Why does Smith think that the government should stay out of economic affairs?

In looking at this question, it's important to understand who was in charge of the government at that particular time. In Adam Smith's Britain, it was mainly the landed aristocracy in charge. In relation to the economy, it was generally thought vulgar for gentlemen to get involved directly in trade or commerce; land was the source of wealth, prestige, and status for the aristocrat. That being the case, Smith doesn't believe that you can really entrust such people with the running of the economy; they simply don't understand how it works. If they interfere in what should be the natural operations of the market, then they are likely to do more harm than good. Economic policy should not be devised by well-meaning amateurs.
The spontaneous, self-interested decisions of actors in the market place—businessmen, consumers, farmers, and traders—eventually conduce to the common good, to growing economic prosperity. This is a completely unintended consequence; it's just what happens when people are allowed to go about their business without the government becoming too deeply involved. The law of unintended consequences also applies to government intervention in the economy. However well-meaning, however beneficial a specific policy may be, it can lead to harmful consequences further down the line. Government shouldn't stay out of economic affairs completely; it still has an important regulatory role to play. But that role is very broad indeed. What the government should do, according to Smith, is to establish general rules that allow the maximum degree of economic freedom, then stand back to allow the invisible hand of the market economy to do its thing.

How do Scout and Jem meet Dill in To Kill a Mockingbird?

In To Kill a Mockingbird, Scout Finch stays with her brother called Jem, and their single father named Atticus, in the quiet Alabama city of Maycomb. Great Depression has hit Maycomb, but since Atticus is a prominent lawyer, he has been able to cater for his small family’s financial needs smoothly. During the summer holiday, Dill visits his aunt who is a Finch's neighbor at Maycomb. Scout and Jem meet Dill when they are glancing over the fence after hearing some noise and finds him seated in his aunt’s collard pitch where they befriend. The Finch’s tell Dill the story of Boo Radley, their neighbor who ever remains indoors. Dill becomes curious of how he appears and sees this as his role of getting him out of the house. The trio uses their whole summer planning how they are going to make him move out of the house. It is apparent that Boo knows what is transpiring. It is Dill who makes Scout and Jem see Boo.

In Chapter 1, Scout and Jem are playing in their backyard when they hear something coming from Miss Rachel Haverford's collard patch. They walk over to the fence expecting to find a puppy, and instead discover a small boy sitting down, staring directly at them. The boy introduces himself as Charles Baker Harris and mentions that he can read. When Jem asks Dill how old he is, Jem is surprised to learn that Dill is seven years old. Jem initially thought Dill was four-and-a-half because he was so small. Dill says he is from Meridian, Mississippi and is staying with his aunt, Miss Rachel Haverford, for the summer. After Dill tells Jem that he's seen the movie Dracula, Jem begins to respect him. Jem and Scout quickly become close friends with Dill, and the three children play together every day during the summer. 

Describe how important the narrator’s point of view is to the telling of The Iliad and if that narrative point of view is effective.

The Iliad gives us a third person omniscient, or god's eye view, which is appropriate as the action that transpires outside the walls of Troy is all part of a divine plan.
Everything that happens in the poem has been fated by the gods, who often give the impression that mortals are there to be manipulated and controlled for their own pleasure. Adopting a third person omniscient point of view allows Homer to take a step back and make some sense of the enormous carnage that takes place during this epic conflict.
If the poem had been told from the standpoint of a participant in the conflict—Achilles, say—then it would've been much more difficult for us to get a handle on events. Achilles may be the most important character in the poem, but like everyone else, he's subject to fate, a plaything of the gods. The third person omniscient point of view emphasizes the inevitable nature of what happens to Achilles, as to all other participants in this long, bloody, and bitter war.

The Iliad is told in the third person, from an omniscient point of view. (It's important to note the narrator is the Muse, different from Homer, the poet.) The narrator's point of view is above the action, as if floating over it, viewing the entire world spread out, so to speak. This includes the thoughts and actions of the gods above, which are tightly woven into the narrative. This world is bigger than mere mortals, and we know it because the narrator constantly reminds us of the active presence of the gods in the affairs of humankind.
The narrator begins in media res, or the middle of the story, thereby capturing our attention immediately, but also takes us backwards and forwards in time. For example, Minerva foretells the future to Achilles:

"I come from heaven, if you will hear me, to bid you stay your anger. Juno has sent me, who cares for both of you alike. Cease, then, this brawling, and do not draw your sword; rail at him if you will, and your railing will not be vain, for I tell you—and it shall surely be—that you shall hereafter receive gifts three times as splendid by reason of this present insult. Hold, therefore, and obey."

This narrator knows what the gods think: For example, when Achilles calls an assembly of the people, the narrator tells us with confidence that Achilles was 

moved thereto by Juno, who saw the Achaeans in their death-throes and had compassion upon them.

This wide-ranging narrative point of view is important and effective, because it allows Homer to juxtapose and contrast the various ways different characters, including the gods, think and understand events. Homer can describe a whole world, its beliefs and preoccupations, while honing in on the most important actions and details that characterize this world. From the opening, we are in the hands of a narrator confident of what is going on and how to interpret it, able both the describe the warrior code of honor and the desire for riches and honor that drove this society, and to critique the cost of it as well in terms of "ills" and death, a theme set out from the beginning:

Sing, O goddess, the anger of Achilles son of Peleus, that brought countless ills upon the Achaeans. Many a brave soul did it send hurrying down to Hades, and many a hero did it yield a prey to dogs and vultures, for so were the counsels of Jove fulfilled from the day on which the son of Atreus, king of men, and great Achilles, first fell out with one another.

While Homer tells a complicated tale that raises questions about war, honor, revenge and death, we can as readers can sink back and enjoy a story told by a confident narrator who knows what is going on and why. 
 
 
 

Is self-reliance the same as self-trust?

I do not believe that self-reliance and self-trust are the same thing.  
I see self-trust as being more associated with internal feelings, guidance, and perhaps even conscience.  Self-reliance deals more with a person's ability to do something without the aid of anybody else.  
From an early age, people develop a great deal of self-trust.  They trust their own thoughts and feelings about who to be friends with, what color is their favorite, what foods they like, and when their body is tired.  They trust their internal thoughts and feelings.  As a person ages though, that trust may diminish as peer pressure asserts itself.  That would be diminishing self-trust, but that person might be very self-reliant in a variety of areas.  He or she could be fully capable of changing the oil in their car or purchasing groceries for the week.  No outside help is needed.  That person is self-reliant because he/she doesn't need nor want outside help; however, that person also might not have much self-trust.  He/she is capable of doing the work but is not confident in which oil to use for the car or which grocery store is best for their needs.  Perhaps several people gave conflicting advice, and now the person doesn't trust himself to make the best decision.  I come across students like this every so often.  A student is completely capable of doing the assignment, but that student has zero trust in themselves that it is done well. 

How old is the Washington Monument?

The Washington Monument is one of the most recognizable sights in Washington DC, situated on the National Mall and near the Lincoln Memorial. It is one of several monuments that were constructed in celebration of George Washington, but because of its sheer size, it was both expensive and time-consuming to construct. While the first stone was laid in 1848, the monument was not officially opened for another forty years: it was October 1888 before this could happen.
One key reason it took so long to build this monument was the intervention of the American Civil War. Not only was there a lack of labor, the US government was financially depleted by the devastation of the Civil War, which rendered it unable to justify spending money on the construction of this monument until 1877, when construction resumed after its halt in 1854.

Beginning Algebra With Applications, Chapter 2, 2.3, Section 2.3, Problem 94

Translate the phrase "the sum of five more than the square of a number and twice the square of the number" into a variable expression. Then simplify the expression.

$
\begin{equation}
\begin{aligned}
& \text{The unknown number: } n && \text{Assign a variable to one of the number quantities}\\
\\
& \text{Square of the number: } n^2 && \text{Use the assigned variable to write an expression for any other unknown quantity.}\\
\\
& \text{Twice the square of the number: } 2n^2 \\
\\
& \text{Five more than the square of the number: } n^2 + 5\\
\\
&= (n^2 + 5) + (2n^2) && \text{Use the assigned variable to write the variable expression.}\\
\\
&= 2n^2 + n^2 + 5&& \text{Use the Commutative Property of Addition}\\
\\
&= 3n^2 + 5 && \text{Simplify}
\end{aligned}
\end{equation}
$

What are the industry and leisure classes in Veblen's The Theory of the Leisure Class and how do they compare to Marx’s two-class model of stratification?

Veblen believed the leisure class was made of people who did not need to do industrial work and who had types of occupations that were of higher status. He wrote in The Theory of the Leisure Class: 




The upper classes are by custom exempt or excluded from industrial occupations, and are reserved for certain employments to which a degree of honor attaches. (2)

While the industry class toils in industrial work (that is, work related to providing for the material needs of people), the leisure class occupies jobs in fields such as government, religion, warfare, learning, and sports in what Veblen called the "barbarian" culture that preceded modern culture. He believed these distinctions between the industry and leisure class continued in modern times. 
Marx, on the other hand, believed in two classes: the proletariat and the bourgeoisie. The bourgeoisie own the means of production (which are land, labor, and capital), while the proletariat must sell their labor to survive. Veblen's two-class structure is different than that of Marx because Veblen believed that Marx's theory of labor did not account for the role of technology, which was becoming increasingly important in modern society. He thought that Marx's theory was not complicated enough to account for the role of technology and its importance in the economy. In addition, unlike Marx, Veblen did not see the classes as engaging in class warfare. Instead, Veblen thought that the industry class was corrupted by the values of the upper class, which the industry class sought to emulate.

y=(x-1)/(x+5) Graph the function. State the domain and range.

y=(x-1)/(x+5)
First, determine the vertical asymptote of the rational function. Take note that vertical asymptote refers to the values of x that make the function undefined. Since it is undefined when the denominator is zero, to find the VA, set the denominator equal to zero.
x+5=0
x=-5
Graph this vertical asymptote on the grid. Its graph should be a dashed line. (See attachment.)
Next, determine the horizontal or slant asymptote. To do so, compare the degree of numerator and denominator.
degree of numerator = 1
degree of the denominator = 1
Since they have the same degree, the asymptote is horizontal. To get the equation of HA, divide the leading coefficient of numerator by the leading coefficient of the denominator.
y=1/1
y=1
Graph this horizontal asymptote on the grid. Its graph should be a dashed line.(See attachment.)
Next, find the intercepts.
y-intercept:
y=(0-1)/(0+5)
y=-1/5
So the y-intercept is  (0, -1/5) .
x-intercept:
0=(x-1)/(x+5)
(x+5)*0=(x-1)/(x+5)*(x+5)
0=x-1
1=x
So, the x-intercept is (1,0) .
Also, determine the other points of the function. To do so, assign any values to x, except -5. And solve for the y values.
x=-15, y=(-15-1)/(-15+5) = (-16)/(-10)=8/5
x=-11, y=(-11-1)/(-11+5)=(-12)/(-6)=2
x=-7, y=(-7-1)/(-7+5)=(-8)/(-2)=4
x=-6, y=(-6-1)/(-6+5)=(-7)/(-1)=7
x=-3, y=(-3-1)/(-3+5) = (-4)/2=-2
x=4, y=(4-1)/(4+5)=3/9
x=15, y=(15-1)/(15+5)=14/20=7/10
Then, plot the points (-15,8/5) ,   (-11,2) ,   (-7,4) ,   (-6,7) ,   (-3,-2) ,   (0,-1/5) ,   (1,0) ,   (4,3/9) and (15,7/10) .
And connect them.
Therefore, the graph of the function is:

Base on the graph, the domain of the function is (-oo, -5) uu (-5,oo) . And its range is (-oo, 1) uu (1,oo) .

Summarize beginning, middle, end plot of the Awkakening by doing a 3 by 3( only use 3 words for each) Example: about Cinderella Evil forbids ball- beginning Hope sneaks freedom- middle Happiness snags prince- end

To create a literary three by three for The Awakening by Kate Chopin, one must first consider the essence of each part of the novel. 
The beginning establishes Edna Pontellier as a bored wife and mother who defines herself by her duties to her family. That boredom comes to a head when she spends the summer on Grand Isle with her family. During the week, the men go to work while the women stay with the children.
She spends most of that summer with Robert. For the first time, she's able to see herself as a complete person outside of her family. It creates a change in her character and sends her on an emotional quest to find herself.
This quest takes the form of new activities, like painting. She also makes new friends and ignores her traditional responsibilities to her family. Robert has left, concerned that they're getting too close and out of respect for her marriage. Edna finds out from a friend that he's still thinking of her.
She leaves her husband and has an affair. Robert returns and confesses his love but then leaves to protect her from shame. Edna returns to Grand Isle and walks into the ocean, swimming out to sea to commit suicide.
So the beginning of the story is about establishing Edna's character. The second part is about her search for a personal identity and freedom from her familial duties. The final part is about losing the person she loves and choosing to commit suicide rather than return to her life.
Beginning: Married mother boredMiddle: Seeking personal freedomEnd: Desertion prompts suicide
Beginning: Duties create resentmentMiddle: Rejecting society's chainsEnd: Death overcomes despair
Beginning: Routine breeds dissatisfactionMiddle: Exploring other alternativesEnd: Devastation chooses death

What does Frederick Douglass understand a man to be?

In discussing Frederick Douglass’s concept of humanity, or what he considers a man to be, one can pretty much begin with a quick reference to French philosopher René Descartes’s oft-quoted dictum “cogito, ergo sum,” or “I think, therefore I am.” For Douglass, the essence of the discussion was encapsulated in the fundamental distinction between humans and animals—in effect, that the former can be defined by the pursuit of knowledge. Perhaps nowhere was this adage better articulated than in an address Douglass gave in 1872 titled “Self-Made Men.” Recognizing at the outset of his remarks the propensity for individuals to interpret that phrase—“self-made men”—as indicative of one who has propelled himself upward socially, professionally, and economically entirely of his own accord, Douglass immediately rejected any such notion without going to another extreme by suggesting that personal initiative and skill played no role at all in one’s success. Rather, Douglass applied the phrase in a broader, more philosophical manner, evident in the following passage from this speech:

The tendency to the universal, in such discussion, is altogether natural and all controlling: for when we consider what man, as a whole, is; what he has been; what he aspires to be, and what, by a wise and vigorous cultivation of his faculties, he may yet become, we see that it leads irresistibly to this broad view of him as a subject of thought and inquiry.

As the distinguished and intellectually-formidable former slave emphasized, the nature of man, as distinct from other animals, was precisely the pursuit of knowledge, and that “by no other is human life so affected and colored.”
It is within this context that Douglass, as he had decades earlier in a series of essays he penned, emphasized the vital role of knowledge in the perpetuation of the institution of slavery. From his own experiences as a slave and from his observation of the role of government and law in preserving this most inhumane of human practices, Douglass noted the importance placed upon maintaining the ignorance of African slaves for the continuation of slavery. An educated black person was not going to submit or be so vulnerable to bondage and forced labor in perpetuity. The more knowledge the slave attained, the more he would question his circumstances and reject the relationship between slave and master.
To Frederick Douglass, man is defined by his capacity to reason. His own experiences in life as well as those of other slaves and descendants of slaves imbued in him a strong sense that the only difference between caucasian and African was the former’s determination to deny the latter the same opportunities for education and social and economic advancement. Additionally, and returning to his focus on the notion of a “self-made man,” he asserts that we are all ultimately dependent upon each other. As Douglass stated, “I believe in individuality, but individuals are, to the mass, like waves to the ocean. . . We differ as the waves, but are one as the sea.”
http://monadnock.net/douglass/self-made-men.html

https://www.libertarianism.org/publications/essays/you-are-man-so-am-i

https://www.theobjectivestandard.com/2018/02/frederick-douglasss-vision-manhood/

Douglass's Autobiography makes a distinction between "slave" and "man." It is a common theme throughout his writings and speeches that the institution of slavery robs the enslaved (and, in a different way, slaveholders) of their humanity. After enduring consistent abuse at the hands of Mr. Covey, Douglass tells us:

I was broken in body, soul, and spirit. My natural elasticity was crushed, my intellect languished, the disposition to read departed, the cheerful spark that lingered about my eye died; the dark night of slavery closed in upon me; and behold a man transformed into a brute!

So slavery had transformed a "man" into a "brute," by which Douglass meant an unthinking creature like a farm animal. Eventually, however, the sixteen-year old Douglass resisted, physically manhandling Covey, a notorious "slave-breaker." Having beaten Covey, who fears losing his reputation for being tough with slaves (i.e. his sense of his own masculinity), Douglass feels liberated, and like a man again:

It rekindled the few expiring embers of freedom, and revived within me a sense of my own manhood. It recalled the departed self-confidence, and inspired me again with a determination to be free. 

For Douglass, slavery was the antithesis of manhood. It completely negated everything that he understood as masculine in the male slave, robbing him of intellect, liberty, the ability to be a father, and control of his own body. Freedom, then--intellectual, spiritual and physical freedom--was essential to become a man. 
https://www.owleyes.org/text/narrative-life/read/chapter-10

Byzantine, Islamic, and Frankish worlds had replaced what was the Roman Empire. Which state most deserves the title of Rome’s successor and why?

Intriguing question. Each of these three "worlds" can be argued to have replaced a part of the Roman Empire. In the end none of them replaced it completely.
The Byzantine or Eastern Roman Empire never "replaced" the greater Roman Empire, but it continued aspects of its heritage for some time to come. Its height was during the reign of Justinian I, not long after the fall of Rome (ca. mid-6th c. BCE). Thereafter the Byzantine Empire remained solvent but was constantly defending itself from Islamic incursions from the later middle ages on, and it finally fell to the Ottomans in the mid-15th c. While one could say it was the best candidate to be a Roman successor, this is complicated by some things. For one, Orthodox Christianity was quite different from Catholicism.
The Islamic Empire expanded rapidly after the death of Muhammad. The initial Caliphates took control of the Arabian Peninsula, Asia Minor, and North Africa in rapid succession. The Umayyad Caliphate was the largest (this was the period when Muslims captured Spain from the Visigoths), but the Abbasid Caliphate was the most stable Islamic Empire, existing from the mid-8th to the mid-13th century. Again, while these Islamic empires were impressive in their extent, none of them captured Europe. And none of them, obviously, were Christian.
The Franks, while they ruled the smallest of the three Empires mentioned here, have perhaps the strongest claim to replacing the Roman legacy. The most elaborate expression of Frankish rule was the Carolingian Empire, first established by Charlemagne, who was actually crowned the "Holy Roman Emperor" by the Pope in 800 CE. While the Carolingian Empire didn't exist on the scale of the Byzantine or Islamic Empires, it continued Roman traditions most extensively. Charlemagne built churches in the Romanesque style, converted pagans to the Christian faith at the point of a sword, and emphasized the value of education. If, however, one considers which culture best preserved the legacy of Greek and Roman thought and amended that thought as well, then title goes to the Islamic Empire. Before it fell in the mid-13th c., Baghdad was a major cultural center—not rivaling Rome, but nonetheless significant.

How is Romeo and Juliet similar to To Kill a Mockingbird in relation to theme, conflict, dynamic characters, etc.?

At first glance, I think most people would classify Romeo and Juliet as a love story, while To Kill a Mockingbird is a story about racial injustice. But closer examination shows that both stories have to do with forbidden desire and the effect realizing that desire has on their communities. In the case of Romeo and Juliet, their love is forbidden by the conflict between their families, the Montagues and Capulets. This love leads to bloodshed (the death of Mercutio) but also to a recognition that the feud between the families is not based on any real difference (Juliet’s famous “Wherefore art thou Romeo” speech poses the question of how her Romeo, the one she loves, can also be Romeo Montague, the enemy of her family).
In To Kill a Mockingbird, the forbidden relationship at the center of the story, the sexual abuse of Mayella Ewell by her father, Bob, is camoflaged by another social split, this time between whites and blacks. In the same way Juliet finds that Romeo is no different for being a Montague, Mayella finds that Tom Robinson is kind and empathic despite the stereotypes about black people that her community perpetuates. And Mayella’s tentative opening up to Tom results in bloodshed, as in Shakespeare, only this time it is his own life that sacrificed.

The Tragedy of Romeo and Juliet certainly shares some superficial qualities with To Kill a Mockingbird, but one of the most significant points of comparison between the two works has to do with the external conflict between the characters.
Both works concern male and female characters from different families, and both focus on young protagonists. Both works also address tension within the communities of Verona and Maycomb, as well as the decision of some community members to take sides.
In Romeo and Juliet, the external conflict between the Capulets and their friends and the Montagues and their people results in bloodshed when Tybalt kills Mercutio. The same happens in To Kill a Mockingbird, when Tom is shot multiple times trying to escape from jail. The external conflict in both works peaks at the point of these deaths, and the rising action in each builds up the tension so that the reader can anticipate the tragedy before it happens.

Romeo and Juliet is similar to To Kill a Mockingbird because in both works, people who are different from each other learn to love and respect each other. Romeo and Juliet are from feuding families, the Capulets and Montagues, but they fall in love and realize that they are not really different. As Juliet says, "What’s in a name? that which we call a rose / By any other name would smell as sweet" (II.2.47-48). In other words, she does not care if Romeo's last name is Montague (though her family--the Capulets--hates the Montagues), as she values him for himself, not for his name. 
Similarly, in To Kill a Mockingbird, Scout learns to love and appreciate Boo Radley, who is developmentally disabled, and to understand the injustice with which Tom Robinson is treated in a racist society. Atticus, her father, tells her,  "You never really understand a person until you consider things from his point of view...until you climb into his skin and walk around in it.” Atticus means that a person can't understand another until they really try to empathize with that person and see what he or she is experiencing. Therefore, the themes of understanding and intolerance are similar in both works, as are conflicts surrounding misunderstanding based on superficial differences. In addition, there are dynamic characters, such as Scout, Romeo, and Juliet, who change in the works and become more empathetic towards people who are different than they are. 

What is discovered (literally) in Miss Emily's house after her death?

After Miss Emily's funeral, the people of Jefferson discover an old, rotted corpse in a closed room in Emily's house. This corpse belonged to Homer Barron, a character who died almost forty years before the day his body was found. The corpse was found lying in a bed with a deep impression beside him on the pillow, where it is implied that Emily would lay beside him.
The discovery of Homer's body ties together several loose ends in Emily's history. It proves that the arsenic that she purchased was used to poison Homer. She was in love with him, but the story implies he was gay—at the very least, he was disinterested in marrying her. It also proves that the terrible smell that townspeople had chosen to cover up with lime was actually the smell of Homer's rotting body. Finally, this discover leaves the reader wondering if the townspeople really never put all this together for themselves.

Following Miss Emily's funeral, the citizens of Jefferson explore her home and enter the mysterious room on the top floor: a dust-filled bridal suite that has (supposedly) remained untouched for decades. On the bed are the skeletal remains of Miss Emily's former lover, Homer Barron. Homer had disappeared decades ago, while he was still courting Miss Emily. Miss Emily discovered that Homer had no plans of marrying her, which motivated her to purchase arsenic and kill him.
In addition to finding Homer Barron's remains, the townspeople are also shocked to discover a thin strand of iron-gray hair on the pillow next to his skeleton. The iron-gray hair reveals that Miss Emily was sleeping with his corpse and suggests that she engaged in necrophilia, which is a highly disturbing discovery.

Miss Emily Grierson has always been a respected figure in the town, not least because she constitutes a living relic of a romanticized, ante bellum past. She's very rude and rather eccentric, but she gets a pass from the townsfolk on account of her coming from a good family. (She's even exempt from paying local taxes). But the signs are there that she's more than just a tad eccentric. The persistent stench emanating from her house should be a clue that there's something wrong. Yet everyone turns a blind eye; they convince themselves it's probably just the smell of a dead animal, a snake or a rat, perhaps.
It's only after Emily's death that the true source of that revolting stench is finally determined. The locked door of an upstairs room is broken down, and inside is a scene of unimaginable horror. In what looks just like an old-fashioned bridal room, complete with faded rose curtains and lamps with rose-colored shades, there lies upon the bed the rotting corpse of Homer Barron, the man that Emily wanted to marry, but was forbidden to do so by her father. On the pillow next to Homer's corpse is the indentation of a head as well as one of Emily's long gray hairs.

As the narrator foreshadows throughout William Faulkner’s short story, the townspeople of Jefferson discover what they expected to in the closed-up portion of Miss Emily Grierson’s home.
The speaker states that the people at the funeral wait until Emily’s body is buried to open the room, because they think it is improper or rude to do so beforehand. When they open the room, the narrator describes a bridal parlor of sorts: fancy decor, an engraved men’s toilet set, and clothes.
“The man himself” lies in the bed—the skeletal remains of Homer Barron, Emily’s long-ago maybe-lover who had jilted her on and off throughout their relationship. On the pillow next to Barron, the people find a single strand of “iron-gray” hair, which the reader infers is Miss Emily’s, based on earlier descriptions of her.
Thus, the final paragraphs of the story reveal that Miss Emily murdered and entombed Homer Barron, and even slept next to his decaying body.

What are five benefits and five shortcomings of oral storytelling and written storytelling?

This is such an interesting question!  Let's see if we can think through five advantages and five disadvantages for these two vital forms of storytelling.
First, when we tell a story, as opposed to offering it in writing, we are able to adjust to our audience in our style, a disadvantage for the written story.  We will tell a story to a young child in a very different manner than we would to an adult. We might make the story shorter, eliminate some racy aspect of it, and choose simpler vocabulary.  This is a distinct advantage over words that are "frozen" on the page, thus conferring a disadvantage upon the written word, since the written word cannot be changed on the spot.
Second, when we tell a story, this allows us a physical intimacy and immediacy that are not gained with a written story.  The act of reading is by its nature a solitary act, while storytelling is a social act.  Even for reading aloud, the reader's eyes must drop down to do the reading, a barrier between the reader and the audience.  Oral storytelling, even if the audience does not speak, creates a kind of dialogue between audience and reader that is personal and here and now. 
Third, oral storytelling is evanescent, while the written story persists in a form that can last for thousands of years and can travel around the world. We are still reading stories from the ancient Romans and Greeks, for example, and routinely read stories from all over the world. In fact, if we ever get to Mars, we can take our written stories with us! The written word has a powerful advantage this way, while the story told disappears.
Fourth, because of the fleeting nature of the spoken word and the enduring nature of the written one, people can make meaning more easily of the written word than the spoken one.  Listening to a story is a very different kind of act from reading a story. I hear a sentence and the words are gone.  Someone next to me laughs, and I miss the words.  I hear something I like, but I cannot focus on it for an extra second because more words are coming.   But I can read at my own pace, slowly or quickly or somewhere in between.  I can read a passage more than once.  I can go back and check on the name of a character.  I can even cheat and see what the ending of the story is.  As I have these freedoms, the story can be far more meaningful to me than a story I have heard. I am able to take the time to make connections with other stories I have read or with events in my own life.  The written story is able to resonate in a way that the story told aloud simply cannot. 
Fifth, a disadvantage to oral storytelling and an advantage to the story told in writing is that the latter has far more utility for someone who seeks to polish writing and reading skills, which everyone should want to do. When we read, we can come to understand far more easily how a story is constructed. When we read, we can learn new words that we can use ourselves.  When we read, we expose ourselves to different styles of writing.  All of these are helpful as we read more to become better readers and we practice writing. We can emulate a style.  We can create a plot line more easily. We come to understand how to show a reader a character or an idea.  Some of this might be glimpsed in passing with a story told orally, but it is far less likely.
For thousands of years, we could only tell stories orally.  However, once we began to write, oral storytelling was by no means abandoned because, as you can see, it continues to have some powerful advantages.  Reading a story has other advantages, which we would never want to give up.  

How many times was Sgt. Bruce Porthero shot in The Other Wes Moore?

Overall, Sergeant Prothero was shot three times; he later died of his injuries. He was off-duty on that terrible day when he responded to a jewelry store robbery in Baltimore. Sgt. Prothero gave chase to the four robbers—among whom were the other Wes Moore and his brother Tony—before he was shot point blank in the face.
To avoid the death penalty, Tony Moore pled guilty to the shooting, for which he was sentenced to life in prison. As for Wes, he claimed that he wasn't at the crime scene, but he was later found guilty of first-degree felony murder and, like his brother, was sentenced to life in prison.
When the author Wes Moore read about the story, he was fascinated at how someone with the exact same name growing up in a similar neighborhood could end up following such a radically different path in life. And so he reached out to the other Wes Moore, writing him a letter that would change both their lives forever.

Do you see Ibsen's A Doll's House as primarily about the struggle between the needs of the individual and the needs of society or about the conflict between women's roles in the family and in the larger society?

Ibsen's A Doll's House addresses both issues as he critiques Victorian gender roles by illustrating Nora's struggle for independence and conflict with how society perceives and treats women. Neither issue is mutually exclusive, and Nora's battle for independence is directly related to her oppressed gender role in society at large. In Victorian society, women were perceived as weak, helpless individuals who relied solely on their husbands or fathers. Women had few individual rights and were expected to be loving wives and caring mothers. Nora's role in her household is no different from society's expectations at the beginning of the play. She is treated like a helpless child and viewed as Torvald's intellectual inferior. Nora is initially content in her role as a submissive, dependent housewife but experiences a dramatic change after discovering Torvald's genuine feelings about her.
At the end of the play, Nora makes a courageous decision to leave her husband and family in order to find herself and live independently. Nora's remarkable decision opposes Victorian society's expectations of how she should act. Through Nora’s opinions and actions, Ibsen criticizes the unjust Victorian society, which prevents women from obtaining true independence from the men in their lives. Essentially, Nora's individual struggle against her oppressive society reflects the larger issue regarding prejudiced gender roles in Victorian society. Ibsen's play illustrates the importance of marriage equality and champions women's independence.

These notions are not mutually exclusive. Society's needs, or expectations, for Nora are foisted upon her due to her gender. For years, she was unable to see how society's expectations constricted her as a human being. She does not really understand who she is or what her own expectations are because she has simply acted according to the expectations of others, including those of her husband, Torvald.
I think it is helpful, too, to regard the family as a microcosm, or a small sample, of society. At this time, women were only expected to be wives and mothers. They were imagined as nurturing, and as desiring nothing more than to care for their husbands and children. Middle-class women like Nora might entertain themselves by decorating their homes, and would also be expected to manage servants. From the outside, her life looks pleasant, comfortable, and privileged; in some ways, it is, but there is also no exteriority. Nora is not expected to go outside of this house.
The expectations imposed on Nora from within her own family are also those imposed by society. By leaving Torvald to discover who she is, Nora is doing something extremely rebellious, something that would generally be frowned upon. By having his female hero act in such a radical manner, Ibsen communicates his own dissatisfaction with bourgeois ideas about marriage and family, which are especially restrictive for women, and thereby limit the possibilities for society as a whole.

Find the volume of the function y = e^(-x^2) , from x=-1 to x=1, rotated around the line x = 5, using the method of shells.

The method of shells is based on breaking up the solid obtained by the revolution of the curve into thin cylindrical shells, and integrating the surface area of the shells to obtain the volume of the solid. 
The general formula for the shell method is
V = int 2pirhdr
where r is the radius and h is the height of the shells.
Since the revolution of the function y = e^(-x^2)
 in this example occurs around vertical line x = 5, this line will be the axis of the cylindrical shells, which passes through the center of the base of the cylinders. Then, the radius of each shell is r = 5 - x, the distance between the center (at x = 5) and the x-coordinate. Since the given curve is bounded by the points with the x-coordinates -1 and 1, the bounds of the integral will be -1 and 1.
The height of the each cylinder is the y-coordinate of each point on the function:
h = y = e^(-x^2)
Therefore, the resultant volume will be equal to the integral
V = int_(-1) ^1 2pi(5-x)e^(-x^2)dx
This integral breaks up into two:
V = 10piint_(-1) ^ 1 e^(-x^2) dx - 2piint_(-1) ^ 1 xe^(-x^2) dx
The first integral can only be evaluated numerically. The second integral is 0 because it is an integral of an odd function will symmetrical bounds.
The value of int_(-1) ^ 1 e^(-x^2)dx
is approximately 0.683, so 
V = 2pi*0.683 = 4.29
The volume of revolution of the given function is approximately 4.29.
 
 
http://tutorial.math.lamar.edu/Classes/CalcI/VolumeWithCylinder.aspx

Explain how the marriage of Macbeth and Lady Macbeth can be viewed as a study of power.

That's an interesting writing prompt. Macbeth and Lady Macbeth are both powerful people. He is a thane, and she is the wife of a thane. By definition, they are wealthy and powerful people. They have a big home/castle with plenty of servants, and they have a close relationship with the king. By all accounts, they are a powerful couple; however, it is interesting to question which person is more powerful. Is Macbeth or Lady Macbeth the more powerful person in the relationship? I think it could be argued either way with great support, but I would lean more toward Lady Macbeth being the more powerful member of the marriage. Strong supporting evidence can be found in Act I, Scene 7. This is the scene where Macbeth comes in and tells Lady Macbeth to forget the entire murder plan. He can't go through with it.

We will proceed no further in this business.
He hath honored me of late, and I have bought
Golden opinions from all sorts of people,
Which would be worn now in their newest gloss,
Not cast aside so soon.

Lady Macbeth is appalled at her husband and begins to browbeat her husband. She's full of insults and graphic language that calls into question Macbeth's manhood.


When you durst do it, then you were a man;
And to be more than what you were, you would
Be so much more the man. Nor time nor place
Did then adhere, and yet you would make both.



She will not take "no" for an answer. She demands that Macbeth do as they had planned, and he caves.


I am settled, and bend up
Each corporal agent to this terrible feat.



Lady Macbeth stated earlier that she worried about Macbeth's ability to do what needed to be done, so it's likely that Lady Macbeth has used this kind of tactical insulting before to get her way. If we are analyzing their marriage and figuring out where the power is, Lady Macbeth clearly has the lion's share of it.

How do you not take damage in a battle in Pokemon Go?

You cannot take zero damage in a fight.  But you can dodge the attacks and reduce damage taken significantly.  
While you are fighting there will be a yellow screen flash right before your opponent attacks.  When that happens forget everything else, stop attacking, and dodge.  Once you get the hang of dodging you can dodge every attack and make battles a breeze.
Remember that if the servers lag or you have poor reception, you can still take the max damage.  Also there is a time limit: you cannot dodge indefinitely.  But you can still take down a Pokemon with +200cp with ease once you learn how to dodge.
Also remember that you cannot dodge after using a charged attack.  You will take a hit no matter what.  

In your opinion, what is the main message in the book?

The Old Man and the Sea is one of Hemingway's most discussed and significant books. Its theme and setting invite the assumption that the work has some deep allegorical meaning that can be unlocked, but ultimately, the message seems to be "things happen."
In that sense, it's completely up to the reader whether they choose to believe any allegory is intentional on Hemingway's part. The author was known for his Iceberg Theory, for being one of the masters of showing meaning instead of directly telling it.
The Old Man and the Sea definitely offers many possible interpretations. It has been seen as a fable-like tale of man's struggle against nature, a symbol for fighting and being defeated, a religious story showcasing being outmatched by something vastly more powerful than a human being ever could be, and so on. The "trouble" with Hemingway's work is that absolutely all of these interpretations can be argued for successfully.
The message of "things happen" seems to fit into all of them, however, including the disappointing one that perhaps the author never intended for the story to be allegorical at all. After all, in life, things happen. We as human beings give them meaning of good and bad, but in truth, most of the time things happen because of the relation of cause and consequence.
A lot of readers, young and old, have been saddened by the arrival of sharks in the tale. As they eat and eat and eat, the reader feels the poetic justice of the story slipping away. The ending offers some relief for Santiago—a few apologies, his continued friendship with the boy, and so on—but it's still a bittersweet ending, with the big, proud marlin eaten long before he reaches the shore. Why did it happen like that? One could say it was Santiago's fate to suffer such a loss, but another way of seeing it is that there was simply blood in the water. Blood attracts sharks. Shark need to eat. They ate.
The brilliance of Hemingway's writing is that there always seems to be something lurking beneath the surface, like with an iceberg. Possibly, the message of the book is that, just as in real life, people need to assign meaning to events. Everyone in the book acts naturally, according to what they are (human and fish alike). The story resolves the way it does, but it could have gone a million other ways as well. The Old Man and the Sea is, in that sense, a picture of life, and in life, things happen.

I would recommend first examining some of the story's themes, and then pick which one you feel is the message that Hemingway is trying to get across to his readers. I think perseverance, strength, skill, and suffering are all themes present within the book. Santiago hasn't been fishing well lately, but he perseveres through adversity. The giant fish he catches is not an easy catch either. He struggles and perseveres to catch the fish for days, and it is only because of this and his skills as a fisherman that he succeeds in catching the huge fish; however, I do not believe any of those are the main point or message. I think the author is trying to give readers a message about defeat. Santiago successfully catches the fish, but he doesn't get it back to shore with him. The sharks eat the fish, and Santiago is once again without a catch to eat or sell. He is defeated, yet he dreams of lions again. His spirit is not crushed. I think Hemingway is trying to tell readers that there are times when you've struggled and worked so hard for something that you deserve to be rewarded; however, defeat is always possible. What matters is how you handle that defeat.

Why does Jonas's society chose to institute sameness? What are some of the consequences on peoples' lives in this community?

Jonas's society decided to adopt the Sameness for a couple of reasons. The Sameness establishes a uniformity for everything. It's trying to make everything more or less equal, and that will hopefully eliminate discomfort, anger, unhappiness, etc. in society. The people also give up a fair amount of free will for the Sameness, and that wasn't seen as a bad thing. By removing a lot of choice, the people are less likely to make wrong decisions. You can't make a wrong decision if there is not a decision in the first place. Finally, the Sameness is a form of societal control.

"Our people made that choice, the choice to go to Sameness. Before my time, before the previous time, back and back and back. We relinquished color when we relinquished sunshine and did away with differences….We gained control of many things. But we had to let go of others."

The consequences of a society like this varies. The elimination of discomfort and anger sounds nice, but the opposite of those things was also relinquished. The people assume that they are happy because they can't feel sadness, but how can one truly know happiness if one doesn't know what sadness feels like? Jonas doesn't understand this concept until the Giver gives him truly joy filled memories like sledding down a hill and truly horrific memories of war. The more Jonas learns from the Giver, the more Jonas comes to believe that the Sameness is not good for the people. They can't choose anything, and they aren't really feeling anything.

How does "The Lottery" by Shirley Jackson relate to the Holocaust?

Another way of looking at "The Lottery" in relation to the Holocaust is to consider the phenomenon of how ignorance and blind obedience to what a particular group values, despite its clear absence of moral underpinnings, propels people to acts of barbarity.
Though Jackson never explicitly explains what the ritual stoning of a randomly-chosen citizen is thought to accomplish, it is reasonable to infer that it is somehow linked to the harvest or in some way benefits the town. If that is indeed the case, then it is a superstitious and illogical belief that no one has the will or strength of character to effectively challenge. It is said that Nazis hated Jews for reasons that don't lend themselves to logic; among them, their belief that Aryans were biologically superior to Jews.
Jackson observes that, left unchallenged, willful ignorance and blind obedience to unexamined traditional beliefs can unleash indefensible destruction of human lives.

One of the themes explored throughout Shirley Jackson's short story "The Lottery" concerns the psychology behind mass cruelty and violence, which is depicted by the community members' cavalier, malicious attitude toward the unlucky winner of the lottery. Shirley Jackson illustrates how typical, friendly citizens are capable of atrocious acts of cruelty at any moment in time. The shocking image of small-town community members stoning one of their fellow citizens without remorse reveals humanity's primitive, savage nature and suggests that humans are capable of horrific acts of violence when they are part of a group which is influenced by mob mentality. The same psychology of mass cruelty and violence corresponds to the Nazi's treatment of the Jews during the Holocaust. Throughout the Holocaust, Nazi soldiers engaged in horrific, atrocious acts of violence and cruelty while attempting to exterminate the European Jewish population.

Which passages might reflect a specifically Anglo-Saxon philosophy of life? Which passages might reflect a Christian outlook?

Beowulf is generally understood to have been first composed during a pagan era in Anglo-Saxon culture, with the poem being updated later to tether it to the new Anglo-Saxon context of the early medieval period, when it was committed to paper (or, in this case, vellum). Accordingly, we see a struggle between paganism and Christianity in the poem which is at times uncomfortable, a situation we see in many Anglo-Saxon works. In "The Wanderer," for example, a clearly pagan elegy about isolation and the loss of vassalage is tied uncomfortably and abruptly in the conclusion to Christian themes of loyalty to God. In "The Dream of the Rood," this theme of marrying heroic concepts to Christianity reaches its peak in the depiction of Christ as the heroic king of the poem, in true Anglo-Saxon fashion.
In Beowulf, then, we have a poem where the pre-Christian Anglo-Saxon preoccupations form the backbone but where Christian concepts have evidently been inserted later. Beowulf, as a king, is every inch the Anglo-Saxon heroic ideal. He is a warrior with all the trappings: a named sword, super strength, the capacity to hold his breath under water for a superhuman length of time, and so on. The warriors in the poem enjoy Anglo-Saxon ideals of what makes a successful life: they are together in a mead hall, while Grendel is bitter and dejected at being excluded from this kind of pagan warrior unity. Although Grendel is described as the descendant of Cain, a Biblical tether, the passage describing the way he prowls around Heorot in envy of the soldiers is a pure Anglo-Saxon concept: the isolated man who has somehow transgressed against his society, wishing he could return to it. We see this concept in "The Wanderer" and "The Seafarer," and it was a key preoccupation of pre-Christian Anglo-Saxon society. While the author of this poem may have been a Christian, making his depiction of pagan Anglo-Saxon culture slightly inaccurate, the life-cycle of the Danes in the poem is pagan even up to the very point of Beowulf's death, where he receives a decidedly pagan burial surrounded by his treasures. Beowulf is a man whose life is governed by the Anglo-Saxon idea of 'wyrd' or fate, and when he is laid to rest, his treasure and all he has achieved in this life goes with him--"eldum swá unnyt    swá hyt aérer wæs" (as useless to men now as it ever was).
By contrast to these deeply-rooted pagan elements in the poem, the Christian elements are rather superficial, clearly afterthoughts. We can see this, for example, in lines 100-115 when Grendel is described in relation to God in curiously un-Biblical terms--the poem says that "eotenas ond ylfe ond orcnease/swylce gigantas, tha with gode wunnon lange thrage"--"ogres and elves, and spirits from the underworld; also giants...strove with God for an interminable season." Even as the poem attempts to marry these monsters to the new Christian context, they remain distinctly rooted in Anglo-Saxon paganism. Another example of a Christian extension to an existing passage comes in lines 179-188, which talks about "the hope of heathens"--the poet here reflects that the heathens in the poem "ne wiston hie drighten god"--they "were not aware of the Lord God/nor yet the Helm of the Heavens." The poet goes on to lament that all those who do not know God will go to hell, while those who seek the Lord will be saved. This section is quite at odds with what comes before it and is generally believed to be one of the most obvious later additions to the poem.
http://www.heorot.dk/beowulf-rede-text.html

https://mclucas.org/wayback/papers/beowulf.html

Please provide a critical analysis of the story "The Chameleon" by Anton Chekhov.

"The Chameleon," at only four pages, is one of Chekhov's shortest short stories. Despite this, it is crammed with the psychological acuity and profound moral insight one would expect from its author. The story also represents a withering critique of the hierarchical, vertical structure of nineteenth-century Russian society.
The protagonist of "The Chameleon" is an officious police superintendent by the name of Otchumyelov. One day, as he walks across the market square with a parcel under his arm, he hears a sudden commotion. A white Borzoi puppy has bitten Hryukin, the goldsmith, on his finger. At first, Otchumyelov is very sympathetic to the unfortunate victim of the dog bite. This crime is an outrage, and a detailed report must be drawn up immediately.
However, when he discovers whose dog it is, his whole attitude suddenly changes. The dog belongs to a local worthy, General Zhigalov. When the policeman realizes this, he starts questioning the veracity of Hryukin's account of events:

"There's one thing I can't make out, how it came to bite you?" Otchumyelov turns to Hryukin. "Surely it couldn't reach your finger. It's a little dog, and you are a great hulking fellow! You must have scratched your finger with a nail, and then the idea struck you to get damages for it. We all know . . . your sort! I know you devils!"

Here we see Chekhov satirizing the rigid class structure of Tsarist Russia. At first, Otchumyelov appears committed to doing his duty and determined to get to the bottom of the crime. However, because the dog concerned belongs to a General, a man of importance in the town, he displays his toadying deference towards his social betters by accusing the complainant of injuring himself to obtain compensation.
However, Otchumyelov, being the chameleon that he is, has not finished changing just yet. He soon establishes, to his own satisfaction at least, that the dog does not belong to the General. There is no way that a man of such nobility and such breeding would own such an animal. However, some people in the gathering crowd are convinced that the dog does indeed belong to the General. Otchumyelov then effectively absolves himself of responsibility for what has happened; he tells his subordinate to take the dog to the General's house and tells the subordinate to ask them not to let it out into the street again, in case it should be tormented or abused.
Otchumyelov is hedging his bets here. He is not absolutely certain whose dog this is. However, if the dog does turn out to belong to the General, then he can say that he was trying to protect the animal on grounds of welfare rather than public safety. In other words, Otchumyelov is more comitted to not offending the General than he is to ensuring that no one else gets bitten by the dog. Maintaining distinctions of rank and their associated privileges is clearly much more important to the superintendent than upholding the law.
Unsurprisingly, this officious, overbearing chameleon is about to change his colors once more. The General's cook steps forward and adamantly insists that the dog definitely does not belong to his master. This settles the matter for Otchumyelov; the dog is a menace, and it must be put down. Then the cook mentions that the dog in question belongs to Vladimir Ivanitch, the General's brother. Otchumyelov then performs another sudden about-face and lets the cook take the little dog back to the General. It is only a little pup, says the superintendent, a nice little pup. Poor Hryukin stands there in the freezing cold, his finger still hurting, as he is subjected to peals of mocking laughter from the assembled crowd. Worse still, Otchumyelov makes a threatening parting shot:

I'll make you smart yet!

As well as being a satire on Tsarist Russian society, "The Chamleon" also displays an acute insight into human behavior. All too often we adjust our behavior to suit our own needs, irrespective of whether it is the right thing to do. Otchumyelov is a senior police officer sworn to uphold the law without fear or favor. Yet, his ever-changing behavior coupled with his constant moral twists and turns leads to the injured party being publicly humiliated and threatened while those responsible for his injury get away scot-free. The outcome of the story shows us that putting our needs above our duty to others often leads to suffering and injustice.
https://americanliterature.com/author/anton-chekhov/short-story/a-chameleon

What lead to WWII and what were the consequences?

The main cause of World War Two was the aggressive military expansion of the two strongest Axis Powers: Germany and Japan.
Adolf Hitler and his Nazi political party came to power in Germany in 1933. Hitler had campaigned on a series of issues, including strengthening the German economy and regaining the lands lost by Germany at the end of World War One. Hitler advocated for what he called “Lebensraum” or living space; he believed that Germany should expand and include all German-speakers. Hitler envisioned a Germany that included most of Eastern Europe and parts of the Soviet Union. In 1939, the German army invaded Poland. France and Great Britain then declared war on Germany. By mid-1940, Germany had conquered most of mainland Europe.
Hideki Tojo, a leading general of the Japanese Army and later Prime Minister of Japan, wanted his country to expand militarily in order to become the dominant power in Asia and the Pacific. Due to the islands small stature, Japan needed more room for its population to expand, as well as more access to natural resources. Japan invaded Manchuria in 1937 and invaded many other Asian nations across the Pacific. By doing so, Japan came into conflict with the British, French, and Dutch empires. As it expanded its authority across the Pacific, Japan’s relationship with the United States became increasingly tense. On December 7th, 1941, Japan attacked the U.S. naval base at Pearl Harbor, Hawaii. The next day, the U.S. declared war on Japan.
As a result of their military expansion, Germany and Japan eventually came into conflict with the United States, the British Empire, France, the Soviet Union, and China (also known as the Allied Powers). After many hard-fought battles and campaigns in Europe, Asia, and North Africa, the Allies defeated the Axis Powers; Germany surrendered in April 1945 and Japan followed in August 1945. Both nations were militarily occupied by the Allied Powers after their surrender.

College Algebra, Chapter 10, 10.5, Section 10.5, Problem 12

Find the expected value (or expectation) of the games described.

A bag contains eight white balls and two black balls, John picks two balls at random from the bag, and he wins $\$5$ if he does not pick a black ball.

The bag has 10 balls consisting of eight white balls and two black balls. The probability of getting a white is $\displaystyle \frac{8}{1} = \frac{4}{5}$ and the probability of getting a black ball is $\displaystyle \frac{2}{10} = \frac{1}{5}$

Assuming that the ball is not replaced after the first one has been picked, the probability that he picks first white ball is $\displaystyle \frac{8}{10}$ and the probability that he picks second white ball is $\displaystyle \frac{7}{9}$. So the expected winning value is

$\displaystyle 5 \left( \frac{8}{10} \right)\left( \frac{7}{9} \right) = \frac{28}{9} = 3.11$

This means that if you play this game, you will make, on average $\$3.11$ per game.

Single Variable Calculus, Chapter 2, 2.3, Section 2.3, Problem 9

Determine the $\lim\limits_{x \rightarrow 4^-} \quad \sqrt{16-x^2}$ and justify each step by indicating the appropriate limit law(s).


$
\begin{equation}
\begin{aligned}
\lim\limits_{x \rightarrow 4^-} \quad \sqrt{16-x^2} &= \sqrt{\lim\limits_{x \rightarrow 4^-} (16-x^2)} && \text{(Root Law)}\\
\lim\limits_{x \rightarrow 4^-} \quad \sqrt{16-x^2} &= \sqrt{\lim\limits_{x \rightarrow 4^-} 16 - \lim\limits_{x \rightarrow 4^-} x^2} && \text{(Difference Law)}\\
\lim\limits_{x \rightarrow 4^-} \quad \sqrt{16-x^2} &= \sqrt{16 - \lim\limits_{x \rightarrow 4^-}x^2 } && \text{(Constant Law)}\\
\lim\limits_{x \rightarrow 4^-} \quad \sqrt{16-x^2} &= \sqrt{16-(4)^2} && \text{(Power Special Limit Law)}
\end{aligned}
\end{equation}\\
\boxed{\lim\limits_{x \rightarrow 4^-} \quad \sqrt{16-x^2} = 0}
$

Calculus of a Single Variable, Chapter 3, 3.4, Section 3.4, Problem 22

Find the inflection points and discuss the concavity of the function f(x)=x*sqrt(9-x)
The inflection points occur when the second derivative is zero (and changes sign.) A function's graph is concave up if the second derivative is positive, and concave down if the second derivative is negative.
Rewrite the function as:
f(x)=x(9-x)^(1/2)
Find the derivative using the product rule:
f'(x)=(9-x)^(1/2)+x(1/2)(9-x)^(-1/2)
f''(x)=1/2(9-x)^(-1/2)+1/2(9-x)^(-1/2)+x/2(-1/2)(9-x)^(-3/2)
=(9-x)^(-1/2)-x/4(9-x)^(-3/2)
=(9-x)^(-3/2)(9-x-x/4)
Setting the second derivative equal to zero yields:
x=9 or x=36/5.
9 is the right endpoint of the domain so it is not an inflection point. The sign of the second derivative is negative on the domain, so the function has no inflection points and is concave down on its domain.

College Algebra, Chapter 4, 4.2, Section 4.2, Problem 6

Sketch the graph of each function by applying sketch transformations on the standard form $y = x^n$. Indicate all $x$ and $y$-intercept on each graph.
a.) $P(x) = x^4 - 16$
b.) $Q(x) = (x+2)^4$
c.) $R(x) = (x+2)^4 - 16$
d.) $S(x) = -2(x+2)^4$

a.) The graph of $P(x) = x^4 - 16$ is the graph of $y = x^4$ that is shifted 16 units downward. Its $y$-intercept is -16 and the $x$-intercept are 2 and $-2$.



b.) The graph of $Q(x) = (x + 2)^4$ is the graph of $y = x^4$ that is shifted 2 units to the left. Its $y$-intercept is 16 and $x$-intercept is $-2$.




c.) The graph of $R(x) = (x+2)^4 - 16$ is the graph of $y = x^4$ that is shifted 2 units to the left and the result is shifted 16 units downward. To solve for $y$-intercept, we set $x = 0$

$
\begin{equation}
\begin{aligned}
y &= (0 + 2)^4 - 16\\
\\
y &= 16 - 16 \\
\\
y &= 0
\end{aligned}
\end{equation}
$


To solve for $x$-intercept, we set $y = 0$

$
\begin{equation}
\begin{aligned}
0 &= (x + 2)^4 - 16\\
\\
(x + 2)^4 &= 16\\
\\
x + 2 &= \pm \sqrt[4]{16}\\
\\
x + 2 &= \pm 2\\
\\
x &= -2 \pm 2\\
\\
x &= 0 \quad \text{ and } \quad x = -4
\end{aligned}
\end{equation}
$





d.) The graph $S(x) = -2(x + 2)^4$ is the graph of $y = x^4$ that is shifted 2 units to the left then the result is reflected about $x$-axis and stretched vertically but a factor of 2. Its $y$-intercept is $-32$ and $x$-intercept is $-2$.

Read "The Man Who Turned Into a Stick" by Abe Kobo. What existential issues does this story raise?

The word "existential" refers to anything that concerns, relates to, or affirms existence.  This entire text addresses the nature of human existence, namely, the fact that human beings are inherently complacent and fundamentally disposed to stop striving once they feel "satisfied".  Essentially, most of us become metaphorical "sticks" during our lives: as the Man from Hell says, "In short, the stick is the root and source of all tools."  The majority of us -- "98.4 percent" to be precise -- are, at best, tools in the hands of others.  We are used, made to perform in some capacity, scuffed up and scarred by our experiences, sometimes "suffer[ing] rather harsh treatment" that impacts what kind of literal stick we become when we die.  Those 98 out of every 100 of us who become sticks have no "aims," just like the Hippie Girl and Boy; she explains, "Aims are out-of-date."  Our lack of personal goals, our satisfaction with enough, leads to our complacency, and so, when we die, "a living stick [turns] into a dead stick [...]."
Given that this fate awaits some 98% of us, the text suggests that we all possess a predictably human propensity to avoid risk and to fail to take chances that might make our existence more extraordinary or even interesting.  We are neither good enough to have earned a reward (if such a thing exists in the text's world) or bad enough to warrant punishment.  The man who has turned into a stick in the story is simply abandoned in the end, of no note.  The Woman from Hell suggests that they give the stick to the little boy, saying, "At least it ought to serve as a kind of mirror.  He can examine himself and make sure he won't become a stick like his father."  The Man, her supervisor from Hell, laughs in her face and asks why "anyone who's satisfied with himself would do that?"  He explains that the man turned into a stick precisely because he was "satisfied."  This doesn't mean that the man was always happy, that he never wished for anything to be different, it's just that he, apparently, never really made an effort to change what displeased him.  And so he became a stick, just like his son will likely someday do.
Just like we all, or the vast majority of us, will do.  In the final lines of the text, the Man and Woman from Hell speak directly to us; the Man says, "Look -- there's a whole forest of sticks around you.  All those innocent people, each one determined to turn into a stick slightly different from everybody else, but nobody once thinking of turning into anything besides a stick."  The Woman affirms this: our acquiescence to satisfaction is simply a part of our nature, our existence as human beings, or rather sticks.  "You're not alone," she says, "You've lots of friends . . . men who turned into sticks."

Does he go to college?

The short answer is that we do not know. The author certainly sets the ending up to hint at this, but he leaves it a mystery as to whether Lonnie actually makes it to college. The book ends with Lonnie pursuing scholarships and committing to getting into college any way he can, hopefully with the help of his exceptional basketball skills. The mystery is an intentional representation of what the author chooses to indicate through Lonnie’s life—the reality that life is almost always uncertain and unforgiving.
Lonnie mentioned that Cal still had “game,” or some kind of personal character or virtue despite a past marred by gambling. He hoped that he could improve his own “game,” but we are left to wonder if even that noble promise bore fruit in the real world. His last missed shot while attempting to instruct a couple young basketball players leaves readers wondering if Lonnie will make it, in either life and basketball. Readers are thus left to question whether they too can have such certainty that they will reach their desired destinations in life’s journey.

How do we know that Cordelia truly loved her father?

Cordelia is the only one of Lear's daughters who refuses to play along with the public charade in which they're all expected to proclaim their love for the old king. Of course, Cordelia's refusal to flatter her father in this way isn't of itself proof that she loves him. But it's telling nonetheless that the only one of Lear's daughters who does truly love him is reluctant to proclaim her love so publicly. As ensuing events demonstrate, Cordelia believes that love is something you show, not something you say. Talk is cheap, as Regan and Goneril's subsequent behavior attests. They have no hesitation in proclaiming their love for Lear, but once they safely get their grasping hands on his kingdom, they proceed to treat him with contempt and disrespect.
Cordelia shows her love for Lear in a number of ways. First and foremost, she marries the King of France and sets about raising an invading army to defeat her wicked sisters and restore Lear to the throne. If we cast our minds back to act 1 scene 1 we'll recall what Cordelia said to her father:

I love your majesty. According to my bond, no more nor less.

Her bond is not only that of daughter, but of royal daughter no less. And it is in this capacity that Cordelia spearheads an invasion force to try and put her father back upon the throne he so foolishly vacated. When Cordelia's plans come to nothing, she chooses to share her father's fate in prison. There, they will sing like birds in a cage. Cordelia has sacrificed everything for her father, including her life, and Lear is most grateful to her for this. If such selflessness isn't the ultimate act of love, then it's difficult to know what is.

In Okay for Now, how do the main characters change throughout the book?

From the beginning to the end of Okay for Now, the main character Doug and most of his family have changed significantly. Doug begins the story as a rather shy young man who feels stifled by his abusive father and brother. As the story progresses, Doug takes on more responsibility and makes more social connections, bringing him out of his shell. Mr. Powell helps Doug learn to express himself through drawing, while Miss Cowper and Mr. Ferris help him learn to read. Through this process, Doug's communication skills improve both literally and figuratively as he finds his voice through reading. By the end of the story, Doug has become a confident teenager who, as the principal says, can "go wherever he wants to go."
Doug's brothers, Christopher and Lucas, change significantly throughout the story as well. Lucas begins the story as an abusive young man who leaves his family to go to war. After being maimed in action, Lucas returns home broken, bitter and disillusioned. Through Doug's intervention and a friendship with the school's gym teacher, Lucas finds his way in the world and realizes the potential he thought was lost after his injuries.
Christopher also undergoes a significant change as the story evolves. While he was often cold and sometimes cruel to his younger brother at the beginning of the story, being accused of theft humbles Christopher. He realizes that Doug is there for him when no one else is and slowly but surely becomes a brother who can be relied upon for support.
Each one of the Swieteck brothers changes throughout Okay For Now in his own way. Although Doug's transformation is the most dramatic, it has ripple effects on the lives of his family members and everyone around him. By the end of the story, the reader is left with the sense that all of the main characters really will be okay.

In "Do Not Go Gentle into that Good Night," what effect do the repetitions create?

Dylan Thomas repeats alternating lines at the end of each stanza; they are "Rage, rage against the dying of the light" and "Do not go gentle into that good night."
Both lines are imperatives that the poem's speaker is delivering to his father; this is revealed in the poem's final quatrain after a series of five tercets. The repetitions of these lines add emphasis and urgency to the idea that his father must not passively accept his demise; he should, rather, battle to the last moments of his existence. The speaker seems to believe that life is precious and should not be given up without a fight. Moreover, the speaker creates a catalog of men (with "men" being another word that is repeated as a point of emphasis) who did not "go gentle" as a point of comparison and a behavior for his father to emulate. He expresses the wish that his father will also "burn and rave" as his last moments approach.

The repetition of the first and third lines of the poem impress the reader with the speaker's relative desperation that his father fight against death (we learn the narrator of the poem is speaking to his or her father in line 16). It sounds as though the speaker is trying to persuade his or her father that, although continuing to live might be painful or difficult, resisting death is the best thing, the right thing, to do. The speaker repeats these lines in the context of describing all different kinds of men—wise men, good men, wild men, and serious men (or men who are very near death, since "Grave" has two potential meanings here)—and all the different reasons that they choose to stay in "the light." This seems to be an attempt to convince the father that no one else goes "gentle into that good night," so neither should he.

Calculus of a Single Variable, Chapter 2, 2.3, Section 2.3, Problem 50

Note:- 1) If y = sinx ; then dy/dx = cosx
2) If y = cosx ; then dy/dx = -sinx
3) If y = u*v; where 'u' & 'v' are functions of 'x' ; then dy/dx = uv' + vu'
Now,
y = xsinx + cosx
dy/dx = y' = xcosx + sinx - sinx
or, dy/dx = y' = xcosx

Why does the speaker desire peace so much in the poem "The Lake Isle of Innisfree" by Yeats?

There is little explanation of why Yeats is so hungry for peace in his famous poem "The Lake Isle of Innisfree." Rather, Yeats spends most of the poem describing the pastoral beauty and idyllic peace of a quiet existence. However, one can guess that Yeats wants peace from the trials of urban existence. 
Written toward the end of the 19th century, "Innisfree" can be seen as a response to a rapidly changing world. Like the Romantics before him, Yeats appears dissatisfied with conventional existence and yearns to return to an idealized, pastoral lifestyle. Additionally, we can guess that the existence Yeats seeks to escape from is something of an urban, industrialized one. Take, for instance, the poem's final lines:

I hear lake water lapping with low sounds by the shore; 
While I stand on the roadway, or on the pavements grey, 
I hear it in the deep heart’s core. (10-12)

One of the key lines here is the second one, in which Yeats describes "pavements grey." Though brief, this description hints at an urbanized world, and the description of the "grey" pavements suggests a dull, tedious, altogether tiresome existence. In short, we could say that Yeats is describing a classic modern, urban existence, and so it seems plausible to guess that he is seeking peace from this dreary, urbanized world through the idyllic natural beauty of Innisfree. Though Yeats gives us too little context to be absolutely sure about this idea, it seems to be a sound one based on the information he does give us. 
https://www.poetryfoundation.org/poems/43281/the-lake-isle-of-innisfree

y' = 5x/y Solve the differential equation

The general solution of a differential equation in a form of y'=f(x,y) can be evaluated using direct integration. The derivative of y denoted as y' can be written as (dy)/(dx) then y'= f(x) can be expressed as (dy)/(dx)= f(x) .
For the problem: y'=5x/y , we let y'=(dy)/(dx) to set it up as:
(dy)/(dx)= 5x/y
Cross-multiply dx to the right side:
(dy)= 5x/ydx
Cross-multiply y to the left side:
ydy=5xdx
Apply direct integration on both sides:
int ydy=int 5xdx
Apply basic integration property: int c*f(x)dx = c int f(x) dx on the right side.
int ydy=int 5xdx
int ydy=5int xdx
Apply Power Rule for integration: int u^n du= u^(n+1)/(n+1)+C on both sides.
For the left side, we get:
int y dy = y^(1+1)/(1+1)
            = y^2/2
For the right side, we get:
int x dx = x^(1+1)/(1+1)+C
            = x^2/2+C
Note: Just include the constant of integration "C" on one side as the arbitrary constant of a differential equation.
Combining the results from both sides, we get the general solution of the differential equation as:
y^2/2=x^2/2+C
or y =+-sqrt(x^2/2+C)
 

Why does Mercutio keep repeating, "A plague a' both your houses"?

Tybalt comes to challenge Romeo because Romeo went to the Capulets' party the night before. When Romeo arrives, he refuses to fight Tybalt because he is now related to Juliet's cousin by marriage, but because his wedding to Juliet is secret, he cannot say this.
Mercutio feels that Romeo, in refusing to fight, is behaving dishonorably and submissively, and so he steps in to fight Tybalt in Romeo's stead. Romeo comes between them both, trying to keep the peace and get them to stop fighting, and Tybalt mortally wounds Mercutio under Romeo's arm. Romeo effectively blocks Tybalt from Mercutio's view and makes it possible for Tybalt to strike him undetected. Therefore, when Mercutio says, "A plague o' both your houses," he is cursing both the Capulet family (Tybalt's family) and Montague family (Romeo's family) because he sees his death as a consequence of their feud. 
He seems to repeat the curse for emphasis. Perhaps he repeats it to make extra sure that it will take effect. Of course, we know later that both families will indeed be cursed when their children take their own lives because they cannot be together.

Intermediate Algebra, Chapter 4, 4.1, Section 4.1, Problem 36

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

& y = -4x \\
& 8x + 2y = 4

\end{aligned}
\end{equation}
$ by substitution. If the system is inconsistent or has dependent equations.

Since equation 1 is solved for $y$, we substitute $-4x$ for $y$ in equation 2.


$
\begin{equation}
\begin{aligned}

8x + 2(-4x) =& 4
&& \text{Substitute } y = -4x
\\
8x - 8x =& 4
&& \text{Multiply}
\\
0 =& 4
&&

\end{aligned}
\end{equation}
$


Combining the equations give, $0 = 4$ which is a false statement. There are no ordered pairs that satisfy both equations, so there is no solution for the system. Therefore, the system is inconsistent.

In act 4, what new insight does Ophelia's grief evoke?

In act 4 we see the drastic change in Ophelia. The gentleman tells Queen Gertrude that beautiful young girl has been seen roaming singing songs of nonsense and talking about her father in lines that aren't easy to follow.



She speaks much of her father, says she hears
There’s tricks i' th' world, and hems, and beats her heart,
Spurns enviously at straws, speaks things in doubt
That carry but half sense. Her speech is nothing,
Yet the unshaped use of it doth move
The hearers to collection. They aim at it,
And botch the words up fit to their own thoughts,
Which, as her winks and nods and gestures yield them,
Indeed would make one think there might be thought,
Though nothing sure, yet much unhappily.




In act 4, scene 5, Ophelia comes to the castle to speak with the Queen, "the beauteous majesty of Denmark." This new Ophelia is a mess and communicates through seemingly nonsensical song lyrics. She never directly answers Gertrude's questions; instead, she sings a response that may or may not give us insight into the cause of her sadness. When King Claudius talks to her, she speaks, but the responses remain just a cryptic.

As she sings of death it can be assumed she is singing about her father's recent death.



He is dead and gone, lady,

He is dead and gone,

At his head a grass-green turf,

At his heels a stone.



But the song the follows gives us insight into her relationship with Hamlet. Her songs turn from ones about death to songs about men's unfaithfulness. She sings that they way men convince young women to go to bed with them is to promise to marry them but then refusing to marry them afterward because they are no longer virgins.





Tomorrow is Saint Valentine’s day,

All in the morning betime,

And I a maid at your window,

To be your Valentine.

Then up he rose, and donned his clothes,

And dupped the chamber door.
Let in the maid that out a maid

Never departed more.



This leads the audience to believe that Hamlet and Ophelia slept together, and, because she doesn't understand why he's gone to England, believes that he has abandoned her after she expected to be married to him. Our suspicions are confirmed when continues by singing to her boyfriend's parents her warning that men will make promises to their women and then leave the promises unfulfilled the morning after. Her second song includes dialogue between a girl and boy who could illustrate the last interactions between her and Hamlet.



Young men will do ’t, if they come to ’t.
  By Cock, they are to blame.
 Quoth she, “Before you tumbled me,
  You promised me to wed.”

 He answers,
 “So would I ha' done, by yonder sun,
  An thou hadst not come to my bed."






Our last hint that something happened between Ophelia and Hamlet is in the flowers she hands out. When she returns later in the scene she has flowers to give to different members of the court. Just as flowers have meaning to us today, they did to Shakespeare's audience as well. She presents rosemary for remembrance, fennel for strength, columbine for madness, daisies for innocence, and the most important violets for faithfulness and modesty. She pauses and laments that she doesn't have any violets to give them. "I would give you some violets, but they withered all when my father died." Did she lose Hamlet's faithfulness too?

The next time Ophelia is mentioned is when Gertrude is telling is explaining to the audience the circumstances of Ophelia's death. Hamlet leaving would make Ophelia upset, but if he left after sleeping with her we could see another reason for her death.

What is a quote from To Kill a Mockingbird that describes Jem Finch physically?

There are not very many physical descriptions of Jem Finch in To Kill a Mockingbird. We know that he is taller than his younger sister, and taller than Dill, but that doesn’t tell us much about his looks. I found three quotes that give us little snippets of what he looked like physically; I’ll give you one and clues to find the other two.
In chapter 15, Scout, Jem, and Dill follow Atticus into town and find him keeping watch by the jail. The children surprise the group of men that show up that evening. Atticus asks them to go home, but Jem refuses. “Jem shook his head. As Atticus’s fists went to his hips, so did Jem’s, and as they faced each other I could see little resemblance between them: Jem’s soft brown hair and eyes, his oval face and snug-fitting ears were our mother’s contrasting oddly with Atticus’s graying black hair and square-cut features, but they were somehow alike.”
There is another small clue to Jem’s appearance when they find the figures of themselves in the tree knothole in chapter 7. Skim that chapter and you’ll find the section where Jem lets Scout pull the treasure out of the knothole.
Another little detail is found right at the beginning of the book, where we find out that Jem’s arm was broken, and it caused his left arm to be shorter than his right. That should be an easy quote to spot.
Lee, Harper. To Kill a Mockingbird. (Soft Cover). Perennial, 1961.

Calculus: Early Transcendentals, Chapter 7, 7.1, Section 7.1, Problem 19

intz^3e^zdz
If f(x) and g(x) are differentiable functions, then
intf(x)g'(x)=f(x)g(x)-intf'(x)g(x)dx
If we write f(x)=u and g'(x)=v, then
intuvdx=uintvdx-int(u'intvdx)dx
Using the above integration by parts,
Let u=z^3 , u'=3z^2
and let v=e^z, v'=e^z
intz^3e^z=z^3inte^zdz-int(3z^2inte^zdz)dz
=z^3e^z-int(3z^2e^z)dz
=z^3e^z-3intz^2e^zdz
again applying integration by parts,
=z^3e^z-3(z^2inte^zdz-int(d/dz(z^2)inte^zdz)dz
=z^3e^z-3(z^2e^z-int(2ze^z)dz
=z^3e^z-3z^2e^z+6intze^zdz
again applying integration by parts,
=z^3e^z-3z^2e^z+6(zinte^zdz-int(d/dz(z)inte^zdz)dz)
=z^3e^z-3z^2e^z+6(ze^z-int(1*e^z)dz)
=z^3e^z-3z^2e^z+6(ze^z-e^z)
adding constant to the solution,
=z^3e^z-3z^2e^z+6ze^z-6e^z+C

How does Katherine Mansfield use literary features such as language, structure and imagery to generate effect and significance when talking about the aloe plant , her dog or her husband Stanley ?

Stanley is an interesting character, painted by Mansfield as a sardonic, vaguely disgruntled figure—generally well-meaning but always a little out of luck. We can see this in the tone of the imagery used to describe his moods, as when he "gloomed as the chops began to fight the tea in his sensitive stomach." The imagery here personifies the chops and tea and leave Stanley their hapless inactive victim. When Stanley does his daily exercises, he is "like a frog, shooting out his legs." While he does have "amazing vigour," the language and simile here make him appear slightly ridiculous and seem to "set him far away from Linda," his wife, who sees him as rather alien. Stanley's haplessness in the face of inanimate objects seemingly defeating him is a theme throughout Prelude, as when he had "butted into a white shirt only to find that some idiot had buttoned the neck band and he was caught." The irony here is that, of course, the "idiot" was evidently Stanley himself. The reader is invited to laugh at Stanley throughout the story. 
The aloe plant, like the inanimate objects that so perplex Stanley, is personified: it is depicted as something "fat" and "cruel" which keeps its bounty away from Linda. The aloe, she says, blooms "once in a hundred years." The effect here is to suggest that the plant could offer Linda more but it does not, something that mirrors her feelings about Stanley and his money. He is not a rich man, but she feels sometimes that he is "unreasonable" except when she remembers that she has no money of her own and therefore cannot complain. The aloe plant has "curving leaves that seem to be hiding something," and its "claws" instead of roots underline its sinister nature to Linda, yet she knows it conceals something beautiful it could offer if it would only do so. Here we see some insights into how Linda feels she is treated by the world. 
In both Prelude and At the Bay, we see several dogs but are told that "Aunt Linda hated decent dogs." Each dog has its own character, whether it be a mongrel or an old sheep dog which "cut an ancient caper or two and then pulled up sharp, ashamed of its levity." Again Linda seems to understand the dog better than she does her husband, and its motives are described more sympathetically. Linda ascribes a number of very human characteristics to the dog: she fears it is judging her, but also notes that it looks "proud" of the shepherd, its master. There is a vaguely forlorn sense that Linda wishes for a dog of her own that might be proud of her; she seems less detached from the dog--not her own--than from any of her own relatives. 
 

Find the area of the parallelogram whose vertices are at A(0,8), B(-2,6), C(-4,-6) and D(-2,-4).

Hello!
This figure is really a parallelogram, for example because the opposite sides have the same length: |AB| = |CD| = 2sqrt(2) and |BC| = |AD| = 2sqrt(37). Or we can check that the opposite sides have the same slope.
The area of a parallelogram ABCD is twice the area of the triangle ABC (or BCD,  or CDA, or DAB ). Therefore it is |AB|*|BC|*|sin(B)|.
The simplest way to compute this for the points with known coordinates is to note that this expression is the absolute value of the cross product:
A = |vec(BA) xx vec(BC)| = |lt2,2gt xx lt-2,-12gt| =
= |2*(-12)-2*(-2)| = |-24 + 4| = |-20| = 20.
This is the answer. If you don't know the cross product, you can use Heron's formula for any mentioned triangle (and multiply by 2).

In Animal Farm, how are Old Major's original commandments a vice?

In chapter one, Old Major gives the animals a number of commandments. Firstly, anything that walks on four legs is a friend, while anything that walks on two legs is an enemy. Secondly, the animals must not adopt the "vices" of man, like sleeping in a bed or wearing clothes. Thirdly, no animal must harm another animal. Finally, all animals are equal.
These commandments could be considered a vice because of their negative portrayal of humans. For Old Major, every man is a tyrant, just like Mr. Jones, but this ignores the many humans who demonstrate care and compassion toward animals.
In addition, Old Major does not realize that animals are also capable of tyranny. As we see through the character of Napoleon, for example, some animals are so driven by their own desire for power that they treat their fellow animals as cruelly as any human. Many of the pigs, like Napoleon and Squealer, also consider themselves to be superior to the other animals on the farm.
While Old Major hoped that expelling the humans would bring peace to the animals, it ultimately brought even greater tyranny.

How does the theme of the American Dream in Death Of A Salesman and The Great Gatsby compare?

Throughout both works, Miller and Fitzgerald examine the theme of the vain pursuit of the American Dream. The American Dream is the idea that an individual can attain financial security and increase their social status through good fortune and hard work. The protagonists in both works pursue the American Dream, only to live unsatisfying lives as they become corrupted by money or the vain pursuit of financial success. In the play Death of a Salesman, Willy Loman believes that he can become financially successful simply through being charismatic and well-liked. Willy also puts an extreme amount of pressure on his sons, Biff and Happy, to become successful without instilling the qualities of a good work ethic and dedication in them. Willy puts so much emphasis on attaining the American Dream that he fails to appreciate the love and support from his family. His decision to commit suicide in order to provide his family with financial security demonstrates the emptiness of pursuing the American Dream. Similarly, Jay Gatsby's decision to enter the illegal bootlegging business to attain financial success does not manifest as personal happiness. Despite attaining the American Dream by becoming extremely wealthy and entering the upper class, Jay Gatsby becomes corrupted by wealth and is not able to provide stability for Daisy. Although his love for Daisy is genuine, Gatsby has become corrupted by wealth and believes that money can buy him happiness. Unfortunately, Gatsby's wealth is not able to purchase Daisy's love, and he dies a lonely, unhappy man. Both Gatsby and Willy Loman neglect or fail to develop meaningful relationships because of their pursuit of the American Dream. While Willy's pursuit of the American Dream is futile, Gatsby's financial success and upper-class status is also empty because he fails to attain personal happiness.

Calculus of a Single Variable, Chapter 3, 3.4, Section 3.4, Problem 11

g(x)=(x^2+4)/(4-x^2)
differentiating by applying quotient rule,
g'(x)=((4-x^2)(2x)-(x^2+4)(-2x))/(4-x^2)^2
g'(x)=(8x-2x^3+2x^3+8x)/(4-x^2)^2
g'(x)=(16x)/(4-x^2)^2
differentiating again by applying quotient rule,
g''(x)=16((4-x^2)^2-x(2)(4-x^2)(-2x))/(4-x^2)^4
g''(x)=(16(4-x^2)(4-x^2+4x^2))/(4-x^2)^4
g''(x)=(16(3x^2+4))/(4-x^2)^3
There are no points at g''(x)=0,but at x=2 and x=-2 the function is not continuous.
So test for concavity in the intervals (-oo ,-2) , (-2,2) and (2,oo )
g''(-3)=-496/125
g''(0)=1
g''(3)=-496/125
Since g''(-3) and g''(3) are less than 0 , so the graph is concave downward in the intervals (-oo ,-2) and(2,oo )
and g''(0) is greater than 0 , so the graph is concave upward in the interval (-2,2).

Which of these 7 elements (totalitarian government, rigid caste system, society is closely monitored, highly developed technology, violence and pain, environmental disasters, lack of free choice) appear in "The Pedestrian," and give reasons why this is so. You have to discuss all of those that appear. Give detailed reasons where the elements you chose appear in the story. You have to take each element individually (there are 7) and state for each one if it appears in "The Pedestrian" or not. If it does you have to give the reasons, explaining in detail, why this is so.

Based on the wording of the question, it seems that the answer only needs to explain the items that do apply to "The Pedestrian."
Totalitarian government: This applies to the story. The Encyclopedia Britannica defines totalitarianism as follows:

Totalitarianism is a form of government that theoretically permits no individual freedom and that seeks to subordinate all aspects of the individual’s life to the authority of the government.

Readers are not told what kind of government exists in the year 2053; however, by the end of the story, it is clear to readers that individual citizens are not permitted many individual freedoms. The freedom that an individual has is to stay at home and watch the "viewing screen." Leonard Mead doesn't do that. Instead, he goes out for nightly walks. Unfortunately, the society that Mead lives in doesn't allow for that usage of time. Mead is ordered to get into the automated police car, and he is then taken to a psychiatric ward.

"Get in."
[...]
"Where are you taking me?"
The car hesitated, or rather gave a faint whirring click, as if information, somewhere, was dropping card by punch-slotted card under electric eyes. "To the Psychiatric Center for Research on Regressive Tendencies."

I suppose a case could be made that Mead's encounter doesn't indicate a totalitarian government. He isn't technically arrested, and the car never says that Mead is breaking the law. Mead is simply acting in a way that is completely unlike every other citizen. Why do all of the citizens stay in their homes and watch entertainment? It could be government-mandated, or it could be by choice. Readers don't know. What we do know is that Mead isn't given the option to go back home. He's taken and forced to go to a psychiatric hospital by a government "employee." He won't be given the option to explain himself in court. Mead will be treated for his "regressive tendencies" before being allowed back into society. If he doesn't reform himself, then he'll likely be a ward of the state forever. The government has complete control over his final destiny. That sounds like totalitarianism to me.
Rigid caste system: This does not apply in my opinion.
Society is closely monitored: This doesn't apply to the story. Readers are told that Mead frequently goes on his walks and never comes across anybody.

. . . he was alone in this world of A.D. 2053, or as good as alone . . .

Readers are also told that "long ago" Mead began using sneakers to muffle his steps. We are under the impression that Mead has been going on his walks for a long time, and nobody notices. Readers are then told that Mead has been going on his walks for a full decade, and he has never met another person.

In ten years of walking by night or day, for thousands of miles, he had never met another person walking, not once in all that time.

Readers are also told that the police are not likely to notice Mead either. We are told that police are "rare" and that the city only has one police car.

The police, of course, but what a rare, incredible thing; in a city of three million, there was only one police car left, wasn't that correct? Ever since a year ago, 2052, the election year, the force had been cut down from three cars to one. Crime was ebbing; there was no need now for the police, save for this one lone car wandering and wandering the empty streets.

Highly developed technology: This applies to the story, but it does depend on your interpretation of what highly developed technology is. I think an automated police patrol is advanced technology. The police car isn't just self-driving. It is also capable of asking Mead questions, interpreting those answers, and making a judgment based on those answers.
Violence and pain: This does not apply to the story. Mead is not subjected to any kind of violence or pain, nor does he use those things against someone or something else.
Environmental disasters: This does not apply to the story.
Lack of free choice: This applies to the story. Mead is taken by the police car because of his free choice. He chooses to go on nightly walks, and that is seen as questionable behavior. For that reason, Mead doesn't really have a choice of how he uses his free time. He either watches TV, or he runs the risk of being taken away to a psychiatric facility. It's like telling somebody that they can choose any color pen they want as long as it's blue.

Which member of the emerging middle class does Chaucer portray in the most favorable light? In what way does his description of this character differ from other members of this class or estate?

Out of the middle-class characters described, the Wife of Bath gets the most favorable description. Chaucer describes her as "good" and "worthy," even if she has a temper. Compared to the other characters, who are corrupt in some way, there is an openness to the Wife which makes her more likable.
Firstly, she is described as skilled in cloth-making, outdoing many of her peers. She does not get her money from exploiting people or from inheritance, as the upper class and clerical pilgrims usually do, but from her own work.
Secondly, she is an experienced woman in the ways of love. She has been married five times. Chaucer does not paint her in a negative light because of this but rather as a wise woman who understands love and sex better than most other people.
Thirdly, she is independent. She travels alone, which would have been strange for a woman to do in the Middle Ages. It was also dangerous for a woman to travel alone, which suggests the Wife is confident and brave. Considering her temper and willingness to argue, she seems more than a match for anyone who would oppose her. Her hat is even described as being as broad as a shield, suggesting warrior-like qualities.
Compared to the other middle-class pilgrims, such as the Miller and the Guildsman, the Wife is more ambitious, honest (at least in regards to her work), and good-natured. While not a perfect person, she seems the most shining example of the middle class in the whole poem.

Very few of the characters Chaucer describes are given a favorable portrait. Most are either corrupt, deceitful, or phony.
The Miller is one of the most vividly described of the middle-class characters, but Chaucer depicts him as rude and tacky. Even if we let his dirty jokes and boisterous personality go as charming in a way, it's difficult to ignore the statement that he cheats his customers and suppliers.
The Guildsmen don't get much more than a short and rather flat description without any explicit criticism. Still, the narrator does suggest that these men were all three driven by their wives' desires to rise in social stature, suggesting that their success did not come from ambition or business skill. While this may not seem extremely critical, in Chaucer's time, a time when English society was firmly patriarchal, being "hen-pecked" would be seen as a weakness.
The Wife of Bath character may be considered here. Chaucer calls her "worthy" twice, and he suggests that she is good at making cloth, has a good sense of humor, and is wise in matters of love, so the narrator seems to like her. If we put her into the middle-class category (the narrative does not place her social status), she clearly stands out among the others. The most obvious difference is that she is a woman, and as a woman, several details set her apart. She is traveling alone, uncommon for women of the time, and she appears to be independent, again uncommon for women of the time. Unlike the Miller, for whom we get mostly personality description, and the Guildsmen, whom the narrator describes mostly in terms of their nice clothing and accessories, the Wife of Bath gets several lines praising her skills.
Another character you may consider is the Host. He is easy to overlook, but he plays an important role in the frame narrative, acting as a leader of the group and setting the standards for the storytelling contest. He is certainly a member of the emerging middle class of the time. The narrator describes him as hospitable and jovial and describes their stay at the Tabbard as pleasant, so he is good at his job. As with the Wife of Bath, Chaucer spends quite a few lines offering praise of his behavior and manner. He also acts as a subtle moral arbiter, criticizing some of the characters' rude behavior, although not always successfully. The Miller, for instance, cuts in and tells his tale out of turn. However, in his role as the leader, as a guide to the group, and as the one who encourages them to tell their tales, he stands out as a positive character.