What political idea in Russian history does Old Major represent?

Old Major symbolizes the Marxism–Leninism of the Soviet Union. He provides the intellectual foundations of the philosophy of Animalism, which he genuinely believes will liberate the animals from oppression at the hands of their human masters. Although Old Major is largely presented in a positive light, his ideas contain within themselves the seeds of the future dictatorship established at Animal Farm by Napoleon. For one thing, Old Major's political ideas are rather naive and simplistic. He seems to believe that once human power is overthrown, then all will be well. When the animals take control, there will be complete freedom for all; everyone will work together for the common good and no one will dominate or control anyone else. If nothing else, Animalism means equality.
The problem is that Old Major's ideas are, at best, unrealistic. His idealization of animals means that he's blind to the prospect that they too possess all the worst traits of humans. Contrary to what he believes, there is no true brotherhood of animals. Once the humans have gone, and the animals have taken over, all the old problems will still remain much as before. Orwell is satirizing Marxism–Leninism here, especially as it was put into practice by Stalin. What started out in theory as a perfectly admirable political philosophy, one devoted to liberating the oppressed masses, has degenerated in practice to a rigid ideology that enslaves and terrorizes the very people whose interests it's supposed to represent.

How are the themes of industrialism and self-discovery (in other words, science and religion) during the Victorian era revealed in Hard Times by Dickens?

In Dickens's novel Hard Times, the theme of industrialism is juxtaposed against the theme of self-discovery. In the latter, religion and science struggle for ascendancy.
Hard Times is an interesting novel; in it, Dickens highlights the most prominent developments of nineteenth-century England. To understand the novel, we first have to explore its historical underpinnings. Dickens's novel is an unvarnished and candid delineation of the disruptive forces at work in the lives of the English populace.
On one hand, we have the Industrial Age, which heralded the rise of materialism, consumerism, assembly-line production, and labor exploitation. Wealthy industrialists, such as Josiah Bounderby, were wholly committed to their own material welfare. Often, they enjoyed success at the expense of the working-class "hands" they employed. Horrific working conditions at fabric mills, coal mines, and factories led to the disenfranchisement of workers.
In the novel, the factory is at the core of human existence. Coketown (the setting for the story) is unequivocally a town of "red brick." It is a town of machinery, tall chimneys, and smoke. Additionally, it is also a town where nature is as "strongly bricked out as killing airs and gases were bricked in." There are "red-bricked streets" and "red-bricked villas." Even the chapels of "eighteen religious persuasions" are made of "pious" red brick.
Industrialism is emphasized by its stranglehold on every aspect of life; its deadening influence is a blight on creativity, humanity, and self-discovery. The name Coketown is significant. Coke is residual material from the dry distillation of bituminous coal. It is hard and unyielding. Similarly, industrialization robs the populace of its soul: Gradgrind's cold, hard "facts" lie in the dominance of the material at the expense of the spiritual.
Here, it is worth mentioning that many of the political and social ideals championed by Bounderby and his friend, Thomas Gradgrind, originate from prominent nineteenth-century thinkers of Dickens's time. This is revealed in the names of Gradgrind's two children, Adam Smith and Malthus. More on this later.
In the novel, many of the working class eventually join unions in order to negotiate better working conditions and pay structures for themselves. In the midst of this turmoil, science and religion battle for ascendancy in the hearts and minds of the English populace. In the nineteenth century, many saw Darwin's Origin of the Species as an affront to fundamental religious beliefs. Others maintained that science was not antithetical to religion. Still others warned that Darwin's doctrines were a blatant attempt to disrupt the conventions that previously dominated every strata of society.
Now, back to Adam Smith and Malthus. It is significant that Dickens chose to name two of Gradgrind's children after important philosophers. Many have credited Adam Smith as a chief proponent of the theory of self-interest, a central tenet of the Industrial Age. Indeed, the Wealth of Nations champions laissez-faire economics: the state wholly divorced from the market mechanism. Smith's book also advocates specialization and mechanized uniformity: think assembly-line production in which each worker performs a specific task.
Certainly, Smith's doctrine of laissez-faire economics has often been connected to Jeremy Bentham's utilitarian theory of self-interest as the driving influence for societal progress. Meanwhile, Malthus, a popular advocate of population control, championed Darwin's "survival of the fittest" theory, which can be seen in Gradgrind and Bounderby's preoccupation with the material. In the novel, only the strong survive, and the strong are invariably wealthy industrialists and elite statesmen who preside over the working class.
However, many experts have since argued that Adam Smith was not wholly utilitarian in his approach to civilization; they maintained that he was also nonutilitarian in that he rejected the selfishness inherent in materialism (the kind demonstrated by Gradgrind and Bounderby). The Adam Smith Institute describes the main points behind Smith's Theory of Moral Sentiments. In his treatise, Smith advocated compassion and sympathy as a vehicle for social harmony. Smith's ideas can be seen in the character of Sissy Jupe in the story.
Sissy is the antithesis of characters such as Gradgrind. We can clearly see the conflict between the "survival of the fittest" laissez-faire economics and the moral underpinnings of Smith's Theory of Moral Sentiments in chapter 9.

Then Mr. M’Choakumchild said he would try me again. And he said, This schoolroom is an immense town, and in it there are a million of inhabitants, and only five-and-twenty are starved to death in the streets, in the course of a year. What is your remark on that proportion? And my remark was—for I couldn’t think of a better one—that I thought it must be just as hard upon those who were starved, whether the others were a million, or a million million. And that was wrong, too.
And I find (Mr. M’Choakumchild said) that in a given time a hundred thousand persons went to sea on long voyages, and only five hundred of them were drowned or burnt to death. What is the percentage? And I said, "Miss;" here Sissy fairly sobbed as confessing with extreme contrition to her greatest error; "I said it was nothing."
"Nothing, Sissy?"
"Nothing, Miss—to the relations and friends of the people who were killed."

Sissy keeps making "mistakes" in answering questions because her compassion "gets in the way." Dickens presents the themes of industrialization and self-discovery through means such as symbolism (Coketown as a "red-brick" town) and indirect characterization (conversation between characters like Sissy and Mr. M'Choakumchild who hold divergent views).

dy/dx + 2y/x = 3x-5 Solve the first-order differential equation

Given dy/dx+2y/x=3x-5
y'+2y/x=3x-5
when the first order linear ordinary Differentian equation has the form of
y'+p(x)y=q(x)
then the general solution is ,
y(x)=((int e^(int p(x) dx) *q(x)) dx +c)/e^(int p(x) dx)
so,
y'+2y/x=3x-5--------(1)
y'+p(x)y=q(x)---------(2)
on comparing both we get,
p(x) = 2/x and q(x)=3x-5
so on solving with the above general solution we get:
y(x)=((int e^(int p(x) dx) *q(x)) dx +c)/e^(int p(x) dx)
=((int e^(int 2/x dx) *(3x-5)) dx +c)/e^(int 2/x dx)
first we shall solve
e^(int 2/x dx)=e^(2ln(x)) =x^2     
so
proceeding further, we get
y(x) =((int e^(int 2/x dx) *(3x-5)) dx +c)/e^(int 2/x dx)
=((int x^2 *(3x-5)) dx +c)/x^2
=((int (3x^3 -5x^2) ) dx +c)/x^2
= (3x^4 /4 -5x^3/3+c)/x^2
so y(x)=(3x^4 /4 -5x^3/3+c)/(x^2 )

Where did Phileas Fogg live?

Phileas Fogg is the protagonist of Jules Verne’s famous novel Around the World in Eighty Days.
Fogg begins the story living in London, England. As he is living a relatively banal existence, Fogg’s only source of relative excitement is his participation in The Reform Club, which is where he gets the idea to traverse the globe, in a wager with other club members. One could argue, however, that for the majority of the novel, London is not Fogg’s home. Instead, "home" might be the various trains and steamships Fogg travels upon across the globe in countries including Hong Kong and India.
The simple answer, then, is that Fogg permanently resides in London. The more complicated version asserts that Fogg lives in no one fixed place because of his global voyage.

Single Variable Calculus, Chapter 3, 3.6, Section 3.6, Problem 23

Find $\displaystyle \frac{dx}{dy}$ of $x^4y^2 - x^3y + 2xy^3 = 0$ by Implicity Differentiation.
$\displaystyle \frac{d}{dy} (x^4y^2) - \frac{d}{dy} (x^3y) + \frac{d}{dy} (2xy^3) =0$


$
\begin{equation}
\begin{aligned}
\left[ (x^4) \frac{d}{dy} (y^2) + (y^2) \frac{d}{dy} (x^4) \right] - \left[ (x^3) \frac{d}{dy} (y) + (y) \frac{d}{dy} (x^3) \right] +2 \left[ (x) \frac{d}{dy} (y^3) + (y^3) \frac{d}{dy} \right] &= 0\\
\\
\left[ (x^4) (2y) + (y^2)(4x^3) \frac{dx}{dy}\right] - \left[ (x^3)(1)+(y)(3x^2) \frac{dx}{dy}\right] +2 \left[ (x)(3y^2)+(y^3) \frac{dx}{dy}\right] &= 0\\
\\
2x^4y + 4x^3y^2 \frac{dx}{dy} - x^3 - 3x^2y \frac{dx}{dy} + 6xy^2 + 2y^3 \frac{dx}{dy} &= 0\\
\\
4x^3y^2 \frac{dx}{dy} - 3x^2y \frac{dx}{dy} + 2y^3 \frac{dx}{dy} &= x^3 - 2x^4y - 6xy^2\\
\\
\frac{dx}{dy} ( 4x^3 y^2 - 3x^2y + 2y^3) &= x^3 - 2x^4y -6xy^2\\
\\
\frac{\frac{dx}{dy} \cancel{( 4x^3 y^2 - 3x^2y + 2y^3)} }{\cancel{( 4x^3 y^2 - 3x^2y + 2y^3)}} &= \frac{x^3-2x^4y-6xy^2}{4x^3y^2-3x^2y+2y^3}\\
\\
\frac{dx}{dy} & = \frac{x^3-2x^4y-6xy^2}{4x^3y^2-3x^2y+2y^3}
\end{aligned}
\end{equation}
$

In Margaret Fuller's essay "Fourth of July," what does she say America still needs to achieve?

Fuller expresses the view that the United States has not lived up to the ideals upon which it was founded. With independence, she says, should come the responsibility to ensure freedom, and given that slavery was still being practiced and defended at the time of her writing in 1845, the Americans had not succeeded in creating the kind of society they had aimed at 70 years earlier.
Fuller seems to be saying that materialism, the pursuit of wealth, is what Americans value above other things. She mentions Andrew Jackson, who had died a month (June, 1845) before she wrote her article. Jackson's legacy was something that any progressive of that time, or ours, would view negatively or at least ambivalently. He was a strong leader who opposed dominance by the wealthy elites, but he was also a slaveowner and he carried out a ruthless policy against the Native Americans. In many ways Fuller's mention of Jackson is a symbol of what needs to be corrected and reformed in America.
Fuller's article prefigures the speeches of Lincoln in the sense that she, like Lincoln, wished for a "new birth of freedom." Tragically, Fuller did not live to see the abolition of slavery, as she died in a shipwreck in 1850 along with her husband and young son.

In Margaret Fuller's essay "The Fourth of July," which appeared in the New York Tribune in 1845, she writes that America has achieved much since its independence and is a land of "great talent and energy." However, she feels that the ideas that led to the American Revolution have been "tarnished," and that the country is starting to value wealth and power over virtue. America has yet to achieve freedom for all its people. She believes that the continued practice of slavery "takes from the patriot his home." She also believes that Americans' love of wealth and power detracts from their commitment to ideals. She feels that the country must be born again and that there needs to be "a new Dynasty...of Fathers of the Country." To achieve the greatness that is within America's potential, the country needs to turn against slavery and recommit itself to the values present at its founding.

There was a death in Max's early life. Who was it, when was it, and what were the circumstances surrounding their death?

In the novel The Sea, by John Banville, we follow the life of Max Morden, an old man who returns to the seaside town where he spent a summer fifty years earlier. His wife has recently died, and he is revisited by memories of an earlier death that he experienced during the summer that he was there. During that earlier time, he became acquainted with a family, the Graces, who he was infatuated and a little obsessed with. He thought that he was in love with the mother, Connie, but he also had a strange relationship with her daughter, Chloe, and became friends with Chloe's twin, Myles. Throughout their friendship, Chloe made it known that she was attracted to Max, kissing him flagrantly and taking him by surprise. Eventually, he overheard some words between Rose, the nanny, and Mrs. Grace that he thought mean that Rose and Mr. Grace were having an affair. Later, Rose and Max watched helplessly from the shore as the twins drowned in the sea. Max had told them that he believed Rose and Mr. Grace were having an affair. Being twins, Chloe and Myles did everything together; they were inseparable. So it follows that they would have been together when they died. It is a very symbolic incident for Max and one that defines his childhood, because it was a summer in which he "came of age" in more ways than one and learned that all actions have consequences.

The probability density for an electron that has passed through an experimental apparatus is shown in the figure. If 4100 electrons pass through the apparatus, what is the expected number that will land in a 0.10 mm-wide strip centered at x = 0.00 mm? y-axis units are see image below P(x)= [psi(x)]^2(mm^-1)

Hello!
First we determine the probability p of the event that one electron will land in a specified strip. Then the expected number of such electrons will be p*N, where N is the total number of electrons.
By the definition of a probability density P(x), the probability of being between a and b is equal to  int_a^b P(x) dx. Here a=-0.1 mm and b=0.1 mm. Because the given density is an even function,  p = 2 int_0^0.1 P(x) dx.
It is simple to write a formula for P(x) for x between 0 and 3, it is P(x)=1/3 - x/9 (a straight line). Therefore
p = 2 int_0^0.1 (1/3 - x/9) dx = 2 (x/3 - x^2/18)|_(x=0)^0.1 = 2*(0.1/3-0.01/18) approx 0.0656.
And the expected number is about  4100*0.0328 approx 269. This number is dimensionless.
Note that this number is the most probable, but the neighboring numbers are also very probable.

What did Andreas Vesalius contribute to modern science?

Andreas Vesalius contributed to modern science by questioning the existing view of human anatomy. This view was established by Galen, an ancient Greek doctor, who wrote many books and articles on the human body. Galen's understanding of human anatomy, however, was not based on dissections of the human body. In fact, Galen often dissected animals (whose anatomy is very different from humans') and made a number of mistakes as a result.
In contrast, Vesalius believed human dissections were crucial to understand human anatomy. As a young physician, Galen was given access to the bodies of criminals to dissect and use in his studies. In 1543, he published his most influential work, De Humani Corporis Fabrica (On the Fabric of the Human Body), in which he presented his view of human anatomy based completely on his own observations.
For more information, please see the reference link provided.

What diligent qualities does the author present in her story "Sweat"?

Delia Jones demonstrates diligence in "Sweat" through the following actions, character traits, and personal history revealed to us in the short story.
Delia works late on Sunday nights to prepare her workload for the week and save time. She conscientiously sorts clothing by color and soaks soiled items, even though her husband, Sykes, does not approve of her bringing "white folks'" laundry into their home.
We learn that Delia has been faithfully washing clothes for fifteen years, which is the entire length of her marriage to Sykes. She is the breadwinner in the household, and her physical beauty has faded over the years due to her overworked state. Sykes has rarely held a job during this time period and instead wastes their money on frivolous expenses.
Delia steadfastly remains in a physically, emotionally, psychologically abusive marriage in which her husband is publicly unfaithful. She attempts to ignore his affair with Bertha by avoiding public meeting places and local acquaintances, and she changes churches so that she will not be required to take a holy sacrament with him.
Despite a long history of abuse, Delia boldly stands up to Sykes after he brings a pet rattlesnake home to torture her. She expresses her hatred towards him and threatens to expose his actions to the "white folks" if he lays hands on her again.
After Sykes tries to kill Delia by planting the rattlesnake in her laundry basket, she flees the house and waits in the hayloft during the night, then outside of the house once he returns in the morning and is attacked by the snake. After he pleads for her help, she calmly waits beneath a tree in the yard until his inevitable death.

What literary elements can be found in "House Taken Over" by Julio Cortázar?

There are any number of literary elements to choose from in "House Taken Over," but I can outline a few of the major ones here.
Perhaps the simplest is that Cortázar uses a first-person point of view: the story is narrated by someone directly involved, an "I" who tells the story.
The entire story can be considered an allegory for Peronism, or a form of Argentine populism. The narrator and his sister are representatives of the Argentine bourgeois class: they are idle most of the day, with money coming in from land rentals; the narrator reads French novels; there are only two of them but they live in a huge house; they take up more space than they need, in a family home that they did not earn, but rather was passed down to them. And yet their wealth and their space is being taken over by something (allegorically, the populace, the working class), cutting them down to size and leaving them with nothing. The line "Irene never bothered anyone" is critical within this reading of the story: she was minding her own business. She never went out, never contributed to society or the economy—the narrator did those things, and only rarely. The narrator is painting Irene as a victim of the working class's takeover; she loses everything, which is then presumably divided up among those who could not afford it.
On a less political note, Cortázar also uses suspense and foreshadowing to keep the reader on their toes: we never see what it is that is taking over the house; we only know that once they have invaded, there can be no going back. When the narrator first hears them,

The sound came through muted and indistinct....At the same time, or a second later, I heard it at the end of the passage which led from those two rooms toward the door. I hurled myself against the door before it was too late and shut it, leaned on it with the weight of my body; luckily, the key was on our side...

In this scene and the last are the only times we get a sense of urgency on the part of the narrator; he "hurled" himself against the door "before it was too late." The pace is quick here, and the sudden eruption of the existence of this "other" in the house leaves the reader with a suspenseful, ominous sense for the rest of the story. The "other" taking over this part of the house also foreshadows the taking over of the entire house at the end of the story.
The last element I will mention is the motif of collecting or gathering in the story: motes of dust "rise and hang in the air, and settle again a minute later on the pianos and the furniture." The siblings' income from the farms was "piling up"; Irene has hidden stacks of shawls in a drawer; and when the narrator finally flees, he abandons a large stack of money in his bedroom. This could be read (but is not necessarily intended) to be an indication of the wealth amassed by the middle class and the sheer amount of things amassed in capitalist society, despite their relative idleness and lack of need.

Julio Cortázar employs Magical Realism and Gothic techniques in his short story "House Taken Over":
Magical Realism (elements are in italics)
--One aspect of the story that might be identified as "realist description" is the portrait of the house in which the narrator and his sister dwell—it has been owned by generations before them and the siblings love it because it holds memories of ancestors and "the whole of childhood."--Another aspect of Magical Realism is that time is "both history and the timeless" with the historic ancestral home and the occupancy of the siblings, who have both lost their opportunities to marry. They then seal themselves from time with their reclusive routine of cleaning the house and spending the rest of the day occupied with favorite pastimes of knitting and reading.--The reader is torn between two concepts of reality. Apparently, there is a supernatural force that enters the house, but the brother, who narrates, describes the take-over of the house as though it were not unusual:

I'll always have a clear memory of it because it happened so simply and without fuss....The sound came through muted and indistinct....At the same time or a second later, I heard it at the end of the passage which led to those two rooms toward the door....

--After hearing these noises, the brother calmly goes to the kitchen, heats the kettle, and when he returns with their daily maté, he tells his sister that he had to shut the door to the passage. "They've taken over the back part" he says, apparently assuming that his sister knows who "they" are. There are two realms of reality.--The siblings have their identities "broken down" as they surrender the house to the spirits and give up some of their favorite possessions. With an odd passivity, the brother and sister reside in their part of the house. Finally, when they hear noises in the kitchen and other areas which they usually occupy, they abandon the house without a word to each other or without even taking anything with them. Passively, the brother locks the front door tightly and throws the key into the sewer. He narrates with this same passivity:

We had what we had on. I remembered fifteen thousand pesos in the wardrobe in my bedroom. Too late now.

Gothic Techniques
--There is definitely a mysterious atmosphere to the house of the brother and sister.--There are supernatural occurrences as the house becomes occupied by some type of spirits who move about and cause the brother and sister to run from them.--The elements of gloom and horror are present as the brother and sister fearfully hide in the other part of the house where they are trapped and without the items they love. Then, after the brother hears the spirits on their side of the heavy oak door,

We stood listening to the noises, growing more and more sure that they were on our side of the oak door, if not the kitchen, then the bath, or in the hall itself at the turn, almost next to us.

So they must flee part of their house in fear of the spirits that have taken it over.
http://www3.dbu.edu/mitchell/magical.htm

https://www.virtualsalt.com/gothic.htm

Why are the pearl buyers excited about kino's pearl?

The pearl buyers are excited about Kino's pearl because of its magnificent quality and size.
The news has swept the town: "Kino has found the Pearl of the World." It is a fantastic pearl of great size and quality that generates dreams in the minds of all that hear of it. "Every man suddenly became related to Kino's pearl" as he dreams of what he could do with such a pearl. Envy also fills the hearts of people so that Kino now becomes "curiously every man's enemy." (III)
Unfortunately, Kino and his wife Juanita are unaware of the poison of envy in so many that their pearl has created. When the neighbors come to see the beautiful pearl that Kino holds in his hand, some become jealous of Kino, wondering how such luck could come to any man. Kino's brother Tomas asks,"What will you do now that you have become a rich man?" (III)
When the dealers hear of this marvelous pearl, they are excited because they have also learned that a peasant has found it. Such a man knows not how these dealers work together; furthermore, he is not aware that they all work for the same man. So, they conspire together on how they will pretend that the pearl is worth little because it is too big and has imperfections. (IV)

What are the costs and benefits of "outsourcing"? Consider these in regard to both the "home country" and the country in which the products are made.

When an American company outsources some services to a foreign country, it can receive the benefits of a large, relatively inexpensive workforce; the company can pay lower wages.  The United States has a minimum wage, but many of the nations that are the beneficiaries of outsourcing do not.  The dollar travels further there and one can find employees who will work for lower rates, though it is less than what an American worker would require to survive.  Also, outsourcing allows a company to expand faster, since the money not used to employ Americans can be used to hire more foreign laborers quickly.  
There are also numerous costs to outsourcing.  In today's business climate, Americans want to keep as many jobs at home as possible.  Outsourcing and laying off domestic workers can cost a company in terms of public relations.  Also, the company must go through intermediaries overseas in order to deal with the workers, whereas by keeping the jobs in the US, the process is more streamlined--if corporate has a problem with a mid-level manager, someone from the office can go see him/her for a face-to-face meeting.  Also, foreign countries do not have the business regulations of the US.  While this can be good in keeping prices down, it is another public relations nightmare if a report leaks that the company is using child labor or that workers are being treated inhumanely by American standards.

Pick a specific court case. Give the background to the case. Explain its significance and explain how it affects us today. 1 page

There are so many key cases from which to choose. However, one of the most significant court cases, both in terms of its perpetual relevance and its impact in its time, is the Brown v. the Board of Education of Topeka, Kansas.
Prior to 1954, the 1896 decision of Plessy v. Ferguson established the principle of "separate but equal" when it came to black people's ability to access public services, including schools. This doctrine solidified Jim Crow, or legal (de jure) segregation throughout the American South.
Though there had been prior challenges in the Supreme Court regarding segregation in public facilities, particularly rail and bus lines, cases which had been successful, civil rights activists and attorneys thought that segregated schools required more urgent attention.
It is important to remember that, contrary to legal language, separate did not mean equal in practice. Public facilities for blacks were of significantly lower quality than those offered to whites. Public schools for blacks were in decidedly worse condition than those available to whites. A family in Topeka, with the help of Thurgood Marshall, who argued their case in the Warren Court, challenged the constitutionality of segregation.
Linda Brown was eight years old when the National Association for the Advancement of Colored People asked her father, Oliver Brown, to enroll his daughter at a predominately white school, Sumner Elementary School in Topeka. Brown, along with thirteen other black families, were organized by the NAACP to help challenge segregation in Kansas.
It is important to note that Kansas, though a very conservative state, was not as virulently racist as the South. The Brown family lived in a racially-mixed neighborhood and segregation was not as strictly enforced there as in the South. However, Linda was required to walk across railroad tracks and take a bus to school, despite the proximity of Sumner Elementary, due to the segregation of elementary schools in Topeka. Clearly, Marshall and others saw an opportunity in Topeka, due to the relative laxity of segregation laws in Kansas.
The Supreme Court, led by Chief Justice Earl Warren, ruled in favor of the Browns, determining that segregated elementary schools in Topeka violated the Fourteenth Amendment which ensured equal protection under the law. However, it was not until a 1955 follow-up decision for Brown v. Board that the ruling was actually enforced. The 1955 decision set a time-table and requirements for schools in segregated states to integrate. 
History shows us that the South was very resistant to these efforts. Little Rock, Arkansas, New Orleans, and Jackson, Mississippi were all sites of fierce and violent opposition to efforts toward integration.
Despite the illegality of segregation (de jure), segregation remains a practice (de facto). Because of stark income inequality, particularly when comparing black and white families, black children (and many Latino children too) often do not have access to school facilities that are equal to those for white children. States supplement federal funding for education with property taxes. If one lives in a district in which few people own property or live in barely adequate housing, the school system will reflect that.
https://www.biography.com/activist/linda-brown

What was Tom doing when Ben was whitewashing the fence?

While Ben was whitewashing the fence, Tom was relaxing, eating, and planning how to fool more kids.
In chapter 2, Tom is whitewashing the fence, and he is not enjoying it; however, Tom isn't about to let Ben know that. Ben shows up at the fence planning on teasing Tom about having to do work while he plans on having fun.

"Say—I’m going in a swimming, I am. Don’t you wish you could? But of course you’d druther work—wouldn’t you? Course you would!"

Tom, being his crafty self, responds by telling Ben that whitewashing the fence could hardly be called work. Tom then proceeds to act like he is working on a great piece of art. He paints a little, then critiques it, then adds a little touch of paint here and there.

Tom swept his brush daintily back and forth—stepped back to note the effect—added a touch here and there—criticised the effect again—Ben watching every move and getting more and more interested, more and more absorbed.

Tom claims that it's not work because it's something that he doesn't get to do all that often. All of this subtle enticement convinces Ben that he wants to paint the fence, and he begs Tom to let him have a chance. Tom refuses, but then Ben offers to pay Tom for the privilege of whitewashing the fence. Tom "reluctantly" agrees to let Ben work on the fence, and Tom sits on a nearby barrel in the shade while eating an apple and planning to trick more kids.

And while the late steamer Big Missouri worked and sweated in the sun, the retired artist sat on a barrel in the shade close by, dangled his legs, munched his apple, and planned the slaughter of more innocents.

College Algebra, Chapter 7, Review Exercises, Section Review Exercises, Problem 36

Show that the matrices $\displaystyle A = \left[ \begin{array}{ccc}
2 & -1 & 3 \\
2 & -2 & 1 \\
0 & 1 & 1
\end{array} \right]$ and $\displaystyle B = \left[ \begin{array}{ccc}
\displaystyle \frac{-3}{2} & 2 & \displaystyle \frac{5}{2} \\
-1 & 1 & 2 \\
1 & -1 & -1
\end{array} \right]$ are inverses of each other by calculating the products $AB$ and $BA$

We perform the matrix multiplications to show that $AB = I$ and $BA = I$


$
\begin{equation}
\begin{aligned}

AB =& \left[ \begin{array}{ccc}
2 & -1 & 3 \\
2 & -2 & 1 \\
0 & 1 & 1
\end{array} \right]
\left[ \begin{array}{ccc}
\displaystyle \frac{-3}{2} & 2 & \displaystyle \frac{5}{2} \\
-1 & 1 & 2 \\
1 & -1 & -1
\end{array} \right]

=

\left[ \begin{array}{ccc}
2 \cdot \left( \frac{-3}{2} \right) + (-1) \cdot (-1) + 3 \cdot 1 & 2 \cdot 2 + (-1) \cdot 1 + 3 \cdot (-1) & \displaystyle 2 \cdot \frac{5}{2} + (-1) \cdot 2 + 3 \cdot (-1) \\
\displaystyle 2 \cdot \left( \frac{-3}{2} \right) + (-2) \cdot (-1) + 1 \cdot 1 & 2 \cdot 2 + (-2) \cdot 1 + 1 \cdot (-1) & \displaystyle 2 \cdot \frac{5}{2} + (-2) \cdot 2 + 1 \cdot (-1) \\
\displaystyle 0 \cdot \left( \frac{-3}{2} \right) + 1 \cdot (-1) + 1 \cdot 1 & 0 \cdot 2 + 1 \cdot 1 + 1 \cdot (-1) & \displaystyle 0 \cdot \frac{5}{2} + 1 \cdot 2 + 1 \cdot (-1)
\end{array} \right]

=

\left[ \begin{array}{ccc}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{array} \right]
\\
\\
\\
\\
BA =& \left[ \begin{array}{ccc}
\displaystyle \frac{-3}{2} & 2 & \displaystyle \frac{5}{2} \\
-1 & 1 & 2 \\
1 & -1 & -1
\end{array} \right]
\left[ \begin{array}{ccc}
2 & -1 & 3 \\
2 & -2 & 1 \\
0 & 1 & 1
\end{array} \right] =
\left[ \begin{array}{ccc}
\displaystyle \frac{-3}{2} \cdot 2 + 2 \cdot 2 + \frac{5}{2} \cdot 0 & \displaystyle \frac{-3}{2} \cdot (-1) + 2 \cdot (-2) + \frac{5}{2} \cdot 1 & \displaystyle \frac{-3}{2} \cdot 3 + 2 \cdot 1 + \frac{5}{2} \cdot 1 \\
-1 \cdot 2 + 1 \cdot 2 + 2 \cdot 0 & -1 \cdot (-1) +1 \cdot (-2) +2 \cdot 1 & -1 \cdot 3 + 1 \cdot 1 + 2 \cdot 1 \\
1 \cdot 2 + (-1) \cdot 2 + (-1) \cdot 0 & 1 \cdot (-1) + (-1) \cdot (-2) + (-1) \cdot 1 & 1 \cdot 3 + (-1) \cdot 1 + (-1) \cdot 1
\end{array} \right]
=
\left[ \begin{array}{ccc}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{array} \right]

\end{aligned}
\end{equation}
$


The matrices $AB$ and $BA$ both arrive in the same result so the matrices $A$ and $B$ are inverses of each other.

Tort Law: In the following scenario, what framework should I go about using in identifying business/legal issues to identify, explain and provide a solution this: Example: A delivery driver is completing his daily route and is approaching an intersection which allows him the right of way on a green light. He must suddenly brake for a pedestrian who walked out in front of his truck and proceeded to walk across the street against a red light. The delivery truck driver fails to stop in time and hits the pedestrian causing serious personal injuries.

The other two answers are comprehensive with regards to the driver and the pedestrian, but I wanted to address the third party involved in a potential legal action: the driver's employer. To determine whether the employer has "vicarious liability" for the actions of the driver, we must answer two questions.
First: is the driver actually an employee for whom the company is responsible, or is he an independent contractor? Three prongs determine this distinction:
Behavior: does the employer determine the manner in which work is done, or does the worker?
Finance: is the business responsible for maintenance, gas, and other expenses, or is the driver?
Relationship: is the work essential to the business over the long term, or is it sporadic?
Second: was the driver acting in his capacity as an employee when the accident occurred?
Were the driver's actions consistent with his job description?
Was he following workplace guidelines and regulations?
If no to either of the above, could the employer have reasonably foreseen the breach of protocol?
In this case, the driver is completing his regular routine doing deliveries, which means he is probably a long-term employee and is probably acting within the scope of his job. If he is determined to be at fault for the accident, his employer will most likely hold vicarious liability.
https://legal-dictionary.thefreedictionary.com/respondeat+superior

https://www.law.cornell.edu/wex/respondeat_superior

Although it is rather simple to realize how the pedestrian was at fault, it is important to also look at the existing conditions on the driver’s side.
It is important to determine whether the driver was vigilant. The driver needs to have been alert and free from distractions. Talking on the phone is considered a distraction while driving and may impact the results of such a case.
It is also important to determine whether the vehicle’s brakes were fully functional at the time of the accident. All vehicles on the road should be maintained in safe working conditions.
Reasonable speeds should be observed by drivers especially when approaching junctions, corners, and other signaled areas of the road. Thus, the driver’s speed at the time of the accident should be established. Reasonable speed also helps in ensuring that the driver has ample time to yield to errant pedestrians (jaywalkers) despite the driver’s right of way.
https://www.nolo.com/legal-encyclopedia/car-accidents-caused-by-negligence-29537.html

The key question in this tort case will be who was at fault in the incident, and therefore who must pay for the damage and injuries caused. This is more important in some states than others; in "no-fault" states such as Michigan, insurance is required to provide certain coverage for everyone regardless of a determination of fault, while in "fault" states such as California each person's liability is strongly dependent upon who is considered at fault. Key concerns for determining fault include negligence, intent, and strict liability. Strict liability is the simplest; if you are defined by law or contract to have liability, then you have liability, even if you did everything right. This would likely be the case if the driver was carrying some hazardous substances that are strictly regulated, but it is unlikely otherwise.Intent means that the harm was caused on purpose, making this a form of assault; that doesn't appear to be the case here.That leaves only negligence. Was the driver or the pedestrian careless? Was either one violating the law at the time, in such a way that contributed to the injury? This one could actually be argued both ways. The pedestrian was walking against a red light, suggesting that their negligence might make them at fault. (The saying "pedestrians always have the right of way" is not strictly true.) But if the driver was in any way careless about watching for them and failing to yield, the driver or the company that they were working for could still be held liable. The result of this tort would depend on very precise details of the circumstances. But from what was given, it sounds like it is probably not the driver's fault, and thus neither the driver nor the company they work for would be held liable.
https://injury.findlaw.com/car-accidents/fault-and-liability-for-motor-vehicle-accidents.html

https://sargentlawfirm.com/blog/california-pedestrian-right-of-way-laws/

https://www.nolo.com/legal-encyclopedia/car-accidents-caused-by-negligence-29537.html

Calculus of a Single Variable, Chapter 5, 5.6, Section 5.6, Problem 62

Equation of a tangent line to the graph of function f at point (x_0,y_0) is given by y=y_0+f'(x_0)(x-x_0).
The first step to finding equation of tangent line is to calculate the derivative of the given function. To calculate this derivative we will have to use the chain rule (u(v))'=u'(v)cdot v'.
y'=1/(|4x|sqrt((4x)^2-1))cdot4=1/(|x|sqrt(16x^2-1))
Now we calculate the value of the derivative at the given point.
y'(sqrt2/4)=1/(|sqrt2/4|sqrt(16(sqrt2/4)^2-1))=1/(sqrt2/4sqrt(16cdot1/8-1))=1/(sqrt2/4)=4/sqrt2=2sqrt2
We now have everything needed to write the equation of the tangent line.
y=pi/4+2sqrt2(x-sqrt2/4)
y=2sqrt2x+(pi-4)/4
Graph of the function (red) along with the tangent line (blue) can be seen in the image below.

What evidence shows that Doodle is a caring person?

There are two good examples from the text which reveal Doodle as both sensitive and caring despite his physical disabilities. In fact, these disabilities may be the primary reason why Doodle became a caring individual in contrast to his often brutish brother. First, Doodle reveals his sensitive nature when his brother takes him to Old Woman Swamp. Doodle is overwhelmed by the beauty of the place:

His eyes were round with wonder as he gazed about him, and his little hands began to stroke the rubber grass. Then he began to cry.
"For heaven's sake, what's the matter?" I asked, annoyed.
"It's so pretty," he said. "So pretty, pretty, pretty."

The best example of Doodle's caring nature comes when the scarlet ibis falls dead in the family's yard. Doodle, who may have sensed a kinship with the fragile bird that was so out of place in coastal North Carolina, insists on burying the bird and singing over its grave. The incident reveals a boy with a deep sense of the importance of life, and that there are more important things than the simple physical endeavors which his brother covets and are essentially meaningless to Doodle (except in his struggle to please his brother). Doodle has that rare ability to appreciate and cherish the beauty which surrounds him, a characteristic which his brother goes to great lengths to emphasize in the retelling of Doodle's short life from many years afterward. 

Five adjectives about The Wednesday Wars.

The previous post has some great adjectives for Gary Schmidt's The Wednesday Wars. I'll provide 5 more.
Funny. Holling is a hilarious character that is made funnier because the book is written from his perspective. Readers will often find themselves laughing out loud as Holling describes what he looks like in his costume with feathers on the butt.
Relatable. Most people that read this book have been through junior high or are in junior high. Holling's experiences with his friends, parents, siblings, teachers, etc. are all relatable experiences. We've felt awkward when around that certain someone that we like. We've had fights with siblings. The book narrates a lot that many readers will find common ground with.
Inspiring. I'm a teacher, so I find Mrs. Baker a very inspiring teacher. She goes the extra mile to help her students, and she makes efforts to understand her students as people.
Sobering. As a parent, I get very angry at Mr. and Mrs. Hoodhood for essentially ignoring their children. Readers that are parents will likely be upset at the part in the book where Holling's father forgets to pick him up for the baseball signing.
Accessible. Schmidt does an excellent job of making the book accessible to a wide range of readers. He chooses to include common events, locations, and relationships in this text. Additionally, Holling is the story's narrator. This means that Schmidt is forced to write in a way that reflects how a 7th grader would think, act, and talk. The book is accessible to 7th grade readers because it sounds like a real 7th grader is narrating.

Gary Schmidt's 2009 young adult novel The Wednesday Wars was nominated for at least two prestigious literary awards.  Here are five adjectives that can be used to describe it, with a rationale for each.
The novel is humorous. When Holling's teacher forces him to read Shakespeare's The Tempest, he loves it. He figures that she has not read it herself, since it has murders, witches, a monster, and includes people drinking themselves drunk.
The novel is realistic. It is set during the Vietnam War, and Schmidt takes pains to recreate the 1960s.  Walter Cronkite appears on the television news, announcing the numbers of soldiers killed each day.
The novel is poignant.  It traces some common setbacks and problems that adolescent boys experience, such as finding a place to fit in with other people.
Some of the scenes in the novel are surprising. Holling's father, a successful architect, is not a very nice man or caring father.  He neglects Holling and his sister and frequently lets them down. 
The novel is ambitious.  Schmidt creates many different story lines; some are about family, some are about school relationships with peers and teachers, and some are about religious differences. All occur against the backdrop of an unpopular war.  Schmidt is able to balance all the competing narratives and bring them together effectively.

4. You drop a 16-pound bowling ball off of a 50-foot structure. How fast is the bowling ball traveling when it strikes the ground?

This question is missing some basic assumptions, but based on the standard way these questions are typically phrased, I am assuming that the friction and air resistance are irrelevant.
Given that, the weight of the bowling ball is also irrelevant. Gravity on Earth is a constant that affects all objects equally, pulling at approximately 32.2 feet per second per second.
The acceleration is constant but that means the bowling ball's speed is not. The longer it falls, the faster it falls. To account for that discrepancy, the formula for calculating time falling involves the square root of the height:
Time to fall = sqrt ( 2 * height / 32.2 )
If we plug in our initial height into that formula and run it through our calculators, we get ~1.76 seconds until the ball hits the ground.
We can then plug that back into the gravitational constant to determine the bowling ball's final speed. The bowling ball gains 32.2 feet/second of speed for every second of acceleration, so, after 1.76 seconds of acceleration, it is traveling at,
32.2 ft / sec^2 * 1.76 sec = ~56.7 feet / sec
The bowling ball will be going about 56.7 feet per second when it strikes the ground.

log_5(2x-7)=log_5(3x-9) Solve the equation. Check for extraneous solutions.

log_5(2x-7)=log_5(3x-9)
Using one to one property of logarithms,
2x-7=3x-9
=>2x-3x=-9+7
=>-x=-2
=>x=2
Let's plug back the solution in the equation,
log_5(2*2-7)=log_5(3*2-9)
log_5(-3)=log_5(-3)
However logarithm of negative number is undefined,
So the solution is extraneous.

How is Troy’s behavior an instrument for the suffering of others?

Troy's selfish and self-centered behavior hurts his family members and causes them to suffer in "Fences".
Troy cheats on his wife which causes her pain. He actually gets another woman pregnant; after 18 years together, he thought he could be another man with a new woman. Rose is angry about the dreams and hopes that she gave up to be with him and to create a life for them. She agrees to raise the baby but says she won't be Troy's wife anymore.
Troy rejects his son, Cory, because the young man represents dreams that Troy couldn't fulfill. He doesn't want him to play football; he says he doesn't have to like him just because Cory is his son. He ultimately kicks Cory out of the house. Cory goes on to find success in life but is still angry with his father after Troy dies.
Troy also hurts his brother. He wants money and signs his brother to an institution. Gabe's checks will go to Troy and to the hospital. However, at his brother's funeral, Gabe still hopes that Troy will be able to go to Heaven.

Troy hurts others and is an instrument of their suffering. He is never able to show others how much he loves them, and he hurts them with his ways. For example, his wife, Rose, is a loving person who has dedicated herself to Troy, but he has an adulterous affair with Alberta that produces his daughter, Raynell.
In addition, Troy does not really accept his sons, Cory and Lyons. Cory wants to play football in college, but Troy believes it's a white man's game and fights his son on this decision, causing Cory to run off and join the army. Lyons wants to be a jazz musician, but Troy also ridicules him, and Lyons leads a shiftless life. Finally, Troy also commits his brother, Gabriel, to a mental institution. After Troy's death, however, most of the characters forgive Troy, knowing that he was contending with racism and fear.

Troy's behavior is a direct cause of suffering for his wife, Rose, and his son Cory. In a less direct way, Troy also causes suffering on the part of his son Lyons and Troy's brother, Gabriel. Troy behaves selfishly and never considers that he might be wrong, and this causes the other characters grief.
Troy's affair with Alberta causes Rose to suffer emotionally. When that affair leads to the birth of a daughter, Raynell, and Alberta dies in childbirth, Rose suffers even more; she agrees to raise a child her husband had with another woman. Troy's cheating hurts and embarrasses Rose.
Troy's demand that Cory focus on work instead of the possible future he could have as a football player causes Cory to suffer. Though Troy is trying to prevent Cory from experiencing the same disappointment he himself experienced with baseball, Cory feels that Troy is taking a bright future away from him, and their already strained relationship is further damaged by this conflict.
Though Troy's son Lyons is following his dreams of being a jazz musician, he does occasionally need to borrow money from Troy, and Troy does not treat the situation delicately or discreetly. Rather, he uses Lyons's request as an opportunity to condescendingly lecture him about the choices he has made in order to pursue music.
Finally, Troy's brother, Gabriel, who fought and was injured in World War II, suffers due to Troy's behavior. Specifically, Troy uses some of the money Gabriel received from the government to pay for the Maxsons' home. Due to his mental state, Gabriel is not seemingly aware of what Troy has taken from him, but it does affect his life nonetheless.

What are the name of the four major oceans?

Oceans make up about 70 percent of Earth’s surface. There are four major oceans on our planet. They are the Atlantic Ocean, the Pacific Ocean, the Indian Ocean, and the Arctic Ocean.
The Atlantic Ocean is bordered by the Americas on its western shore and by Europe and Africa on its eastern shore. The Atlantic Ocean is located both north and south of the equator.
The Pacific Ocean is bordered by Asia on its western shore and by the Americas on its eastern shore. The Pacific Ocean is located both north and south of the equator.
The Indian Ocean is bordered by Africa on its western shore and by Australia on its eastern shore. Most of the Indian Ocean is located south of the equator.
The Arctic Ocean is connected to both the Pacific Ocean and the Atlantic Ocean. It connects to the Pacific Ocean through the Bering Sea and the Bering Strait and to the Atlantic Ocean through the large opening between Greenland and Scandinavia. Several countries surround the Arctic Ocean, including Canada, Greenland, and Russia.
The four main oceans are the Atlantic, the Pacific, the Indian, and the Arctic.
http://www.marinebio.net/marinescience/01intro/woocean.htm

What are ten nouns in "The Rime of the Ancient Mariner" by Samuel Taylor Coleridge?

As noted above, a noun is a word that represents a person, a place, or a thing. Nouns can be either abstract or concrete. Abstract nouns try to briefly represent a concept, whereas concrete nouns are more specific. Because this is a long poem and because Coleridge is trying to paint vivid visual images, he uses many concrete nouns that help us experience what the Mariner experienced. What can make this exercise confusing is that the same word in English can function as a different part of speech, depending on its context. For example, the word love can function as an abstract noun but also as a verb. So we need to look for words that are functioning primarily to denote a person, a place, or a thing, not an action.
Some examples follow. When the Mariner describes his ship entering the cold regions of the antarctic, he describes the area using such nouns as "mist," "snow, and "ice," which a paint a picture of the environment. He goes on to talk about "clifts" (cliffs) and to note that there are no "men" or "beasts" around, just "ice." A few stanzas later, the Mariner introduces the "Albatross," another noun, then "fog," then "food" and "helmsman."
To recap, some nouns used in stanzas 13–17 include: mist, snow, ice, clifts, men, beasts, albatross, fog, helmsman, and food.

Samuel Taylor Coleridge's "The Rime of the Ancient Mariner" marked the shift to British Romanticism and the modernity of poetry. This poem was published in 1798 and describes the experiences of a mariner who shot an albatross after getting caught in icy Antarctic waters.
Let's make a list of some of the nouns that occur in this poem. First, let's make sure we understand the meaning of a "noun." A noun is a word the represents or names a person, place, thing, quality, event, or idea. I will bold the nouns as they appear in the lines of poetry:

"'By they long grey beard and glittering eye."
"The guests are met, the feast is set"
"The Wedding-Guest sat on a stone."
"The ship was cheered, the harbor cleared."
"The bride hath paced into the hall"

As this is a very long poem, there are plenty of other nouns within it, but this is a good start!

h(t) = ln(t)/t Find the derivative of the function.

We'll use the formula of the derivative of a quotient:  (u/v)' = (u'v-u v')/v^2.  Here u=ln(t) and v=t, therefore u'=1/t and v'=1. So
h'(t) = (1/t *t - ln(t))/t^2 = (1 - ln(t))/t^2.

How are Toussaint Louverture and Nat Turner similar and different?

Both Louverture and Turner were leaders of rebellions by enslaved people. Apart from this, and the fact that both were of African descent, there are probably more differences between the two men, and their individual stories, than there are similarities. The latter, however, are significant.
Louverture's revolutionary activities took place over a period of more than a decade. The large-scale rebellion of the enslaved people of Saint-Domingue (Haiti) began in 1791 and eventually succeeded in abolishing slavery and creating an independent country under the leadership of African American (or African West-Indian) people. Louverture was a participant in and then leader of this movement. He fought with or against the European powers, and was involved in negotiations with them and, through emissaries, the US administration of John Adams in 1798. Unfortunately, Louverture was arrested by the French in 1802 and transported to prison in France, where he died the following year.
Nat Turner's rebellion was by contrast a brief and unsuccessful action. He believed he had received visions from God, and that his mission was to free the enslaved people of Virginia and the US as a whole. The uprising was premature, for it was unrealistic to believe that sufficient numbers of enslaved people and free African Americans could be recruited in the 1830's to take part in it. The rebellion was quickly put down and Turner was arrested within just over two months after it began.
In spite of these differences, both Louverture and Turner became symbols of freedom and were extolled in the collective consciousness of progressive people in general, and in European and American literature. Wordsworth's sonnet on Louverture expresses the tragedy of his ultimate fate, and William Styron's novel about Turner, though a controversial work, has made Turner's story familiar to many who might otherwise have known nothing about him. A final similarity between Louverture and Turner is that both ended up defeated despite their accomplishments. Louverture died in prison, probably of natural causes, and Turner was hanged less than two weeks after being arrested.

What was the reason Dr. Mannette was imprisoned?

Dr. Mannette was imprisoned in the Bastille, a notorious fortress prison that stood as a hated symbol of pre-Revolutionary France and whose fall is generally thought to represent the start of the French Revolution. He rotted away in that hellhole for eighteen long years: his lengthy period of incarceration taking a terrible toll on both his mental and physical health.
Dr. Mannette was imprisoned for informing on Darnay's father and his uncle, the wicked Marquis St. Evrémonde. They were responsible for the rape of a peasant woman and the murders of her husband and brother. The Evrémonde brothers obtained what's called a lettre de cachet to keep Dr. Mannette quiet and send him to prison.
A lettre de cachet was a sealed letter from the king that contained his express orders, normally relating to the punishment without trial of certain individuals. There was no appeal against a lettre de cachet, and they were wide open to abuse, often used to settle scores or personal vendettas. That's precisely what happened to Dr. Mannette. Two aristocrats were able to get away with breaking the law; not only that, but they were able to send an innocent man to prison for eighteen years, and all because he had the courage to do the right thing. It's no wonder that the revolutionaries hated the Bastille and the manifestly unjust system it represented.

An acrostic of the first letters of Factionless-Abnegation-Candor-Amity-Dauntless-Erudite spells FACADE. How is this significant to the story?

Roth's Chicago is ruled by a government that claims to have identified the five essential components of virtuous character. The city's leaders tout the effectiveness of their segregated society, but the entire social paradigm is a mirage worthy of a Potemkin village. The term "Potemkin" refers to any social structure that hides the true conditions of a situation, and this is what Roth's futuristic Chicago encapsulates. In this city, social interaction between the members of the five factions is actively discouraged, and faction customs dictate both work and recreation choices, supplanting even individual preferences.
Meanwhile, the yearly aptitude tests are designed to identify divergents for execution, and defectors to other factions are subjected to social stigma for their choices. In the five-faction system, civilians are largely divorced from the political process. For example, civilians do not know why soldiers from the Dauntless faction must guard the Fence that surrounds the city. Meanwhile, the factionless are consigned to a dilapidated sector where many of the roads have collapsed, and open sewer systems endanger the health of its poverty-stricken populace. Accordingly, the acrostic "FACADE" is significant to the story in the sense that it alerts us to the dysfunction and malevolence of a world based on a rigid social stratification system.

Calculus: Early Transcendentals, Chapter 4, 4.6, Section 4.6, Problem 30

This function is defined only on [-c,c] (we can assume that c is positive) and infinitely differentiable inside the interval.
f'_c(x) = sqrt(c^2-x^2)+x*(-2x)/(2sqrt(c^2-x^2)) = (c^2-2x^2)/sqrt(c^2-x^2).
f''_c(x) = (-4x*sqrt(c^2-x^2)-(c^2-2x^2)*(-2x)/(2sqrt(c^2-x^2)))/(c^2-x^2) = (x*(2x^2-3c^2))/(c^2-x^2)^(3/2).

f' is negative for x in (-c,-c/sqrt(2)) and in (c/sqrt(2),c), f decreases there, and f' is positive for x in (-c/sqrt(2),c/sqrt(2)), f increases.
So -c/sqrt(2) is a local minimum, c/sqrt(2) is a local maximum.
About f'': 2x^2-3c^2 is negative on (-c,c) so f'' is positive on (-c,0) and is negative on (0,c). f is concave upward on (-c,0) and is concave downward on (0,c). So x=0 is an inflection point.
The general shape of the graph is the same for all c's.
Please look at the graphs here: https://www.desmos.com/calculator/4a0q7l7sec

How old is Luke at the end of the story?

Margaret Peterson Haddix is the author of the novel Among the Hidden, which is a part of a series of books in the Shadow Children sequence.
In chapter seven, dialogue reveals that Luke, the third child born in a society where it is only legal to have two children in a family, is twelve years old. From that chapter until chapter twelve, the text mentions harvest time and late October. So readers could infer that the novel begins in summer, and has spanned about three to four months at this point. In chapter nineteen, November is referenced. Luke's father is playing cards with him on Luke's bed because there is no work for him to do.

"'Again?' Dad asked, shuffling the cards.
'If you don't have any work you've got to do.'
'In November? With no livestock? Only work I've got now is figuring out how we're going to pay our bills once the hog money runs out.'"

Chapter twenty is set in mid-January, and chapter twenty-one begins in mid-February. Chapter twenty-two begins with April rain. The next chapters span the remainder of that month. Chapter twenty-six opens a week and a half after the rally, which is probably the beginning of May.
I couldn't find any other definite time markers longer than a day or two from chapter twenty-six to the end of the book, chapter thirty. So, we can infer that Luke is still twelve, and the events of the novel take place in just under a year's time.

List some of Montag's conversational mannerisms.

During Montag's first interaction with Clarisse, the reader gets a sense of his mannerisms. Montag attempts to portray himself as an amiable person who does not take his job too seriously. Montag is used to having superficial conversations, which usually amount to dismissive small talk. However, Clarisse is an extremely introspective, curious person who begins to make Montag feel awkward and anxious. Montag does not seem comfortable when Clarisse pauses during their conversation, and he prefers to continue elaborating on senseless topics to keep their conversation moving.
When Clarisse mentions that she heard firemen used to put out fires in the past, Montag reveals his typical mannerism of abruptly laughing. Clarisse responds by questioning Montag about why he instinctively laughed when she did not say anything funny. As their conversation continues, Montag instinctively breaks out into laughter several more times because he is uncomfortable. Bradbury also mentions that Montag "clenches" when there are silent gaps in their conversation.
Overall, Montag's mannerisms indicate that he is an anxious individual who is not used to having enlightening conversations and feels more comfortable engaging in small talk. His mannerisms include abruptly laughing, attempting to keep the conversation moving, clenching, and engaging in rather fragmented speech without deeply elaborating on specific topics of conversation.

Who contradicts the Wife of Bath in her discourse on marriage?

The Pardoner, unsurprisingly, is the one who takes issue with the Wife of Bath's feminist discourse.
Why, one may ask, do I say "unsurprisingly"? The Pardoner's own nature and character are, like anything in literature, open to interpretation. Teachers and critics often see him as an exemplar of both sinfulness and, paradoxically, perfection. Those whose business was the "selling of indulgences" were usually considered mercenary and unsavory people. Yet the tale told by the Pardoner after he completes his sermon of a prologue is often regarded as the most beautiful and artistically perfect section of The Canterbury Tales. The stark and frightening story of the three men coming to grief through their own greed, in the midst of a plague-time all too familiar to Chaucer's readers, is a warning not only against greed but against any type of sin. One might consider all the things Chaucer reveals to us about the Pardoner throughout the Tales, and ask why he, of all the travelers in the group, should take such exception to the frank and pleasure-loving tone of the Wife of Bath. But perhaps the most remarkable thing in the Tales overall is that Chaucer shows us a woman who stands up so forcefully for women's rights, nearly 600 years before the modern feminist movement of our own time.

What were the reasons for the revolts and rebellions that occurred in the American colonies?

There were many factors that led American colonists to rebel against the British, but the French and Indian War (1756–1763)—or the Seven Years War for Europeans—is a good starting point.
American colonists believed they played their part well in the fight against the French and the Indians. So when the British Parliament, and King George III, began imposing new laws and taxes (Sugar Act, Currency Act, Quartering Act, Stamp Act) on the colonists, to pay for the war and to reduce British debt, the colonists felt betrayed and proceeded to try to reduce the effect of these laws. They generally succeeded in doing so. But the British didn't quit, and they began to impose even more laws on the colonists.
Acts of resistance, like the Boston Tea Party, were small but significant gestures meant to demonstrate to the British that the colonists were resolved not to be taxed to pay off British debt. Moreover, there were no colonial representatives in the British Parliament representing colonial views on anything. Hence, the colonial response to any new British tax was "No taxation without representation!"
But during this time, the people in the thirteen colonies were not united, and they really had no plan to become united. Nevertheless, the British imposed a new set of laws, the Intolerable Acts, which included the Boston Port Act, that punished the colonists for their continued resistance.
The colonists had had enough as well, and in 1774, twelve of the thirteen colonies sent representatives to the First Continental Congress in Philadelphia, PA. They had hoped to reverse the effects of the sanctions imposed by the Intolerable Acts. Among other things that came out of that one-and-a-half month long conference was the decision to boycott the purchase of all British goods.
It was in the following year, however, that the "Shot Heard Round the World" set off hostilities between the British and the American Colonists on April 19, 1775 that began the American Revolutionary War.
As you can see, there were many factors that impacted the American Revolution, but the fact that the colonists kept rebelling and kept responding to the laws imposed on them is what eventually led to the beginning of the war.

While it is somewhat popular to believe that the Thirteen Colonies were economically and politically unified, nothing could be further from the truth. Throughout the colonies, differing political and economic goals often led to conflict.  Even within each individual colony, a strict social stratification was taking place.  An elite class was emerging that was quickly becoming politically powerful and economically advantaged.  It is the emergence of this aristocratic class that led to several rebellions throughout colonial history.  The most famous of the rebellions was led by Nathaniel Bacon in Virginia in 1676.  Disheartened by the lack of opportunity afforded to middling planters, and angered by the governors lack of interest in defending the frontier against Indian attacks, Bacon led a rebellion. Bacon and thousands of disgruntled farmers led a revolt against Governor Berkeley and burned the capital.  This is one of several examples of social unrest within the colonies themselves.  
https://www.ushistory.org/us/7e.asp

What is Lady Capulet's opinion of Juliet and Romeo?

It looks like the answer to your question is located in act 3, scene 5.
Here, Lady Capulet completely misunderstands Juliet's grief. It is clear that her distorted perception is occasioned by her lack of discernment. Lady Capulet accuses Juliet of overindulging in her grief for Tybalt. She even suggests that Juliet is not really weeping for her kinsman; she insists that Juliet is sad because Tybalt's killer remains a free man.
Meanwhile, Lady Capulet thinks of Romeo as a "villain" and a "banished runagate" (vagabond or fugitive). Her desire is that Romeo should die for killing Tybalt. She tells Juliet that she is ready to send one of their servants to Mantua to poison Romeo. 
Privately distressed at this suggestion, Juliet presents an alternative: she will make sure the poison is properly concocted if her mother can find a man to "bear a poison" to Mantua. At this point, we get the idea that Lady Capulet thinks of her daughter in superficial terms. Her lack of discernment causes her to miss the real reason for her daughter's anguish. On a deeper level, Lady Capulet is satisfied with her own interpretation of Juliet's grief and does not feel the need to draw it out.
Because of her lack of discernment and her tendency to railroad her daughter into performing her will, Lady Capulet is unable to fully bond with Juliet. This tragic state of affairs is highlighted when Juliet voices her refusal to marry Paris: Lady Capulet simply becomes furious and takes to wishing that the "fool were married to her grave." Lady Capulet's opinion of Juliet is that she is a spoiled, ungrateful child who refuses to consider her parent's wishes. She does not entertain any other interpretation of her daughter's seemingly baffling behavior.
Meanwhile, Lady Capulet's opinion of Romeo is extremely negative as well. She thinks of Romeo as a killer, who deserves to die for committing murder. Certainly, she does not want to see her daughter marry such a "villain." 

What is the significance of the Virginian roping the pony?

Wister uses the episode of the eponymous Virginian roping a recalcitrant pony as an opening illustration in his novel to show us the character of his protagonist and to underscore his skill as a horseman. The pony, Wister says, is one who "would not be caught, no matter who threw the rope." As such, the mysterious protagonist who can approach, and successfully rope, a pony who has neatly avoided capture by all others who have tried is set aside: through this episode, he is proven exceptional.
Wister describes the pony as akin to a "skilful boxer" and describes in detail how it outwits those who attempt to capture it, remaining "undistracted" throughout. At the side of the corral, the narrator observes "a man" who is also watchful and who approaches the pony with "the undulations of a tiger." Unlike the others, who have whirled their rope showily, the man watches quietly and approaches with no false showmanship but with an understanding of what the pony's attitude is and how it tends to move and react. Animal imagery is used again to describe the natural way in which the man approaches his task: like "a sudden snake," the rope ensnares the pony. The reaction of the passenger in the train epitomizes what Wister wants us to take from this story: "That man knows his business."

What trouble did George and Lennie have in Weed in Of Mice and Men?

They were run out of town. Lennie likes to touch soft things; he likes the way they feel in his hand. That's why he is constantly stroking rabbits and mice. His dream is to one day look after the rabbits on a ranch he's going to buy with George. Unfortunately, Lennie's penchant for stroking soft objects often gets him into trouble. It certainly does near the end of the story in relation to Curley's wife. And back in Weed it was a similar story, though without the tragic consequences. Lennie touched a girl's dress. His motives were completely innocent, but the girl and the townsfolk inevitably got the wrong idea. Not surprisingly, Lennie is perceived as a threat, so he and George have to escape Weed as soon as they can in order to avoid a possible lynching.

In 'A Midsummer Night's Dream,' how (in what ways) does Shakespeare convey the theme of love?

Shakespeare portrays love as mad, magical, and difficult. Theseus and Hippolyta are engaged, Oberon and Titania are married, and Lysander and Hermia wish to elope. Meanwhile, Demetrius pursues Hermia, and Helena, his former girlfriend, pines for him. The lovers are mad in the sense that they are irrational, particularly Helena and Demetrius. Helena observes that she is as worthy of Hermia, as beautiful and virtuous, and concludes, “Love looks not with the eyes, but with the mind; / And therefore is wing'd Cupid painted blind.”
The magical element arises when a spell is introduced. Oberon and Puck infect Titania, Lysander, and Demetrius with a love potion. Titania falls for Bottom, whose head has been transformed into a donkey’s. This makes no difference to her, demonstrating that love, whether enchanted or not, is like a sudden spell. Lysander abandons Hermia for Helena, even rationalizing his preference, and Demetrius attempts to fight Lysander for Helena.
Almost every couple in the play experiences the difficult aspects of romance. As Lysander says, “The course of true love never did run smooth.” Theseus and Hippolyta warred before marrying, Oberon and Titania quarrel over the adoption of a child, and Egeus, Hermia’s father, opposes her marriage to Lysander. Both Demetrius and Helena are unrequited in their love, and even the ridiculous Pyramus and Thisby features lovers who are cruelly parted by a wall. In A Midsummer Night’s Dream, love is wild and ridiculous, but, in the end, it all works out.
http://shakespeare.mit.edu/midsummer/full.html

Do you agree that Barton has no choice but to let Marilyn die?

This is an interesting question from the vantage point of our modern sensibilities. Today, we live in the era of vast technological accomplishments. For example, we are experiencing the emergence and implementation of 5G now. Briefly, 5G is the new generation of wireless technology, set to revolutionize AR (augmented reality) and VR (virtual reality) applications in the business, healthcare, autonomous vehicle, and gaming industries.
We also have AI (artificial intelligence) and machine learning applications that are changing the way we protect sensitive consumer data and how we deliver accessibility in terms of customer service. So, in our modern era, we can't conceive of the kinds of limitations we read about in The Cold Equations.
Now, if we analyze the pilot's predicament based on the story's principles, it would be impossible to blame Barton for his difficult choice.

There could be no alternative. Additional fuel would be used during the hours of deceleration to compensate for the added mass of the stowaway, infinitesimal increments of fuel that would not be missed until the ship had almost reached its destination. Then, at some distance above the ground...the unmissed increments of fuel would make their absence known; the EDS would expend its last drops of fuel...Ship and pilot and stowaway would merge together upon impact as a wreckage of metal and plastic, flesh and blood, driven deep into the soil.

The following are some important questions to ask in order to arrive at an answer to your question:
1) Should Barton sacrifice himself, will Marilyn be able to pilot the EDS and reach the required destination safely?
2) Should Barton sacrifice himself?
3) Should Barton take a chance and keep Marilyn on the EDS ship, potentially sacrificing the lives of six other individuals?

Barton's confronted with a profound moral dilemma. If he allows Marilyn to remain on board ship, then he potentially jeopardizes his own safety as well as the success of what is essentially a mission of mercy. On the other hand, jettisoning Marilyn into space will lead to her certain death. The dilemma boils down to whether the individual is more important than the collective, or the wider community.
One could argue that Marilyn is being selfish in hitching a ride aboard the Emergency Dispatch Ship. The ship's carrying an essential cargo—desperately-needed medical supplies. Even if Marilyn thought that she'd only get off with a fine or a warning for stowing aboard ship, she must have known the ship's purpose and how important it was not to disrupt its vital mission. Tough situations require tough decisions, and although ejecting Marilyn into the icy wastes of deep space would be a tough decision indeed, it would also be justified under the circumstances.

What are some literary devices in Robert Frost's "The Sound of Trees"?

Robert Frost's "The Sound of Trees" employs a first person speaker to meditate on the relationship between humans and trees.
The speaker begins with a rhetorical question:

I wonder about the trees.
Why do we wish to bear
Forever the noise of these
More than another noise
So close to our dwelling place? (1-5)

The speaker "wonder[s]" why people choose to live in such close company to trees. He asks why we choose to hear the "noise of these / More than another noise." Some of the word choice has a slight negative connotation: "to bear" and "the noise," for example. These phrases suggest that humans "put up with" the sounds that come from trees, as though there is not something inherently pleasant or peaceful about them. The entire poem, as we can see from these first few lines, is written in free verse, with no set rhyme scheme or stanza structure. The lines also feature enjambment, where the speaker's thoughts flow from one line to the next, usually without punctuation at the end of every line. This style more effectively mirrors the speaker's meandering thought process than a more structured form would do.

The speaker continues the ideas first established in lines 2-5 in the following several lines:


We suffer them by the day
Till we lose all measure of pace,
And fixity in our joys,
And acquire a listening air. (6-9)



The word "suffer" is another example of significant diction with a negative connotation. He describes the effect of the trees on the speaker and other humans, however, in a less negative way when he says they "acquire a listening air" from previously "los[ing] all measure of pace."

Next, the speaker writes,


They are that that talks of going
But never gets away;
And that talks no less for knowing,
As it grows wiser and older,
That now it means to stay. (10-14)



The unusual repetition of the word "that" in line ten makes the reader pause and read carefully. The trees represent "that that talks of going / But never gets away." The trees are stable and permanent, and they are also personified when the speaker describes them as "wiser" and ascribes intention to them ("it means to stay.").

The final section of the poem shifts focus back on to the speaker, as he writes,

My feet tug at the floor
And my head sways to my shoulder
Sometimes when I watch trees sway,
From the window or the door.
I shall set forth for somewhere,
I shall make the reckless choice
Some day when they are in voice
And tossing so as to scare
The white clouds over them on.
I shall have less to say,
But I shall be gone. (15-25)

Here, the imagery conveys the similarity between the speaker and the tree. The speaker feels more firmly planted, like a tree, and moves like a tree sways in the wind. Further, the speaker echoes the previous notion about trees in lines ten and eleven when he says, "I shall set forth for somewhere / I shall make the reckless choice." This indicates that the speaker sits there fixed but thinks of moving on and going elsewhere. He also juxtaposes the previous description of trees as "wiser" with his own perception of himself as having the capacity for "reckless[ness]." The speaker ends the poem with an image of the trees in the future, "tossing so as to scare / The white clouds over them on." The difference is that the speaker will be dead, and he will no longer be there to hear the trees' "voice[s]," as he is now. The speaker ends with a reflection on the permanence of the trees versus his own mortality.

Calculus of a Single Variable, Chapter 8, 8.5, Section 8.5, Problem 28

int5cos(x)/(sin^2(x)+3sin(x)-4)dx
Take the constant out,
=5intcos(x)/(sin^2(x)+3sin(x)-4)dx
Now let's apply integral substitution:u=sin(x)
=>du=cos(x)dx
=5int1/(u^2+3u-4)du
Now to use partial fractions, denominator of the integrand needs to be factored,
Let's split the middle term,
1/(u^2+3u-4)=1/(u^2-u+4u-4)
=1/(u(u-1)+4(u-1))
=1/((u-1)(u+4))
Now let's write it as sum of partial fractions:
1/((u-1)(u+4))=A/(u-1)+B/(u+4)
Multiply the above by the LCD,
=>1=A(u+4)+B(u-1)
1=Au+4A+Bu-B
1=(A+B)u+4A-B
Equating the coefficients of the like terms,
A+B=0 -----------------------------(1)
4A-B=1 ----------------------------(2)
Solve the above linear equations to get the values of A and B,
Add equation 1 and 2,
5A=1
A=1/5
Plug the value of A in equation 1,
1/5+B=0
B=-1/5
Plug in the values of A and B in the partial fraction template,
1/((u-1)(u+4))=(1/5)/(u-1)+(-1/5)/(u+4)
=1/(5(u-1))-1/(5(u+4))
int1/(u^2+3u-4)du=int(1/(5(u-1))-1/(5(u+4)))du
=int1/5(1/(u-1)-1/(u+4))du
Take the constant out,
=1/5int(1/(u-1)-1/(u+4))du
Apply the sum rule,
=1/5(int1/(u-1)du-int1/(u+4)du)
Now use the common integral:int1/xdx=ln|x|
=1/5(ln|u-1|-ln|u+4|)
Substitute back u=sin(x)
=1/5(ln|sin(x)-1|-ln|sin(x)+4|)
int5cos(x)/(sin^2(x)+3sin(x)-4)dx=5(1/5(ln|sin(x)-1|-ln|sin(x)+4|)
Simplify and add a constant C to the solution,
=ln|sin(x)-1|-ln|sin(x)+4|+C

In Crooks’ opinion, why does George travel with Lennie?

In chapter four of Steinbeck's novella Of Mice and Men, Crooks pours his heart out to Lennie about his loneliness. Like Curley's wife in the next chapter, Crooks seems to feel comfortable telling Lennie the most intimate details of his life. He senses that Lennie, who is mentally challenged, is a safe person to share secrets with because, he says, "A guy can talk to you and be sure you won't go blabbin'." He suggests that this is why George travels with Lennie. Crooks believes it is important for two people to be together, sharing the same experiences and, most of all, having another person to talk to. It doesn't really matter if Lennie understands what is being said (he usually doesn't). Rather it is the experience of two men talking that is important. Crooks says,

"I seen it over and over—a guy talkin' to another guy and it don't make no difference if he don't hear or understand. The thing is, they're talkin', or they're settin' still not talkin'. It don't make no difference, no difference...George can tell you screwy things and it don't matter. It's just the talking. It's just bein' with another guy. That's all."

Indeed, the idea of simple companionship is one of the important themes in the book. George travels with Lennie because it is far better than traveling alone and having no one to talk to. Crooks and Curley's wife are two of the characters in the novella who do not have that companionship but yearn for it, and that is why Lennie is a sounding board for their hopes and fears. Similarly, George carries on and on about his dream farm to Lennie, who doesn't understand much of it other than the idea of tending rabbits.
 

Mr. Pignati told the kids to take care of two things until he returned. What were those two things?

At the hospital, Mr. Pignati asks Lorraine and John to take care of his house and Bobo (the baboon at the zoo).
Bobo is Mr. Pignati's favorite animal at the zoo. Since Mr. Pignati is in the hospital, he will not be able to visit Bobo until he is released. As a result, he asks John and Lorraine to feed Bobo properly when they next see him at the zoo; they are to make sure that Bobo gets dry-roasted peanuts from the yellow package (not the red package) and half a hot dog. Mr. Pignati tells John and Lorraine that Bobo never eats the whole hot dog.
Mr. Pignati also tells the teenagers to take care of his home. He invites them to make themselves at home in his house and to use anything there they want. John and Lorraine take Mr. Pignati up on his offer, but their good intentions are soon obscured by their desire to have fun. They hold a party at Mr. Pignati's house, and a terrible fight breaks out between John and Norton (a classmate), resulting in the destruction of many of Mr. Pignati's pig figurines.
Mr. Pignati never fully recovers from his grief and later dies from a second heart attack.

Why was Gulliver given the name "Quinbus Flestrin"?

Gulliver sees the words "quinbus flestrin" on the inventory of his pockets which the Lilliputians took early in his stay in Lilliput. He says that he interprets the words to mean "great man-mountain," as a result of his huge size in comparison to the natives of this land. Later, he reads the words again in the articles of impeachment against him. Compared to the Lilliputians, Gulliver is the bigger person, so to speak, both literally and figuratively. He is, physically, many many times their size, but he is also more generous and compassionate than they are. When the emperor wants Gulliver to completely destroy the fleet of Blefuscu, a move which would allow the emperor to bring "'a free and brave people into slavery,'" Gulliver refuses him this request, inviting the emperor's ire and wrath. It shows, however, that—though Gulliver is certainly a smaller person (literally and figuratively) than many of the Brobdingnagians he meets on his next voyage—he is greater in most ways than the Lilliputians.

During his stay in Lilliput, Gulliver is given the name "Quinbus Flestrin" by the tiny Lilliputians. According to Swift, this name means something along the lines of  "the Man-Mountain" or "the Great Man Mountain," and so it's easy to assume that the Lilliputians give Gulliver this name because he is so much larger than they are. Indeed, it's suggested that the Lilliputians are only a few inches high compared to Gulliver, and so his name illustrates his astronomical size in comparison with his minuscule hosts. Moreover, it illustrates a major theme in Gulliver's Travels: perspective. While Gulliver might seem average-sized to other humans, the vastly different perspective of the Lilliputians turns him into a "Man-Mountain" of immense size. In short, Gulliver's nickname shows how a change in perspective can drastically change the meaning of a situation, experience, or individual. 
https://www.owleyes.org/text/gullivers-travels-jonathan-swift/read/part-i-chapter-i

https://www.owleyes.org/text/gullivers-travels-jonathan-swift/read/part-i-chapter-ii

What are the obstacles that prevent Troy from having what he wants?

In Fences, social problems along with a lack of emotional connection all represent obstacles that prevent Troy from having what he wants.
Troy believes he is socially marginalized.  Racial prejudice and institutional bias are factors that prevent him from achieving what he wants.  Troy feels that there is a challenge in being a man of color in America.  For example, he feels that racial integration of baseball helped to ruin his chances of pursuing his dream as a major league ballplayer. Additionally, he feels that racial bias prevents him from advancing in his job with the sanitation department. For example, Troy confronts his boss as to why whites drive the trucks but "the colored" are lifting the trash.  Troy feels that racial discrimination will never allow him to get a "paper job," a profession that affords him more money and greater social respect.  He believes that racial prejudice impedes him from the wealth and social status that could allow him to be happy, preventing him from having what he wants.
Troy is also denied from having what he wants because of emotional alienation. On many levels, Troy is divided from happiness because he is unable to emotionally bond with his family.  He feels that his family uses him for money and cannot give him what he needs.  This can be seen when he remarks to them,  "You all line up at the door with your hands out. I give you the lint from my pockets. I give you my sweat and my blood. I ain't got no tears. I done spent them."  Troy feels that his family weighs him down, and this burden separates him from what he wants.  At the same time, when Troy talks about his own father being "trapped," he intimates that he himself experiences the same reality. Troy's entire desire to build the fence is a symbolic way to separate himself from a group of people who he feels will never be able to give him what he needs.  As a result,  Troy feels that his relationships with his family will never be able to yield what he wants.

College Algebra, Chapter 5, 5.5, Section 5.5, Problem 40

A power mower has the noise of 106 dB. The noise level at a rock concert was measured at 120 dB. Determine the ratio of the intensity of the rock music to that of the power mower.



Recall that the formula for Sound Intensity in dB is represented as

$\displaystyle B = 10 \log \frac{I}{I_0}$

where

$B$ = intensity level in dB

$I$ = Sound intensity

$I_0 = 10^{-12} W/m^2$ reference intensity

If we let $I_1$ be the intensity of the rock concert and $I_2$ be the sound intensity of the power mower, then we need to find $\displaystyle \frac{I_1}{I_2}$, so

@ rock concert


$
\begin{equation}
\begin{aligned}

120 =& 10 \log \frac{I_1}{I_0}
\\
\\
12 =& \log \frac{I_1}{I_0}
\\
\\
10^{12} =& \frac{I_1}{I_0}
\\
\\
I_0 =& \frac{I_0}{10^{12}}
\qquad \text{Equation 1}

\end{aligned}
\end{equation}
$


@ power mower


$
\begin{equation}
\begin{aligned}

106 =& 10 \log \frac{I_2}{I_0}
\\
\\
10.6 =& \log \frac{I_2}{I_0}
\\
\\
10^{10.6} =& \frac{I_2}{I_0}
\\
\\
I_0 =& \frac{I_2}{10^{10.6}}
\qquad \text{Equation 2}

\end{aligned}
\end{equation}
$


By using equations 1 and 2


$
\begin{equation}
\begin{aligned}

\frac{I_1}{10^{12}} =& \frac{I_2}{10^{10.6}}
&& \text{Multiply each side by $10^{12}$ and divide both sides by } I_2
\\
\\
\frac{I_1}{I_2} =& \frac{10^{12}}{10^{10.6}} = 25.12
&&

\end{aligned}
\end{equation}
$

How might "The White Man's Burden" have impacted Europeans' views of imperialism and the peoples in the places being imperialized?

Some nineteenth-century British writers popularized the idea of the white man's burden. These authors included the illustrious Rudyard Kipling, who coined the term in his famous poem of the same title. "Take up the white man's burden— / Send forth the best ye breed— / Go bind your sons to exile / To serve your captives' need," Kipling wrote.
The racist idea behind the "white man's burden" was that benevolent rule would uplift "primitive" peoples. Western leaders eagerly embraced the doctrine of the white man's burden because it was a convenient justification for their expansionist policies. Far from "uplifting" native populations, however, white colonizers brutally exploited indigenous people. As a rule, indigenous peoples did not welcome the supposedly beneficial rule of Westerners.
Social Darwinism was the psuedo-scientific justification for the white man's burden and imperialism. Charles Darwin's theories explained how certain species thrived while others did not. Proponents of social Darwinism applied Darwin's concept of "survival of the fittest" to human societies and nations. They argued that Western nations were obvious the fittest on earth, so they had a duty to spread their advanced ideas and culture to backward areas of the globe. In fact, Darwin's ideas were only applicable to biology. Today, it is known that there is no scientific basis for Social Darwinism, but many late nineteenth-century Western leaders were under its sway.

Rudyard Kipling’s poem "The White Man's Burden" puts forward the idea that colonization is a great responsibility and a labor that often goes unrewarded or is even condemned in the colonized or imperialized areas.
Two possible reactions among the peoples in the colonizing powers are increased and decreased support for their nation’s actions. Those holding either position might still view subjected peoples as inferior and needy. While many white Europeans joined the service of empire, others were recruited or conscripted into the military. The governments generally promoted idea that it was both a privilege and a burden to extend what they saw as “civilization” to “wild” people elsewhere. The terms that Kipling uses for the subject peoples are in accord with widely accepted ideas in Europe, enhanced by the racist, eugenicist, and distorted philosophy of Social Darwinism, which claimed all other races were inferior to Caucasians. Kipling refers to them as “half-devil and half-child.”
Opposition to imperialism is also supported in the poem. Kipling uses an ironic undertone which is often ignored. He acknowledges that people at home may reject taking up this burden because it does not benefit them directly, but enriches the dominant sectors of society: “to seek another’s profit/ And work another’s gain.” Because this poem and related prose works responded directly to the US actions in the Spanish-American war, which was not universally popular, the criticism of armed conflict and the loss of life is significant: “the savage wars of peace” and “mark them with your dead.” Organized political opposition to the high costs of war, both monetary and human, showed erosion of national confidence in the imperial project.
http://www.kiplingsociety.co.uk/poems_burden.htm

https://monthlyreview.org/2015/07/01/imperialism-and-anti-imperialism-in-africa/

The "White Man's Burden" implies that whites (represented by the white populations of Europe and the United States) are doing other ethnic groups a favor when they run their countries and impose Western culture. In this telling of the story, they are giving "primitive" people the valuable gift of civilization. According to this narrative, white Europeans are sacrificing themselves to make life better for childlike people who can't properly run their own societies.
If this is your outlook, you are going to look down on the people you colonize as inferior. Rather than regard yourself as an invader or exploiter harming the cultures you are in charge of, you will see yourself as a savior of a backward society. Rather than seeing your interference as abusive or damaging, you are likely to expect the people you have power over to be grateful to you for bestowing your superior culture on them.
The attitude is likely to have made people in Europe feel justified in pursuing imperialism and less questioning of it as a possibly immoral or unethical usurping of other nations' sovereignty. It is an attitude that breeds arrogance and makes the imperial power less likely to want to learn from or know about the people it is subjugating. This can be very alienating, breed deep resentments, and lead to destructive blunders and misunderstandings.

In Bud, Not Buddy by Christopher Paul Curtis, does Bud use Rule Number 16 to survive or thrive？

In Chapter 7, Bud is in the library and asks the librarian for Miss Hill. The librarian responds by saying, "Miss Hill? My goodness, hadn't you heard?" (Curtis 55). Bud instantly remembers one of his rules. According to Rule Number 16,

"If a Grown-up Ever Starts a Sentence by Saying "Haven't You Heard," Get Ready, 'Cause What's About to Come Out of Their Mouth Is Gonna Drop You Head first into a Boiling Tragedy" (Curtis 56).

Bud braces himself for some bad news because he associates the statement "haven't you heard" with finding out that somebody has just passed away. He elaborates by saying that not only does the statement imply that someone is dead, but also that the person they are referring to typically died in a tragic, grotesque manner. Bud then tries to prepare himself to receive the tragic news about Miss Hill. Fortunately, the librarian informs Bud that Miss Hill moved to Chicago with her new husband. Rule Number 16 would be classified as a "survival" rule because Bud uses the rule to remind himself to be prepared to receive bad news. Bud realizes that if he can prepare himself to hear tragic news, then he will be able to maintain his composure and protect himself emotionally.

What is the symbolism of the dragon in Beowulf?

As has been mentioned by the other answers, the dragon in Beowulf represents absolute evil. It is greedy (hoarding a trove of gold) and destructive (killing many people). This is the opposite of Beowulf's conduct as a king. Beowulf is generous in sharing wealth with his warriors, and he loves his people enough to put his life on the line to save them, even though he is, at this point in the epic, an old man.
The dragon is also Beowulf's antithesis because it is essentially an antisocial creature. Unlike Beowulf, who is a generous king willing to die to save his people from destruction, the dragon lives alone and only seems to prize its treasure hoard. This quality links the dragon with the other two monsters Beowulf faced in his youth: Grendel and Grendel's mother. Both of those characters were outcasts descended from Cain, who was cursed to wander the earth after murdering his brother, Abel, out of jealousy. However, the dragon is, in a way, worse than Grendel or his mother, since at least those two characters (violent outcasts though they were) had one another as a small family and therefore deserve a little sympathy, even if their actions were evil. The dragon has no sense of community at all, making it even more unsympathetic.
So in the end, the dragon is the ultimate threat to Beowulf's community and represents pure evil.

The dragon in Beowulf symbolizes malice, destruction, and death. In the poem, the dragon is characterized as being malicious. Even the roof of the dragon’s barrow is described as malicious. The destructive and horrific actions of the dragon are evident when it burns the homes of the Geats. The dragon also symbolizes death. In the poem, the dragon kills people and completely razes homes. When Beowulf embarks on a mission to kill the dragon, he dies together with the creature. The fact that Beowulf dies when fighting the dragon symbolizes the inevitability of death (Beowulf's just happened to come in the form of a dragon). Everyone has to die at some point in time, one cannot fight death and emerge victorious—not even Beowulf.

In addition to its avaricious symbolic significance, the dragon is wholly representative of absolute evil.
To explain this, one must consider that the dragon is Beowulf’s ultimate adversary that he must face at the end of the epic. Just prior to Beowulf killing the dragon, the dragon’s lethal venom courses through his veins. Knowing that his death is imminent, Beowulf musters all of his might to kill the dragon, thereby vanquishing evil.
While it is certainly true that the dragon is a miserly beast, its final battle with Beowulf represents the triumph of good over evil. If Beowulf represents good in this situation, then the dragon represents evil.
If one considers the Christian influence on medieval literature, then this final battle is analogous to the triumph of God over Satan in the Christian Bible.

The dragon in Beowulf could be said to symbolize several things, but many readers have noted that it likely symbolizes abstract ideas like greed, hoarding, and destruction. Indeed, the dragon is the opposite of the generous and kind Beowulf, who benevolently gives gifts to his loyal followers and rewards virtue and good actions. The dragon, on the other hand, greedily amasses gold and riches and refuses to share its vast store of wealth. Even worse, the dragon does not use this hoarded wealth in any constructive fashion. Rather, the dragon sits on its hoard and guards it jealously simply because it doesn't want others to have a share in its riches. In this way, it's easy to see how the dragon symbolizes negative qualities in opposition to Beowulf's just and benevolent reign. 
https://public.wsu.edu/~delahoyd/beowulf.monsters.html

Who is Malala Yousafzai?

Malala Yousafzai is acclaimed as the youngest Nobel Peace Price winner. Born on July 12, 1997 in Swat Valley in Pakistani, she is known and celebrated the world over for her efforts in advocating for the right to education for girls in her native Pakistani.
Malala's consciousness and awareness on the issue of gender inequality started from a very young age. The book "I am Malala", tells of Malala's life story. She was born in Swat Valley in Pakistani. Her father was a teacher and ran a girl's school. this gave Malala a good foundation which ultimately led to her finding her calling as an activist.
Despite the traditions of the Pashtun people which celebrated the birth of a son but payed little to no mind to the birth of a daughter, Malala's father Ziauddin Yousafzai strived to give her all the opportunities a boy could have.
In the village which she and her family visited twice a year, Malala witnessed the continued degradation of women. In the village, the women were meant to cook and bear children for their men. Young girls were sold off to elder men who wanted younger wives.
women were also expected to cover their faces and avoid communicating with any men they were not related to. Malala, even as a teenager refused to cover-up to the displeasure of one of her male cousins. Her resolve was strengthened by the fact that her father stood by her decision and did not try to make her conform.
When the Taliban arrived in Pakistani from Afghanistan, there was an aggressive push to close down girls' school and later the girls' madrasas. The girls that kept attending classes were insulted and berated in public and those that left school were applauded and promised heaven.
With her father's support, Malala attended various TV interviews and openly spoke up against the atrocities committed by the Taliban against the girl.
One day in 2012, due to her outspoken nature, Malala was shot in the head by a gunman. She was then flown out of Pakistan to Birmingham, where she was treated and rehabilitated before rejoining her family which had re-located to the United Kingdom.
Due to her advocacy and activism, Malala was nominated for the International Children's peace Prize in 2011, and was awarded the Pakistani's National Youth Peace Prize. In 2013 she was nominated for the Nobel Peace Prize but did not win the same. She was re-nominated for the same in 2014 which she won.
She was also awarded the Sakharov Prize for Freedom of Thought by the European Parliament in 2013, and was appointed the U.N. Messenger of Peace to promote girls education in 2017 for an initial period of two years.
Malala is currently a student at the Oxford University where she is studying philosophy, politics and economics.

Malala is an amazing young woman who is from Pakistan, a country where the Taliban have wreaked havoc with women's rights. She is intelligent, religious, clever, and passionate about equality for women when it comes to their education. She was raised to believe that women deserve to be treated equally to men and was able to get an education in her father's school. From a young age, she became a public figure who openly spoke out about the injustices that the Taliban inflicted on Pakistani women and anyone who spoke against their policies. She became such a threat to the Taliban that they eventually try to kill her by shooting her on a school bus when she was in high school. She survived, moved to England, and continues to do the important work of fighting for women's education. She is an incredible role model of courage and strength for women's equality in education.

Malala Yousafzai is a Nobel Prize laureate for her activism regarding the rights of all children to have access to education. She is twenty years old and was born and grew up in the Swat region of Pakistan. In 2009, at eleven years old, Malala began blogging for the BBC about life in Taliban-controlled Pakistan. In January of 2009, the Taliban declared that girls would no longer be allowed to attend school; this ban was later lifted. Malala went on to appear in a New York Times documentary and was interviewed by multiple local and international news sources. She publicly advocated for female education. In 2011, Malala was the first Pakistani girl nominated for the International Children's Peace Prize. Later that same year, Malala won Pakistan's National Youth Peace Prize. As her public profile increased, she received death threats, and by 2012, the Taliban had decided to kill her. On October 9, 2012, fifteen-year-old Malala was shot in the head by a Taliban gunman on a bus on her way home after taking an exam. Malala was airlifted to Peshawar, where she received multiple surgeries, and a few days later, she was flown to Germany to receive the best medical care possible. The attempted murder received worldwide media coverage and outrage. Since her recovery, Malala has continued to work as an advocate for education, women's rights, and children's rights around the world. She has also published multiple books about her story, including a couple children's books.