Why was non-violent action so effective in the civil rights movement?

The nonviolent protests of the 1950s and the 1960s were very successful for several reasons. For example, the Montgomery Bus Boycott showed that African-Americans were very determined to achieve their goals. They walked, biked, or carpooled for 381 days, regardless of the weather, until they got what they wanted. They took these actions in a peaceful manner, not destroying property or hurting people.
Another reason why the nonviolent method was successful was that it showed the rest of the country who was really being violent. When the police in Birmingham turned the fire hoses on the protesters and used dogs to attack them, it showed the brutal methods that law enforcement was using. When the police beat the marchers as they attempted to march from Selma to Montgomery, it also showed how violently the police were responding to the nonviolent protests. These actions were captured by the news media covering these events. The whole country was able to watch and see these events unfold. This helped sway public opinion in favor of the nonviolent protesters. This helped to pressure Congress to act and led to the passing of the Civil Rights Act of 1964 and the Voting Rights Act of 1965.
Another factor that supported the nonviolent protesters was that those who were against integration went after black churches and killed black children. People were horrified when the 16th Street Baptist Church was bombed and young, black children were killed.
The constant use of nonviolent protests helped to sway public opinion and some lawmakers to take actions to deal with the civil rights’ injustices facing our country.
http://www.pbs.org/independentlens/februaryone/civilrights.html

https://www.voanews.com/usa/non-violence-was-key-civil-rights-movement

Single Variable Calculus, Chapter 3, Review Exercises, Section Review Exercises, Problem 46

Determine $\displaystyle \lim\limits_{t \to 0} \frac{t^3}{\tan^3 2t}$


$
\begin{equation}
\begin{aligned}
\lim\limits_{t \to 0} \frac{t^3}{\tan^3 2t} &= \lim\limits_{t \to 0} \frac{\frac{t^3}{\sin^3 2t} }{\cos^3 2t} = \lim\limits_{t \to 0} \frac{t^3}{\sin^3 2t} \cdot \cos^3 2t && \Longleftarrow \text{If we introduce } \frac{8}{8} \text{ such that...}\\
\\
\lim\limits_{t \to 0} \frac{t^3}{\tan^3 2t} &= \lim_{t \to 0} \frac{8t^3}{\sin^3 2t} \cdot \frac{\cos^3 2t}{8} && \Longleftarrow \text{we can rewrite the limit as...}\\
\\
\lim\limits_{t \to 0} \frac{t^3}{\tan^3 2t} &= \lim_{t \to 0} \left( \frac{2t}{\sin 2t} \right)^3 \cdot \frac{\cos^3 2t}{8} && \Longleftarrow \text{recall that } \lim_{t \to 0} \frac{\sin t}{t} = 1\\
\\
\lim\limits_{t \to 0} \frac{t^3}{\tan^3 2t} &= \lim_{t \to 0} (1)^3 \cdot \lim_{t \to 0} \frac{\cos^3 2(0)}{8}\\
\\
\lim\limits_{t \to 0} \frac{t^3}{\tan^3 2t} &= 1 \cdot \frac{1}{8}\\
\\
\lim\limits_{t \to 0} \frac{t^3}{\tan^3 2t} &= \frac{1}{8}

\end{aligned}
\end{equation}
$

Describe the opposing attitudes toward Great Britain that colonists held prior to and during the Revolutionary War. How did different social groups respond? What factors influenced their decisions to support the patriots, support the British, or remain neutral?

There were different attitudes in the colonies toward Great Britain prior to and during the Revolutionary War. Each group had reasons for supporting the side they did. Since you have asked several questions in this post, I will mainly focus on your first statement and briefly touch upon the others.
There were people who believed we should remain loyal to Great Britain. These people believed that Great Britain had the right to run the colonies in any manner that they wanted. They believed that Great Britain took a risk in establishing and in running the colonies. This gave them the authority to do what they felt what was necessary in order to make them successful. These people also were concerned there would be chaos if Great Britain was defeated.
Some people wanted to remain loyal to Great Britain for economic reasons. The colonists got many products from Great Britain that were not made in the colonies. Some people worked for the British government. These people would have lost their jobs if Great Britain was defeated.
Other people wanted to remain loyal for religious reasons. The King of England was the head of the Anglican Church. These people felt they couldn’t disobey the King since he was the leader of the Church of England.
The Native Americans and some slaves tended to be on the side of the British. The Native Americans didn’t trust the colonists and feared the colonists would take away their land. Some slaves supported the British because they were promised their freedom if Great Britain won the war.
There were other people who believed we needed to be free from the rule of the British. They believed the British were violating the rights of the colonists. They felt the tax laws were illegal because the colonists had no representatives in Parliament that could vote on the taxes. They felt the British were trying to control them by preventing the colonists from moving to the new lands that we had just gained from France as a result of the French and Indian War. They were unhappy with the Proclamation of 1763 and with the Quartering Act. The Quartering Act required the colonists to provide housing for the British troops that were enforcing the unpopular Proclamation of 1763.
More people began to feel the colonists should be free from the British rule after there were violent confrontations with the British. People became concerned after five colonists were killed in the Boston Massacre. After the Intolerable Acts were passed to punish the colonists for the Boston Tea Party, the colonists formed their own militias as they expected some fighting to occur. After the battles at Lexington and at Concord, during which both sides suffered casualties, many people believed it was only a matter of time before we would declare our independence. Throughout the war, these people believed we were fighting for our rights and to stop the abuses of the British government.
Each group of people had various reasons for supporting the rule of the British or for joining the colonists in their fight for freedom.
https://www.ushistory.org/us/11b.asp

https://www.ushistory.org/us/13c.asp

Why was Doon disappointed about his first day on his job?

In approaching this question, it's important to understand what kind of person Doon is. He's a very serious, studious young man, with a real taste for knowledge. As such, he's none too popular with his classmates, who tend to regard him as a bit of an oddball. In the City of Ember, when students graduate, they're assigned jobs. Given Doon's prodigious knowledge, in particular his knowledge of technology, one might think that he'd be given a job appropriate to his aptitude and skills. Unfortunately for him, that doesn't happen. Much to his disgust, Doon's given the job of messenger, which as the name implies involves delivering messengers to the people of the City of Ember.
Doon's incredibly annoyed at being given what he considers such a meaningless job. The city's whole infrastructure is in the process of collapsing; there are chronic shortages of just about everything; and the lights are always going out. If these problems aren't addressed then there won't be anyone left to deliver messages to. Doon rightly believes that his talents would be much better employed as a Pipeworks laborer. That's the job that Lina's been assigned, but she's none too pleased about it. In fact, she'd much rather be a messenger. So Doon and Lina make a trade and Doon goes off to the Pipeworks to start his new job.
His first day on the job, however, leaves something to be desired. Doon's intellectual curiosity extends to insects; he takes care of a moth larvae that's about to develop into a cocoon. While working at the Pipeworks, he also collects a variety of bugs, which he finds an endless source of fascination. Sadly for Doon his co-workers don't share his interests. They subject him to mockery, teasing him mercilessly about collecting bugs for his lunch. But Doon will have the last laugh. His curiosity about the natural world may not earn him the respect of his work colleagues, but it eventually proves crucial in helping him and Lina find a way out of the city.

How has Karana's attitude toward the island changed when she returns?

Karana originally leaves the island with her people, sailing aboard a ship belonging to white missionaries. Her brother Ramo is meant to come along on the voyage too, but he gets left behind. Karana is very close to her brother and simply will not leave without him. So she dives from the ship into the sea and swims back to the island.
Once she's returned to the island, Karana's whole attitude changes, especially after Ramo is killed by a pack of wild dogs. All alone on the island, Karana becomes fiercely self-reliant. When she lived with her tribe, she was restricted to certain menial tasks such as cooking and washing, which were reserved for women. But now that he's on her own, Karana engages in the kind of activities that, according to tribal custom, are the sole preserve of men, such as hunting and fishing. For Karana, the island is now no longer a place to live but a harsh wilderness to be tamed.

Precalculus, Chapter 1, 1.1, Section 1.1, Problem 34

Plot the points $A = (4,-3), B = (4,1)$ and $C = (2,1)$ and form the triangle $ABC$. Verify that the triangle is a right triangle. Determine its area.








$
\begin{equation}
\begin{aligned}

AB =& \sqrt{(4-4)^2 + [1-(-3)]^2}
\\
=& \sqrt{0+16}
\\
=& \sqrt{16}
\\
=& 4
\\
BC =& \sqrt{(2-4)^2 + (1-1)^2}
\\
=& \sqrt{4+0}
\\
=& \sqrt{4}
\\
=& 2
\\
AC =& \sqrt{(2-4)^2 + [1-(-3)]^2}
\\
=& \sqrt{4+16}
\\
=& \sqrt{20}
\\
=& 2 \sqrt{5}
\\
(AC)^2 =& (AB)^2 + (BC)^2
\\
(2 \sqrt{5})^2 =& (4)^2 + (2)^2
\\
(4 \cdot 5) =& 16 + 4
\\
20 =& 20


\end{aligned}
\end{equation}
$


Thus, $\Delta ABC$ is a right triangle.

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


$
\begin{equation}
\begin{aligned}

\Delta ABC =& \frac{1}{2} (4)(2)
\\
\\
=& \frac{8}{2}
\\
\\
=& 4 \text{ square units}

\end{aligned}
\end{equation}
$

What is Daisy Buchanan's background?

The reader knows about Daisy from Jordan Baker's recollections, as Jordan grew up with her. Daisy, whose maiden name was Fay, grew up in Louisville, where she was a very popular young woman, around 1917. She drove a little white roadster, and the officers from Camp Taylor constantly called her and asked her out. One of these officers was Jay Gatsby.
Daisy was the subject of rumors—for example, that her mother had found her packing to go to New York to bid farewell to a soldier who was going overseas. This incident caused Daisy not to be on speaking terms with her family for a while and to only date men who weren't in the military. After the end of the war, she had a debut, and she eventually married Tom Buchanan in a lavish ceremony. On the day of Daisy's wedding, Jordan found her drunk and in tears. Daisy was clutching a letter in one hand (which she even took into the bath with her until it disintegrated) and the very expensive pearl necklace Tom had given her in the other. Ultimately, Daisy's wealthy and constricted upbringing greatly affected her life as an adult.

Where does Pip transition from boyhood to manhood?

Pip begins the transition from boyhood to manhood after he goes to London in Stage II; then in Stage III of Great Expectations, Pip reaches full maturity.
Before he goes to Satis House to play with Estella at Miss Havisham's Satis House, Pip is an innocent boy. But after Estella is cruel to him and calls him "common," Pip perceives himself as inferior; consequently, he desires to be a gentleman and attain a social status that cannot be ridiculed. This urgent desire of Pip's to become a gentleman seems possible after Mr. Jaggers arrives with the announcement that Pip is to have "great expectations." Elated that his wish may come true, Pip leaves his sister and Joe without misgivings and takes the stagecoach to London. There he lives with a relative of Miss Havisham's, Herbert Pocket. They become fast friends, but both of the young gentlemen do not exercise frugality, and so they get themselves into debt. Worse than this, Pip becomes a snob. When Joe Gargery, whom Pip has loved like a father, comes to London to visit, Pip is embarrassed by Joe's speech and his awkwardness in his new clothes. When the perceptive Joe realizes that Pip is ashamed of him, he returns to the marshes.
After this visit, Pip continues on the path of believing that social position is equated with happiness. However, as Mr. Jaggers has warned him, he "goes wrong." Pip loses sight of the values that are real. When he learns that Estella is coming to London, Pip is convinced that Miss Havisham means for him to court her. However, he soon realizes that Estella is interested in a brutish young man named Bentley Drummle. To add to his disappointment and dismay, Pip is visited one night by Abel Magwitch, the convict from the prison ship. Pip learns from Magwitch that this old convict, not Miss Havisham, is his benefactor (Ch.39).
In Book Three, it is after he and Herbert try to help Magwitch/Provis elude his enemy Compeyson who has come to London to kill him that Pip begins to realize a person's social position is not the most essential quality that someone possesses. It is then that Pip reaches full maturity as a man. The love that Joe and Magwitch have for him is real, and it is love that matters the most. Unlike social position, which has brought no comfort or delight to Miss Havisham or Estella, love provides a person true happiness.

Which persuasive devices does the inspector use in his final speech?

As the inspector is leaving the Birlings' house, he says that although Eva Smith is dead, "there are millions and millions of Eva Smiths and John Smiths still left with us, with their lives, with hopes and fears." He reminds the family that members of society are responsible for each other. The persuasive device that the inspector is using is pathos, or appealing to the emotions of the Birling family, to convince them that what they all did to Eva Smith is wrong and that they have a responsibility for people in the working class. He also says that if people don't learn that lesson, they will eventually have to learn it "in fire and blood and anguish." Again using pathos, he reminds the audience of the anguish that they will continue to cause if they don't amend their ways. To reinforce his point, he also uses the device of repetition, as he repeats the words "millions" and "with." His repetition of these words reinforces the idea that the society is made up of countless people like Eva Smith, who upper class people like the Birlings are taking advantage of.

What are some interesting words from Milkweed by Jerry Spinelli?

There are a lot of interesting words in Milkweed, including the title word itself, "milkweed." Some others are Jackboot, Stawki Station, Stopthief, runt, strawberry babka, lopped-off, resettlement, deportation, ghetto, locomotive, dried herring, flamethrowewr, cannibals, nickered (a soft breathy whinny from a horse) and cuckoo (an Eastern Hemisphere songbird immortalized in cuckoo clocks). I'll discuss some of these and explain their interest.
First is milkweed. Its Latin name is Asclepias syriaca. It is a herbaceous perennial with 140 species and is native to North America, among other places. Most interestingly, milkweed is the chrysalis ground for Monarch butterflies, the population of which is recently cut down by 90%. Several movements to save the Monarch request that people plant milkweed, having very lovely blossom clusters, in their gardens to give Monarchs shelter. Also interesting is that milkweed is poisonous, as are the butterflies that feed upon them.
Stawki Station was an actual train station just to the east of Warsaw, Poland, where Jews were boarded onto trains for their "resettlement," or transportation out of Poland to resettlement camps, which we now know as extermination camps or forced labor concentration camps.
Strawberry babka is a traditional sweet Polish coffee cake. Babkas are generally made with orange peel for orange babka, but strawberry babka is a common variation on orange babka. Other ingredients in this sweet, raised-dough coffee cake are raisins, rum and almonds. Coffee cake is so named because it is traditionally served for breakfast or morning visits along with coffee; hence, coffee cake: cake served with coffee.

How is Scout naive in To Kill a Mockingbird?

There's one lovely scene in To Kill a Mockingbird where Scout shows her naivety. Maycomb is experiencing its first snowfall since the end of the Civil War—that's about 70 years in all. Most adults in the town have never seen snow falling, let alone the children. So when Scout looks out the window that morning, she's absolutely terrified by what she sees. As Scout has never experienced snow before, she doesn't know how to handle it. It's all so strange to her that it genuinely seems like the end of the world. She screams out loud as the flakes gently fall outside her window, causing Atticus to rush into her bedroom to see what's wrong. Scout wants Atticus to do something—anything—to stop the impeding apocalypse. But it's just a rare Alabama snowfall, nothing more.

Being that Scout is five years old at the beginning of the story, many of the events described are narrated from her naive point of view. She lacks the maturity and ability to comprehend different situations throughout the story and is unaware of the overt prejudice throughout her community. Scout continually displays her childhood innocence by asking numerous questions concerning explicit subjects. Scout asks Atticus what the term "nigger-lover" means and inquires about the definition of "rape" from Calpurnia. Scout lacks the ability to grasp the gravity of the situation when she enters the circle of men outside of the Maycomb jailhouse in chapter 15 and does not fully understand the significance of her father's defense of Tom Robinson.
Scout also portrays her naive personality by fearing her reclusive neighbor and believing nearly every story that Jem tells her. As the novel progresses, Scout matures and gains perspective on the world beyond her self. Following Tom's trial, Scout begins to perceive the overt prejudice throughout Maycomb and views Boo as a shy, compassionate man, instead of a "malevolent phantom."

What is the situational irony in "The Story of an Hour"?

The core situational irony in "The Story of an Hour" relies on the historical context of the society in which Mrs. Mallard lives. The story depicts her societal place in the late 1800s, a time when women were afforded precious few opportunities for self-fulfillment and were expected to take great satisfaction in taking care of their husbands and families.
Before she receives the news, Mrs. Mallard "only yesterday...had thought with a shudder that life might be long." She is weary of the monotony of caring for others, particularly her husband. She longs for more.
Thus, the situational irony is that she is expected to deeply grieve the loss of her husband but is instead filled with joy, and "she did not stop to ask if it were or were not a monstrous joy that held her." This (mistaken) turn of events has allowed her a freedom she longs for, and she welcomes both his death and the change.
Furthering the situational irony, Josephine comes to the door, believing that Mrs. Mallard is making herself ill with the grief of her loss. Instead, this wife who believes herself a widow is " drinking in a very elixir of life."
The situational irony comes to new light when Mrs. Mallard realizes that her husband is very much alive, and it is she who ends up dead at the story's close—not her husband. This ironic twist shows that so much can happen within the span of an unpredictable hour.

Situational irony occurs when something is expected to happen, but the opposite happens instead. Kate Chopin's short story "The Story of an Hour" has great examples of this literary device. This short story takes place within one hour, in which the protagonist, Mrs. Mallard, learns of her husband's death.
The story begins with the line "Knowing that Mrs. Mallard was afflicted with a heart trouble, great care was taken to break to her as gently as possible the news of her husband's death." When she hears this news, Mrs. Mallard does grieve and weep as expected, but then she retreats into her bedroom alone. Here, it is expected that she will continue mourning, and her sister becomes worried about her being alone. However, Mrs. Mallard is no longer sad. She feels as if she will now be free and able to live a joyous life.
Another example of situational irony occurs at the end of the story when her husband returns home alive and well. It is expected that she will react joyfully and be ecstatic that he was not killed in the train accident as suspected. However, she suffers a heart attack and dies upon seeing him. The doctor explains her death as "joy that kills." However, we know the opposite to be true.

In this story, all the neighbors and Mrs. Mallard's sister think Mrs. Mallard is overwhelmed with grief when she hears her husband has been killed in a train accident. In fact, even Mrs. Mallard doesn't at first understand her own feelings:

There was something coming to her and she was waiting for it, fearfully.

It is only after she stops to think that the realization dawns on her: she is feeling joyful and liberated about her husband's death, not grief-stricken. This is ironic, because it is not how she or anybody else around her expects her to feel. She is not living by the "distraught widow" script. She is, as she thinks, "free, free, free!"
She, in fact, relaxes, joyfully realizing she can now be her own person.
As a final twist, however, when her husband appears and she learns the reports of his death were mistaken, she dies. All of this happens within a single hour. The irony here is that people think she has died of joy over seeing her husband alive, when the opposite is true.

Situational irony occurs in a story when the outcome of an event is the opposite of what one expects. Two paired instances of situational irony create the structure of Kate Chopin's "The Story of an Hour," both hinging on Mrs. Mallard's heart trouble and her husband's life. 
The first sentence of the story introduces Mrs. Mallard's heart trouble, implying immediately that the news of her husband's death might precipitate a heart attack. Thus, the expectation is solidified beyond what readers would already anticipate: a woman who learns of the untimely death of her husband in a train accident will be overcome with grief. The irony is that Mrs. Mallard, after retreating to her room ostensibly to grieve, finds herself experiencing joy instead. She imagines the years of freedom spreading before her and focuses on her unexpected but welcome liberation, rather than on her loss. 
The second instance of irony, which caps off the story, occurs when Mr. Mallard appears in the doorway. He has not died after all. Normally, a wife would greet such news and such an appearance with joy, relief, and even euphoria. Readers would expect the wife, when she finds out that her husband is still alive and sees him standing there, to rush to him, embrace him, and possibly weep for joy. Instead, Louise drops dead of a heart attack. Her reaction is so unusual, the doctor ascribes her death to "the joy that kills," which is ironic since it was not what really killed her.
The impact of Chopin's story depends on the skillful use of situational irony; Louise reacts to the news of her husband's supposed death (and is happy) and to his appearing before her alive and well (and dies) in the opposite fashion of what we would expect. 

How did the Mayflower Compact shape the formation of politics in America?

The Mayflower Compact was the first attempt at self-government in America.  The Compact was written down and agreed to by the male members of the Mayflower voyage.  It was meant to provide for "order and preservation" of the people and to provide for "just and equal" laws.  The signers of the Compact pledged to follow the laws of the colony.  In this one can also see the beginning of a social contract system in which the members of a body politic promise to follow the laws and the government promises order and equality under the law.  This would be important as the Framers of the Constitution sought to create an orderly system of government with equality under the law with the citizen's responsibility being to follow the laws provided by the government.  The Mayflower Compact was the first attempt at self-government in the New World, and in it one can see the beginnings of how the future government of the United States would operate.  
https://www.usconstitution.net/mayflower.html

What is the diction, imagery, and figurative language in the poem "Full Moon" by Robert Hayden?

Diction refers to an author's word choice and even, sometimes, syntax, or sentence structure. How formal or informal is it? The diction of this poem is certainly higher than conversational; I would classify it, then, as "standard"—the kind of diction one might expect to see in formal, polished writing, the King's English. Words and phrases like "brilliant challenger of rocket experts," "white hope of communications men," "radiance on the exile's path," and "mooted goal" seem to mark the diction as being a step above what one might use in an everyday, casual conversation.
Imagery is language that attempts to convey sensory information, and all of the imagery in this poem is visual: describing something that could be seen. The phrases "throne of a goddess," "bubble house," and "tumbling Mother Goose man" all convey such visual images. Likewise, we can vividly see the image created by the line, "Pierced their ears for gold hoop earrings" or "the full moon dominates the dark." We might also be able to imagine the sight of the moon "spread[ing] its radiance on the exile's path" or "burn[ing] in the garden of Gethsemane, / its light made holy by the dazzling tears / with which it mingled."
The moon is described, figuratively, as the one-time "throne of a goddess to whom we pray" and the "bubble house of childhood's / tumbling mother Goose man." We no longer think of the moon in these ways, though at one time people did worship the moon and children still do imagine it in fanciful terms like these. The moon is personified by the word "emphatic" in line 4, given the human ability to move with purpose and determination. It "challenge[s]" experts in the field of space exploration. It is metaphorically compared to the sun in the fifth stanza, when the speaker says that the moon "burned" in Gethsemane. In the last stanza, it is compared, via metaphors, to a "mooted goal" (a goal already reached), "an arms base," and "a livid sector."

This poem is an exploration of the endurance of the moon, itself unchanging while it endures through humanity's changing beliefs, experiences, and ambitions. It is dense with imagery and figurative language, so this can form the core of your writing about it. The first stanza depicts the moon as it is imagined by children—"a bubble house of childhood's tumbling Mother Goose man"—and packages this alongside the image of that same moon as "the throne to a goddess to which we pray." Many cultures across history have prayed to a moon goddess, such as the Greek Selene (Roman Luna). These beliefs about the moon, as a figurative "bubble house" or "throne," the poet says, are "no longer." In these instances, the poet's figurative language—the moon is not literally a throne or bubble house, nor has it ever been—serve to establish vivid imagery of the moon as a castle in the sky, the seat of long-ago daydreams. The following stanza describes the moon in terms of, by contrast, the concrete issues it provides for scientists: the "challenger" encouraging them to reach it and the "white hope of communications experts." There is a degree of figurative language here, as the moon does not have the agency to set itself up as a challenger, but by contrast to the first stanza, this one lacks imagery or fanciful language, underlying its description of science rather than fantasy. The moon, instead, is "emphatic," steadfast in its purpose, enduring. The following two stanzas, however, revisit the imagery and lush language of the fanciful, as the poet describes what the moon has meant to his family. The imagery here calls to mind travelers, or other country people, believing that certain elements of their lives depended upon the moon as it "waxed and waned—the times at which they "planted seeds, trimmed their hair," pierced their ears for "gold earrings," which the language of the poem almost invites us to imagine glinting under the moon. The poet, however, undercuts this imagery harshly: "the moon shines tonight upon their graves," outlasting with its unchanging nature all their beliefs and acts of service to it. Stanzas five and six revisit the familiar imagery of Gethsemane, underlining the length of time for which the moon has accompanied humanity through its most significant events. Here it "burned in the garden," and the poet emphasises with repetition that its light was "made holy." The moon's light catches in Christ's "dazzling" tears and lights his path "with radiance." The imagery is vivid and the language elevated: "The Glorious One," "His Holiness." In the final stanza, again, then, the poet repeats his tactic of contrasting this rich imagery with the scientific, but in this case, the moon-as-challenger, too, is described evocatively. "A mooted goal" now that it has been conquered, the poet muses darkly that it may perhaps next be "an arms base, a livid sector." For now, though, the moon outlasts all human meddling and "dominates the dark."

Is Hamlet crazy, or is everyone else just suspicious? Give evidence from the text to prove if Hamlet is crazy, or if Hamlet is not crazy.

Madness, real and pretend, is a recurring motif in Shakespeare’s Hamlet. The title character, Hamlet, tells his friends after meeting the ghost of his father and learning his father was murdered by his uncle, "I perchance hereafter shall think meet / To put an antic disposition on" (1.5.171-172). Hamlet is warning them that he plans to behave strangely. While he doesn’t say why it is assumed that he plans to act like he is crazy so that King Claudius is distracted and fails to notice he is planning revenge.
Later, Ophelia tells her father, Polonius, about Hamlet’s strange visit to her closet. She describes him as entering with his shirt undone, his socks around his ankles, his knees knocking together, and with no hat on his head. To add to the strangeness of the visit she reports Hamlet only grabbed her by the wrist, then let go and backed away, saying nothing. He seems to be mad in this scene, and she immediately tells her father, who assumes he is lovesick. This scene seems to accomplish what Hamlet may have hoped—instead of being suspicious of his actions Polonius is focused on his behavior being the result of a broken heart. Later on, the King and Queen summon childhood friends of Hamlet’s to learn what has caused his “transformation.” While Hamlet is implementing his plan to prove Claudius’s guilt with the play the actors will perform Claudius is distracted by Hamlet’s “madness,” allowing him to plan without notice.
In another scene, Hamlet has an absurd conversation with Polonius that finds Hamlet using wild puns and acting eccentrically. After his encounter, Polonius still believes the behavior is caused by Ophelia’s break up with him, though he may be starting to think it is more than that, saying "Though this be madness, yet there is method in't" (2.2.205-206). Midway through Act 3, Ophelia exclaims after a brutal confrontation with the unstable Hamlet, "O, what a noble mind is here o'erthrown!" (3.1.150).
Hamlet’s behavior continues to deteriorate throughout the play and some people believe that while he intended to act like he is crazy at the start, he may have literally lost his sense of reason due to the pressure of planning revenge and the sadness of losing Ophelia. Throughout the play, though, right up until the end, Hamlet’s soliloquies are beautiful and well-reasoned; they are measured attempts to show his growing determination to enact his revenge. This is why it seems likely that Hamlet was indeed just playing mad in order to be able to fulfill the promise he made to his father’s ghost and avenge his father’s murder.

College Algebra, Chapter 8, Review Exercises, Section Review Exercises, Problem 42

Identify the type of curve which is represented by the equation $\displaystyle x^2 + 4y^2 = 4x + 8 $
Find the foci and vertices(if any), and sketch the graph

$
\begin{equation}
\begin{aligned}
x^2 - 4x + 4y^2 &= 8 && \text{Subtract } 4x\\
\\
x^2 - 4x + 4 + 4y^2 &= 8 + 4 && \text{Complete the square; Add } \left( \frac{-4}{2} \right)^2 = 4\\
\\
(x - 2)^2 + 4y^2 &= 12 && \text{Perfect square}\\
\\
\frac{(x-2)^2}{12} + \frac{y^2}{3} &= 1 && \text{Divide by 12}
\end{aligned}
\end{equation}
$


The equation is an ellipse that has form $\displaystyle \frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1$ with center at $(h,k)$ and horizontal major axis.
Since, the denominator of $x^2$ is bigger. The graph of the shifted ellipse is obtained by shifting the graph of $\displaystyle \frac{x^2}{12} + \frac{y^2}{3} =1$
by 2 units to the right. This gives us $a^2 = 12$ and $b^2 = 3$. So, $a = 2\sqrt{3}, b = \sqrt{3}$ and $c = \sqrt{a^2 - b^2} = \sqrt{12-3} = 3$. Thus,
by applying transformatioms, we have

$
\begin{equation}
\begin{aligned}
\text{center } & (h,k) && \rightarrow && (2,0)\\
\\
\text{vertices: major axis} & (a,0)&& \rightarrow && (2\sqrt{3},0) && \rightarrow && (2\sqrt{3}+2,0) && = && (2\sqrt{3}+2,0)\\
\\
& (-a,0)&& \rightarrow && (-2\sqrt{3},0) && \rightarrow && (-2\sqrt{3}+2,0) && = && (-2\sqrt{3}+2,0)\\
\\
\text{minor axis }& (0,b)&& \rightarrow && (0,\sqrt{3}) && \rightarrow && (0+2, \sqrt{3}) && = && (2, \sqrt{3})\\
\\
& (0,-b)&& \rightarrow && (0,-\sqrt{3}) && \rightarrow && (0+2, -\sqrt{3}) && = && (2, - \sqrt{3})\\
\\
\text{foci }& (c,0)&& \rightarrow && (3,0) && \rightarrow && (3+2,0) && = && (5,0)\\
\\
& (-c,0)&& \rightarrow && (-3,0) && \rightarrow && (-3+2,0) && = && (-1,0)
\end{aligned}
\end{equation}
$

Therefore, the graph is

In A Gathering of Old Men, what do you think of Mapes’s tactics when he questions and strikes the black men, and why does he behave this way?

After driving up the dusty road and arriving at Mathu's place, Sheriff Mapes steps out of his squad car in his gray suit with a red tie. He assesses the situation and then questions the old men, employing the tactics of a sheriff in the South of a former day: He seems brutal and bigoted. 
In Chapter 8 of A Gathering of Old Men, the old black men walk through the graveyard in a symbolic gesture of their remembrance of loved ones who died dissatisfied or were harmed under the cruel feudal-like system of the South. They then enter the yard of Mathu with fervor and a new resolve to assume the blame for the death of the Cajun Beau Bauton, and, in so doing, assert the manhood they have sacrificed in the past.
When Sheriff Mapes arrives in his squad car that is shrouded in a cloud of dust, the burly man steps out, looks around, and asks what has occurred. Candy insists that she killed Beau; however, the sheriff looks at Mathu, who remains quietly squatting on the porch. Since there are yet residuals of the methods of the Old South, Sheriff Mapes slaps the almost eighty-year old Uncle Billy and others that he interrogates when they each claim responsibility for having shot Beau.
Even in the 1970s and later, sheriffs wielded much power, and on this day Mapes is brutal. Furthermore, he knows these old men have compromised their manliness in the past because of their fears of "the man" when racial cruelty was allowed. Therefore, he hopes to intimidate them in a similar fashion and learn who is the real perpetrator of the murder.
Mapes's brutish behavior suggests that he does not truly care what precisely has occurred; he simply wants to find the culprit and arrest him before Beau's father Fix hears of the death of his son and further conflicts develop. Mapes's desire overrides any real investigation of the motives and details in connection to the death of Beau demonstrate the sheriff's desire to preserve the status quo.

Calculus of a Single Variable, Chapter 8, 8.3, Section 8.3, Problem 30

Before we can begin to find the integral, we must do some rearranging using some trig identities so that we have integrals that we can work with. We will need to remember the following identities as we work through this problem:
tan^2(x)=sec^2(x)-1
tan(x)=(sin(x))/(cos(x))
So, to begin, we will split up the tan^3 like so:
int tan^3(3x)dx=int tan(3x)*tan^2(3x)dx
Next, we will use the first identity above to rewrite tan^2:
int tan(3x)*tan^2(3x)dx=int tan(3x)(sec^2(3x)-1)dx
We will then distribute and separate it into two integrals:
int tan(3x)sec^2(3x)-tan(3x)dx=
= int tan(3x)sec^2(3x)dx-int tan(3x)dx
Now we can use the second trig identity above to rewrite the second integrand:
int tan(3x)sec^2(3x)dx-int (sin(3x))/(cos(3x))dx
We can now use u-substitution on each integral. We will also need the chain rule on the 3x when finding du. So the u-substitution for the first integral is:
u=tan(3x)
du=sec^2(3x)*3dx
1/3 du=sec^2(3x)dx
For the second integral, we will use a v for our u-substitution so as not to confuse the two as we work through them. So the "v"-substitution for the second integral is:
v=cos(3x)
dv=-sin(3x)*3dx
-1/3dv=sin(3x)dx
Now, we will substitute these back into the integrals and integrate, as shown below:
1/3 int udu-(-1/3)int (1/v)dv=(1/3)(u^2/2)+(1/3)ln|v|+C
We can now substitute back in for u and v to find our final indefinite integral:
int tan^3(3x)dx=1/6tan^2(3x)+1/3ln|cos(3x)|+C

What are the pros and cons of tenure for K-12 teachers?

The important context for thinking about this is salary levels. Teachers are paid substantially less than other professionals with similar levels of education. They also tend to work high levels of unpaid overtime in a job that is extremely stressful. The teaching profession also has a high attrition rate of approximately 40 percent annually. Some areas and specializations are facing significant teacher shortages. Even worse, education is not a major attracting the best qualified applicants, with prospective education majors scoring in the bottom half of standardized tests such as the SAT and ACT compared to students interested in other majors.
What this means is that tenure, which offers a form of job security, is one of the few things that might attract and retain highly qualified applicants to the profession. It is also important to ensure that teachers can grade fairly, rather than feeling compelled to give students higher grades or teach exclusively to standardized tests to hold on to their jobs.
On the negative side, tenure will protect weaker teachers from being fired.

I’m doing a type of annotation essay/assignment for my English class, but I’m having a hard time understanding what would be relevant when doing annotations within an essay. What should I be looking for when annotating "Crusoe in England" by Elizabeth Bishop?

An annotation is just an explanation or comment added to a text. For example, Bibles are often annotated with footnotes throughout, offering explanations for historical context, translation difficulties/ambiguities, or relationships to other texts. Annotation is also a practice that any reader can undertake. You can take any text and create your own annotations by highlighting, scribbling notes in, or providing notes that point to related information in the same text or in others. 
It is hard to give specific direction without knowing exactly what your assignment is, but presumably you are being asked to annotate the text of "Crusoe in England" by Elizabeth Bishop. Alternatively, it may be that you are being asked to write an essay that leans upon the text and refers to it consistently throughout. Either way, your approach can be the same. You will need to break the text down and focus on specific passages and phrases to support whatever your argument is. 
Are you being asked to focus on the symbolism or themes in the poem? Bishop uses the character of Robinson Crusoe to make points about her own thoughts and concerns; the entire poem is an extended metaphor used to make these points. Crusoe's return to England and the associated emotions represent Bishop's own concern for her inability to produce poetry and express herself through her art. 
Are you being asked to focus on the structure of the poem? It could be described as a dramatic monologue, which includes the following characteristics:
A single person, who is patently not the poet, utters the speech that makes up the whole of the poem, in a specific situation at a critical moment.
This person addresses and interacts with one or more other people; however, we know of the auditors' presence, and what they say and do, only from clues in the discourse of the single speaker.
The main principle controlling the poet's choice and formulation of what the lyric speaker says is the speaker's temperament and character, which must be revealed to the reader in a way that enhances interest in the poem. 
You could also describe the poem as an elegy in tone, as elegies are mournful laments. 
Regardless of the topic, list out concrete points that you are trying to make and then associate them to specific moments in the poem. This will allow you to strongly support the points you are making, and a list of concrete points will keep you focused in your analysis. Some of the links below may help. Good luck!
http://www.modernamericanpoetry.org/criticism/susan-mccabe-crusoe-england

https://seapoetry.wordpress.com/2012/02/08/elegy-exile-elizabeth-bishops-poem-crusoe-in-england/

https://www.modernamericanpoetry.org/dashboard

How many bonds can a sulfur atom form?

This answer depends on how technical of an answer you are looking for. Most of the time a sulfur atom can form two bonds. It is in the same column of the periodic table of elements as oxygen is and oxygen will form two bonds. Most people would say that sulfur will do the same thing because it has six valence electrons. That means it has two more spots to fill in order to have a full outer shell. Of course sulfur is not oxygen, so it does not behave exactly the same way that oxygen behaves. For example, sulfur can form up to six bonds, which is what is the case in something like sulfuric acid -- (H2)SO4.   

The rejection of established religion in "The Open Boat" is shown by _____, _____, and the descriptions of humans as holy.

We see the rejection of established religion through the repetition of the men's appeal to the "seven mad gods," who they evidently used to believe would operate on some principle of justice, juxtaposed with the injustice of the men's situation. They repeat,

If I am going to be drowned—if I am going to be drowned—if I am going to be drowned, why, in the name of the seven mad gods, who rule the sea, was I allowed to come thus far and contemplate sand and trees?

There is something so unjust about being allowed to survive one's ship sinking only to drown in a lifeboat after suffering so much already. It's ironic and unfair, and the men seem to realize—especially after Billie's death—that their situation is evidence that no such gods exist, that no one cares about whether they live or die except themselves.
We also see the rejection of established religion through the men's reliance on their "subtle brotherhood" rather than a god. No one speaks of it, "But it dwelt in the boat, and each man felt it warm him." They rely on one another in every way, comfortable with the roles the little society they establish within the confines of the boat, and they are comforted only by one another. They are, in fact, they only comfort to be had in the face of harsh natural elements such as the appearance of the shark.

"The Open Boat" regards the arbitrary power of nature as the driving force of life and death rather than subscribing to the notion of an all-powerful "God" belonging to an established religion (like Christianity). In the midst of a stormy night aboard the boat, the text remarks on a man's attitude towards life and death while he is in mortal danger:

When it occurs to a man that nature does not regard him as important, and that she feels she would not maim the universe by disposing of him, he at first wishes to throw bricks at the temple, and he hates deeply the fact that there are no bricks and no temples.

Here, the author makes it quite plain that the text and the characters within believe that nature, not some God casting moral judgments, is the deciding factor in who lives and who dies. This revelation is what deepens one's resentment of the hypocrisy, even the absurdity, of established religious doctrine; this is what makes one want to "throw bricks at the temple."
In addition to the pervasive attitude towards nature as the true "God" of life, the story also conflates the absurd and the sacred to show that religion incorrectly defines both. This question references how the story describes people as "holy," which is true at many points; religious diction is used to valorize camaraderie among the crew. Yet there is also an important relationship between a notion of the "sacred" (holy) and the "profane" (obscene or absurd). At the end of the story, a completely naked man, typically a profane or absurd image, comes to the rescue of the crew. The naked man appears to "shine like a saint" though he is "naked as a tree in winter."
To summarize, Crane and his characters reject established religion by revering nature (rather than God) as the true all-powerful life-force and by conflating absurd and sacred images so that they are one in the same.

In The Outsiders, a church catches fire where Ponyboy and Johnny were staying. Why are there kids inside the burning church in the first place?

After killing Bob, a Soc, Johnny and Ponyboy escape to this church out in a pretty remote, mountainous location (which is wonderfully symbolic after Ponyboy's dreams of a simple life in the country) based on Dally's advice. After staying there for a while, Dally comes to check on them and takes them for a quick meal before leaving them again.
Interestingly, it is just before they are all aware of the fire that Johnny has a couple of pertinent revelations. First, he considers turning himself in to the police because he sees that as the best possible outcome for both him and Ponyboy. He also asks whether his (abusive) mother has asked about him, and Dally tells him that she hasn't. Pony realizes that as much as the group of friends support and love Johnny, they are no replacement for the actual love of a mother that Johnny has never had.
When they return the the church, they stop short when they realize that it is on fire. A group of kids has gathered in what seems to be a school picnic, and someone becomes frantic, yelling that some of the kids are missing.
Johnny and Pony leap into action, believing the church is ablaze because of one of their cigarettes. They knock out a window, climb into the church, and get all the kids out. Unfortunately, Johnny is hurt badly in the process.

In The Outsiders, Ponyboy and Johnny are hiding in the abandoned church because Johnny killed a Soc during a fight. Although he did this to keep the Socs from killing Ponyboy, Johnny and Ponyboy are scared they'll be arrested. They go to Dally for help, and he gives them money and tells them where to find an old abandoned church where they can hide.
After Johnny and Ponyboy have been hiding for a few days, Dally comes to check on them. He takes the boys to get food and fills them in on news of their fight with the Socs. On the way back to their hideout, they notice the church is on fire and that a group is gathered outside the church. Asking the first grownup he sees, Ponyboy finds out that the children are there for a school picnic on the mountain. A lady soon remarks that "some of the kids are missing" and shares that she told them not to play in the church. They hear faint yelling from inside, and it is at this time that Ponyboy and Johnny go into the burning church to save the children. Dally soon follows them.

Based on the Preface, Introduction, and Chapters 1-4 of Ian Haney López's "Dog Whistle Politics: How Coded Racial Appeals Have Reinvented Racism and Wrecked the Middle Class," what are the three types of racism and how are they used? What is strategic racism?

According to the author, the three types of racism are hate, structural racism, and implicit bias.
The racism-as-hate model is overt and easily identifiable; it emphasizes "discrete acts of bigotry by malicious individuals." Modern examples of this model include the obnoxious neo-Nazi skinheads who preach a white supremacist message. In America, this overt form of racism has been relegated by many to the dustbin of historical aberration. After all, the Ku Klux Klan no longer presents a dominant force in mainstream society; Klan members do not stand at street corners and harass black students whose only crime is to go to school. So, this "malice conception of racism" is used by those who prefer not to confront the covert forms of racism that still exist today.
Structural racism is another type of racism; it is also known as institutional racism. This type of racism confronts racism on a structural rather than on an individual level. It shows how "past mistreatment drives current inequalities." Examples of institutional or structural racism include the convict leasing systems in the South after the Civil War. Because of decades of incarceration and exploitation, affected black families faced vast deficits in health and wealth, compared to their white counterparts.
A third type of racism is implicit bias, where racism results from unconscious and instinctive thought. Implicit bias basically involves a preference for one's own race. However, the author prefers to think of implicit bias as common-sense racism, where individuals are biased not because of race but because of cultural constructs that assign value to societal stereotypes. For example, darker skin colors are deemed negatively as opposed to lighter skin tones. Lopez states that "the settled idea of whites as decent folks and blacks as dangerous work animals resolved for many, at the unconscious level, the moral rightness of convict leasing."
Essentially, Lopez uses the three types of racism to explain the biases that led to the proliferation of the convict leasing system.

This abhorrent system was an amalgam of hate-filled cruelty, deeply structured inequality from the slavery era that facilitated a new yet similar system of institutionalized exploitation and unconscious racial biases that allowed many to turn a blind eye to a ghastly arrangement.

Strategic racism refers to the practice of manipulating entrenched racial constructs to gain wealth and power. For example, the European conception of race focused on the supposed "differences" between the races. This race construct was used to justify European mistreatment and exploitation of the aboriginal races from Africa and North America. It was not until the 1700s that the people were divided into white, black, and red races, with "red and black savagery justifying the expropriation of Native American land and the enslavement of African labor."

What are the properties of magnets?

All the magnets have two types of poles: north-seeking poles or north poles and south-seeking poles or south poles.
The magnetic strength is the strongest at the poles of the magnet.
When you freely suspend a bar magnet in a horizontal position, the magnetic field of the bar magnet will interact with the magnetic field of the Earth. This will cause the bar magnet to come to rest in a north-south direction, where the north pole of the magnet points to the north pole of the Earth.
Like poles repel and unlike poles attract. (just as like charges repel and unlike charges attract).
Magnets attract magnetic materials such as iron, steel, cobalt and nickel.
The stronger a magnet, the larger will be the attractive or repulsive force between other magnets.
The closer together the two magnets are, the greater is the magnetic force between them.

Magnets have the following properties:
1. Magnets attract ferromagnetic materials, such as iron, nickel, and cobalt.
2. All magnets have two poles: north pole and south pole. There are no magnets containing only one pole.
3. Like poles of two magnets repel each other; opposite poles of two magnets attract each other.
4. The magnetic force of a magnet is stronger at its poles than in the middle.
5. The stronger the magnets and the closer two magnets are to each other, the greater the magnetic force exerted on each other.
6. When a bar magnet is suspended by a thread freely in horizontal position, its north pole will move towards the North Pole of the earth and its south pole will move towards the South Pole of the earth. This is because the earth is a giant magnet, and its geographical north pole is its magnetic south pole, and vice versa.
7. There are two types of magnets: permanent magnets and temporary magnets. Permanent magnets remain magnetized even without the influence of external magnetic field, such as a horseshoe magnet. Temporary magnets may lose their magnetism when removed from the external magnetic field, such as an iron pin.

x + y = 4 , y = x , y = 0 Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis.

We can use a rectangular strips to represent the region bounded by x+y=4, y=0 , and y=x revolved about the x-axis. As shown on the attached graph, we consider two sets of rectangular strip perpendicular to the x-axis (axis of revolution) to be able to use the Disk Method.  This is the case since the upper bound of the rectangular strip differs before and after x=2 .
 In this method, we follow the formula: V = int_a^b A(x) dx since we are using a vertical orientation of each rectangular strip with a thickness =dy.
Note: A = pir^2 where r= length of the rectangular strip.
 We may apply r = y_(above) - y_(below) .
For the region within the boundary values of x: [ 0,2] , we follow r = x-0=x
For the region within the boundary values of x: [ 2,4] , we follow r = 4-x-0=4-x
Note: x+y=4 can be rearranged as y=4-x.
Then the integral set-up will be:
V = int_0^2 pi*(x)^2dx+int_2^4 pi*(4-x)^2dx
For the first integral: int_0^2 pi*(x)^2dx , we may apply Power rule of integration: int x^n dx = x^(n+1)/(n+1) .
int_0^2 pi*(x)^2dx= pi* x^((2+1))/((2+1))|_0^2
                        =(pix^3)/3|_0^2
Apply definite integration formula: int_a^b f(y) dy= F(b)-F(a) .
(pix^3)/3|_0^2 =(pi(2)^3)/3-(pi(0)^3)/3
          =(8pi)/3- 0
          =(8pi)/3
For the indefinite integral of int_2^4 pi*(4-x)^2dx , we may u-substitution by letting u =4-x then du =-dx or (-1)du =dx .
The integral becomes :
int pi*(4-x)^2dx =int pi*u^2*(-1) du
Apply basic integration property: intc*f(x) dx = c int f(x) dx.
int pi*u^2*(-1) du = -pi int u^2 du
Apply power rule for integration: int x^n dy= x^(n+1)/(n+1).
-pi int u^2 du =-pi* u^((2+1))/((2+1))
                      = (-piu^3)/3
Plug-in u=4-x on (-piu^3)/3  we get:
int_2^4 pi*(4-x)^2dx =(-pi(4-x)^3)/3|_2^4 or ((x-4)^3pi)/3|_2^4
Apply the definite integral formula: int _a^b f(x) dx = F(b) - F(a) .
((x-4)^3pi)/3|_2^4 =((4-4)^3pi)/3-((2-4)^3pi)/3
                  = 0 - (-8pi)/3
                = (8pi)/3
Combing the two definite integrals, we get:
 
V = int_0^2 pi*(x)^2dx+int_2^4 pi*(4-x)^2dx
V = (8pi)/3+(8pi)/3
V =(16pi)/3 or 16.76 (approximated value).

What is the plot of "The Lady or the Tiger" by Stockton?

"The Lady, or the Tiger?" is set in a kingdom whose king had determined to turn justice into a spectacle determined solely by chance. He has built an arena in which accused criminals are faced with two doors and given free choice between them. Behind one door is a tiger, which kills and devours the chooser (thus confirming the guilt of the accused, at least in the king's mind). Behind the other door is a woman, to whom the accused (having been found innocent) would be immediately married upon choosing that door. In this way, guilt and innocence, punishment and reward, are all tied together in a single unbiased spectacle, determined solely by chance.
In this specific trial, we are watching the main character, a courtier who has pursued a romantic relationship with the princess (which was later found out by the king). For his transgressions, he receives that same trial by fortune—behind one door, a tiger, and the other, a wife.
However, this story ultimately hinges upon the princess, who is watching this spectacle and has successfully managed to find out which fate lies behind each door. Thus, the courtier looks to her for guidance, and she signals him an answer. The conundrum, however, lies in the princess's own motives. She is passionately in love with the courtier and likely jealous at the thought that he might marry another. So, is she going to save his life, or would she rather see him dead than married to another?
The answer to this question is not revealed. We see him select his door, in accordance with her signal, but his fate is left unwritten.

The plot of the story begins with a description of a king who constructed an arena where crime and virtue were punished and rewarded purely on chance. In the arena, the accused was expected to choose between two doors, which presented different fates. A marauding tiger was behind one of the doors and a lady behind the other. Selection of the door with the tiger led to death, while the door with the lady was followed by a wedding ceremony.  As the story unfolds, the king’s daughter and one of the palace’s courtiers fell in love and soon the king discovered the affair. The young man was thrown into prison to await his fate in the arena. The princess learned what each door presented. In addition, she knew the lady behind the door and suspected that she had feelings for the courtier. The princess was forced to decide whether to allow the youth to marry the lady or face the tiger. In the arena, the princess signaled the youth to open the door on the right after they exchanged glances. The plot ends after the youth opens the door on the right and the reader is left in suspense, not knowing what came forth.

In "Old Love" by Jeffery Archer, why did William take his life after his wife died?

Based on the story's context, William simply felt that he couldn't bear to be apart from Phillipa, even in death. In all the years of their marriage, "they were never apart for more than a few hours." In fact, the couple had been together since the day they jointly won the Charles Oldham Memorial Prize.
Also, both Phillipa and William had been naturally competitive with each other before Phillipa's death. There is every indication that William wanted to best Phillipa, even after her death: "Forgive me, but I had to let her know." What this quote means is that William wanted to let Phillipa know there was such a word as "whym-wham" in the Oxford English Dictionary. He decided to follow her into the grave (and presumably into the afterlife) in order to let her know this.
On the surface, this might seem a little extreme. Why would a man kill himself simply to prove the existence of an obscure word? To answer the question, we must remember that William had always enjoyed sparring with Phillipa while she lived. From the moment he fell in love with her, his affection for Phillipa had been wrapped up in a friendly rivalry. The narrative implies that William would be lost without Phillipa and that he would find it unbearable to live without the pleasure of the good-natured rivalry they had always enjoyed.
The story of why William took his life actually began with a crossword puzzle. For many mornings, Phillipa had relished completing the Times crossword before William got to the breakfast table. On one particular morning (to William's great amusement), Phillipa failed to complete an entry. So, based on the clue "Skelton reported that this landed in the soup," William filled in the word "whym-wham" for the last entry. Although Phillipa argued against the existence of such a word, William was adamant that the word existed.
Phillipa died of a heart attack before William could win his bet. By the time the Senior Tutor and Master at Merton College (one of Oxford University's 38 colleges) knocked on William's door, the elderly professor was already dead from a self-inflicted gunshot wound. William preferred to die rather than live without his beloved Phillipa.

What stood in the way of Napoleon's plan of rebuilding France's empire in North America?

Napolean never, at least publicly, expressed interest in rebuilding the lost French colonies it once had in North America. Instead, he was more focused on building and maintaining a European empire. To attempt to retake its former colony in Quebec would have proved too expensive and risky to do while trying to gain supremacy across the Atlantic.
After the defeat of the French fleet at the Battle of the Nile in 1798, it would have been very difficult, if not impossible, for France to fight a war across the ocean. The British navy was simply too strong for the fragmented and weak French navy.
After Napoleon won control of Spain, the Louisiana territory came under the control of France. Napolean viewed this territory as too big and too unimportant to his interests to bother delegating resources to defend. By selling the territory to the United States, Napolean eliminated the need to defend a large territory in North America from the British. Instead, he could focus on fighting them closer to home in Europe.
Also, by the beginning of the nineteenth century, France was already struggling to hold on to the few territories in the hemisphere that it already had. The Haitian Revolution was a humiliating defeat for France that cost the nation one of its most profitable territories and destroyed an entire army. Napoleon decided it was better to cut his losses in the region, at least until he could secure an unquestioned foothold in Europe.

What is Appointment in Samarra about?

Appointment in Samarra is about the events in the last three days of Julian English’s life. Julian is a well-to-do white, Anglo-Saxon, Protestant man living in a small Pennsylvania town in 1930. He runs a Cadillac dealership and lives with his wife, Caroline, on the sought-after Lantenengo Street. The story narrates Julian’s self-destruction, starting with his disruption of the rules of respectable behavior and ending with his suicide. However, the novel is not just about Julian English. It is also about Gibbsville, a microcosm of American life on the cusp of the Great Depression, and about the meaning of life, work, money, marriage, sex, and death for each of the social groups in the town.

How does the Winslow Boy give you a holistic understanding of the political, social, and economic climate of England? Support with references from the play and base on analyses of language, form, and structure of the play.

I think the theme of "family honor," and the lengths to which the Winslows will go to protect it, is used by Rattigan as the basis for a complex critique of British notions of justice, marriage, and the class system.
Justice: The play draws a distinction between "justice," or the finding of the Admiralty, and the notion of "let right be done," or finding the actual truth of the matter. Ultimately, what is at issue is less Ronnie's alleged crime of stealing five shillings and more the tradition and bureaucracy that mandates his expulsion from school and his eventual trial. The scene in act II where Sir Robert examines Ronnie and is convinced of his innocence is meant to be understood as a moment in which the truth comes out, but, in fact, Sir Robert's involvement only facilitates what can only be thought of as a kind of transaction: the Admiralty does give up its case, but only after the process has consumed the Winslow fortune and left their "honor" a hollow shell. (In this sense the play recalls the Chancery suit in Dickens's Bleak House.)
Class: The Winslows are representative of the rising British middle class because they are not truly wealthy, but nevertheless aspire to a higher social standing. Much of the first act is concerned with the father discussing (or criticizing) his children's prospects for the future. Although Ronnie, according to his father, is a brighter prospect than his brother, who is currently studying at Oxford and looking forward to a career in the civil service, it is Ronnie's expulsion that throws the brother's future into doubt, since the family can no longer afford his tuition. There is a kind of dissonance in the Winslow's apparent prosperity and the sacrifices they must make to pursue Ronnie's case. While on the face of it it may seem like a noble sacrifice, there is also something degrading about it.
Marriage: Ronnie's brilliant suffragette sister, Catherine, is also affected by the trail and its outcome. Catherine has entered into an engagement with an Army officer, the transactional nature of which is made plain in the first act when the father discusses the twelve hundred pounds he has set aside for her dowry. The engagement ends in act three when it becomes clear that Catherine's fiancé is more concerned about the dwindling Winslow finances than he is with Catherine herself. Catherine's intelligence and independence, best exemplified by her urging her father to pursue the case over her fiance's objections, prove to be of little value in helping her family improve their social standing. The play closes with her marriage prospects still in doubt.
It is perhaps ironic that the entire play is set in that symbol of British gentility, the Winslow's drawing room. While Ronnie's vindication may seem like a vindication of the Winslow name, the personal and financial costs of that victory are very high and serve to undercut their ability to attain a higher social status.

Single Variable Calculus, Chapter 6, 6.2, Section 6.2, Problem 20

Find the value generated by rotating $\mathscr{R}_1$ about $OC$



If you rotate $\mathscr{R}_1$ about $OC$, its cross section form a circular washer with outer radius 1 and inner radius $\sqrt[3]{y}$. Thus, the cross sectional area can be computed by subtracting the area of the outer circle to the inner circle. Hence, $A_{\text{outer}} = \pi (1)^2$ and $A_{\text{inner}} = \pi \left( \sqrt[3]{y}\right)^2$


Therefore, the value is...

$
\begin{equation}
\begin{aligned}
V &= \int^1_0 \left[ \pi (1)^2 - \pi (\sqrt[3]{y})^2 \right] dy\\
\\
V &= \pi \left[ y - \frac{y^{\frac{5}{3}}}{\frac{5}{3}}\right]^1_0\\
\\
V &= \pi \left( \left[ 1 - \frac{(1)^{\frac{5}{3}}}{\frac{5}{3}}\right] - \left[ 0 -\frac{(0)^{\frac{5}{3}}}{\frac{5}{3}} \right] \right)\\
\\
V &= \frac{2\pi}{5} \text{ cubic units}
\end{aligned}
\end{equation}
$

How does the American Revolution and the American people appear in Rip Van Winkle? How do we learn history from fiction, and how does fiction reshape history?

One of the points of "Rip Van Winkle" is to contrast the old, lazy, apathetic mindset of America under British rule with the vigor, enthusiasm and energy of the newly independent United States. Rip is a representative of the old way of thinking: he is happy to be under the rule of King George III, doesn't work hard, and doesn't have much interest in bettering himself.
After he awakes from his twenty years of sleep, he discovers a whole new world in his once sleepy village:

The very character of the people seemed changed. There was a busy, bustling, disputatious tone about it, instead of the accustomed phlegm and drowsy tranquillity. ... a lean, bilious-looking fellow, with his pockets full of handbills, was haranguing vehemently about rights of citizens—elections—members of Congress—liberty—Bunker’s hill—heroes of seventy-six—and other words, which were a perfect Babylonish jargon to the bewildered Van Winkle.

The town has gone from apathetic to alive. People, on fire about an upcoming election, question Rip as to whether he is "Federal or Democrat." Suddenly, politics matter, and people want to do more than discuss old news. They are actual participants in their own governance.
In reading the story, we learn that history changed during a twenty year period while Rip slept: The thirteen British colonies achieved their independence and formed a republic. But the story also shapes history: independence is not presented as a value-neutral change. In depicting, in an exaggerated way, the transformation of a village from apathy to energy, Irving participates in creating an American mythology: independence has wrought self-sufficiency and great positive changes in average people. Clearly, the American people were, on the whole, vigorous and energetic before the Revolution (or they wouldn't have survived in a hostile land), but Irving's story highlights and helps form a new spirit of national optimism.

What are the striking differences between the personalities of a mother and a friend?

Alhough a mother and a friend may both have love for the individual in consideration, these roles typically have significantly different approaches in how they think of and interact with their child or friend.
Mothers try to have their child's best interests at heart, especially when they consider long-term goals and security. While friendships also involve care and well-wishes, friends may not have as much foresight as parents when it comes to making big decisions. For example, if a person was really passionate about music, a mother would be more likely to suggest that this person get a degree in music, while a friend might suggest the individual take his or her band on the road. Both are potentially good decisions, but the mother's suggestion, in this case, would offer far more long-term job security.
The differing personalities of mothers and friends can sometimes create conflict in a person's life. Young people are still mentally and emotionally developing and need time and space to figure themselves out and experiment with identities. With that in mind, friends can have positive or negative influences on each other. Social deviation encouraged by friends can be a good learning experience, but also often brings heavy consequences. Mothers are less likely to encourage their children to participate in social deviation, often because they've learned lessons from their own experiments! 
The relationship roles of mother and friend both carry the unfortunate fact that we often think of people as existing only in their relationship to us. It can be hard for a mother to imagine her child as anyone but the specific person she knows, and vice versa. I can certainly say I sometimes have a hard time imagining my mother as anyone but my mom. Friends, too, may be limited in their understanding of a person. I would argue that where mothers and friends differ in their understanding of a person is that a mother is more likely to know her child's fine-tuned emotional nature, while a friend is more likely to know a person's outward, socially-presented, personality.
In general, I think mothers take far more responsibility when it comes to their child's actions and how those actions might reflect upon them. A friend may feel a sense of distance from a person whose actions do not reflect upon them personally. When things are seriously tough, a friend might even have the option to walk away from the friendship, while a mother-child relationship is for life.

How do you think Harper Lee felt when she was writing To Kill A Mockingbird?

She was most probably thinking about how best to do justice to her own experiences of growing up in Alabama during the 1930s, as well as using her background to make general points that would resonate with people who hadn't shared those experiences. To Kill a Mockingbird is a heavily autobiographical work, and so, in writing the book, Harper Lee will have wanted to share some of her life experiences—especially with those who wouldn't have seen or encountered the kind of things that she had.
Doubtless it must have been very important for her to present as truthful an account as possible of what life in a small Southern town was like in those days. This was her world, after all, a world with its own unique rhythms, traditions, and conventions. It's against the background of small-town Southern life that Harper Lee set out to explore more universal themes.
Of course we cannot be absolutely sure as to what Harper Lee felt when she was writing To Kill a Mockingbird, but it seems a fair assumption that she wanted to deal with both the particular (the details of Southern life) and the general (broad themes such as growing-up, racial intolerance and empathy).

Find all the real and complex roots of 8.

Your question is equivalent to solving for x  when x^3-8=0 .
Since we know that the real cube root of 8 is 2, we can divide by x-2  to get (x^3-8)/(x-2)=x^2+2x+4=0 (Use long division).
This equation can now be solved by completing the square:
x^2+2x=-4 
x^2+2x+1=-3
(x+1)^2=-3
x+1=+-isqrt(3)
X=-1+-isqrt(3)

Let the complex number z=8 . Rewrite this in polar form as z=8e^(i(0+2pi*n)) .
z^(1/3)=(8e^(i(0+2pi*n)))^(1/3)
z^(1/3)=2e^(i(0+(2pi*n)/3))
Here, theta becomes 3 distinct angles for all integers n . 0^@ , 120^@ , and 240^@ . The value at 0^@ is the real root, and the other two are complex roots. These can be represented as equal points around a circle of radius 2 in the complex plane.
The roots in cartesian coordinates are
8^(1/3)={2, -1+i sqrt(3), -1-i sqrt(3)}

Describe what the use of italics signals to the readers.

Italics are used in a couple of different ways in this book.
First, italics are used when writing the name of a ship. For example, the author writes Andrea Gail in italics to alert readers that he is talking about the ship. This is a fairly standard grammatical format, and I don't think that this is what the question is asking about.
The other main use of italics in the book is for conversations that are taking place between people; however, italics are not used for every conversation. They are only used for conversations or communications that are happening over radio or telephone.

What's also key about the dialogue in this book is whether or not it has quotation marks around it. The author has stated that no dialogue was made up; however, some of the dialogue is based on people's recollections. If it's not in quotation marks, the dialogue does not represent word-for-word what that person actually said. If the dialogue is actually a verbatim quote, then quotation marks are used.

A runner covers a distance of 23.5 miles in 2hrs a. What is the runner's velocity? b What is the runner's velocity in m/s ? (1mi=1609.3)?

The first part of this question requires you to know the definition of velocity:
a) Velocity, in this case, is defined as distance traveled over a period of time (distance/time).
The runner moves a distance of 23.5 miles in 2 hours. The velocity of the runner is therefore (23.5 miles)/(2 hours), which is equal to 11.75 miles/hour.
The second part of this question requires you to know the conversion between miles and meters and hours and seconds:
b) Meters are a unit of measurement, meaning that they have a direct conversion value to miles. That number is 1609.344 meters to 1 mile.
We now need the number of seconds in an hour. This conversion is well-known. There are sixty minutes in an hour and sixty seconds in a minute. This means that the number of seconds in an hour is (60 x 60) or 3600 seconds.
Now that we have the number of meters in a mile and the number of seconds in an hour, we are ready to convert our equation.
 
(11.75 miles/hour) * (1609.344 meters/1 mile) * (1 hour/3600 seconds) = 5.25 meters/second.
 
 

First, let us find the runner's velocity in miles per hour. The velocity v can be found as the distance by the time during which the distance was traveled:
v = 23.5/2 = 11.75 miles per hour (mph).
To convert the velocity from the miles per hour to meters per second, consider that 1 mile = 1.6093 kilometers = 1609.3 meters and 
1 hour = 60 minutes = 60*60 = 3600 seconds.
Then, 11.75 mph = 11.75* (1609.3 m)/(3600 s) = 5.253 m/s
So, if the runner covers a distance of 23.5 miles in 3 hours, his velocity in meters per second is 5.253 m/s.

What are five items that Scout and Jem find in the Radleys' tree?

Scout’s finding of items in the tree is an interesting part of the novel. It all begins in chapter 4 when Scout finds gum in the tree knot. At first, she does not know what to do with it, but she winds up taking it. Here is the quote:

I stood on tiptoe, hastily looked around once more, reached into the hole, and withdrew two pieces of chewing gum minus their outer wrappers.

On the next day, Jem and Scout find something else. They are wrapped in velvet: Indian-head pennies. Later, they find a gray ball of twine. By this time, the children are really perplexed. Is someone leaving these things for them, or will someone come back for them? Here is what Scout says to Jem:

“Don’t take it, Jem,” I said. “This is somebody’s hidin‘ place.”
“I don’t think so, Scout.”

The gifts in the tree knot do not stop here. Jem and Scout also find carved soap figures that look like them. They also find more gum, a spelling medal, and a pocket-watch.
In the end, Mr. Radley comes and puts cement in the knot of the tree to end the exchange of gifts. There is a small inkling that Boo might be the one leaving these gifts, but no one can say for sure—certainly not the children

Jem and Scout find several small items in the knothole of the Radley tree. Boo Radley is the anonymous gift giver, who gives the children an entire pack of Wrigley's Double-Mint chewing gum, two scrubbed and polished Indian Head pennies, a ball of twine, two carved soap figures, a tarnished spelling bee medal, and a broken pocket watch on a chain. These small gifts are tokens of Boo Radley's friendship and appreciation. When Jem and Scout write a letter to the anonymous gift giver, Jem is unable to put the note into the knothole of the oak tree because Nathan Radley filled it with cement. Nathan Radley then lies to Jem by telling him that he was forced to fill the knothole of the tree with cement because it was dying.

Calculus of a Single Variable, Chapter 9, 9.10, Section 9.10, Problem 23

Recall binomial series follows:
(1+x)^k=sum_(n=0)^oo (k(k-1)(k-2)...(k-n+1))/(n!)x^n
or
(1+x)^k = 1 + kx + (k(k-1))/(2!) x^2 + (k(k-1)(k-2))/(3!)x^3 +(k(k-1)(k-2)(k-3))/(4!)x^4+...
To evaluate given function f(x) =sqrt(1+x) , we may apply radical property: sqrt(x)= x^(1/2) . The function becomes:
f(x) =sqrt(1+x)
= (1+x)^(1/2)
or (1+x)^(0.5)
By comparing "(1+x)^k " with "(1+x)^(0.5) ”, we have the corresponding values:
x=x and k =0.5
Plug-in the values on the formula for binomial series, we get:
(1+x)^(0.5) =sum_(n=0)^oo (0.5(0.5-1)(0.5-2)...(0.5-n+1))/(n!)x^n
=1 + 0.5x + (0.5(0.5-1))/(2!) x^2 + (0.5(0.5-1)(0.5-2))/(3!)x^3 +(0.5(0.5-1)(0.5-2)(0.5-3))/(4!)x^4+...
=1 + 1/2x -0.25/(2!) x^2 + 0.375/(3!)x^3 -0.9375/(4!)x^4+...
=1 + x/2 -x^2/8 +x^3/16 -(5x^4)/128 +...
Therefore, the Maclaurin series for the function f(x) =sqrt(1+x) can be expressed as:
sqrt(1+x)=1 + x/2 -x^2/8 +x^3/16 -(5x^4)/128 +...

Why did Brian improve his shelter and protect his food in Hatchet?

In chapter 14, Brain decides to rebuild his shelter after he learns that it is not sufficient to keep out animals. One night, he awakens to a skunk digging up his stashed turtle eggs. This episode goes badly for him, as he ends up painfully blinded for a few hours after getting sprayed by the skunk. It becomes absolutely clear to Brian that he must be able to protect his food, or he will starve.
The next day, Brian tears down his old shelter and spends three days building a better one. He constructs walls of tightly woven branches that he feels should be sufficient to keep out any creatures that are after his food stores. He converts a hollow in the rock above his shelter into a food pantry by constructing a door to cover it. He also creates a little wall in the pond in which he can trap fish to more efficiently catch them as needed.
Food, Brian has realized, is the most important part of survival. The episode with the skunk has taught him that he has to be strategic and think ahead about preserving the food that he has gathered.

In chapter 14 of Hatchet, Brian learns that there isn't room for mistakes in survival. He wakes in the middle of the night to find a skunk trying to steal the turtle eggs he buried for food. Brian almost smiles when he first sees the skunk but then quickly realizes that he may lose his food supply. After throwing a handful of sand, Brian learns a most unpleasant lesson as the skunk sprays him. In his rush to get to the lake to wash his eyes, he destroys his shelter.
Brian comes to the realization that "food is all," and he needs to take steps to protect whatever food he has. His shelter needs to do more than just protect him from the elements; it needs to provide safety and protection. He proceeds to build a more effective shelter, because he knows that in nature there is a constant competition for food. Brian continues to learn lessons from his predicament, the latest of which is "nothing in nature was lazy."

College Algebra, Chapter 2, 2.3, Section 2.3, Problem 18

Determine an appropriate viewing rectangle for the equation $y = x(x+6)(x-9)$ and use it to draw the graph.

We can determine the appropriate viewing rectangle easier by getting the $x$ and $y$-intercept at the equation. So, if we set $y=0$

$
\begin{equation}
\begin{aligned}
0 &= x(x+6)(x-9) && \text{Solve for } x\\
\\
x &= 0 , x = -6 \text{ and} x =9
\end{aligned}
\end{equation}
$

Thus, the $x$-intercept are at $(0,0), (-6,0)$ and $(9,0)$

Next, solving for $y$-intercept, where $x = 0$

$
\begin{equation}
\begin{aligned}
y &= 0(0+6)(0-9)\\
\\
y &= 0
\end{aligned}
\end{equation}
$


The $y$-intercept is at $(0,0)$
Hence, we assume that the appropriate viewing rectangle is $[-10,10]$ by $[-300,300]$

Where was the place of execution?

The unfortunate Egeon of Syracuse is being led to his execution in Ephesus. He's been found guilty of the very serious crime of traveling between the two cities. Syracuse and Ephesus don't get on very well; they're commercial rivals and perceive each other as serious strategic and economic threats. Relations are so strained between the two cities that anyone from Syracuse caught in Ephesus must pay a heavy fine of 1,000 marks. If they're unable to pay, then they will be executed. Unfortunately for Egeon, he doesn't have any money, hence his being led off to be executed. Thankfully, however, Egeon is able to earn the sympathy of Solinus, the Duke of Ephesus, who gives him the opportunity to save his life. Egeon has twenty-four hours to find someone who'll pay for his ransom. If not, then the law must take its course.

Precalculus, Chapter 5, 5.3, Section 5.3, Problem 27

3tan^3(x)=tan(x)
3tan^3(x)-tan(x)=0
tan(x)(3tan^2(x)-1)=0 =>
tan(x)=0 , (3tan^2(x)-1)=0
General solutions for tan(x)=0 are,
x=0+pin
Solutions in the range 0<=x<=2pi are,
x=0 , pi ,2pi
solving (3tan^2(x)-1)=0
3tan^2(x)=1
tan^2(x)=1/3
tan(x)=+-1/sqrt(3)
General solutions for tan(x)=-1/sqrt(3) are,
x=(5pi)/6+pin
solutions in the range 0<=x<=2pi are
x=(5pi)/6 , (11pi)/6
General solutions for tan(x)=1/sqrt(3) are
x=pi/6+pin
solutions in the range 0<=x<=2pi are,
x=pi/6 , (7pi)/6
Therefore solutions are,
x=0 , pi/6 , pi , (5pi)/6 , (7pi)/6 , (11pi)/6 , 2pi

Based on "The Love Suicides at Amijima" by Chikamatsu Monzaemon, provide information that can be used to write a background on the author and discuss how it influenced him to write the story.

Chikamatsu Monzaemon was a drama writer who made his name writing historically themed dramas. Rather than being performed by actors in a theatre setting, Chikamatsu's work was chanted by storytellers. In many cases, his works were also told through rudimentary puppet shows and artistic backdrops. The author was born in 1652 in what is the modern-day Fukui prefecture of Japan. Although he became a famous playwright, Chikamatsu was born into a family of samurai warriors. After his father gave up his military career, Chikamatsu's family moved to Kyoto. It is not clear how Chikamatsu came to be interested in theatre, but he began writing Kabuki plays shortly after his move to Kyoto and eventually moved to Osaka to pursue his career. There are actually two similarly titled stories by Chikamatsu, including "The Love Suicides at Sonezaki" and "Double Suicide at Amijima." "The Love Suicides at Sonezaki" marked a turning point in Chikamatsu's career. Previously, his work had focused on embellished historical tales of the nobility. "The Love Suicides at Sonezaki" and his newer works focused on everyday people, including average families, criminals and merchants. The dramatic tale of a double suicide was so popular that it inspired the author to write many others like it, effectively dividing his body of work into two distinct genres. Years later, he wrote "Double Suicide at Amijima," which focused on similar subject matter. Chikamatsu was so moved by the event that he finished his work almost immediately after he learned of it. Although the inspiration for Chikamatsu's earlier works is largely unknown, it is clear that the report of the actual double suicide "The Love Suicides at Sonezaki" was based on was responsible for sparking his interest in contemporary drama. When you consider that his early works were embellished stories of actual events, it becomes clear that Chikamatsu was more heavily influenced by the world around him than by fantasy or other works of fiction. From that point on, he continued to write about both historical and contemporary drama.
https://www.britannica.com/biography/Chikamatsu-Monzaemon

How does the play resolve the philosophical questions raised by Jocasta's judgment of the oracles?

The play resolves the philosophical questions raised by Jocasta's judgment of the oracle and of prophecy in general when all of the prophecies are shown to have come true. Laius was, in fact, killed by his child, despite his and Jocasta's best efforts to avoid the prophecy by ordering Oedipus's murder when he was a baby. Oedipus did, in fact, kill his father and marry his mother, despite his best efforts to avoid the prophecy by refusing to return to Corinth, the city he believes to be his home and the home of his parents. Teiresias also proved to be absolutely correct in his knowledge of both past and future events. Jocasta is shown to be absolutely wrong in her estimation of the value and accuracy of prophecy.

In Oedipus Rex Jocasta displays a marked skepticism towards the prophecies of the Delphic oracle. There could be more than an element of self-preservation involved here. After all, the oracle predicts that Jocasta and Laius's child would grow up to marry her and kill him. As far as Jocasta is concerned, that simply cannot happen. Her child was abandoned, exposed out in the open air; there is just no way he could have survived. It is in Jocasta's interests for the oracle's prophecies not to be true, and so it's not surprising that she should be so dismissive.
In response to Jocasta's skepticism, the Chorus makes clear just how serious a matter insolence towards the gods really is, how it brings utter ruin upon all those who display it. This feeds into a broader philosophical consideration of the relationship between gods and mortals. It's never clearly established whether Jocasta is skeptical of prophecies in general or just those that predict terrible consequences for her and her family. If it's the former, then she is indeed displaying insolence towards the gods. The resolution of this philosophical problem comes when the full, terrifying truth of the prophecy is made manifest and ruin is indeed brought crashing down upon Jocasta and her whole family.

After Soraya tells Amir about her past, she says, "I'm so lucky to have found you. You're so different from every Afghan guy I've met” (180). How do Afghan women fare in America? Are they any better off than they were in Afghanistan before the Taliban seized power? There is a noticeable absence of women in the novel. How is this significant?

Afghan women are treated with sexism in America. For example, Amir says that while fathers and sons can speak openly about women, no Afghan daughter can ever openly discuss a man with her father. In addition, a father would not bring up a man with his daughter unless the man were an approved suitor whose father has asked the girl's parents' permission for marriage (147). While boys run around and largely do as they wish, girls are expected to remain virtuous and prepare for their weddings. Soraya tells Amir that she was living with a man, and her father threatened to shoot the man and himself if Soraya did not return home. One might argue that, in the book, women are not much better off in America than they were in Afghanistan before the Taliban.
The absence of women in the novel shows that women are cloistered away. Afghan boys spend most of their time with other boys and men. The role of women in the context of this society has been reduced to the point at which they are barely noticeable. Instead, men are figures who take part in society, while women are behind closed doors.

what are some examples of research questions about mathematics in elementary grades?

Here are some areas of interest and questions that arise in mathematics teaching in the elementary grades:
Curriculum -- What content should be taught? When should it be taught? What are the objectives to teaching a specific idea or group of ideas? How should the content be arranged within a particular year and across the elementary grades? When should algebraic ideas be introduced?
Learning -- How important is discovery learning? How can discovery learning best be utilized in the classroom? What is the most effective use of manipulatives? Which fosters better retention - teaching for understanding or practical applications?
General -- How effective is homework? How much time should be devoted to practicing skills? How should classes be organized? How can we implement differentiated instruction especially as related to gifted or remedial students? Should we insist that elementary teachers be math specialists? Should we integrate computer assisted instruction, and if so what are the long term ramifications and limitations? How should gender inequality be addressed at the elementary level?
https://eric.ed.gov/?id=ED052033

I have to write an essay using Aristotle's definition of a tragic hero to compare the tragic stories of Othello and Oedipus, and then after that, I have to state which is a better tragic hero than the other. How do I start off this essay, and how do I compare them?

A good place to start such an essay might begin with a definition of the term, “tragic hero,” as defined by Aristotle in Poetics, and how that particular character elicits an emotional connection in and builds a relationship with his audience. While doing this, one might also touch upon the reasons why audiences are drawn to tragedies and what they gain from indulging in an instance of fictional schadenfreude.
With the definition of tragic hero firmly in place, one might next begin an examination of the characters, Othello and Oedipus, noting how each embodies (or perhaps does not embody) the Aristotelian ideal: how do they elicit respect, fear, and pity in their audiences? What fatal flaws lead to their respective downfalls, what do they learn as a result, and lastly, how does each accept or reject their fate? A thorough examination of the character arc--the journeys that Othello and Oedipus make--as well as a discussion of these, might also prove very useful when arguing the last section of your question, that of tragic degree.
Although some scholars and critics consider the character of Oedipus the penultimate tragic hero, your experience might differ. It might be helpful to think about whom you respected or related to more at the start of each play, whose journey engaged you more, and ultimately, which ending you found more satisfying.  
 
 
http://www.classics.upenn.edu/myth/php/tragedy/index.php?page=oedhero

Single Variable Calculus, Chapter 3, 3.1, Section 3.1, Problem 10

a.) Determine the slope of the tangent to the curve $\displaystyle y = \frac{1}{\sqrt{x}}$ at the point where $x = a$

Using the equation

$\displaystyle m = \lim \limits_{h \to 0} \frac{f(a + h) - f(a)}{h}$

Let $\displaystyle f(x) = \frac{1}{\sqrt{x}}$. So the slope of the tangent to the curve at the point where $x = a$ is


$
\begin{equation}
\begin{aligned}

\displaystyle m =& \lim \limits_{h \to 0} \frac{f(a + h) - f(a)}{h}
&& \\
\\
\displaystyle m =& \lim \limits_{h \to 0} \frac{\frac{1}{\sqrt{a + h}} - \frac{1}{\sqrt{a}}}{h}
&& \text{Substitute value of $a$}\\
\\
\displaystyle m =& \lim \limits_{h \to 0} \frac{\sqrt{a} - \sqrt{a + h}}{(h)(\sqrt{a}) (\sqrt{a + h})}
&& \text{Get the LCD on the numerator and simplify}\\
\\
\displaystyle m =& \lim \limits_{h \to 0} \frac{\sqrt{a} - \sqrt{a + h}}{(h)(\sqrt{a}) (\sqrt{a + h})} \cdot
\frac{\sqrt{a} + \sqrt{a + h}}{\sqrt{a} + \sqrt{a + h}}
&& \text{Multiply both numerator and denominator by $(\sqrt{a} + \sqrt{a + h})$}\\
\\
\displaystyle m =& \frac{a - (a+ h)}{(h)(\sqrt{a})(\sqrt{a + h})(\sqrt{a} + \sqrt{a + h})}
&& \text{Combine like terms}\\
\\
\displaystyle m =& \frac{-\cancel{h}}{\cancel{(h)}(\sqrt{a})(\sqrt{a + h})(\sqrt{a} + \sqrt{a + h})}
&& \text{Cancel out like terms}\\
\\
\displaystyle m =& \frac{-1}{(\sqrt{a}) (\sqrt{a + h})(\sqrt{a} + \sqrt{a + h})} = \frac{-1}{(\sqrt{a}) (\sqrt{a + 0}) (\sqrt{a} + \sqrt{a + 0})}
&& \text{Evaluate the limit}\\
\\
\displaystyle m =& \frac{-1}{2a \sqrt{a}}
&& \text{Slope of the tangent}

\end{aligned}
\end{equation}
$


b.) Determine the equations of the tangent lines at the points $(1, 1)$ and $\displaystyle\left(4, \frac{1}{2}\right)$

Solving for the equation of the tangent line at $(1, 1)$

Using the equation of slope of the tangent in part (a), we have


$
\begin{equation}
\begin{aligned}

a =& 1
&& \text{So the slope is }\\
\\
m =& \frac{-1}{2a \sqrt{a}}
&& \\
\\
m =& \frac{-1}{2(1) \sqrt{1}}
&& \text{Substitute value of $a$}\\
\\
m =& \frac{-1}{2}
&& \text{Slope of the tangent line at $(1, 1)$}\\
\end{aligned}
\end{equation}
$

Using point slope form

$
\begin{equation}
\begin{aligned}

y - y_1 =& m ( x - x_1)
&& \\
\\
y - 1 =& \frac{-1}{2}(x - 1)
&& \text{Substitute value of $x, y$ and $m$}\\
\\
y - 1 =& \frac{- x + 1}{2} + 1
&& \text{Get the LCD}\\
\\
y =& \frac{- x + 1 + 2}{2}
&& \text{Combine like terms}
\\
y =& \frac{-x + 3}{2}
\end{aligned}
\end{equation}
$

Therefore,
The equation of the tangent line at $(1,1)$ is $ y = \displaystyle \frac{-x + 3}{2}$

Solving for the equation of the tangent line at $\displaystyle \left(4, \frac{1}{2}\right)$

Using the equation of slope of the tangent in part (a), we have $a = 4$. So the slope is


$
\begin{equation}
\begin{aligned}

m =& \frac{-1}{2a \sqrt{a}}
&& \\
\\
m =& \frac{-1}{2(4)\sqrt{4}}
&& \text{Substitute the value of $x, y$ and $m$}\\
\\
m =& \frac{-1}{16}
&& \text{Slope of the tangent line at $\left(4, \frac{1}{2}\right)$}

\end{aligned}
\end{equation}
$


Using point slope form



$
\begin{equation}
\begin{aligned}

y - y_1 =& m ( x - x_1)
&& \\
\\
y - \frac{1}{2} =& \frac{-1}{16} (x - 4 )
&& \text{Substitute value of $x, y$ and $m$}\\
\\
y =& \frac{-x + 4}{16} + \frac{1}{2}
&& \text{Get the LCD}\\
\\
y =& \frac{-x + 4 + 8}{16}
&& \text{Combine like terms}
\\
y =& \displaystyle \frac{-x + 12}{16}
\end{aligned}
\end{equation}
$


Therefore,
The equation of the tangent line at $\displaystyle\left(4, \frac{1}{2}\right)$ is $ y = \displaystyle \frac{-x + 12}{16}$


c.) Graph the curve and both tangent lines on a common screen.

Compare and contrast the subject matter of the Iliad and Dante's Inferno.

Homer's Iliad and Dante's Inferno are both epic poems that examine the negative consequences of unbridled human emotion—of giving in to unethical personal desires that harm others.
A big difference between the two works is the role of the gods and of destiny. A background story to The Iliad explains the role of the gods in setting up the conditions that lead to the Trojan War, the subject of the poem. Why does Paris of Troy abduct Helen, Queen of Sparta and wife of Menaleus, setting into motion the Trojan War? The goddesses Eris and Aphrodite had already set him up to carry out this brazen and selfish act. It was his destiny.
Sometime before the Trojan War begins, Zeus holds a banquet for the wedding of the goddess Thetis and King Peleus (parents of Achilles) and does not invite Eris, goddess of discord. She shows up anyway, determined to make trouble in revenge for the snub. She brings a golden apple for "the fairest." Zeus gives the touchy assignment of judging who is the fairest to Paris, a Spartan prince. When he chooses Aphrodite over Athena and Hera, the goddess of love rewards him with the most beautiful woman in the world: Helen, Queen of Sparta (later known as Helen of Troy). So Helen, though already married, and Paris become entwined by destiny as well as by unethical desires, thereby bringing about the Trojan War and all the loss, death, and brutality that ensues. Helen herself is a child born (hatched) as a result of one of Zeus's many indiscretions—the seduction of the mortal Leda while in the form of a swan.
In the ancient Iliad and its background stories, we see deities who can be both wanton and selfish, and we see flawed humans who, like the deities they worship, sometimes make choices based on unbridled desire, without thought given to the greater implications of their choices and the harm that could be caused to others.
Dante, on the other hand, writes from a worldview that is highly informed by the precepts of Christianity and the concept of free will. The Christian God and Christ are nothing like the deities of Homer's age. Christians must uphold a code of behavior that is ever-mindful of controlling passions that can harm others. In fact, Helen, Paris, and Achilles appear in the first of the nine circles of Hell in The Inferno (where each circle is increasingly more punitive) for the sins of lust and infidelity, while Odysseus is placed in the eighth circle for his far more serious sins of premeditated deception.
One might explore the question of why Dante did not place the gods and goddesses of the Greek pantheon in the circles of Hell as well.

Homer's Iliad is the story of part of the Trojan War concerned with the "wrath of Achilles." At the beginning of the epic, Achilles has a disagreement with Agamemnon concerning a war prize and withdraws from the fighting. Being the greatest of the Greek warriors, Achilles's absence limits the abilities of the Greeks to succeed on the battlefield. At the end of the epic, he returns to the fighting and kills Hector, the greatest of the Trojan heroes. It is a pagan poem, grounded in polytheism, and a story of a war, describing in detail many battles, discussions of strategy, and issues of honor in battle.
Dante's Inferno is a Christian poem detailing an imaginary journey through the circles of Hell as the narrator is escorted by the Latin poet Virgil. We encounter many famous historical people on the journey within the context of Christian religion. The narrator at the end of the poem emerges from his journey on Easter day.
While both poems are important works that became both standard reading and symbols of cultural greatness, they are very different, with one focusing on war and the other on religion and one belonging to oral tradition and the other to literary practice.
The major similarity between them is that ancient Greece and Renaissance Italy were not actually nations but rather collections of city states and territories united by cultural and linguistic ties. Thus poetry and other cultural performances gave them a sense of unity that did not exist in the political realm.

Homer's other great epic, the Odyssey, probably has more in common with Dante's Inferno than the Iliad. Indeed, the Odyssey, like the Inferno, involves the hero descending into the underworld and returning after encountering its inhabitants. But both the Iliad and The Divine Comedy in general are epic poems, emphasizing the complex relationship between humanity and the divine. Perhaps the most obvious connection between the two poems is not really thematic, though. Dante populates hell with many of the figures from Homer's poems, including the blind poet himself. (Remember that the Roman epic poet Virgil is actually Dante's guide in Inferno). In Canto IV we discover Homer, along with other poets, including Horace, Ovid, and Lucan—all poets who would have been familiar to Dante's readers—and Hector, one of the main characters in the Iliad. These men are in the First Circle of Hell, reserved for those who were not evil people, but had been born before Christ and were therefore not able to be saved. One circle deeper into Hell, Dante encounters Achilles and Paris, two major figures in the Iliad, who are there for the sin of lust. Helen of Troy is there, too, for her betrayal of her husband, Menelaus. Their actions essentially set the events portrayed in the Iliad in motion. Odysseus, one of the most important characters in the Iliad, is in the Eighth Circle of Hell for his trickery. So there are many connections between Dante's Inferno and the Iliad, and a good essay might take this a step further by considering the reasons that Dante chose to portray these characters in Hell.