Beginning Algebra With Applications, Chapter 5, 5.2, Section 5.2, Problem 98

Determine the $x$ and $y$-intercepts for $\displaystyle y = \frac{2}{3}x - 4$.

$x$-intercept:


$
\begin{equation}
\begin{aligned}

y =& \frac{2}{3}x - 4
&& \text{Given equation}
\\
0 =& \frac{2}{3}x - 4
&& \text{To find the $x$-intercept, let } y = 0
\\
\frac{-2}{3} x =& -4
&& \text{Subtract } \frac{2}{3}x
\\
x =& 6
&& \text{Multiply both sides by } \frac{-3}{2}

\end{aligned}
\end{equation}
$


The $x$-intercept is $(6,0)$

$y$-intercept:


$
\begin{equation}
\begin{aligned}

y =& \frac{2}{3} x - 4
&& \text{Given equation}
\\
y =& \frac{2}{3} (0) - 4
&& \text{To find the $y$-intercept, let } x=0
\\
y =& -4
&&

\end{aligned}
\end{equation}
$



The $y$-intercept is $(0,-4)$

How can I discuss five terms of plot for "The Red Convertible" by Louise Erdrich? (These terms of the plot may be suspense, foreshadowing, conflict, gaps, epiphany, etc.)

"The Red Convertible" is a poignant story about lost youth, lost hope, and lost love. In the narrative of this short story, Louise Erdrich employs the plot elements of foreshadowing, symbolism, tone, conflict, and effect.
There is rather extensive foreshadowing:
--Henry's death is foreshadowed in the opening paragraph as the narrator/brother named Lyman states that he and his brother were co-owners of the red convertible 

...until his boots filled with water on a windy night and he bought out my share.

--There is the prefiguring of disaster in the way in which the brothers pay for the red convertible: Lyman has procured his money with the insurance settlement from the destruction of his business by a tornado; Henry has received his last paycheck and another check as severance pay from the Jewel Bearing Plant.--Henry narrates that when he and his brother first see the red convertible, it seems to "repose." This word repose is often used in funeral arrangements or ceremonies (as in "the body will repose in...").--Later in the story, Lyman narrates that Henry sits absolutely still in front of the television, much like a rabbit "when it freezes before it will bolt."
There is symbolism:
--The red convertible.
The convertible is a complex symbol because its meaning changes as the narrative progresses.
The color of the convertible is red, the color of passion and love. It represents the feelings of the brothers for one another. The car, jointly owned by the brothers, symbolizes their bond of brotherhood. It also represent hope.Once Henry dies, the convertible has no meaning for Lyman, so he drives it into the river. Now, it represents the loss of hope.
--Susy's hair
When Susy's hair is wrapped in buns on each side of her head, they symbolize the qualities of people that are often not recognizable. Later, Susy undoes these buns and her long tresses fall; the brothers are astonished, and they realize how extraordinary her hair is.
--The television
When Lyman purchases this item in order to distract Henry, it instead brings reality and the world's problems to the tranquil reservation where people love each other. The television symbolizes the intrusion of the world's problems into the otherwise peaceful home.
--The seasons
The summer in Alaska is a halcyon time in which the brothers engage in innocent enjoyment of the long, sunny days. The end of summer marks the end of their good times. The following winter Henry begins to withdraw, but in the spring he seems renewed somewhat. Unfortunately, it is only temporary.
--The river
The river represents life's course, the changes and trials that a person endures. Henry undergoes much trauma until his soul overflows and he is drowned in his agony and mental torture.
--Alaska
With its long summer and placid atmosphere, Alaska is heavenly compared to Vietnam and Henry's experiences there.
There is a certain tone to the narrative 
In "The Red Convertible," tone, or the author's attitudes about characters and the plot, suggests the author's admiration for the resiliency and endurance of Lyman, who persists in his attempts to return his troubled brother to some sense of normalcy.
Throughout the narrative, the brother is solicitous of Henry, trying to engage Henry in fixing the convertible. He closely observes his brother as he "grips the armrests of the chair" and he hears Henry's

"...teeth click at something bitten through his lip. Blood flows down his chin."

The conflicts are both internal and external
Henry is content until he enters the army. When he returns with his postwar illness, no amount of solicitation from the brother can prevent Henry from his act of suicide; the experience of war has altered him. The mother consoles Lyman,

"They don't fix them in those places," Mom said, "they just give them drugs."

Lyman tries many things to help his brother: He purchases the car with him, he goes on a trip with him, and he buys him a television. He even releases the red convertible into the same water where his brother died.
The effect
The ending of Erdrich's story is rather disturbing as Henry finally despairs of adjusting to life again. Henry walks out into the water and lets himself drown. Witnessing this, Lyman turns on the ignition of the red convertible and sends the car into the same water:

The headlights reach in... searching, still lighted. The wires short out. It is all finally dark. And then, there is only the water, the sound of it going and running and going and running and going.

The utter futility of Lyman's attempts to help his beloved brother leaves him in despair, and the effect of the ending is chilling.

Please share a summary of Adichie's Purple Hibiscus?

Purple Hibiscus, a novel that takes place in Nigeria, begins on Palm Sunday when the protagonist, a 15-year-old girl named Kambili Achike, describes an incident that begins the dissolution of her family. On that day, her older brother, Jaja, refuses to get communion at church. As a response, their father, a devout, wealthy Catholic named Eugene, throws a prayer book that breaks the mother's figures on the etagere.
Kambili then goes back in time to her family's history before this event, and she describes the emotional torture and control that her father exercises over her family. Kambili and her brother must, for example, earn perfect grades in school and follow their father's detailed wishes. Her mother tells Kambili that she is pregnant. Later, her father, annoyed that her mother does not get out of the car to greet a priest because she feels sick, beats his wife until she has a miscarriage. The newspaper Eugene runs becomes increasingly critical of the new government.
Ifeoma, Eugene's sister who is a university professor, convinces him to allow Jaja and Kambili to stay with her. She allows her three children far more freedom, and they practice a form of Catholicism that is combined with local Igbo beliefs. Though they are not rich, their way of life seems far preferable to that of Eugene in Kambili's eyes. While living with her aunt, Kambili comes to know a young local priest named Father Amadi, whom she feels attracted to. He practices a loving kind of Catholicism through which he helps local children. Eventually, Papa-Nnukwu, Ifeoma and Eugene's father, comes to live with Ifeoma, but he dies while he is visiting. Eugene becomes upset that his children were living with his father because he considers his father to be a heathen, as the father does not practice Catholicism. After a brief visit home, during which Eugene beats Kambili, they return to Ifeoma's house, although their aunt is engaged in controversy against the new administration at her university. She and her children eventually leave for America.
The end of the novel returns to the fateful Palm Sunday on which Jaja refuses to take confession. Their father dies, and the mother confesses to her children that she poisoned him. Jaja takes the blame for the crime, and he goes to prison. The book concludes three years later, when Jaja is about to be released from prison.

How does Dickens present Scrooge's response to Marley's warnings in A Christmas Carol?

Scrooge reacts with fear when he first encounters the ghost of his long-dead partner, Jacob Marley. Marley’s ghost appears for the first time as a glowing face on the doorknocker of Ebenezer Scrooge’s house. Scrooge is shaken by the apparition, but he unlocks the door, enters his house, and lights a candle. He examines the door before he closes it and tries to shake off his uneasiness. Scrooge is too cheap to light more candles, but he does check all the rooms in the house. Scrooge tries to begin his usual ritual of cooking the evening meal, but he continues to think about Marley’s face. When Marley’s ghost comes into the room, Scrooge examines him cautiously.
Scrooge admits to the apparition that he doesn’t believe in ghosts. Then he makes a joke, a practice that is unusual for the typically cranky Scrooge, but the joke is just an attempt to deflect his own attention from the rising fear he feels in the presence of Marley’s ghost. Scrooge is even more terrified when the ghost’s jaw drops to his chest after he unwraps the bandage from his head. Scrooge begs the ghost for comforting words. “I have none to give,” Marley says.
Marley then tells Scrooge that the only hope Scrooge has is to listen to the three Christmas ghosts who will soon visit him. Having experienced the horror of seeing his dead partner’s ghost, Scrooge says, “I think I’d rather not.” When he learns that the ghosts will arrive one at a time, Scrooge requests that they visit all at once because he dreads the experience and wants to get it over with. Marley’s ghost explains that the three apparitions will appear one at a time. Scrooge is exhausted from the experience and falls asleep immediately.

The ghost of Jacob Marley, Scrooge's former business partner who died seven years before, appears before Scrooge in chains on the anniversary of his death. He tells Scrooge this same fate awaits him if he does not dedicate himself to his fellow men and women but instead only cares about making money. Scrooge makes many feeble defenses of Marley that he, Scrooge, would also apply to himself, including that Marley was a good man of business and that he was a good friend to Scrooge. To Scrooge's protestation that Marley was good at business, Marley replies, "Mankind was my business," intimating Scrooge should have dedicated himself to other people, not just to making money (23). Scrooge is clearly afraid of Marley's ghost, but he doesn't yet heed his message. After Marley leaves, Scrooge immediately goes back to sleep.

What were Daniel Boone's characteristics?

Daniel Boone's greatest characteristic was his wanderlust. Boone was involved in land speculation; in the latter part of the eighteenth century, this was a big business in which many prominent statesmen dabbled. While Boone was a horrible speculator in that he sometimes sold the same plot of land to more than one person, he was one of the few people in the wilderness actively exploring. Boone guided frontier families through the Cumberland Gap to settle in Kentucky and Tennessee. Boone also assisted with the building of towns. Many places in the Southeast still bear Daniel Boone's name.
Daniel Boone's wanderlust led him to keep traveling west. Boone eventually settled down as a farmer in Missouri. His eyesight failed him in his latter years. Boone represents the pioneer ethos of early America: opportunities abounded, provided one was willing to take big risks to get them. Boone was the precursor to the mountain men who helped settle the West and blazed the trails for Oregon and California.

Analyze the character of Scrooge.

Ebenezer Scrooge of Charles Dickens's A Christmas Carol is one of the quintessential villains of literature.  However, he also represents one of its greatest heroes.  At the start of the novel, Scrooge is "a tight-fisted hand at the grindstone."  He is rich but miserly and moves through life shirking all human contact.  Even his own clerk isn't given a name until Scrooge is forced by the Ghost of Christmas Present to realize that Bob, the clerk, is a human being with a real family.  There are a number of reasons why Scrooge is such an unpleasant person.  His early conversations with his nephew, Fred, suggest that there was some moment in Scrooge's past where he lost a love and has subsequently rejected the idea of love and marriage ever since.  During his time with the Ghost of Christmas Past, it is revealed that Scrooge is the son of an abusive father and was sent away to boarding school at a very young age.  Upon revisiting this memory, Scrooge thinks back to a young boy whom he treated harshly and wishes he had the chance to give him something.  Clearly Scrooge makes the connection between the loneliness he felt as a child and the loneliness he caused for another as an adult.  Beyond the affinity he developed for reading, the only source of love and compassion in his young life was his sister, Fan, who died young, sometime after she gave birth to Fred.  It is also revealed that Scrooge was in love with a woman named Belle, but as Scrooge's love for money grew, his love for her declined until she eventually released him from what she refers to as their "agreement."  Belle goes onto marry and have children, and Scrooge is deeply upset as he sees a vision of what he could have had.As stated above, Scrooge's time with the Ghost of Christmas Present allows him to witness the life of his clerk, Bob Cratchit.  He sees Bob's home life and his family, including his youngest: a sickly boy named Tiny Tim.  Despite their poverty and the concerns for Tim's health, the Cratchit family is genuinely happy for what they have; even if it is only one another, it is enough, and they make do.  As he watches this vision, Scrooge begins to feel a connection to Tiny Tim and a desire to help him.  Time grows short for the second ghost who, after furthering Scrooge's unease by introducing him to two wolfish, dirty, feral, yet pathetic children, referred to as Ignorance and Want, disappears.  Shortly afterward, the final spirit presents Scrooge with a glimpse of the future, which contains not only the death of Tiny Tim and Scrooge, but a view of the pillaging of Scrooge's possessions and even the degradation of his corpse by greedy, opportunistic urchins.  By this point, Scrooge had already started to shift his perspective.  He felt regret upon seeing his younger self; he wished he had treated his clerk better after seeing how his own boss, Fezziwig, treated him at a younger age, and he has developed a genuine desire for Tiny Tim to get better.  However, these final visions push Scrooge over the edge and he begins to repent for the life he has led, promising to change.  The dark spirit vanishes, and Scrooge finds himself in his own bedroom on Christmas morning.  Immediately, Scrooge makes good on his word.  He joins his nephew for Christmas dinner, he gives Bob Cratchit a raise and sees to the health of Tiny Tim.  He becomes the man he should have always been, and proves that it is never too late to change one's ways.  He is an extremely dynamic character, and represents one of the greatest changes to take place in all of literature.

What type of whale is Moby-Dick?

The whale in the novel Moby-Dick was actually based on a notorious albino sperm whale killed off the southern coast of Chile near Mocha Island who was called Mocha Dick. The whale was notorious for attacking whaling ships. At the time of its publication, whaling was a very prosperous industry in the United States and whalers traveled all over the world in search of whale oil for lamps and valuable ambergris for perfume. Although the right whale was considered the most valuable, the sperm whale was also prized for its ambergris. The sperm whale could also be quite aggressive and many whalers lost their lives,as a wounded whale could become vengeful at sea.
The story Moby-Dick was inspired by the real-life account of George Pollard, captain of the whaling vessel Essex which was attacked in the Pacific Ocean by a sperm whale. Pollard and his crew had to endure months at sea facing starvation, dehydration, and cannibalism.
https://governmentshutdown.noaa.gov/

What are Keller's reasons for describing the garden as the paradise of her childhood?

Helen Keller was drawn to nature. Like her father, Helen appreciated being out in nature. The garden near her house was a place of solace for her. When Helen was young, she would go to the garden when she became frustrated. She found peace there among the flowers and vines. She could not see or hear, but she used her senses of smell and touch to enjoy the garden. Helen especially loved the flowers in the garden. Roses were her favorite of all. Though she traveled to many places in her life, Helen never experienced roses like the ones at home.
The garden was like a paradise to young Helen. She experienced joy and comfort when she spent time there. Being in the garden made her happy. Helen described her time spent in the garden before Ms. Sullivan came to be her teacher:

There, too, after a fit of temper, I went to find comfort and to hide my hot face in the cool leaves and grass. What joy it was to lose myself in that garden of flowers, to wander happily from spot to spot... (The Story of My Life, Chapter I) 

In Of Mice and Men, what message does Steinbeck convey to the reader about the American Dream, and how does he go about presenting this information through his characters?

In Of Mice and Men, Lennie and George dream about owning their own farm and living off of the land.
The American dream is the belief that everyone has an equal opportunity for success, provided that they work hard. Of Mice and Men is set during the era of the Great Depression when, despite extreme shortages, people still clung to the idea of the American dream. Ultimately, what Steinbeck demonstrates with Lennie’s death is that for some people, despite determination and drive, the American dream is unattainable and can even be somewhat of a trap. However, Lennie and George's dream is what keeps them together (see quote below) and striving for something greater. So, although the American dream is just a fantasy, perhaps it is necessary for living a fulfilling life.

Guys like us, that work on ranches, are the loneliest guys in the world. They got no family. They don't belong no place....With us it ain't like that. We got a future.... An' why? Because...because I got you to look after me, and you got me to look after you, and that's why.

Another event illustrating the futility of the American dream is Curley’s wife’s death. She revealed that her dream was to be a movie star, but she is unable to escape her unhappy marriage and life on the ranch. Her dream was unlikely to ever materialize, but Steinbeck absolutely crushes even the possibility by penning her death at the hands of Lennie.
Crooks also allows himself to become carried away with the thought of hoeing the garden on George and Lennie’s future farm, but the underlying sense is that this will never happen. Moreover, Crooks himself explicitly says that American dreams are impossible:

I seen hunderds of men come by on the road an’ on the ranches, with their bindles on their back an’ that same damn thing in their heads. Hunderds of them. They come, an’ they quit an’ go on; an’ every damn one of ‘em’s got a little piece of land in his head/ An’ never a God damn one of ‘em ever gets it. Just like heaven. Ever’body wants a little piece of lan’. I read plenty of books out here. Nobody never gets to heaven, and nobody gets no land. It’s just in their head. They’re all the time talkin’ about it, but it’s jus’ in their head.

Steinbeck conveys the message that the American Dream—which can be defined in the context of this book as people's ability to control their own land and destiny—is not available to the American working person. Steinbeck conveys this message about the inaccessibility of the American Dream through the fate of his main characters, Lennie and George. They dream of owning their own farm where they can raise crops and rabbits and are not subject to the management of cruel farm owners. This dream is not realized, though, because George mistakenly kills a woman, so Lennie must kill him to avoid the authorities further inflicting damage on George. Candy, an elderly farm worker, symbolizes the working man's inability to achieve the American Dream. He becomes entranced by the dream Lennie and George have of owning their own farm, but he also fails to achieve this dream. It is clear that the farmhands in the book will meet tragic ends in which they either die or face lives of unending work with little to show for it.

What are Darry’s physical and personality traits?

Darry is Ponyboy's eldest brother, and the reader learns about Darry through the eyes of Ponyboy, the narrator of The Outsiders.
Darry is twenty years old, and Ponyboy explains that Darry's rigid personality and unfriendly manner is the result of having to grow up too fast. When the three Curtis boys, Ponyboy, Darry, and Sodapop, the middle brother, lost their parents in a car accident, Darry stepped in to look after the other boys and to become the head of the family. Darry's need to mature quickly turned him into a cold person, and Ponyboy is scared of him.
Ponyboy describes Darry as looking like their father, tall and muscular, but Darry's eyes set his looks apart from their dad's. They are cold and green-blue, and Ponyboy thinks that Darry would be good-looking if his eyes weren't so cold.

What are three ways Elie Wiesel's father helped him stay alive in the camps, as detailed in Night?

In the story, Elie's father is instrumental to his son surviving the Holocaust. Elie's father gives his son valuable advice, shares his rations of food with Elie, prevents Elie from falling asleep in the snow, and motivates his son to continue living despite their appalling, tragic circumstances. Elie's father is his source of comfort during the Holocaust and remains by Elie's side until he passes away. Shortly after arriving at Auschwitz, Elie mentions that he was terribly hungry and engulfs his ration of bread and margarine. Elie's father then advises him to eat sparingly before giving him his ration. Elie's father also offers him words of encouragement during extremely difficult, dangerous situations, which gives Elie the strength to endure the transports, constant violence, exhausting marches, and threatening prisoners. Elie's devotion to his father also inspires him to keep living. In one scene, Elie attempts to lay down and sleep in the snow after an arduous journey. Elie's father saves his life by preventing him from falling asleep, which would mean sure death. When Elie's father becomes extremely ill, Elie shares his rations with him and is motivated to make sure his father survives. Tragically, Elie's father passes away and Elie completely loses hope. Following the death of his father, Elie begins to walk around like a lifeless corpse.

Despite the fact that his father is often a burden to Elie, the older man's presence in the camps is one of the major reasons why Elie ultimately survived. Throughout their internment, Elie is constantly concerned with his father's well being and considers himself indispensable to his father's survival. This attitude probably helped keep Elie from succumbing to exhaustion and starvation. There are two good examples of this in section six. During the forced march from Buna to Gleiwitz, Elie suggests that his survival was prompted by his father's presence running at his side. He believed that if he faltered and could not go on, his father would also certainly perish:

My father's presence was the only thing that stopped me....He was running at my side, out of breath, at the end of his strength, at his wit's end. I had no right to let myself die. What would he do without me? I was his only support.

A little later in this section, Elie is again on the verge of giving in to exhaustion when his father saves him. After marching (more like running) forty-two miles, he drops to the snowy ground to sleep. His father pleads with him to move on and not to fall asleep on the frozen "carpet" of snow:

"Don't let yourself be overcome by sleep, Eliezer. It's dangerous to fall asleep in the snow. You might sleep for good. Come on, come on. Get up."...I got up, gritting my teeth. Supporting me with his arm, he led me outside.

Even though Elie's father does not survive the camps, it could certainly be argued that Elie lived on primarily because he had a purpose in life during the horrible year he spent imprisoned. In his book Man's Search for Meaning, Victor Frankl, also a camp survivor, argued that apathy and lack of purpose was one of the major reasons why prisoners died. They simply gave up because they could see no reason to carry on such an abominable existence. For Elie, no matter how bad things got, he always had his father (his father died shortly before the liberation of Buchenwald) to give him a purpose and a reason for living.

Point slope linear equation is y-4=3(x+1) . on a parallel line find the ordered pair where x=2.

We are given the point-slope form of a line: y-4=3(x+1) . We are then asked to find the ordered pair (coordinates) of the point lying on a line parallel to the given line with x value 2. (Note this is the same as finding the intersection of the vertical line x=2 and the constructed line parallel to the given line.)
From the alternate description of the question, it is clear that there are an infinite number of answers. The line x=2 will intersect every line parallel to the given line.
First note that the slope of the given line is 3. (We also know that it passes through the point (-1,4).) Every line with slope 3 is parallel to this line, and as stated above each of these lines will intersect the vertical line x=2.
Assume the coordinates of the point of intersection between the constructed lines and the line x=2 are of the form (2,k), where k is a real number. Then the point-slope form for every line of this type is y-k=3(x-2)
Here are some graphical examples:

The red line is the original line (with a slope of 3, containing (-1,4)). The black lines are parallel to the red line, and you can see, from top to bottom, that they intersect x=2 at (2,19), (2,16), (2,13), (2,11), (2,9), and (2,7) respectively.
** If there was more information given in your original problem, you could pinpoint which of these lines was required. For example, if the line goes through the origin, the equation would be y=3(x-2). **
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http://mathworld.wolfram.com/Point-SlopeForm.html

How is Lord Capulet presented in act 1, scene 2, of Romeo and Juliet (using literary techniques and context)?

Lord Capulet is introduced as a sensible man who, while not willing to reach out to Lord Montague to end the feud, is willing to not initiate any new conflicts. His age is a governing factor in this, as he says, "... And 'tis not hard, I think, / For men so old as we to keep the peace" in the first part of this scene. One can infer he is weary of the feud and just tries his best to not stoke the long-existing enmity between the two families.
Shakespeare contrasts Capulet with the young Count Paris in this scene, emphasizing the older man's patience. Paris is eager to marry Juliet right away, even before the two are introduced. Capulet advises Paris to wait until Juliet is older. The interaction between these two characterizes Capulet as cautious, advising against impulsive action, since "too soon marred" are girls who marry and have children before they are emotionally ready to do so.
Capulet's words about Juliet mark him as a loving father. He describes Juliet as "the hopeful lady of my earth" and claims "Earth hath swallowed all my hopes but she." Juliet is an only child, so the hope that the line will continue rests on her. However, Capulet wants to respect Juliet's wishes in choosing a husband. He tells Paris he must "get her heart" before Juliet shall be his to marry.
Overall, Capulet's introduction presents him as a wise family man, looking out for the best interests of his loved ones. This has the effect of making his later tyrannical behavior all the more tragic, since they go against the two impressions the audience receives in this scene: his desire to stay out of the feud and his patient love for Juliet.

We know that Capulet is an older man who would prefer to "keep the peace" as opposed to engaging in a fight with the Montagues. This is important for the audience to know in relation to Capulet's character, which is why Shakespeare privileges it by opening the scene with this comment from Capulet himself.
In this scene, Paris is attempting to persuade Capulet to accept his "suit," but Capulet is wary. This is a further example of his cautiousness as a character: he suggests that they "let two more summers wither in their pride/Ere we may think [Juliet] ripe to be a bride." The use of the rhyming couplet here draws attention to the sentiment and gives a sense that this is Capulet's final, resolved conclusion, as rhyming couplets are commonly used in Shakespeare to bring scenes or ideas to an end. When Paris argues that "younger than she are happy mothers made," Capulet counters that such women are "too soon marr'd."
Capulet's approach to his daughter is forward-thinking; his language—"consent," "choice," "get her heart"—suggests strongly that he respects his daughter's authority and will not override her wishes. He attempts to imbue Paris with some of his own natural patience, offering an invitation to "an old accustom'd feast" as a suggestion to Paris as to how he might gently win Juliet's favor. Capulet's language is measured and elegant, his use of verse (rather than prose) marks him out as an erudite and aristocratic character. He uses natural imagery to persuade Paris that the "fresh female buds" he will find at Capulet's house will justify the young man's attendance.
All in all, this scene presents Capulet to the audience as a respectable older man who has seen enough in his life to take a cautious approach to change, which stands in contrast to the rather brash young Paris.

According to the narrator, what four things remain as they were in the period from 1874 to 1890?

You can find the answer to this question in Owen Wister's preface to his novel The Virginian. In this preface, he addresses the reader on the question of what constitutes a historical novel and whether The Virginian is one. According to Wister, although the novel is set at a point not far distant in the past from the time in which Wister is writing, it must be considered a historical novel because it accurately and faithfully portrays a "vanished world" which can no longer be reached outside of the memories of those who experienced it.
Not everything in Wyoming has changed, but according to Wister, the only things which remain unchanged are elements of the natural landscape. The buffalo have departed, and the horsemen, and the sheer wildness of the landscape as it once was. Indeed, the only four elements which are unchanged are the mountains, the sunlight, "the infinite earth," and "the air that seems forever the true fountain of youth."
The type of horseman depicted in this novel, Wister says, has died out since the days the novel depicts, and the Wyoming of the book is a bygone world. The pioneer age, which saw men like the eponymous Virginian fashioning Wyoming into the state it now is, represented an earlier stage in American history. Now, the America of Wall Street has emerged, and an inevitable transition has taken place.

How would you prove that Guiseppe Mazzini's The Duties of Man can support and explain romanticism?

Romanticism is a broad term. In this address, Mazzini gives voice to a liberal nationalism that was associated with the Romantic movement. In particular, he argues that one's nation or country is something elemental, something a person was given by God. Romantic nationalists thought that nations were bodies of people bound together by a common history, language, and culture (a concept that was just beginning to emerge in the nineteenth century). They believed that for centuries, monarchs and empires had denied people the ability to express their national identities—to share a polity with others like them. As Mazzini writes,

Evil governments have disfigured the Divine design. . . . They have disfigured it by their conquests, their greed, and their jealousy even of the righteous power of others. . . . These governments did not, and do not, recognize any country save their own families or dynasty, the egoism of caste. But the Divine design will infallibly be realized; natural divisions and the spontaneous, innate tendencies of the peoples will take the place of the arbitrary divisions, sanctioned by evil governments.

Mazzini believed that the "map of Europe would be redrawn" in ways that better reflected the fundamental ties between different groups of people. This was a departure from the thinking of both dynastic monarchies and Enlightenment philosophers, who generally spoke of divinely-endowed universal rights. To Romantic nationalists like Mazzini, rights, identity, and other such things came from God. However, they only made sense through a nation-state formed with other people connected to them in fundamental ways. As he said in summation,




O, my brothers, love your Country! Our country is our Home, a house God has given us, placing therein a numerous family that loves us, and whom we love; a family with whom we sympathize more readily and whom we understand more quickly than we do others.

This sentiment may seem somewhat xenophobic and chauvinistic to modern readers, but to Mazzini and other Romantic nationalists, it made sense that liberal reforms would be more likely to adhere in homogenous societies, in which people had a sense of fellow feeling with others. In this way, The Duties of Man is an example of the nationalistic strain in Romanticism.

In Elie Wiesel's Night, how does Moishe the Beatle change throughout the pages 3-22 (at first, then, finally)?

At first Moishe the Beadle kept to himself. A very poor man, he managed to avoid the scorn often heaped on the poor by staying out of people's way. Moishe had "mastered the art of rendering himself insignificant, invisible," Weisel writes. The reader becomes acquainted with Moishe through Elie, who has talked often with him about the mysteries of Kabbalah. Moishe's deportation from Sighet is the transformative moment in his life. He escapes a certain death and returns to the town with horrific tales of the atrocities committed against the deportees by the Gestapo. He is no longer "invisible," as he goes from house to house trying to warn the people of the fate that awaits deported Jews. But he is anguished to find that nobody will listen to him:

Moishe was not the same. The joy in his eyes was gone. He no longer sang. He no longer mentioned either God or Kabbalah. He spoke only of what he had seen...[He said] "I no longer care to live. I am alone. But I wanted to come back to warn you. Only no one is listening to me...."

Over time, Moishe withdrew again: "drifting through synagogue or through the streets, hunched over, eyes cast down, avoiding people's gaze." He is as shattered by the unwillingness of the people to heed his warnings as he was by his own deportation. When the Germans enter the town, and eventually begin arresting the Jews, Moishe comes to Elie's house, and shouts "I warned you," before quickly leaving. This is the last time Elie sees Moishe, who tried and failed to warn the Jews of Sighet that they faced utter destruction.

Why does Mercutio choose to fight Tybalt when Romeo backs down?

I'd like to start this answer by reminding readers that Mercutio is just about as hot tempered as Tybalt.  Tybalt always gets the blame for having a quick temper, but Mercutio is just as bad.  Benvolio even states the fact in Act 3, Scene 1. 

"An I were so apt to quarrel as thou art, any manshould buy the fee-simple of my life for an hour and a quarter."

That is the same scene where Mercutio and Tybalt fight each other too.
I believe that Mercutio chooses to fight Tybalt for a few reasons.  First, the day is hot.  Benvolio states the fact at the very beginning of the scene, and he says that the hot weather always puts people in hot tempered moods.  Mercutio likes fighting in the first place, and the weather is making him crankier.  
Second, Mercutio is still upset that Tybalt sent a formal challenge to Romeo.  Mercutio knows that Tybalt is dangerous, and as Romeo's friend, Mercutio feels the need to protect his friend.  
Third, when Romeo finally shows up, Romeo essentially just stands there and takes insult after insult from Tybalt.  Mercutio is angered by the insults and angered that Romeo isn't willing to do anything about it.  Mercutio eventually gets to the point where he can't idly stand by and watch anymore.  He feels compelled to jump into the fray and fight Tybalt.  Unfortunately Mercutio's actions get himself killed.  

How, and to what ends, has J.D Salinger incorporated family relationships into The Catcher in the Rye?

The mental descent of Holden Caulfield in The Catcher in the Rye begins with the death of his brother Allie several years before the novel begins. To Holden, Allie maintained these qualities: he was "nicest" in the family, was more "intelligent" than Holden, and "had very red hair." When he died of Leukemia, Holden lost his mind and "broke all the goddam windows [in the garage]" with his fist, "just for the hell of it."
In the novel, Holden also clings to his 10-year-old sister Phoebe, whom he says, "[S]he knows exactly what the hell you're talking about." It's Phoebe's love for Holden that keeps him going off the rails. He wants to see her and even buys her a record. It's her threat to run away with him that knocks some sense back into Holden.
One important factor about family to consider is the absence of Holden's father. He continues to send Holden to boarding schools despite the fact that Holden seems to be failing at every turn. When Holden does return home, they are noticeably absent with Phoebe's repetition of "Daddy's going to kill you" being the only reminder of him. Holden also mentions that his father is a corporate lawyer, but Holden doesn't really want to be like him.

How does Rikki-Tikki's friend help him?

Darzee the tailor-bird initially helps Rikki-Tikki at the beginning of the short story by warning him about Nagaina's ambush. While Rikki-Tikki is speaking to Nag for the first time, Nagaina sneaks up behind him and Darzee yells "Behind you! Look behind you!" to Rikki-Tikki, who instantly jumps into the air to avoid Nagaina's attack. After Rikki-Tikki kills Nag, he asks Darzee where Nagaina is located and she tells him that Nagaina is mourning her deceased husband by the rubbish heap. Darzee then informs Rikki-Tikki that Nagaina's eggs are located in the melon bed, on the end nearest the wall. Darzee once again helps Rikki-Tikki by acting like she broke her wing to get Nagaina's attention while Rikki-Tikki destroys her eggs in the melon bed. Overall, Darzee helps Rikki-Tikki by warning him about Nagaina's ambush, telling him where Nagaina hides her eggs, and distracting Nagaina by feigning a broken wing, which gives Rikki-Tikki time to destroy Nagaina's eggs.

I believe the friend the question is referring to is Darzee's wife. Darzee's wife helps lure Nagaina away from her snake eggs so Rikki-tikki can sneak up to them and destroy most of the eggs.
Darzee's wife is an intelligent and brave bird. She knows Nagaina's eggs, if allowed to hatch, will produce dozens of deadly cobras. She wants those eggs destroyed, and she is willing to put herself in harm's way to help Rikki-tikki do that. Her plan is to fake an injury and lure Nagaina away. Darzee's wife flies to the ground and begins hobbling around and moaning in pain. She keeps crying out that the boy broke her wing. Nagaina can't resist the easy target, and Nagaina begins to stalk Darzee's wife. Darzee's wife continues to play up the injury while hobbling away from the cobra's nest. Rikki-tikki realizes the opportunity he is being given and seeks out Nagaina's eggs. He destroys all the eggs except one. 

Address Brutus's leadership abilities.

Overall, one could argue that Brutus is temperamentally unsuited to a position of leadership. For one thing, he's far too noble, too unselfish to survive for very long in such a treacherous, cutthroat environment. Brutus is an idealist; he loves the Roman Republic more than anything else. In some respects, this is a very important quality in a leader. But the problem is that the other assassins aren't motivated by the same noble aims as this most honorable of Romans. Brutus kills Caesar because he wants to save Rome from tyranny; his coconspirators stick the knife in—literally—for purely personal gain. Brutus actually believes in something, believes in a higher cause, and for a potential leader of Rome that's a fatal handicap.
Brutus's leadership qualities—or lack of them—are much in evidence on the field of battle. While the much more grounded Cassius understands the necessity of adopting defensive tactics in relation to Mark Antony's forces, Brutus foolishly decides to take the fight to the enemy at Philippi, with catastrophic results. Brutus has had his head well and truly turned by the responsibilities that military leadership entails. Instead of dealing with the practicalities of defeating the enemy, he's become enamored of his own legend, seeing himself as playing a lead role in a gigantic cosmic drama. It is his destiny to engage with the enemy at Philippi, he thinks.
Ironically, Brutus, who sacrifices his dear friend for the greater good of Rome, has now sacrificed the cherished cause of Roman republicanism to fulfill his vague, ill-defined sense of destiny. For that reason more than any other, his abilities as a leader must be called into serious question.

What does Mr. Underwood think about Tom’s death?

In Chapter 25, Scout elaborates on Braxton Bragg Underwood's editorial in The Maycomb Tribune concerning Tom Robinson's death. Although Mr. Underwood is a racist, he considers it a sin to kill cripples. Scout says he likened Tom's death to the senseless killing of songbirds. As Scout reads Mr. Underwood's article, she realizes that Tom was a dead man before he set foot in court. Mr. Underwood understands that Tom Robinson was an innocent, crippled man who became a victim of racial injustice. He doesn't believe Tom should have died and is disgusted that the prison guards murdered a crippled man. Scout mentions that the majority of Maycomb's citizens read Braxton's article and believed he was simply trying to be poetic enough to get a reprint in The Montgomery Advertiser.

How did the Crusades lead to the discovery of the New World?

The Crusades were a series of military expeditions in the 11th, 12th, and 13th centuries. European Christians believed it their duty to recapture the Holy Land from the growing Muslim Ottoman Empire. By the end of this pursuit, many Crusaders had returned home with exotic goods like spices, silks, and gold they had acquired in the Holy Land. With a hunger for these exotic goods from as far off as China and the Indian subcontinent, European nations began seeking a quicker, cheaper route for getting their hands on what they wanted. 
When the Crusades ended in the 13th century, trade for exotic goods did not entirely come to a halt. Rather, the flow of goods had to pass through many hands, over many miles of land and sea, before being traded from Muslim merchants to Italian merchants, and from Italy to the rest of Europe. With each trade being made, prices went up! Imagine the poor people of Britain who just wanted a little pepper for their soup! 
In response to this high-demand, high-price situation, the Portuguese established a navigation school and quickly became the major players in European exploration and trade. The Portuguese were the first to round the tip of Africa and find a sea passage to India, where silver, spices, and textiles could be acquired. They were also the first to reach Southeast Asia, and second in the New World. Before the Portuguese, the Italian sailor Christopher Columbus sailed to the New World on behalf of Spain.
When Columbus made his fateful voyage in 1492, he wasn't looking for a "new world" or Biblical paradise... he was seeking a sea route to Asia to the west! He believed that Spain could get a leg up on Portugal by going across the Atlantic rather than around Africa. Of course, where he landed was not India or China at all, but the Americas. There he and other explorers found resources they already knew to be valuable (gold and gems) as well as new luxuries to be exported (tobacco, chocolate, potatoes.) European desire to have exotic goods at reasonable prices, combined with a sense of duty to spread Christianity- which served as an excellent tool for justifying Colonialism- the Americas were rapidly conceptualized as a land of resources waiting to be shipped across the Atlantic.
https://www.britannica.com/event/Crusades

https://www.britannica.com/topic/European-exploration

Intermediate Algebra, Chapter 4, Review Exercises, Section Review Exercises, Problem 16

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

4x - y =& 2 \\
3y + z =& 9 \\
x + 2z =& 7

\end{aligned}
\end{equation}
$. If a system is inconsistent or has dependent equations, say so.


$
\begin{equation}
\begin{aligned}

12x - 3y \phantom{+z} =& 6
&& 3 \times \text{ Equation 1}
\\\
3y + z =& 9
&& \text{Equation 2}

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

\phantom{12x - 3y + z = 15}
\\
\hline

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

12x \phantom{-3y} + z =& 15
&& \text{Add; New Equation 2}

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

12x + z =& 15
&& \text{Equation 2}
\\
x + 2z =& 7
&& \text{Equation 3}

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

-24x - 2z =& -30
&& -2 \times \text{ Equation 2}
\\
x + 2z =& 7
&& \text{Equation 3}


\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

\phantom{-23x + 2z = -23}
\\
\hline

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

-23x + \phantom{+ 2z} =& -23
&& \text{Add}
\\
x =& 1
&& \text{Divide each side by $-23$}
\\
1 + 2z =& 7
&& \text{Substitute $x = 1$ in Equation 3}
\\
2z =& 6
&& \text{Subtract each side by $1$}
\\
z =& 3
&& \text{Divide each side by $2$}
\\
\\
4(1) - y =& 2
&& \text{Substitute $x = 1$ in Equation 1}
\\
4 - y =& 2
&& \text{Multiply}
\\
-y =& -2
&& \text{Subtract each side by $4$}
\\
y =& 2
&& \text{Divide each side by $-1$}


\end{aligned}
\end{equation}
$


The ordered triple is $(1,2,3)$.

What effects did slavery have on Mississippi?

Prior to the end of the Civil War, slavery was common in Mississippi.  Like in other southern states, large plantations produced cotton and other crops.  Slaves made up almost the entire workforce on plantations.  Typically, overseers were the only white employees on a plantation.  Some slaves worked in and around the plantation house, while most worked in the fields.  These slaves planted, cared for, and harvested crops.
Mississippi relied on a primarily agricultural economy.  Without slave labor, Mississippi farmers and plantation owners would have been without workers.  The agricultural industry depended on slave labor.
Slaves generally lived in harsher conditions in Mississippi than in other slave states.  Emancipation was prohibited in most cases.  Few freed blacks lived in the state, and because of this almost all paying jobs were held by whites.
After the Civil War, plantation owners had to pay their workers.  The sharecropping system rose in popularity during this time.  Former slaves became sharecroppers.  Many Mississippi plantation owners faced financial hardships after the Civil War.
 

Who is the father of economics?

Adam Smith is considered to be the father of economics. This is not because Adam Smith was the first person to consider many of the ideas he is credited with, but instead because he was the first person to put many of those ideas into a format that could easily be read and understood.
Smith was a proponent of a free market and "laissez-faire" policies in which the government had little involvement in the economy. Smith believed in the "invisible hand," which would guide the economy through competition and supply and demand. In his thinking, individuals acting in their own self-interest were also working in a way that was best for society. For example, one could not charge too much for a good or people would not buy it, thus depriving the seller of a profit and ultimately leading to their own failure.
Smith's thinking also focused on the idea of division of labor, which gave birth to modern ideas on manufacturing. Smith argued that one person working on a product that requires multiple steps could only make a limited amount per week. Smith further argued that if the steps were broken up and each step assigned to a different worker, who could then become especially skilled in their specific step, production would be much greater.
For his ideas regarding the free market, supply and demand, and division of labor, as well as his ability to express these ideas, Adam Smith became known as the father of economics. Many of Smith's theories, although hundreds of years old now, are still relevant to economics today.
https://www.investopedia.com/updates/adam-smith-economics/

Most people would say that Adam Smith is the father of economics. However, there were others who came before him. One of those people was Richard Cantillon. He was an Irish banker and merchant who wrote a document four decades before Adam Smith wrote The Wealth of Nations.
Around 1730, Cantillon wrote a document in French titled Essai sur la nature du commerce in général. While this was not published due to censorship restrictions of that time period, it was circulated in literary circles and in intellectual circles. This treatise has been referred to as “the first systematic presentation of the field of economics.” He was able to free economics from being intertwined with ethical and political concerns. He was also one of the first people to use the tool of economic abstraction, which is now referred to as economic reasoning.
Therefore, Richard Cantillon can be called the father of economics.

Did Cassius's bad feeling during the battle make him interpret his army's victory as defeat and then cause his suicide?

This is actually a really interesting question (and perhaps more complicated than it at first appears). First, be aware: Shakespeare tends to be open to multiple lines of interpretation, and I'd suggest this is certainly the case here. It's an entirely valid interpretation to suggest that Cassius's own psychological mindset going into the battle (shaped by his dreams beforehand) influenced events as they played out on the battlefield. In fact, this seems like a very realistic point of view.
However, I would suggest that where things get interesting, and more complicated, is when we consider the nature of Cassius's misgivings within the larger context of the play. Do note that, within the world of Julius Caesar itself, omens and prophesy play a major role within the setting. In that respect, Cassius's dream is not an isolated occurrence. Consider the prophesies surrounding Caesar's death, for example, in act 1, scene 2, when the Soothsayer warns Caesar to "beware the ides of March" or later when Caesar's wife Calpurnia dreams of Caesar's own death.
This is where your question becomes more complicated, because now one can ask (given that Cassius's defeat was itself possibly subject to prophesy) whether or not the events on the battlefield might well have been fated. Did his dreams influence his mindset, which in turn influenced the events on the battlefield, or was it rather the reverse? Did the outcome on the battlefield influence the dream? Furthermore, one might suggest that both these options are true simultaneously: if fate had doomed Cassius, by being aware of it, he may have had a role in shaping it.
This is where Shakespeare gets really interesting from an analytic perspective, because it can get really complicated when you dive into these thematic questions, and you can argue for a multiplicity of different answers. I don't think there's one clear right answer here. Various perspectives can be defended.

In act 5, scene 3, Cassius receives word that Antony's troops have surrounded them and commands Titinius to find out whether the approaching soldiers are their allies or enemies. Cassius then asks Pindarus to mount the hill and watch Titinius. Pindarus then reports that Titinius has been captured by the enemy soldiers and Cassius immediately expresses despair by saying,

Oh, coward that I am, to live so long To see my best friend ta'en before my face! (Shakespeare, 5.3.37-38).

He then asks Pindarus to take his sword and stab him while his eyes are shut. Pindarus follows Cassius's instructions by killing him, and Cassius's last words are "Caesar, thou art revenged, Even with the sword that killed thee" (Shakespeare, 5.3.48-50). Unfortunately, Pindarus misinterpreted what he saw, and Titinius arrives to announce that Brutus's troops have overtaken Octavius's soldiers.
According to the conversation between Titinius and Messala following Cassius's death, they believe Cassius killed himself because he thought that Titinius would never return and he would lose the battle. Before the battle, Cassius lacked faith in Brutus's ability to lead troops and also disagreed with his decision to meet Octavius and Antony at Philippi. Cassius's final decision to commit suicide was a result of his belief that he would lose the battle. Rather than be captured by Antony and Octavius, Cassius chooses to commit suicide.

How does Top Girls by Churchill present its protagonist in both a positive and negative light?

The play Top Girls by Caryl Churchill investigates what constitutes female success and paints a nuanced portrait of its flawed protagonist, Marlene, an ambitious business woman who leaves her child in the care of her sister in order to pursue her career. Marlene's choices are neither sanitized nor demonized by the play. Instead, she, along with her own conception of what "success" entails, are shown in both a positive and negative light depending on context.
The play opens with Marlene hosting a dinner party at a restaurant for various famous real and fictional women from throughout history to celebrate a recent promotion at work. This scene places Marlene and her ambitions in historical context and includes her in a pantheon of women who have achieved great things in spite of the patriarchal society that attempted to keep them down. In this scene, the portrayal of Marlene is overwhelmingly positive. Marlene's promotion is presented here, at least in Marlene's own mind, as being on the level of Pope Joan pretending to be a man and ascending to the highest role in the Catholic Church or explorer Isabella Bird's many discoveries. Though none of the women present can agree on what constitutes female success or the best way to achieve it, the play embraces the dialectical nature of their conversation. Marlene's way—climbing the corporate ladder—is not the only way, but it is no worse than any other.
The following scenes of the play are written in a decidedly more realist mode, with characters from the present day only. The difference between the positive portrayal of Marlene in act 1, scene 1—which is a celebration of female empowerment—and the grittier, negative portrayal of her in the scenes that follow is partially due to this tonal shift.
In the Top Girls office, the audience is privy to Marlene's hard, no-nonsense business persona. Here, she is cold and conservative. The point of the Top Girls Agency is to help women advance in their careers, but it seems that Marlene's philosophy in doing this is to become more traditionally masculine, embracing competition and toughness. She values individualism and works toward the advancement of singular ambitious women, rather than liberation of the group as a whole.
It is perhaps in the scene between Marlene and Joyce, accompanied by the revelation that Marlene is Angie's mother, that Marlene's portrayal becomes most complex. Though the audience can understand her values and the decisions she has made, her strained relationship with her sister and her lack of a relationship with her own daughter drive home the point that she has chosen her own advancement over all else. Though she tries to help her sister financially, money, which Marlene has sacrificed so much to gain, is not enough to restore her familial relationship.

Does Harry Potter and the Sorcerer's Stone have religious undertones?

Religious undertones exist both in Harry Potter and the Sorcerer's Stone and in the series as a whole. As mentioned in the other answers, Harry is a Christ figure, a chosen one who is destined to end the tyranny of Voldemort, who represents evil.
Sacrificial love is a strong concept in the Christian religion, since Christ's love for humanity led to the cross, and it is much the same in Harry Potter and the Sorcerer's Stone, where Harry's mother died saving him. Her love continues to protect Harry from evil, as represented in Voldemort when Quirrell tries to kill Harry during the climax before the Mirror of Erised. Harry is knocked unconscious during this confrontation, which is presented as a metaphorical death, since he confronted Quirrell in order to protect the school and, indeed, the wizarding world at large from Voldemort.
The Sorcerer's Stone itself contains religious connotations as well. The stone is said to grant eternal life, which is why Voldemort wishes to possess it. In contrast, Harry is willing to risk his life to procure the stone but not use it. This element of the story could be linked to the Bible verse Matthew 16:25, "For whosoever will save his life shall lose it: and whosoever will lose his life for my sake shall find it." At the end of the novel—and at the end of the series—Voldemort's violent quest for immortality ends in death, while Harry, who sacrifices time and again, ultimately gets to live a life filled with love and companionship.
The unicorn blood has similar religious significance. In medieval Christianity, the unicorn was a symbol of Christ, since it was associated with purity and goodness. To kill a unicorn is to kill something truly good. As Firenze tells Harry in the woods, "The blood of a unicorn will keep you alive, even if you are an inch from death, but at a terrible price. You have slain something pure and defenseless to save yourself, and you will have but a half-life, a cursed life, from the moment the blood touches your lips." Firenze's lines are reminiscent of the biblical verse "What will it profit a man if he gains the whole world, yet forfeits his soul?" (Matthew 16:26). Voldemort's killing a unicorn further cements his position as an evil, even Satanic, figure, opposed to the values represented by Harry, the Christ figure protagonist.
https://biblehub.com/matthew/16-25.htm

In Harry Potter and the Sorcerer's Stone, there are religious undertones. First, it is understood that the magical world is caught in an epic battle between good and evil, with the evil Voldemort gaining power. Voldemort represents evil; Harry represents good.
Further, love is identified as the chief attribute of the good, which is a strongly Christian concept. Harry is identified with love because his mother, Lily, sacrificed herself out of love to save him from Voldemort. This love is symbolized by the scar on his forehead, which gives Harry extra protection against evil: love is depicted as a powerful force, like a lightning bolt, that repels wickedness.
Sacrifice is strongly associated with religious belief. In sacrificing herself, Lily has acted as a Christ figure, dying that others may live. The parallels with the Christ story are imprecise. Harry, however, carries on the Christ-figure legacy. He is "everyman," as his ordinary name indicates, and he too has been asked to risk his life to defeat evil and protect other people.

Harry Potter and the Sorcerer's Stone has religious undertones in the Christ-like figure that Harry is made into.
The comparisons between Jesus Christ and Harry Potter begin wherein Harry is described as The Chosen One. Harry was a miraculous child that survived a vicious attack from Lord Voldemort, thus defeating the Dark Lord. In The Bible, Jesus Christ is referred to as a chosen son of God to walk the Earth in God's image. In Christianity, it is often believed that Jesus is the only way Satan will be kept at bay. Jesus is also a miracle child in that he was born to the virginal Mary.
As the story of The Sorcerer's Stone progresses, a lot of myth and wonder surrounds Harry. When he meets wizards and witches for the first time, they reach out to shake his hand and thank him for the kindness he has done in ridding the world of Lord Voldemort. Jesus Christ plays a similar role in The Bible, healing lepers and sinners alike. Men and women gather to see Jesus in real life, often asking to touch his body and thanking him for the miracles he has performed.
Lastly, Harry sacrifices himself in order to defeat Lord Voldemort at the end of the book. He is resurrected from a comatose state under Albus Dumbledore's care, a character with God-like qualities. Within Christianity, Jesus was nailed to a cross and subsequently died. Later, Jesus is resurrected by God. The celebration of Easter for Christians and the final feast at the Great Hall in Sorcerer's Stone are akin to each other in that both celebrations focus on a resurrected savior.
With these examples present, one need not look far for comparisons between Harry Potter and Jesus Christ in Harry Potter and the Sorcerer's Stone.

y = x^2/2 - ln(x) Locate any relative extrema and points of inflection.

We are asked to locate the relative extema and any inflection points for the graph of y=x^2/2-lnx :
Extrema can occur only at critical points; i.e. points in the domain where the first derivative is zero or fails to exist. So we find the first derivative:
y'=x-1/x   This is a continuous and differentiable function everywhere except x=0, which is not in the domain of the original function. (The domain, assuming real values, is x>0.)
Setting the first derivative equal to zero we get:
x-1/x=0 ==> x=1/x ==> x^2=1 ==> x=1   (x=-1 is not in the domain.)
For 01 it is positive, so there is a minimum at x=1. This is the only minimum or maximum.
Inflection points can only occur when the second derivative is zero:
y''=1+1/x^2 ==> y''>0 forall x so there are no inflection points.
The graph:

How specifically did comic books reflect or contribute to New Deal America in the 30s?

Hello! You have a very interesting question. Comic books both reflected and contributed to the popular culture of New Deal America.
Some of the most well-known characters of the comic book industry were created in the 30s, just as America was starting to crawl its way out of the Great Depression. Entertainment was very much a form of escapism, but the heroes had changed. American audiences no longer trusted the idea of the "self-made man" who became rich, because they had seen what greed had done to the economy. They also did not swing the other way and pick leftist heroes from reality. Instead, they found heroes in comic-book-form who could be both an "everyman" reflection of themselves and the thrilling hero who can do things normal people cannot do.
Superman's popularity helped take those values that the writers felt were uniquely American—confidence, sense of justice, care of the poor, valuing people over money—and fed them to the wide audience of readers he had. One also needs to look at the creators of these characters, and many writers of comic books at the time were Jewish. For them, these characters—very much in particular Superman—was a reflection of what they thought it was to be truly American in a country that still struggled with accepting Jews as Americans. Superman's comics also dealt with him dispensing justice to everyone—something that a lot of Americans of the time wanted to see from Washington. Many of Superman's early adventures had him doing everything from stopping abusive husbands to hunting down company owners who valued money over their workers. Even though he was not born in America, there was the idea that he was raised with American values, and that became a central theme for Superman comics during the New Deal era. The comics were both explicit and subtle about echoing FDR as he fought for New Deal policies and helped form a popular culture that reflected the celebration of the common man and the rejection of corporate greed.
Sources: 
Comic Book Nation: The Transformation of Youth Culture in America - Bradford W. Wright
Captain America and the Struggle of the Superhero - edited by Robert G. Weiner
"Was Superman a New Dealer?" - Essay by Robert Parkinson (link below).

In Kate Chopin’s “The Story of an Hour” and “Desiree’s Baby” the stories involve the reader in the experiences of their characters and perhaps misguide us in our assumptions about what is going on. What are some techniques the author uses to compress information into a short space?

Kate Chopin is able to write complex short stories in brief lengths for several reasons. In both of the examples listed, Chopin uses a third person limited point of view and spare figurative language.
The third person limited point of view allows Chopin to focus on just one or two characters’ inner thoughts and emotions, which prevents the story from being consumed by too many characters.
In addition, Chopin uses dialogue and interior monologue as primary plot devices. She does not use elaborate metaphors, symbols, or flowery imagery to convey her points. Instead, Chopin is most interested in character development and irony. In each story, the protagonist is a victim of irony at the hands of her husband.
Mrs. Mallard has a heart attack because she discovers her husband is alive; and she is not happy about this. Desiree essentially commits suicide and infanticide because Armand allows her to believe she is black; the reader learns in the last paragraph that it is Armand, in fact, who is black. Each of these ironic revelations is not discussed until the final paragraph of the story. Ultimately, Chopin is able to mislead and hook the reader into a complex story because of her ability to hone in on the most important parts of a narrative rather than tricks of language.

What similarities or differences do you see between Etruscan and Egyptian burials and funerary practices?

The Etruscans were a civilization that reigned in Italy before the Roman Empire. Prior to the foundation of Rome in 509 BCE, the Etruscans ruled as a monarchy.
The ancient Egyptians are one of the older agricultural civilizations, starting as a river valley civilization in 3,100 BCE until it was incorporated into the Roman Empire.
Both the Etruscans and Egyptians used burial urns and sarcophagi. Burial urns are used to store cremated remains, and sarcophagi are stone coffins that house the deceased. Egyptian burial urns could be used for either cremated remains or particular organs; these were known as canopic jars and often featured the heads of some of their gods, like Horus or Ra. Etruscan burial urns could also function as holders for cremated remains or organs, but unlike the Egyptian urns, it displayed their human's image as opposed to one of a deity.
The Etruscan sarcophagus, however, is more animated than their Egyptian counterparts. The Etruscan sarcophagus, true to Etruscan art, focuses more on liveliness and energy; many Etruscan artworks and potteries feature figures dancing (see image linked below). Etruscan sarcophagi sometimes feature a couple as opposed to a single person. In one famous Etruscan sarcophagus, called "Sarcophagus of the Spouses," the couple is sitting up and holding one another almost as if they are in bed, looking out in the distance. In another, a couple in laying down together, staring at one another, as if in bed. I've attached a quick google search link to see these sarcophagi.
Egyptian sarcophagi are more serious in tone, flatter, and the subject is laying down facing upwards. Unlike the Etruscan sarcophagi, Egyptian ones can be more decorated, with gold and other jewels and dyes, used to signify importance. More important sarcophagi, like the ones of pharaohs, are portrayed with a mask and wrapped beard.
https://www.google.com/search?q=etruscan+sarcophagus&tbm=isch&ved=2ahUKEwjTlP_OwIvmAhWSFd8KHXueCNoQ2-cCegQIABAA&oq=etruscan+sarcophagus&gs_l=img.3..0l7j0i8i30l3.37928.40103..40258...0.0..0.122.818.10j1......0....1..gws-wiz-img.......0i67.qBx6GL0CUfk&ei=UQ

While the ancient Etruscans and Egyptians had very different cultures and religious practices, their funerary art does indeed share a number of notable characteristics. For one thing, they both placed a very heavy focus on depicting life beyond death. Both cultures viewed death as just the first step on a long journey to the world of the dead. Consequently, their burial practices were done to please the souls of the dead and help speed them along on their journies. The Egyptians believed that lifelike and accurate funerary masks helped the deceased find acceptance by the gods once they reached the afterlife. The Etruscans also believed that lifelike imagery depicting the dead helped them reach the afterlife. Offerings, such as food and jewels, were also left in tombs, which, it was believed, could help the dead on their journey.
Of course, being such different cultures in most regards, there are striking differences. Etruscan funerary art often depicts scenes that reflect everyday life. It is thought that the Etruscans believed that happy scenes of life would please the dead and free them to leave the world of the living. The Egyptians, on the other hand, used imagery that of the journey to the afterlife itself. It was believed that the deceased could use this as a map or guide on their journey.

While both cultures had elaborate funeral rites and beliefs about the soul's journey to the afterlife, there are two key differences between them. For one thing, the Egyptians wanted to preserve the corpse as much as possible. The body was considered important, even after life had left it. The Etruscans did not care as much since they cremated their dead.
The artistic styles used for funerary art are different. Images on Etruscan tombs and sarcophagi emphasize liveliness. One famous Etruscan sarcophagus called the Sarcophagus of the Spouses features a couple in a relaxed, affectionate pose. Compare this to the images seen in Egyptian tombs, which are two dimensional and formal. The art there seeks to immortalize the dead's deeds rather than emphasize how they were in daily life.

There are several similarities that can be found between the funeral practices of the Etruscans and the Ancient Egyptians. Both cultures placed heavy emphasis on death and the afterlife. As such, heavy emphasis and importance was placed on the care of the dead and the process of preparing the dead for each cultures' ideas of the afterlife. Both cultures left offerings for their dead loved ones in order for them to be well prepared on their journey to the afterlife. Both the Etruscans and the Ancient Egyptians took great care to decorate and adorn the burial tombs of their dead loved ones.
While the Ancient Egyptians practiced mummification, the Etruscans actually cremated their dead, but ultimately put the cremated remains in elaborately designed sarcophaguses. The Etruscans believed that in order for their loved ones to pass on to the afterlife, that they must be pleased with the decorations of their tombs. Or else, the dearly departed may end up haunting the mortals who failed to properly decorate their sarcophaguses. As such, the Etruscans painted elaborate and intricately designed scenes of lavish banquets and festivities upon the tombs in order to give their departed loved ones that best chance of reaching a happy after life.

The Etruscan and Egyptian beliefs about the afterlife were somewhat similar, and this is reflected in similarities in their burial and funerary practices. Both societies could be said to have had an obsession with death, and their cultural approach to the dead should be seen through this lens. Both societies featured burial elements that were quite elaborate: carefully constructed tombs, lavishly decorated sarcophagi, and extensive rituals involving the preparation of the dead.
The fundamental difference between the two cultures was the process of mummification. Etruscan funerary rights did not really involve mummification to the same degree as in Egypt. The Egyptians turned mummification into a science. The process, which took about two months, involved special salts to dry the body, the preservation of the organs in canopic jars, and the embalming and wrapping of the body in layers of resin and linen laced with gems and jewels. The Etruscan approach was less elaborate in this respect, and many bodies were cremated. The decoration of the coffins (sarcophagi) was also quite different—more artistic and sculptural in Etruscan culture and more representational in Egyptian.
Interestingly, there is another unexpected connection between the two cultures as regards funerary practices. The longest extant Etruscan text, the Liber Linteus, was actually written on linen and remains preserved because it was used to wrap an Egyptian mummy in the Ptolemaic period.

Single Variable Calculus, Chapter 3, 3.2, Section 3.2, Problem 52

According to the definition, the left hand and right hand derivatives of $f$ at $a$ are defined by



$\displaystyle f'_- (a) = \lim\limits_{h \to 0^-} \frac{f(a+h) - f(a)}{h} \qquad \text{ and } \qquad
f'_+ (a) = \lim\limits_{h \to 0^+} \frac{f(a+h)-f(a)}{h} $


Suppose that these limits exists.
a.) Determine $f'_- (4)$ and $f'_+ (4)$ for the function
$
\displaystyle
f(x) = \left\{
\begin{array}{c}
0 & \text{if} & x \leq 0\\
5-x & \text{if} & 0 < x < 4\\
\frac{1}{5-x} & \text{if} & x \geq 4
\end{array}\right.
$

b.) Sketch the graph of $f$
c.) Where is $f$ discontinuous?
d.) Where is $f$ not differentiable?

a.)
For Left Hand,

$
\begin{equation}
\begin{aligned}
f'_- (x) &= \lim\limits_{h \to 0^-} \left[ \frac{5-(x+h)-(5-x)}{h}\right]\\
f'_- (x) &= \lim\limits_{h \to 0^-} \left[ \frac{\cancel{5}-\cancel{x}-h-\cancel{5}+\cancel{x}}{h}\right]\\
f'_- (x) &= \lim\limits_{h \to 0^-} -\frac{\cancel{h}}{\cancel{h}}\\
f'_- (x) &= \lim\limits_{h \to 0^-} -1\\
f'_- (4) &= -1
\end{aligned}
\end{equation}
$


For Right Hand,

$
\begin{equation}
\begin{aligned}
f'_+ (a) &= \lim\limits_{h \to 0^+} \frac{\left[\frac{1}{5-(x+h)}-\left(\frac{1}{5-x}\right)\right]}{h}\\
f'_+ (a) &= \lim\limits_{h \to 0^+} \frac{\frac{5-x-[5-(x+h)]}{(5-(x+h))(5-x)}}{h}\\
f'_+ (a) &= \lim\limits_{h \to 0^+} \frac{\frac{\cancel{5}-\cancel{x}-\cancel{5}+\cancel{x}+h}{(5-(x+h))(5-x)}}{h}\\
f'_+ (a) &= \lim\limits_{h \to 0^+} \frac{\cancel{h}}{(5-x-h)(5-x)\cancel{h}}\\
f'_+ (a) &= \lim\limits_{h \to 0^+} \frac{1}{(5-x-h)(5-x)}\\
f'_+ (a) &= \lim\limits_{h \to 0^+} \frac{1}{(5-x-0)(5-x)}\\
f'_+ (a) &= \lim\limits_{h \to 0^+} \frac{1}{(5-x)^2}\\
f'_+ (4) &= \frac{1}{(5-4)^2} = \frac{1}{(1)1^2} = 1\\
f'_+ (4) & = 1
\end{aligned}
\end{equation}
$

Therefore, $f'(4)$ doesn't exist since $f'_- (4) \neq f'_+ (4)$

b.)



c.) Based from the graph
The function $f$ is discontinuous at $x=0$ because of jump discontinuity.
Also, $f$ is discontinuous at $x=5$ because of infinite discontinuity

d.) The function $f$ is not differentiable at $x=0$ and $x=5$ because the function is discontinuous
at that points. Also, the function is not differentiable at $x=4$ since $f'_- (4) \neq f'_+ (4)$ based
from definition.

What criticism has Stan Lee gotten over the years?

Stan Lee is a famous cartoon artist who worked as a creative force at Marvel Comics in the 1960s and 1970s, then moved on to be a publisher. During his time at Marvel, he worked to create several of the most iconic cartoon figures of all time--The X-Men, Iron Man, Thor, Spider Man, The Avengers, and The Incredible Hulk, among others. Many credit him with creating pop-culture legends that have only grown in popularity over time. He made his heroes remarkably human, as opposed to archetypes of perfection as earlier superheroes had been, and he also introduced a colloquial way of speaking that also helped his audiences relate to his characters. He also created a shared fictional universe of comic characters and created the Black Panther, the first major black hero in comics. 
However, despite his role in creating pop-culture phenomena, according to some sources (see the link in Vulture below), there are doubts that he almost singlehandedly created these characters, as he and Marvel have claimed. There is a consensus among some scholars that he and Marvel downplayed the work of collaborators who helped to create the comic book characters Lee claims as almost his own. For example, in an article in Inc. (see the link below) published on November 1, 2009, he said "All the characters at Marvel were my ideas." He is now chairman emeritus of Marvel and has moved on to his own company, POW! 
https://www.inc.com/magazine/20091101/how-i-did-it-stan-lee-of-marvel-comics.html

https://www.vulture.com/2016/02/stan-lees-universe-c-v-r.html

In "Young Goodman Brown," what social institutions do Deacon Gookin, Goody Cloyse, and the minister represent?

On Goodman Brown's journey to the Black Mass in the forest, he witnesses a conversation between the Devil and Goody Cloyse, who taught him his catechism in youth and is a revered spiritual leader in his Puritan community. In addition to witnessing Goody Cloyse have a conversation with the Devil, Brown also overhears a discussion between Deacon Gookin and the minister regarding the unholy ceremony as they travel deep into the forest.
During the Black Mass, all three characters participate and worship the Devil as Goodman Brown and his wife take part in the unholy communion. Hawthorne offers a sharp critique of Puritan religion and culture by depicting presumably righteous spiritual leaders participating in the Black Mass.
Collectively, Deacon Gookin, Goody Cloyse, and the minister symbolically represent the Christian church, which is the foundation and cornerstone of Puritan society. They represent a standard of piety and godliness in Brown's community and are highly respected individuals. However, Hawthorne portrays them as deeply flawed, wicked individuals, who hide their sins behind their pure reputations and holy personalities.

The three individuals mentioned in the question represent the church. The minister is somewhat obvious. In many ways, he is the voice of a church, because he is the person delivering spiritual messages and teachings to the people in attendance. Deacon Gookin has a similar church leadership role as a church deacon. Deacons are elected members of a church to be servant-leaders. They are often in charge of the church's finances, and they are also the church members tasked with intentionally finding ways to help people within the church. Goody Cloyse might not be an elected member of the church council; however, her knowledge of the faith and the denomination are deep enough for her to be entrusted with teaching young people their catechism. The catechism is a summary of the principles of the Christian religion. It is formatted in a question and answer style.

When the devil points out Goody Cloyse on the path, young Goodman Brown notes that she is the elderly woman of unimpeachable reputation in town who taught him his catechism when he was young; in fact, she is still, along with the minister and Deacon Gookin, a spiritual advisor for Brown.  These three people, jointly, represent the church.  They are all thought to be beyond moral reproach, and they are responsible for helping to lead the community down a righteous path.  It is very ironic, then, that Brown spots Goody Cloyse, and later hears the deacon and minister, on the path because he would never have expected them to be on their way to the witches' Sabbath.  They are the community's best examples of morality, and so if even they are in league with the devil, it seems that there can be little hope, if any, for anyone else to maintain innocence.
Their guilt also seems like an indictment of Puritan society by Hawthorne.  If even the most moral folks in this community are corrupt, then that says nothing positive about Puritans: instead, they seem hypocritical and false.

What is a topic to research in the classroom?

If you are talking about doing empirical pedagogical research, your first step should be thinking about what sort of research project you can do in a feasible manner. For example, if you are a professor teaching a multi-section course, you can set up studies with students in 4 sections assigned to use one learning strategy and 4 sections assigned a different one and compare results. You need to be able to create two groups containing at least 40-50 people per group (more is better) to have useful statistical results.
If you do not have enough study subjects for statistical analysis (a basic rule of thumb is that N=50 is the minimum for significance), you will need to to some form of ethnography, watching and closely describing an individual learner or pedagogical method. 
You may be able to do historical research as well, doing something like looking through archives of syllabi for a given course and analyzing how they have changed over a 10 or 20 year period. 
 

I definitely recommend choosing a research topic that you are interested in.  If a bunch of topics sound equally appealing, choose the one that will be the most beneficial to your readers or the school.  Here are ten that I think are particularly interesting. 
Does teacher feedback actually help improve student learning?
Does homework improve student learning?
What types of homework are most effective for student learners?
Does the classroom seating arrangement have any effect on student learning?
Does the classroom seating arrangement have any effect on classroom management?  
Does listening to music while studying for tests and taking tests improve test scores?
Does technology improve student learning?  
Do male students perform better in math and science related courses than female students perform?  
Athletes technically have fewer hours to work on schoolwork; therefore, their grades and completion rates should be lower than students who do not participate in sports.  Is this true or is the opposite true?  
What type of learner are most students?  Visual, auditory, or kinesthetic learners?   Do teachers effectively balance all three teaching and learning styles?  

College Algebra, Chapter 4, 4.2, Section 4.2, Problem 20

Sketch the graph of polynomial function $\displaystyle P(x) = \frac{1}{5}x (x - 5)^2$ make sure the graph shows all intercepts and exhibits the proper end behaviour.
The function has an odd degree 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 $x$-intercept, we set $y = 0$.


$
\begin{equation}
\begin{aligned}
0 &= \frac{1}{5}x (x - 5)^2\\
\\
0 &= x \quad \text{and} \quad (x - 5)^2 = 0
\end{aligned}
\end{equation}
$


We have,
$x = 0$ and $x = 5$

To solve for the $y$-intercept, we set $x = 0$
$\displaystyle y = \frac{1}{5} (0) (0 - 5)^2 = 0$

Single Variable Calculus, Chapter 2, 2.5, Section 2.5, Problem 63

Prove that the function
$f(x) = \left\{
\begin{array}{cc}
x^4 \sin \left( \frac{1}{x} \right) & \text{ if } x \neq 0 \\
0 & \text{ if } x = 0
\end{array}
\right.
$ is continuous everywhere.

Using the Squeeze Theorem to prove that the left and right hand limits are equal...


$
\begin{equation}
\begin{aligned}

& -1 \leq \sin \left( \frac{1}{x} \right) \leq 1\\
\\
& -x^4 \leq x^4 \sin \left( \frac{1}{x} \right)\leq x^4\\
\\
& \lim \limits_{x \to 0} (-x^4) = -(0)^4 = 0\\
\\
& \lim \limits_{x \to 0} (x^4) = 0^4 = 0

\end{aligned}
\end{equation}
$


The Squeeze Theorem gives us $\displaystyle\lim \limits_{x \to 0} x^4 \sin \left( \frac{1}{x} \right) = f(0) = 0$. Therefore, the given function is continuous on $(-\infty, \infty)$

The 1950s and 60s are often considered polar opposites, but were the 1950s as placid and conflict-free as they seemed? Also, why did the 1960s begin on such an optimistic note yet end rather darkly?

The 1950s were not as calm as portrayed in popular culture, as this period marked the beginning of the Civil Rights Movement. This was the decade where the jailing of Rosa Parks launched the Montgomery Bus Boycott. This was also when Eisenhower sent in the National Guard, in order to protect the "Little Rock Nine" and thus desegregate the schools and uphold the Brown v. Board Supreme Court ruling.
The decade also saw extreme paranoia situated as it was in the McCarthyism era. Many were accused of being Communist, simply because they backed leftist agendas during the 1930s. Many actors and screenwriters were punished because they would not incriminate others. The period was also bad for women, as they had lost much of the autonomy they had gained during WWII and were now expected to go back to low-paying work and homemaking.
The 1960s began on a relatively positive note. The United States had a young dynamic president who promised to put a man on the moon by the end of the decade. He also launched the Peace Corps, which promised to both spread American ideals and make the world a better place. Kennedy also rose above the Southern Democratic party base and helped to establish civil rights, though his successor, Lyndon Johnson, would do more of this upon Kennedy's assassination. Johnson even declared war on poverty in his Great Society platform. The decade ended darkly, as Vietnam, a war which had gradually escalated from advisers to ground troops, turned into America's nightmare. The "living room war" showed American casualties and not enough winning of key battles. It also showed thousands of defenseless Vietnamese being put in inhumane conditions. Martin Luther King Jr. was shot in Memphis in 1968, touching off race riots all over the country. The 1968 Democratic National Convention was picketed by protesters chanting "The Whole World is Watching!" as police beat them away from the convention. Richard Nixon won the election by promising "Peace with Honor" in Vietnam, but he actually escalated the war by invading Laos and Cambodia. The United States did land a man on the moon in 1969; this was one of the bright spots of that year. All of this made the 1960s a decade which started with such promise but ended with more questions unanswered.

int tan^5 (x/2) dx Find the indefinite integral

Indefinite integrals are written in the form of int f(x) dx = F(x) +C
 where: f(x) as the integrand
           F(x) as the anti-derivative function 
          C  as the arbitrary constant known as constant of integration
To evaluate the given integral problem int tan^5(x/2) dx , we may apply u-substitution by letting: u = x/2 then du =1/2 dx or  2du= dx .
The integral becomes:
int tan^5(x/2) dx =int tan^5(u)* 2 du
Apply the basic properties of integration: int c*f(x) dx= c int f(x) dx .
int tan^5(u)* 2 du =2 int tan^5(u)du
Apply integration formula for tangent function:  int tan^n(x)dx = (tan^(n-1)(x))/(n-1)- int tan^(n-2)(x)dx .
2 int tan^5(u)du= 2 *[(tan^(5-1)(u))/(5-1)- int tan^(5-2)(u)du]
                        = 2*[(tan^(4)(u))/(4)- int tan^(3)(u)du]
Apply another set integration formula for tangent function on  int tan^(3)(u)du .
int tan^(3)(u)du = (tan^(3-1)(u))/(3-1)- int tan^(3-2)(u)du
                         = (tan^(2)(u))/(2)- int tan^(1)(u)du
                         =(tan^(2)(u))/(2)-ln (sec(u))+C
Applying  int tan^(3)(u)du =(tan^(2)(u))/(2)-ln (sec(u))+C , we get:
2 int tan^5(u)du=2*[(tan^(4)(u))/(4)- int tan^(3)(u)du]
                        =2*[(tan^(4)(u))/(4)- [(tan^(2)(u))/(2)-ln (sec(u))]]+C
                        =2*[(tan^(4)(u))/(4)-(tan^(2)(u))/(2)+ln (sec(u))]+C
                       =(tan^(4)(u))/2-tan^(2)(u)+2ln (sec(u))+C
Plug-in u = x/2 on (tan^(4)(u))/2-tan^(2)(u)+2ln (sec(u))+C , we get the indefinite integral as:
int tan^5(x/2) dx=(tan^(4)(x/2))/2-tan^(2)(x/2)+2ln (sec(x/2))+C

What allowed the Europeans to explore further into Africa and eventually conquer more?

During the nineteenth century, Europeans were able to advance into the interior of Africa. Improved military, communications, and transportation technology allowed them to do so, and more effective drugs to fight malaria helped as well.
The specific “tools of imperialism” that facilitated Europe’s colonial conquests in Africa included breech-loading repeating rifles, light field artillery, smokeless gunpowder, iron-hulled steamships, railroads, quinine, and, later, machine guns. The introduction of submarine telegraph cables enabled European colonial authorities to communicate by telegraph; this allowed them to use their limited resources in a more effective way and to send reinforcements where they were badly needed.
Quick-firing British and French rifles and artillery were important in helping British and French forces to conquer parts of Western Africa in the late nineteenth century, and the new Maxim machine guns played a decisive role in the defeat of the large-scale Sudanese Mahdi uprising against the British in the battle of Omdurman (1898). Many thousands of rebels died, but the British and Egyptian forces lost just a few dozen of their own people. The Maxim machine guns devastated the courageous Ndebele warriors in South Africa (1893), thus defeating one of the strongest states that opposed the British colonial advance.
Where European troops did not have an overwhelming technological advantage and African forces were reasonably well-trained in the use of modern weapons, the European invading armies sometimes experienced crushing defeats. The Ethiopian victory over Italian forces in the battle of Adwa (1896) is a notable example of this.

Who is Raymond Sintes and what is the word around the neighborhood regarding Raymond?

Raymond Sintes is a foil to Meursault. This means that he provides a contrast to the protagonist, emphasizing certain characteristics of his. If Meursault is amoral, his neighbor Sintes is completely immoral. He's a pretty unpleasant character, to put it mildly. He is a macho chauvinist who physically abuses his mistress and generally treats her like dirt. It is Sintes's contempt for his mistress that leads to Meursault becoming embroiled in a scheme that ultimately ends in murder. Sintes is devious and manipulative and thus is able to get Meursault to do his bidding.
The reputation that Sintes has in the neighborhood is that of a pimp. And he certainly gives the impression of being one, with his flashy clothes and his reputation of violence towards women. Sintes is indeed subsequently exposed as a pimp in court, but he remains somewhat cagey about what he does for a living. Despite everything, Sintes still seems keen to maintain a certain reputation in the neighborhood.

During the 1950s, who did advertisers begin to target?

Television changed advertising in the 1950s.  Millions of American families watched TV and the commercials that ran.  Popular celebrities starred in commercial ads showing new products.  Ads began to target children and teenagers.  Ads targeted toward children showed new and exciting toys.  Ads for teenagers showed everything from phonographs to sodas to clothes.
The 1950s were a time of increased consumerism.  The previous two decades had been filled with hardships.  The Great Depression of the 1930s and World War II in the 1940s had forced consumers to cut back.  The economy was flourishing by the 1950s, and American consumption reflected this.  It was in the 1950s that advertisers began researching their demographics.  They wanted ads to target specific demographics.  Besides children and teenagers, women were frequently targeted.  Many women were housewives, so ads for cleaning products were common.  Smoking was a common habit for adults, and cigarette ads dominated the television screens during Prime Time.

What ailment might the narrator suffer? How does the narrator use personification throughout the story?

It seems that the narrator is suffering from what we would call postpartum depression, though they did not have such a diagnosis when Gilman wrote the story. The narrator's husband, a doctor, tells friends and family that she has only a "temporary nervous depression—a slight hysterical tendency." A diagnosis of hysteria tended to function as a sort of catchall for any mental problems that seemed particularly associated with women: in fact, the word hysteria comes from the Greek word for uterus. Further, the narrator talks about how glad she is that "Mary is so good with the baby. Such a dear baby! And yet I cannot be with him, it makes me so nervous." Her confession that being with her baby makes her feel nervous is a good indicator that the state of her mental health has a great deal to do with the fact that she's recently given birth and that she is not, perhaps, connecting with her child in the way that one might hope or expect.
Throughout the story, the narrator routinely personifies the wallpaper in her room. For example, she says,

There is a recurrent spot where the pattern lolls like a broken neck and two bulbous eyes stare at you upside down [....]. Up and down and sideways they crawl, and those absurd, unblinking eyes are everywhere [....]. I never saw so much expression in an inanimate thing before, and we all know how much expression they have! I used to lie awake as a child and get more entertainment and terror out of blank walls and plain furniture than most children could find in a toy-store. I remember what a kindly wink the knobs of our big, old bureau used to have, and there was one chair that always seemed like a strong friend.

She gives the design of the wallpaper a neck and eyes and the ability to crawl. Not only does she attribute life to the wallpaper itself, but it also seems to have been a pattern with her, throughout her life, to personify all kinds of objects. She talks about how inanimate things always seem to have a great deal of expression to her: a pretty atypical description of things like walls and wardrobes. This helps gives us some insight into her imagination as well; she is clearly very creative and thoughtful and that must make it all the more frustrating and upsetting for her that her husband has removed all means of mental stimulation from her room.

Can you help me with writing a descriptive essay on the experience of a classroom without a teacher?

Since you are tasked with describing something you must imagine, your first step is to close your eyes and visualize a teacher-less classroom. What does that look like in your mind's eye? Jot short notes or phrases that will help you remember what you're seeing. The more clearly you visualize, the better your essay will be. Imagine you are a student in this classroom. What does it feel like? How do you like it? Note any feelings or sensations associated with your image.
Using your imagined picture, choose a thesis statement. It might be something like, "A classroom without a teacher is total chaos," or "Students learn better without a teacher." Let your image lead you. Then, organize your essay around your thesis. A good hook might be to describe your classroom to the reader; try to make readers see your classroom the same way you do. Throughout the essay, keep picturing your teacher-less classroom. Use that image to support your thesis.
For example, in your imagination are the students engaged and learning? How can you tell? What are they doing? Their actions and expressions are what you want to describe. Why do students learn better without a teacher? Because you "saw" them working individually at computers, and helping each other with questions. You "saw" how much more efficient it was. Or maybe you pictured unruly kids talking, throwing things, and running around the class. Describing this scene to your readers supports a thesis that a classroom without a teacher is total chaos.
It is said a picture is worth 1,000 words. Create a clear picture in your mind, and you'll have no trouble writing a few-hundred word essay. Have fun with it! And remember there is no right or wrong description of what this new type of classroom would be like. Your experience is unique to you.

A descriptive essay is an essay topic that English or writing teachers like to frequently give at some point in the year. At first look, the process can be daunting, but the writing prompt given is fairly specific, so that will help a great deal. I'm not allowed to write the essay for you; however, it does seem like a potentially really fun topic. The descriptive essay itself is an essay that asks a writer to describe something. It could be an object, place, person, experience, emotion, or situation. There is a lot of flexibility within the form of this essay, but the main goal is that the piece paints a vivid image in the mind of the reader. With that in mind, I'd like to offer some tips to get you going in the right direction.
One of the first things to decide is what the topic is going to be. This has been decided for you, but that's only a small part of the rhetorical situation. Another thing that has to be decided is who is narrating. Will you, as a student within this classroom, be the person that is narrating the story? This is where the story's flexibility comes in because your narrator doesn't have to be you or even another student within the classroom without a teacher. Your narrator could be a literal fly on the wall. You could even get creepy and have your narrator watching the events from a control room using hidden cameras and microphones throughout the room. You also have to decide on what genre you are going to write. Will your essay be a comedy, a horror story, a news piece, or something else? Finally, another thing to think about is where your essay will take place. What grade level doesn't have a teacher? A first grade classroom without a teacher is going to be a very different place than a college classroom.
The next thing to do is create an attention grabbing hook. You need to get your reader's attention right away. The first sentence is key. You could start by asking your reader a question in order to get them thinking about the situation. You could start with a quote. This could be interesting to play around with because the quote could be completely made up. It could be a piece of dialogue that a fictional student shouts out at the top of his/her lungs about the teacher being gone. The hook could be a bold, declarative sentence that sets the reader on edge. This worked amazingly well for Andy Weir's book The Martian.
Now that the first sentence is done, you can begin writing about the experience that a classroom without a teacher is to your narrator. An important thing to remember throughout the descriptive essay is to describe what the situation is like. Use vivid language to really help the reader understand what is it like in the classroom. Use similes and metaphors more than you normally would for a school essay. If you are drawing a blank on how to describe something or what to actually describe, consider your five senses. Tell your reader what it is that you see, smell, hear, feel, and even taste. For example, "It was five minutes into the class period, and the teacher was still absent. The students were all starting to get the same feeling. They could practically taste the freedom that was slowly wafting into the classroom like the smell of freshly fried bacon."
A final recommendation is to stay organized. You might be tempted to write this essay in a stream of consciousness style. That could definitely work, but I don't recommend it. I understand that writing it in stream of consciousness makes sense, but it makes sense to you. Your reader is not you, and his/her stream flows slightly differently. The stream of consciousness will likely be a very jarring read for your reader, so stick with an organized format. Perhaps write each paragraph about what each of your senses are experiencing. This organization isn't perhaps realistic, but it does allow you to guide your reader into reading and experiencing each item in full detail in the order that you want the reader to experience it in.
https://owl.purdue.edu/owl/purdue_owl.html