y = 2/(x+1) , y=0 , x=0 , x=6 Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis.

For the region bounded by y=2/(x+1) ,y=0 , x=0 and x=6 and revolved about the x-axis, we may apply Disk method. For the Disk method, we consider a perpendicular rectangular strip with the axis of revolution.
As shown on the attached image, the thickness of the rectangular strip is "dx" with a vertical orientation perpendicular to the x-axis (axis  of revolution).
We follow the formula for the Disk method:V = int_a^b A(x) dx  where disk base area is A= pi r^2 with r =y=f(x) .
For the r, we consider the length of the strip= y_(above) - y_(below).
 Then r =f(x)= 2/(x+1)-0
        f(x) = 2/(x+1)
The boundary values of x will be a=0 to b=6 .
Plug-in the f(x) and the boundary values to integral formula, we get: 
V = int_0^6 pi (2/(x+1))^2 dx
V = int_0^6 (4pi)/(x+1)^2 dx
 To solve for the indefinite integral, we may apply u-substitution by using u = x+1 then du =dx .
The integral becomes:
V = int (4pi)/(u^2) du
Apply basic integration property: int c f(x) dx = c int f(x) dx .
V =4pi int 1/u^2 du
Apply Law of exponent: 1/x^n = x^(-n) and Power rule of integration: int x^n dx = x^(n+1)/(n+1)
V =4pi int u^(-2) du
V= 4pi u^((-2+1))/((-2+1))
V=4pi* u^(-1)/(-1)
V=(-4pi)/u
 
Plug-in u=x+1 on V=(-4pi)/u , we get:
V=(-4pi)/(x+1) with boundary values a=0 to b =6 .
Apply definite integration formula: int_a^b f(y) dy= F(b)-F(a) .
V = (-4pi)/(6+1) -(-4pi)/(0+1)
V =(-4pi)/7 +4pi)
V =(24pi)/7 or  10.77  (approximated value)

Which country controlled most of western Africa?

French West Africa existed from 1895 to 1959 and included the areas of modern-day Senegal, Togo, Dahomey, Côte d’Ivoire (the Ivory Coast), Mali, Niger, Guinea, and Mauritania. In the fifteenth century, the Portuguese were the first Europeans to arrive in West Africa, followed by the Dutch, English, and French. The European powers initially traveled along the coast, as they were interested in developing trade ports. As the Transatlantic Slave Trade progressed, slave markets dominated West Africa from the seventeenth through the nineteenth centuries. Other goods such as peanuts and gold increased European activity as well.
As the age of colonialism continued, there was a land grab in Africa leading to the consolidation of French West Africa. 
Due to the abolition of slavery, European interest in West Africa began to decline. However, the European imperial powers would hold on to as many of their colonial territories as they possibly could, even regaining some territories lost during WWII. At this point colonialism had fallen out of fashion, and world leaders encouraged granting independence to colonies. By 1960, all territories of West Africa had gained independence.
https://www.africa.upenn.edu/K-12/French_16178.html

What is the best way to memorize Robert Frost's "The Road Not Taken"?

The best way to memorize a poem is to find key features of the poem's structure that create a pattern to you or stand out to you. These you will remember, so construct your memorization around them.
In Robert Frost's "The Road Not Taken," there are connections of ideas in each stanza; there is a chronological design: 
The speakers sees the two paths [roads] and looks down one of them
The speaker takes the other path because it was grassy and not worn, although they look essentially the same
He keeps the first "road" for another day
He will tell "this" with a sigh
Once you get these ideas in your mind--the main ideas--along with their pattern, you can memorize the first lines of each stanza thoroughly as they will "ignite" your memory of the ones that follow.
If you can easily learn songs, then committing to memory the meter of the poem and its rhyme is a good way to remember it. (Some students memorize the last words of each line, rather than the first.) Reading the poem aloud over and over will assist the "ear" to remember the lines.-OR-Since poems often progress through associative images, you can write down these images and look at the words as you begin to memorize. Sometimes when a student gets "stuck," these images will ignite the memory. Memorizing key phrases helps, also, as they act as connective tissue.
-OR-Memorizing the first letter of each line, or the first word, helps to "jog" the memory sometimes. This is very helpful if students are asked to write the poem from memory, since they can quickly write those letters down, then fill in the poem from the beginning. Often that one letter will jog the memory.________________________________________________
Read the poem aloud several times and practice, practice. Nothing is better than repetition. Hearing it helps, too. As the lines become more familiar to you, say them without looking at the page. Then, see if you can write it without looking at anything.
https://masterofmemory.com/poetry/

What were three effects on family life during World War II?

I will focus on the United States and three significant effects on Americans' family life. The first was the huge mobilization of troops needed to fight a war on two fronts in Europe and Asia. Most able-bodied men under age 38 were either drafted or chose to enlist in the armed forces. This left many young families with absentee fathers. Second, the loss of male workers combined with the need for factories to run nonstop to support the war effort threw masses of women into the workforce. Women earned their own money and had a taste of freedom, but children were often left in daycare or, if older, to fend for themselves. Finally, rationing, which conserved resources for the war effort, left most families with little to buy and, because of gas rationing, few opportunities to travel. Instead, families were encouraged to grow Victory Gardens so more food would be available and to collect tin cans and other resources that could be recycled for the war effort. Families, when they did have leisure time together, were more likely to focus on life's simpler pleasures.

How does Thoreau answer the question implied in the title "Where I Lived and What I Lived For"?

In this chapter of Walden, Thoreau makes explicit his goal in moving to the spartan cabin he constructed on the shore of Walden Pond in the chapter's opening words: "I wished to live deliberately, to front only the essential facts of life."
Thoreau wanted "simplicity, simplicity, simplicity" in his life and so turned temporarily away from life in Concord to live in his cabin for close to two years.  He believed that humanity gets caught up in progress and materialism and loses sight of life's essential meaning.  He asks and then answers the rhetorical question, "Why should we live with such hurry and waste of life," by asserting that "if we respected only what is inevitable and has a right to be, music and poetry would resound along the streets" and "petty fears and petty pleasures are but the shadow of the reality." Thoreau said that to read one news report is to read them all, that most mail he receives is not worth reading, and that the speed of railroad travel is unnecessary if we are content to stay home.  Thoreau felt that materialism and progress really only created artificial wants that people confuse with actual needs.

Provide an analysis of The Phantom of the Opera.

The play version of the Phantom of the Opera is based on a French novel by Gaston Leroux, published in serial format from 1909-1910. The novel is in part based on true stories and myths about events that took place in the Paris Opera. 
Much of the analysis of Leroux's book and the play has been through a psychological lens. Christine, the main character, is asked to turn to the dark side in order to achieve greatness as a singer. She must abandon her regular life and her boyfriend to go to a literal and metaphorical land of seduction and darkness. Christine, who is a Christ-like figure, must sacrifice herself to Erik, who is a devil-like creature who dwells in darkness, to achieve greatness as an artist.
This story is the classical choice between good and evil, and it can be analyzed through the writings of Jung, a psychoanalyst who studied good and evil. Jung believed that evil was one side of the devil and that evil was not separate from humans but something that dwelled within them. People often cast the idea of evil onto others through a process that Jung referred to as casting a shadow. In a Jungian analysis, Christine's association with Erik, the phantom, can be analyzed as her process of casting her own shadow onto Erik. In other words, Christine has both evil and good within her. Her sense of evil comes from her willingness to do anything to become a great singer, while her sense of goodness comes from her love for Raoul, her boyfriend. In the end, by recognizing Erik, the phantom, she becomes whole again and is no longer threatened by him. Instead, Erik lets her go, with a promise that she will return when he dies. The phantom can be seen as an extension of herself and of her own evil desires. 
https://fisherpub.sjfc.edu/cgi/viewcontent.cgi?referer=&httpsredir=1&article=1063&context=nepca

Why did Pip not enjoy the Christmas dinner in Great Expectations by Charles Dickens?

The Christmas dinner is described in Chapter 4 of Great Expectations. Pip does not enjoy it because all of the adults, with the exception of the kindly Joe Gargary, make derogatory comments about him. He tells the reader:

But they wouldn't leave me alone. They seemed to think the opportunity lost, if they failed to point the conversation at me, every now and then, and stick the point into me. 

Unfortunately, there are many adults who make mealtimes unpleasant for children by using these occasions to instruct them on good table manners and other aspects of deportment. The fact that Pip's sister permits and encourages this at the Christmas dinner characterizes her as a woman who aspires to social advancement. This will explain why she attaches so much importance to the fact that Pip has the opportunity to become acquainted with the wealthy Miss Havisham and her adopted daughter Estella. It also explains why Pip's sister is so unhappy about being married to a humble working man like Joe Gargary.
The following excerpts from the dinner-table conversation are examples of the way Pip's sister and her guests displayed their own bad manners by "sticking the points" of their moralizing into Pip.

My sister fixed me with her eye, and said, in a low reproachful voice, “Do you hear that? Be grateful.”


“Especially,” said Mr. Pumblechook, “be grateful, boy, to them which brought you up by hand.”


Mrs. Hubble shook her head, and contemplating me with a mournful presentiment that I should come to no good, asked, “Why is it that the young are never grateful?” 

In addition to suffering under the disapproving scrutiny of all the adults except his good friend Joe, Pip is not delighted with his dinner because his sister serves him the meanest portions.

I was regaled with the scaly tips of the drumsticks of the fowls, and with those obscure corners of pork of which the pig, when living, had had the least reason to be vain. 

Pip also has a guilty conscience because he stole so many things from his sister's larder to give to the convict, as described in Chapter 3, and stole a file from Joe for the same purpose. The poor boy is living in dread of the moment when his sister will discover the pork pie is missing.
It is no wonder that Pip is shy, sensitive, inhibited, and solitary, considering the kind of environment he has to grow up in. He is fortunate to have one good friend in Joe Gargary. Although Joe cannot protect Pip from all the cruel digs he receives during this unhappy Christmas meal, Joe does his best to soften them.

Joe's station and influence were something feebler (if possible) when there was company, than when there was none. But he always aided and comforted me when he could, in some way of his own, and he always did so at dinnertime by giving me gravy, if there were any. There being plenty of gravy to-day, Joe spooned into my plate, at this point, about half a pint.

What is the central theme of A House for Mr. Biswas?

Two central themes of V. S. Naipaul's novel A House for Mr. Biswas are the absurdity of human desire and the diminished scope of the modern Western bourgeois experience.
It is correct to say, as it is often said, that the protagonist's most acute desire is for a home. But Naipaul complicates this desire by repeatedly depicting the crucial—and tragicomic—difference between the desire for a house and the desire for a home. Mr. Biswas desires both, and he keeps trying to find a sense of home by associating that sense with an actual house. But the houses he lives in are all failures. His childhood home, a mud hut, is a space of deprivation and fear. The Tulsi house is characterized by an oppressive tedium that is almost suggestive of death. And the house that he finally obtains for his own family is a pathetic shambles.
The desire for a home can never match up with the desire to own a house. The former is a vast, insatiable longing; the latter can be satisfied, though only in a way that ironically connotes no corresponding sense of satisfaction. The epic longing for home that, in Western literature, is associated with the Homeric Ulysses is, in this novel, anatomized and shown to be a mixture of a bourgeois wish for the pride of possession as well as a deep and moving longing for a place in the world.

One of Mohun Biswas's most cherished dreams is to build a house of his own. Mr. Biswas was raised in a simple mud hut and has since led an itinerant lifestyle, moving around from place to place without ever feeling truly settled. It's not surprising, then, that a home of his own is a very important goal in his life.
Mr. Biswas makes a number of attempts to build his own house, but all end in failure due to extreme weather conditions and fire. It seems as if he will never make his dream come true. But one day, almost on the spur of the moment, he buys a dilapidated old house from a solicitor's clerk. It's not much, but it's a place he can finally call home.
I'd like to suggest that Mr. Biswas's quest for a place of his own is symbolic of his native Trinidad's struggle for independence, which is the main theme of the story. As with all anti-colonial struggles, Mr. Biswas encounters a number of setbacks in his attempts to lead an independent life. And even when he finally does obtain a place of his own, it's quite a rickety old structure, requiring a lot of hard work to make it tolerably habitable. So it was with the independence of Trinidad, or indeed any former colony. Once freedom had finally been achieved, then the hard work really started.

lim_(n->oo) root(3)((n+1)^2) -root(3)((n-1)^2)

Hello!
We'll use an identity a^3 - b^3 = (a - b)(a^2 + ab + b^2) in the form a - b = (a^3 - b^3) /(a^2 + ab + b^2)  for  a = root(3)((n+1)^2)  and  b = root(3)((n-1)^2).
This way we obtain
root(3)((n+1)^2) - root(3)((n-1)^2) = ((n+1)^2 - (n-1)^2) / ((n+1)^(4/3) + (n+1)^(2/3)(n-1)^(2/3)+(n-1)^(4/3)) =
=(4n) /((n+1)^(4/3) +(n+1)^(2/3)(n-1)^(2/3)+(n-1)^(4/3)).
All three terms in the denominator are equivalent to n^(4/3) as n->oo. Therefore the limit is the same as  lim_(n->oo) (4n) / (3n^(4/3)) = lim_(n->oo) (4) / (3n^(1/3))= 0.
This is the answer (zero), and it is true for n->+oo and n->-oo.
To prove that, say,  (n+1)^(4/3)  is equivalent to  n^(4/3),  consider
(n+1)^(4/3) / n^(4/3) = ((n+1)/n)^(4/3) = (1+1/n)^(4/3), which tends to 1 as as n->oo.
 

Read chapter three of The Metamorphosis. What questions arise as you go?

Below you will find my annotations of Chapter Three of The Metamorphosis, including comments and/or questions for each page you asked for:
Page 449: If the apple which has become lodged in Gregor's back makes Gregor's family recall that he is one of them, not an "enemy," and owed "nothing but patience" as a result of duty, why does no one bother to remove the apple for him? This seems like it would be the first and foremost act of "patience" to perform for a family member--to alleviate his pain. 
Page 450: My comment here is that Gregor's father seems to be a greater source of trouble for the family than Gregor himself. His lack of attention to his own hygiene and appearance, his insistence upon falling asleep in his chair, and his theatrics about being helped off to his room seem to make him sound like a giant vermin his own self. 
Page 451: Why does Gregor maintain the meticulous attitudes of his previous human form now that he is an insect/vermin? Wouldn't he naturally adapt to these dirty conditions, as actual insects and vermin do?
Page 452: The text says that the charwoman had a frame which "enabled her to survive the worst a long life could offer" and that she "by no means recoiled from Gregor." What kind of incidences would be so bad in her life that she would not take fright in seeing an enormous insect in a man's room? 
Page 453: My comment here is that it is interesting how Gregor's attention to detail seems to be heightened by his transformation. He notices small things which he might not have before: how the lodgers bend over their food before consuming it, the sound of their teeth while chewing and the implications this has, the presence of the violin-playing, etc.
Page 454: Is it really the artistic satisfaction of hearing beautiful music that Gregor craves, or is it the company of his sister? If it's the latter, why this sudden change when Gregor had just proclaimed his "surprise at his growing lack of consideration for the others"?
Page 455: I find this particular page bizarre. It's clear that the lodgers are manipulating the discovery of Gregor into a situation in which they can financially take advantage of Gregor's family. They don't strike me as the most cleanly or "proper" bunch, which would explain why their initial reaction to seeing him would be fascination rather than disgust. Gregor's sister's impulse to go make their beds and tidy their rooms seems silly given this knowledge; that kind of action isn't going to calm these men down.
Page 456: Gregor's family seems to believe that he can't understand them, although he can. My question for Gregor would be: why don't you make greater efforts to facilitate some sort of communication between you and your family, no matter how difficult or impossible the task seems? 
Page 457: Why does the charwoman manage to "[credit] [Gregor] with every kind of intelligence" when--as I just mentioned--his own family can't recognize him as a thinking, feeling being? 
Page 458: Do any of Gregor's family members experience true grief at his passing? Do they recognize that Gregor had internalized their death wish for him?
Page 459: Another point of interest here to me is the fact that the lodgers are ordered to leave immediately after Gregor's death. It seems like they themselves were a kind of vermin--predatory men looking to profit off the family's unfortunate circumstances by any means necessary. 
Page 460: Why does the conclusion of the novella place such emphasis on Gregor's sister's body and her marriageability?  

What is Jem And Scout's relationship in chapter 1?

Jem and Scout have a relatively typical sibling relationship in chapter 1. Jem is the somewhat authoritative older brother, and Scout tags along with him and their new friend Dill. Scout pays close attention to anything her brother says and believes him wholeheartedly. When Jem gives his fantastic description of Boo Radley, Scout believes Jem and trusts that Boo is actually the creature Jem describes in gruesome detail. Jem views himself as Scout's superior, and she retaliates by making smart comments that contradict her older brother. When Jem tells Dill that he is not scared of the Radley's home, Scout makes sure to include the fact that Jem runs past the Radley home each day. After Dill bets that Jem will not knock on the Radley's door, Jem hesitates and tells Dill that he has a younger sister to think of, which Scout recognizes as a weak excuse. Scout mentions,

When he said that, I knew he was afraid. Jem had his little sister to think of the time I dared him to jump off the top of the house (Lee, 14).

Overall, Jem and Scout are portrayed as typical siblings, who hang out constantly and influence each other significantly. Jem is portrayed as the obvious leader, while Scout is depicted as the younger sister who tags along and follows Jem everywhere.

What was the Church of England like with King Henry VIII in charge?

Henry VIII's religious policy has been described as "Catholicism without the Pope." Though a crude exaggeration, it does contain more than a grain of truth, for Henry was always quite conservative when it came to religion. He distrusted Protestant reformers such as Luther and Calvin, and personally retained many of the old beliefs. At the same time, Henry wanted to divorce Catherine of Aragon and marry his mistress Anne Boleyn. This put him directly at odds with the Pope. As Henry was unable to get his way, he broke from Rome and declared himself head of the Church of England.
For the remainder of Henry's reign, official church policy veered this way and that, depending on changing circumstances. To a large extent, the necessities of foreign policy dictated developments. If Henry needed to ally with Catholic powers in Europe, then life became harder for English evangelicals, many of whom were executed as heretics. On the other hand, if Henry wanted to develop closer relations with Protestant rulers then it was the turn of Catholics to feel the full, crushing weight of state persecution.
In Henry's time, politics and religion were inextricably linked in a manner unthinkable today. With the monarch as its head, the Church of England became an even more overtly political institution than previously, an instrument used by a tyrannical ruler to increase and consolidate his power.

To what extent was propaganda the Third Reich's most powerful tool?

Propaganda can be defined as information of a biased or misleading nature. Over the twelve-year course of the Third Reich, it proved to be a potent weapon in the hands of the Nazi regime. As with any other totalitarian dictatorship the Third Reich imposed a total ban on any independent sources of information. The government only wanted its message to get out; it sought total control over the hearts and minds of the German people and propaganda was a highly effective weapon in achieving this aim.
The Nazis refined propaganda almost to an art form, achieving at times a high degree of sophistication. Reich Propaganda Minister Goebbels was particularly effective in embracing the power of media such as radio, cinema, and newspapers to convey the Nazi creed. Films such as Triumph of the Will were incredibly innovative in their use of cinematic techniques, achieving great critical acclaim despite the unacceptable nature of its message.
At other times, Nazi propaganda could be willfully crude. It largely depended on which particular policy was being pushed at the time. Propaganda against the Jews, for example, showed none of the sophistication or aesthetic worth of Triumph of the Will. It was uniformly vulgar, pandering to the basest instincts of a population increasingly whipped up with anti-Semitic hatred. Although the ostensible message of such propaganda was explicit, its underlying message was more subtle. The Nazis were attempting, little by little, to dehumanize the Jews in order to prepare the German people for a more systematic policy of exclusion and ethnic cleansing.
If nothing else, Nazi propaganda was remarkably adaptable. Despite being a dictatorship, the government of the Third Reich couldn't completely afford to ignore public opinion. For example, the state policy of murdering those deemed physically or mentally disabled was deeply unpopular with the country at large, particularly among practicing Christians. So the Nazis had to tread carefully. And their circumspection was reflected in their propaganda, which refrained from addressing this controversial issue except through the language of scientific advancement.
There can be little doubt that propaganda kept the Nazi regime going longer than it ought to have done. Even when it was obvious that the war was lost and that the so-called "thousand year" Reich would last only twelve, most Germans still displayed a remarkable degree of personal loyalty to Hitler. This, more than anything, shows the cumulative effectiveness of several years of systematic propaganda by the state. The German people had internalized the pernicious Nazi narrative of a pure race fighting for its very existence against the barbarous hordes of Jewish-controlled Communists. Instead of challenging the regime, Germans looked to it to provide security in the face of Allied aggression.
One of the Nazis' main articles of faith was the belief in a complete unity of government and people, Reich and Volk, all fanatically struggling together to fulfill their historic destiny. It was, of course, a complete myth. But thanks to arguably the most sophisticated, innovative propaganda machine in history, that myth contained more of the truth than it really ought to have.
https://encyclopedia.ushmm.org/content/en/article/nazi-propaganda

Why do you think Anna Avalon did not reach out for her husband while he was falling in "The Leap"?

Anna Avalon chose life rather than death as she fell through the air.
Anna always contended that a person can think of many things as he/ she is in the act of falling. As lightning strikes the big top, Anna Avalon realizes she cannot save her tumbling husband. Instead, she turns in the air and twists her body toward the heavily braided wire, saving herself and her unborn child.
Unfortunately, Anna hemorrhages after her fall from the trapeze, and her baby is stillborn. She does regain her health, though, and her broken arm heals well, thanks to the attentive care of her physician, who falls in love with her. They marry, and their only child is the narrator, who declares that her mother's words about being able to think during the brief time that one is falling are absolutely veracious.
Louise Eldrich's narrative soars on its own as the protagonist leaps from one daring act of love to the next, proving the strength and agility of the human spirit that fortifies its existence with the love necessary to make the leap to the next challenge. For, whenever one is in the air "there is always time to think." And, with the impetus of love, there is always time to change the course of one's life.   

In "The Leap," Harry Avalon is killed when a freak bolt of lightning hits the main pole of the tent, causing him to fall to the ground. When describing this tragic accident, the narrator mentions that her mother, Anna, could have possibly saved his life:

"As he swept past her on the wrong side, she could have grasped his ankle, the toe-end of his tights, and gone down clutching him."

But Anna did not do this. Instead, she changed the direction of her body and clung on to a "heavy wire" which burned her hands but enabled her to climb safely to the ground.
As Anna was seven months pregnant at the time of the performance, it is likely that saving her unborn child was her priority. In that split second, she realised that she could not save her husband and her child so she chose the latter, perhaps driven by maternal instinct.
In fact, Anna's desire to protect her children is one of her defining characteristics, as we see later when she rescues the narrator from a burning house. It is, therefore, part of her nature to put the lives of her children before anyone else, even her own husband. 

Who initiates the mending of the wall?

I am going to assume that this question is referring to the Robert Frost poem "Mending Wall."  
The narrator of the poem is the person that initiates the mending of the wall.  When the poem begins, the narrator is contemplating the fact that something exists that simply doesn't want walls to exist.  

Something there is that doesn't love a wall,

The speaker then goes on to give two examples of "something" that repeatedly destroys his wall.  The first thing is the weather.  Alternating freezes and thaws eventually put large gaps in the wall.  The second thing is hunters that tear apart the wall, so their dogs can hunt the rabbits. 

Where they have left not one stone on a stone,
But they would have the rabbit out of hiding,
To please the yelping dogs.

The narrator then brings his reader back to the task at hand.  He is mending the wall; however, the poem says "we."  This lets readers know that the poem's speaker is not the only person present at the wall. 


The gaps I mean,
No one has seen them made or heard them made,
But at spring mending-time we find them there.



The other person is the narrator's neighbor, and the narrator states that he let his neighbor know about the wall needing to be repaired.  The two men meet on a predetermined date and each work on their own side of the wall to mend its broken sections.  


I let my neighbour know beyond the hill;
And on a day we meet to walk the line
And set the wall between us once again.

What is the greatest problem of the present day world?

I think that you mean to ask, "What is the greatest problem of the present-day world?" The answer to this question is a matter of personal opinion, but one that should be based on the issues that are most frequently discussed with concern. People, depending on their nationality, level of education, and other factors, will have varying opinions about the level of importance of the things that impact us the most.
Globally, most people are concerned with the environment, particularly the long-term effects of climate change. This is a global concern because the effects of the warming of the Earth will impact everyone, albeit in different ways. The accelerated melting of ice caps in the Arctic causes rising sea levels, which leads to flooding in low-lying areas. Also, very hot parts of the world, such as the Middle East, North Africa, and Sub-Saharan Africa, will get hotter. When conditions in these regions make them uninhabitable for humans, natives will have to move to northern climes. Once again, we will probably see a backlash against refugees, as well as concerns about overcrowding and the dilution of national culture by foreign influence. Climate change can also lead to food shortages.
Concerns about starvation also exist. In the United States, we talk frequently about "food deserts," communities that lack access to stores with fresh fruits and vegetables and whole grains.
Other global concerns include the rights of minorities and the equal treatment of women and girls. The current "ethnic cleansing" of the Rohingya Muslim minority in Burma is an example of how the rights of minorities are still elusive.

Precalculus, Chapter 7, 7.4, Section 7.4, Problem 46

(x^3+2x^2-x+1)/(x^2+3x-4)
Since the rational expression is an improper expression , we have to express the expression as a sum of simpler fractions with the degree of the polynomial in the numerator less than the degree of the polynomial in the denominator.
Dividing using the long division yields,
(x^3+2x^2-x+1)/(x^2+3x-4)=x-1+(6x-3)/(x^2+3x-4)
Polynomials do not completely divide , so we have to continue with the partial fractions of the remainder expression,
Let's factorize the denominator of the remainder fraction,
x^2+3x-4=x^2+4x-x-4
=x(x+4)-1(x+4)
=(x-1)(x+4)
Let (6x-3)/(x^2+3x-4)=A/(x-1)+B/(x+4)
=(A(x+4)+B(x-1))/((x-1)(x+4))
=(Ax+4A+Bx-B)/((x-1)(x+4))
:.(6x-3)=Ax+4A+Bx-B
6x-3=x(A+B)+4A-B
equating the coefficients of the like terms,
A+B=6 ----- equation 1
4A-B=-3 ------ equation 2
Now we have to solve the above equations to get the solutions of A and B,
Adding the equation 1 and 2 yields,
A+4A=6+(-3)
5A=3
A=3/5
Plug the value of A in equation 1 ,
3/5+B=6
B=6-3/5
B=27/5
(6x-3)/(x^2+3x-4)=3/(5(x-1))+27/(5(x+4))
:.(x^3+2x^2-x+1)/(x^2+3x-4)=x-1+3/(5(x-1))+27/(5(x+4))

What aspects of Gothic literature appear in “Confessions of an English Opium Eater” by Thomas De Quincey? How are these aspects significant to Gothic Literature themes?

"Confessions of an English Opium Eater" is an autobiography, rather than a piece of Gothic fiction, but it certainly contains several aspects that might be more at home in a Gothic novel. De Quincey's lush prose was much criticized as a paean to the very drug he supposedly sought to warn readers away from, and his languid, unfortunate narrator—his fictionalized self—could certainly be compared to the archetypal brooding Gothic hero.
Specifically, Gothic elements in this work include:
1. The landscape as a character. London, in this work, is described lavishly, and presented as somewhere mysterious, dark, and concealing hidden depths where anything can happen. De Quincey's descriptions of London at night foreshadow the urban Gothic of Stephenson and Wilde.
The idea of the hinterland, or borderlands, as part of a landscape is key to Gothic literature. It suggests a blurring of the lines, a place where all things are possible, and creates an aura of mystery. In this work, Oxford Street becomes a "stony-hearted stepmother," a symbol of the underworld in which iniquity thrives. The narrator presents it almost always as it was at night, with the cover of darkness, once again echoing Gothic tropes.
2. The Gothic archetype of the "doomed" woman, cloaked in shadow, almost a ghost as she lives—look at the descriptions of the narrator's "benefactress" in Oxford Street, "one of that unhappy class who subsist upon the wages of prostitution." This woman lives in the shadows, is the narrator's "partner in wretchedness," and yet is presented with a Gothic preoccupation that focuses on the fall of the innocent. A prostitute, she is nevertheless "noble-minded Ann," full of "bounty and compassion" and yet brought low by some sinister element.
3. A fixation on dreams, and the symbolism of dreams. The idea of being "haunted" appears again and again in this work: the narrator refers to his past misdeeds as having "tyrannised over my dreams" and "haunted my sleep." Elsewhere, however, dreams approach the Gothic ideal of the sublime, driven by the power of "mighty opium," which "to the guilty man for one night givest back the hopes of his youth," providing an "oblivion" in which the beauty of a man's thought approaches "Paradise." The Sublime is made possible through the ecstasies of opium, which produce "more than earthly splendour" in the narrator's dreams, but at the same time, "deep-seated anxiety and gloomy melancholy" overcome him. Gothic literature developed hand in hand with advances in psychology, and we often see an interest in what happens in dreams and how this is connected to the events of waking life and the affect of the dreaming character. This work explores this idea in depth, and inspired many others to pursue psychological storylines in their Gothic work.

y' + y/x = 0 , y(2) = 2 Find the particular solution of the differential equation that satisfies the initial condition

Given y'+y/x=0 and find the particular solution at y(2)=2
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'+y/x=0--------(1)
y'+p(x)y=q(x)---------(2)
on comparing both we get,
p(x) = 1/x and q(x)=0
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 (1/x) dx) *(0)) dx +c)/e^(int(1/x) dx)
first we shall solve
e^(int (1/x) dx)=e^(ln(x)) =x     
so
proceeding further, we get
y(x) =((int e^(int (1/x) dx) *(0)) dx +c)/e^(int(1/x) dx)
=(0 +c)/(x)
=c/x
so y(x)=c/x
now let us find the value of c at y(2) =2
so,
y(x)=c/x
=> 2=c/2
=> c=4
so at y(2) =2 the particular solution is y(x) =4/x

Based on their actions in North America, why were Dutch respectful of other cultures?

The Dutch prided themselves in a society of openness.  They usually supported freedom of religion.  They also lived peacefully among those who were different.
When the Dutch established New Netherland in North America, they carried on this culture of acceptance.  The Union of Utrecht provided for freedom of religion, and the laws of this document were followed in New Netherland. 
The purpose of setting up the Dutch colony was a financial one and not one related to Christian evangelism.  This led to a colony that was more secular than other nearby ones.  Jews settled in New Netherland.  The diversity of New Netherland can also be revealed through the languages spoken there.  Over a dozen different languages were spoken in New Netherland.  Many people who were not Dutch settled there peacefully.  Most of the governing bodies in New Netherland allowed others to live there despite cultural differences.  It was a place of overall acceptance.
 
https://www.upenn.edu/pennpress/book/14980.html

What would happen to the memories if Jonas fell in a river and drowned?

As Receiver-in-Training, Jonas is tasked with not just containing all the memories of the community but also all of the emotions. When the novel first opens, the reader is unaware that the community is built on only law and order and practicality; as the story progresses and more is revealed, primarily through interactions the Giver has with Jonas, it becomes clear that the community is sheltered from a true and meaningful life experience. They don't hold painful memories (as the Receiver/Giver hold those for them), but they also do not have memories of love. Families are structured based on their compatibility and everyone agrees to cooperate for the betterment of the community. When Jonas realizes how much the community could be, he really struggles with how they choose to interact with each other, devoid of all emotional connections.
The Receiver cannot die before his memories are transferred to the next Receiver-in-Training (which is a highly selective process) because all the memories that the Receiver holds would be released to the community. Not only would they then know of love, but they would also know of hate and sorrow. The community members have no understanding of these feelings, and it would lead to massive confusion as they all tried to simultaneously process these previously unknown emotions. Nevertheless, Jonas continues pondering the idea of somehow releasing the memories to his community because, as he tells Gabriel, "There could be love" (Chapter 16). This idea continues to gain momentum in his thoughts as the novel nears its end.

In the unfortunate event that Jonas should fall into the river and drown, the community would be able to access the difficult memories Jonas received from the Giver during his training, and chaos would ensue. The Giver explains to Jonas that the community suffered greatly when the previous Receiver of Memory requested release, which is why Jonas is not allowed to request to be released. According to the Giver, when the previous Receiver of Memory requested release, her memories drifted into the atmosphere, where the community had access to them. The painful, difficult memories caused chaos and panic throughout the community because the citizens could not handle the traumatic memories. In Jonas's community, comfort and safety are paramount, and citizens are not exposed to the difficult memories and experiences that Jonas and the Giver understand. Since being released is simply a euphemism for dying, the community would suffer from Jonas's loose memories the same way they suffered when the previous Receiver of Memory was released.

What was the conflict of The Cold Equations?

The conflict of Tom Godwin's short story "The Cold Equations" is that because of a mistake, Marilyn has to die, and Barton has to be the one to send her to her death.
Set in a more scientifically advanced future, Barton is piloting an Emergency Dispatch Ship carrying much-needed medicine to a colony of people that live on another planet called Woden. He discovers that a young woman named Marilyn, naive to the consequences of her actions, snuck onto the ship before takeoff, hoping that she would be able to get to see her older brother Gerry, who is currently working on Woden.
What Marilyn does not know before deciding to stow away on this ship is that it only holds enough fuel to reach its destination with one person inside. If she remains on the ship long enough, it will run out of fuel before it reaches Woden. That would mean not only the death of herself and Barton, but also the people on Woden waiting for the serum that the ship is carrying.
By law, in order to save fuel and save lives, Marilyn must be jettisoned out of the ship and into space, meaning she will die. Barton talks with his Commander to see if there's anything he can do to save her, but its no use. Marilyn goes through a lot of emotions, as would be expected, but she eventually understands that her fate cannot be changed. At the end of the story Marilyn steps into the airlock and says "I'm ready," and Barton has to pull the lever that releases her into space. The last line of the story shows us that Barton will not be getting over the guilt of this death any time soon:

It seemed, almost, that she still sat, small and bewildered and frightened, on the metal box beside him, her words echoing hauntingly clear in the void she had left behind her: I didn’t do anything to die for...I didn’t do anything...

Why is Mrs. Dubose lengthening the sessions each time?

In chapter 11, Jem and Scout walk by Mrs. Henry Lafayette Dubose's home on their way to the store and listen as she begins calling Atticus derogatory names. Jem tries his best to ignore Mrs. Dubose but loses his temper after she calls Atticus a "nigger-lover." On their way home from the store, Jem takes Scout's new baton and proceeds to destroy Mrs. Dubose's camellia bush before he snaps Scout's baton over his knee.
Later that evening, Atticus makes Jem apologize to Mrs. Dubose. When Jem comes home from Mrs. Dubose's home, he tells Atticus that she requested that he read to her for two hours every weekday and Saturday afternoon for an entire month. Atticus ends up making Jem read to Mrs. Dubose daily, and Scout tags along. When Jem first begins reading to Mrs. Dubose, she nods off early into their sessions, and the children have to leave when her alarm goes off. As the month progresses, Mrs. Dubose stays awake for longer periods of time and their reading sessions become longer. Scout says,

"It suddenly came to me that each day we had been staying a little longer at Mrs. Dubose’s, that the alarm clock went off a few minutes later every day, and that she was well into one of her fits by the time it sounded" (Lee, 113).

After Mrs. Dubose passes away, Atticus explains to the children that Mrs. Dubose was addicted to morphine and was determined to conquer her addiction. Jem's reading occupied her mind between morphine doses until she was able to quit using morphine altogether. The reason Mrs. Dubose would lengthen Jem's reading sessions by two minutes each day was to acclimate her body to not using morphine every two hours until she was able to conquer her addiction completely.

Should cloning be used to assist in management of species close to extinction?

As an opinion based question, the answer to this could go either way. It is a debated topic, so there is evidence that supports using clones to bolster dwindling populations, and it is equally supported that using clones should not be done. In my opinion, using cloning in species that are at risk of extinction is a bad idea. It sounds like a viable solution. A species that has dangerously low numbers of individuals could all of a sudden have population numbers that look sustainable. The problem is a genetic diversity one. Cloning does not increase genetic diversity. There is no shuffling of the gene pool. The population might be huge due to cloning; however, the gene pool for breeding is just as small as it always was. All that the cloning did was create a very large population of inbreeding. Inbreeding rarely works out, and a limited gene pool leads to inbreeding. The Florida panther is a good example of how low species numbers forced a species to begin inbreeding. Researchers discovered all kinds of genetic abnormalities such as kinked tails, undescended testicles, and structural heart problems as a result. Creating clones of those few individuals creates a larger population, but the available DNA to mix for future generations stays small, and that is why cloning as a form of species management should be avoided.
https://www.researchgate.net/figure/The-kinked-tail-of-a-Florida-panther-on-the-left-and-an-x-ray-of-a-kinked-tail-on-the_fig4_273968104

What are three negative effects a sewing machine has on the environment?

When considering the environmental impact of a sewing machine, it is unlikely that this common household appliance immediately conjures images of ecological threat. However, the sewing machine plays a leading role in the fashion industry, which, according to a report by the Ellen MacArthur Foundation, is one of the largest sources of pollution in the world. The report suggests that the textile and fashion industries produce more pollution than aviation and international shipping combined.
Also, with the production of sewing machinery projected to exceed $7 billion this year in China alone, the distribution of those machines will have a massive impact on greenhouse gas emissions. The mass production and distribution of sewing machines, both industrial and domestic, also requires tons of packaging material which negatively impacts the environment. Lonely Whale and the Point Break Foundation estimate that by 2025 there will be one ton of plastic for every three tons of fish in the ocean. Even more alarming, the United Nations suggests that by 2050 there will be more plastic than fish.
Modern domestic sewing machines are made from plastics and polymers, which increases affordability. It also increases the likelihood that consumers will replace rather than repair, especially in the case of handheld sewing machines, which are a growing novelty. With sewing machines constituting an increasing proportion of the millions of tons of household appliances which end up in landfills, this also poses a significant environmental concern.
https://www.ellenmacarthurfoundation.org/publications/a-new-textiles-economy-redesigning-fashions-future

https://www.lonelywhale.org/ticktock/

The sewing machine uses electricity. Since electricity can be taken from coal-powered power plants, the use of the sewing machine can indirectly increase greenhouse gases. Sewing machines also allow people to produce more clothes. As clothes wear out, people can throw them away, thus leading to filling landfills. The sewing machine makes clothes easier to obtain and people will think less of patching clothing if they realize that they can have an entirely new garment sewn. An increased demand for inexpensive clothing also leads to an increased demand for fabrics. Mass-produced cotton requires fossil fuels for farm machinery and the chemicals used for cotton can lead to groundwater and soil contamination. There is also the question of an increased number of potentially harmful dyes used in clothing manufacturing. As more clothes are produced, more dyes can potentially seep into the water supply. While the sewing machine might not be the only cause of this, the device does lead to an increase in consumerism and all consumerism ultimately leads to pollution and a strain on Earth's resources.

lim_(x->oo)lnx/x^2 Evaluate the limit, using L’Hôpital’s Rule if necessary.

Given to solve,
lim_(x->oo) lnx/(x^2)
as x->oo then the lnx/(x^2) =oo/oo form
so upon applying the L 'Hopital rule we get the solution as follows,
as for the general equation it is as follows
lim_(x->a) f(x)/g(x) is = 0/0 or (+-oo)/(+-oo) then by using the L'Hopital Rule we get  the solution with the  below form.
lim_(x->a) (f'(x))/(g'(x))
 
so , now evaluating
lim_(x->oo) lnx/(x^2)
= lim_(x->oo) ((lnx)')/((x^2)')
= lim_(x->oo) (1/x)/((2x))
= lim_(x->oo) (1/(2x^2))
upon plugging inx= oo  , we get
= (1/(2(oo)^2))
= 1/oo = 0

Is the life lesson to listen to your elders?

Yes, to a certain degree. At the beginning of The Devil's Arithmetic, before she is taken back in time, it is made very clear that young Hannah does not understand what her older family members went through as Jews during the Holocaust. She is embarrassed by their behavior, especially her Grandfather's, and wishes that they would forget the past.
When Hannah returns to the present after her journey through the past, having lived as a prisoner in a concentration camp, she now fully and completely understands why her family cannot forget and does not want to forget the Holocaust.
So yes, one could interpret the "life lesson" of The Devil's Arithmetic to be "listen to your elders," but I believe this lesson works in combination with another: Don't judge a man until you've walked a mile in his shoes. As a child who had never before known what it meant to suffer, Hannah found it easy to judge her family and be embarrassed by them. When she suffered as they had, Hannah knew that she had been wrong to feel this way, and cherishes her family in a way that probably would not have been possible beforehand.

Single Variable Calculus, Chapter 7, 7.2-2, Section 7.2-2, Problem 62

Find the derivative of $\displaystyle y = \sqrt[4]{\frac{x^2 + 1}{x^2 - 1}}$ by using logarithmic differentiation.

By taking logarithms of both sides..

$\displaystyle \ln y = \ln \sqrt[4]{\frac{x^2 + 1}{x^2 - 1}}$

If we apply the Laws of logarithm, we have


$
\begin{equation}
\begin{aligned}

& \ln y = \frac{1}{4} \ln \frac{x^2 + 1}{x^2 - 1}
&& \text{recall that } \ln x^k = k \ln x
\\
\\
& \ln y = \frac{1}{4} [\ln (x^2 + 1) - \ln (x^2 - 1)]
&& \text{recall that } \ln \frac{x}{y} = \ln x - \ln y
\\
\\
& \ln y = \frac{1}{4} [\ln (x^2 + 1) - \ln (x - 1)(x + 1)]
\\
\\
& \ln y = \frac{1}{4} [\ln (x^2 + 1) - (\ln (x -1) + \ln (x + 1))]
\\
\\
& \ln y = \frac{1}{4} \ln (x^2 + 1) - \frac{1}{4} \ln (x - 1) - \frac{1}{4} \ln (x + 1)


\end{aligned}
\end{equation}
$


By taking the derivative implicitly, we have..


$
\begin{equation}
\begin{aligned}

& \frac{\displaystyle \frac{d}{dx} (y) }{y} = \frac{1}{4} \left( \frac{\displaystyle \frac{d}{dx} (x^2 + 1)}{x^2 + 1} \right) - \frac{1}{4} \left( \frac{\displaystyle \frac{d}{dx} (x - 1)}{x - 1} \right) - \frac{1}{4} \left( \frac{\displaystyle \frac{d}{dx} (x + 1)}{x + 1} \right)
\\
\\
& \frac{\displaystyle \frac{dy}{dx}}{y} = \frac{1}{4} \left( \frac{2x}{x^2 + 1} \right) - \frac{1}{4} \left( \frac{1}{x - 1} \right) - \frac{1}{4} \left( \frac{1}{x + 1} \right)
\\
\\
& \frac{dy}{dx} = \frac{y}{4} \left( \frac{2x}{x^2 + 1} - \frac{1}{x - 1} - \frac{1}{x + 1} \right)
\\
\\
& \frac{dy}{dx} = \frac{\displaystyle \sqrt[4]{\frac{x^2 + 1}{x^2 - 1}}}{4} \left( \frac{2x}{x^2 + 1} - \frac{1}{x - 1} - \frac{1}{x + 1} \right)



\end{aligned}
\end{equation}
$

Do you think the hyperbole in Plath's "Daddy" about Hitler and Dracula is justifiable?

The confessional nature of Plath's "Daddy" makes the use of powerful imagery justifiable.
Plath writes "Daddy" from a confessional frame of reference. The interactions Plath had with her father had a profound impact on her identity. They were difficult to understand, and her poetry is a way for her to make sense of it.
Plath sees her father as dominating. She feels he denied her voice and expression. He was a "black shoe" in which Plath "lived like a a foot," afraid to "breathe" or sneeze. Plath writes how she had "always been scared" of her father. Her trepidation in communicating with him is seen in lines such as "the tongue stuck in my jaw." It conveys the fear that prevented a daughter from being able to speak to her father.
The use of "Hitler" communicates this emotional dynamic. Plath compares herself to someone who is Jewish living at the time of concentration camps. In likening herself to a Nazi victim, Plath conveys the extent to which her father denied her voice. He "killed" off a part of her identity. Plath's father made her believe she "may well be a Jew." Plath's argument that her father robbed a portion of her identity makes the Hitler comparison fitting, if extreme. What Hitler did on a political level to millions of people is what Plath feels her father did to her on a personal level.
Plath feels her father took something from her. He took her happiness. His dominance over her was similar to how Dracula wielded power over his victims. Both malevolent forces take the lifeblood of their victims. Her call to drive a "stake in your fat black heart" reflects how Plath wants to restore power. Just as Dracula has to be killed to make people feel safe, Plath believes she must do the same to her "vampire" of a father. In "Daddy," the relationship between Plath and her father makes the images of Dracula and Hitler highly effective.

log_4(-x)+log_4(x+10)=2 Solve the equation. Check for extraneous solutions.

To evaluate the given equation log_4(-x)+log_4(x+10)=2 , we may apply the logarithm property: log_b(x)+log_b(y)=log_b(x*y) .
log_4(-x)+log_4(x+10)=2
log_4((-x)*(x+10))=2
log_4(-x^2-10x)=2
To get rid of the "log" function, we may apply the logarithm property: b^(log_b(x))=x.
Raise both sides by base of 4 .
4^(log_4(-x^2-10x))=4^2
-x^2-10x=16
Add x^2 and 10x on both sides of the equation to simplify in standard form: ax^2+bx+c= 0.
-x^2-10x+x^2+10x=16+x^2+10x
0=16+x^2+10x orx^2+10x+16=0.
Apply factoring on the trinomial.
(x+2)(x+8)=0
Apply zero-factor property to solve for x by equating each factor to 0 .
x+2=0
x+2-2=0-2
x=-2
and
x+8=0
 x+8-8=0-8 
x=-8
Checking: Plug-in each x on log_4(-x)+log_4(x+10)=2 .
Let x=-2 on  log_4(-x)+log_4(x+10)=2 .
log_4(-(-2))+log_4(-2+10)=?2
log_4(2)+log_4(8)=?2
log_4(2*8)=?2
log_4(16)=?2
log_4(4^2)=?2
2log_4(4)=?2
2*1=?2
2=2        TRUE
Let x=-8 on log_4(-x)+log_4(x+10)=2.
log_4(-(-8))+log_4(-8+10)=?2
log_4(8)+log_4(2)=?2
log_4(8*2)=?2
log_4(16)=?2
2=2        TRUE
Therefore, there are no extraneous solutions.
Both solved x-values: x=-2 and x=-8 are real solution of the equation log_4(-x)+log_4(x+10)=2 .

Calculus and Its Applications, Chapter 1, 1.6, Section 1.6, Problem 4

Take the derivative of $g(x) = (3x - 2)(4x + 1)$: first, use the Product Rule; then,
by multiplying the expression before differentiating. Compare your results as a check.

By using Product Rule,

$
\begin{equation}
\begin{aligned}
g'(x) = \frac{d}{dx} \left[ (3x - 2)(4x + 1) \right] &= (3x - 2) \cdot \frac{d}{dx} (4x + 1) + (4x + 1) \cdot \frac{d}{dx} (3x - 2)\\
\\
&= (3x - 2)(4) + (4x + 1)(3)\\
\\
&= 12x - 8 + 12x + 3\\
\\
&= 24x - 5
\end{aligned}
\end{equation}
$


By multiplying the expression first,

$
\begin{equation}
\begin{aligned}
g(x) &= (3x - 2)(4x + 1) = 12x^2 + 3x - 8x - 2 = 12x^2 - 5x - 2\\
\\
g'(x) &= \frac{d}{dx} \left[ 12x^2 - 5x - 2 \right] = 24x - 5
\end{aligned}
\end{equation}
$


Both results agree.

Single Variable Calculus, Chapter 3, 3.2, Section 3.2, Problem 31

The table below represents the unemployment rate $U(t)$ in percent of the US labor force from 1993 to 2002.



$
\begin{array}{|c|c|c|c|c|}
\hline\\
t & U(t) & & t & U(t)\\
\hline\\
1993 & 6.9 && 1998 & 4.5\\
1994 & 6.1 && 1999 & 4.2\\
1995 & 5.6 && 2000 & 4.0\\
1996 & 5.4 && 2001 & 4.7\\
1997 & 4.9 && 2002 & 5.8\\
\hline
\end{array}
$



a.) State what is the meaning of $U'(t)$ and its corresponding units.



b.) Contruct a table of values for $U'(t)$


$\quad$ a.) The meaning of $U'(t)$ is the rate at which the percentage of the unemployed varies with
respect to time. Its unit is $\displaystyle \frac{\text{percent}}{\text{year}}$.

$\quad$ b.) Using the formula $\displaystyle U'(t) = \frac{U(t+h)-U(t)}{h}$ where $h$ is 1.


$
\quad
\begin{array}{|c|c|}
\hline\\
t & U'(t)\\
\hline\\
1993 & -0.8 \\
1994 & -0.5\\
1995 & -0.2\\
1996 & -0.5\\
1997 & -0.4\\
1998 & -0.3\\
1999 & -0.2\\
2000 & 0.7\\
2001 & 1.10\\
2002 & 0\\
\hline
\end{array}
\qquad
\begin{equation}
\begin{aligned}
U'(1993) &= \frac{U(1994)-U(1993)}{1}\\
U'(1993) &= \frac{6.1-6.9}{1}\\
U'(1993) &= -0.8 \frac{\text{percent}}{\text{year}}
\end{aligned}
\end{equation}
$

Did Lewis and Clark achieve their goals? What were the lasting effects of their work?

The goals of the Lewis and Clark expedition were to explore and map the new territory gained by the United States with the Louisiana Purchase, establish ties with the native peoples of the region, and catalog the plants and animals there. In all three respects, the expedition can be considered a success.
The Lewis and Clark expedition produced some 140 maps of the region between the Mississippi River and the Pacific Northwest. They accurately charted the course of the Missouri and Columbia Rivers as well as a significant portion of the Rocky Mountains. They found and mapped a reasonable route to the Pacific Coast. All this information was unknown to Americans previously. As a result, Americans could now begin confidently moving into the territory to establish their own presence before other European powers could.
Most of the encounters that the expedition had with Native Americans were peaceful. They encountered many different tribes that provided them with assistance and provisions throughout their journey. While relations between the United States and many of these tribes would, to put it mildly, become strained in future generations, these early encounters did much to foster goodwill. Trade agreements were established with some of these tribes as well. Much was learned about these peoples through the expedition. Lewis and Clark returned with many Native American artifacts, such as bows and cloth, that they had traded for.
Lewis and Clark brought with them a number of books with blank pages. They used these to record their observations of many plants and animals that were previously unknown to Europeans. They also returned with a number of unknown animal pelts, plant samples, and seeds.
As a result of the Lewis and Clark expedition, the United States had a decent idea of what the territory included. They had solidified American claims to the land. They had found a route to the Pacific that other travelers could use. They established trading ties with Native Americans and had cataloged many new species of flora and fauna. Perhaps most importantly, Lewis and Clark brought back information that sparked the imagination of many Americans in the east, who then chose to explore and settle the land themselves.
https://oregonencyclopedia.org/articles/lewis_and_clark_expedition/

Was Nat ever becalmed?

In Carry On, Mr. Bowditch, the word "becalmed" refers to a ship without wind in the sails and which therefore cannot move. Nat's toiling away as an apprentice chandler when he hears the phrase being used disparagingly of him by a regular visitor to the store, a certain Ben Meeker:

"Nat Bowditch, eh? I've heard of you. Master Watson's brightest student you were." He shook his head dolefully. "And now you're becalmed . . ."

Ben uses the term as a not-so-subtle way of reminding Nat that he's going nowhere in life; he's like a ship that doesn't move. In one sense, he's right. Nat is a bright, highly-motivated boy who's keen to be successful, but he doesn't seem to be able to find a way to move on, to make his dreams come true. On the other hand, Ben's comment seems a tad unfair, as Nat has already overcome a lot of sadness and adversity in his life. He's also using his apprenticeship as an opportunity to improve himself, acquiring new knowledge in the process.
Sam Smith's more encouraging. He tells Nat that when a ship is becalmed, a strong man sails by "ash breeze." This means that when a ship stops moving, the sailors get out the oars (made of white ash) and start rowing. Sam clearly uses this as a metaphor for someone working hard to get on in life when the chips are down. Or, as we might say today, "When the going gets tough, the tough get going."
And that is precisely what Nat proceeds to do. But is it fair to say that he was "becalmed" before then? Perhaps just a little. But, to extend the sailing metaphor, he always had the inner drive and determination to "sail by ash breeze," so there was never a chance that he would remain "becalmed" for very long.

Who is Emerson's intended audience in "Self-Reliance"?

Emerson's essay is aimed at young men--and we must emphasize men--graduating from college or in other ways about to embark on a life of opportunity. In other words, he writes to persuade privileged white American males like himself.
Emerson, like all of us, has blind spots because of the times in which he lived. While he was a strong abolitionist, for example, he did carry with him the racism of his time period, once likening blacks to animals ("elephants") and seeing them as having less reasoning capacity than whites. While he did embrace women intellectuals, such as Margaret Fuller, and would have wanted women to develop their God-given destinies, the use of pronouns and the assumption that his readers are deciding on a career (at a time when the vast majority of white women were homemakers) shows he was visualizing a male audience.
He assumes that his audience has the privilege of making choices about vocation and that their struggle is with the temptation of abandoning their destinies in order to conform to society and earn its rewards of wealth, honor, and power. Many people would not have this kind of choice to pick one path or another, but Emerson is not speaking to them.

In his day, Ralph Waldo Emerson was something like a rock star. Crowds came to listen to his lectures. Young people hearkened to his message that American society was on the verge of a new age; intellectuals responded to his philosophical ideas, and society in general responded to his optimism.
His essay "Self-Reliance" and its appeal to the young people was effected by his arguments that they were on the verge of a new age. In addition, many responded to his optimism and philosophical ideas, ideas about the relationships of humanity, nature, and God. Also popular was his belief that

[N]o government or church can explain a man’s heart to him, and so each individual must resist institutional authority.

Further, Emerson appealed to young people because he advocated acting from impulses, rather than rules, contending that the "self-reliant will triumph over the tyranny of time." This idea of trusting one's instincts and believing in one's unique talents and passions greatly appealed to many, especially the young, who felt that the nation—also young—was headed for greatness.

Why is acid rain unevenly distributed across the world?

Acid rain is unevenly distributed around the world, and even across some countries, because this weather pattern is highly dependent upon environmental conditions. 
As an overriding factor, parts of the world where rain generally does not fall (such as deserts or the poles) are not likely to experience acid rain. More importantly, acid rain is a result of the environmental concentration of sulfur dioxide and nitrogen oxide. When these emissions are circulating in the air, they react with water and oxygen to create acids. Sulfur dioxide and nitrogen oxide do occur naturally as a result of, respectively, volcanic eruptions and lightning strikes. Human activity and industrialization produce relatively large amounts of these emissions and contribute to greater concentrations of these basic ingredients for acid rain. 
Most of these emissions released into the environment are the result of burning fossil fuels for energy. In areas where many cars burn gasoline or factories use fossil fuels, there are likely to be higher environmental concentrations of sulfur dioxide and nitrogen oxide. These emissions alone aren't necessarily enough to cause acid rain; there must also be sufficient humidity in the air. When acid rain does fall, it isn't always right on top of the people and machines who provided the ingredients. Winds may push acid rain clouds far away from their point of origin, causing trouble for people who may not have contributed to the formation of acid rain at all.
https://www.britannica.com/science/acid-rain

https://www.epa.gov/acidrain/what-acid-rain

How did the movement West affect our nation?

This is a big question with many possible answers ranging from the impact of westward expansion on American politics to the influence of it on modern day pop culture.  Here is a look at some of the big picture implications of westward expansion.
1. The move West was a catalyst for the Civil War.  The Civil War likely would have happened sooner or later anyway but the addition of western states and territories escalated tensions.  Both abolitionists and pro-slavery groups wanted to bolster their numbers and eventually get more votes for their side in Congress by claiming the new Western areas as either free or slave territories.  While many compromises, including the Mason-Dixon line, attempted to keep things evenly balanced, there was always a new frontier to be contested.  While politicians on both sides might have been content if the opposing side could be limited geographically, both sides also could see the potential for the new western areas to tip the balance of power to one side or the other.  The Kansas-Nebraska Act in 1854 allowed settlers in new territories to make their own choice regarding slavery.  In response both sides sent people to Kansas hoping to influence policy one way or the other.  They elected two conflicting territorial governments and started a violent conflict known as "Bleeding Kansas".  While many western territories did not experience the same outright violence over slavery as Kansas did, the status of western territories in regards to slavery continued to be a question of great political weight and conflict.
2. The move of European settlers through the Western United States led to the genocide and forced removal of Native American tribes.  Conflicts between Native Americans and Europeans had been a constant since European colonization of the United States began.  In the West, however, the United States government adopted policies intent on the eradication of Native American peoples.  One of these policies was the wide-scale hunting of bison.  Buffalo served as a primary food source for Native Americans living on the Great Plains.  Without the herds of buffalo, many tribes were driven by starvation to accept resettlement on government reservations.  Through armed conflict, forced resettlement, and the introduction of new diseases not only did many Native Americans lose their lives, but also their culture, language, and religion.  In the 1960's and 70's the American Indian Movement or AIM staged a series of protests and occupied various locations in an attempt to force the government to address the continuing repercussions of European settlement.  In 2008 AIM staged a walk from San Francisco to Washington DC to again bring attention to these issues.  The actions taken against Native Americans during westward expansion are likely to continue to impact the country's future.
3. The resources of the West were the basis of the fortunes of many influential men throughout history.  Mining concerns, railroads, and the fur trade were the basis of wealth for many.  John Jacob Astor made much of his money in the fur trade and later established the New York Public Library.  The Astor family dominated New York social circles and the family name even inspired the naming of the neighborhood of Astoria.  George Hearst became wealthy through several mining ventures throughout the West.  He served as a senator in California and his son, William Randolph Hearst, would go on to revolutionize American journalism.  Leland Stanford earned his wealth as a merchant in the California gold rush and then later became president of the Southern Pacific Railroad.  Stanford would eventually establish Stanford University.  These are just a few examples of the economic impact of western resources.  Wealth accumulated in the West would have far-reaching consequences for the nation as a whole.

What's Euripides's view on religion?

Euripides's view of religion is considerably more nuanced than that of many of his fellow Athenians. For one thing, he displays a fair degree of skepticism throughout his works, not just in relation to the gods, but towards certain key elements of ancient Greek religion. The notion of blind faith, though common at the time, is not one that appears to be shared by Euripides. Nor would it seem that he has much time for soothsayers and prophets, whose words were treated by the ancient Greeks with such astonishing reverence.
Yet it is the gods of Olympus who are the main target of Euripides's withering skepticism. With good reason, Samuel Taylor Coleridge described Euripides as never being more happy than when he was administering a great slap to all the gods. His portrayal of them is less than flattering, to say the least. They are greedy, lustful, treacherous, and vain, treating men like mere playthings as part of a gigantic cosmic game whose rules have been rigged to favor the immortals. In Ion, the lead character chastises the gods for their shameless double-dealing and hypocrisy:

How is it then just that you, who gave the laws to mortals, should yourselves transgress those laws?

Euripides does not call into question the existence of the gods as such. He does, however, question whether they deserve to be worshiped, given their appalling behavior. Implicit in Ion's lament is the assumption that gods ought to lead by example if they are to earn the respect, as opposed to fear, of those who worship them.
In Herakles Euripides allows Amphitryon to voice an even more bitter condemnation of the gods and their destructive impact on mortal man:

Even I, though but a mortal, surpass thee in virtue. I have not betrayed the sons of Hercules. As for thee, thou knewest how to steal in secret to the bed of another's wife, but to save thy friends thou knowest not. A feeble god, or a treacherous, art thou.

Even more boldly, Hercules implies that a god who doesn't behave in a morally exemplary manner isn't really a god at all:

Never will I believe, that the gods pursue unlawful loves, or that they throw their kindred into bonds, or that one is master of the other. God, if he be a true god, has need of nothing. These are but the pitiful fables of poets.

Yet that is precisely how the gods do behave in Greek mythology, time and time again. The gods are being measured against human standards and found wanting, not just in relation to their morals, but even their very status as immortals.
Having said that, Euripides, like the philosopher Plato, understands the overriding value of public religion for the good order and long-term stability of Athens. But it's the nature of that religion, its rites, beliefs, and practices, which is of cardinal importance for Euripides. And it is here that he shows a consistent hostility to the various elements of superstition, folklore, and myth that have accrued to the city-state's religious life over the course of time.
Euripides harbors a particular animus towards oracles, seers and soothsayers of various kinds. His motives would appear to be political. Athens' defeat in the Peloponnesian War led to a huge backlash against the use of divination to determine the timing and conduct of military expeditions. In common with many of his fellow Athenians, Euripides came to see the whole rich panoply of superstitions as tending to the destruction of the polis. Once again, Euripides appears to suggest that humans must look to themselves to determine what ought to be done, instead of wasting their time consulting oracles or worshiping unworthy, amoral deities. A classic statement of this proto-humanistic concept is provided in Helen:

False and worthless are the utterances of soothsayers, nor is wisdom to be found in flames of fire, or in the voices of the feathered tribe. 'Tis folly to hope that birds can bring benefit to mortal men.... Let us rather, at our sacrifices, beseech the gods to send us blessings, and let us pay no heed to oracles.... Wisdom and prudence are the wisest soothsayers.

As we said at the outset, however, Euripides's approach to religion is nuanced. His skepticism, though significant, is far from destructive. Indeed, in plays such as The Bacchae and Hippolytus Euripides appears keen to highlight the folly of intellectual pride and of turning one's back on established religious norms. In The Bacchae, for instance, King Penteus's skepticism regarding the propriety of Dionysiac ritual leads directly to his own gruesome death.
In his famous comedy The Frogs, Aristophanes has a lot of fun at the expense of Euripides, as he does with all the great Athenian tragedians. He satirizes him as someone who abuses his undoubted gifts as a dramatist to try and convince the people that there are no gods. Yet this is no more than a comic exaggeration. There's no evidence to suggest that Euripides denied the gods' existence. If he seriously had, then his plays would simply not have been staged in the first place.
However, there can be no doubt that Euripides encouraged his fellow Athenians to examine more closely the nature of their beliefs, while at the same time maintaining an appropriate degree of respect for the established religious rites and practices, even if only from a utilitarian perspective. Fables, myths, and stories may not literally be true, suggests Euripides, but they do still serve an important purpose, nonetheless. If they conduce to the well-being and stability of the city-state, all well and good. If they do not, however, then they must be exposed to contempt and ridicule in the hope that they will be purged altogether. In other words, for Athenian public religion to be preserved and maintained it is necessary for it to develop a more questioning, self-critical edge. And it is that which Euripides, more than any of the great tragedians of antiquity, provides in abundance.

What was their most profitable venture

Buddy and his friend made money in a variety of ways: selling berries, selling jars of homemade preserves, hosting rummage sales, picking bouquets to sell for weddings and funerals, and by making fruit cakes to sell during the holidays. Although most of these ventures resulted in them earning little more than spare change, the two managed to garner some larger amounts by winning contests. Their most profitable venture, however, occurred the summer two years prior to the story’s start, when the two turned an empty woodshed in the backyard into a Fun and Freak Museum. After paying a modest admission fee, attendees could view slides of major cities using a hand-held device and then, behold the venue’s freakish live attraction: a three-legged chicken. Although Buddy and his friend charged only two cents for children and a nickel for adults, their attraction was an enormous success, earning about twenty dollars in revenue that summer. Unfortunately, their Fun and Freak Museum's success died with the demise of the biddy hen.

Beginning Algebra With Applications, Chapter 5, 5.4, Section 5.4, Problem 48

Determine the equation of the line through the points whose coordinates are $(-6,19)$ and $(2,7)$.

Using the Slope Formula with $(x_1, y_1) = (-6,19)$ and $(x_2, y_2) = (2,7)$

$\displaystyle m = \frac{7-19}{2-(-6)} = \frac{-12}{8} = \frac{-3}{2}$

The slope of the line is $\displaystyle \frac{-3}{2}$.

Using the point slope formula with $\displaystyle m = \frac{-3}{2}$ and $(x_1, y_1) = (-6,19)$


$
\begin{equation}
\begin{aligned}

y - y_1 =& m(x - x_1)
&&
\\
y - 19 =& \frac{-3}{2} [x- (-6)]
&& \text{Substitute } m = \frac{-3}{2}, (x_1, y_1) = (-6,19)
\\
y-19 =& \frac{-3}{2}x - 9
&& \text{Apply Distributive Property}
\\
y =& \frac{-3}{2}x + 10
&& \text{Write the slope-intercept form}

\end{aligned}
\end{equation}
$

arcsinx + arcsiny = pi/2 , (sqrt(2)/2, sqrt(2)/2) Use implicit differentiation to find an equation of the tangent line at the given point

arcsin(x) +arcsin(y) = pi/2
First, take the derivative of both sides of the equation using implicit differentiation.
d/dx[arcsin(x) + arcsin(y)] = d/dx (pi/2)
d/dx[arcsin(x)] + d/dx[arcsin(y)]=d/dx(pi/2)
Take note that the derivative formula of arcsine is
d/dx[arcsin(u)] = 1/sqrt(1-u^2)*(du)/dx
And the derivative of a constant is zero.
d/dx(c) = 0
Applying these two formulas, the equation becomes
1/sqrt(1-x^2) *d/dx(x) + 1/sqrt(1-y^2)*d/dx(y) = 0
1/sqrt(1-x^2) *1 + 1/sqrt(1-y^2)*(dy)/dx=0
1/sqrt(1-x^2) + 1/sqrt(1-y^2)*(dy)/dx = 0
Then, isolate (dy)/dx .
1/sqrt(1-y^2)*(dy)/dx = -1/sqrt(1-x^2)
(dy)/dx = -1/sqrt(1-x^2)*sqrt(1-y^2)/1
(dy)/dx = -sqrt(1-y^2)/sqrt(1-x^2)
Then, plug-in the given point to get the slope of the curve on that point.  The given point is (sqrt2/2,sqrt2/2) .
(dy)/dx = -sqrt(1- (sqrt2/2)^2)/sqrt(1-(sqrt2/2)^2)=-1
Take note that the slope of a curve at point (x,y) is the slope of the line tangent to that point.  Hence, the slope of the tangent line is
m = (dy)/(dx) = -1
Now that the slope of line that is tangent to the graph of function at (sqrt2/2,sqrt2/2) is known, apply the point-slope form to get the equation of the line.
y-y_1 = m(x- x_1)
Plugging in the values, it becomes
y - sqrt2/2=-1(x - sqrt2/2)
y-sqrt2/2=-x + sqrt2/2
y = -x+sqrt2/2+sqrt2/2
y = -x + (2sqrt2)/2
y = -x + sqrt2
 
Therefore, the equation of the tangent line is y = -x + sqrt2 .

Why is Mrs. Jensen contemptuous of men?

In the book, Mrs. Jensen is Lorraine's mother. She's a private nurse and often works the night shift. Her patients are usually elderly and terminally ill. Lorraine and her mother have a difficult relationship, as Mrs. Jensen is a deeply unhappy woman. According to Lorraine, her father left them fifteen years ago when his parents got a legal separation. Since Lorraine's father is now deceased, Lorraine states that the separation between her parents is permanent.
Mrs. Jensen has a great distrust of men due to her husband's actions during their marriage. Accordingly, he had contracted a venereal disease while she was pregnant with Lorraine. She discovered his illness when the doctor called and warned her not to engage in any sexual intimacy with her husband until he was cured. When Mrs. Jensen found out that her husband had actually cheated on her, she filed for a legal separation. According to Lorraine, this is the main reason that her mother is contemptuous of men. Mrs. Jensen equates all men with her faithless husband; she sincerely believes that all men are untrustworthy and that they are only interested in sex.
Because of her hangups about men, Mrs. Jensen is always warning Lorraine about boys. She tells Lorraine not to get into a car with any boy and warns her that men "have dirty minds, and they’re only after one thing." Lorraine imagines that a good psychiatrist would be able to help her mother, but she concludes that her mother's problems are so "deep-rooted she’d need three years of intensive psychoanalysis" just to see some results.

The bulk density of a soil is 1.33g/cm cubed. What is its bulk density in kg/m cubed?

This is a problem of converting units. I prefer to do these with fractions. I first set up the unit I am starting with, and write the unit I want to get to.
(1.33g)/(1cm^3) ......   [kg]/m^3
Then, I multiply by fractions that cancel out the current units and get me to the units I need. For this example, I will start with the units of grams to kilograms.
[1.33g]/[1cm^3]*[1kg]/[1000g] .....    [kg]/m^3
I now have grams on the top and bottom, so they cancel, and because there are 1000 grams in a kilogram, I divided by 1000. Next, I convert the units of cm^3 to m^3. Because these are cubed, I will expand the numbers, just to be sure.
[1.33g]/[1cm*1cm*1cm]*[1kg]/[1000g]*[100cm*100cm*100cm]/[1m*1m*1m]  ......     [kg]/[m^3]
Each of the units will cancel out, leaving behind just the kg and m^3. All that is left is to do the math, giving you 1330[kg]/[m^3] .

How can I compare and contrast the images, tone, and themes of the poems "My Last Duchess" by Robert Browning and "Richard Cory" by Edwin Arlington Robinson?

"My Last Duchess" is a dramatic monologue spoken in first person by the Duke; "Richard Cory" is a ballad narrated in first person by a citizen who knew Cory from a distance. The poems have much in common but have many differences as well.
The images in "My Last Duchess" center around artwork, specifically the painting of the Duke's former duchess and a sculpture of Neptune. The woman is objectified by these images, as well as the association with other objects such as her "white mule" and a "bough of cherries." Similarly, Richard Cory is objectified by the townspeople by his clothing and his glittering appearance. Both the Duchess and Cory spoke with kindness to others; the Duke reacted negatively, but the townspeople responded positively. "Richard Cory" contains images of poverty and hardship among the lower class citizens; "My Last Duchess" has only images consistent with upper-class life.
The tone of each piece is quite distinct from the other. The tone of "Richard Cory" is measured, calm, and somewhat detached. The tone of "My Last Duchess" is somewhat manic and unpredictable as the Duke vacillates among the emotions of pride, irritation, rage, and desire to please. However, there is some similarity in tone in that the narrator of each poem is primarily focused selfishly on himself rather than being overly saddened by the passing of the person being discussed. A feeling of jealousy also pervades each poem.
The themes of the poems are similar in that both contemplate the effects of jealousy. In "Richard Cory," the jealousy of the townspeople may have resulted in Cory feeling increasingly alienated, which may have furthered the depression that perhaps led to his suicide. In "My Last Duchess," the Duke's jealousy leads him, presumably, to having his wife killed. Thus both poems show the destructive power of jealousy. Another strong theme in both poems is that money can't buy happiness. Cory was so unhappy that he ended his life, despite being "richer than a king." The Duke has immense wealth from being at the highest level of aristocracy, yet he allows himself to be made miserable by perceived slights from his wife. Each of the poems has a unique theme it does not share with the other. "Richard Cory" has a strong theme of depression, alienation, and suicide, while "My Last Duchess" has a theme of the corrupting nature of power.
Although "My Last Duchess" and "Richard Cory" are different types of poems, they share similarities of tone, images, and theme while remaining distinct in many ways.

What does Baldwin mean by "black people, mainly, look down or look up but do not look at each other, not at you, and white people, mainly, look away"?

What Baldwin is referring to is the fact that racism separates black people, not just from whites, but from each other. The indignities of racism have instilled a certain mindset in African Americans that makes them seek a kind of artificial dignity in class distinctions. Essentially, they internalize society's racism and then use it to construct barriers between themselves and other African Americans on the basis of class. So, as well as constantly having to "look up" at white people, lower-class African Americans also have to do the same to their alleged social superiors of the same race.
Among other things, this means that black people are divided from each other when they should be united. Instead of coming together to fight racism and oppression, they're too busy trying to create a distinct social hierarchy that keeps a whole segment of black society down, oppressed by both white racism and black middle-class snobbery. In the meantime, white society can just look away, ignoring what goes on among African Americans, safe in the knowledge that, in this unequal society, and with black America divided among itself, white society remains firmly in control.

Baldwin, in my view, is stating that many or most black people are unable actively to come to grips with the general conditions in which African Americans have been placed by white society. At the time he wrote The Fire Next Time,the civil rights movement was only in its infancy. It still appeared to many that there were no obvious solutions to racial oppression, and in Baldwin's opinion, African Americans, in "not looking at each other," were still unable to evaluate their situation in objective terms and still felt largely powerless to effect change.
In saying "white people look away," Baldwin is indicating that most whites simply do not wish to acknowledge the fact of racial oppression and, still less, to take any action to correct it. He also means that too many whites (up to that time and, tragically, still today) have considered African Americans to be invisible or have regarded them as somehow not truly a part of America. Though much progress has been made in the fifty-five years since The Fire Next Time was published, many of the points Baldwin makes are unfortunately still valid today.

Baldwin is addressing the way in which race has created a hierarchy whose strictures are obeyed by both whites and blacks. 
Black people "look up" at those within the race who are of a higher economic class and/or whose skin is of a lighter hue. They "look down" on those who are poorer or darker. Black men might be inclined to "look down" on black women; heterosexuals may also "look down" on homosexuals.
Racism, sexism, homophobia, and classism, which often coincide, have dissuaded efforts at black unity and even the basic acknowledgement that another black person's life, however degraded or different, is still important and invaluable. If members of the community were able "to look at each other," as fellow individuals, this understanding would be obvious. The "not at you" is a reference to Baldwin's nephew, to whom the letter in The Fire Next Time is addressed.
Whites, he argues, "look away," unable to see the presence of black people at all. To look away from someone is to refuse to acknowledge their existence. In his impassioned argument, Baldwin spares no white American—neither conservatives nor liberals—from his accusation that they do not think that black lives matter as much as their own; he also says that their concerns over rioting and unrest at the time were not in response to conditions in ghettos, but instead a reaction to possible intrusion onto their property. When one's first response, in face of another's pain, is to talk about oneself, there is not only no concern for the other, there is no sense that he is there at all.

Why do Don Quixote and Sancho need to leave La Mancha for their adventures to occur? How does the role of the journey in this text compare with other texts where journeys play a central role? Do our characters make the hero’s journey as explained by Joseph Campbell?

Don Quixote and Sancho Panza leave La Mancha because Don Quixote has read chivalric romances that make him want to right all the wrongs in the world. As Cervantes writes:

In short, his wits being quite gone, he hit upon the strangest notion that ever madman in this world hit upon, and that was that he fancied it was right and requisite, as well for the support of his own honour as for the service of his country, that he should make a knight-errant of himself, roaming the world over in full armour and on horseback in quest of adventures, and putting in practice himself all that he had read of as being the usual practices of knights-errant; righting every kind of wrong, and exposing himself to peril and danger from which, in the issue, he was to reap eternal renown and fame.

Don Quixote goes insane reading the chivalric romances of his time, and his brain is so addled that he sets out to become like the knights-errant he has read about. His goal is to correct the wrongs of the world and to win honor and glory for himself. Sancho Panza, for his part, accompanies Don Quixote because he hopes to get money from Don Quixote, even though he knows that Quixote is insane and delusional.
In this sense, Don Quixote does not go on a typical hero's journey (such as that in Homer's Odyssey), which involves not only leaving home but also undergoing a kind of transformation. As conceived by Campbell and others, the hero's journey includes not only a call to adventure but a crossing into a supernatural frontier and a trial that results in a kind of change or rebirth. While Don Quixote and Sancho Panza go on a journey, they are not transformed by their ordeals.
It is only at the very end of the book that Don Quixote realizes that he has labored under a delusion about his capacity to be a hero; however, he makes this realization just before his death. He is sickened by his inability to achieve the unrealistic dreams he wanted to make reality. Cervantes writes that Don Quixote's friends believe Quixote suffers from "grief at finding himself vanquished, and the object of his heart, the liberation and disenchantment of Dulcinea, unattained." Don Quixote fails to free Dulcinea, and he is not able to truly experience a rebirth or transformation in a way that affects or betters his life. He says at the end of the book, "Now I see through their absurdities and deceptions, and it only grieves me that this destruction of my illusions has come so late that it leaves me no time to make some amends by reading other books that might be a light to my soul." In other words, though Don Quixote realizes that reading chivalric romances has destroyed his mind and that these books are not good for him, he has no time to read other books to compensate for his mistakes. He dies still unfulfilled.

In the book, how do different characters learn to empathize?

To show empathy is to understand the feelings of others. Many characters in To Kill a Mockingbird learn empathy during the novel. In chapter 2, after a rough day at school, Atticus advises Scout by telling her, "You never really understand a person until you consider things from his point of view." Scout learns to apply these words of wisdom in her understanding of Boo Radley. While he is terrifying to her in the beginning, she learns to understand him. Near the end, Scout recognizes that to bring attention to Boo for his role in rescuing the children from Bob Ewell would be "sort of like shootin‘ a mockingbird." She empathizes by showing awareness of Boo's feelings and personality.
Jem also shows empathy. Each time the word "guilty" is read at the end of Tom Robinson's trial, Scout recalls that Jem's "shoulders jerked" as if he experiences pain. Jem is upset about the verdict and becomes quite emotional. As the son of a lawyer, Jem is convinced that Atticus effectively proves his case that Tom is innocent. Once he hears otherwise, Jem tells Atticus, "It ain’t right." Jem empathizes with Tom and knows he has been treated unfairly because of the color of his skin.
Dill is another character that feels empathy for Tom. During the trial, Dill becomes so upset that Scout has to take him outside. Dill doesn't like the way Mr. Gilmer, the prosecuting attorney, speaks to Tom and calls him "boy." Scout attempts to help by telling Dill that Tom is "just a Negro," but Dill says, "It ain’t right, somehow it ain’t right to do ‘em that way."
Atticus remains a caring and empathetic man throughout the story, even showing empathy for Mayella Ewell. Although he knows that Mayella falsely accuses Tom of rape, Atticus understands that Mayella's life at home is difficult. In chapter 23, Bob Ewell approaches Atticus and spits in his face. Angry about the way in which Atticus handles the case with Tom, Bob threatens him. Atticus explains to Jem that if Bob "spitting in my face and threatening me saved Mayella Ewell one extra beating," he will accept it. Atticus shows concern for Mayella and the other Ewell children.

What is significant about time switching back and fourth in The Brief Wondrous Life of Oscar Wao?

Diaz shifts not only back and forth in time, but also between different narrators, for a couple of different reasons.
First, the book itself focuses on Oscar, but it is also the story of his family. His mother, Beli, and his sister, Lola, are featured prominently throughout the novel. By going back and forth in time, Diaz introduces readers to these characters at different points in their lives and from different perspectives. Because his family plays such an important role in Oscar's life, it makes sense that Diaz wants us to know their backgrounds and motivations, and skipping around in time helps him to do this very effectively.
Second, just as the book is about Oscar's family, it is also about Dominican culture. There are multiple pressures on Oscar, and these pressures often arise as a result of his family's Dominican background. Although Oscar grew up in New Jersey, his family's Dominican culture is still very much an influence in his life, and we see this especially from his mother, Beli. By going back in time to her earlier years, we get a better understanding of what the Dominican Republic was like when she was growing up, what influenced her, and how all of those experiences have shaped her as a woman and a mother. This also allows Diaz to tell some of the history, political and otherwise, of the Dominican Republic and illustrate how that history has current effects on Dominicans, whether they currently live in the Dominican Republic, or elsewhere.
Ultimately, shifting between timeframes in any story is a fairly common rhetorical and strategic choice of many authors. These shifts allow them to tell deeper, more complex, and more layered stories that may span generations, just like we see in The Brief Wondrous Life of Oscar Wao.

Within works of fiction, flash backs (analepses) and flash forwards (or prolepses) are literary devices that an author uses to interrupt the current time in the novel and take the narrative backward or forward in time. Often, these inset stories within the larger narrative arc serve a bigger literary purpose. Introducing character and plot details at intentional moments within the larger story has bearing on how characters and themes develop.
 
In The Brief and Wondrous Life of Oscar Wao, Junot Diaz's narrative moves frequently not only from one time to another, but from one narrator to another as well. Like the Dominican culture around which the story revolves, the narrative texture is varied and colorful. In addition to mirroring the Dominican spirit, Diaz's narrative choices also serve a higher literary goal. Throughout Oscar Wao, Diaz describes the juxtaposing aspects of the Dominican-American experience. A few of the overarching themes include colonization vs. belonging, superstition vs. science, and masculinity vs. female power. 
 
By continually switching time periods throughout the novel, Diaz continues his examination of opposites, applying that same scrutiny on time: present vs. past. In my opinion, Diaz is using that juxtaposition to make the reader ask How different are these two things actually? Throughout the novel, we see parallels and similarities between each of Diaz's juxtaposed pairs, including present and past. Prolepsis and analepsis are just two devices Diaz uses to bring the reader's attention to the novel's central themes.

Which tragic news come to Helen in February 1896?

Although we have not heard of the gentleman in the memoir before this point, Helen Keller writes at end of chapter 12 of the death of Mr. Spaulding:

these bright days were darkened by the greatest sorrow that I have ever borne, except the death of my father. Mr. John P. Spaulding, of Boston, died in February, 1896.

Keller goes on to explain that he was a person who

made every one happy in a beautiful, unobtrusive way, [and] was most kind and tender to Miss Sullivan and me.

She states that Mr. Spaulding always took a great interest in the work she and Miss Sullivan were doing and that they all always felt safe with his protection of their interests at hand. Helen continues by saying that Spaulding's death has left a "vacancy" that has been unfilled.
Toward the end of the memoir, she includes a letter she wrote to Mr. Spaulding. It appeals for his help in a difficulty and gives some insight into how they worked together for charitable causes. She and Miss Sullivan were having a tea to raise money for a kindergarten for blind children. However, the house where they had planned to hold it could not fit more than fifty people, and they expected many more. Keller appeals to Mr. Spaulding for help in finding a bigger space. In response, his sister does open her own home for the event. The tea raises $2,000. According to the inflation calculator, that $2,000 would be worth more than $50,000 today.

In February 1896 Helen was brought the tragic news that John P. Spaulding of Boston had passed away. It's a measure of just how highly regarded Mr. Spaulding was by Helen that her sorrow at his passing was exceeded only by the death of her father, someone else she deeply loved, cherished, and admired. Mr. Spaulding had been a close friend of the family, a source of great comfort and support to Helen. An elderly bachelor, he was a wealthy man known as "The Sugar King" of Boston. He donated large sums of money from his sugar business to various philanthropic ventures and generously acted as a financial benefactor to Helen and her family. He was a warm, caring man, someone who had been immensely supportive and encouraging both to Helen and her close friend and assistant, Annie Sullivan. As Helen puts it herself, Mr. Spaulding's passing left a vacancy in their lives that would never be filled.

What is the relevance of Brave New World today?

Huxley's Brave New World remains relevant in today's society because this fictional civilization, in many ways, parallels America's affinity for sex, science, and pharmaceuticals. In Huxley's future society, promiscuity is considered healthy, while monogamous relationships are taboo. Since having a child is considered a dirty affair, birth control is prevalent, and women immediately have abortions when they learn they are pregnant. In today's society, casual sex is increasingly accepted, and women also have access to birth control. Huxley also satirically examines the increasing dependence and reverence for science. In Brave New World, Henry Ford is revered as a deity in the society that values efficiency, production, and consumerism. Babies are also mass produced in an elaborate cloning process, and technology is applied to nearly every facet of life. The increasing reliance on technology in today's society and devotion to science resembles Huxley's fictional society. Huxley also explores the prevalence of pharmaceuticals, particularly emotional stabilizing medications, which is currently an issue in today's society. In the fictional society, citizens take a drug called soma, which relieves negative emotions. Soma resembles many different benzodiazepines, which are used to treat anxiety, panic disorder, seizures, or sleep disorders. The brilliance of Huxley's work is evident in his ability to accurately predict many of society's current trends. 

If Lance Armstrong were to be sued in a US Court for using illegal performance-enhancing drugs and perjury, should he be sued in a federal court or a state court? Make sure you discuss "jurisdiction" over Mr. Armstrong, both "subject matter" and "personal jurisdiction."

If this is a question for a class, I do suggest you seek some clarification of the question.  A situation in which someone would sue Lance Armstrong for the use of illicit drugs seems quite unlikely, and no one can sue another person for perjury.  As you have stated this, these are both crimes.  So, the question would appear to be whether Armstrong could be prosecuted in state or federal court.  And the answer to that is that it depends. If Lance is in a particular state and in the United States and has violated the laws of either or both, they may both have jurisdiction, the state only may have jurisdiction, or the federal government only may have jurisdiction.  Subject matter jurisdiction lies in a criminal court and is almost irrelevant to the inquiry, since people are prosecuted only in criminal court, not in civil court. 
Most criminal law is the domain of the states, but there are federal laws concerning drug use, so if there is a federal law that preempts a state law, jurisdiction would lie in a federal criminal proceeding. For example, many states now allow the use of marijuana, either medically, recreationally, or both. But federal law makes the use of marijuana a crime.  So even a person in a state that allows its use can be tried in federal court in a criminal prosecution. We say that the federal law preempts the state law in a situation like this.  I do not know which performance enhancing drugs Armstrong has taken and which are actually illegal.  For instance, it may or may not be illegal to do an autologous blood transfusion, one performance-enhancing means athletes use, in a particular state or in the United States crimes code. 
Which court system would have jurisdiction regarding perjury is a function of to whom Armstrong perjured himself. If he lied to a state official under oath, that state would have jurisdiction over him for this crime. If he lied to a Congressman or a federal marshal, the federal government would have jurisdiction over him.
You can see how little subject matter jurisdiction matters under circumstances such as these. Different courts are allowed to try different kinds of cases, so that a bankruptcy would need to be filed with the federal bankruptcy court and if I sue another person over a private contract, the federal courts are not likely to have jurisdiction. If I seek an injunction, I must file in a court of equity.  But if a person is being prosecuted for a crime, he or she must, of course, be prosecuted in criminal court.