitis.
Classification of Uveitis
The Standardization of Uveitis Nomenclature (SUN) Working group guidance on uveitis terminology categorizes uveitis anatomically as follows;
- Anterior uveitis; localized primarily to the anterior segment of the eye, involving iris and pars plicata.
- Intermediate uveitis; localized to the vitreous cavity and pars plana
- Posterior uveitis; localized to the choroid and retina.
- Panuveitis; inflammation involving anterior, intermediate and posterior uveal structures.
- Exogenous infections: due to the introduction of organisms into the eye through perforating wound or ulcer.
- Secondary infections: the inflammation of the uveal tract due to its spread from other ocular tissues- cornea, sclera or retina.
- Endogenous infections: organisms primarily lodged in another organ of the body reach the eye through the bloodstream. These include bacterial infections such as syphilis, tuberculosis; viral infections such as mumps, smallpox or influenza; and protozoal infections such as toxoplasmosis.
- Immune-related inflammation: sensitized ocular tissues excite an immune response on contact with the organisms such as in Behcet syndrome.
Some intraocular malignancies such as retinoblastoma, iris melanoma, and systemic haematological malignancies such as leukemia, lymphoma and histiocytic cell sarcoma can present with features of panuveitis termed ‘masquerade syndromes’.
Blunt or penetrating ocular trauma can produce features of panuveitis. Surgical trauma from intraocular procedures such as cataract extraction, trabeculectomy, and vitreoretinal surgery can produce postoperative panuveitis.
The clinical presentation of panuveitis involves the summation of symptoms and signs of anterior, intermediate, and posterior uveitis.
- Watery discharge
- Blurring of vision
- Diminution of vision
- Flashes of light
- Reduced Visual acuity
- Lid Oedema
- Ciliary injection
- Keratic Precipitates(KPs)- deposits on the corneal endothelium composed of inflammatory cells such as lymphocytes, plasma cells, and macrophages.
- Anterior chamber:
- Cells in the anterior chamber
- Hypopyon–whitish purulent exudate composed of myriad inflammatory cells in the inferior part of the anterior chamber forming a horizontal level under the influence of gravity.
- Aqueous flare: haziness of the normally clear fluid in the anterior chamber due to protein in the aqueous present as a result of the breakdown of the blood-aqueous barrier.
- Fibrinous exudates
- Iris nodules- including Koeppe nodules which are the site of posterior synechiae formation, Bussaca nodules which are a feature of granulomatous uveitis, and yellowish nodules seen in syphilitic uveitis.
- Iris pearls- seen in lepromatous uveitis
- Iris crystals
- Posterior synechiae
- Iris atrophy- seen in herpetic uveitis
- Heterochromia iridis
- Iris neovascularization
- Intraocular pressure may be increased or reduced
- White snowball like exudates near the ora serrata
- Mild peripheral phlebitis
- Macular edema
- Papillitis or Disc edema
- Vitreous hemorrhage
- Exudates in the choroid and retina
- Retinal hemorrhages
- Choroidal Neovascularization
- Retinal detachment
Toxoplasmosis is caused by Toxoplasma gondii, an obligate intracellular protozoan. It is the most common cause of infectious retinitis in immunocompetent individuals and commonly occurs due to reactivation of prenatal infestation, but postnatal infestation may also occur. Reactivation commonly occurs between 10-35 years. Ocular findings include:
- Retinitis, retinochoroiditis,
- Papillitis, optic neuritis
- Vasculitis (arteritis, phlebitis)
- Deep retinal infiltrates
- Subretinal neovascularization
- Vitreous strands and membranes
- Detachment (PVD) posterior hyaloid face covered with inflammatory precipitates.
- Posterior synechiae
Intraocular TB can be due to direct infection of Mycobacterium tuberculosis or indirect immune-mediated hypersensitivity response to mycobacterial antigens when there is no defined active systemic lesion elsewhere, or the lesion is thought to be inactive. Ocular findings include:
- Mutton-fat keratic precipitates and posterior synechiae
- Macular edema, retinal vasculitis, neuroretinitis, solitary or multiple choroidal tubercles, multifocal choroiditis, choroidal granulomas, subretinal abscess
- Serous retinal detachment
- Anterior optic neuritis, neuroretinitis, retrobulbar optic neuritis, optochiasmatic arachnoiditis, optic nerve tuberculoma or papilledema
VKH Syndrome is an idiopathic multisystem autoimmune disease featuring inflammation of melanocyte containing tissues such as the uvea, skin, ear, and meninges. It predominantly affects Hispanic, Japanese and pigmented individuals. The following criteria are required to make a diagnosis of VKH syndrome.
- The absence of a history of penetrating ocular trauma
- Absence of other ocular disease entities
- Bilateral panuveitis
- Neurological and auditory manifestations
- Integumentary findings, not preceding the onset of central nervous system or ocular disease such as alopecia, poliosis, and vitiligo
Behcet disease is an idiopathic multisystem syndrome characterized by recurrent aphthous oral ulcers, genital ulcerations, and panuveitis. It typically affects patients from Turkey, Middle, and the Far East, with a lower prevalence in Europe and North America. Relapsing/remitting acute onset panuveitis with retinal vasculitis and often spontaneous resolution without treatment is the classical pattern of eye involvement. Retinal vascular disease (vasculitis and occlusion) is the main cause of visual impairment.
Sarcoidosis is a chronic disorder of unknown cause, manifesting with noncaseating granulomatous inflammatory foci. It is one of the most common systemic associations of panuveitis. It is more common in colder climates but affects people of black ethnicity more than whites. The International Workshop on Ocular Sarcoidosis (IWOS) identified seven key signs in the diagnosis of intraocular sarcoidosis.
- Mutton fat KPs and/or small granulomatous KPs and/or iris nodules.
- Trabecular meshwork nodules and/or tent shaped Peripheral Anterior Synechiae (PAS)
- Vitreous opacities; snowballs and/or ‘strings of pearls’
- Multiple chorioretinal peripheral lesions
- Nodular and/or segmental periphlebitis (with/without candlewax drippings) and/or retinal macroaneurysm in an inflamed eye.
- Optic disc nodules/granulomas and/or solitary choroidal nodule.
Syphilis is a great mimic of panuveitis due to infection with Treponema pallidum.
The ocular findings include:
- Multifocal chorioretinitis
- Focal areas of chorioretinal atrophy associated with pigmentation
- Optic neuritis
- Optic atrophy
Sympathetic Ophthalmitis is a bilateral granulomatous panuveitis occurring after penetrating trauma; it may also occur following intraocular surgery especially multiple vitreoretinal procedures. It occurs due to immune sensitization to melanin or melanin associated proteins in uveal tissues. The findings include:
- Koeppe nodules
- Mutton fat KPs
- Retinal edema
- Disc edema
A careful history and detailed clinical examination are usually sufficient in making a diagnosis. However, investigations may be necessary especially in recurrent and bilateral cases of panuveitis.
- FBC – Eosinophilia - parasitic infections such as Toxoplasmosis
- Lymphocytosis – Chronic infections
- Erythrocyte Sedimentation Rate – a non-specific indication of systemic disease.
- Antibody titre: Toxoplasmosis
- Angiotensin-converting enzyme: Sarcoidosis
- Tuberculin test- Tuberculosis
- Kveim test – Sarcoidosis
- Behcetin (pathergy) test– Behcet’s disease
- Behcet’s disease: HLA-B51.
- Sympathetic Ophthalmia: HLA-A11.
- Vogt-Koyanagi-Harada disease: MT-3, BW22J/DR5, DW15.
- Skull x-ray: Calcification in toxoplasmosis
- Chest x-ray: Tuberculosis, Sarcoidosis, Malignancies
- Gallium scans: Lungs, Salivary glands, Lacrimal glands for sarcoidosis.
- Ultrasound Scan
- CT scan: Chest CT in Sarcoidosis
Non Specific Treatment
- Give comfort by relieving iris sphincter and ciliary muscle spasm,
- Prevent formation of posterior synechiae
- Break down synechiae
- Reduction of leukocytic and plasma exudation
- Maintenance of cellular membrane integrity with inhibition of tissue swelling
- Inhibition of phagocytosis and lysozymal release from granulocytes.
- Increased stabilization of intracellular lysosomal membranes.
- Suppression of circulating lymphocytes.
Systemic immunosuppressive agents
- Alkylating agents - Cyclophosphamide and Chlorambucil-These agents work by suppression of T – lymphocytes and to a lesser extent B – lymphocytes.
- Antimetabolites- Azathioprine (impairs purine metabolism inhibiting the synthesis of DNA, RNA and protein) and Methotrexate (impairs folate synthesis by inhibiting dihydrofolate reductase, an enzyme that participates in the synthesis of folic acid)
- T cell inhibitors - Cyclosporine A, Tacrolimus-Inhibits T-cell lymphocyte activation
- Infliximab, Adalimumab, Etanercept; Inhibit alphaTNF (Tumour Necrosis Factor)
Based on Underlying Disease.
- Syphilis: Penicillin. Penicillin-sensitive patients can be treated with oral Tetracycline or Erythromycin
- Tuberculosis: Standard antitubercular therapy (Isoniazid, Rifampicin, Ethambutol, Pyrazinamide)
- Toxoplasmosis: Clindamycin, Sulphadiazine, Pyrimethamine, Cotrimoxazole, Atovaquone, Azithromycin
Panuveitis is a major cause of blindness and visual morbidity. The prognosis for people with panuveitis varies depending on the underlying cause and severity. When the condition is unrecognized or inadequately treated, profound and irreversible vision loss can occur. Therefore early detection and proper management is a necessity in every case of panuveitis.
- Moorthy RS, Basic and Clinical Science Course, Section 9, 2013–2014. Courtesy of Albert T. Vitale, MD. © 2019 American Academy of Ophthalmology American Academy of Ophthalmology. Severe sarcoid panuveitis. https://www.aao.org/image/severe-sarcoid-panuveitis. Accessed July 08, 2019.
- Sihota R, Tandon R. Parsons’ diseases of the eye. Elsevier India; 2015. 641 p.
- Jabs DA, Nussenblatt RB, Rosenbaum JT, Standardization of Uveitis Nomenclature (SUN) Working Group. Standardization of uveitis nomenclature for reporting clinical data. Results of the First International Workshop. Am J Ophthalmol. 2005 Sep;140(3):509–16.
- Bowling B (Bradley). Kanski’s clinical ophthalmology : a systematic approach. Elsevier; 2016. 928 p.
- Friedman NJ, Kaiser PK, Trattler B. Review of Ophthalmology. Elsevier; 2017. 413 p. | <urn:uuid:bcdf22f6-d062-473e-b842-8e2ae1da5bdc> | {
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# Estimating coefficient in linear regression
Given: $$y = b_0 + b_1x$$
I am wondering what is the explanation behind this formula for estimating the $$b_1$$ coefficient:
$$b_1 = \frac{\sum_{i=1}^n( x_i-\bar{x})(y_i-\bar{y})}{ \sum_{i=1}^n( x_i-\bar{x})^2 }$$
What are the steps to derive this formula?
Part 1 Update -March 18 2021:
When tried to substitute $$\bar{y} - b_1\bar{x}$$ for $$b_0$$ in
$$b_0 \bar{x} + b_1 \overline{x^2} = \overline{xy}$$ I got stuck with $$b_1$$ in both sides of the equations.
$$b_1 \overline{x^2} = \overline{xy}-(\overline{x} \bar{y} - b_1\overline{x^2})$$
Can you please guide me in further derivation steps. Thanks
Part 2 Update
With another help from @MartinVesely, I realized that this should be:
$$b_0 \bar{x} + b_1 \overline{x^2} = \overline{xy}$$
$$((\bar{y} - b_1\bar{x})\bar{x}) + b_1 \overline{x^2} = \overline{xy}$$
$$(\bar{x}\bar{y} - b_1(\bar{x})^2) + b_1 \overline{x^2} = \overline{xy}$$
$$( - b_1(\bar{x})^2) + b_1 \overline{x^2} = \overline{xy} - \bar{x}\bar{y}$$
$$b1( -(\bar{x})^2 + \overline{x^2}) = \overline{xy} - \bar{x}\bar{y}$$
$$b1= \frac{\overline{xy} - \bar{x}\bar{y} }{ \overline{x^2} -(\bar{x})^2}$$
• Are you asking what is the meaning of the formula or how to derive it? Mar 16, 2021 at 9:37
• Mar 16, 2021 at 10:15
• @martin yes I want to know how to derive it. Mar 16, 2021 at 10:27
• @Edville: Please see my derivation below, I hope it helps. Mar 17, 2021 at 7:56
• @Edville: There is $\bar{x}$ in formula for $b_0$ (i.e. average of $x$), while in the other equation there is $\overline{x^2}$, i.e. average of $x$ squares. You cannot interchange $(\bar{x})^2$ and $\overline{x^2}$. Mar 18, 2021 at 9:05
A derivation of the formula is done with the least square method.
Firstly write down a function $$L = \sum_{i=1}^n (y_i - b_0 - b_1 x_i)^2$$. This is a sum of squared differences between actual output data $$y_i$$ and output given by a regression line.
Our goal is to minimize a difference between actual data and theregression line. This means that we need to calculate first derivatives with respects to $$b_0$$ and $$b_1$$:
$$\frac{\partial L}{\partial b_0} = -\sum_{i=1}^n 2(y_i - b_0 - b_1 x_i)$$
$$\frac{\partial L}{\partial b_1} = -\sum_{i=1}^n 2x_i(y_i - b_0 - b_1 x_i)$$
Now, by setting $$\frac{\partial L}{\partial b_0}$$ and $$\frac{\partial L}{\partial b_1}$$ equal to zero and dividing by -2 we have
$$\sum_{i=1}^n (y_i - b_0 - b_1 x_i) = 0$$
$$\sum_{i=1}^n x_i(y_i - b_0 - b_1 x_i) = 0$$
Rewriting leads to $$\sum_{i=1}^n (y_i - b_0 - b_1 x_i) = \sum_{i=1}^n y_i - b_1\sum_{i=1}^n x_i - nb_o = 0$$
$$\sum_{i=1}^n x_i(y_i - b_0 - b_1 x_i) = \sum_{i=1}^n x_iy_i - b_1\sum_{i=1}^n x_i^2 -b_0\sum_{i=1}^n x_i = 0$$
Now, if we divide both eqautions by $$n$$ and rearranging them, we have $$b_0 + b_1 \bar{x} = \bar{y}$$
$$b_0 \bar{x} + b_1 \overline{x^2} = \overline{xy},$$
where $$\bar{x}$$ is average of $$x_i$$ values (similarly for $$y_i$$) and $$\overline{xy}$$ is average of products $$x_iy_i$$.
Clearly $$b_0 = \bar{y} - b_1\bar{x}$$. After substituing this to the other equation we get $$b_1 = \frac{\overline{xy} -\bar{x}\bar{y}}{\overline{x^2}-(\bar{x})^2}.$$
Since $$\overline{xy} -\bar{x}\bar{y}$$ is covariance of $$x$$ and $$y$$ and $$\overline{x^2}-(\bar{x})^2$$ is variance of $$x$$ we have your formula, because $$\frac{1}{n}\sum_{i=1}^n (x_i - \bar{x})^2$$ is variance of $$x$$ and $$\frac{1}{n}\sum_{i=1}^n (x_i - \bar{x})(y_i - \bar{y})$$ is covariance of $$x$$ and $$y$$.
• Thank you very much for your help! Mar 17, 2021 at 16:14 | crawl-data/CC-MAIN-2022-27/segments/1656104204514.62/warc/CC-MAIN-20220702192528-20220702222528-00758.warc.gz | null |
The Barents Sea – offering a high biological production
Due to the North Atlantic drift, the Barents Sea has a high biological production compared to other oceans of similar latitude.
The fresh water from the melting ice makes up a stable water layer on top of the sea water, thus enabling the spring bloom of phytoplankton to start quite early. The phytoplankton bloom feeds zooplankton such as Calanus finmarchicus, Calanus glacialis, Calanus hyperboreus, Oithona spp., and krill.
The southern half of the Barents remains ice-free year round due to the warm North Atlantic drift. In September, the entire Barents Sea is more or less completely ice-free.
There are three main types of water masses in the Barents Sea: warm, salty Atlantic water from the North Atlantic drift (temperature >3°C, salinity >35), cold Arctic water (temperature <0°C, salinity <35) from the north, and warm, but not very salty coastal water (temperature >3°C, salinity <34.7).
Between the Atlantic and Polar waters, a front called the Polar Front is formed. In the western parts of the sea this front is determined by the bottom topography and is therefore relatively sharp and stable from year to year. In the east it can be quite diffuse and its position can vary a lot between years.
The lands of Novaya Zemlya attained most their early Holocene coastal deglaciation approximately 10,000 years before present.
The Barents Sea was formerly known to Russians as Murmanskoye Morye, or the ‘Sea of Murmans’ – i.e. Norwegians. The sea was given its present name in honor of Dutch navigator and explorer Willem Barents. Barents was the leader of expeditions to the far north at the end of the sixteenth century.
During the Cold War, the Soviet Red Banner Northern Fleet used the southern reaches of the Sea as a ballistic missile submarine bastion, a strategy that Russia continues. Nuclear contamination from dumped Russian naval reactors is an environmental concern in the Barents Sea.
Oil exploration in the Barents Sea began in the 1970s with discoveries made on both the Russian and Norwegian sides. For decades there was a boundary dispute between Norway and Russia, with the Norwegians favouring the Median Line and the Russians favouring a meridian based sector. A compromise treaty announced in 2010 settled the border in the approximate middle of these two stances.Source: Wikipedia | <urn:uuid:104c78c6-5818-42a4-893a-0d4a8c35245e> | {
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What are synchronous communication and asynchronous communication?
Synchronous communication is a communication method which matches the timing of data transmission by sender and the one of data reception by recipient. On the other hands, asynchronous communication is a communication method which doesn’t match these timings of data exchange.
The meaning of the word “Synchronous” changes according to the context. For example, at the physical level, it means to synchronize clock frequencies in communication. In web application, it means to synchronize the timing to send request to the server and the timing to get response from the server. The following is a description in the context of a web application.
Synchronous communication on the web matches the timing when the client send the request and the timing when the client get the response from the server. In other words, client does no process once it sends the request until it receives the response.
Examples of synchronous communication
Waiting for loading when accessing a web page
Waiting for page move after pressing the button to send the answer
Advantages and disadvantages of synchronous communication
- Client can surely get a response to the request
- The order of processing does not change
- Cannot operate until response is obtained
- It sometimes takes a long waiting time
Asynchronous communication on web allows user to do another process while waiting response. Users can continue to operate after request sending because the reception processing will be done without freezing after receiving the response.。
Examples of asynchronous communication
- On the search page a suggestion is displayed when you enter a search term
- Users can search and move while loading the map (Reference: Google Maps)
Advantages and disadvantages of asynchronous communication
- No perceived waiting time
- It is possible to refresh only a part of the page (other parts can be operated during that time)
- Implementation is complicated
- A large amount of asynchronous communication increases the load on the server
What is AJAX?
For example the following are techniques of Ajax. (reference: AJAX Documentation)
How Ajax works
In Ajax, the 2 system “sending the request and getting the response from the server” and “get the data from the browser and reflect the received data to the browser” are separated. So users can operate on the browser while waiting the response.
The system which manage exchange of the data between server and client is called “Ajax engine”.
Advantages of Ajax
Ajax has the same advantages as the asynchronous communication’s advantages above such as “No perceived waiting time”.
Additionally, ajax enables the display change without page transition. Generally, the HTTP response body contains html itself. So, a new html page will be received and page transition will occur after waiting. (Related article: What is http request/response?). Ajax can change the contents without causing this page transition.
Implementation of Ajax
XMLHttpRequest (XHR) can be used for Ajax implementation.
Please check “Implementation Of Ajax (Search Suggestion)” for a concrete example. | <urn:uuid:de4a640a-fa44-451d-a94a-59f08853789d> | {
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Group B streptococcus (GBS) is a topic seldom talked about, yet is a common bacterium carried in the intestines or lower genital tract. It is generally harmless yet can cause infections in adults who suffer from specific chronic medical conditions such as liver disease or diabetes. Surprisingly, many adults carry group B strep within the body – most commonly in the throat, bladder, vagina, bowels, and rectum. This specific bacterium is not sexually transmitted, nor is it spread through food or water. Those adults at an increased risk for the bacterium include diabetics, having a compromised immune system such as HIV, have liver disease, or cancer.
A great deal of attention is paid to pregnant women carrying GBS because they can (but may not) pass it off to their babies during labor. Statistics from the CDC indicated that women who test positive but are not in a high risk category stand a one in 200 chance of delivering a baby with GBS if antibiotics are not given and a one in 4000 chance if they are. This is the reason why the CDC has recommended routine screening between the 35th and 37th week of pregnancy for vaginal strep B for all women who are pregnant. Early onset group B for infants may include fever, kidney problems, instability of the heart, sepsis, lethargy and difficulty feeding. With late onset which might occur in as little time as a week or up to a month or two following delivery, the infant may exhibit dyspnea (difficulty breathing), acquire meningitis, have a fever, become irritable, and have a hard time feeding. Treatment is commonly in the form of intravenous antibiotics, possibly oxygen and other medications, as well. It should be noted that to test positive for group B strep simply implies the woman is a carrier.
In adults, the disorder may cause endocarditis (infected heart valves), sepsis (bloodstream infection, cellulitis (a skin infection), meningitis (inflammation of the fluid that surrounds the brain and spinal cord, urinary tract infections, infections of bones and joints, and pneumonia (lung inflammation).
Diagnosis is made by growing cultures of fluid samples collected. On the downside, the cultures will take two or three days to grow which may delay treatment which, for adults, is antibiotics. The specific antibiotic chosen depends on the severity of the infection, its location, and the patient’s medical history.
While unavailable at this time, researchers are attempting to perfect a group B strep vaccine that can help prevent infections in adults. | <urn:uuid:54af3bcc-c9e7-48a7-b5a4-2c7251fc3dba> | {
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Bastian Schaefer and his team at Airbus have a vision of a more sustainable future for aviation, a future that should incorporate social as well as environmental and economic value. To help make this dream a reality, have come up with a disruptive structure that mimics the design of bone, or more accurately a skeleton, somewhat as it occurs in nature.
Schaefer explains what this means:
So how does nature build its components and structures? So nature is very clever. It puts all the information into these small building blocks, which we call DNA. And nature builds large skeletons out of it. So we see a bottom-up approach here, because all the information, as I said, are inside the DNA. And this is combined with a top-down approach, because what we are doing in our daily life is we train our muscles, we train our skeleton, and it’s getting stronger. And the same approach can be applied to technology as well. So our building block is carbon nanotubes, for example, to create a large, rivet-less skeleton at the end of the day. How this looks in particular, you can show it here. So imagine you have carbon nanotubes growing inside a 3D printer, and they are embedded inside a matrix of plastic, and follow the forces which occur in your component. And you’ve got trillions of them. So you really align them to wood, and you take this wood and make morphological optimization, so you make structures, sub-structures, which allows you to transmit electrical energy or data. And now we take this material, combine this with a top-down approach, and build bigger and bigger components.
New design rules and 3D printing will help to fulfill the dreams of the Airbus team in producing aircraft designs that are stronger and yet weigh less, leading to the obvious cost and environmental benefits. | <urn:uuid:3bf2c6a9-40be-4bc4-b7fb-8403a3f9b7db> | {
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# What's a math trick that is not very well-known?
• What's a math trick that is not very well-known?
• Here are some of the math tricks that i know which are not that well known :
Square of a number using unit digit :
Let us find out the square of say 11 using the formula :
11^2 = 11 + 1/1^2 = 12/1 = 121 (^2 is being used for : to the power 2)
• Slash is used just as a separator.
• So we basically add the unit digit of the number to be squared to the number,followed by the square of the unit digit.
• The number of digits after the slash can only be one,if they exceed one,then we place the rightmost digit on the extreme right after the slash,and the remaining digit gets added to the number on the left hand side of the slash.
For example : 19^2 = 19 + 9/9^2 = 28/81 = 361 (Here note that the 8 from the 81 has been added to 28 resulting in 36)
We can work up like this upto 19.If we wish to find out square of higher numbers, the following steps should be followed :
The steps remain the same only with a slight change
21^2 = 2*(21+1)/1^2 = 222/1 = 441
We multiply the left side of the slash by 2 because now we are operating in 10
2 zone.
Similarly, for numbers 31 to 29,we will multiply the left side of the slash by 3 and so on.
Using the above method, we can easily find out the squares of numbers upto 99.
Square of a number using (a+b)^2 formula :
We all know from school : (a+b)^2 = a^2 + 2ab+ b^2
Ever wondered we can use this to find square's of numbers?
So this is how it goes :
Lets say we want to find the square of 12 :
• We take a=1 and b=2
• We substitute the values of a and b in the formula
• Ignore all the +'s,just consider them like the slash we used before.
So (12)^2 = 1^2 2(1)(2) 2^2
= 1 4 4
Even here if any one the term exceeds single digit, we have to sort of carry it to the left.
For example :
14^2 = 1^2 2(1)(4) 4^2
= 1 8 16
= 1 9 6
(Here the unit digit 6 is retained as a part of the answer and 1 is added to the 8 in the left making it 9)
One more example :
26^2 = 2^2 2(2)(6) 6^2
= 4 24 36
= 4 27 6
= 6 7 6
(Here the unit digit 6 was retained and 3 was added to 24 making it 27,now since even 27 is not a single digit number, 7 was retained and 2 was added to 4 making it 6)
Cube of a number using (a+b)^3 formula :
We do the same thing like in (a+b)^2 here.
(a+b)^3 = a^3 + 3(a^2)(b) + 3(a)(b^2) + b^3
Lets find the cube of 12 :
Steps :
• First term is 1^3 = 1
• Second term is 3(1^2)(2)=6
• Third term is 3(1)(2^2)=12
• Fourth term is 2^3=8
Put them all in a row :
1 6 12 8
1 7 2 8
(Here the unit digit 2 was retained and 1 was added to 6 making it 7)
So in most of these tricks, we always use this method.Unit digit is considered and the other part is carried to the left.
For example : Cube of 16
16^3 = 1^3 3(1^2)(6) 3(1)(6^2) 6^3
= 1 18 108 216
= 1 18 129 6
= 1 30 9 5
= 4 0 9 6
(So same way here, 6 was retained, 21 was added to 108 making it 129,9 is retained, 12 is added to 18 making it 30 and we end up with 4096 which is the answer)
All The Best !!! | crawl-data/CC-MAIN-2020-16/segments/1585371604800.52/warc/CC-MAIN-20200405115129-20200405145629-00177.warc.gz | null |
The lymphatic system is an extensive drainage network that helps keep body fluid levels in balance and defends the body against infections. It is made up of a network of lymphatic vessels that carry lymph — a clear, watery fluid that contains protein molecules, salts, glucose, urea, and other substances — throughout the body.
The spleen, located in the upper left part of the abdomen under the ribcage, works as part of the lymphatic system to protect the body, clearing worn-out red blood cells and other foreign bodies from the bloodstream to help fight off infection.
About the Spleen and Lymphatic System
One of the lymphatic system's major jobs is to collect extra lymph fluid from body tissues and return it to the blood. This is crucial because water, proteins, and other substances are always leaking out of tiny blood capillaries into the surrounding body tissues. If the lymphatic system didn't drain the excess fluid from the tissues, the lymph fluid would build up in the body's tissues, causing them to swell.
The lymphatic system also helps defend the body against germs (viruses, bacteria, and fungi) that can cause illnesses. Those germs are filtered out in the lymph nodes, which are small masses of tissue located along the network of lymph vessels. The nodes house lymphocytes, a type of white blood cell. Some of those lymphocytes make antibodies, special proteins that stop infections from spreading by trapping disease-causing germs and destroying them.
The spleen also helps the body fight infection. The spleen contains lymphocytes and another kind of white blood cell (called macrophages) that engulf and destroy bacteria, dead tissue, and foreign matter and remove them from the blood passing through the spleen.
The lymphatic system is a network of very small tubes (or vessels) that drain lymph fluid from all over the body. The major parts of the lymph tissue are located in the bone marrow, spleen, thymus gland, lymph nodes, and the tonsils. The heart, lungs, intestines, liver, and skin also contain lymphatic tissue.
One of the major lymphatic vessels is the thoracic duct, which begins near the lower part of the spine and collects lymph from the pelvis, abdomen, and lower chest. The thoracic duct runs up through the chest and empties into the blood through a large vein near the left side of the neck. The right lymphatic duct is the other major lymphatic vessel and collects lymph from the right side of the neck, chest, and arm, and empties into a large vein near the right side of the neck.
Lymph nodes are round or kidney-shaped. Most lymph nodes are about 1 cm in diameter but they can vary in size. Most of the lymph nodes are found in clusters in the neck, armpit, and groin area. Nodes are also located along the lymphatic pathways in the chest, abdomen, and pelvis, where they filter the blood. Inside the lymph nodes, lymphocytes called T-cells and B-cells help the body fight infection. Lymphatic tissue is also scattered throughout the body in different major organs and in and around the gastrointestinal tract.
The spleen helps control the amount of blood and blood cells that circulate through the body and helps destroy damaged cells.
How A Healthy Lymph System Works
Carrying Away Waste
Lymph fluid drains into lymph capillaries, which are tiny vessels. The fluid is then pushed along when a person breathes or the muscles contract. The lymph capillaries are very thin, and they have many tiny openings that allow gases, water, and nutrients to pass through to the surrounding cells, nourishing them and taking away waste products. When lymph fluid leaks through in this way it is called interstitial fluid.
Lymph vessels collect the interstitial fluid and then return it to the bloodstream by emptying it into large veins in the upper chest, near the neck.
Lymph fluid enters the lymph nodes, where macrophages fight off foreign bodies like bacteria, removing them from the bloodstream. After these substances have been filtered out, the lymph fluid leaves the lymph nodes and returns to the veins, where it re-enters the bloodstream.
When a person has an infection, germs collect in the lymph nodes. If the throat is infected, for example, the lymph nodes of the neck may swell. That's why doctors check for swollen lymph nodes (sometimes called swollen "glands" — but they're actually lymph nodes) in the neck when your throat is infected.
Problems of the Lymphatic System
Certain diseases can affect the lymph nodes, the spleen, or the collections of lymphoid tissue in certain areas of the body.
- Lymphadenopathy. This is a condition where the lymph nodes become swollen or enlarged, usually because of a nearby infection. Swollen lymph nodes in the neck, for example, can be caused by a throat infection. Once the infection is treated, the swelling usually goes away. If several lymph node groups throughout the body are swollen, that can indicate a more serious disease that needs further investigation by a doctor.
- Lymphadenitis. Also called adenitis, this inflammation of the lymph node is caused by an infection of the tissue in the node. The infection can cause the skin overlying the lymph node to swell, redden, and feel warm and tender to the touch. This infection usually affects the lymph nodes in the neck, and it's usually caused by a bacterial infection that can be easily treated with an antibiotic.
- Lymphomas. These cancers start in the lymph nodes when lymphocytes undergo changes and start to multiply out of control. The lymph nodes swell, and the cancer cells crowd out healthy cells and may cause tumors (solid growths) in other parts of the body.
- Splenomegaly (enlarged spleen). In healthy people, the spleen is usually small enough that it can't be felt when you press on the abdomen. But certain diseases can cause the spleen to swell to several times its normal size. Usually, this is due to a viral infection, such as mononucleosis. But in some cases, more serious diseases such as cancer can cause it to expand. Doctors usually tell someone with an enlarged spleen to avoid contact sports like football for a while because a swollen spleen is vulnerable to rupturing (bursting). And if it ruptures, it can cause a huge amount of blood loss.
- Tonsillitis. Tonsillitis is caused by an infection of the tonsils, the lymphoid tissues in the back of the mouth at the top of the throat that normally help to filter out bacteria. When the tonsils are infected, they become swollen and inflamed, and can cause a sore throat, fever, and difficulty swallowing. The infection can also spread to the throat and surrounding areas, causing pain and inflammation. A child with repeated tonsil infections may need to have them removed (a tonsillectomy).
Reviewed by: Yamini Durani, MD
Date reviewed: May 2015 | <urn:uuid:e8d2de86-a707-4052-917d-f9e6c8cdfaee> | {
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Condensation is by far the most common cause of dampness in buildings, probably accounting for the majority of damp problems reported. It affects both old and new buildings, but it appears to be a significant problem where the building has been modernised.
Condensation is directly associated with mould growth. It is this that the occupier sees first, and it gives an indication of the potential scale of the problem. The mould is usually found on decorative surfaces, especially wallpapers, where it can cause severe and permanent spoiling. In many cases, the mould and its spores ('seeds') give rise to complaints about health, and cause the "musty" odour frequently associated with a damp house.
The obvious places for condensation to occur are on cold walls, wiondows, and floors, but it can also occur in roof spaces and in sub-floor areas where there is a timber suspended floor; in the latter case, it can lead to dry rot or wet rot developing in floor timbers.
It is a fact that warm air can hold more water as vapour than cool air. Condensation is caused when moisture-laden air comes into contact with a cold surface – the air is cooled to the point where it can no longer hold its burden of water vapour. At this point, known as the "dewpoint," water begins to drop out of the air, and is seen as condensation on surfaces. On impervious surfaces such as glass and gloss paint, beads or a film of water collect. On permeable surfaces such as wallpaper and porous plaster, the condensing water is absorbed into the material. Therefore, the problem is not always initially obvious.
Condensation is very much a seasonal problem, occurring during the colder months – October to April. During the summer, the problem is seen to go away.
During the winter, ventilation of the house is usually low (due to windows and doors being closed, draught-proofing takes place). This allows build up of water vapour in the house, which, in some cases is sufficient to cause condensation. This condensation becomes apparent from the following symptoms:
- Water droplets form on cold, impervious surfaces such as glass and paint.
- Slightly damp wallpaper (often not noticed).
- Development of moulds, usually black mould.
In some cases, condensation may be long term, but intermittent, forming only at certain times of the day or night. In these cases, the only sign of condensation may be mould growth, as the moisture may have evaporated by the time moisture measurements are taken.
One should also be aware that the problem can occur well away from the site of most water vapour production. E.g. water vapour produced in the kitchen may diffuse through the house into a cold bedroom where it will condense on cold walls.
If one wishes to confirm that there is a condensation risk, then a Humiditect card can be affixed to the surface where condensation is suspected for 7 days (due to the intermittent nature of the problem). Spots of colour printed on the card will gradually bleed depending on the severity of the problem.
Control of Condensation
The control of condensation is based on two very simple primary measures, supported by a number of secondary measures.
Primary Measure 1 – Improve Ventilation
This will sweep away the internal moisture-laden air and replace it with drier air from the outside (yes, external air is drier than internal air most of the year!)
Primary Measure 2 – Improve Heating
Coupled with ventilation, heating should be set or applied to give a low-level background heat. This will ensure no rapid changes to the environment, and will facilitate slight warming of wall surfaces over a period of time, thus reducing the risk of condensation.
- Remove excess moisture sources – e.g. paraffin heaters, indoor drying of clothes.
- Insulate cold surfaces.
- Prevent possible water penetration.
- Install a dehumidifier.
- Use an anti-mould paint.
In situations where a condensation problem is persistent, it may be necessary to employ the services of a professional company to correctly diagnose the factors causing the condensation problem and implement measures to control it. If you would like a quote from a professional company in your area that offers a condensation control service, please call our technical department on 01403 210204 or visit our technical support page. | <urn:uuid:c6bc92ef-11dc-4e48-ac00-bbf4f8e75277> | {
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Iowa's Southern Boundary
How did Iowa come to have the shape it has today? Determining the location of Iowa’s borders was an essential step in our path to statehood.
A Line Is Drawn
The western boundary of Iowa was disputed because the words "the middle of the main channel of the Missouri River" did not point to a real place that was always easy to find. The same was true for what would become the southern boundary of Iowa. When Missouri— the state that is directly south of Iowa— wrote its constitution, it described the state's northern boundary as "the rapids of the river Des Moines." This description was used in their state constitution when Missouri voters accepted statehood in 1821. Later, trouble started because state and federal governments could not agree on where "the rapids of the river Des Moines" really were.
In 1816, before Missouri or Iowa became states, Colonel John C. Sullivan surveyed and marked what would soon become the northern boundary of Missouri. His survey was supposed to be a "parallel of [the] latitude which passes through the rapids of the river Des Moines," but he made a mistake. He did not adjust his compass as he moved eastward from the Missouri River. This caused his boundary line to angle upward until it was four miles further north on the east (Mississippi River) side than on the west (Missouri River) side. Few people knew this though, and it would only become important when many people began to settle the area.
Where Missouri Ends and Iowa Begins
As settlers quickly moved into the Iowa country after 1833, they started farms and towns. As these grew, the settlers wanted to know just where the northern Missouri boundary line was. One of the reasons they wanted to know was because of slavery. Missouri was a slave state and many people in the area did not want to live where laws allowed one man to own another man.
Missouri officials also wanted to be sure just where the boundary was. They believed that the Des Moines rapids were much farther north than the Sullivan line. Therefore, Missouri officials sent Joseph C. Brown to re-survey the boundary line in1837. He was supposed to begin at "the rapids of the river Des Moines" and then mark his line as he moved westward toward the Missouri River. He found a place on the Des Moines River near Keosauqua which he thought was the spot described by the words. This place, Great Bend, was 63 miles upstream from the mouth of the Des Moines River where it flows into the Mississippi River. He marked his line from Great Bend to a parallel spot near the Missouri River. Missouri then claimed Brown's line as its northern boundary.
The difference between the two lines was about 2,600 acres. Most of the settlers living on the disputed strip of land thought they had settled in the Iowa country. Much of it was rich farm land, which officials from both Missouri and Iowa Territory claimed as part of their jurisdiction. But in 1839 Missouri sheriffs tried to collect taxes from settlers in the disputed strip. Iowa Territorial Governor Robert Lucas warned Missouri Governor Lilburn Boggs that the Missouri sheriffs would not be permitted to do this. Governor Boggs warned Governor Lucas that the Missouri militia might be brought out to make sure the taxes were collected.
The "Honey War"
So when another Missouri sheriff tried to collect taxes, an Iowa sheriff arrested him. Of course this angered Missouri officials, and in the icy cold December of 1839 the Missouri militia was ordered to the border area. In response, Governor Lucas called for Iowa volunteers to meet at the border town of Farmington. As troops gathered from both sides, people in the area began to think that there might really be war between Iowa and Missouri.
William Willson reported that while on business in Missouri he and his crew had been stopped and searched by soldiers. The soldiers were looking for ammunition. Other reports told of Iowa citizens who had been held in Missouri as spies.
Before things had gotten to this state, Albert Miller Lea had been sent by President Martin van Buren to decide which line was the correct boundary between Iowa Territory and Missouri. Lea wrote that it was general knowledge that "the rapids of the river Des Moines" were in the Mississippi River, not the Des Moines River. He suggested that the Sullivan line was not an accurate one, yet it had often been used in legal papers as the northern boundary of Missouri. But when the war was about to start, the federal government had not made a decision. Just when it looked as though the first shot would be fired, the Missouri troops were dismissed, and Missouri's jurisdiction was withdrawn back to the Sullivan line. The Iowa troops gladly went home. The "war" was over, and no one had been killed. These events were later called the "Honey War" because early in the conflict someone had destroyed some valuable honey-filled bee trees which were growing in the disputed strip. A poem was later written about the war and set to the tune of Yankee Doodle. It made fun of the two governors for their part in creating the needless conflict.
A Line Is Drawn Again
Even though the "Honey War" had ended, the boundary issue was not settled right away. The United States Supreme Court finally decided the boundary issue in 1851. The court decided that the Sullivan line was the best boundary because it had been used so often in treaties. The court also ordered that the Sullivan line be re-surveyed and re-marked, correctly this time. Big cast iron monuments, each weighing about 1,600 pounds, were placed at the east and west ends of the line. Smaller cast iron posts were placed every tenth mile, and wooden posts were placed every mile along the boundary line.
One more survey was done in 1896, again at the request of the United States Supreme Court. A few of the wooden mile markers were replaced at that time with stone monuments. Some of these cast iron and stone markers can still be found today along Iowa's southern boundary. | <urn:uuid:1e66a01e-a6aa-4b4e-b525-1986b7fe3a60> | {
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The United States has a long and troubling history of race-based housing segregation. Until the Fair Housing act was passed in 1968, municipalities and private realtors were able to legally force African Americans to live in separate neighborhoods. The long-term consequences of these policies, coupled with the continuing trend of white flight, has entrenched segregation and the resulting inequalities in U.S. metropolitan areas.
There are many negative effects of ongoing segregated housing in U.S. metropolitan areas. For example, black families in America tend to have lower incomes than white families, and so largely black neighborhoods are far more likely to be highly impoverished. In the largest metropolitan areas, 25% of the black population lives in poverty, compared to 9% of whites. In some of the cities on this list, more than one-third of black residents live in poverty.
A number of studies have shown that people living in highly poor neighborhoods suffer from negative consequences that extend beyond poverty. Because of both the higher likelihood that African Americans live in poverty and because of racial segregation in cities, the concentrated poverty rate in the largest metro areas is virtually nonexistent for whites — just 1.4% of the white population lives in highly poor neighborhoods. Meanwhile, 12.4% of black residents live in such neighborhoods.
In these highly segregated cities, black residents are even more likely to live in extreme concentrated poverty. In seven of the cities on this list, more than 20% of black residents live in neighborhoods where at least 40% of the population is poor. In Detroit, the most segregated major metropolitan area in the country, 1 in 3 black residents live in highly impoverished neighborhoods.
Another serious consequence of segregation in these metropolitan areas is the effect it can have on the public school system. School funding is largely determined by property tax revenues. In metropolitan areas with low-income black neighborhoods and affluent white areas, the white schools will likely be much better funded. This means the children living in black neighborhoods face much greater obstacles for success.
Not surprisingly, the less racially integrated metropolitan areas in particular have poor educational outcomes for African Americans. In New Orleans, for example, 90.8% of white adults have a high school diploma, while the high school attainment rate for black adults is 79.6%.
To identify America’s most segregated cities, 24/7 Wall St. calculated the percentage of metropolitan area black residents who live in predominantly black census tracts — statistical subdivisions with an average of about 4,000 people. The greater the share of black metro residents living in the area’s racially homogenous neighborhoods, the greater the degree of segregation. We only considered census tracts with at least 500 residents in the 100 largest metropolitan areas. Population data are based on five-year estimates through 2015 from the U.S. Census Bureau’s American Community Survey. For the purpose of this story, we only considered segregation of white and black populations.
Because a certain level of racial diversity is necessary for segregation to be measured with confidence, only 74 of the 100 largest metro areas could be compared. The remaining 26 were not considered because they do not contain any predominantly black census tracts.
While racial segregation was the primary focus of our analysis, segregation by income is also an important component. Our analysis included the share of a metro area’s population living in extreme poverty — census tracts with poverty rates higher than 40%. This portion of our analysis excluded tracts with fewer than 500 residents, as well as tracts where more than 50% of the population was enrolled in either undergraduate or graduate school.
We also reviewed median household income, poverty rates, educational attainment rates, unemployment rates, and homeownership rates among black and white populations in each metro area from the ACS. All data are five-year estimates. | <urn:uuid:396baf80-c17c-4da8-b317-35d7e8aa96e9> | {
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Where Does All the Carbon Go?
This oil-burning power plant is located in the middle of New York City. Its smokestacks are equipped with scrubbers. These are devices that remove many of the pollutants from the exhaust gases. But the smokestacks still release gases.
The Back Story
- Oil is a fossil fuel. Like all fossil fuels-and the living things from which they form-oil consists mostly of carbon. What happens to the carbon in a fossil fuel like oil when it burns? There doesn’t appear to be anything left from the fire. Is the carbon destroyed in the flames?
- Actually, the carbon still exists because matter can’t be destroyed. Matter is always conserved in chemical reactions. If you don’t believe it, watch this video in which some middle school “scientists” try to demonstrate the law of conservation of matter (or mass):
What Do You Think?
At the link below, watch a dramatic example of how matter is conserved in the formation and burning of a fossil fuel. Then answer the questions that follow.
- What is the law of conservation of mass?
- How did the students in the first video demonstrate the law of conservation of mass?
- When something burns, it undergoes a combustion reaction. Describe a combustion reaction. How does it follow the law of conservation of mass if there appears to be nothing left after the substance burns?
- Identify where the carbon in a fossil fuel goes when it burns.
- What do you think? How does the burning of fossil fuels contribute to the greenhouse effect and global warming? | <urn:uuid:564d760a-9e15-4134-a573-54a252197450> | {
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Arithmetic Problems To Prepare For IBPS PO Exam
Dear Reader,
Below are four problems on numbers dealing with the arithmetic calculations.
Question 1
Which of the following expression is equal to 13786?
a) 8459 + 4617 + 2714 - (713x9)
b) 8594 + 4167 + 2417 - (731x8)
c) 8495 + 4716 + 2714 - (713x3)
d) 8549 + 4761 + 2147 - (713x8)
Answer : c) 8495 + 4716 + 2714 - (713x3).
Solution:
From option a,
Given, 8459 + 4617 + 2714 - (713x9) = 15790 - 6417 = 9373 which is not equal to 13786.
From option b,
Given, 8594 + 4167 + 2417 - (731x8) = 15178 - 5848 = 9330 which is not equal to 13786.
From option c,
Given, 8495 + 4716 + 2714 - (713x3) = 15925 - 2139 = 13786 which is equal to the given value.
Hence the answer is option c.
Question 2
Which of the following is equal to 3002?
a) -48 x 39 + 5016
b) -41 x 29 + 5084
c) -40 x 19 + 5853
d) none of these.
Answer : d )none of these.
Solution:
From option a,
Given, -48 x 39 + 5016 = -48(40-1) + 5016 = -1920 + 48 + 5016 = 3144 which is not equal to 3002.
from option b,
Given, -41 x 29 + 5084 = -41(30-1) + 5084 = -1230 + 41 + 5084 = 3895 which is not equal to 3002.
From option c,
Given, -40 x 19 + 5853 = -40(20-1) + 5853 = -800 + 40 + 5853 = 5093 which is not equal to 3002.
Therefore, none of the given options is equal to 3002.
Hence the answer is option d.
Question 3
Which of the following is equal to 15318 ?
a) 21101 + 2407 - 1598 - 6939
b) 21000 + 2074 - 1895 - 6993
c) 21891 + 2157 - 1913 - 6817
d) 21731 + 2890 - 1816 - 6718
Answer : c) 21891 + 2157 - 1913 - 6817
Solution :
From option a,
Given, 21101 + 2407 - 1598 - 6939 = 23508 - 8537 = 14971 which is not equal to 15318.
From option b,
Given, 21000 + 2074 - 1895 - 6993 = 23074 - 8888 = 14186 which is not equal to 15318.
From option,
Given, 21891 + 2157 - 1913 - 6817 = 24048 - 8730 = 15318 which is equal to the given value.
Hence the answer is option c.
Question 4
Which of the following is equal to 125802 ?
a) 3007314 - 2908113
b) 3097383 - 2807016
c) 3097383 - 2816032
d) 3029613 - 2903811
Answer : d) 3029613 - 2903811
Solution :
From option a,
Given, 3007314 - 2908113 = 99201 which is not equal to 125802.
From option b,
Given, 3097383 - 2807016 = 290367 which is not equal to 125802.
From option c,
Given, 3097383 - 2816032 = 281351 which is not equal to 125802.
From option d,
Given, 3029613 - 2903811 = 125802 which is equal to the given value.
Hence the answer is option d.
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### Question 3. Solve the following simultaneous equation. x + 7y = 10; 3x – 2y = 7
Question 3.
Solve the following simultaneous equation.
x + 7y = 10; 3x – 2y = 7
Multiply Eq. I by 2 and Eq. II by 7
x=3
Substituting x= 3 in Eq. I
7y=7
y=1
∴ Solution is (x , y) = (3, 1)
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Practice Set 1.1
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(WEAU)--Physics students at Cameron High School are taking the classroom out of the learning equation today--trading their paper and pencils for what's called... Punkin' Chuckin.
We define physics at the beginning of the year and it’s the study of how things work," said Brent Whittenberger.
There is no better way to learn how something works than to try it yourself
Whittenberger says math and science can be intimidating on paper, but this brings physics to life.
"The kids get excited over this. Instead of using some boring story problem this is real and it makes the problem more complex because they have to find the angles and use the math they already know,” said Whittenberger.
Using a 5 pound pumpkin and the catapult behind me the students will calculate how far the pumpkin travels and how fast
"We're collecting data and then use this data to extrapolate the velocity," said Alexander Birkholz
"We could do a virtual thing but then it’s a perfect situation. Here there are all kinds of factors like obviously it’s raining and the cameras aren’t picking up the pumpkins as well as we’d like but we are working through it and the kids are collaborating,” said Whittenberger.
And while it’s not every day you shoot a pumpkin out of a cannon, Whittenberger says problem solving is a skill students use daily.
“You understand it so much better if you take a pumpkin and smash it collect the data and they put in the equation than if you are just given the numbers,’ said Theresa Papantonatos. | <urn:uuid:a0052aff-1e1f-4f5d-9023-5bc63d3cb5b8> | {
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