Precalculus, Chapter 7, 7.3, Section 7.3, Problem 32

(1) 2x+y+3z=1
(2) 2x+6y+8z=3
(3) 6x+8y+18z=5

Using Equations (1) and (2) eliminate the x. Multiply equation (2) by -1.
2x+1y+3z=1
-2x-6y-8z=-3
----------------------------
-5y-5z=-2
(4) -5y-5z=-2

Using Equations (2) and (3) eliminate the x. Multiply equation (2) by -3.
-6x-18y-24z=-9
6x+8y+18z=5
--------------------------------
-10y-6z=-4
(5) -10y-6z=-4

Using equations (4) and (5) eliminate the y. Multiply equation 4 by -2.
10y+10z=4
-10y-6z=-4
-----------------------
4z=0
z=0

Use equation (4) to solve for y.
-5y-5z=-2
-5y-5(0)=-2
y=2/5

Use equation (1) to solve for x.
2x+y+3z=1
2x+2/5+3(0)=1
x=3/10

The solution set is (3/10, 2/5, 0).

You may check your answers by plugging in the x, y, z values into the original equations.
(1) 2(x)+y+3z=1
2(3/10)+(2/5)+3(0)=1

6/10+2/5=1
6/10+4/10=1
1=1

(2) 2x+6y+8z=3
2(3/10)+6(2/5)+8(0)=3
6/10+12/5=3
6/10+24/10=3
30/10=3
3=3

(3) 6x+8y+18z=5
6(3/10)+8(2/5)+18(0)=5
18/10+16/5=5
18/10+32/10=5
50/10=5
5=5

Consider the essay "Library Card" by Richard Wright as a tale of transgression; what are the particulars of trespass or violation as the author portrays them?

On the most basic level, Wright's "transgression" is the mere act of wishing to take out books from a library in the Jim Crow South. Though Mr. Falk agrees to let him use his library card, Wright must still forge the notes purportedly from him in order to request the specific books he wants to read—at first, those of H.L. Mencken.
The more profound "violation" that underlies this is Wright's desire to enter the intellectual world, the world of books, from which the whites have excluded him. He's thus rebelling against the whole mindset of the segregated South, where African Americans were perceived, and treated, in a harsh, dehumanizing way. The subtext of this racist thinking was, of course, the whites' fear that if black people were permitted to read and to acquire knowledge, they would be in a position to overturn the status quo and bring an end to Jim Crow—which, of course, they were eventually able to do.
It is significant that Wright names Mencken as the writer whose books first attracted him. Mencken was an iconoclast who shattered many of the notions around which Americans had built their self-mythologizing. He was against organized religion, for example. In the antebellum South and in the Jim Crow period of the hundred years after the Civil War, whites had used Christianity to justify slavery and segregation. So, by choosing Mencken to read, Wright was making the deepest kind of "transgression" possible as he entered the world of books and intellectualism that had been denied to him.

Who is the protagonist in Toni Cade Bambara's story "Raymond's Run"?

Squeaky is the protagonist of "Raymond's Run" because she is the main character who undergoes some conflict and change in attitude.
As the narrator, Squeaky mentions her antagonists as Gretchen, against whom she competes for a medal on May Day at the local park, and Cynthia Proctor, who wins the spelling bees, but pretends that she does not study. Another one is Mary Louise Williams, who mocks Raymond's mental handicap. 
Squeaky undergoes changes in her attitudes after the race. Her feelings toward Gretchen and toward Raymond both are altered. As she sprints along, Squeaky sees Raymond on the other side of the fence with his arms stretched behind him and his palms upward much in the manner in which geese run with their necks stretched and wings straight behind them. She is absolutely amazed at his skill. After the race, she narrates, "...it occurred to me that Raymond would make a very fine runner."
Also at the end of the race, after Squeaky races across the finish line, she leans over to catch her breath, and she notices Gretchen, who has also overshot the finish line. "I sort of like her a little for the first time," Squeaky immediately remarks. Later, after Gretchen is given second place, Squeaky indicates to Gretchen her change of heart:

....And I smile. Cause she's good, no doubt about it. Maybe she'd like to help me coach Raymond.

Clearly, Squeaky is the protagonist of "Raymond's Run" since she changes her opinions of both Gretchen and Raymond. Now, she realizes that they are richer in heart and talent than she had previously thought.

Why might religious people from Chaucer's time have been upset with Chaucer's view of the Monk and the way he described him in The Canterbury Tales?

In Chaucer's The Canterbury Tales, the author paints a less-than-complimentary view of "the Monk," one who has sworn to serve the Roman Catholic Church during the Middle Ages. The Church was the central authority at the time, with no separation between church and state. The Church not only made the laws that governed the people, but it also set the tone for the people's spiritual welfare. With this in mind, the Monk should have made himself humble, selling all that he had to give it to, and serve, the people. The Monk is one of several members of the clergy on the pilgrimage, although only the Parson is a true man of God.
In that the people completely supported and did not question the authority of the Church, many believers of the time might have felt Chaucer's writing was disrespectful. It is important to note that some people may have been aware of the Monk's behavior (or that of other clergy members in their parishes), however, and might have applauded Chaucer's exposure of these sneaky, greedy, and unethical members of the cloth. (Chaucer was a student of human nature; rather than creating problems, he wanted simply to describe the kinds of people he met in real life: those who were what they espoused to be, and others who lied and took advantage.)
Chaucer describes the Monk. The Monk was a man of venery (he had a deep love of hunting). He owned a horse, and the horse wore a fine harness (which was not cheap). By not living in a cloister, his time was not spent in service to others as much as it was spent following his own pleasures. The narrator sarcastically questions why a monk would ever spend time studying—to what end? What good would he do breaking a sweat?
Hunting was dear to his heart:

Therefore he was a rider day and night; Greyhounds he had, as swift as fowl in flight. Since riding and the hunting of the hare Were all his love, for no cost would he spare (25-28).

The Monk had greyhound dogs (known for their speed). He also had no qualms about spending as much money as necessary in his hunting exploits. He was, however, a man who was supposed to have given up his worldly goods and serve God's people.
The Monk wore clothes that were expensive (only the best for him): his cloak (fur-lined) was adorned with a pin—a gold love-knot. Why would a man of God be dressed in such expensive clothes, and why would he wear a love-knot pin?

I saw his sleeves were lined around the hand With fur of grey, the finest in the land; Also, to fasten hood beneath his chin, He had of good wrought gold a curious pin: A love-knot in the larger end there was (29-33).

There seemed little time or interest on the part of the Monk to serve others. Chaucer does not come right out and censor the Monk. He makes observations and lets the reader make his or her own decisions.
People of the time might have sensed criticism from the author; they might have resented what seemed to be fault-finding. Students of human nature (like Chaucer) would be able to identify the contradictions in behavior among many members of the clergy. Some might have seen these observations as a reflection of the Church's lost of control over its people, a poor reflection on the Roman Catholic Church.
At that time, the Church was in charge of every aspect of life. With those clerics in Chaucer's writings far outside the guidelines by which they were to live their lives, one wonders if they should not have been watched more closely.
https://www.owleyes.org/text/canterbury-tales/read/the-monk/root-218780-1

What is the game they play at the pier?

Navy Pier is an old, abandoned part of the city with a carousel, a Ferris wheel, and many crumbling and empty buildings. It is located in an old part of Chicago, which is no longer inhabited.
Tris is a new Dauntless initiate, having transferred from Abnegation. During the first part of their training, the Dauntless initiates have to face a number of challenges in order to prove themselves worthy, such as fighting sessions. One of these challenges is a game of capture the flag, a Dauntless tradition. The initiates are divided into two teams; each team must hide their own flag and make it hard to find, and then find the opposing team's flag. The first team to find the other team's flag wins.
Tris understands that the Ferris wheel can be a great vantage point and allow her to see what the other team is doing, so she climbs up, followed by Four. She manages to see where the other team has hidden the flag and climbs down the Ferris wheel. She almost falls and is saved by Four. Once she gets down, she is able to tell her team where the other team has hidden the flag, and this leads to her team's victory.

Who was King Henry VIII?

Henry VIII was one of the most significant monarchs of England. Most famous for having six wives during the course of his tumultuous reign, he also did much to build England as a powerful nation-state, and, perhaps most significantly, separated the kingdom from the Catholic Church. Unable to conceive a male heir, Henry petitioned the Pope to annul his marriage to his first wife, Catherine of Aragon. When the Pope denied the King's request, he took the revolutionary step of declaring himself head of the Church of England, separating the kingdom from the Catholic Church. This move ushered in a decades-long conflict between England and Spain, the dominant Catholic power on the continent. It also significantly strengthened the English monarchy, and Parliament, by stripping the Church of lands and authority in England. Henry would go on to marry five more times, executing his wives Anne Boleyn and Catherine Howard for adultery, and divorcing Anne of Cleves. Jane Seymour died before Henry, and Katherine Parr was his wife at his death. He had one son, Edward VI, who succeeded him, but died soon after. Edward was succeeded by first Lady Jane Grey and then Henry's daughters Mary and Elizabeth, who became one of the most important monarchs in English history.
https://www.biography.com/royalty/henry-viii

Why do you think Grandin prefers animals to people?

Temple Grandin prefers animals to people because she can relate to them more easily. Temple has autism, a neurological disorder that essentially makes people with the condition live in a world of their own. People with autism like Temple think visually; this is one aspect of their condition that gives them an often greater degree of empathy with animals than with other human beings. Animals lack the power of speech, so naturally their thoughts are also visible.
From these images in her mind, Temple constructs associations—something she notices is common among animals, for instance in horses. These associations are important in that they are highly determinative of animal behavior. For example, if a rat is shocked on entering a passageway in a maze, it will associate that experience with fear and so will never go back there again. Fear and associative thinking also combine in autism. People with the condition tend to see the outside world as an intensely hostile, dangerous place. They see themselves almost as prey in much the same way that animals do.
These insights allow Temple to devise a humane method of slaughtering cattle on farms and in processing plants. The whole procedure of slaughter can be made more efficient and less frightening for the cows if their fear and capacity for associative thinking can be taken into consideration.

In the Declaration of Independence, by whose authority do the representatives declare independence from Britain?

The answer to this question can be found at the end of the Declaration of Independence.  It is at that point that the signers actually come around and say that they are breaking away from England.  Before that, the document had been giving reasons why the colonists would be justified in breaking away, but it never actually said that they were.  Towards the end, the signers explicitly state that they are breaking away and they say that they are doing so by the authority of the people of the American colonies.
In the Declaration of Independence, Thomas Jefferson (who did most of the work of writing the document) emphasizes the importance of democracy.  He says, among other things, that government can only have legitimate authority if the people consent to be ruled by that government.  If Jefferson is going to say that democracy is important, he needs to appeal to democracy when he says that the colonies are breaking away from England.  He has to say that the people approve of this step or else the step will not be democratic and will be illegitimate.  This is why Jefferson says that

We, therefore, … do, in the Name, and by Authority of the good People of these Colonies, solemnly publish and declare, That these United Colonies are, and of Right ought to be Free and Independent States…

Clearly, then, the representatives who signed the Declaration of Independence are claiming that the authority of the people of the colonies is what gives them the right to declare independence. 
https://www.archives.gov/founding-docs

What is Ibsen's use of his set design throughout the play? What is the purpose of minor characters, especially Dr. Rank, Krogstad, and Mrs. Linde?

The most striking set design element in A Doll's House is the letter box Nora fearfully watches in expectation of Krogstad's letters to her husband. The box is almost a symbol, like the Nibelung's ring in Norse myth, holding a supernatural power that will determine her fate, and the fact that her husband holds the key shows her powerlessness. In a quite different way the piano and the festive set surrounding it during the party are a vivid, ironic prison in which Nora is locked as she frantically dances "for her life."
The functions of the "minor" characters are crucial to the plot and Ibsen's overall "message." Dr. Rank, in his selfless and pure love for Nora, and in his courage in the face of death, is a foil to the other male characters. Torvald is, of course, a domineering and arrogant husband typical of that time and later. He loves Nora in his way but does not respect her as a person or have any real regard for her feelings. He considers himself an "expert" on everything, including dancing, complaining that Nora, as she rehearses, has forgotten all he (supposedly) taught her, and he viciously abuses her when Krogstad threatens to reveal her "crime," though she had forged her father's signature to save Torvald's life. Krogstad, despite his obvious sliminess and criminality, at least seems less self-deluded than Torvald. Again, Dr. Rank, though the casual viewer might doubt he is essential to the plot, serves as a contrast to Torvald and Krogstad and demonstrates kindness and warmth in a man.
Mrs. Linde also represents a rare selflessness in helping Nora by giving herself to Krogstad. Though Ibsen is not "judging" Nora for her traditional housewife role (normal, of course, for the great majority of women at that time) Kristine has been a businesswoman and thus an example of what women were already achieving in an age when they still could not vote. It is only at the very end of the play that Nora is forced to find the courage to become independent and leave the paternalistic world of her husband's dominance.

In Someone Knows My Name, what are some examples that show inhumanity, barbarism, and racism? Also, what are some examples of inhumanity, barbarism, and racism in real life?

After Aminata arrives on the plantation, the slave owner, Appleby, brutally rapes her. She describes the rape in the following way: "the pain was terrible as he plunged deep inside my body where no one belonged but me." After she is raped, Aminata is covered in blood and ashamed of what happened to her.
When Aminata later becomes pregnant with Chekura's child, she knows Appleby will not let her marry. In another instance of brutality, he does not allow his slaves to marry. When Appleby sees Aminata dressed up in fine clothes, he makes her burn them, and then he shaves the hair she is so proud of. When Aminata's son, Mamadu, is only ten months old, Appleby sells him for five pounds. Appleby laughs at Aminata, and he won't tell her where her son has been sold.

There are several examples of barbarism in the novel. Some of these examples are from Aminata's youth in West Africa, where she was born in 1745. For example, Aminata's mother explains to her daughter, in Aminata's words, that "some people have their womanly parts torn apart and put back together improperly" and that this must be done to the women in her mother's tribe in West Africa so that men will marry them. This is a form of female genital mutilation, and some girls die during the procedure.
The episode in which Aminata is captured by slave traders is another example of extreme barbarism and inhumanity. The captors strike her mother and likely kill her and shoot her father. As Aminata describes the murder of her father, "Fire exploded from the stick and blew Papa onto his back. He turned his head to look for me, but then his eyes went blank." The captors seize a young girl and put a noose over her head, and they also kill her parents in front of her. Another example of inhumanity is that the captors force the enslaved people to walk naked. Aminata experiences her first menstrual period while she is naked, and blood runs down her legs.
During the Middle Passage, the enslaved men are chained on deck--another instance of barbarism and racism. They are fed so little that Aminata describes one man in the following way: "His ribs were showing, and he looked utterly spent." He is tossed overboard because he is sick. Another example of barbarism is when the assistant cracks his whip on deck and the men are forced to dance. The slaves' captors treat them with extreme barbarism because they are racist and believe Africans' lives are worth little, save for the labor they can provide.
In today's world, there are still unfortunately far too many examples of barbarism. Slavery still exists today. According to the link below, there are 21 million enslaved people today who are treated with barbarism and inhumanity to force them to work in fields such as mining, farming, ranching, and other areas. In addition, 22% of enslaved people today are forced into slavery involving forced sex, and 26% of enslaved people are children. Many of these children are also forced into slavery involving prostitution. These people are regarded as worthwhile only for their labor and are not valued as humans, just as the slaves in the novel were treated.
https://www.freetheslaves.net/our-model-for-freedom/slavery-today/

Single Variable Calculus, Chapter 1, 1.3, Section 1.3, Problem 32

We need to find (a) $f \circ g$, (b) $g \circ f$, (c) $f \circ f$, and (d) $g \circ g$ and state their domains


$ f(x) = x-2 , \qquad g(x) = x^2 + 3x + 4 $


$
\begin{equation}
\begin{aligned}

\text{(a)} \qquad \quad f \circ g &= f(g(x))
&& \text{ Substitute the given function $g(x)$ to the value of $x$ of the function $f(x)$}\\

f(x^2+3x+4) &= x-2 && \text{ Simplify the equation}\\


f(x^2+3x+4)&= x^2+3x+4-2 && \text{ Combine like terms}
\end{aligned}
\end{equation}
$


$\boxed{f \circ g =x^2+3x+2}$


$\boxed{\text{ The domain of this function is } (-\infty,\infty)} $



$
\begin{equation}
\begin{aligned}

\text{(b)} \qquad \quad g \circ f &= g(f(x))\\
g(x-2) &= x^2+3x+4 && \text{ Substitute the given function $g(x)$ to the value of $x$ of the function $f(x)$}\\
g(x-2)&= (x-2)^2+3(x-2)+4 && \text{ Simplify the equation}\\
g(x-2) &= x^2 - 4x+4+3x-6+4 && \text{ Combine like terms}

\end{aligned}
\end{equation}
$



$\boxed{g \circ f=x^2-x+2} $


$\boxed{\text{ The domain of this function is }(-\infty,\infty) }$


$
\begin{equation}
\begin{aligned}
\text{(c)} \qquad \quad f \circ f &= f(f(x)) \\

f(x-2) &= x-2 && \text{ Simplify the equation}\\

f(x-2) &= x-2-2 && \text{ Combine like terms}
\end{aligned}
\end{equation}
$


$\boxed{f \circ f=x-4}$


$\boxed{ \text{ The domain of this function is } \,(-\infty,\infty)}$



$
\begin{equation}
\begin{aligned}
\text{(d)} \qquad \quad g \circ g &= g(g(x)) \\

g(x^2+3x+4) &= x^2+3x+4 && \text{ Substitute the given function $g(x)$ to the value of $x$ of the function $f(x)$}\\


g(x^2+3x+4) &= (x^2+3x+4)^2+3(x^2+3x+4)+4 && \text{ Simplify the equation}\\


g(x^2+3x+4) &= x^4+3x^3+4x^2+3x^3+9x^2+12x+4x^2+12x+16+3x^2+9x+12+4 && \text{ Combine like terms}



\end{aligned}
\end{equation}
$



$\boxed{g \circ g= x^4+6x^3+20x^2+33x+32}$


$\boxed{ \text{ The domain of this function is} (-\infty, \infty)}$

What was the arena built for in "The Lady or the Tiger?" by Frank Stockton?

The king in this story is described as "semi-barbaric," meaning that he is, in his essence, barbaric by nature, but has borrowed some more civilized ideas from some of the gentler nations which surround his kingdom. The public arena which he builds is actually, in its origin, one of these "borrowed notions" intended to reduce the barbarism of the nation by offering a space to display exhibitions of valor, which would supposedly refine and culture his subjects.
However, being at heart a barbaric king, the king warped this idea in the arena which he built. He doesn't have any interest in showcasing gladiators or religious people fighting with tigers in the hopes of improving their minds this way, as the Romans did. Instead, he prefers to use his vast amphitheater as an "agent of poetic justice," used for punishing crimes and rewarding virtues based on chance alone. When an interesting enough crime was committed, the fate of the supposed criminal would be decided in the king's arena.

The king's arena in Frank Stockton's short story "The Lady or the Tiger?" was a "vast amphitheater" built in order to deliver the king's justice. It was large enough to house the king's subjects, "encircling galleries," "mysterious vaults," and "unseen passages." The king believed his arena was the agent of an "incorruptible" justice. When someone was accused of a crime, they were taken to the arena, where their judgment was in their own hands. They were given the choice of two doors. One of the doors would reveal a tiger, which promptly killed the accused and rendered him guilty. Behind the other door was a lady who "immediately" married the accused because, by choosing so judiciously, he had proven his innocence. The narrator refers to it as "poetic justice" because the accused could never know from which door might spring the tiger or the lady. Unfortunately, like all things supposedly incorruptible, the justice of the arena becomes corrupted when the king's daughter discovers the secret of the doors.

In Maniac Magee by Jerry Spinelli, what kind of career does Grayson have in the Minor Leagues? How does Grayson appear different when he tells Jeffrey he had been a pitcher?

Grayson had experienced a fairly long career as a Minor League Baseball player.  He had played as a pitcher on several different baseball teams.  He had once had a chance to impress a scout for a team that was "one short step from the Majors" (Maniac Magee, Chapter 25).  Instead of impressing the scout, Grayson had pitched a horrible game.  His chances of someday playing Major League Baseball were over.  He continued to play on Minor League teams until he was about forty.  His last team was in Mexico.  The years had left him unable to play with the necessary skill.  He retired from baseball, and became a janitor.
When Grayson told Maniac Magee that he had been a pitcher in his younger years, the boy was shocked.  Maniac had never expected Grayson to reveal such a secret.  Grayson was not a "rickety, whiskered worm chow" (Chapter 25).  Instead, he had been a baseball pitcher for many years.  Maniac was in awe.  He begged Grayson to tell stories from his baseball days.

Calculus: Early Transcendentals, Chapter 3, 3.6, Section 3.6, Problem 25

You need to find the first derivative of the function, using the chain rule, such that:
y' = (ln(x+sqrt(1+x^2)))'
y' = (ln'(x+sqrt(1+x^2)))*(x+sqrt(1+x^2))'
y' = (1/(x+sqrt(1+x^2)))*(1+(2x)/(2sqrt(1+x^2)))
y' = (1/(x+sqrt(1+x^2)))*(1+(x)/(sqrt(1+x^2)))
y' = (sqrt(1+x^2)) + x)/((sqrt(1+x^2))(x+sqrt(1+x^2)))
Reducing like terms, yields:
y' = 1/(sqrt(1+x^2))
You need to evaluate the second derivative, differentiating the first derivative, with respect to x,using the quotient and chain rules, such that:
y'' = ((1)'(sqrt(1+x^2)) - 1*(sqrt(1+x^2))')/(1+x^2)
y'' = -(x)/((1+x^2)^(3/2))
Hence, evaluating the first and the second derivatives, yields y' = 1/(sqrt(1+x^2)) and y'' = -(x)/((1+x^2)^(3/2)).

What is one characteristic trait of Brutus from Act 5?

In light of Roman military ethics, it can be argued that Brutus was both courageous and honorable. We can also say that he was noble.
Brutus was raised as a Stoic by his uncle, Cato the Younger, who vigorously opposed the rule of Julius Caesar. In temperament, Cato was both unyielding and implacable; he certainly impressed upon Brutus the need to battle compromise in all areas of life.
In Roman military culture, every good warrior sought glory on the battlefield; there, his physical prowess was tested, and he was immortalized by his courageous acts. To retain honor, the Roman warrior needed a strong will and the energy to succeed. As a stoic, Brutus maintained iron control over his emotions; he was self-sufficient and self-possessed. The Stoics believed that destructive emotions (such as anger or anxiety) crippled the psyche and had to be brought under the control of the will. Thus, a man's character was defined by his ability to navigate perilous challenges without complaint. The Stoics called this pursuit of virtue man's greatest objective in life; an honorable man endured all for the common good, as Brutus believed he did.
Brutus' opposition to Julius Caesar was based on his strict moral code; he felt that Caesar's ambitions threatened the Roman state and the freedom of its citizens. So, Brutus fought to save the Roman republic, and he endured the atrocities of the battlefield in order to secure the common good. However, his limited focus fueled his naivety, and he failed to recognize the duplicity of the conspirators. In the end, Brutus was defeated in battle, and in line with his honorable character, chose to fall upon his own sword. In dying this way, Brutus expended his complete being for the good of the Republic. His sacrificial actions allowed him to exert one last control over his body and emotions; in his eyes, he retained his masculine courage and honor to his last breath. 
Hint: If you're looking for pictures that characterize Brutus as honorable, try picking examples from search engines that match pictures of warriors with words describing the warrior code of honor. 
Source:
Roman Honor: The Fire in the Bones by Carlin A. Barton.

What was the significance of the exploits of Christopher Columbus?

Christopher Columbus made four voyages across the Atlantic Ocean for Spain. The Spanish sponsored his explorations in hopes of finding a shorter route to Asia. Columbus believed it might be possible to find a shorter route to Asia by heading west. The King and Queen of Spain also hoped he would find valuable minerals that would enhance Spain's treasury. Spain also hoped to spread Christianity to the places he would find. His voyages were significant.
As a result of Columbus's voyages, Europeans began to increase their interest in the Americas. It should be noted that Columbus didn’t discover the Americas, but he prompted many explorations to the Americas by the European colonial powers. European countries eventually set up colonies in the Americas. These explorations eventually led to the discovery of many minerals that greatly benefited the European countries. There also was an increase in trade between Europe and the Americas. The people who lived in the Americas suffered greatly as a result of these explorations. Europeans brought diseases that killed many of the native people because they had no immunities to these illnesses. The Europeans also enslaved some of the native people and took away their land.
https://www.history.com/topics/exploration/christopher-columbus

How does Shakespeare employ the rhetorical method of syntax in Hamlet's soliloquy "To be or not to be"?

When we talk about syntax, we essentially mean sentence structure. How are the words in a sentence arranged, and what is the effect of arranging them that way? Different syntactical structures can impact the understanding, mood, tone, or emphasis of a passage.
In analyzing the syntax of a sentence, it's often helpful to look for things like punctuation, sentence length, patterns (or where a pattern breaks down), first or last words of sentences, and/or repetition.
Hamlet's "To be or not to be" soliloquy has a lot of interesting things happening with its syntax, although the interpretations that different readers or actors take away from the same syntax is variable.
One of the things to consider in this soliloquy is the word order. Hamlet begins by saying "to be or not to be - that is the question" (3.1.64). This has a very different effect than saying "The question is: To be or not to be?". Starting this soliloquy with a question instead of statement sets the tone for this entire passage. The audience should be curious and puzzled from the first few words and empathize with Hamlet's thoughts because this question has drawn them in. The same is true later when Hamlet says "to die, to sleep - / no more" (3.1.68-69). Hamlet starts with "to die" instead of something like "Sleeping is just like dying" because beginning with the words "to die" at the start of the thought has a greater impact.
Another consideration is the punctuation in the soliloquy. At the beginning, the text is full of punctuation that makes the reader (or the actor) slow down. The first phrase ends with a colon, and many of the other sentences in the first half of the soliloquy include dashes or periods, whereas there are longer sentences punctuated by commas in the second half of the soliloquy. The effect on reading this is that the first half is slower and more contemplative, while the second half speeds up. In terms of content this makes sense because the first half of the soliloquy is Hamlet thinking and processing this information and asking the audience to contemplate with him, while in the second half there is a long list of life's injustices. The first phrase "To be or not to be - that is the question:" contains the only colon. This punctuation makes sense here, because this really is the big question and takes the most thought, so this punctuation should make the reader pause for the longest time before considering the rest of the speech.
https://www.folgerdigitaltexts.org/html/Ham.html

How does immigration impact the United States?

Rather than examine the impact of immigration in an economic light, I will examine it from a socio-cultural perspective with a historical focus. The relationship between the United States and immigration to the United States can at times be complicated. Almost all Americans today can trace their heritage back to at least one immigrant group. Even many people of Native American descent can find evidence of immigrant ancestors from Europe, Africa, Asia, or especially more recently, Central and South America. Many Americans also hold their ancestral heritage as a sense of pride, and in some cases still maintain traditions brought from abroad.
Although many Americans have strong pride in their ancestry, and many Americans would likely agree that immigration is one of the factors that has made America great, there is still a significant part of the population opposed to immigration. This is an interesting phenomenon that has existed since the earliest days of the United States, and even before the country was independent. In 1751, for example, Benjamin Franklin complained of the arrival of German immigrants who settled in Pennsylvania. Anti-immigrant sentiment continued in the mid-19th Century with the formation of the Know-Nothing Party. The Know-Nothing Party stood on a platform that opposed immigration, particularly immigration by Roman Catholics and those whose native language was not English. Many of these immigrants came from places like Germany and Ireland. In 1882, the United States government aimed to limit immigration from China through the Chinese Exclusion Act. Chinese immigrants were particularly discriminated against and mistreated in the western United States in the late 1800s.
In the late 19th and early 20th centuries there was opposition to the major immigrant groups of the time. These immigrants came from places like Ireland, Italy, and Eastern Europe in search of jobs. It was common to see help-wanted signs warning that "no Irish need apply". Anti-immigrant sentiment of the time declared these new immigrants to be inferior to Americans who had lived in the United States for generations.
Today opposition to immigration is once again a divisive issue. President Trump's statements on immigration have caused great outrage, but also help to explain how he was elected. Today the major source of immigration to the United States comes from Central and South America, with immigrants coming for many of the same reasons they came in the past. Immigrants are leaving countries like Mexico, El Salvador, and Guatemala to escape poor conditions, violence, and a lack of economic opportunities. In the United States they, like earlier generations of immigrants, see a new and better life. They see the opportunity to earn more money, live without constant fear of violence or intimidation, and provide a brighter future for their children. The reaction to these immigrants has led to a divide in American culture, with many Americans supportive of these new immigrants but many also opposed. If we look at our history we will realize that this divide is nothing new. History also tells us that the opposition to these new groups of immigrants should eventually pass as is it did in past generations.
Why do we see this trend of opposition to new immigrants throughout our history? The explanation for this comes from fear. People often fear things that are different from what they know. They fear that these new immigrants may change the culture they are so familiar with and that they might be left behind. They are afraid that new immigrants will take their jobs and hurt them economically. They are afraid that new immigrants will bring the troubles of their home countries with them. It is normal for people to fear uncertainty, and this is why we see this response from a significant portion of the U.S. population.
Immigration has had an enormous impact on the United States in a number of ways. We can see that immigration causes fear and division within the population, and sometimes leads to harsh backlash against it. We also know that immigration has brought a tremendous diversity to American society. It has brought diverse cultures, food, religions, innovations, and ways of thinking. This diversity is something that has helped the country to thrive and develop into the global power it is today. Immigration has ultimately made the United States into a truly unique nation, but it has not occurred without some struggle, opposition, and division along the way.
http://www.iwm.at/transit-online/the-impact-of-immigration-on-american-society/

https://www.britannica.com/topic/Know-Nothing-party

Economists differ in their opinions on the impact that immigration has on the United States economy. On the one hand, some economists believe that immigration has a net-positive impact. Economists theorize that the influx of low-skilled workers fills jobs that many Americans won’t do such as seasonal positions in the farming industry, low-wage jobs in the service sector, and others. Another economic benefit of immigration is that low-wage workers help to keep prices low on many products and services. The low cost of labor saves companies money that they would otherwise have to spend to purchase expensive equipment or hire others at higher wages. The savings are passed on to the consumer in the form of lower prices.On the other hand, some economists argue that immigration has a negative impact on the United States economy. They point to the large numbers of immigrants who sign up for social welfare benefits. This represents a significant cost to American taxpayers.Another point economists make in favor of immigration having a negative impact on the economy involves the fact that many immigrants send a large portion of the money they earn in the US to their families in their home countries. While some of the money immigrants earn is spent in the US, there is a large outflow of capital to other countries.FURTHER READING:https://www.usnews.com/news/articles/2016-09-23/study-examines-immigrations-economic-costshttps://www.hoover.org/research/economic-effect-immigration

Economists assert that the impacts of immigration are largely positive.
They have argued against the theory that immigrants take jobs away from citizens. Economists suggest that although there is competition in the labor market, the money made by the immigrants is still spent within the economy, thus increasing demand for goods and services. The demand in the economy translates to more jobs.
The additional labor and increased demand for products and services have been shown to force companies to increase investments in both labor and productivity. The situation also helps improve wages in the long term. Thus, both citizens and immigrants get to enjoy better-paying jobs.
Immigrants are also credited with increased innovation and talent in the economy. The situation helps in introducing new products and processes for improving existing businesses.  Additionally, citizens are also pushed to higher-paying jobs to match the pace of innovation in the economy.
Immigrants also have the effect of keeping the population young and fit for productivity, especially in a situation where the native population is aging.
https://budgetmodel.wharton.upenn.edu/issues/2016/1/27/the-effects-of-immigration-on-the-united-states-economy

https://www.nbcnews.com/news/latino/5-things-know-about-immigration-u-s-economy-n179196

Calculus: Early Transcendentals, Chapter 3, 3.6, Section 3.6, Problem 40

y=(e^-x*(cos(x))^2)/(x^2+x+1)

Taking the natural logarithm of both sides and applying the properties of logarithms, we get

logy=loge^-x+2logcosx -log(x^2+x+1)
logy=-x+2logcosx-log(x^2+x+1)

Differentiating both sides with respect to x, we get

1/y dy/(dx)=-1+(2/cosx)(-sinx) -(1/(x^2+x+1))(2x+1)
1/y dy/(dx)=-1-2tanx-(2x+1)/(x^2+x+1)
dy/dx=y(-1-2tanx-(2x+1)/(x^2+x+1))
dy/dx=((e^-x(cos(x)))^2/(x^2+x+1))(-1-2tanx-(2x+1)/(x^2+x+1))
dy/dx=-((e^-x(cos(x))^2)/(x^2+x+1))(((x^2+x+1+2(x^2+x+1)(tanx)+2x+1))/(x^2+x+1))
dy/dx=-((e^-x(cos(x))^2)(x^2+3x+2+2(x^2+x+1)tanx))/(x^2+x+1)^2

Precalculus, Chapter 6, 6.4, Section 6.4, Problem 32

You need to use the formula of dot product to find the angle between two vectors, u = u_x*i + u_y*j, v = v_x*i + v_y*j , such that:
u*v = |u|*|v|*cos(theta)
The angle between the vectors u and v is theta.
cos theta = (u*v)/(|u|*|v|)
First, you need to evaluate the product of the vectors u and v, such that:
u*v = u_x*v_x + u_y*v_y
u*v = 3*4 + 2*(0)
u*v = 12
You need to evaluate the magnitudes |u| and |v|, such that:
|u|= sqrt(u_x^2 + u_y^2) => |u|= sqrt(3^2 + 2^2) =>|u|= sqrt13
|v|= sqrt(v_x^2 + v_y^2) => |v|= sqrt(4^2 + 0^2) => |v|= 4
cos theta = (12)/(4sqrt13) => cos theta = (3)/(sqrt13)
Hence, the cosine of the angle between the vectors u and v is cos theta = (3)/(sqrt13) , so, theta ~~ 34^o.

Why did Poe say there were 3 species: man, woman, and Margaret Fuller? Why did Margaret Fuller create a fictional character of a nineteenth-century woman to talk with?

There are many theories for why Poe made the assertion that "humanity is divided into men, women, and Margaret Fuller."
However, the most popular theory rests on how the men of Fuller's time related to her. I will endeavor to address this by referring to Edgar Allen Poe's criticism of Fuller and her work. You can read Poe's critique here.
If you prefer, you can search for the critique by its title: Criticism by Edgar Allan Poe, The Literati of New York City - No. IV. (B), Godey's Lady's Book, August 1846, pp. 72-78.
During her most prolific years, Margaret Fuller was admired by men for her incisive intelligence, wit, and powers of analysis. Despite this, however, few men found her attractive, perhaps because her feisty and dominant persona often made them uncomfortable. Emerson proclaimed that Margaret "carried too many guns." Certainly, men found her assertiveness abrasive. Edgar Allen Poe expressed male ambivalence towards Fuller best when he proclaimed that "humanity is divided into men, women, and Margaret Fuller."
To Poe, Fuller was a conundrum. Although she was biologically female, her behavior was seen as neither feminine nor representative of the best of her sex. In Poe's critique of "Woman in the Nineteenth Century," Fuller is represented in ambivalent terms. Men admired her intellectual gifts but were turned off by her unabashedly insistent nature. Poe admitted that few women could have written her treatise, even as he insisted that her conclusions were "radical."
At the same time, he allowed that her theories were neither "too novel, too startling, or too dangerous in their consequences." The only objections he had were that Fuller distorted too many "premises" and ignored important "analogical inferences." He criticized Fuller for ignoring the fact that sexual differences were divinely ordained.
Poe also maintained that Fuller was not wholly objective in her treatise: after all, she appeared to judge all women "by the heart and intellect of Miss Fuller," despite the fact that there were "not more than one or two dozen Miss Fullers on the whole face of the earth." At the same time, Poe lambasted the "silly, condemnatory criticism" of Fuller's work. At the end of the critique, Poe insisted that although Fuller was reasonably attractive, the distinctive thrust of her upper lips often conveyed "the impression of a sneer." So, Poe's assertion about humanity is centered on male ambivalence towards Fuller.
In Woman In The Nineteenth Century, Fuller addressed a fictional character. The text gives us some clues as to who this character represents: the American "everywoman." Fuller hoped that the average American woman would listen to what she said and support her conclusions about feminine intellect, female agency, and gender roles. Fuller spoke to the American woman because she believed that women were the female gender's best advocates and supporters.
Fuller maintained that women should love truth and excellence. To this end, she argued that they should resolutely reject their coquettish nature:

It must happen, no doubt, that frank and generous women will excite love they do not reciprocate, but, in nine cases out of ten, the woman has, half consciously, done much to excite. In this case, she shall not be held guiltless, either as to the unhappiness or injury of the lover. Pure love, inspired by a worthy object, must ennoble and bless, whether mutual or not; but that which is excited by coquettish attraction of any grade of refinement, must cause bitterness and doubt, as to the reality of human goodness, so soon as the flush of passion is over.

So, Fuller created a fictional female character to talk to because she believed that her conclusions about female agency would be better accepted by members of her own sex.

I believe that, at present, women are the best helpers of one another.
Let them think; let them act; till they know what they need.

These are likely the conclusions that Poe criticized. He maintained that Fuller neither gave credence to divine appointment of sexual differences nor acknowledged the possibility that female objections to her thesis would arise.
For her part, Fuller was especially interested in promoting the concept that men and women possessed both female and male energies in themselves ("There is no wholly masculine man, no purely feminine woman."). Thus, amity between the sexes could not occur until both acknowledged this sexual dichotomy within themselves.

What is a plane mirror?

A plane mirror is a mirror whose surface is planar or “flat.” The familiar mirrors found in bathrooms and dressing rooms are normally plane mirrors. The shape of a mirror’s surface affects the image seen in the mirror, as can be observed in funhouse mirrors, which distort our images in various ways.
Mirrors used in optics, as in lasers and telescopes, may be plane mirrors or convex or concave curved mirrors. Depending on the purpose, spherical, parabolic, or even cylindrical curved mirrors may be selected. The reflecting surfaces of these curved mirrors have the shapes of portions of the solids named in the description.
Differently shaped mirrors have different effects on the rays of light that strike them. One way of describing the effect of a particular mirror shape is to specify details of the image it produces. All plane mirrors produce a virtual image. This means that when an object is viewed in a plane mirror, the object appears to be behind the mirror. Furthermore, this virtual image is the same size as the reflected object, and the object and image are the same distance from the plane mirror’s surface. Images in a plane mirror are always upright, which does not seem extraordinary unless you are familiar with the various mirror and lens shapes that produce inverted (upside-down) images.
A final characteristic of images in plane mirrors is that they appear to be be left-right reversed. Most of us have noticed at some point that graphics and lettering on our clothing appear backwards when viewed in a plane mirror, and if we part our hair on the side, we may be startled to see that photographs of our faces are the reverse of what we see in the mirror.
More information on plane mirrors may be found on the page from The Physics Classroom linked below.
https://www.physicsclassroom.com/class/refln/Lesson-2/Image-Characteristics

What mostly causes Bruno to recognize that he and Shmuel are dissimilar?

In The Boy in the Striped Pajamas, Bruno finally recognizes that he and Shmuel are dissimilar when Gretel corrects him on his pronunciation of "Out-With" to Auschwitz and explains that the Jews live on the other side of the fence to stop them from mixing with other people. When Bruno further questions Gretel concerning what his family is, she responds by saying they are the "opposite" (183). Before this episode, Bruno thought the children chose to remain on opposite side of the fence.
However, ironically, it is shortly after this discussion between Bruno and Gretel that the children discover they have lice. When father shaves off Bruno's hair, he realizes that he looks more like Shmuel than he thought before. Therefore, even though Bruno finally begins to realize the differences between himself and the children on the other side of the fence, he also begins the self-realization that he and Shmuel are alike in many ways on a deeper level, which foreshadows the end of the novel.

int (sec(2x) + tan(2x)) dx Find the indefinite integral.

int(sec(2x)+tan(2x))dx=
Use additivity of integral: int (f(x)+g(x))dx=int f(x)dx+int g(x)dx. int sec(2x)dx+int tan(2x)dx=
Make the same substitution for both integrals: u=2x, du=2dx=>dx=(du)/2
1/2int sec u du+1/2int tan u du=
Now we have table integrals.
1/2ln|sec u+tan u|-1/2ln|cos u|+C
Return the substitution to obtain the final result.
1/2ln|sec(2x)+tan(2x)|-1/2ln|cos(2x)|+C 
http://integral-table.com/

What is autobiographical element in The Tempest by William Shakespeare?

The question of whether The Tempest is autobiographical has long been a source of speculation among scholars and literary critics alike. One of the main pieces of evidence offered in support of the autobiography thesis is the nature of the work itself. Previously, Shakespeare had almost always used preexisting source material as the basis for his plays. He always managed to transform such material into something wholly unique, but it was still preexisting material, all the same.
But this is not so with The Tempest. There is simply no precedent for the elements that Shakespeare, in a Prospero-like way, conjures up to create the magical world in which this, his final play, is set. The Tempest is all Shakespeare, conception as well as execution. And it's telling that when John Heminges and Henry Condell—fellow actors and friends of Shakespeare—compiled the first complete edition of his plays, they ignored the order in which the plays were written and put the last one, The Tempest, first. This could be taken to suggest that Heminges and Condell saw the play as not just the ultimate example of Shakespeare's original power as a dramatist but a unique expression of his personality.

There are strong links between The Tempest and William Shakespeare's own life. These revolve around the character of Prospero, his powers, and where he is in his "career" on the island.
Start with the basics: both are men of mature age. That's basic, but what follows is less basic.
Prospero is a wizard. On this island, people do what he says. They move according to his wishes. He organizes the drama early in the play, and the narrative twists and turns throughout it. At times, his magic makes them see things that aren't really there.
Shakespeare is a playwright, not a wizard, but on stage, people do what he says. Characters move according to his wishes. He structures the drama throughout his plays, and, when he moves into his poetic moments, like in the monologues, he makes us all see things that aren't there.
At the end of the play, Prospero sets his staff (his magic) aside. This furthers the comparison between Prospero and Shakespeare because The Tempest was Shakespeare's final play.
https://www.theguardian.com/books/booksblog/2014/apr/15/prospero-the-tempest-shakespeare-reading-group

How is Sid different from Tom?

Sid is a great foil for Tom in the book. Unlike Tom, Sid is quiet and mindful of his manners. The text tells us that he has no "adventurous, trouble-some ways."
In short, Sid is the total opposite of the mischievous and rambunctious Tom. In the story, Sid exposes Tom for going swimming, and Tom promises to get his revenge.
Of course, Aunt Polly prefers Sid to Tom. Upset that Tom is always misbehaving and getting the better of her, she orders him to whitewash the fence. You can read all about it in chapter 2. For his part, Tom isn't about to whitewash the fence if he can get someone else to do it.
In the same chapter, you'll read about how Tom manages to trick other boys into doing his work. And that's not all: Tom even accepts a reward (an apple) from Aunt Polly for his supposed industry. On his way out, he manages to steal a doughnut from right under Aunt Polly's nose. The poor woman never discovers the truth about Tom whitewashing the fence.
Basically, Tom managed to manipulate other boys into doing his work by portraying whitewashing as an enviable task, fit only for the best boys. In other words, Tom portrayed whitewashing the fence as an exclusive activity.
Tom's wily ways present a total contrast between him and Sid. On the way out, Tom throws a hail of mud clods at Sid, who is caught off guard. To Tom, this is a satisfactory way of paying Sid back "for calling attention to his black thread and getting him into trouble."
Sid's good behavior may put him on good terms with adults, but his smug attitude often puts him at odds with Tom. Both Tom and Sid are total opposites. The former is mischievous and thrill-seeking, while the latter is virtuous to a fault.

Sid really couldn't be more different to Tom if he tried. For one thing, he's a real goody-two-shoes. You'd never catch Sid playing hooky to go swimming, or getting into fights, or running off to play pirates and pretending to be dead. The boy has no sense of adventure. He always does as he's told and never gives Aunt Polly the slightest trouble.
It's no surprise that Sid doesn't get on with Tom, given their huge differences in personality. Sid resents Tom for his waywardness and lack of discipline, and he is always looking for ways to get Tom into trouble. Sid is a real sneak and has no hesitation in telling on Tom to Aunt Polly. We see this when Sid observes that the thread on Tom's collar is a different color to what it was when he set out for school that morning. This alerts Aunt Polly to the fact that Tom has been playing hooky to go swimming and has fixed his collar with a different color thread.

y = 9-x^2 , y=0 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.

Given the curves
y=9-x^2,
y=0
we have to find the volume using the shell method.
so , the volume of vertical rotation is given as
V=2*pi int_a^b p(x)h(x) dx
where p(x) is a function of  average radius and h(x) is a function of height
so as the solid is rotating with respect to y=0 ie x axis
sop(x) =x
and height h(x) = 9-x^2
now let us find the range of x on the x axis by the intersection of the curves  y=9-x^2 and y=0
=> 0=9-x^2
=> x= +-3
now the volume is =2*pi int_a^b p(x)h(x) dx
 
= 2pi int_-3^3 (x)(9-x^2) dx
=4pi int_0^3 (9x-x^3) dx
=4*pi *[(9x^2)/2-x^4/4]_0 ^3
= 4*pi *[[(9(3)^2)/2-(3)^4/4]-[0]]
=4*pi*81/4
= 81pi
is the volume

Single Variable Calculus, Chapter 1, Review Exercises, Section Review Exercises, Problem 7

State the domain and range of the following functions.


$
\begin{equation}
\begin{aligned}

y =& 1 + \sin x\\
\text{ domain:} & [-\infty, \infty]\\
\text{ range:} & [0,2]

\end{aligned}
\end{equation}
$


Recall that the range of $y = \sin x$ is $[-1, 1]$


$
\begin{equation}
\begin{aligned}

\text{So }, y =& 1 + \sin x\\
=& 1 + (-1)\\
=& 0\\
y =& 1 + \sin x\\
=& 1 + (1)\\
=& 2

\end{aligned}
\end{equation}
$




Therefore, the range of $y = 1 + \sin x$ is $[0, 2]$

y = sqrt(x+2) , y = x , y = 0 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 x-axis.

To be able to use the shell method, the rectangular strip from the bounded plane region should be parallel to the axis of revolution.
By revolving multiple rectangular strip, it forms infinite numbers of hollow pipes or representative cylinder.
  In this method, we follow the formula: V=int_a^b (length * height * thickness)
This can be also expressed as:
 V=int_a^b (2pi* radius * height *thickness of rectangular strip)
or  V=int_a^b (2pir * length of rectangular strip *thickness of rectangular strip) where r = distance of the rectangular strip from the axis of rotation.
For the bounded region, as shown on the attached image, the rectangular strip is parallel to x-axis (axis of rotation). We can let:
radius=y
height=y -(y^2-2) = y-y^2+2
Note: When we squared both sides of y =sqrt(x+2) , we get: y^2 =x+2.
It can be rearranged into x= y^2-2.
thickness=dy
the boundary values of y is a=0 to b=2
Then the integral set-up will be:
V= int_0^2 2 pi *y * (y-y^2+2) *dy
Simplify:V= int_0^2 2 pi ( y^2-y^3+2y)dy
Apply the basic integration property: int c f(x) dx - c int f(x) dx
V= 2pi int_0^2 ( y^2-y^3+2y)dy
Apply basic integration property: int (u+-v+-w) dx = int (u) dx +- int (v) dx+- int (w) dx.
V= 2pi [int_0^2 ( y^2) dy-int_0^2(y^3)dy+int_0^2(2y)dy]
Apply Power rule for integration: int x^n dx = x^(n+1)/(n+1) .
V= 2pi [y^3/3 - y^4/4+2*y^2/2]|_0^2
V= 2pi [y^3/3 - y^4/4+y^2]|_0^2
Apply the definite integral formula: int_a^b f(x) dx = F(b) - F(a) , we get:
V= 2pi [(2)^3/3 - (2)^4/4+(2)^2]-2pi [(0)^3/3 - (0)^4/4+(0)^2]
V =2pi[8/3 -4+4] -2pi[0-0+0]
V= (16pi)/3 -0
V= (16pi)/3  or 16.76 ( approximated value)

With what literary movement is the book Red Scarf Girl by Ji-Li Jiang associated?

Red Scarf Girl is a form of literary memoir. The author, Ji-Li Jiang, is writing about her own experiences during the Cultural Revolution, which took place in China in the mid 1960s to mid 1970s. The story begins as the Cultural Revolution is starting in China, and the author narrates her experiences dealing with the events of the Cultural Revolution as they affect her. For example, the author is impressed with the dancers of the Liberation Army that come to her school, but she realizes over time that she cannot take part in the Liberation Army because of her relatively upper-class background. The book is a literary memoir because it follows the narrative of a story and contains the types of themes and literary devices that a fictional book does. The book could also be considered a form of historical memoir, as it discusses events in history and discusses how those events affected the author.

College Algebra, Chapter 8, Review Exercises, Section Review Exercises, Problem 38

Identify the type of curve which is represented by the equation $\displaystyle 2x^2 + 4 = 4x + y^2 $
Find the foci and vertices(if any), and sketch the graph

$
\begin{equation}
\begin{aligned}
y^2 - 2(x^2 -2x) &= 4 && \text{Factor and group terms}\\
\\
y^2 - 2(x^2-2x+1) &= 4 -2 && \text{Complete the square; Add } \left( \frac{-2}{2} \right)^2 =1 \text{ on the left and subtract 2 from the right}\\
\\
y^2 - 2(x - 1)^2 &= 2 && \text{Perfect square}\\
\\
\frac{y^2}{2} - (x - 1)^2 &= 1 && \text{Divide by 2}
\end{aligned}
\end{equation}
$


The equation is hyperbola that has the form $\displaystyle \frac{(y - k)^2}{a^2} - \frac{(x-h)^2}{b^2} = 1$ with center at $(h,k)$ and vertical transverse axis.
The graph of the shifted hyperbola is obtained from the graph of $\displaystyle \frac{y^2}{2} - x^2 = 1$ by shifting it 1 unit to the right. This gives us a
$a^2 = 2$ and $b^2 = 1$, so $a = \sqrt{2}, b = 1$ and $c = \sqrt{a^2 + b^2} = \sqrt{2+1} = \sqrt{3}$. Then, by applying transformation

$
\begin{equation}
\begin{aligned}
\text{center } & (h,k) && \rightarrow && (1,0)\\
\\
\text{vertices } & (0,a)&& \rightarrow && (0,\sqrt{2}) && \rightarrow && (0+1,\sqrt{2}) && = && (1, \sqrt{2})\\
\\
& (0,-a)&& \rightarrow && (0,-\sqrt{2}) && \rightarrow && (0+1,-\sqrt{2}) && = && (1,-\sqrt{2})\\
\\
\text{foci } & (0,c)&& \rightarrow && (0,\sqrt{3}) && \rightarrow && (0+1,\sqrt{3}) && = && (1,\sqrt{3})\\
\\
& (0,-c)&& \rightarrow && (0,-\sqrt{3}) && \rightarrow && (0+1,-\sqrt{3}) && = && (1,-\sqrt{3})
\end{aligned}
\end{equation}
$

Then, the graph is

Why does Higgins agree to educate the flower girl in George Bernard Shaw's Pygmalion?

Henry Higgins, a linguist, happens to overhear Cockney flower seller Eliza Doolittle speaking in lower class dialect at Covent Garden. He brags that:

in three months I could pass that girl off as a duchess at an ambassador's garden party.

He goes home, thinking no more of that passing comment or of the Cockney flower seller.
In her cold room, however, Eliza ponders what Higgins said about teaching her to speak like lady. She'd like a better life for herself, so she boldly shows up at his doorstep the next day. She demands lessons and offers to pay a shilling apiece for them.
Higgins is ready to throw her out when Colonel Pickering, who happens to be there, offers to pay. He also holds Higgins's feet to the fire, betting him that he won't be able to pass Eliza off as a duchess. Higgins rises to the challenge and agrees to the bet. In this way, Eliza ends up being educated to act, dress and speak like a lady.
This has nothing to do with Higgins having any compassion for Eliza. He plans to throw her out again once the bet is over.

Higgins first encounters the flower girl outside Covent Garden and transcribes her speech. He boasts to Colonel Pickering that by means of his skills as a speech coach he could pass her off for a duchess at an ambassador's garden party in a period of three to six months of instruction. To Higgins' surprise, the flower girl, who reveals her name to be Eliza Doolittle, appears at his house the next day and offers to pay him for speech lessons so that she can get a job at a flower shop.
Higgins agrees to teach her for several reasons. First, he finds the project intriguing and an interesting professional challenge. Second, he makes a bet with Colonel Pickering, and wants to win the bet. Also, Colonel Pickering agrees to pay the expenses of the project, including appropriate clothing for Eliza. 

Calculus of a Single Variable, Chapter 6, 6.2, Section 6.2, Problem 38

It is impossible to predict when a particular atom will decay. However, it is equally likely to decay at any instant in time. Therefore, given a sample of a particular radioisotope, the number of decay events −dN expected to occur in a small interval of time dt is proportional to the number of atoms present N, i.e.
-(dN)/(dt)propto N
For different atoms different decay constants apply.
-(dN)/(dt)=\lambda N
The above differential equation is easily solved by separation of variables.
N=N_0e^(-lambda t)
where N_0 is the number of undecayed atoms at time t=0.
We can now calculate decay constant lambda for carbon-14 using the given half-life.
N_0/2=N_0e^(-lambda 5715)
e^(-5715lambda)=1/2
-5715lambda=ln(1/2)
lambda=-(ln(1/2))/5715
lambda=1.21 times 10^-4
Note that the above constant is usually measured in seconds rather than years.
Now we can return to the problem at hand. Since the charcoal contains only 15% (0.15N_0 ) of the original carbon-14, we have
0.15N_0=N_0e^(-1.21times10^-4t)
Now we solve for t.
e^(-1.21times10^-4t=0.15)
1.21times10^-4=-ln 0.15
t=-(ln0.15)/(1.21times10^-4)
t=15678.68
According to our calculation the tree was burned approximately 15679 years ago.

Calculus and Its Applications, Chapter 1, 1.8, Section 1.8, Problem 14

Determine the $f'(x)$ of the function $\displaystyle f(x) = x^3 - \frac{5}{x}$
We have $f(x) = x^3 - 5x^{-1}$, so

$
\begin{equation}
\begin{aligned}
f'(x) = \frac{d}{dx} \left( x^3 - 5x^{-1} \right) &= \frac{d}{dx} (x^3) - 5 \cdot \frac{d}{dx} (x^{-1})\\
\\
&= 3x^2 - 5(-1) x^{-1-1} \\
\\
&= 3x^2 + 5x^{-2} \text{ or } 3x^2 + \frac{5}{x^2}
\end{aligned}
\end{equation}
$


Then,

$
\begin{equation}
\begin{aligned}
f''(x) &= 3 \cdot \frac{d}{dx} (x^2) + 5 \cdot \frac{d}{dx} (x^{-2}) \\
\\
&= 3 \cdot 2 x^{2-1} + 5(-2) x^{-2-1} \\
\\
&= 6x - 10 x^{-3} \text{ or } 6x - \frac{10}{x^3}
\end{aligned}
\end{equation}
$

How is resilience is presented through the poem Invictus written by William Ernest Henley?

Resilience, or the speaker's "unconquerable soul," is presented in this poem as standing firm against the onslaught to which it is subjected by life. Henley uses the metaphor of night, "black as the pit," to suggest that the speaker may feel lost and isolated, and yet he thanks the "gods" for the fact that his soul, even in this situation, is "unconquerable." Without even the promise of light, only "the Horror of the shade" beyond the darkness, the speaker's resilience is such that he is "unafraid," even in the most seemingly dire circumstances.
It is clear, too, that attempts have been made to conquer the inconquerable. The "bludgeonings of chance" and the "fell clutch of circumstance"—both vivid, near-tangible metaphors—have assailed the speaker to the extent that he is figuratively "bloody," and yet he does not bend under the blows, remaining "unbowed." The language is violent, creating a sense that resilience of the soul means withstanding a relentless barrage from all sides.
In the final stanza, the speaker seems to summon his courage and conviction, giving an indication of how he is able to maintain such resilience. The parallelism—"I am the master of my fate, / I am the captain of my soul"—emphasizes the speaker's self-reliance, which seems to be the key to his endurance of the "night" he describes.

What is Montresor's attitude toward revenge, or punishment in "The Cask of Amontillado"?

Throughout the short story, Montresor mentions that he had been wronged a thousand times by Fortunato and felt justified in taking his revenge. Montresor mentions at the beginning of the story that in order to right a wrong, he finds it necessary to make Fortunato pay for his hurtful actions. Montresor understands the delicate, careful manner that he must approach his revenge and makes sure not to reveal anything about his plans to anybody. Montresor also mentions that in order to enact the perfect revenge, he must not suffer as a result of his actions, which is why he approaches his plan with such care. Montresor also believes that Fortunato needs to know that he is paying for his actions and that it is Montresor who is making him pay. Clearly, Montresor's attitude towards revenge is specific and direct. The fact that he carefully plans his revenge by making sure his servants are not home and by enticing Fortunato to follow him under the guise of drinking a rare wine reveals Montresor's calculated plot and deliberate ideas about revenge. Fortunato's death is also terrifying and brutal, which again illustrates Montresor's seriousness about enacting revenge. Also, Montresor is telling the story nearly fifty years after enacting revenge, which indicates that his crime went unpunished, and he met his own standards. 

It is apparent that Montresor feels revenge is justifiable when insults and injuries go beyond the pale [outside the boundaries of normal behavior].
Poe's unreliable narrator explains to his audience that he has endured multiple injuries until the point that they become so excessive—"a thousand injuries"—as well as compounded with "insult" that he feels compelled and justified to avenge himself. Nevertheless, there are certain stipulations for seeking true revenge:
The act of revenge must punish, and it must punish without any risk to the avenger. (In his act of luring Fortunato into the catacombs, Montresor takes no risk as he commits this act during the Carnival in which people are distracted in their celebrations; furthermore, Fortunato is disguised by his costume.)
The revenge must "punish with impunity." There must be no consequences that result from this act of retribution. (Apparently, there have been no consequences for Montresor since it has "half a century" and "no mortal has disturbed" the remains of Fortunato.)
The avenger must not himself be the recipient of any retribution for his act. (Montresor has received no punishment for his crime. No one has avenged Fortunato's death against him, either.)
The revenge is not accomplished if the victim is not aware of the identity of the avenger. (Fortunato certainly has known that he was being walled in to die by Montresor.)

What effect did the Native Americans have on Europeans?

In a practical sense, Native Americans influenced the European diet in profound ways. Native Americans cultivated foods that were unknown to the Europeans before first contact. Important foods introduced to Europe included tomatoes, potatoes, and maize (corn). These are now such staples that it is hard to imagine there was a time when Europeans did not eat them. Potatoes were so easy to grow and so nutritious that the Irish, for example, relied on them too heavily. When a potato blight came and potato crops were destroyed, many starved.
In a more philosophical sense, the cultural contact and cultural differences led Europeans thinkers to question their own values and way of life. The idea of the "Noble Savage" developed, which saw the Native Americans as superior to the Europeans because of their simpler way of life.

What's the presentation of suicide, talk of suicide, and self-harm in Macbeth?

Although Lady Macbeth's suicide occurs off stage and is reported after the fact, the famous scene leading up to and foreshadowing it occurs at the beginning of Act V. Here, we witness her sleepwalking. She tries, in her sleep, to wash the blood from the various murders she's been involved with off her hands. Of course, although she attempts to scrub away the bloodstains, she really has no physical blood on her hands. The "blood" represents her guilty conscience and the way the murders she and Macbeth have perpetrated torment her.
The scene is eerie and unsettling as we watch an unstable, mentally tortured person unwittingly confess her guilt. Her servants find this display, which they say has been repeated over and over, night after night, deeply unsettling. It is also ironic: Lady Macbeth was the one who pooh-poohed her husband's doubts about murdering Duncan by boasting of her hard heart and manlike strength of will. She had claimed she could dash her baby's brains out without a second thought. After the initial murder, she tells Macbeth to man up and get over it when he says in horror that Duncan's blood could turn the green seas red, but now she is the one suffering the unbearable pangs of guilt and remorse.

What are five reasons why the Declaration of Independence was written?

There were several reasons why the Declaration of Independence was written. One reason was to inform the world that the colonists were declaring their independence from Great Britain, and they were now no longer connected to the British government. A second reason was to tell the world the specific reasons why the colonists were declaring their independence. They wanted the world to know what British government and the King of England had done to lead them to declare independence.
There were other reasons for writing the Declaration of Independence. The colonists wanted to explain their beliefs about what rights people should have. The Declaration of Independence explained that all people have the right to life, liberty, and the pursuit of happiness. The colonists also wanted to explain that the job of the government is to protect the rights of the people. They wanted to let the world know that when a government does not protect the rights of the people, the people must replace the government. Since the colonists felt the British government was no longer protecting their rights, they had to declare their independence from Great Britain.
https://billofrightsinstitute.org/founding-documents/declaration-of-independence/

What is the instrument used for broadcasting?

Transmitter is the name of the equipment used for broadcasting. A transmitter is an electronic device which generates and amplifies a carrier wave, which it mixes with the information to be disseminated and then broadcasts the resulting signal from an antenna.
Transmitters do this by first converting electric power from a battery or electrical mains into radio frequency. An electronic information signal in the form of an audio (sound) signal from a microphone or a video (image) signal from a video device such as a camera or a computer is mixed with the radio frequency generated by the transmitter through a process called modulation. The radio waves generated by the process of modulation is called the carrier signal.
The carrier signal is then transmitted from an antenna. The antenna may be enclosed in the same case as the transmitter, as in portable devices, or it may be mounted on top of a building or on a separate tower, as it is in TV or radio stations.

Woodenplank.

How is memory shown?

The theme of memory in Tears, Idle Tears by Tennyson is shown as both beautiful and painful. 
The speaker contemplates his life and thinks about past days, the "days that are no more," which were beautiful and full of passion but now have passed. Even the happiest moments are temporary and must end, leaving only memories behind. For this reason, they are truly beautiful but also tinged with sadness and melancholy, as the speaker knows it will be impossible to relive these experiences. These past times and memories only live on in our minds as time goes by, causing "tears, idle tears" when they are remembered. 
This poem focuses on the theme of the passing of time and the consequent realization that everything must end in death, especially our own lives. It is this poignant realization however that pushes us to create beautiful things and truly appreciate life, as we know that we will not get the chance to relive certain experiences.

What is the significance of fire in Lord of the Flies?

Fire is a complex symbol in Golding's classic novel Lord of the Flies. In the story, fire is both destructive and necessary for survival at various moments in the story. When the boys initially attempt to light a signal fire, they pile too much dry wood onto the fire and accidentally catch an entire side of the mountain on fire. Tragically, the littlun with a mulberry-colored birthmark dies in the forest fire. Towards the end of the story, Jack instructs his hunters to burn the forest in hopes of smoking Ralph out of his hiding place. By doing so, Jack and his savages set the entire island on fire and narrowly avoid death at the end of the story. These examples indicate that fire has the potential to be destructive like the disastrous decisions the boys make on the island.
The signal fire symbolically represents the hope of rescue, is the boys' connection to the outside world, and can be used as a gauge to measure the boys's civility. Initially, Jack and his hunters are in charge of maintaining the signal fire at the top of the mountain. The boys hope that a passing ship will see the smoke and eventually rescue them. Ralph, who is an outspoken proponent of civilization, continually reminds the boys about the importance of maintaining the signal fire. Tragically, the hunters allow the signal fire to go out and they miss a rare opportunity for rescue when a ship passes.
After relighting the signal fire, Samneric mistake a dead paratrooper on the top of the mountain for the beast and once again let the signal fire go out. Ralph, Simon, and Piggy then attempt to build a small signal fire on the beach but cannot maintain it because the other boys join Jack's tribe of savages and there is not enough dry wood around to feed the flames. The absence of the signal fire corresponds with the absence of civility and loss of hope on the island. Without the signal fire, the boys rapidly descend into savagery, and there is virtually no hope of rescue.

As a symbol of technology—generated by Piggy's glasses, no less—fire purifies the boys' primitive surroundings by introducing into their new surroundings a feature of the modern life they left behind in England. It allows them, then, to maintain a connection with what is comforting and familiar in the midst of this harsh, scary environment. So long as the boys can keep this fire going, there is always hope that they will one day be rescued and return to their former lives.
That's why it's rather telling that Jack and his gang make no effort to keep the fire burning. Truth be told, they don't want to go back home any time soon. They're doing just fine on the island, thank you every much, and see it as nothing more than an awfully big adventure. Jack's association with the fire going out is instructive; it shows us that Jack offers no hope for the other boys, only brutal domination and control. So long as Jack's around, any hope that the other boys have will always be tinged with fear.

The fire from Lord of the Flies is significant because it symbolizes both hope and destruction.  
When the novel first begins, Ralph is adamant that a signal fire is kept lit.  His hope rests on the belief that the fire will be able to attract the attention of a passing ship.  

“There’s another thing. We can help them to find us. If a ship comes near the island they may not notice us. So we must make smoke on top of the mountain. We must make a fire. . . We’ve got to have special people for looking after the fire. Any day there may be a ship out there“ –- he waved his arm at the taut wire of the horizon -– “and if we have a signal going they’ll come and take us off.”

Unfortunately that initial fire wound up being more destructive than anything else.  By then end of chapter two, the fire had burned completely out of control, didn't signal any rescue whatsoever, and killed one of the boys.  
While fire may have gone from a symbol of hope to a symbol of destruction in the beginning of the book, fire does the opposite at the novel's conclusion.  Jack has gone ballistic by the end of the book, and he wants to hunt and kill Ralph.  Part of Jack's plan is to use fire to smoke Ralph out into the open.  To Jack's credit, that part of the plan is successful; however, the fire and smoke are also seen by a passing ship.  Rescue arrives just in time to save Ralph's life.  Fire has once again been turned into a symbol of hope and rescue.

The fire reached the coconut palms by the beach and swallowed them noisily. A flame, seemingly detached, swung like an acrobat and licked up the palm heads on the platform. The sky was black.
The officer grinned cheerfully at Ralph.
“We saw your smoke." 

The liver is an important organ in detoxication of harmful substances. What organelle in liver cells is active in this process?

The question is correct in stating that the liver plays an important role in detoxification of harmful substances. The liver, being an organ, is made up of liver tissue, and tissue is made of cells. Cells then contain subunits called organelles that perform specific functions inside the cell. The organelle that this question is asking about is the smooth endoplasmic reticulum (smooth ER). It is smooth because it is not studded with ribosomes like the rough endoplasmic reticulum. Both types are present in animal and plant cells; however, cells that specialize in producing lipid and steroid hormones have a greater amount of smooth ER. The smooth ER is also devoted to the metabolism of lipids. In the liver, one of the main functions of the smooth ER is to metabolize and detoxify ethanol (alcohol) and specific drugs like barbiturates.
https://biologywise.com/smooth-endoplasmic-reticulum

https://bscb.org/learning-resources/softcell-e-learning/endoplasmic-reticulum-rough-and-smooth/

Metaphor in the poem the red wheelbarow

There is only one metaphor in this incredibly short poem, and it's expressed by the following lines:

"a red wheelbarrowglazed with rainwater..."

The red wheelbarrow is presented to us as being "glazed," that is to say, shining, and with a certain hardness to it. The narrator sees the wheelbarrow just after a shower of rain and with the sun peeping through the clouds. The sun makes the wet surface of the wheelbarrow shine; it also makes the white chickens gleam.
The metaphorical use of the word "glazed" implies a certain fixity in the hard surface of the wheelbarrow. The weather will change, and the seasons will come and go, but normality will always return. The chickens will emerge from their hiding place after the storm has passed, and life will go on as before. Yes, such moments of storm and stress will continue to recur throughout our lives, but they never last. What matters is the sense of stability, the normal rhythm of our daily lives to which we return after the moments of turbulence have elapsed. And it is upon those solid foundations that "so much depends."
 

Precalculus, Chapter 7, 7.2, Section 7.2, Problem 24

7x+8y=6
-14x-16y=-12
From the first equation,
7x=6-8y
x=(6-8y)/7
Substitute the value of x obtained in the second equation,
-14((6-8y)/7)-16y=-12
-2(6-8y)-16y=-12
-12+16y-16y=-12
-12+0y=12
The equations has an infinite number of solutions.
If the equations are of the form,
a_1x+b_1y+c_1=0
a_2x+b_2y+c_2=0
and if,
a_1/a_2=b_1/b_2=c_1/c_2
then the equations have an infinite number of solutions.

What steps does Shylock take to ensure that Antonio is bound to the condition in the bond?

As Act I, Scene III, of William Shakespeare’s The Merchant of Venice begins, the character of Shylock, a Jewish moneylender, is introduced to the audience. The tense relationship between Shylock, Bassanio, and Antonio is quickly established despite some cordiality during the formalities. Bassanio’s invitation to Shylock to join him and Antonio for dinner is quickly and rudely rebuffed: “I will buy with you, sell with you, talk with you, walk with you, and so following, but I will not eat with you, drink with you, nor pray with you.” The topic of Bassanio’s need of money and of Antonio’s agreement to borrow that money on his friend’s behalf has been broached, and the moneylender is indeed interested.
The issue, then, becomes one of collateral, and it is here that the crux of the matter will be established, providing for the play’s dramatic tension and for the eventual and humiliating rejection of Shylock’s demand for payment from Antonio. The step that Shylock takes to ensure that Antonio is bound to the condition of the bond—a pound of the latter’s flesh in the event he is unable to repay the loan (“If you repay me not on such a day, / In such a place, such sum or sums as are / Express'd in the condition, let the forfeit / Be nominated for an equal pound / Of your fair flesh, to be cut off and taken / In what part of your body pleaseth me”)—is the court system. Shylock places his faith in the strength of his argument and the wisdom of the juror. Little does he know that Portia will intervene in the legal proceedings to his detriment. The trial in Act IV of The Merchant of Venice provides both for Shylock's final denunciation and for his heartfelt plea for justice considering his and his people’s history of dehumanization at the hands of the Christians who dominate Venice.

Shylock has a conversation with Antonio before they agree on the bond. First, Shylock ensures Antonio that he is able to provide the amount of money Bassanio intends to borrow from him. Next, Shylock mentions Antonio’s belief in lending money without charging interest and uses a story from the Bible to argue against it. Being a Christian, Antonio is much irritated by Shylock’s comments, saying that Shylock is like a devil who cites the Bible to suit his own purpose. Then Shylock further increases Antonio’s anger by pointing out that Antonio has insulted him many times before, and so asks why he should lend money to Antonio. Antonio says this is just a business transaction, and he will pay the penalty if he breaks the bond. After getting this word, Shylock puts on a friendly face and offers to lend him the money free from interest on the condition that he gets a pound of Antonio’s flesh if he fails to pay back. He further assures Antonio that it’s just a game and his flesh would be of no use to him. Antonio is probably prepared to pay a very high interest initially, but Shylock’s offer appears to be a lot more favorable than he has expected. He is also quite confident about this venture capital and does not take this condition seriously. Therefore, he gladly accepts it without hesitation and thinks Shylock grows kind.

In "The War of the Wall," what was the painter lady doing in town?

The painter lady has come to town ostensibly with the purpose of painting a mural. It is not until much later that her real objective is made apparent to the youths who resent her presence at "their wall."
From the children's point of view, the painter lady has no right to do anything to the neighborhood wall, where they play handball and the old people sit in the shade. The narrator is especially displeased to think that this woman may paint over their friend's name, which she has carved as a memorial to a soldier killed in Vietnam. Ironically, the children who criticize the painter for invading their territory and marking off spaces on the wall are surprised on Monday after school when they come to spray paint over the artist's work.
On this once-chipped wall, the artist has depicted people from the neighborhood, along with the faces of famous people such as Harriet Tubman, Martin Luther King, Malcolm X, "a handsome dude in a tuxedo seated at a piano" (perhaps Duke Ellington or Count Basie), and portraits of people from the neighborhood. These include the narrator's father and the narrator herself looking at a row of books. Her friend Lou spins a globe on the tip of his index finger as though it were a basketball. Suddenly, Lou drops the bag of black paint and rushes to the wall, running his fingers over the painted rainbow where Jimmy Lyons's name had been chiseled. Now the name is painted into this rainbow. The dedication of this beautiful mural reads as follows:

To the People of Taliaferro StreetI Dedicate this Wall of RespectPainted in Memory of My CousinJimmy Lyons

What is evidence that "Zaabalawi" by Naguib Mahfouz can be interpreted as a spiritual quest, portrait of mental illness/ obsession, desperate search for companionship or support, or pursuit of self-knowledge.

In "Zaabalawi," the main character is afflicted with a serious illness that medical doctors cannot cure. Determined, he sets off on a quest to find Zaabalawi, a man who is rumored to have great healing powers. This quest can be seen through multiple perspectives, and the author leaves the reader to determine which is correct.
Spiritual Quest
The events in "Zaabalawi" can be interpreted as a spiritual quest since the main character is seeking a healer with metaphysical powers. The protagonist himself implies that his affliction is spiritual with the line, "I became afflicted with that illness for which no one possesses a remedy."
Zaabalawi is believed by many to be a holy man and, in his quest to find this healer, the protagonist himself goes on a journey that is both spiritual and physical. In a sense, Zaabalawi could represent God, while the protagonist's journey represents man's search for spiritual fulfillment and enlightenment.
Mental Illness and Obsession
Another interpretation of "Zaabalawi" is that the character suffers from mental illness. There is evidence for this in his admission that he "was overcome by despair" and his physicians have been unable to find a physical cause for his illness. Throughout the course of the story, the protagonist's focus on finding Zaabalawi turns to obsession. Although he finds some semblance of relief from his suffering after discovering Zaabalawi was with him while he dreamed, he continues to search for this mysterious figure.
Companionship and Support
"Zaabalawi" can be seen as a quest for companionship or support as the protagonist acknowledges his own loneliness and expresses a desire for friendship with Zaabalawi. He first visits one of his late father's friends in an attempt to find out more about Zaabalawi's current whereabouts and when the man mentions his father, he is overcome with sadness.

The very pain that had driven me to go there now prevailed upon me to stay.

This line implies that the protagonist is motivated by a deep loneliness and desire for companionship, and there are many examples of his encounters with the other characters he meets on his journey that you could use to illustrate this point.
Pursuit of Knowledge
A more subtle—yet equally compelling—interpretation of "Zaabalawi" is that the main character is seeking knowledge rather than a literal person. Zaabalawi embodies hidden knowledge and mystery that the main character hopes will enrich his life and heal him in both body and spirit. This theory is shown by the portion of the text in which the protagonist encounters Zaabalawi in his dream.

There was an extraordinary sense of harmony between me and my inner self, and between the two of us and the world, everything being in its rightful place, without discord or distortion.

This excerpt supports the theory that Zaabalawi represents knowledge. When the protagonist was united with him, even though it was only in a dream, he felt "a sense of harmony" with his inner self. This description coincides with many philosophical ideas about the pursuit of knowledge and the peace that comes with it.
Each of these interpretations is valid in its own right, and the story ends on an ambiguous note with the protagonist in continued pursuit of the titular "Zaabalawi." This could be seen as a metaphor for the continual process of seeking spiritual truth or knowledge. You could also take this as evidence that the main character is seeking companionship, which he finds elusive in those around him. A fourth interpretation is that the protagonist's continued obsession with Zaabalawi suggests he is still suffering from mental illness at the end of the story.
https://pls.nd.edu/assets/131608/zaabalawi/

How was the spread of the Buddha’s more radical teachings a gradual process in India?

The Buddha's teachings spread mostly through the merchant class. The merchant class in India was unsympathetic to the Brahmin aristocracy. Brahmin faith contained a great deal of ritual and ceremony. Some rituals were caste-specific and could only be performed by Brahmin priests. Thus, the merchant class viewed the Brahmin faith as an expression of caste-based elitism.
The merchant class was mobile, wealthy, and open to religious reformation. Through their extensive travels, merchants brought the Buddha's teaching to major cities across northern and southern India. The cities of Khotan, Bukhara, and Merv were particularly recipient to Buddhist teachings. In these diverse and populous cities, Buddhist teachings evolved and merged with preexisting religious and cultural norms. The Buddha's teachings were simple and did not involve a lot of ritual. For this reason, the teachings were easy to export to peoples of different cultures and ethnicities.

College Algebra, Chapter 1, 1.3, Section 1.3, Problem 86

The formula $\displaystyle P = \frac{x}{10} (300 - x)$ represents the profit (in dollars) generated by producing $x$ microwave ovens per week, where $0 \leq x \leq 200$. How many ovens must be manufactured in a given week to generate a profit of $\$ 1250$?


$
\begin{equation}
\begin{aligned}

P =& \frac{x}{10} (300 - x)
&& \text{Model}
\\
\\
1250 =& \frac{x}{10} (300 - x)
&& \text{Substitute the given}
\\
\\
1250 =& 30x - \frac{x^2}{10}
&& \text{Apply Distributive Property}
\\
\\
12500 =& 300x - x^2
&& \text{Multiply both sides by } 10
\\
\\
x^2 - 300x + 12500 =& 0
&& \text{Add $x^2$ and subtract } 300x
\\
\\
(x - 250)(x - 50) =& 0
&& \text{Factor}
\\
\\
x - 250 =& 0 \text{ and } x - 50 = 0
&& \text{ZPP}
\\
\\
x =& 250 \text{ and } x = 50
&& \text{Solve for } x
\\
\\
x =& 50
&& \text{Choose } x = 50, \text{ since } 0 \leq x \leq 200

\end{aligned}
\end{equation}
$


In order to generate a profit of $\$ 1250$, $50$ ovens must be manufactured.

Does the image of the respected poet “poking/ among the meats” in "A Supermarket in California" strengthen the poem’s impact or undercut any serious “message” the poem might have?

I would argue the incongruent image of the respected poet “poking/ among the meats” in the supermarket strengthens the poem’s impact.
In the poem, Allen Ginsburg addresses two poets (Federico Garcia Lorca and Walt Whitman) as he peruses the fruits and vegetables in the supermarket. Walt Whitman is said to be "poking among the meats in the refrigerator and eyeing the grocery boys." Meanwhile, Ginsburg wonders what Garcia Lorca is doing "down by the watermelons." Although neither Whitman nor Lorca are present, Ginsburg brings them into his supermarket experience because he's as lonely as he imagines his admired poets were when they were alive.
LikeGinsburg, Garcia Lorca and Whitman were homosexuals. In the poem, Ginsburg muses about whole families (husbands in the aisles, "wives in the avocados," and "babies in the tomatoes") in the supermarket, all enjoying their shopping experience. Meanwhile, Ginsburg is alone and feels himself so detached from the scene that he has to imagine Whitman walking with him down corridors, "tasting artichokes, possessing every frozen delicacy, and never passing the cashier," in order to refrain from feeling out of place.
Ginsburg basically uses the incongruent image of the poets to highlight his loneliness and detachment from society. He dreams of the "lost America of love" as he walks through the supermarket. At the end of the poem, he imagines asking Whitman about the kind of America he knew when he was alive. In Greek mythology, anyone who drank from the waters of Lethe would completely forget how they lived during their mortal lives. The learned were advised to seek the river of memory, Mnemosyne, instead.
Yet, in the poem, Ginsburg suggests that Whitman may have needed to drink from the waters of Lethe to forget his mortal life in the America he knew. Although the images of the poets seem incongruent, Ginsburg is raising some pretty serious questions here. He's asking his readers to consider the image of the America he knows and whether materialism ("automobiles in driveways") is conducive to happiness. He's also wondering what his place in America is, just as he imagines both Whitman and Lorca must have wondered about their own worlds when they were alive. His last words in the poem lead us to question whether a poet like him should drink of the waters of Lethe in order to survive in the America he's living in.

In “How to Date a Browngirl, Blackgirl, Whitegirl, or Halfie,” by Junot Diaz, why does the narrator include his reference to the tear gas used by the United States when the Dominican Republic was invaded?

In the story, the narrator includes the reference to the tear gas to make a point about his self-image: as an immigrant living in an American suburb of New Jersey, the narrator is ever aware of his "foreignness" to most people. Additionally, he believes that this "foreignness" often gets in the way of his having a successful date, especially with a white American girl. Essentially, the narrator feels self-conscious about his racial and national heritage.
He references the tear gas used during the American invasion of the Dominican Republic but admits that he would never divulge this part of his heritage to a white girl. So, the reference is for us readers rather than for the white girls he hopes to impress. The text tells us that he will only mention the tear gas as a factor in some fantastic story about "the loco who'd been storing canisters of tear gas in his basement for years, [and] how one day the canisters cracked and the whole neighborhood got a dose of the military-strength stuff." However, he will not mention why and how his mother easily recognizes the smell of tear gas.
The narrator sees the story of his neighbor as an exciting story that will impress a white girl, and that's all that matters to him. However, he will stop short of alluding to any past conflict between the United States and the Dominican Republic (where he or his family are originally from.) He fears that doing so will alert the girl to his "foreignness" and so, destroy his chances of gaining sexual fulfillment. He admits, "The white ones are the ones you want the most, aren't they...."
So, the historical background behind the tear gas reference is for us readers. The narrator is telling us how he really feels about himself and how much he fears his "foreignness" will get in the way of him successfully having relations with white girls.

What does the reference to "a soldier" tell you about the time period of the story?

The reference tells us that the story is set during wartime. Specifically, it is set in French Algeria during the Second World War. France had been speedily conquered by German forces, and a large part of the country came under their direct control. The rest of the country was placed under the authority of a puppet regime based in the spa town of Vichy. The new regime was racist, authoritarian, and reactionary and maintained control over French Algeria. Prejudice and bigotry towards France's Arab colonial subjects were widespread, leading to the development of a growing resistance movement.
Official discrimination against the indigenous population provides a background against which the main action of The Stranger unfolds. Meursault shoots and kills an Arab without the slightest compunction; the violent pimp Sintes beats his Arab girlfriend and generally treats her with contempt; and when Meursault is finally brought to trial for the murder he's committed, his lack of concern for his late mother appears to have more significance for the court than the life of an Arab.
The Stranger does indeed take place during wartime, as already mentioned. But there are a number of wars running throughout the story—seething, undeclared conflicts that change the lives of those concerned more completely than the more formal conflict raging in the background.

How do others' actions before the race starts affect Squeaky?

Squeaky generally likes to arrive just before the May Day race starts, as she does not like the rest of the May Day program and only wants to lie in the grass before her race is announced. While waiting for the race to start, she notices other kids participating in May Day events and carrying their instruments. Mr. Pearson, who is organizing the race, comes by to sign up Squeaky, and he asks her if she is going to let someone else win this year. He begins to say it would be nice if Gretchen and Squeaky both win the race, but Squeaky fixes him with a stare that makes him silent. Squeaky thinks to herself, "Grown-ups got a lot of nerve sometimes."
Even though she doesn't see Gretchen, her main rival, until right before the race, Squeaky feels "so burnt" from talking to Mr. Pearson and realizing he wants her to share the glory of winning the race. Right before the race, Squeaky sees Gretchen stretching "like a pro," and she sees Raymond bending down like he knows how to run. During the race, she realizes Raymond could be a good runner, so she thinks about what she has noticed before the race while she is running.

What do potential energy and kinetic energy make together?

When potential energy and kinetic energy are combined, they indicate total mechanical energy.  Mechanical energy is the energy that an object has due to its motion and/or due to its position.  Energy of motion is kinetic energy, and energy of position or shape is potential energy.  Think of mechanical energy like you would an addition problem.  
Mechanical energy = kinetic energy + potential energy
All three of those energies are measured in Joules, so there is no need to even worry about converting units.  
When I teach my students about mechanical energy, I like to use a roller coaster as an example.  When the roller coaster is at the top of the highest hill, it has all gravitational potential energy (just pretend the roller coaster stops for a second before going down the hill).  Halfway down that hill, the roller coaster is moving quickly, so it has kinetic energy; however, it still has potential energy because it's only halfway down. At the bottom of the hill, all of the potential energy has been converted to kinetic energy.  Due to the law of conservation of energy, the total energy of the roller coaster system must remain the same.  That means the total mechanical energy within the system stays the same.  Let's put some numbers to it.  
At the top of the hill, the roller coaster has 5,000 J of potential energy and 0 J of kinetic energy.  
Mechanical energy = potential energy + kinetic energy
5,000 J = 5,000 J + 0 J
Halfway down the hill, the equation would look like this.  
5,000 J = 2,500 J + 2,500 J
At the bottom of the hill, it would look like this.
5,000 J = 0 J + 5,000 J
As you can see, the mechanical energy of the system is conserved, and it is the sum total of the potential energy and kinetic energy within the system. 
http://www.eschooltoday.com/energy/kinds-of-energy/what-is-mechanical-energy.html

https://www.physicsclassroom.com/class/energy/Lesson-1/Mechanical-Energy

What are some universal lessons learned from Fast Food Nation: The Dark Side of the All-American Meal?

Two lessons emerging from Fast Food Nation: The Dark Side of the All-American Meal relate to consumer vigilance.
Schlosser's work is designed to raise public awareness about "the All-American meal."  He does this in two distinct ways.  The first is in his display of the food preparation process.  An important lesson emerges through displaying situations like livestock care, health and safety issues, and the presence of chemical additives.  As consumers, we must be aware of what fast food corporations are doing in the name of profit to the food we eat:

The medical literature on the causes of food poisoning is full of euphemisms and dry scientific terms: coliform levels, aerobic plate counts, sorbitol, MacConkey agar, and so on. Behind them lies a simple explanation for why eating a hamburger can now make you seriously ill: There is s**t in the meat.

Schlosser demonstrates why it is so important to hold corporations responsible for the food products they generate.  There is a public health concern when we think about the mass consumption of such food.  For example, the "Happy Meal" cheerful packaging belies the chemicals used to prepare its food.  Children eating such products are unaware of the dangers.  When the most vulnerable of our society is at risk, the lesson is that consumers must be vigilant.  Consumers must be aware of food preparation practices that do not meet stringent health and safety standards. The public must hold corporations accountable for not meeting these standards.  After reading Schlosser's work, it is clear that simply trusting fast food corporations could be dangerous to our collective health.
Along these lines, Schlosser's work illuminates another lesson.  The world is no longer defined by political ideologies as much as it is defined by a globalized economic reality.  This materialist reality is far more insidious:

The history of the twentieth century was dominated by the struggle against totalitarian systems of state power. The twenty-first will no doubt be marked by a struggle to curtail excessive corporate power.

Schlosser suggests that we should be more mindful of the influence that corporations have in our world.  It impacts our lives on nearly every level. Schlosser's work details how millions of lives are changed as a result of corporate influence and power.  One of the most important lessons regarding this reality is that we need to be mindful of the excesses of corporate power. Public sector initiatives to safeguard public health and safety need to be developed and maintained.  Consumers and governments must ensure that corporations follow established rules.  Blind faith in corporations does not benefit consumers.  The need to carve out a public space where the abuse of corporate power can be effectively checked is one of the most important lessons from Schlosser's work.