Beowulf is able to defeat evil in the form of Grendel and Grendel’s mother, yet he loses his life when he battles the dragon. What theme does this suggest about the struggle between good and evil?

It can be hard to assign values such as "good" and "evil" to the events in Beowulf. For Beowulf, "good" is that which gains him glory; the point of a warrior’s life is to perform great deeds that will be remembered. This, after all, is what brings him to Heorot in the first place—the opportunity to show himself to be a man of great strength and valor. Beowulf’s subsequent reign over the Geats is successful in that his reputation has secured them from invasion.
In a way, his final battle with the dragon is a fitting end to his story. It is far better for Beowulf to go out in battle defending his people than to die quietly in his bed. Beowulf’s death, however, is a great evil for the Geats, who now are open to attack from their enemies and lack a great warrior to defend them.

A possible theme would be that the struggle between good and evil often results in a Pyrrhic victory.
The word "Pyrrhic" refers to the results of the conflict, where the victor's losses are almost as great as those sustained by the conquered. In a Pyrrhic victory, there is the sense that the victor's gains have been nullified by the extreme losses incurred. If you're interested, please refer to the link below about the origins of the phrase "Pyrrhic victory" and a history of such victories on the battlefield.
In Beowulf, the protagonist's final victory is won at great cost to himself. He kills the dragon but sustains a fatal wound. In his final moments, Beowulf voices his regret that he has no son to bequeath his legacy to. Yet, he comforts himself that, during his fifty-year reign as king, no other monarch dared to openly challenge him in battle. During his last moments on earth, Beowulf also rejoices that his death will not leave his people helpless; the dragon's hoard will enrich his subjects. So, the conflict between Beowulf and the dragon suggests that evil is often defeated at great cost to the good.
https://www.warhistoryonline.com/history/thermopylae-bunker-hill-and-2-other-pyrrhic-victories-throughout-history-winning-isnt-always-worthit-m.html

In Lee's To Kill a Mockingbird, what is the compromise that Atticus suggests?

In Chapter 14 of To Kill a Mockingbird, Scout becomes overwhelmed with all of the people in her life who are telling her what to do. Aunt Alexandra has recently moved in with them, and it is difficult for Scout to mind this new woman who openly disapproves of her. To add salt to the wound, Jem attempts to tell her what to do in order to bring peace to the household. This doesn't sit right with Scout because she sees Jem as her equal, not her superior. As a result, Scout provokes him into a fistfight that Atticus has to break up. Atticus asks the children who started the fight and Scout blames Jem because he was telling her what to do. She asks her father if she has to mind Jem from then on, too. Atticus makes the following compromise:

"Let's leave it at this: you mind Jem whenever he can make you. Fair enough?" (138).

This seems to satisfy Scout because it gives her some support for a time that Jem might tell her what to do in the future. In fact, Scout uses this during the Tom Robinson trial when Jem tells her to go home. Scout responds by saying the following:

"'You gotta make me first,' I said, remembering Atticus's blessed dictum. Jem scowled furiously at me . . ." (173).

Therefore, the compromise is that whenever Jem bosses Scout around, she doesn't have to obey him unless he can make her obey.

12yy' - 7e^x = 0 Find the general solution of the differential equation

For the given problem: 12yy'-7e^x=0 , we can evaluate this by applying variable separable differential equation in which we express it in a form of f(y) dy = f(x)dx .
 Then, 12yy'-7e^x=0 can be rearrange into 12yy'= 7e^x
Express y'  as (dy)/(dx) :
12y(dy)/(dx)= 7e^x
Apply direct integration in the form of int f(y) dy = int f(x)dx :
12y(dy)/(dx)= 7e^x
12ydy= 7e^xdx
int12ydy= int 7e^x dx
For the both side , we apply basic integration property: int c*f(x)dx= c int f(x) dx
12 int ydy= 7int e^x dx
Applying Power Rule integration: int u^n du= u^(n+1)/(n+1) on the left side.
12int y dy= 12 *y^(1+1)/(1+1)
               = (12y^2)/2
               =6y^2
Apply basic integration formula for exponential function: int e^u du = e^u+C on the right side.
7int e^x dx = 7e^x+C
Combining the results for the general solution of differential equation:
6y^2=7e^x+C
or 
(6y^2)/6=(7e^x)/6+C
y^2 = (7e^x)/6+C
y = +-sqrt((7e^x)/6+C) 

Why did the Old Man kill his own father?

The Old Man killed his father because the latter squandered the wealth that belonged to the Old Man's mother. In the Old Man's mind, his father (by squandering his wife's wealth) also defrauded his child (the Old Man) of his rightful inheritance.
In the play, the Old Man tells his sixteen-year-old son that his mother once owned a grand mansion. In her youth, she had fallen in love with one of her grooms. She married him, despite her own mother's wishes. After the marriage, her mother disowned her and never spoke to her again.
The Old Man relates that his mother never knew how his father squandered her wealth. She died while giving birth to the Old Man. After her death, the Old Man's father spent the wealth of her estate on horses, women, drink, and cards. To pay for his accumulating debts, the Old Man's father even had the trees on the property cut down. The Old Man tells his son that he will never forgive his father for laying waste to an illustrious mansion, especially one that was inhabited by the great men of his age. The Old Man describes his father's actions as a "capital offence."
As we can see, the Old Man still resents his father for squandering his mother's fortune, and he also hates him for defrauding him of his inheritance. The Old Man is also angry that his father never provided him with an education. Instead, the Old Man had to learn how to read from a gamekeeper's wife, and he had to rely on a Catholic curate in order to learn Latin. Eventually, the Old Man had to earn a living as a lowly peddler. So, the Old Man killed his father for what he considers were immoral actions against him and his mother.

The Old Man's father was a dissolute wastrel, a chronic alcoholic who shamelessly frittered away the family fortune. As a boy, the Old Man was prevented by his father from attending school, and so to this day, he still harbors resentment towards him for his ignorance. The Old Man's son seems unconcerned by his late grandfather's character. Rather, he appears more interested in the glittering world of wealth and privilege his family once inhabited.
At the same time, the young man is aware of certain unpleasant rumors concerning his father, the Old Man. One night, the Old Man's father got drunk as usual, only this time he burned down the family home. The boy has heard that the Old Man killed his father that night. When asked about it, the Old Man admits that the rumors are indeed true.
It would appear that the Old Man was motivated primarily by revenge. His mother married beneath herself and the result was the destruction of a great family and its ancestral home. The Old Man is also eaten up with resentment over his reduced status in life, directly caused by his father's profligacy. Although he couldn't have foreseen how his life would turn out when he stabbed his father to death amid the burning wreckage of the family home, the years since have confirmed to the Old Man's satisfaction that he made the right decision.

Single Variable Calculus, Chapter 5, 5.4, Section 5.4, Problem 56

A particle moves along a line so that its velocity at time $t$ is $v(t) = t^2 - 2t - 8$ (measured in meters per second).
a.) Find the displacement of the particle during the time period $1 \leq t \leq 6$ from the formula.

$
\begin{equation}
\begin{aligned}
\int^{t_2}_{t_1} v(t) dt &= s (t_2) - s(t_1)\\
\\
\int^{t_2}_{t_1} v(t) dt &= \int^6_1 \left( t^2 - 2t - 8 \right) dt\\
\\
\int \left( t^2 - 2t - 8 \right) dt &= \int t^2 dt - 2 \int t d t - \int 8 dt\\
\\
\int \left( t^2 - 2t - 8 \right) dt &= \frac{t^{2+1}}{2+1} - 2 \left( \frac{t^{1+1}}{1+1} \right) - 8 \left( \frac{t^{0+1}}{0+1} \right)\\
\\
\int \left( t^2 - 2t - 8 \right) dt &= \frac{t^3}{3} - \frac{\cancel{2}t^2}{\cancel{2}} - 8t\\
\\
\int \left( t^2 - 2t - 8 \right) dt &= \frac{t^3}{3} - t^2 - 8t\\
\\
\int^6_1 \left( t^2 - 2t - 8 \right) dt &= \frac{(6)^3}{3} - (6)^2 - 8 (6) - \left[ \frac{(1)^3}{3} - (1)^2 - 8 (1) \right]\\
\\
\int^6_1 \left( t^2 - 2t - 8 \right) dt &= \frac{216}{3}-36-48-\frac{1}{3}+1+8\\
\\
\int^6_1 \left( t^2 - 2t - 8 \right) dt &= 72-36-48-\frac{1}{3}+9\\
\\
\int^6_1 \left( t^2 - 2t - 8 \right) dt &= \frac{-10}{3} \text{ meters or } -3.33 \text{ meters}
\end{aligned}
\end{equation}
$


This means the particle moved $3.33$m toward the left.
b.) Find the distance traveled during this time period
Note that $v(t) = t^2 - 2t - 8 = (t- 4)(t+2)$ and then $(t-4)(t+2) = 0$
$t = 4$ and $ t = -2$
Only $t = 4$ is in the interval $[1,6]$, thus, the distance traveled is...

$
\begin{equation}
\begin{aligned}
\int^6_1 |v(t) | dt &= \int^4_1 - v(t) dt + \int^6_4 v(t) dt\\
\\
\int^6_1 |v(t) | dt &= \int^4_1 \left( -t^2 + 2t + 8 \right) dt + \int^6_4 \left( t^2-2t - 8 \right) dt\\
\\
\int^6_1 |v(t) | dt &= \left[ -\frac{t^3}{3} + t^2 + 8t \right]^4_1 + \left[ \frac{t^3}{3} - t^2 - 8t \right]^6_4\\
\\
\int^6_1 |v(t) | dt &= \frac{-(4)^3}{3} + (4)^2 + 8 (4) - \left[ \frac{-(1)^3}{3} + (1)^2 + 8(1) \right] + \left[ \frac{(6)^3}{3} - (6) - 8(6) - \left[ \frac{(4)^3}{3} - (4)^2 - 8(4) \right] \right]\\
\\
\int^6_1 |v(t) | dt &= \frac{-64}{3} + 16 +32 + \frac{1}{3} - 1 - 8 + 72 - 36 - 48 - \frac{64}{3} + 16 + 32\\
\\
\int^6_1 |v(t) | dt &= \frac{98}{3} \text{ meters } \qquad \text{ or } \qquad \int^6_1 |v(t) | dt = 32.67 \text{ meters}
\end{aligned}
\end{equation}
$

How was the World War II era not a watershed for the Civil Rights Movement?

This is a difficult question to answer, because most historians would argue that World War II was a watershed moment for the Civil Rights Movement, for many reasons. To argue against this consensus, though, one might look at the realities of life in the Deep South, where the movement for civil rights met the most resistance. The war ended in 1945, and Southern cities (like Atlanta, Montgomery, Mobile, and New Orleans), their populations swollen by war industries, became crucibles for racial conflict. This was because thousands of African Americans had moved to these cities to take advantage of economic opportunities during the war. Southern cities responded by doubling down on Jim Crow (segregation) laws. Many of these would be directly challenged by African American activists (like, for example, Rosa Parks in Montgomery.) Even this line of argument suggests that World War II was an important impetus for civil rights. But looking at the situation through the eyes of an African American in the rural South, one might see little social change resulting from the war—indeed, things got worse before they got better. While civil rights workers protested segregation on public transport and at lunch counters, the vast majority of black men and women in the South remained desperately poor and lived in small rural communities. They would have seen very little change in the aftermath of the war. Even the most famous victories of the Civil Rights Movement came two decades after the end of World War II. So citing World War II as the "watershed" event in the Civil Rights Movement makes some assumptions that may seem simplistic. It falsely suggests that the urban black experience in the South was the dominant one. It suggests a certain inevitability that would not have been evident to people at the time. Finally, it oversimplifies the movement, which had many different facets and even factions.
https://www.history.com/topics/black-history/civil-rights-movement

While significant desegregation and nullification of Jim Crow laws would not take place until after World War II, the war years saw African Americans begin to nudge their way toward equality. Led by the charismatic President of the Brotherhood of Sleeping Car Porters, A. Phillip Randolph, civil rights groups of the early 1940s organized the first March on Washington as a protest to what they saw as a double standard in the country regarding race. On one hand, America was fighting for the world's freedom against a regime in Germany founded on racism. On the other hand, blacks were still treated as second-class citizens. They were treated as lesser than white soldiers, and they were often paid much less than white workers in the nation's defense industry.
Organizers estimated that over one hundred thousand marchers were prepared to descend on Washington DC in the summer of 1941. Alarmed by such a demonstration, President Franklin D. Roosevelt issued Executive Order 8802 which sought to eliminate prejudicial hiring in the defense industry. (The prior Democrat, Woodrow Wilson, oversaw unprecedented segregation in the federal government.) The order's title read, "Reaffirming Policy Of Full Participation In The Defense Program By All Persons, Regardless Of Race, Creed, Color, Or National Origin, And Directing Certain Action In Furtherance Of Said Policy."
Although it was just a baby step on the road to desegregation, the act was integral in later eliminating racial discrimination in all federal hiring. In 1948, the military followed suit by allowing black and white soldiers to serve side by side in the nation's armed forces. The 1941 March on Washington was ultimately cancelled because of the passage of Executive Order 8802. A more consequential March on Washington would take place in 1963 with Martin Luther King Jr. giving his famous "I Have a Dream" speech.
Perhaps the most consequential executive order involving civil rights took place early in 1942 when President Franklin Roosevelt, responding to hysteria over the Japanese attack at Pearl Harbor, signed Executive Order 9066 expelling those of Japanese ancestry from military areas "as deemed necessary and desirable." The resulting order caused the forced evacuation of 112,000 Japanese Americans to camps throughout the West Coast. Many established Japanese Americans lost their jobs, their businesses, their farms, and the respect from white Americans they had been fostering for many decades. Moreover, conditions in the relocation camps were poor and the Japanese often received brutal treatment from military guards. For nearly two years the United States government denied the rights of its own citizens, setting the trajectory of civil rights backwards.
In California, then-Governor Earl Warren was an early proponent of Roosevelt's "Removal Order," arguing vehemently that the West Coast needed to be kept safe from sabotage. He said, “If the Japs are released, no one will be able to tell a saboteur from any other Jap. . . . We don’t want to have a second Pearl Harbor in California. We don’t propose to have the Japs back in California during this war if there is any lawful means of preventing it.”
During the war, only ten Americans were convicted of spying for Japan. Warren, in his memoirs many years later, admitted that his treatment of the Japanese during the war had been wrong. He wrote that he had, over the years, come to regret "the removal order and my own testimony advocating it, because it was not in keeping with our American concept of freedom and the rights of citizens."
For more in-depth study on the internment during World War II, I would point to three excellent portrayals of the Japanese American problems of the time. First, Jeanne Wakatsuki Houston's Farewell to Manzanar is an effective memoir of her childhood in the relocation center in the California desert. Second, John Okada's No-No Boy is about a young Japanese man who refused to join the U.S. military and was sent to prison. Some Japanese American men did serve, especially in the famous 442nd Regiment in Europe. More than 800 Japanese Americans were killed in action. Finally, George Takei, of Star Trek fame, has penned an entertaining and revealing musical, Allegiance, about his experience as a child being uprooted from his family's farm in the Salinas Valley to the Heart Mountain Relocation Center in Wyoming.
https://www.blackpast.org/african-american-history/march-washington-movement-1941-1947/

https://www.theatlantic.com/politics/archive/2015/11/wilson-legacy-racism/417549/

What does Kino offer the doctor as payment for the doctor's treatment?

In chapter 1, Coyotito is bitten by a poisonous scorpion and Juana suggests that they take their son to the doctor in town. When Kino and Juana arrive at the doctor's residence with their ill son, the doctor's native servant answers the door. After Kino explains why Coyotito needs the doctor's attention, the servant relays the message to the doctor, who is uninterested in helping the "little Indians." Kino then offers to pay the doctor with eight small, misshapen seed pearls, which are of little value. The doctor reveals his racist, callous nature by refusing to treat Coyotito.
After Kino finds the largest pearl ever to be discovered in the region, he gains attention from his community, and the word spreads throughout town. The doctor ends up visiting Coyotito in Kino's village, and it seems as if Coyotito is recovering from the poisonous sting. However, the greedy doctor gives Coyotito a mysterious capsule filled with powder, which ends up making Coyotito sick. After the doctor leaves, he returns promptly in an hour and gives Coyotito three drops of ammonia, which calms the infant. The doctor then feigns ignorance about Kino's massive pearl and asks him how he plans on paying for his services. Kino responds by telling the doctor that he will pay him back once he sells the pearl. The doctor then offers to put Kino's pearl in his safe before he leaves the village.

What do you know about the Canterville Ghost? How was his soul liberated?

In the first chapter of the story, we learn that the Canterville Ghost is Sir Simon de Canterville, a former resident of Canterville Chase. In 1575, Sir Simon murdered his wife, and nine years later, he died in very mysterious circumstances. His body was never found and his "guilty spirit" has haunted the house ever since, terrifying generations of guests.
In Chapter Five, we learn even more about Sir Simon when he has a conversation with Virginia Otis. He tells her, for example, that he murdered his wife because she was a poor housekeeper and that he was killed by his wife's family. We also learn that he is very tired and is desperate to enter the Garden of Death where his soul can be at peace.
In order to do this, he must enlist a girl who is pure of heart and can pray for him and the sins he committed in life. When he explains this to Virginia, she agrees to help him, and, together, they are successful. Sir Simon finally enters the Garden of Death and is never seen at Canterville Chase again.

Sir Simon, the Canterville ghost, has his soul liberated through the actions of Virginia Otis, the American girl living in Canterville Hall.
She stumbles across him by accident one day in the tapestry room. She sees he looks sad. In conversation with him, she learns that he is tired of being a ghost and wishes he could die. He became a ghost as a punishment for murdering his wife. He has been haunting Canterville Hall for hundreds of years and is weary.
The only way he can be liberated, according to the prophecy in the tapestry room window, is to have a pure young woman pray and intercede for him with God. Virginia agrees to do that. As a result, Sir Simon fully dies and is finally at peace.

How are George and Hazel Bergeron described? What sort of life do they lead?

Hazel Bergeron is described as being "perfectly average" in intelligence. This description implies that she cannot ponder anything because her thought processes are shallow. She cannot recall much, and her attention span is very short. When, for instance, she views the television, Hazel forgets what she has seen almost instantly. On the other hand, George Bergeron is innately highly intelligent. Consequently, he is required to always wear in his ear a "little mental-handicap radio." This radio is tuned to a government transmitter that sends sharp noises into his ear "to prevent him from taking unfair advantage of his brain."
Hazel and George Bergeron lead lives that are entirely controlled by their government. They have had to surrender their civil rights. Their genius son Harrison has been imprisoned for plotting to overthrow the government. Harrison is later killed when he breaks out of prison and tries to take over the television station. Due to the oppressive government's demand that everyone be "equal every which way," those who are better-looking, stronger, more athletic, more graceful, more talented, more intelligent, more artistic, or more of any quality that makes them superior to others are forced to become "average," a condition which is non-threatening to the government.
While Hazel is too dull to know what she misses, her husband George lives a burdensome and painful life. His handicaps prevent him from using his intelligent mind and sturdy body: his body is weighed down with birdshot, while his head rings from the shrill and irritating noises sent through his mental-handicap radio. Never is he allowed to be creative or analytical. He cannot express ideas of any complexity or enjoy anything genuinely pleasurable to him. George's son was taken from his home and shot—all because Harrison rebelled against governmental oppression. George's life is one of tragic subjection, deprivation, and physical torture.

Hazel and George have different levels of mental and physical abilities, and Vonnegut uses those contrasts to illustrate the effects of the equality measures their society enforces. Hazel is of "average" or "normal" intelligence, and therefore she doesn't have to use any handicapping devices to disrupt her thinking. She already thinks only in "short bursts" and has difficulty remembering anything for more than a few minutes. George, on the other hand, is intelligent enough to think through issues and their consequences. Every time he starts to think deeply about something, however, his handicapper radio emits a painful signal and his thoughts crash. George also has to wear a 47-pound bag of birdshot around his neck to make his life as physically challenging as if he were as weak as Hazel. 
Hazel and George lead a very boring life. It's not clear whether Hazel is employed. But when George comes home from work, their life consists mostly of sitting around and watching TV. Although they experienced great emotional trauma when their son, Bergeron, was arrested and removed from their home, they are prevented from the effect of that trauma by Hazel's natural ignorance and George's enforced ignorance. Even seeing her son murdered on TV cannot bring enduring sadness to Hazel, and George missed watching the entire event when he went to get a beer.
By making society equal, the government ensures its citizens are boring, compliant people who lead boring, compliant lives.

What is a quote from The Outsiders that explains a simalarity between the Socs and Greasers?

In S.E. Hinton's classic novel, The Outsiders, the relationship Ponyboy develops with Cherry Valance reveals that Socs and Greasers have more in common than they think. 
The novel is set in the 1960s, and there are definite distinctions between the classes. Greasers, named for the way they wore their hair, are poorer and of the working class. The Socs are affluent and have designer clothing and nice cars. 
Ponyboy narrates the novel, and he meets Cherry Valance at the drive-in movies one night. He knew who she was before that night, but had never spoken to her due to their class differences. Prior to meeting Cherry, Ponyboy spent a fair amount of time thinking about the differences between the Socs and the Greasers. Here is an example of his musing: 

But most looked at us like we were dirt—gave us the same kind of look that the Socs did when they came by in their Mustangs and Corvairs and yelled "Grease!" at us. I wondered about them. The girls, I mean... Did they cry when their boys were arrested, like Evie did when Steve got hauled in, or did they run out on them the way Sylvia did Dallas? But maybe their boys didn't get arrested or beaten up or busted up in rodeos.

On the night that Cherry and Ponyboy are at the drive-in movies, Ponyboy starts to describe the things that had been done to Johnny when he was jumped by a group of Socs. Cherry doesn't want Ponyboy to think badly of her, and so she takes the opportunity to address the stereotype most people have of her social class, the Socs. In the quote below, she describes a similarity between the Greasers and the Socs:

Cherry no longer looked sick, only sad. "I'll bet you think the Socs have it made. The rich kids, the West-side Socs. I'll tell you something, Ponyboy, and it may come as a surprise. We have troubles you've never even heard of. You want to know something?" She looked me straight in the eye. "Things are rough all over."

Cherry lets Ponyboy know that the Socs lives aren't as perfect and privileged as they appear to be. She divulges that they have troubles of their own and that life is hard no matter what social class you belong to. That is one example of the similarities between the Greasers and the Socs. Toward the end of the novel, when Ponyboy is having a conversation with Randy, there are similarities revealed again.

In his "Letter from a Birmingham City Jail," how does King feel about the Birmingham Police Department and how they act “'nonviolently’ in public”?

In his “Letter from a Birmingham City Jail,” Dr. Martin Luther King, Jr. says that we should not think highly of the Birmingham city police just because they have acted nonviolently during the recent protests.  Instead, he says, we should realize that their relative nonviolence has been a moral tactic deployed in support of an immoral cause.  We should realize, then, that it is only moral to be nonviolent if one’s goals are worthy.
Just before the passage you cite, King takes issue with the idea that the Birmingham police really are truly nonviolent.  He talks about how they treat black men and women very poorly.  He writes about police “dogs sinking their teeth into unarmed, nonviolent Negroes.”  He describes how the police “slap and kick old Negro men and young boys.”  He essentially says that they are not as nonviolent as his critics say they are.
However, King then goes on to admit that the police have been relatively nonviolent with regard to the recent protests.  He says that

the police have exercised a degree of discipline in handling the demonstrators. In this sense they have conducted themselves rather "nonviolently" in public.

Even so, he says, this does not make them worthy of praise.  The fact that they have acted nonviolently does not make them moral.  He points out that the police have acted nonviolently in order to “preserve the evil system of segregation.”  This, he says, makes their actions immoral even though they are nonviolent.  He argues that it is wrong “to use moral means to preserve immoral ends.”  Because the Birmingham police are doing this, King feels that they are immoral even if they are acting relatively “nonviolently” in public.
https://www.africa.upenn.edu/Articles_Gen/Letter_Birmingham.html

Is the world portrayed in To Kill a Mockingbird by Harper Lee a fair one?

The world that Harper Lee portrays in her classic novel To Kill a Mockingbird is not a fair world where people are treated equally and justice is administered fairly. The novel is set in the small town of Maycomb, Alabama during the 1930s, which was a time when southern states enforced Jim Crow laws. Jim Crow laws imposed racial segregation, discriminated against black citizens, and severely limited the civil rights of black people.
In the small town of Maycomb, Alabama, Scout's father, Atticus Finch, is given the difficult task of defending a black man named Tom Robinson, who is falsely accused of assaulting and raping Mayella Ewell. Atticus and his children are criticized and ridiculed by their racist neighbors for his decision to defend Tom Robinson, and their well-being is even jeopardized in chapter 15 by a lynch mob. In addition to portraying the extent of racial discrimination in the South, Harper Lee depicts the destructive nature of racial prejudice during the Tom Robinson trial, where Scout, Jem, and Dill witness racial injustice firsthand as Tom is wrongly convicted by prejudiced jurors simply because he is a black man. Tom's wrongful conviction is the most prominent example of injustice and unfair nature of Maycomb's society, as well as a critique of the Jim Crow South.

No, not at all. The world portrayed in To Kill a Mockingbird is deeply unfair. In common with much of the South at that time, racial prejudice is rife in Maycomb. African Americans aren't treated equally and are subjected to official discrimination. The criminal justice system is stacked against them, as we see in the case of Tom Robinson. Tom's convicted on a trumped-up charge of rape and assault, despite there being absolutely no evidence whatsoever of his guilt. He's been convicted purely and solely because he's an African American and his accuser is white.
But Maycomb is unfair in other ways too. With such a small town mentality, this is no place for an outsider, anyone a little different from the norm. A good example of this would be Boo Radley. The townsfolk have turned him into a scary boogie-man on the basis of gossip and hearsay. And yet he ultimately proves himself to be a kind and gentle man, a complete contrast to the terrifying urban legend spun by ignorant gossip-mongers. 

Is there a contradiction between Adam Smith’s Wealth of Nations and his Theory of Moral Sentiments?

I would argue that there isn't a contradiction here. As one of the greatest thinkers of the Enlightenment, Adam Smith has been singularly ill-served by many of his most vocal advocates, who've turned him into some kind of free-market zealot or an apostle of "greed is good." In actual fact, Smith's whole philosophy was a good deal more subtle than this caricature would suggest—and it's as a whole that Smith's thought should be evaluated.
That being the case, we will find that there is no real contradiction between the ideas expressed in The Wealth of Nations and those in The Theory of Moral Sentiments. In both works, Smith attempts to demonstrate how apparently conflicting facets of human nature can be combined and shaped for the good of society as a whole. Smith believes that human beings are both self-interested and sympathetic. There's nothing contradictory here, simply an acknowledgement that we are all individuals as well as members of society. The key for Smith is to establish institutions that will maintain the appropriate balance between our individual and social selves.
For instance, in The Wealth of Nations, Smith argues that competition is actually the most tried and trusted method for keeping self-interest in check. If self-interest is allowed to prevail, then the result will be the formation of monopolies, which Smith believes are bad for both the economy and society as a whole. That's why it's a mistake to regard Smith as some kind of rampant individualist, or high priest of libertarianism.
Just as economic competition disciplines those who enter the market-place, commercial interaction cultivates virtue, which is the main focus of The Theory of Moral Sentiments. Virtue requires the approval of others, and such approval is best displayed through adherence to the values of commercial society. If firms and producers engage in practices that do not earn them the respect and approval of others (i.e., behavior that isn't considered virtuous), then they will be unable to flourish. In other words, far from there being a contradiction between virtue and the values of commercial society, they are inextricably linked.

The Wealth of Nations is Adam Smith's best known work, and its subject matter—economic principles—is quite different from The Theory of Moral Sentiments, which dealt with the origins of morality in people. We might see, from a twenty-first century perspective, a number of contradictions between a book that argues for the importance of economic self-interest and one that focuses on individual morality. But if Smith thought there was any contradiction between these two books, he never raised it publicly. Moreover, there are many ways in which the two works are intellectually consistent. In both, Smith uses a heuristic to describe how people reach economic decisions and how they form a system of morality. In The Wealth of Nations, he argues that people are guided by an "invisible hand" of self-interest to make economic decisions, and that the sum total of these decisions—i.e., the economic activity of a nation—will be improved by allowing people to make these decisions without restraint. In The Theory of Moral Sentiments, he claims that people imagine an "impartial spectator" whose judgment guides us toward making moral decisions, based on our sympathy (i.e., the ability to think about feelings) for other people. If people heed the "advice" of the "invisible hand" on the one hand and the "impartial spectator" on the other, society will be better for it. Smith also suggests that both morality and economics are social, and can only be understood in the context of organic, unified systems. But at the same time, these systems are basically aggregates of individual human actions. While he does reject the pursuit of wealth as a means to achieve happiness in The Theory of Moral Sentiments (this, to an extent, contradicts the spirit of The Wealth of Nations), his understanding of morality and economics are at least analogous if not entirely unified.
https://plato.stanford.edu/entries/smith-moral-political/

I need help developing a proposal for a paper on the topic of the cultural effects of globalization. I need to come up with a thesis about positive or negative effects. I also need some help finding credible resources for my bibliography.

A normal starting point for developing a thesis about a topic is to narrow the topic into something manageable. You cannot possibly talk about every cultural effect of globalization in every aspect of the lives of people in every country in the world; such a project would occupy several lifetimes rather than a single semester. This means that you should choose a single region and a single cultural area. 
For example, if you are interested in food, you could look at how globalization has effected the human diet, and especially whether the dietary changes in particular countries resulting from globalization have been beneficial or harmful to the health of local residents. Often the new diets, which might include fast food, are less healthy than traditional diets, but globalized food chains can also prevent or ameliorate famines. 
Another possible area you could study would be a genre that fuses western and local cultural traditions, such as the Indian film industry (Bollywood) or South Korean video gaming. You could then look at the specific effects of these genres on the local cultures.
To find reliable sources, you could search for articles about your topic on Google Scholar, a version of Google that only searches reputable sources such as peer-reviewed journals. Another excellent starting point for research is the scholarly databases available at your university library website. Most university libraries have reference librarians available to help students learn how to do research; many also offer short workshops on doing research for university-level papers. 
https://www.reuters.com/article/us-food-diet-idUSKBN0LR1R120150223

College Algebra, Chapter 2, 2.4, Section 2.4, Problem 62

Determine the area of the triangle formed by the coordinates axes and the line $2y + 3x - 6 = 0$

Solving for $y$ intercept, where $x = 0$


$
\begin{equation}
\begin{aligned}

2y + 3(0) - 6 =& 0
\\
\\
2y - 6 =& 0
\\
\\
2y =& 6
\\
\\
y =& 3

\end{aligned}
\end{equation}
$


The $y$ intercept is at $(0,3)$

Solving for $x$ intercept, where $y = 0$


$
\begin{equation}
\begin{aligned}

2(0) + 3x - 6 =& 0
\\
\\
3x - 6 =& 0
\\
\\
3x =& 6
\\
\\
x =& 2

\end{aligned}
\end{equation}
$


The $x$ intercept is at $(2, 0)$

Since the $y$ intercept is at $(0,3)$, notice that the height of the triangle will be $h = 3$. Consequently, if the $x$ intercept is at $(2, 0)$, then the base of the triangle will be $b = 2$. Thus, the area is..

$\displaystyle A = \frac{1}{2} bh = \frac{1}{2} (2)(3) = 3 $ square units

Why did Keller compare the climbing roses of her greenhouse with the asphodels of God's garden?

From an early age, Helen has always found the natural world to be a source of great comfort, a haven of peace and repose from the myriad frustrations of home life. She seems to have a connection with the world of nature that she simply doesn't have with other people. As she casts her mind back to the time before she lost her sight, Helen reminisces nostalgically about the climbing roses in her family's greenhouse—their cooling petals, their leaves and flowers, and the soothing effect they had upon her.
There's something almost paradisiacal about the Kellers' greenhouse, like the Garden of Eden. It's telling that Helen describes the roses as being "untainted by any earthly smell." It's as if they're so beautiful, so fresh, and so soft that they're not of this world. Little wonder, then, that in her effusive description of the roses, Helen likens them to the asphodels of God's garden. It's almost as if they're reaching up towards heaven.

Keller was long fascinated with nature, and she found refuge in the natural world before and after the illness that made her blind and deaf as a young child. She writes that after she had a tantrum as a baby (before her illness), "I went to find comfort and to hide my hot face in the cool leaves and grass." She writes that she never found in the greenhouses of the North the beautiful kinds of climbing roses that grew in her house in Alabama. She writes, "I could not help wondering if they did not resemble the asphodels of God's garden." Homer's The Odyssey describes the afterworld as being covered in asphodel flowers. For example, Achilles's ghost walks across a field of asphodels to the afterworld. Keller's comparison implies that her roses were heavenly in appearance and scent. They are a cherished memory of the period of her childhood when she had sight.  

College Algebra, Chapter 4, 4.2, Section 4.2, Problem 18

Sketch the graph of polynomial function $P(x) = (2x-1)(x+1)(x+3)$ make sure the graph shows all intercepts and exhibits the proper end behaviour.
The function has an odd degree of 3 and a positive leading coefficient. Thus, its end behaviour is $y \rightarrow \infty \text{ as } x \rightarrow \infty \text{ and } y \rightarrow -\infty \text{ as } x \rightarrow \infty$. To solve for the $y$-intercept, we set $x = 0$

$
\begin{equation}
\begin{aligned}
y &= (2(0)-1)(0+1)(0+3)\\
\\
y &= (-1)(1)(3) = -3
\end{aligned}
\end{equation}
$

To determine the $x$-intercept, we set $y = 0$. In this case, we have
$\displaystyle x = \frac{1}{2}, -1$ and $-3$.

In "The Umbrella Man," what do the girl and her mother find out about the gentleman after he enters the pub?

The mother and daughter learn they have both been deceived about the little old man with the umbrella.
The man's deception of the woman is rather cleverly accomplished: He tells the narrator's mother that he has forgotten his wallet and he needs the fare for a taxi because he has walked too far and his "old legs" are tired. He offers to sell his twenty-pound umbrella for just one pound for the taxi-fare.
The mother feels it wrong to purchase a silk umbrella for twenty pounds, so she suggests she just give the little man a pound. She tells the old gentleman that she does not feel right about taking his umbrella. The little old man insists that she take his umbrella, saying,

But now it’s of no importance so long as I can get home and rest these old legs of mine.

The mother provides the old gentleman with the pound he desires. Afterwards, the mother congratulates herself on judging the man's character correctly. Just then, her daughter sees the man scurrying down the street. The mother decides to follow him as he dodges in and out of places where people stand. Finally, the mother and daughter see him enter a pub where he lays down the pound note given him and orders a "treble whisky," a whisky that is three shots. The daughter and her mother realize the mother has been tricked. Then she watches as the man departs. He goes to the hook where his coat is hung, but while doing so, he grabs an umbrella. He then goes out of the building with his new prize.

College Algebra, Chapter 7, 7.2, Section 7.2, Problem 24

Suppose the matrices $A, B, C, D, E, F, G$ and $H$ are defined as



$
\begin{equation}
\begin{aligned}


A =& \left[ \begin{array}{cc}
2 & -5 \\
0 & 7
\end{array}
\right]

&& B = \left[ \begin{array}{ccc}
3 & \displaystyle \frac{1}{2} & 5 \\
1 & -1 & 3
\end{array} \right]

&&& C = \left[ \begin{array}{ccc}
2 & \displaystyle \frac{-5}{2} & 0 \\
0 & 2 & -3
\end{array} \right]

&&&& D = \left[ \begin{array}{cc}
7 & 3
\end{array} \right]
\\
\\
\\
\\
E =& \left[ \begin{array}{c}
1 \\
2 \\
0
\end{array}
\right]

&& F = \left[ \begin{array}{ccc}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{array}
\right]

&&& G = \left[ \begin{array}{ccc}
5 & -3 & 10 \\
6 & 1 & 0 \\
-5 & 2 & 2
\end{array} \right]

&&&& H = \left[ \begin{array}{cc}
3 & 1 \\
2 & -1
\end{array} \right]


\end{aligned}
\end{equation}
$


Carry out the indicated algebraic operation, or explain why it cannot be performed.

a.) $3B + 2C$


$
\begin{equation}
\begin{aligned}

3 \left[ \begin{array}{ccc}
3 & \displaystyle \frac{1}{2} & 5 \\
1 & -1 & 3
\end{array} \right]
+
2 \left[ \begin{array}{ccc}
2 & \displaystyle \frac{-5}{2} & 0 \\
0 & 2 & -3
\end{array} \right]

=&

\left[ \begin{array}{ccc}
9 & \displaystyle \frac{3}{2} & 15 \\
3 & -3 & 9
\end{array} \right]

+

\left[ \begin{array}{ccc}
4 & -5 & 0 \\
0 & 4 & -6
\end{array} \right]

\\
\\
\\
\\

=& \left[ \begin{array}{ccc}
9+4 & \displaystyle \frac{3}{2} - 5 & 15 + 0 \\
3+0 & -3+4 & -6+9
\end{array} \right]
\\
\\
\\
\\

=& \left[ \begin{array}{ccc}
13 & \displaystyle \frac{-7}{2} & 15 \\
3 & 1 & 3
\end{array} \right]


\end{aligned}
\end{equation}
$


b.) $2H + D$


$
\begin{equation}
\begin{aligned}

2 \left[ \begin{array}{cc}
3 & 1 \\
2 & -1
\end{array} \right] +

\left[ \begin{array}{cc}
7 & 3
\end{array} \right]


\end{aligned}
\end{equation}
$


$H + D$ is undefined because we can not add matrices of different dimensions.

What would you retitle the book Tunes for Bears to Dance To by Robert Cormier and why?

One example of an alternative title for Tunes for Bears to Dance To by Robert Cormier is It Takes a Village, as Mr. Levine builds the village of his former town destroyed in the Holocaust. George Graham explains to Henry that Mr. Levine is building the village to cure himself of his troubling memories. George says, "This is his real cure. Better medicine than the hospital." (39) In addition, the village is important because by deciding not to destroy the village, even when Mr. Hairston orders him to do so, Henry develops a conscience and chooses what is good over what is evil and self-serving (as Mr. Hairston had promised to reward Henry for destroying the village). Finally, the well-known expression "it takes a village" refers to the need for everyone in a community to help children develop as moral and ethical beings, and many people in the novel help Henry develop into a moral person.
The other examples are up to you. They can revolve around the idea of Henry's developing a moral sense and grieving for his brother, Eddie, who has died. Throughout the book, Henry wants to place a stone on Eddie's grave and winds up putting a baseball and bat on the grave. Is there a title you can develop that involves the idea of baseball and of winning a battle (or scoring a home run)? This type of title would use Eddie's interest in baseball to imply that Henry finally triumphs in his battle to defeat the evil Mr. Hairston. Or you could develop a title using the idea that Henry tells Doris, Mr. Hairston's daughter, to stand up to her father. Mr. Hairston constantly says that Doris falls down, though it's apparent that Mr. Hairston might shove her. Is there a title you can develop that uses the idea of standing up, literally and figuratively, to negative forces in one's life and doing what's right? 

Beginning Algebra With Applications, Chapter 5, 5.4, Section 5.4, Problem 24

Using the point slope formula, find the equation of the line that passes through the point whose coordinates are $(0,0)$ and has slope of $\displaystyle \frac{-1}{5}$


$
\begin{equation}
\begin{aligned}

(x_1, y_1) =& (0,0)
&& \text{Let $(x_1, y_1)$ be the given point}
\\
m =& \frac{-1}{5}
&& \text{$m$ is the given slope}
\\
y - y_1 =& m(x- x_1)
&& \text{Point slope formula}
\\
y - 0 =& \frac{-1}{5} (x-0)
&& \text{Substitute $$ for $x$, $$ for $y$ and } \frac{-1}{5} \text{ for $m$}
\\
y =& \frac{-1}{5}x
&& \text{Rewrite the equation in the form } y = mx+b

\end{aligned}
\end{equation}
$

What does the son mean when he tells his mother that she is already “wealthy”?

What the son means is that his mother already has everything she needs in life. More than this, her grateful attitude encompasses the whole of her existence. By modern standards, she has achieved what many consider impossible: contentment through a simple life that is rich in love and peace. So, this is why the son tells his mother that she is already wealthy.
In the story, Samuel is the son who speaks these words to his mother, Berlcha. He has come from America for a visit and brings money to renovate his parents' village, Lentshin. However, his parents tell him that the village will have no need of the money. This surprises Samuel very much, until he sees the coins his parents saved from cashing his money orders.
When Samuel asks Berl, his father, why they did not spend the money, the latter gives a surprising answer. He tells Samuel that their needs are provided by their garden, the cow, the goat, and the chickens. Also Berlcha sells chickens and eggs, and the profits are enough to purchase flour for bread. Both Berl and Berlcha rely on the land and their animals for all of their daily needs. In the winter evenings, Berl sits quietly while Berlcha spins flax at the spinning wheel.
Samuel returns to Lentshin after forty years, and he is determined to help his old village. However, he soon learns that his conception of poverty and wealth are based on faulty, preconceived notions. To his astonishment, he discovers that every single one of the villagers is happy with the simple life in the country. This is why he concludes that his mother is already wealthy and, therefore, has no need to pray for wealth.

Were military coups across Africa inevitable following decolonization? Were democracies in the French and British models doomed to fail?

It is somewhat difficult to make counterfactual statements about historical events as we cannot actually know for certain what would have happened had given conditions been different. What we do know, however, is that most African countries did not immediately and successfully transition to a form of western liberal democracy after the departure of colonial powers. 
A hidden assumption in this question that we should also note is that this question assumes democracy is somehow a natural end point of political evolution and that other forms of government are somehow failures. This may be a Eurocentric model of thinking about political systems. Chinese political philosophers, for example, would not agree with it. 
For democracy to become established, several forms of civic and technological infrastructure need to be in place. In Africa, many of the civic institutions were either weak or associated with the colonial powers. Even worse, democracy generally takes hold in societies that are somehow cohesive in ethnicity, language, culture, and religion. In Africa, many of the postcolonial "countries" were territories defined by lines drawn on maps by colonial administrators dividing up spheres of influence with little attention paid to such issues as tribal boundaries, meaning that the cohesive sense of "nation" was absent. Many civic institutions on which such a sense could have been established were either absent or distrusted as instruments of colonial power. Only a small group of elites, often educated in the colonial traditions, were literate or even familiar with large scale administrative skills and methods, and those elites were quite distant from the people they ruled in culture and lifestyle, having been to a large degree influenced and educated within European traditions. Even the physical infrastructure needed for voting was not in place.
The groups that led independence movements naturally tended to move into power at independence. There was no natural opposition or multiparty system. Instead, factions tended to be determined by tribal affiliation, and power seen as a way to control lucrative government largesse; there was little concept of rights of minorities. Thus even in countries that held elections, rather than engendering a sense of power sharing and minority rights, election results tended to confirm the exclusive grip on power of the largest faction that would use that power to benefit other members of their tribe. 
As Africa has developed an educated urban middle class, many countries (e.g. Kenya and Nigeria) have seen a democratic transition; educated urban professionals have weaker tribal affiliations and a greater amount of sophistication and power than people living in remote villages. This change, though, is relatively recent and was present in few countries at independence. Thus even when weak democratic structures were put in place by departing colonial powers, because they were imposed from above rather than rooted in local culture, they tended to evolve into authoritarian governments organized on tribal lines. 
Thus it does seem as though it was highly probably that democratization in postcolonial Africa would be a gradual and uncertain process. 

Glencoe Algebra 2, Chapter 2, 2.3, Section 2.3, Problem 36

Given the slope of the line passes through (x,y)= (-2, -3) is m = oo
so the line is a vertical line and is parallel to x = 0
as it passes through the point (-2,-3)
so the desired line is x = -2
the line is plotted and is given in the attachments
the point (-2,-3) is plotted with a yellow dot

How is Lady Macbeth controlling?

Lady Macbeth controls her husband using a combination of shame and manipulation. She uses shame through repeated attempts to emasculate Macbeth. She questions his commitment to the murder of Duncan, calling him a "coward" (I.vii.47) for equivocating as he does. She draws on her own experience as a mother, saying that if she were to be in his position, she would be so resolute as to smash in her own child's brains (I.vii.61-66). This bastardization of the ultimate image of womanhood - being a mother - suggests that Lady Macbeth sees a reversal in the gender roles of her and her husband.
This is clearly a successful tactic and allows Lady Macbeth's manipulation to land. Her husband responds by reaffirming his commitment to their plot. His words of affirmation echo hers of manipulation from earlier in the play. He ends Act I by stating "False face must hide what false heart doth know" (I.vii.95). This is the literal interpretation of Lady Macbeth's much more eloquent subversion to "Look like the innocent flower,/But be the serpent under 't" from two scenes earlier (I.v.76-7). It is almost as though through exuding her own power over her husband, Lady Macbeth's strength, thoughts, and resolve are manifested in him.
This cycle of shame driving manipulation continues but wanes as the play progresses, with the murder of Duncan being Lady Macbeth's high point of control. Later, as Macbeth plans Banquo's murder and his subsequent assassinations in his power-hungry climb to the top, Lady Macbeth's control decreases as he becomes the primary agent. As her power and control recede, chaos and instability reign through the reign of the new king.

What you will notice about Lady Macbeth is that she is very controlling towards her husband, Macbeth. When she finds out about the witches' prophecies in a letter from Macbeth, for example, her controlling nature becomes apparent. She is determined that Macbeth will murder Duncan and immediately makes preparations for this event. These preparations include asking the spirits to "unsex" her so that she can be crueler and choosing the murder weapon. Her controlling nature, therefore, makes it impossible for Macbeth to take charge of this situation.
In addition, when Macbeth has second thoughts about killing Duncan, Lady Macbeth immediately manipulates him. She attacks his masculinity to ensure that he bends to her will. Lady Macbeth, therefore, controls Macbeth psychologically and uses humiliation to make him do as she says.

College Algebra, Chapter 8, 8.4, Section 8.4, Problem 28

Complete the square to determine whether the equation represents an ellipse, a parabola, a hyperbola, or a degenerate conic. If the graph is an ellipse, find the center, foci, vertices and lengths of the major and minor axes. If it is a parabola, find the vertex, focus and directrix. If it is a hyperbola, find the center, foci, vertices and asymptotes. Sketch the graph of the equation. If the equation has no graph, explain why.


$
\begin{equation}
\begin{aligned}

2x^2 + y^2 =& 2y + 1
&& \text{Group terms}
\\
\\
2x^2 (y^2 - 2y) =& 1
&& \text{Complete the square: add } \left( \frac{-2}{2} \right)^2 = 1
\\
\\
2x^2 + (y^2 - 2y + 1) =& 1 + 1
&& \text{Perfect square}
\\
\\
2x^2 + (y - 1)^2 =& 2
&& \text{Divide both sides by } 2
\\
\\
x^2 + \frac{(y - 1)^2}{2} =& 1
&&

\end{aligned}
\end{equation}
$


The equation is an ellipse that is shifted so that its center is at $(0, 1)$. It is obtained from the ellipse $\displaystyle x^2 + \frac{y^2}{2} = 1$ with center at the origin by shifting $1$ unit upward. The endpoints of the major and minor axis of the unshifted ellipse are $(0, \sqrt{2}), (0, - \sqrt{2}), (1, 0)$ and $(-1, 0)$. By applying transformations, the corresponding end points will be..


$
\begin{equation}
\begin{aligned}

(0, \sqrt{2}) \to (0, \sqrt{2} + 1) =& (0, \sqrt{2} + 1)
\\
\\
(0, - \sqrt{2}) \to (0, - \sqrt{2} + 1) =& (0, - \sqrt{2} + 1)
\\
\\
(1, 0) \to (1, 0 + 1) =& (1,1)
\\
\\
(-1,0 ) \to (-1, 0 + 1) =& (-1, 1)

\end{aligned}
\end{equation}
$


To find the foci of the shifted ellipse, we first find the foci of the unshifted ellipse. Since $a^2 = 2$ and $b^2 = 1$, then $c^2 = 2 - 1 = 1$, so $c = 1$. So the foci are $(0, \pm 1)$. By applying transformation, the foci will be

Therefore, the focus is at

$(0, 1) \to (0, 1 + 1) = (0, 2)$

$(0, -1) \to (0, -1 +1) = (0, 0)$

Therefore, the graph is

People wonder how U.S. soldiers could mistreat prisoners so badly at Abu Ghraib, or how Nazi soldiers could systematically kill so many Jews and others during WWII. Using any three of the following concepts and research, describe how the concept or research finding could be applied to one of the situations listed above. Milgram’s research Zimbardo prison experiment Foot in the door phenomenon Bystander effect In group/out-group Normative social influence

The Milgram Experiment focused on the effects of authority on individual conscience—if the boss tells us to do something we know is wrong, can we justify obeying? In this experiment, the test subjects believed that they were harming another person with electric shocks. Even when they protested, every one of them continued to administer the shocks when the experimenter told them that they had to keep going. Milgram concluded that obedience to authority is ingrained, and we are likely to follow orders, even if we disagree with them. The soldiers in your examples may have objected personally to the way the prisoners were being treated, but perhaps they felt that since they were “just following orders,” they didn’t have a choice and couldn’t be responsible.
The “foot in the door phenomenon” is a compliance technique that starts out by making a small request of someone, and when they agree, progresses to larger, more substantial requests. The theory is that once someone agrees to something minor, they begin to feel “involved," and are more likely to comply with the larger requests. The prisoners probably weren’t subjected to extreme cruelty right away. As the situation escalated, the soldiers may have felt that since they were already committed to this path, they should continue.
We’ve heard stories about people in big cities being murdered right on the sidewalk in front of several onlookers who do nothing to help: this is the “bystander effect." It occurs when a group of people witness a disturbing event together. They all may be moral, ethical individuals who would quickly step in to help if they were the only other person there. But in a group, they each believe that one of the others will do something about it... and then nobody does. Maybe the soldiers all assumed that someone else would take the lead.
http://faculty.babson.edu/krollag/org_site/soc_psych/freed_fras_foot.html

https://greatergood.berkeley.edu/article/item/we_are_all_bystanders

Single Variable Calculus, Chapter 5, 5.4, Section 5.4, Problem 22

Find the integrals $\displaystyle \int^0_{-2} \left( u^5 - u^3 + u^2 \right) du$

$
\begin{equation}
\begin{aligned}
\int \left( u^5 - u^3 + u^2 \right) du &= \int u^5 du - \int u^3 du + \int u^2 du\\
\\
\int \left( u^5 - u^3 + u^2 \right) du &= \frac{u^{5+1}}{5+1} - \frac{u^{3+1}}{3+1} + \frac{u^{2+1}}{2+1} + C\\
\\
\int \left( u^5 - u^3 + u^2 \right) du &= \frac{u^6}{6} - \frac{u^4}{4} + \frac{u^3}{3} + C\\
\\
\int^0_{-2} \left( u^5 - u^3 + u^2 \right) du &= \frac{(0)^6}{6} - \frac{(0)^4}{4} + \frac{(0)^3}{3} + C - \left[ \frac{(-2)^6}{6} - \frac{(-2)^4}{4} + \frac{(-2)^3}{3} + C\right]\\
\\
\int^0_{-2} \left( u^5 - u^3 + u^2 \right) du &= C - \frac{64}{6} + \frac{16}{4} + \frac{8}{3} - C\\
\\
\int^0_{-2} \left( u^5 - u^3 + u^2 \right) du &= -4
\end{aligned}
\end{equation}
$

How might you recognize a peer-reviewed journal article?

A peer-reviewed journal is a scholarly publication in which experts discuss research and analysis in a particular field of study. In order to identify whether an article comes from a peer-reviewed journal, one can look for the following things:
The title of the publication often includes the word “journal.”
The article usually contains headings to label sections of the article, such as abstract and methodology.
The reader will notice domain-specific vocabulary or jargon that might be difficult to understand without knowledge of the field.
The text will contain numerous citations that refer to other bodies of research from experts in the field.
The intended audience of the article is the same as the author: an expert in their field of study. For instance, an article about an analysis of a work of literature is directed at literary scholars.
A peer-reviewed article will have been evaluated by a number of experts who reached a consensus that the article in question was worthy of publication. One traditional way of determining whether an article was peer-reviewed is to consult the masthead of the publication and note how articles are submitted.

According to Nat, what is odd about winter so far this year? What do you think the description of the cold and black ground early in the story foreshadows?

Nat notes it has been a very mild autumn until the weather turns overnight on December 3, and it becomes cold and winter arrives suddenly. He notices great flocks of birds have been arriving on the peninsula since the fall, and they are incredibly restless. They seem to dive and wheel in the sky continuously, and they do not seem interested in eating from the rich autumnal soil. Instead, they constantly take to the skies, as if they sense death is coming.
The cold and black ground, covered with frost, symbolizes the impending death of humans and the land. The sky becomes leaden, and the hills, which had shone in the sunlight the day before, suddenly become black. Winter has arrived in a single day. The darkness of the ground and sky foreshadows the beginning of the birds' attacks and the demise of humans as a result.

In the opening paragraphs of "The Birds," Nat notices that the winter is so far quite different than that of previous years. The birds are more "restless," for example, and appear to be unsatisfied, even when they feed. In addition, there are more birds than usual, a fact which is supported by the observations of the farmer, Mr Trigg.
After the attack on Nat's house, Du Maurier describes the cold ground and how it has the "hard, black look of frost." This, perhaps, foreshadows Nat's attempt to bury the dead birds which have attacked his family. The ground is too hard to dig, however, and Nat is forced to take the birds to the beach. While he is there, he sees the gulls riding the waves and realises that the birds will return to attack his home. He must now take action to safeguard his home so that his family is protected. 

In Hatchet, what does Brian think about in the plane？How does he feel about this topic and why？

In the book Hatchet, thirteen-year old Brian Robeson is the only passenger on a tiny plane bound for the northern woods of Canada. At first, he thinks it’s interesting to be flying in the small plane, and stares at the control panel in wonder. The pilot gives him a great opportunity by letting him have control of the plane.  
Soon, however, Brian’s thoughts turn to his parents, who are getting a divorce. He feels very angry at the lawyers, and pretty much at everybody, for trying to tell him how he’s supposed to feel and how the divorce will affect his life. Brian begins to think about something that he refers to as “the secret,” though we have no idea at this point what it is.
While thinking about these things, Brian feels as though he’s going to cry, but he attempts to hold his tears back. He’s ashamed and nervous about his feelings, and doesn’t want the pilot to see him crying. The thoughts of the divorce lead to thoughts of his parents, who are not in agreement about the whole thing, leading us to believe that Brian feels torn between them and split in two.
His father has no idea why his mother wants the divorce and is torn up about it, while his mother wants to comfort him. We learn that she’s unaware that Brian knows “the secret,” but we feel that it might have something to do with the divorce. There is a sense that Brian feels like he must protect both of his parents from the secret and the fact that he knows it. For a thirteen-year old boy, he is under an immense amount of pressure.
 
 

Discuss Malcolm’s belief that conking one’s hair was a step towards self-degradation.

In the Autobiography of Malcolm X, Malcolm X discusses his discovery of the hairstyle called a "conk" when he is living in Roxbury, an African American neighborhood of Boston. He sees that many African American men straighten their hair through this process so that they appear to look more like white men. He later receives a conk himself, which he finds very painful.
He writes, "This was really my first big step towards self-degradation: when I endured all of that pain, literally burning my flesh to have it look like a white man's hair" (56). Malcolm X associates the conk with self-debasement because African American people endure pain to meet white beauty standards. He finds it degrading that they destroy their bodies to try to look like whites and, in the process, ignore their own beauty. He believes that it is part of the process of "brainwashing," in his words, that African Americans receive by which they begin to believe what is white is beautiful. In making themselves look more white, African Americans debase themselves.

Intermediate Algebra, Chapter 3, 3.3, Section 3.3, Problem 44

Determine an equation of the line that satisfies the condition "through $(6,-1.2)$; slope $0.8$".

(a) Write the equation in standard form.

Use the Point Slope Form of the equation of a line with $(x_1,y_1) = (6,-1.2)$ and $m = 0.8$


$
\begin{equation}
\begin{aligned}

y - y_1 =& m (x - x_1)
&& \text{Point Slope Form}
\\
y - (-1.2) =& 0.8(x - 6)
&& \text{Substitute $x = 6, y = -1.2$ and } m = 0.8
\\
y + 1.2 =& 0.8x - 4.8
&& \text{Distributive Property}
\\
-0.8x + y =& -4.8 - 1.2
&& \text{Subtract each side by $(0.8x + 1.2)$}
\\
-0.8x + y =& -6
&& \text{Standard Form}
\\
\text{or} &
&&
\\
0.8x - y =& 6
&&

\end{aligned}
\end{equation}
$



(b) Write the equation in slope-intercept form.


$
\begin{equation}
\begin{aligned}

-0.8x + y =& -6
&& \text{Standard Form}
\\
y =& 0.8x - 6
&& \text{Slope Intercept Form}

\end{aligned}
\end{equation}
$

Single Variable Calculus, Chapter 6, 6.5, Section 6.5, Problem 2

Determine the average value of the function $f(x) = \sin 4x $ on the interval $[- \pi, \pi]$


$
\begin{equation}
\begin{aligned}

f_{ave} =& \frac{1}{b - a} \int^b_a f(x) dx
\\
\\
f_{ave} =& \frac{1}{\pi - (- \pi)} \int^8_1 \sin 4x dx
\\
\\
\text{Let } u =& 4x, \text{ then}
\\
\\
du =& 4dx

\end{aligned}
\end{equation}
$


Also, make sure that the upper and lower limits are now in terms of $u$.


$
\begin{equation}
\begin{aligned}

f_{ave} =& \frac{1}{2 \pi} \left(\frac{1}{4} \right) \int^{4(8)}_{4(1)} \sin u du
\\
\\
f_{ave} =& \frac{1}{8 \pi} \int^{32}_4 \sin u du
\\
\\
f_{ave} =& \frac{1}{8 \pi} [- \cos u]^{32}_4
\\
\\
f_{ave} =& \frac{1}{8 \pi} [- \cos (32) - (- \cos (4))]
\\
\\
f_{ave} =& -0.059

\end{aligned}
\end{equation}
$

How can I write a great thesis on the topic of setting in stories? How does the setting of a story affect the character? What role does the setting of a story play?

Character, setting, and plot are intricately woven together in order to form a cohesive story.  Without a setting, a character would exist in a vacuum.  He or she wouldn't be able to affect anything or be affected by anything.  I don't want to make a blanket statement and say that the setting of a story is what always drives the plot, because that isn't always true; however, there are frequently times when the setting of a story drives the characters and the plot.  Let's take Lord of the Flies as an example.  I feel that a fairly strong case could be made that characters like Jack and Roger never descend to such moral lows without the plane crash and deserted island.  I don't believe that Timothy and Phillip from The Cay ever bond without the island that they are on.  1984's Winston Smith wouldn't be who he is if he wasn't surrounded by the totalitarian government of Oceania.  In each of those cases, the characters are shaped and driven by the setting of the story.  Setting and character are integral to each other.  
I feel that the above relationship of setting and character is more common, but there are times when the setting is nothing more than a backdrop for the events of the story.  Take Winnie-the-Pooh as an example.  The stories told about Pooh and his friends are stories about curiosity, wonder, friendship, and helping each other.  Those stories happen to take place in a forested area, but they could also happen in a jungle or an open field.  
In order to write your thesis, you need to choose how you feel about the importance of setting and character.  A thesis statement is a statement of opinion, and it's an opinion that you have to defend through the body of your paper.  The statement can't be a fact.  If it was a fact, there wouldn't be anything to debate. 
I recommend writing a two-part, either/or style thesis.  You will begin the thesis with the world "although" because it guarantees a dependent clause.  The first half of the thesis statement will be the part that you intend to disprove.  The second half of the statement is the part that you believe in.  For example, you could write a thesis that goes something like this: "Although it might seem that the setting of a story has minimal impact on characters, the setting of a story is actually one of the most important and integral parts to driving a plot forward and to characterizing each character." 
https://literarydevices.net/setting/

College Algebra, Chapter 5, 5.3, Section 5.3, Problem 52

Combine the expression $\displaystyle 2 (\log_5 x + 2 \log_5 y - 3 \log_5 z)$, using the Laws of Logarithm


$
\begin{equation}
\begin{aligned}

2 (\log_5 x + 2 \log_5 y - 3 \log_5 z) =& 2 \left( \log_5 x + \log_5 y^2 - \log_5 z^3 \right)
&& \text{Law of Logarithm } \log_a (A^C) = C \log_a A
\\
\\
2 (\log_5 x + 2 \log_5 y - 3 \log_5 z) =& 2 \left( \log_5 xy^2 - \log_5 z^3 \right)
&& \text{Law of Logarithm } \log_a (AB) = \log_a A + \log_a B
\\
\\
2 (\log_5 x + 2 \log_5 y - 3 \log_5 z) =& 2 \log_5 \left( \frac{xy^2}{z^3} \right)
&& \text{Law of Logarithm } \log_a \left( \frac{A}{B} \right) = \log_a A - \log_a B
\\
\\
2 (\log_5 x + 2 \log_5 y - 3 \log_5 z) =& \log_5 \left( \frac{xy^2}{z^3} \right)^2
&& \text{Law of Logarithm } \log_a (A^C) = C \log_a A

\end{aligned}
\end{equation}
$