Can you give an example of four prominent themes found in Capote's In Cold Blood?

In Cold Blood, by Truman Capote, features multiple strong themes throughout the narrative, some subtle while others are overt. These themes include life in rural America, the American dream, violence, and trust.
Life in Rural America
In Cold Blood is a non-fiction novel that takes place in communities all across America. The main character, Perry, travels with his family from Texas to Oregon and later to Florida, Texas and Nevada as well as to the country of Mexico. Through Perry's travels, Capote explores the similarities between rural American communities despite the distance between them. Perry's childhood is spent traveling from one place to another, and it is this sporadic upbringing that contributes to his identity as a loner. The text explains that he "washed dishes in an Omaha restaurant, pumped gas at an Oklahoma garage, and worked a month on a ranch in Texas."
As the story progresses, the superficial differences between the states Perry has lived in are woven into the tapestry of what Capote considers the myth of America. Despite the differences in each location he travels to, Perry identifies a common loneliness and dissatisfaction among the rural populace he encounters.
The American Dream
The American Dream and life in rural America are themes that are closely intertwined throughout the narrative. Perry and Dick are motivated to commit violent crimes by perversions of the American dream, which was a prominent topic in the 1950s. As a self-made farmer, Herbert is living the traditional American dream. Perry and Dick seek to obtain the rewards of that dream without putting in any of the honest work it takes to achieve success. To do this, they devise a plan to murder Herb and his family and use their money to further their own dreams.
Violence
The central story of In Cold Blood revolves around the planned murder of Herb Clutter and his family. Perry Smith and Dick Hickock believe that the Clutters have thousands of dollars hidden somewhere in their home and kill the family in cold blood to obtain the money. In reality, they find only $40 in Herb's wallet. The ruthless ambition of Perry and Dick is used to showcase the reality of violence, which is so often inflicted for the sake of petty gain.
Trust
Capote grows close to Perry in an attempt to obtain his confession. He works to gain Perry's trust over time and becomes something of a kindred spirit, even as he comes to the conclusion that Perry and Dick are cold-blooded killers. Both men are isolated and consider themselves loners, which contributes to the trust that is built between them over time. In a subtler sense, the idea of trust in an orderly world is also explored through this narrative. Herb is a pillar of the community and he has no reason to believe that anyone would wish to hurt him. This trust is violated when two men he has no direct connection to break into his home and perpetuate violence against him and his family.

What contributions to the world did the Mayans and Aztecs make?

The Mayans were great innovators in the fields of art and architecture. Using minerals and plants, they created paint for highly sophisticated murals depicting famous battle scenes, religious ceremonies, and sacrificial rituals.
In architecture, the Mayans were renowned for the elaborate construction of huge temple pyramids from hand-cut limestone bricks. The stones of each temple were stacked in such a way that they formed an unusual triangular archway, a unique feature of Mayan architecture.
The Mayans developed a very complex system of writing based on hieroglyphics or picture symbols. Over time, Mayan hieroglyphics developed to such an extent that scribes were able to convey a whole panoply of sophisticated words, concepts, and ideas.
As for the Aztecs, they made enormous strides in technology, which enabled them to construct the massive island city of Tenochtitlán. Their technological expertise further allowed them to enlarge the city by creating a number of floating islands called chinampas.
In addition, the Aztecs designed a series of causeways connecting Tenochtitlán to the mainland. During the rainy season, when the waters rose, the causeways acted as dikes, preventing the city from being flooded.

The Mayans developed the idea of zero and advanced the field of mathematics. They also managed to develop a more accurate calendar that showed a year had more than 365 days. Mayans established the production and processing of cotton, which they shared with the Europeans through earlier trade interactions. The Mayans also shared their technique of performing intracranial surgeries and advanced the field of medicine. Aspects of their writing system have been adopted in modern systems.
The Aztec civilization emphasized the importance of education by making it mandatory for the entire population, regardless of class or gender. Most civilizations limited education to the nobility. The Aztecs advanced the field of medicine through the use of antispasmodic medicine during surgery. The Aztecs introduced chocolate to the Spanish before it was introduced to other parts of the world.
http://www.aztec-history.com/aztec-inventions.html

https://www.history.com/topics/ancient-americas/mayan-scientific-achievements

What things do Leo and Stargirl have in common?

One trait that Leo and Stargirl both share is their confidence in their unique individuality. Granted, Stargirl is way more comfortable and confident in being her own person than Leo is. He is still much more affected by peer pressure, but readers do get to see how Leo has confidence in himself liking things that are considered weird or not trendy. For example, he likes porcupine ties:

When I was little, my uncle Pete had a necktie with a porcupine painted on it. I thought that necktie was just about the neatest thing in the world. . . . I loved that porcupine tie so much that I decided to start a collection.

Both Leo and Stargirl are capable of loving people by accepting the other person's actions or personality. Again, Stargirl is better at this than Leo. It's why she is able to kiss Hillari after being slapped. Leo shows his ability to love people regardless of their quirkiness by being friends with Stargirl and Archie. Archie is basically the neighborhood goof, but that doesn't stop Leo from talking to him and seeking his advice. The love of people and goodness that Leo and Stargirl share is also demonstrated in their missions of random acts of kindness.

Is Meursault capable of love?

The simple answer is we do not know. But irrespective of whether or not Meursault does have a capacity for love, there is little doubt that he does not display much in the way of loving behavior toward anyone, at least not in the conventional sense. Meursault shows all the signs of being a sociopath, and those afflicted with this personality disorder tend not to be the most loving of individuals.
Later on in the story, Meursault finds himself on trial for his flouting of established social conventions as much as for the Arab's murder. The prosecutor presents Meursault's relationship with his girlfriend Marie as existing purely to satisfy his own carnal lusts. The prima facie evidence for this contention is quite overwhelming. After a night of passionate lovemaking, Meursault calmly tells Marie that it did not mean anything. The prosecutor also makes hay with Meursault's borderline sacrilegious indifference to his late mother.
However, if we delve a little deeper, a more complex picture begins to emerge. There are a number of examples in the story where Meursault appears to show some semblance of true feeling towards Marie. Whether we can call it love is a moot point, but at the very least, it gives a more rounded picture of this most mercurial of characters. For instance, when the chaplain asks him if he ever sees the face of God in the prison walls, Meursault replies that the only face he looks for is Marie's. His actions are in vain, too.
Perhaps Meursault is lying to himself when he expresses the opinion that love is just a meaningless, abstract concept. The question of whether or not we accept that Meursault is capable of love boils down to the further question of whether we agree with him that love is indeed just an abstract concept or whether we feel that it has a much deeper meaning that Meursault himself chooses to overlook in his relationship with Marie.

Top three rhetorical devices that were the most effective in JFK's Inaugural Address?

JFK delivered his inaugural address on January 20, 1961. His speech was carefully crafted with the help of a few of his closest advisors. So how did he use rhetorical devices (techniques a speaker uses to persuade or sway an audience to agree with his perspective) to appeal to his audience? Let's go over the key points, and you can choose which three you'd like to write about.
Brevity: at 1,355 words, the speech was relatively short. He held the audience's attention because he wasn't speaking for very long.
Phrasing and diction: in the interest of clarity, JFK intentionally used short phrases and short words. These are three separate lines from the speech:

The world is very different now.
This much we pledge—and more.
We dare not tempt them with weakness.

Repetition: Kennedy repeated key words again and again to strengthen his message. Look at the structure of the speech. many lines begin with the same phrase:

Let both sides explore what problems unite us . . .
Let both sides seek to invoke the wonders of science . . .
Let both sides unite to heed in all corners of the earth the command of Isaiah . . .

Rhetorical questions or ideas: these involve the audience, making them consider their own positions instead of just listening passively.

And so, my fellow Americans: ask not what your country can do for you—ask what you can do for your country.

Flattery: JFK makes his audience feel good about themselves by using complimentary language.

The torch has been passed to a new generation of Americans—born in this century, tempered by war, disciplined by a hard and bitter peace, proud of our ancient heritage . . .

How did Egeon contrive means for the safety of the children?

Egeon and Emilia have set sail from Epidamnum on the Adriatic. Their destination is Syracuse, their home town. The couple take with them four children: the twin boys born to Emilia and another pair of baby twins born to a poor couple who sold them to Egeon and Emilia. These boys will grow up to be slaves to Egeon and Emilia's own children.
Disaster strikes when, far from Syracuse, their ship springs a leak. The crew make good their escape, leaving Egeon and his young family behind. To save their children, Egeon and Emilia each tie two infants to the mast, one of their own children together with one of the slaves. They then secure themselves to the mast in the hope that they will escape death. However, the ship hits a rock and splits in two. Emilia and two of the children are swept away in one direction, Egeon and the other two in another. Emilia winds up having her children taken away from her by some Corinthian fishermen, whereas Egeon is more fortunate, returning to Syracuse, where his son Antipholus grows up alongside his slave, Dromio.

Calculus of a Single Variable, Chapter 6, 6.3, Section 6.3, Problem 1

(dy)/dx = x/y
This differential equation is separable since it can be re-written in the form

N(y)dy = M(x)dx
So separating the variables, the equation becomes
ydy = xdx
Integrating both sides, it result to
int y dy = int x dx
y^2/2 + C_1 = x^2/2 + C_2
Isolating the y, it becomes
y^2/2 =x^2/2+C_2-C_1
y^2=x^2 + 2C_2 - 2C_1
y=+-sqrt(x^2+2C_2-2C_1)
Since C2 and C1 represents any number, it can be expressed as a single constant C.
y = +-sqrt(x^2+C)

Therefore, the general solution of the given differential equation is y = +-sqrt(x^2+C) .

Rewrite the final scene of the play. How could the play have ended peacefully?

One problem with the question is to define what we mean by "peacefully." The only way the play could end entirely peacefully would be for Fortinbras to decide not to march on Denmark.
But before we get to that, if by a peaceful ending we mean avoiding the bloodbath that leaves the stage littered with dead bodies, there are other ways the final scene could go. Hamlet, for example, could act on his gut instinct that something is wrong, as well as Horatio's urging that he not fight, and refuse the rapier battle with Laertes. That would knock the poisoned rapier out of the action and also give Claudius no reason to put the poisoned "union," or pearl, in the wine goblet. Of course, one of the problems with this scenario is that Laertes would still be angry and out for vengeance. Also, Claudius would not be killed, so the ending would have to find a way to bring him to justice. One possibility would be to have Claudius poison the wine anyway and for Laertes to see it and realize what is going on. This could jolt him to sense that he is no better than Claudius in planning to kill Hamlet in an underhanded way. This could dissipate Laertes's anger.
If Laertes called out that Claudius poisoned the wine goblet, Hamlet could have Claudius ordered arrested, and Laertes could tell the court about the poisoned rapier. In this scenario, Claudius could be sent to justice with a long jail term but not bloodshed. Hamlet could be named king. Laertes and Gertrude would survive, and Hamlet would make amends to Laertes.
Finally, Fortinbras would have a change of heart and decide, just as Hamlet thinks, that sacrificing so many lives for a small piece of land isn't worth it. He would send Hamlet greetings and head back home. This ending lacks some dramatic gusto, but it could work.

I am sure that there are multiple ways of writing a different ending for this play that doesn't end in the bloodbath that Shakespeare wrote. The tough part is that the question specifies that the rewrite has to happen to the final scene of the play. That makes the peaceful ending much harder to obtain, because by this point the events are almost equivalent to a runaway train. I think the best opportunity for a peaceful ending occurs when Hamlet apologizes to Laertes. Hamlet offers his apology and a bit of an explanation for his previous actions.

Give me your pardon, sir. I’ve done you wrong.
But pardon ’t, as you are a gentleman.
This presence knows,
And you must needs have heard, how I am punished
With sore distraction.

Laertes accepts the apology; however, he is unwilling to back down from the challenge, because it might taint his honor.


I am satisfied in nature,
Whose motive in this case should stir me most
To my revenge. But in my terms of honor
I stand aloof, and will no reconcilement
Till by some elder masters, of known honor,
I have a voice and precedent of peace
To keep my name ungored.



If Laertes would have accepted the apology and not been so driven to uphold his honor, I think the entire final fight scene wouldn't have happened. The poisoned sword would not have been used on Laertes or Hamlet, and no poison would have been consumed by the Queen.

What was unusual about the telescreen in Winston's apartment?

The telescreen is located in a position that does not command a view of Winston's entire room; in this way, Winston is able to write his diary in the little corner hidden from the screen. If this anomaly of construction hadn't existed, he would never have dared keep a diary, which he knows is an act forbidden by the Party.
Interestingly, we're told that what Winston is doing is not actually illegal. Nothing is really illegal because "there were no longer any laws." This is the apparent paradox embedded within a totalitarian society: nothing is explicitly prohibited, but everything a person does is suspect in the eyes of the regime, because its power is arbitrary. Another extraordinary concept in 1984, from the point of view of our own democratic (though still somewhat imperfectly so) society, is that "most of the proles did not even have telescreens in their homes." In one sense the telescreen, or at least part of its functionality, that Winston so fears and has to hide from is also, paradoxically, something we consider indispensable. To be without one would be like not having a smartphone, the absence of which would drive most of us crazy in our world of high-tech expectations. The proles, however, are both deprived of it (therefore living under "primitive" conditions) and simultaneously granted a degree of freedom Outer Party members such as Winston do not have. This accords with the Party's dictum that "the proles are not human beings." They are considered so inferior and beyond the pale that they do not need to be surveilled.
Orwell's implication is that technology will eventually be used as an instrument of oppression. When the ability to transmit and receive was combined in the same device, he tells us, "private life came to an end." One wonders if Winston could have been saved if the randomness of design in his old-style flat hadn't permitted him to keep a diary. Writing things down, expressing himself on paper, emboldens him to transgress further and further against the Party. Yet we're also told that the Thought Police can do just what is implied in their title: read people's minds—in which case Winston would have been doomed anyway.

To answer this question, take a look at Part One, Chapter One. First of all, you'll notice that it's not called a television. In Oceania, this television is, in fact, called a telescreen. Secondly, it does not have the same purpose as modern televisions. That is, it's not about providing news and entertainment to the viewers. In Winston's world, the telescreen transmits messages directly from the Party.
In addition, there is something else rather unusual about the telescreen, as Winston describes:

The instrument (the telescreen, it was called) could be dimmed, but there was no way of shutting it off completely. 

The telescreen cannot be turned off for an unusual, and rather sinister, reason: the Party uses it to monitor the every moment and conversation of Party members. It is like having a CCTV camera in Winston's apartment which live streams his every move to the Inner Party members.
The telescreen is, therefore, an important tool in keeping control of the people of Oceania, which explains its unusual functions.

Explain the quote "There's no art to find the mind's construction in the face." How does it relate to Lady Macbeth in Macbeth?

In Act l, scene lV, King Duncan speaks these lines about the Thane of Cawdor, who has betrayed him. He has just discovered that Cawdor was executed after he confessed his treason and begged the king's forgiveness.
What Duncan means is that no one can determine what another is thinking by looking at his or her appearance or the expression on such a person's face. It is impossible, therefore, to judge whether the person bears you any ill will or not by reading his or her face. He acknowledges that the Thane of Cawdor deceived and misled him. He trusted the thane and believed that he was loyal. This fact is further supported by his earlier statement in Act l, scene ll, when he ordered that Cawdor be killed and Macbeth be given his title:

No more that thane of Cawdor shall deceiveOur bosom interest.

Lady Macbeth, from the outset, is intent on misleading others. She, for example, commands her husband to "appear the innocent flower but be the serpent underneath." She tells him that he must put on a face of conviviality and friendship when he meets Duncan and his entourage when he is, in fact, plotting his malice. Indeed, when she welcomes the king to their castle at Inverness in Act l, scene Vl, she puts on a show and warmly welcomes him:

All our serviceIn every point twice done and then done doubleWere poor and single business to contendAgainst those honours deep and broad wherewithYour majesty loads our house.

Her exaggerated welcome hides her true intentions. She has already decided that Duncan should be murdered and that his visit will give her and her husband the ideal opportunity to enact their perfidy. Prior to this, she called on the powers of darkness to hide her malicious intent and empower her to commit evil. 
It is obvious that Lady Macbeth is sly and ruthless. She is intent on implicating others by creating the illusion that they are responsible for what she and Macbeth are about to do. She informs her husband that:

. . . what not put uponHis spongy officers, who shall bear the guiltOf our great quell?

She intends getting Duncan's guards so drunk that they will be incapable of defending him during the assassination. They will not remember anything and will be easy to blame for a crime that she and her husband are about to commit. She and Macbeth will, after "learning about" Duncan's murder, put up such a show of grief that others will be convinced of their loyalty and love for their now-deceased liege and will, therefore, not suspect them of any wrongdoing.
In addition, she has convinced Macbeth that their task will not fail. He eventually succumbs to her will and agrees about putting on an act. He states, at the end of Act l:

False face must hide what the false heart doth know.

Lady Macbeth's conniving and plotting tie in well with the theme of appearance and reality. Her sole purpose is to illegitimately gain power. She will deceive and mislead to ensure that she and her husband achieve their goal. It is ironic that she is the first to eventually succumb to remorse. She is overwhelmed by guilt and becomes so overwrought that she commits suicide. 

The quote you reference is originally spoken by King Duncan in Act 1, Scene 4 of Shakespeare's Macbeth. In context, the quote references how the former Thane of Cawdor fooled Duncan and betrayed him. Basically, in this quote Duncan is acknowledging how difficult it is to know what's going on in someone else's mind based on their outward appearance. In other words, it's easy for someone to hide his or her real feelings in order to betray someone.
This quote could certainly apply to Lady Macbeth on multiple occasions, as she proves adept at hiding her true feelings for most of the play (until, of course, she's goes crazy and dies). The most obvious example of this is Act 2, Scene 3, at which point King Duncan's murder is discovered. At this point, we know Lady Macbeth had a role to play in the murder. That said, you wouldn't guess it from the way she pretends to be surprised, and then emotionally/physically weakened by the grisly "revelation." Indeed, Lady Macbeth carefully hides her guilty conscience by pretending she is too "weaK" to deal with the news of Duncan's murder. As such, at this point in the play Lady Macbeth's outward appearance certainly masks her "mind's construction."

Is Luke O'Neill in the Thorn Birds more like Amir from The Kite Runner or Rasheed from A Thousand Splendid Suns?

Colleen McCullough's Thorn Birds highlights the story of the Cleary family over the course of 54 years, emphasizing the life of Meghann "Meggie" Cleary who lives at Drogheda, a sheep station in the Australian Outback. Meggie is eventually courted by Luke O'Neill, a miserly and misogynistic ranch worker at the station. Luke and Meggie unenthusiastically marry each other, but Luke doesn't stick around for long, leaving her to cut sugarcane in North Queensland, stealing her wages and savings in the process. 
Luke is more like Rasheed in Khaled Hosseini's A Thousand Splendid Suns. Rasheed is a shoemaker from Kabul who marries the much younger Mariam and is incredibly abusive toward her. Rasheed also later abuses the other female protagonist, Laila, who bears his son. 
Amir, from Khaled Hosseini's The Kite Runner, is much more passive than the two aforementioned characters. He does witness a horrific act of violence and chooses not to intervene, but he does not play an active role in injuring anyone. Thus, I would say Luke, who is very aggressive, is not really like Amir.

How and why did the Holocaust begin?

Historians generally feel that the beginning of the Holocaust was the date that Adolf Hitler was appointed chancellor of Germany (January 30, 1933). This is a compelling argument because much of the reason for the Nazi party's success was its propaganda against the communists and the Jews even before their ascendancy. The Germans were very desperate for a leader that could solve the economic hardships, particularly unemployment and inflation.  The state of desperation the Germans were facing allowed them to be convinced that the Jews were the root of all of their problems. There also was an element of fear in opposing the viewpoints of the Nazis.  
Hitler was able to turn the propaganda into law in September of 1935 with the Nuremberg Laws.  This anti-Jewish legislation established a firm legal ground on which to persecute the Jews in Germany.
 
 
https://www.jewishvirtuallibrary.org/an-introductory-history-of-the-holocaust

int (x^3 - 8x)/x^2 dx Find the indefinite integral.

int (x^3-8x)/x^2dx
To solve, express the integrand as two fractions with same denominators.
=int (x^3/x^2-(8x)/x^2)dx
Simplify each fraction.
=int (x - 8/x)dx
Express it as difference of two integrals.
=int xdx - int8/xdx
For the first integral, apply the formula intx^ndx= x^(n+1)/(n+1)+C .
And for the second integral, apply the formula int 1/xdx=ln|x|+C .
= int xdx - 8int1/xdx
=x^2/2-8ln|x|+C
 
Therefore, int (x^3-8x)/x^2dx = x^2/2-8ln|x|+C .

How did the Fugitive Slave Act affect sectional division between the South and the North?

The Fugitive Slave Act was one of the most controversial pieces of legislation in the antebellum (pre-Civil War) era and was a contributor to the sectional divisions between the North and the South.
After the Mexican-American War (1846-1848), in which the U. S. took the land that it now the southwest of the country, intensified the debate between the North and the South over the extension of slavery. The key question became: Could slavery be extended to the newly acquired land from Mexico and how would that be determined? Many in the North, primarily abolitionists and "free-soilers" (those who wanted to keep the new territories free) disapproved of the expansion of slavery to the West. The South thought the expansion essential to their way of life. One of the first compromised to try to solve this sectional view was the Compromise of 1850, engineered by Illinois Democrat Senator Stephen Douglas. One of the key facets of the law was a pro-South provision, the Fugitive Slave Act, which allowed southern slave owners, with support of the federal government, to go to the North to retrieve runaway slaves.
The act outraged many in the North who believed it was a violation of their position as free states to allow slave holders come into their territory to forcibly take African Americans back into slavery. Frederick Douglass, the former slave and abolitionist leader, saw the law as a violation of American liberties, stating,

Human government is for the protection of rights; and when human government destroys human rights, it ceases to be a government, and becomes a foul and blasting conspiracy; and is entitled to no respect whatever.

Northerners were also upset at the abuses of the law as in the case of Solomon Northrup, a free African American who was captured by southern bounty hunters and sold into slavery (see his book Twelve Years a Slave). Lastly, it contributed to sectionalism because many Northerners saw it as an attempt of the South to control the federal government, and further extend the system of slavery.
The South, obviously, supported the law and tried to put it into strong effect. The Compromise of 1850 had given the North some provisions, such as bringing California into the union as a free state, so they were fairly giving the right to capture their runaway slaves in the North. A result that most angered the South was the North's blatant disregard for the law. In many cases where runaway slaves were brought to trial, Northern juries refused to hand them over to bounty hunters and therefore put them into slavery, a violation of the Fugitive Slave Act according to Southerns. It also led the South to believe that the North was trying to limit their rights as slaveholders.

The Fugitive Slave Act was part of a raft of legislation known as the Compromise of 1850. This was an attempt to take the heat out of growing tensions over the deeply contentious issue of slavery. In actual fact, it had almost the exact opposite effect. The highly controversial Act stipulated that all runaway slaves had to be returned to their masters, and that free states and their officials were required to assist in their return.
To many in the North, the Fugitive Slave Act was an outrage, both morally and legally. In terms of the latter, it was widely resented as an attack on the rights of the Northern states to manage their own affairs. The Southern states, while forever insisting on the importance of their rights being respected, were at the same time infringing on the rights of free states. This attitude was seen in the North as hypocritical in the extreme. More seriously, it appeared to confirm what many Northerners had long believed: that the South enjoyed disproportionate political power in the United States, which they were flagrantly abusing in order to defend a cruel, immoral institution. In the North at least, the Compromise of 1850 was regarded as anything but. It merely served to heighten tensions and drive a further wedge, politically and culturally, between North and South.

College Algebra, Chapter 8, 8.2, Section 8.2, Problem 40

Determine the equation for the ellipse with end points of minor axis $(0, \pm 3)$ and distance between foci $8$.
The equation $\displaystyle \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ is an ellipse that has endpoints on major axis at
$(0,\pm a)$ and endpoints on minor axis at $(0,\pm b)$ with foci on $(0,\pm c)$ where $c^2 = a^2 - b^2$ and the distance
between the foci is determined as $2c$. So, $b = 3$ and if $2c = 8$, then $c = 4$. Thus,

$
\begin{equation}
\begin{aligned}
c^2 &= a^2 - b^2 \\
\\
a^2 &= c^2 + b^2\\
\\
a^2 &= 4^2 + 3^2 \\
\\
a^2 &= 25\\
\\
a &= 5
\end{aligned}
\end{equation}
$

Therefore, the equation is
$\displaystyle \frac{x^2}{3^2} + \frac{y^2}{5^2} = 1 \text{ or } \frac{x^2}{9} + \frac{y^2}{25} = 1$

Calculus of a Single Variable, Chapter 2, 2.4, Section 2.4, Problem 80

You need to find the equation of the tangent line to the given curve, at the point (pi/4,2), using the formula:
f(x) - f(pi/4) = f'(pi/4)(x - pi/4)
You need to notice that f(pi/4) = 2.
You need to evaluate the derivative of the given function, using chain rule, such that:
f'(x) = (2(tan x)^3)' => f'(x) = 2*3(tan x)^2*(tan x)'
f'(x) = 6tan^2 x*(1/(cos^2 x))
You need to evaluate f'(x) at x = pi/4 , hence, you need to replace pi/4 for x in equation of derivative:
f'(pi/4) = 6tan^2 (pi/4)*(1/(cos^2 (pi/4)))
f'(pi/4) = 6*1/(1/2) => f'(pi/4) = 12
You need to replace the values into equation of tangent line, such that:
f(x) - 2 = 12(x - pi/4) => f(x) = 12x - 3pi + 2
Hence, evaluating the equation of the tangent line to the given curve, at the given point, yields f(x) = 12x - 3pi + 2 .

Which document did the Pilgrims write and sign as a plan of government that said they would have "just and equal laws . . . for the general good of the colony"?

The document you are referring to is known as the Mayflower Compact. In November of 1620, the Mayflower had landed at Cape Cod in what would become the Colony of Massachusetts. There were 102 passengers on board. Only forty-one of these passengers were the religious dissenters known as Pilgrims. The rest were craftsmen, merchants, mercenaries, and indentured servants. The Pilgrims referred to these people as Strangers.
The necessity for a document defining a local government came up shortly after landing at Cape Cod. Their original destination had been Virginia, but navigational error had brought them well off course. Now they found themselves well outside the protections of the English government. A conflict between the Strangers and the Pilgrims soon arose as the former group began arguing that, since they were outside the jurisdiction of the Virginia Colony, the laws of the colonial government no longer applied. There threatened to be a rift between the two groups that could sabotage the whole venture.
To avoid this calamity, the leaders aboard the Mayflower decided it was necessary to make a mutual agreement between all the parties. They would need to create a governing body that would recognize the rights and duties of the colonists and create a means to prevent internal turmoil.
The Mayflower Compact was a tool to create a self-governing body. In England, the authority to rule came from the monarchy. Isolated across the Atlantic Ocean, the colonists aboard the Mayflower had to rely on themselves. The Mayflower Compact still affirmed them to be loyal subjects of the English king but also set up a system of governors and ministers to safeguard the civil and religious rights of the passengers. The document is relatively short, but it bound the colonists into a single civic unit created to protect the "general good of the colony." It was signed on November 11, 1620 on board the Mayflower by the adult males on board. It became the first legal document drafted by colonists in North America.
https://historyofmassachusetts.org/the-mayflower-compact/

Single Variable Calculus, Chapter 3, Review Exercises, Section Review Exercises, Problem 40

Find $y'$ of $y = \sin^2 \left( \cos \sqrt{\sin 'pi x}\right)$


$
\begin{equation}
\begin{aligned}
y' &= \frac{d}{dx} \left[ \sin^2 \left( \cos \sqrt{\sin 'pi x}\right) \right]\\
\\
y' &= \frac{d}{dx} \left[ \sin^2 \left( \cos \sqrt{\sin 'pi x}\right) \right]^2\\
\\
y' &= 2 \sin \left( \cos \sqrt{\sin \pi x} \right) \frac{d}{dx} [\sin(\cos\sqrt{\sin \pi x})]\\
\\
y' &= 2 \sin (\cos\sqrt{\sin \pi x}) \cdot (\cos \sqrt{\sin \pi x}) \frac{d}{dx} (\cos\sqrt{\sin \pi x})\\
\\
y' &= 2 \sin (\cos\sqrt{\sin \pi x}) \cdot (\cos \sqrt{\sin \pi x}) \cdot (-\sin\sqrt{\sin \pi x}) \frac{d}{dx} (\sqrt{\sin \pi x})\\
\\
y' &= 2 \sin (\cos\sqrt{\sin \pi x}) \cdot (\cos \sqrt{\sin \pi x}) \cdot (-\sin\sqrt{\sin \pi x}) \frac{d}{dx} (\sin \pi x)^{\frac{1}{2}}\\
\\
y' &= 2 \sin (\cos\sqrt{\sin \pi x}) \cdot (\cos \sqrt{\sin \pi x}) \cdot (-\sin\sqrt{\sin \pi x}) \cdot \left( \frac{1}{2}\right)(\sin \pi x)^{\frac{-1}{2}} \frac{d}{dx} ( \sin \pi x)\\
\\
y' &= 2 \sin (\cos\sqrt{\sin \pi x}) \cdot (\cos \sqrt{\sin \pi x}) \cdot (-\sin\sqrt{\sin \pi x}) \cdot \left( \frac{1}{2}\right)(\sin \pi x)^{\frac{-1}{2}} \cdot (\cos \pi x) \frac{d}{dx} (\pi x)\\
\\
y' &= \cancel{2} \sin (\cos\sqrt{\sin \pi x}) \cdot (\cos \sqrt{\sin \pi x}) \cdot (-\sin\sqrt{\sin \pi x}) \cdot \left( \frac{1}{\cancel{2}}\right)(\sin \pi x)^{\frac{-1}{2}} \cdot (\cos \pi x)(\pi)\\
\\
y' &= \frac{-\pi \sin(\cos\sqrt{\sin \pi x})\cos(\cos\sqrt{\sin \pi x}) \sin \sqrt{\sin \pi x} \cos \pi x}{(\sin \pi x)^{\frac{1}{2}}} \qquad \text{or} \qquad y' = \frac{-\pi \sin(\cos\sqrt{\sin \pi x})\cos(\cos\sqrt{\sin \pi x}) \sin \sqrt{\sin \pi x} \cos \pi x}{\sqrt{\sin \pi x}}
\end{aligned}
\end{equation}
$

How did life start on Earth?

How did life Start on Earth?
This is an excellent question that has challenged scientists for many years. The answer to this question is still in the realm of theoretical speculation however, this does not mean that there are not strong theories about how life first appeared on Earth. The earliest evidence of life on Earth can be found in fossilized matts of cyanobacteria in Greenland that are about 3.7 billion years old. Whereas this is the first concrete evidence of the beginning of life, there is other evidence dating back to around 4.1 billion years which indicates a form of carbon that is believed to be connected to life.
There are many competing theories about the beginnings of life on Earth. One of them is known as panspermia which stipulates that life actually exists throughout the universe and is carried to knew planets through the impact of comets and meteorites on lifeless planets. Another theory postulates that life started off with amino acids and polypeptides and through a combination of chemical processes and electric sparks via lightning life started.
Today's life is dominated by DNA which drives is code of life. However, this is believed to not always to have been the case. It is believed by many scientists that RNA was once the driving molecule of life. RNA today still has a role to play in all cells as a integral part to play in protein synthesis and also can be found in mitochondria. Mitochondria are the engines of the cell and many scientists believe that they were primitive life that later joined with other cell for mutual symbiotic advantage. It could be that there have been many genesis of life on earth given that over 99 percent of life that has ever existed has gone extinct.
References:
https://www.livescience.com/1804-greatest-mysteries-life-arise-earth.html
http://www.nature.com/scientificamerican/journal/v197/n1/pdf/scientificamerican0757-131.pdf

There is evidence that early Earth was different than Earth today. The atmosphere had no free oxygen—instead it consisted of methane, ammonia, water vapor, and hydrogen gas. It has been proven by experiments like one done by Stanley Miller in the 1950s that organic compounds can be formed spontaneously in the absence of living organisms, given the proper conditions. There was volcanic activity and lightning that provided an energy source along with an abundance of elements in the early Earth that reacted together and formed organic compounds.
Eventually, they would have accumulated and would have been stable for a long period of time—like a hot, rich organic soup. As molecules collided, larger, more complex molecules formed. These are polymers. Their formation is known as spontaneous polymerization.
It is thought that eventually, these chemicals became able to self-replicate and produce proteins capable of catalyzing chemical reactions that would be a key step to life evolving on Earth. Self-replicating polynucleotides—the building blocks of proteins—were established on Earth 3.5 billion years ago. It is believed that this brought about RNA, which can be used as a catalyst and can act as a template for replication. RNA is a single-stranded nucleic acid and was probably the first molecule on early Earth to carry the genetic information necessary to make proteins.
It is next hypothesized that the first cell arose on ancient Earth when a self-replicating RNA, along with its protein products, was surrounded by a phospholipid "bubble," which acted like a cell membrane, enclosing the RNA and its proteins. This would then be a primitive cell since RNA was capable of self-replicating.
Later on, DNA arose, which is a more stable molecule consisting of a double helix. In modern cells, DNA in the nucleus directs the production of proteins indirectly because it is transcribed into RNA first, and then during translation of the RNA by a ribosome, proteins are produced. This is the central dogma—DNA to RNA to protein—and describes the flow of information within a cell. Due to the endless combinations of nucleic acids, there is a large variety of life on Earth.
On ancient Earth, the first cells depended on the rich organic materials in the sea broth for food, and these early organisms were heterotrophic: dependent on pre-formed organic molecules to feed on. These organisms eventually multiplied, and as the organic substances began to be consumed, any organism with the ability to manufacture organic nutrients from simple molecules would have an advantage, as it could produce its own food. Therefore, autotrophs arose next on early Earth. These are producers.
As autotrophs like early blue-green algae accumulated, oxygen would accumulate in the atmosphere as a by-product of their metabolism. The atmosphere changed from an anaerobic to an aerobic one, and evidence shows oxygen accumulated on ancient Earth around 2 billion years ago. The oxygen would be toxic to the early bacteria accustomed to an anaerobic environment. Those that couldn't adapt would only be able to live in anaerobic parts of the biosphere. Other aerobic bacteria evolved. The accumulation of oxygen allowed eukaryotic one-celled organisms to arise around 1 billion years ago. And from then on, the wealth of multicellular organisms on Earth evolved into every part of the biosphere.
https://en.wikipedia.org/wiki/Miller%E2%80%93Urey_experiment

Calculus of a Single Variable, Chapter 3, 3.4, Section 3.4, Problem 42

Given the function f(x)=2sinx+cos(2x) in the interval [0,2pi]
Taking the first derivative we get,
f'(x)=2cosx-2sin(2x)
Inorder to find the critical points we have to equate f'(x)=0.
So we get,
2cosx-2sin(2x)=0
i.e. cosx-2sinxcosx=0
cosx(1-2sinx)=0
implies, cosx=0 and 1-2sinx=0
So cosx=0 implies x=pi/2, 3pi/2 in the interval [0,2pi].
1-2sinx=0 implies, x=pi/6, 5pi/6.
Therefore the critical points are: pi/2, (3pi)/2,pi/6,(5pi)/6
Now taking the second derivative of f(x) we get,
f''(x)=-2sinx-4cos(2x)
Applying second derivative test we have,
f''(pi/2)=4>0
f''(3pi/2)=4>0
f''(pi/6)=-3<0
f''(5pi/6)=-3<0
Therefore the function has relative minima at x=pi/2, (3pi)/2
and the minimum value is f(x)=1
The function has relative maxima at x=pi/6,(5pi)/6
and the maximum value is f(x)=1.5

What was bad about this deal?

The land-greedy peasant Pahom thinks he's made the bargain of the century with the seemingly naive Bashkirs. Their chief has told Pahom that he can have as much land as he can walk around in one day. And all for the knockdown price of one thousand rubles. But there's one condition: Pahom needs to return to the exact point where he started.
Pahom thinks he's got the better of the deal; all that land for a hardly anything. What an unbeatable bargain! Unfortunately, however, his greed gets the better of him, and in his frenzied desire to grab as much land as possible, dies in the attempt. Despite his astute business brain and experience in the acquisition of land, it's fair to say that Pahom ends up losing out on the deal. And all because he got too greedy. How much land did Pahom really need? Just enough to bury him in, the same as everyone else.

Calculus of a Single Variable, Chapter 8, 8.6, Section 8.6, Problem 46

Recall indefinite integral follows int f(x) dx = F(x)+C
where:
f(x) as the integrand
F(x) as the antiderivative of f(x)
C as the constant of integration.
From the table of integrals, we follow the formula:
sqrt(x^2+-a^2) dx = 1/2xsqrt(x^2+-a^2)+-1/2a^2ln|x+sqrt(x^2+-a^2)|
From the given problem int_0^3 sqrt(x^2+16) dx , we have a addition sign (+) in between terms inside the square root sign. Then, we follow the formula:
int sqrt(x^2+a^2) dx = 1/2xsqrt(x^2+a^2)+1/2a^2ln|x+sqrt(x^2+a^2)|
Take note that we can express 16 = 4^2 then the given problem becomes:int_0^3 sqrt(x^2+4^2) dx .
The x^2 +4^2 resembles the x^2 +a^2 in the formula. Then by comparison, the corresponding values are: x=x and a=4.
Plug-in x=x and a=4 on the formula, we get:
int_0^3 sqrt(x^2+16) dx =[1/2xsqrt(x^2+4^2)+1/2*4^2ln|x+sqrt(x^2+4^2)| ]|_0^3
=[1/2xsqrt(x^2+16)+1/2*16ln|x+sqrt(x^2+16)|]|_0^3
=[1/2xsqrt(x^2+16)+8ln|x+sqrt(x^2+16)|]|_0^3
Apply definite integral formula: F(x)|_a^b = F(b) - F(a) .
[1/2xsqrt(x^2+16)+8ln|x+sqrt(x^2+16)|]|_0^3
=[1/2*3sqrt(3^2+16)+8ln|3+sqrt(3^2+16)|]-[1/2*0sqrt(0^2+16)+8ln|0+sqrt(0^2+16)|]
=[3/2sqrt(9+16)+8ln|3+sqrt(9+16)|]-[0*sqrt(0+16)+8ln|0+sqrt(0+16)|]
=[3/2*5+8ln|3+5|]-[0*4+8ln|0+4|]
=[15/2+8ln|8|]-[0+8ln|4|]
=15/2+8ln|8| -0-8ln|4|
=15/2+8ln|8| - 8ln|4|
=15/2+8(ln|8| - ln|4|)
Apply natural logarithm property: ln(x)- ln(y) = ln(x/y) .
=15/2+8ln|8/4|
=15/2+8ln|2|
Apply natural logarithm property: n*ln(x) = ln(x^n) .
=15/2+ln|2^8|
=15/2+ln|256| or 13.05 ( approximated value)

What does Sophocles' Antigone communicate to the audience?

In addition to the classic issue of hubris, or excessive and unrelenting pride, which is a perennial one in Greek tragedy, Antigone poses two related questions about the nature of citizenship and political power.
First, the dilemma posed to Antigone revolves around the perspective of the citizen or subject: is every decree of a ruler to be obeyed, or are there duties that may be more important than civic statutes? Antigone is never in doubt about the answer, even in her opening dialogue with Ismene:

IsmeneYou plan to bury him—when it is forbidden to the city?
AntigoneYes, he is my brother, and yours too, even if you wish it otherwise. I will never be convicted of betraying him.
IsmeneHard girl! Even when Creon has forbidden it?
AntigoneNo, he has no right to keep me from my own. (44-48)

Later, in her confrontation with Creon, she explicitly states than her disobedience to his decree was just,

since it was not Zeus that published me that edict, and since not of that kind are the laws which Justice, who dwells with the gods below, established among men. Nor did I think that your decrees were of such force, that a mortal could override the unwritten and unfailing statutes given us by the gods. (450-455)

Creon's dilemma is from the perspective of the ruler: should he demand obedience, or should he be open to critique and correction from the citizens or subjects? His clearest answer is given when challenged by his own son, Haemon, where Creon begins with a speech in which he states:

whomever the city may appoint, that man must be obeyed in matters small and great and in matters just and unjust...But there is no evil worse than rejection of the ruler (anarchia). (lines 666-667, 672)

The argument between Creon and Haemon leads to this furious stichomythia:

CreonShall the city prescribe to me how I must rule?
HaemonSee, there, how you have spoken so much like a child.
CreonAm I to rule this land by the will of another than myself?
HaemonThat is no city, which belongs to one man.
CreonDoes not the city by tradition belong to the man in power?
HaemonYou would make a fine monarch in a desert. (734-739)

Creon's demand for total and unquestioning obedience in all things turns out to be the truly tragic decision of the play, since his law against the burial of Polyneices brings pollution on the city (line 1015) and the deaths of Antigone and his own son.
The play's answer to both questions, then, is in favor of Antigone and Haemon's view that there are limits to the ruler's power, and that both the citizens and the ruler should recognize this.
An important addendum as to the message of Antigone has to do with the role of women. Creon's demands of obedience are crucially intertwined with his refusal to listen to a woman:

Therefore we must defend those who respect order, and in no way can we let a woman defeat us. It is better to fall from power, if it is fated, by a man's hand, than that we be called weaker than women. (677-680)

This is seen as well in his argument with Haemon, where Creon repeatedly condemns and insults his son for supporting a woman (740, 746, 756).
The fact that the play vindicates Antigone's actions and perspective on political authority and its limits, over against Creon's tyranny and misogyny, lead many to consider Antigone to be a striking, early example of feminist social critique.
http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0186%3Acard%3D1

In Antigone, Sophocles communicates the importance of being humble. 
At the end of Antigone, there is a profound sense of emptiness.  We have seen Creon and Antigone collide with one another because they believed in the authenticity of their convictions.  Antigone believed she was doing right by her beliefs.  Creon is equally adamant in his unwillingness to compromise.  Family members appeal to both of them to change their mind.  However, neither one sacrifices their ego and, as a result, the unthinkable takes place.  While Creon does relent, it is too late.  The deaths of Creon's son and wife along with Antigone's death represent sadness resulting from human foolishness. 
Sophocles communicates the danger of self-aggrandizement.  He conveys the calamity that can await when we believe that we are better, smarter, and stronger than we really are.  This is revealed at the drama's conclusion. Creon appears before the Chorus and the audience as a broken man:

Let this rash man be led out of the way,who, my child, unwillingly slew you,and this woman, you, too—alas! I haveno where to turn to, nothing to lean on,for everything goes cross in my hands,and a difficult fate falls on my head.

Creon's language is very different from the bluster he displayed throughout the drama.  He has recognized that living a life without humility has made him a "rash man." He knows that his hubris resulted in the deaths of his son and wife.  He is forced to admit his limitations, a reality he would not previously entertain. Creon communicates how "a difficult fate" crushes us when we do not limit our ego and listen to others' counsel.
Sophocles communicates how we need to live within our limitations in order to find happiness.  In the drama's final lines, the Chorus communicates how we must be different than Creon or Antigone:   

Knowledge truly is by far the most important partof happiness, but one must neglect nothingthat the gods demand.Great words of the over-proudbalanced by great fallstaught us knowledge in our old age.

We are punished through "great falls" when we live as "the over-proud." Sophocles tells the audience that knowledge and wisdom mean living with humility and deference to something larger than ourselves.  Creon and Antigone communicate the dangers of living otherwise.

What was Kristallnacht?

Kristallnacht (German for "Crystal Night") was the night of November 9–10, 1938, during which Nazis attacked Jewish people and property. The night is also referred to as Reichskristallnacht, Pogromnacht, and Novemberpogrome. The Crystal Night or Night of the Broken Glass gets its name from the litter of broken glass left in the streets after the destruction caused by the anti-Semitic pogroms that led to the death of approximately a hundred Jews. During the night, Jewish stores, homes, and schools were terrorized and robbed; nearly 1,000 synagogues were burned. In the immediate wake, nearly 30,000 (if not more) Jews were arrested and sent to concentration camps.
Anti-Semitism had been rampant in Germany since the rise of Adolf Hitler (1933), who frequently lambasted Jews as the reason for Germany's defeat in the First World War (1914–1918) and the subsequent economic collapse. Hitler's propaganda made Jews easy scapegoats for all of Germany's administrative and economic problems, and this dehumanization was key to the German populace's acceptance of—and participation in—the anti-Jewish pogroms, including Kristallnacht.
The immediate catalyst for Kristallnacht was the shooting of Ernst vom Rath (a German diplomat) in Paris on November 7, 1938, by the student Herschel Grynszpan (a Polish Jew). When news of this reached Munich, where the Nazis were celebrating the anniversary of the Beer Hall Putsch, Joseph Goebbels (the Nazi minister of propaganda) created a public frenzy with calls of revenge and easily organized Nazi storm troopers into "protesters" who demonstrated all over the country. Heinrich Muller (a Gestapo chief) on November 9th informed the German police that acts of violence against German Jews were soon to take place—and that the police were not to attempt to stop them; instead they were to aid the hate crimes and arrest victims.
While the Nazi Party had always been both covertly and overtly anti-Jewish, Kristallnacht symbolised a break from a policy of mostly hate speech and non-violent anti-Semitism. The night marked the transition to full-scale state-sponsored violence. The latter would come to dominate Hitler's Germany.

Kristallnacht was a seminal moment in Nazi Germany's war against its Jewish population. It provided the pretext for a sweeping range of anti-Semitic laws that drove Jews out of the German economy. It was a pivotal step in the nation's progression from merely discriminating against Jews to expelling them from society to expelling them from the nation to the ultimate Final Solution.
Kristallnacht purportedly was a spontaneous reaction to the assassination of a minor German government official by a Jewish expatriate in Paris in November 1938, a reaction to the Nazis expelling thousands of Jews of Polish descent across the border into Poland. On the nights of November 9th and 10th, mobs of angry German citizens roamed the streets throughout the nation, breaking the windows of Jewish-owned businesses, homes, and synagogues—hence the name Kristallnacht, or the Night of Broken Glass.
The Germans eventually blamed the Jews for Kristallnacht and enacted a series of laws that basically rid Jews from the German economy as well as levied billions of marks worth of fines and penalties for the death of the German official and to pay back insurance companies for payouts.
Kristallnacht is considered by some as the beginning of the Holocaust because it marked the turning point in Nazi Germany's dealings with its Jewish population. No longer would Jews be tolerated in the nation; their dealings went from mere harassment to violence, and when the German population didn't object to the pogrom, the Nazis knew they could enact their Final Solution without much pushback.
https://www.aish.com/ho/o/48956531.html

https://www.history.com/topics/holocaust/kristallnacht

https://www.jewishvirtuallibrary.org/background-and-overview-of-kristallnacht

"The Cask of Amontillado" is told in chronological order to create suspense. "Sonny's Blues" uses flashbacks to establish depth of character. Discuss these two methods of narration, showing how they work in these two stories.

"The Cask of Amontillado" builds towards a suspenseful conclusion by presenting, in a chronological way, the method that the narrator uses to get revenge on Fortunato. At the beginning of the story, the reader knows that the narrator, Montresor, seeks revenge, as he says of Fortunato, "when he ventured upon insult I vowed revenge." The reader also knows that Fortunato has what the narrator calls "a weak point"--his pride in his knowledge of wine. However, the reader does not know how Montresor will use Fortunato's weakness to get revenge. As Montresor leads Fortunato through the damp vaults and Fortunato begins to cough, Montresor attends to Fortunato with what appears to be kindness. The reader does not quite understand how Montresor will get revenge on Fortunato merely by bringing Fortunato to a vault, and Montresor is so seemingly kind to Fortunato that it seems uncertain that he will ultimately get revenge.
By taking the reader through each stage of Fortunato's descent through the vault, Poe builds suspense. There are clues that Montresor is bent on his friend's destruction, such as when he tells Fortunato that the Montresor family crest is one in which "the foot crushes a serpent rampant whose fangs are imbedded in the heel." This symbolizes Montresor's eventual murder of his friend. Montresor then takes Fortunato to part of the crypt where "the walls had been lined with human remains," another sign that death is coming before Montresor finally buries the drunken Fortunato in the crypt forever.
Unlike "The Cask of Amontillado," the suspense in "Sonny's Blues" is on a psychological level. The narrator wonders why his brother has been arrested for selling heroin. The story begins, "I read about it in the paper, in the subway, on my way to work. I read it, and I couldn't believe it, and I read it again." The story uses flashbacks to help the narrator--and the reader--understand how Sonny has gotten to this point.
The narrator begins to remember the past. He thinks:




"This was because I had begun, finally, to wonder about Sonny, about the life that Sonny lived inside. This life, whatever it was, had made him older and thinner and it had deepened the distant stillness in which he had always moved."

Sonny's deeper psychological motivations are a mystery to his brother until the narrator goes further and further back into time and into his family's history. The narrator realizes that Sonny and his father never got along; he says, "the principal reason that they never hit it off is that they were so much alike." The narrator also realizes that he has been dismissive towards his brother's dreams. When Sonny tells him that he wants to be a musician, the narrator thinks, "I simply couldn't see why on earth he'd want to spend his time hanging around nightclubs, clowning around on bandstands, while people pushed each other around a dance floor." It is only at the end of the story, as the narrator sees Sonny playing music, that the narrator understands his brother's struggles. This form of flashback narration works because the narrator needs to go back in time, to mine his brother's past, to understand what makes his brother tick and why his brother has suffered so much. Presenting the events of the story in a chronological way would not achieve the effect of going back in time to understand the present.

What is the American Dream? The traditional goals of achieving a happy, fulfilling life after hard work and dedication were challenged in the wake of a country experiencing devastation from war and economic collapse. (In this module, you have examined how the age of Modernism developed and the new forms of literature that it cultivated. )..I read "Of Mice and Men" and "Winters Dreams." You also looked at how the American Dream manifested itself into the very marrow of American culture. 1.How does the quest for this dream shape the lives of Americans today? 2.Is the dream alive today, and is it even possible to achieve? 3.Or is this dream just a reminder of what once was or can never be? I need these three questions answer please.

The American Dream is the ideal that anyone who lives in the United States can achieve a meaningful life and meet all of his or her needs through hard work and determination. "Of Mice and Men" and "Winter Dreams" address this theme directly, albeit in different ways. "Of Mice and Men" tells the story of two migrant workers who buy into the American dream, while "Winters Dream" tells of a young man named Dexter who is faced with the death of his own, more specific American dream.
1. How does the quest for this dream shape the lives of Americans today?
The American dream may have changed since the era of the Great Depression, but it still shapes the lives of all Americans. The American Dream is what fuels people to devote their lives to the pursuit of education and a career, through which they hope to achieve relative economic stability and the ability to live freely and pursue their interests.
2. Is the dream alive today, and is it even possible to achieve?
The ability to achieve the American dream is dependent upon both the protection of freedoms by the government and economic stability. The 2008 recession and housing market crash resulted in the perceived loss of the American dream for many citizens and immigrants alike, but economic recovery has led to a resurgence in believe in the American dream today. For many, the lavish American dream of the pre-Depression era in the 1920s is no longer a reality. Today's American dream has shifted to more moderate terms for most people, but it is still alive and well.
3. Or is this dream just a reminder of what once was or can never be?
Whether this dream is possible to achieve is a matter of perspective, but as long as Americans maintain the basic freedoms of speech and the ability to earn a living through honest work, the dream will always be possible to achieve, if improbable. Like George in "Of Mice and Men," many Americans have been forced to re-evaluate their ideas of what it means to be free and successful in America. Like Dexter, many are forced to abandon idealistic dreams of perfection and youthful naivete, but with that abandonment comes perspective.
As Dexter realized that his own American dream was unrealistic, modern Americans are often forced to determine which qualities and achievements are truly fundamental to the American dream. Living in a mansion and driving expensive cars may not be a feasible American dream for everyone, but it is always the prerogative of the next generation to improve upon the American dream of their predecessors and redefine it in terms of the qualities that are most important to them. As long as people continue to think about the American dream and work earnestly towards achieving it, it will always be possible.

When Gene visits the tree, what does it resemble?

The tree is a very important symbol in A Separate Peace. For Gene, it represents many different things, such as the need for self-discipline and overcoming your innermost fears. He associates it with his schooldays at Devon when his roommate Finny egged him on to make a daring leap from the tree into the river. Initially, the tree presents quite a forbidding spectacle to Gene; it's tall, majestic, a "steely black steeple." But when he returns as an adult to Devon School fifteen years later, the tree takes on a completely different appearance. Now it seems shriveled and weak, much smaller than he remembers it. In the words of Gene, it seems to resemble

[T]hose men, the giants of your childhood, whom you encounter years later and find that they are not merely smaller in relation to your growth, but that they are absolutely smaller, shrunken by age. In this double demotion the old giants have become pigmies while you were looking the other way.

Gene reflects on how fearful he was when he was a schoolboy at Devon, and he deliberately seeks out those places on campus he always associated with that fear, one of which is the tree. But it no longer holds any such fears for Gene. In actual fact, the tree hasn't really changed all that much but he has. He's gone through so many experiences, most notably during the war, in which he's had to show courage that the tree now symbolizes not so much fear, but the quiet, bookish young schoolboy who didn't really understand its true meaning.

What is the climax of The Wind in the Willows?

The storyline of “The Wind in the Willows” is fairly episodic, so it can be hard to point to a specific single climax for the book. Nevertheless, if we understand the book to be about Toad’s change from a dangerously impulsive, immature character to a functioning adult, then the highest point of the action must be the retaking of Toad Hall, in the chapter entitled, “The Return of Ulysses.” Toad, after his escape from jail, returns to the riverbank to find his house inhabited by weasels and stoats. With the help of his friends Badger, Rat, Otter, and Mole, Toad is able to retake his house using a secret tunnel to gain access. 
The climax is a significant moment in the development of Toad’s character. He learns that he needs the help of his friends to reclaim his home. Mole also learns that he is a brave and capable person, since it is his “reconnaissance“ mission to Toad Hall that draws the weasels out of the building, giving Toad and his allies a significant advantage in the attack.

The climax of The Wind of the Willows takes place after Toad escapes from prison and evicts the stoats and weasels that have taken over his house, Toad Hall. With the help of Badger, Mole, and Rat, Toad follows a secret tunnel into his house and attacks the intruders, who flee. At the celebration that Toad gives afterward, he humbly thanks his friends and is finally aware of the value of their friendship. This marks the climax of the action because the book has been filled up until this point with ongoing action, including Toad's constant road accidents and his failure to heed his friends. After Toad and his friends retake Toad Hall, Toad recognizes what is truly valuable--his friends--and decides to live peacefully and responsibly ever after. The action falls after Toad retakes his house and settles down to a quiet and happy life with his friends.

Precalculus, Chapter 1, 1.1, Section 1.1, Problem 30

Plot the points $A = (-2,5), B = (12,3)$ and $C = (10,-11)$ and form the triangle $ABC$. Verify that the triangle is a right triangle. Determine its area.








$
\begin{equation}
\begin{aligned}

AB =& \sqrt{[12-(-2)]^2 + (3-5)^2}
\\
=& \sqrt{196 + 4}
\\
=& \sqrt{200}
\\
BC =& \sqrt{(10-12)^2 + (-11-3)^2}
\\
=& \sqrt{4+196}
\\
=& \sqrt{200}
\\
AC =& \sqrt{[10 - (-2)]^2 + (-11-5)^2}
\\
=& \sqrt{144+256}
\\
=& \sqrt{400}
\\
=& 200

\end{aligned}
\end{equation}
$


$(AC)^2 = (AB)^2 + (BC)^2$, thus $\Delta ABC$ is a right triangle.

The area of $\displaystyle \Delta ABC = \frac{1}{2} AB \cdot BC$. So


$
\begin{equation}
\begin{aligned}

\Delta ABC =& \frac{1}{2} (\sqrt{200}) (\sqrt{200})
\\
\\
=& \frac{200}{2}
\\
\\
=& 100 \text{ square units}

\end{aligned}
\end{equation}
$

Can you help me write a journal entry from the perspective of a British subject living in London during the Blitz? What precautions would you have to take? How did you react to the relentless bombing of your city?

I will provide you with details about every day life in London during the Blitz. You can use this information to create a journal entry. When writing a journal entry about such a traumatic period of time, it will be important for you to show fear and emotion. My own great-grandmother lived through the Blitz in London and developed severe anxiety from the almost constant bombings. She eventually abandoned London altogether and spent the rest of her life in the country. This was a common story among Londoners. Those who survived the Blitz were left with emotional scars.
Life during the Blitz was extremely difficult. The worst of the bombing in London lasted for over fifty days in a row in September and October of 1940. Bombings occurred during the day and at night. Air raid sirens signaled coming attacks from the Germans. People evacuated to underground shelters in basements, Tube stations, or backyard shelters. Metal tables were sometimes used in homes if people did not have time to exit to a safer place. Often, people emerged from their shelters to find their homes damaged or destroyed. While many people took precautions by seeking shelter, others left London entirely. Some parents sent their children to live in the country while they stayed in London. If possible, sometimes the entire family would relocate. People reacted to the bombings by supporting the war efforts in Great Britain, though some petitioned the government for better safety measures and shelters.  Some people left London in despair, while others sought to rebuild and help their neighbors.  Regardless, Londoners lived in fear and many had to deal with the emotional trauma of the Blitz. Even after the city rebuilt, people carried emotional scars. It was a time of uncertainty in London, and it led to different reactions.

College Algebra, Chapter 4, 4.2, Section 4.2, Problem 80

a.) How many $x$-intercepts and local extrema does the polynomial $P(x) = x^3 - 4x$ have?
b.) How many $x$-intercepts and local extrema does the polynomial $Q(x) = x^3 + 4x$ have?
c.) Suppose that $a > 0$, how many $x$-intercepts and local extrema does each polynomials $P(x) = x^3 - ax$ and $Q(x) = x^3 + ax$ have? Explain your answer.

a.)


Based from the graph $P(x) = x^3 - 4x$ has 3 $x$-intercepts and 2 local extrema.
b.)


Based from the graph $Q(x) = x^3 + 4x$ has 1 $x$-intercept and 0 local extrema.
c.) The number of $x$-intercepts and local extrema always depends on the number degree of the function. The maximum number of $x$-intercepts is equal to the degree of the function. While the number of the local extrema can never be greater than $n -1$, where $n$ is the degree of the function. This is true for all functions. However, it depends on the orientation of the function. For example, like $Q(x) = x^3 + 4x$, the function is always increasing, that's why it has only 1 $x$-intercept and 0 local extrema but the number of the $x$-intercept does not exceed the degree of the function as well as the local extrema.

What made life meaningful to the narrator of the poem?

In the poem "Annabel Lee" by Edgar Allan Poe, the speaker of the story is deeply in love with his wife, Annabel Lee, who has tragically died. He describes their love as "more than a love" and explains the following:

[She] lived with no other thoughtThan to love and be loved by me.

The narrator explains that the angels in heaven so envied the love they shared that they sent a wind "chilling and killing my Annabel Lee." After her death, Annabel Lee is placed in a sepulcher, a monument built of stone, by the sea. The narrator describes how he stays connected to her, now that she is gone, by visiting her every night.

And so, all the night-tide, I lie down by the side Of my darling—my darling—my life and my bride, In her sepulchre there by the sea— In her tomb by the sounding sea.

From the description of their love as "stronger by far than the love of those who were older than we," the reader can gather that the narrator and Annabel Lee were young and in love in a way that people rarely are as they age. Their love is eternal, because Annabel Lee dies before they are able to grow up and out of love.
https://www.poetryfoundation.org/poems/44885/annabel-lee

What church does Calpurnia attend?

Calpurnia attends First Purchase African M.E. Church and invites Jem and Scout to attend Sunday service with her in chapter 12. After Atticus leaves town for business, Calpurnia takes the Finch children to Sunday service at First Purchase, which is a unique, eye-opening experience for Jem and Scout. Aside from the prejudiced Lula, the congregation greets Jem and Scout with open arms, and the children take note of the differences between Calpurnia's black church and their regular white church. Scout notices that there is no piano, hymn books, or church programs at Cal's church and is astonished to witness how the congregation sings hymns in unison using a technique known as "lining." They also witness Reverend Sykes's unique preaching style, where he specifically chastises individuals for their sins and locks the church doors in order to collect ten dollars for Tom Robinson's family. In addition to enjoying the service, Jem and Scout also gain valuable insight into Calpurnia's personal life. Overall, the children enjoy their visit to First Purchase African M.E. Church in chapter 12.

In To Kill a Mockingbird, Calpurnia invites Jem and Scout to go to church with her while Atticus is away working with the state legislature. Calpurnia remembers that on a previous Sunday when Atticus was away, the children's class at church "tied Eunice Ann Simpson to a chair and placed her in the furnace room." Calpurnia appears concerned that a similar event will happen, although Scout promises they'll behave. Calpurnia spends Saturday night making sure Scout is sufficiently bathed and that Scout's dress is adequately starched.
Calpurnia, along with the other African American citizens of Maycomb, attends First Purchase African M.E. Church, located outside of the town limits. It is known as First Purchase because "it was paid for from the first earnings of freed slaves." While it is used for gambling by some of the white men during the week, its purpose on Sundays is for worship.

Describe the town using details from the novel.

Maycomb is an old, sleepy southern town during the Great Depression. It is described as the kind of place in which rains turn the roads to red mud and "the courthouse sags in the square" (page 5). In other words, its buildings exist in a state of disrepair. It is often a hot place, where everything wilts and people have to move slowly. People aren't in a rush because, as Lee writes, "there is nowhere to go, nothing to buy and no money to buy it with" (page 6). Maycomb is an Alabama farm town in which most people have very little money, particularly during the Great Depression, and in which people know very little beyond the boundaries of the town.
In addition, it is a town in which everyone knows each other and each other's business. For example, everyone knows that the Ewells are a disgraceful family. It is also a town in which people often help each other; for example, during the fire at Miss Maudie's house, the men of the town help carry the furniture out of her house. Finally, it is a segregated town in which most white people subscribe to racist beliefs and in which a white woman's word--for example, that of Mayella Ewell--always counts more than that of a black man such as Tom Robinson. 

Describe the town using details from the novel.

Discuss the heroic code and the values of war in the Iliad with respect to Achilles and Hector.

The most important aspect of the heroic code is honor. For the Achaeans and Trojans alike, honor is won primarily on the field of battle, displayed in countless acts of physical courage. Achilles, the Achaeans' finest warrior, exemplifies this code more than anyone else. If anything, his taste for battle is too great, and he derives enormous satisfaction from hacking his opponents to pieces and reveling in their pitiless slaughter.
The actions of Achilles seem extraordinarily reckless; when he finally returns to battle after his lengthy sulk, he throws himself at the enemy without a moment's reflection, utterly heedless of the potential consequences. Honor can take many forms, but for Achilles it's strictly personal; he fights for his own honor, not the honor of the Achaeans, and that honor has been sorely offended by Hector's killing of Patroclus, Achilles's close friend and companion.
Hector's understanding of the heroic code has marked similarities to Achilles's, but there are important differences. For one thing, Hector fights primarily for the honor of his family and his city. He's every bit as brave as Achilles, but lacks his utter recklessness and disregard for human life. Saving the lives of his men is more important to Hector than winning personal glory. Hector kills Patroclus, along with many other Achaean warriors, but he kills them because he has to.
Unlike Achilles, his fidelity to the warrior code means that he feels himself bound to a higher law, a set of standards that should always determine his conduct. Achilles, on the other hand, is a law unto himself; the heroic code simply allows him the opportunity to indulge his taste for unrestrained violence and self-aggrandizement. In the respective figures of Achilles and Hector, we can see that the heroic warrior code of the Iliad has both individual and social dimensions.

Discuss how the author has emphasized the "Americanness" of the Otis family?

Wilde uses a variety of techniques to indicate how American the Otis family is. He, for example, uses repetition by consistently referring to Mr. Otis as "the American Minister" or, alternatively, "the United States Minister." Furthermore, he focuses on the American lifestyle and the manner in which they conduct themselves in various aspects of their lives.
Mr. Otis, for instance, tells Lord Canterville:

I come from a modern country, where we have everything that money can buy;

Also, he speaks about:

...all our spry young fellows painting the Old World red, and carrying off your best actors and prima-donnas.

America was seen as the New World, and Mr. Otis's statement alludes to this fact. The Americans were seen as pioneers and entrepreneurs, and Mr. Otis's statement confirms this assumption. America had become a land of opportunity, and all the best talent in Britain left for the United States to seek new opportunities and expand their horizons. His reference to the ghost being placed in a museum or a roadshow further illustrates the spirit of American entrepreneurship.
Wilde contrasts the manner in which the English do things with the American way. Lord Canterville tells Mr. Otis "You are certainly very natural in America," suggesting that the Americans do not assume the snobbish airs and graces so ubiquitous in the English middle and upper classes.
The author also makes particular references to the Otis family heritage to illustrate their Americanness. He mentions, for instance, that,

Mrs. Otis, who, as Miss Lucretia R. Tappan, of West 53rd Street, had been a celebrated New York belle

and that the Otis's had christened their eldest son Washington "in a moment of patriotism." The younger twin boys, similarly, were nicknamed "The Stars and Stripes," alluding to the numerous punishments they received with a switch for their misdemeanors.
Wilde also expresses the political sentiments of the family as wholly American. He states that "They were delightful boys, and with the exception of the worthy Minister the only true republicans of the family."
The references to "Pinkerton's Champion Stain Remover and Paragon Detergent" and "Tammany Rising Sun Lubricator" further relates to entrepreneurial spirit and consumerism, which had become typically American qualities.
The following paragraph probably best sums up how Wilde accentuates the Otis's typically American identity:

The subjects discussed, as I have since learned from Mr. Otis, were merely such as from the ordinary conversation of cultured Americans of the better class, such as the immense superiority of Miss Fanny Davenport over Sara Bernhardt as an actress; the difficulty of obtaining green corn, buckwheat cakes, and hominy, even in the best English houses; the importance of Boston in the development of the world-soul; the advantages of the baggage check system in railway travelling; and the sweetness of the New York accent as compared to the London drawl.

Give me some basic points on democracy.

There are various kinds of democracy. In a direct democracy, all of the eligible voters gather to vote on laws and to make important decisions. The Athenians used this method of government.
Another form of democracy is a representative democracy. This kind of democracy exists in the United States. In a representative democracy, the voters elect leaders to make decisions for them. The elected representatives are elected for a specific period of time before they must run again for reelection unless there are term limits in place. The theory behind a representative democracy is that it would be very difficult if every citizen had to vote on every issue that required action. In a representative democracy, the elected representatives are supposed to listen to the wishes of the majority of their constituents, and then they would cast their votes accordingly. In this form of democracy, the people need to be in communication with their elected officials so that these officials are able to know what the majority of the people want them to do.
In a democracy, the people have more influence and involvement in their government and in their government's activities than in other, nondemocratic forms of government. They either are directly involved in the government or they determine who will represent them in the government to make decisions for them.
https://mocomi.com/what-is-democracy/

https://www.thenation.com/article/what-was-democracy/

What did the poet wish to do when he took the path that he had not been able to choose in "The Road Not Taken" by Robert Frost?

The speaker says he wishes he could go back and take the other road after having chosen one.
"The Road Not Taken" is about a person who comes to a fork in a road and has to choose between two roads. He comments in the beginning that he wishes he could travel both. Since he can only choose one road, the speaker stops and thinks about his choice for a while. He notices one of the roads is grassier than the other one. It is fall, so leaves cover the road.

Two roads diverged in a yellow wood,
And sorry I could not travel both
And be one traveler, long I stood
And looked down one as far as I could
To where it bent in the undergrowth 

Eventually, the speaker chooses one path, and says he will come back for the other one. He also comments that, given how life usually turns out, he doubts he will ever be back again to take that other path. 

And both that morning equally lay
In leaves no step had trodden black.
Oh, I kept the first for another day!
Yet knowing how way leads on to way,
I doubted if I should ever come back.

The speaker tells us his decision to take the less-traveled path made all the difference for him. We can assume this means he never went back to try the other one. He seems to be pleased with the less-traveled path, though.
The poem can be seen as a metaphor for life. In life, you cannot make two decisions simultaneously. You might make a decision and then try to go back and make the other choice, but that option is often no longer open to you.

What are some literary devices employed in Robert Frost's "The Ax Helve"?

This poem, about an encounter with a peasant over an ax-helve (or handle), is written in a prosaic style, as if it is a plain narrative account of a conversation and a visit. At the same time, however, the poem uses literary devices to signal that it is, indeed, a poem. One would be the use of the archaic, Middle English term for handle: helve. This jars readers out of the ordinary and leads us to expect an unusual encounter.
The poem also uses alliteration. Alliteration is repeating the same consonant at the beginning of different words placed closed together. This creates a sense of rhythm, as in "forth" and "favor."

When all my strength put forth was in his favor....

The poem uses dialect to show class and education differences. Baptiste, who criticizes the narrator's axe handle, has less formal education than the narrator, as we can hear when Baptiste says,

“You give her 'one good crack, she's snap raght off.Den where's your hax-ead flying t'rough de hair?”

However, Baptiste is clearly much wiser about practical objects, such as axes, than the narrator.
The poem also uses simile, which is comparing two dissimilar things using "like" or "as." Here, Frost uses both "as" and "like" to describe how slender and flexible Baptiste likes his helve:

He liked to have it slender as a whipstock,Free from the least knot, equal to the strainOf bending like a sword across the knee.

The poem also uses personification, likening the ax-helve to a woman with a "chin" who "cock[s] her head:"

Thick hand made light of, steel-blue chin drawn downAnd in a little—a French touch in that.Baptiste drew back and squinted at it, pleased:“See how she's cock her head!”

What key moments would have had to have been altered in order for a positive outcome to be created for the characters within Hamlet?

This, of course, depends on what we mean by a positive outcome. If we take that to mean that Claudius alone should have paid for the crime of murdering Hamlet's father, a positive outcome would be Claudius's death in the absence of all the other corpses littering the the stage at the end of the play.
One way this could have happened is the following: once Hamlet had confirmed throughout the Mousetrap play that Claudius was truly a murderer, he could have immediately gone, with several reliable witnesses, and forced Claudius to confess to his crime. Then, Hamlet could either have killed Claudius or, even better, brought him before a court or tribunal. That way, Hamlet would not be taking the law into his own hands.
Either way, the key point is that to have a good outcome, it would be best to avoid having Hamlet mistakenly murder Polonius. Polonius's death, especially with Claudius still in power and able to manipulate Laertes, set off the the chain of events that led to the final tragic ending. 

In what ways was the League of Nations unjust?

The greatest success of the League of Nations is that it served as a precursor to the United Nations. Its greatest failure, however, is that it failed to keep the peace among nations, as evidenced by the rise of the Third Reich, resulting in World War II.
Primarily, historians consider the League unjust due to its punitive approach toward Germany. The Treaty of Versailles, where the League of Nations was formed, disarmed Germany, levied large debts, and redistributed territory as reparation to other nations for World War I. While reparations could be considered appropriate, these sanctions hobbled Germany's ability to recover from the war in the homeland.
In addition, the League singled out Germany as ineligible for membership even though other powers who fought alongside them (Bulgaria and Austria-Hungary, for example) were permitted to join. If the League's stated goal was to maintain peace among nations, giving Germany a voice would seem essential. Germany was later allowed to join the League in 1924, but Germany withdrew after Hitler's appointment as chancellor.

Calculus of a Single Variable, Chapter 7, 7.3, Section 7.3, Problem 21

We can use a rectangular strips to represent the region bounded by x+y=4, y=0 , and y=x revolved about the x-axis. As shown on the attached graph, we consider two sets of rectangular strip perpendicular to the x-axis (axis of revolution) to be able to use the Disk Method. This is the case since the upper bound of the rectangular strip differs before and after x=2 .
In this method, we follow the formula: V = int_a^b A(x) dx since we are using a vertical orientation of each rectangular strip with a thickness =dy.
Note: A = pir^2 where r= length of the rectangular strip.
We may apply r = y_(above) - y_(below) .
For the region within the boundary values of x: [ 0,2] , we follow r = x-0=x
For the region within the boundary values of x: [ 2,4] , we follow r = 4-x-0=4-x
Note: x+y=4 can be rearranged as y=4-x.
Then the integral set-up will be:
V = int_0^2 pi*(x)^2dx+int_2^4 pi*(4-x)^2dx
For the first integral: int_0^2 pi*(x)^2dx , we may apply Power rule of integration: int x^n dx = x^(n+1)/(n+1) .
int_0^2 pi*(x)^2dx= pi* x^((2+1))/((2+1))|_0^2
=(pix^3)/3|_0^2
Apply definite integration formula: int_a^b f(y) dy= F(b)-F(a) .
(pix^3)/3|_0^2 =(pi(2)^3)/3-(pi(0)^3)/3
=(8pi)/3- 0
=(8pi)/3
For the indefinite integral of int_2^4 pi*(4-x)^2dx , we may u-substitution by letting u =4-x then du =-dx or (-1)du =dx .
The integral becomes :
int pi*(4-x)^2dx =int pi*u^2*(-1) du
Apply basic integration property: intc*f(x) dx = c int f(x) dx.
int pi*u^2*(-1) du = -pi int u^2 du
Apply power rule for integration: int x^n dy= x^(n+1)/(n+1).
-pi int u^2 du =-pi* u^((2+1))/((2+1))
= (-piu^3)/3
Plug-in u=4-x on (-piu^3)/3 we get:
int_2^4 pi*(4-x)^2dx =(-pi(4-x)^3)/3|_2^4 or ((x-4)^3pi)/3|_2^4
Apply the definite integral formula: int _a^b f(x) dx = F(b) - F(a) .
((x-4)^3pi)/3|_2^4 =((4-4)^3pi)/3-((2-4)^3pi)/3
= 0 - (-8pi)/3
= (8pi)/3
Combing the two definite integrals, we get:

V = int_0^2 pi*(x)^2dx+int_2^4 pi*(4-x)^2dx
V = (8pi)/3+(8pi)/3
V =(16pi)/3 or 16.76 (approximated value).

What are the tables in Ab Jones’s bar made of?

The tables in Ab Jones's bar are made out of stone, gravestones, to be precise. This is just the kind of thing we might expect from Cormac McCarthy, with his heightened sense of the macabre. Ab Jones's novel use for gravestones is also expressive of his anti-establishment personality. He's an African American at a time and a place (1950s Tennessee) when racial prejudice was almost universal, and Ab's often on the receiving end of savage beatings from officers of the Knoxville Police Department. Like most African Americans of the time, he's subjected to bigotry and hatred on virtually a daily basis. It's not surprising, then, that he has such a deeply ingrained distrust of authority.
Ab's use of gravestones for bar tables is indicative of a society in which little of any real value is fixed or permanent. The graves are predominantly those of the poor and downtrodden, their graves washed away by the building of the great Tennessee dams. In his own unique way, Ab is preserving the memory of these long-forgotten folks. As a victim of daily oppression, he can empathize with these people and how they were ignored and disrespected by the authorities both before and after their deaths.
 

What is the girls' fascination with the name Ernest and how does it reflect an idealistic romanticism?

According to the Oxford English Dictionary, "earnest" means "seriousness, as opposed to jest or play." If you've read this play, you know that it is entirely in "jest" and never serious. Thus, we see Wilde using the name "Ernest" in an ironic way. The man going by "Ernest" is, of course, Jack, and his act of deceit is not "earnest" at all. Rather than exemplifying honesty and sincerity, Jack spins lies.
When Gwendolen says, "My ideal has always been to love some one of the name of Ernest. There is something in that name that inspires absolute confidence," we see that she loves the idea of the name, not the person who has the name. When Gwendolen adds, "The moment Algernon first mentioned to me that he had a friend called Ernest, I knew I was destined to love you," we see the superficiality of Gwendolen's "affections" for Jack.
Her reasons for loving Jack are absurd; they are the equivalent to saying, "I love people who wear baseball caps" and then falling in love with the next person you see wearing the aforementioned baseball cap. The idealistic romanticism you mention is Wilde's way of poking fun at the social rituals we enact during courtship. Gwendolen and Cecily have whimsical ideas about the qualities their future lovers will have. These ideas are shaped by what society has deemed "admirable" in a partner.
Yet—as we see as the play unfolds—these ideas rest on shallow traits. Because of Gwendolen's desire to be with a man named Ernest, she ultimately finds herself with a man who has proven himself to be a liar and a trickster. Wilde mocks Victorian society here, exposing the emptiness of its values and the hypocrisy of its standards.

In Oscar Wilde's play The Importance of Being Earnest, dramatic irony arises from the use of the name Ernest.
At the beginning of the play, two friends, Jack and Algernon, are enjoying tea together. Jack admits that he goes by Jack in certain settings and Ernest in others, as he has a made-up younger brother named Ernest.
Algernon states that he "always suspected [Jack] of being a confirmed and secret Bunburyist." As Algernon explains, "Bunbury" is a fictional invalid that Algernon cares for. Whenever Algernon needs an excuse to take a vacation, he cites his ailing friend Bunbury as the reason. Whoever invents such a character is, likewise, a "Bunburyist." Jack is a Bunburyist because he has invented a brother named Ernest.
Shortly, Jack woos Gwendolen, who loves him simply because she thinks his name is Ernest. Then, Algernon goes to visit Jack's relations, assuming the identity of Jack's (fictitious) brother, Ernest. Jack's young aunt, Cecily, falls in love with Algernon (alias Ernest). Like Gwendolen, she loves him for being Ernest.
The irony is that each man calls himself "Ernest," a play on the word "earnest," which means "open or honest." The idealist lovers are enamored with the name, because they naively conclude that a man named Ernest will be frank and genuine. Of course, assuming a false identity is deceptive. Thus, the men called Ernest are not truly earnest at all.

Why were the pilgrims so miserable once they got to the New World?

First, the Pilgrims had already endured a rough Atlantic voyage. Ships back then did not carry much in the way of fresh fruit and vegetables, so the Pilgrims were already in dire need of vitamins. Also, sanitation was an afterthought on these ships. Fresh water was at a premium, so bathing was out of the question. There was also the issue of crowding. The Pilgrims arrived in the New World already distressed and short of food, and they had to face the New England winter under these conditions.
Many died on board the ship while they waited for housing to be built in the new colony. There was also fear—no one knew about the nature of the Native Americans who lived in the area. The initial goal of the Pilgrims was to arrive further south and closer to the Jamestown area, so they were definitely in uncharted territory. While the Pilgrims were thankful to have a new place to practice their religion, there was still much anxiety as to how to fill basic needs.  

Precalculus, Chapter 1, 1.2, Section 1.2, Problem 34

Plot the point $(-1,-1)$ then plot the point that is symmetric to it with respect to (a) the $x$-axis; (b) the $y$-axis; (c) the origin

a. The $x$-axis

If the point $(-x,-y)$ is reflected over the $x$-axis, then the image is the point $(-x,y)$. So

$(-1,-1) \to (-1,1)$







b. The $y$-axis

If the point $(-x,-y)$ is reflected over the $y$-axis, then the image is the point $(x,-y)$. So

$(-1,-1) \to (1,-1)$







c. The origin

If the point $(-x,-y)$ is reflected over the origin then the image is the point $(x,y)$. So

$(-1,-1) \to (1,1)$

Calculus of a Single Variable, Chapter 5, 5.7, Section 5.7, Problem 16

For the given integral: int 3/(2sqrt(x)(1+x)) dx , we may apply the basic integration property: int c*f(x) dx = c int f(x) dx .
int 3/(2sqrt(x)(1+x)) dx = 3/2int 1/(sqrt(x)(1+x)) dx .

For the integral part, we apply u-substitution by letting:
u = sqrt(x)
We square both sides to get: u^2 = x .
Then apply implicit differentiation, we take the derivative on both sides with respect to x as:
2u du =dx .
Plug-in dx= 2u du , u =sqrt(x) and x= u^2 in the integral:
3/2int 1/(sqrt(x)(1+x)) dx =3/2int 1/(u(1+u^2)) (2u du)
Simplify by cancelling out u and 2 from top and bottom:
3/2int 1/(u(1+u^2)) (2u du) =3 int 1/(1+u^2) du
The integral part resembles the basic integration formula for inverse tangent:
int 1/(1+u^2) du = arctan (u) +C
then,
3 int 1/(1+u^2) du = 3 * arctan(u) +C
Express in terms x by plug-in u =sqrt(x) :
3 arctan(u) +C =3 arctan(sqrt(x)) +C
Final answer:
int 3/(2sqrt(x)(1+x)) dx = 3arctan(sqrt(x))+C

What does Matt think is the purpose of a gift?

It's fair to say that Matt doesn't really get the concept of what a gift entails. This is a direct consequence of his chaotic, unstable background. Matt is a wild child, a vagabond from the wrong side of the tracks—the Fen, to be precise: a dirt-poor neighborhood of the village. In such a bleak environment, the law of the jungle prevails. It's every man, woman, and child for themselves, forced to compete with each other for the most basic means of subsistence. It's not surprising, then, that the very notion of a gift, something you give to someone else without thought of recompense, is just too weird for Matt to comprehend.
Kira patiently tries to explain to Matt exactly what a gift means. She says it's something special you give to someone you care about. Matt can only laugh. Back in the Darwinian jungle that is the Fen, giving something special involves kicking someone up the behind.

How did the logic of the cold war shape American foreign policy in Central America? What kinds of regimes were supported because of this policy? With what results?

American foreign policy during the Cold War was driven by the ideological struggle between the capitalist United States and the communist Soviet Union. Throughout the world, the Soviet Union backed governments or insurgent groups willing to either adopt or ally themselves with communism, while the United States backed governments or insurgent groups willing to fight communism. The results in Central America were often highly destructive.
In 1954, the Guatemalan leader Jacobo Arbenz legalized the nation's communist party and attempted to seize lands owned by an American fruit company. The United States orchestrated his overthrow by Colonel Carlos Castillo Armas, leading to a civil war that began in 1960 and claimed more than 200,000 lives over the next 36 years.
After the Cuban dictator Batista was overthrown in 1959, US policy makers began to fear that Central America might also become communist. As Cuba's revolutionary leader Fidel Castro aligned himself more and more closely with the USSR, the US took steps to prevent communism from spreading to other nations in the region. This included multiple attempts to overthrow or assassinate Castro, as well as pressure on other nations in the region to keep Cuba diplomatically isolated. The US intervened either directly or indirectly in other Latin American nations such as Chile to prevent communism from expanding its foothold.
In Central America itself, Cuba and its Soviet allies supported the FMLN's communist insurgency in El Salvador through the 1980s, as well as the revolutionary government of the Sandinista movement in Nicaragua. The United States supported the right wing government of El Salvador in its efforts to defeat the communist insurgency while simultaneously supporting the Contra insurgency against the Nicaraguan government. The war in Nicaragua ended when the Sandinista government agreed to allow elections in 1990. The civil war in El Salvador lasted for 12 years before an end to the war was negotiated in 1992.
In all of these civil wars, government or insurgent forces backed by both sides were notorious for committing massacres and other war crimes. Hundreds of thousands of people were killed and society was destabilized to the extent that organized crime was allowed to flourish. Although the Cold War is over, the ideological hatred from that era is still a factor in Central American politics.
https://cja.org/where-we-work/el-salvador/

https://wcfia.harvard.edu/files/wcfia/files/jd_us_latin.pdf

https://www.pbs.org/newshour/health/latin_america-jan-june11-timeline_03-07

Single Variable Calculus, Chapter 7, 7.4-1, Section 7.4-1, Problem 84

Determine the volume of solid obtained by rotating the region under the curve $\displaystyle y = \frac{1}{x^2+1}$ from 0 to 3 about the $y$-axis.

By using vertical strips, and applying the shell method, notice that the strips have distance from $y$-axis as $x$ and if you rotate this length about $y$-axis, you'll get a circumference of $c = 2\pi x$. Also, the height of the strips resembles the height of the cylinder as $\displaystyle H = y_{\text{upper}} - y_{\text{lower}} = \frac{1}{x^2+1} - 0 = \frac{1}{x^2+1}$. Theus,

$
\begin{equation}
\begin{aligned}
V &= \int^3_0 c(x) H (x) dx\\
\\
V &= \int^3_0 3(2 \pi x) \left( \frac{1}{x^2+1} \right) dx
\end{aligned}
\end{equation}
$

Let $u = x^2 + 1$, then
$du = 2x dx$

Make sure that the upper and lower units are also in terms of $u$

$
\begin{equation}
\begin{aligned}
V &= \pi \int^{(3)^2+1}_{(0)^2 +1} \frac{1}{u} du\\
\\
V &= \pi \int^{10}_1 \frac{du}{u}\\
\\
V &= \pi [ \ln u]^{10}_{1}\\
\\
V &= \pi [\ln10-\ln1]\\
\\
V &= \pi \ln(10) \text{ cubic units}
\end{aligned}
\end{equation}
$

ANALYSE ELEGY FOR A STILLBORN CHILD

This beautiful poem by Seamus Heaney is, as the title indicates, an elegy, a poem of lament. Traditionally, an elegy contains three sections: an expression of grief, an expression of praise for the dead, and then an offering of solace in the conclusion. Heaney's poem adheres to this, broken down as it is by the poet into three numbered sections. Part 1 laments how the "collapsed sphere" of the stillborn child "extinguished itself in our atmosphere." Part 2 expresses what the child achieved in its short life, functioning as a "cartographer" to chart its father's path "from husband towards father." Part 3, the conclusion, offers an element of reflection as consolation, the final image of the poet "on lonely journeys" and the world "full to the brim with cloud" suggesting that the journey of life continues on toward unknown new horizons.
Heaney makes the decision to address the poem directly to its subject, the unborn child: "you." This underlines for the reader the fact that the child is, though unborn, a person with a soul, who existed, even if only in its mother's womb. This forms an interesting contrast with the description of the child as a "weight of seed-flesh and bone-curd," as others might view it.
This contrast is in line with Heaney's use of opposites throughout the poem, which is, after all, on the seemingly opposite themes of birth and death, both combined in the body of this stillborn child and its emergence into the world. The baby's mother is "heavy with the lightness in her," and the "globe" the father imagined is shattered when "the pole fell, shooting star, into the ground."
The imagery used in the poem could be interpreted as nautical. A simile compares the baby's mother to "an empty creel" (a creel is a wicker basket usually used to hold fish). Meanwhile, the "intimate nudge and pull" of the baby inside her suggests the nudge and pull of guide ropes on a boat. In the second section of the poem, the baby becomes a metaphorical "cartographer," or map maker, charting a father's journey like an explorer; the trappings of exploration, such as the "globe" and the "pole" (which suggests a pole star or guiding star) also feature in this stanza. The child, in its "six months" of life, seemed a guiding star through previously uncharted waters for these parents, until it fell away, leaving them untethered. The "collapsed sphere" metaphor in the first stanza, too, suggests a star which "extinguished itself in our atmosphere."
The final section of the poem is distinct from the others in that the heavy use of figurative language falls away, demarcating this as the passage of consolation and reflection. The images in this section, as the poet contemplates "birth of death, exhumation for burial," are evocative, but literal: "a wreath of small clothes, a memorial pram." The poet marks, in this stanza, a return to the real world, much as the baby's parents must also return to real life eventually. The image of the "bare road" on which the poet is driving is not prepossessing at the moment—"under a drizzling sky, a circling rock"—but we see promise in the "mountain fields" and the "white waves riding home on a wintry lough." The poem ends on a note not only of reflection, but also of assurance that life will go on, and there may yet be a new "cartographer" to chart the journey.