Calculus and Its Applications, Chapter 1, 1.8, Section 1.8, Problem 68

If the distance function is $s(t) = 0.1t^4 - t^2 + 0.4$, illustrate $s, v$ and $a$ over the
interval $[-5,5]$. Then use the graph to determine the point(s) at which the velocity will switch
from increasing to decreasing or from decreasing to increasing.

We have, $s(t) = 0.1t^4 - t^2 + 0.4$, so

$
\begin{equation}
\begin{aligned}
v(t) &= s'(t) = 0.4t^3 -2t\\
\\
a(t) &= v'(t) = 1.2t^2 -2
\end{aligned}
\end{equation}
$


Then, the graph is



Based from the graph, the velocity switches at $t \approx -1.25$ from increasing to decreasing.
On the other hand, the velocity switches at $t \approx 1.25$ from decreasing to increasing. These values
are obtained by looking at the peaks of the graph of the velocity function or by looking at the values where
the acceleration function crosses the $x$-axis because the slope and time peaks of the velocity is zero.

How is Antony a wiser leader than Brutus?

This is a great question. While Brutus is often considered the tragic hero of Shakespeare's Julius Caesar, many readers and audiences of the play have insightfully noted that Brutus, for all his honor, is not always the best leader. Indeed, it could be argued that Antony is the wiser leader, as he is able to skillfully navigate and manipulate the complex political climate of Rome while also increasing his own power simultaneously.
Let's compare the two men: Brutus is famous for his honor and nobility, and he ultimately joins the conspirators to protect Rome's republican politics from a tyrannical dictator. These sentiments are entirely honorable and admirable to be sure, but they also illustrate a fatal flaw. Since he is so wrapped up in honor and justice, Brutus naively assumes that other individuals will act with the same selfless attitude. This assumption ultimately proves to be the downfall of both himself and his fellow conspirators. By foolishly letting Antony speak at Caesar's funeral, Brutus inadvertently gives Antony the chance to manipulate the passions of the mob against the conspirators. Indeed, Antony proves to be a cunning politician, as he is able to use carefully crafted rhetoric to influence the masses of Rome and many prominent politicians to turn against Brutus and his companions. As such, though he is less honorable, Antony proves to be the better leader, as he skillfully manipulates Rome's political system to amass personal power.

Why did Andy join a gang?

Ironically, Andy joined a gang to gain what he believed would be a worthy identity. The text tells us that the Royals and the Guardians were two of the biggest gangs in his area. Andy was especially proud when the Royals accepted him; at the time, he believed that he had gained a worthy title as a Royal gang member.
However, as he lay dying, he no longer reveled in being a Royal. He suddenly realized that he had never envisioned dying at such a young age. After all, he was only sixteen. There were still many things he wanted to do in life. Above all, he had hoped to one day marry Laura, his girlfriend.
As Andy lay dying, he wondered whether the Guardian member who stabbed him saw him as an individual. Andy did not want to die as a Royal gang member. He desperately needed to be known as an individual in his own right. In the last moments of his life, he concluded that a so-called title was little good if one was dead. The story is a sad one: eventually, Andy dies alone, with none of the Royals on hand to comfort him in his last moments.

What is hidden in Montag's ventilator grill of his house?

Montag has hidden a small collection of books behind the ventilator grill in his home. Montag is a jaded firefighter who has been questioning his life and occupation after meeting Clarisse. Montag has been dissatisfied with his life for some time and has been secretly taking books while on duty. Books are illegal to own in Bradbury's dystopian society, which is why Montag is forced to hide the novels behind his ventilator grill. He believes that the ventilator is an adequate hiding spot to place the books, and he stares directly at the grill several times in part one when he begins to question his happiness. Montag believes that the answers to many of life's most difficult questions could be written in books and contemplates quitting his job. After having a tense conversation with Captain Beatty, Montag takes the hidden books out of his ventilator and begins reading them.

Montag has books hidden in his ventilator grill at his house. 
Although he has not read any books before meeting Clarisse, his brief encounter with her causes him to be reminded of these books when he returns home:

He stood looking up at the ventilator grill in the hall and suddenly remembered that something lay hidden behind the grill, something that seemed to peer down at him now.

Montag must have had some spark of curiosity about the contents of the forbidden objects that he burns or he would not have stolen them. Now, after talking with the girl named Clarisse, Montag begins to wonder what it is that the books contain. When the books seem to "peer down at him," he "move[s] his eyes quickly away" as though he wishes not to think of them, or, perhaps, out of fear that he does desire to examine them. Clarisse has awakened something in Montag, something that he wants to experience, but, at the same time, he fears doing so because it is forbidden.

What is a brief character sketch of Uncle Podger from Jerome's Three Men in a Boat?

I will definitely try to be more brief than the narrator is during his description of Uncle Podger.  The narrator begins chapter three with a long description of Uncle Podger.  The narrator does this because he tells readers that Harris is exactly like his Uncle Podger, so instead of telling us about Harris, we get to read a long, comical section about his uncle.  

That’s Harris all over—so ready to take the burden of everything himself, and put it on the backs of other people.
He always reminds me of my poor Uncle Podger.

Uncle Podger is the kind of person that considers himself a real handyman, and he wants everybody to know that he's working on a particular project.  

“Oh, you leave that to me. Don’t you, any of you, worry yourselves about that. I’ll do all that.”

The project in this particular case is the simple act of hanging a picture on the wall.  Instead of just getting the tape measure, level, hammer, and nail himself and hanging the picture within ten minutes, Uncle Podger recruits the entire family to help him with the job.  He sends a person out to get a nail, a different person to get the hammer, a different person to do something else, etc.  

“Now you go and get me my hammer, Will,” he would shout; “and you bring me the rule, Tom; and I shall want the step-ladder, and I had better have a kitchen-chair, too; and, Jim! you run round to Mr. Goggles, and tell him, ‘Pa’s kind regards, and hopes his leg’s better; and will he lend him his spirit-level?’ And don’t you go, Maria, because I shall want somebody to hold me the light; and when the girl comes back, she must go out again for a bit of picture-cord; and Tom! — where’s Tom?—Tom, you come here; I shall want you to hand me up the picture.”

He doesn't perform any task completely by himself, and when he does, he messes it up.  In the narrator's example, Uncle Podger finally gets to the point of actually hitting the nail in the wall; however, he hits his finger instead of the nail.  Then he puts the hammer through the wall because he hit the nail too hard.  By the time the job is finished, hours have passed by, and the picture isn't even on the wall straight.  

Then we had to find the rule and the string again, and a new hole was made; and, about midnight, the picture would be up—very crooked and insecure, the wall for yards round looking as if it had been smoothed down with a rake, and everybody dead beat and wretched—except Uncle Podger.

Basically, Uncle Podger is the kind of person that can't do simple tasks, but he thinks he can.  Additionally, he's the kind of person that makes simple tasks more complex because of the number of people he recruits to help him do the simple task.  
The narrator sees this trait in Harris, so when Harris says that he'll do a simple job and asks for the narrator's help, the narrator immediately puts a stop to what he believes will be an ensuing fiasco.  

“Now, the first thing to settle is what to take with us. Now, you get a bit of paper and write down, J., and you get the grocery catalogue, George, and somebody give me a bit of pencil, and then I’ll make out a list.”
[...]
“No; you get the paper, and the pencil, and the catalogue, and George write down, and I’ll do the work.”

J., the narrator of Three Men in a Boat, tells a lengthy story about his Uncle Podger in Chapter III. Here is a man who thinks he knows how to do something – maybe, he thinks he knows how to do many things -- when in fact, he’s quite helpless and needs the assistance, verification, and admiration of everyone else around him to do the simplest task. The incident J. recalls is when his uncle once decided to hang a picture on the wall. The task only required the framed picture, a nail, a hammer, a step-ladder, and perhaps a pen or pencil to mark the spot where the nail should go. But Podger made a big deal of the challenge. He called on all of family members to bring him the tools. Then he kept “losing” some of them. He dropped the picture and cut his finger on the glass. He hit his thumb with the hammer. And on and on the ordeal went until near midnight, when the picture finally hung crookedly on the wall, the room was in a state of shambles, and Uncle Podger commended himself on a job well done. He had sapped the strength of everyone around him.

Do you think the poet should have stopped near the woods and enjoyed the beauty of nature in the poem "Stopping by Woods on a Snowy Evening"? Give a reasoned reply.

Robert Frost was a great admirer of Henry David Thoreau, author of the classic Walden. Frost evidently made an early decision to lead a life of rustic simplicity so that he could devote all his time and thought to writing poetry, which was obviously his calling. This may have forced him to become a "nature poet" whether that was his original inclination or not. He derived inspirations from nature, and like all poets he never could know when he might receive an inspiration. But he must have learned that such inspirations were of the utmost importance to him in his chosen career. And the sight of the woods filling up with snow on a snowy evening was a great deal more important than a pretty picture that would look good on a Christmas card. It was an inspiration for a now-famous poem. He had to sit there while the inspiration sank in--although he didn't have to compose the poem itself before he started for home. No doubt the poem "Stopping by Woods on a Snowy Evening" was written later on in the comfort of a lighted room with a warm fireplace. But Frost not only "should" have stopped to look at that scene; it was a necessity. What if he hadn't stopped and the poem didn't exist?

Because this is a "what do you think" question, there is not a 100% correct answer.  Different readers will have different opinions.  You can safely state your opinion, but do be sure to clearly explain why you think what you think.  
I'd like to play the Devil's advocate for my answer.  Most people would probably answer "yes, it's fine that the man stopped by the woods because nature is beautiful, and he's not hurting anybody;" however, I would like to provide an answer that goes the other direction.    
No, I do not think that the man should have stopped by the woods to enjoy nature.  The poem states that it is a dark and cold night.  

The darkest evening of the year.

Snow is beginning to fall too. Enough snow to begin filling the woods.

To watch his woods fill up with snow. 

For the speaker's safety and the safety of his horse, he should not be out wasting time.  He needs to minimize his exposure to the elements and get to shelter sooner rather than later.  This is especially true since the end of the poem says that he has many more miles to go before his destination.  I read "To Build a Fire."  That guy died from exposure to the cold.  I also read "The Outcasts of Poker Flat.  Most of those characters froze to death in a winter storm because they didn't hurry to their destination.  The man in the poem is perfectly welcome to admire the beauty of nature, but he should do so through a window on the inside of a nice, warm house. Additionally, the poem ends with the speaker admitting that he has promises to keep. He needs to stop procrastinating, get to his destination, and honor his commitments.   

Precalculus, Chapter 4, 4.4, Section 4.4, Problem 62

sin(7pi/6)=sin(pi+pi/6)=-sin(pi/6)=-1/2
cos(7pi/6)=cos(pi+pi/6)=-cos(pi/6)=-sqrt(3)/2
tan(7pi/6)=tan(pi+pi/6)=tan(pi/6)=1/sqrt3

Which of the five senses does the third stanza concentrate on? List examples.

William Wordsworth's 1849 poem pays respect to the steady habits of a village blacksmith, a widower who works hard, practices faith, and lives simply. The third stanza has many appeals to the reader's sense of hearing.

"Week in, week out, from morn till night,You can hear his bellows blow;You can hear him swing his heavy sledge,With measured beat and slow,Like a sexton ringing the village bell,When the evening sun is low."

A bellows is a tool that produces air to feed a fire. When it is operated, it produces a whooshing sound. In using it, the fire would respond by flaring, which would also produce sound.
The sledge that is mentioned in line three is a sledge hammer, a tool composed of a wooden handle and a blunt iron head. A blacksmith uses a sledge hammer to shape hot metal by pounding it on an iron anvil. The sound that it produces is rhythmic and clamorous as metal hits metal. It is a clanging sound. The poem's speaker describes the sound as slow, meaning that the blacksmith pounds slowly and methodically. Using a simile, he compares it to the ringing of a church bell for evening prayers.

How in the book A Mercy by Toni Morrison did Jacob Vaark receive mercy?

Morrison portrays Jacob Vaark as a character who gives mercy freely to others throughout the book, but he himself is the recipient of mercy at multiple points in the story. Vaark is plucked from his degrading life in the poor house by a job offer from a prestigious law firm. In this way, he is able to change his station in life and develop a platform of wealth that he uses to help the disenfranchised. Jacob also experiences mercy when his mail-order bride turns out to be a compatible partner in life. While both Jacob and his bride took a risk in accepting the arrangement, he is rewarded with a companion who shares his burdens and his joys.
The primary mercy that Jacob receives is the fact that he did not survive to see the ruin of his estate. While the counterweight to this mercy is the fact that he did not survive to achieve the vast, wealthy mansion he had dreamed of building for so long, he died with the prospect of hope for what he left behind. As Jacob tells his wife, "What a man leaves behind is what a man is." At the time of his death, his wife was still well and there were many possibilities ahead of him, despite the tragedy in his past.

How can I write a caption on the back of the attached book cover that I designed for the short story "The Ship Who Sang" by Anne McCaffrey?

To provide a caption for this picture, you should credit its source. You can also provide a short description of what is going on in the picture. This is up to you, but it can be something along the lines of, "Helva, a brainship, has the energy and brains to travel through space." 
The back cover also usually provides a short summary of the novel or story. You may want to include something along the lines of the following: "Helva, a cyborg, becomes a 'shell person,' living her life beneath titanium as her superior brain pilots her spaceship. She is not an ordinary person, but she still struggles with human emotions. Though she is by nature not a defeatist, she goes on her journeys with a sense of loss after her lover, Jennan, is killed, and with worries about whether she'll ever be able to pay off the considerable debts that she owes for her training. Will she ever find the right brawn to partner with her and to provide her with the companionship she has long wanted?" (The short story stops a bit short of including her continued search for a new brawn, so you can cut that part if you are writing only about the short story and not the novel.)

Why was the term "stirrings" chosen by the committee used to describe the wanting and sexual desires that Jonas felt in the dream, this state of growth?

In The Giver (Lowry), the Elders use euphemisms to deal with the aspects of life that they seek to control.  Death becomes "release," for instance, and sexual desire becomes "stirrings." The Elders do not want the people in the community to have sex, and so they rename it and repress desire with drugs.  We think that if we do not call something by its proper name, we can somehow make it go away or at least ignore its implications. This is the reason we refer to white meat and dark meat on a turkey, because people did not want to refer to a breast or a thigh.  This is the reason some people think that sex education for young people is a bad idea.  To call a healthy and natural part of human life "stirrings" is to disguise it, to trivialize its power, and to control it better.  This effort on the part of the Elders is quite successful. There is no indication in the story that anyone ever has sex, and babies are produced in some way that avoids this, perhaps with Birthmothers' eggs fertilized and implanted back in them. This is speculation, though, since the book is never clear on how those babies do get produced. 

What are the different forms of state (unitary, federation, and confederation)?

A government consists of a set of legal and political institutions that control relationships between society and outsiders and the relationships among the members of the society. There are various systems of government, including confederation, federation, and unitary.
In a unitary system, the federal government performs all government functions. The federal government carries out police powers, taxation, and lawmaking responsibilities. Subnational national units are responsible for matters within their jurisdiction. However, the power of these units comes from the federal government. Many countries have a unitary system of government. In some instances, the regional units of government have a good deal of power and authority. This is true in Great Britain, where Northern Ireland, Scotland, and Wales have a good deal of autonomy. In France, the federal government has strict control over the regional units of government.
In a confederation, the federal government has limited power. The states have a great deal of power. Only powers that are needed for continuing the confederation are given to the federal government. The states make their own laws and levy their own taxes. In the United States, the first plan of government was a confederation. It was called the Articles of Confederation. The federal government had very little power, which eventually led to problems and to the writing of a new plan of government. No modern nations have a confederation form of government. However, the British Commonwealth of Nations and the North Atlantic Treaty Organization have aspects of confederation principles.
In a federation, there is a strong federal government. The states also have a good deal of power. The United States is an example of a federation. The federal government has more power than the state governments, but the state governments have a good deal of power and authority. Local units of government, such as cities, towns, and villages, also exist within this system. The local forms of government also have significant powers within their areas of jurisdiction. In the United States, both the state and the federal government share some powers, such as taxation. However, some powers are given only to the federal government, such as the power to declare war. There are also some powers set aside only for the state governments, such as the power to determine educational policies within that state. However, no state law can contradict a federal law, and the states must follow the federal laws. The same is true for the local government units.
https://junior.scholastic.com/pages/content-hubs/us-constitution.html

In chapter 34, why does Huck become so passive and deferential?

Tom Sawyer comes up with a new plan to save Jim because he thinks Huck's plan isn't romantic and exciting enough. Tom reads a lot of adventure stories, so he wants reality to conform to what he sees and enjoys in fiction on a regular basis. Huck admits this plan could get them all killed, even if it is "worth fifteen" of his plans on the basis of style alone.
Huck defers to this plan for two reasons: one, he is pretending to be Tom at this point and does not want his cover blown by Tom, and two, he feels the plan could at least work, so the end will be the same whether they go by his plan or Tom's—Jim will be free. So while Huck is still being realistic in knowing the plan is a bit silly and more than a little dangerous, he still admires Tom enough to take a chance on it. He is still, after all, a boy.

Huck and Tom are trying to figure out a way to free Jim from his captivity on the Phelps property. Huck comes up with the idea of stealing the key to the shed where Jim is being kept and then taking off with him into the night. Tom is none too impressed. Huck's plan is just way too unimaginative; there is no sense of adventure about it. For a boy like Tom Sawyer, that is a major consideration.
As a result, Tom hatches a much more daring rescue plan. Huck goes along with it even as he admits that it might get them all killed. He is not by nature a particularly passive individual, but he always defers to Tom when it comes to dreaming up exciting and adventurous plans. Huck admits that Tom's ruse to free Jim is much more stylish than anything he could ever come up with. Accordingly, Huck is more than willing to go along for the ride.

Why did Osama-Bin Laden target the United States of America

Osama-bin Laden disagreed with the American way of life.  He did not like American consumerism or its immodest values.  He did not like its secular nature.  He also did not approve of its foreign policy of meddling in the Middle East to ensure its oil supply.  Finally, he disapproved of the formation of the Israeli state and therefore hated America as one of Israel's most vital allies.  Bin-Laden was part of a group of radical fundamentalists who believed that the best government was controlled via Sharia law.  His attacks against monuments to American capitalism and American military might on September 11 were meant to send a statement--that the Middle East could find vulnerabilities in Western might.  Bin-Laden, a Saudi by birth, hid on the border of Afghanistan and Pakistan during the early stages of the Global War on Terror where he organized extremist groups via the internet to attack Americans in Iraq and Afghanistan and at various embassies throughout the Middle East and Africa.  

A prison warden's managers have described him as distant, cold, uninvolved, and apathetic. How would you analyze his leadership repertoire?

A "leadership repertoire" is the combination of leadership skills, drawn from leadership styles, that are put to use, when they are needed the most, for the common good of the organization. 
According to Daniel Goleman's book Primal Leadership, the six most common leadership styles stem from an individual's emotional intelligence. The six styles are:

Afiliative: "Let's keep the group together. Everything will be okay."
Authoritative: "Let us all work together to achieve the goal."
Coaching: "I will take the time to mentor each of you."
Coercive: "My way or the highway."
Democratic: "Let's all decide together for an outcome."
Pace-Setting: "Here's the goal. It may be high, but reach it anyway."

The warden described in this hypothetical scenario is described as cold, uninvolved, and apathetic. Let's define these adjectives and attach each to a potential style, or antistyle.
While "cold" is a descriptor that entails lack of physical emotion or emotional connection, it is also an adjective that depends entirely on the eye of the beholder. What may be considered "cold" or "unemotional" in one culture or group may not be considered so by another.
Therefore, the fact that someone chooses to remain emotionally disconnected to the dynamics of the workplace has less to do with leadership style and more to do with personal defense mechanisms, especially in a hostile environment like the prison system.
To give the warden credit, his choice to be "cold" may actually be a good one, and will be part of an authoritative style from which his repertoire includes:

avoiding attachments with prisoners
preventing mental manipulation from potential sociopaths (which a fair number of criminals are)
maintaining objectivity 
averting mistakes made by hindered objectivity

All of this affects the work environment, particularly the specific work environment of a prison, in a way that nulls any potential "enmeshment" of emotion and vulnerability. A warden may have to appear unapproachable and cold, especially to the prisoners. This skill can actually work well with supervisors. The less emotional connected the warden is, the more objective he can become (ideally speaking).
Part of being cold may also include remaining uninvolved, or aloof from what is going on. Being uninvolved in situations that require regrouping, voting, goal-setting, and active participation, however, negatively affects the work environment. 
Just think what would happen if this warden did not become involved in rule-setting, defining limits between wardens and prisoners, or voting on the proper consequences for infractions? This person's repertoire lacks all six of the leadership styles. Therefore, this person's  repertoire also lacks

decision making
authority
initiative
cohesiveness
connection

Finally, the warden is also considered apathetic. Someone who is apathetic shows neither emotion nor interest. The latter is the real problem. Not having interest means not possessing the internal or external motivation to accomplish anything. The problem with lacking motivation is that it immediately cancels out any potential leadership skill because the primary factor is missing: wanting to do anything. This warden will, therefore, also lack

initiative
problem-solving skills
goal-setting or -reaching 
cohesiveness
decision making

The warden may, however, be so self-absorbed that all he cares about is what is "in it for him." That is also a huge problem because it means he will not consider the best interests of the community for which he works. For all we know, the warden is a non-entity at work. He does not do much to better any situation, but his attitude can affect a lot of people: he has the potential of infecting others with his lack of spirit, and may even work his way into manipulating others to disregard the importance of teamwork. 
https://cmoe.com/blog/apathetic-leader/

Do you think that regeneration or redemption is the main theme of Silas Marner?

One could certainly argue that redemption and regeneration are important themes in George Eliot’s Silas Marner.
This applies first to Silas’s journey in the text. A bitter, miserly old weaver, Silas is despondent when Duncey steals all of his precious gold coins. Silas has isolated himself from human relationships and contact after the failure of his first engagement. He was also framed for a crime he never committed. However, when Silas takes in a motherless child and names her Eppie, he finds renewed purpose in life. The closeness he eschewed for so long becomes a rejuvenating force in his life; Eppie becomes his surrogate daughter and companion, and without her, Silas would have easily died a penniless, grouchy old man by choice. This shows that love and human kindness can rejuvenate the soul.
Redemption is also a factor in Godfrey Cass’s story. Because of his embarrassment, Godfrey denies ever having been married to Eppie’s biological mother—even after the discovery of her corpse in the snow. This causes him to neglect Eppie as his child, even though he helps Silas care for her via financial support. However, Godfrey realizes that he was wrong to abandon his only child after Dunsey’s skeleton is found with Silas’s stolen gold. Godfrey’s guilty conscience forces him to confess to Nancy the truth about Molly and his daughter. Even though Eppie does not want to move in with her father and Nancy, Godfrey still redeems himself by remodeling Silas’s house once Eppie gets married. This shows that people who make bad decisions always have the ability to redeem themselves; it is never too late.

What did Charlemagne do to avoid war with the Byzantine Empire?

Both Charlemagne, who ruled the Franks, and the Byzantine Empire claimed to be the inheritors of what used to be the Roman Empire. This caused a great deal of tension between them, but it never led to direct war for a number of reasons. First, Charlemagne himself had been crowned by the pope, whose authority was recognized by the Byzantines. Although the Byzantines did not acknowledge Charlemagne as Roman emperor, they could not openly defy the pope. Crucially, the Byzantine Empire was not at this time in a position to fight a war against Charlemagne. By the time of his coronation by the pope, he already controlled much of Europe, and although the Byzantines were a formidable force in Italy, they did not have the confidence to defeat Charlemagne in a military conflict.

What are the elements of orientalism in the film Lawrence of Arabia directed by David Lean?

Despite the meticulous craftsmanship that went into David Lean's Lawrence of Arabia, much of the film is dated and portrays typically stereotyped and "orientalist" attitudes about "the East" and the Arab world.
Much of the detail of the film is unrealistic, showing Lawrence (Peter O'Toole), though a flawed person, as also in some ways a nearly superhuman character, riding through the desert without a pith helmet, evidently because Lean wished to emphasize his courage and his blondness. The sudden ways in which Lawrence arrives at his inspirations on how to defeat the Turks are also a bit hard to take.
Apart from Omar Sharif as Sherif Ali, nearly all of the major roles are played by western actors. Regardless of the historical veracity of much of the script, the impression one gets from watching the film is that a European was required to lead the "easterners." Other epic films from the same period (the 1960s) show a similar approach, such as Khartoum, starring Charlton Heston as General Gordon, besieged by the "Muslim hordes" who attempted to expel the British from Sudan.
Near the end of Lawrence of Arabia,the Arab leaders are shown bickering with each other and unable to unify. This fits in with the British/French narrative that the Arab lands needed to remain European protectorates for as long as possible, and that even after independence was granted, the western countries had to stay on to guide them. While there is a grain of truth in this, the film seems, as stated, to reinforce stereotypes, and is a clear example of what Edward Said called "orientalism."

Examples of orientalism in David Lean's 1962 film Lawrence of Arabia can be said to exist, but an argument can be made that the film goes some distance in presenting the Arab population in question in a reasonable light, especially if one is a serious student of the Middle East. Inspired by T.E. Lawrence's Seven Pillars of Wisdom, and embellished considerably with respect to Lawrence's role relative to other "Westerners," Lean's film is nevertheless a highly sympathetic portrait of the indigenous tribes that populated the Arabian Peninsula during the early-20th Century.
Lawrence of Arabia can be said to reflect the Western perspective of Arabia by virtue of its Western production. The screenplay was written by a Westerner and the film was directed by a Westerner. A Mexican-born actor named Anthony Quinn, fitted with a preposterous prosthetic nose to appear more Semitic, portrayed a key Arab figure in the film, Auda abu Tayib. Most significantly, the film reflects the condescending perspective of non-Westerners towards "Third World" populations that is a key characteristic of orientalism. Western ways are modern and, consequently, better. The Arabs are portrayed as simple, backwards people in need of Western guidance. One of the film's most important characters, Sherif Ali, is a cold-blooded killer, but evolves into one of the film's most noble figures. This nobility is reflected in his desire to study Western -- read: superior -- political systems. At one point, the American journalist Jackson Bentley, noticing that Sherif Ali is carrying a Western-published children's book on politics, inquires as to the Arab figure's aspirations. When Ali's answer proves murky, he innocently asks the wise journalist whether he, Ali, answered well, prompting Bentley's reply, "You answered without saying anything. That's politics."
Lawrence himself, highly sympathetic of Arabs and suspicious of his own government's intentions towards Arabia, displays an arrogance toward Arabs that exposes his own jaundiced view of these people: "So long as the Arabs fight tribe against tribe, so long will they be a little people, a silly people -- greedy, barbarous, and cruel, as you are." Throughout Lawrence of Arabia, Arabs are portrayed as weak and riven with divisions that allow them to be prey to stronger, European powers. Lawrence of Arabia can be considered to be "orientalist," but, it can in some ways be viewed as a film that respects its subjects, especially given its criticism of British policies and ambitions in the Middle East.

What would be a good thesis statement for a comparative essay, with topics of power and ignorance, on the books "The Use of Force" and "The Giraffe" by Mauro Senesi?

If you're writing a comparative essay, you may decide to discuss the relationship between power and ignorance in both stories.
However, before you do that, you will need to decide what sort of differences or similarities the stories share. In "The Giraffe" and "The Use of Force," power appears to rest in the hands of the adults. In "The Giraffe," it is the adults who motivate a change in the boys' plans. Initially, the boys had planned to keep the giraffe in town. After the adults threaten to kill the animal, however, the boys take their new pet into the countryside.
In "The Use of Force," the doctor exerts his power over his little patient. Because of his superior physical strength, she must submit to his ministrations.
In both stories, ignorance rears its head. In "The Use of Force," the ignorance seems to lie chiefly in the young patient. On the other hand, adults are portrayed as the ignorant ones in "The Giraffe." After the animal is caught spying on people and devouring the church flowers, the townsfolk adopt a defensive posture towards the giraffe. Additionally, because the adults lack the knowledge required to look after a giraffe, they come to the erroneous conclusion that the animal must be killed.
So, on the surface, we have very clear examples of ignorance in both stories. However, as we explore the stories a little more, we discover ignorance in other characters. In "The Use of Force," the mother's use of the word "hurt" in connection with the doctor's efforts makes matters worse. The little girl rears up in rage and attacks the doctor. Embarrassed and humiliated, the mother scolds her daughter for attacking the "nice man."
It's clear that both parents have failed to grasp the psychology behind their daughter's behavior. They don't realize that she is furious at what she perceives to be her lack of power. Additionally, their placating behavior does little to impress upon her mind the seriousness of her condition. Because of their ignorance and accompanying emotional angst, the parents are unable to properly (and safely) restrain their daughter.
A similar ignorance shows up in "The Giraffe." At first glance, the ignorance displayed by the adults is quite clear for all to see. As we further explore the story, we see that the boys are also ignorant. Like the adults, they know little about caring for a giraffe. Their lack of experience in this area leads to the unintentional and tragic death of their cherished new pet.
So, now back to our thesis statement. It's clear from the stories that ignorance can be manipulated by a superior will (or power). Think about how the adults lay down the law, so to speak, in "The Giraffe." In "The Use of Force," the doctor holds all the cards.
However, the accomplishment is superficial at best. This main idea (thesis) is true for both stories, but it is only in "The Giraffe" that the manipulation ends in death. Essentially, the collective ignorance of two parties (the boys and the adult townsfolk) result in tragedy. I hope this premise makes it easier for you to come up with a working thesis statement. Happy writing!

Is there any occasion in Shakespeare's play Othello where Othello reflects on his own race, possibly relating to his insecurity?

In Act 3, Scene 3, Othello does refer to his race. He uses the reference in a monologue after the devious Iago has manipulated him into believing that Desdemona was involved in an inappropriate liaison with his lieutenant, Cassio. Iago has, throughout their conversation, made suggestions by using innuendo, intimations and equivocation to encourage the general's jealousy and then, ironically, suggesting that he should 'beware of jealousy.'
Othello is overcome by Iago's scheming and deceit and seeks justification for Desdemona being involved with Cassio. He is quite honest about himself and exposes his insecurities.
He mentions: 

Haply, for I am blackAnd have not those soft parts of conversationThat chamberers have, or for I am declinedInto the vale of years,--yet that's not much--She's gone.

The implication here is that it is a matter of chance that he is black and thus lacks the ability to speak softly, gently or sweetly as fashionable or intriguing men do. He believes that since he has not constantly whispered sweet nothings in Desdemona's ear, she might have turned from him. Othello's admission here links to his earlier contention in Act 1 when he also mentioned his inability to use beautiful or florid language, where he stated that he 'is rude in speech.'
Later, in Act 3, Scene 3, when Othello is fully convinced about Cassio and Desdemona's adulterous affair, he again refers to his race. In this passionate statement, he swears to take revenge on them for cuckolding and humiliating him. Iago has convinced him that Cassio, through his behavior, has definitely proven that he is having an affair with Desdemona. He also tells the highly upset general that he had seen Cassio wipe his beard with the napkin Othello had given Desdemona as a gift. Othello passionately cries out:

O, that the slave had forty thousand lives!One is too poor, too weak for my revenge.Now do I see 'tis true. Look here, Iago;All my fond love thus do I blow to heaven.'Tis gone.Arise, black vengeance, from thy hollow cell!

The general then kneels and makes a vow to take revenge. Iago kneels with him and promises allegiance. Othello then, out of gratitude for Iago's 'exceeding honesty,' awards him the title of lieutenant, which is the greatest irony of all. 

Besides this one
Haply for I am black,And have not those soft parts of conversationThat chamberers have; or for I am declinedInto the vale of years—yet that’s not much— She’s gone. I am abused, and my reliefMust be to loathe her. O curse of marriage,That we can call these delicate creatures oursAnd not their appetites! I had rather be a toadAnd live upon the vapor of a dungeonThan keep a corner in the thing I loveFor others’ uses. Yet ’tis the plague of great ones;Prerogatived are they less than the base.’Tis destiny unshunnable, like death. (III.iii.267–279)

Summarize paragraph 5-24 in Peter Singer's essay "The Singer Solution to World Poverty."

This part of Singer's essay is about the questions NYU philosophy professor Peter Unger devised to investigate our understanding about whether it's ethically wrong to live well when people around the world are suffering from preventable diseases. Singer provides some examples, such as that of a man who has an expensive car who could destroy it to stop a train that will run over a child but doesn't do so. While most people would deem this person's actions wrong, they still don't give the $200 or so that it would take, according to Unger, to allow a sickly two-year-old to develop into a healthy six-year-old. However, it is difficult to determine if there is a moral difference between the man who does not save the child on the tracks and the wealthy westerner who does not give $200 to save suffering children. Singer concludes that since governments, such as that of the U.S., give less than what the United Nations recommends in international humanitarian aid and many westerners do not give any aid, we have a moral imperative to give surplus wealth to help suffering people around the world. 

College Algebra, Chapter 10, Review Exercises, Section Review Exercises, Problem 28

Find the probability that the indicated card is drawn at random form a 52-card deck.

a.) An ace

There are four aces in a deck of a card. Thus, the probability in this case is

$\displaystyle \frac{4}{52} = \frac{1}{13}$

b.) An ace or a jack

Since an ace can never be jack, then the probability of this mutually exclusive event is

$\displaystyle \frac{4}{52} + \frac{4}{52} = \frac{8}{52} = \frac{2}{13}$

c.) An ace or a spade

Since there is an ace of spades we have an intersection of two events. Thus, the probability of union of this two events is

$\displaystyle \frac{4}{52} + \frac{13}{52} - \frac{1}{52} = \frac{4}{13}$

d.) A red ace

We know that there are only two red aces. Precisely ace of diamonds and ace of hearts. Thus, the probability in this case is

$\displaystyle \frac{2}{52} = \frac{1}{26}$

Why does the wanderer go into exile?

Although the code of behavior in Anglo-Saxon England did expect that one of the king's thanes would fight to the death at the king's side, it was not always the case that a surviving thane was dishonored. For example, Beowulf himself, the greatest of heroes in Old English poetry (at least what is extant), survives the battle in which his king and kinsman, Hygelac, is killed, and returns home alone (anhaga, which is also used to describe the Wanderer in lines 1 & 40). His people actually ask Beowulf to be king at that point, but he refuses, instead serving as regent or protector to Hygelac's son Heardred--until Heardred is also killed. Then, in spite of having failed to defend not one but two kings, Beowulf is still made king. (See Beowulf, lines 2354-2390 for this sequence of events.)
In "The Wanderer" itself, we do not find any sense of guilt or shame, but only sorrow. Furthermore, this sorrow is not just for the king or for himself, but for much greater loss:

Where is the horse? Where is the young warrior? Where is the giver of treasure?Where are the seats of the banquets? Where are the joys in the hall?
Alas the bright cup! Alas the mailed warrior! Alas the glory of the prince!
How the time has gone, vanished under night’s helm, as if it never were! Now in place of a beloved host stands a wall wondrously high, decorated with the likenesses of serpents.
The powers of spears took the noblemen,weapons greedy for slaughter; fate the renowned, and storms beat against these rocky slopes, falling snowstorm binds the earth, the noise of winter, then the dark comes. The shadow of night grows dark, sends from the north a rough shower of hail in enmity to the warriors. All the kingdom of earth is full of trouble, the operation of the fates changes the world under the heavens.
Here wealth is transitory, here friend is transitory, here man is transitory, here woman is transitory, this whole foundation of the earth becomes empty. (lines 92-110)

If this response was only because of a sorrow that was deserved because of his failure, the Wanderer would seem consumed by self-pity and would be an object of contempt and not compassion.
For these reasons, Christopher Dean's reconstruction of the events that led to the Wanderer's exile is preferable:

The Wanderer's lord and companions met their deaths in battle. The Wanderer must have been absent from the battle, for no reproach attaches to him for not dying by his lord's side. Returning to the hall, he found the bodies, some preyed upon by birds and wolves. He carried out his last duty to the lord that he loved, and...buried his lord. He then set up a wall around the mound, some at least of the stones carrying carved ornamentation. The whole made a fitting memorial. Then his search for a new lord began. As an old man, he remembers his lord still and the memorial that he raised to him. His memory of his lord and of the memorial is the only thing that can survive the universal decay.
http://www.heorot.dk/beowulf-rede-text.html

https://www.journals.uchicago.edu/action/cookieAbsent

The Wanderer's predicament is heavily based on the historical context in which it was written. It is an Old English elegy, which is a poem depicting loss and loneliness. During the the time of the Anglo Saxons in England, the most important relationship was that between the lord and his knight (vassal). From a fairly young age, a vassal pledges his loyalty to a lord who provides for him in return for his service and protection in battle. Therefore the most honorable thing a vassal could do for his lord is to die for him. In "The Wanderer," the narrator is lamenting the death of his lord and is feeling regret and shame for not being the one who was dead. He either chooses to exile himself, or is shunned by his family and friends out of dishonor. When he tries unsuccessfully to find another lord, he finds himself sailing alone on the unforgiving seas to reminisce about the good times he had with his lord and company, ruminate on the sufferings of man, and finally realize that without a lord the only comfort he has is in God.

"The Wanderer" is an elegiac poem whose theme, that of exile and loneliness, is one common to Anglo-Saxon poetry— see also "The Wife's Lament" and "The Seafarer." In this case, the wanderer explains exactly why he was forced to go into exile far from his kinsmen. He explains that "siþþan geara iugoldwine minne hrusan heolstre biwrah" (long years ago, I hid my lord in the darkness of the earth). What the wanderer is saying here is that, because he did not die in battle with his lord, as a vassal should, he has been left without honor and without a meadhall to which he might belong or a "giver of treasure" to pledge allegiance to.
The Anglo-Saxon audience would understand the wanderer's reasoning, as it derives very much from societal context. This wanderer is seemingly either the last survivor of his hall or group, or someone who has been ostracized by his kinsmen because of his failure to meet expectations as a vassal and die in defense of his lord.

What are literary techniques in "The Storm" by Kate Chopin?

Kate Chopin uses colloquial speech to aid in the characterization of Bobinôt and Bibi, seen in Bibi's response to his father's suggestion that Calixta had Sylvie helping her: "No; she ent got Sylvie. Sylvie was helpin' her yistiday."
Chopin also uses varying settings as she moves between Bobinôt and Bibi, and Calixta and Alcée. The story opens with father and son at Friedheimer's store, and then the narrative moves to Bobinôt and Calixta's home.
Imagery is another technique Chopin uses in "The Storm" to describe the weather and the physical attraction of Calixta and Alcée, as seen in this line: "The rain was coming down in sheets obscuring the view of far-off cabins and enveloping the distant wood in a gray mist."
Chopin uses a simile in her physical characterization of Calixta: "Her lips were as red and moist as pomegranate seed."
Though Bobinôt has done nothing wrong in staying at the store during the storm, he fears that he has upset Calixta and approaches her carefully when he returns, rehearsing "explanations and apologies which he had been composing all along the way."  This is situational irony, given that Calixta has just had a sexual liaison with Alcée during the storm.

Why were the mountains dear to him and terrible?

The mountains are dear and terrible to Jody for two reasons. First, he knows little about the mountains surrounding his home. They remain a mystery to him, and since he is not allowed to explore them on his own, the mountains take on an added charm for him.
Second, the mountains are terrible to Jody because they are so imposing. They tower above everything in his surroundings, and all he can see of them are jagged ridges and dangerous cliffs.
To Jody, the mountains are a mystery. His parents know little about them and aren't especially interested in the secrets they hold. When Jody voices his desire to explore the mountains, his father scoffs at the notion. He tells Jody that there is nothing in the mountains worth discovering. Meanwhile, his mother placates him with a reference to a line from a popular children's song: "The bear went over the mountain, To see what he could see."
Jody becomes exasperated and decides to ask Billy, the ranch hand, about the possibility of there being ancient lost cities in the mountains. Billy's answer corresponds with that of Jody's father. These unsatisfying answers further increase Jody's curiosity about the mountains. The mountains are dear and terrible to him at the same time. They represent an unknown but important aspect of his surroundings. Yet, their imposing heights are terrifying to him.

According to one model of bird flight, the power consumed by a pigeon flying at velocity v (in m/s) is P(v)=17v^-1 +10^-3*v^3 . Find the velocity that minimizes power consumption.

The function is obviously defined only for v gt 0 and is continuously differentiable on this interval. When v approaches zero the function tends to +oo, when v tends to +oo, the function also tends to +oo.
Thus it must have at least one local (and global) minimum and it is reached at the point(s) where P'(x) = 0.  Let's solve this equation:
P'(x) = -17 v^-2 + 3*10^-3*v^2 = 0.
This is equivalent to  17 v^-2 = 3*10^-3*v^2, or  v^4 = 17/3*10^3.
The only solution is  v = root(4)(17/3*10^3) approx  8.7 (m/s). This is the answer.
 

Take the derivative of P(v) .
P'(v)=-17v^-2+3*10^-3v^2
Set P'(v) equal to zero and solve for the critical values.
-17v^-2+3*10^-3v^2=0
-17+3*10^-3v^4=0
3*10^-3v^4=17
v^4=17/3*10^3
v^4=17/3*10^3
v=(17/3*10^3)^(1/4)~~8.676 m/s
We can check graphically that this is indeed a minimum.

why did jefferson believe it was important to acquire the port of new orleans

President Jefferson wanted to acquire the Port of New Orleans to protect the right of merchants and farmers west of the Appalachian mountains to trade and navigate along the Mississippi River. In 1798, the Spanish had revoked the United States' right to navigate the river and deposit goods in New Orleans. This caused an economic crisis in the Ohio River Basin. That same year, Spain gave the territory of Louisiana over to the French. Many southerners feared that Napoleon would free the slaves in that territory, which could potentially spark a slave rebellion in the United States.
Jefferson felt it necessary that the United States secure the port in order to safeguard American interests in trade once and for all. Napoleon was more focused on events in Europe than in the Americas, and therefore his representatives were eager to sell the entire territory. Nearly overnight, the United States doubled in size. Now the country had secure rights to navigate along the Mississippi River and use New Orleans as a port for international and domestic trade.
https://www.monticello.org/thomas-jefferson/louisiana-lewis-clark/the-louisiana-purchase/

What did Ferdinand and Isabella do to fund Columbus's voyage?

Christopher Columbus was an old-time entrepreneur. He was willing to take great risks and expose his credibility to ridicule in order to obtain a profit. After being denied financial compensation from several sources, he eventually approached the thrones of King Ferdinand and Queen Isabella of Spain hoping to find them in a giving mood.
Recently turned away by the King of Portugal, Columbus made his case before the Spanish monarchy. Imagine a scene not unlike a modern-day episode of Shark Tank. Columbus had the challenge of convincing his audience that it was a shorter journey to the Indies by going west. Conventional wisdom of the day held that east was the proper course to take.
The task was not an easy one. Spain was just wrapping up a war to drive Muslims from the nation. Advisers to the monarchs strongly recommended sending Columbus away without the benefit of any donation.
However, the monarchs were interested. If Columbus could get to the Indies faster, they could gain an advantage in trade over their European rivals. They also were interested in spreading Catholicism to areas around the world. Columbus was willing to bring some financing to the table himself—financing he had obtained from creditors outside of Spain. The Spanish crown would contribute a much larger amount from its treasury in the Spanish currency of the day (maravedí). Even after this generous donation, more was needed to embark on such a journey.
Enter the city of Palos. The King and Queen ordered the port city to provide two ships to Columbus for a year. This was done to settle an outstanding court case in which the city still owed payment. At last Columbus had the necessary funding to begin his famous voyage. As part of the deal, Columbus was allowed to keep a small percentage of any riches he would find.

In "The Black Cat," the narrator begins the story by speaking directly to the reader. The narrator continues this practice periodically throughout the story. How does the author's use of this structure create mystery in the story?

Knowing that the narrator is speaking directly to you as the reader and giving only his perception of what happened leads to questions of whether or not he is a reliable narrator and lends an air of mystery to the story. In the opening of the story he even says he does not expect to be believed and that his “senses reject their own evidence,” so the reader cannot be sure of what is true. This uncertainty about the truth also adds a sense of mystery to the tale.
From the beginning of the story, we only have the narrator’s word that he was a kind animal lover early in his life. The only actions we see, starting with his confession of intemperate language and violence toward his wife, contradict that and add to the questions about what has really happened. The reader has no way of deciphering what actually happened.
Later in the story, we still have only dubious ideas of what led up to the murder of the narrator's wife. He claims to see an image of a hanged cat on the wall of his burned-down house, but he makes no mention of anyone else noting this image. Later, he says that the second cat had a white mark that was at first no particular shape but slowly took on the shape of a gallows. We have no way of knowing if the mark actually changed or if his perception of it changed.
Overall, this is a story of more questions than answers. As the story goes on, we learn that the narrator is sinking further into alcoholism, and his comments become more suspect until, by the end of the story, the reader is left unsure of whether this is a story of a man’s descent into alcohol-induced madness or a story of supernatural revenge.

Referencing Huston Smith's The World's Religions and Durkheim's The Elementary Forms of Religious Life, how did the emergence of sacred thought affect the development of early societies? In what ways was this influence expressed?

Smith and Durkheim both maintain that sacred thought was a primary motivator in early societies. Huston Smith from his post-World War II perspective, aims to counter the dominance of secular views, while Émile Durkheim formed his ideas in the late 19th century. Smith, while clearly influenced by Durkheim in positively valuing the belief systems that predated organized religion, does not see religion as primarily social, which was Durkheim’s position. Also similarly to Durkheim, Huston Smith bases much of his analysis in Australian Aboriginal society; both analyze their contemporary beliefs for insights into religion in ancient times.
Huston Smith discusses the earliest or “primal religions” as moral guides that encoded positive values and enabled society to develop. He also calls them “tribal religions,” noting how they reflect the tribal thinking that binds people. Claiming that they predate writing and were transmitted orally, he emphasizes the importance of memory at the heart of religion and the social connectedness of person-to-person transmission. Because these religions helped people to understand the “mystic world” around them, they contributed to social formation and continuity. He emphasizes tribal peoples’ immediate involvement with nature, often shown through their selection of animal “totems” symbolizing potent forces as embedded within people and aiding their comprehension of the greater natural world in which they live.
While Smith discusses these “primal” systems as religions, he also distinguishes between supernatural forces and “gods.” For example, he maintains that the aboriginal Dreaming, through which they accessed their ancestors, was not worship. For him, religion contributed to but was not subsumed within the collective cohesion that created, maintained, and enforced social behaviors among groups of humans. Yet the tribal character of early societies, generally linked to specific places and locally understood natural phenomena, were limiting factors in the expansion of religious views and of social growth.
Durkheim, writing fifty years earlier, had taken a pioneering role in presenting religion as primarily social. He veered away from the then-accepted view that religion consisted mainly of the human quest to understand supernatural phenomena. Instead, he aimed to analyze the ways that what had become solidified into “religion” was another aspect of society. For Durkheim, it was the essentially social character of human beings that was expressed in religious practices. Not only what people believed but what they did helped form society. Those practices, both through selectively performed rituals and daily behavior, upheld the norms by which people lived their lives. His definition included not only what people should do but prescribed behavior—“things set apart” and emphasized human membership in a “moral community.” Thus, while he explored the importance of the “sacred,” he saw its intersection with the “profane,” and the idea of a strict difference between them, as equally significant in social development.

In The Elementary Forms of Religious Life, Durkheim defined religion as composed of rites (modes of action) and beliefs (collective representations). He writes that all religious beliefs do the following:

They presuppose a classification of all the things, real and ideal, of which men think, into two classes or opposed groups, generally designated by two distinct terms which are translated well enough by the words profane and sacred.

In other words, the emergence of the idea of the sacred made it necessary to protect the sacred from the profane. Early societies developed systems in which sacred things and their differentiation from profane things were represented in religious beliefs. Religious rites developed as means of conduct that governed how people should behave in the presence of the sacred. Durkheim writes the following:

A religion is a unified system of beliefs and practices relative to sacred things, that is to say, things set apart and forbidden—beliefs and practices which unite into one single moral community called a Church, all those who adhere to them.

That is, religion is the set of beliefs around what is sacred and the practices that unite everyone who follows them. The emergence of the sacred unified people who shared rites and beliefs. Different primitive religions had different ideas of the sacred. For example, animism believed that the sacred was in the spirits that filled natural objects. 
Huston Smith, author of The World's Religions, quotes the anthropologist Paul Radin, who writes, "Only when we have fully grasped the mystic and symbolic meanings inherent in most of the activities of primitive man can we hope to understand him." In other words, primitive people had a sense of the sacred in their everyday lives, and this sense helped them make meaning in their lives. By understanding the idea of the sacred in primitive societies, modern people can understand how primitive people made sense of their lives. By understanding what primitive people found sacred, we can understand what they valued and what they set apart from the everyday, or the profane. 

Single Variable Calculus, Chapter 2, 2.3, Section 2.3, Problem 41

Determine the limit $\lim\limits_{x \rightarrow 0.5^-} \displaystyle \frac{2x-1}{|2x^3-x^2|}$, if it exists. If the limit does not exist, explain why.


$
\begin{equation}
\begin{aligned}
\lim\limits_{x \rightarrow 0.5^-} \displaystyle \frac{2x-1}{|2x^3-x^2|} & = \lim\limits_{x \rightarrow 0.5^-} \displaystyle \left[ \frac{2x-1}{-(2x^3-x^2)}\right]
= \lim\limits_{x \rightarrow 0.5^-} \displaystyle \frac{\cancel{2x-1}}{-\cancel{(2x-1)}(x^2)} && \text{(Get the factor and simplify)}\\
\lim\limits_{x \rightarrow 0.5^-} \displaystyle \frac{1}{-x^2} & = -\frac{1}{(0.5)^2} && \text{(Substitute value of } x)
\end{aligned}
\end{equation}\\
\boxed{\lim\limits_{x \rightarrow 0.5^-} \displaystyle \frac{2x-1}{|2x^3-x^2|} = -4}
$

How does the westward expansion affect our time today?

The expansion of the United States has significant consequences for the nation today. The nation was able to spread from thirteen original colonies to fifty states. The United States has become the breadbasket of the world with the fertile grain growing areas in the Midwest. The mineral resources found in the far west, especially gold in California and Alaska, helped to drive the economy then as well as now. Much of the United States' oil wealth can be found in the West. Tourism is a considerable business as well, as millions come from all over the world to see the wonders of the Western United States. The promise of cheap land encouraged immigrants from all over the world to come to the United States—here was a rich land with room for seemingly everyone. Because of westward expansion, the United States was able to grow significantly and it still benefits from having such a large pluralistic population today. The United States can also trade easily with the growing markets in Asia thanks to its numerous Pacific seaports. The United States is still reaping the benefits of its westward expansion movement.

What were issues that the Constitutional Convention dealt with? How were these issues resolved? Describe George Washington's administration. Name and describe two of his achievements.

There were several issues that were resolved at the Constitutional Convention. One issue dealt with the structure of the legislative branch. The small states were afraid that the big states would have too much power. The Virginia Plan proposed having a legislature where the large states would have more representatives than the small states. The small states countered with the New Jersey Plan, which stated that there would be equal representation in Congress. A compromise, called the Great Compromise, was reached where there would be a two-house legislature. In the House of Representatives, representation would be based on the size of the state. The large states would have more representatives than the small states. In the Senate, each state would have two senators, regardless of the size of the state.
Another issue that was resolved was how the executive branch would be structured and how much power it would have. There was a concern that a strong executive might abuse the power given to that person. An agreement was reached that allowed for the President to have significant power, but that person could be removed from office if power was abused or if the person broke the law.
The question of whether slaves would be counted towards a state’s population count was resolved. The South wanted each slave to be fully counted while the North didn’t want slaves to be counted at all. An agreement was reached, known as the Three-Fifths Compromise, which stated that every five slaves would be counted as three people.
There was also a question about the trading of slaves. Northerners wanted to stop the slave trade while Southerners wanted it to continue. It was agreed that there would be no restriction regarding the trading of slaves for twenty years, until 1808.
There was a question of how much power the federal government should have. The reason for writing a new plan of government was that the federal government created by the Articles of the Confederation was too weak to deal with issues facing the country. The federal government was given more power, such as the ability to levy taxes and require the people to join the military. Additionally, the federal government could tax imports, but it wouldn’t be able to tax exports. After the Constitution was written, some people were concerned that the federal government might be able to take away the rights of individual citizens. As a result, an agreement was made after the Constitutional Convention ended to add a Bill of Rights that would guarantee the rights that each citizen had.
There were many issues that were resolved at the Constitutional Convention.
http://www.digitalhistory.uh.edu/disp_textbook.cfm?smtID=3&psid=163

https://www.thoughtco.com/compromises-of-the-constitutional-convention-105428

What is a key event related to the voluntary migration in America and what is its impact on history?

One key historical event that led to the migration of American citizens was the discovery of Gold at Sutter's Mill in California in 1848.  At first, this was supposed to be kept secret, but Sutter's workers spread the news and suddenly people from all over the world came to take advantage of the California Gold Rush.  Indigenous tribes suffered, as the new settlers took the land of the hunter-gatherers of the region.  Cities such as San Francisco sprang up overnight.  Some people made their riches in the goldfields, while others made a living from selling things to the miners, many of whom were single men with few domestic skills.  The California Gold Rush marked the first rush of Asian immigration to the United States--this sparked a wave of xenophobia which would end with the Chinese Exclusion Act in 1882.  California became a state without having to go through the territorial process--its admission as a free state temporarily broke the balance of power between free states and slave states in Congress and necessitated the Compromise of 1850.  

Single Variable Calculus, Chapter 1, 1.1, Section 1.1, Problem 57

A rectangular piece of cardboard is used to construct a box with an open top having a dimensions 12 inches by 20 inches, by cutting out equal squares of side $x$ at each corner and then folding up the sides as shown in the figure. Express the volume $V$ of the box as a function of $x$






By thorough investigation, the dimensions of the open top box could be...






The volume of the box is equal to the product of its length, width and height. By using the dimension of the box, the volume we obtain is...



$
\begin{equation}
\begin{aligned}

\rm{Volume} &= x(20-2x)(12-2x) && (\text{Distribute } x \text{ in the equation})\\
\rm{Volume} & = (20x-2x^2)(12-2x) && (\text{Using FOIL method.})\\
\rm{Volume} & = 240x - 40x^2-24x^2 +4x^3 && (\text{Combine like terms.})\\
\end{aligned}
\end{equation}
$



$
\fbox{$\rm{Volume} = 240x - 64x^2+4x^3$}
$

Explain the photoelectric effect.

Photoelectric effect commonly refers to the behavior of electrons that are ejected from the surface of a metal due to the light shining on the metal. Photoelectric effect was first noticed by Hertz at the end of the 19th century in the course of his experiments involving electromagnetic waves. The unusual characteristics of the current (stream of electrons) emitted from the metal were later (in the beginning of the 20th century) explained by Einstein.
In order for an electron to be ejected from the surface of the metal, it needs to posses a certain amount of energy in order to overcome the electric forces binding it to the metal. This amount of energy is called work-function and it depends on the type of metal. 
According to the laws of classical physics, it would be expected that the kinetic energy with which electrons leave metal would depend on the intensity of incident light, because more intense light would impart more energy to the electrons. However, this is not what was observed. The kinetic energy was measured to be dependent not on intensity, but instead, on the frequency of the incident light. Again, this was surprising because the energy carried by light, thought of as electromagnetic wave, depends only on the wave's amplitude, but not frequency. Moreover, it was found that if the frequency of the incident light was too low, no electrons were emitted at all, no matter how intense the light was.
Einstein explained these results by using the Planck hypothesis that the light can be thought of as composed of quanta ("pieces") of energy proportional to its frequency:
E = hnu
Here, h is the Planck's constant and 
nu
is the frequency. 
The photoelectric equation, obtain experimentally, is
K= hnu - phi , where 
K = mv^2/2 is the kinetic energy of electrons (proportional to the square of the speed) and
phi is the work-function of the metal. From here, it can be seen that if the frequency nu is too low, there is no sufficient energy for the electrons to leave the metal. The threshold frequency is determined by setting K = 0, corresponding to the electrons leaving the metal with no extra energy. Then,
the threshold frequency equals
nu = phi/h
No electrons is emitted if the light incident on the metal has the frequency below this value.
These results were significant because they supported the understanding of the dual nature of light: light can behave either as an electromagnetic wave, or as a stream of massless particles called photons.
http://hyperphysics.phy-astr.gsu.edu/hbase/mod2.html

What quotes could prove that the main conflict of Jane Eyre is between Jane's true love and her responsibility to God?

In Jane Eyre, Jane feels a strong moral responsibility to God that she has spent years cultivating into a need to do what she sees as the right thing. These beliefs, along with her moral compass, have been perhaps the only thing that sustained her and gave her purpose throughout her difficult upbringing—that is, until Mr. Rochester came along and she fell madly in love with him. Still, there are points at which Jane seems to come to an impasse; she's not quite sure how to reconcile her love with Mr. Rochester with her desire to appease God. This is especially difficult for her, because not only is Mr. Rochester still married, which Jane finds out right before they are about to complete their own nuptials, but he keeps massive secrets from her and others about the state of his private life and his relationships. She finds these pieces of information to be in direct opposition to her own sense of morality, causing her to be confused about the choices she must make.
Near the end of Chapter 27, Jane is nearly convinced to acquiesce to Mr. Rochester's attempts to get her to stay with him, even though she has just found out about Bertha, his estranged wife: "Who in the world cares for you? or who will be injured by what you do?” Still indomitable was the reply: “I care for myself. The more solitary, the more friendless, the more unsustained I am, the more I will respect myself. I will keep the law given by God; sanctioned by man. I will hold to the principles received by me when I was sane, and not mad—as I am now." Here, Jane questions what she will do and who she will turn to, as Rochester is the only person in the world who loves her. Still, she holds tight to her beliefs and her responsibility to herself. When she leaves him, the conflict she feels about being torn from him and doing the right thing is evident:

Gentle reader, may you never feel what I then felt! May your eyes never shed such stormy, scalding, heart-wrung tears as poured from mine. May you never appeal to Heaven in prayers so hopeless and so agonized as in that hour left my lips; for never may you, like me, dread to be the instrument of evil to what you wholly love (Chapter 27).

Jane feels staying with Rochester would be seen as evil in the eyes of God, so she must leave; she has no choice in the matter.
In another passage, in Chapter 34, St. John asks for Jane's hand in marriage. As she is still in pain over Mr. Rochester, and wishes to do the good work of God, Jane almost relents. Here, we can see her inner turmoil:
"As his curate, his comrade, all would be right: I would cross oceans with him in that capacity; toil under Eastern suns, in Asian deserts with him in that office; admire and emulate his courage and devotion and vigour: accommodate quietly to his masterhood; smile undisturbed at his ineradicable ambition. . . I should suffer often, no doubt, attached to him only in this capacity."
Still, even though his ideals fit perfectly with hers, Jane doesn't think marrying St. John would be a good idea because she does not love him as she does Mr. Rochester.

Why does Grandfather think he has been a fool?

Grandfather thinks he has been a fool because he failed to see the inherent threat in the yellow fever. In Chapter 5, Lucille (Matilda's mother) wanted to send Matilda to the Ludingtons at Gwynedd. However, Matilda's grandfather would not hear of it; he maintained that the Ludingtons were not family and that Matilda would fare better by staying put.
Matilda's grandfather believed that they would only need to accommodate the fever for a few weeks. He insisted that life would soon return to normal and cautioned against panicking.
In Chapter 11, Matilda and her grandfather are abandoned after the armed men determine that the latter is too sick to be allowed passage through their town. The two are left without food and water, and Matilda's grandfather eventually laments his foolish stubbornness. He admits that Lucille was right to worry and that they should have left town before any of them caught the fever. So, Grandfather thinks himself a fool because he resisted the idea of moving.

Can we consider Cooper as a racist in his book The Last of the Mohicans?

This question is difficult because Cooper's views are outdated in the present day. However, upon examination of the novel in the context it was written, the answer would, most likely, be "no." Remember, that in the nineteenth century, sexual relations between different races was illegal in the United States. However, Cora is presented as a woman of strength and courage—even though she considers herself "a violation of nature" due to her interracial background—and she is willing to give up her life for her sister, Alice.
With that being said, Cooper does portray many of the characters as stock characters such as the "noble savage." More interesting, however, is that Cooper kills off Cora and Uncas (rather than allowing their union), which could be interpreted as his abhorrence for racial mixing. But, on a deeper level, perhaps Cooper intended their death to illustrate and delve into the problematic moral issues facing the new republic—those based upon oppressing indigenous peoples and implementing racial division, which began with the founding fathers.

Calculus of a Single Variable, Chapter 7, 7.2, Section 7.2, Problem 2

To find the volume of a solid by revolving the graph of y =4-x^2 about the x-axis, we consider the bounded region in between the graph and the x-axis. To evaluate this, we apply Disk method by using a rectangular strip perpendicular to the axis of rotation. As shown on the attached image, we consider a vertical rectangular strip with a thickness =dx.
We follow the formula for the Disk Method in a form of: V = int_a^b pir^2 dx or V = pi int_a^b r^2 dx
where r is the length of the rectangular strip.
In this problem, we let the length of the rectangular strip=y_(above)-y_(below) .
Then r = (4-x^2) - 0 = 4-x^2
Boundary values of x: a= -2 to b=2 .
Plug-in the values on the formula V = pi int_a^b r^2 dx , we get:
V =pi int_(-2)^2 (4-x^2)^2 dx
Expand using FOIL method:(4-x^2)^2 = (4-x^2)(4-x^2)= 16-8x^2+x^4 .
The integral becomes:
V =pi int_(-2)^2 (16-8x^2+x^4) dx
Apply basic integration property:int (u+-v+-w)dx = int (u)dx+-int (v)dx+-int(w)dx to be able to integrate them separately using Power rule for integration: int x^n dx = x^(n+1)/(n+1) .
V = pi[ int_(-2)^2(16) dx -int_(-2)^2(8x^2)dx+int_(-2)^2(x^4)dx]
V = pi[16x-(8x^3)/3+x^5/5]|_(-2)^2
Apply definite integration formula: int_a^b f(y) dy= F(b)-F(a) .
V = pi[16(2)-(8(2)^3)/3+(2)^5/5]-pi[16(-2)-(8(-2)^3)/3+(-2)^5/5]
V =pi[32-64/3+32/5]-pi[-32-(-64)/3+(-32)/5]
V =pi[32-64/3+32/5]-pi[-32+64/3-32/5]
V=(256pi)/15 -(-256pi)/15
V=(256pi)/15 +(256pi)/15
V=(512pi)/15 or 107.23 (approximated value)

Who were the Romans and how did they conquer Greece?

Rome was a civilization that started in Central Italy and eventually went on to conquer the entire Mediterranean and much of Europe. A complete history of the Romans is too complex and extensive to give here. Basically, Rome was founded as a small city-state in 753 BCE. Until 509 BCE they were ruled by kings. In that year, the kings were overthrown and Rome became a republic ruled by elected senators and counsels. It was during its time as a republic that Rome began expanding its borders by conquering its neighbors, including Greece. In 27 BCE, the Roman Empire was established by Augustus. Rome remained an empire until it was conquered by barbarians in the 5th Century CE.
The Romans themselves were a mix of ethnicities. They started off as members of the Latin tribe in Central Italy. As they spread across Italy and then across the Mediterranean and Europe, the Romans absorbed many more ethnicities. Many of these other groups became Romanized, meaning they adopted the culture and customs of the Romans and essentially became Roman themselves.
The Roman conquest of Greece began in 146 BCE after the Battle of Corinth when the Romans took control of Macedonia. The rest of Greece was added piecemeal to Rome over the next century. The province of Pergamon came to Rome through peaceful means in 133 BCE when its king left it to Rome in his will. The revolt of Athens in 88 BCE led the Romans to directly conquer the city and its region and place it under direct Roman administration. The Roman Civil Wars were fought largely on Greek soil, leaving the region in ruins. After the wars, Emperor Augustus placed southern Greece under the administration of the governors of the Achaea Province.
Interestingly, although it was the Romans who conquered Greece, Greek culture survived and was readily appropriated by the Romans. Many Roman aristocrats began adopting Greek customs and patronizing Greek-inspired arts. Many consider the conquest of Greece to be the catalyst for bringing civilization to Rome. As Horace, the 1st Century Roman poet, wrote "Captive Greece took captive her savage conqueror and brought the arts to rustic Latium."
https://uts.nipissingu.ca/muhlberger/2055/L33ANC.HTM

What are the reasons behind each rule in The Giver?

The answer to this question could go two ways, so I'll attempt to answer both.
In general, the reasons behind each rule are the same. Rules are a very important part of the society in The Giver. To the members of the society, rules are good because they make life manageable. Everything is neat and orderly. The rules make life predictable and simple, which is what the people wanted when they adopted the Sameness. Of course The Giver is a dystopian story. The society might like the rules, but readers come to see the rules as devices that take away any individuality and freedom of choice. No matter what the rule is, it still functions to limit a person, a family, and/or the society in some way.
The question might be asking for a brief explanation of each rule in the book. There are a lot of rules in Jonas's society, so here are a few rules with some possible explanations for why that particular rule exists.
Families are limited to four people: a mother, father, son, and daughter. This rule serves two functions. First, it serves as population control. Two parents that eventually die are replaced by two children. The population size neither grows nor shrinks. Second, the rule ensures a gender-equal society. There should be the same number of men and women in the society.
Fighting and lying are prohibited. This rule helps maintain peace and order.
Strong feelings are not to be experienced. This helps maintain the Sameness.
Modesty is to be maintained at all times. Nakedness is forbidden for everybody except the very young and very old. This rule is likely there to help control the Stirrings.
Adolescents are required to report when the Stirrings begin and then take medication for it. This rule is tied to the rule about not being allowed to have strong feelings.
Each family member must share his/her dreams in the morning and share their feelings in the evening. This rule sounds like it exists to encourage family bonding; however, it is more likely that the rule is there so each family can monitor whether or not any of its members are becoming abnormally emotional.
Children's comfort objects are taken away at age 8. This is probably to help the child realize that they are getting closer to being a contributing member of society. This rule can be seen as a form of oppression: what the child wants or feels is irrelevant.
Objects cannot be removed from designated areas. This rule sounds like it helps people not misplace or lose objects. On the surface, it seems like a simple, non-invasive rule. However, this rule also sounds like a rule that helps keep everything in its place. That's what all of these rules are geared to do: keep people in their place.

In what ways might RFID technology be used to serve customers better? What problems might arise? Do you think that the technology might be valuable when implanted in animals or people?

RFID stands for Radio Frequency Identification. It is a type of wireless technology and basically has three components to it: a tag, a reader, and a computer system.
The tag consists of a microchip and radio antenna. The microchip in the tag contains essential information about a product or item. To transmit this information to a reader, the tag uses radio signals. After picking up the signals, the reader delivers the information to a computer system. From the computer system, companies can easily track the kinds of products consumers like to buy. This allows companies to position advertisements, sales, and product placements in stores according to their customer's preferences. Also, using RFID technology increases productivity: it is much easier to use, is more accurate, and less error-prone than traditional bar-coding. Thus, increased productivity leads to greater profits for companies.
As for consumers, the benefits of RFID technology are numerous. For example, it minimizes wait times at toll booths, and this in turn reduces traffic congestion during busy hours on a highway. In hospitals, nurses immediately know which medication patients need by referring to their RFID tags. At the store, customers can pay for their purchases by waving credit cards (embedded with RFID technology) under special readers. The most important benefit to consumers is the convenience they enjoy. Wait times at checkout lines will be reduced if customers can rely on RFID technology.
Companies can quickly replace perishable items or recalled items from the shelves; they can also replenish their shelves quickly when popular items run out. This will reduce customers' frustrations when they go to their favorite stores. Yet, with all these benefits, there may be some concerns about RFID technology.
The main concern centers on consumer or personal privacy. For instance, companies can use the technology to track the spending habits of consumers. The claim is that this helps companies tailor advertisements and product releases according to their customers' preferences. Yet, the concern lies in how the gathered information will be used and how many third parties the companies will share the information with.
As for implanting RFID chips into humans and animals, the technology may prove useful in tracking down Alzheimer's patients or even lost pets. Employees who work for government agencies that handle sensitive intelligence data can only enter specific buildings they have received clearances for; their implanted RFID chips will determine exactly what buildings they can enter. Meanwhile, for those patients who have heart conditions, medical professionals can keep track of and even disable pacemakers from a laptop, if necessary. However, this raises a frightening question: what if this technology is abused? It is a chilling thought that this technology can expose a patient to the prospect of sabotage, whether intentional or otherwise.
So, you can see that there are advantages and disadvantages to using RFID technology in our daily lives. For more, please refer to the links below.
http://www.rfidc.com/docs/introductiontorfid_business.htm

https://www.vice.com/en_us/article/kwxwjn/pros-and-cons-of-getting-a-microchip-283

In "Sinners in the Hands of an Angry God," what is the writer's main purpose?

Jonathan Edwards’s main goal in writing and delivering his sermon “Sinners in the Hands of an Angry God” was to persuade people to love God and give their hearts to him.  If they do this, Edwards believes they can be saved.
Before the Great Awakening (of which Edwards was a part), many religious Americans believed in predestination. They believed God had already decided whether they were going to Heaven or Hell and that there was nothing they could do to change their fate. Preachers of the Great Awakening disagreed. They believed people deserved to be damned but could save themselves by accepting God’s love and loving God in return. 
The main purpose of Edwards’s sermon is to convince the people who are listening that this is true. He warns them about how they are in danger of going to Hell, and claims they would completely deserve that fate. He says, there is an opportunity for them, though; they can accept God and improve their chances for salvation. Edwards tells his listeners that God has given them

an extraordinary opportunity, a day wherein Christ has flung the door of mercy wide open, and stands in the door calling and crying with a loud voice to poor sinners.

He tells them that many other people have already accepted God’s love and that their

hearts [are] filled with love to him that has loved them and washed them from their sins in his own blood, and rejoicing in hope of the glory of God.

He urges them to do the same so they might be saved as well and be able to live with God in Heaven. His main goal in this sermon is to get people to accept God’s love and to love him back so they can be saved from damnation.

Why do the pigs start walking upright?

In Animal Farm, the pigs start walking upright in the final chapter of the story and there are a couple of possible explanations for this. Firstly, the pigs have devoted a lot of time and effort to emulate humans. We have seen this earlier in the story when they, for example, start sleeping in beds, wearing clothes, and drinking alcohol. Although they hated their human masters, the pigs regard humans as the pinnacle of authority and power, so it is, perhaps, not surprising that the pigs would want to emulate this ability, even if it is very ironic.
Secondly, walking upright is symbolic of the pigs' elevated status above the other animals. Like their better rations and ability to change the rules, walking upright demonstrates that the pigs are not like the other animals on the farm. They represent a different class—the ruling class—and, by walking upright, this point is reinforced to everyone.

What is the meaning of transparency?

Transparency in politics means that government is open, honest, available, and accountable. When a government is being transparent, it means that the government holds meetings, hearings, and sessions of the legislature at reasonable times and with advanced notice to the public. It also means that the people will know what will be happening in these meetings, hearings, and legislative sessions. When a legislature meets late at night and adds special items into, or deletes items from, a bill without the public having an opportunity to speak about these additions or deletions, that is an example of nontransparent government.
A transparent government also makes all documents, agendas, and minutes available to the public. The people should be able to examine any documents that are being discussed or that are used for discussion. When a request is made for some information that doesn’t involve personnel, the government should willingly provide that information.
Transparent government means that the government will show how it is using taxpayer money. Revenues and expenses will be clearly identified. Government budgets should also be available for public examination and should be easy to understand.
Some people feel that elected officials should share information regarding their personal income, expenses, and tax returns. These people believe that by doing so, it adds to the transparency of the government and its leaders.
https://ballotpedia.org/Government_transparency

What does "Mario and the Magician" teach us about moral choice, normative ethics, and how we ought to live?

The short story "Mario and the Magician" suggests that moral choice is an individual decision. It dictates how we choose to behave in our everyday lives. In terms of normative ethics, the story teaches us that our moral centers differ based on how we define our ethical parameters.
In normative ethics, there are two ways in which basic moral standards are derived. The first is teleological and the second is deontological. Teleological theories define a good action based on the consequences it brings about. So, if an action brings about positive results, it is labeled as a "good" action. In contrast, deontological theories are focused on inherent moral absolutes: an action is good because it is right.
In the story, Cipolla is a domineering, obnoxious, and vulgar performer. Accordingly, he uses hypnotism to get his audience to perform demeaning acts of self-subjugation. While many members of the audience are disgusted by Cipolla's behavior, others remain fascinated.
The narrator notes that not one person chooses to leave during the intermission, despite the freedom to do so. Here, the audience knows how it would prefer Cipolla to behave, but it is too captivated by his bold indifference to care. By his actions, Cipolla is able to hypnotize the entire audience into a state of emotional paralysis. The atmosphere is "queer, uncomfortable, troublesome, tense, [and] oppressive." Yet, no one can muster the will to leave.
So, here, the teleological theory of normative ethics dominates: Cipolla entertains the audience, and the audience in turn is mesmerized by his performance. Thus, Cipolla's actions are "good" because they result in pleasure. But, at what cost comes the pleasure of the masses?
Cipolla humiliates each member of the audience he calls on stage. For example, he hypnotizes Signor Angiolieri's wife, to the point that she will respond to no other voice but his own. During the entire performance, Cipolla mocks the woman's husband, ordering him to call his wife to him. The poor husband's cries of "Sofronia" are ignored.
In due time, Cipolla snaps the wife out of her reverie and returns her to Signor Angiolieri, cruelly saying

"Here is your wife. Unharmed, with my compliments, I give her into your hands. Cherish with all the strength of your manhood a treasure which is so wholly yours, and let your zeal be quickened by knowing that there are powers stronger than reason or virtue, and not always so magnanimously ready to relinquish their prey!"

So, the question begs to be asked: does Signora Angiolieri ignore her husband because she chooses to? It certainly is an uncomfortable question.
Again, is moral choice an individual decision? It seems that Cipolla's last guest on stage answers the question for us. In Mario, we see personal agency in action. Although he initially succumbs to Cipolla and humiliates himself on stage, Mario later does an about-turn. He fatally shoots Cipolla, and almost immediately, the crowd snaps out of its strange trance. People jump on Mario to disarm him, while others shout for the police and the doctor.
Mario's actions show that an authority figure cannot compel us to obedience without our consent. Thus, moral choice is a decision and that decision is based on how we define ethical conduct.
https://www.britannica.com/topic/normative-ethics

In Stockton's "The Lady, or the Tiger?" what is unique about the king's arena?

The king's arena in Stockton's "The Lady, or the Tiger?" is not unique because there is a 50% chance that the accused will die an ignominious death. Roman arenas provided such gut-wrenching death scenes as well. The king's arena in this story is unique because the outcome doesn't depend on a criminal's strength or skills in battle. For the person who faces the choice of what is behind two doors, the outcome is determined by chance. The narrator describes the king's justification behind creating such an arena for justice as follows:

This was the king's semibarbaric method of administering justice. Its perfect fairness is obvious. The criminal could not know out of which door would come the lady. . . and the thinking part of the community could bring no charge of unfairness against this plan; for did not the accused person have the whole matter in his own hands?

Based on the information provided from the passage, the unique qualities of this king's arena is that the criminal gets to choose his fate; then, whatever comes out from behind the door is the accused's final reward or punishment.
In Roman arenas, slaves would fight gladiators more than once or until they died. Roman arenas weren't used as courtrooms, either. They were used purely for violent entertainment. As a result of the philosophy behind the arena, the king supplies his subjects and himself with a partially civilized way of dealing with criminals; of course, the civilized part emerges only if criminals choose the lady's door. On the other hand, the arena is also barbaric because of the deaths which occur if criminals choose the door with the tiger behind it. Ultimately, there is hope in the king's arena because there is a choice; and when there is a choice, there is an opportunity for the criminal to escape the punishment of a tiger. The arena is also unique because of the intrigue it provides its audience each time a new criminal is released in it.

College Algebra, Chapter 5, 5.4, Section 5.4, Problem 48

Solve the Logarithmic Equation $\log_5 x + \log_5 ( x + 1) = \log_ 5 20$ for $x$.

$
\begin{equation}
\begin{aligned}
\log_5 x + \log_5 ( x + 1) &= \log_ 5 20\\
\\
\log_5 x (x + 1) &= \log_5 20 && \text{Laws of Logarithms } \log_a AB = \log_a A + \log_a B\\
\\
5^{\log_5 x ( x + 1)} &= 5^{\log_5 20} && \text{Raise 5 to each side}\\
\\
x (x + 1) &= 20 && \text{Property of } \log\\
\\
x^2 + x &= 20 && \text{Distributive Property}\\
\\
x^2 + x - 20 &= 0 && \text{Subtract 20}\\
\\
(x - 4)(x + 5) &= 0
\end{aligned}
\end{equation}
$

Solve for $x$

$
\begin{equation}
\begin{aligned}
x -4 &= 0 &&\text{and}& x + 5 &= 0 \\
\\
x &= 4 &&& x &= -5
\end{aligned}
\end{equation}
$

The only solution in the given equation is $x = 4$, since $x = -5$ will make the term a negative value.

In Freak the Mighty by Rodman Philbrick, are the main characters trying to achieve something or overcome a particular problem?

The main character of Rodman Philbrick's Freak the Mighty is Maxwell Kane, the son of Kenneth "Killer" Kane, who was convicted for murdering Maxwell's mother via strangulation. Maxwell's struggle throughout the book is to overcome his low self-esteem (he frequently refers to himself as a "butthead") and his reputation as a frightening presence in the community due to his resemblance to his father. 
Maxwell finds a friend in the form of another major character, Kevin, the titular "freak." Kevin's struggle throughout the book is to cope with the birth defect (Morquio syndrome) which has left him dramatically smaller than other children his age and which requires him to use leg braces and crutches to walk. 
Together, Max and Freak go on many adventures, including evading bullies, visiting the "Bionics Department" of a hospital, returning the lost purse of the wife of a motorcycle gang leader, and turning over Max's murderous father to the police after he is released from prison on parole. 

Name three ways that white Southerners restricted African Americans’ right to vote.

White Southerners restricted the African American right to vote in various ways. These restrictions began with the ratification of the 15th Amendment in 1870 up until the passing of the Voting Rights Act by President Lyndon B. Johnson on August 6th, 1965. This period would be known as the Era of Jim Crow (based on a minstrel show character that negatively portrayed African Americans) as mostly white southerners did everything they could to segregate themselves, intimidate minorities, and stop African Americans from voting.
First, many Southerners simply used fear and violence to stop African Americans from voting. Groups such as the Ku Klux Klan (Founded in Pulaski, Tennessee) and The White League (Founded in Louisiana) quickly spread to other parts of the South and took part in marches, riots, and even murder to stop African Americans from going to the polls. For example, during election season in 1876, a group known as the Red Shirts executed four African Americans in Hamburg, South Carolina in what would become known as the Hamburg Massacre.
Second, whites during this era also used political power to stop African Americans from having the right to vote. One way in which they did this was through the use of the Grandfather Clause and Poll Taxes. The Grandfather Clause stated that any man whose grandfather did not vote, could not vote either. Therefore, the majority if not all of African Americans could not vote as most of their grandfathers had been slaves. Poll Taxes were taxes that forced African Americans to pay for their right to vote. Due to the fact that African Americans were just coming out of slavery, many were unwilling or did not have the money to pay such taxes. Poll taxes were even written into many Southern State Constitutions in the late 19th and early 20th centuries.
Finally, African Americans were disenfranchised with the use of literacy tests that forced them to prove that they could read before they were allowed to vote. A common example of this would be the Eight Box Law. This law created a system where ballot boxes were set up in front of voters. If the voter could not read the ballot boxes and place their ballot in the correct box, then their vote did not count. Tests and laws such as these were common place in the American South throughout the Jim Crow Era.

The first way the Southerns restricted African Americans from voting was by imposing a poll tax on their constituents. With this measure placed in the laws, many people received a tax when going to vote. The tax was about $25 to $50 dollars with inflation included in this estimate. This tax was applied to all voters, black and white, so people with low incomes found themselves unable to pay the tax and therefore unable to vote. The next restriction was in-acting literacy test on all citizens. Thus, voters were ask to take a test to see if they understood what was read to them, if they did they could vote and if they didn't they couldn't vote. But their was one major problem back in that era, many people were illiterate, which meant many people at that time were denied the opportunity to vote. It was even found that voting officers' claimed that many of the whites understood what was read to them and the blacks even if the did understand, were unable to comprehend the passage read to them. And lastly, was the violence that was put upon African Americans just because they voted or attempted to vote. For example many people were intimidated, beaten and killed and even in some cases their families were harmed. So in some situations people would pass the requirements to vote but they took a risk for doing so.

One way was intimidation through hate groups such as the Ku Klux Klan. The Klan beat up influential African Americans and stood guard over polling places to ensure minimal black participation. Sometimes they even resorted to lynchings. Another way was a poll tax. Poor whites who promised to support the Democratic Party usually could get access to the funds to vote, but these funds were denied to African Americans, who primarily supported Republicans in elections. Poll taxes were abolished in 1964 as part of the civil rights movement. Another rule was the grandfather clause. This rule stated that if one's grandfather could vote in 1860, then one also had the right to vote. Of course, this ruled out African Americans—even if they were free, they could not legally vote.
A fourth barrier to the polls was the literacy test. As the South did not receive public education until after the war, many poor people in the South could barely read or write. Poor whites who promised to uphold the system were often given the simplest things to read, while African Americans were given a passage from the Constitution to analyze. These barriers, both customary and legal, curtailed African American voter turnout until the Democratic Party regained power in the South after 1877.