Use Hooke's Law to determine the variable force in the spring problem. A force of 250 newtons stretches a spring 30 centimeters. How much work is done in stretching the spring from 20 cm to 50 cm?

As per Hooke's Law, the force needed to stretch/compress a spring x units from its natural length is
F = kx
where F is the force in Newtons (N), x is the displacement of the object from its equilibrium position (x=0) in meters and k is the spring constant.
To determine the variable force using the Hooke's Law, the spring constant should be solved. To do so, plug-in F = 250N and x = 0.30m.
250 = k * 0.30
250/0.30=k
2500/3=k
Plugging this to the formula of Hooke's Law, the force needed to stretch the spring x units from its natural length is
F = 2500/3x
Now that the expression that represents the variable force is known, let's determine the amount of work done in stretching the spring from 20 cm to 50cm.
Take note that if the force applied is constant in moving an object from x=a to x=b, the formula is
W =F * Delta x
However, if the force is not constant, the amount of work done in moving an object from x=a to x=b is
W = int_a^b Fdx
Applying this formula, the integral needed to compute the work done in stretching from x=20 cm to 50 cm is:
W = int_0.2^0.5 2500/3x dx       (Take note that the x should be in meters.)
 
W = 2500/3 int_0.2^0.5 xdx
To take the integral of this, apply the formula int x^n dx = x^(n+1)/(n+1) .
W = 2500/3 *x^2/2  |_0.2^0.5
W = (1250x^2)/3 |_0.2^0.5
W = (1250*0.5^2)/3 - (1250*0.2^2)/3
W=87.5
Therefore, the amount of work done in stretching the spring from 20cm to 50 cm is 87.5 Joules.

Solve the integral int 8/(16-x^) dx

Solve int 8/(16-x^2)dx
Factor the denominator and pull the 8 outside the integral.
=8int 1/((4-x)(x+4))dx
Preform partial fraction decomposition on 1/((4-x)(x+4)) .
1/((4-x)(x+4))=A/(4-x)+B/(x+4)
1=A(x+4)+B(x-4)
1=Ax+4A+Bx-4B
1=(A+B)x+4(A-B)
Sine the left hand coefficients must be equal to the right hand side coefficients, (A+B) must be equal to zero to make x vanish and 4(A-B) must equal 1 .
A+B=0
A=-B
1=4(A-B)
1/4=A-B
1/4=2A
1/8=A, -1/8=B
Then the integral becomes:
=8int (1/8)[1/(4-x) -1/(x+4)]dx
=int 1/(4-x)dx-int 1/(x+4)dx
Use u-substitution on the first integral.
4-x=u , and du=-dx
on the 2nd integral.
x+4=v , dv=dx
=-int 1/(u)du-int 1/(v)dv
=-ln|u|-ln|v|+C
=-ln|4-x|-ln|x+4|+C
=-ln((4-x)/(x+4))+C
=ln(((4-x)/(x+4))^-1)+C
Then finally,
int 8/(16-x^2)dx=ln((x+4)/(4-x))+C
https://www.purplemath.com/modules/partfrac.htm

Where do Della and Jim live in "The Gift of the Magi"?

While the setting of O. Henry’s short story “The Gift of the Magi” isn’t explicitly stated, clues and the tone of the story lead us to believe the story takes place in New York City.
The story begins the day before Christmas, in the apartment of Jim and Della Young. Della laments that, despite having worked to save money for months, she only has $1.87 saved to purchase a gift for her husband. She soon realizes the only thing she has left to sell is her hair—the hair Jim loves so much. She looks at herself and worries about what her husband will say about her short hair. She alludes to a New York landmark: Coney Island, a well-known amusement park area in Brooklyn. She says to herself, “before he takes a second look at me, he’ll say I look like a Coney Island chorus girl.” The Coney Island chorus girls were women who danced in the chorus line as a part of the shows at Coney Island.
The description of their second-floor apartment also leads us to imagine the couple’s New York home. O. Henry delicately describes the couple's home as having “not exactly beggar description, but it certainly had that word on the lookout for the mendicancy squad.” The eight-dollar-a-week flat fits the couple’s tight financial times.

Mr. and Mrs. James Dillingham Young live in a flat in New York City. There are two allusions to identifiable places in New York: Coney Island and Broadway. It was not unusual for O. Henry to use New York City as a setting because he lived there for years himself.  In fact, several stories of O. Henry's are set in New York; among these stories are "The Last Leaf," "A Madison Square Arabian Night," "After Twenty Years," "The Cop and the Anthem," and "The Tale of the Tainted Tanner." 
"The Gift of the Magi" is characteristic of the humorous and sentimental stories written by O. Henry. It is a Christmas story of a loving, but poor young married couple who live in a New York flat. Unfortunately, Jim has a lower salary than he had when they first moved into this apartment and there is no extra cash for gifts and such. Nevertheless, each is determined to buy a present worthy of the other. Della decides to sell her luxurious hair to a wig shop so that she can purchase a platinum fob chain for Jim's heirloom watch. After she looks at her shortened hair, Della thinks Jim will say that she looks "like a Coney Island chorus girl." Jim sells his treasured watch so that he can buy beautiful hair combs that Della has "worshiped for long in a Broadway window." These combs are of pure tortoise shell with jeweled rims that are the perfect shade to match Della's hair. So, while neither can use the Christmas present, they both receive the most significant gifts, those of unselfish love.

In "The Gift of the Magi," Della and Jim live in a larger city described as being colorless ("grey") in a very humble apartment that lacks furnishings—rough or otherwise. Within the city itself are other grey elements in their lives: a grey fence and cat both figure into the narrative, reinforcing the drabness of Della and Jim's belongings. The doorbell and the mailbox are both broken, perhaps as symbols of how financially broke Della and Jim are. Their home is austere at best. The description of their home drives home how impoverished they are.
Although William Sydney Porter (pen name O. Henry), the author, does not name the city in the text of the story, readers can speculate the setting is New York City because there is a reference made to Coney Island, which already was a popular New York attraction when Porter wrote the story. Additionally, Porter lived in New York at the time he wrote the story and published it in a New York newspaper, so most biographers are comfortable labeling the setting as New York City. 
The term flat could throw readers off somewhat; it seems to be a little more "British" than apartment, but nothing else in the story gives it a British flair. Furthermore, Porter seemed determined to portray the lives of everyday Americans that reflected those he had known along the way growing up in North Carolina, working in Texas and New Orleans, spending a brief time in jail in Ohio, and finally settling in New York City.
https://www.biography.com/writer/william-sydney-porter

What were Bakhtin's main concerns regarding language? How does he treat language?

Bakhtin viewed language as an ever-changing interaction. Language is not some rigid structure wherein the rules and meanings are set in stone. Rather, language is a fluid product of individuals interacting with one another. Bakhtin devoted a lot of thought to Dostoyevsky and the novel. In Dostoyevsky, he found what he called "polyphony" or "many voices." Although each character in a Dostoyevsky novel is singular, all characters are informed by all other characters. This is a very simplistic way of saying everyone affects everyone else. Bakhtin goes into much more depth in this manner. He focuses on dialogue and the novel in particular as a literary genre because the novel contains characters, different dialogues, contexts, description, and socio-historical elements.
Bakhtin uses the term "carnival" to describe the idea of voices and people interacting. This conveys the idea of many different voices, maybe even something chaotic. But this helps to describe the diversity of interacting voices and how they (voices), in the context of a society, create meaning.
Another Bakhtinian term to be familiar with is "heteroglossia." Similar to polyphony, this term means differences in a language. We see this in a country as diverse as America, but this exists in any social group and even in a single individual.
Bakhtin's view of language is that it is the product of social, cultural, and historical factors. Meaning comes from the many ways these things factor in but also from the many ways in which we speak (heteroglossia). Consider the ways a single person speaks and makes meaning in a typical day. One speaks a certain way to her mother, to her husband, to her boss, or to some other kind of authority figure. So, there are different ways of speaking in the individual, different voices in a social group, different factors shaping culture, and Bakhtin felt that the novel showcased these interactions better than any other literary genre.

Precalculus, Chapter 5, 5.2, Section 5.2, Problem 32

Verify the identity. cos(x)-[cos(x)/(1-tan(x))]=(sinxcosx)/(sinx-cosx)
[cos(x)(1-tan(x))-cos(x)]/[1-tan(x)]=[sin(x)cos(x)]/[sin(x)-cos(x)]
[cos(x)-tan(x)cos(x)-cos(x)]/(1-tan(x))=[sin(x)cos(x)]/[sin(x)-cos(x)]
[-tan(x)cos(x)]/[1-tan(x)]=[sin(x)cos(x)]/[sin(x)-cos(x)]
Rewrite the tan(x) terms as the quotient sin(x)/cos(x).
-[[sin(x)/cos(x)]cos(x)]/[1-(sin(x)/cos(x))]=(sin(x)cos(x))/(sin(x)-cos(x))
-sin(x)/[(cos(x)-sin(x))/cos(x)]=(sin(x)cos(x))/(sin(x)-cos(x))
-[sin(x)/1]*[cos(x)/(cos(x)-sin(x))]=(sin(x)cos(x))/(sin(x)-cos(x))
(sin(x)cos(x))/-(cos(x)-sin(x))=(sin(x)cos(x))/[sin(x)-cos(x)]
(sin(x)cos(x))/[-cos(x)+sin(x)]=(sin(x)cos(x))/(sin(x)-cos(x))
(sin(x)cos(x))/(sin(x)-cos(x))=(sin(x)cos(x))/(sin(x)-cos(x))

What laws have we recently tried to pass that infringe on the second of FDR’s "Four Freedoms"?

The "Four Freedoms" speech is the term commonly used for President Franklin D. Roosevelt’s fourth State of the Union Address, or Annual Message to Congress, which he delivered in January 1941. Roosevelt, the only president ever elected to a fourth term, spoke for US support for its allies in World War II, which the nation had not yet entered. The first two freedoms about which he spoke, speech and religion, are also the first two mentioned in the First Amendment to the US Constitution (religion is actually mentioned first).
In the United States, laws can be passed at both the state and federal level. Proposed legislation that is considered by a legislature is known as a “bill”; after passage, it can become “law.” Further approval by the executive branch may be required.
For the decade from 2007 to 2017, research published by the Pew Research Center shows American attitudes toward some religious components suggested by federal laws, as well as restrictions on religious freedom in state laws.
The Affordable Care Act (also known as the ACA, the Patient Protection and Affordable Care Act, or Obamacare) is a federal law which guarantees health insurance to Americans. Some people believe that the ACA restricts religious freedom because it requires businesses to provide health benefits that include family planning and abortion, which some people oppose on religious grounds.
In the 2010s, several states passed laws restricting the use of religious law in court decisions. These include Arizona, Kansas, Louisiana, Oklahoma, South Dakota, and Tennessee, which enacted laws specifically mentioning sharia law. In many other states, bills were introduced but not passed.
https://www.fdrlibrary.org/four-freedoms

https://www.pewforum.org/2013/04/08/state-legislation-restricting-use-of-foreign-or-religious-law/

https://www.pewforum.org/2016/09/28/where-the-public-stands-on-religious-liberty-vs-nondiscrimination/

The second of Franklin Delano Roosevelt's Four Freedoms is the freedom of worship.  This freedom is, of course, codified in the First Amendment to the United States Constitution, in which establishing a state religion is forbidden and the state may not impede people's rights to freely exercise their respective religions.  The only law that comes to mind is one that has been under discussion during this presidential campaign, which could be said to have been referenced in the comments of one candidate who seeks to keep all Muslims out of the United States. There is a Supreme Court decision that you might be thinking of, that some people will argue interferes with the freedom of religion, but I disagree with their position on this. You will have to decide for yourself what you think. 
If we place a religious restriction on immigration, we are clearly interfering with Roosevelt's second freedom.  If we are going to be a nation that allows immigrants at all, the government cannot pick and choose which religions to allow in. People who are here lawfully have constitutional rights, too.  And it is a slippery slope once we prohibit people of one particular religion from emigrating here. From there, it would be quite easy to make Muslim worship completely illegal, along with Hinduism, Judaism, and whatever other minority religion we choose to eliminate.  We might say this can't happen today, but it happened in the Spanish Inquisition, it is happening now with ISIS, and it has happened in plenty of other times and places, too.  Once we choose one religion to stigmatize, it is easy to keep going down that path.
In Obergefell v. Hodges, (2015) the Supreme Court held that gay people have the right to marry one another, with the same protections and privileges afforded by law to heterosexual couples. The argument is that anyone who believes, as a matter of religion, that the LGBT community is an "abomination unto God" is being denied the right to practice his or her religion by signing a gay marriage license or by doing the photography or flowers for a gay wedding. The decision is also disingenuously held to stand for the proposition that clergy must perform gay marriage ceremonies.
There are a few separate threads to these arguments that must be untangled. First, signing a marriage license is an act of a public official who has no freedom whatsoever to exercise religious judgement on the job. Second, if an establishment is open to the public, if we allow it to discriminate on the basis of sexual preference, there is nothing to stop it from discriminating on the basis of race.  Both are immutable characteristics.  This is another slippery slope that is antithetical to American values.  Most of us have done business with people we do not approve of in one way or another from time to time. This does not mean that we sanction them in any way whatsoever.  A public entity needs to be open to the public, not just to those whom we approve of.  This in no way detracts from someone's exercise of religion. Third, any law that would force any member of the clergy to perform any wedding at all would be a violation of the First Amendment.  Religious institutions have the absolute freedom to delineate whom they will admit, whom they will marry, and whom they will serve. No minster, priest, rabbi, or imam can be forced to officiate in any marriage ceremony in the United States.
I am not sure if the Supreme Court decision is the "law" being contemplated in your question or if perhaps the proposals of one presidential candidate are what you have in mind. Certainly, the response of Congress has been largely negative regarding this suggestion.  While there may be those who believe that the court decision interferes with their second freedom, the fact is that a converse decision would have interfered with the religious rights of many gay people, who would have had to forego the sanctity of marriage. If someone believes there is something religiously wrong with being gay, that person can be assured that no decision or statute will ever force that person to engage in any gay behavior.  
https://www.law.cornell.edu/supremecourt/text/14-556

College Algebra, Chapter 7, 7.4, Section 7.4, Problem 28

Find the determinant of the matrix $\displaystyle A = \left| \begin{array}{cccc}
-2 & 3 & -1 & 7 \\
4 & 6 & -2 & 3 \\
7 & 7 & 0 & 5 \\
3 & -12 & 4 & 0
\end{array} \right|$, using row/column operations.

If we add 3 times column 3 to column 2, we get

$\displaystyle \left| \begin{array}{cccc}
-2 & 0 & -1 & 7 \\
4 & 0 & -2 & 3 \\
7 & 7 & 0 & 5 \\
3 & 0 & 4 & 0
\end{array} \right|$

So,

$\displaystyle \det (A) = -7 \left| \begin{array}{ccc}
-2 & -1 & 7 \\
4 & -2 & 3 \\
3 & 4 & 0
\end{array} \right|$

Now, adding $\displaystyle \frac{-4}{3}$ times column 1 to column 2, we get


$
\begin{equation}
\begin{aligned}

\det (A) =& -7 \left| \begin{array}{ccc}
-2 & \displaystyle \frac{5}{3} & 7 \\
4 & \displaystyle \frac{-22}{3} & 3 \\
3 & 0 & 0
\end{array} \right|
\qquad \text{Expand this by column 1}
\\
\\
=& -7 (3) \left| \begin{array}{cc}
\displaystyle \frac{5}{3} & 7 \\
\displaystyle \frac{-22}{3} & 3
\end{array} \right|
\\
\\
=& -7 (3) \left[ \frac{5}{3} \cdot 3 + \frac{22}{3} \cdot 7 \right]
\\
\\
=& -1183


\end{aligned}
\end{equation}
$

Why did Pope Pius XI want Reconstruction of the Social Order?

In the text Quadragesimo Anno: Reconstruction of the Social Order, Pope Pius XI examined the potential effects of laissez-faire capitalism as well as totalitarian socialism on human freedom, and argued for a solidarity-based social order. This text was written in 1931, and the social context of the late 1920s influenced this examination of different economic systems. Stalin's first Five-Year Plan was established in 1928, and the USSR's transition to a totalitarian socialist economy created massive social upheaval, nationwide famine, and millions of deaths due to starvation, forced labor, and the Great Purge. Within the context of this transition, as well as the Great Depression in the U.S. and the rise of fascism under Mussolini in Italy, examining the shortfalls of different socio-economic systems was a very relevant question. Pius XI wrote the text to promote an economic system away from the extremes of unfettered capitalism or totalitarian communist states, instead arguing for societies based in solidarity with freedom and equal opportunity for all people.

In the novel The Outsiders how is Johnny in the beginning of the book?

S.E. Hinton's classic The Outsiders is told from the point of view of Ponyboy Curtis. Johnny Cade is his best friend. They are both Greasers. 
Chapter 1 contains a hint as to what happened to Johnny; he was jumped by a bunch of Socs. Ponyboy is bleeding because he was cut by a Soc carrying a blade. Darry and Sodapop, his brothers, come to his rescue. Ponyboy compares his experience to an earlier one that Johnny had: 

You just don't cry in front of Darry. Not unless you're hurt like Johnny had been that day we found him in a vacant lot. Compared to Johnny, I wasn't hurt at all.

Johnny is described as being the gang's pet. He's one of the smallest people in the gang. He's nervous and suspicious not just because of the beating that was alluded to, but also because of his home life.

His father was always beating him up, and his mother ignored him, except when she was hacked off at something, and then you could hear her yelling at him clear down at our house. I think he hated that worse than getting whipped. He would have run away a million times if we hadn't been there. If it hadn't been for the gang, Johnny would never have known what love and affection are.

Johnny is also sensitive and doesn't conduct himself the same way that other members of the gang do. He likes to watch the stars with Ponyboy. Cherry and her friend don't judge him harshly like they do Dally, they can see that he is different, and not a threat to them.

I'm a high school student, and English is my second language. I'm really struggling with understanding the Island: The Complete Stories by Alistair MacLeod. Could you please help me with summarizing stories such as: 1. "The Boat" 2. "The Return" 3. "Island" 4. "The Vastness of the Dark" ... Thanks.

The narrator, the "I" of the story, frames his narrative with his present-day life in which he awakens with the old feelings and the old urgency from the time when he stayed by his father's side and fished the sea from May first to the end of November, when the North Atlantic seas became brutal with man-killing waves. He establishes the reality of his present-day life by saying that, after dreams of the old days, and four a.m. walks through bitter cold to chase off memories, he rushes off to teach at "a great Midwestern university." A reminiscent tone of jolting sorrow in a life once lived is established by this narrative frame, which isn't enough to prepare the reader for the jolting ending.
In a broad allusion to Dickens' David Copperfield, an allusion later brought into clear relief, the narrator starts his life's story with a recollection of his early consciousness of "the boat" and of his father's "gigantic rubber boots," boots seen from the vantage point of the floor when an infant. Later, from the vantage point of his father's shoulders, he became conscious of the "galumphing along the gravel beach" of his father's rubber boots, accompanied by his father's song.
The boat to which he was introduced and his father shared the same "odour of the salt." The boat was part of everyday conversation: mended clothes were "'torn in the boat'," prepared food was "'to be eaten in the boat'," his mother always looked out the kitchen window for sight of "'the boat'." "Well, how did things go in the boat today?" A "Cape Island boat," it was "named Jenny Lynn." The people who knew to call it a Cape Island boat had ancestors from Ireland, from Scotland's Highlands and from the Tories fleeing the thirteen colonies after the American Revolution left them unfavorably disenfranchised from England.
The most important room in the house, for the fact of its belonging to the most important person in the house and of its being the most disordered room in the house, was his father's room. The repository of old cigarettes and volumes of magazines and books to read (both being the enemy of the narrator's mother), no one went into the father's room unless given permission. And when someone by some misguided fancy thought of cleaning it, or at least of getting rid of the cigarette litter, they soon were captured by the words of the volumes' pages--volumes like David Copperfield--until the mother forcibly put an end to it (in the end, her intervention doing no good). It was also home to the "woollen sweaters, mitts and socks which [the] mother knitted for him." The narrator's mother "despised the room and all it stood for and ... despised disorder ... [and] had not read a book since high school."
The father disapprove of the "daughters of the house" playing by the wharf, but this was a point of contention because the mother, a woman of the sea, said, "'Nothing will happen to them there" or "They could be doing worse things in worse places.'" After disobediently reading books in the father's room, the daughters "grew restless" and soon began to work "as waitresses at the Sea Food Restaurant ... [that] catered to the tourists" from Boston, the wealthy tourists from Boston. Despising "the whole operation," the mother protested that that lot were not "our people."
In another point of conflict between father and mother because of the vacationer crowd, she expected they'd get "knocked up," and he was irate that she'd suggest it. The narrator, unseen on the porch, wondered if his father "would kill [his] mother while [he] stood there ... [with] three foolish mackerel in [his] hand." The daughters would talk to the father in his room late on "hot summer nights," their voices "blending with the music from his radio into a mysterious vapour-like sound floating softly up the stairs" to where the mother waited with exasperating questions.
The mother's daughters married Boston vacationers. The mother didn't understand. The men did no physical work. She couldn't see where their earnings came from: their earnings didn't come from "the boat." She "had each of her daughters for fifteen years, then lost them for two [years] and finally forever. None married a fisherman." In the end, she stopped caring because the men were "not of her people ... not of her sea." The mother and father age noticeably, and there are "only three" in the house, now empty but for them. When the narrator was fifteen, his father took to his bed with illness.
May first opens the fishing season and, with the father in bed beginning in January, they are far behind on their preparations, like knitting "lobster trap headings" from sharp twine, even with the mother's fisherman brother helping (he with twelve children). In a state of worry and uncertainty because the boat would not be ready "with her gear and two men," the narrator said "good-bye" to his schooling and to David Copperfield and The Tempest. Yet, his father sat up in his sick-bed to ask--not tell--him to go back to school the day after he quit school. A great conflict emerged from this because the mother, following her son out to porch the next morning, in her hatred of all but the sea said:

"I never thought a son of mine would choose useless books over the parents that gave him life."

Miraculously, the boat and the gear and the men were ready and the Jenny Lynn painted "by the last two weeks of April .... On the first day of May the boats raced out as they had always done. [...] And at night my mother asked, 'Well, how did things go in the boat today?'" The narrator's father had never wanted to be a fisherman; he had wanted to go to university. The narrator dismissed his father's saying this as something absurd, like wanting to do tightrope walking. The narrator learns to believe that it "was very much braver to spend a life doing what you really do not want rather than selfishly following forever your own dreams and inclinations."
He resolves to forever protect his father against the "iron-tipped harpoons which [his] mother would forever hurl into his soul because he was a failure as a husband and a father who had retained none of his own [for the sea]." As his father's room piles high with books and more books and pictures of "small red-headed grandchildren and baseball bats"--grandchildren who, to the mother's wistful sorrow, would "never know the sea in hate or in love"--he promises to stay with his father "as long as he lived" and to "fish the sea together."
Fishing through the autumn and into early winter, the boy now at the tiller, "in the place and manner of [his] uncle," the father withstood the snow, salt and ice freezing his eyelids shut and stood in the stern. But on November twenty-first, on what seemed to be the last run of the winter, the narrator looked toward the stern and his father was not there, and he "knew even in that instant that he never would be again." Even if the fierce Atlantic winter storm waves would allow for turning around for a search, even if the "burden" so lost over the stern would stay in the spot it fell rather than go a mile or more away, his father, in "the final irony ... cannot swim a stroke." After this, no one from near or far can fish those waters. Buoys are mysteriously cut if they try. Gear is mysteriously destroyed if any try. To his mother and others, "the [fishing] grounds are sacred and they think" the fishing grounds wait for the narrator to return to them to fish them.
The mother is alone with no husband, no son, no son-in-law who walks from the house to the boats nor from the boats to the house. She "looks on the sea with love and on [the narrator] with bitterness." The father was found on November twenty-eighth "ten miles to the north. ... There was not much left of [his] father, physically, as he lay there with the brass chains on his wrists and the seaweed in his hair." In a jolting realization, we understand, as did the narrator back on November twenty-eighth, brass chains hold "such a burden" down, deep down, and it seemed as before that the "bracelets of brass chain which he wore to protect his wrists from chafing seemed abnormally large...."
Interview with Alistair MacLeod, William Baer, Michigan Quarterly Review
https://www.lrb.co.uk/the-paper/v23/n18/elizabeth-lowry/little-red-boy

https://www.theguardian.com/books/2001/jul/07/fiction.reviews

Drawing from his article titled "The Case for Reparations," why does Ta-Nehisi Coates think that reparations are important?

In his June 2014 article in The Atlantic titled "The Case for Reparations," African American journalist and writer Ta-Nehisi Coates traces the history of one particular African American family, with special attention to Clyde Ross, born and raised in formally segregated and thoroughly racist Mississippi. Ross's birth in 1923 coincided with the passage and implementation of what were known as "Jim Crow" laws, formal statutes passed by state legislators across the American South, that institutionalized racist policies like the mandatory use of separate restrooms and water fountains. As Coates notes in his article, however, the inferior and often violent treatment of African Americans extended beyond the Jim Crow laws that governed a huge chunk of the country. Those laws and policies extended to the federal government, which systematically discriminated against African Americans in its implementation of social welfare policies ostensibly intended to serve all American citizens irrespective of ethnicity, race, or religion. Discussing New Deal programs to aid Americans during the depths of the Great Depression, Coates describes one such effort as follows:

"In 1934, Congress created the Federal Housing Administration. The FHA insured private mortgages, causing a drop in interest rates and a decline in the size of the down payment required to buy a house. But an insured mortgage was not a possibility for Clyde Ross. The FHA had adopted a system of maps that rated neighborhoods according to their perceived stability. On the maps, green areas, rated 'A,' indicated 'in demand' neighborhoods that, as one appraiser put it, lacked 'a single foreigner or Negro.' These neighborhoods were considered excellent prospects for insurance. Neighborhoods where black people lived were rated 'D' and were usually considered ineligible for FHA backing. They were colored in red. Neither the percentage of black people living there nor their social class mattered. Black people were viewed as a contagion. Redlining went beyond FHA-backed loans and spread to the entire mortgage industry, which was already rife with racism, excluding black people from most legitimate means of obtaining a mortgage."

As Coates continues to trace Clyde Ross's history, he also continues to emphasize the formidable and sometimes impossible obstacles confronting not only Ross but millions of other African Americans as well. From slavery to the brutality of the Ku Klux Klan to the Jim Crow laws of the South to the prejudicial practices of governments at all levels (e.g., federal, state, and local), to the treatment of blacks in supposedly egalitarian institutions like the Armed Forces, African Americans have endured horrific levels of racial prejudice throughout American history. Financial services industries systematically discriminated against African Americans, as did most other industries. The net effect of that prejudice was the creation of an underclass denied opportunities available to others and overrepresented in the nation's criminal justice system.
This, then, is the context in which Coates and others argue for reparations. Coates believes that reparations are important because of the substantial benefit that would accrue from financial remunerations. Among the subjects Coates discusses at length in his article is the history of efforts by African Americans and others on their behalf for some form of reparations—efforts that trace to the nation's founding, all without success. Coates believes such compensation is fully warranted by virtue of the history of racial discrimination and terrorism to which African Americans have been subjected. More than merely being denied opportunities, the author emphasizes, they were blatantly robbed of what was rightfully theirs. Land owned by African Americans was stolen, and fines and fees were inappropriately levied on them. African Americans, Coates argues, should receive compensation for what was taken from them without compensation in the first place, as well as for the legacy of being denied wages and other benefits on par with those provided to others.

Explain this quote: “he was an intruder in the land of fine deeds.”

The quote that this question is asking about appears a little more than halfway through the story. Fred Collins finally gets permission from an officer to go get the water, and Fred begins to move away from the other men. Readers are told that as Fred begins to make his way toward the water, he is very much aware of the fact that he is not feeling any of the fear that he believes that he should be feeling. He then makes a connection that actually makes him feel somewhat uncomfortable. Fred realizes that he always thought that men that don't feel fear in dangerous situations must be heroes. Fred realizes that he must then be a hero too.

He wondered why he did not feel some keen agony of fear cutting his sense like a knife. He wondered at this, because human expression had said loudly for centuries that men should feel afraid of certain things, and that all men who did not feel this fear were phenomena—heroes.
He was, then, a hero.

Fred is actually disappointed in this realization. He is mentally aware enough to understand that a hero is meant to be revered by other people. They are supposed to be a perfected member of society that we look to in order to feel better about ourselves. Fred doesn't believe that he fits the hero mold because he has done shameful things. Fred feels in some way that he is tainting what it means to be a hero. He is intruding into a group in which he doesn't belong because he is supposedly not as worthy as "true heroes."

He saw that, in this matter of the well, the canteens, the shells, he was an intruder in the land of fine deeds.

The statement implies that Fred Collins is not used to being brave or heroic. This is a whole new experience for him. As he risks his life to go fetch some water, he starts turning over in his mind whether or not he really is a hero. He certainly doesn't feel like one. After all, he once borrowed $15 from a friend, promised to pay him back the next day, and avoided him for ten months. There's nothing very heroic about that. And when he was growing up on the farm, he was often lazy and disrespectful to his late mother. This is not the kind of material from which heroes are usually made. But what this episode shows us is that war can often make heroes out of people who've previously done nothing with their lives. Crane is suggesting here that heroes are made, not born.

int sin(sqrt(theta)) / sqrt(theta) d theta Find or evaluate the integral

int (sin sqrt theta)/sqrt theta d theta
To solve, apply u-substitution method.

u=sqrt theta
u= theta ^(1/2)
du = 1/2 theta^(-1/2) d theta
du = 1/(2theta^(1/2))d theta
du =1/(2 sqrt theta) d theta
2du =1/sqrt theta d theta

Expressing the integral in terms of u, it becomes:
= int sin (sqrt theta) * 1/sqrt theta d theta
= int sin (u) * 2du
= 2 int sin (u) du
Then, apply the integral formula int sin (x) dx = -cos(x) + C .
= 2*(-cos (u)) + C
= -2cos(u) + C
And, substitute back  u = sqrt theta .
= -2cos( sqrt theta) + C
 
Therefore, int (sin sqrt theta)/sqrt theta d theta= -2cos( sqrt theta) + C .

What is the main argument about class in chapter 3?

Chapter three of A People's History of the United States addresses the inequalities that lay at the heart of seventeenth-century American society. These class inequalities, as Zinn shows, emerged with violent force in Bacon's Rebellion of 1676. The title of the chapter, "Persons of Mean and Vile Condition," refers specifically to the indentured servants who embraced the rebellion in Virginia. The incident was especially frightening to elites because it raised the specter of interracial cooperation between poor whites (indentured servants and former indentured servants) and African Americans. In most colonies, these elites sought to govern these unruly people through a number of strategies, the most important being cultivating the support of what was then called "the middling sort." These artisans, merchants, independent farmers, and others were courted by elites who could "make concessions. . . without damage to their own wealth or power, at the expense of slaves, Indians, and poor whites" (58). "Middling" whites were enlisted in the media, granted the right to vote, and mobilized in support of the British, all in an effort to maintain elite control. This chapter is very typical of the overarching narrative of A People's History, which emphasizes class struggle throughout its entirety.

What is the significance/theme of the repeated phrase Je ne parle pas francais in the story "Je Ne Parle Pas Francais" by Katherine Mansfield?

The title of Mansfield's story, Je ne parle pas français, is expressive of the lack of communication and social meaning in the main characters.
There is little, if anything, which reflects a culture more than a language. So, the "stale phrase" of Je ne parle pas français—I do not speak French—is thematic of Mansfield's stream-of-consciousness story narrated by the male prostitute, Raoul Duquette.
This phrase, so commonly repeated by those who do not belong to the French culture, reflects the theme of sexual ambiguity—not belonging in a single sexual category—since Raoul will go with men or women, as does Dick Harmon. Also, the woman called "Mouse" that Dick brings to Paris has some masculine traits, such as her "boyish" hands. Her act of holding out her hand "in that strange boyish way Englishwomen do" also conveys a certain sexual ambiguity. 
A story set in the years after World War I, a time in which France lost its moral center just as did other countries, "Je ne parle pas français" has a narrator and main character, Raoul Duquette, who hedonistically focuses solely upon the satisfaction of his own desires. He presents himself as a writer, but in reality he merely uses this pretense to frequent a cafe where he can prostitute himself to women or men, although he never propositions them. The title phrase, Je ne parle pas français, then, is also expressive of Duquette's amorality and nihilism, the belief that life is without real meaning, purpose, or intrinsic value. He simply enjoys what pleasures he can while acting under the pretense of having a literary profession. In essence, then, he does not really speak French, a historically precise language of philosophy, love, human truths, and war.
Another theme of Mansfield's story is that of the masque. Certainly, Duquette wears a social mask as he is not truly a writer, as he pretends. As an example of his pretense and self-deceit, at one point in the story, he narrates that he stands before his mirror, practicing his pose as a "man of letters." After all, he decides, if a person looks the part, he must be that part. Clearly, then, Raoul does not speak the language of reality; he merely pretends to do so.
Dick Harmon also pretends to be other than what he is. He masques as a heterosexual man, but has relations with Raoul, and is involved in some sort of odd relationship with his mother. He abandons the woman who believes he will marry her, writing her a letter that explains that he is controlled by his mother, whom he writes to Mouse is "dragging me back to her—calling."

Who are Hamlet's closest friends?

Hamlet's closest friend, certainly, is Horatio. Horatio has come all the way from Wittenberg for Hamlet's father's funeral, unasked, which shows both his loyalty and respect. When Hamlet mockingly suggests that Horatio actually came for his mother's wedding, Horatio responds honestly, that "it followed hard upon" his father's funeral (1.2.177). He doesn't sugarcoat a response or fawn over the prince; he is straightforward and honest, without being unkind to Hamlet's mother. Horatio also delivers the news to Hamlet that the ghost of old King Hamlet has been seen, more than once, on the castle ramparts. He seems to be Hamlet's equal in intelligence and wit, and he is certainly faithful to the prince throughout the entire play. He is the only person to whom Hamlet divulges his plans for Claudius, and Horatio keeps Hamlet's secrets. After it is clear that Hamlet will die of the wounds he sustains in the duel with Laertes, Horatio is even prepared to drink the poison left in the cup in order to accompany him in death, saying, "Here's yet some liquor left" and raising it to his lips (5.2.343). Hamlet intercepts this, and Horatio vows to tell the true story of all that happened in the Danish court.
Horatio contrasts with Rosencrantz and Guildenstern, two other students from Wittenberg, who only come to Elsinore at the king and queen's behest. They try to lie to Hamlet when he asks why they've come—they've agreed to report on his behavior back to Claudius. Hamlet is painfully aware of this. Although they do not realize they are helping a murderer, they certainly do not seem very loyal to Hamlet, especially contrasted with Horatio.

What is your favorite color?

Red.

There are instinctual connotations that surround this colour. We are taught when we are young that red relates to danger for it is the colour of blood and fire, yet I am drawn to it. Fire engines streak through the city in red like a beacon of destruction, yet it is mildly comforting to know we have individuals putting their lives on the line to save others deep within that red vehicle. We see red everywhere for Christmas and Valentine's Day - symbolising love. How contrasting are these images? Danger and love.
This is is why red has been my favourite colour for many years. It can be whatever you want it to be. It can help you feel the rage of heartbreak or the warmth of love. But then again, it's just a colour. Right?

Interesting question.
I usually say that my favorite color is blue, but of course it really depends on what the color is part of. I like blue shirts but not blue walls. It's weird, but that's humanity for you.
According to Livescience.com, blue is the most common favorite color of both men and women. While blue has a big lead over runner-up green among guys, ladies like purple almost as much as blue. It might be a little surprising to find out that pink is only the fifth favorite color choice for women.
Some people particularly like certain combinations of colors. I happen to like the combination of orange and blue, probably because those are my college colors (University of Florida). I also like red with a little yellow, like the St. Louis Cardinal baseball team wears on their jerseys. 

What led the United States to build its military forces after winning a successful war? Were the Soviets afraid of Americans as much as Americans were afraid of them? Would the recommendations contained in these documents be appropriate responses to national security threats since the end of the Cold War (for example, al-Qaeda)?

First, one should note that the United States did not single-handedly succeed in winning a war. Instead, World War II was won by the Allied forces who were aligned against the Axis powers. A crucial factor in the victory was the participation of the Soviet Union after Hitler's unsuccessful invasion. The opening of an Eastern Front weakened Hitler and was a major factor in his eventual downfall.
Although the United States emerged from the war in a powerful position, it still was involved in a Cold War with the Soviet Union and not entirely secure in its victory. The development of the nuclear bomb and long range missiles meant that the Atlantic Ocean no longer protected the United States to the east and Pearl Harbor demonstrated insecurity to the west. The launch of Sputnik, shortly after the end of World War II, heightened this insecurity.
From the point of view of the Soviet Union and many other countries, the United States was and has remained the only country ever to have used nuclear weapons against a civilian population. Moreover, despite a temporary alliance, the United States was firmly committed to overthrowing communism in the Soviet Union which was legitimately concerned that the United States and NATO had hostile intentions towards it.
Security documents that plan responses to major power wars really are not relevant to dealing with terrorism, which is a different sort of strategic threat.

After World War II, the U.S. was convinced that it had to build up its military forces to combat the growing threat from the Soviet Union. Even during the end of World War II, the Soviets had stopped their attack on Warsaw, Poland, which was then controlled by Nazis, to defeat anti-Communist forces in Poland. The U.S. had detonated two atomic bombs in Hiroshima and Nagasaki, Japan, in August of 1945 in an attempt, some historians believe, to frighten Soviets at the beginning of the Cold War. Therefore, the origins of the Cold War lie within the end of World War II. According to historian David Trowbridge, author of U.S. History, Volume 2, "both nations came to view the other as aggressive and committed to global domination by the early 1950s." Therefore, there is research that suggests that the Soviets were just as afraid of American aggression, in part resulting from the detonation of the atomic bombs, as Americans were afraid of Soviets. 
I'm not sure which documents you are referring to in the question, but the American Cold War policy was guided by documents such as NSC-68, written in 1950 by the National Security Council. This document stated that the Soviets wanted “to impose its absolute authority over the rest of the world.” NSC-68 established an aggressive approach to fighting communism. These types of approaches would likely not be successful in fighting current or recent threats, such as al-Queda, because terrorist groups are not a conventional enemy. It is therefore difficult to know how to oppose their expansion. 

Who are the main characters in The Wednesday Wars?

The main character is Holling Hoodhood. He is a 7th grader at his school, and he happens to be the only Presbyterian at a school filled with either Catholic or Jewish students. He has a sister, but readers do not discover her name until very late in the novel. Her name is Heather, and she and Holling antagonize each other like a stereotypical brother and sister. She is older than Holling and tests the boundaries with her parents repeatedly. She is more or less a developing hippie. Holling's parents are present in the novel, but not in any major way. Mrs. Hoodhood is a flat character that doesn't express her own wishes or desires. She goes along with whatever Mr. Hoodhood demands. Mr. Hoodhood is an architect and incredibly ambitious in that career. That ambition comes at a cost. He is not a great father figure to Holling or Heather. Although Mrs. Baker, Holling's English teacher, doesn't get along with Holling in the beginning of the novel, she winds up being a sort of surrogate parent to Holling. She does have a husband, but he is overseas fighting in the Vietnam War. Holling is not a super popular kid at school, but he does have three very close friends. They are Danny, Meryl Lee, and Doug. Doug's older brother is another major character in the book, and he is the school's bully.

The protagonist of the book is Holling Hoodhood, a seventh grader at Camillo Junior High in Long Island during the 1960s. He thinks his teacher, Mrs. Baker, hates him, and he has to spend Wednesday afternoons with her because he does not go to Hebrew school or Catechism like the other students. Mrs. Baker is a strict teacher whose husband is sent to fight in Vietnam, but she turns out to be a very caring person. The other main characters are Holling's sister, Heather, who is an idealistic hippie, and his tuned-out parents, Mr. Hoodhood (an architect) and Mrs. Hoodhood. Holling's nemesis is Doug Sweiteck, a fellow student who is troublesome and has an older brother. Holling also spends time with Meryl Lee Kowalski, who has been in love with Holling for a number of years.

Why was Rikki-tikki-tavi's fight with Karait important?

Rikki-tikki is a mongoose, an animal similar to a weasel with a reputation for being a particularly effective enemy of snakes. Rikki-tikki is washed out of his home by a flood, and arrives half-drowned in the garden of a British family, who essentially adopt him (although Rikki-tikki, arguably, adopts them as well), particularly their young son, Teddy. Teddy's mother is nervous about allowing Rikki-tikki, a wild animal, into such close confidence with their child, but Teddy's father insists that having a mongoose around the house is better than having a dog.
Rikki's primary enemies are Nag and Nagaina, a pair of cobras. Karait is a smaller, but equally deadly snake, and Rikki's fight with Karait allows Rikki to be established as a successful snake-hunter, and therefore a hero, without encountering the main antagonists. From a literary perspective this amplifies the tensions and sets up their rivalry for a greater final conflict. From the perspective of the plot, Rikki's fight with Karait allows him to demonstrate his protective nature, and assure Teddy's mother that he is a benefit rather than a threat.

Calculus of a Single Variable, Chapter 8, 8.5, Section 8.5, Problem 27

intsin(x)/(cos(x)+cos^2(x))dx
Apply integral substitution: u=cos(x)
=>du=-sin(x)dx
=int1/(u+u^2)(-1)du
Take the constant out,
=-1int1/(u+u^2)du
Now to compute the partial fraction expansion of a proper rational function, we have to factor out the denominator,
=-1int1/(u(u+1))du
Now let's create the partial fraction expansion,
1/(u(u+1))=A/u+B/(u+1)
Multiply the above equation by the denominator,
=>1=A(u+1)+B(u)
1=Au+A+Bu
1=(A+B)u+A
Equating the coefficients of the like terms,
A+B=0 ------------------(1)
A=1
Plug in the value of A in equation 1,
1+B=0
=>B=-1
Plug in the values of A and B in the partial fraction expansion,
1/(u(u+1))=1/u+(-1)/(u+1)
=1/u-1/(u+1)
int1/(u(u+1))du=int(1/u-1/(u+1))du
Apply the sum rule,
=int1/udu-int1/(u+1)du
Now use the common integral:int1/xdx=ln|x|
=ln|u|-ln|u+1|
Substitute back u=cos(x)
=ln|cos(x)|-ln|cos(x)+1|
intsin(x)/(cos(x)+cos^2(x))dx=-1{ln|cos|x|-ln|cos(x)+1|}
Simplify and add a constant C to the solution,
=ln|cos(x)+1|-ln|cos(x)|+C

Did Patrick Henry also say, "This is not a constitution that will safeguard our liberties?"

Though I cannot validate this quote, I can guarantee that Henry shared the sentiment. 
Patrick Henry, a revolutionary best-known for his "Give me liberty, or give me death" speech, delivered at the Virginia Convention in 1775, was vehemently opposed to a strong centralized government. In other words, he was an anti-Federalist. His speech in Richmond encouraged the formation of militias to protect Virginians from British aggression.
In 1787, the lawyer and politician was invited to participate in a convention to revise the Articles of Confederation, otherwise known as a Constitutional Convention.
Henry feared that the document would set up "the Founding Fathers" as masters of a new government -- a prospect that he strongly opposed. When the Constitution was ratified the following year, he remained a fierce critic.
In 1789, Congress sent a list of twelve amendments to the states to be ratified. These twelve amendments were the first draft of The Bill of Rights. Still a tough customer, Henry refused them, arguing that these amendments did not sufficiently safeguard our liberties. He called for a new convention -- a request that went unheeded. The state of Virginia approved the amendments without his support. Ten of the proposed amendments were ratified by all of the states and ended up in the Constitution as The Bill of Rights. 
https://billofrightsinstitute.org/educate/educator-resources/founders/patrick-henry/

https://www.history.com/news/patrick-henrys-liberty-or-death-speech-240-years-ago

Why did Edmund Burke believe the French Revolution was doomed to fail?

Edmund Burke believed the French Revolution was doomed to failure because the French would not know how to properly use the liberty they had suddenly achieved for themselves. Unlike other thinkers of the time (notably Thomas Paine), Burke did not believe conceptualizing unfettered liberty as a natural right was a good thing, and he was a critic of what we might call the Radical Enlightenment.
Burke's understanding of liberty is best summarized by a passage from a letter he wrote to a Frenchman named Depont in 1789:

Permit me then to continue our conversation, and to tell you what the freedom is that I love, and that to which I think all men entitled. This is the more necessary, because, of all the loose terms in the world, liberty is the most indefinite. It is not solitary, unconnected, individual, selfish liberty, as if every man was to regulate the whole of his conduct by his own will. The liberty I mean is social freedom. It is that state of things in which liberty is secured by the equality of restraint. A constitution of things in which the liberty of no one man, and no body of men, and no number of men, can find means to trespass on the liberty of any person, or any description of persons, in the society. This kind of liberty is, indeed, but another name for justice; ascertained by wise laws, and secured by well-constructed institutions.

Burke believed the ability to use liberty properly was something that had to be learned. In Reflections on the Revolution in France, he argues that liberty is an "entailed inheritance" and famously describes a social contract "between those who are living, those who are dead, and those who are to be born." Throughout the text, he argues that the British have spent generations--going all the way back to the Magna Carta (1215)--protecting and generally improving their conception of liberty.
On the other hand, the French, who had long been under the rule of an absolute monarch, did not have a tradition of liberty to pass down. Burke believed that, without knowledge of how to be free, sudden liberation could be dangerous. (In making this argument, Burke is drawing upon Locke's famous distinction between "liberty" and "license" from the Two Treatises on Government.) He believed France would be susceptible to all the vices of populism. In one of the closing passages of the Reflections, he writes:

But when the leaders choose to make themselves bidders at an auction of popularity, their talents, in the construction of the state, will be of no service. They will become flatterers instead of legislators, the instruments, not the guides, of the people. If any of them should happen to propose a scheme of liberty, soberly limited and defined with proper qualifications, he will be immediately outbid by his competitors who will produce something more splendidly popular. Suspicions will be raised of his fidelity to his cause. Moderation will be stigmatized as the virtue of cowards, and compromise as the prudence of traitors, until, in hopes of preserving the credit which may enable him to temper and moderate, on some occasions, the popular leader is obliged to become active in propagating doctrines and establishing powers that will afterwards defeat any sober purpose at which he ultimately might have aimed.

Burke has been seen by his supporters as a bit of a prophet. The Reflections were written in 1790, and the Terror, a violent period of purges, occurred from 1793–4. He also wrote of the dangers of a military general taking power:

In the weakness of one kind of authority, and in the fluctuation of all, the officers of an army will remain for some time mutinous and full of faction until some popular general, who understands the art of conciliating the soldiery, and who possesses the true spirit of command, shall draw the eyes of all men upon himself. Armies will obey him on his personal account. There is no other way of securing military obedience in this state of things. But the moment in which that event shall happen, the person who really commands the army is your master — the master (that is little) of your king, the master of your Assembly, the master of your whole republic.

Napoléon Bonaparte took power in France two years after Burke's death.
https://oll.libertyfund.org/quotes/473

How does Scout handle the situation with Cecil Jacobs differently from the situation with Walter Cunningham?

One day at school, Cecil Jacobs taunts Scout by yelling that her father defends n*****s. His use of this notorious racial epithet is sadly all-too-common in Maycomb, even among the children. Scout does not quite understand the full import of Cecil's hurtful words, but she knows it cannot be good. That night, she talks to Atticus about what happened, and he tells Scout that he is defending Tom Robinson in court. He advises Scout to practice tolerance, despite how unpleasant such playground taunts are. The next day Scout tells Cecil to take back what he said. He does not, so Scout readies herself to let fly with her fists. But at the last moment, she recalls what Atticus said to her, and she walks away.
Scout displays considerably more maturity in relation to Cecil Jacobs than to Walter Cunningham Jr. On the first day of school, Scout intercedes with the hapless, inexperienced teacher Miss Caroline so that she does not lend him money for his lunch, as the Cunninghams do not accept charity from anyone. All she gets for her trouble is a spank with a ruler. Scout cannot very well fight back against her teacher, so she takes out her frustration on poor old Walter by rubbing his nose in the dirt.

What effect did the Venezuela crisis have on Anglo-American (Britain and U.S.) relations in the short term and long term?

The crisis of 1895 came about as the result of a seemingly minor territorial dispute between Great Britain and Venezuela. Initially, the United States under President Cleveland was unwilling to intervene, despite repeated requests to do so from the Venezuelan government. Domestic opinion in the United States was also hostile to British actions as they were thought to be in clear contravention of the Monroe Doctrine, which famously opposed any colonialist expansion in the Americas.
Under pressure from Congress, Cleveland signed into law an act recommending that a settlement be reached by means of arbitration. The British, however, wouldn't budge and Anglo-American relations suffered a short-term lull. Cleveland, for his part, was caught between those in his cabinet and in Congress who thought he was insufficiently robust in defending the Monroe Doctrine and those who believed that, if anything, he'd been too belligerent.
Cleveland's public posture became increasingly bellicose, but in truth neither his administration nor the British government ever seriously entertained the prospect of war. His public stance was largely for domestic political consumption, and his actions spoke otherwise. By setting up a commission to look into the dispute Cleveland expertly took the heat out of an increasingly tense diplomatic situation.
Both the short and long-term consequences of the crisis were largely beneficial to Anglo-American relations. In the short-term the British received a fairly generous settlement as a result of the arbitration process. (Although the Venezuelans felt humiliated by the outcome.) In the long-term a tacit understanding developed between the United States and Great Britain about their respective spheres of interest. The Venezuelan crisis essentially put the Monroe Doctrine into effect by way of an increasingly active foreign policy. At the same time, this allowed Great Britain to concentrate on running its already enormous empire. By keeping the two great English-speaking nations apart, the resolution of the 1895 Venezuelan crisis ironically brought them closer together diplomatically.
https://history.state.gov/milestones/1866-1898/venezuela

Why is "The Souls" a good name for these students?

In the novel, "The Souls" refers to Nadia, Julian, Noah, and Ethan. "The Souls" is presumably a good name for the students because it highlights the transformative journey each of them has taken.
You can find the answer to your question in Chapters 8 and 11. In Chapter 8, Mr. Singh confronts Mrs. Olinski. He makes a mysterious proclamation: he knows she almost chose Hamilton Knapp to be the fourth member of the Epiphany Academic Bowl team. Then, he proceeds to surprise her even further by saying that Hamilton Knapp would have been a "disastrous" choice. 
Mrs. Olinski becomes defensive, mostly because she feels unsettled by Mr. Singh's uncanny revelation. However, Mr. Singh makes another mysterious proclamation:

"Think of the atom, Mrs Olinski. There are energies within that tiny realm that are invisible but produce visible results . . ."

According to Hinduism, each soul goes through a cycle of life, death, and rebirth before it obtains moksha, or liberation from the earthly existence and all its accompanying challenges. Every soul that is reborn into a new body often keeps its previous experiences and acquired wisdom intact.
In Chapter 11, Mr. Singh tells Mrs. Olinski that the children have all gone on important journeys. Each has made a significant discovery on their journeys: that there is kindness in others and that this same kindness can be found in them as well.
So, The Souls is a good name for the students because it perfectly reinforces the journeys they have taken and the important life lessons they have learned along the way. The students' journeys mimic the soul's journey through the cycles of life, death, and rebirth.

How does Ray Bradbury develop the mood in "All Summer in a Day"?

Ray Bradbury creates a leitmotif that expresses repeatedly the idea of rain with recurring phrases; this repetition generates the major atmospheric effect, or mood, of his story. It is an oppressive mood of grey anxiety and cynicism. Here is an example of the use of leitmotif:

It had been raining for seven years; thousands upon thousands of days compounded and filled from one end to the other with rain, with the drum and gush of water, with the sweet crystal fall of showers and the concussion of storms so heavy they were tidal waves come over the islands.

The monotony of this ever-present rain that has killed forests and flowers and any vegetation is rather overpowering. The effect of the grey atmosphere and unceasing rain is reflected in the children's behavior, as well. They bully the one girl who has come from Ohio and seen the sun and remembered it. To the other children, she has committed "the biggest crime of all." So, in their envy and cynical doubt of Margot's truth about the sun, the children lock her in a closet, causing Margot great anxiety. Only they get to enjoy the sun's powerful rays and joyous light and warmth. 
In her imprisonment, Margot suffers her worst oppression and anxiety as she is denied the vision of a sunny sky, a vision for which she has long been anxious; she has always remembered and yearned for it. She is also prohibited from the added satisfaction of erasing the cynicism that looms over her from other children who are skeptical of her description of the sun. Certainly, too, the behavior of these other children underscores the narrator's tone of cynicism with regard to human nature.

Bradbury uses lyrical language to convey a mood of longing and loss in this story of a Venus where the sun only emerges once every seven years. This mood is reinforced by the personality of the main character, Margot, a sensitive, melancholy little girl whose soul's sadness seems reflected in the ever present rain. The sun in this story becomes the metaphor for all our longings and desires. 
Bradbury doesn't just say it rained all the time, but describes the rain: "the sweet crystal fall of showers and the concussion of storms so heavy ... A thousand forests had been crushed." Likewise, Bradbury lingers over descriptions of the sun. It is like "gold" or a "lemon crayon," "flaming bronze" and a "warm iron." 
Bradbury repeatedly uses similes and poetic language to describe this sun and this world. Rather than hurtle us forward from event to event in this story, Bradbury encourages us, through his description, to stop and to experience being drenched in what it is like to be on this imaginary Venus. Only two things happen in terms of plot: the sun comes out and Margot, who longs so deeply to see it, is locked away in a closet by the other children. The rest is the longing mood Bradbury evokes. 

Calculus: Early Transcendentals, Chapter 6, 6.2, Section 6.2, Problem 15

You need to evaluate the volume of the solid obtained by the rotation of the region bounded by the curves y = x^3 , y = 0, x = 1 , about x = 2, using washer method, such that:
V = int_a^b (f^2(x) - g^2(x))dx, f(x)>g(x)
You need to find one endpoint, hence you need to solve the following equation:
x^3 = 0=> x = 0
You may evaluate the volume
V = pi*int_0^1 (2 - root(3) y)^2dy
V = pi*int_0^1 (4 - 4 root(3) y + root(3) (y^2))dy
V = pi*(int_0^1 4dy - 4*int_0^1 y^(1/3)dy + int_0^1 y^(2/3) dy)
V = pi*(4y - 4*(3/4)*y^(4/3) + (3/5) y^(5/3))|_0^1
V = pi*(4y - 3*y^(4/3) + (3/5) y^(5/3))|_0^1
V = pi*(4 - 3 + (3/5) )
V = pi*(1 + 3/5)
V = (8pi)/5
Hence, evaluating the volume of the solid obtained by the rotation of the region bounded by the curves y = x^3 , y = 0, x = 1 , about x = 2, yields V = (8pi)/5 .

Why are the Olympics important?

The modern Olympics represent one of the few times when people from all over the world not only compete peacefully together, but watch or listen together as a global audience. The competing athletes and their teams form bonds that often last a lifetime, and the audiences seeing them have a chance to learn about other cultures, as many profiles are aired about the host city or area during the Games.
There are often opportunities provided by the Games that extend beyond sports. For example, the just-concluded Winter Olympics had South and North Korean athletes competing as one team, and there is at least a possibility that the door may have cracked open for additional talks; this coming at a time when tensions have been extremely high.
Again using the 2018 Winter Games as an example, the open acknowledgement by a number of athletes (notably Americans Adam Rippon and Gus Kenworthy) of their LGBTQ sexual identities and the media attention this received makes it easier for other athletes worldwide to do the same, and by extension, other non-celebrities as well.
http://westchester.news12.com/story/37586234/openly-gay-athletes-make-history-at-2018-olympics

In order to understand the significance of the Olympics, it is vital that we first examine some of the history of the Olympics.  According to the official website of the Olympics, the first ancient Olympic games occurred in the year 776 BC, and though the modern Olympics began much later, generally, events that have that type of longevity are culturally significant traditions with timelines that predate most modern nations.  For instance, consider that the Olympic games are currently approximately 2,792 years old, while our nation, the United States, is just 240 years old. The Olympics are an event with a lot of history behind them.
Now let us consider the number of nations that generally compete in the Olympics.  The countries competing may have disputes militarily, economically, or socially, yet these countries are competing against one another on the same stage.  As time progressed, so did the number of countries participating in the Olympics.  For instance, the 1920 Olympics saw just 24 countries compete.  The 2012 Olympics, on the other hand, had 204 countries represented by over 10,000 athletes in 300 events.
Imagine the amount of pride winning a specific Olympic event brings to one's country, considering that most nations on our planet are represented.  This honor proves that one's country is distinguished in a certain event or activity, and it is for these reasons that the Olympics are important in our global culture and society.   
https://engineeringsport.co.uk/2012/06/26/why-are-the-olympics-important/

https://www.olympic.org/ancient-olympic-games/history

What clues to the identity of Charles can you find in the opening paragraph of the story?

The opening paragraph of Shirley Jackson's short story "Charles" foreshadows the truth that is revealed in the end: Charles does not exist outside of Laurie's imagination. Laurie created Charles to deflect from his own outrageous behavior, and even take credit for it. His parents continue under the delusion that Laurie is a well-behaved child even despite the instances of bad behavior he displays throughout the story, beginning with the opening paragraph: 

The day my son Laurie started kindergarten he renounced corduroy overalls with bibs and began wearing blue jeans with a belt; I watched him go off the first morning with the older girl next door, seeing clearly that an era of my life was ended, my sweet-voiced nursery-school tot replaced by a long trousered, swaggering character who forgot to stop at the corner and wave good-bye to me.

Jackson's choice of the word "renounced" to describe Laurie's attitude toward overalls suggests there was a battle of some degree over wardrobe between parent and child. Many parents accompany their children on the first day of kindergarten, but the narrator is denied this privilege, watching him walk away with a next door neighbor. It would be reasonable to infer that this was not necessarily the narrator's choice. Since she is lamenting the loss of her sweet-voiced nursery school tot, it suggests she is not ready to award the independence Laurie has taken—that it wasn't her idea. 
The narrator also describes Laurie as a swaggering character, which suggests the confidence and arrogance of teenage rebellion more than kindergarten excitement. 
The narrator also states that Laurie forgot to stop and wave good-bye, which suggests he has been instructed to do so. If he had been instructed to do so, this is a failure to comply with his mother's reasonable request, which foreshadows the rebellion and insolent behavior to come. 
 

While Charles's true identity is only revealed at the end of the story, Shirley Jackson gives us some clues in the opening paragraph when she describes the changes Laurie is undergoing. On the day Laurie starts kindergarten, he no longer likes wearing the same clothes: he swaps his "overalls with bibs" for "blue jeans" and a belt. Similarly, Laurie's demeanor also changes significantly: he is no longer a "nursery-school tot" but instead is described by his mother as a "swaggering character" who does not wave to her from the street corner anymore.
These clues are important because they foreshadow the birth of Laurie's alter ego, Charles, and his many bouts of bad behavior. They are subtle enough, however, to go almost unnoticed by the reader, and this makes the story's surprise ending (in which Charles's true identity is revealed) even more effective.

What are two pieces of evidence that back up Atticus's quote that "Simply because we were licked a hundred years before we started is no reason for us not to try to win" in chapter 9?

Atticus discusses the reasons why he is defending Tom Robinson to Scout in chapter 9 of Lee's To Kill a Mockingbird. Scout asks him why he continues to fight for the case when he knows he will lose and everyone thinks he shouldn't take it in the first place. Atticus responds by saying, "Simply because we were licked a hundred years before we started is no reason for us not to try to win" (76).
When Scout hears this coming from her father, it reminds her of Cousin Ike Finch saying something similar:

The Missouri Compromise was what licked us, but if I had to go through it agin I'd walk every step of the way there an' every step back jist like I did before an' furthermore we'd whip 'em this time (76).

Not only does Cousin Ike mention the word "licked," which means getting beaten down or losing a battle, but the principle behind what he says is the same as what Atticus implies. Both men are saying that just because the odds are stacked against a person doesn't mean the battle isn't worth fighting. Atticus believes in this principle so much that he is willing to risk people hating him because of it.
One other person who fights a battle, even though she may lose, is Mrs. Dubose. Atticus thinks she is the bravest person he knows because she wins the fight against her addiction to morphine before she dies in chapter 11. Atticus explains to his children what it means to fight important battles even though a person knows he or she might lose in the following passage:

I wanted you to see what real courage is, instead of getting the idea that courage is a man with a gun in his hand. It's when you know you're licked before you begin but you begin anyway and you see it through no matter what. You rarely win, but sometimes you do. Mrs. Dubose won, all ninety-eight pounds of her. According to her views, she died beholden to nothing and nobody. She was the bravest person I ever knew (112).

Notice again that the word "licked" is used, followed by the explanation that a brave person is one who commits to a specific goal and sticks to it no matter how hard it is to accomplish. Atticus specifically says Mrs. Dubose won her fight because she died having fought a battle for herself and she achieved her goal. The same is true for Atticus when he defends a black man in a white court. Even though the odds are stacked against him and he most likely won't win, the battle still needs to be fought.

Single Variable Calculus, Chapter 8, 8.2, Section 8.2, Problem 6

Determine the integral $\displaystyle \int \frac{\sin^3 (\sqrt{x})}{\sqrt{x}} dx$

Let $u = \sqrt{x}$, then $\displaystyle du = \frac{1}{2 \sqrt{x}} dx$, so $\displaystyle \frac{1}{\sqrt{x}} dx = 2du$. Thus,


$
\begin{equation}
\begin{aligned}

\int \frac{\sin^3 (\sqrt{x})}{\sqrt{x}} dx =& int \sin^3 (\sqrt{x}) \cdot \frac{1}{\sqrt{x}} dx
\\
\\
\int \frac{\sin^3 (\sqrt{x})}{\sqrt{x}} dx =& \int \sin^3 u \cdot 2du
\\
\\
\int \frac{\sin^3 (\sqrt{x})}{\sqrt{x}} dx =& 2 \int \sin^3 u du
\\
\\
\int \frac{\sin^3 (\sqrt{x})}{\sqrt{x}} dx =& 2 \int \sin^2 u \sin u du
\qquad \text{Apply Trigonometric Idendities } \sin^2 x = 1 - \cos^2 x
\\
\\
\int \frac{\sin^3 (\sqrt{x})}{\sqrt{x}} dx =& 2 \int (1 - \cos^2 u) \sin u du

\end{aligned}
\end{equation}
$


Let $v = \cos u$, then $dv = - \sin u du$, so $\sin u du = -dv$. Thus,


$
\begin{equation}
\begin{aligned}

2 \int (1 - \cos^2 u) \sin u du =& 2 \int (1 - v^2) \cdot -dv
\\
\\
2 \int (1 - \cos^2 u) \sin u du =& - 2 \int (1 - v^2) dv
\\
\\
2 \int (1 - \cos^2 u) \sin u du =& -2 \left( v - \frac{v^{2 + 1}}{2 + 1} \right) + c
\\
\\
2 \int (1 - \cos^2 u) \sin u du =& -2 \left( v - \frac{v^3}{3} \right) + c
\\
\\
2 \int (1 - \cos^2 u) \sin u du =& -2 \left( \cos u - \frac{\cos ^3 u}{3} \right) + c
\\
\\
2 \int (1 - \cos^2 u) \sin u du =& -2 \left[ \cos (\sqrt{x}) - \frac{\cos^3 (\sqrt{x})}{3} \right] + c
\\
\\
2 \int (1 - \cos^2 u) \sin u du =& -2 \cos (\sqrt{x}) + \frac{2 \cos^3 (\sqrt{x})}{3} + c
\\
\\
\text{or} &
\\
\\
2 \int (1 - \cos^2 u) \sin u du =& \frac{2 \cos ^3 (\sqrt{x})}{3} - 2 \cos (\sqrt{x}) + c

\end{aligned}
\end{equation}
$

What impacted World War II politically?

World War II spanned the globe and shaped political decisions in dozens of countries. For the purposes of this question, we’ll consider only domestic politics and we’ll confine the discussion to the political decisions that precipitated the United States’ entry into WWII.
The United States fought WWII in two theaters, in the Pacific against Japan and in Europe against Germany and Italy. Franklin Roosevelt was president throughout the conflict and had to grapple with political and policy decisions unique to each theater of the war.
Decisions surrounding the war against Japan
In 1937 Japan invaded China and a swath of Pacific islands, seizing territory and greatly expanding its sphere of influence. The United States was on good terms with China but FDR couldn’t risk direct action because he didn’t want to alienate a Congress that favored neutrality. FDR decided to impose trade sanctions which gave the appearance of action but didn’t anger domestic isolationists.
On September 27, 1940, Japan entered into an alliance with Nazi Germany and fascist-controlled Italy (the Tripartite pact) which allowed the three nations to cooperate to further their respective ambitions. FDR now had a freer hand to act because the American electorate had come to see Hitler as an enemy, and Japan, by association, became an enemy too. FDR took advantage of this swing in popular opinion and began sending weapons and supplies to China. Seeing FDR’s posture in the Pacific as a direct threat to its ambitions, the Japanese attacked Pearl Harbor on December 8, 1941. For FDR, Congress, and the American people, the decision to declare war was the only possible response.
Decisions surrounding the war in Europe
Since 1937, Nazi Germany and Italy had been aggressively taking territory in central Europe and North Africa but met with little resistance from France, Britain, and the United States. FDR was under no direct pressure to act until the Tripartite pact made it impossible to declare war on Japan without also declaring war on Germany and Italy. Germany’s subsequent invasion of France made it impossible for FDR to avoid the conflict given that the United States, Britain, and France were long-time allies.
Short of mobilizing American soldiers, FDR began sending military equipment and financial support to Britain. He also instituted the draft and committed enormous resources to expanding the American military. These decisions signaled that the US was fully committed to defeating Germany and Japan.
Unlike previous wars, the American public began to see newsreels showing the atrocities being committed in Asia and in Europe, and the radio brought first-hand accounts of the war into every living room. FDR made use of these technologies to sell his political decisions to the American people by speaking on the radio and by harnessing patriotic, pro-war newsreels.
https://history.state.gov/milestones/1937-1945/lend-lease

https://www.history.com/this-day-in-history/the-tripartite-pact-is-signed-by-germany-italy-and-japan

It seems that this question is asking what political situations impacted the outbreak of war. The main political development that led to World War II was the rise to power of dictatorships in Germany, Italy, and the Soviet Union, as well as a militaristic regime in Japan. Nazi Germany and Imperial Japan were especially aggressive militarily, and their attempts to expand their possessions destabilized Europe and the Pacific, respectively. The Soviet Union, too, was viewed as a major threat by many Western powers, a fact that accounts for their inaction in the face of Hitler's expansion. Another major political development was the breakdown of the League of Nations, an international organization that was supposed to be a forum for peacefully resolving conflicts. It was almost totally ineffectual in dealing with the threats posed by Hitler's Germany, Mussolini's Italy, and Japan. Finally, another key political development was the isolationist stance taken by the United States. The fact that the most powerful nation in the world was not willing to take a firmer stance in the face of aggression was a major reason that Germany in particular was able to behave as it did.
https://www.history.com/topics/world-war-ii

I need a thesis statement for "The Yellow Wallpaper" by Charlotte Gilman.

Certainly, you could argue that Charlotte Perkins Gilman opposes the sexist practices of the nineteenth-century medical community, which largely excludes women from having a say in their own treatment and determines that their medical problems are the result of their own imaginations. Obviously, the narrator's sense of her own needs is not marked by her husband and doctor, John. The boredom which is brought on by her "treatment"—likely one called the "rest cure," which advocated for the absence of all mental or intellectual stimulation so that the woman's body could restore proper blood flow away from her brain and back to her sexual organs—causes her to become obsessed with the wallpaper. With nothing else to focus on, she focuses her significant powers of intellect—evidenced by her vocabulary and evident knowledge of many areas—on the paper. The narrator claims that a little conversation and stimulation would do her good, but her opinion is unheeded, and she is threatened with having to go to a well-known doctor, Weir Mitchell, who actually pioneered this "treatment." Her husband/doctor even constantly belittles her as well as her condition, saying things like "Bless her little heart! [. . .] she shall be as sick as she pleases!", implying that the narrator is actually responsible for her own disease and that she could simply choose to no longer have it, if she wanted.
The narrator's mental degeneration throughout the story is quite clearly caused by her "treatment," established by the male profession of medicine and the fact that she's been locked up on the top floor of a strange house that she does not like by the person who's supposed to love her the most: her husband. She begins with a condition we would likely refer to as postpartum depression, and she ends with a complete mental breakdown where she no longer recognizes her own identity, even referring to herself as "Jane" in third person, after experiencing hallucinations and extreme paranoia. Clearly, Gilman points the finger at those who administer the treatment rather than the one who is treated.

I was always taught a thesis statement should be a miniature encapsulation of the essay as a whole. In that way, it should give the main concept, following by roughly three evidences that support that argument or line of thinking. So, the first objective is to select an argument from the book on which to take a stance. I would go with something like “the woman’s postpartum depression begins an ever increasing spiral into insanity.”
Next, you choose three examples or pieces from the work that act to support your argument. In this case I would say “this is evidenced by her growing suspicion of her husband, her obsession with the wallpaper, and her belief in the spirits in the house.” Combine it all together for a cohesive thesis statement: “The woman’s postpartum depression begins an ever increasing spiral into insanity, as evidenced by her growing suspicion of her husband, her obsession with the yellow wallpaper, and her belief in this spirits in the house.” This will also define your essay’s structure and composition.

A thesis statement should be both arguable and specific. To be arguable, the thesis has to state an opinion and defend it by using quotes from the story as evidence.
To determine an opinion about the story which you can defend, you first need to decide what the story means: what point is Gilman trying to make? This, of course, can be understood through the themes of the story.
It is often argued that Gilman's story is critiquing gender divisions in nineteenth-century society. One possible thesis statement could argue that it is wrong for a man (or men) to decide, on the basis of gender, that a woman should "naturally" be happy in the home and that the "cure" for her postpartum depression or "temporary nervous depression" should be the deprivation of all of her intellectual stimulation. This thesis could say something like the following: in "The Yellow Wallpaper," Gilman shows that, just like men, women need intellectual stimulation to stave off depression and that depriving them of intellectual stimulation leads to madness.
You would then need to find examples that show how terrible the woman's situation is and how her current situation is not helping her in any way.
Another theme of the story is that of freedom and autonomy. Does the narrator achieve freedom in her madness? She says she does—"I've got out at last"—but has she really? Obviously, she is still physically imprisoned, but has she liberated her soul through madness? If you argue against madness as a real liberation, your thesis would say something like the following: Gilman is critiquing a situation in which insanity is the only way a woman can achieve liberation from captivity.
You would then show that the narrator, despite what she thinks, is still in a terrible situation, as she is locked in a room that she crawls around in like an animal.
These are simply some suggestions. Whatever thesis you pick, be sure to back it up with examples and quotes from the story.

Jack London's story "the white silence" is about people trying to survive in the cold harsh winter up north. What type of conflict BEST describes this situation? A. Conflict with another person B. Conflict with a force of society C. Conflict with a force of nature D. Conflict within oneself

It seems reasonable to say that the conflict is best described as one with the forces of nature. Indeed man versus nature is a common theme throughout Jack London's work, especially in his short stories. In "The White Silence," three people are slowly making their way across the frozen wastes of the Yukon trail. The environment is harsh and unforgiving—cold, lifeless and barren. Any journey in such a pitiless landscape is going to be a struggle against the often brutal forces of nature. And so it proves.
As the party of travelers pauses for a much-needed rest, an old tree falls down and crushes Mason, the man leading the journey. Just about every bone in his body has been broken, and it's just a matter of time before he passes away. Yet the Malemute Kid cheats nature of its final victory by shooting Mason dead instead of watching him die a slow, painful death in the snow. And in the figure of Mason's unborn child, still safe and warm inside Ruth, man scores another victory over nature. Ruth and her baby will undoubtedly live on, unvanquished by the icy wasteland.
The message of the story appears to be that, however harsh nature can sometimes get, however hard humankind may struggle against it, it cannot achieve a final victory over us. We must respect nature, neither exploiting it nor being overawed by it. The conflict with nature can never truly be won by either side; all that can be hoped for is some kind of reasonable accommodation.

What does the reader learn from the stranger about his best friend Jimmy and what is his attitude towards this man in After Twenty Years?

When the policeman, who checks doorways on his beat finds a stranger standing in a store's door that used to belong to "Big Joe' Brady's restaurant, the man claims he is standing there as he waits to meet an old friend, who was a great friend, although somewhat of a "plodder."
This waiting man assures the policeman that everything is all right; he is just waiting for his old friend named Jimmy, with whom he dined twenty years ago. After this meal the friends parted, but they agreed to come back to their favorite restaurant in two decades after they had settled into their adult lives. While Jimmy was the truest of friends and they corresponded for a while, they had lost track of one another. The waiting man says that Jimmy was kind of a "plodder," but he has sought his fortune in the West, and because he was "hustling," and moving so much, he had lost track of Jimmy.

"But I know Jimmy will meet me here if he's alive, for he always was the truest, stanchest old chap in the world. He'll never forget. I came a thousand miles to stand in this door tonight, and it's worth it if my old partner turns up."

Clearly this man holds Jimmy in high regard, having traveled so far to reunite with his old friend. Even after he reads Jimmy's note, the man knows that Jimmy is still a true friend. For, he has not the heart to arrest 'Silky Bob' himself, although he knows that he must do his duty, too.

In the book Hoot, how does the main character contribute to the development of the theme?

Roy Eberhardt is the main character in Hoot. A strong theme in the book is that one should get involved and stand against injustice. Roy contributes to the development of this theme in three important ways.
As the book starts out, when Roy is on the school bus, he sees a barefoot boy running across lawns as the other children are going to school. He is intrigued by the mysterious boy and goes in search of him. When he finds the strange boy living by himself in the woods, he wants to find out more and gives him a pair of his own shoes. He keeps pursuing the mystery boy, despite threats from Beatrice Leep. He stands in sharp contrast to Beatrice's father, who is so uninvolved in his step-son's life that he doesn't even know he has run away from school. Roy is willing to get involved where others aren't. 
Roy also supports the theme of getting involved and standing against injustice when he defies Dana Matherson, the bully. Dana terrorizes new and younger kids on the bus and at school with impunity. No one stood up to him before Roy. He almost chokes Roy, but Roy fights back, breaking Dana's nose. When the school fails to discipline Dana for fear of a lawsuit, Roy takes matters into his own hands and lures Dana into committing a crime, for which Dana is arrested and sent to juvenile detention. When Dana gets locked up, Roy "felt guilty about making up the bogus cigarette story, [but he] also couldn't help but think that putting Dana behind bars was a public service." Again, Roy gets involved where others have let the matter slide, and justice is achieved in the end.
Finally, Roy's attempt to save the owls is an example of how an everyday citizen, even a minor, can get involved in community issues and stand against injustice. Mullet Fingers tries to protect the owls, and instead of brushing the boy off as crazy Roy investigates and learns the owls are protected by law. Roy then attempts to find out whether Mother Paula's has followed the law, and he even goes to city hall to try to look at the company's file. He raises the issue in his history class, which inspires many of his classmates to come out to rally against the groundbreaking. Because of his efforts, the story garners local and then national media attention, and the pancake house company's illegal actions are exposed. By getting involved and taking a stand against injustice, Roy creates positive change in his community and beyond.
Roy demonstrates that ordinary citizens, even teens, can impact society positively when they get involved and take a stand against injustice.

What lesson does the fakir want to teach?

The Sergeant-Major tells the Whites that an old fakir, or holy man, put a spell on the monkey's paw. By doing so, he wanted to show people that fate ultimately rules their lives and that it's both foolish and dangerous to defy it. Among other things, this means not wishing for something you don't already have. The story is a prime illustration of the old adage "Be careful what you wish for, you might just get it." Unfortunately, the Whites ignore the fakir's sage advice and proceed to treat the whole legend as a bit of a joke. Eventually, after the tragedy of losing his son, the most skeptical member of the family, Mr. White, finally realizes the truth of the fakir's warning, which is why he uses his third and final wish to stop the chilling knock at the door.

A uniform line charge that has a linear charge density λ equal to 3.5 nC/m is on the x axis between x = 0 and x = 5.0 m. What is its total charge? Find the electric field on the x axis at x = 6.0 m.

First, use the definition of λ to find the total charge of the line of charge. Integrate the line of change along the axis to find electric field. The line of charge is positive, and since the point p also lies directly on the x-axis, the field will point entirely in the +x direction.

what motivates the students to do what they do to Margot?

Th students, especially William, envy Margot because she is the only one of them who can remember seeing the sun. All the rest arrived on Venus when they were two. They are nine now, and the sun only comes out for about an hour once every seven years. It is about to come out again, but the last time they would have seen it, they would have been two: too young to remember.
Margot, however, only came to Venus five years ago. She remembers what the sun was like in Ohio when she was four. She tries to tell the other students about the sun, but they don't believe her.
Because she is depressed about being on Venus, she doesn't want to join in and play with the other children. She keeps herself apart. This also makes the children angry, as it seems to them as if she thinks she is better than they are. Therefore, right before the sun comes out, they lock her in a windowless closet.

How do kite flying and kite fighting develop the themes in the novel?

In The Kite Runner, the kite is both a positive and negative symbol. As such, kite flying and kite fighting simultaneously trace the themes of betrayal, generational conflict, and redemption as the story progresses.
Amir, ever cognizant of his fragile relationship with Baba, takes up kite-flying in his childhood years; it is the one activity that allows him to relate to Baba on a personal level. As a former champion kite fighter, Baba is partial to the sport; Amir sees it as the only means by which he can redeem himself in his father's eyes for his lack of prowess in other, more tactile sports.

Baba and I lived in the same house, but in different spheres of existence. Kites were the one paper thin slice of intersection between those spheres.

Preparation for each year's kite-fighting competition can be surprisingly brutal on young hands. Amir relates how "by the time the snow melted and the rains of spring swept in, every boy in Kabul bore telltale horizontal gashes on his fingers from a whole winter of fighting kites." As a warring sport, kite-fighting also symbolizes the inner conflicts in Amir's life. For example, the blue kite represents Amir's abandonment and subsequent betrayal of Hassan (it is while acting as Amir's kite runner that Hassan falls into Assef's hands and is brutally raped). Later, Amir basks in Baba's applause and admiration rather than admit his winning kite is tainted by Hassan's blood and pain.
The kite also develops the theme of Amir's redemption. By the time he flies the kite with Sohrab at the end of the book, Amir has redeemed himself. He has retrieved Sohrab (Hassan's son) from the orphanage, and, however clumsily, done his part in freeing Sohrab from Assef's cruel custody. In teaching Sohrab the principles of kite-fighting, Amir is gifting Sohrab with Hassan's legacy of selflessness and courage and redeeming himself of his past sins.

I did it perfectly. After all these years. The old lift and dive trap. I loosened my grip and tugged on the string, dipping and dodging the green kite. A series of quick sidearm jerks and our kite shot up counterclockwise, in a half-circle. . . "Do you want me to run that kite for you?" His Adam's apple rose and fell as he swallowed. The wind lifted his hair. I thought I saw him nod. "For you, a thousand times over," I heard myself say.

To what extent does ‘Sir Gawain and the Green Knight’ conform to the conventions of quest narrative?

Sir Gawain and the Green Knight conforms quite closely to the conventions of a classic quest. What are those conventions, and how does the story follow them?
First, in a conventional quest, a character (a character who will eventually be the hero of the story) hears a call to action and feels compelled to leave his current surroundings in pursuit of something. In this case, that hero is Sir Gawain. He's attending a New Year’s Eve feast at King Arthur’s court when an unexpected visitor, the Green Knight, arrives at the party. The Green Knight challenges someone in the party to join him in a game, then he mocks King Arthur. Sir Gawain takes this as his call to action. He doesn't want to participate in the game with the Green Knight, but he accepts this duty.
Second, in any quest, the hero faces trials and tribulations along his journey. Examples of Sir Gawain's challenges include his interactions with Lady Bertilak, who tries to seduce him. Gawain is terrified of offending her husband, who has offered him accommodation during the journey. But he must fend off Lady Bertilak's advances without offending her, too.
A classic quest also includes kind souls along the way who help the hero on his mission. In this case of that story, one of those figures is Bertilak de Hautdesert, the lord of a castle that Sir Gawain stumbles upon, and where he ends up staying before he encounters the Green Knight again.
A quest always includes fighting an enemy. Here, that's represented in the axe battle with the Green Knight: the "game" that the Green Knight initially proposed to the court at King Arthur's party.
Finally, a conventional quest typically ends in the hero achieving his aim, and if he doesn't, at least learning something about himself in the process. This particular story ends in an unusual way: Sir Gawain learns that the Green Knight invented the whole situation (including, confusingly, using magic to transform himself into Bertilak, Gawain's friendly host) as a way of testing Gawain's nerve. So although Sir Gawain doesn't exactly defeat his opponent, he does return to his home honorably. 
 

In Browning's "My Last Duchess," the speaker says, "E'en then would be some stooping; and I chose never to stoop." Is this irony or not?

The Duke is telling the envoy about the fraught relationship he had with his late wife, the Duchess. In the course of the discussion, the Duke reveals aspects of his wife's personality and behavior which he found particularly annoying. When his wife was alive, the Duke never saw fit to inform her of the seemingly inexhaustible ways she displeased him. Yet he has no compunction whatsoever in revealing such information to a complete stranger:

E’en then would be some stooping; and I choose Never to stoop.

In other words, no matter how disgusted the Duke was with his wife—highly disgusted, as it turns out—he never stooped so low as to discuss the matter with her. The Duke clearly thinks this would've been highly improper for someone of his noble status; it would've breached some ancient aristocratic code of behavior.
The Duke's words are indeed ironic. For though he never stooped to discuss his wife's annoying habits with her, out of a sense of propriety, he nevertheless did stoop to killing her, violating every decent moral standard there is. For a haughty nobleman such as the Duke, social etiquette appears to be so much more important than morality.

How does the description of the wallpaper change over time?

As the narrator of Charlotte Perkins Gilman's short story "The Yellow Wallpaper" descends into madness, her descriptions of the wallpaper change. The color and the appearance of the wallpaper intensifies, and eventually, the wallpaper takes on a life of its own as the narrator's grip on reality loosens completely.
At the start of the short story, the wallpaper is unappealing to the narrator. It appears to her a sickly sort of color, and the jaundiced look of the walls in her bedroom disgusts her. The pattern on the wallpaper appears frenzied and chaotic, annoying the narrator. John, the narrator's husband, ignores her discomfort and her preference to be elsewhere in the house they have rented for the summer, and his dismissal of her request to move is the first gesture of many that expedites the narrator's decline.
As the narrator's mental state breaks down, her perception of the wallpaper changes. The pattern animates and her language describing the pattern take on a violent quality. The lines and curves "strangle" against the backdrop of rotten yellow. Eventually, as the condition of the narrator worsens, the narrator describes the wallpaper as it begins to move and change shape; soon the narrator sees something moving around underneath the wallpaper. When she begins to rip apart the wallpaper, her madness emerges, in the form of an imagined woman, once trapped and now freed by the narrator. At the end of the story, the wallpaper is described as being in bits on the floor, evidence of the narrator's loss.

"The Yellow Wallpaper" details, in first-person voice, the gradual mental deterioration of a young woman, and its description of the wallpaper itself mirrors her worsening mental state. Even so, if we look across the entire span of the short story, from beginning to end, we'll find a near continuous fixation on that piece of wallpaper (though the nature of that fixation will evolve over time).
The topic of the wallpaper comes up from the very earliest journal entries as a critical theme in her account. She voices a detestation of the wallpaper, and even in that very first journal entry, she puts significant effort into describing it. She speaks about its color (which she finds odious), as well as its shape and pattern, noting that:

It is dull enough to confuse the eye in following, pronounced enough to constantly irritate, and provoke study, and when you follow the lame, uncertain curves for a little distance they suddenly commit suicide—plunge off at outrageous angles, destroy themselves in unheard-of contradictions.

From the very beginning, this wallpaper exerts a hold on her imagination, but in those early entries, it's not entirely all-consuming. She writes about her day, her complaints and frustrations, her interactions with her husband, and while the wallpaper is a critical component in those recollections, it does not dominate the entries as it will later. Eventually, there will be entire entries where the wallpaper is all that she seems to think about (the wallpaper and/or the woman associated with it). Thus, as the story proceeds, we see a growing obsession with and fixation on the wallpaper, alongside her conviction that there is a woman on the other side of it. Thus, these descriptions of the wallpaper (and the degree to which they dominate these entries) will mirror her own deteriorating mental state.

As the main character in “The Yellow Wallpaper” transforms mentally, so does her description of the wallpaper in the room. As the story is clearly about her deteriorating mental and emotional state, the symbolism of the wallpaper directly correlates to the main character’s break with reality. From the beginning, the wallpaper is seen as undesirable, hideous, and grotesquely unattractive to the woman. At every moment, she is fixated on the wallpaper, finding new and more complex elements occurring within the pattern. This analysis will follow the progression of her description of the wallpaper as it directly relates to her own psychosis.
She begins by describing the paper as dead (1). She purports having never seen a “worse paper in my life” (3) and asserts that the paper is horrid (5). But as she deteriorates, so does her interpretation of the wallpaper. She asserts that "there are things in that paper that nobody knows but me, or ever will” (9). It is here that she begins to elaborate on the patterns and designs, further revealing her psychological state. She explains that "dim shapes get clearer every day. It is always the same shape, only very numerous . . . it is like a woman stooping down and creeping about behind that pattern" (9). The narrator begins to describe in more detail the imprisoned woman that is trapped in the wallpaper. Obviously, this description parallels her own condition, as she too is locked in a room with bars on the windows. She explains how at night the pattern "becomes bars . . . and the woman behind it is as plain as can be" (12). As her condition continues to worsen, she begins to state that the wallpaper has “a yellow smell” (14). Totally disgusted by the paper, the woman begins to tear off the wallpaper with her nails and teeth. The story ends with the main character having worked to shake and pull the wallpaper from the wall to free the imprisoned woman on the other side. She gives a most chilling final description that is as disturbing as the woman’s psychological state. She decries that “the pattern just enjoys it! All those strangled heads and bulbous eyes and waddling fungus growths just shriek with derision” (17).
The final lines of the story have the main character hysterically telling her husband, “I've pulled off most of the paper, so you can't put me back!” (18). It is in this final statement that the reader comes to understand that the main character is the woman in the wallpaper and “setting her free” represents the pinnacle of her psychotic break.
Work Cited:
Gilman, Charlotte P. The Yellow Wallpaper and Other Writings. Bantam Classic, 2006.