What was F. Scott Fitzgerald's main purpose for writing The Great Gatsby?

According to the foreword to the novel written by Charles Scribner III, Fitzgerald wanted to write a book that was "consciously artistic" and "beautiful and simple and intricately patterned."
Having had commercial success with This Side of Paradise, Fitzgerald hoped, in other words, to write a literary masterpiece. Fitzgerald started to write this novel as a satire called Trimalchio, based on the Roman satire the Satyricon, but the novel transcended that form. Gatsby was modeled on Trimalchio, a nouveau riche former slave who gave lavish parties, but Gatsby transformed in Fitzgerald's hands into a figure of tragic romance.
Fitzgerald also wanted to explore the American Dream, as the novel does through Gatsby's desire to start anew and wipe away the past, which is part of the larger American dream of coming to a new continent and creating a new and improved society. In Gatsby's case, the dream means regaining Daisy and acting as if the years they were apart never happened.
Fitzgerald succeeded in writing a novel that was lyrical, short, and "intricately patterned"—there is an enormous attention to detail in this work. Though not a success on its first release, the novel is now solidly in the canon of great American literature.
https://bigthink.com/purpose-inc/f-scott-fitzgerald-on-writing-the-great-gatsby

There are many purposes in the novel. We look at the disillusionment of the materialistic world, how excessive it is and how corrupted wealth is.

Despite its slim size, The Great Gatsby encompasses a diverse array of important themes, commenting on everything from the state of capitalism to gender relations. As such, it's very difficult to pinpoint a major purpose. That said, if there is a major purpose in the novel, it is most likely Fitzgerald's critique of the classical American Dream.
Simply put, the American Dream is the widespread notion that any American citizen can achieve happiness and fulfillment by simply working as hard as possible. Fitzgerald deconstructs this idea by showing that, though Gatsby works hard and acquires a vast store of riches, he does not ever achieve true happiness or fulfillment. For Gatsby, true happiness involves earning the lasting love of Daisy. However, though Daisy loves him in her own way, she is not able to love him as fully as he would prefer, and in the end Daisy abandons Gatsby. Thus, no matter how hard Gatsby works to gain material wealth, he ultimately dies alone, and so much of the novel's major purpose is to ultimately critique the mythology of the American Dream.    

Intermediate Algebra, Chapter 4, 4.1, Section 4.1, Problem 16

Solve the system $
\begin{equation}
\begin{aligned}

x - 4y =& -4 \\
3x + y =& 1

\end{aligned}
\end{equation}
$ by graphing.

To graph these linear equation, we plot several points for each line.

$x - 4y = -4$

$\begin{array}{c|c}
x & y \\
\hline \\
-4 & 0 \\
0 & 1 \\
4 & 2
\end{array} $

$3x + y = 1$

$\begin{array}{c|c}
x & y \\
\hline \\
-1 & 4 \\
0 & 1 \\
1 & -2
\end{array} $







Based from the graph, the point of intersection is $(0,1)$.

Therefore, the solution to the system is $(0,1)$.

How was Helen Keller a daring and adventurous girl?

Helen Keller was daring and adventurous in childhood and throughout her life. After becoming deaf and blind due to an illness at only eighteen months of age, Helen had to survive on her own perseverance and persistence from early childhood to adulthood.
In that era, blind children were referred to as “children of the silent night,” and they would typically demonstrate difficult behavior. Helen was no exception to having temper tantrums. Helen was a troublemaker in the household, but no one had the heart to punish her, especially her mother.
However, it was that rambunctious spirit that held Helen together in her most trying times. Helen also met Dr. Alexander Graham Bell when she was six years old. Her parents wanted him to meet her so they could get advice regarding Helen’s future.
While some people would find blindness and deafness a disadvantage, Helen could not accept defeat. It was her daring and adventurous spirit that helped her throughout her endeavors. Relying on the help of her family and friends, Helen learned to find light and hope in her dark visual world. She got help from her teacher, Anne Sullivan, at the Perkins Institute for the Blind.
While training with her teacher, Helen learned to feel objects and then associate them with words spelled out on the palm of her hand. She could also read sentences by feeling raised words on cardboard. She then learned to lip read by placing her hands on the throat and lips of the speaker while words were spelled out for her.
While at the Perkins Institute, Helen met other blind children and connected with them. Sullivan also took Helen to Cape Cod for one summer, and Helen notes wonderful memories by the seashore. Helen loved the outdoors and the changing seasons. She loved the snow and icicles, and she loved to toboggan in the winter. She also later learned how to manage canoeing and sailing. She even visited Niagara Falls and was captured by its magical power.
At age of sixteen, Helen entered Cambridge School for Young Ladies in Massachusetts; she later entered Radcliffe College. In college, she was always enthusiastic about reading books and learning. Helen has stated that “the best and most beautiful things in the world cannot be seen or even touched. They must be felt with the heart.”
https://archive.nytimes.com/www.nytimes.com/books/first/h/herrmann-keller.html

https://www.britannica.com/biography/Helen-Keller

Before Miss Sullivan arrives, Helen shows her sense of adventure and daring by getting into much mischief. She and Martha Washington, for example, steal a cake and eat it by the woodpile. Helen also locks her mother in a pantry.
After Miss Sullivan has a civilizing effect on Helen, Helen channels her sense of adventure into more constructive goals. For example, she is determined to go to Harvard, which in those days, for a woman, meant Radcliffe, despite the problems posed by being blind and deaf. A less daring person might not have taken on the challenge in a time before colleges provided accommodations for people with disabilities. Nevertheless, she faces the challenge head on, preparing by going to school, then successfully coping with the many obstacles in her path, such as a lack of textbooks in Braille. At a time when the vast majority of women didn't attend college at all, this was quite an achievement.

Why did the Greeks have different types of columns?

The different Greek columns reflect the evolution of architectural styles over time.
The earliest Greek order of column, the Doric, evolved from earlier wooden models. That is why it is a simpler and stockier version of the other orders of columns. It usually lacks the decorative functions of a base.
The Ionic order of columns originated in the sixth century BCE. Ionic columns tend to be more slender than the earlier Doric columns. They have added decorative elements, such as a stylized capital. This reflects advances in stone working technology and a changing aesthetic in style. As tastes in art and architecture changed, so too did the columns.
The Corinthian order of columns is the most elaborate and decorative of the three. It employs the most stylization of any Greek column. By comparing these orders, we can see that the Greeks had different types of columns as tastes and styles evolved over time. More stylization was desired in later periods than before, and columns evolved to meet this.

Calculus of a Single Variable, Chapter 3, 3.2, Section 3.2, Problem 18

The Rolle's theorem is applicable to the given function, only if the function is continuous and differentiable over the interval, and f(a) = f(b). Since all trigonometric functions are continuous and differentiable on R, hence, the given function is continuous and differentiable on interval. Now, you need to check if f(0) = f(2pi).
f(0) = cos 0 = 1
f(2pi) = cos (2pi) = 1
Since all the three conditions are valid, you may apply Rolle's theorem:
f'(c)(b-a) = 0
Replacing 2pi for b and 0 for a, yields:
f'(c)(2pi-0) = 0
You need to evaluate f'(c):
f'(c) = (cos c)' => f'(c) = - sin c
Replacing the found values in equation f'(c)(2pi-0) = 0
-2pi*sin c = 0 => sin c = 0 => c = 0, c = pi, c = 2pi
Since c = {0,2pi} !in (0,2pi), the only valid value for c is pi .
Hence, in this case, the Rolle's theorem may be applied for c = pi .

At the end of the story, what answer is given to the question of the title, "How Much Land Does a Man Need?"

The story portrays Pahom’s greed and the devil’s mischief. The devil overheard Pahom boast about how he would not fear the devil if he had enough land. The statement was made during a conversation between Pahom’s wife and her sister from the city. The sister bragged about how they had better lives in the city compared to what Pahom’s wife and her family had in the countryside. She talked about the exciting social life and advanced amenities in the city. Pahom’s wife in defense stated that although they did not enjoy the benefits of city life, they had less complicated lives with minimal risks to their fortunes. Pahom took the opportunity to state that the only problem facing people in the countryside was insufficient access to land and it was in the same breath that he made the boast.
The devil lured Pahom into his trap by offering him land. Pahom’s greed got the best of him, and he made a fatal mistake when the Bashkir’s made him an offer to acquire their land. In attempts to carve out a huge piece of land, Pahom walked too far and died of extreme exhaustion in front of the Bashkirs and their chief.  Pahom’s demise proved that he did not need all the land he tried to acquire because after death he left it all behind. He was buried in a six feet long grave, which was all the land he needed after all.

His servant picked up the spade and dug a grave long enough for Pahom to lie in, and buried him in it. Six feet from his head to his heels was all he needed.

Why Chris is irresponsible?

Chris could be described as irresponsible in that he shames his father so badly that he commits suicide. Yet in challenging his father's fraudulent behavior, he wants his family to recognize that there are people outside the Keller family to whom they have responsibilities. There is a clear conflict here between family and social responsibilities. Joe tries to reconcile this conflict, but without success. Chris, too, in his own way, tries to do likewise, but is also unable to do this. In fact, as he admits to Annie, he's something of a moral coward, and this confession makes him seem not quite the pillar of integrity we've been led to believe he is. Despite angrily confronting his father over his cutting of corners, Chris still feels Joe's influence. He now recognizes that he, too, has the spirit of practicality, a spirit he's inherited from his father. It's this realization that makes Chris shirk his responsibility of seeing that Joe should be brought to justice for what he's done.

Why does Nick go East and when does he do it?

We can find the answer to this question right at the beginning of the book when Nick Carraway is explaining who he is and the background to the current story. He explains that after his graduation from New Haven his career was then interrupted by the Great War, after which he felt very "restless" when he came back to the Midwest, which "now seemed like the ragged edge of the universe." For this reason, and to quell his own sense of restlessness (we can assume that Nick, like most returning soldiers, was probably suffering from shell shock on some level, and certainly from culture shock), Nick decided to go east and "learn the bond business."
Nick broached this idea to his family, having come up with it because many of his other single male friends were in the bond business, so it seemed like a good option. There is no suggestion that Nick was particularly drawn to it for any other reason, but his family approved of the idea, and so Nick did go east in 1922.

What happened at the end of the book Hoot by Carl Hiaasen?

Carl Hiaasen's novel Hoot consists of twenty-one chapters and an epilogue. In chapter twenty, the groundbreaking ceremony for the new Mother Paula's pancake house is taking place. Mullet Fingers, whose real name is Napolean Bridger Leep, has been trying to stop construction through various tricks. He wants to stop construction in order to save the burrowing owls on the property. During the groundbreaking ceremony, Mullet Fingers has buried himself in one of the owl dens with only his head sticking out. He has a bucket of "snakes" with him that he threatens to let out if they go forward with construction. Chuck Muckle, the vice president of the Mother Paula's organization, calls his bluff by taking his gold-painted shovel and hacking the snakes to pieces. They are made out of rubber. 
Roy tells the crowd that there are owls on the property and the pancake house will destroy their habitat. He tries to prove his point, but the pictures they took to prove the owls lived on the property were grainy and dark. The students who are at the groundbreaking ceremony join hands to prevent the bulldozers from beginning the groundbreaking. At the end of chapter twenty, a burrowing owl lands on Mullet Fingers's head, proving their existence. 
In chapter twenty-one, the press, present for the groundbreaking ceremony, reports the entire story in the newspaper the next day. Roy's family meets Kelly Colfax, a reporter Chuck Muckle assaulted during the groundbreaking. Roy's dad gives Kelly Colfax an envelope that contains the file for the Mother Paula's project. Roy's father got the file from the courthouse and had it examined by lawyers who were experts in environmental law. The file was missing the environmental impact statement, which proves Chuck Muckle and Curly Branitt knew about the owls and tried to cover it up. 
In the epilogue, the Gazette reports that the environmental impact statement turned up in the golf bag of Councilman Grandy, along with an envelope containing $4,500. This scandal permanently shuts down construction of the restaurant on the property at East Oriole and Woodbury. Chuck Muckle was demoted to Assistant Junior Vice President and was court-ordered to take an anger management class. Mother Paula's company pledges to create an owl sanctuary on the property. 
Mullet Fingers ends up in juvenile detention when his mother reports that he stole her valuable toe ring. He manages to escape juvenile detention by using his cell mate, Dana Matherson, as a decoy.

College Algebra, Chapter 4, 4.3, Section 4.3, Problem 12

Two polynomials $P(x) = 6x^3 + x^2 - 12x + 5$ and $D(x) = 3x - 4$. Use either synthetic or long division to divide $P(x)$ by $D(x)$, and express the quotient $\displaystyle \frac{P(x)}{D(x)}$ in the form $\displaystyle \frac{P(x)}{D(x)} = Q(x) + \frac{R(x)}{D(x)}$.

Using Long Division







The process is complete at this point because $5$ is of lesser degree than the divisor $3x - 4$. We see that $Q(x) = 2x^2 + 3x$ and $R(x) = 5$, so


$
\begin{equation}
\begin{aligned}

\frac{6x^3 + x^2 - 12x + 5}{3x - 4} =& 2x^2 + 3x + \frac{5}{3x - 4}

\end{aligned}
\end{equation}
$

Why has Boldwood's disturbance caused by Bathseba's valentine been compared with 'first floating weed to Columbus" in 'Far from the Madding Crowd'

As the remainder of this quote indicates, the meaning here is that the valentine is a small thing that hints at potentially enormous change, or  "contemptibly little suggesting possibilities of the infinitely great." 
To understand that comparison, you need to know about what Columbus and his men experienced on their voyage of discovery in 1492 -- information that Hardy assumes his audience shares.
About a week after the sailors finally lost sight of the land they had departed from, Columbus (writing in his log) wrote that they began to encounter

"large patches of weeds very green, and which appeared to have been recently washed away from the land."

This caused excitement and hope, because the men

"concluded that it must come from some nearby land. But at the same time, it caused some of them great apprehension because in some places it was so thick that it actually held back the ships."

Weeks later, they were still at sea -- longer than anyone had anticipated -- and the men were openly expressing their fears and doubts that they would ever reach land.

"Some feel that they have already arrived where men have never dared to sail and that they are not obliged to go to the end of the world."

But the sightings of floating weed continued. It was a persistent feature in their lives--a sign that a mysterious new land was near, and that they were on the verge of a huge, life-altering change.
So when Boldwood receives the valentine, it represents for him that sort of sign. We've been told in Chapter 12 that Boldwood is

"erect in attitude, and quiet in demeanour. One characteristic pre-eminently marked him — dignity."

He is the only man in the market who ignores Bathsheba, giving rise to the impression of someone "wrapt up and indifferent, and seemingly so far away from all he sees around him." This, says Liddy is probably due to a failed romance in his past.
The valentine Boldwood receives was sent as a cruel joke, but he doesn't know that. He spreads it out on his mantelpiece and studies every clue it might contain. But there is very little to go on--just a child's rhyme  ("The rose is red, The violet blue, Carnation's sweet, And so are you") on a flimsy piece of paper, and an envelope with his name written on it and a red seal bearing the words "marry me."
He obsesses over the mystery of who wrote the letter, dreams about the unknown woman of his imagination, and experiences "nervous excitability" that bothers him. He is accustomed to being dignified, standoffish, and in control. Clearly, he is intrigued about the idea that an admirer wants to marry him, and the prospect of this future represents a new world that is both exciting and a bit frightening.
https://sourcebooks.fordham.edu/source/columbus1.asp

How does Hansberry make the opening scene of A Raisin in the Sun a significant one?

Lorraine Hansberry opens the play with a description of the Younger's old, cramped apartment, which is much too small for the rather large family. The apartment and the worn-down furniture correspond to the family's current situation. The play begins with Ruth waking up Travis, who sleeps on the couch, before she begins making breakfast for her husband, Walter. When Walter enters the scene, he immediately asks Ruth about the insurance check, and the couple begins to bicker with each other. Ruth and Walter's relationship is clearly strained, and Walter proceeds to give Travis money, despite Ruth's disapproval. After Travis leaves for school, Walter begins talking about his business idea with Willy Harris, and Ruth mentions that his business partner is a "good-for-nothing loudmouth." Walter responds to Ruth's comment with a passionate speech about being tired and stressed out all of the time. Through Walter's speech, Hansberry illustrates his dream of using the insurance check to invest in his liquor business. However, Ruth simply replies to her husband's dreams by telling him to eat his eggs. Walter's plea and Ruth's response creates sympathy for his character.
When Beneatha enters the scene, she is portrayed as a young, educated woman who is as intense as her brother. Walter once again mentions the insurance check, and Beneatha responds by telling him that it belongs to Mama. Walter then criticizes Beneatha for wanting to become a doctor, and she responds by ridiculing his plan to invest in a liquor business. Their interaction illustrates the tension among the family members and further develops the theme of attaining one's dream.
After Walter leaves for work, Lena enters the scene and has a conversation with Ruth. Ruth attempts to influence Lena's decision to let Walter invest in the liquor business in the hopes that he will be happy and their marriage will prosper. However, Lena detests the idea of going into the liquor business and expresses her own dream of buying a home. Hansberry further characterizes Beneatha by portraying her as an ambivalent girl with fleeting interests. Hansberry also depicts the tension between Ruth and Lena's views regarding men, which contrast with Beneatha's modern ideas of romance. When the conversation shifts to the topic of God, Beneatha mentions that she does not believe in God. Lena responds by powerfully slapping Beneatha in the face and making her say, "In my mother's house there is still a God" (Hansberry, 9). Lena's display of authority establishes her as the head of the household, which indicates that she has the final say in how the insurance money will be spent. The scene ends with Lena talking to Ruth about her "strong-willed" children, and Ruth loses consciousness as Lena is watering her plant.
Hansberry depicts the conflicts of interest regarding how to spend Lena's insurance check while simultaneously characterizing each member of the Younger family. While Walter Jr. is the play's protagonist, Lena is depicted as the authority figure in the home. The tension between each character is illustrated, and the audience wonders whose dream will come to fruition. Both Walter and Beneatha are portrayed as strong-willed individuals, and nobody in the family seems content with their current situation. The decision regarding how to spend the insurance money drives the plot, as each character wishes to improve their life.

Why were the Ottoman Turks during this time period relatively tolerant of religions other than Islam while the Europeans were definitely not tolerant of any religion other than their particular type of Christianity?

For the early Ottoman rulers, religious tolerance proved an excellent political choice, as it facilitated Ottoman expansion in Europe. Throughout the Balkans, Cyprus, Crete, and Greece, society at that time was religiously divided; the Catholic nobility generally ruled over Greek or Slavic Orthodox peasants and artisans. Various western Catholic states, especially Venice, established control over many locations in the Eastern Mediterranean after the crusaders sacked Constantinople (1204) and established the Latin Empire and divided the remnants of Byzantium among themselves. The restored Byzantine Empire (1261–1453) was a mere shadow of its former self and never managed to recapture most of its lost territories.
Persistent weakness drove the late Byzantine rulers towards union with Rome, which promised to help Byzantium fight off the Turks if the Byzantine Church would accept the authority of the pope. Many Eastern Orthodox people, including influential religious and political figures, resented the imperial readiness to accept Catholicism. They considered Catholics heretics and regarded them as greedy and aggressive; some Eastern Orthodox people openly declared that Ottoman domination would be preferable to Catholicism. As a result, when the Ottomans conquered the Southern Balkans in the late fourteenth century, the reasonably tolerant Muslim rulers could count on at least some of the Orthodox Slavs and Greeks to accept them as a lesser evil compared to Catholic rule.
Sufi dervish orders exercised a strong influence on the early Ottoman rulers and shaped their religious policy. The Sufis were generally quite tolerant towards other faiths, as they believed in the universality of mystical religious revelation. As a result, Ottoman policy generally allowed members of other religions, especially Christians and Jews, to maintain their religious identities with little discrimination.
That minimal discrimination benefited the government substantially and provided a huge economic incentive to welcome millions of loyal non-Muslim subjects. As non-Muslims, they had to pay the jizya tax. They also provided thousands of boys (one in every five boys per village) to the Sultan’s army, which converted them to Islam and then raised and educated as future Ottoman officials or soldiers. These ex-Christian soldiers made up the famous Janissary corps, the shock troops of the Ottoman army.

e^(2x) = sinh(2x) + cosh(2x) Verify the identity.

e^(2x)=sinh(2x)+cosh(2x)
Take note that hyperbolic sine and hyperbolic cosine are defined as

sinh(u) = (e^u-e^(-u))/2

cosh(u)=(e^u+e^(-u))/2
Apply these two formulas to express the right side in exponential form.
e^(2x)=(e^(2x)-e^(-2x))/2 + (e^(2x)+e^(-2x))/2
Adding the two fractions, the right side simplifies to
e^(2x) = (2e^(2x))/2
e^(2x)=e^(2x)
This proves that the given equation is an identity.
 
Therefore,  e^(2x)=sinh(2x)+cosh(2x)  is an identity.

Precalculus, Chapter 8, 8.1, Section 8.1, Problem 69

x+2y-3z=-28
4y+2z=0
-x+y-z=-5
The equations in the matrix form can be written as,
[[1,2,-3,-28],[0,4,2,0],[-1,1,-1,-5]]
Add Row 1 and Row 3
[[1,2,-3,-28],[0,4,2,0],[0,3,-4,-33]]
Multiply Row 2 by 2 and Add it to Row 3
[[1,2,-3,-28],[0,4,2,0],[0,11,0,-33]]
Now the equations can be written as,
x+2y-3z=-28 ----- equation 1
4y+2z=0 ------ equation 2
11y=-33 ----- equation 3
From equation 3,
y=-33/11=-3
Substitute back y in equation 2,
4(-3)+2z=0
-12+2z=0
2z=12
z=12/2=6
substitute back y and z in equation 1,
x+2(-3)-3(6)=-28
x-6-18=-28
x=-28+18+6
x=-4
So the solutions are x=-4, y=-3, z=6

Is The Duchess of Malfi a revenge tragedy?

A revenge tragedy, made popular in Elizabethan and Jacobean Britain, typically tells the story of a protagonist seeking revenge against the murderous actions of an antagonist. Shakespeare's Hamlet is probably seen as the most typical revenge tragedy of those times and the play that popularized many of the genre's conventions, including soliloquies, madness, action-packed scenes, bloody murders, important noble figures, suicide, and the use of disguise.
The Duchess of Malfi is also seen as a revenge tragedy, just not a typical one.
It is a revenge tragedy because, firstly, it features a character, Bosola, who seeks revenge for the murders of the play's most noble characters. Secondly, it features some of the genre's most typical characteristics: soliloquies, sensational murders, madness, and Machiavellian characters.
Soliloquies
Bosola is the only character in the play who gives the audience insight into his true state of mind by speaking his thoughts aloud. For example, at the end of act 4, he shows guilt for arranging to kill the Duchess of Malfi by telling the audience,

All our good deeds and bad, a perspectiveThat shows us hell! That we cannot be suffer'dTo do good when we have a mind to it!This is manly sorrow

Sensational murders
Perhaps the most sensational murder of many is when Bosola orders the executioner to kill the Duchess and her children at the end of act 4. Just before the executioner strangles her, the Duchess says,

What would it pleasure me to have my throat cutWith diamonds? or to be smotheredWith cassia or to be shot to death with pearls?I know death hath ten thousand several doorsFor men to take their exits. . . .


Dispose my breath how please you.

With the Duchess dead, Bosola tells his men,

some other strangle the children.

Madness
Like Hamlet loses his mind after the death of his father, the Duchess's brother Ferdinand loses his mind in act 5, scene 2 after the death of his sister. At one point he attempts to throttle his own shadow.

Eagles commonly fly alone: they are crows, dawsand starlings that flock together. Look, what's that follows me?I will throttle it.

Machiavellian characters
The Cardinal is probably the play's Machiavellian character and, though professing to be a man of God, kills his lover by tricking her into kissing the cover of a poisoned bible:

Now you shall never utter it; thy curiosityHath undone thee; thou 'rt poison'd with that bookBecause I knew thou couldst not keep my counselI have bound thee to 't by death

Where The Duchess of Malfi is different from most revenge tragedies is that the protagonist revenging the deaths of the principle characters, Bosola, is the one that either killed them or played a hand in their deaths. Not only that, but he doesn't decide to take revenge until the end of act 5, scene 4, when he says,
I have this cardinal in the forge already;Now I'll bring him to th' hammer O direful misprison.
Up to that point, the play could just as easily have been a tragedy in the vein of Romeo and Juliet.

It is indeed appropriate to describe The Duchess of Malfi as a revenge tragedy, albeit one that departs in some respects from the traditional definition. Nonetheless, most of the key elements are present. Let's now look at some of them in greater detail:

Horrors. There are numerous horrors in the play. One thinks of the scene where the Duchess kisses a dead man's severed hand, believing it to belong to the Duke. The grotesque spectacle of the wax figures of the dead bodies of Antonio and the children being presented to the Duchess is yet another particularly creepy example.

Madness. The Duke deliberately attempts to drive the Duchess mad, yet he is the one who ends up going insane. The theme of madness also feeds into the different angle on revenge presented by Webster, which departs from the traditional conventions of revenge tragedy. In The Duchess of Malfi it's the villains, not the heroes, who seek revenge. The Duchess's wicked brothers are effectively driven mad by their desire to get even; in that sense, they are the victims of their own revenge.

Characters of noble birth. According to the prevailing dramatic conventions, only the suffering of characters of noble birth were a fit source for revenge tragedy (or any kind of tragedy, for that matter). The nobility had more to lose and further to fall. Indeed, being brought low was in itself thought to be tragic for someone of noble birth such as the Duchess. Tragedy implies some kind of fall, and that's precisely what happens, not just to the Duchess, but also to her evil brothers, who are morally corrupted by their insane, all-consuming desire for revenge.

First, we should think about the definition of a "revenge tragedy." The term was first used by the American Shakespeare scholar Ashley H. Thorndike (1871–1933) in a 1902 article "The Relations of Hamlet to Contemporary Revenge Plays." It has since become a common term in literary criticism used to elucidate the common characteristics of many Elizabethan and Jacobean dramas. The characteristics include
a plot involving some form of revenge, usually for a past injustice
a convoluted and action-packed plot structure
madness
disguise or other forms of pretense
violent murders
many characters dying in the fifth act
extremely evil villains
cannibalism
highly wrought figurative language
exotic setting (Italy, Spain, etc.)
The play is set in Italy. Ferdinand, the duke of Calabria, is a typical revenge tragedy villain. The plot is extremely convoluted and includes the ruse to send Antonio away and keep the children safe. Many of the characters are murdered near the end of the play.
Although The Duchess of Malfi does not have the classic plot arc of a single avenger seeking and obtaining justice for a past injustice, it has many of the other characteristics of revenge drama and, as a result, most critics consider it a revenge tragedy. 

Why does the narrator call attention to Robbie’s, Nettle’s, and Mace’s acts of kindness?

Atonement is a 2001 novel written by Ian McEwan. Early in the novel, the narrator, Briony Tallis, witnesses her sister, Cecilia, and Robbie sharing an intimate moment in the family's library. She believes that Robbie is being sexually aggressive toward her sister, so later in the novel, when Robbie asks Briony to deliver a letter to Cecilia, she reads it to find an explicit confession of Robbie's true feelings for Cecilia. Because Briony is only a child, she doesn't quite understand what the letter means. She is confused by Robbie's confessions and is not keen on his relationship with her sister.
Later that evening, when the twins go missing during dinner, Briony discovers her cousin Lola being sexually assaulted during the search. Although Briony did not clearly see who committed the crime, she thinks back to the scene in the family's library and tells the police that it was Robbie who raped her cousin. Despite his innocence, the police take Robbie away.
As the novel follows Briony's life as a writer, she learns more about life itself, which includes the situation that took place that fateful night at her family's home. She begins to understand that Robbie was not only innocent, but that he truly loved Cecilia. Throughout the book, she mentions others' acts of kindness toward her. She believes that writing the story of Robbie and Cecilia's life is her way to atone (hence the title of the book) for what she had done as a child. For example, in the epilogue, Briony mentions how the letters Nettle sent her helped her recreate Robbie's trip to Dunkirk, which further developed the story she was writing.
At the end of the novel, Briony states, ”I like to think that it isn't weakness or evasion, but a final act of kindness, a stand against oblivion and despair, to let my lovers live and unite them at the end. I gave them happiness, but I was not so self-serving as to let them forgive me." Briony is speaking of Robbie and Cecilia, who in her version of the story end up living together happily. At this point in the novel, Briony is now an elderly woman who truly understands the extent of the damage she caused by lying to the police. Although she has written a life where Cecilia and Robbie end up together, she knows this is not the reality her sister and Robbie faced, thus the latter half of the line. Briony considers Robbie, Mace, and Nettle's acts of kindness, recognizing that they were kind to her when they had no reason to be.

Single Variable Calculus, Chapter 8, 8.1, Section 8.1, Problem 38

Evaluate $\displaystyle \int \sin (\ln x) dx$ by making a substitution first, then by using Integration by parts.
If we use $z = \ln x$, then $e^z = x$ so $dx = e^z dz$
Thus,


$\displaystyle \int \sin (\ln x) dx = \int \sin z \left( e^z dz \right) = \int e^z \sin z dz$
By using Integration by parts, if we let $u = e^z$ and $dv = \sin z dz$ then,
$du = e^z dz$ and $v = -\cos z$

Thus,

$
\begin{equation}
\begin{aligned}
\int e^z \sin z dz = uv - \int vdu &= -e^z \cos z - \int (-\cos z) (e^z dz)\\
\\
&= -e^z \cos z + \int e^z \cos z dz
\end{aligned}
\end{equation}
$

Again by using Integration by parts, if we let

$
\begin{equation}
\begin{aligned}
u_1 &= e^z && \text{and}& dv_1 &= \cos z dz \text{, then}\\
\\
du_1 &= e^z dz && \text{and}& v_1 &= \sin z
\end{aligned}
\end{equation}
$

So,
$\displaystyle \int e^z \cos z dz = u_1 v_1 - \int v_1 du, = e^z \sin z - \int \sin z(e^z dz)$

Going back to the first equation,
$\displaystyle \int e^z \sin z dz = -e^z \cos z + \left[e^z\sin z - \int \sin z \left( e^z dz \right) \right]$

Combining like terms, we obtain

$
\begin{equation}
\begin{aligned}
2 \int e^z \sin z dz &= -e^z \cos z + e^z \sin z\\
\\
\int e^z \sin z dz &= \frac{e^z(\sin z - \cos z)}{2}

\end{aligned}
\end{equation}
$

but $z = \ln x$,

Therefore,


$
\begin{equation}
\begin{aligned}
\frac{e^z(\sin z - \cos z)}{2} &= \frac{e^{\ln x} (\sin (\ln x) - \cos (\ln x))}{2}\\
\\
&= \frac{x}{2} [ \sin (\ln x) - \cos (\ln x)] + c
\end{aligned}
\end{equation}
$

Why would African Americans be concerned about the United States allowing thousands of Filipinos to become a part of the United States?

Black Americans occupied the lower rungs of the socioeconomic ladder following the end of slavery—and many still do so today. Immigrants tend to come from lower socioeconomic levels in their home country, but this is certainly not always the case. When immigrants go to any country, whether the US or anywhere else, they often have to take tough jobs in order to survive. This is due to several reasons, including a lack of a family to support them, the lack of a social network, as well as the lack of a social safety net in case they run into financial trouble. Historically, immigrants, whether they are from Europe, Asia, or Africa, are often known to be hard working because they do not have those things that native-born individuals already have.
As with any immigrant group, Filipinos began to create their own communities and businesses. Many times these were in areas already occupied by minorities, such as black Americans. Growing communities of immigrants can slowly displace groups already in an area, creating friction between the two as the native-born population sees jobs and businesses being dominated by others. But as you can see, this is not necessarily an issue between two specific groups but rather an issue that can develop between any native-born group and immigrant group. 
https://www.migrationpolicy.org/article/filipino-immigrants-united-states

Monarchs across Europe worried about the revolution happening in France, why?

From the Middle Ages onward, much of Europe operated under the feudal system. In feudalism, the king owns all of the land in his kingdom but gives large parcels of it to nobles to rule in exchange for military service. The nobles then designate smaller portions of land to be lived on and worked by the peasantry, who are in turn protected by the nobles. The kings and nobles, along with the peasants, represent two parts of the Three Orders of society: bellatores (those who fight, the nobles) and laboratores (the working peasantry.) The third Order was oratores (those who pray,) including all of the religious monastics and clergymen in society. These Three Orders were considered to be the natural forms and functions of a society, and as long as everyone fulfilled their role, everything was perfect... right?
Not so much! The feudal system became increasingly complex and troubled as nobles might break up their land among lesser nobles, often resulting in an individual being obliged to more than one superior! In addition, times of environmental stress created a difficult situation for the peasants. Crop failure was considered to be the fault of the peasantry (or punishment from God) while the nobility were still demanding a significant portion of the food produced. Peasant riots shared the same sentiment which later drove the revolution.
Here is something important to bear in mind: though peasants were not skilled in the arts of war and diplomacy, they far outnumbered both the religious and noble of society. As the feudal system continued to disintegrate or become more convoluted over time, it made things harder on the largest portion of society. Pretty much across the board, life for the peasantry was the same in every kingdom: survive on meager foods and work until you die. When the French peasantry became fed up with being exploited under the Ancien Regime, which developed out of feudalism, it signified a possibility that was previously unthinkable: the peasantry could overcome the nobility. 
Monarchs across Europe were rightly frightened because their power in society, and the entire way their kingdom functioned, developed out of the feudal system and likely suffered the same complications as in France. The combination of social inequality and increased education and literacy for the peasantry proved deadly for many a noble. Scholars like Marx and Engels later described these revolutions as the naturally occurring result of an unsustainable socioeconomic system which exploits the proletariat (working class) and impedes human development. Perhaps the monarchs of Europe heard of the Revolution in France, took a long look at their own kingdoms, and realized that they, too, were unsustainable.
https://www.britannica.com/event/ancien-regime

https://www.britannica.com/event/French-Revolution

https://www.britannica.com/topic/feudalism

Speaking on the Senate floor in May 1970, Senator Frank Church (D-Id) observed that the Vietnam War “has already stretched the generation gap so wide that it threatens to pull the country apart.” The Vietnam War exposed many tensions, in addition to the generational! Throughout the 1960s, the war and stateside movements (the Civil Rights Movement, the Free Speech Movement, the Feminist Movement, the Antiwar Movement, etc.) revealed fissures within society that divided Americans generationally, by class, by race, and often alienated them from the government. Select three movements on which to focus in your essay about “the Sixties.” How did the key issues for those movements reflect the fundamental transformation that American society underwent between the “age of consensus” of the 1950s and the famously “turbulent” Sixties? Your answer should define what “the Sixties” were and when “the Sixties” happened. Did “the sixties” span 1960-1970, 1961-68, 1963-1975, for example, or other dates?

There is no foolproof way of delineating the sixties as a cultural epoch beyond stating the actual years of its beginning and end—1960 and 1969. That said, the first two or three years of the decade were relatively "quiet" in comparison with what came about later. And the "turmoil" of the period surely spilled over into the 1970ss, with events like the Kent State shootings and the release of the Pentagon Papers. So perhaps we will end up talking mainly about the years from 1963 until late 1972, when the decision was finally made to withdraw US combat troops from Vietnam.
Of the three "movements" to focus on, I would first choose Civil Rights. After the March on Washington in August, 1963, it was (or should have been) impossible for white Americans to persist in their belief that race was not a major issue or that the US could continue with the old, segregated way society was run. When he took office after President Kennedy's assassination, Lyndon Johnson, to his credit, fully backed civil rights legislation and appointed Thurgood Marshall as the first African American Supreme Court justice. Yet there was huge resistance in the South to the integration of schools and of public life generally. Conservatives in the North as well during this period acted as if the country was "going downhill" because of the racial changes that were, in fact, inevitable. Police brutality and the rioting in reaction to it in Los Angeles in 1965 and Detroit and Newark in 1967, among other cities, led some pundits to state that the US was approaching "a state of anarchy." But in spite of the violence and turmoil, it's undeniable that by the end of the decade, the racial dynamic had changed for the better. The open, undisguised oppression against African Americans that had characterized the South and to an extent even northern states prior to the sixties had become, or at least was becoming, forever a thing of the past.
A second issue to examine would have to be, of course, the Vietnam War. Though the engagement of US combat forces had begun under JFK, it was not until over a year after his assassination that the US public began really to take notice of the war, as LBJ radically increased the number of troops and escalated the conflict. As the war continued over the years 1965–1967, it became increasingly apparent that no "progress" was being made. The US was evidently bombing the Vietcong and North Vietnamese to Kingdom Come, but the "Communists" showed no signs of giving up. The US "victory" of the Tet Offensive in early 1968 did nothing to bring the war closer to an end. By that year, even conservative people were questioning the wisdom of US involvement. Young people in urban areas, especially on the east and west coasts, were almost universally opposed to the war. The whole idea of being drafted to fight in a war halfway around the world began to seem ridiculous, as it was. Few educated people under the age of 30 continued to believe in the old bromides of "my country, right or wrong," and "Communism must be stopped!" and "we've gotta fight 'em over there so we don't have to fight 'em here." The violence that broke out at the Democratic convention in Chicago in 1968 was emblematic of the disordered state in which America found itself. The assassinations of the decade—JFK in 1963, Malcolm X in 1965, and Martin Luther King, Jr. and Robert Kennedy in 1968—exacerbated the awareness, especially of young people, that the world the "older generation" had created was deeply flawed. It was impossible not to be "disillusioned" during such a time. In 1970, when the war was escalated into Cambodia by Richard Nixon—who had gotten himself elected saying he had a "secret plan" to end the war—the shooting of student protesters at Kent State led to strikes by students at multiple universities. It would not be until nearly three years after this, in early 1973, that US combat engagement in Southeast Asia finally was brought to an end.
The third point about the decade involves the social changes involving sexuality, previously taboo subjects, and the portrayal of conflicts relating to these issues in television, film, and music. The introduction of the birth-control pill in 1960 led to greater sexual freedom. Because of this and the entry of more and more women into the work force, marriage was increasingly postponed and considered simply an option in relationships. The discussion of sexual topics in film became more and more explicit. By the middle to latter part of the decade with movies such as Who's Afraid of Virginia Woolf?, The Graduate, Bonnie and Clyde, and Midnight Cowboy, there was a startling (at the time) increase in frankness about sex, nudity, explicit language, and graphic violence. In television, though it lagged behind film in those pre-cable days, boundaries began to be pushed as well, especially in comedy revue-type programs such as The Smothers Brothers and Laugh-In. The Smothers Brothers were thrown off the air because they went too far with their political satire. These shows set the stage for Saturday Night Live and the freedom that is a normal part of the media today. Similarly, in music, the British Invasion destroyed the insular nature of the US popular culture. Though the Beatles' early songs were innocent and fun, by 1967, with the release of Sgt. Pepper, pop music dealt openly with the formerly taboo subject of drugs, as did music by others such as the Rolling Stones, the Doors, and Jimi Hendrix.
Each of these factors: civil rights, Vietnam, and freedom of sexuality and of expression, were dividers between conservatives and progressives and old and young in the sixties. Though the changes of that decade have in some sense been irrevocable—there is no going back, and there should not be—it's significant that many of the conflicts that led to those changes are still with us today.

What is the final temperature when 8 kg of ice at -5 deg C is mixed with 2 kg of steam at 126.8 deg C. The heat capacity of steam is 1.901 kJ/kg-deg C and the heat capacity of ice is 2.108 kJ/kg-deg C. The heat capacity of water is 4.183 kJ/kg-deg C.

This is a tricky problem because we do not know what the mixture of steam and ice look like after they come to the thermal equilibrium. Since there is such a large amount of ice (8 kg, compared to 2 kg of steam), let's calculate whether the heat given off by the cooling and condensation of steam will be enough to melt all of the ice.
The heat that the steam gives off while cooling to 100 degrees C is
Q_1 = c_sm_s(100 - T_(is)) = 1.901*10^3*2*26.8 = 1.019*10^5 J
The heat that the steam gives off while condensing at the constant temperature of 100 degrees is
Q_2 = L_v*m_s = 2.265*10^3*2 = 4530 J
Here, L_v is the latent heat of vaporization of water/steam.
While the condensed steam cools off to 0 degree C, it will give off heat equal to
Q_3 = c_w*m_s*(100 - 0) = 4183*2*100 = 8.366*10^5 J
 
The total heat released by stem during these three processes is
Q_1 +Q_2 +Q_3= 9.429*10^5 J .
The heat it would take to melt 8 kg of ice at the temperature of 0 degrees C is
Q_4= L_f*m_i = 334*10^3*8 = 2.672*10^6 J
Here, L_f is the latent heat of fusion of water/ice. 
Since the heat released by steam is less than the heat required to melt all ice, only some of the ice will melt while the steam will condense and cool down to 0 degrees. Thus, the final temperature of the mixture will be 0 degrees C.
It can be calculated how much ice will melt, Deltam , from considering that the heat released by steam will heat up the ice to 0 degrees and melt some of the ice:
Q_1 + Q_2 + Q_3 = c_i*m_i*(0 - T_(ii)) + L_f*Deltam
9.429*10^5 = 2108*8*5 +334*10^3*Deltam
Delta m = 2.57 kg
The final temperature is 0 degree C, with 2.57 kg of the ice melted and all steam condensed to water.
 
 
 
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/phase.html

https://www.physicsclassroom.com/class/thermalP/Lesson-2/Calorimeters-and-Calorimetry

"'Can't repeat the past?' he cried incredulously. 'Why of course you can!'" What does this quote mean?

Jay Gatsby makes this response to Nick Carraway’s statement, “You can’t repeat the past.” Their conversation occurs after Daisy and Tom Buchanan have left a party at Gatsby’s house. It is the first one they have attended, and Gatsby can tell that Daisy did not like it. Nick is encouraging him to realize that he is asking a lot of Daisy. Gatsby is incredulous in part because of what Nick says, and in part because he had thought Nick was entirely on his wavelength in his plan to rekindle Daisy’s love.
Gatsby does not want to repeat the entire past, only select moments of the past. He wants to believe he can pick and choose the best fragments of his shattered past and in doing so block out the unpleasant ones. Rather than the horrors of war, for example, he remembers the months he spent at Oxford. The focus of this selective reinvention is Daisy. While she has been his ideal, the corporeal aspect of their relationship centered on a single perfect kiss. The build up to that kiss has created an idyllic vision in his mind. It remains unfocused in his mind that it is part of himself that he is trying to recover. Nick says, “He wanted to recover something, some idea of himself perhaps, that had gone into loving Daisy.”
What Gatsby does not—or will not, or cannot—understand is that it was that anticipation and that hint of physical contact that made the moment so perfect for both of them. He tries to convince himself that he, Daisy, and Tom can meet socially as a way to get closer to her. The effect, of course, is to make her nervous and Tom jealous. His next step will be to stop socializing and have Daisy come to his house alone.

This is an important quote. Gatsby says this to Nick as he is reuniting with Daisy for the first time in five years. Gatsby's whole life since they parted has revolved around seeing her again and starting over. He is emotionally invested in the idea that he can turn back the clock and rekindle his relationship with her as if the past five years never happened.
Nick tries to warn him that this can't be done. Gatsby's response shows that he completely rejects Nick's commonsense warning.
Gatsby's tragedy is that he can't accept that the passage of time changes circumstances. Daisy has a husband and child. She is not the person she was five years ago. Nevertheless, Gatsby, as the quote shows, persists in believing he can will a moment from the past back into being and bring it into the present. He is living in a fantasy, but the fantasy has become so important to him that he can't give it up.

How can I present a persuasive argument as to whether the employee leave granted by the Family and Medical Leave Act (FMLA) represents an undue burden on employers required to comply with the act?

The act requires that employers grant employees job-protected and unpaid leave for qualified medical and family reasons. Qualified medical and family reasons include personal or family illness, family military leave, pregnancy, adoption, or the foster care placement of a child.
Your argument should consider the following points:
Would the employer suffer any serious financial losses if leave is granted?
Does job-protection for an employee mean a loss in working hours and thus affect production, or may the employer hire a replacement for the period concerned?
How do restrictions on employees who need to take leave benefit the employer? Or are they a disadvantage to the employer?
The following post should help:

The FMLA was intended "to balance the demands of the workplace with the needs of families." The Act allows eligible employees to take up to 12 work weeks of unpaid leave during any 12-month period to attend to the serious health condition of the employee, parent, spouse or child, or for pregnancy or care of a newborn child, or for adoption or foster care of a child. In order to be eligible for FMLA leave, an employee must have been at the business at least 12 months, and worked at least 1,250 hours over the past 12 months, and work at a location where the company employs 50 or more employees within 75 miles. The FMLA covers both public- and private-sector employees, but certain categories of employees are excluded, including elected officials and their personal staff members.

Remember, the focal point of your argument is "undue burden." Define this in your introduction and thesis statement. Your argument should be supported by strong statements either in support or against the topic. Since your word limit is quite restricted, you need to be succinct and to the point. Use the detail provided in the above post for support. The following guidelines should also help:
Take a strong stance on the topic in your thesis statement
Use plain and direct topic sentences to begin each paragraph. 
Use short sentences.
Be authoritative and sound like an expert.
Use persuasive techniques such as repetition and validation. One or two well-placed rhetorical questions in such a short piece can also work.
A brief conclusion which reiterates your thesis statement should bring an effective end to your piece.
https://en.wikipedia.org/wiki/Family_and_Medical_Leave_Act_of_1993

At Belmont, what reason does Portia give Nerissa for being weary of the world?

Great question. Some readers suggest that Portia is weary of the world because life has been too easy for her. She is weary of having so much luxury and ease. In act 1, scene 2, Nerissa points out the easy living, wealth, and good fortunes that Portia has had throughout her life. Portia then elaborates on what is bothering her:

Portia: . . . O me, the word “choose!” I may neither choose whom I would nor refuse whom I dislike—so is the will of a living daughter curbed by the will of a dead father. Is it not hard, Nerissa, that I cannot choose one nor refuse none?

In this passage, Portia explains why she is weary of her father's plans for her future marriage. Though her father is dead, he left specific rules in his will about who she can marry. Anyone who wants to marry her has to go along with her father's game. This game involves suitors selecting one of three caskets, gold, silver, and lead. Only one casket allows them the right to marry Portia. Additionally, suitors must agree not to marry anyone else, even if they choose the wrong casket. Though many men want to marry Portia, Portia has no right to choose a husband for herself. Additionally, she doesn't find many of the suitors particularly interesting.
When Portia tells Nerissa that she is weary with the world, she means that she is bored by her father's marriage game. Portia has no power in choosing her own husband; instead, she has to wait for a suitor to win her father's game. She is bored of waiting for her future husband to arrive, and she worries that she may not like the man who eventually wins the right to marry her.

Summarize the book Terrorism and the Ethics of War by Stephen Nathanson. From the link following: https://ssandhbooks2.files.wordpress.com/2015/05/terrorism-and-ethics-of-war.pdf

This book asks several ethical and philosophical questions about terrorism, including why terrorism is wrong and why moral condemnations of terrorism are lacking in credibility. The author begins by defining terrorism. The author states that it has been difficult to come to a definition of terrorism because people making the definition have vested political interests. He determines that one of terrorism's main features is that it is "violence directed against innocent people" (5).  The author then critiques this definition, discussing whether it is free of subjectivity, and examines what comprises "innocent" people and whether unintentional acts can be terrorism. He also examines what makes terrorism wrong. The author also discusses the idea that only non-governmental organizations can be terrorists. He believes that governments can also be agents of terrorism and writes, "we can see that any inquiry about the moral status of terrorism must widen its scope to include traditional wars" (72).
The author then goes on to show why moral condemnations of terrorism lack credibility from the point of view of utilitarian theory, political realism, and other schools of thought. He also uses Michael Waltzer's book Just and Unjust Wars to examine the idea that proponents of the just war theory condemn terrorism while approving of killing people in other situations, such as through collateral damage. The author then advocates the idea that it is always wrong to kill or attack civilians in war and that we cannot condemn terrorism unless we condemn all attacks on civilians. The author condemns the idea that "collateral damage," or the unintentional killing of civilians, is permissible by showing that the focus on intent is not relevant. In other words, people can be guilty of killing others even when it's not intentional. 
 

Why is the work a scalar quantity?

A scalar quantity is a quantity that can be measured by one number. This is in contrast to a vector quantity, that has to be represented by two, or more, numbers. For example, velocity is a vector quantity because it indicates how fast an object is moving, and in what direction.
Force is also a vector quantity, because it represents the strength of the push or pull, and also the direction of that push or pull. Work, however, is a quantity that indicates the result of the force's action: it combines the force with displacement that occurred in the direction of that force. Mathematically, it is expressed as follows:
W=vecF*Deltavecx
This is called a scalar product of the two vectors: the force vector and the displacement vector. It is a scalar because the result of it is just one number, calculated as follows:
W =|vecF||Deltavecx|*cos(theta).
So, work is the product of the magnitudes of the force and the displacement, and the cosine of the angle between them (theta ).
Work can also be thought of as a change in the kinetic energy of and object. The kinetic energy is
K = 1/2mv^2 , where m is the mass and v is the speed of the object. Since mass and speed are scalar quantities (speed is a magnitude of velocity, and this a scalar), kinetic energy is also a scalar quantity, so the work, which equals the change in kinetic energy, is also a scalar quantity.
 
https://en.wikipedia.org/wiki/Work_(physics)

In "Everything That Rises Must Converge," what are the similarities and differences between these two mothers and two sons?

In terms of differences, Mrs. Chestny and Julian, her son, are white. They, apparently, come from a family that used to be somewhat wealthy, as Mrs. Chestny is proud of the fact that her family once owned a plantation and two hundred slaves. In contrast, Carver and his mother are black. While Mrs. Chestny is relatively at ease and comfortable on the bus, especially before any black people get on, Carver's mother wears an expression that broadcasts the message, "Don't tamper with me." In fact, "Her face was set not only to meet opposition but to seek it out." Carver's mother seems prepared to do battle, while Julian's mother is, to Julian, irritatingly serene, even social. She begins "a general conversation meant to attract anyone who felt like talking." It seems clear that these two mothers have been treated quite differently in their lives: one has been privileged, while the other has not. One expects to be met with peace, whereas the other expects to be met with offense. Further, Julian has just graduated from college, while Carver is a young boy; it is likely that their mothers are likewise separated by age.
In terms of similarities, the most obvious one is that Carver's mother gets on the bus wearing the exact same hat that Julian's mother recently purchased. Ironically, the sales lady actually told Mrs. Chestny that she would not "meet [her]self coming and going," meaning that the hat is somewhat unusual (and implying that it is somewhat special—a notion that would seem to gratify Mrs. Chestny). It will set her apart. Ultimately, however, it is a symbol of how the races have begun to "converge"—as the title acknowledges—and how Mrs. Chestny is not alone in her ability to purchase such a hat. Carver, the child, is immature, playfully pushing his mother's buttons and eliciting a reaction from her. Likewise, Julian (though he is much older) is also immature, though he viciously pushes his mother's buttons in order to teach her a lesson.

What hints do you get from the story "Engine Trouble" that it is not going to end badly for the narrator?

In the story, there are two hints that things will not end badly for the narrator.
First, the swami's assistant manages to start up the road engine. This means that the engine can now be moved without extensive human assistance. Second, a devastating earthquake causes the road engine to be moved away from the compound wall.
In the story, the narrator wins a massive road engine at the fair. He is initially happy to have won the prize but soon becomes disillusioned with his win. This is because he cannot move the engine off the fairgrounds by his own strength. As a poor man, he also has few resources at his disposal.
The narrator is forced to pay rent to the Gymkhana Grounds in order to keep his engine there. Eventually, the administrators of the fairgrounds demand that the narrator remove his engine immediately. This is because a cattle show is coming to town. The narrator desperately asks for help, but no one seems to be able to offer him any assistance. In the end, the priest of a local temple offers the narrator the use of the temple elephant.
The narrator also engages the services of an unemployed driver and fifty coolies. The coolies are to push the engine from behind while the driver steers the machine. Things do not go according to plan, however. The elephant drags the engine along, but the machine has great difficulty moving in a straight line. The coolies try to help, but the resultant "confused" maneuvering leads the engine straight into a nearby compound wall. The engine demolishes the wall, and this causes the elephant to panic.
In its panic, the elephant stomps down another portion of the compound wall. This in turn causes the fifty coolies to flee in fear. Eventually, the police come and take the narrator away. Now, he must pay for all of the damages caused. Meanwhile, the narrator's wife threatens to return to her father's home. She objects to pawning the remainder of her jewels to pay for the damages.
As for the narrator, he thinks about running away. He also decides that he will encourage his wife to return to her father's home. However, two important events occur that turn the tide in his favor.
First, a swami comes to town. During one of his performances, the swami insists that he will live even if he is run over by a road engine. The narrator is ecstatic upon hearing the swami's proclamation, and he immediately offers the use of his road engine. He takes the swami and his assistant to the compound wall, where the engine still sits. The swami's assistant manages to start up the engine. However, the town officials refuse to allow the swami to carry out his stunt. As a result, the engine continues to sit by the compound wall.
That night, a terrible earthquake occurs. The next morning, the narrator discovers to his glee that the engine is no longer at its previous location. A search party finds the engine closing up the mouth of a disused well. The owner of the well tells the narrator that he is thrilled with this state of affairs. With the engine in its present location, he no longer has to pay exorbitant municipal fees to close up the well. The story ends happily with the owner of the well offering to pay the narrator's previous expenses.

Contrast Prospero's attitude towards Ariel and Caiban

Prospero uses his magic to control both Ariel and Caliban, albeit in different ways. In that sense his attitude towards them is inherently exploitative. Ariel and Caliban exist to serve him, and how they perform their duties will largely determine how they are treated. Caliban, for instance, is treated by Prospero in a malicious, vengeful manner. Prospero's magic is used to control Caliban, to keep him in a permanent state of subjugation. It's no wonder that Caliban is so surly and resentful towards his master. But ultimately he has no choice; through the exercise of his magic powers Prospero has a hold on him:

I must obey. His art is of such pow’r It would control my dam’s god, Setebos, And make a vassal of him (Act I Scene ii).

It's different with Ariel. Whereas Prospero uses his magic to subjugate Caliban, he uses it to set Ariel free from the curse of Sycorax, the evil witch. Because of this, Ariel adopts a submissive posture towards Prospero; he feels forever in his debt. Even so, Ariel makes so bold as to ask his master if he might one day be released from his authority:

Is there more toil? Since thou dost give me pains, Let me remember thee what thou hast promised, Which is not yet performed me . . . My liberty (Act I Scene ii).

Yet Prospero immediately puts Ariel back in his box. He threatens to imprison him in an oak tree for twelve years. Wisely, Ariel reverts to his supine attitude:

Pardon, master. I will be correspondent to command And do my spiriting gently (Act I Scene ii).

So even though Prospero has a more benevolent attitude towards Ariel, he still makes it abundantly clear that he is firmly in charge. Until he's finally granted his liberty, Ariel's relationship to Prospero is characterized by domination and control no less than Caliban's.

Calculus of a Single Variable, Chapter 9, 9.3, Section 9.3, Problem 31

The Integral test is applicable if f is positive and decreasing function on the infinite interval [k, oo) where kgt= 1 and a_n=f(x) . Then the series sum_(n=1)^oo a_n converges if and only if the improper integral int_1^oo f(x) dx converges. If the integral diverges then the series also diverges.
For the given series sum_(n=1)^oo 1/n^(1/4) , the a_n = 1/n^(1/4) then applying a_n=f(x) , we consider:
f(x) = 1/x^(1/4) .
As shown on the graph of f(x), the function is positive on the interval [1,oo) . As x at the denominator side gets larger, the function value decreases.

Therefore, we may determine the convergence of the improper integral as:
int_1^oo 1/x^(1/4) = lim_(t-gtoo)int_1^t 1/x^(1/4) dx
Apply the Law of exponents: 1/x^m = x^(-m) .
lim_(t-gtoo)int_1^t 1/x^(1/4) dx =lim_(t-gtoo)int_1^t x^(-1/4) dx
Apply the Power rule for integration: int x^n dx = x^(n+1)/(n+1) .
lim_(t-gtoo)int_1^t x^(-1/4) dx=lim_(t-gtoo)[ x^(-1/4+1)/(-1/4+1)]|_1^t
=lim_(t-gtoo)[ x^(3/4)/(3/4)]|_1^t
=lim_(t-gtoo)[ x^(3/4)*(4/3)]|_1^t
=lim_(t-gtoo)[ (4x^(3/4))/3]|_1^t
Apply the definite integral formula: F(x)|_a^b = F(b)-F(a) .
lim_(t-gtoo)[ (4x^(3/4))/3]|_1^t=lim_(t-gtoo)[ (4*t^(3/4))/3-(4*1^(3/4))/3]
=lim_(t-gtoo)[(4t^(3/4))/3-(4*1)/3]
=lim_(t-gtoo)[(4t^(3/4))/3-4/3]
= oo
The lim_(t-gtoo)[ (4x^(3/4))/3]|_1^t= oo implies that the integral diverges.
Note: Divergence test states if lim_(n-gtoo)a_n!=0 or does not exist then the sum_(n=1)^oo a_n diverges.
Conclusion: The integral int_1^oo 1/x^(1/4) diverges therefore the series sum_(n=1)^oo 1/n^(1/4) must also diverges.

What is the effect of James's many references to Daisy's prettiness in so few pages?

There are a number of references to Daisy's prettiness in the span of a few pages. The use of such a literary maneuver impresses upon us Winterbourne's first distinct feelings about Daisy. He thinks of her as innocence personified; to him, Daisy embodies a virginal wholesomeness that is set off to perfection by her fresh, wholesome beauty.
The effect of so many references to Daisy's prettiness is that our attention is drawn to her physical attractiveness ad nauseam. The effect is simultaneously cloying and intriguing.

The young girl's eyes were singularly honest and fresh. They were wonderfully pretty eyes; and, indeed, Winterbourne had not seen for a long time anything prettier than his fair countrywoman's various features—her complexion, her nose, her ears, her teeth.

James's use of repetition causes us to question his reasons for doing so, and he doesn't disappoint in providing the answer. In the story, he demonstrates the difference between American and European views of female virtue. In noticing Daisy's fresh beauty and all-embracing openness, Winterbourne becomes filled with questions about American female honor.
He questions whether Daisy's outward freshness hides the taint of promiscuity:

He thought it very possible that Master Randolph's sister was a coquette. . . Certainly she was very charming, but how deucedly sociable! Was she simply a pretty girl from New York State? Were they all like that, the pretty girls who had a good deal of gentlemen's society? Or was she also a designing, an audacious, an unscrupulous young person?

The European view of overly-friendly young women is that they must be "coquettes," whose only aim is to ensnare men in their debauchery. Ultimately, Winterbourne concludes that Daisy doesn't exactly fit the picture of an ideal "coquette." She is pretty, but she is also unassuming and chaste in her conduct. In the end, he decides that Daisy is just a "pretty American flirt," not one of those "dangerous, terrible women."
The repetitive description of Daisy's prettiness is a literary device that highlights the theme of differing European and American prejudices regarding the outsider, female virtue, and class hierarchies.

Anton Chekhov's short story "Misery" has a subtitle "to whom shall I tell my grief?" Discuss the significance of the two titles and how they relate to each other.

Clearly, the title and subtitles complement one another. The title "Misery" refers not just to the main situation of the story, but also to the overall mood of the tale in itself. 
Our main character, Iona, is an old cabman who is poor, tired, has an old mare as his working animal, and is currently suffering the worst pain any human being can undergo: he is grieving the death of his only son. 
The entire situation is miserable as it is. The man lives in dire conditions, works under dire circumstances at his old age, and endures the abuse of bad patrons that neither pay well nor treat him with any degree of decency.
The poor man is so used to the abuse, and so far gone in his own pain, that he does not even have the capacity to differentiate the abuse that he suffers. All he wants to do is tell someone about the death of his son.
Like any human, he wishes to let his thoughts out; to properly put an end to that chapter of his life. He wants to express his emotions, explain how it all happened, and render some sort of homage to his child, even if it is in conversation. Nobody listens to him. Here is where the second title, "To Whom Shall I tell my Grief," comes in.
Iona is a widower, and his daughter is somewhere in the country. Being that these are the days prior to any type of electronic communication or social media interaction, you may be able to picture the extreme degree of loneliness that this man must be feeling, alone in the world, and with nobody to talk to. The man tries to tell his pain to the military officer that he first drives. He then tries to tell the rowdy youngsters who needed his services and ended up abusing him. He tried to tell someone at the place where he lives, but that person just turned around and kept sleeping.
In the end, there was no other choice but to go straight to the mare, and speak to it. The animal, who was eating hay at the time, simply continued to chew as the man was finally able to say what he had to say. 

"That's how it is, old girl.... Kuzma Ionitch is gone.... He said good-by to me.... He went and died for no reason.... Now, suppose you had a little colt, and you were own mother to that little colt. ... And all at once that same little colt went and died.... You'd be sorry, wouldn't you?..."

Therefore, the story reads as a critique of society and the narcissistic and selfish ways of people who look down on others; people with no empathy or humanity who rest importance to the vicissitudes of a fellow man. That an animal ended up being the only one listening to Iona's sad tale speaks volumes of the type of society that Chekov based his story upon. 

Describe the main character throughout the story "Facing the Forests" by A.B. Yehoshua. What is the process he undergoes from the first time he meets the mute Arab until he returns to his town?

A. B. Yehoshua's protagonist in "Facing the Forests" is a weak and passive forest guard. The protagonist is a graduate student who has accepted a six-month job as a guard to keep a fire watch over the forest. He is characterized by aimlessness and poor vision. Although the guard has small transformations throughout the story, he ends back where he started as a weak and passive young man.
Yehoshua crafts his story by developing the relationship between the Arab, the forest, and the guard. The forest is a new stand of young trees planted there after the destruction of an Arab village. An old Arab man lives there with his young girl.
At the start, the guard complains about his post. He likens his contract at the forest to a prison term. He feels alienated and distant from the forest and escapes to the familiar world of books. Eventually, however, he begins to leave his post and explore the forest. From that moment, we see a transition occur. The guard begins to feel closer to the trees and farther from the world of words, representing a character shift toward decisiveness and away from passivity in the protagonist. 
The guard's feelings toward the forest parallel his sentiments toward the old Arab, who is mute because his tongue was cut out during the war. The guard's thoughts reveal that he cares little for the Arab at this moment in the tale:

The Arab turned out to be old and mute. His tongue was cut out during the war. By one of them or one of us? Does it matter?

As the guard begins to feel closer to the forest, he also begins to be more interested in the Arab. The guard's progression away from his aloof self indicates a transition away from the past and toward the future. 
 
The guard's progression is redirected when he learns of the Arab village and the fire. A village once existed where the forest now stands. Israelis burned the village during the war and planted the forest in its place. When the guard makes this discovery, it changes the course of the narrative. The guard begins to look for the remains of the village. Now, instead of the passive and weak character we met at the beginning of the story, we see a purposeful guard who actively ventures out into the forest and maps his findings as he seeks the remains. The guard's interest in the village makes him more interested in communicating with the old Arab.
 
In the Arab's hut, the guard notices some cans of kerosene, which the guard suspects he will use for arson. Instead of reporting the Arab, the guard tries to draw him out by building a bonfire of his own. Together without words, the Arab and the guard develop an understanding that they will burn the forest. We see the guard's transformation as he now is extremely interested in the Arab and longs to connect with him:

The Arab speaks to him out of the fire, wishes to say everything, everything at once. Will he understand?

At the climax of the story, the Arab commits arson and burns the forest with the unspoken consent of the guard, who merely looks on as the forest burns. It is ironic that in the guard's most decisive moment, he is still just a passive onlooker. 
 
After the forest fire, the police come to investigate. They thoroughly question the guard, who ultimately gives up the Arab. By the end of the story, the guard has betrayed his job by burning the forest and betrayed the Arab by pointing him out as a suspect. At this point in the story, the guard's term as a guard is up, and he goes back to the city.
 
Once everything is over--the forest, the guard's job, the relationship with the Arab--the guard retreats back to the way he was. The guard regards his actions passively, musing that the forest was probably insured. By the end of everything, the connection the guard felt with the forest is gone. There is evidence, however, that although the guard acts passively about his actions, some trace of sorrow remains with him.

At night, in some shabby hotel room, he is free to have a proper sleep, to sleep free from obligations for the first time, just sleep without any further dimensions. Except that he will not fall asleep, will only go on drowsing. Green forests will spring up before his troubled eyes. He may yet smart with sorrow and yearning, may feel constricted because he is shut in by four walls, not three. 

This ending passage suggests that the guard is sad to leave his post as guard and sad about the way things ended. However, he is still plagued by personal incapacity. Though he does feel some remorse for his actions, he cannot close the distance between himself and the world, and he returns to his passive mode of existence.
https://jewishstudies.rutgers.edu/docman/zerubavel/17-forest-national-icon/file

int 1 / (sqrt(x)sqrt(1-x)) dx Find the indefinite integral

Recall  that int f(x) dx = F(x) +C   where:
f(x) as the integrand function
F(x) as the antiderivative of f(x)
C as the constant of integration..
 For the given problem, the integral: int 1/(sqrt(x)sqrt(1-x))dx
does not yet resemble any formula from table of integrals.
To evaluate this, we have to apply u-substitution by letting:
u =sqrt(x)
Square both sides: (u)^2=(sqrt(x))^2 , we get: u^2 =x
Then plug-in u^2 =x in sqrt(1-x) :
sqrt(1-x) = sqrt(1-u^2) .
Apply implicit differentiation on u^2 =x , we get: 2u du = dx .
Plug-in sqrt(x) =u , sqrt(1-x) = sqrt(1-u^2) , and dx= 2u du , we get:
int 1/(sqrt(x)sqrt(1-x))dx =int 1/(u*sqrt(1-u^2))*(2u du)
                         =int (2u du)/(usqrt(1-u^2))
 Cancel out common factor u:
int 1/(usqrt(1-u^2))*(2u du)=int (2 du)/sqrt(1-u^2)
Apply the basic integration property: int c*f(x) dx = c int f(x) dx :
int(2 du)/(sqrt(1-u^2))= 2int(du)/sqrt(1-u^2)
The integral part resembles the basic integration formula for inverse sine function:
int (du)/sqrt((a^2 -u^2)) = arcsin(u/a) +C
Then,
2int(du)/sqrt(1-u^2) =2arcsin(u/1) +C
                    =2 arcsin(u) +C
Express it in terms of x by plug-in u =sqrt(x) for the final answer :
int 1/(sqrt(x)sqrt(1-x))dx =2 arcsin(sqrt(x)) +C

What is Miss Kinnian teaching Charlie?

As the story opens, Miss Kinnian is teaching Charlie spelling and reading at a night school. He writes in his journal in response to a question about how he found the class that:

sumbody told me where I shud go to lern to read and spell good.

We learn that Charlie is very determined to go to the night school because he wants to learn and become smart. This is also why he is willing to submit to the operation that will boost his brain power, even though he is warned it will probably only be temporary. It's also clear that he doesn't fully understand the implications of what he is getting himself into.
We learn as well that Miss Kinnian thinks Charlie is the person in her class who would be best for the operation and that she thinks he deserves it most of all.

Calculus of a Single Variable, Chapter 3, 3.4, Section 3.4, Problem 34

I) Find the first derivative -> f'(x) = -3x^2 + 14x - 15 and set it equal to zero to solve. This will find the x-values of your "critical points". A critical point is where the graph humps. Solving, you get x = 5/3 and x = 3, meaning there is a hump (relative extrema) at those values. Because we don't/can't graph the function, we don't know if those humps are hills or valleys. If necessary, you can find the exact point of those critical points by plugging 5/3 into the original function to determine the y-value (and likewise for x = 3).

II) Find the second derivative -> f''(x) = -6x + 14. The second derivative will help you find the exact point on a graph where a graph changes from a hill to a valley (or vise versa). This concept is called "concavity." Plug the critical points from Part One into the second derivative: f''(5/3) = a positive number -- the number four to be exact, but that won't matter to you -- and f''(3) = a negative number -- again, the number negative four to be exact, but that won't matter to you. Why does the exact value not matter to you, you ask? If the second derivative gives you a positive number, then your graph is "concave up" (or CUP UP or a VALLEY) and if the second derivative gives you a negative number, then your graph is "concave down" (or CUP DOWN or a HILL). [A cup that is up would make a valley, but a cup that is upside down would make a hill].

Why was Chips startled when Ralston gave him a soft reminder to think about retirement?

When Ralston suggests that Chips should retire, it's a total surprise. Chips has never liked Ralston. He feels that he's more of a hyper-efficient bureaucrat than a teacher, certainly not a molder of boys into men. He's obsessed with increasing the number of rich pupils attending the school, which has led to something of a snob culture developing at Brookfield. Chips is also disillusioned about the academic changes that Ralston's introduced, especially the new way of pronouncing Latin. Ralston, for his part, looks upon Chips as a bit of an old dinosaur, an unwelcome reminder of the school's past. Chips's eccentricities, such as his tatty old master's gown, are also a source of irritation.
So why is Chips surprised when Ralston suggests he should retire? Over the years Chips has shown outward loyalty to Ralston despite his personal animosity towards him and his misgivings about the school's change of direction. He's witnessed firsthand the ruthlessness with which Ralston deals with masters who get in his way. But Chips thought it would be different for him. He thought that his age and seniority would somehow protect him. Chips is hugely popular in the school, with boys and masters alike, so he also thought that his popularity would protect him.

I am from India and have recently qualified in a PhD entrance examination. My specialization is English language teaching (ELT). I have to fill in an admission form including my research topic soon. Can you please suggest to me two or three topics on ELT?

First, as someone who has served on PhD program admissions committees, I would suggest that the point of this part of the form is to help people on admissions committees see if your research interests are a good fit for the department. This means that you need to spend time thinking carefully about a topic in which you would like to immerse yourself for the next 4 to 5 years rather than just seeing it as a hoop to jump through.
Your first way of narrowing your choice of research fields might be by types of student. You could focus on primary school, secondary school, university, or adult learners. You could also think about different types of English. Teaching migrants who aim for near native fluency is different than teaching business English or English for tourists or a reading knowledge of English for graduate students.  Also, students' own backgrounds and native languages raise different pedagogical issues. You could also, for example, blend TESOL and disability studies by focusing on teaching English as a second language to deaf students or students with other disabilities.
Another important and growing area is computer aided pedagogy of various sorts. Increasingly, education is delivered online to remote students. Research and specialization in online TESOL pedagogy (especially a pedagogy that can be implemented on mobile phones) is a growing area and particularly relevant to India.
Finally, "gamification" is an important area of study within language pedagogy. You could develop research on how to gamify TESOL for specific student populations. 

Please give five examples of the theme of dehumanization in 1984.

Enumerating things up to a specific number is not always the best way of dealing with literary issues, BUT, in 1984 there are so many elements of dehumanization that coming up with five or more of them should not be hard. The constant surveillance makes it impossible for anyone to have a private life. The children are trained to dislike their parents and spy on them. The food is scanty, substandard, and monotonous. A huge segment of the population, the proles, are explicitly dehumanized by official policy. We hear the phrase more than once that “the proles are not human beings.”
The deepest form of dehumanization, however, would seem to be that no one trusts anyone else. It is not just the children who are spying on their parents, but everyone is a potential member of the Thought Police or at least has the likelihood of giving information about a colleague or acquaintance if that person slips up and says something heretical. Fear is the largest single factor in the Party’s objective of turning the population into so many automatons. At the stage in which we are shown this vision of the future, it hasn’t quite happened yet, but Orwell makes us believe that the process is practically inevitable, as the despairing close of the novel indicates.

1. The Party dehumanizes citizens by spying on them 24/7. This allows people no privacy or private lives. One's whole life is intended to be dedicated to the advancement of the Party, not their own desires.
2. Marriage is sanctioned only by the Party's wishes. Even sexual relations between a husband and wife are not allowed the possibility of fruitlessness—sex is for creating more citizens, not pleasure or emotional bonding. The relationship between Winston and his brainwashed wife shows this, since she only had sex with him with the hopes of pregnancy and was distraught when she could not fulfill this duty to the Party.
3. The very concept of Hate Week is dehumanizing. Citizens are basically expected to transform themselves into mindless, angry hordes for the sake of propaganda. The Hate Week practices turn individuals into a mob, which is dehumanizing and beneficial to the state keeping its power over the hearts and minds of its subjects.
4. Party members are forced to wear the same uniform, stripping them of personal expression and individuality.
5. Freedom of speech is decidedly not a thing in Oceania. You either support the Party or you are a traitor.

1. The Party dehumanizes its members by constantly watching them and creating a surveillance state. Party members have literally no privacy, and Big Brother watches them via strategically placed telescreens in their homes, at work, and throughout society.
2. The Party deprives the citizens of typical amenities, which are hard to find and are in scarce supply throughout Oceania. The Party economically deprives the population in order to keep them oppressed and weak.
3. The Party controls whether or not its members are allowed to have relationships with other members. Marriages and relationships are sanctioned by the Party, which dehumanizes its members.
4. The Party members are required to wear the official outfit of blue overalls, and women are forbidden from wearing makeup. The official uniform of the Party diminishes a person's individuality and further dehumanizes them.
5. The Party members are also forbidden from expressing their true feelings about Big Brother and anything deemed unorthodox is punishable by death. Winston Smith and Julia are forced to pretend they agree and support the Party at all times in order to survive in the hostile nation of Oceania.

Which Enlightenment philosopher most directly influenced the Declaration of Independence? Use evidence from the Declaration of Independence to support your answer.

Many people would argue that Thomas Jefferson himself was an Enlightenment philosopher, but if we are looking for someone besides Jefferson, the answer would be John Locke. While Locke was active as a writer before the eighteenth century Enlightenment, his works were very influential among the thinkers and writers generally associated with the Enlightenment. Jefferson famously asserted that Locke was, along with Francis Bacon and Isaac Newton, one of the three greatest men who ever lived. Locke's influence can be found in the first section of the Declaration. Here Jefferson and the members of the Continental Congress assert that "all men are created equal" and that they are "endowed by their Creator with certain unalienable rights," including "life, liberty, and the pursuit of happiness." In his Second Treatise on Civil Government Locke had asserted the following:

Man being born, as has been proved, with a title to perfect freedom, and an uncontrolled enjoyment of all the rights and privileges of the law of nature, equally with any other man, or number of men in the world, hath by nature a power, not only to preserve his property, that is, his life, liberty and estate...

The similarities should be obvious. Locke and Jefferson both argued that man was born free and equal to all other men, and that each man had a natural right to life, liberty, and property. The Declaration goes on to say that the purpose of government was to "secure," or protect, these rights, and that if a government instead takes those rights away, men had a right to replace the government with another. This too was a Lockean idea, derived from this passage (among others) from the Second Treatise:

but in such cases...[that the people] are persuaded in their consciences, that their laws, and with them their estates, liberties, and lives are in danger, and perhaps their religion too; how they will be hindered from resisting illegal force, used against them, I cannot tell.

 

Why does Hughes set up "A Dream Deferred" as a question? What point does this make?

One of the purposes of poetry is to open up possibilities in the reader's mind, to get the person to think about something. This would be very important in Langston Hughes' context, being an African American writer at a time when racism was seriously overt. He was writing at the time of Jim Crow laws and even restrictions of African Americans in northern cities. 
A Dream Deferred covers the difficult realities of so many African American people. Much like today, many had little hope for their lives, certainly not the hopes of the wealthy (mostly whites) who can go to college and choose to focus on something they like. Young people with ambition were and are regularly forced to abandon such dreams.
When African Americans read the poem, they may find that it speaks to their lives and conditions. Hughes' white readers might off-handedly reject the poem because its realities are bitter. By asking questions, Hughes makes a bitter pill a little easier to swallow. 
At the same time, the questions communicate something truly significant. Why have there been protests and riots that began some time after Hughes was writing and continue today with Black Lives Matter? Hughes' answer is that this is what happens when dreams are deferred. The next question readers have to ask themselves is, how can I be part of a solution rather than being part of the problem? How can we help people to realize their dreams?

Is there an essential question about Geraldine Connolly's poem, "The Summer I was Sixteen" -- a question that helps students consider the poem's main meaning?

I would suggest something like this:
"How does the poet convey the vivid, subjective impressions of a 16-year-old, while also indicating that the narrator has evolved, and now sees these memories in a different light?"
Here's why.
Obviously, deciding if a question is "essential" depends on a certain amount of subjectivity. But this poem is clearly presented as the recollection of an older woman about her experiences and perceptions as an adolescent. It is just as clearly concerned with evoking vivid sensory impressions, and it makes us aware of two, sometimes conflicting perspectives: The teenager's and the adult narrator's.
So while readers may disagree about shades of meaning, I think most will acknowledge that the meaning of the poem concerns these two points:
(1) what it felt like to be a sixteen-year-old enjoying a carefree summer day, and
(2) what it feels like to revisit those feelings from a different perspective -- the perspective of an older, wiser person whose sense of self and the world has expanded or become more complex.
That's what gives the poem its distinctive emotional character: It isn't just a nostalgic collection of sensory memories. It's a poetic reflection on the distance between the current self and the past self -- on our ability to re-experience vivid memories of the past while also considering them from another, more mature perspective.
So if you want a question that asks a student to discuss these meanings, I think the question above is on the right track.
A student answering such a question will be forced to consider not only the imagery that evokes the teenager's experiences. The student will also need to address the evidence of conflict in the poem -- the conflict between the teenager's perceptions and the narrator's understanding.
It is essential, for instance, to notice that the past self "did not exist beyond the gaze of a boy," and that the teenager and her friends tossed a glance through the fence at "an improbable world." We can surmise that the narrator now feels differently about these things.
She knows she exists beyond the gaze of boy, and accepts, with apparent amusement, that her teenage self did not. The bigger world beyond the fence is no longer "improbable." She has had to venture beyond the fence, and learn first-hand what the world is like.
In light of these contradictory perspectives, and the vivid imagery of this poem, it may be helpful to read an interview that the poet gave in 2010 (see link below). In it, Connolly said:

I have a visual mind and imagination. I would have like to have been a painter. I think of an image as a word picture, an intense electric connection between the eyes of the writer and the mind of the reader.

So imagery is essential to her. But in this interview she also noted that she's  intrigued by images that are in some way self-contradictory or paradoxical, referring to examples from Emily Dickinson and other poets.
In particular, note what she says at the end of this quote about contradiction feeling honest or true (words I've printed in boldface):

Some of the other great image makers are Dickinson: “frost, a blonde assassin—”; T.S. Eliot’s singing mermaids who do not sing to him; Wallace Stevens’s “downward to darkness, on extended wings.” I love the way that image of pigeons’ wings descends and expands simultaneously. All of these images that come to mind include paradox. There’s something about contradiction that feels honest and true to me.

 

Calculus: Early Transcendentals, Chapter 7, 7.4, Section 7.4, Problem 27

int (x^3+x^2+2x+1)/((x^2+1)(x^2+2))dx
To solve, apply partial fractions decomposition.
To express the integrand as sum of proper rational expressions, set the equation as follows:
(x^3+x^2+2x+1)/((x^2+1)(x^2+2)) = (Ax+B)/(x^2+1)+(Cx+D)/(x^2+2)
Multiply both sides by the LCD.
x^3+x^2+2x+1=(Ax+B)(x^2+2)+(Cx+D)(x^2+1)
x^3+x^2+2x+1=Ax^3+2Ax+Bx^2+2B + Cx^3+Cx+Dx^2+D
x^3+x^2+2x+1=(A+C)x^3+(B+D)x^2+(2A+C)x+2B+D
For the two sides to be equal, the two polynomials should be the same. So set the coefficients of the polynomials equal to each other.
x^3:
1=A+C (Let this be EQ1.)
x^2:
1=B+D (Let this be EQ2.)
x:
2=2A+C (Let this be EQ3.)
Constant:
1=2B+D (Let this be EQ4.)
To solve for the values of A, B, C and D, isolate the C in EQ1.
1=A+C
1-A=C
Plug-in this to EQ3.
2=2A+C
2=2A+1-A
2=A+1
1=A
Plug-in the value of A to EQ1.
1=A+C
1=1+C
0=C
Also, isolate the D in EQ2.
1=B+D
1-B=D
Plug-in this to EQ4.
1=2B+D
1=2B+1-B
1=B+1
0=B
And plug-in the value of B to EQ2.
1=B+D
1=0+D
1=D
So the partial fraction decomposition of the integrand is:
(x^3+x^2+2x+1)/((x^2+1)(x^2+2)) = (1x+0)/(x^2+1)+(0x+1)/(x^2+2)=x/(x^2+1)+1/(x^2+2)
Taking the integral of this result to:
int(x^3+x^2+2x+1)/((x^2+1)(x^2+2))dx
=int (x/(x^2+1) + 1/(x^2+2))dx
= int x/(x^2+1)dx + int 1/(x^2+2)dx
For the first integral, apply u-substitution method.
u=x^2+1
du=2xdx
(du)/2=xdx
= int 1/u*(du/2) + int 1/(x^2+2)dx
=1/2 int 1/u du + int 1/(x^2+2)dx
= 1/2ln|u| + 1/sqrt2 tan^(-1) (x/sqrt2)+C
And, substitute back u = x^2+1 .
=1/2ln |x^2+1|+1/sqrt2tan^(-1)(x/sqrt2)+C

Therefore, int (x^3+x^2+2x+1)/((x^2+1)(x^2+2))dx=1/2ln |x^2+1|+1/sqrt2tan^(-1)(x/sqrt2)+C .

How did French officers and soldiers learn about the freedoms gained by American citizens?

When the American Revolution started in 1776, France immediately saw it as an opportunity to weaken the British Empire. They secretly began sending supplies to the colonies, especially gunpowder. During this time, Benjamin Franklin was appointed as the American ambassador to France. During his time as ambassador, Franklin earned the respect and admiration of the French and he served as a shining example of American democracy. In 1777, after the Americans had beaten the British at the Battle of Saratoga, the French realized that the Americans had a real chance at winning the war. They continued to send supplies, but they also began to send soldiers and ships to aid the Americans in the war effort. The soldiers and officers that France sent to America worked closely with American soldiers, spent their money on American goods, and endeared themselves to the local populace. Meanwhile, France was being ruled by an absolute monarch, and the upper classes of French society lived in luxury while the majority of people starved and suffered. Many French soldiers and officers were tired of the monarchy and they were inspired by the American Revolution and the idea of a democracy built on equality for all. 
http://www.pbs.org/benfranklin/l3_world_france.html

https://www.ushistory.org/us/11g.asp

To what extent do you agree that The Crucible is only about courage and honesty?

As a "what do you think" type of question, you can feel free to answer this in a variety of ways. As the question suggests, it is your support that is most important.
I do not believe that this play is only about courage and honesty. Lies, deceit, and power are also a big part of the play. Abigail is the main person that is behind this theme, and she lets audiences and characters know right from the beginning of the play that she has no problems with lying and exerting power over the other girls in order to control a situation.

BETTY: You did, you did! You drank a charm to kill John Proctor's wife! You drank a charm to kill Goody Proctor!ABIGAIL, smashes her across the face: Shut it! Now shut it!BETTY, collapsing on the bed: Mama, Mama! (She dissolves into sobs.)ABIGAIL: Now look you. All of you. We danced. And Tituba conjured Ruth Putnam's dead sisters. And that is all. And mark this. Let either of you breathe a word, or the edge of a word, about the other things, and I will come to you in the black of some terrible night and I will bring a pointy reckoning that will shudder you. And you know I can do it; I saw Indians smash my dear parents' heads on the pillow next to mine, and I have seen some reddish work done at night, and I can make you wish you had never seen the sun go down! (She goes to Betty and roughly sits her up.) Now, you—sit up and stop this!

Even a character as good and honest as John Proctor isn't immune from lying to people, attempting to deceive them, and forcefully exerting his will. He obviously tried to keep his affair with Abigail a secret, and he wasn't immediately forthcoming to Elizabeth that he had an exchange with Abigail about the trials. It was during that exchange with Abigail that John even threatened to hit Abigail if she kept talking about his wife.

ABIGAIL, with a bitter anger: Oh, I marvel how such a strong man may let such a sickly wife be—PROCTOR, angered at himself as well: You'll speak nothin' of Elizabeth!ABIGAIL: She is blackening my name in the village! She is telling lies about me! She is a cold, sniveling woman, and you bend to her! Let her turn you like a—PROCTOR, shaking her: Do you look for whippin'?

A fundamental Anglo-Saxon belief is that human life is shaped by fate. How is this belief reflected in “The Seafarer”?

Before turning to the poem itself, we need to clarify what fate meant to the Anglo-Saxons. This is actually a very complex issue, in large part because we do not have direct, written access to pagan Anglo-Saxon mythology. Based on early English texts like Beowulf, we can infer that Anglo-Saxon mythology likely resembled other branches of Germanic paganism (e.g. Norse mythology); although these written sources all postdate the introduction of Christianity (or, at least, were revised in keeping with Christianity), they contain traces of an earlier belief system. In other words, Anglo-Saxon literature often draws on two competing ideas of destiny. In the Christian worldview, one can take comfort in the knowledge that God is the ultimate arbiter of fate; human life may be difficult, but the promise of salvation after death ensures a kind of happy ending. By contrast, the pagan Anglo-Saxon worldview was likely more stoic; fate is an all-powerful force but not necessarily a kind one, and the best humans can hope for is to endure their destinies with courage."The Seafarer" draws on both these conceptions of fate. It is largely a Christian poem, and the speaker ends by cautioning us not to lose sight of our ultimate destiny, which is to join God in heaven: "Let us consider where our true home is; / and then let us think how to come thither" (117–18). This, he says, will give us strength in adversity and ensure that we do not devote our lives to the kinds of worldly, sinful pursuits that might expose us to God's anger: "gold is no aid to a soul full of sins / in face of God's terror, his awful power" (100–101). Interwoven with this Christian idea of destiny, however, is a more pagan sense that fate is unknowable but (likely) harsh. The poem speaks mournfully, for instance, of a glorious past that seems fated to have vanished: "Wanes all this noble host; joys have departed; / weaker remain and rule this world, / live here afflicted" (86–88). In thinking about the role that fate plays in "The Seafarer," then, it might be helpful not only to look at lines that explicitly mention God or destiny (e.g. lines 115–116, which reiterate the power of both), but also to think about how the speaker combines the pagan idea that the world is basically in decline with a Christian understanding of human destiny.
https://lightspill.com/poetry/oe/seafarer.html