What is the relationship between the Curate and the narrator in War of the Worlds?

The narrator, like just about everyone else in the book, finds the curate a constant source of irritation and annoyance. Even worse for the narrator is that he ends up being stuck in a house with this man, who everyone considers to be such an insufferable bore, for nine whole days, having to put up with his endless shouting and wittering to himself and his insatiable gluttony. (Which, ironically for a man of God, is one of the seven deadly sins.) When faced with a full-scale Martian invasion, the curate's explanation is that the unwelcome visitors are instruments of divine wrath; they are God's punishment for our sins, including gluttony, one presumes.
The narrator's response to the curate's seemingly never-ending string of loud lamentations is often violent and will doubtless find resonance among many of The War of the Worlds' readers—he beats and kicks the curate "madly," as he puts it. He also attempts to bribe him with a bottle of Burgundy to get him to keep his mouth shut. Sadly, that doesn't work, and so the curate carries on with his unhinged ranting, potentially alerting the Martians to where he and the narrator are hiding out.
Drastic situations call for drastic measures; the narrator grabs hold of a meat chopper and whacks the curate with the butt of the blade. He falls to the floor. Peace reigns. But not for long, because soon a Martian tentacle starts slithering around in the kitchen. After briefly examining the curate's body, this particular instrument of divine wrath drags him outside, where, presumably, a sumptuous Martian feast awaits.

What is the setting of Alan Paton's story "The Wasteland"?

Setting refers to the time and place in which events in a story unfold. The setting can also refer to the mood, circumstances, weather, social status of the characters, historical period, and immediate surroundings in which the characters find themselves.
In Alan Paton's short story, the plot unfolds during the evening at the end of a work week (most probably a Friday) when the main character returns home from work carrying his wages. He has just stepped off a bus and has to walk the rest of the way home. The atmosphere is thick with the man's fear, for he realizes that he will be robbed by the young men he has noticed. It is obvious that they plan to accost him, and he is frightened that he might be killed.
Most of the action occurs in an area known as the wasteland—a place filled with discarded waste and derelict cars. The man realizes that it is the only place he can go to escape being robbed and hurt. It is very dark, and the abandoned cars and other trash mean that he can hide and evade his malicious pursuers.
In the darkness, the man strikes at a figure looming up at him, and he hears it cry out in pain. He eventually escapes by hiding underneath a truck. He ironically learns that his son, Freddy, is a member of the gang who planned to accost him when they speak about him, and one mentions that "your father's got away." His son had evidently arranged, with the gang, to attack him and take his hard-earned money. It is also tragically ironic that the man discovers that the young man he had hit with his heavy stick has died, and that it is his son.
The story illustrates the kind of crime prevalent in the townships of South Africa, especially during the Apartheid era. Black people were displaced and forced into areas where poverty and crime were allowed to fester and grow. The authorities did very little to fight crime in such areas, and this, amongst other atrocities, led to the type of situation depicted in the story.

"The Wasteland" takes place in a South African town at night. More specifically, the setting is a lot with old cars, wire, and iron. The story takes place during apartheid, the system of legal racial segregation that was in place in South Africa from 1948 to 1994. The protagonist, an old man pursued by robbers, must escape to this lot because the only other place in sight is a convent, which has been barred to the public. In this lot, the old man at first runs into wire and cars, and the lot is so dark that he cannot see his attackers. In this darkness, he hits one of the men pursuing him with a stick. He then has the insight to hide beneath a truck, where he realizes that the man he has killed is his son, who urged the other men to attack his own father.

Thomas Jefferson wrote that all men are created equal, but he owned hundreds of slaves. He believed in a weak federal government, but strengthened it, as president. Does this make him a hypocrite? Why or why not? What does this tell you about the role of a president?

Thomas Jefferson probably did not consider himself a hypocrite. While he wrote that all men were created equal, this, to the founding fathers, meant that all white men who owned property were created equal. Slavery was commonly used throughout the South, and it was an acceptable form of labor for that time period in southern society.
Jefferson also wanted a weak federal government and in some ways, this occurred. He did reduce taxes. For example, the tax on whiskey ended. He also reduced the size of the military and reduced the number of federal workers. While the Louisiana Purchase increased the power of the federal government since he used a power not specifically mentioned in the Constitution, it shows that there are times when a president needs to make decisions that go against his personal beliefs if the action is in the best interests of the country. Abraham Lincoln was against slavery, yet he allowed slavery to exist where it was already established when he took office. There are times when the President must put aside his own beliefs and do what is best for the country.
http://www.digitalhistory.uh.edu/disp_textbook.cfm?smtid=2&psid=2981

https://www.loc.gov/exhibits/jefferson/jefffed.html

https://www.mattbrundage.com/publications/jefferson-equality/

What is the setting of Journey to the Center of the Earth, and why is it important?

Large portions of the setting for this story are fictional. At the time that Verne wrote this book, geologists were not sure what the interior of Earth was like. In typical Verne fashion, the text weaves known science with fiction. After descending through a volcano into the Earth's interior, the setting is fictional locations inside Earth. Regarding actual locations, the story begins in Hamburg, Germany in the spring of 1863. The story begins with Axel explaining to readers that Otto Lidenbrock had discovered a manuscript written by a 16th century Icelandic man. The manuscript supposedly narrates a path to the center of Earth, and the path begins at Mount Snaeffels in Iceland. The men then travel to Reykjavik, Iceland in order to gain access to the starting location. The story ends with the men being ejected from Stromboli's vent in Italy.
The setting is important mainly because it gives readers a believable exploration story. Readers know that hollow spaces exist in Earth. Big caves and caverns have been known about for centuries. Additionally, it makes a certain amount of sense that the throat of a volcano could give a person access to Earth's interior. Unfortunately, Earth's interior is not nearly as full of big, hollow, and open spaces as Verne's story would lead us to believe, but it still makes a great story.

The setting begins in Germany, where Professor Lidenbrock lives with his nephew, Axel. They journey to Iceland, where they have learned lies the entrance of a passage to the center of the earth. The story takes the two men, along with their guide Hans, through the subterranean passages that lead to an underground world. In this world they find an ocean, along with dinosaurs and prehistoric men.
The setting is important, of course, because it provides the way along which they journey. It has hidden dangers in abundance, and there is no quick escape route along the way (until the very end). These dangers move the plot along by providing adventures for the travelers, which they always manage to escape. Unlike many of Jules Verne’s stories, the scientific background for this passage to the center of the earth is unfounded. It is now believed that the earth is molten rock for much of the center, making such a passage impossible. Yet much of the geology has some scientific basis, and thus gives the illusion of scientific truth.

How is it that, although the Creature clearly warns Victor that he will be with him on his wedding night, Victor goes ahead and marries Elizabeth, showing no concern for the danger in which he will be placing his bride?

There appear to be two likely reasons for Victor's behavior.
First, Victor believes that the monster is only targeting him, not Elizabeth. Second, Victor believes that he can repel any attack the monster unleashes on him.
The text tells us that Victor does not once suspect that the monster will harm Elizabeth:

"I WILL BE WITH YOU ON YOUR WEDDING-NIGHT." That, then, was the period fixed for the fulfillment of my destiny. In that hour I should die and at once satisfy and extinguish his malice. The prospect did not move me to fear; yet when I thought of my beloved Elizabeth, of her tears and endless sorrow, when she should find her lover so barbarously snatched from her, tears, the first I had shed for many months, streamed from my eyes, and I resolved not to fall before my enemy without a bitter struggle.
Great God! If for one instant I had thought what might be the hellish intention of my fiendish adversary, I would rather have banished myself forever from my native country and wandered a friendless outcast over the earth than have consented to this miserable marriage. But, as if possessed of magic powers, the monster had blinded me to his real intentions; and when I thought that I had prepared only my own death, I hastened that of a far dearer victim.

Victor is resolved to fight the monster to the death. He prepares emotionally for a "bitter struggle" but cannot imagine that the monster would stoop so low as to hurt a woman. In their exchange, the monster begs Victor to create him a mate. For his part, Victor refuses. He balks at the idea of creating another monster that is equal in wickedness to that of the creature before him.
Upon hearing Victor's answer, the monster flies into a rage. He promises Victor that he will exact his revenge on him. However, Victor thinks that he is ready for anything that the monster will try.
Victor has totally misinterpreted the monster's motives and behavior. However, either by naivety or overconfidence, Victor chooses not to take precautions. This is why he goes ahead and marries Elizabeth, showing no apparent concern for the danger he will be placing his bride in.

In Shakespeare's Hamlet, do you think the characterization of Gertrude and Ophelia as passive and dependent on men is accurate?

I do think the characterization of Gertrude and Ophelia as passive and dependent on the men in their lives is accurate.  Gertrude is so dependent on men that she cannot bear to be alone even for two months after the death of her first husband, and she quickly remarries a man she later comes to see as quite inferior to old King Hamlet.  However, she only arrives at this conclusion as a result of being scolded by her son, Hamlet.  After they speak, she agrees to act according to his instructions rather than her new husband's, King Claudius's.  She seems to need to be constantly led, and she really displays little to no independence until the very end, ironically, when she disobeys her husband and drinks the poisoned wine that kills her.  So much for independence.
Ophelia, likewise, is in love with Hamlet and believes him to be in love with her, but she takes the counsel of her father and brother and breaks off their relationship.  She follows her father's orders until Hamlet finally kills him, and then she goes mad and is unable to keep herself alive in the absence of a man to direct her.  Both Gertrude and Ophelia seem to simply exist as ill-fated players in others' plots, casualties of the schemes of the men around them.

How do waves transfer energy?

Waves can be thought of as propagation of disturbance without movement of matter. We come across waves all the time: light waves, sound waves, radio waves, and so on. With the propagation of disturbance, energy is also transferred. Think of sound waves when someone speaks to us. Air particles get disturbed and that disturbance of the air particles travels towards us enabling us to hear what was said. In this case, each air particle that gets vibrated transfers the energy to the adjoining air particle and comes back to rest, thus propagating the energy through the air. In this motion, the air particles themselves remain (more or less) at the same place, while the motion takes place and energy is transferred.
Similar is the case with water waves—say, in an ocean. Each wave transfers the energy to the next wave, thus enabling energy transfer over large distances without much actual movement of the mass of water.
Another example of energy transfer is the kinetic energy transfer between molecules during an earthquake. When an earthquake takes place, the seismic (or earthquake) waves travel by transferring the kinetic energy from particle to particle. This may result in the momentary motion of the ground until the wave passes.
In summary, one can say that waves transfer energy by disturbance or vibrations of the particles; in other words, particle-to-particle energy transfer takes place.
In case of electromagnetic waves, a medium is not needed for wave propagation. Such waves transfer energy by oscillations of the electric and magnetic fields.
Hope this helps.

Kate changes from a shrew to an obedient wife in Shakespeare's Taming of the Shrew. Please provide 3 reasons to prove this statement with examples. Please include ideas for thesis statement to prove this.

We have to keep in mind that the Taming of the Shrew is a play within a play, meaning that Shakespeare is going to pains to actually show us the unreality of a man actually being able to successfully "tame" his wife as Petruchio does.
That being said, this is an easy thesis to prove because the text provides plenty of evidence that Kate has become a docile wife by the end of the action. One way Petruchio tames her is through killing her with "kindness": being so over solicitous about food and drink that Kate can neither eat nor sleep. He also whisks her away from her wedding very quickly and isolates her away from friends and family. With no one to turn to, not enough to eat, and no sleep, three main methods Petruchio uses to control her, she capitulates. What he does is sadistic, but apparently—at least in this fictive universe—effective.
Proof of Kate's new role as obedient wife can be found in the following quote from act 5:

Thy husband is thy lord, thy life, thy keeper,
Thy head, thy sovereign, one that cares for thee,
And for thy maintenance commits his body
To painful labor both by sea and land,
To watch the night in storms, the day in cold,
Whilst thou liest warm at home, secure and safe,
And craves no other tribute at thy hands
But love, fair looks and true obedience—
Too little payment for so great a debt.


In a thesis statement you could mention that Kate's transformation from a shrew to an obedient wife is depicted in act 5 through her many words that show she now regards her husband as her ruler.

Katherine becomes the image of a dutiful wife by the end of “Taming of the Shrew” because Petruchio embarrasses her publicly, isolates her from her family and friends, and wears her down with constant tortuous methods.
The embarrassment begins on their wedding day, when Petruchio arrives late to the ceremony, causing Katherine to flee in tears. When he finally does arrive, he is accoutred in a mismatched, shabby outfit and riding a broken-down, diseased horse. The crowds in Padua who have gathered to witness the marriage delight in the hideous spectacle of Petruchio’s appearance. This embarrassment is the first tactic Petruchio uses to control Katherine. To prevent future embarrassment, Katherine knows she will have to change her ways.
To make things worse, Petruchio insists on whisking Katherine away immediately after their vows, not even allowing her to receive congratulations from her guests, father, and sister. When she objects, Petruchio asserts that she is now his property and must do as he instructs. Because he physically separates her from familiar surroundings so soon after the wedding, Katherine is compelled to do as he says or face total isolation from any other living soul. He makes her dependent upon him, which forces her to change her habits.
Once they arrive at his country estate, Petruchio employs a variety of techniques to further grind down Katherine’s independent spirit. First, he prevents her from eating dinner by pretending that the food his servants have prepared is unfit to eat. Then, he prevents her from sleeping because he fusses about the bed being uncomfortable. In doing these things, Petruchio exaggerates his rage and throws ostentatious tantrums that are much worse than the “shrewish” behavior Katherine earlier displayed. Sleep deprived, hungry, and aghast at her new husband’s disagreeableness, Katherine finally gives up.
To prove Katherine’s full transformation as an obedient wife, Petruchio makes a bet with Lucentio and Hortensio at the banquet as their wives leave to talk amongst themselves. To Lucentio and Hortensio’s amazement, Katherine proves herself the most subservient of all: she is the first to return at her husband’s request, she retrieves the other wives, and she even delivers a speech in front of everyone about the proper way a wife should behave.
Katherine becomes the perfect wife because Petruchio emotionally and psychologically manipulates her until she has no other choice but to conform to his expectations.

Why do you think Stevenson chose to tell the story from Utterson's point of view rather than using Jekyll and Hyde from the beginning? How does this choice increase the suspense of the novel?

Utterson is a respectable Victorian gentleman. In fact, he's the very epitome of Victorian respectability. He's just the kind of man that people would instinctively trust, despite the fact that he's a lawyer and no matter how strange a story he has to tell.
As an upstanding member of the legal profession, Utterson has a reputation to maintain. And that reputation would be seriously damaged were he to spin us some kind of shaggy-dog story about the weird, sensational events associated with his friend, Dr. Jekyll.
Stevenson understands that the tale he tells has so many bizarre, fantastical elements in it that his readers may well conclude that his is yet another tiresome entry in the Gothic genre. But as Stevenson is uninterested in reviving a worn-out literary genre, and as he wants to say something about contemporary society, he chooses to make his narrator someone to whom his audience can relate, someone who finds the unfolding action every bit as weird, disturbing, and grotesque as they do.
So he recounts the action of the story through the eyes of a respectable, middle-aged lawyer. And Utterson—for it is he—acts as the reader's guide through the dark, seedy underbelly of Victorian London, through the fog-wreathed streets stalked by the unspeakable Mr. Hyde.

Eight of the ten chapters in The Strange Case of Dr. Jekyll and Mr. Hyde are, although written in a third-person narrative, focused through Mr. Utterson's point of view. One reason why Mr. Utterson's point of view is chosen is because he is a reliable narrator. Stevenson begins the story by emphasizing this point. Mr. Utterson is introduced as a lawyer, who has "an approved tolerance of others," is not easily agitated, and is not judgmental. These characteristics, and also his profession, mean that we can trust what Mr. Utterson tells us over the next eight chapters. When he describes strange happenings, we trust that he is not exaggerating. We believe that those strange happenings occurred in just the way that he describes, and this in turn makes the questions we ask about those happenings all the more curious. If we didn't believe what the narrator was telling us, then our questions would be less urgent and the suspense less gripping.
Another reason for having Mr. Utterson as the narrative point of view is that he becomes the detective. He declares in chapter 2 that "If he be Mr. Hyde . . . I shall be Mr. Seek." Having Mr. Utterson in this detective role, and the story told from his point of view, means that the reader also becomes a detective. We share the detective role with Mr. Utterson because we see things only from his point of view. We follow him and discover clues, one by one, along with him, knowing no more and no less than he does at any point in the story. Each clue generates more and more questions, to which neither Mr. Utterson nor we, the readers, know the answers. We get to share the suspense with him. We also, of course, get to share with him the moments of revelation toward the end of the story, which are our rewards for the detective work we have done alongside Mr. Utterson up until those moments.
If Robert Louis Stevenson had chosen Dr. Jekyll as the narrator from the beginning, or Mr. Hyde, instead of Mr. Utterson, the reader would have known straight away that Jekyll and Hyde are two manifestations of the same person, and the shock of that climactic revelation at the end of the book would have been lost.

The narrative structure of The Strange Case of Dr. Jekyll and Mr. Hyde by Robert Louis Stevenson is complex. The novel has a third person narrator who generally follows the viewpoint of Mr. Utterson and has full access to Utterson's thoughts, perceptions, and actions. Utterson is a good choice of narrator as he is intelligent, observant, and reliable.
Utterson, however, is not initially in full possession of the facts concerning the mysterious Mr. Hyde and must go through many steps, including reading documents, to ascertain what actually happened. The fact that Utterson does not know all the details of what is happening to Jekyll allows Stevenson to build suspense. Readers gradually piece together the story along with Utterson, encountering troubling incidents and pieces of information to increase suspense.
It should be noted that two final chapters which provide the resolution to the story actually are embedded narratives with first person narrators, namely "Dr. Lanyon’s Narrative" and "Henry Jekyll's Full Statement of the Case."

Stevenson likely chose to have Utterson narrate the story so that the audience would see the story unfold as he does, increasing suspense and tension as we must wonder with him what on earth is going on with Dr. Jekyll and Mr. Hyde.  If either Jekyll or Hyde were the narrator, there would be almost no suspense because either one would be able to explain to us, from the beginning, what the nature of their relationship is and how they are connected.  However, as it is, whenever Utterson is confused and suspicious, so are we.  Whenever he lacks information, so do we, and so Stevenson succeeds in creating a great deal more suspense by revealing the strange case to us as it is revealed to Utterson.  Then, as he pieces the full story together from Lanyon's narrative as well as Jekyll's letter, we see the big picture at the same time, finally relieving the tension for all of us. 

Who is the book The Virginian dedicated to?

At the beginning of The Virginian, we find a dedication to Theodore Roosevelt, in which Wister expresses his "changeless admiration" for a man who has seen and praised parts of the novel already. Wister also states that parts of the novel have been rewritten because Roosevelt "blamed," or criticized them. He calls Roosevelt his "dear critic."
Owen Wister, who wrote The Virginian in 1902, was a close friend of Theodore Roosevelt, whom he met when the two were students at Harvard together. Wister, in fact, wrote a memoir describing his friendship with Roosevelt, published in 1930. The two shared a love of the West and often discussed Wister's writing; there is a letter held in the Library of Congress from Roosevelt to Wister, in which Roosevelt expresses admiration for the way Wister has transformed the short stories upon which The Virginian was based into a "remarkable novel." Roosevelt particularly praises the chapter "Superstition Trail," and says that if he were not President, he would love to write a favorable review of the novel. I have attached a link to this letter below, as it offers some insight into the relationship between these two men and the nature of their correspondence, which Wister refers to in his dedication.
The dedication in full is as follows:

To Theodore Roosevelt
Some of these pages you have seen, some you have praised, one stands new-written because you blamed it; and all, my dear critic, beg leave to remind you of their author's changeless admiration.
https://www.theodorerooseveltcenter.org/Research/Digital-Library/Record/ImageViewer?libID=o182488

How does the author of "The Monkey's Paw" use foreshadowing in the first chapter to suggest that the spell placed on the paw might not bring happiness to whoever possesses it?

The author of "The Monkey's Paw" uses the words and behavior of Sergeant-Major Morris as ominous foreshadowing of what is likely to happen to the person who possesses the mummified paw on which an Indian fakir supposedly placed a spell. Here are a few examples of how Sergeant-Major Morris foreshadows what is to come.

"The first man had his three wishes. Yes," was the reply; "I don't know what the first two were, but the third was for death. That's how I got the paw."


"If you don't want it, Morris," said the other, "give it to me.""I won't," said his friend, doggedly. "I threw it on the fire. If you keep it, don't blame me for what happens. Pitch it on the fire again like a sensible man."
"Hold it up in your right hand and wish aloud," said the sergeant-major, "but I warn you of the consequences."

The reader is certainly prepared to expect something very bad to happen if Mr. White makes his three wishes. In fact, something strange and uncanny seems to happen even as he is in the process of making his first wish, thereby augmenting Sergeant-Major Morris' foreshadowing of evil. White drops the monkey's paw with revulsion and explains to his wife and son:

"It moved," he cried, with a glance of disgust at the object as it lay on the floor. "As I wished, it twisted in my hand like a snake."

Mr. White's experience may have been nothing more than his imagination intensified by his being startled by the crashing chord Herbert played on the piano at the moment he made his first wish. Throughout the story the reader can never be quite sure that the monkey's paw has any magical power at all. As Mr. White explains in Part II of the story:

"Morris said the things happened so naturally," said' his father, "that you might if you so wished attribute it to coincidence."

All of the foreshadowing at the beginning of the story is apparently intended by the author to prepare the reader to believe that the results of Mr. White's three wishes are not coincidences but the granting of those wishes by some supernatural power. The reader, however, will never know for sure and is left wondering.
 
 
 

Calculus of a Single Variable, Chapter 9, 9.4, Section 9.4, Problem 13

Limit comparison test is applicable, if suma_n and sumb_n are series with positive terms. If lim_(n->oo)a_n/b_n=L where L is a finite number and L>0 , then either both series converge or both diverge.
Given series is sum_(n=1)^oon/(n^2+1)
We can compare the series with sum_(n=1)^oon/n^2=sum_(n=1)^oo1/n
The comparison series sum_(n=1)^oo1/n is a divergent harmonic series.
a_n/b_n=(n/(n^2+1))/(1/n)=n^2/(n^2+1)
lim_(n->oo)a_n/b_n=lim_(n->oo)n^2/(n^2+1)
=lim_(n->oo)n^2/(n^2(1+1/n^2))
=lim_(n->oo)1/(1+1/n^2)
=1>0
Since the comparison series sum_(n=1)^oo1/n diverges, so the series sum_(n=1)^oon/(n^2+1) diverges as well, by the limit comparison test.

What is ironic about the newscaster?

The premise of Kurt Vonnegut's short story "Harrison Bergeron" is that in this futuristic society, everyone has become equal. Anyone who has an extraordinary talent or any kind of superior physical attributes is handicapped in various ways by the Handicapper General's office so that no one has an unfair advantage over anyone else.
The irony of the newscaster is that he can't do his job. He has a speech impediment that makes it impossible for him to report the news. He ends up handing the news bulletin to a ballerina who had been dancing on the show before the news bulletin that interrupts programming. The narrator explains in the story that all news announcers had a speech impediment, but stops short of saying that it is a handicap they all receive. Readers can infer that there is a good possibility that all news announcers receive a speech impediment as a handicap or that they are chosen for the job due to their challenges. Either way, it is ironic that someone whose job it is to report the news is unable to do so due to speech difficulties.

The television program was suddenly interrupted for a news bulletin. It wasn't clear at first as to what the bulletin was about, since the announcer, like all announcers, had a serious speech impediment. For about half a minute, and in a state of high excitement, the announcer tried to say, "Ladies and Gentlemen." He finally gave up, handed the bulletin to a ballerina to read. "That's all right," Hazel said of the announcer, "he tried. That's the big thing. He tried to do the best he could with what God gave him. He should get a nice raise for trying so hard."
"Ladies and Gentlemen," said the ballerina, reading the bulletin.

What is the relationship between Walter and Ruth in Scene 1.1?

In A Raisin in the Sun, Ruth and Walter Younger are a married couple in their thirties. They live in a small apartment with Walter's mother and his sister Beneatha, and Ruth and Walter's son Travis. The opening scene of the play introduces us to these characters and their relationship. Ruth is first seen trying to wake up her son Travis to go to school and she also does the same for her husband Walter. This shows that Ruth is the most responsible member of the family and also that her husband is almost treated like another child. She must wake up the boy and the man and then make their breakfast. While Walter waits for his breakfast, he mentions headlines from the newspaper to his wife, who is described as indifferent in the stage directions. She is obviously busy with her daily tasks and doesn't have the free time to wake up slowly and relax like her husband does. 
Later in the scene, Walter talks to Ruth about a plan he has with his friends to buy and operate a liquor store. He wants Ruth's help talking to his mother so she will approve of him spending his father's life insurance money on this business venture. Ruth seems to think the store is a bad idea, and Walter is insulted, telling his wife "A man needs for a woman to back him up..." (I.1). This will be an ongoing conflict in the play. Walter believes that other family members, including Ruth, do not support or believe in his dreams. The family is poor and struggles to make ends meet; the insurance money would be helpful to them in many ways, and different characters have opposing ideas for how to spend that sum. Walter believes that he would be helping the family in the long run, by running a profitable business, but Ruth thinks it's too risky. Walter lashes out at her, saying she has no respect for or interest in his dreams or his relationship with his friends.
At the same time, we can tell that Ruth and Walter have been married for some time and know each other fairly well. The circumstances of their lives, however, have caused conflict to be the centerpiece of their relationship when we meet them at the start of the play. 

sum_(n=2)^oo n/ln(n) Determine the convergence or divergence of the series.

sum_(n=2)^oo n/(ln (n))
To determine if the series is convergent or divergent, apply the nth-Term Test for Divergence.
It states that if the limit of a_n is not zero, or does not exist, then the sum diverges.

lim_(n->oo) a_n!=0      or      lim_(n->oo) a_n =DNE
:. sum a_n   diverges

Applying this, the limit of the term of the series as n approaches infinity is:
lim_(n->oo) a_n
=lim_(n->oo) n/ln(n)
To take the limit of this, use L’Hospital’s Rule.
=lim_(n->oo) (1)/(1/n)
=lim_(n->oo) n
=oo
Therefore, by the nth-Term Test for Divergence, the series diverges.

In Twelve Angry Men, which juror is particularly anxious to make a quick decision?

Juror #11 comments “Facts may be colored by the personalities of the people who present them.”  Does this occur in the movie?  Give examples to support your answer.

In Twelve Angry Men, the juror who wishes to hurry the vote is Juror No. 7.
A loud and superficial man, Juror No. 7 is a sarcastic salesman who is quick to form opinions. He is essentially a bully who disguises his cowardliness. No sooner is he inside the jury room than he begins to make quick judgments, saying,

How did you like that business about the knife? Did you ever hear a phonier story?

As the foreman calls the men to order, Juror No. 7 expresses his personal exigency in a flippant tone, saying

This better be fast. I've got tickets to The Seven Year Itch tonight. . . OK, your honor start the show.

When the first vote is called for by the foreman and only Juror No. 8 votes no, Juror 7 immediately questions him, "So what'd you vote not guilty for?" He then becomes somewhat combative with No. 8, who claims he voted in the negative because it is not "so easy" for him to raise his hand and give a boy the death penalty without any discussion. "Who says it's easy for me?" is his retort. When No. 8 calmly responds, "No one," No. 7 responds,

What? just because I voted fast? I think the guy's guilty. You couldn't change my mind if you talked for a hundred years.

Juror No. 7 continues to gripe about wasting time discussing a "kid like that" and complaining, "Some of us've got better things to do than sit around a jury room." When a secret vote is taken among the jurors, No. 7 demands to know who else voted "Not guilty."
When No. 5 later asks to change his vote to "not guilty," No. 7 becomes angry, "Oh, brother!" Further, he tells No. 8, "You sit in here and pull stories out of thin air." He criticizes some of No. 8's perceptive observations, later sarcastically asking, "Why don't we have them run the trial over just so you can get everything straight?"
Juror No. 7 is very critical of others. He ridicules No. 11, an immigrant. When No. 11 later accusing No. 7 of just voting as the majority does and not having "the guts to do what you think is right," No. 7 backs down.
It is not long, however, before he does exactly what No. 11 accuses him of. No. 7 complains he is "sick of this whole thing." He then suggests, "Let's break it up and go home. I'm changing my vote to not guilty. I've had enough." Of course, he is challenged on this opinion by No. 11, who asks him "What kind of a man are you?" No. 7 hesitantly says, "I told you. Not. . . guilty." In Act Three, No. 7 sincerely changes his mind to "Not guilty," making the vote unanimous.

lim_(x->1) lnx/sin(pix) Evaluate the limit, using L’Hôpital’s Rule if necessary.

lim_(x->1) (ln(x))/(sin(pix))
To solve, plug-in x = 1.
lim_(x->1) (ln(x))/(sin(pix)) = (ln(1))/(sin(pi*1)) = 0/0
Since the result is indeterminate, to find the limit of the function as x approaches 1, apply L'Hopital's Rule. So, take the derivative of the numerator and the denominator.
lim_(x->1) (ln(x))/(sin(pix)) =lim_(x->1) ((ln(x))')/((sin(pix))') = lim_(x->1) (1/x)/(pi cos(pix)) = lim_(x->1) 1/(pix cos(pix))
And, plug-in x = 1.
= 1/(pi*1*cos(pi*1))=1/(pi*cos(pi)) = 1/(pi*(-1)) = -1/(pi)
 
Therefore,  lim_(x->1) (ln(x))/(sin(pix))=-1/pi .

3, -6, 12, 4, 20 what is the next number in the pattern

In number sequences, in order to determine what comes next, it is important to look into the differences between the adjacent numbers. In most cases, the pattern is immediately recognizable by going through a few of the numbers. However for this particular problem, it becomes clear that the whole sequence needs to be looked into closer.
That said these are the answers we get when we subtract the previous number from the succeeding one:
2nd - 1st = (-6) - 3 = (-9)
3rd - 2nd = 12 - (-6) = 12 + 6 = 18
4th - 3rd = 4 - 12 = (-8)
5th - 4th = 20 - 4 = 16
Looking further, we see that the answers have a pattern themselves which are:
(-9), 18, (-8), 16
We see that the negative numbers are increasing while the positive numbers are decreasing. Using this pattern, we can see that the pattern of the answers is:
(-9), 18, (-8), 16, (-7)
Going back to the original problem, what this means is that
6th - 5th = (-7) or
6th = (-7) + 5th = (-7) + 20 = 13
Therefore the next number in the pattern is 13.

One of the ways to find patterns in the sequence of numbers is to examine differences between the adjacent numbers. In this case, we would find that:
2nd - 1st = -6 - 3 = -9
3d - 2nd = 12 - (-6) = 18
Notice that second difference can be obtained from the first by multiplication by (-2).
4th - 3rd = 4 - 12 = -8. This is 1 greater than the first difference, -9.
5th - 4th = 20 - 4 = 16. This can be obtained from the previous difference by multiplication by (-2), again.
To continue in this fashion, the next difference, between the 6th and the 5th term, must be greater than -8 by 1. Since -8 + 1 = -7, the 6th term can be obtained by subtracting 7 from the 5th term, 20:
20 - 7 = 13
To get the next, 7th term, multiply (-7) by (-2) and add it to the 6th term: 13 + (-7)(-2) = 13 + 14 = 27.
So the next two numbers in the sequence would be 13 and 27. The longer sequence (check the following numbers using the same pattern) would be
3, -6, 12, 4, 20, 13, 27, 21, 33...
This is one of the possibilities of how the given sequence of numbers is formed. There might be others.

What are some of Fortunato's weaknesses? How do you know?

Fortunato, Montresor's enemy and eventual victim in Poe's "The Cask of Amontillado," is not a very clearcut character to the reader, but he does exhibit a few character flaws according to Montresor's descriptions.
First of all, Fortunato is already drunk when he encounters Montresor, so he may have a weakness for alcohol. Related to his fondness for alcohol is Fortunato's excessive pride in his own knowledge of wine. Additionally, Montresor reports that Fortunato has somehow insulted him, but Fortunato is unaware of his offense. Two possible interpretations of this situation exist: it is possible that Montresor is an unstable person and he is oversensitive and overreactive, or it is possible that Fortunato has done something so hurtful to Montresor that his mistake leads him to his own death. If the second case is true, then another flaw of Fortunato's is his lack of self-awareness.

What is an oxymoron in The Hound of the Baskervilles?

An oxymoron is a literary device in which two opposing concepts or words are juxtaposed against each other. 
We can find a great example of an oxymoron in chapter eight of The Hound of the Baskervilles, "First Report of Doctor Watson."
On October 13th, Watson writes to Holmes from Baskerville Hall to describe how being there is like leaving behind all traces of contemporary England. He describes the graves that are scattered throughout the hillsides and the gray stone huts that are there too. He goes on to report the facts concerning Sir Henry Baskerville and to mention the escaped convict who is prowling the moor.
In the opening passage of his letter, we can find the oxymoron. Watson states that the longer he stays there, the more the spirit of the moor sinks into his soul—both its vastness and its "grim charm."
"Grim charm" is an oxymoron which juxtaposes a positive quality (charm) against a negative descriptor (grim). Watson is suggesting that while the moor is initially frightening, one can become accustomed to it. 

What are some ideas to help me with writing "The Ugly Duckling" in the voice of the Ugly Duckling?

When you write a short story, consider it as three parts, called the story sequence. Part I introduces the characters and the setting. In this part you show the main character in his or her normal setting and describe what the characters are like in the beginning of the story. For this story, you would describe where the ducks live, what they do on a normal day, and introduce the Ugly Duckling and, perhaps, name a couple of other ducks as characters.
Part II of your story is the Problem/Conflict section. Here you want to elaborate on the main character's want or need. Begin by having something bad happen to the Ugly Duckling, an incident of teasing. Describe from the Ugly Duckling's perspective how the teasing makes him feel and what he wishes his life was like, instead. You may have a couple of increasingly unkind instances of teasing in this section.
Part III of the story is the Climax/Resolution section. Here the rising action of the story, the increasing cruelty of the other ducks, reaches a peak. Something pushes the main character over the edge, so he has to make a decision that sets up the resolution of the conflict. In this story, he flies away in the spring and joins a group of beautiful birds, thinking he will be killed by them because of how ugly he is. But they welcome him. When he sees his reflection, he sees he is one of them. That is the resolution. He lives happily ever after, so describe how he feels upon seeing his own beauty and being part of a group who accepts him.
Writing from the Ugly Duckling's perspective doesn't mean you have to tell the story in first person (using "I" and "me"), but that is probably the easiest way to do it. Just keep in mind the three-part format of the story as you write: Setting, Conflict, and Climax/Resolution.

College Algebra, Chapter 1, 1.4, Section 1.4, Problem 14

Find the real imaginary part of the complex number $2 -\sqrt{-5}$

$
\begin{equation}
\begin{aligned}
& 2 - \sqrt{-5} && \text{recall that } i^2 = -1\\
\\
& 2 - \sqrt{5 i^2} && \text{Simplify}\\
\\
& 2 - i \sqrt{5} && \text{The real part is 2 while the imaginary part is } \sqrt{5}
\end{aligned}
\end{equation}
$

How does Susan Glaspell use imagery in her play Trifles?

Most of the imagery in Glaspell's one-act play Trfiles centers around the Wright home, which is also the crime scene being investigated. The key images become the clues that the women—Mrs. Hale and Mrs. Peters—use to solve the crime, while their husbands come up empty using traditional investigative methods.
Mr. Wright has been murdered, and his wife is being held at the prison. The men who are investigating the crime scene bring their wives along to gather some items for Mrs. Wright. As the women look around the house, they notice several key pieces of evidence ignored by their husbands. First, they notice the kitchen work that Mrs. Wright left unfinished. The imagery of the unfinished canning is the first clue that something went amiss and also the first detail that kick starts the women's empathy with Mrs. Wright. The image of Mrs. Wright's knitting is another major image that also serves as a clue for the women. They notice that Mrs. Wright dropped a stitch in her otherwise perfect knitting, indicating her disturbed state of mind. The most significant images are those of the birdcage and the dead bird. These are the clues that seal Mrs. Wright's motive in the women's minds. They seem the damaged birdcage without a bird and then find the body of the dead bird. This bird becomes symbolic of Mrs. Wright, nee Minnie Foster. One of the women remembers her when she used to sing. They piece together the information in the house and past knowledge of Minnie to determine that Mr. Wright would not let her sing and killed her bird. That is what made her snap and murder her husband. The act of taking the dead bird with them also shows that the women are going to protect Minnie and they understand why she committed the crime.
These major images serve as clues to help the women solve the crime. Significantly, these items and details are also seen as "trifles" by the men, so they are not able to uncover Mrs. Wright's motive.

In "Bullet In the Brain" by Tobias Wolff, in the first part of the story, how is the third-person point of view utilized to depict the characters? How is speech and thought presentation used to shape the reader's understanding of the events and characters in the passage?

"Bullet in the Brain" is, among other things, a story about criticism and critical distance. The use of third person in the story creates a kind of ironic separation between the events of the story, Anders' reaction to them, and the narrator's voice. Take, for instance, the words Anders exchanges with a woman waiting in line when a teller suddenly closes her window:

"Oh, that’s nice,” one of them said. She turned to Anders and add, confident of his accord, “One of those little human touches that keep us coming back for more.”
Anders had conceived his own towering hatred of the teller, but he immediately turned it on the presumptuous crybaby in front of him. “Damned unfair,” he said. “Tragic, really. If they’re not chopping off the wrong leg, or bombing your ancestral village, they’re closing their positions.”
She stood her ground. “I didn’t say it was tragic,” she said. “I just think it’s a pretty lousy way to treat your customers.”
“Unforgivable,” Anders said. “Heaven will take note.”

The narrator understands the attitudes of both Anders and the woman; it is through the narration that we come to see their short dialog as a kind of fight. At the same time, the narration serves as a commentary on Anders' thinking. Anders is a person who clearly hates everything, but the phrase "towering hatred" can only be understood as meant to belittle Anders and paint him as a prig. The fact that the narrator says the woman "stood her ground" implies a kind of approval of this woman's resistance to Anders' rudeness, which suggests that the narrator is functioning as a kind of critic of Anders' own over-developed critical sensitivities. In fact, Anders seems unable to separate reality from text: everything is subject to his critical judgement, even the speech of the hold-up men. It's possible that Anders' sense of distance from the events he witnesses suggests that he confuses himself with the narrator of his story, someone who cannot be affected by the events he narrates.

In Tobias Wolff's short story "Bullet in the Brain," third-person omniscient narration serves a dual purpose. First, by describing the activity in the bank in third person, the author provides a glimpse of many characters without championing the narrative of one. Though the reader gets a better sense of Anders's personality than that of any of the other characters, the setting is immediately relatable to anyone who has had to wait in line for service. The impatience of the customers and disinterest of the tellers are not personal; they are part of a common shared experience.
The second purpose of third-person is to reveal the bank robbers to the reader as they would be revealed to anyone standing in the bank. In contrast, if the story were told in first-person by any character, the reader would automatically be concerned with the fate of just one character. Because of the omnipotent third-person narration, the reader is left wondering what will happen, watching the interaction between the gunman and Anders as anxiously as anyone in the bank. Additionally, because of the omniscient voice, the point of view of the story could shift at any time, adding to the suspense.
The characters' words do not necessarily convey their feelings. For example, Anders is as frustrated with the teller closing her position as the woman in front of him, but he does not give the woman the satisfaction of agreeing with her. Instead, he says, “Tragic, really. If they’re not chopping off the wrong leg, or bombing your ancestral village, they’re closing their positions" (para. 3), minimizing the woman's frustration. This interaction proves to be illustrative of Anders's personality, as he can't keep himself from antagonizing the gunman, even upon threat of harm.  

What are the basic points in The Work of Art in the Age of Mechanical Reproduction?

The primary thesis of Benjamin's "The Work of Art in the Age of Mechanical Reproduction" is that mechanical reproduction has rendered art useless to fascism. Benjamin explicitly claims that reproduction has eradicated "a number of outmoded concepts, such as creativity and genius, eternal value and mystery—concepts whose uncontrolled (and at present almost uncontrollable) application would lead to a processing of data in the Fascist sense." To support this claim, Benjamin presents a thorough and complicated argument that grounds itself in the examination of certain concepts. These concepts are as follows: 1) the "aura" of the artwork, 2) art's origins as a "cult of ritual," and 3) the relation of the masses to works of art.
According to Benjamin, the "aura" of a work of art resides in "its presence in time and space, its unique existence at the place where it happens to be," and the historical authority this presence grants to the object. The erasure of the aura (the artwork's unique presence in space and time is elided by mechanical reproduction) results in a freeing from tradition, which leads into Benjamin's arguments about the "cult" nature of art.
Benjamin claims that "originally the contextual integration of art in tradition found its expression in the cult," and he then goes on to identify different types of artistic cults, such as the cult of religion and the cult of beauty. Whether the cult is religious or secular, Benjamin argues, "the unique value of the 'authentic' work of art has its basis in ritual, the location of its original use value." For Benjamin, erasing the aura is key to freeing art from "its parasitical dependence on ritual," which is important because art then becomes "based on another practice—politics." This shift from ritual to politics is the lynch pin of Benjamin's argument and leads into the last major topic of his essay, which is the relation of the masses to the artwork.
While Benjamin does talk about literature, he spends most of his time discussing film and how it, more than any other form of art, embodies the changes he is discussing. He frequently compares film to other art forms, such as painting and live theater performances, arguing throughout that the amount of technology involved in creating a film—and the ways this technology mediates the relationship between the audience, the artist, and the art object—creates a distinctly new understanding of art. This new understanding of art is grounded in the idea that "the greater the decrease in the social significance of an art form, the sharper the distinction between criticism and enjoyment by the public" (Benjamin).
Benjamin ends his essay by returning to the idea of fascism and how fascist ideology "seeks to give them [the working-class masses] an expression while preserving property. The logical result of Fascism is the introduction of aesthetics into political life." Benjamin goes on to say that this sort of aesthetic distraction inevitably results in war and that the politicization of art (due, of course, to the eradication of the "aura") is the communist defense against fascism.
https://www.marxists.org/reference/subject/philosophy/works/ge/benjamin.htm

What are some important quotations between Prospero and Caliban in The Tempest?

Caliban and Prospero see their rancorous relationship differently. Their first conversation reveals how they both view themselves as victims of one another. Prospero claims Caliban’s father was “the devil himself,” and it appears Caliban’s mother Sycorax was a witch who was on the island before Prospero. Both Caliban and Prospero curse one another, but only Prospero’s curses work thanks to his indentured servant Ariel, a magical spirit.
The two enemies agree Prospero was initially kind to Caliban, who describes how his surrogate father cared for and taught him:

When thou camest first,Thou strokedst me and madest much of me, wouldst give meWater with berries in't, and teach me howTo name the bigger light, and how the less,That burn by day and night:

Caliban says he also provided for Prospero, but now Prospero imprisons and enslaves him out of a desire for power. Prospero denies this, claiming he enslaves Caliban because he attempted to violate Prospero’s daughter Miranda. Caliban retorts, “You taught me language; and my profit on't / Is, I know how to curse.” Throughout the rest of the play, Prospero plagues Caliban and Caliban conspires to overthrow and kill Prospero. This conversation sets the stage for their conflict.
http://shakespeare.mit.edu/tempest/full.html

Why does Brutus choose to commit suicide at Philippi in Julius Caesar?

Choice A is the correct answer: To ancient Romans, suicide was an honorable way to die if it helped one avoid defeat and humiliation.    
 In Ancient Rome, suicide was considered an honorable alternative to being humiliated by the enemy.  Brutus and Cassius did not want to be captured by Antony and Octavius and marched in triumph through Rome.  A triumph was a military parade where the victor showed off his spoils and his captives.  It would have been the ultimate defeat for Brutus and Cassius. 
Before the battle, Brutus and Cassius discuss their plans if things go wrong.  They do not plan to be Antony’s captives.  This is a civil war.  To be marched in their own city as captives is unthinkable. 

CASSIUS
Then, if we lose this battle,You are contented to be led in triumphThorough the streets of Rome?
BRUTUS
No, Cassius, no: think not, thou noble Roman,That ever Brutus will go bound to Rome;He bears too great a mind.  … (Act 5, Scene 1) 

What do you do then?  If victory is out of grasp and it looks like there is a certain defeat, Brutus and Cassius agree that they will kill themselves.  In fact, each of them do.  Cassius thinks that he sees his enemies surrounding his men, when in fact it is a victory celebration he sees. He commits suicide prematurely, on his birthday. 
Brutus commits suicide later, when he knows that all is lost. 

… Countrymen,My heart doth joy that yet in all my lifeI found no man but he was true to me.I shall have glory by this losing dayMore than Octavius and Mark AntonyBy this vile conquest shall attain unto.So fare you well at once; for Brutus' tongueHath almost ended his life's history … (Act 5, Scene 5) 

Antony later calls Brutus the noblest Roman of them all.  He believes that unlike some of the other members of the conspiracy, Brutus was not involved for fame or power. He really was doing what he thought was best for Rome.
 
 

Which statement best expresses the theme of "The Laugher"?

“The Laugher” by Heinrich Böll is full of contradictions, so much so that they themselves become the main framework of the story. The narrator’s last statement beautifully encapsulates this absurd theme:

"So I laugh in many different ways, but my own laughter I have never heard."

In the first half of the story, the unnamed narrator describes his work, that of a professional laugher. He tells us of his versatility and range and the breadth of his knowledge of the art of cachinnation. However, he also makes a point of telling us how much he is attached to the truth—he won’t represent himself as an actor to others, because he feels he does not have all the skills of an actor and so cannot truthfully claim that title. Yet, his entire means of earning his keep is a lie (who hires someone to laugh when a subject is truthfully funny?), and so a dichotomy is set up between his avowed love of truth and his means of earning his keep.
The second half of the story only adds another layer to the split between what the narrator professes and his profession. He himself, as he says, is a solemn man, never laughing while off duty, and notes that he was that way since he was a boy. Laughter never occurs in his home, only occasional smiles. In fact, during his work hours he is responsible for the promotion and spread of laughter; at home, he suppresses it, and he has suppressed it so long and so successfully that his wife also laughs no longer.
Further, laughter itself is generally considered—leaving aside instances of laughter intended to be mocking or hurtful—to be an unfeigned and uncalculated response to humor or an unexpected situation. Yet the narrator’s entire vocation is the deliberate opposite. He provides laughter upon demand, in any quality or variety, regardless of (and, in the cases of the poor comedians, in direct contradiction to) natural instinct.
All of these contradictions are wrapped up in the ultimate sentence, which in itself adds the capstone: this man, whose job it is to spread laughter and expression of joy to others, has never himself been so joyful as to discover what his own laughter sounds like. Truly a sad—but apt—end to a funny little story.

What is the analysis of the story "How to Tell Renata"?

In the short story "How to Tell Renata," we are introduced to a first person narrator, Renata's daughter, who is fifteen years old and is soon starting high school. She has taken to reading the dictionary because her mind is on other things that worry her. Her worry is her mother's boyfriend, Jerry, who has started looking at her oddly and showing her inappropriate attention when her mother is at work.
The first word she sees in the dictionary is fact, something that really exists—emphasizing her situation with Jerry. The second word she reads is chimera,which means a creation of the imagination. She hopes that Jerry's attention is her imagination. The second word is realization; at this point, she knows his attention is not her imagination. The next word is ripe, which connotes maturity. She knows she will have to tell Renata about the situation, but she does not know how. She dreads telling her mother because she does not know whether her mom will believe her or not. Her mother cares for Jerry, so someone will be hurt. The last word is illuminate. This is a fitting word for the end of the story. The reader does not know what caused Renata's breakup with Jerry, but when the daughter comes home after trying to stay out late, his clothes are gone. He has moved out. Therefore, the situation is resolved before any further damage is done. Mother and daughter are safe.

How can we link conflict theory to child poverty?

Conflict theory is one of the main sociological theories. According to this theory, society is in a state of constant conflict because the elite try to maintain power and their share of resources by oppressing those without resources. This theory explains the existence of childhood poverty because the wealthy in society take far more resources, leaving little for the poor and the children of the poor. For example, the wealthy live in areas with better schools or send their children to private schools, and the society invests little money in improving education for poor children. In addition, the children of the poor cannot generally access high-quality medical care and other resources that improve their chances, and this situation perpetuates poverty. The elite class is not invested in changing this situation, as they hope to maintain a hold on the society's resources to help their own children.

Conflict Theory is a term coined by Karl Marx to explain that society is always in conflict over a small number of resources. For example, in the former Soviet Union, while everything was centralized and socialized, there was a limited amount of food to go around, and so people needed to line up in the streets outside of food distributors to ensure they received food.
Child poverty is related to this theory in that resources are being distributed unfairly, and the children are not able to successfully compete in order to attain adequate resources. Children are unable to provide income or contribute to competition for resources, and so in low economic areas, people with children tend to struggle more due to the lack of resources and natural competition for what is available. This disparity in resources and the inability of children to contribute means that those families with children suffer more and have less money, food, and other resources to go around. All of this contributes further to child poverty.

Conflict theory is one of the three main sociological perspectives.  It holds that all conditions and institutions in society come about through conflict between two or more groups within society.  Groups with different interests come into conflict with one another and whoever prevails in that conflict gets to make the rules for that particular aspect of society. 
If every aspect of society comes about because of conflict, then child poverty must be caused by conflict.  In the United States, at least, we can identify at least two types of conflict that cause child poverty.  First, we can say that child poverty arises from conflict between the poor and others.  People who are not poor want to keep the poor in poverty.  This ensures a cheap source of labor, allowing others in society to, for example, enjoy relatively cheap restaurant food and yard maintenance services.  The non-poor also set up rules that keep poor children from getting ahead so that those children will not be able to compete with their own children later in life.  In the United States, child poverty could also be linked to racial or ethnic conflict.  We know that disproportionate numbers of black and Hispanic children are poor.  Conflict theorists would say that these non-white children are poor because their race/ethnicity has lost out in conflict with whites (and perhaps with Asians).  In this view, racial and ethnic prejudice has caused conflict between these groups.  Whites have won this conflict and have set up a society that helps them prosper while making it harder for African Americans and Hispanics to do so.  This causes children from the two non-white groups to suffer from poverty more often.
In these ways, it is possible to link child poverty to the ideas of the conflict perspective.

College Algebra, Chapter 7, Review Exercises, Section Review Exercises, Problem 54

Express the system of linear equations $
\left\{
\begin{array}{ccccc}
2x & & +3z & = & 5 \\
x & +y & +6z & = & 0 \\
3x & -y & +z & = & 5
\end{array}
\right.$ as a matrix equation then solve the matrix equation by multiplying each side by the inverse of the coefficient matrix.

The equivalent matrix equation of the system is

$\left[
\begin{array}{ccc}
2 & 0 & 3 \\
1 & 1 & 6 \\
3 & -1 & 1
\end{array}
\right] \left[ \begin{array}{c}
x \\
y \\
z
\end{array} \right] = \left[ \begin{array}{c}
5 \\
0 \\
5
\end{array} \right]$

If we let

$\displaystyle A = \left[ \begin{array}{cc}
6 & -5 \\
8 & -7
\end{array} \right] \qquad X = \left[ \begin{array}{c}
x \\
y
\end{array} \right] \qquad B = \left[ \begin{array}{c}
1 \\
-1
\end{array} \right]$

Then the matrix can be written as

$AX = B$

We solve this matrix equation by multiplying each side by the inverse of $A$


$
\begin{equation}
\begin{aligned}

AX =& B
&&
\\
A^{-1} (AX) =& A^{-1} B
&& \text{Multiply each side by } A^{-1}
\\
(A^{-1} A) X =& A^{-1} B
&& \text{Associate Property}
\\
I_3 X =& A^{-1} B
&& \text{Property of Inverses}
\\
X =& A^{-1} B
&& \text{Property of Identity Matrix}

\end{aligned}
\end{equation}
$


Solving for the inverse of $A$

Add identity matrix to the right of the matrix

$\displaystyle \left[ \begin{array}{ccc|ccc}
2 & 0 & 3 & 1 & 0 & 0 \\
1 & 1 & 6 & 0 & 1 & 0 \\
3 & -1 & 1 & 0 & 0 & 1
\end{array} \right]$

Using Gauss-Jordan Elimination

$\displaystyle \frac{1}{2} R_1$

$\displaystyle \left[ \begin{array}{ccc|ccc}
1 & 0 & \displaystyle \frac{3}{2} & \displaystyle \frac{1}{2} & 0 & 0 \\
1 & 1 & 6 & 0 & 1 & 0 \\
3 & -1 & 1 & 0 & 0 & 1
\end{array} \right]$

$\displaystyle R_2 - R_1 \to R_2$

$\displaystyle \left[ \begin{array}{ccc|ccc}
1 & 0 & \displaystyle \frac{3}{2} & \displaystyle \frac{1}{2} & 0 & 0 \\
0 & 1 & \displaystyle \frac{9}{2} & \displaystyle \frac{-1}{2} & 1 & 0 \\
3 & -1 & 1 & 0 & 0 & 1
\end{array} \right]$

$\displaystyle R_3 - 3 R_1 \to R_3$

$\displaystyle \left[ \begin{array}{ccc|ccc}
1 & 0 & \displaystyle \frac{3}{2} & \displaystyle \frac{1}{2} & 0 & 0 \\
0 & 1 & \displaystyle \frac{9}{2} & \displaystyle \frac{-1}{2} & 1 & 0 \\
0 & -1 & \displaystyle \frac{-7}{2} & \displaystyle \frac{-3}{2} & 0 & 1
\end{array} \right]$

$\displaystyle R_3 + R_2 \to R_3$

$\displaystyle \left[ \begin{array}{ccc|ccc}
1 & 0 & \displaystyle \frac{3}{2} & \displaystyle \frac{1}{2} & 0 & 0 \\
0 & 1 & \displaystyle \frac{9}{2} & \displaystyle \frac{-1}{2} & 1 & 0 \\
0 & 0 & 1 & -2 & 1 & 1
\end{array} \right]$

$\displaystyle R_2 - \frac{9}{2} R_3 \to R_2$

$\displaystyle \left[ \begin{array}{ccc|ccc}
1 & 0 & \displaystyle \frac{3}{2} & \displaystyle \frac{1}{2} & 0 & 0 \\
0 & 1 & 0 & \displaystyle \frac{17}{2} & \displaystyle \frac{-7}{2} & \displaystyle \frac{-9}{2} \\
0 & 0 & 1 & -2 & 1 & 1
\end{array} \right]$

$\displaystyle R_1 - \frac{3}{2} R_3 \to R_1$

$\displaystyle \left[ \begin{array}{ccc|ccc}
1 & 0 & 0 & \displaystyle \frac{7}{2} & \displaystyle \frac{-3}{2} & \displaystyle \frac{-3}{2} \\
0 & 1 & 0 & \displaystyle \frac{17}{2} & \displaystyle \frac{-7}{2} & \displaystyle \frac{-9}{2} \\
0 & 0 & 1 & -2 & 1 & 1
\end{array} \right]$

So the inverse is

$\displaystyle A^{-1} = \left[ \begin{array}{ccc}
\displaystyle \frac{7}{2} & \displaystyle \frac{-3}{2} & \displaystyle \frac{-3}{2} \\
\displaystyle \frac{17}{2} & \displaystyle \frac{-7}{2} & \displaystyle \frac{-9}{2} \\
-2 & 1 & 1
\end{array} \right]$

Then,


$
\begin{equation}
\begin{aligned}

X =& A^{-1} B
\\
\\
X =& \left[ \begin{array}{ccc}
\displaystyle \frac{7}{2} & \displaystyle \frac{-3}{2} & \displaystyle \frac{-3}{2} \\
\displaystyle \frac{17}{2} & \displaystyle \frac{-7}{2} & \displaystyle \frac{-9}{2} \\
-2 & 1 & 1
\end{array} \right] \left[ \begin{array}{c}
5 \\
0 \\
5
\end{array} \right]
\\
\\
X =& \left[ \begin{array}{c}
\displaystyle \frac{7}{2} \cdot 5 + \left( \frac{-3}{2} \right) \cdot 0 + \left( \frac{-3}{2} \right) \cdot 5 \\
\displaystyle \frac{17}{2} \cdot 5 + \left( \frac{-7}{2} \right) \cdot 0 + \left( \frac{-9}{2} \right) \cdot 5 \\
-2 \cdot 5 + 1 \cdot 0 + 1 \cdot 5
\end{array} \right]
\\
\\
X =& \left[ \begin{array}{c}
10 \\
20 \\
-5
\end{array} \right]


\end{aligned}
\end{equation}
$

How can I take a position that explains to what extent the American Dream is real and achievable? I should synthesize the following sources: Wilson—the movie Fences Fitzgerald—The Great Gatsby Roosevelt—Fireside Chats Rawlings—The Hard Path to Citizenship Ehrenreich—Since When Is It a Crime to Be Poor?

The late American historian James Truslow Adams famously originated the phrase, if not the concept, of "the American Dream." As Adams defined it, "The American Dream is that dream of a land in which life should be better and richer and fuller for everyone, with opportunity for each according to ability or achievement." For much of the nation's history, the notion of an "American Dream" has sustained innumerable immigrants and citizens of less-developed countries who looked to the United States as the land of opportunity. There have, over the decades, been particularly difficult periods, in which the vision of a land of opportunity has waned, such as during the Great Depression. Tough economic times invariably force even the most idealistic or imaginative to reassess their notions of specific venues where the opportunities for advancement are markedly superior.
The student's question includes a number of sources comprised both of fictional accounts of life in America and nonfiction depictions of individuals (e.g., President Franklin Roosevelt) who have commented upon or inspired in some way a new evaluation of the concept of "the American Dream." F. Scott Fitzergald's tragedy The Great Gatsby is often cited as a example of a novel that dissects that concept and concludes, somewhat ambiguously, that the dream remains ephemeral. The Great Gatsby, of course, is about a young, somewhat naïve aspiring bond trader who leaves his Midwestern roots for the glamour and excitement of Wall Street.
Told from Nick Carraway's perspective, the book follows his adventures among the elite of Long Island from the vantage of the new money section known in the book as West Egg. Nick's neighbor, Jay Gatsby, is the novel's center insofar as the ideal of an American Dream drives the narrative. Gatsby, formerly James Gatz, is driven by the pursuit of success. His other obsession is Daisy Buchanan, Nick's second cousin who married into great wealth. Gatsby is determined to win back this lost love but knows that, if he is to succeed, he must attain the kind of wealth to which Daisy has become accustomed. The American Dream dictates that hard work is the key to material success, and Gatsby works hard to achieve his goal. The problem, though, is that Gatsby's chosen path to success is entirely criminal. He cannot succeed, although the odds are against him anyway. He cannot have what Tom Buchanan has no matter how much he earns through vice and, in the end, is just one more casualty of the endless struggle for wealth and social acceptance. Note, in this regard, the novel's final passage, after Gatsby has been killed and the Buchanans continue on as before:

"Gatsby believed in the green light, the orgastic future that year by year recedes before us. It eluded us then, but that’s no matter — tomorrow we will run faster, stretch out our arms farther. . . . And one fine morning ——
"So we beat on, boats against the current, borne back ceaselessly into the past."

In playwright August Wilson's Fences, Troy Maxson is imbued with a bitterness from the experience of having his life dictated by his ethnicity. As an African American baseball player whose peak coincided with the era of racial segregation, he knows that his chance at success are behind him. His sense of the American Dream is entirely cynical, born of that experience. His bitterness, however, extends to  his son Cory, a promising football player with a chance to attend college on an athletic scholarship. Observe in the following passage from Fences Troy's take on the American Dream during an exchange with his wife Rose:

Rose: Cory done went and got recruited by a college football team.
Troy: I told that boy about that football stuff. The white man ain't gonna let him get nowhere with that football. . .He ought to go and get recruited in how to fix cars or something where he can make a living."

Once, Troy was a young, skilled athlete. He is also black. To be black during the 1940s and 1950s was to be segregated from white society and denied opportunities that were supposed to be an integral component of the social contract known as the American Dream.
These are the fictional works inspired by their author's real-life observations of America and the road to success. Both are cynical, suggesting that the American Dream, if it exists at all, is only for a select few to whom material wealth is already promised. That Fitzgerald wrote his novel during an era when immigration and xenophobic sentiments were at a peak and displays of ostentatious wealth were common (even as the Great Depression loomed over the horizon), is testament to the prism through which he viewed the American Dream. It was these authors' mission to puncture the balloon.
President Franklin Delano Roosevelt was elected during the period when the balloon had burst. The Great Depression was four years old and unemployment was alarmingly high. While few Americans were cognizant, or cared, about the darkening clouds gathering over Europe—Adolf Hitler ascended to the chancellorship of Germany that same year—Roosevelt knew that the public's morale had to be lifted. His series of "Fireside Chats" were intended to lift the public's spirits. Television had yet to be invented, and families were reliant on radio as well as theaters and the printed media for their news and entertainment. Roosevelt understood that by bringing a soothing, confident voice of authority into American homes via these radio-delivered speeches and homilies, he could help an emotionally wounded people recover some of their confidence. And, he was right. By addressing the economic and social challenges confronting Americans, he was able to provide a measure of assurance that a steady, capable hand was at the helm, and that conditions would improve.
What did Roosevelt's "fireside chats" mean for the American Dream? Plenty. When tens of millions are out of work and the concept of bread lines has replaced notions of an American Dream, the president's discussions of the New Deal and the programs designed to put people back to work were more than a little welcome. Roosevelt's ability to trumpet the New Deal and the promise of a better future helped reinvigorate the American public's mental outlook and once again make the American Dream a viable option.
The Time magazine column penned by First Lieutenant Nate Rawlings is a contemporary attempt at addressing the current issue of immigration within the context of the concept of an American Dream. Lt. Rawlings raises a valid point when suggesting that those who enlist in the Armed Forces of the United States deserve an opportunity to pursue that dream.
Whether one believes that the American Dream exists is entirely subjective. Yes, hard work and perseverance can lead to professional success and material wealth. They are, however, no guarantee of success and wealth. Forty years in the coal mines is extremely admirable. Those forty years, however, are more likely to have lead to respiratory illnesses than to material comfort. Too many examples of ostentatious wealth derive more from mastery of arcane financial instruments intended to subvert regulatory structures rather than from manual labor.
https://www.history.com/topics/great-depression/fireside-chats

https://www.thebalance.com/what-is-the-american-dream-quotes-and-history-3306009

What is a detailed summary of the poem "Phenomenal Woman" by Maya Angelou?

From the outset it is pertinently clear that the speaker in the poem has an overwhelming pride in who she is and what she represents. She is no ordinary woman who subscribes to a stereotype. She is different and amazing. She has to be seen to be believed. She is special, extraordinary and powerful. 
 
The first stanza makes it clear that she does not deem herself "pretty." She does, however, exude a power and charisma that so-called pretty women want to learn about, for they want to know her secret. When she confirms that whatever she has is no secret, they don't believe her. It is clear that she deems everything about her special. It's not that she has any specific characteristic that makes her stand out. What makes her special is simple—she is a woman. It is being a woman that makes her remarkable. She asserts the fact by positively stating at the end of the stanza: "That's me."
 
In stanza two, the speaker emphasizes her greatness and continues in the same vein by confidently proclaiming that her entrance into a room immediately draws men's attention. She enters without making a fuss and they either stand up out of respect or, out of servile duty, bend their knees to her authority. It is as if these men have no choice—their reactions are automatic and each one, without exception, instinctively and simultaneously, reacts to her amazing presence. They then all surround her—she becomes the queen bee, surrounded by willing acolytes, ready to do her bidding. Once again, the speaker lists the qualities she has that make these "fellows" respond so obligingly to her: it's the fact that she exudes a supreme confidence through her eyes, her smile, the way she swings her waist and how she walks. The assertion is extended—she is a woman, an exceptional and extraordinary being. She has these attributes and this power because she is a woman, and that is what makes her so exceedingly special.
 
The third stanza is a couplet which repeats her earlier declaration that she is sensational. The fact that this statement stands on its own further accentuates the power she believes she has.
 
The fourth stanza suggests that men see her as an enigma. They don't know what it is about her that they find attractive. It is not something tangible and, therefore, it is out of their reach. Her power is a mysterious force that they cannot comprehend even when she tries to show them exactly what it is. Once again, the speaker exclaims that her grandness lies in a number of qualities that she possesses followed by the repetition that she is a woman and that her incredible stature lies therein.
 
The fifth and final stanza offers somewhat of a resolution to the enigma of who or what the speaker is. Here she explains why she does not behave in the stereotypical manner in which she may be expected to. She does not demurely bow her head, nor does she seek attention by jumping about or talking loudly. Her appearance and her stature should be enough to make anyone proud because she exudes, and is, the epitome of pride. The speaker again refers to a number of attributes which, in part, define her, the most significant of which is the fact that she is needed by those who seek care. The word "'cause" brings clarity, for it explains why the speaker is so supremely special—she is a woman and being one makes her an outstanding member of the human race.
 
One could say that the poem carries a universal message to all women. It is a positive and clear pronouncement that women should be proud of who and what they are. They should celebrate the fact that they are extraordinary in every way. Each part of what they have makes them who they are—it is for this reason that the speaker, throughout the poem, mentions certain feminine traits—each one a part of the whole. The speaker believes that women should walk with their heads held high and should not succumb to stereotypes and the expectations of others. They should not allow themselves to be judged on individual qualities but as a complete whole—a fact that they should repeatedly assert, just as the speaker does.

What is a statement of theme for Twilight by Stephenie Meyer?

A statement of theme means that you are being asked to state (write) what a central theme of a piece of literature is.  Theme can be defined as a main idea or underlying meaning of a literary work.  Generally a statement of theme needs to be followed up with supporting evidence.  It's not good form to state that a theme is present without providing evidence to support that claim.    
One theme that is present in Twilight (and the rest of the series) is love and desire.  Bella and Edward are hopelessly in love with each other.  Jacob is in love with Bella.  The rest of the Cullen couples are in love with each other.  The book is full of teenage love and desire.  
I think another theme is the theme of mortality and immortality.  That theme is closely tied with the theme of choices as well.  Bella is mortal, and the Cullens are immortal.  Bella has a choice throughout the series to become like the Cullens, and a great deal of time is spent discussing the positives and negatives of such a choice.  
https://literarydevices.net/theme/

Number of cities Phileas Fogg visited in India

At Suez, Phileas Fogg and Passepartout board a steamer bound for Bombay. Also with them is the doggedly determined Inspector Fix, hot on the heels of a notorious bank robber who bears more than a passing resemblance to the intrepid gentleman explorer. The travelers arrive two days ahead of schedule. From Bombay they make their way by train to Calcutta. Fogg is somewhat miffed to realize that the Daily Telegraph was wrong after all; the railroad actually ends at Kholby and then starts again another 50 miles further on at Allahabad.
The ever-resourceful Fogg buys himself an elephant, hires a local guide, and begins the long trek towards Allahabad. On the way there he sees a young widow by the name of Aouda, who's about to be thrown on her late husband's funeral pyre, in accordance with ancient Hindu tradition. Fogg and Passepartout hatch a daring plan to rescue the unfortunate young lady. Passepartout swaps places with her late husband's corpse. His subsequent "resurrection" scares off the assembled priests, allowing Passepartout to whisk Aouda off to safety. Fogg loses two days of traveling time due to this little escapade, but he doesn't mind. Saving Aouda was the right thing to do.

Single Variable Calculus, Chapter 1, 1.3, Section 1.3, Problem 36

We need to find (a) $f \circ g$, (b) $g \circ f$, (c) $f \circ f$, and (d) $g \circ g$ and state their domains



$f(x) = \frac{x}{1+x} , \qquad \quad g(x) = \sin 2x$


$
\begin{equation}
\begin{aligned}
\text{(a)} \qquad \quad f \circ g =& f(g(x))\\


\displaystyle f(\sin 2x)=& \frac{x}{1+x}
&& \text{ Substitute the given function $g(x)$ to the value of $x$ of the function $f(x)$}\\


\end{aligned}
\end{equation}
$


$\boxed{\displaystyle f \circ g = \frac{\sin 2x}{1+ \sin 2x}}$

$\boxed{ \text{The domain of this function is } \displaystyle (-\infty, \frac{-\pi}{4}) \bigcup\displaystyle(\frac{-\pi}{4}, \infty)}$


$
\begin{equation}
\begin{aligned}
\text{(b)} \qquad \quad f \circ g =& g(f(x))\\


\displaystyle g \left(\frac{x}{1+x}\right) =& \sin 2x
&& \text{ Substitute the given function $g(x)$ to the value of $x$ of the function $f(x)$}\\

\displaystyle g \left(\frac{x}{1+x}\right) =& \sin 2\left(\frac{x}{1+x}\right)
&& \text{ Simplify the equation }
\end{aligned}
\end{equation}
$



$\boxed{\displaystyle f \circ g= \sin \left(\frac{2x}{1+x}\right)}$


$\boxed{ \text{The domain of this function is } (-\infty, -1) \bigcup(-1,\infty)}$




$
\begin{equation}
\begin{aligned}
\text{(c)} \qquad \quad f \circ f =& f(f(x))\\


\displaystyle f\left(\frac{x}{1+x}\right) =& \frac{x}{1+x}
&& \text{ Substitute the given function $g(x)$ to the value of $x$ of the function $f(x)$}\\

\displaystyle f\left(\frac{x}{1+x}\right)=& \frac{\frac{x}{1+x}}{1+\frac{x}{1+x}}
&& \text{ Get the LCD of the numerator and the denominator}\\

\displaystyle f\left(\frac{x}{1+x}\right)=& \frac{\frac{x}{\cancel{1+x}}}{\frac{1+x+x}{\cancel{1+x}}}
&& \text{ Cancel out and combine like terms}

\end{aligned}
\end{equation}
$


$\boxed{\displaystyle f \circ f = \frac{x}{2x+1}}$

$\boxed{\text{ The domain of this function is } \displaystyle(-\infty, \frac{-1}{2}) \bigcup \displaystyle(\frac{-1}{2},\infty)}$


$
\begin{equation}
\begin{aligned}
\text{(d)} \qquad \quad g \circ g =& g(g(x))\\

g(\sin 2x)=& \sin 2x
&& \text{ Substitute the given function $g(x)$ to the value of $x$ of the function $f(x)$}\\

g(\sin 2x)=& \sin 2(\sin 2x)
&& \text{ Simplify equation}

\end{aligned}
\end{equation}
$


$\boxed{g \circ g= \sin(2 \sin 2x)}$


$\boxed{\text{ The domain of this function is }(-\infty,\infty)}$

What kinds of landscapes do we see in "Crossing Brooklyn Ferry" by Walt Whitman? What roles do the ferry and nature play in the poem?

Whitman’s poem describes what he sees on a ferry crossing between Brooklyn to Manhattan. But the poem uses this landscape as a way of imaginatively casting himself into the future. Whitman’s description of his trip is addressed to “you that shall cross from shore to shore years hence”; there is something about the specificity of his experience, as captured in this poem, that enables him to directly address a future reader.
The things Whitman sees, of course, are the day-to-day workings of ships on the river; he sees the “Twelfth-month sea-gulls... oscillating their bodies”; he sees himself reflected in the water below, and “Look’d at the fine centrifugal spokes of light round the shape of my head in the sunlit water”; he also sees the people aboard their passing boats, the “sailors at work in the rigging” or the steamer pilots “in their pilot-houses,” and then, the “gray walls of the granite storehouses by the docks,” or, on shore, “the foundry chimneys burning high and glaringly into the night.” Whitman does not present these details in a romanticized way. His point is that they don’t need to be romanticized—to be alive in the world is enough. As he says, addressing his future reader across the centuries,

What is more subtle than this which ties me to the woman or man that looks in my face?
Which fuses me into you now, and pours my meaning into you?
We understand then do we not?

Walt Whitman's "Crossing Brooklyn Ferry" is a poem that exemplifies Whitman's abilities as a leading proponent of the transcendentalism literary movement. The poem depicts a thoughtful narrator taking the Brooklyn ferry home. He absorbs the entire scene, and early in the poem he has an uncanny sense in his observations of the throng of humanity taking the ferry:

Flood-tide below me! I see you face to face!
Clouds of the west—sun there half an hour high—I see you also face to face.
Crowds of men and women attired in the usual costumes, how curious you are to me! (1057)

In this everyday scene, the narrator has a transcendent moment in which he realizes that this same ferry will host future generations long after its current passengers have died. He pictures the ebb and flow of a constant ocean, the buzzing streets of Manhattan, the hills of Brooklyn, and several other striking images. In the poem, the ferry plays a role as a potent metaphor: it is the bridge between the present and the future.

Fifty years hence, others will see them as they cross, the sun half an hour high,
A hundred years hence, or ever so many hundred years hence, others will see them,
Will enjoy the sunset, the pouring-in of the flood-tide, the falling-back to the sea of the ebb-tide (1058).

Nature plays a similar role as something that remains constant in the face of a changing, evolving mass of humanity:

Flow on, river! flow with the flood-tide, and ebb with the ebb-tide!
Frolic on, crested and scallop-edg'd waves!(1061)

The vivid, grandiose imagery Whitman presents is made more potent because he is focusing on what many would consider to be a mundane scene. He casts the ferry as a bridge between the present and the future, and exalts the natural scenery he depicts as a reminder of the constancy of our world.
All line numbers were retrieved from The Norton Anthology of American Literature, Volume 1 7th Ed

In the second sentence, the narrator asserts that "you," the reader, "know the nature of [his] soul." What do we know about the narrator when he first makes this claim and what do you know about him by the end of the story?

We know very little about Montresor, the narrator, by the second sentence of the story. We do realize from the first sentence that he is a proud and vengeful man who vows to punish when he is insulted. This opening statement provides a hint that he is not a saintly and forgiving human being.
By the end of the story, we know that Montresor is a man capable of cold-bloodedly walling up his enemy in a cold, moldy catacomb and leaving him alone to die. This act indicates that Montresor's soul, from a spiritual point of view, is not in good order. He has committed a heinous sin, and now, fifty years later, he wants to talk about it. His statement near the end that "my heart grew sick" and his confession of what he did indicates that he does feel some remorse for his act.

How do the views and outlooks and accomplishments of Greece and Rome compare to those of Western Europe during the Middle Ages and Renaissance?

This question seems to be addressing the intellectual and cultural achievements of the classical world versus those of medieval and Renaissance Europe. So this answer will not include a discussion of the military, diplomatic, or, for the most part, political achievements of either. The simplest way to answer such a broad question is to say that the cultural achievements and indeed the outlook of the medieval period and Renaissance era were heavily influenced by the Greeks and the Romans. While we usually associate the medieval period as a sort of intellectual backwater, it actually featured a great deal of creative thought. While the outlook was decidedly religious in nature, tending to regard mankind as debased in comparison with the divine, it nevertheless drew on a classical worldview advanced by Aristotle. The medieval philosophy known as Scholasticism, often associated with Thomas Aquinas, for example, was strongly influenced by Aristotle. 
The most explicit evocation of Greek and Roman thought, however, came with the Renaissance. Humanism, the philosophy that guided Renaissance thinkers, writers, and artists, emphasized a return to what were believed to be the classical ideals of the ancient Greeks and Romans. Scorning what they thought to be medieval ignorance, they turned especially to Roman writers like Livy and Ovid to celebrate man, his achievements, and his potential. They viewed Greek and Roman philosophers and writers as possessing knowledge that had been lost during the Middle Ages. In terms of outlook, we must speak very generally, but it is safe to say that the worldview of the Italian Renaissance in particular had more in common with the secularism of some Greek and Roman philosophers (Epicurus, for example) than that of the medieval period. The critical worldview embraced by the Greeks in particular resonated with Renaissance philosophers, and the example of participatory government based on a virtuous citizenry set by Romans of the Republican period was emulated by Machiavelli, among others. 

What was Oedipus's tragic flaw?

For many years there's been a fairly intense debate raging in academia as to precisely what constitutes Oedipus's tragic flaw. It's not possible to provide a definitive answer to the question here, but there are a couple of possibilities that we can examine.
The first of these is pride, or hubris, as the Greeks called it. When Oedipus visits the Oracle at Delphi, she tells him that one day he will kill his father and marry his mother. Understandably, Oedipus is shocked at hearing this, as anyone would be. Less understandably, however, he chooses to defy fate, displaying extraordinary hubris in the process. Ironically, his act of overweening pride ultimately leads to his downfall. It's precisely because Oedipus refuses to return to Corinth that he ends up meeting his birth father, Laius, on the road, where he subsequently kills him.
A slightly less convincing case could be made for anger as Oedipus's tragic flaw. After all, it's anger that leads Oedipus to kill his father. There are two problems with this approach, however. First of all, although anger does indeed lead directly to Laius's death, it has nothing whatsoever to do with the other part of the Oracle's prophecy: that Oedipus will marry his mother. In fact, this has more to do with the hubris that Oedipus displayed in solving the riddle of the Sphinx, for which he was rewarded with Jocasta's hand in marriage.
The second problem with the anger case is that Oedipus's killing of Laius could reasonably be justified on the grounds of self-defense. Certainly, most of the audience watching Oedipus Rex will have arrived at the same conclusion. After all, Oedipus, like Laius himself, is a king, and as such would be expected to defend his honor, by force if necessary.
On balance, then, hubris would seem to be the most likely answer to your question. However, the matter is far from settled. The important thing is to read the play carefully and make up your own mind.
 

What is the main conflict in My Side of the Mountain by Jean George?

I would say the main conflict of My Side of the Mountain is an external man vs. nature conflict. In the beginning of the book, Sam Gribley decides to live on his own out in the wilderness. He does this in a manner befitting an extreme survivalist because when he leaves civilization, he has minimal supplies. Sam doesn't take food or a lot of tools. He leaves New York in May with “a penknife, a ball of chord, an ax, and $40,” as well as flint and steel for making fires.
That is an exceptionally small amount of gear. I like camping, but Sam puts me to shame. Throughout the novel, he is continually in conflict with the nature that surrounds him. Not only does he have to deal with the challenges of finding decent shelter, but he also has to hunt and forage for food. Because his diet is so meager, Sam struggles with vitamin deficiencies and very low calorie intakes. As winter approaches, Sam discovers his meager supplies cannot adequately deal with winter conditions.


Toward the end of January I began to feel tired, and my elbows and knees were a little stiff. This worried me. I figured it was due to some vitamin I wasn't getting, but I couldn't remember which vitamin it was or even where I would find it if I could remember it.


As the book moves toward its conclusion, Sam's conflict turns into an internal conflict. Sam must decide to continue living on his own or return to his family.

Sam Gribley is a city kid who runs away from New York city to live in a tree on his ancestral land in the wilderness of the Catskill Mountains. The main conflict of the plot is man versus nature. Sam has read about and studied some outdoor and survival skills, but this is the first time he has a chance to use these techniques. Each day is a learning experience for him. He learns about edible plants. He trains a young falcon to help him hunt for meat. He makes his own tools, and hollows out a large hemlock tree to use as a house. The case could also be made that an additional conflict is man versus civilization. Sam wants to be on his own, and he doesn’t want to be found. He goes into town on occasion, but only when he needs to. After about six months on the mountain, a few people begin to find him, too.

Single Variable Calculus, Chapter 7, Review Exercises, Section Review Exercises, Problem 46

Differentiate $\displaystyle y = x \tan h^{-1} \sqrt{x}$


$
\begin{equation}
\begin{aligned}

y' =& \frac{d}{dx} (x \tan h^{-1} \sqrt{x})
\\
\\
y' =& x \frac{d}{dx} (\tan h^{-1} \sqrt{x}) + \tan h^{-1} \sqrt{x} \frac{d}{dx} (x)
\\
\\
y' =& x \cdot \frac{1}{1 - (\sqrt{x})^2} \frac{d}{dx} (\sqrt{x}) + \tan h^{-1} \sqrt{x}
\\
\\
y' =& \frac{x }{1 - x} \frac{d}{dx} (x^{\frac{1}{2}}) + \tan h^{-1} \sqrt{x}
\\
\\
y' =& \frac{x}{1 - x} \cdot \frac{1}{2} x^{\frac{-1}{2}} + \tan h^{-1} \sqrt{x}
\\
\\
y' =& \frac{x}{2x^{\frac{1}{2}} (1 - x)} + \tan h^{-1} \sqrt{x}
\\
\\
y' =& \frac{x^{\frac{1}{2}}}{2(1 - x)} + \tan h^{-1} \sqrt{x}
\\
\\
& \text{or}
\\
\\
y' =& \frac{\sqrt{x}}{2 (1 - x)} + \tan h^{-1} \sqrt{x}
\end{aligned}
\end{equation}
$

Why do you think should Hrothgar find confidence in someone like Beowulf?

Hrothgar confidently puts his hopes (for safety and victory against Grendel) in Beowulf for a variety of reasons. One very superficial reason is that Beowulf looks the part of a big, strong, brave, experienced warrior. Early in the narrative, Beowulf is on his way to see Hrothgar. A guard stops Beowulf and wants to know Beowulf's purpose, and the guard also comments on what Beowulf looks like:

"Nor have I seenA mightier man-at-arms on this earthThan the one standing here: unless I am mistaken,He is truly noble. This is no mereHanger-on in a hero’s armour."

This is the same image that Hrothgar will eventually see. Beowulf also has some very strong and heroic stories tied to his name. For example, we are told that Beowulf has the strength of thirty men.

"Who valuable gift-gems of the Geatmen carriedAs peace-offering thither, that he thirty men’s grappleHas in his hand, the hero-in-battle."

These things would help to give Hrothgar confidence in Beowulf as an experienced and strong warrior. The final thing that I think would give Hrothgar confidence is that Beowulf seeks him out. Beowulf wants to step into this fight. Beowulf isn't going into this fight because he is cornered and there is no other option—he is confident that he can defeat Grendel, and Hrothgar has to feel confident as well because of that. Beowulf isn't likely to step into a fight that is a guaranteed loss.

Hrothgar has enormous confidence in Beowulf, not least because Beowulf has such enormous confidence in himself. When Beowulf arrives at Heorot, he regales the assembled throng with tales of how he battled courageously against fierce sea monsters and other vicious beasts, before slaying them in the icy wastes off the coast of Finland. Beowulf may come across as a bit of a braggart, but it was considered perfectly normal for warriors in that culture to boast about their legendary exploits; indeed, it was expected of them.
After hearing of Beowulf's tales of daring, Hrothgar knows he's found the right man to take on Grendel. He also knows that Beowulf isn't engaged in idle boasting; his reputation for bravery and fearlessness precedes him and goes back many years. As subsequent events will prove, Hrothgar has every right to repose his trust and confidence in the great Geatish warrior.

College Algebra, Chapter 2, 2.1, Section 2.1, Problem 32

(a) Plot the points $(2,13),(7,1)$ in the coordinate plane. (b) Find the distance between them. c) Find the midpoint of the segment that joins them
a.)




b.) By using distance formula.

$
\begin{equation}
\begin{aligned}
d &= \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}\\
\\
d &= \sqrt{(7-2)^2 + (1-13)^2}\\
\\
d &= \sqrt{(5)^2 + (-12)^2}\\
\\
d &= \sqrt{25+144}\\
\\
d &= \sqrt{169}\\
\\
d &= 13 \text{ units}
\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}
\text{c.) } x &= \frac{2+7}{2} = \frac{9}{2}\\
\\
y &= \frac{13+1}{2} = \frac{14}{2} = 7
\end{aligned}
\end{equation}
$

Thus, the midpoint is $\left( \frac{9}{2},7 \right)$

What are the circumstances surrounding Janet Waking?

The narrator is Janet's father whose helplessness to prevent his beloved daughter's exposure to life's pain and suffering drive the story as it unfolds.  The physical context of John Crowe Ransom's poem "Janet Waking" is a normal domestic morning for Janet as she greets her parents when she wakes up before dashing to visit her pet hen, Chucky.  The normalcy is shattered when Janet discovers that the hen is dead.  The poem's deeper context is Janet confronting the sudden knowledge that death is real, catapulting her from childhood innocence and initiating her into adult pain. Also shattered is her father's role as hero in his child's life.  The broader context speaks to the agony both father and daughter feel when unable to protect a loved one.

What is Thomas Paine trying to tell the colonists and soldiers in his book, The Crisis?

The Crisis is a series of articles written by Thomas Paine that encourages support for the American Revolution. In his articles, he talks about the difficulty of obtaining freedom. He wants the American people to know that it is worth fighting for something as important as freedom. He reminds the people and the soldiers that this will be a difficult struggle, but a struggle that is worth fighting. He is trying to inspire the American people and soldiers.
He reminds the colonists why we need to fight for freedom. He states that most people would agree that a separation from Great Britain is inevitable. He urges the American people to make this separation in their time so their children can have freedom and peace.
He speaks negatively about the British and those who support them. He urges people to support our leaders, at times suggesting that G-d is on our side. He also tells the people to be wary of those Americans who support the British. He is very critical of the British generals.
Thomas Paine wants the American people to know we are fighting for the right reasons. The British have treated us poorly, and we are fighting to eliminate that poor treatment.
The Crisis was designed to boost our spirits as well as the spirits of the soldiers fighting the Revolutionary War. One purpose of these articles is to continue to push for people to support our efforts in the Revolutionary War.
https://www.ushistory.org/paine/crisis/

https://www.ushistory.org/paine/crisis/c-01.htm

How did Plato Teach ?

Plato was one of the most important educators in history. This should come as no surprise, considering his mentor was Socrates, who many consider the greatest teacher in history. In c. 387 BC, Plato founded a school known simply as the "Academy." Located in Athens, this school was likely the first "university" in the Western world.
Plato's Academy exhibited Socratic teaching methodology. Plato and the other "senior members" of the Academy would present questions and problems to their students, and it would be their mission to solve them cooperatively, through discussion. Often called dialectic, Plato taught using the same inquisitive discourse which Socrates uses in Plato's dialogues. However, historians note that there is some evidence that teachers would give occasional lectures to their students.