Explain Wiesel’s purpose in including Madame Schächter in the memoir. What function does she serve?

Elie Wiesel, the author of Night, includes Madame Schachter as a harbinger of coming events. She serves to foreshadow the horrifying events that are coming for the Jews.
Madame Schachter appears fairly early on in the narrative. Moishe the Beadle is the first one who warns the Jews in the Hungarian ghetto what is coming. He had survived being taken and was on a mission to warn the Jews, but they would not listen.
Madame Schachter appears in chapter 2. She is with her son on the cattle cars that are taking the Jews to the concentration camps. Her husband and two older sons were deported separately from her. Elie describes her as having lost her mind. She would moan and cry and repeatedly ask why she had been separated from the rest of her family. Then, her cries become hysterical. She claims to have seen a furnace with flames roaring out of it.

On the third night, as we were sleeping, some of us sitting, huddled against each other, some of us standing, a piercing cry broke the silence: "Fire! I see a fire! I see a fire!" There was a moment of panic. Who had screamed? It was Mrs. Schächter. Standing in the middle of the car, in the faint light filtering through the windows, she looked like a withered tree in a field of wheat. She was howling, pointing through the window: "Look! Look at this fire! This terrible fire! Have mercy on me!" Some pressed against the bars to see. There was nothing. Only the darkness of night.

From this quote, you can see how the other passengers would have thought she was crazy. She woke them all up screaming about something that wasn't even there. But later on, they find out that she wasn't necessarily crazy. She had had a vision or a premonition that was absolutely correct.

In Elizabeth Warnock Fernea's "Guests of the Sheikh," how does Fernea’s distinction between “women of the tribe” and “women of the town” offer us a sense of the multiple ways of being a Muslim woman? Give at least one example from the text to support your argument. Reflect on Fernea’s use of the ethnographic strategy of “thick description,” that is, her writing in a very detailed way about as much of a situation as possible—accounting for the people, the event, the surroundings, the time, and the reasons all the people may be there. How does this strategy affect how she tells the story of her time in El Nahra?

In the book, Fernea's distinction between women of the tribe (or harem) and women of the town highlights the multiple ways of being a Muslim woman. During her visit to the women's quarters, Fernea finds herself an object of curiosity among the sheikh's wives. The youngest, Selma, is the sheikh's favorite, and she wears no abayah. Although this is unusual for a traditional Muslim woman, Selma's dress and education demonstrates the sheikh's progressive attitude (and indulgence) toward female agency. Selma's sky-blue satin dress and largely uncovered hair is a manifestation of the similar independence women of the town enjoy.
In the book, the women of the town who socialize with Fernea include several teachers (Aliyah, Hind, etc.), the mayor's wife (Um Saad), the engineer's sister (Khadija), and the doctor's wife (Nadia). While the sheikh's wives are only expected to cater to the sheikh's needs, to remain chaste, and to raise his children, more is expected of women like Khadija. Khadija's engineer brother, Jabbar, expects her to learn how to socialize with men so that she can be both an engaging companion and a matchless homemaker when she marries. Despite her discomfort, Khadija humors her brother. In Khadija, we see how the traditional Muslim woman must reconcile the old ways with modern interpretations of womanhood.
Um Saad (pedigreed, wealthy, and educated) is the epitome of the modern Muslim woman. Her mayor husband, although privately progressive on the subject of women's rights, prefers to take a moderate stance in public. As a devoted wife, Um Saad obliges him, but she continues to excel in her academic pursuits in private. Muslim women such as Um Saad, Selma, and Khadija embody the best of Muslim womanhood: while demonstrating the multiple ways of being a Muslim woman, all three demonstrate that "a good woman is the same in both spheres: her reputation for fidelity is above reproach, she is hard-working, a devoted wife and mother, a good cook and housekeeper, and a quiet obedient companion to her husband." Above all, a Muslim woman's influence is matchless, regardless of which sphere she belongs to.
As for the second part of your question, I will offer some clues on how to tackle this. First, provide a brief definition of thick description. Next, provide an example from the book that illustrates the benefits of this ethnographic method. For an example, I recommend Fernea's description of the bed Selma shares with Sheikh Hamid and Selma's narrative about the photographs on the walls. By describing the layout of the room, Selma's (and Hamid's) bed, Hamid's portraits, the clothes worn by Abdul Emir (Hamid's father), as well as Abdul Emir's illustrious warrior past, Fernea helps us to understand Sheikh Hamid's background, his present opulence, and his continuing influence in his society. Fernea's strategy of thick description also allows her to illustrate her personal growth as she navigates Iraqi society and immerses herself in the culture. Additionally, in studying the details of her surroundings and describing them, Fernea also makes Iraqi culture accessible to her readers.

What is ROI?

ROI stands for Return on Investment, which is a performance measure. Usually, it is used when an investment opportunity is in question. Businesses use this measure to evaluate the efficiency of an investment. It calculates the amount of return on an investment, which means the profit, generated due to a certain amount invested. Businesses also use ROI to make a comparison between different investment scenarios, in order to decide which is the most profitable one. It is calculated by dividing the profit of an investment by the cost of the investment and expressed as a percentage. Profit means revenue minus costs. The formula of Return on Investment is as follows:
ROI= (Gain from Investment - Cost of Investment) / Cost of Investment x 100
Multiplying the result by 100 makes it a percentage.
Assume that the gain is $210, and the cost is $140. Then ROI is:
ROI= (210-140) / 140 = 0.50 x 100= 50%

ROI is an acronym which stands for Return on Investment. Return on Investment is a business term which calculates whether an investment made by a business has returned a loss or a gain—that is, whether or not it has been a profitable and sound investment. There is a simple calculation to find ROI, provided that you know how much profit has resulted from the investment, and the cost of the investment itself.
For example, let's say you invest $20 in purchasing materials from which you knit four sweaters. You then sell each sweater for $8. Your total investment is $20, and your total profit is the sales value minus the original investment. In this case, you have made $32, so your profit is $12. So, to calculate your ROI, you use the following calculation:
(Net Profit/Cost of Investment) * 100 = ROI
12/20 * 100 = 60%
Therefore, your ROI for this investment is 60%.
https://investinganswers.com/dictionary/r/return-investment-roi

Why did Lady Montague die and when?

Lord Montague comes to Juliet's grave and announces to the Prince that:

Alas, my liege, my wife is dead tonight.
Grief of my son’s exile hath stopped her breath.
What further woe conspires against mine age?

From this statement, we know that Lady Montague has died the night before of grief brought on by the endless feud, culminating, she thinks, in her son's exile. Lord Montague doesn't know at this instant that events are even worse than he already imagines. Only a moment later, however, Lord Montague will realize his son is dead and exclaim in sorrow:


O thou untaught! What manners is in this,
To press before thy father to a grave?

How, he asks his dead son, can you so upset the order of things that you, the son, die before the father?

In some sense, it is a mercy that Lady Montague has been spared the knowledge of her son's death.

Though neither character has a large role in the play, both Montague parents show themselves to be loving and caring towards their son. Lord Montague's worry over Romeo's mooning around is what leads Benvolio to invite Romeo to the Capulet's party, leading to the fateful encounter with Juliet. Lady Montague's unhappiness over being separated from her son seems to have the final straw in her distress over the feud—we remember her trying to stop her husband from joining the street brawl in the play's opening scene. The otherwise loving feelings the Montagues exhibit emphasize how destructive and aberrant the feud is.

In Act 5, Scene 3 of the play, Lord Montague enters the stage declaring that “grief of my son’s exile hath stopped her [Lady Montague’s] breath.” He also gives a time frame for the death, saying that it has occurred “this night”. The suddenness of the death gives some clue as to its nature; although it was actually believed in the Elizabethan period that it was possible to die of grief, these sorts of deaths were usually preceded by prolonged periods of depression where the person would confine themselves to bed. As Lady Montague’s death was so sudden, we can infer that she had probably been overcome with shock upon hearing of her son’s exile, resulting in a heart attack or similar sudden death caused by shock.

How did Sir Simon get peace and become able to sleep?

Sir Simon is finally able to get the eternal rest that he so desperately desires only because Virginia Otis agrees to help him by praying on his behalf. Virginia Otis is the only member of the Otis family that is not antagonistic toward Sir Simon. Because Virginia is kind to him, Sir Simon explains his situation to her. He tells her that he desperately wants to get his eternal rest, and that he has been searching for it for 300 years. He tells her about the Garden of Death, and Sir Simon explains that Virginia is a person that is capable of helping him cross over to his eternal resting place.

"Yes, death. Death must be so beautiful. To lie in the soft brown earth, with the grasses waving above one's head, and listen to silence. To have no yesterday, and no to-morrow. To forget time, to forget life, to be at peace. You can help me. You can open for me the portals of death's house, for love is always with you, and love is stronger than death is."

She is pure, innocent, and beautiful, and that is exactly the kind of person that he needs to intercede on his behalf.

"They mean," he said, sadly, "that you must weep with me for my sins, because I have no tears, and pray with me for my soul, because I have no faith, and then, if you have always been sweet, and good, and gentle, the angel of death will have mercy on me. You will see fearful shapes in darkness, and wicked voices will whisper in your ear, but they will not harm you, for against the purity of a little child the powers of Hell cannot prevail."

Fortunately for Sir Simon, Virginia Otis agrees to pray on his behalf.

"I am not afraid," she said firmly, "and I will ask the angel to have mercy on you."

Sir Simon the ghost is able to make a connection with Virginia when she stumbles across him one day in the tapestry room. Because she is kind to him, he is able to explain to her how desperately he would like to go to his final rest—to finally be able to die, rather than to continue on forever as a ghost. However, he has sinned in murdering his wife. He needs someone pure to intercede and pray for him. Virginia, who is pure, agrees to do so.
Although it is hard on her, Virginia's prayers on Sir Simon's behalf are successful, and he is able, finally, to die. He is given a big funeral, attended by the Otises and the Cantervilles. 
When Virginia sees the withered almond tree in bloom, which a prophecy says will happen when Canterville Hall is at peace, she knows that Sir Simon is finally forgiven and at rest.

What happened in the election of 1824?

The U.S. presidential election of 1824 was historically significant for a number of reasons. Won by John Quincy Adams, it nevertheless is remembered for the ascent to national political prominence of Andrew Jackson, as well as for being one of just three elections decided by the House of Representatives (and the only one decided under the provisions of the Twelfth Amendment.) Andrew Jackson, enormously popular with many ordinary Americans, finished with more electoral votes (99) than either John Quincy Adams (84,) Henry Crawford (41) or Henry Clay (37.) The House ultimately voted to give the Presidency to Adams. Jackson, whose followers had clashed bitterly with Clay's in the newspapers during the campaign, charged that Clay, as Speaker of the House, had reached a "corrupt bargain" with Adams, who appointed Clay Secretary of State upon assuming the Presidency. The election laid the foundations for what historians call the "second two-party system," as Jackson's Democratic Party forged a coalition of western farmers, southern planters, and working-class northerners that would be opposed by Clay's Whig Party.

What did the poet wish to do in the future in "The Road Not Taken"?

The poet wishes to explore or walk the other path in the future. Despite his best intentions, however, he admits that he probably won't return to realize his inclination. In the poem, the poet confesses that he regretted not being able to take both paths. He relates how he took a long time to choose his path.
In the end, he took the path less traveled, the path that was grassy and "wanted wear." However, as he continued to ponder his choice, he came to the conclusion that both paths were similarly worn in nature. Neither was more worn than the other. In fact, the poet maintains that both paths had leaves that no human steps had yet trodden "black." After thinking at length, he reluctantly decides that he will leave the first path for another day. All in all, he philosophizes that there's little chance he'll be back to fulfill this particular goal.
The last stanza is interesting and can be interpreted in one of two ways. The poet tells us that he took the road less traveled, and that his choice made all the difference. However, he also admits that he will be telling his story with a sigh for a long time. The first interpretation could center on the poet's regret for his decision. Perhaps the path he took led to some ostensibly negative consequences.
However, another interpretation could center on the fact that his chosen path led to some unexpected consequences. Perhaps they were simultaneously positive and negative in nature. In other words, his choice led to results he both liked and disliked (thus, the sigh). Because he didn't travel the first path, he will forever wonder about its possibilities.

This reference comes in the third stanza, with the lines:

Oh, I kept the first for another day!
Yet knowing how way leads on to way,
I doubted if I should ever come back.

The narrator had already chosen one of the two paths, “the one less traveled by.” Now he says at first that he could always come back and follow the other path on some other day in the future. But just as quickly, he understands how life works. He knows that even though he can have the best of intentions to someday return to the point where the two routes divide, the reality is that he probably won’t come back. Another “future” scene appears in the final stanza, when the narrator says that from this moment on, he will be explaining to people how and why he made the decision he did. Will he then be happy about his past choice? This is the question we debate.
https://www.poetryfoundation.org/poems/44272/the-road-not-taken

In Fahrenheit 451, the family dynamic has changed. How do families function in the society? Is it a positive or negative relationship for people?

In Bradbury's dystopian society, the vast majority of citizens are depicted as superficial, ignorant consumers, who spend most of their leisure time watching the interactive parlor walls, driving extremely fast on the highways, or dozing off while listening to their Seashell radios. Montag's meaningless, hollow relationship with his wife gives an in-depth look at the typical family dynamic in Bradbury's dystopian society. Montag and his wife are extremely distant, rarely discuss significant, insightful topics, and do not have a healthy relationship with each other. Mildred's friends also comment on the typical family units as Mrs. Bowles brags about shutting her children inside their rooms to watch the parlor walls each night. Mrs. Phelps also casually mentions that her husband is at war and says that she would never mourn his death.
Essentially, the citizens are conditioned to not develop meaningful, loyal relationships with each other, and the family unit has severely suffered. Children rarely interact with their parents, who do not even care about their spouses. Clarisse and her family stand in stark contrast to the callous, superficial family units of Bradbury's dystopian society. Clarisse and her family are considered abnormal because they enjoy having conversations and spending alone time together. Overall, the family unit in Bradbury's dystopian society is virtually non-existent as family members rarely enjoy quality time together or genuinely care about one another.

In this novel, the family is vastly different when compared to our society. This is clearly shown through the conversation between Mildred's friends, Mrs. Phelps and Mrs. Bowles, in Part Two. According to Mrs. Bowles, for example, children spend most of their time at school. When they are at home, which might only be for three days a month, they are put in the parlor and left to watch the walls. For Mrs. Bowles, children are an inconvenience to her life. Instead of acting as a motherly figure to them, she would rather "kick back" and enjoy some entertainment.
Clearly, this family dynamic has negative consequences for people in this society. As we see from Clarisse's comments about her classmates, children have become violent and reckless. She tells Montag, for instance, that six of her friends have been shot and ten have died in car accidents.
What we see, then, is that a bond between families does not exist in this society. Instead, parents and children are consumed by a need for entertainment which overshadows their love and care for one another.

In Fahrenheit 451, the only family we see up close is Montag's, but we get insights into the typical family from Montag's conversation with Clarisse. She tells him how different her family is:

Oh, just my mother and father and uncle sitting around, talking. It's like being a pedestrian, only rarer. My uncle was arrested another time—did I tell you?—for being a pedestrian. Oh, we're most peculiar.

In contrast, Montag's relationship with his wife is fairly typical of family life in his society. Mildred watches a tremendous amount of television on her viewscreens, and they do not have much to say to each other. Montag hardly seems to know Mildred, and Mildred hardly seems to know him. When he tries later in the book to share his feelings (and a desire for books) with her, she is frightened and returns to her viewscreens.
We learn that what Clarisse's family does—talking together and taking walks—is highly unusual. Most of the rest of the society is encased and isolated by technology, be it cars speeding from place to place or endless television. This has a negative impact on people, as evidenced by Mildred's suicide attempt.

What was the influence of Jane Austen on American authors?

This is an interesting question, as most often we trace Austen's influence on other British writers, such as George Eliot, who was influenced by her realism. The American writer who first comes to mind, however, as an early fan and advocate for Austen was William Dean Howells. His good friend Henry James was also influenced by her work. James wrote quite a bit about her, some of it critical, but it is clear he studied her carefully and incorporated her realism and cool detachment into his own novels.
Mark Twain, in contrast, famously criticized her. He said he hated her novels, which he saw as out of the American literary tradition, but he also exaggerated his dislike of her as part of a running public debate with Howells.
With the explosion of interest in Jane Austen in the last 40 years has come a profrusion of American written sequels, prequels, and take-offs of her work—the most popular probably being Pride and Prejudice and Zombies.

How does crowd react when the demonstrators bow their heads in prayer?

Anne Moody's become deeply involved in a campaign by the NAACP to stage sit-ins at segregated lunch counters in Jackson. One of the sit-ins turns particularly violent, as Anne and a number of other civil rights activists are attacked by a baying mob of white supremacists.
The atmosphere was already tense when Anne entered Woolworth's with students from the historically black Tougaloo College. But when a mob of white students shows up, tensions rise to boiling point. They start making threats of violence, but the response from the activists is entirely non-violent. They bow their heads in prayer, drawing upon their faith for strength and spiritual sustenance at such a dangerous moment. At that moment, all hell breaks loose. That's when the mob begins to attack the civil rights activists, while ninety Jackson police officers outside watch through the window, doing absolutely nothing to stop the violence.

Intermediate Algebra, Chapter 3, 3.2, Section 3.2, Problem 28

(a) Determine the slope of the ling through the pair of points $(-3,-3)$ and $(5,6)$.

Let $(-3,-3) = (x_1, y_1)$ and $(5,6) = (x_2,y_2)$ in the slope formula

$\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{6 - (-3)}{5-(-3)} = \frac{9}{8}$

The slope is $\displaystyle \frac{9}{8}$.

(b) Based on the slope, indicate whether the line through the points rises from left to right, falls from left to right, is horizontal, or is vertical.

Based on the slope, the line through points $(-3,-3)$ and $(5,6)$ rises from left to right.

What will happen if New York stays in the loyalist camp?

I'm not sure if this question is asking a general historical question, or if the question is asking for an answer about Isabel.  I'll go a little bit through both.  
If New York remains in Loyalist control, then Britain has a strategic stronghold.  New York is prime military ground.  It has access to Patriot forces over land, it has a good harbor for the British Navy, and it already has defenses in place.  Additionally, because it's a big city, it has plenty of places to house British troops.  If New York stays Loyalist, many Patriots will vacate the city.  That will open up room for British forces.  
For Isabel, if New York stays under Loyalist control, she isn't likely to get free of Madam Lockton.  The Locktons are Loyalists, so if New York stays friendly to Loyalists, the Locktons have no reason to leave.  If New York were to be taken over by Patriot forces, Isabel stands a bit better of a chance at escape and/or freedom.  

After his second appearance, the family left the ghost feeling dejected. Discuss this idea.

In "The Canterville Ghost," the ghost make his second appearance in Chapter Three. In this instance, the ghost disturbs the family when he tries to wear his old suit of armour which is hanging on display in the downstairs hallway. This attempt, however, is an unmitigated disaster which results in the ghost being attacked by the family. This causes him to feel to dejected and humiliated, as we learn from the description in the text:

On reaching his room he entirely broke down, and became a prey to the most violent agitation.

The ghost feels this way because the twins attacked him with their pea-shooters and Mrs Otis offered him a "tincture" for indigestion, instead of being afraid of his "most horrible laugh." Unable to scare them, the ghost has no choice but to turn "faintly phosphorescent" and return to his room.

Calculus of a Single Variable, Chapter 8, 8.2, Section 8.2, Problem 12

Recall that indefinite integral follows int f(x) dx = F(x) +C where:
f(x) as the integrand function
F(x) as the antiderivative of f(x)
C as the constant of integration.
For the given integral problem: int5 x/e^(2x) dx , we may apply Law of exponent: 1/x^n =x^(-n) then 1/e^(2x) = e^(-2x) .
int5 x/e^(2x) dx =int5 x*e^(-2x) dx
Apply the basic integration property: int c*f(x) dx = c int f(x) dx .
int5 x*e^(-2x) dx= 5int x*e^(-2x) dx
Apply integration by parts: int f *g' = f*g - int g *f'du .
Let : f =x then f' = dx
g'=e^(-2x) dx then g = -1/2e^(-2x)
Note: g = int g'= int e^(-2x) dx . Apply u-substitution using u =-2x then du = -2dx or (du)/(-2) =dx .
int e^(-2x) dx =int e^(u) * (du)/(-2)
= -1/2 int e^u du
= -1/2 e^u
Plug-in u =-2x on -1/2 e^u , we get: int e^(-2x) dx =-1/2 e^(-2x) .

Following the formula for integration by parts, we set it up as:
5int x*e^(-2x) dx =5[ x*(-1/2 e^(-2x)) - int (-1/2 e^(-2x)) dx]
=5[ x*(-1/2 e^(-2x)) - (-1/2) int ( e^(-2x)) dx]
=(-5xe^(-2x))/2 + 5/2int ( e^(-2x)) dx
Plug-in int e^(-2x) dx =-1/2 e^(-2x) , we get:
5int x*e^(-2x) dx=(-5xe^(-2x))/2 + 5/2int ( e^(-2x)) dx
=(-5xe^(-2x))/2 + 5/2*[-1/2 e^(-2x)] +C
=(-5xe^(-2x))/2 - (5 e^(-2x))/4 +C
or (-5x)/(2e^(2x)) - 5/(4 e^(2x)) +C

What are some good points to put in my essay on the Proclamation of 1763?

For your essay to be complete, I think you should have to give the history of the Proclamation of 1763. This line was designated by the British so that no American colonists could legally settle west of the Appalachians. It was done to reward Native American allies during the French and Indian War as well as prevent friction between settlers and natives. Colonists were angry because they did not think that the Native Americans should be rewarded when for generations native tribes had attacked colonial settlements.
Land speculation was also popular, especially among the upper classes. When the land available for this speculation shrank, many worried that this would stagnate the colonial economy. There was also the fear that the line was drawn at the mountains so that British tax collectors would have an easier time controlling the colonists. Finally, the colonial population was growing and the dream of many young American colonists was to own farmland. Many young people were worried that this land would not be available. Those who had already moved west of the mountains had already established homes there and would not be willing to leave.
If I were you, I would structure the essay by writing the point of view of both the colonists and the British. I would also write about how this is important in understanding the American Revolution.

How can I summarize the article "The New York Safe Act: A Thoughtful Approach to Gun Control, or a Politically Expedient Response to the Public's Fear of the Mentally Ill?"

This article discusses the New York Secure Ammunition and Firearms Enforcement Act of 2013 (“SAFE Act”), passed to protect the public from mentally ill people with guns. The act states that a mental health professional who suspects that a person with a gun is likely to pose a danger to themselves or others must report this situation to a Director of Community Services, who, if she or he agrees, must report this person to the criminal justice system. At that point, the person's license to hold a gun will be revoked, and the weapon will be seized. Critics of the act feel that it is unconstitutional and believe that it interferes with patient-therapist relationships. They also feel that people with mental illness perpetrate very few crimes involving guns and that this law unnecessarily stigmatizes people with mental illness.
The article discusses the recent history of cases related to gun ownership, including District of Columbia v. Heller (2008), in which the Supreme Court upheld an individual's right to have a gun. In McDonald v. City of Chicago (2010), the Supreme Court applied this right to the states through the 14th Amendment's Due Process Clause. The author also reviews long-standing prohibitions of gun ownership by mentally ill people. 
The author determines that the SAFE Act is unconstitutional because, unlike other long-standing prohibitions on gun ownership by the mentally ill, the act does not require someone to be judged mentally ill or committed to a mental institution before that person's firearm is taken away. In the past, a person's weapon could only be taken away if that person was diagnosed with mental illness or sent to a mental institution. The author presents reasoning about why the SAFE Act's revocation of the right to possess a firearm in the home is likely unconstitutional. The author states that the SAFE Act is not the least restrictive means of providing for public safety and that the law stigmatizes people with mental illness. The author believes that gun rights should be revoked based on indications of people's dangerousness, not based on mental illness. 

Why was Marbury v. Madison significant to anyone outside of William Marbury's immediate family?

Marbury v Madison (1803) is arguably the most important legal case in American judicial history. Why? Because the case established the principle of judicial review, the power of the United States Supreme Court and other federal courts to strike down acts of Congress which they deem unconstitutional.
The principle of judicial review is of immense importance in the development of the Supreme Court as one of the three branches of federal government. Marbury vs. Madison gave life to the philosophy of the Founding Fathers that governments should be of laws, not men. Who is it that interprets the law? It should not be politicians (who make the law), but judges. A Constitution made by "We, the People" then becomes a document whose meaning is decided by "We, the Judges."
To that end, the case enshrined the principle that the Supreme Court has the right to determine what is, or is not, constitutional. That right has been jealously guarded by the Court ever since and passionately debated by friend and foe alike. Marbury vs. Madison has been such a contentious case because the Constitution is both a political and a judicial document. This raises the question of precisely who should be charged with its interpretation. Should it be democratically-elected representatives, even if they lack appropriate judicial training? Should it be legally-qualified judges, even though they are not elected and are therefore not subject to democratic control or recall?
The debate continues.
https://www.thoughtco.com/marbury-v-madison-104792

Prove that when using the quadratic formula for the two complex solutions, the radicand in the final answer is always 3 (sqrt3). (Sums and differences of cubes)

This is not a very clear question, but it seems that you need to show that the complex solutions of the equation of the form
x^3 + a^3 = 0 or x^3 - a^3 = 0   will contain a radical of 3 (sqrt(3) ). Here, a is assumed to be a positive real number.
This can be shown by factoring the left side using the formula for the sum of cubes (or difference of cubes, for the second equation):
(x + a)(x^2 -ax + a^2) = 0
This is satisfied when x = -a (this is the real solution) or when x^2 - ax + a^2 = 0 . The quadratic equation can be solved by using the formula:
x = (a +-sqrt(a^2 - 4a^2))/2 = (a +-isqrt(3)a)/2
These are two complex solutions, as the radical of the negative number -3a^2 is an imaginary number isqrt(3)a . No matter what the value of a is, the equation of the form shown above will always have two complex solutions which contain the square root of 3, and one real solution.
The same can be shown for the equation of the form x^3 - a^3 , except the real solution will be x = a and the complex solutions will be
x = (-a +-isqrt(3)a)/2 .

What is the final impression of Rip Van Winkle?

Assuming you mean what final opinion readers are left with about Rip Van Winkle, it would be that he is a throwback to the sleepier times before the Revolution, a symbol of the apathy in the land before people became the bustling and engaged citizens of a democracy. Rip returns to his old ways of sitting on the bench outside the inn and regales people with his story of falling asleep for twenty years. The final impression is that Rip is unchanged, which highlights all the more thoroughly the way the world around him has energized and transformed itself. The narrator says this about Rip:

Having nothing to do at home, and being arrived at that happy age when a man can be idle with impunity, he took his place once more on the bench at the inn door, and was reverenced as one of the patriarchs of the village, and a chronicle of the old times “before the war.”

If the question means, however, what is Rip's final impression of all that has happened, he leave off on a happy note. He no longer has a bossy wife to contend with. He is past the age when anything is expected of him. He can idle away his life happily and without ambition, honored as a representative of a former time.

Please explain "To Sleep," a poem by William Wordsworth.

Overall, someone who has been suffering from insomnia describes his difficulties in Wordsworth’s poem, “To Sleep.”
The title and the first two lines of the poem hint at the theme of sleeplessness even before it is clearly identified. For instance, the idea of counting sheep to put oneself to sleep is very common in the face of sleeplessness—even to a contemporary audience.
In the first four lines, Wordsworth describes the images that come into the speaker's mind as he tries to fall asleep.

A flock of sheep that leisurely pass by,  One after one; the sound of rain, and bees  Murmuring; the fall of rivers, winds and seas,  Smooth fields, white sheets of water, and pure sky... (1-4)

The speaker lists the things he has laid awake imagining, in an attempt to sleep. "One by one" gives reference to the act of counting sheep. "Leisurely" refers to the rolling gait and relaxed pace of the moving sheep (1-2). The speaker refers to the soothing sounds of rain, "bees murmuring" and waterfalls—"fall of rivers" (2-3). He also describes the visions of "smooth fields" (perhaps a part of an afternoon nap in the country), as well as a "pure sky," with no hint of storm and nothing in it that would cause anything but a quiet calm within, conducive to falling asleep (3-4).
In lines 5-8, Wordsworth's speaker explains that he has done all he can think of to bring sleep upon himself (5). However, he has had no success—he has remained awake all night long—until he finally hears the sound of birds that utter in the orchard, breaking the silence with their song in the early morning, we imagine just before dawn (5-6). Even the first cuckoo makes a melancholy: we can assume it is because the speaker is still awake to hear it, having had no respite from the day before. Note that the bird does not sing, but cries—it is a sound of distress (7-8):

I have thought of all by turns, and yet do lie  Sleepless! and soon the small birds' melodies  Must hear, first uttered from my orchard trees;  And the first cuckoo's melancholy cry. (5-8)

The theme of sleeplessness continues into the next three lines, giving the reader a deeper insight into the depth of the speaker's difficulty: for it is not just this one sleepless night, but the third in a row—

Even thus last night, and two nights more, I lay,  And could not win thee, Sleep! by any stealth;  So do not let me wear tonight away... (9-11)

With all the tricks he has tried to use, the insomniac has not been able to even steal—"Sleep! by any stealth..." (10)—any relief. In line 11 the speaker directly addresses sleep (as if it were a living, hearing thing), asking that it not allow him to remain in the same condition as he faces the approach of another night.
The poem's last three lines describe just how important sleep is:

Without Thee what is all the morning's wealth?  Come, blessed barrier between day and day,  Dear mother of fresh thoughts and joyous health! (12-14)

The "morning's wealth" (12) refers to all of the wonders of a new day. "Wealth" indicates that the morning is filled with things that are extremely valuable. He has already pointed out the sound of birds that welcome the day. They are a blessing at the beginning of the day, but only after a time of rest; the sound is very different when one has remained unable to experience rest, but instead has counted the long hours until the day breaks. What good, what joy is to be found in the coming of morning without rest from the night before?
The speaker praises sleep, referring to the "blessed barrier" (13), the thing that separates one day from another. He goes on to provide details of the benefits of a good night's sleep: "fresh thoughts" and "joyous health." (14)
Whereas the title might first lead the reader to believe the poem is about the pleasures of sleep, the content demonstrates that it is actually about the hardships created when one is unable to sleep; it points out the negative ramifications—most especially when the insomnia continues over subsequent nights.
 

Single Variable Calculus, Chapter 4, 4.7, Section 4.7, Problem 50

Determine the equation of the line through the point $(3,5)$ that cuts off the least area of the first quadrant.



By using Point Slope Form, we can determine the equation of the line that pass through the point $(3,5)$.

$
\begin{equation}
\begin{aligned}
y - 5 &= m(x-3)\\
\\
y &= mx - 3m + 5
\end{aligned}
\end{equation}
$


So the $y$-intercept when $x=$ will be,
$ y = m(0) - 3m + 5$

And the $x$-intercept when $y = 0$ will be,

$
\begin{equation}
\begin{aligned}
0 &= mx - 3m + 5\\
\\
x &= 3 - \frac{5}{m}
\end{aligned}
\end{equation}
$







$
\begin{equation}
\begin{aligned}
\text{So, the area of the triangle will be }A &= \frac{1}{2} \left( 3-\frac{5}{m}\right) \left( 5-3m\right)\\
\\
A &= 15 - \frac{25}{2m} - \frac{9m}{2}
\end{aligned}
\end{equation}
$


If we take the derivative of $A$, we get...
$\displaystyle A' = \frac{25}{2m^2} - \frac{9}{2}$

when $A'=0$,

$
\begin{equation}
\begin{aligned}
\frac{25}{2m^2} &= \frac{9}{2}\\
\\
m^2 &= \frac{25}{9}\\
\\
m &= -\frac{5}{3} \text{ and } m = \frac{5}{3}
\end{aligned}
\end{equation}
$


$\displaystyle m = \frac{-5}{3}$ respects a minimum since $\displaystyle A''\left( \frac{-5}{3} \right) > 0$

$
\begin{equation}
\begin{aligned}
\text{Therefore, the equation of the line is } y &= mx - 3m + 5 = - \frac{5}{3} x - 3 \left( \frac{-5}{3}\right)+5\\
\\
y &= \frac{-5}{3}x + 10
\end{aligned}
\end{equation}
$

College Algebra, Chapter 5, 5.4, Section 5.4, Problem 32

Solve the equation $e^x - 12e^{-x} - 1 = 0$

$
\begin{equation}
\begin{aligned}
e^x - 12e^{-x} - 1 &= 0\\
\\
e^x - \frac{12}{e^x} - 1 &= 0 && \text{Law of exponent } a^{-n} = \frac{1}{a^n}\\
\\
\frac{e^{2x}-12-e^x}{e^x} &= 0 && \text{Get the LCD}\\
\\
e^{2x}-e^x-12 &= 0 && \text{Multiply both sides by } e^x\\
\\
(e^x - 4)(e^x + 3) &= 0 && \text{Factor using trial and error}
\end{aligned}
\end{equation}
$

Solve for $x$

$
\begin{equation}
\begin{aligned}
e^x - 4 &= 0
&&&
e^x + 3 &= 0\\
\\
e^x &= 4
&&\text{Add 4}&
e^x &= -3 && \text{Subtract 3}\\
\\
\ln e^x &= \ln 4
&&\text{Take $\ln$ of each side}&
\ln e^x &= \ln(-3) && \text{Take $\ln$ of each side}\\
\\
x &= \ln4
&&\text{Property of $\ln$}&
x &= \ln(-3) && \text{Property of $\ln$}
\end{aligned}
\end{equation}
$

The only solution to the given equation is only $x = \ln 4$, since $\ln (-3)$ is undefined.

What does it mean vaporized mean in the book 1984?

To be vaporized in 1984 means to be treated as if you had never been alive, no matter how important you might once have been. It means being regarded as if you had never been born. Winston thinks about this as he contemplates the woman in the next cubicle:

He knew that in the cubicle next to him the little woman with sandy hair toiled day in day out, simply at tracking down and deleting from the Press the names of people who had been vaporized and were therefore considered never to have existed.

Vaporization is a means of social control in Oceania. Anyone who could conceivably harbor an independent thought is in line for being vaporized. Winston learns this is deliberate policy when O'Brien gives him the secret book called The Theory and Practice of Oligarchic Collectivism by Emmanuel Goldstein. In it, Winston reads the following:

vaporizations are not inflicted as punishment for crimes which have actually been committed, but are merely the wiping-out of persons who might perhaps commit a crime at some time in the future.

Before he is arrested, Winston calculates which people he knows will inevitably be vaporized and puts himself on the list. He later comes to understand that the vaporizing is part of the Party's attempt to control all of reality. By wiping out all records and traces that someone existed, the Party can control history. In a sense, that person never did exist, because no memory remains of his or her existence. This ability to will into being its own reality is the kind of power the Party craves.

How did Jane try to compose her nerves?

In Chapter 15 of Jane Eyre, Rochester reveals to Jane some of the murkier aspects of his past. He tells her that Adele—the girl for whom Jane has been acting as a governess—is the daughter of a Frenchwoman called Celine. Years before, Rochester had had an affair with Celine. After he caught her cheating on him, he ended the relationship, but not before shooting and injuring her lover in a duel. Rochester doesn't think that Adele is his daughter, but he felt sorry for her anyway, not least because her mother had abandoned her, so he took her back to England with him.
As she tosses and turns in bed that night, Jane can't stop thinking about Rochester's scandalous story. She feels agitated and unnerved, her anxiety made worse by a sudden sound at her bedroom door. Jane quickly reassures herself that it's most probably Pilot, Mr. Rochester's Newfoundland dog. Silence returns to the house and settles Jane's fraught nerves. Now she feels herself gently falling into a deep slumber once more. But it doesn't last for very long; soon Jane will be disturbed once again, this time by a fire.

College Algebra, Chapter 4, 4.4, Section 4.4, Problem 52

Determine all the real zeros of the polynomial $P(x) = 3x^3 - 5x^2 - 8x - 2$. Use the quadratic formula if necessary.

The leading coefficient of $P$ is $3$, and its factors are $\pm 1, \pm 3$. They are the divisors of constant term $-2$ and its factors are $\pm 1, \pm 2$. Thus, the possible zeros are

$\displaystyle \pm 1, \pm 2, \pm \frac{1}{3}, \pm \frac{2}{3}$

Using Synthetic Division,







We find that $\displaystyle 1, 2, \frac{1}{3}, \frac{2}{3}, -1$ and $-2$ are not zeros but that $\displaystyle \frac{-1}{3}$ is a zero and that $P$ factors as

$\displaystyle 3x^3 - 5x^2 - 8x - 2 = \left( x + \frac{1}{3} \right) (3x^2 - 6x - 6)$

We now factor the quotient $3x^2 - 6x - 6$ using the quadratic formula


$
\begin{equation}
\begin{aligned}

x =& \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\\
\\
x =& \frac{- (-6) \pm \sqrt{(-6)^2 - 4(3)(-6) }}{2(3)}
\\
\\
x =& 1 \pm \sqrt{3}

\end{aligned}
\end{equation}
$


The zeros of $P$ are $\displaystyle \frac{-1}{3}, 1 + \sqrt{3}$ and $1 - \sqrt{3}$.

Is race and gender discrimination moral? From the perspective of Rawls's A Theory of Justice, discuss.

Rawls did not really directly address racial nor gender discrimination in his famous work A Theory of Justice. He was, of course, aware of these issues, and they could certainly be made to fit within his theoretical framework. The theory of justice outlined by Rawls was based on a thought experiment usually described as a "veil of ignorance." He asked the following question: If a person had a choice of how their society would be structured, and they were forbidden, by a "veil of ignorance," from knowing what their socioeconomic status would be in this society, what would be the characteristics of this society?
Rawls argued that a rational person would choose a society that did the best job of taking care of the least fortunate. This was because the person behind the "veil of ignorance" could not be certain that they themselves might not be among the least fortunate. Rawls did not really discuss the issues of race or gender in this formulation, but given the close associations between race and poverty, and the dearth of opportunities historically afforded to women, if race and gender were also obscured by the "veil of ignorance," it would make sense that a person would choose a society that did everything it could to prevent discrimination based on race or gender.
Rawls viewed "justice as fairness," and in his view, morality was fairly close to the same thing as justice. He argued that these had a rational foundation, and it should be fairly clear that neither racism nor sexism would have been part of a society founded upon a rational social contract. So racial and gender discrimination would not be moral under Rawls's theory of justice. On the other hand, as many critics have pointed out, the failure to discuss these issues in A Theory of Justice is a substantial and important oversight.
https://halshs.archives-ouvertes.fr/halshs-01163932/document

https://plato.stanford.edu/entries/rawls/

What are three reasons why some people were against the Louisiana Purchase?

The biggest reason people were against the Louisiana Purchase was a financial one. The United States was a very young country and had many debts to pay. When Thomas Jefferson sent envoys to France, they were initially only going to purchase the port of New Orleans; purchasing the the rest of Louisiana required borrowing even more money. Some people (predominantly New England Federalists) argued that the acquisition was unconstitutional and that Jefferson was bending the rules for his own benefit. Really, they were concerned about the economic strain such a purchase might require.
Additionally, the acquisition created problems for the inhabitants of the Louisiana Territory. French and Spanish settlers lived in Louisiana, as well as free black people. The treaty between France and the United States declared that all of these people would be granted citizenship, but some members of Congress did not believe these people upheld American values and therefore did not deserve citizenship.
Finally, Spain objected to the purchase because it did not want the United States to grow even larger. Louisiana had been in the process of transferring from Spanish ownership to French, and when James Madison originally approached Spain about purchasing New Orleans, Spain told him he would have to take it up with France. Spain retracted this argument as soon as it became apparent that the French were going to hand over the territory.
Despite the initial unpopularity of the purchase, fifteen states formed out of the territory. Without the Louisiana Purchase, the United States would be nowhere near the large and powerful nation it is today.
https://history.state.gov/milestones/1801-1829/louisiana-purchase

College Algebra, Chapter 1, 1.1, Section 1.1, Problem 82

Determine the solution of the equation $\displaystyle \frac{1.73 x}{2.12+x} = 1.51$ correct to two decimals

$
\begin{equation}
\begin{aligned}
\frac{1.73 x}{2.12+x} &= 1.51 && \text{Multiply both sides by } (2.12 +x)\\
\\
\cancel{(2.12+x)} & \left[ \frac{1.73x}{\cancel{2.12+x}} = 1.51 \right] (2.12+x) && \text{Cancel out like terms}\\
\\
1.73 x &= 1.51(2.12+x) && \text{Apply Distributive Property}\\
\\
1.73 x &= 3.2012 + 1.51 x && \text{Combine like terms}\\
\\
1.73x - 1.51x &= 3.2012 + 1.51 x - 1.51 x && \text{Simplify}\\
\\
0.22x &= 3.2012 && \text{Divide both sides by 0.22}\\
\\
\frac{\cancel{0.22}x}{\cancel{0.22}} &= \frac{3.2012}{0.22} && \text{Simplify}\\
\\
x &= 14.55
\end{aligned}
\end{equation}
$

What is the central theme in the novel? How is the theme conveyed through characters, the setting, symbolism, and so on? What are examples of this theme as it appears throughout the novel? Explain why you chose this as the central theme.

There are many themes we could choose to discuss in Geraldine Brooks's novel Caleb's Crossing (2011). These include the significance of names, the contrast between country life and city life, and the cycle of life and death.
However, one theme that I think would be particularly interesting to highlight is the importance of individual identity. What makes us who we are? How do the characters find their identities, and how do they struggle in the process? Let us talk about this with respect to the novel's various elements you mentioned in your question: characters, setting, and symbols.
CHARACTERS
Bethia is the novel's protagonist. The story opens when she is 15. Her name means "servant," and she struggles with it: she is a young modern woman. She lives in a conservative place (in a Puritan settlement on Martha’s Vineyard). She studies in secret, even though she is not supposed to. Additionally, she wants to be treated with the same fairness and respect as her brother, but she knows that the society she lives in considers him her superior. She does not want to be a "servant," although her name, given at birth, designates that role for her. She is somewhat at odds with her identity as a female. Additionally, she has more interest in the spirituality of the island's indigenous group than in the religion she is being raised in.

I had come to think that the Wampanoag, who dealt so kindly with their babes, were wiser than we in this. What profit was there in requiring little ones to behave like adults? Why bridle their spirits and struggle to break their God-given nature before they had the least understanding of what was wanted of them?

This brings us to the next point.
Caleb, the book's other main character, also struggles with his identity. He is part of the island's indigenous tribe, the Wampanoag. Early in the book, he becomes friends with Bethia. He is interested in the book she is reading.

I held it out and Caleb took it. This was the first book he had held in his hands. He made me smile, opening it upside down and back to front, but he touched the pages with the utmost care, as if gentling some fragile-boned wild thing. The godliest among us did not touch the Bible with such reverence as he showed to that small book.

When he asks her for it, she says it is not hers to give. Caleb has no grasp of the idea of personal property—he was raised in another culture, with the Wampanoag—and he is hurt. He does not fit in with Bethia's world any more than she fits in with his. However, they are both curious about the worlds outside their own communities, and they both struggle to define themselves in that larger context.
SETTING
The setting of the book involves two specific settings that rarely overlap despite the fact that they are right next to each other. Bethia's Puritan community and Caleb's community, where the Wampanoag live, both constrain identity to a certain set of social norms, traditions, and behaviors. As mentioned above, it is difficult for a person from one of these settings to find (or feel comfortable in) his identity in the other.
SYMBOLS
Books are important symbols in Caleb's Crossing. As we saw in the passage quoted above, Bethia's father's book is a symbol of his identity, and the identity he wants for his daughter. Caleb wants the book because he is drawn to what it means and what it contains.
Books also represent escape from one's identity, especially as it pertains to social roles. As Bethia observes, her father uses his books to avoid intimacy with his wife:

My mother was an excellent woman. Pious, virtuous. Kind. But she was not the intellectual equal of my father. Not by any means. I do not speak of book learning. I speak of a certain innate quality of mind, a superior understanding. Because she had it not, their companionship was—diminished. Father looked to his books, rather than to his wife.

Books, whether between Bethia and Caleb or between Bethia's parents, symbolize the gap between two identities.

What happens when the narrator, Jing-Mei, performs at the talent show?

Jing-Mei's performance in the talent show is disastrous in "Two Kinds" by Amy Tan. 
For a whole year Jing-Mei halfheartedly practices her piano skills under the tutelage of her deaf, myopic music teacher. She is quick to realize she can be lazy and inaccurate while she works with him. Unfortunately, her mother arranges for her to take part in a talent show. Having high expectations for her daughter, and in her excitement, she invites all of her friends from the Joy Luck Club to the performance.

For the talent show I was to play a piece called "Pleading Child," from Schumann's Scenes from Childhood. It was a simple, moody piece that sounded more difficult than it was.

Jing-Mei dressed in a beautiful white dress for the performance and she felt confident in her piano skills until she played the first wrong note. Her performance was horrible as she played one wrong note after another. After her dreadfully embarrassing recital, Jing-Mei feels faint and is overcome with embarrassment as she overhears a young boy express his feelings about her talent to his mother.

By then I saw my mother's face, her stricken face. The audience clapped weakly, and I walked back to my chair, with my whole face quivering as I tried not to cry, I heard a little boy whisper loudly to his mother. "That was awful," and mother whispered "Well, she certainly tried."

After the performance, Jing-Mei and her mother have an argument that creates a permanent rift between the two.

What were the causes and long-term effects associated with the New Deal?

There were several causes that led to the launching of the New Deal. Prior to the beginning of the Great Depression, a laissez-faire attitude existed regarding the involvement of the government in the economy. That approach didn’t work once the Great Depression began. The depression was so severe that it required a lot of government intervention in the economy.
Conditions in the United States had deteriorated since the start of the Great Depression. At one point, about 25% of the American workforce was unemployed. Many people had lost their savings when the banks failed and the stock market crashed. Many people either lost their homes or farms or were in danger of losing their homes or farms because they couldn’t pay their mortgages. The American people looked to the government to try to ease these very difficult situations.
One long-term effect of the New Deal is that people still believe the government should act as a safety net when tough times occur. Whether it is a natural disaster or a serious problem with the economy, people expect the government to act in these situations.
Another long-term effect of the New Deal is that some government programs that were created during the New Deal still exist today. People depend on Social Security for all or part of their income when they retire. People also depend on unemployment benefits when they lose their job. People rely on the Federal Deposit Insurance Corporation to protect the money in their savings accounts.
There were many factors that led to the start of the New Deal. There also were long-term effects associated with it that still exist today.
https://www.history.com/topics/great-depression/new-deal

What are the positive aspects of George and Lennie's friendship in Of Mice and Men?

Although a study of Of Mice and Men has to focus on the negatives and what eventually happens to Lennie, it is unfair to say there are no positive aspects of George and Lennie's friendship. The friendship provides Lennie an opportunity to participate in a world that would otherwise be very unaccommodating to him; for George, the friendship provides a focus that takes him beyond merely day-to-day survival.
Lennie's disability is not clearly defined in the novella, but it is historically accurate to say a person with an intellectual disability at the time at which the story is set would have had very few options available to him. Before George takes Lennie under his wing, Lennie is cared for by his aunt. For the time period, that is believable. People with disabilities were frequently hidden away by family or institutionalized. (For historical context, consider President John F. Kennedy had a sister who was kept out of the public eye in an institution for most of her life—and she was from a wealthy, respected family.) When it came to dealing with the handicapped, the goal of the time period was not to provide rich stimulation; instead, the goal was "out of sight, out of mind." Once Aunt Clara dies, Lennie has no one obligated to care for him, so George's friendship truly does provide Lennie with entrance to a world that would never have accepted Lennie on his own. Even something as mundane as keeping track of his work card is too much for Lennie to handle by himself, but George makes sure Lennie has opportunities to work for pay in a time when jobs were hard to find even for those without handicaps. Without George, Lennie would have not had entry into a workforce where his tremendous strength could be viewed as an asset. With George, Lennie can fit in and even be quietly admired for his abilities instead of maligned for his disability.
For George, Lennie provides a purpose and meaning to everyday work. George and Lennie's shared dream of having a small parcel of land to call their own makes George different from the other men who drift and squander their paychecks on visits to bars or brothels. Although George complains about Lennie and says he could be like those other men, it is clear Lennie provides an excuse for George to have the loftier goal of their shared future plans. Being friends with Lennie sets George apart on a ranch where characters are judged harshly for marrying hastily or caring for an old pet. 
Both Lennie and George gain something from their shared friendship. Interestingly enough, Lennie gains the sense that he can be just one of the guys instead of being set apart, while George gains the reputation of being set apart because he is not like the other guys.

Why is it important that the accused people come out underneath the place where the king and his party sit in the arena in the story "The Lady or the Tiger?"

The location of the king’s party is important because the princess is able to secretly signal her lover.
It is important that the king and the accused can see each other, because the king feels that fate is at play in his system of justice.  He is not the one condemning the accused or pardoning him.  That is done by fate.  The accused person chooses between two doors.  One kills him and the other sends him to his wedding to a beautiful maiden.

Directly opposite him, on the other side of the enclosed space, were two doors, exactly alike and side by side. It was the duty and the privilege of the person on trial to walk directly to these doors and open one of them. 

However, it probably never occurred to the king that someone in his party might find out what was behind each door and signal the accused.  When his daughter’s lover was sent into the arena, she took it upon herself to find out what was behind which door.  She used her position to signal him.

Her right arm lay on the cushioned parapet before her. She raised her hand, and made a slight, quick movement toward the right. No one but her lover saw her. Every eye but his was fixed on the man in the arena.

He knew that she would find out, and he knew she would signal him.  The interesting thing about this story’s ambiguous ending is that we do not know what she signaled him.  She might have sent him to his death, because she did not want another woman to have him.  However, she might have also decided she could not live without him.  We do not know what the signal was, we only know that there was a signal, and he saw her signal.

Calculus of a Single Variable, Chapter 8, 8.6, Section 8.6, Problem 39

For the given problem: int_0^1 xe^(x^2) , we may first solve for its indefinite integral. Indefinite integral are written in the form of int f(x) dx = F(x) +C
where: f(x) as the integrand
F(x) as the anti-derivative function
C as the arbitrary constant known as constant of integration
We omit the arbitrary constant C when we have a boundary values: a to b. We follow formula: int_a^b f(x) dx = F(x)|_a^b .
Form the table of integrals, we follow the indefinite integral formula for exponential function as:
int xe^(-ax^2) dx = - 1/(2a)e^(-ax^2) +C
By comparison of -ax^2 with x^2 shows that we let a= -1 .
Plug-in a=-1 on -ax^2 for checking, we get: - (-1) x^2= +x^2 or x^2 .
Plug-in a=-1 on integral formula, we get:
int_0^1 xe^(x^2) =- 1/(2(-1))e^((-(-1)x^2))| _0^1
=- 1/(-2)e^((1*x^2))| _0^1
= 1/2e^(x^2)| _0^1
Applying definite integral formula: F(x)|_a^b = F(b)-= F(a) .
1/2e^(x^2)| _0^1 =1/2e^(1^2) -1/2e^(0^2)
=1/2e^(1) -1/2e^(0)
=1/2e -1/2 *1
= 1/2e -1/2 or 1/2(e-1)

College Algebra, Chapter 4, Chapter Review, Section Review, Problem 44

If $P(x) = x^4 - 2x^3 - 2x^2 + 8x - 8$, then

a.) Find all zeros of $P$, and state their multiplicities.

b.) Sketch the graph of $P$.



a.) To find the zeros of $P$, we apply synthetic division with the possible rational zeros of the factor of $8$ which are $\pm 1, \pm 2, \pm 4$ and $\pm 8$. Then,

By trial and error,







Again, by applying Synthetic Division







Thus,


$
\begin{equation}
\begin{aligned}

P(x) =& x^4 - 2x^3 - 2x^2 + 8x - 8
\\
\\
=& (x - 2)(x^3 - 2x + 4)
\\
\\
=& (x -2)(x + 2)(x^2 - 2x + 2)

\end{aligned}
\end{equation}
$



Therefore, rational zeros of $P$ are $2$ and $-2$. Also, all the zeros have multiplicity of $1$.

b.) To sketch the graph of $P$, we must know first the intercepts of the function. The values of the $x$ intercepts are the zeros of the function, that is $ 2$ and $-2$. Next, to determine the $y$ intercept, we set $x = 0$ so, $P(0) = ( 0 - 2)(0 + 2)(0^2 - 2(0) + 2) = (-2)(2)(2) = -8$.

Since the function has an even degree and a positive leading coefficient, then its end behavior is $y \to \infty$ as $x \to -\infty$ and $y \to \infty$ as $x \to \infty$. Then, the graph is

I need the page numbers of sixty locations in Maycomb in To Kill a Mockingbird by Harper Lee. I am not sure of the edition, but the treehouse is described on page 9 ("between two trees"), Ms. Dubose's house is on page 7 ("two doors to the north of us"), and the Radleys' place is on page 8 ("three doors to the south").

In my edition, the "treehouse that rested between giant twin chinaberry trees in the back yard" is on page 8. In yours, it is on page 9. The following locations (with page numbers) have been adjusted to correspond with your edition.
Page 7: mentions the Finch home on the main residential street in town, "Mrs. Henry Lafayette Dubose’s house two doors to the north . . . and the Radley Place three doors to the south." Miss Rachel Haverford, who lives next door to the Finches, is also mentioned.
Page 10: the Maycomb school grounds is said to adjoin the back of the Radley lot. In fact, the two locations are so close that nuts from pecan trees in the Radley yard often end up on school grounds.
Page 17: mentions that Miss Caroline Fisher lives across the street from the Finches, one door down in Miss Maudie Atkinson's upstairs front room.
Page 36: describes where Cecil Jacobs and Mrs. Dubose live in relation to the Finches (Atticus, Scout, and Jem).
Page 52: this page locates Mr. Avery's house across from that of Mrs. Henry Lafayette Dubose.
Page 56: mentions Deer's Pasture, located behind the Finch home.
Page 105: V.J. Elmore's is mentioned.
Page 106: on this page, the O.K. Cafe is said to be on the north side of the town square. V.J. Elmore's, where Scout buys her baton, is also mentioned.
Page 120: mentions the First Purchase African M.E. Church as located in the Quarters, outside the southern town limits. This church is said to be the only one in Maycomb with a steeple and bell.
Page 151: the carhouse is mentioned. This is where Atticus parks his Chevrolet.
Page 152: describes the office building that houses the Maycomb Tribune, on the south side of the town square. Mr. Underwood lives in the office building, above the Maycomb Tribune office. When he looks out his window, he can see the jail and courthouse.
This page also mentions the county toilet and the courthouse. The text tells us that Atticus's law office was initially located at the courthouse. However, its new location is at the Maycomb Bank building.
Page 153: describes the Maycomb jail, which is said to be "one cell wide and two cells high, complete with tiny battlements and flying buttresses." On this page, the Maycomb jail is said to be situated between Tyndal’s Hardware Store and the Maycomb Tribune office. The Jitney Jungle is also mentioned.
Page 173: mentions the Ewells living behind the Maycomb dump in what used to be a slave cabin.
Page 174: states that the African American settlement is situated five hundred yards beyond the Ewell residence.

The following questions are in reference to chapters 5-9 of Ian Haney López's Dog Whistle Politics: How Coded Racial Appeals Have Reinvented Racism and Wrecked the Middle Class: What are the author’s criticisms of Obama’s policies during his first term? What was the Gates Affair?

Dog Whistle Politics: How Coded Racial Appeals Have Reinvented Racism and Wrecked the Middle Class addresses numerous aspects of racial tensions in the United States as they relate to the actions (or inaction) of those in positions of political power, including President Obama.
What are the author’s criticisms of Obama’s policies during his first term?
In Chapter 9, the author focuses on what he terms President Obama's post-racial strategy. He explains his views that Obama "sidestepped" the issue of race with his first-term policies, thus tacitly reinforcing the so-called dog whistle politics being perpetuated by Republican politicians and many Democrats. Haney-López's primary argument is that by not doing enough to address the issues underlying dog whistle politics in his first term, Obama himself became complicit in reinforcing that narrative. Throughout the book, the author takes the view that if someone is in a position of power, he or she has the responsibility not only to refrain from actively participating in dog whistling but to stop it wherever possible as well.
In addition to a lack of active participation in decoding racial appeals made by other politicians, Haney-López also criticizes the President's lack of intervention in racialized mass incarceration during his first term. He view's Obama's post-racial policies as a hindrance to addressing issues such as the mass incarceration of racial minorities. The author also addresses the various ways in which the public and media fed into the post-racial narrative with belief that the election of an African-American President would mean an end to racism. In this sense, the author argues that Obama's first term led to complacency among those who believed that racial tensions in the country would be solved simply through his election and without the need for direct policy changes
The Gates Affair
The Gates Affair refers to the arrest of a well-known African American Harvard professor named Henry Louis Gates, Jr.. Gates was arrested on charges of disorderly conduct at his home after returning from a trip in 2009. After being unable to enter his own home, the police were called by a neighbor who saw Gates trying to enter the house and believed he was breaking in. Gates was questioned and there was an argument between the professor and the arresting officer that led to allegations of misconduct on both sides. The matter drew national media attention when Gates was taken to the police station in Cambridge, Massachusetts. Although the charges against him were later dropped, the matter gained media traction when it became known that Gates and the President were friends. While Obama made a statement to the press regarding the incident, Haney-López criticized him for not directly condemning the police for approaching members of minority groups with what he described in a subsequent article as "an aggressive disrespect and a quick resort to physical domination."
https://digitalcommons.macalester.edu/cgi/viewcontent.cgi?referer=&httpsredir=1&article=1043&context=maccivicf

https://www.law.berkeley.edu/php-programs/courses/fileDL.php?fID=7213

Why were Sacco and Vanzetti innocent and what was the significance of the case?

Nicola Sacco and Bartolomeo Vanzetti were two Italian American anarchists convicted of murder and armed robbery in 1920, crimes for which they were executed seven years later. Their executions came at a time in American history when there was widespread fear and mistrust of radical politics, which was associated in the popular mind with violence and disorder. The case was a polarizing one, with many high-profile public figures campaigning against what they saw as a major miscarriage of justice.
Even at the time of their conviction, the case against Sacco and Vanzetti was seriously flawed in many important respects. Eyewitnesses for the prosecution gave conflicting evidence of the defendants' involvement in the crime and in some cases even changed their story. The prosecution case against Vanzetti was especially flimsy, as many eyewitnesses testified that he was at work during the time of the fatal robbery.
The case has been pored over by countless lawyers, jurists, and scholars ever since. Most seem to agree that there was reasonable doubt as to the defendants' guilt. Others have suggested that Sacco did indeed pull the trigger but that Vanzetti was not involved in the actual robbery. In any case, the general consensus is that Sacco and Vanzetti did not receive a fair trial, not least because of the open bias and partiality of the presiding judge, Webster Thayer. The lack of basic fairness in the conduct of the trial was acknowledged in 1977, when the then governor of Massachusetts, Michael Dukakis—the future Democratic presidential candidate—formally proclaimed that Sacco and Vanzetti had been unfairly tried and convicted.
What is significant about the case is that the defendants were on trial for their deeply unpopular, "un-American" political opinions as much as anything. The prosecution persistently used Sacco and Vanzetti's avowed radicalism as a means of establishing circumstantial guilt. Their background as Italian immigrants, their broken English, and their social views were all ruthlessly exploited by the prosecution to convey the impression that, even if they were not guilty of the actual crimes for which they had been charged, they were still dangerous radicals—dangerous foreign radicals—and needed to be punished accordingly.
https://www.theatlantic.com/magazine/archive/1927/03/the-case-of-sacco-and-vanzetti/306625/

How did Maniac pay for Russell and Piper’s school tuition?

Russell and Piper McNab grow up in chaos and squalor. With a drunk for a dad and a seemingly absent mother, they're pretty much left to their own devices. Unsurprisingly, the McNab kids lack the necessary discipline and sustained application for formal education. Maniac's own family background isn't a million miles away from the McNabs', but unlike Russell and Piper, he appreciates the value of an education. So he effectively bribes the two boys to get them to go to school.
First, he gives them pizza if they agree to go. But the McNab boys are cunning little critters and soon realize that they're in a position to negotiate a better deal. From pizza, they graduate to demanding that Maniac perform all kinds of crazy dares and heroic feats. He does so, hitting a telephone pole with a stone sixty-one times in a row; he takes off his shoes and socks and walks barefoot through the rat-infested dump at the foot of Rako Hill; he climbs over the zoo's fence and into the bison enclosure, where he proceeds to kiss a baby buffalo. In performing such bizarre (yet heroic) feats, Maniac is "paying" for Russell and Piper's tuition.

How can I write an essay of 2-3 pages comparing the settings and the themes between "The Yellow Wallpaper" and Annie John?

Though both works are very different, each has an over-arching theme in common—the subjugation of women and girls. In both works, this theme manifests in similar ways.
Firstly, there is the limitation imposed on women and girls' self-expression. In Gilman's story, the narrator is a writer whose creative outlet is discouraged by her husband. Her journal, which serves as the narrative, is forbidden by her husband, John: "There comes John, and I must put this away—he hates to have me write a word." In Annie John, Annie's mother scolds her and calls her a "slut" for talking to a group of boys. Though the implications are different for each behavior—the first is discouraged because John does not want his wife to develop her creative and critical faculties, and the the second is discouraged due to its perceived sexual connotations—both behaviors go against ideas about traditional femininity.
Secondly, there is the problem of attachment. In "The Yellow Wallpaper," the narrator's husband tells her what to do, how to think, and how she feels. He refers to her as "little girl." The narrator thinks that this is a demonstration of love:

He is very careful and loving, and hardly lets me stir without special direction. . . . he takes all care from me, and so I feel basely ungrateful not to value it more.

In Annie John, Annie struggles with feelings of her childhood attachment to her mother, as well as her mother's diminishing love and excessive criticism. Annie's mother projects her own fears and sexual anxieties onto her daughter, as well as an internalized double-standard that condemns Annie for talking to boys, but says nothing in response to Annie's father's infidelities. To separate effectively from her mother, she leaves Antigua to study nursing in England.
In regard to setting, the two works are very different—"The Yellow Wallpaper" is set in "a colonial mansion" at "a hereditary estate" in an unnamed part of the country, while Annie John is set in tropical Antigua. However, Antigua was a British colony during the time in which the novel is set. Both are beautiful places. The mansion is surrounded by gardens and plenty of greenery, just as Antigua is a lush place.
In both works, the colonial aspect could serve as a metaphor for restriction and the demand to follow established patterns. In Gilman's story, the yellow wallpaper in the house—a remnant of bygone days—becomes the site of the narrator's descent into madness. She wants to change it, but her husband refuses, believing that it will only lead to her wanting to make more renovations, which he finds unnecessary in a summer house. In Kincaid's novel, she describes the formality of British schools and how they forbid critical thinking and the demonstration of aspects of folk culture, such as singing benna, or Antiguan calypso.
I hope that this helps you in constructing your own essay.

Find and copy three passages which describe Count Dracula as he stands in the doorway.

Throughout Stoker’s classic novel, doorways function as liminal spaces in which either side of the threshold represents an alternate reality. In literature, liminal spaces symbolize a sense of uncertainty about one’s transition from the present to the future. In the following examples, Dracula in a doorway functions within this context.
The narrator describes Dracula at the door of his castle, saying, “Within, stood a tall old man, clean shaven save for a long white moustache, and clad in black from head to foot, without a single speck of colour about him anywhere. He held in his hand an antique silver lamp, in which the flame burned without a chimney or globe of any kind, throwing long quivering shadows as it flickered in the draught of the open door.” This quote appears in chapter 2. Based on this description, Dracula is a mysterious figure who evokes a sense of death. The black clothing and colorlessness of his person are both associated with mortality. In addition, once Jonathan enters into the castle, his fate will be sealed.
Moments later, Jonathan remarks, “He made no motion of stepping to meet me, but stood like a statue, as though his gesture of welcome had fixed him into stone. The instant, however, that I had stepped over the threshold, he moved impulsively forward, and holding out his hand grasped mine with a strength which made me wince, an effect which was not lessened by the fact that it seemed cold as ice, more like the hand of a dead than a living man.”
This further indicates Dracula’s association with death. In addition, the comparison to a statue suggests that Jonathan notices something odd about Dracula. In other words, his first impression, that Dracula is pretending to be normal but is so obviously not, makes Jonathan feel uneasy. Dracula’s apparent delight at getting Jonathan to enter of his own accord indicates that the Count has plans for his new guest.
In chapter 4, Dracula pretends to let Jonathan return to England when he unlocks the great door of the castle. However, Jonathan hears and sees the wolves that seem to be under Dracula’s control: “But still the door continued slowly to open, and only the Count’s body stood in the gap.” In this quote, the Count serves as a barrier between imprisonment and escape. Escape, however, also means tortuous death, in this case. Dracula uses doors as a way to conceal and control, even using himself as part of the liminal space in this example.

What dose fathers office look like in the boy in striped pyjamas

Just like his father's office in heir former home in Berlin, Bruno knows that his father's office in Out-With is "Out of Bounds, With No Exceptions." In fact, that is the title of Chapter 5, in which Bruno actually gets to see the interior of the forbidden room. In this chapter, Bruno desperately wants to speak with his father about his displeasure concerning the move to the new home, so he enters his father's office to speak with him.
The first thing that Bruno notices is that this room is different from the gloomy rooms that occupy the rest of the house. The office has a very high ceiling and a soft wall to wall carpet. The walls are entirely lined with tall mahogany bookshelves that are full of books. Across from the door are large windows overlooking the garden with a seat in front of them. The room is dominated by his father's large oak desk which is placed in the center of the office. His father's chair is behind the desk. There are at least two large armchairs in front of the desk for visitors and petitioners. Bruno is very impressed by the magnificence of the room.

One of the most important rules that Bruno must follow at home is to never enter his father's office. Bruno's father is a high-ranking Nazi commandant who conducts business from his home office and does not want his son disturbing him. Bruno obeys his father's rule that his office is "Out Of Bounds At All Times And No Exceptions" and has only been inside his father's office a few times.
In chapter 5, Bruno finally gets a chance to step into his father's new office at their house in Out-With. Bruno recalls seeing high ceilings and feeling the luxurious carpet underneath his feet throughout the office. There are also rich mahogany shelves aligning the walls, where books are neatly stacked and resemble the walls of a library. In the center of the office is a massive oak desk that sits in front of two high windows, which overlook the garden outside. Bruno is impressed with his father's luxurious office and is surprised at all the expensive features inside.

Why does Holmes let Ryder go?

Ryder is the thief who is found to have stolen the blue carbuncle in "The Adventure of the Blue Carbuncle." However, at the end of the story after Ryder has confessed himself and begged, "God help me! God help me!", Holmes seems moved by compassion and tells the man to get out of his flat, without making any move to prosecute Ryder. He explains to Watson that he is doing this because he does not believe that it is his responsibility to "supply the deficiencies" of the police, and moreover, the failure to prosecute Ryder cannot result in the conviction of another innocent man. He feels that Ryder has been "too terribly frightened" by this case to continue on and commit any other crime, but "send him to gaol now, and you make him a gaol-bird for life."
Holmes is also somewhat moved by the fact that it is Christmas, "the season of forgiveness." His primary concern, however, seems to be the fact that Ryder is not a born criminal and is more likely to become one if sent to prison for this act than if simply allowed to go free on this occasion. Holmes knows he is committing a "felony" of his own in doing this but ultimately judges it the best course of action.

Discuss how the Cold War between the United States and the Soviet Union affected other nations and/or regions of the world.

Whether they liked it or not, most of the world's countries had to take sides during the Cold War. The United States, then as now, was the world's biggest superpower, with the world's largest economy. It was virtually impossible for any country to avoid having to deal with the United States; the only question was how. Countries such as India adopted what could be described as a flexible posture with regards to the Cold War, playing the United States and the Soviet Union off against each other, depending on the circumstances.
In the developing world, both new nations and anti-colonialist movements alike came under the influence of the USSR, which was seen as a useful ally against Western imperialism. For its part, the United States also involved itself in the affairs of the developing world, often propping up dictatorships that were hostile to Communism. Continents such as Africa and South America became battlegrounds in this epic ideological struggle, with both the Americans and the Soviets jockeying for strategic primacy in advancing their respective goals.
As the United States and the Soviet Union were nuclear powers, a direct confrontation between them was unthinkable. So the two Cold War superpowers used proxies to fight their battles for them. A prime example of this can be seen in the Angolan Civil War, where two rival liberation movements—the Marxist MPLA (backed by the Soviets) and the more right-wing UNITA (backed by the United States)—engaged in a long, bloody and bitter struggle for nigh on thirty years. The war was prolonged by massive shipments of arms to both sides in the conflict from their respective Cold War backers.
Many Angolans simply wanted independence; they weren't too concerned about the wider geopolitical issues involved. Nonetheless, they found themselves caught up in the middle of another conflict which caused significant suffering and misery to their country. What happened in Angola is symptomatic of how the world was divided up during the Cold War and of how some kind of involvement was almost inescapable, especially for the world's poorest and least-developed countries.

The Cold War affected the entire world, not just members of the two nations primarily involved.  The United States and the Soviet Union fought a series of proxy wars in the developing world.  Both the Soviet Union and the United States initially sent advisers to North and South Vietnam respectively before moving to send combat forces, the United States sending ground troops and the Soviet Union sending fighter pilots.  The United States and the Soviet Union also fought a proxy war in Afghanistan, with the Soviets sending ground troops and the United States arming the mujaheddin rebels.  Both of these proxy wars served to destabilize both countries.  Millions of Vietnamese, Laotians, and Cambodians died as a result of the Vietnam War, and the world is still experiencing the results of extremism as a result of the chaos that was created in Afghanistan during the 1970s.  
Even regions that did not experience war directly were affected by the Cold War.  Germany remained divided between East and West well after World War II was over.  Even today, American troops are a presence in Germany.  Cuba received Soviet aid for decades; this nearly led to the island being invaded in 1962 and has led to sanctions that has affected all Cubans.  Many armies  and paramilitary groups around the world still use Soviet-era weapons.  

Calculus: Early Transcendentals, Chapter 7, 7.4, Section 7.4, Problem 21

Integrate int(x^3+4)/(x^2+4)dx
Rewrite the given function using long division.
int[x+(-4x+4)/(x^2+4)]dx
=intxdx-int(4x)/(x^2+4)dx+int4/(x^2+4)dx

Integrate the first integral using the pattern intx^n=x^(n+1)/n+C
intx=x^2/2+C

Integrate the second integral using u-substitution.
let u=x^2+4
(du)/dx=2x
dx=(du)/(2x)
-int(4x)/(x^2+4)dx
=-4intx/u*(du)/(2x)

=-2ln|x^2+4|+C
=-2ln(x^2+4)+C

Integrate the third integral using the pattern
int(dx)/(x^2+a^2)=(1/a)tan^-1(x/a)+C
int4/(x^2+4)dx=(4)(1/2)tan^-1(x/2)+C=2tan^-1(x/2)+C

The final answer is:
1/2x^2-2ln(x^2+4)+2tan^-1(x/2)+C

What is the first thing that Scout finds in the oak tree on the edge of Boo Radley's property? How does Jem react when he learns about Scout's discovery?

As a first grader, Scout gets out of school thirty minutes earlier than Jem does, which means she must walk home without him. She runs past the Radley place each day because the children have made Arthur Radley into a legendary monster, even though they've never seen him. One day as she is running past, she notices a piece of tinfoil "winking at me in the afternoon sun" from one of the two oak trees on the Radley lot. The tinfoil is sticking out of a knot-hole that is about as high off the ground as Scout is tall. She reaches into the knot-hole  and takes out two pieces of chewing gum--without their wrappers. Not wanting to spend any more time than necessary on Radley property, she runs home quickly with the gum in her hand. She sniffs it and examines it once she reaches the safety of her front porch. She thinks it looks fine, but she still licks it and waits a while before cramming it into her mouth. At that point she can tell that it's Wrigley's Double-Mint gum.
When Jem comes home and notices her chewing a huge wad of gum, he wants to know where she got it. She divulges that she found it inside one of the Radleys' trees, and he commands her to spit it out immediately. He stamps his foot and warns her that she'll get killed if she even touches a Radley tree. He tells her she must gargle or he'll tell Calpurnia on her, and she reluctantly complies, not wanting to rinse the taste away but fearing Calpurnia's wrath.

In Chapter 4, Scout is passing the Radleys' home and notices a shiny object coming from the knothole of the giant oak tree in the Radleys' yard. Scout runs over to the tree and grabs two sticks of Wrigley's Double-Mint chewing gum out of the knothole. When she gets home, she unwraps the gum and sniffs it to make sure it isn't poisonous. Jem returns home and asks Scout where she got the wad of chewing gum. Scout tells Jem she found it sticking out of the tree in the Radley yard and Jem yells at her to immediately spit out the gum. Scout obeys Jem by spitting out the gum and then informs him she's been chewing it all day. Jem is still under the impression that everything associated with the Radleys is harmful and tells Scout she's not even supposed to touch the Radleys' trees, let alone eat anything she finds in them. Jem insists what Scout did was deadly and commands her to gargle the taste out of her mouth.

Should consumers buy goods from countries or producers that use child labor?

This question is strictly an opinion question. An argument could be made for either side of the issue. Those who would say we should boycott buying products from countries or producers who use child labor are appealing to the moral and emotional side of the issue. Most people believe children should not be working long hours for low pay. They believe children should be in school getting an education in order to help themselves make a better life in the future. Without an education, it is hard to accomplish this. They also may say that child labor may harm the development of the child.
Those who would be opposed to boycotting buying products from these countries or producers would say that using child labor helps to keep the cost of the product lower. This gives these countries or producers an advantage over other countries or producers who have to pay higher wages and then charge higher prices. The goal of a business is to keep expenses low in order to maximize profit. With higher expenses come higher prices, putting that producer at a disadvantage. Some people would also say that any money a child earns may be helpful to a family that is struggling economically.
https://campaign.worldvision.com.au/wp-content/uploads/2013/04/It-is-better-for-children-to-work-debate-kit.pdf

Choose two words from this group that are related. a. shout b.carefully c. create d. laugh

There are at least two ways to answer this question. This is because it is not clear exactly what it means for two words to “be related.”
First, you could say “create” and “carefully” are related. These are related because they could be used together. When a person creates something, he or she might do so carefully. Because you might create something carefully, the two words are, in a sense, related.
Second, you could say “laugh” and “shout” are related. I would say this is the better answer. These two words are related in two ways. They are related because they are both verbs. They are also related because they are both actions people can do with their own bodies. People can, without anything or anyone else, shout or laugh.
These are two options for this answer. I prefer the second option because those two words are connected to one another in two different ways.

College Algebra, Chapter 5, 5.3, Section 5.3, Problem 48

Combine the expression $\displaystyle \log_5 (x^2 - 1) - \log_5 (x - 1)$, using the Laws of Logarithm


$
\begin{equation}
\begin{aligned}

\log_5 (x^2 - 1) - \log_5 (x - 1) =& \log_5 \left( \frac{x^2 - 1}{x - 1} \right)
&& \text{Law of Logarithm } \log_a \left( \frac{A}{B} \right) = \log_a A - \log_a B
\\
\\
\log_5 (x^2 - 1) - \log_5 (x - 1) =& \log_5 \left[ \frac{(x - 1)(x + 1)}{(x - 1)} \right]
&& \text{Factor } x^2 - 1
\\
\\
\log_5 (x^2 - 1) - \log_5 (x - 1) =& \log_5 (x + 1)
&& \text{Cancel out like terms}

\end{aligned}
\end{equation}
$

Who paid for Vasco Núñez de Balboa’s exploration?

Unlike other Spanish explorers and conquistadors, Vasco Nunez de Balboa was not the leader of an expedition and was not financed by royalty when he first went to the New World. Instead, he joined an expedition in 1500 led by Rodrigo de Bastidas and received a share of earnings from Bastidas as a member of his team. They explored the coast of present-day Columbia and then went to the island of Hispaniola.
As a planter and pig farmer on Hispaniola, Balboa got into debt. He stowed away on a ship bound for the coast of Columbia. When he was discovered, the captain's first impulse was to abandon Balboa on a deserted island, but he eventually brought him to the colony of San Sebastian. Balboa helped some of the men win a victory over natives in the region of Darien, and when they defeated them, they plundered the native settlement and found numerous gold ornaments.
Balboa eventually became mayor of the new settlement, which was named Santa Maria la Antigua del Darien. After much political maneuvering with rivals, Balboa became governor of Veragua in 1511. As governor, Balboa continued raiding the villages of the local natives, gathering more gold in the process. He did not earn this gold as pay, though, but took it by force. His colony also received some supplies from Hispaniola and also from Spain.
In 1513, Balboa wrote to the King of Spain asking for men, weapons, and supplies to build a fleet of ships for further exploration. While waiting for an answer, he heard of another sea and natives with a vast wealth of gold on its shores. With a group of men and some native guides, Balboa crossed the Isthmus of Panama. From a mountain peak, he saw the Pacific Ocean and claimed the lands on all its shores for the King of Spain.
When Balboa got back to Santa Maria, he and his men brought a treasure of gold and pearls. He sent news of his discoveries and a portion of the treasure to the King. A large fleet of 17 ships and 1,500 men arrived from Spain, but Balboa was deposed as mayor and governor.
The new governor, Pedrarias Davila, gave Balboa some men and materials to build ships and explore a small area of the Pacific Coast, but when Balboa returned, Pedrarias had him arrested and beheaded in 1519.
In conclusion, we can see that Balboa was first paid by Bastidas, then made his living as a pig farmer, then accumulated wealth by warring with natives and seizing gold and other treasures, and finally, near the end, received some supplies from the King of Spain and Pedrarias.
https://www.biography.com/explorer/vasco-nunez-de-balboa

https://www.history.com/topics/exploration/vasco-nunez-de-balboa

Balboa is most famous for being the first Spaniard to reach the Pacific Ocean by crossing the Isthmus of Panama. Born in Spain, he belonged to a noble family that had become cash-poor, and, as a result, he sought to make a fortune in the New World like many of his fellow conquistadores.
His initial voyage with Don Rodrigo de Bastidas explored the coast of what is today Colombia and Venezuela, and they actually discovered what is now modern-day Panama in the process. This voyage was financed by the Spanish crown.
Eventually, however, Balboa settled in Hispaniola, only to leave for Panama because he saw opportunity for riches in the failing settlement (in Panama) of San Sebastien. After emerging to prominence, and creating a new settlement called Darien in Panama, Balboa set off through the dense rain forests to explore the western regions of the isthmus. This expedition took almost two months and involved several dozen Spaniards and hundreds of Native people. Balboa, eager to earn more riches, financed it himself.
This risk paid off, as he encountered what was then known as the "South Sea," (i.e., the Pacific Ocean), and he became the governor of Panama. Eventually, he was executed amid rivalries and infighting—which often characterized Spanish colonial politics—but in the short term, his self-financed expedition through the jungle earned him fame and power.
https://exploration.marinersmuseum.org/subject/vasco-de-balboa/

Vasco Nunez de Balboa led the first European expedition to the Pacific Ocean. One of the more remarkable parts of his story is that he did so with relatively little outside support and funds. His 1513 expedition across the Isthmus of Panama was carried out on a shoestring budget and was predominantly funded by himself.
Balboa had indeed requested funding from the authorities of Hispaniola. However, his rival, Fernández de Enciso, who Balboa had previously usurped as mayor of Santa Maria in Panama, had beat him there. Enciso had informed colonial leaders of Balboa's power grab in Panama and was in the process of bringing charges against him. As a result, Balboa found no support in Hispaniola. He therefore sent his comrade, Enrique de Colmenares, to Spain to make a case for funds. Unfortunately for Balboa, Spanish authorities were already aware of Enciso's case against Balboa and were making moves to have him replaced. He would find no support from Spain.
As a result, Balboa's expedition was funded by himself. Using only what resources he had on hand in Panama, including ten native canoes and one small ship, he set out on September 1, 1513, with 190 Spaniards and a handful of natives to cross the Isthmus of Panama.
In short, Balboa's "discovery" of the Pacific Ocean received no official funding from any government or patron. His unpopularity in Spain and Hispaniola meant that no one would back him financially on his voyage. Therefore, he used only the limited resources he had available when he and his men set out to find the Pacific Ocean.
https://www.gutenberg.org/files/34802/34802-h/34802-h.htm

Are United States military interventions and wars absolutely necessary to preserve democracy and freedom?

I believe it is fair to say that, in most cases, the United States needs to be involved in military interventions or in wars to preserve democracy and freedom. There are several examples that support this position. During the 1920s and the 1930s, the United States and other European countries actively followed an isolationist foreign policy for various reasons. This backfired as aggressive countries, led by dictators such as Hitler and Mussolini, began to take over other countries. One message this whole set of events suggested is that aggression cannot be ignored.
After World War II, the United States, our allies, and, at times, the United Nations took an active role to prevent the spread of communism to non-communist countries. It is fair to say that if the United States, France, and Great Britain did not organize the Berlin Airlift, West Berlin would have fallen into communist hands. The same case can be made in South Korea in 1950. Even with help from the United Nations, South Korea nearly was conquered by communist North Korea. With the help of forces from the United Nations, led by the United States, South Korea remained free and does so to this day. Currently, there is a growing threat from North Korea with its development of nuclear weapons, and the United States is supporting South Korea.
The United States developed the European Recovery Program to help nations that were fighting the spread of communism in Europe after World War II. The United States gave aid to Greece and Turkey to help them avoid being taken over by communist forces. The Cuban Missile Crisis is another example where American involvement was needed. The United States could not allow the Cuban government and the Soviet Union to put missiles with offensive capabilities in Cuba. The United States needed to act to protect the American people and other countries in the Western Hemisphere.
In each of these cases, the United States was acting to preserve freedom and democracy in countries where it already existed and was being threatened by the actions of other countries. It is reasonable to conclude that the United States needs to be involved when threats are made to democratic governments and to freedom.
https://www.history.com/topics/cold-war/berlin-airlift

https://www.history.com/topics/cold-war/cuban-missile-crisis

https://www.thoughtco.com/the-korean-war-an-overview-2360860

College Algebra, Exercise P, Exercise P.1, Section Exercise P.1, Problem 24

If a fruit crate has square ends and is twice as long as it is wide.

a.) Find the volume of the crate if its width is 20 inches.
Recall that the volume of a box is $V = L \times W \times H$. Since the box has a square ends, its width and height are equal. So,

$
\begin{equation}
\begin{aligned}
V &= L \times W \times H \text{ ,where } W = H \text{ so}\\
\\
V &= L \times W \times W\\
\\
V &= L \times W^2 \text{ ,also from the condition } L = 2W \text{ so}\\
\\
V &= 2W \times W^2\\
\\
V &= 2W^3 && \text{model}\\
\\
V &= 2(20 \text{in})^3 && \text{Substitute } W = 20\text{in}\\
\\
V &= 16,000 \text{in}^3 && \text{Volume of the crate}
\end{aligned}
\end{equation}
$


b.) Find a formula for the volume $V$ of the crate in terms of its width $x$.
From the model in part(a), we solve $V= 2W^3$ for $W = x$, so

$
\begin{equation}
\begin{aligned}
\frac{V}{2} &= \frac{\cancel{2}x^3}{\cancel{2}} && \text{Divide both sides by 2}\\
\\
\sqrt[3]{\frac{V}{2}} &= \sqrt[3]{x^3} && \text{Take the cube root of both sides}\\
\\
\sqrt[3]{\frac{V}{2}} &= x && \text{model}\\
\\
& \text{or}\\
\\
x &= \sqrt[3]{\frac{V}{2}}
\end{aligned}
\end{equation}
$

What sacrifices do people make to ensure their own or someone else's survival?

In cases where we are talking about ensuring survival, we can assume that lives are at stake. This means that people will behave in extreme ways.
The idea of a "sacrifice" suggests selflessness, and indeed people will sometimes behave selflessly in order to protect their loved ones, particularly their children. There have been many recorded instances of parents sacrificing their own lives so that their children can live, from the sadly mundane—women choosing to give birth to their children under dangerous circumstances, knowing they are likely to die in the process—to the disastrous and unexpected. When a child can only escape from a home made unstable by an earthquake if a parent steadies the building for them, parents have repeatedly sacrificed themselves to secure their children's escape. Where there is a limited supply of food or water, parents will sacrifice their own share for their children. This is a natural instinct.
Arguably, however, parents' overwhelming need to provide for their children can be selfish, too. If there are two children and enough food only for one of them, will a parent feed their own child over someone else's? Often, yes.
In the same way, what we will "sacrifice" to save our own lives, where no loved ones are involved, is sometimes selfish, too. People sometimes sacrifice their moral compass, choosing to make decisions which result in someone else dying first. Or we may sacrifice the laws of society: in order to survive, humans have resorted to cannibalism. Humans have also tried to ensure their own survival by sacrificing parts of their own bodies, as when the climber Aron Ralston amputated his own right arm with his pocketknife in order to escape a rock which was trapping him.
So, humans have been known to sacrifice both selfishly and selflessly in order to ensure the survival of themselves and their families. What precisely is sacrificed depends on the extremity of the circumstance.