Single Variable Calculus, Chapter 3, 3.8, Section 3.8, Problem 20

At what rate is the boat approachng the dock when it is 8m from the dock?
Illustration:







Required: $\displaystyle \frac{dx}{dt}$ when $x = 8m$

Solution:

By using Pythagorean Theorem we have,

$z^2 = 1^2 + x^2 \qquad$ Equation 1

taking the derivative with respect to time


$
\begin{equation}
\begin{aligned}

\cancel{2} z \frac{dz}{dt} =& \cancel{2}x \frac{dx}{dt}
\\
\\
\frac{dx}{dt} =& \frac{z}{x} \frac{dz}{dt} \qquad \text{Equation 2}

\end{aligned}
\end{equation}
$


We can get the value of $z$ by substituting $x = 8$ in equation 1


$
\begin{equation}
\begin{aligned}

z^2 =& 1^2 +x^2
\\
\\
z^2 =& 1^2 + 8^2
\\
\\
z =& \sqrt{65} m

\end{aligned}
\end{equation}
$


Now, using equation 2 to solve for the unknown


$
\begin{equation}
\begin{aligned}

\frac{dx}{dt} =& \frac{\sqrt{65}}{8} (1)
\\
\\
\frac{dx}{dt} =& \frac{\sqrt{65}}{8} m/s

\end{aligned}
\end{equation}
$


This means that the boat is approaching the dock at a rate of $\displaystyle \frac{\sqrt{65}}{8} m/s$ when the boat is $8 m$ from the dock.

Analyze the development of the character of Scout. Support this analysis with evidence from the text, such as major developments in the plot.

Whether or not Harper Lee studied Piaget's stages of cognitive development or not, Lee did an admiral job of showing readers a character that is moving from the preoperational stage to the concrete operational stage. The preoperational stage tends to exist when a person is between the ages of 2 and 7 years old. One of the characteristics of this stage is that a child tends to be egocentric and struggles to see things from another person's perspective. When the book begins, Scout is just about 6 years old, and readers can see Atticus trying to help Scout consider things from another person's perspective:

"First of all," he said, "if you can learn a simple trick, Scout, you'll get along a lot better with all kinds of folks. You never really understand a person until you consider things from his point of view—"
"Sir?"
"—until you climb into his skin and walk around in it."

At the book's conclusion, Scout is 8 years old. She has technically moved into Piaget's concrete operation stage which exists between 7 and 11 years of age. It is during this developmental stage when a child begins losing some of their egocentric tendencies. Kids become better at thinking about how other people might feel or see a particular situation. I believe that her final interaction with Boo helps readers see this change in Scout. In the book's final paragraphs, Scout is talking about a character from the story Atticus was reading, but the subtext hints that she is also referring to her newfound attitude and opinion about Boo as well:

"Atticus, he was real nice . . ."
His hands were under my chin, pulling up the cover, tucking it around me.
"Most people are, Scout, when you finally see them."

Scout develops from an innocent, impulsive child to a more knowing and caring young girl as the novel progresses. At the beginning, Scout is somewhat careless with her language and her tone of voice when speaking to others, but by the end of the novel, she is more considered and thoughtful in her speech. This change reveals the development in her character very clearly.
For example, in Chapter 2, Scout doesn't think carefully before speaking out loud in class, and she creates a difficult situation for herself with the teacher and with Walter Cunningham. She means to be helpful, but she doesn't think it all through, and Scout ends up frustrated and tearful at being so misunderstood. Later, in Chapter 3, Scout and Calpurnia clash because, yet again, Scout innocently speaks her mind, and her curiosity about Walter Cunningham's table manners leads to another difficult situation.
An example of change takes place later in the book when Scout shows more thoughtfulness and restraint in her speech, signifying growth and maturity. In Chapter 15, during one of the most poignant moments in the whole novel, Scout speaks carefully and politely to Mr. Cunningham during the mob scene. Her childish good intentions are tempered by her awareness of the men and her learning to be more thoughtful, and she single-handedly contains the mob and the men disperse. Here, the power of Scout's newfound handle on language is apparent as well as her maturing awareness.

How is Jerry's growth and evolving maturity reflected in his relationship with his mother in "Through the Tunnel" by Doris Lessing?

In the beginning of the narrative of "Through the Tunnel," Jerry stays close to his mother, asking permission to part from her, then returning to her after going to the rocky bay; later, he demands goggles and goes independently to the rocky bay.
Dependence upon his mother
Because his mother is a widow and Jerry an only child, she is protective of her son; likewise, Jerry feels emotionally tied to her. At the beach, when she feels that he is not with her, she quickly turns around,

"Oh, there you are, Jerry!" ....Contrition sent him running back to her, And yet, as he ran, he looked back over his shoulder at the wild bay; and all morning...he was thinking of it." 

As Jerry's yearning to explore the rocky bay waxes, his mother senses that she may be keeping him too close to her now that he is eleven years old. So, although she is anxious, she gives Jerry permission to go the big beach. Jerry is excited to go, but still turns to find his mother on the beach:

When he was so far out...he floated on the buoyant surface and looked for his mother.

A burgeoning independence
After his experiences with the boys who swim under the water and rebuff him, Jerry swims back to the other beach and returns to the villa where he and his mother are staying. He waits for her, and as soon as his mother enters, Jerry demands swimming goggles, "pant[ing], defiant, and beseeching." She agrees, but he "nagged and pestered" her until she takes him to a shop. Then, Jerry grabs the goggles and runs off without asking permission.
As quickly as he can, Jerry swims to the big barrier rock. Adjusting his goggles on his face, Jerry dives into the deep water. However, the force of the dive knocks his goggles out of place; so, he fills his lungs and adjusts his goggles in order to see below.
Jerry explores the rock and finds the hole. Then, he practices and practices until he feels dizzy. But, when his nose bleeds that night, his mother cautions him and insists that he accompany her the next day.

It was a torment to him to waste a day of his careful self-training, but he stayed with her...[where it] now seemed a place for small children....It was not his beach.

Independence from his mother and a new maturity
The next day, Jerry does not ask permission to go to "his beach." Instead, he leaves before his mother has time to consider the "complicated rights and wrongs of the matter." When he arrives at the wild bay, Jerry ponders trying to go through the tunnel, but "[A] curious, most unchildlike persistence, a controlled impatience" leads him to wait.
After his mother tells Jerry that they must return home in four days, Jerry realizes that he must attempt to swim through the tunnel "if it killed him." So, he dives down, controlling himself, but feeling panic along with a sense of victory that he is moving through the tunnel. He knows that he must continue or he will drown. Finally, Jerry reaches the surface, although he feels that he may not be able to swim back to the rock. Yet, he manages, and when he removes his goggles, they are filled with blood.In a little while, Jerry returns to the shore and makes his way up the path to the villa. He rushes to the bathroom to wash away the blood and the tear stains, but his mother senses that Jerry is too pale under his suntan. "How did you bang your head?" she asks him, while at the same time warning herself not to worry. Jerry only tells her that he can remain under water for three minutes, at least. Moreover, "it was no longer of the least importance to go to the bay" as he has already completed his rite of passage. 

Calculus: Early Transcendentals, Chapter 4, Review, Section Review, Problem 1

You need to evaluate the local absolute extrema of the function, hence, you need to find the zeroes of the equation f'(x) = 0.
You need to evaluate the derivative such that:
f'(x) = 3x^2 - 12x + 9
You need to solve for x the equation f'(x) =0:
3x^2 - 12x + 9= 0 => x^2 - 4x + 3 = 0
x_(1,2) = (4+-sqrt(16-12))/2
x_(1,2) = (4+-2)/2
x_1 = 3 ; x_2 = 1
You need to evaluate the function at critical points:
f(1) = 1^3 - 6*1^2 + 9*1 + 1
f(1) = 1 - 6 + 9 + 1
f(1) = 5
f(3) = 3^3 - 6*3^2 + 9*3 + 1
f(3) = 27 - 54 + 27 + 1
f(3) = 1
You need to evaluate the function at the end points of interval:
f(2) = 2^3 - 6*2^2 + 9*2 + 1 = > f(2) =8 - 24 + 18 + 1 = 3
f(4) = 4^3 - 6*4^2 + 9*4 + 1 => f(4) = 64 - 96 + 36 + 1= -3
Hence, the absolute maximum of the function, on the interval [2,4], is 5 and it occurs at x = 1 and the absolute minimum of the function is -3 and it occurs at x = 4.

3^(2x) = 75 Solve the equation accurate to three decimal places

Problem: 3^(2x)=75 is an exponential equation.
  To simplify, we need to apply logarithm property: log(x^y) = y*log(x)
 to bring down the exponent that is in terms of x.
 Taking "log" on both sides:
log(3^(2x))=log(75 )
(2x)log(3)=log(75)
Divide both sides by log(3) to isolate "2x ":
(2x * log (3)) /(log(3))= (log(75))/(log(3))
2x=(log(75))/(log(3))
Multiply both sides by 1/2 to isolate x:
(1/2)*2x=(log(75))/(log(3))*(1/2)
Note: You will get the same result when you divide both sides by 2.
The equation becomes:
x=(log(75))/(2log(3))
x~~1.965    Rounded off to three decimal places
 
To check, plug-in x=1.965 in 3^(2x)=75 :
3^(2*1.965)=?75
3^(3.93)=?75
75.0043637 ~~75  TRUE
 
Conclusion: x~~1.965 is the final answer.

The protagonist in "The White Heron" changed in the resolution of the story. Describe her in the exposition and resolution to show the change. Describe the change in two to three sentences and use quotations from the story to support your answer. I know in the beginning she was described as being young, scared of people, and likened to a wretched geranium, which is in the exposition. In the resolution, she shows she has grown from a girl to a young lady. She decided that she would put nature ahead of "the money" and "the hunter," which shows maturity. But I can't seem to tie them together correctly to answer the teacher's question.

In Sarah Orne Jewett's short story "The White Heron," the protagonist, Sylvia, changes from a vulnerable young girl seeking approval to a strong person who knows that nature is more valuable than money. Passing over the temporary pleasures of money or momentary kindness from the hunter, she protects the white heron, as she feels that the birds and the natural world they come from are far more valuable. In a short time, she has grown from being a shy girl to one who can stand up for what she believes in.
Here are some quotes to explain Sylvia's transformation. At the beginning of the story, in the exposition, she has just begun to flourish in the Maine countryside. Sylvia "had tried to grow for eight years in a crowded manufacturing town," but it is not until she comes to live on the Maine farm with her grandmother that she can truly develop physically and emotionally. To Sylvia herself, "it seemed as if she never had been alive" before she moved to the farm, where she is immersed in the world of nature and its delights, such as finding the lost cow in the huckleberry bushes. She also has seen the white heron: "She knew that strange white bird, and had once stolen softly near where it stood in some bright green swamp grass." She is alert to the wonders of nature, including the majestic white heron. Her grandmother, old Mrs. Tilley, understands how much Sylvia has grown since coming to the country, and she "thought often with wistful compassion of a wretched geranium that belonged to a town neighbor." The geranium is a flower that wilts in the town but thrives in the countryside, so it is a symbol for Sylvia. However, at the beginning of the story, Sylvia is so shy that she can barely speak to the handsome hunter who comes to her grandmother's house. 
In the resolution of the story, Sylvia climbs a pine tree and observes the wonders of nature. She is described as one with nature; as she climbs the tree, her "face was like a pale star." She has become something magical and a part of the natural world. Though she sees the heron and knows where it is, and though she wants the approval of the sympathetic hunter and the money he offers to her and her poor grandmother, she refuses to tell him where the bird is. All at once, the mysteries of nature come to her:

"The murmur of the pine's green branches is in her ears, she remembers how the white heron came flying through the golden air and how they watched the sea and the morning together, and Sylvia cannot speak."

The majesty of nature has won her over, and she knows that it's more powerful than the money or approval the hunter can offer her. She has gone from being a shy child to one who knows what she stands for and refuses to tell adults where the white heron is hiding.

Why were the Americans justified in fighting the British?

The Americans were justified in fighting the British. There are several reasons why this is true. One reason was that the British began to violate the rights of the colonists. When the British passed the Stamp Act and the Townshend Acts, the colonists didn’t have representatives in Parliament that could speak about and vote on these taxes. This is a right all British citizens have. However, the Parliament still passed these laws without the colonists having representation in Parliament.
The colonists were concerned that the British were trying to control them. The Proclamation of 1763 restricted the colonists from moving to the new lands that the British had gained from France in the French and Indian War. The British also required the colonists to provide housing for the British troops that were enforcing this unpopular law.
Eventually, events became more violent. Five colonists were killed in the Boston Massacre in March 1770. When the colonists destroyed the tea that was on the ships in Boston Harbor by throwing the tea into the harbor, the British responded with the Intolerable Acts. The Intolerable Acts were designed to punish the colonists, mainly those in Massachusetts, for the Boston Tea Party. The colonists began to form their own militias. When the British marched to Lexington and to Concord in April 1775, fighting occurred with both sides suffering casualties. After this event, many colonists believed it was only a matter of time before they would declare their independence from Great Britain. This would lead to the Revolutionary War.
The colonists were justified in fighting the British.
https://www.revolutionary-war.net/causes-of-the-american-revolution.html

What smashes into Piggy and kills him?

Piggy is crushed by a boulder shoved by Roger down the mountainside. Ralph manages to dodge the massive rock, but Piggy is not as lucky. The rock crushes Piggy and throws him off the mountainside. He lands on the rocky surface below and dies.
Ralph, Piggy, Sam, and Eric go to Jack’s camp to recover Piggy’s glasses that had been taken by Jack’s group. When they arrive, they meet guards at the camp. Shortly after, Jack and the hunters show up with a dead pig. A confrontation ensues between Ralph and Jack. Ralph tries to reason with Jack to give them back the glasses so that they could reinstate the signal fire. However, Jack calls for the capture of Sam and Eric. A fight ensues between Ralph and Jack. Piggy tries to speak, but Roger shoves the boulder, which kills him.

Why does Lena hate birds?

Boesman and Lena are forced to wander from place to place after their home has been bulldozed—a common practice in apartheid-era South Africa. Their enforced wanderings constitute a parody of the freedom enjoyed by birds: like birds, they can wander, but they cannot settle down in one place for any length of time.
That's why Lena resents the birds for possessing the freedom that, as a woman of color in South Africa, she is routinely denied. If a bird's nest is destroyed, it can always be rebuilt elsewhere. But Lena and Boesman can't do the same with their ruined shacks. The racist apartheid state dictates where they can and can't live, while the birds remain proverbially free to go wherever they like. The very presence of the birds acts upon Lena as a constant reminder of her complete lack of freedom. It's almost like the birds are taunting her as they fly overhead. Lena's hardscrabble existence is resolutely earthbound, but the birds have the freedom to soar high into the sky. It's little wonder, then, that Lena hates them so much.

Athol Fugard's Boesman and Lena is centered on a "coloured" couple living in South Africa during the era of Apartheid. The play was first performed in South Africa in 1969.
Near the beginning of act 1, we come to a brief moment where the stage directions describe Lena watching and yelling at a bird flying slowly out of her view. 
Essentially, Lena does not like birds because she is jealous of them, because they have a freedom that she does not. Birds can fly away, while she and Boesman have to stay on the ground, "in the mud." Lena cannot even choose where to stay on the ground. She and Boesman have to move from place to place, as white men keep bulldozing the shantytowns where homeless "coloured" people live, telling them to "Clear out!" She feels that the place they have come to is "rotten," but for now she has no choice but to stay there.

In Maniac Magee, what is the relationship between Maniac and Grayson?

As the other educator points out, Maniac and Grayson share a father-son relationship. Grayson is also a mentor and a male role model to Maniac.
When Maniac discovers that Grayson played in the Minor Leagues, he is impressed. The young orphan is even more impressed when he learns that Grayson played as a pitcher. The knowledge that Grayson played in such a pivotal position completely changes Maniac's perspectives about his mentor.
Suddenly, Grayson is no longer just a park maintenance man and someone who lives at the YMCA. Before Grayson knows it, Maniac is begging for stories about his time in the Minors. Grayson begins by telling Maniac how he got his start playing for the Bluefield Bullets in West Virginia.
Maniac is fascinated when he learns that Grayson ended up washing dishes at a restaurant on his first day in Bluefield. Apparently, a gas station attendant played a joke on Grayson. He told Grayson that every rookie got a free meal at the Blue Star restaurant. Upon hearing this, Grayson went over and ordered a sixteen-ounce steak, half a broiled chicken, and two pieces of rhubarb pie. Grayson relates how shocked he was to discover that he'd been played. Accordingly, Grayson eventually spent the day washing dishes to pay for his "free" meal at the Blue Star restaurant.
To hear more about Grayson's early experiences about playing in the Minors, Maniac tags along when the old man goes to work. The young orphan helps Grayson raise a new fence around the children's petting yard. When the park supervisor comes around, Grayson tells him that Maniac is his nephew.
The text tells us that Maniac follows Grayson to work every day after this first collaboration between them. In due time, Maniac can be found working with Grayson at many park tasks. These include mending fences, trimming trees, and patching asphalt. The two also eat all their meals together and spend every day together.
So, the relationship between Maniac and Grayson is one between a mentor and his mentee. Grayson also doubles as a role model and father figure to Maniac. Above all this, Maniac and Grayson are good friends.

A standard way to answer this question is going to say that the relationship between Maniac and Grayson is a father and son type relationship.  Maniac has run away from home, and he is searching for some kind of family.  Grayson, for a short time, fills that role.  He takes Maniac in and acts as a supporting father should.  At times Grayson is a caretaker, and other times Grayson is a friend to Maniac.  Maniac in turn sees Grayson as an authority figure.  Additionally, Maniac sees Grayson as a source of fatherly wisdom about life in general.  
The relationship does change at one point though to become a teacher and student relationship.  That occurs when Maniac decides to teach Grayson how to read.  I believe that Grayson and Maniac are practically made for each other, which is why it is so sad that Grayson dies.  

Questions about Dystopia: Please answer the followings questions about Bradbury’s “The Veldt”: 1. What makes this story Dystopian? How is this world different from our own? How is it similar? 2. What type of Dystopia is this story: Ecological, Economic, Political, Spiritual, or Science/Technology? Explain. 3. How are people in the story different from us? How are people in the story similar to us? 4. How is language shaped or warped by the world in which it is practiced? Questions about Bradbury’s “The Pedestrian”: 1. What makes this story Dystopian? How is this world different from our own? How is it similar? 2. What type of Dystopia is this story: Ecological, Economic, Political, Spiritual, or Science/Technology? Explain. 3. How are people in the story different from us? How are people in the story similar to us? 4. How are people categorized or represented? Please number your answer and use 1 more detail or quote from the story for each answer.

1. "The Veldt" is dystopian in that the technology that is supposed to bring the Hadley family happiness only brings them misery and, for the parents, death. The world is different from our own in that the technology the house offers—the extent to which it cares for the family—is more advanced than our own:




They walked down the hall of their soundproofed Happylife Home, which had costthem thirty thousand dollars installed, this house which clothed and fed and rocked them to sleep and played and sang and was good to them.

Mostly, however, this seems to be a middle-class suburban world still very familiar to how many live in the United States.



2. The story depicts a science/technology dystopia. Instead of serving people, the technology of the house harms people. It has taken control of their lives and sets the children against the parents:




“That’s just it. I feel like I don’t belong here. The house is wife and mother now, and nursemaid. Can I compete with an African veldt? Can I give a bath and scrub the children as efficiently or quickly as the automatic scrub bath can? I cannot. And it isn’t just me. It’s you. You’ve been awfully nervous lately.”




3. The people are different in reflecting a 1950s ethos. For example, Mrs. Hadley expects to find her fulfillment through being a homemaker. Like us, however, people believe material goods will bring them happiness. Similar us, too, the Hadley turn to a mental health professional for guidance on dealing with their children. The psychologist says:




My advice to you is to have the whole damn room torn down and your children brought to me every day during the next year for treatment.




4. Concepts of "happiness" in this world are defined solely in terms of material and technological well-being. Happiness is having everything done for you. Happiness, people are told, can be purchased for a price. The Hadley realize too late that happiness is primarily a spiritual state.
1. In "The Pedestrian" people have become so divorced from the natural world and so wedded to technology that Leonard Mead is arrested for taking a walk. This world is different from ours in that walking is treated as social deviancy. For deviating from social norms, Mr. Mead is taken to "the Psychiatric Center for Research on Regressive Tendencies." In other words, he is being treated as insane for walking, as well as for not having a viewing screen and not being married. Today, we are more tolerant of difference. However, this world is like ours in that people tend to be more divorced from nature than previous generations.
2. "The Pedestrian" is another technological dystopia. Technology has displaced nature as the center of people's lives, and it dictates that people behave in rigidly conformist ways. It is also a political dystopia: the police enforce conformity. When Mr. Mead walks, he is arrested:




A metallic voice called to him:
"Stand still. Stay where you are! Don't move!"
He halted.
"Put up your hands!"




3. As mentioned, people in this story seem to be much more conformist than we are. They are like us in that we are also wedded to our technology and more likely to be watching a scene of nature on our screens than out in nature. Bradbury calls their homes "tombs:'




The tombs, ill-lit by television light, where the people sat like the dead, the gray or multicolored lights touching their faces, but never really touching them.




4. People are categorized as either normal and sane if they conform to the culture or as potentially insane if they don't.

I need examples of Romeo's love among his friends and himself.

Romeo enjoys a lot of love within his group of friends; Mercutio is one of his closest friends, and Benvolio is another good friend, and both characters show their love and loyalty to Romeo during a particularly tense moment in the play, when Romeo and Tybalt have a confrontation.
One example of Mercutio's love for Romeo is when Mercutio decides to take on Tybalt, of the Capulets, in a fight. Romeo's honor is compromised when he refuses to fight Tybalt, so Mercutio steps in instead to preserve Romeo's good name. Mercutio dies in the fight with Tybalt, giving his life for his friend's benefit.
Benvolio shows his love for Romeo when Mercutio dies, and Romeo impulsively decides to avenge Mercutio's death by killing Tybalt. Benvolio seems to be a voice of reason for Romeo, encouraging Romeo to go away to save himself, rather than stay and face the consequences of Romeo's impetuousness. Benvolio puts Romeo's interests ahead of anyone else's at this point in the play, showing his concern for Romeo's well-being.

Why is breaking down cultural barriers a valid theme for Alexie's "Superman and Me" essay?

In Sherman Alexie's touching essay "Superman And Me," the writer discusses the idea of the "smart Indian." The essay revolves around Alexie's perception that people expected him and other members of his culture to be uneducated and unintelligent. Alexie writes, "They wanted me to stay quiet when the non-Indian teacher asked for answers, for volunteers, for help. We were Indian children who were expected to be stupid." Nonetheless, regardless of these expectations, he strove to succeed in his academic pursuits; in school, he studied hard, he learned very much, and he became a renowned writer. Starting with a simple Superman comic, Alexie learned to read in his youth.
The essay is very much about the breaking down of cultural barriers primarily because of the expectations set up by both Natives and non-Natives alike. The expectation from all directions was for Alexie, and Natives in general, to struggle with the traditional academia that many white students could easily thrive in.
Alexie broke down these cultural barriers through his success as a student and, eventually, as a novelist. Determined not to be oppressed, broken down, or held back by others due to his race, Alexie read many books and eventually formed a unique and powerful literary voice that is studied in classrooms across the country.

As Alexie notes in the essay, his fellow classmates on the reservation "wanted me to stay quiet" when it came to questions posed by the teacher. He goes on to say, "We were Indian children who were expected to be stupid." Being interested in books and wanting to engage in literary discussions made Alexie a social outlier among his peers. But, Alexie takes pains to underscore that his classmates' antipathy toward literacy was context specific: they didn't like displays of ability in the classroom but were, say, talented storytellers around the dinner table, or they'd be submissive toward their teachers but would "slug it out with the Indian bully who was 10 years older." What emerges here is that his peers were highly capable in a multitude of ways not always seen by the outside "white" world. So, Alexie challenges cultural barriers from both sides: he refuses to conform to what others would have him be on the reservation, but so too does he seek to overturn notions that Native students on the reservation weren't impressive in their own right.

Alexie declares "a smart Indian is a dangerous person, widely feared and ridiculed by Indians and non-Indians alike" to explain why, in his opinion, the Indians he lived with on the Spokane Reservation did not value formal education in the reservation schools. Alexie recognizes that his peers had plenty of intelligence, citing the complexity of their stories, songs, and jokes, but that they did not want to display it.  
Alexie's family was different: they provided a home rich in books, and as he grew up, he sought out anything with text: auto repair manuals, cereal boxes, and books from the library and secondhand shops. He realizes his attitude is different from other Indians he knew, writing "I refused to fail. I was smart. I was arrogant."
Near the end of his essay, Alexie observes that in today's reservation schools, he sees two kinds of Indian students: voracious readers who write their own poems, stories, and novels and "sullen and already defeated Indian kids who sit in the back rows. . . the pages of their notebooks are empty. They carry neither pencil nor pen."
Alexie broke through cultural barriers—the pervasive culture of low expectations—to embrace education and the life of a writer, and in this essay he writes of his intention to keep visiting schools and trying to inspire Indian students because he is "trying to save our lives.

When and why did Eliezer begin to hate the Hungarian police?

When German troops entered Hungary in the spring of 1944, the Hungarian police immediately began to cooperate with them and to carry out measures against the Jewish population in accordance with the Nazi agenda. It is first the Hungarian police who burst into Jewish homes and confiscate gold and other valuables and to give the order that Jews must wear the "yellow star." The Hungarians behave brutally, striking people with rifle butts and truncheons. One of the police inspectors apparently tries to help the Wiesels because he's a friend of Eliezer's father, but nothing comes of the attempt.
The Jewish population of Hungary were taken aback by the complete subservience of the Hungarians to the Nazis. At least subconsciously among Jewish people, the expectation was probably that because Hungary had been an independent country since the end of World War I, there was no reason for Hungarians to follow the orders of the Germans, and especially to do it so enthusiastically.

The Hungarian police prove themselves to be willing participants in the Nazis' campaign of genocide against the Jews. When it is time to evacuate the ghetto, they act with appalling brutality, forcing the Jews out with clubs and rifles and screaming abuse at them. Elie hates them for this, not least because these are his friends and neighbors who are being rounded up and treated so badly. The Jews are going to be sent to the camps, so it is a traumatic experience for everyone. However, the situation is made even worse by the thuggish behavior of the Hungarian policemen. The police are supposed to uphold law and order, yet here they are, actively participating in a monumental crime against humanity. For Elie, the Hungarian police are the face of evil, his first oppressors, and he hates them for it.

Is Hard Times a realist novel?

Hard Times was one of Charles Dickens's shorter works and was actually written with the intention of garnering more sales for his other works. It, like most of his other novels, takes a hard, often harsh, look at society and the living conditions of the people of Britain. As to whether it can be classified as a "realist" novel, there are two ways of looking at this.
The first way is to take in the fact that one of the main characters, Thomas Grandgrind, looks at life with no sympathy, and no rose-colored glasses, whatsoever. He teaches his children, Louisa and Tom, to be "settlers": people who just take what they can get and never try to achieve their dreams, or want for anything more than what is available to them at the moment. As a result of this, Louisa marries a man much older than her that she doesn't love (and eventually cheats on), and her brother Tom convinces her to do it so that he can benefit from the financial stability the older man provides. This way of thinking that life is what it is and there is no point in trying to change anything could be argued to be "realist." A realist just sees what is in front of them and decides to deal with it, without expecting or hoping anything will change or trying to see things in a different light.
The second way of looking at this story, though, is to think of it as less of a realist novel, and more of an exaggeration. By focusing on these harsh times in a work that was also written to criticize the social and economic changes brought about by the Industrial Revolution (which Dickens did not support), the author is perhaps making things look bleaker than they really are in order to drum up support from his readers. So, perhaps in a way the novel is a realist one, but its readers must ask themselves, is it realistic?

What did Grandpa do that made Billy feel proud in Chapter 15?

In chapter 15 of Where the Red Fern Grows, Billy, Papa, and Grandpa are on their way to the campground when they decide to stop for the night. While they’re waiting for supper to be ready, Grandpa suggests that Billy feed his dogs some corned-beef hash. Grandpa soon learns that Old Dan will only eat his food when Little Ann has been given her share. Grandpa is amazed by Billy’s dogs and comments that he’s “always felt like there was something strange about those dogs.” He notices that the dogs are always watching Billy.
As they’re preparing to eat, Grandpa does something that causes Billy to feel a sense of pride. As Grandpa pours the coffee, he pours a third cup for Billy. Billy feels like he is one of the men, noting that his head “swelled up as big as a number-four washtub.” He knows that Grandpa must also feel proud about how well Billy has done with his dogs.

What is the meaning of the "The Lazy Mist" by Robert Burns? How can I analyze it?

The main theme in "The Lazy Mist" is the ephemeral quality of life.
In the poem, the narrator's attention is drawn to the "lazy mist" and how it heralds a change in season. He decides that the mist reminds him of the stealthy advance of "Autumn to Winter." 
More than anything, the narrator laments that the "forests are leafless, the meadows are brown, and all the gay foppery of Summer is flown." The seasons are capitalized, demonstrating their importance as markers of time for the narrator. Essentially, the passing seasons are metaphorical for the swift advance of the narrator's years on earth.
The narrator tries to remove himself from the phenomenon of passing time ("Apart let me wander, apart let me muse"), but his efforts are in vain. Time flies by quickly, pursued by Fate. The narrator laments that he may have lived his life in vain, and he grieves that so little time is left to him on earth ("How little of life's scanty span may remain"). 
However, he is helpless to change the fact that everyone must die. The narrator anguishes over the fact that Fate (which appears to hasten death) will rob him of the progress he has made in life and the connections he has formed during his years on earth. He laments the futility of a life that amounts to such loss and argues that, if life is to be worth living, man must have something beyond his existence on earth.

How foolish, or worse, till our summit is gain'd!And downward, how weaken'd, how darken'd, how pain'd!Life is not worth having with all it can give,For something beyond it poor man sure must live.

In This Is What It Means to Say Phoenix, Arizona, why can Victor be described as a realist, while Thomas can be described as a dreamer?

Without question, there are character differences between Victor and Thomas-Builds-the-Fire.
Thomas maintains more of his Indian identity than Victor does.
Thomas-Builds-the-Fire lives on the reservation, and he tells stories; he also speaks of dreams, employs Indian phrases, and invokes legends. He seems to know things without having been told anything.
The young men cannot be warriors because, as Thomas says, "All the horses were gone;" that is, they are confined to a reservation, and there are no people against whom they can demonstrate their warrior spirit and skills.  Nevertheless, Thomas-Builds-the-Fire does not surrender to these deterrents as does Victor. For Thomas speaks of dreams; he believes in the power of dreams. When Victor's father runs off, Thomas goes to Victor and tells him in the heartfelt language of dreams,

"I heard it on the wind. I heard it from the birds. I felt it in the sunlight." Only then does he admit, "Your mother was just in here crying." 

This Indian spirit and a deep feeling for his father is lost to Victor. After they reach Phoenix, Thomas tries to rekindle it in Victor by asking him if there is anything valuable in the man's trailer. "I thought his money was in the bank," Victor replies, demonstrating his rationality. Thomas explains, "It is. I was talking about pictures and letters and stuff like that."  
Thomas extends his love and understanding toward Victor despite their no longer being friends. Victor, in turn, begins to appreciate Thomas and promises to listen to one of his stories.
As Victor sits at his kitchen table, realizing that he does not have enough money to travel to Phoenix to pick up his father's remains, Thomas-Builds-the-Fire appears at the door, saying "Ya-hey, Victor . . . I knew you'd call me." He offers to pay for the flight to Phoenix, but only on the condition that he accompany Victor.
While they travel, Thomas tells Victor of the dream he once had that led him to Spokane; he hopes that this retelling will give Victor more understanding of his father. Thomas begins by saying that his dream told him to wait for a sign. As he waited at a falls, Victor's father approached Thomas. The man asked him what he was doing there, warning him that he could get mugged. So, Victor's father buys Thomas dinner and drives him back to the reservation. After this account, Thomas tells Victor, "For a long time, I was mad because I thought my dreams had lied to me. But they hadn't. Your dad was my vision."
Once they return to the reservation, Thomas-Builds-the-Fire asks Victor only one favor. He asks Victor if he will just once stop and listen when he tells a story. Victor agrees to do so; then, Victor turns his truck toward home. Thomas closes his door and hears a new story coming to him.

How can Gulliver's Travels by Jonathan Swift be related to George I?

The Emperor of Lilliput is a satirical version of King George I. The Lilliputian emperor's preference for people who wear low heels symbolizes his favoring of the Whig party, which preferred what was referred to as the "low church" (the church stripped of Catholic elements). The high heels that the king does not favor are representative of the opposition party in England at the time, the Tories, who favored the "high church," the Church of England. Candidates for public office in Lilliput must literally carry out an elaborate rope dance, which they are trained for since birth. The rope dance symbolizes the way in which people in the royal court in England had to curry favor with the king to gain favor or office. 
The Emperor of Lilliput is also convinced of his own grandness. He is described as a sovereign "whose dominions extend five thousand blustrugs (about twelve miles in circumference) to the extremities of the globe." In this sense, the emperor is similar to the king of England, whose powerful navy extended his country's reach to different parts of the globe.

Swift's Lilliput is a satirization of England at the time of his writing (1725-6). Therefore, it follows that the Lilliputian emperor is a satirical representation of the King of England at that time, George I, and that the two political factions in Lilliput, the Tramecksans and the Slamecksans, represent the two main political parties in England, the Tories and the Whigs, respectively. The Tramecksans wear only high heels on their shoes—a reference to the Tories, the conservative party in England that favored the Catholic influence in the Church of England (the “high church”). On the other hand, the low-heel Slamecksans are a reference to the the low-church (pro-Protestant) supporting Whigs. Like George I, who was strongly pro-Whig, the Lilliputian emperor only appoints Slamecksans to important government posts; also like George I, the emperor is obsessed with destroying neighboring Blefuscu, a reference to England’s war with France over Spanish territories in the War of Spanish Succession (1701-1714).

The emperor of Lilliput is representative of George I, the king on the throne when Gulliver's Travels was published.  The pro-Whig George I persecuted the High Church Tories.  When Gulliver details the conflict between the two warring parties in Lilliput, the Tramecksans and Slamecksans, those who wear high heels and low heels on their shoes, respectively, Swift is satirizing the conflict between the Tories and Whigs, respectively.  He says that the emperor has determined to "make use of only low Heels" in his administration, and this parallels King George's favor of the Low Church Whig party.  The Whigs were the more liberal party; the Tories more conservative. 
Further, the Lilliputian emperor is highly susceptible to influence and manipulations by his administration's ministers, and this parallels the belief that George I was too easily influenced by those people that he trusted (and, perhaps, that those people were not altogether reliable). 

Opposition to anything that oppresses the human spirit dominates Songs of Innocence and Songs of Experience. To what extent do you agree?

Blake wrote at a time when the European and American worlds were being transformed through war and revolution. He was an 18th-century progressive, his circle including the reformers William Godwin, Mary Wollstonecraft, and Thomas Paine, so it is not surprising that in his own writings he empathized with the weak and oppressed.
In Songs of Innocence the poem "The Chimney Sweeper" is a criticism of the exploitation of children on both the societal and individual level: "....my father sold me while yet my tongue / Could scarcely cry 'weep, 'weep, 'weep, 'weep.'" Both the child and the parents are oppressed victims of society: the general conditions of poverty in which the English working class lived have evidently caused the mother's death and the father's need to "sell" the child, now forced to work as a chimney sweep. (In a later time the same thought is expressed in the melancholy song of the Chimney Sweep in Mary Poppins, where he ironically sings that a "chimney sweep's lucky as lucky can be.")
A more subtle and ambiguous example in Songs of Innocence is in "Holy Thursday." Blake's attitude to religion was complex and, by conservative standards, rather heretical. The children in this poem are described in a way that suggests cattle being marched to the slaughter, as they are led by "grey-headed beadles." Blake was anti-clerical and believed in a new, radical form of Christianity, as opposed to that of the Established Church. In Songs of Experience the corresponding "Holy Thursday" poem makes the implied radicalism of the earlier poem explicit, with its reference to "Babes reduced to misery, / Fed with cold and usurous hand." And of course, the same is true of the corresponding Chimney Sweeper poem in the Experience cycle, with the child crying in its "notes of woe," while the mother and father are "gone up to the church to pray," the Church again representing the Establishment which seemingly neglects the poor and oppressed in order to serve the rich.
One can say these are critiques of material, rather than spiritual, oppression, but in Blake the two forms are mirror images of each other. "The Garden of Love," though not as famous as "The Tyger" and several of the other poems, is perhaps the one poem in which Blake's various themes are brought together: "The gates of this Chapel were shut," and "priests in black gowns were walking their rounds / And binding with briars my joys and desires." This is not simply a criticism of the religious system for taking little heed of the poor. It gets to the heart of Blake's view that religion stifles the inner (spiritual) needs of people by essentially teaching that joy and happiness should be denied to them, and that they should feel guilty about experiencing them. And in "The Tyger," the animal itself represents a primal force of nature and desire which cannot be denied, though Blake is ambivalent about it. In the verse "When the stars threw down their spears / And watered heaven with their tears," the suggestion is that God, or heaven, regretted the creation of this force and the negative factors it carries with it. The poem "London," in which the speaker notes the "marks of weakness, marks of woe" throughout the city, is a kind of culmination of Blake's awareness of and sympathy for both the materially and spiritually deprived in society.
Blake's work is replete with contradictions, above all the fact that he was religious but anti-church; these examples overall show that an overriding concern was his sympathy for the weak and dispossessed in the world.

How could I go about writing a monologue about a character from The Crucible?

One way to write an effective monologue based off of a character in The Crucible is to choose a complex character and explore the depth of their experience.
One complex character is Abigail.  She plays such an important role in the drama's development.  She is the reason why the trials reach such a fevered pitch.  She initiated many of the accusations and stirred the emotionally contagious pot that Salem became.  However, she simply disappears at drama's end.  We really have no idea what has become of her.  It might be very interesting to write about Abigail's life once she leaves Salem.  A monologue that talks about what she experienced, whether she still thinks of Salem and John Proctor, or even what she hoped to gain out of leaving Salem could be very effective.  It would delve into the thoughts and motivations of one of the drama's most important characters.
Another topic for an emotionally intense monologue would be Giles Corey.  He occupied such an important role in Act III.  His legal challenge to Danforth and Hathorne was significant to the drama.  He is hauled off to jail and the only information we have about him comes from Elizabeth when she talks about his death.  It might be unique to get into his mind while he is in jail. He knows that he will refuse to speak.  Exploring the motivations behind his silence might be very persuasive.  The monologue could even take place as he is sentenced.  It could examine his thoughts as the stones are added upon him.  There could be a delving into the physical pain he experiences as well as his emotional resolve to continue with it.  His cry of "More weight" is synonymous with resistance in the face of intense pressure.  Entering into this mindset might be very worthwhile in monologue form.
You can select any character from Miller's drama for an effective monologue. The idea would be to enter their mind and explore what they might have felt and experienced as a result of the emotionally draining witch trials. 

What are the specialties of the dog Eel?

Eel is one of the two dogs that like to hang around Vanka’s grandfather, Konstantin Makarich. The other dog is called Kashtanka. The text describes Eel as a black dog with a “long weasel-like body.” He appears highly respectful of the people around him yet is actually “spiteful and malicious.” He is a specialized thief, quick at stealing all sorts of things, and is continually hunted down and beaten for this. He has been badly hurt by the beatings that he receives for his crimes, yet he is unable to turn a new life. He always survives the injuries he gets from his daily transgressions, and one wonders at his ability to brave it all. His other specialties are “snapping at people’s feet, creeping into the ice-house," or stealing chicken belonging to the neighbors. Eel is a sly dog who, it seems, likes adventures, no matter how risky they are.
Eel’s master, Konstantin, is a nice man of about sixty-five years of age. He has a bubbly personality and is always smiling or talking cheerfully with his fellow workers at Zhivarev’s estate. He seems to like his dogs. They follow him around the estate in the night while he is attending to his duties as the estate watchman.

A strong underlying force in this film is the relationship between Amir and Hassan. Discuss their friendship. Why is Amir afraid to be Hassan's true friend and why does he constantly test Hassan's loyalty? Also, why does Amir resent Hassan? After the kite running tournament, why does Amir no longer want to be Hassan's friend?

Amir and Hassan have a deeply complicated and tragic relationship. In all honesty, it's very hard to characterize it as a "friendship" past a certain moment in time, and that point is far before the horrific day that ultimately breaks everything.
Kids aren't born into the world with prejudices. They pick them up from their parents, their friends, the society around them, and so on. It seems to have been the same way with Amir and Hassan—when they were young and more or less in the dark about all the things that would become problems later, they genuinely were friends and liked each other. The moment things truly went awry was when both boys started to become aware of the fact that the world didn't think the two of them were as similar as they thought. Amir was a Pashtun, the son of a wealthy man, and Hassan was a Hazara. Both he and his father were servants of Amir's family. Now, it's probably unlikely that there was a time when they didn't know there was a social class between them, but it wasn't initially as big of an issue as it was later.
As the boys both start realizing how the world around them worked, the relationship between them changes completely. Amir starts feeling pressure not to develop a close friendship with a Hazara, and Hassan feels that he should keep in his own place and be more of a squire than a friend to Amir. The difference between the two comes from how they handled that situation; this also provides the answer to the question of Amir's resentment.
In addition to coming from different backgrounds, the boys are actually not that alike as people, either. Hassan has a good heart and a strong sense of loyalty, while Amir proves to be a cowardly, petty person. Amir dislikes the fact that Hassan is actually better than him—as a person and as a kite runner—but he is also painfully aware of how true it is. In a situation like that, a person can go two ways: they can try to be better, or they can try to make the other person worse. Amir keeps testing Hassan, becoming mean toward him, but Hassan remains who he is. That only infuriates Amir further and feeds the bitterness in his heart. Amir's father's affection toward Hassan only adds to that.
After the kite tournament, where Amir witnesses Hassan getting raped by some bullies and doesn't intervene (because of his own fear), the friendship between them is utterly lost. Hassan figures out that Amir saw and didn't help him, but he can't confront Amir about this. Instead, he becomes even more silent and reserved than before, heartbroken to find out that Amir wasn't a good friend to him when he needed him the most. Amir, in turn, starts to resent Hassan even more because of how badly he hates himself for letting it happen. This leads to Amir sinking even further, falsely accusing Hassan of a robbery and letting his friend take the blame.
The rest of the story concerns Amir's guilt and, ultimately, his attempts to make up for it, but even then the reader can see how his childhood fears hold him back from doing the right thing for Hassan's son for a long time. The Kite Runner is a powerful story of how artificial constructs like prejudice and class ruin people, how children carry their scars for the rest of their lives. The novel doesn't inspire much sympathy toward Amir, who could be called an anti-hero, but the truth is that he was born into an unjust and uncaring environment. He could have made different choices, could have stood up for Hassan, but we can't know if things would have been easier for them for it.

Amir and Hassan have a close relationship and enjoy playing together as children. They are essentially best friends, but Amir refuses to acknowledge this fact because Hassan is a Hazara and he is a Pashtun. It would be considered socially unacceptable for Amir to develop a mutual friendship with Hassan openly. Also, Amir is jealous of Hassan because Hassan is pure and talented. Amir continually tests Hassan's loyalty because he cannot comprehend how a person can be so loyal and morally upright. Amir also gets a kick out of teasing and playing tricks on Hassan. Amir resents Hassan because Hassan is the epitome of everything Amir is not. Hassan is athletic, naturally intelligent, and has a pure heart. While Baba ignores Amir, he admires Hassan, which is another reason Amir resents him. After the kite tournament, Amir witnesses Hassan getting raped and does not take action to stop Assef. Amir is filled with guilt because he did nothing to prevent Hassan from being raped. Amir can no longer be friends with Hassan because Hassan only reminds him of his cowardly decision to stand idly by and watch Hassan get raped.

How was Harriet Tubman fearless?

Harriet Tubman was a fearless woman. One reason why she was fearless was that she survived being a slave. She had endured horrible treatment, including having been beaten several times. She eventually escaped to freedom, leaving her entire family behind as she fled. Trying to escape to freedom was a very risky thing for a slave to do.
After she got her freedom in the North, she worked very hard to help other slaves, including her own family members, escape to freedom. She was actively involved in the Underground Railroad. She went back to the South a minimum of 19 times to help other slaves escape to freedom. There were offers of big rewards for her capture, but that didn’t stop her from taking the risk to help other slaves become free.
During the Civil War, Harriet Tubman worked with the North. She served as a nurse to help soldiers of all races. She also served as a spy and as a guide.
Harriet Tubman was clearly a very fearless woman.
https://www.history.com/topics/black-history/harriet-tubman

What is the cause of violence in Romeo and Juliet, act 3, scene 1?

Tybalt is the instigator in act three, scene one when he arrives on the scene and demands that Romeo draw his sword. Tybalt is portrayed as a hot-headed, belligerent man who champions honor and seeks revenge on Romeo for intruding on his uncle's ball. When Tybalt draws his sword on Romeo, Romeo attempts to ease his tensions by explaining that he loves Tybalt more than he knows.
Mercutio is unaware of Romeo's secret wedding to Juliet and comes to Romeo's defense by challenging Tybalt. Mercutio and Tybalt begin fighting, and Romeo throws himself between the two men to act as a human barrier. Tragically, Tybalt manages to fatally wound Mercutio, and Romeo responds by killing Tybalt, which results in his exile. Overall, Tybalt starts the fight in an attempt to get revenge on Romeo for intruding on his uncle's ball.

In Act 3, scene 1, Tybalt comes looking for Romeo to challenge him to fight because Tybalt is mightily offended that Romeo went to the Capulets' feast the night before.  If you'll recall, Tybalt pointed Romeo out to Lord Capulet, but Lord Capulet told Tybalt that he was not allowed to attack Romeo at the party, because it would ruin the festivities and upset the other guests.  Now, however, Tybalt wants to protect his family's honor by challenging Romeo.  
At first, Romeo refuses to fight because he has just married Juliet in secret, and so Tybalt is now actually his relative by marriage.  However, Mercutio thinks Romeo is behaving like a coward, and so he steps in to fight Tybalt instead.  Romeo comes between them to try to keep the peace, and Tybalt stabs Mercutio under Romeo's arm.  After Mercutio dies, having cursed both families, Romeo kills Tybalt and then flees.

How would you analyze the poem "Song" by Alun Lewis?

The poem “Song” was written by the Welsh poet Alum Lewis, who died in India during World War II.
The themes addressed in the seven stanza poem are love, loss, and ultimately, the acceptance of loss. The tone is melancholy and forlorn.
In the poem, which is spoken from the wife’s point of view, a young soldier leaves his wife to join the fight. His leaving makes her miserable enough to feel ill.  It is their hope that she is pregnant. Unfortunately, both are disappointed when she is not.

And where he's left his promise
Life did not turn or kick
The seed, the seed of love was sick.

In her grief, she misses him dearly, but the months of his absence pass until he dies in a shipwreck and is lost at sea. She explains that they never planned for life as it occurred but slowly, she learns to live without him and to accept her loss. The process of acceptance is slow and difficult but ultimately, it does happen.  
Each of the seven stanzas follows an ABCBB rhyming pattern, and contains vivid imagery and similes.

And my bed was like a grave
And his ghost was lying there.

The first stanza describes how the wife felt when her love left, and she discovered she was not carrying his child. The second stanza describes her grief and loneliness; while the third brings her to the realization his ship is lost at sea. In the fourth stanza, which corresponds with the fourth month of his absence, she imagines him to command her not to think of him in his permanent absence. In the fifth stanza, Lewis describes, with vivid sea life imagery, the soldier’s watery grave. Stanza six finds the wife lamenting life’s twists and turns, and it describes how the coral reef continues to grow while her husband lays dead in its midst. This is a metaphor for how life progresses even in the face of a loved one's death.  Finally, in the seventh stanza, as time passes, she, with great difficulty, comes to accept his loss.  

The turning seasons wither in my head;
All this slowness, all this hardness,
The nearness that is waiting in my bed,
The gradual self-effacement of the dead.

A group of protestors was arrested after they acted violently by burning the American flag and destroying public property. They claim their actions are protected by the First Amendment. Do you think their defense will be successful?

The First Amendment of the United States Constitution offers protections for certain types of speech and expression. Only some of the actions taken by the protesters fall under the protections of the First Amendment. Americans have the right to freedom of religion and freedom of expression that is free from government interference, provided those expressions do not violate any existing laws. The First Amendment allows the government to prohibit speech that causes a breach of the peace or results in violence. By destroying public property, the protesters clearly violated this aspect of the Constitution and their attempt to use the First Amendment as a defense will not likely be successful in this regard.
The Right to Assemble
The right to assemble is a primary component of the First Amendment, but it is often misunderstood. Americans have the right to gather together for "peaceful and lawful purposes." Any demonstration that results in violence or causes a breach of the public peace is not a protected form of protest. The government may also prohibit Americans from gathering in groups that are known to promote illegal activities.
Flag Desecration Law
The U. S. Supreme Court has determined that the Constitution's First Amendment does afford protesters the right to desecrate the American flag. It is believed that outlawing such practices, while they are generally regarded as offensive, would do greater damage to the country legally and ethically than allowing flag burning to take place. While Congress has attempted to pass anti-desecration laws on many occasions, it has not been successful at convincing the Supreme Court of the constitutionality of these laws. Burning the flag is considered an act of political expression and thus, as long as it is not accompanied by violence or other disorderly conduct, is not a criminal activity in itself. The protesters burned the flag in the process of illegal conduct, however, so they will not likely be successful in using the First Amendment to defend their actions.
Landmark Cases
The 1989 case of Texas v. Johnson began when Gregory Lee Johnson burned the American Flag in protest. He was arrested and charged with violating a Texas statute that covered the desecration of all venerated objects, including the nation's flag. Johnson appealed on the grounds that his actions were protected by the First Amendment, and the Supreme Court agreed. One year later, the United States v. Eichman case confirmed this ruling on a federal level.
While the protesters can successfully argue that their flag burning was protected under the First Amendment of the United States Constitution, the First Amendment does not protect their other actions. Violence, damaging public property, and disturbing the peace are criminal acts that are punishable by law, and protections for protesters only extend to peaceful and lawful assemblies.
https://www.law.cornell.edu/wex/first_amendment

https://www.uscourts.gov/educational-resources/educational-activities/facts-and-case-summary-texas-v-johnson

https://www.uscourts.gov/educational-resources/educational-activities/texas-v-johnson

Single Variable Calculus, Chapter 7, 7.3-2, Section 7.3-2, Problem 38

Differentiate $\displaystyle g (x) = \sqrt{x} e^x$


$
\begin{equation}
\begin{aligned}

g'(x) =& \frac{d}{dx} (\sqrt{x} e^x)
\\
\\
g'(x) =& \sqrt{x} \frac{d}{dx} (e^x) + (e^x) \frac{d}{dx} (\sqrt{x})
\\
\\
g'(x) =& (x)^{\frac{1}{2}} \frac{d}{dx} (e^x) + (e^x) \frac{d}{dx} (x)^{\frac{1}{2}}
\\
\\
g'(x) =& (x)^{\frac{1}{2}} e^x + (e^x) \left( \frac{1}{2} \right) (x)^{\frac{-1}{2}}
\\
\\
g'(x) =& x^{\frac{1}{2}} e^x + \frac{e^x}{2 \sqrt{x}}
\\
\\
g'(x) =& \sqrt{x} e^x + \frac{e^x}{2 \sqrt{x}}
\\
\\
& \text{or}
\\
\\
g'(x) =& \sqrt{x} e^x + \frac{e^x}{2 \sqrt{x}} \cdot \frac{\sqrt{x}}{\sqrt{x}}
\\
\\
g'(x) =& \sqrt{x} e^x + \frac{\sqrt{x} e^x}{2x}

\end{aligned}
\end{equation}
$

Is Gatsby blind to his pursuit of ambition?

Yes. In a way, Jay Gatsby is not aware of the dangers of becoming corrupted by the pursuit of attaining the American Dream. As a young, naive man, Gatsby is driven to become wealthy and enter the upper-class. Gatsby's ambition blinds his sense of right and wrong and motivates him to enter the illegal bootlegging industry, where he becomes business partners with Meyer Wolfsheim. Essentially, Gatsby believes that he will be able to buy his happiness, and ends up sacrificing his morals and identity. Gatsby then transforms himself into an aristocrat, who hails from a wealthy family. Gatsby's ambition to marry Daisy also blinds him into believing that he will be able to have a genuine relationship with her. Overall, Gatsby's ambition motivates him to sacrifice his morals, integrity, and identity in order to attain the American Dream.

Describe the socioeconomic and political environment in the thirteen colonies of New England.

The king of England chartered and appointed governors to the colonies of New England.  Despite the overarching authority established by England's parliamentary monarchy, pilgrims in the colonies did participate in their government without being fully democratic.  The Colonial Legislature was formed through the election of candidates by land owning males.  The Atlantic Ocean was a physical barrier between England and the colonies, giving pilgrims a greater perception of self-governance.  Eventually, in 1774, the colonies realized they had more leverage in negotiations with England if they worked together.  Thus, the Continental Congress was established.
The colonies were a valuable commodity in England's trade; many laws imposed by the king revolved around the colonies' roles as consumers and producers.  The Sugar Act of 1764 was a commodity taxation aimed at generating revenue for England.  The Tea Act of 1773 eliminated competition from the tea market in the colonies. Tea, rather than coffee, was consumed daily in most households. This act generated revenue for an English company called the British East India Tea Company. New England and England struggled to balance each others needs for autonomy and revenue within merchant trade. 
https://www.history.com/this-day-in-history/british-parliament-adopts-the-coercive-acts

https://www.masshist.org/revolution/sugar.php

How did the French relations with the Native Americans compare with those of Great Britain and Spain?

The French, British, and Spanish encountered the Native Americans when they established colonies in the Americas. However, only the French had a good relationship with the Native Americans.
The French treated the Native Americans well. They traded with them. They made it clear they didn’t want to take away their land. They also learned the languages of the Native American tribes. In addition, they married the Native Americans. There was respect between the French and the Native Americans.
The British and Spanish didn’t have a very good relationship with them. These countries wanted to take away the land of the Native Americans. The Spanish enslaved them and exploited their land for minerals. They also tried to convert them to Christianity. The Native Americans resented these actions. The British viewed the Native Americans as inferior. The British tried to impose their laws upon them. This also led to poor a relationship with them.
The French had a good relationship with the Native Americans because they treated them well, unlike the British or the Spanish.

Calculus: Early Transcendentals, Chapter 6, 6.1, Section 6.1, Problem 24

y=cos(x) , y=1-cos(x) ,0<=x<=pi
Refer the attached image, y=cos(x) is plotted in red color and y=1-cos(x) is plotted in blue color.
From the graph,
cos(x) is above (1-cos(x)) from 0 to pi/3 and
(1-cos(x)) is above cos(x) from pi/3 to pi.
Area of the region enclosed by the given curves A=int_0^(pi/3)(cos(x)-(1-cos(x)))dx+int_(pi/3)^pi((1-cos(x))-cos(x))dx
A=int_0^(pi/3)(2cos(x)-1)dx+int_(pi/3)^pi(1-2cos(x))dx
A=[2sin(x)-x]_0^(pi/3)+[x-2sin(x)]_(pi/3)^pi
A=((2sin(pi/3)-pi/3)-(2sin(0)-0))+(pi-2sin(pi)-(pi/3-2sin(pi/3))
A=(2*sqrt(3)/2-pi/3)+pi-pi/3+2*sqrt(3)/2
A=sqrt(3)-pi/3+pi-pi/3+sqrt(3)
A=pi/3+2sqrt(3)~~4.511

Suggest why triglycerides are more valuable to a small desert mammal as a food store than carbohydrates.

Based on the wording of the question, it appears that you can suggest multiple possible reasons as to why you think a small desert animal finds a greater benefit from triglycerides as energy storage than carbohydrates. One possible reason is a simple caloric benefit. A calorie is a unit of food energy. Carbohydrates offer 4 calories per gram of food; however, fats offer 9 calories per gram of food. Triglycerides are a type of fat, so an animal that uses them for its diet is getting nearly double the calorie intake and storage than it would be if it were eating mainly carbohydrate food sources. If food was plentiful, a high fat diet wouldn't be ideal; however, food sources are not plentiful in the desert. By focusing on higher fat diets, a small dessert mammal is better able to meet its caloric needs between longer fasting periods.
https://oli.cmu.edu/jcourse/webui/guest/activity.do?context=df3e40f50a0001dc60503ae4fb6d4193

What are a few quotes from To Kill a Mockingbird that go with the theme of bravery?

In Lee's To Kill a Mockingbird, the topic of bravery is explored in different ways with different characters. First, the children first view bravery as a thing to be demonstrated by facing terrifying situations and then overcoming them. For example, Dill challenges Jem's manhood by daring him to get Boo Radley to come out of the house. Then Dill modifies the challenge, which requires Jem only to touch Boo Radley's house instead of making the man come outside. Jem fulfills this mission with a quick run through the yard and back, but he does it because he "wanted Dill to know once and for all that he wasn't scared of anything" (14). In this case, bravery is a matter of honor as demonstrated by an act of courage.
However, Atticus shows what calm, cool, and collected bravery looks like when he shoots a mad dog in chapter 10 and saves the neighborhood. As a result, the kids want guns for Christmas, but they are confused when their father won't teach his own kids how to shoot them. The answer to their confusion comes in chapter 11 when Atticus teaches Jem what he believes bravery really is--and that it isn't found using guns. For Atticus, bravery is found in people like Mrs. Dubose who overcomes her addiction to morphine before she dies. Atticus explains as follows: 

"I wanted you to see what real courage is, instead of getting the idea that courage is a man with a gun in his hand. It's when you know you're licked before you begin but you begin anyway and you see it through no matter what. You rarely win, but sometimes you do. Mrs. Dubose won, all ninety-eight pounds of her. According to her views, she died beholden to nothing and nobody. She was the bravest person I ever knew" (112). 

This lesson from Atticus paints a different picture of bravery than what the children think. They discover that bravery is not about proving to others that a scary task can be accomplished; rather, it is facing fears or weaknesses and holding one's self accountable no matter what the outcome.
Finally, another example of bravery demonstrated in the novel is when Aunt Alexandra faces a room full of smug and self-righteous women after finding out that Tom Robinson has died while attempting to escape from prison. Moments before discovering the unfortunate news, these intolerant guests imply that Atticus defending a black man in court hurts the social status quo in Maycomb. It is overwhelming and intimidating for Aunt Alexandra to go back to her guests after discovering that Tom is dead. This fact may cause more problems in the community, and her "friends" might blame Atticus for it. Nevertheless, Aunt Alexandra must keep her head held high in the presence of these intolerant women. She must show them that she is strong, supports her brother's efforts, and is proud to be a Finch. Scout recognizes her aunt's personal resolve and courage by describing how Aunt Alexandra readies herself before facing her guests again:

"Aunt Alexandra rose and smoothed the various whalebone ridges along her hips. She took her handkerchief from her belt and wiped her nose. She patted her hair and said, 'Do I show it?'" (237).

This passage shows Aunt Alexandra preparing herself to be brave in front of the community's gossips. Scout is impressed and decides to follow Aunt Alexandra's example by saying, "After all, if Aunty could be a lady at a time like this, so could I" (237). In this situation, Aunt Alexandra and Scout show social bravery by going back out to their guests and holding their heads high. They could have stayed in the kitchen and cried over the situation, or lost their tempers by yelling at their guests, but they decide to face life with strength--even if that means acting like a lady and not crumbling down into tears like a little girl.

In Hemingway's "A Clean and Well Lighted Place," who are the protagonist and antagonist?

The protagonist is the older waiter. He is the character who embodies the story's overriding theme of existential angst in the face of nothingness. He is a world weary soul who's abandoned the certainties of faith and succumbed to despair. We see this in his parody of the Lord's Prayer, where he inserts the word nada (nothing) into various places.
But how to escape from this crushing sense of despair in a bleak and seemingly Godless universe? The cafe in which he works provides a place of refuge. It is "a clean, well-lighted place" where a sense of order and stability prevails. Yet this can only be a brief respite, and no more. At some point the older waiter will need to go home to bed, where he will be alone with this thoughts once more and also bitterly aware that he is all alone in the universe as he struggles to impose some meaning on an inherently meaningless existence. The futility of the attempt merely adds to his crushing sense of despair.
The younger waiter is the antagonist. His youthful naivety and ignorance of the ways of the world give him a radically different perspective from that of his older work colleague. He doesn't openly acknowledge the fundamental nothingness at the heart of life, but the valuation he puts on worldly goods shows that he is unknowingly seeking to avoid the question of his death by losing himself in endless distractions. Unlike the older waiter and the deaf old man, he has a wife. His marriage provides him with a link to the world of other selves, a world from which the other two men in the story have been almost completely cut off. In short, he appears to have something to live for. His world is indeed "clean and well-lighted."
The younger waiter cannot understand why someone as rich as the deaf old man would ever contemplate taking his own life. Nor can he begin to comprehend the cynicism and depression of the older waiter. But perhaps in the story's protagonist we can catch a glimpse of what the antagonist will become once his worldly attachments no longer constitute the "clean, well-lighted place" he thinks they do.

Single Variable Calculus, Chapter 4, 4.8, Section 4.8, Problem 18

Use Newton's Method to find all roots of $x^5 = 5x - 2$ correct to six decimal places.

We rewrite the equation in standard form

$x^5 - 5x + 2 = 0$

So we let $f(x) =x^5 - 5x + 2$, then


$
\begin{equation}
\begin{aligned}

f'(x) =& \frac{d}{dx} (x^5) - 5 \frac{d}{dx} (x) + \frac{d}{dx} (2)
\\
\\
f'(x) =& 5x^4 - 5

\end{aligned}
\end{equation}
$


Using Approximation Formula


$
\begin{equation}
\begin{aligned}

x_{n + 1} =& x_n - \frac{f(x_n)}{f'(x_n)}
\\
\\
x_{n + 1} =& x_n - \frac{x^5_n - 5x_n + 2}{5x^4_n - 5}

\end{aligned}
\end{equation}
$








To find the initial approximation, we graph $y = x^5$ and $y = 5x - 2$. Based from the graph, they have three intersection points in $x$-coordinate where they are very close to $-1.6, 0.4$ and $1.4$. So we have $x_1 = -1.6, x_1 = 0.4$ and $x_1 = 1.4$

So we get


$
\begin{equation}
\begin{aligned}

& x_2 = x_1 - \frac{x_1^5 - 5x_1 + 2}{5x^4_1 - 5}
&&
&&&
\\
\\
& x_2 = -1.6 - \frac{(-1.6)^5 - 5 (-1.6) + 2}{5 (-1.6)^4 - 5}
&& x_2 = 0.4 - \frac{(0.4)^5 - 5 (0.4) + 2}{5 (0.4)^4 - 5}
&&& x_2 = 1.4 - \frac{(1.4)^5 - 5 (1.4) + 2}{5 (1.4)^4 - 5}
\\
\\
& x_2 \approx -1.582506
&& x_2 \approx 0.402102
&&& x_2 \approx 1.373378
\\
\\
& x_3 = -1.582506 - \frac{f(-1.582506)}{f'(-1.582506)}
&& x_3 = 0.402102 - \frac{f(0.402102)}{f'(0.402102)}
&&& x_3 = 1.373378 - \frac{f(1.373378)}{f'(1.373378)}
\\
\\
& x_3 \approx -1.582036
&& x_3 \approx 0.402102
&&& x_3 \approx 1.371886
\\
\\
& x_4 = -1.582036 - \frac{f(-1.582036)}{f'(-1.582036)}
&&
&&& x_4 = 1.371886 - \frac{f(1.371886)}{f'(1.371886)}
\\
\\
& x_4 \approx -1.582036
&&
&&& x \approx 1.371882
\\
\\
&
&&
&&& x_5 = 1.371882 - \frac{f(1.371882)}{f'(1.371882)}
\\
\\
&
&&
&&& x_5 \approx 1.371882

\end{aligned}
\end{equation}
$


Therefore, the roots are $x \approx -1.582036, x \approx 0.402102$ and $x \approx 1.371882$

y = e^(-x^2/2)/sqrt(2pi) , y = 0 , x = 0 , x = 1 Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the y-axis.

Using the shell method we can find the volume of the solid generated by the given curves,
y = e^(-x^2/2)/sqrt(2pi), y = 0 , x = 0 , x = 1
 
Using the shell method the volume is given as
V= 2*pi int _a^b p(x) h(x) dx
where p(x) is the function of the average radius  =x
and
h(x) is the function of height =  e^(-x^2/2)/sqrt(2pi)
and the range of x is given as 0 to 1
So the volume is  = 2*pi int _a^b p(x) h(x) dx
= 2*pi int _0^1 (x) (e^(-x^2/2)/sqrt(2pi)) dx
=(2*pi)/(sqrt(2pi)) int _0^1 (x*e^(-x^2/2)) dx
=(2*pi)/(sqrt(2pi)) int _0^1 (x*e^(-x^2/2)) dx
let us first solve
int (x*e^(-x^2/2)) dx
let u = x^2/2
du = 2x/2 dx = xdx
so ,
int (x*e^(-x^2/2)) dx
= int  (e^(-u)) du
= -e^(-u) = -e^(-x^2/2)
 
So,  V=(2*pi)/(sqrt(2pi)) int _0^1 (x*e^(-x^2/2)) dx
 =(2*pi)/(sqrt(2pi)) [-e^(-x^2/2)]_0^1
=(2*pi)/(sqrt(2pi)) [[-e^(-(1)^2/2)]-[-e^(-0^2/2)]]
=(2*pi)/(sqrt(2pi)) [[-e^(-1/2)]-[-e^(0)]]
=(sqrt(2pi)) [1-[e^(-1/2)]]
= 0.986
is the volume

How ancient Greek Drama is different from our contemporary experience at the movies or at the theater.

The biggest difference between Greek drama and modern day entertainments is that the former was largely religious in nature. Dramas weren't staged in Ancient Greece purely, or even mainly, for the purposes of entertainment. They took place as part of elaborate religious rituals in which the whole community was invited to participate. Attending the modern-day theater or going to the cinema to catch a movie doesn't have quite the same communal value. It's certainly not a religious experience, nor is it intended to be.
The scholarly consensus is that Greek tragedy emerged out of rituals in which Dionysus, the god of fertility—and later theater—was worshipped by devotees wearing masks. This is widely held to form the basis of the mask-wearing tradition in both Greek tragedy and comedy.
In terms of subject matter, it is no accident that Greek drama often explored the relations between gods and mortals or that it also provided an in-depth commentary on religious practices. All surviving Greek plays draw extensively upon a rich mythological heritage in which the immortals play such a crucial part. The gods aren't there to entertain but to remind the audience of their sacred duty towards the immortals and to the importance of paying them their due homage.

Ancient Greek drama was a central part of the social and entertainment lives of the Ancient Greek people. Each year, there was a drama competition held as part of the Festival of Dionysus. The plays would each be performed for the large audience and one playwright would win recognition for having written the best play. Winning this prize was a great honor, even though it was not accompanied by a large financial sum or other physical object: the prize was more about the reputation of the playwright and bragging rights. The community would gather to watch the plays, and in the case of tragedies, would experience catharsis. This means that through watching the tragic fall of the hero, the audience would purge their emotions, feeling cleansed by the experience. The community also saw itself represented in the Chorus, which provided both entertainment and social commentary during the plays. Finally, as part of the Festival of Dionysus, one of the Greek gods, the drama festival and competition were inherently religious rites. The masks worn by characters in the play were also part of a religious ritual, in addition to serving the practical purpose of allowing actors to play more than one role.
In some ways, an experience of going to a contemporary film or play is similar because our dramas are so influenced by the Ancient Greek classics. We do gather communally in theaters and sometimes experience catharsis when watching a movie or play. We do still recognize "the best" of the products in awards shows like the Oscars and the Tonys. We do still respect writers and directors who are involved in the creation of "the best" movies and plays. The major difference is probably that our movie-and-theater-going experiences are really not linked to religious practices, in most cases. Also, we do not gather together as one community to watch one or a few plays on a given day. We have more options for watching entertainment, and we are more widely dispersed as we enjoy these productions.

int_0^oo xe^(-x/3) dx Determine whether the integral diverges or converges. Evaluate the integral if it converges.

We will use integration by parts
int udv=uv-int vdu
int_0^infty xe^(-x/3)dx=|[u=x,dv=e^(-x/3)dx],[du=dx,v=-3e^(-x/3)]|=
-3xe^(-x/3)|_0^infty+3int_0^infty e^(-x/3)dx=
(-3xe^(-x/3)-9e^(-x/3))|_0^infty=
lim_(x to infty)[-3e^(-x/3)(x-3)]+3cdot0cdot e^0+9e^0=
To calculate the above limit we will use L'Hospital's rule:
lim_(x to c)(f(x))/(g(x))=lim_(x to c)(f'(x))/(g'(x))
lim_(x to infty)[-3e^(-x/3)(x-3)]=-3lim_(x to infty) (x-3)/e^(x/3)=
Apply L'Hospital's rule.
-3lim_(x to infty)1/e^(x/3)=0
Let us now return to the integral.
0+0+9=9
As we can see the integral converges and it has value of 9.  
The image below shows graph of the function and area under it representing the value of the integral. Looking at the image we can see that the graph approaches x-axis (function converges to zero) "very fast". This suggests that the integral should converge. 

To whom does John call out to as his mother dies in Brave New World?

As his mother, Linda, dies, John calls out, "Oh, God, God, God..." and he repeats this to himself.
John realizes that Linda has died sooner than she normally would have because she has been taking excessive amounts of soma so that she could feel the state of euphoria which she used to feel when she was younger. She has also desired to ease herself from the judgment and the shame that she has felt in the presence of those of the New World to which she has returned. Indeed, the residents of this world have found Linda repulsive because they know that she has actually given birth the old natural way and, unlike others of the New World, she has aged and become fat.
Perhaps, too, John calls out to God because he realizes that his romantic idea of the New World has dissolved, and he perceives the tragic results of a society that desensitizes its citizenry to real human emotions and desires. At any rate, it is a tragic end for his mother who never knew the meaning of real love, real friendship, or real life. John is also hurt when, before she dies, she mistakes him for Popé and not her son. He begins to despair, too, after his disappointing experience with Lenina in the previous chapter. "Oh, God, God, God..." John cries as his vision of a romanticized "brave new world" dissolves before him.

Single Variable Calculus, Chapter 3, 3.3, Section 3.3, Problem 70

If $f$ is a differentiable function, find an expression for the derivative of the following functions:

$
\begin{equation}
\begin{aligned}
\text{a. ) } y &= x^2 f(x) &&& \text{b. ) } y &= \frac{f(x)}{x^2}\\
\\
\text{c. ) } y &= \frac{x^2}{f(x)} &&& \text{d. ) } y &= \frac{1+xf(x)}{\sqrt{x}}
\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}
\text{a.) } y &= x^2 f(x)\\
\\
y'&= x^2 \frac{d}{dx}[f(x)] + f(x) \frac{d}{dx}(x^2) && \text{Using Product Rule}\\
\\
y'&= x^2 f'(x) + f(x)(2x) && \text{Simplify}\\
\\
\end{aligned}
\end{equation}\\
\quad \boxed{y'=x^2f'(x)+2xf(x)}
$



$
\begin{equation}
\begin{aligned}
\text{b.) } y &= \frac{f(x)}{x^2}\\
\\
y' &= \frac{x^2 \frac{d}{dx} [f(x)] - \left[ f(x) \frac{d}{dx} (x^2) \right]}{(x^2)^2}
&& \text{Using Quotient Rule}\\
\\
y' &= \frac{x^2 f'(x) - f(x)(2x)}{x^4}
&& \text{Factor } x \text{in the equation}\\
\\
y' &= \frac{\cancel{x}[xf'(x)-2f(x)]}{\cancel{(x)}(x^3)}
&& \text{Simplify the equation}\\
\\
\end{aligned}
\end{equation}\\
\quad \boxed{\displaystyle y' = \frac{xf'(x)-2f(x)}{x^3}}
$



$
\begin{equation}
\begin{aligned}
\text{c.) } y &= \frac{x^2}{f(x)}\\
\\
y'&= \frac{f(x) \frac{d}{dx}(x^2)- \left[ x^2 \frac{d}{dx} f(x)\right]}{[f(x)]^2}
&& \text{Using Quotient Rule}\\
\\
y'&= \frac{f(x)(2x)-x^2f'(x)}{[f(x)]^2}
&& \text{Simplify the equation}\\
\\

\end{aligned}
\end{equation}\\
\quad \boxed{\displaystyle y'= \frac{2xf(x) - x^2 f'(x)}{[f(x)]^2}}
$



$
\begin{equation}
\begin{aligned}
\text{d.) } y &= \frac{1+xf(x)}{\sqrt{x}}\\
\\
y'&= \frac{(x)^{\frac{1}{2}}\frac{d}{dx}[1+xf(x)]-\left[ (1+xf(x)) \frac{d}{dx}(x^{\frac{1}{2}})\right]}{(\sqrt{x})^2}
&& \text{Using Quotient Rule}\\
\\
y'&= \frac{(\sqrt{x})[0+xf'(x)+f(x)(1)] - [ 1+xf(x)] \left(\frac{1}{2\sqrt{x}}\right)}{x}
&& \text{Simplify the equation}\\
\\
y'&= \frac{2x^2f'(x)+2xf(x)-1+xf(x)}{2x\sqrt{x}}
&& \text{Combine like terms}\\
\\
\end{aligned}
\end{equation}\\
\quad \boxed{\displaystyle y'= \frac{2x^2f'(x)+3xf(x)-1}{2x\sqrt{x}}}
$

y=(8x+3)/(2x-6) Graph the function. State the domain and range.

We are asked to graph the function y=(8x+3)/(2x-6) :
There is a vertical asymptote at x=3. Since the degrees of the numerator and denominator agree, the horizontal asymptote is y=4.
The y-intercept is -1/2. The x-intercept is -3/8. The graph is a hyperbola. Using long division we can rewrite as y=27/(2(x-3))+4 . Using y=1/x as the base function, the graph we want is a transformation of the graph of the base function: horizontal translation 3 units right, vertical translation 4 units up, and a vertical dilation of factor 27/2.
The graph:

What are some film techniques and scenes involving rebellion in Metropolis?

Fritz Lang's 1927 masterpiece of silent cinema Metropolis, is often widely regarded as one of the finest films ever made. Released at the tail-end of the German Expressionist film movement, Metropolis utilized a wide range of cinematic themes, styles, and techniques that would later continue to be significantly influential for decades.
Metropolis takes place in a dystopian society in which a significant division of wealth separates (quite literally) businessmen from laborers. Classist dissent and economic equality serve as one of the film's primary themes. In what is perhaps one of the most famous and heavily studied scenes of the film, Freder—the film's protagonist and the son of the leader of Metropolis—watches as one of the city's factory machines explodes and kills several workers. Freder experiences a hallucination in which the machine becomes the Canaanite deity Moloch to which the workers are fed. This cinematic technique, which implements a touch of surrealism, creates a strong thematic metaphor of labor; quite specifically, the laborers are portrayed as sacrifices to a heartless and insatiable entity that perpetually needs to be fed.
As the film progresses, an android with the likeness of a woman enters the workers' area of the city, causing anger, dissent, and hatred among the crowds of workers. This android serves as a contrast to Maria, whose likeness the android had taken, who aims to bring the workers and businessmen together in peace. Lang's use of duality with these two figures shows two possible options of erasing the classist divide: peace and rebellion.
One technique, Lang's liberal use of extras (it's estimated that roughly 37,000 were used in the finished film), serves the purpose of showing the power of rebellion. With such a staggering number of workers in the rebelling crowd, Lang see
Other techniques, such as lavish set design and cutting-edge special effects, lent to the futuristic and dystopian style of the film. These techniques also assist in strongly implementing another of the film's themes: the danger and wearisome nature of technology and industrialism. This theme seems to inherently tie into the theme of the classist divide, for industrialism demands increased labor.
As a whole, Metropolis takes a peek into a dystopian future in which workers and businessmen are divided both economically and physically. Through technological cinematic advances, expressionist metaphors, and the use of a significant number of extras, Fritz Lang succeeds in creating a not-too-distant future in which class dissent leads to rebellion and violence.

Discuss the similarities and differences in the character of Louise Mallard and Mathilde Loisel.

Louise Mallard is the protagonist from Kate Chopin's short story "The Story of an Hour." Mathilde Loisel is the protagonist from Guy de Maupassant's "The Necklace." Both women come to find out that life gives and takes without care and concern for mankind.
The women possess far more differences than similarities. Of the few similarities, one that stands out is that each functions as the protagonist in their respective text. The other similarity concerns their downfall in life. Both fail to find success in life.
Louise Mallard is an oppressed woman. This characterization is provided as Louise "mourns" the death of her husband, Brently Mallard. Readers come to find out that Louise has been "repressed" by her husband.

There would be no one to live for during those coming years; she would live for herself. There would be no powerful will bending hers in that blind persistence with which men and women believe they have a right to impose a private will upon a fellow-creature. A kind intention or a cruel intention made the act seem no less a crime as she looked upon it in that brief moment of illumination.
And yet she had loved him—sometimes. Often she had not.

It is obvious that Louise will not miss her husband. She is actually happy he is dead. His death allows her to move on with her life, free to do as she wishes. Brently, in this story, functions as her antagonist. Although readers do not come to know him through anything but Louise's thoughts, they are made painfully aware of the abuse she suffers from his oppressive nature. In the end, as a result of poor communication, Brently shows up at home, and Louise dies. The idea of freedom being taken away from her again kills her.
Mathilde's husband, on the other hand, does not oppress her. In fact, he does everything in his power to help her feel important and successful. In the story, Monsieur Loisel, Mathilde's husband, gets an invitation to the Palace of Ministry. He hopes she will be pleased with the opportunity to attend such a formal event, but Mathilde throws the invitation across the table in disgust. She has no formal attire to wear to such an event. Broken by her poverty, she refuses to go. In the end, her husband gives her money to buy a new gown (money that he had saved for a gun for himself). Ecstatic at the thought, she begins to prepare herself for the event. The only thing she is missing is jewelry. She borrows a necklace from her friend Madame Forestier, a woman whom Mathilde believes has everything. Unfortunately for Mathilde, she loses the necklace, which puts her family into dire financial straits. In the end, Mathilde ends up poorer than when she began.
Unlike Louie, Mathilde's antagonist is societal expectations and poverty. Her end, essentially, comes when she meets Madame Forestier years later. Mathilde admits that she lost the necklace and took out loans, which ruined her and her family, to replace the lost necklace. Forestier, shocked at Mathilde's appearance, tells her the necklace was a fake, simply "paste." Mathilde ruined her life to replace a worthless neckless.
Both women sought out their own personal freedoms, and both failed. Both women lost more than they had to lose in the first place.

One possible interpretation of the play is as follows: “Oedipus is punished not for any fault in himself, but for his ignorance. Not knowing his family history, unable to recognize his parents on sight, he is blameless; and in killing his father and marrying his mother, he behaves as any sensible person might behave in the same circumstances.” Do you agree with this interpretation?

I think there's a strong case to be made that Oedipus is not without blame. When he visits the oracle at Delphi, the mouthpiece of the god Apollo, and hears the prophecy that he will kill his father and marry his mother, he decides that he would not go home to Corinth. Oedipus thinks that he can avoid the prophecy, proudly believing that his will can overcome that of fate or that of a god. In thinking that he can outwit Apollo, he moves to Thebes, surmising that he can never fulfill the prophecy if he is not near the individuals he believes to be his parents, and yet this is precisely the action that leads him to kill his father (on the road to Thebes) and marry his mother (once he gets there and is named king). He does not understand that the gods know more than he does, or that he—a mere mortal—is fallible. Had he not been ruled by pride, who knows what might have happened? As it is, Oedipus's pride compels him to think himself more powerful than fate, and he pays a heavy price.

How will a nation try to overthrow a foreign country which reigns over it?

There are at least two main ways in which people or nations have tried to overthrow foreign countries that have ruled them.  These two ways are violence/military action and protests/persuasion.  A colonized country can use one or both of these methods to try to gain their independence.
In the United States, for example, both were used, but military action was more important than protests.  After the British government started to impose taxes on the colonists, there were many protests.  The colonists tried to persuade the British to give them more autonomy.  However, because the British did not agree to these requests, the colonists ended up fighting a war against the mother country.  It was in this way that they were able to gain their independence.  Similar things happened in Latin America to allow those countries to become independent from Spain.
In other situations, violence has been less important.  A major example of this is India.  In the history of British rule over India there were, of course, incidents of violent attempts to overthrow British rule.  However, in the end, it was protest and persuasion (along with WWII) that actually brought about Indian independence.  It was Congress’s program of protest and persuasion, rather than a violent rebellion, that overthrew British rule.
Thus, violence and persuasion/protest are the two main ways in which a nation might attempt to overthrow a foreign country that rules it.
http://www.bbc.co.uk/history/british/modern/independence1947_01.shtml

What is the resolution of "Désirée's Baby"?

The resolution of a story takes place after the climax. It is the part of the story where the conflict comes to an end. In Kate Chopin's "Désirée's Baby," the resolution comes after Désirée and her baby leave the plantation. 

She disappeared among the reeds and willows that grew thick along the banks of the deep, sluggish bayou; and she did not come back again.

Weeks after her disappearance, Armand orders his slaves to put up a huge fire. In it, he burns all of the things that used to belong to Désirée and the baby. There were also letters thrown in the fire, some from Désirée, and others from Armand's own mother. Chopin ends the story by citing the writing on the letter, in which Armand's mother states that she is very grateful to God for her husband's love. However, she was even more grateful for the fact that Armand will never have to find out that she, his mother, is African American. 
This is significant because the entire reason Désirée leaves Armand is because their baby has developed African American physical traits. These were the days before the Civil War, and slavery was in full swing. That the baby was black meant that either Armand or Désirée was also of the same descent. Armand, who is a cruel and difficult man, automatically blames Désirée for it and insists that she is the one who carries this heritage—that it is her fault that their child is of "the race that is cursed with the brand of slavery."
In total despair, Désirée leaves the plantation, presumably to go see her mother. What she does, however, is drown herself and the baby in the bayou.
Therefore, the resolution is tragic and ironic because it is now clear that Armand is the one who carries the African American genes in his blood, from his mother, and he has just caused the unnecessary and cruel deaths of his wife and child.

Deputy Governor Danforth tells Proctor that Elizabeth is pregnant and will not be harmed until after the baby is born. What does Procter do after that?

After Deputy Governor Danforth tells John Proctor that Elizabeth, John's wife, has declared that she is pregnant, and that she will be saved for at least a year as a result, John explains that his friends' wives are also accused. Therefore, he feels that he cannot drop his case against the accusing girls. He explains to Danforth that Mary Warren has admitted that she and the other girls were pretending when they claimed to see spirits and lying when they accused people of witchcraft. He eventually names Abigail Williams as a "whore" and insists that Elizabeth fired her as a result of her discovery of his affair with Abigail. Danforth tests this story by questioning Elizabeth, who John has sworn cannot lie; however, she does lie and inadvertently helps to condemn John as a result.

How is the Old South represented in Faulkner's "A Rose for Emily"?

The character of Emily Grierson is used by Faulkner to symbolize the Old South and its decline. She is a living monument of a romanticized past—based on a rigid social hierarchy and its associated code of chivalry. This explains why the townsfolk hold Emily in such high esteem. In a defeated, postbellum South, the Grierson name acts as a nostalgic reminder of the so-called glory days before the Civil War. The people of Jefferson want to hang on to the memory of yesteryear for as long as they possibly can, and so Emily gets a pass for her eccentricity and evident disdain for her social inferiors.
In "A Rose for Emily," Faulkner holds up a mirror to the society of the Old South. In its reflection we see a society that is stuck in the past, unable to move on, unwilling to acknowledge that the world outside Jefferson has changed forever. Although slavery may have been abolished, the old social hierarchies remain. And they corrupt the town's public life. Everyone can smell the revolting stench emanating from the Grierson residence, but instead of launching a proper investigation, the authorities merely send out some men to go and neutralize the smell. The old ways continue to exert such a hold on the minds of the townsfolk that their values are warped, and they become complicit in immoral acts. So long as Emily lives, and the Grierson name continues to exude its strange, bewitching magic, such moral corruption will live on.

College Algebra, Chapter 4, 4.4, Section 4.4, Problem 42

Determine all rational zeros of the polynomial $P(x) = x^5 - 4x^4 - 3x^3 + 22x^2 - 4x - 24$, and write the polynomial in factored form.

The leading coefficient of $P$ is $1$, so all the rational zeros are integers. They are divisors of the constant term $-24$. Thus, the possible candidates are $\pm 1, \pm 2, \pm 3, \pm 4, \pm 6, \pm 8, \pm 12, \pm 24$.

Using Synthetic Division







We find that $1$ is not a zeros but that $2$ is a zero and $P$ factors as

$x^5 - 4x^4 - 3x^3 + 22x^2 - 4x - 24 = (x - 2)(x^4 - 2x^3 - 7x^2 + 8x + 12)$

We now factor the quotient $x^4 - 2x^3 - 7x^2 + 8x + 12$. Its possible zeros are the divisors of $12$, namely

$\pm 1, \pm 2, \pm 3, \pm 4, \pm 6, \pm 12$

Using Synthetic Division







We find that $-1$ is a zero and $P$ factors as

$\displaystyle x^5 - 4x^4 - 3x^3 + 22x^2 - 4x - 24 = (x - 2)(x + 1)\left( x^3 - 3x^2 - 4x + 12 \right)$

We now factor the quotient $x^3 - 3x^2 - 4x + 12$. Its possible zeros are the divisors of $12$, namely

$\pm 1, \pm 2, \pm 3, \pm 4, \pm 6, \pm 12$

Using Synthetic Division







We find that $2$ is a zero and $P$ factors as

$x^5 - 4x^4 - 3x^3 +22x^2 - 4x - 24 = (x - 2)(x + 1)(x - 2)(x ^2 - x - 6)$

We know factor the quotient $x^2 - x - 6$ using trial and error. We get

$x^5 - 4x^4 - 3x^3 + 22x^2 - 4x - 24 = (x - 2)(x + 1)(x - 2) (x - 3)(x + 2)$

The zeros of $P$ are $2, 3, -1$ and $2$.

Why was HEC so mean?

I am pretty sure that by "HEC" the question is asking about Herman E. Calloway. Additionally, I am sure that the question is implying that Calloway is being mean to Bud.
Calloway is mean to Bud because Calloway knows that Bud is lying about being his son. Bud believes that Calloway is his father, so Bud goes looking for Calloway in order to live with a family member again. Calloway knows that he only fathered a daughter, so he knows that Bud isn't his son. This causes Calloway to think that Bud is just some runaway looking to get some easy room and board.  

You see, kid, you ain't the only one trying to get on Mr. C's good side.

The story takes place during the Great Depression, and Calloway is one of the fortunate individuals that can maintain some kind of employment. He is financially successful at a time when people are struggling to put food on their plates. Bud is probably not the first person trying to con Calloway out of some money. Calloway sees no reason to be nice to a kid that he knows is not his son.  

He was so doggone mean and hard to get along with it just didn't seem like it was true that he could be anyone's daddy. The way he was so worried about me stealing stuff from him before he even knew if I was honest or not made me wonder if someone who was so suspicious could ever be kin to me.

Of course all of that changes when Calloway realizes that Bud is his grandson. Calloway feels horrible for how he treated Bud all while being happy that he has a grandson from his daughter.  

You can't help but feel sorry for him, even if he's been mean to you from the minute he first had eyes on you, even if he's crying 'cause he found out the two of you were kin.