Why does the narrator lead the policemen to the old man's room? Why does he say the police "knew" that the body was hidden there? Do you agree with his perception? Comment

The Tell-Tale Heart is Edgar Allan Poe's signature story in his inimitable style of suspense writing. The narrator has murdered the old man even though he says, " I loved the old man. He had never wronged me. " Yet the " vulture eye" of the old man bothers him to such an extent that he kills the old man in a cold blooded manner.  Since then he labours under the guilt which keeps on slowly building in him. He is quite pleased with himself over having committed a perfect murder. " I had been too wary for that. A tub had caught it all - ha! ha!" 
He feels so secure in no one detecting his crime that he brings the policemen straight to the old man's room in his overconfidence. " I smiled - for what had I to fear?" As the narrator himself says, he bade them sit and himself joined them " in the wild audacity of my perfect triumph". He is at first at ease but his inherent madness gets stimulated further by his guilt and he fancies that he can hear the old man's heart beating. In his guilt-ridden insanity, the narrator can no longer maintain his casual behaviour and talks loudly, gesticulating wildly to allay any suspicion that he feels the police might have of him. However as the noise of the beating heart in his ears increases, so does his madness, until he feels that there was no way that the police could not hear the noise and were in fact pretending to chat pleasantly, while all the time baiting him. 
The crescendo in the narrator's guilty insane mind builds to such a volume that he concludes that the police did indeed know of his crime and were merely mocking him. His guilt becomes agonising to him and he shrieks out his confession to the police. 
If the narrator had been able to maintain his sang-froid, perhaps his crime could have gone undetected for some more time, since the policemen did not suspect anything wrong and were merely spending some time pleasantly with the narrator. However , it was the narrator's own psychotic mind coupled with his guilt that resulted in his arrest. Throughout the story he tries to show that he is perfectly sane and therein also lies the irony of the story.
 
 
 
 

Insanity or madness is a central theme throughout much of Edgar Allan Poe’s work. In his short story “The Tell-Tale Heart,” it is in the narrator’s forceful protestations in defense of his sanity that the depth of his insanity is apparent. Notice in the following plea the narrator’s exhortation to be taken seriously and not be judged harshly in terms of his frame of mind:

“TRUE!—nervous—very, very dreadfully nervous I had been and am; but why will you say that I am mad? The disease had sharpened my senses—not destroyed—not dulled them. Above all was the sense of hearing acute. I heard all things in the heaven and in the earth. I heard many things in hell. How, then, am I mad?”

Poe’s narrator shares a home with an old man for whom he professes great affection (“I loved the old man. He had never wronged me. He had never given me insult. For his gold I had no desire”). Yet, unnerved by the old man’s deformed eye, the narrator decides to kill his elderly harmless roommate, all the while continuing to assert that his actions were entirely the actions of a sane, rational human being (“You fancy me mad. Madmen know nothing. But you should have seen me. You should have seen how wisely I proceeded”).
What the reader learns in reading “The Tell-Tale Heart” is that the narrator’s protestations regarding his sanity are in fact the ravings of a lunatic—and a homicidal one at that. The narrator is psychologically impaired. His decision to kill the kindly old man solely because of his deformed eye and his confession in carefully planning the act and carrying it out are all the indications one needs to conclude that he is, indeed, quite mad. To paraphrase Queen Gertrude in William Shakespeare’s Hamlet, the narrator "doth protest too much." If he is in fact insane, however, the narrator’s insanity is exhibited in another manner: The depth of his conscience is greatly expanded by virtue of his mental illness. That is why he hears the beating of his victim’s heart, while the police officers hear nothing. The narrator has killed and dismembered the old man’s body and buried it beneath the floorboards. He is so stricken with guilt, though, that he imagines that he is hearing the beating of the old man’s heart. As the police officers continue to remain oblivious to the sounds the narrator hears, the latter grows increasingly agitated until the extent of his madness is revealed by his exhortation to his uninvited guests to “tear up the planks! Here, here!”
When the narrator thinks about the oblivious officers (“They heard!—they suspected!—they knew!”), he is again revealing the extent of his madness. He has transitioned from a cold, calculating killer to a remorseful and guilty maniac. The police officers do not know that the old man’s body is buried nearby, and they do not hear the beating of the old man’s heart because it is all in the narrator’s head. He leads them to the old man’s remains because his madness has manifested itself in such a manner that he must confess his sin.

What does the novella Anthem foreshadow?

The term for what Rand warns against or "foreshadows" for a society in which individuals refuse to think and act for themselves is called collectivism. This philosophy promotes the idea that society can dictate a person's life and make them do things that have no concern for the individual, but only for how they benefit society (or a government) as a whole. Equality expresses this belief of his society when he says "there is no life for men, save in useful toil for the good of their brothers."
Rand allows us to see the negative results of this collectivism by allowing us to view the primitive setting of Equality's world. When a government determines the place and value of an individual and subjects them to its beliefs with force and punishment, an individual's potential to create and achieve is limited. Limiting the individual in this way also limits the society itself, as some of the most important inventions of history were created by individuals who ignored society's opinions. These individuals' creations provided wonderful things for the whole of society to use for its advancement. Rand cautions us that without this individual freedom of thought and action, we are doomed to stall not only in terms of innovation and technology, but also in terms of in personal fulfillment.
Rand warns that a collectivist government or group can destroy personal happiness. She implies that to be truly happy, we must embrace the "I" in a society that rules through "we." Equality expresses her message when he states, "We lived not when we toiled for our brothers, we were only weary." Equality only finds true happiness when he embraces his own individual gifts and emotions, refusing to let the values and mores of his society hold him back.

Ayn Rand's Anthem is a cautionary tale, meant to warn against the dangers of collectivism. Rand lived in the Soviet Union as a teenager and so experienced life in a communist dictatorship firsthand before coming to the United States in 1926. She wrote Anthem in 1937, a time of Stalinist excesses.
The book celebrates individualism. Foreshadowing is not exactly the right term to describe what the book does. It would be more accurate to call it a cautionary tale, warning readers not to allow too much groupthink or conformity to take hold in a society. When nobody is allowed to pursue excellence or think for themselves, then society as whole backslides into barbarism. Trying to enforce complete equality means, according to Rand, that the most talented people are dragged down into mediocrity. Rand's work is deliberately very simple, opposing an extreme version of repressive collectivism that suppresses heroic individualism.
Most societies, in fact, thrive by both promoting individualism and assuring some social equality so that the culture doesn't descend into the chaos of ruthless social Darwinism.

What is the significance of loyalty in the book The Hunger Games?

Loyalty is an important theme in the novel The Hunger Games written by Suzanne Collins. The theme is present in the entire series as well.
Throughout the series, Katniss Everdeen exudes loyalty. She is loyal first and foremost to her family. Katniss takes care of her mother and sister by acting as a parent-figure. She cleans the house, hunts for food, and trades for goods. A major point in the story where loyalty is shown is when Katniss wishes to protect her sister, Prim, and therefore volunteers herself as tribute to participate in the games.
Once Katniss arrives at the games, she must remain loyal in her alliances with other competitors in the games in order to survive. Katniss is especially loyal to Rue, a young tribute, and to Peeta, the male tribute from her district. Katniss shows compassion for Rue after Rue's death by singing to her and covering her with flowers. Katniss proves her loyalty to Peeta when they are the last two remaining tributes and must decide who will live and win the games and who will die. Katniss creates a plan where both her and Peeta can survive or they can both die and ruin the games entirely. This moment is a pivotal point in the series because it sparks the rebellion against the Capitol that is led by Katniss.
Katniss is loyal enough that she is willing to sacrifice herself for those in her life who are important to her.

The importance of loyalty is a consistent theme in The Hunger Games series. Katniss is fiercely loyal to her friends and family, and it is her commitment that drives much of the action of the book and part of her rebellion against the Capitol. One example of Katniss's loyalty is her decision to volunteer for the Hunger Games in order to protect her younger sister Prim. Katniss is also loyal to Peeta and Rue within the Hunger Games; she risks her life to get lifesaving medicine for Peeta, and comforts Rue at the end of her life by singing to her, even though the sound could have gotten her killed. Additionally, her loyalty to Peeta inspires her to create their feigned double-suicide attempt in order to save both of their lives. Katniss becomes a contestant in the Hunger Games and risks her life due to her commitment to the people she cares about, and at the end of the book she even defies the powerful Capitol in order to save the life of her friend.

The nineteenth century was a time of unmatched imperialism, heightened nationalism, and the emergence of scientific racism. In this essay I want you to think about the connections between these phenomena. How did imperialism and nationalism influence and mutually reinforce each other? What about imperialism and racism? How about nationalism and racism?

Competition for empire had been going on long before the huge wave of nationalistic feeling that swept Europe after the Enlightenment, and with even greater strength as a result of the Napoleonic Wars. The ideal of the nation state that emerged was especially strong in those countries that had not yet unified: Germany and Italy—and perhaps even more so among the Greeks and the Slavic nationalities that had lived under foreign domination for a long period. After unification the Germans and Italians soon engaged in this “great game” of competition for overseas possessions. At the end of the eighteenth century Britain, having lost its American colonies, at first thought the loss was disastrous but was then stimulated to even greater aggression in other parts of the world, eventually establishing direct rule in India, turning the Ottoman Empire into more or less a client state, and increasing its interests elsewhere in Asia and in Africa.
All of this imperialism was probably less the direct result of nationalism (though it still played a part) than of the need for raw materials prompted by industrialization. Yet the competition over colonies was a kind of sublimated form of the usual antagonism played out perpetually through wars on the European continent itself. For nearly a hundred years (1815 to 1914) the wars fought within Europe itself were on a relatively small scale. But the emergence of newly unified Germany (Italy less so) and its competition for empire was clearly a factor in the new and unprecedented outbreak of violence in 1914.
”Scientific racism” was a response to the need to rationalize the taking over of foreign lands. In the earlier, pre-Enlightenment period, thinking was primitive enough to allow people to believe it was simply their right to conquer, and it was seen as a given that non-white peoples were inferior, or that their subjugation could be rationalized through the need to convert them to the white man’s values, especially Christianity. But in the more advanced nineteenth century this rationale was inadequate. It was a scientific age, so a scientific facade was needed to justify conquest. Theories of racial hierarchy were no less primitive, and were rooted in the same tribal mentality, but there was a veneer of modernity and sophistication to them, just as there was in the theorizing about the relative superiority of one European nation with respect to others. So ultimately we do see a convergence of nationalism, imperialist intentions within Europe (the Ottoman and Austrian Empires in Europe were held together as long as possible and then, the latter was partly recreated by the Nazis) as well as outside of it, and a pseudo-scientific rationale for all of this re-emergence of primitivism.

Imperialism was in many ways inextricably linked with the ideologies of nationalism and racism. Nationalists saw the acquisition of overseas territories as a means of asserting national power, not to mention fostering pride in the nation. In a very famous speech in 1898, US senator Albert Beveridge claimed the United States, as a democratic nation, had a "nobler destiny" than European nations, because it would take over territories around the world to spread democratic principles. This brand of nationalism was common among Western powers. Imperialism promoted nationalistic beliefs, and nationalists urged imperialistic policies. In the late nineteenth century, as Social Darwinistic theories gained popularity, the idea that Anglo-Saxon nations were inherently more advanced than others was used to justify imperialism in two ways. One was to characterize relations between nations as a brutal struggle for existence, one which justified aggressive foreign policy as a means of survival. Many Americans, for example, justified the annexation of the Philippines after the Spanish-American War on the grounds that Germany would take the islands if the United States did not. Others saw in scientific racism a "white man's burden," one which mandated that whites "civilize" supposedly less advanced peoples by taking them over. As should be evident by now, nationalism was steeped in racism. German, American, and British nationalists in particular argued for a national destiny that was connected to their supposed superiority to other peoples. This superiority, they claimed, was supported by scientific thinking on race.
https://books.google.com/books?id=T5rR1ypxfvwC&printsec=frontcover&dq=american+imperialism&hl=en&sa=X&ved=0ahUKEwjC_8fotfLeAhXxs1kKHdrdC9gQ6AEIMDAB

Your answer to this question must be guided by the course materials you have been provided. There is a very close connection between nationalism, imperialism, and scientific racism starting in the nineteenth century.
In the 1870s, Europe's second wave of the Industrial Revolution spurred European nations' desire for access to raw materials. As a result, many European nations wanted overseas empires. For example, King Leopold II of Belgium began to enslave the people of the Congo in his pursuit of ivory and, later, rubber. When other nations saw his actions, they were motivated by a sense of nationalism (or the idea that their nation was destined for greatness) to pursue overseas colonies in Africa, Asia, and the Middle East. (The United States was also motivated to be imperialist, mainly in the New World but also in the Pacific.) Many nations such as Germany had just united (in 1871), driving these recent countries to use imperialism to promote their new nations and unite their people.
The philosophy of scientific racism developed in part from Darwin's monumental work, On the Origin of Species (1859), which uncovered the mechanisms of heredity. Other thinkers, such as Francis Galton, who was Darwin's cousin, applied Darwin's ideas to the study of human heredity and determined (falsely) that human ability is entirely heritable. Galton began the study of eugenics, the creation of a "master race" through genetic engineering. The idea of a superior race fueled nationalism and imperialism, as Europeans and Americans believed that they were superior to other people and had a right to conquer others and "civilize them." Therefore, these three ideas were closely interconnected. 

What values of the time period does Martin Luther King Jr.'s "I Have a Dream" speech communicate?

Two values of the 1960s embodied in Dr. King's "I Have a Dream" speech are transformation and community.
Transformation was an important value in the 1960s.  The time period changed the way people viewed the world.  It was evident in music, art, and literature.  It was also a significant part of the political landscape of the time period.  The shifting dynamics of race, class, gender, and sexual identity were all addressed in the 1960s.  Dr. King's speech embraces this idea of change.  "I Have a Dream" is significant because it moved the issue of civil rights to the forefront of American consciousness. The speech transformed how people viewed racial equality. The speech forced the issue that racial injustice must change. It made civil rights a moral issue. Americans of all backgrounds could no longer claim that it was a "political" or "state" issue.  Rather, the language and imagery that Dr. King employed made racial justice a spiritual necessity, something that found its root in Scripture.  Dr. King's speech caused people to change their thinking about civil rights.  In doing so, "I Have a Dream" embraced a significant value of the 1960s.
The value of community was important to the 1960s. From communes that became socially acceptable to the idea that inclusivity of voices was important to American identity, the 1960s emphasized a collective cultural identity.  "I Have a Dream" places importance on community.  Dr. King is deliberate in suggesting that racial equality can only be accomplished when everyone comes together, and can "sit down at the table of brotherhood." Dr. King uses references from Christianity to enhance the community, showing that civil rights is not an issue that only applies to one group.  Rather, he affirms that it is a reality that impacts everyone.  In employing "My Country, Tis of Thee" and ending with “from every mountainside, let freedom ring,” the speech strongly underscores community. In doing so, Dr. King echoes a value from the 1960s, and indelibly links his speech to the time period.

In Homer's Odyssey, who is Theoclymenus and why should Telemachus treat him kindly?

Theoclymenus is a seer who is fleeing Argos for killing a man of his own race. He tells Telemachus that the kinsmen of the murdered man seek to avenge themselves on him; this is why he lives in exile.
Theoclymenus is actually a very important guest; as he is a seer, he can see the future and interpret omens. If Telemachus treats him kindly, he will benefit from Theoclymenus' psychic abilities. In the story, Theoclymenus' clairvoyant skill is demonstrated when he observes a hawk fly by Telemachus' right hand. The hawk is clutching a dove in its talons, and in mid-flight, it tears the feathers of the dove off. The feathers fall between Telemachus and the ship. Theoclymenus interprets this as a good omen. He tells Telemachus that he, Telemachus, will remain a powerful man and that no house in Ithaca will be as royal as his own.
As time progresses, Theoclymenus becomes more and more important to Telemachus. His ability to interpret omens is a gift that encourages Telemachus and those who are faithful to Odysseus' house. In Book 17, Theoclymenus tells Penelope (the wife of Odysseus) that he can divine the future. He tells her that her husband "himself is even now in Ithaca, and, either going about the country or staying in one place, (and) is inquiring into all these evil deeds and preparing a day of reckoning for the suitors."
In Book 20, Theoclymenus prophesies that the suitors will eventually meet their doom:

But Theoclymenus said, "Eurymachus, you need not send any one with me. I have eyes, ears, and a pair of feet of my own, to say nothing of an understanding mind. I will take these out of the house with me, for I see mischief overhanging you, from which not one of you men who are insulting people and plotting ill deeds in the house of Ulysses will be able to escape.

From the text, we can see that Telemachus' welcome of Theoclymenus is not misplaced. His kind treatment of his exiled guest has earned him the loyalty of a seer who has psychic abilities. At each stage of the mission to reclaim Odysseus' household, Theoclymenus uses his clairvoyant abilities to encourage Telemachus and his allies. So, Theoclymenus is an asset to Telemachus.

Find f '(t) using the definition of derivative. f(t) = (1-3t)/(2+t)

The definition of derivative of a function  is
  (the limit of the quotient of the difference between f(x + h) and f(x) and h, as h approaches zero.)
To apply this definition to the given function  , fist find f(t + h) by plugging in t+h instead of every t:

Then, find the difference between f(t + h) and f(t):

Simplify the numerator by using distributive property:

Dividing this by h results in

Finally, consider the limit when h approaches zero. Then, the expression above approaches the value of the derivative of f(t):

We can use the quotient rule to solve this derivative.
f(t) = (1-3t)/(2+t)


where g(x) = 1-3t and h(x) = 2+t
f'(t) = [-3(2+t) - 1(1-3t)]/[(2+t)^2]
=-7 /(2+t)^2

The definition of derivative of a function f(x) is
f'(x) = lim_(h ->0) (f(x+h) - f(x))/h  (the limit of the quotient of the difference between f(x + h) and f(x) and h, as h approaches zero.)
To apply this definition to the given function f(t) = (1-3t)/(2+t) , fist find f(t + h) by plugging in t+h instead of every t:
f(t + h) = (1 - 3(t + h))/(2 + (t + h)) = (1 - 3t-3h)/(2 + t + h)
Then, find the difference between f(t + h) and f(t):
f(t+h) - f(t) = (1 - 3t-3h)/(2 + t + h)-(1-3t)/(2+t) = ((1-3t-3h)(2+t) - (1-3t)(2+t+h))/((2+t+h)(2+t))
Simplify the numerator by using distributive property:
f(t+h)-f(t) = ((1-3t)(2+t)-3h(2+t) - (1-3t)(2+t)-h(1-3t))/((2+h+t)(2+t)) =(-6h-3ht-h+3ht)/((2+h+t)(t+h)) = (-7h)/((2+h+t)(t+h))
Dividing this by h results in
(f(t + h)-f(t))/h=(-7)/((2+t+h)(2+t))
Finally, consider the limit when h approaches zero. Then, the expression above approaches the value of the derivative of f(t):
f'(t) = lim_(h->0) (f(t+h)-f(t))/h = -7/(2+t)^2
This result can be confirmed by taking the derivative of f(t) using the quotient rule and the chain rule:
f'(t) = ((1-3t)'(2 + t) - (2+t)'(1-3t))/(2+t)^2 = (-3(2+t) - 1(1-3t))/(2+t)^2 = -7/(2+t)^2