What did Akiba Drumer ask the others to do for him?

Akiba Drumer has always been noted for his unshakeable optimism and unbending faith in God, even in the midst of the camp's unspeakable horrors. As well as a deep commitment to his faith, Akiba is also heavily into numerology, using it to predict immanent deliverance for the inmates from their terrible ordeal.
Eventually, however, Akiba is broken by his experiences of the camp, and he loses not just his faith but also his will to live. When he's selected by the Germans to be sent to the crematorium he asks his fellow inmates to say the Kaddish for him. In Judaism, Kaddish is the prayer for the dead. Although Akiba has lost his faith, he still feels it appropriate that the relevant religious rites should be observed. Unfortunately, however, no one remembers to say the Kaddish. The last few days had been particularly harsh and brutal, even by normal standards, so it's not surprising that the inmates' minds were focused elsewhere, on the daily struggle to survive.

What does "whose horrid image doth unfix my hair and make my seated heart knock at my ribs" mean in Shakespeare's Macbeth?

In act one, scene three, Macbeth receives a seemingly favorable prophecy from the Three Witches, who tell him that he will be named the Thane of Cawdor and become the future King of Scotland. Shortly after receiving the prophecy, Ross and Angus arrive to inform Macbeth that King Duncan has just given him the title Thane of Cawdor. Both Macbeth and Banquo are astonished by the news, and Macbeth immediately begins thinking about ways to attain the Scottish throne.
In an aside, Macbeth contemplates the positives and negatives associated with the witches' prophecy. Macbeth then begins to imagine assassinating King Duncan in order to become king, which is a horrifying, unsettling thought. Macbeth describes his feelings regarding the nature of the prophecy by saying,

If good, why do I yield to that suggestion Whose horrid image doth unfix my hair And make my seated heart knock at my ribs, Against the use of nature? (Shakespeare, 1.3.137-140)

Macbeth is essentially saying that the thought of committing regicide makes his hair stand on end and heart pound against his ribs in an unnatural way. These comments reveal Macbeth's ambitious nature and conscience. Judging from Macbeth's aside, the "horrid image" of murdering King Duncan is evidently disturbing and unsettling to him at this point in the play.

Macbeth was told by the Weird Sisters that he would become Thane of Cawdor and King of Scotland, and then, lo and behold, Ross and Angus arrive, bringing the news that he has, indeed, been named Thane of Cawdor. Now Macbeth really begins to believe, in earnest, that the more significant prophecy could come true, and he begins to entertain ways in which it might. He says,

I am thane of Cawdor.If good, why do I yield to that suggestionWhose horrid image doth unfix my hairAnd make my seated heart knock at my ribs,Against the use of nature?

In other words, he is now Cawdor, as the Weird Sisters said he would be. However, if this is a good thing, he asks himself, then why does he now find himself considering the murder of the current king, which is such a horrible idea that it makes his hair stand up on end and his heart pound loudly within his ribcage in such an unnatural way? Macbeth is already considering the nearest way to the throne, and he is unnerved by how quickly he has jumped to regicide as a possibility.

What was Pennsylvania's role in the abolitionist movement and the Civil War?

Quakers made up a significant portion of Pennsylvania's population. William Penn, the state's founder, was an English Quaker who had been granted a large piece of land by King Charles II in 1681 to pay off a land debt. Several thousand Quakers left England and followed Penn to the state that he would found. Initially, they were politically active, and they held positions of political influence until deciding that politics often compromised their values, particularly their pacifism.
Instead, they were early devotees of social justice. First, they pursued the protection of Native Americans' rights. Shortly thereafter, they reached an anti-slavery consensus. By the 1780s, slave ownership among Quakers was forbidden. Quakers were among the first abolitionists and participated in the Underground Railroad, harboring slaves until they reached their final destination which, after the passage of the Fugitive Slave Act in 1850, had to be Canada in order to avoid being captured and sent back to the South.
In regard to the Civil War, the most important battle—the Battle of Gettysburg—was fought in Pennsylvania. The battle was decisive, for it resulted in great losses on the Confederate side, as well as General Robert E. Lee's infamous retreat back into Virginia. Lee took his army north with the dual goals of gaining the support of Northern copperheads who were sympathetic to the Confederate cause and winning a battle in the interest of getting the Confederacy recognized by Britain and France.
Instead, 28,000 men were killed—a third of Lee's army. Union losses were not modest either. Union casualties amounted to 23,000. Lee was so dejected that he offered his resignation as general to Confederate president Jefferson Davis, who refused to accept it. The Confederacy went on to win other battles, but Gettysburg, along with Ulysses S. Grant's triumph at the Battle of Vicksburg in Mississippi, set the Union on the course to win the war.
https://www.history.com/topics/american-civil-war/battle-of-gettysburg

https://www.history.com/topics/immigration/history-of-quakerism

Did the last candidate die?

In the short story "The Knife Thrower," the last candidate is a young girl named Laura. During the night, Hensch performed a series of impressive knife throwing acts that left his audience in awe of his prowess. During the last segment of his performance, he inflicts the artful wound on three volunteers: his assistant, a high schooler named Susan, and a fifteen-year-old boy named Thomas. However, it is Hensch’s final performance that baffles his audience.
After the assistant invites a brave volunteer to come on stage for the "ultimate sacrifice," a mark that could be received only once in a person’s lifetime, the crowd is hesitant. Nevertheless, Laura raises her hand and makes her way to the front. The narrator states that after this, things happened so fast that they neither had time to protest nor stop what was about to happen. Soon after, Hensch released his knife and Laura’s body fell to the floor.
According to the narrator, it is unclear whether or not the last candidate died. The people believed that Hensch was so hell-bent on securing his reputation as the greatest knife thrower that he would be willing to stage the Laura act. However, the narrator also recounts numerous rumors involving the police and charges as well as countercharges that arose after Hensch’s performance. The narrator also asserts that even though they acknowledge that it is necessary for Hensch to develop new acts in order to stay relevant in a highly competitive environment, they agree that he crossed the line by endangering people’s lives.

y = sqrt(9-x^2) , -2

The function y = sqrt(9-x^2) is rotated about the x-axis and the surface area that is created in this way is a surface of revolution.
The area to be calculated is definite, since we consider only the region of the x-axis x in [0,3] , ie x between 0 and 3.
The formula for a surface of revolution A is given by
A = int_a^b (2pi y) sqrt(1 + (frac(dy)(dx))^2) dx
The circumference of the surface at each point along the x-axis is 2pi y and this is added up (integrated) along the x-axis by cutting the function into infinitessimal lengths of sqrt(1 + (frac(dy)(dx))^2) dx
ie, the arc length of the function in a segment of the x-axis dx in length, which is the hypotenuse of a tiny triangle with width dx , height dy . These lengths are then multiplied by the circumference of the surface at that point, 2pi y to give the surface area of rings around the x-axis that have tiny width dx yet have edges that slope towards or away from the x-axis. The tiny sloped rings are added up to give the full sloped surface area of revolution. In this case,
frac(dy)(dx) = -frac(x)(sqrt(9 -x^2))  
and since the range over which to take the arc length is [-2,2] we have a = -2 and b=2 . Therefore, the area required, A, is given by
A= int_(-2)^2 2pi sqrt(9-x^2) sqrt(1 + frac(x^2)(9-x^2)) dx
which can be simplified to
A = int_(-2)^2 2pi sqrt(9-x^2 + x^2) dx = int_(-2)^2 6 pi dx
so that 
A = 6pi x|_(-2)^2 = 6 pi (2 + 2) = 24pi
 
http://mathworld.wolfram.com/SurfaceofRevolution.html

An undergraduate engineering student, Ann, wants to secure a prestigious internship with company C in the summer before her senior year. Ann believes—rightly, let’s suppose—that if she secures that internship she will be hired by company C once she graduates, and she will go on to do important (and well-paid) work designing and building safe and useful objects for years to come. In her quest to get this internship, Ann comes to learn that one of company C’s current employees named Beth is a graduate of Ann’s college. A positive word from Beth can go a long way in helping a person get the coveted internship. Ann also comes to learn that Beth is a friend of a friend of hers (more precisely: an acquaintance of a friend of an acquaintance of hers) and that Beth will be at a party that Ann is going to this weekend. Intrigued, Ann looks around online for info about Beth. (For example, she checks out her LinkedIn page.) At the party, Ann goes out of her way to meet and speak with Beth, not about company C or the internship, but about general life stuff. Ann charms Beth quite successfully, which is not surprising given how much Ann knows about Beth, their shared college, the fact that they are both engineers, and so on. They exchange phone numbers and, in short order, they are hanging out regularly. Their budding friendship, if you can call it that, is initially built and sustained by Ann. Ann typically sends the first text, Ann requests to be Facebook friends with Beth, and so on. Over the course of a couple of months, it comes to be mutual and balanced. Eventually, they see each other a few times a week and talk (at least via text) almost every day. A few weeks after meeting Ann, Beth learns that Ann is applying for the internship. Ann does not make a big deal about it—and neither does Beth—but Beth wishes her luck. She also mentions how cool it would be if they could work together. Ann eventually applies for the internship and, unfortunately, does not get it. Beth even puts in a good word for Ann, as Ann really hoped she would—that’s why she tried to befriend Beth in the first place, after all—but it is not enough. Once Ann finds out that she did not get the internship, she cuts Beth off completely. She stops responding to her (many) texts, she unfriends her on Facebook, and so on. Ann is not angry at Beth. Ann just no longer sees any reason to keep talking to her, given that she did not get the internship. Why would Immanuel Kant almost certainly think that Ann acted immorally in this scenario?

One would be safe to conclude that Immanuel Kant would have disapproved of Ann’s actions. By meticulously cultivating a relationship with Beth over a period of time solely for the purpose of securing an important internship and then, upon failing to secure said internship, precipitously and rudely terminating all vestiges of that relationship, Ann violated Kant’s “categorical imperative” regarding human relations.
In his Grounding for the Metaphysics of Morals, Kant addresses the definition of morality and how it should, optimally, constitute the rules under which humans interact. In one of this treatise’s most frequently cited rules, the late German philosopher wrote, “Act so that you use humanity, as much in your own person as in the person of every other, always at the same time as end and never merely as means.” Kant was, in a sense, postulating a variation of the oft-cited “Golden Rule” or “ethic of reciprocity,” which can be traced to antiquity and which commands one to love his or her neighbor as he or she loves himself or herself. The “Golden Rule’s” most well-known variation is in the New Testament, Matthew 7-12: “Therefore all things whatsoever ye would that men should do to you, do ye even so to them: for this is the law and the prophets.” Kant, of course, had a complicated view of religion. He believed it in direct conflict with scientific reasoning but did not discount the presence of God in his life. His philosophy of ethics, however, represented a continuation of the “Golden Rule.”
In summary, Ann has deliberately exploited another human being for her own purpose and then further betrayed that human being’s trust by cavalierly cutting off all communications between Beth and herself. There is no question that Kant would disprove of Ann’s highly-questionable sense of morality. He would probably repeat another of his more frequently cited comments: “If man makes himself a worm, he must not complain when he is trodden upon.” Ann has violated the categorical imperative and has invited some form of retribution upon herself, whatever form that retribution might take.

According to Justice Harlan, what did the railroad claim was its motivation for the decision to separate passengers?

Justice Harlan wrote the dissenting opinion in the 1896 Supreme Court case Plessy v. Ferguson. This case stated that it was constitutional for states to have "separate but equal" public facilities, including schools, until it was overturned (related to schools) in the 1954 Supreme Court case Brown v. Borad of Education. 
In Plessy v. Ferguson, the court ruled that Louisiana could have separate railroad cars for black people and white people. In Harlan's dissent, he dismissed the idea that the railroad did not discriminate against either race but used the same rules to apply to both races, as they had claimed. Harlan wrote:

"The thing to accomplish was, under the guise of giving equal accommodations for whites and blacks, to compel the latter to keep to themselves while travelling in railroad passenger coaches. No one would be so wanting in candor as to assert the contrary."

In other words, Harlan said that under the pretense of giving separate accommodations to whites and blacks, the railroad's real motivation was to keep black people in their own coaches. The railroad intended to discriminate against blacks. Harlan wrote, "But in the view of the Constitution, in the eye of the law, there is in this country no superior, dominant, ruling class of citizens." That is, he said that under the Constitution, no race is superior and that all citizens have equal rights under the law.