Charles Walluas says that they can’t make decisions based on fear. Do you agree? Please explain.

I agree because IT is doing its best to get control of the children's minds. IT is already in control of their father. Though fear tempts the threesome to turn and run away from Central Central Intelligence, as Charles Wallace notes, they won't make the decisions that will free their father if they give into fear. They need, instead, to face their fears. As Calvin says, quoting Mrs. Who, who was quoting Franklin Delano Roosevelt, the only thing the children had to fear was fear itself.
IT is trying to hypnotize the children. If they keep thinking, rather than allowing themselves to be paralyzed by fear, they can block out IT and avoid mind control. They have to keeping thinking thoughts that are not IT's thoughts and that means overcoming their terror. 

Calculus and Its Applications, Chapter 1, 1.4, Section 1.4, Problem 38

Determine the $f'(x)$ of the function $\displaystyle f(x) = \frac{2x }{x + 1}$

$
\begin{equation}
\begin{aligned}
\frac{f(x + h) - f(x)}{h} &= \frac{\left[ \frac{2(x + 1)}{(x + h) + 1} \right] - \left[ \frac{2x}{(x + 1)} \right]}{h}\\
\\
&= \frac{\frac{2(x + h)(x + 1) - 2x (x + h + 1)}{(x + 1)(x + h + 1)}}{h}
&& \text{Get the LCD}\\
\\
&= \frac{2x^2 + 2x + 2xh + 2h - 2x^2 - 2xh - 2x}{h(x + 1)(x + h + 1)}\\
\\
&= \frac{2h}{h(x + 1)(x + h + 1)}\\
\\
&= \frac{2}{x^2 + xh + x + x + h + 1}\\
\\
&= \frac{2}{x^2 + xh + 2x + h + 1}
\end{aligned}
\end{equation}
$

Thus,

$
\begin{equation}
\begin{aligned}
f'(x) = \lim_{h \to 0} \frac{ f(x + h) - f(x) }{h} &= \frac{2}{x^2 + x(0) + 2x + 0 + 1}\\
\\
&= \frac{2}{x^2 + 2x + 1} \text{ or } \frac{2}{( x + 1)^2}
\end{aligned}
\end{equation}
$

What happened in the “Robber’s Cave” experiment? Why is that study significant?

The Robber's Cave experiment was conducted in 1954 by a famous social psychologist, Muzafer Sherif. In this experiment, 22 12-year-old boys from white, middle-class, Protestant backgrounds with two parents were brought to Robber's Cave State Park in Oklahoma. They did not know each other before the study and were randomly assigned to one of two groups. Each group spent a week developing their own group norms without being aware of the other group. One group called itself the Rattlers, while the other group called itself the Eagles. During the competition part of the experiment, the boys engaged in competitions that led to all-or-nothing awards (the winners got everything, while the losers got nothing). For example, picnics were staged in which the first group to arrive ate all the food. The conflict between the groups started as verbal harassment and developed into stealing each other's property and then physical attacks. During the last two days of the experiment, the boys spoke in a debriefing exercise of the negative qualities of the other group and the positive qualities of their group. The conflict between the groups was lessened through inter-group activities that involved teamwork. 
The experiment is important because it corroborates Sherif's Realistic Conflict Theory, which states that conflicts between groups are an outgrowth of limited resources and situations in which only one group can achieve rewards. This type of conflict results in the members of one group developing negative stereotypes about the other group, even if the individuals in one group are quite similar to the individuals in the other group.

Where are Antonio and his friends, and what does Antonio say about his sadness in the opening scene of The Merchant of Venice?

Antonio and his friends are on a street in Venice, a city of "psychic, dark corners," as Shakespearean critic Harold Bloom describes it. Antonio has fallen into one of these "dark corners" in his mind, and his friends Salerio and Salanio express their concern. 
When Antonio tells the two men that he knows no cause for his sadness--"In sooth I know not why I am so sad (1.1.1.)--Salerio suggests that Antonio may be anxious about his merchant ships: "Your mind is tossing on the ocean" (1.1.8). However, Antonio denies that this is the cause. Not convinced by Antonio's reply, Salanio provides Antonio with another opportunity to admit his concerns as by observing that he would certainly be worried about everything that could go wrong were he in Antonio's place. Nonetheless, Antonio is adamant that nothing about his business disturbs him.
When Salanio suggests that he might, then, be in love, Antonio replies heatedly, "Fie! fie!" At this, Salerio cleverly amends Salanio's question in order to ameliorate the situation:

Not in love? Then let us say you are sad,Because you are not merry: and 'twere as easyFor you to laugh and leap and say you are merry,Because you are not sad. (1.1.49-52)

At this point, Bassanio, Lorenzo, and Gratiano enter and Salerio and Salanio make their departure, bowing to "worthier friends."
Perhaps, then, the very beginning of this play is meant to set a tone that complements the sometimes incongruous, foreboding, and "psychic" city of Venice, as well as to foreshadow the misfortune of Antonio which is to come.

To whom is Miss Maudie referring when she asks, “His food doesn’t stick going down, does it?” Why does she ask this?

Miss Maudie is referring to Atticus in this question. This incident occurs during Aunt Alexandra’s social event with the other ladies in town, which Scout unwillingly attends wearing a clean, starched dress instead of her preferred tomboy clothing. The ladies have an extremely hypocritical discussion about missionary work in Africa and how wonderful it is that J. Grimes Everett is helping the poor people there, before immediately turning around and making negative comments about Atticus’s work defending Tom Robinson. Miss Maudie takes offense to this, not only because she is friends with Atticus and thinks he is doing the right thing, but also because they are all sitting in Atticus’s house and eating his food. Miss Maudie thinks Mrs. Merriweather is being quite rude to criticize Atticus while enjoying his hospitality. Hence her comment, “His food doesn’t stick going down, does it?” In other words, she is saying to Mrs. Merriweather, You are criticizing this man, but you sure don’t have a problem eating his food.

In chapter 24, Scout attends Aunt Alexandra's missionary circle and listens as the local ladies discuss J. Grimes Everett's missionary work in African before discussing current community affairs. Mrs. Merriweather then proceeds to comment on how her black servants have been acting depressed following the Tom Robinson trial.
She then indirectly criticizes Atticus for defending Tom by referring to him as "Good, but misguided." Miss Maudie responds to Mrs. Merriweather's indirect criticism of Atticus by saying, "His food doesn’t stick going down, does it?" (237) Miss Maudie is referring to Atticus (and his food) when she questions Mrs. Merriweather. Rather than directly confront Mrs. Merriweather about criticizing a man who has allowed her to dine in his home, Miss Maudie passively reproaches Mrs. Merriweather by asking her a question that gets her attention and makes her consider her comments.

What did Malcolm do to almost get killed by Archie?

At this stage of the story Malcolm is living in Harlem, making a living as a low-level criminal. One of the criminal enterprises he gets mixed up in is the numbers racket: an illegal lottery. But Malcolm doesn't just sell lottery tickets; he starts playing the numbers as well. He becomes more deeply involved in gambling, placing bets with a formidable character by the name of West Indian Archie. One day, Archie and Malcolm fall out over a bet. Archie accuses Malcolm of collecting on a wager he never actually made. Malcolm, for his part, is equally insistent that he did indeed make the bet and is entitled to keep his winnings.
Neither man wants to back down, but Archie forces the issue by giving Malcolm twenty-four hours to pay back the money. This is a low point in the story for Malcolm. Not only is he a criminal; he's also taking drugs and getting deeper into debt. Worse still, he's constantly looking over his shoulder, worried that at any moment he might get killed by Archie, not to mention the hustler he's just punched and the Italian gangsters who think he's robbed one of their craps games.

How is Rochester portrayed as a loving person in Jane Eyre?

Mr. Rochester's behavior throughout the entire novel is one that easily confuses readers. The question always stands "If he really loved Jane Eyre, then why did he keep such a big secret from her?"
One way a person could look at Mr. Rochester is by looking at his merciful nature. The people that he kept around him were people that he obviously adored, but chose not to create a connection due to his fear of rejection and possibly damaging them with his own issues. So therefore, when it came down to Mr. Rochester and love, he seemed to fall easily and hard towards those that have a sense of innocence about them.
Then, with Jane Eyre, he seems to instantly want to have her at his side, but know that he cannot have the best of both worlds with him being married to Bertha. Nevertheless, he was drawn to Jane and carried himself with a tender, but somewhat guarded nature that even put Jane in a state of confusion with her constantly asking the question "Is he mocking me or is he being serious?" Rochester, on the other hand, finds himself at odds with not just his own ability to love Jane in the way that he knows and wants to love Jane Eyre, but he also has to deal with reality.
"I have for the first time found what I can truly love-I have found you. You are my sympathy-my better self-my good angel-I am bound to you with a strong attachment..."
After years of keeping a distance to keep the true innocent, Rochester finds himself unable to keep his distance from Jane Eyre. He is drawn to her because he felt that she had exactly what he needed, but could not possibly tell Jane Eyre about his wife because then, the mask would be away. There would no longer be a sense of innocence to keep and all of his disdainful behavior would have been for nothing.

Mr. Rochester's love is problematic through much of the novel. For example, he shows love for his illegitimate daughter Adele by caring for her, giving her gifts, and hiring her a governess in the form of Jane Eyre, but he also dismisses the child as affected and not very intelligent. Therefore, his love for her is mixed with distaste.
Rochester's love for Jane is also mixed: in this case, it is tainted with selfishness and deception. He loves her, and he believes her strength of character and purity can save him and make him a happy man, but he doesn't love her enough to tell her the truth about his situation of being married to Bertha Mason. He shows what imperfect love he has by proposing marriage to her, such as when he states:

"My bride is here," he said, again drawing me to him, "because my equal is here, and my likeness. Jane, will you marry me?"

He tries to express to her how much he loves her, even though he is not being honest with her:

You— you strange, you almost unearthly thing!—I love as my own flesh. You—poor and obscure, and small and plain as you are—I entreat to accept me as a husband.

He is willing to trick her into bigamy, which is what marrying means while Bertha is still alive. While we do not doubt that Rochester loves Jane, he is ready to sacrifice her moral values, which he knows matter deeply to her, for his own happiness. At this point, his love is selfish.
It's not until the end of the novel, when he has become blind and mutilated from the fire that consumed Thornfield that he has been humbled enough to truly love Jane as an equal.
When they reunite, he speaks these loving words to her:

My living darling! These are certainly her limbs, and these her features; but I cannot be so blest, after all my misery. It is a dream; such dreams as I have had at night when I have clasped her once more to my heart, as I do now; and kissed her, as thus—and felt that she loved me, and trusted that she would not leave me.

Later, Jane testifies to the love they share as husband and wife, this time an unselfish love on both sides:

We talk, I believe, all day long: to talk to each other is but a more animated and an audible thinking. All my confidence is bestowed on him, all his confidence is devoted to me; we are precisely suited in character— perfect concord is the result.

Rochester has grown, through painful experience, into a man who can love Jane as she deserves.

College Algebra, Chapter 1, 1.6, Section 1.6, Problem 42

Solve the nonlinear inequality $\displaystyle x^2 < x + 2$. Express the solution using interval notation and graph the solution set.


$
\begin{equation}
\begin{aligned}

& x^2 < x + 2
&& \text{Given}
\\
\\
& x^2 - x - 2 < 0
&& \text{Subtract $x$ and $2$}
\\
\\
&(x -2)(x + 1) < 0
&& \text{Factor}

\end{aligned}
\end{equation}
$


The factors on the left hand side are $x - 2$ and $x + 1$. These factors are zero when $x$ is $2$ and $-1$ respectively. These numbers divide the real line into intervals

$(- \infty, -1), (-1, 2), (2, \infty)$







From the diagram, the solution of the inequality $x^2 < x + 2$ is

What is Steinbeck trying to convey in the novella Of Mice and Men when he compares Lennie to various animals?

Throughout the novella, Steinbeck compares Lennie to various animals. Lennie is compared to a bear dragging its paws, a horse drinking water, a disobedient terrier, a terrified sheep, and a dog seeking comfort. Lennie's mental and physical character traits are illuminated by Steinbeck's comparisons. Mentally, Lennie is depicted as subhuman and unintelligent like animals. Similar to animals, Lennie acts on his instincts and does not process situations or thoughts the same way a normal person would. Lennie follows and listens to George like a dog. George even tells Slim that Lennie would jump into a river if he were told to. Lennie's dog-like personality also demonstrates his loyalty to George.
Similar to an animal, Lennie is also physically imposing and hard to control. His animal-like strength, tireless work ethic, and massive physique provide the reader with a visual reference point. Also, Lennie's animal-like personality portrays his innocence, and the reader does not hold him accountable for his actions. Steinbeck's references essentially convey to the reader that Lennie is both mentally and physically comparable to an animal.

Which animal does Zaroff consider to be the most dangerous game?

General Zaroff is the antagonist in Richard Connell's short story "The Most Dangerous Game." He owns a secluded island in the Caribbean Sea where he indulges in his favorite pastime, hunting. When Sanger Rainsford, a big game hunter from New York, blunders onto Zaroff's island, the general invites him to dinner and describes his passion for hunting. The general has hunted all over the world and pitted his skills against dangerous animals such as tigers, grizzlies, and the Cape buffalo. Unfortunately, Zaroff discovers that he has grown bored with hunting such animals. For him, it has become too easy. He admits to Rainsford that he had to "invent a new animal" which would provide more of a challenge or else, Zaroff believed, "he would go to pieces." Rainsford, of course, is quite interested in this new animal until Zaroff admits that he actually hunts men. The general understood that only a reasoning animal could provide the type of danger he craved. Thus, he began hunting the sailors who had become shipwrecked on his island. Zaroff rationalizes this abhorrent practice by believing that it is his right, as a superior human being, to hunt men of lesser intellectual prowess. He tells Rainsford,

I hunt the scum of the earth—sailors from tramp ships—lascars, blacks, Chinese, whites, mongrels—a thoroughbred horse or hound is worth more than a score of them.

When Zaroff invites Rainsford to hunt with him, the American refuses, calling the general uncivilized. Because he is steadfast in his refusal, Rainsford eventually becomes one of Zaroff's new animals, and the second half of the story recounts Zaroff's pursuit of Rainsford through the island's jungles.
The title of the story is an example of verbal irony. The term "game" has two meanings in this title. First, it describes a hunted animal as being dangerous game because it can sometimes turn violently on the hunter. Second, the title refers to the dangerous game being played between Zaroff and Rainsford in which Zaroff is ultimately killed.

Calculus of a Single Variable, Chapter 9, 9.3, Section 9.3, Problem 16

The Integral test is applicable if f is positive and decreasing function on infinite interval [k, oo) where kgt= 1 and a_n=f(x) . Then the series sum_(n=k)^oo a_n converges if and only if the improper integral int_k^oo f(x) dx converges. If the integral diverges then the series also diverges.
For the given series sum_(n=2)^oo 1/(nsqrt(ln(n))) , the a_n =1/(nsqrt(ln(n))) then applying a_n=f(x) , we consider:
f(x) =1/(xsqrt(ln(x))) .
The graph of f(x) is:

As shown on the graph above, the function f(x) is positive and decreasing on the interval [2,oo) . This implies we may apply the Integral test to confirm the convergence or divergence of the given series.
We may determine the convergence or divergence of the improper integral as:
int_2^oo 1/(xsqrt(ln(x)))= lim_(t-gtoo)int_2^t 1/(xsqrt(ln(x)))dx
To determine the indefinite integral of int_2^t1/(xsqrt(ln(x)))dx , we may apply u-substitution by letting:
u = ln(x) and du = 1/x dx .
The integral becomes:
int 1/(xsqrt(ln(x)))dx=int 1/sqrt(ln(x)) *1/x dx
=int 1/sqrt(u) du
Apply the radical property: sqrt(x)= x^(1/2) and 1/x^m = x^(-m) .
int 1/sqrt(u) du=int 1/u^(1/2) du
=int u^(-1/2) du
Apply the Power rule for integration: int x^n dx = x^(n+1)/(n+1) .
int u^(-1/2) du =u^(-1/2+1)/(-1/2+1)
=u^(1/2)/(1/2)
=u^(1/2)*(2/1)
= 2u^(1/2) or 2sqrt(u)
Plug-in u=ln(x) on 2sqrt(u) , we get:
int_2^t1/(xsqrt(ln(x)))dx=2sqrt(ln(x))|_2^t
Apply the definite integral formula: F(x)|_a^b = F(b)-F(a) .
2sqrt(ln(x))|_2^t =2sqrt(ln(t))-2sqrt(ln(2))
Applying int_1^t1/(xsqrt(ln(x)))dx=2sqrt(ln(t))-2sqrt(ln(2)) , we get:
lim_(t-gtoo)int_1^t 1/(xsqrt(ln(x)))dx=lim_(t-gtoo)[2sqrt(ln(t))-2sqrt(ln(2))]
= oo -2sqrt(ln(2))
=oo
Note: lim_(t-gtoo)2sqrt(ln(2))=2sqrt(ln(2)) and
lim_(t-gtoo)2sqrt(ln(t))= 2lim_(t-gtoo)sqrt(ln(t))
=2sqrt(lim_(t-gtoo)ln(t))
=2sqrt(oo)
=oo
The lim_(t-gtoo)int_2^t 1/(xsqrt(ln(x)))dx= oo implies that the integral diverges.
Conclusion: The integral int_2^oo 1/(xsqrt(ln(x))) diverges therefore the series sum_(n=2)^oo 1/(xsqrt(ln(x))) must also diverges.

What is the role of the narrator in "A Sound of Thunder"?

The third-person narrator of "A Sound of Thunder" sets the scene of the various parts of the story as seen through the eyes of Eckels, who is the main character. The narrator also puts the reader inside the mind of Eckels so that we know what his thoughts and emotions are as the story unfolds.
The narrator conveys both what Eckels physically experiences and his inner sense of wonder. For example, in the paragraph below, the first sentence show us the sight and sound of the time machine as Eckels experiences it. The second, much more lyrical sentence, tells us how the time machine seems imaginatively to Eckels:

Eckels glanced across the vast office at a mass and tangle, a snaking and humming of wires and steel boxes, at an aurora that flickered now orange, now silver, now blue. There was a sound like a gigantic bonfire burning all of Time, all the years and all the parchment calendars, all the hours piled high and set aflame.

For much of the central part of the story, the narrator disappears and we overhear the dialogue between the characters. But it is the narrator who introduces us to the T-Rex, describing all the wonder and terror of Eckels seeing one for the first time:

Each lower leg was a piston, a thousand pounds of white bone, sunk in thick ropes of muscle, sheathed over in a gleam of pebbled skin like the mail of a terrible warrior.

The narrator also recounts Eckels leaving the trail, the killing of the T-Rex, and the reactions of all the men. At the end of the story, the narrator allows us back into the mind of Eckels, as he returns to the present day. We experience the eerie sense that Eckels does of everything being not quite right:

Beyond this room, beyond this wall, beyond this man who was not quite the same man seated at this desk that was not quite the same desk ...

The narrator is able to get beyond dialogue to describe what is going on emotionally with Eckels. And finally, the narrator has the ability to stand back and describe the sound of thunder as Travis shoots Eckels.

Why is Roger unable to say what he wants to say to Mrs. Jones at the end of the story in "Thank you, M’am" by Langston Hughes?

Roger is overcome with emotion at the end of “Thank you, M’am” by Langston Hughes, which leaves him unable to say more than a simple “thank you.”
Roger is a young man who is the product of his Harlem environment. There is no evidence of family support in his young life. When he attempts to snatch the purse off the shoulder of Mrs. Luella Bates Washington Jones, he is in for the lesson of a lifetime.
 Mrs. Jones does not report him to authorities, but instead takes him to her rooming house, where she shows him kindness and understanding. She has him wash up before they eat a meager dinner together. More importantly, she respects his circumstances and shares some of her background with him. While he is in her company, she allows him to learn how to be trustworthy.
When it is time for her to rest, she hands him the money he needs to buy the blue suede shoes that drove him to steal in the first place. Roger is unaccustomed to this type of treatment and he finds it so overwhelming that he is virtually speechless. Deep within, Roger realizes Mrs. Jones gave him much more than the money for those shoes.

College Algebra, Chapter 4, 4.4, Section 4.4, Problem 40

Determine all rational zeros of the polynomial $P(x) = 6x^4 - 7x^3 - 12x^2 + 3x + 2$, and write the polynomial in factored form.

The leading coefficient of $P$ is $6$ and its factors are $\pm 1, \pm 2, \pm 3, \pm 6$. They are the divisors of the constant term $2$ and its factors are $\pm 1, \pm 2$. The possible rational zeros are $\displaystyle \pm 1, \pm 2, \pm \frac{1}{2}, \pm \frac{1}{3}, \pm \frac{1}{6}, \pm \frac{2}{3}$

Using Synthetic Division







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

$6x^4 - 7x^3 - 12x^2 + 3x + 2 = (x - 2)(6x^3 + 5x^2 - 2x - 1)$

We now factor the quotient $6x^3 + 5x^2 - 2x -1$. The factors of 6 are $\pm 1,\pm 2, \pm 3, \pm 6$. The factors of 1 are $\pm 1$. The possible rational zeros are
$\displaystyle \pm 1, \pm \frac{1}{2}, \pm \frac{1}{3}, \pm \frac{1}{6}$
Using synthetic division



We find that $-1$ is a zero and $P$ factors as
$6x^4 - 7x^3 -12x^2 + 3x + 2 = (x-2)(x+1)(6x^2 - x - 1)$

We now factor $6x^2 - x - 1$ using trial and error. We get,

$6x^4 - 7x^3 - 12x^2 + 3x + 2 = (x - 2)(x + 1)(6x + 1)(x - 1)$

The zeros of $P$ are $2, 1, -1$ and $\displaystyle \frac{-1}{6}$.

If you had to pick a famous actor to play Mercutio, who would it be?

Just a few further thoughts on the above:
In deciding on an actor for Mercutio, there aren't, as I said, any guidelines on his age or race (he was played, famously, by Harold Perrineau as a cross-dressing black man in Baz Luhrmann's filmed production), but you might consider the other characteristics of Mercutio when making your casting choice.
Mercutio is often best portrayed by rather flamboyant actors--he is often interpreted as being in love with Romeo himself, which sometimes means a gay actor is cast, or he is coded as gay in the production. He is also, in many ways, the comedic star of the play, so an actor who is excellent with wordplay but also able to evoke pathos when necessary is required. Mercutio also must serve as the older and wiser influence on Romeo, despite his loud and sometimes dirty wit. The actor you cast should certainly be older than your casting choice for Romeo and have a world-weary aspect—able to convey the suggestion that his jokes convey something deeper.
I would be interested in seeing Jim Carrey as Mercutio, an actor who gained fame as a comic but has also showcased the ability to convincingly evoke audience sympathy in such films as The Truman Show. Another interesting, quite different choice might be Aaron Paul—capable of cutting and quickfire wit but with the air of weary wisdom suggesting there is much beneath the surface. Mercutio is a funny character, but, as with many of Shakespeare's fools, there is far more to him than meets the eye. The actor you choose must be able to convey that.

What a fun question! Of course, this is entirely up to you. The great thing about Mercutio is that his qualities can be interpreted very differently. He is a knowing, cunning character who is more worldly and wise than Romeo and able to advise him. It is not stated anywhere in the text how old Mercutio is or what he looks like. In a recent Kenneth Branagh production of the play, the director made the interesting choice of casting Derek Jacobi, who is almost eighty, as Mercutio. This was a very different interpretation of the character than is normally seen but is definitely not disallowed by the text.
So, who would you enjoy seeing as this great Shakespeare character? You could make a case for whoever is your favorite actor, provided he has the comedic and dramatic skills.

Calculus: Early Transcendentals, Chapter 6, 6.3, Section 6.3, Problem 21

The shell has the radius x, the cricumference is 2pi*x and the height is x*e^(-x) , hence, the volume can be evaluated, using the method of cylindrical shells, such that:
V = 2pi*int_(x_1)^(x_2) x*x*e^(-x) dx
You need to find the next endpoint, using the equation x*e^(-x) = 0 => x = 0
V = 2pi*int_0^2 x^2*e^(-x) dx
You need to use integration by parts to evaluate the volume, such that:
int udv = uv - int vdu
u = x^2 => du = 2xdx
dv = e^(-x) => v = -e^(-x)
int_0^2 x^2*e^(-x) dx = -x^2*e^(-x)|_0^2 + 2int_0^2 x*e^(-x)dx
You need to use integration by parts to evaluate the integral int_0^2 x*e^(-x)dx.
u = x => du = dx
dv = e^(-x) => v = -e^(-x)
int_0^2 x*e^(-x)dx = -x*e^(-x)|_0^2 + int_0^2 e^(-x) dx
int_0^2 x*e^(-x)dx = -x*e^(-x)|_0^2 - e^(-x)|_0^2
int_0^2 x*e^(-x)dx = -2*e^(-2) - e^(-2) +0*e^(0)+ e^(0)
int_0^2 x*e^(-x)dx = -2/(e^2) - 1/(e^2) + 1
int_0^2 x*e^(-x)dx = -3/(e^2)+ 1
int_0^2 x^2*e^(-x) dx = -x^2*e^(-x)|_0^2 + 2(-3/(e^2)+ 1)
int_0^2 x^2*e^(-x) dx = -2^2*e^(-2) - 6/(e^2) + 2
int_0^2 x^2*e^(-x) dx = -4/(e^2) -6/(e^2) + 2
int_0^2 x^2*e^(-x) dx = -10/(e^2) + 2
V = 2pi*(-10/(e^2) + 2)
Hence, evaluating the volume, using the method of cylindrical shells, yields V = 2pi*(-10/(e^2) + 2).

Calculus of a Single Variable, Chapter 6, 6.4, Section 6.4, Problem 66

Given equation is yy'-2y^2=e^x
=> y' -2y=e^x y^(-1)
An equation of the form y'+Py=Qy^n
is called the Bernoulli equation .
so, to proceed to solve this equation we have to transform the equation into a linear equation form of first order as follows
=> y' (y^-n) +P y^(1-n)=Q
let u= y^(1-n)
=> (1-n)y^(-n)y'=u'
=> y^(-n)y' = (u')/(1-n)
so ,
y' (y^-n) +P y^(1-n)=Q
=> (u')/(1-n) +P u =Q
so this equation is now of the linear form of first order
Now,
From this equation ,
y' -2y=e^x y^(-1)
and
y'+Py=Qy^n
on comparing we get
P=-2 Q=e^x , n=-1
so the linear form of first order of the equation y' -2y=e^x y^(-1) is given as

=> (u')/(1-n) +P u =Q where u= y^(1-n) =y^2
=> (u')/(1-(-1)) +(-2)u =e^x
=> (u')/2 -2u=e^x
=> (u')-4u = 2e^x

so this linear equation is of the form
u' + pu=q
p=-4 , q=2e^x
so I.F (integrating factor ) = e^(int p dx) = e^(int -4dx) = e^(-4x)

and the general solution is given as
u (I.F)=int q * (I.F) dx +c
=> u(e^(-4x))= int (2e^x) *(e^(-4x)) dx+c
=> u(e^(-4x))= int (2e^x) *(e^(-4x)) dx+c
=> u(e^(-4x))= 2 int (e^(-3x)) dx+c
=>u(e^(-4x))= 2 int (e^(-3x)) dx+c
=>u(e^(-4x))= 2 (1/(-3)*e^(-3x))+c as int e^(ax) dx = 1/a e^(ax).
=>u(e^(-4x))= (-2/3)*e^(-3x)+c
=> u = ((-2/3)*e^(-3x)+c)/(e^(-4x))
but u= y^2 so ,
y^2 = ((-2/3)*e^(-3x)+c)/(e^(-4x))
y= sqrt((-2/3e^(-3x)+c)/(e^(-4x)))
=sqrt((-2/3e^(-3x)+c)*(e^(4x)))
= sqrt((-2/3e^(x)+ce^(4x)))
=e^(x/2)sqrt((-2+3ce^(3x))/3)
is the general solution.

The wave function for a particle is psi(x)=Axe^(-x^2/a^2) where A and a are constants. Where is the particle most likely to be found? Assume that a = 2.49 nm. Is the particle most likely around 2.49 nm because that is the constant/max.

Hello!
The probability of finding a particle within some set R is int_R |Psi(x)|^2 dx. The probability to find a particle at a specific point is zero, but there is a correct question: "what is the point x_0 such that the probability of finding the particle within a small interval with the center in x_0 is maximal?"
Since our Psi(x) is continuous, the integral over a small interval is almost equal to Delta x*|Psi(x_0)|^2. So, we have to find the point(s) x_0 where |Psi(x_0)|^2 has its maximum. This is the same as the |Psi(x_0)| maximum.
The factor |A| has no effect on x_0, thus it is sufficient to find the maximum of f(x) = x e^(-x^2/a^2) for xgt=0 (for xlt0 the values are the same). At x=0 the value is zero, at +oo the limit is also zero, so the maximum is somewhere in between. The necessary condition is f'(x_0) = 0, so the equation is:
f'(x) = (x e^(-x^2/a^2))' =e^(-x^2/a^2) - x*(2x)/a^2e^(-x^2/a^2) =e^(-x^2/a^2)(1-(2x^2)/a^2) = 0.
The only such x_0 = |a|/sqrt(2) (so there are two points of a maximum, |a|/sqrt(2)  and -|a|/sqrt(2)). Numerically for a=2.49 nm   x_0 approx +-1.76 nm.

What are the good things Rikki-Tikki-Tavi does in the story?

Rikki-Tikki-Tavi rids the family's bungalow of the two wicked cobras and secures the premise for the future by destroying Nag and Nagaina's eggs. Initially, Rikki-Tikki-Tavi saves Teddy's life by killing Karait, an extremely venomous snake who attempts to bite the young boy. That night, Rikki-Tikki-Tavi runs into Chuchundra and learns that Nag is in the bungalow preparing to bite Teddy's father in the morning. Rikki-Tikki-Tavi then sneaks into the bathroom at night, spies on Nag as he is sleeping, and ends up killing him before Nag can bite Teddy's father. After saving another family member and killing Nag, Nagaina mourns the loss of her husband, which gives Rikki-tikki enough time to destroy every egg in her nest except one. Nagaina then enters the bungalow, where she threatens to bite Teddy's leg. Fortunately, Rikki-Tikki-Tavi distracts Nagaina by showing her the last egg, and she quickly abandons her mission of killing Teddy. Rikki-Tikki-Tavi then follows Nagaina into her underground hole, where he kills Nagaina and destroys her last egg, effectively securing the bungalow and its premises.

Rikki-Tikki-Tavi does a number of good things in the story. As the main protagonist, Rikki-Tikki-Tavi proves himself to be an altruistic hero. For example, after he is rescued by the family, Rikki-Tikki-Tavi takes it upon himself to take care of and protect them. This is seen in a number of instances. The first time is out in the garden, when the young boy, Teddy, is threatened by a small snake named Karait. Rikki-Tikki-Tavi immediately takes it upon himself to kill the snake to help Teddy. Later, the cobra Nag sneaks into the family's bathroom, and he waits to bite them. Rikki-Tikki-Tavi kills Nag before anything bad can happen. Finally, Rikki-Tikki-Tavi kills Nagaina, Nag's wife, in order to protect the family.
https://www.vma.is/static/files/enska/Bokmenntir/Short%20Stories/RikkiTikkiTavi_Kipling.pdf

Why did Sor Juana Inés de la Cruz write her reply to the Bishop of Puebla?

Sor Juana Inés de la Cruz's letter to the Bishop of Puebla was a response to his own pseudonymous letter criticizing her for her attention to and concern of earthly matters and quest for knowledge. This was considered very unbecoming for a woman at the time. Sor Juana's letter is a defense of a woman's right to education and the pursuit of learning. She uses her letter to showcase her intelligence in an age and place where women were considered less intelligent and capable of knowledge than men. She even provides a framework of how a woman can properly learn so as to improve society as a whole.
Cleverly, she opens her letter by stating that she is not as smart as others may think, but then she shows her wit and wisdom by incorporating language and ideas throughout the piece that highlight her intelligence. Her letter responds to the Bishop's arguments and shines a light on her own abilities at the same time. Throughout the letter, she deconstructs many of the patriarchal practices of her society and promotes a woman's right to an education. Sor Juana Inés de la Cruz's letter is thus seen as an early work of feminism.

Sor Juana Inés de la Cruz (1648?–1695) was a well-educated Mexican woman who was renowned for her knowledge and literary ability. Seeking to further her knowledge, she entered a convent and remained there until her death. Her study of non-religious subjects made her a target of criticism in both political and religious circles.
In 1690, a person masquerading as "Sor Filotea de la Cruz," who was actually the Bishop of Puebla, Manuel Fernandez de Santa Cruz, published, without Sor Juana's approval, a letter that she had written criticizing a sermon. Sor Filotea also took Sor Juana to task for the secular nature of her studies and reading. In her famous response, Sor Juana defended her right as a woman to gain an education and stated that her secular studies made her more able to understand the scriptures. Her scholarly and eloquent letter is regarded as among the first defenses of a woman's right to an education.

What factors led to the Commercial Revolution in Europe?

The 15th Century saw a renewed interest in trading in Europe. One of the primary reasons for this was the contact that the Europeans experienced with the East during the Holy Crusades. The Crusaders brought back food goods such as spices, coffee, tea, and rice that were immediately in high demand. Porcelain, silks and perfumes were also introduced and there was a high demand for those goods in Europe. This interest in goods from the East motivated nations to explore trade routes to India. These routes led to the expansion of trade and conquest along the coast of Africa and into the New World. The colonial conquests of Britain, Spain, and Portugal increased the wealth of these imperial powers which further expanded trade in Europe. The continent was introduced to new goods from both the east and west. This early form of capitalism, which was called mercantilism, motivated nations to trade. A nation achieved its economic and political strength by gaining trade surpluses over its neighbors under mercantilism.
 
 

How does the change in Laurie's clothing on his first day of school signal a change his behavior?

The change in Laurie's clothing is described in the first paragraph of Shirley Jackson's short story, "Charles." It foreshadows the behavioral changes in Laurie, as manifested through the character Charles, whom Laurie invents. 
Here is the paragraph: 

The day my son Laurie started kindergarten he renounced corduroy overalls with bibs and began wearing blue jeans with a belt; I watched him go off the first morning with the older girl next door, seeing clearly that an era of my life was ended, my sweet-voiced nursery-school tot replaced by a longtrousered, swaggering character who forgot to stop at the corner and wave good-bye to me.

Jackson's word choice and description of Laurie's new attire foreshadow the behavioral changes to come. First, she uses the word "renounced." Synonyms for this word include shun, reject, and disown. This shows that Laurie is asserting his independence with his clothing choice. One can infer that his mother made the clothing choices up to that point. Now Laurie is casting aside the clothing he used to wear and choosing blue jeans with a belt, a more grown-up choice. His mother, the narrator, describes him as "swaggering," which suggests Laurie feels more grown up and impressive in his new attire.  
The mother describes watching her sweet-voiced preschooler being replaced by a child who swaggers. He also wears clothing that shows he is leaving behind a part of his childhood. He even forgets to turn around and wave to his mother, showing that he doesn't think he needs her as much as he did previously.

Why did the author write in third person?

This is an interesting question for this story, because I have always thought that the story wouldn't be that much different if it was written in the first person perspective. While the narration of this story is third person, it is not third person omniscient. It is third person limited. The narration is almost exclusively focused on Connie. Readers know her thoughts, actions, and feelings, and we do not know much of that information about any other character. This makes Arnold Friend as mysterious and creepy to readers as he is to Connie. We feel her fear, and we have no idea what Friend is up to and about. All of that can be accomplished with a first person perspective, yet this story is told from the third person perspective. This allows the narrator to explore Connie's world in a little bit more depth than would be possible in first person. The opening paragraphs are a good example of this. They give readers information about Connie, her sister, and her mother. The third person narration allows the narrator to give information that is beyond Connie's limited teenage perspective.

Her mother, who noticed everything and knew everything and who hadn't much reason any longer to look at her own face, always scolded Connie about it. "Stop gawking at yourself."

The other thing that the third person perspective does is create a bit of distance. This limited perspective creates distance from other characters, but the third person perspective creates distance from Connie's narrow worldview. The point of view allows the story to be more of an allegorical/moral/symbolic story. First person narration would make the story a horrific account of a young girl's abduction. The third person perspective still tells that story; however, it also conveys an "and let this be a lesson to you" message. The story could be interepreted as a warning for young girls like Connie in all places.

College Algebra, Chapter 2, 2.2, Section 2.2, Problem 28

Make a table of values and sketch the graph of the equation $y = - \sqrt{4 - x^2}$. Find the $x$ and $y$ intercepts.

$
\begin{array}{|c|c|}

\hline\\
\text{Let } x & y = - \sqrt{4 - x^2} \\
\hline\\
-2 & 0 \\
\hline\\
-1.5 & - \displaystyle \frac{\sqrt{7}}{2} \\
\hline\\
-1 & - \sqrt{3} \\
\hline\\
-0.5 & - \displaystyle \frac{\sqrt{15}}{2} \\
\hline\\
0.5 & - \displaystyle \frac{\sqrt{15}}{2} \\
\hline\\
1 & - \sqrt{3}\\
\hline\\
1.5 & - \displaystyle \frac{\sqrt{7}}{2}\\
\hline\\
2 & 0\\
\hline

\end{array} $

To solve for $x$ intercept, where $y = 0$


$
\begin{equation}
\begin{aligned}

0 =& - \sqrt{4 - x^2}
\\
\\
0 =& \sqrt{4 - x^2}
\\
\\
0 =& 4 - x^2
\\
\\
x^2 =& 4
\\
\\
x =& \pm 2


\end{aligned}
\end{equation}
$


Thus, the $x$ intercept is at $(2,0)$ and $(-2, 0)$

To solve for the $y$ intercept, we set $x = 0$


$
\begin{equation}
\begin{aligned}

y =& - \sqrt{4 - (0)^2}
\\
\\
y =& - \sqrt{4}
\\
\\
y =& -2

\end{aligned}
\end{equation}
$


Thus, the $y$ intercept is at $(0, -2)$

In I Am China by Xiaolu Guo, how can Jian's loss of identity be explained, and what role does his status as an asylum-seeker play?

To properly answer this question, let us establish a bit of context with respect to the setting and main characters.
Kublai Jian (along with his love interest, the poet Deng Mu) is one of the main characters in Xiaolu Guo's novel I Am China. When the story begins, just after the historic events of Tiananmen Square have unfolded, Jian is a punk rocker living in Beijing.
The third character at the center of this book is a literary translator named Iona Kirkpatrick. She works for a publishing house in London, and she is in the process of sorting through and translating Jian's letters and diaries. In reading these materials, she learns about the two-decade-long love story between Jian and Mu. She realizes that they have been separated (though she does not know how at first, she will eventually learn that Jian is at a psychiatric hospital in England, seeking asylum, while Mu is searching for Jian back in Beijing) and feels increasingly compelled to find them and help them to reunite.
Now, to get back to the question at hand. How can we explain Jian's loss of identity? To what extent is his status as someone seeking asylum important?
First, let us talk about Jian's identity in general and how it changes in the course of the narrative. Jian is living in Beijing when the book opens. He is not fully Chinese, however: he identifies as half Mongol and half Han Chinese. There is something essentially disorienting about his identity, even before he leaves China and ends up going to live for stints in Switzerland and France before seeking asylum in the UK. His constant dislocation, both physical and emotional (he is separated from Mu, as she is touring internationally as a poet while he is jumping from one country to the next), means that he has already lost a sense of identity before he ever gets to England.
The reason for Jian's departure from China, too, is a major contributor to his loss of identity. As Iona discovers in her translations, Jian wrote a political manifesto that forced him to go into exile. The last lines of that manifesto inspired the title of the book, and they also speak to Jian's estrangement from his native country:

I am China. We are China. The people. Not the state.

So, how does Jian's status as someone seeking asylum play into his loss of identity? On one hand, being in exile frees him from the expectations and norms of the place he is from. However, he does not have any particular status in the place where he seeks asylum. He is isolated and alone, and he struggles internally with his political ideals and his personal nostalgia for the place he used to call home. This is well expressed in one of his letters to Mu that Iona translates:

Dearest Mu, The sun is piercing, old bastard sky. I am feeling empty and bare. Nothing is in my soul, apart from the image of you. I am writing to you from a place I cannot tell you about yet.

Being a seeker of asylum renders him vulnerable and even weak—he is at the mercy of the system. It is worth mentioning that the author herself, Chinese by birth, has been living in England since 2002. This novel is in part a product of her personal experience.

Single Variable Calculus, Chapter 7, 7.7, Section 7.7, Problem 24

Show that the formulas for the derivatives of the functions a.) $\cos hx$, b.) $\tan hx$, c.) $\csc hx$ ,d.) $\sec hx$ and e.) $\cot hx$

a.) $\cos hx$


$
\begin{equation}
\begin{aligned}

\cos hx =& \frac{e^x + e^{-x}}{2}
\\
\\
\frac{d}{dx} (\cos hx) =& \frac{d}{dx} \left( \frac{e^x + e^{-x}}{2} \right)
\\
\\
\frac{d}{dx} (\cos hx) =& \frac{\displaystyle (2) \frac{d}{dx} (e^x + e^{-x}) - (e^x + e^{-x}) \frac{d}{dx} (2) }{(2)^2}
\\
\\
\frac{d}{dx} (\cos hx) =& \frac{2 [e^x + (-e^{-x})]}{4}
\\
\\
\frac{d}{dx} (\cos hx) =& \frac{e^x - e^{-x}}{2}

\end{aligned}
\end{equation}
$


We know that $\displaystyle \sin h(x) = \frac{e^x - e^{-x}}{2}$, so

$\displaystyle \frac{d}{dx} (\cos hx) = \sin hx$

b.) $\tan hx$


$
\begin{equation}
\begin{aligned}

\tan hx =& \frac{\sin hx}{\cos hx}
\\
\\
\frac{d}{dx} \tan hx =& \frac{d}{dx} \left( \frac{\sin hx}{\cos hx} \right)
\\
\\
\frac{d}{dx} \tan hx =& \frac{\displaystyle (\cos hx) \frac{d}{dx} (\sin hx) - (\sin hx) \frac{d}{dx} (\cos hx) }{(\cos hx)^2}
\\
\\
\frac{d}{dx} \tan hx =& \frac{(\cos hx) (\cos hx) - (\sin hx)(\sin hx)}{\cos h^2 x}
\\
\\
\frac{d}{dx} \tan hx =& \frac{\cos h^2 x - \sin h^2 x}{\cos h^2 x}


\end{aligned}
\end{equation}
$



We know that $\cos h^2 x - \sin h^2 x = 1$, so


$
\begin{equation}
\begin{aligned}

\frac{d}{dx} \tan hx =& \frac{1}{\cos h^2 x}
\\
\\
\frac{d}{dx} \tan hx =& \sec h^2 x

\end{aligned}
\end{equation}
$


c.) $\csc hx$


$
\begin{equation}
\begin{aligned}

\csc hx =& \frac{1}{\sin hx}
\\
\\
\csc hx =& (\sin hx)^{-1}
\\
\\
\frac{d}{dx} (\csc hx) =& \frac{d}{dx} (\sin hx)^{-1}
\\
\\
\frac{d}{dx} (\csc hx) =& -(\sin hx)^{-2} \frac{d}{dx} (\sin hx)
\\
\\
\frac{d}{dx} (\csc hx) =& - (\sin hx)^{-2} (\cos hx)
\\
\\
\frac{d}{dx} (\csc hx) =& \frac{-1}{\sin h^2 x} \cdot \cos hx
\\
\\
\frac{d}{dx} (\csc hx) =& \frac{- \cos hx}{\sin hx} \cdot \frac{1}{\sin hx}
\\
\\
\frac{d}{dx} (\csc hx) =& - \cot hx \csc hx


\end{aligned}
\end{equation}
$


d.) $\sec hx$


$
\begin{equation}
\begin{aligned}

\sec hx =& \frac{1}{\cos hx}
\\
\\
\sec hx =& (\cos hx)^{-1}
\\
\\
\frac{d}{dx} (\sec hx) =& \frac{d}{dx} (\cos hx)^{-1}
\\
\\
\frac{d}{dx} (\sec hx) =& - (\cos hx)^{-2} \frac{d}{dx} (\cos hx)
\\
\\
\frac{d}{dx} (\sec hx) =& - (\cos hx)^{-2} (\sin hx)
\\
\\
\frac{d}{dx} (\sec hx) =& \frac{-1}{\cos h^2 x} \cdot \sin hx
\\
\\
\frac{d}{dx} (\sec hx) =& \frac{- \sin hx}{\cos hx} \cdot \frac{1}{\cos hx}
\\
\\
\frac{d}{dx} (\sec hx) =& - \tan hx \sec hx

\end{aligned}
\end{equation}
$


e.) $\cot hx$


$
\begin{equation}
\begin{aligned}

\cot hx =& \frac{\csc hx}{\sin hx}
\\
\\
\frac{d}{dx} (\cot hx) =& \frac{d}{dx} \left( \frac{\cos hx}{\sin hx} \right)
\\
\\
\frac{d}{dx} (\cot hx) =& \frac{\displaystyle (\sin hx) \frac{d}{dx} (\cos hx) - (\cos hx) \frac{d}{dx} (\sin hx)}{(\sin hx)^2}
\\
\\
\frac{d}{dx} (\cot hx) =& \frac{(\sin hx)(\sin hx) - (\cos hx)(\cos hx)}{\sin h^2x}
\\
\\
\frac{d}{dx} (\cot hx) =& \frac{\sin h^2 x - \cos h^2 x}{\sin h^2 x}
\\
\\
\frac{d}{dx} (\cot hx) =& \frac{- (\cos h^2 x - \sin h^2 x)}{\sin h^2 x}

\end{aligned}
\end{equation}
$


We know that $\cos h^2 x - \sin h^2 x = 1$


$
\begin{equation}
\begin{aligned}

\frac{d}{dx} (\cot hx) =& \frac{-1}{\sin h^2 x}
\\
\\
\frac{d}{dx} (\cot hx) =& - \csc h^2 x

\end{aligned}
\end{equation}
$

Do powerful lobbyists help or hurt the legislative process, and why?

There are arguments to be made for lobbyists being beneficial to the legislative process and arguments to be made that they are harmful to the legislative process.  Bear in mind that lobbying is a legal activity, and indeed, is protected by the First Amendment of the United States Constitution, and any argument against lobbying must take this into account.  Your opinion on this matter, for or against lobbying, should be a considered one, certainly, so let's look at the pros and cons. 
On the positive side, there are arguments to be made. Lobbying is simply the act of trying to influence the legislative process, and this is completely consistent with democratic aims, to allow a constituency to voice concerns and opinions. When you or I write to our legislatures, we are lobbying, within the pure meaning of the word.  When a group bands together and selects someone to represent it to the legislature, the dynamic is at least theoretically the same.  Legislators cannot legislate in a vacuum in which they have no awareness of what the people want.  Lobbying to some degree solves that problem.  Also, lobbyists will tell you, and it's true, that they can perform an important function for legislators, which is to educate them.  Legislators are expected to make laws in myriad areas, from housing to gas lines, from wage regulation to food safety.  They cannot possibly be knowledgeable in all of the areas that they must address, much less have any expertise in them.  Lobbyists are quite knowledgeable in their respective areas and often have a certain amount of expertise. The fact that what they do is completely self-serving does not take away from the fact that they can and often do educate legislators, who can then go on to enact statues that are not completely ill-informed.  Since every special interest group (with the exception of hate groups or terrorist groups) can have a lobbyist, an additional benefit is that a legislator can be exposed to different and diverse points of view. That, too, is consistent with the aims of a democracy, which are to represent the will of the people, people who inevitably do not all hold the same opinions on matters.
On the other hand, in politics today, lobbying has results that are quite troubling for the state of democracy, since certain kinds of interests have the wherewithal to spend millions and even billions of dollars on this activity, while other special interests do not have the financial means to do so.  The interests of banks or the National Rifle Association come to mind.  If their interests are in conflict with those of poor people or people who have been victimized by the lack of gun control, there is little money available from these constituencies to hire lobbyists.  The interests of the wealthy hold sway in lobbying, with an ever-spiraling movement of legislation that advances their agendas, a vicious cycle that leaves poor people poorer and even less able to voice their concerns and needs.  Another example that comes to mind is the dismantling of public education, accomplished at the federal and state level with legislation that has permitted the privatization of schools.  This has been effectuated by wealthy interests that stand to benefit from this change.  Poor people, many less educated with each generation as our public schools lie in virtual ruins in many cities,  are not in a position to hire lobbyists to counteract this movement. So, lobbying has some consequences that are ugly for the majority of American citizens and residents. 
Whatever your opinion is on this matter, be sure you support it with good reasoning and examples to help you make your point. My own opinion is that lobbying does more harm than good today, but we cannot make it go away.  
 

Is it appropriate for Romeo to deny his family name for love?

This question is an opinion question, so my answer may be very different than yours. However, we have to consider the same basic points to reach our respective conclusions, so let's go through some pros and cons.
Reasons Romeo should deny his family name:

His name doesn't define him. As Juliet said, "a rose by any other name would smell as sweet." 

Love conquers all. To many people, love is one of the most important things in the world. Romeo and Juliet both think so, given the lengths to which they go to be with one another. If you agree, that's a strong reason to leave.

His family name is tainted. In the opening scenes of the play, the Prince has made it clear that he's sick and tired of the feud between the Montagues and Capulets. Yet this feud shows no sign of stopping. Abandoning his name might be a wise decision even without Juliet, making it all the more attractive if love is his reward.
Reasons Romeo should keep his name:

He owes it to his parents. Romeo's parents bore, raised, cared for, and educated him. And as a Christian, Romeo is commanded to honor his father and mother. His moral and religious duty requires him to stay true to his family.

He was raised to think the Capulets are the bad guys. Romeo tries to make peace with the Capulets after his secret wedding to Juliet, but up until that point, he is a Montague. You and I know that the narrative message behind the feud is that it's pointless and destructive and Romeo would be well rid of it. But Romeo may not know that. And is allowing evil to go unpunished an appropriate price to pay for love?

Is it really love? A recurring question about Romeo and Juliet is whether to interpret their relationship as a true love cursed by fate, or a flaring teen passion that clouded the lovers' judgement. It may eventually be correct for Romeo to abandon his name for love, but it's too early, given that the entire play takes place over the course of a week.
Take a look through the points, decide which are most compelling, and form your opinion on this basis. Good luck!
 

In The Joy Luck Club by Amy Tan, how does An-mei's mother show motherly love towards An-mei?

In The Joy Luck Club, An-mei's mother's sacrifice displays maternal love.
An-mei's mother was dealt a terrible blow in being Wu-Tsing's fourth wife. When An-mei's mother comes back to her, all she has to do to show how much she loves her daughter is touch her "smooth-neck scar."  This shows An-mei that while her mother has been absent, she never stopped loving her. When she finds the wound that only a mother would know, it conveys love and devotion towards An-mei. 
An-mei's mother further displays love in the way she tries to give her daughter the strength she lacks.  An-mei's mother teaches An-mei the importance of strength and why sadness and suffering cannot be swallowed. This is another way that love is shown because she is teaching her daughter the lessons that life has so brutally taught to her.  When she has to return to Tientsin, An-mei's mother shows love towards her daughter by respecting her wishes:  "An-mei, I am not asking you.  But I am going to back to Tientsin now and you can follow me."  There is a respect for her daughter underscored with love.
An-mei does go with her mother and learns more about suffering, pain, and the way to combat them.  The classroom for such instruction is An-mei's mother's life as a fourth wife for Wu Tsing.  An-mei's mother teaches An-mei about the ways of men and marriage:  "You can see now, a fourth wife is less than a fifth wife. An-mei, you must not forget.  I was a first wife, yi yai, the wife of a scholar.  Your mother was not always Fourth Wife, Sz Tai!" When An-mei's mother breaks the necklace that Second Wife gave An-mei, it is one of the strongest examples of love that a mother can show a daughter:  "You do not believe me, so you must give me the necklace.  I will not let her buy you for such a cheap price."  An-mei realizes how much her mother truly loves her: "That necklace that had almost bought my heart and mind now had one bead of crushed glass."  An-mei's mother wants her to "recognize what is true" and avoid that which is false, a lesson forged out of love.
An-mei's mother loves her so much that she wants her to learn from her own example.  She wants her daughter to look at her own life as how not to live. When An-mei's mother dies, An-mei knows why.  While others believe she swallowed too much opium, An-mei knows the truth about her mother's death:  "She would rather kill her own weak spirit so she could give me a stronger one."  This shows the highest form of love that a parent can have for a child. It is the reason why An-mei is able to scream, raising her voice against an injustice.  An-mei is able to demand that her mother in death is respected more than she was in life.  She is able to right the wrongs done to her mother, and prove that the best love a parent can show to a child is teaching them the value of strength and honor.  An-mei's mother's sacrifices are a testament to both this lesson and the love she had for her daughter.

sum_(n=1)^oo ln(n)/n^2 Confirm that the Integral Test can be applied to the series. Then use the Integral Test to determine the convergence or divergence of the series.

The Integral test is applicable if f is positive and decreasing function on infinite interval [k, oo) where kgt= 1 and a_n=f(x) . Then the series sum_(n=k)^oo a_n converges if and only if the improper integral int_k^oo f(x) dx converges. If the integral diverges then the series also diverges.
For the given series sum_(n=1)^oo ln(n)/n^2 , the a_n =ln(n)/n^2 .
Then applying a_n=f(x) , we consider:
f(x) =ln(x)/x^2
The graph of f(x) is:

As shown on the graph, f is positive on the finite interval [1,oo) . To verify of the function will eventually decreases on the given interval, we may consider derivative of the function.
Apply Quotient rule for derivative: d/dx(u/v) = (u'* v- v'*u)/v^2 .
Let u = ln(x) then u' = 1/x
      v = x^2 then v' = 2x
Applying the formula,we get:
f'(x) = (1/x*x^2- 2x*ln(x))/(x^2)^2
       = (x-2xln(x))/x^4
       =(1-2ln(x))/x^3
Note that 1-2ln(x) lt0 for larger values of x which means f'(x) lt0 .Based on the First derivative test, if f'(x) has a negative value then the function f(x) is decreasing for a given interval I . This confirms that the function is ultimately decreasing as x-gt oo . Therefore, we may apply the Integral test to confirm the convergence or divergence of the given series.
We may determine the convergence or divergence of the improper integral as:
int_1^oo ln(x)/x^2dx= lim_(t-gtoo)int_1^t ln(x)/x^2dx
To determine the indefinite integral of int_1^t ln(x)/x^2dx , we may apply integration by parts: int u *dv = u*v - int v* du
u = ln(x) then du = 1/x dx . 
dv = 1/x^2dx then v= int 1/x^2dx = -1/x  
Note: To determine v, apply Power rule for integration int x^n dx = x^(n+1)/(n+1).
int 1/x^2dx =int x^(-2)dx
                =x^(-2+1)/(-2+1)
                = x^(-1)/(-1)
                = -1/x
The integral becomes: 
int ln(x)/x^2dx=ln(x)(-1/x) - int (-1/x)*1/xdx
                    = -ln(x)/x - int -1/x^2dx
                    =-ln(x)/x + int 1/x^2dx
                    =-ln(x)/x + (-1/x)
                    = -ln(x)/x -1/x
Apply definite integral formula: F(x)|_a^b = F(b) - F(a) .
-ln(x)/x -1/x|_1^t =[-ln(t)/t -1/t] -[-ln(1)/1-1/1]
                      =[-ln(t)/t -1/t] -[-0-1]
                      =[-ln(t)/t -1/t] -[-1]
                      = -ln(t)/t -1/t +1
Apply int_1^tln(x)/x^2dx= -ln(t)/t -1/t +1 , we get:
lim_(t-gtoo)int_1^tln(x)/x^2dx=lim_(t-gtoo) [-ln(t)/t -1/t +1]
                                  = -0 -0 +1
                                = 1
Note: lim_(t-gtoo) 1=1
         lim_(t-gtoo) 1/t = 1/oo or 0
      lim_(t-gtoo) -ln(t)/t =[lim_(t-gtoo) -ln(t)]/[lim_(t-gtoo) t]
                             =-oo/oo
Apply L' Hospitals rule:
lim_(t-gtoo) -ln(t)/t =lim_(t-gtoo) -(1/t)/1
                        =lim_(t-gtoo) -1/t
                        = -1/oo or 0
The  lim_(t-gtoo)int_1^tln(x)/x^2dx =1  implies that the integral converges.
Conclusion: The integral int_1^oo ln(x)/x^2dx   is convergent therefore the series sum_(n=1)^ooln(n)/n^2 must also be convergent. 

What are some examples of a strong thesis statement and three topic sentences about "The Lesson" by Toni Cade Bambara?

You could say that a thesis statement is an opinion which you will be arguing throughout your essay. I like to think of a yes or no question and frame my thesis statement around an answer.
For example, in "The Lesson" I might ask, "Is it necessary to become aware of injustice?"
In the story, Miss Moore takes the kids into a rich part of town and shows them expensive toys which the kids know they cannot afford. She's making them confront their situation and think about the poverty and injustice that surrounds them. Does this make a difference? Does anything change in the way Sylvia thinks and asks? Will knowing that she is poor help her make a positive impact in the future?
Think through these questions, or come up with questions of your own, and then decide how you want to answer. Your thesis can come from those answers, such as "Becoming aware of injustice is a necessary step in improving one's situation." Or, on the flip side, you could argue "One does not need to become aware of injustice in order to make a difference."
Once you've come up with a thesis statement you need to answer the question "why?" Come up with three reasons your statement is true, then find examples and evidence from the story to support these statements, which will become your topic sentences and will help you frame the outline of your essay.

Your thesis statement and topic sentences depend on what you plan to prove in your essay. "The Lesson" is a powerful story with many themes, including the nature of poverty and injustice and how children learn about these concepts. A strong thesis statement makes an argument that is supported by each of the topic sentences (which begin the body paragraphs). 
One topic you might write about is what Sylvia, the African American girl from Harlem who narrates the story, learns by going on the shopping trip to Fifth Avenue in Manhattan with Miss Moore. If you think about three things Sylvia learns, such as the unfairness of the society (as well as two other things), each of these smaller lessons can be a topic sentence for one of your body paragraphs. Your thesis can be the overall lesson that she learns or the three smaller lessons she takes away.
You might also write about how Sylvia changes over the course of the story. At first, she is reluctant to believe that Miss Moore can teach her anything. When she is on Fifth Avenue, she starts to make some realizations. When she returns home to Harlem, she really internalizes what she has learned. You can focus one body paragraph (and its topic sentence) on how Sylvia thinks before the lesson, one paragraph on what she thinks during the lesson, and one paragraph on how she thinks after the lesson. Your thesis statement would summarize the overall change that she goes through during the story.

What prayers does Crispin make to saint Giles at the end of chapter 26? Why?

Father Quinel is a good friend to both Crispin and his mother Asta. He also knows the true identity of Crispin's father, and this makes him a threat to the wicked John Aycliffe. Aycliffe brutally murders Father Quinel before he can tell Crispin the whole truth about his father. When Crispin finds Father Quinel's body, he's absolutely devastated. He feels all alone in the world, as if everyone's abandoned him, even God. Nevertheless, Crispin is still sufficiently devout to get down on his knees and pray to St. Giles. Crispin is petrified, frightened at what's in store for him. Like the vast majority of people in the Middle Ages, his faith provides a source of comfort in times of great fear and sorrow.
In medieval Christianity, St. Giles was one of the so-called Fourteen Holy Helpers, a group of saints thought to be particularly helpful in interceding on behalf of believers. If Crispin ever needed the assistance of a saint, then it's now. Trembling, he falls to his knees and prays to St. Giles, imploring his blessings on the departed priest and on himself.

Did you find this to be a disturbing story?

The definition of "disturbing" is when peace and harmony are interrupted or interfered with. In O'Connor's "A Good Man is Hard to Find," the peace and tranquility of the family traveling for a holiday are fatally interrupted when they take a wrong road and come in contact with The Misfit and his gang. The family may have escaped unharmed if the grandmother had not identified the men as escaped convicts, which makes one feel sorry for the family. Probably the most disturbing fact of the story, however, is the polite, yet carefree, way that the deaths are carried out. For example, the Misfit says the following:

"Lady, . . . would you and that little girl like to step off yonder with Bobby Lee and Hiram and join your husband?"

Then the mother simply says, "Yes, thank you," and walks her daughter and herself into the woods to be killed like her husband just was. The mother doesn't put up a fight, or argue, or try to escape! Another disturbing thought is how easily the other men carry out The Misfit's orders. These men kill men, women, and children without a second thought! After the surprise of such evil wears off, a reader might realize just how desensitized and callous some people can become; however, each reader might find a different part of the story that disturbs him or her in a different way. Which part of the story upsets you?

What does Rosicky value most for his children?

Rosicky values a happy life living off the land for his children. His greatest hope is that his children never have to contend with the worst of human nature.
In the story, Rosicky worries about Rudolph, his eldest son. Rudolph is married to Polly, but the relationship between the two is strained. The weather has not cooperated lately, and the crops have been poor. Rosicky also suspects that Polly misses city life, so he decides to cheer the couple up. He goes over to Rudolph and Polly's house and offers them the use of the family car. 
In order to encourage the couple to go into town, Rosicky offers to do the dishes and to clean up the kitchen for Polly. He tells his daughter-in-law that he means to watch out for her and to make sure that her life is a happy one. 
In the story, we learn that Rosicky deeply values the agricultural lifestyle. He believes that city life is unnatural because it is divorced from the land that sustains humankind. His greatest fear is that Rudolph will move back to the city and take up a job there. To Rosicky, a wage earner is a "landless man" and a slave. 
Although Rosicky recognizes that farmers are subject to the whims of weather cycles, he insists that they have more freedom than city workers. After all, farmers are not subject to the "foulness and misery and brutality" of city life, and they do not have to contend with the conflicting interests of "bosses and strikers." 
Accordingly, Rosicky values a simple, happy existence on the land away from "the cruelty of human beings" as the best thing his children can attain.

What do we learn about where Mrs. Jones lives in "Thank You, M'am" by Langston Hughes?

In "Thank You, M'am," we learn that Mrs. Jones's home is a modest one.
When Mrs. Jones drags Roger to her home, she is not taking him to an opulent mansion.  Hughes gives us specific details about how her home reflects a limited economic condition.  Mrs. Jones lives in a house with other "roomers."  When Roger hears them laughing, he knows that "they were not alone."  Roger notices the home's "large kitchenette furnished room at the rear of the house."  There is a day-bed where Mrs. Jones talks to Roger about her life of economic limitation.  We are struck by the intimate, modest setting that contains a "gas plate and an icebox."  Roger does not wash his face in a large bathroom, but rather at a sink.   
Mrs. Jones' home bolsters her lesson to Roger.  Mrs. Jones emphasizes how Roger should reject immorality.  His poverty does not justify such behavior.  As Mrs. Jones reprimands Roger for stealing, she is speaking from the perspective of economic challenge.  If Mrs. Jones's home were a palace that reflected vast sums of wealth, her lesson of not needing to steal to get money would ring hollow.  However, when Roger sees where she lives, it is clear that she shares some common experience with him. He knows that she knows a life of financial limitation.  As a result, he can understand her moral instruction.

How does Wuthering Heights present the possibilities of women as heroic?

In a different interpretation than the other educator, I would argue that there is only one female hero in the text. Both Isabella and the elder Catherine are victims, in a sense, of the men who prey upon them. Additionally, each is destructive in her own way: a quality that often runs contrary to the notion of heroism.
The younger Catherine does not really perform any acts of courage or heroism either. In the end, the noblewomen in the text are not to be idealized.
However, Ellen “Nelly” Dean stands apart from the rest of the women in Bronte’s novel. Nelly is the only character in the text who is both compassionate toward the Earnshaws, Lintons, and even Heathcliff after he transforms into a sort of villain. Dean is somewhat heroic in that sense that she has the moral fortitude to remain an essentially good person amidst so much pain and chaos.

A hero is a person who others see as courageous or bold. In that sense, Catherine Earnshaw could be understood as heroic. She is fearless. She marries Edgar Linton, in large part, as she tells Nelly Dean, to try to save Heathcliff from degradation. After Heathcliff has gone away and mysteriously returns a gentleman, she does her best to pull him into her life. She is willing to defy Linton to protect Heathcliff. In the end, she chooses death rather than a life without Heathcliff. Despite her bouts of madness, she is courageous in death, facing it unflinchingly when she is reunited with Heathcliff for a last meeting. She states boldly that she does not belong in heaven. She believes her happiness will come if, after she dies, God throws her spirit out to wander her beloved moors. The novel relentlessly shows her as strong and fierce in contrast with the weaker Lintons, especially her weak, conventional husband. 
Her daughter Catherine and her sister-in-law Isabella show courage in the face of cruel, abusive marriages. Bronte depicts ways women can be courageous in the face of a patriarchy in which all the power in the social and economic system goes to men.

C.S. Lewis writes that Uncle Andrew was "vain as a peacock" and that was why he had become a magician. What connection can you make between vanity and wanting to be a magician?

The first connection that comes to mind between vanity and being a magician is power. Someone who believes they are better than everyone else is also likely to believe they should be able to have access to more power as a reflection of their greatness. In the book, for example, Uncle Andrew is able to use his powers to access the other world, which he expects will give him considerably more knowledge and influence (both forms of power) than if he were not a magician. Of course in the book we see that instead of giving him power, it brings Jadis into his life, who enslaves him in spite of his magical abilities.
The second connection I see between vanity and becoming a magician is control. Again, individuals who exhibit vanity would not want things to be outside of their control because it might affect their power or station. Uncle Andrew views learning magic as an additional tool to provide him with a greater ability to control what is happening to him.

Use the disk method to verify that the volume of a right circular cone is 1/3 *pir^2h where r is the radius of the base and h is the height.

To verify the volume of a right circular cone, we consider the radius of the base (r) as an interval along the x-axis  and height (h) as an interval along the y-axis. As shown in the attached image, a red line revolves about the y-axis to form a right circular cone. For the equation of the red line, we consider the points: (0,h) and (r,0) where:  x_1= 0 , y_1=h , x_2=r , and y_2=0 .
 
The point (0,h) is a y-intercept point therefore  it follows  (0,b) then  b =h in y=mx+b .
To solve for m, we follow m = ((y_2-y_1))/((x_2-x_1)) .
m= ((0-h))/((r-0)) = -h/r
Then  plug-in m= -h/r and b = h, we get the equation of the red line as: y =-h/rx+h .
This can be rearrange into x = -(y-h)*r/h   or   x= ((h-y)r)/h .
Using the Disk Method, we consider a rectangular strip perpendicular to the axis of revolution.
For a horizontal rectangular strip with a thickness of "dy", we follow the formula for Disk Method as: V = int_a^b pi r^2 dy .
 To determine the r, we consider the length of the rectangular strip = x_2-x_1 .
Then, r= ((h-y)r)/h - 0 = ((h-y)r)/h  .
Boundary values of y: a=0 to b=h .
Plug-in the values on  the formula: V = int_a^b pi r^2 dy , we get:
V = int_0^h pi (((h-y)r)/h)^2 dy
V = int_0^h pi (r^2/h^2)*(h-y)^2dy
Apply basic integration property: int c*f(y) dy = c int f(y) dy .
V =( pir^2)/h^2 int_0^h (h-y)^2 dy
To find the indefinite integral, we may apply u-substitution by letting u = h-y then du = -dy or (-1)du = dy .
V =( pir^2)/h^2 int (u)^2 *(-1)du
V =( -pir^2)/h^2 int (u)^2 du
Apply Power rule for integration: int y^n dy= y^(n+1)/(n+1) .
V =( -pir^2)/h^2* u^(2+1)/(2+1)
V =( (-pir^2)/h^2)* u^3/3
Plug-in y = h-y  on (( pir^2)/h^2)* u^3/3 , we get:
V =(( -pir^2)/h^2)* (h-y)^3/3|_0^h
Apply definite integration formula: int_a^b f(y) dy= F(b)-F(a) .
V =((- pir^2)/h^2)* (h-h)^3/3-((- pir^2)/h^2)* (h-0)^3/3
V =(( -pir^2)/h^2)* (0)^3/3-(( -pir^2)/h^2)* (h)^3/3
V =0 -(( -pih^3r^2)/(3h^2))
V = 0 +(pih^3r^2)/(3h^2)
V =(pih^3r^2)/(3h^2)
V = (pihr^2)/3 or 1/3pir^2h
 
Note: Recall the Law of Exponent: y^n/y^m= y^((n-m))
then h^3/h^2= h^((3-2)) = h^ 1 or h .
 

What precautions must the Franks and van Daans take to remain undiscovered in the annex?

The Diary of Anne Frank, as the title tells us, is the true-life diary of Anne Frank, who spent years in hiding with her family in an attempt to stay alive and not be taken away by the Nazis. Anne tells us every single detail of her life, big or small, and we learn a lot about her.
One of the things we learn very well is how important it is for Anne, her family, and the van Daan family to take precautions so that they are not discovered. The most paramount of these precautions is to stay quiet during the day, so as not to alert the people working downstairs to their presence. The family spoke very little during daylight hours, and moved around very little, so as not to make the floorboards creak. They never flushed the toilet until the end of the day either, so no one would become suspicious or suspect that someone was living or working upstairs.
They also made sure to keep the curtains drawn during the day, so that no one out on the street could see inside. All of the windows were kept closed, with the one exception being a window in the attic. Occasionally they would open the windows a bit at night to let fresh air in, but other than this, the annex was kept sealed and covered.
To outsiders, it may have appeared that there was not even a room there at all—or, at the very least, that if there was a room, it was unused. When people came by to bring the families food, they made sure to do so at night, under the cover of darkness, so no attention would be brought to it.
https://www.annefrank.org/en/

Calculus: Early Transcendentals, Chapter 4, Review, Section Review, Problem 70

You need to evaluate f(u) using the antiderivative of the function f'(u), such that:
int f'(u) du = f(u) + c
int (u^2 + sqrt u)/u du = int (u^2)/u du + int (sqrt u)/u du
int (u^2 + sqrt u)/u du = int u du + int u^(1/2 - 1) du
int (u^2 + sqrt u)/u du = u^2/2 + (u^(1/2 - 1+1))/(1/2 - 1+1) + c
int (u^2 + sqrt u)/u du = u^2/2 + 2sqrt u + c
Hence, f(u) = u^2/2 + 2sqrt u + c
You need to evaluate the constant c, using the information f(1) = 3, such that:
f(1) = 1^2/2 + 2sqrt 1 + c
3 = 1/2 + 2 + c => c = 3 - 2 - 1/2 => c = 1 - 1/2 => c = 1/2
Hence, evaluating the function f under the given conditions yields f(u) = u^2/2 + 2sqrt u + 1/2.

How does Squealer use rhetorical devices to further convey pathos, logos, and ethos?

As Napoleon's protege and a character allusion to the historical Vyacheslav Molotov, who was Stalin's head of Communist propaganda, Squealer is a master of rhetoric and oration. Squealer serves as a figurehead for Animal Farm as Napoleon is seen less and less as corruption begins to thrive in the upper ranks of the farm. Throughout the book, Squealer uses several rhetorical devices to sooth any misgivings the animals may have. Squealer does not possess a great deal of basis for his ethos, but he uses it as an effective tool to convince the animals regardless. For example, when the animals figuratively raise their eyebrows at the idea of the pigs being allowed milk and apples, Squealer insists that it is simply science that pigs should need such foods to sustain their superior intelligence. Furthermore, he claims that certain "documents" that have been left behind prove that Snowball was in league with Jones from the start. While it does add an air of credibility to his argument, a few animals notice that they have no way of verifying that this is true. Squealer's logos primarily consists of gaslighting the animals and using circular reasoning to convince them that what the pigs want is also in their best interest. One example of this is when the pigs plan to open the farm for trade and the animals cite the previous agreement to never do this. Squealer makes a logical argument for the benefit of trade and insists that the animals simply dreamed up this resolution. Squealer is undoubtedly the most rhetorically powerful in terms of pathos. He addresses all of the animals as "comrade," immediately establishing a connection with them and implying that they are equals. He seems to have the ability to cry on cue, adding whirlwinds of emotion to any argument. He paints a picture of the pigs's duty as tiresome and arduous, insisting that they do not enjoy the burden of their leadership. This is the most effective way that squealer hides the true nature of the pigs.

Napoleon's propagandist-in-chief Squealer uses a number of time-honored rhetorical tropes to get the animals to believe what the regime wants them to believe. In one of his speeches to the animals, Squealer uses pathos, an appeal to the emotions:

I trust that every animal here appreciates the sacrifice that Comrade Napoleon has made in taking this extra labour upon himself. Do not imagine, comrades, that leadership is a pleasure! On the contrary, it is a deep and heavy responsibility.

It's tough at the top, and Squealer wants the animals to have sympathy towards Napoleon for the awesome burden of governance that he's placed upon his shoulders.
Squealer also uses ethos, an appeal to the speaker's credibility and moral character. Squealer doesn't have either of these, but gives it his best shot anyhow:

Our sole object in taking these things is to preserve our health. Milk and apples (this has been proved by Science, comrades) contain substances absolutely necessary to the well-being of a pig. We pigs are brainworkers. The whole management and organization of this farm depend on us. Day and night we are watching over your welfare. It is for YOUR sake that we drink that milk and eat those apples.

Squealer is trying to convince the animals that the pigs are not lazy or greedy (even though they are really). It's just that their superior intelligence means that they need to eat apples and drink milk. They don't want to—Good Lord, no—but they have to if they're going to continue benevolently watching over the animals and looking out for their best interests.
Finally, Squealer uses logos, an appeal to reason, to add credibility to his propaganda. Things are going disastrously wrong on the farm; there are chronic food shortages and nothing seems to work properly. There must be a good reason for this, and there is—Napoleon and the other pigs aren't up to the job—but of course Squealer can't very well admit that, so he needs to find a convenient scapegoat. Enter Snowball. This traitor to the Animalist revolution has been secretly plotting to destroy the farm, and what's more, says Squealer, we have the documents to prove it:

We had thought that Snowball's rebellion was caused simply by his vanity and ambition. But we were wrong, comrades. Do you know what the real reason was? Snowball was in league with Jones from the very start! He was Jones's secret agent all the time. It has all been proved by documents which he left behind him and which we have only just discovered. To my mind this explains a great deal, comrades.

Precalculus, Chapter 5, 5.4, Section 5.4, Problem 15

You need to evaluate the sine of 105^o , using the formula sin(a+b) = sin a*cos b + sin b*cos a such that:
sin(105^o) = sin(60^o + 45^o) = sin 60^o*cos 45^o + sin 45^o*cos 60^o
sin(105^o) = (sqrt3)/2*(sqrt2)/2 + (sqrt2)/2*1/2
sin(105^o) = (sqrt2)/2*(sqrt3 + 1)/2
You need to evaluate the cosine of 105^o , using the formula cos(a+b) = cos a*cos b - sin b*sin a such that:
cos (105^o) = cos (60^o + 45^o) = cos 60^o*cos 45^o - sin 45^o*sin 60^o
cos (105^o) = 1/2*(sqrt2)/2 - (sqrt2)/2*(sqrt3)/2
cos (105^o) = (sqrt2)/2*(1 - sqrt3)/2
You need to evaluate the tangent of 105^o , such that:
tan 105^o = (sin(105^o))/(cos (105^o))
tan 105^o = ((sqrt2)/2*(sqrt3 + 1)/2)/((sqrt2)/2*(1 - sqrt3)/2)
tan 105^o = (sqrt3 + 1)/(1 - sqrt3)
tan 105^o = ((sqrt3 + 1)*(1 + sqrt3)/(1 - 3)
tan 105^o = -((sqrt3 + 1)^2)/2
Hence, evaluating the sine, cosine and tangent of 105^o , yields sin(105^o) = (sqrt2)/2*(sqrt3 + 1)/2, cos (105^o) = (sqrt2)/2*(1 - sqrt3)/2, tan 105^o = -((sqrt3 + 1)^2)/2.

What is the significance of Desiree's response to Armand's belief that she is not white: "It is a lie; it is not true, I am white! Look at my hair, it is brown; and my eyes are gray, Armand, you know they are gray. And my skin is fair," seizing his wrist. "Look at my hand; whiter than yours, Armand," she laughed hysterically.

The significance of Désirée's response to Armand's belief that she is not white is that her physical features—skin color, hair color, and eye color—are her only proof of being white. She cannot point to any lineage as proof because she was a foundling left at the pillar of the gateway at the Valmondés' home. So she has no further evidence since she does not know her parents' names or race. Désirée's hysterical state demonstrates her fear that she cannot prove she is white, as well as her fear that she may possibly have African blood in her.
Désirée may also recall that her adoptive father, Monsieur Valmondé, "wanted things considered," such as "the girl's obscure origin," before Armand married her. But at the time, Armand felt that her origin did not matter, nor did it matter that she was virtually "nameless." But now that the baby does not appear to be white, Armand Aubigny, whose mother lived and died in France, and his white father assume that Désirée must be responsible for the baby's mixed blood. The tragic irony is the truth that Armand learns after the disappearance of Désirée and her baby. After he has destroyed all items that are reminders of Désirée and the child, Armand throws letters written by Désirée into the fire. But stuck in the back of the drawer from which the other letters have come is a remnant of an old letter to his father. Armand unfolds it and reads the words his mother has written. "...I thank the good God for having so arranged our lives that our dear Armand will never know that his mother, who adores him, belongs to the race that is cursed with the brand of slavery.”

In Kate Chopin's "Desiree's Baby," race, origin, and social status play significant roles. Before Desiree marries Armand, her race had never been questioned even with her mysterious appearance as a baby at the Valmondes's estate. In fact, her adoptive father, Monsieur Valmonde is more concerned about Desiree's "obscure origin" and what that means for her social status when Armand first demonstrates an interest in marrying her. Valmonde knows that for, someone such as Armand, name and class are everything, but impulsive Armand argues that he does not care, even when

reminded that [Desiree] was nameless. What did it matter about a name when he could give her one of the oldest and proudest in Louisiana?

Armand's blase attitude toward Desiree's origin before the birth of their son creates a false sense of comfort for Desiree. Admittedly, she does notice her new husband's cruel treatment of the slaves on his plantation but chooses to overlook it at first. After the baby's birth and Armand's growing detachment from Desiree and the baby because of his skin tone, Armand eventually "accuses" Desiree of not being white. He knows that no one can dispute his claim because of his wife's unknown biological roots. However, when he confronts Desiree about her race and she places her hand next to his to show how much lighter her skin is than his, she ironically and subconsciously identifies what Armand is most afraid of: the truth that he is the one who is biracial and that others will find out what his roots really are.

How did the South react to Abraham Lincoln as president?

The South didn’t react well to the election of Abraham Lincoln as president in 1860. The South was convinced that Lincoln was going to end slavery, even though Lincoln had said he wasn’t going to do that. While Lincoln was against slavery, he stated that he would allow it to remain where it already existed, if doing so would keep the country together. However, many Southerners believed that their way of life would be destroyed, and many people in the South had a difficult time accepting the idea that the slaves would be treated as equals if President Lincoln actually ended slavery. Many Southerners doubted Lincoln would keep his word. As a result, seven states seceded from the union shortly after the election of 1860, forming the Confederacy. After the attack at Fort Sumter, four additional Southern states seceded and joined the Confederacy.
https://www.history.com/topics/19th-century/lincoln-douglas-debates

College Algebra, Chapter 4, 4.6, Section 4.6, Problem 82

Graph the rational function $\displaystyle y = \frac{4 + x^2 - x^4}{x^2 - 1}$ and find all vertical asymptotes, $x$ and $y$ intercepts, and local extrema. Then use long division to find a polynomial that has the same end behavior that has the same end behavior as the rational function, and graph both functions in a sufficiently large viewing rectangle to verify that the end behaviors of the polynomial and the rational function are the same.







Based from the graph, the vertical asymptotes are the lines $x = \sqrt{2}$ and $x = - \sqrt{2}$. Also, the value of $x$ and $y$ intercept is . Then, the estimated local maximum occurs when $x$ is . On the other hand, the estimated value of the local minima of $8$ occurs when $x$ is approximately $2$.

By factoring,

$\displaystyle r(x) = \frac{4 + x^2 - x^4}{x^2 - 1} = \frac{4 + x^2 - x^4}{(x + 1)(x - 1)}$

Based from the graph, the vertical asymptotes are the lines $x = -1$ and $x = 1$. Also, the value of the $y$ intercept is $-4$ and $x$ intercepts are approximately $-1.60$ and $1.60$. Then the local maximum of $4$ occurs when $x$ is . However, the graph shows that the function has no local minima.

Then by using Long Division,







Thus, $\displaystyle r(x) = \frac{4 + x^2 - x^4}{x^2 - 1} = -x^2 + \frac{4}{x^2 - 1}$

Therefore, the polynomial $f(x) = -x^2$ has the same end behavior with the given rational function. Then, their graph is

Satan is frozen in Cocytus, Minos is in charge of examining each soul for judgment, but who is in charge of all of hell?

Satan is indeed in charge of Hell. It's just that Dante presents him as a rather pathetic, impotent figure. Instead of the charismatic, charmingly seductive Satan of Milton's Paradise Lost, we're presented with a hideous but immobile monster, vainly beating his six wings in a futile bid to escape his icy tomb.
There's a sense of anticlimax about Dante's encounter with the Prince of Darkness, and this is intentional on Dante's part. He wants to present Satan as a dumb beast rather than a cunning tempter. He may look pretty fearsome with his monstrous size, three faces, and six huge bat-like wings, but he cannot threaten Dante as he remains firmly trapped in ice.
Satan constantly beats his wings in a desperate bid for freedom. Ironically, though, each time he does so, he simply generates an icy wind that keeps the water beneath him frozen solid. If he didn't struggle, this wouldn't happen, and so he'd be able to make good his escape. But because Satan is so proud, so arrogant, and so full of defiance towards God, he'll continue to keep on trying to fly off, even though it'll leave him trapped in Cocytus for all eternity.

College Algebra, Chapter 1, 1.5, Section 1.5, Problem 34

Find all real solutions of the equation $\displaystyle x + 2 \sqrt{x - 7} = 10$


$
\begin{equation}
\begin{aligned}

x + 2 \sqrt{x - 7} =& 10
&& \text{Given}
\\
\\
2 \sqrt{x - 7} =& 10 - x
&& \text{Subtract } x
\\
\\
(2 \sqrt{x - 7})^2 =& (10 - x)^2
&& \text{Square both sides}
\\
\\
4(x - 7) =& 100 - 20x + x^2
&& \text{Use FOIL method}
\\
\\
4x - 28 =& 100 - 20x + x^2
&& \text{Combine like terms}
\\
\\
x^2 - 24x + 128 =& 0
&& \text{Factor out}
\\
\\
(x - 8)(x - 16) =& 0
&& \text{Zero Product Property}
\\
\\
x - 8 =& 0 \text{ and } x - 16 = 0
&& \text{Solve for } x
\\
\\
x =& 8 \text{ and } x = 16
&&
\\
\\
x =& 8
&& \text{The only solution that satisfy the equation } x + 2 \sqrt{x - 7} = 10

\end{aligned}
\end{equation}
$

In Connell's "The Most Dangerous Game," how do we know Rainsford is an exceptionally fit man?

Sanger Rainsford is Richard Connell's protagonist in "The Most Dangerous Game." The reader first discovers Rainsford is a fit man at the beginning of the story after he falls off the yacht and swims through ocean currents toward Ship-Trap Island. The text says the following about this swim for safety:

Doggedly he swam in that direction, swimming with slow, deliberate strokes, conserving his strength. For seemingly endless time he fought the sea. He began to count his strokes; he could do possibly a hundred more.

From this passage, the reader learns that not only does Rainsford know how to swim with intention, but the swim isn't easy because he has to fight through the ocean.
Rainsford then proves he is at the top of his game physically when he is hunted for three days in a jungle. For instance, Rainsford runs through the forest, climbs trees, digs pits, and makes elaborate traps during this three-day traumatic activity. Not only that, but he does it with very little sleep. 
Additionally, Rainsford proves he is in top shape when he jumps from some island cliffs, survives the fall, and swims around the island at the end of the third day. He then finds his way to General Zaroff's personal quarters. Zaroff is taken completely by surprise as follows:

"Rainsford!" screamed the general. "How in God's name did you get here?"
"Swam," said Rainsford. "I found it quicker than walking through the jungle."

Rainsford does not die of exhaustion, nor does he get injured over the course of such an intense few days. Only a man in the best physical shape could have accomplished what Rainsford does.

If violence is a cornerstone of gang involvement, what explains why some youth join a gang if there is little difference in types of aggression? Explain your answer in detail.

Many youths join gangs for different reasons. Some want acceptance, while others want some sort of family to look up, and forward to. When looking at the different factors that make people want to join gangs, it is important to pay attention to the environment those people are exposed to. Many of the larger cities, such as Los Angeles and Chicago, are so badly plagued by gang violence, the youth of those communities are willing to join the gang solely for protection. Society also plays a large role in why someone will join a gang. Music, television, and movies, all affect how adolescents see themselves and how they see society. Being part of something is important to young people, and many older people as well, and the violence and aggression can be over looked. Stopping and looking at the consequences is something many young people avoid. They tend to act off of impulse and often figure out what they got involved in too late. 
Social Psychology says humans are influenced for different reasons. It could be a real or imagined consequences that they are chasing (power, protection, "family") and only after they see there is no real benefit do they realize how negative the consequences of their choices are. Most gangs operate off of coercion and violence, which can be appealing to young children growing up. Being the most powerful, most feared, and most respected may influence the decision making of an adolescent. For example, the Surenos are a street gang that originated in Southern California (South Siders in English). Many of these gang members join the gang at a young age to make easy money dealing drugs. Along with the "easy" money comes the difficult task of protecting the territory. These young gang members are expected to protect their territory by any means necessary which often times includes violence. Assaults, kidnapping, and murder often send a strong message to rival gangs, and earn respect that is essential to thriving in that lifestyle. After being exposed to this lifestyle for any given amount of time, these young men and women reeducate themselves to their new lifestyle, and the aggression and violence just becomes a way of life, which makes it difficult to see that they are doing anything wrong. 

Violence is definitely a major component of life in a street gang. For many gangs, initiation into the group entails violence, with prospective members forced to conduct physically brutal acts while also, occasionally, being subjected to violence themselves at the hands of fellow gang members. Street and motorcycle gangs depend upon intimidation and violence to accomplish their goals, which include enrichment, enforcement of gang rules, expansion of territory at the expense of rival gangs, and defense of turf from encroachment by rival gangs. Violence defines gangs, both internally and externally.
While violence is a cornerstone of gang activity or involvement, it does not explain the reason so many youth and young adults join gangs. The main reason is entirely sociological. Unsurprisingly, the overwhelming majority of young boys and some girls join neighborhood gangs for a sense of community or family lacking at home. For many susceptible youth, the structure, rules and sense of family that gangs offer serves as a substitute for a broken or otherwise dysfunctional family situation at home. The camaraderie and sense of purpose—defending the gang, hanging with fellow members, depending on each other—represents the most stable environment they have experienced.
Not all members willingly join gangs. Some are forced into gang life by neighborhood gangs forever seeking new “recruits” to expand their numbers. Established gang members using threats of violence against the prospective recruit or his family can compel participation in the gang. Members who want to leave the gang are often prohibited from doing so by the threat of being murdered. Sometimes, the person will only be allowed to leave after enduring a brutal beating by the rest of the gang.
Individuals join gangs for any of several reasons. Few join because of the violence gang activity entails. The violence is an integral component of gang life, but most are motivated to join either out of a sense of family with other gang members or because they were forced to join.

What were some of the issues Americans faced as they emerged from the Gilded Age, and in what ways did the Progressive Movement seek to address them? In what ways can the Progressive Era be viewed as a success? A failure?

Some issues faced during the Gilded Age were consumer safety, governmental corruption, urban planning, and deregulated capitalism. The Food and Drug Act, passed soon after the release of Upton Sinclair's The Jungle, sought to regulate food and medicines and was one of the first ways that the federal government intervened directly in the lives of the American public. This act made American food safer and ended the practice of selling patent medicines. The Pendleton Act created civil service tests that governmental employees had to pass before being offered a job. The goal of this act was to limit officeholders' ability to give jobs to their favorites as a form of patronage—now governmental employees had to have some kind of qualification. The act was passed after the assassination of James Garfield by a disgruntled office-seeker in 1881. Acts concerning zoning were passed due to the tenement system. Many immigrant families lived in tenements during the Gilded Age. Many of these tenements were crowded and dangerous. Many families also were told to bring their work home with them, meaning that they had to work even longer hours when they arrived at home. Urban planning made the tenements safer with fairer conditions. Cities also concerned themselves with sanitation and public safety with publicly funded fire and police forces. Cities also constructed parks for all the people to enjoy. The Sherman Anti-Trust Act and the work of Theodore Roosevelt and William Howard Taft helped to end the era of monopolies in American business as large companies such as Standard Oil were broken up into smaller ones, giving other companies room to start and grow.
The Progressive Era can be considered successful in that it demonstrated the power of the individual in government. Government passed ballot initiatives because of the will of groups of people. Governmental leaders were also held accountable with referendums and recalls, making leadership accountable at all times. This was aided by a rise in investigative journalism. The Progressive Era also made food safer, as the amount of people who died from food-related diseases dropped. The National Park Service was also borne out of the Progressive movement.
The era was a failure in that it did not do enough. By the end of the era, children still worked long hours and workers still had no minimum wage. Businesses could still become quite large and many would manipulate their stock prices, leading to the economic crash in 1929. The greatest experiment of the Progressive Era, Prohibition, failed because of a lack of public support and a lack of funds.

Calculus of a Single Variable, Chapter 10, 10.2, Section 10.2, Problem 5

x=t^3 -----------------(1)
y=t^2/2 -----------------(2)
Draw a table for different values of t and plot the points obtained from the table.Connect the points to a smooth curve.( Refer the attached image).
From equation (1),
t=x^(1/3)
Substitute t in equation (2),
y=(x^(1/3))^2/2
y=x^(2/3)/2
Rectangular equation of the curve is y=x^(2/3)/2

What two enemies does the kingdom of Scotland face? How are they overcome?

At the start of the play, the kingdom of Scotland faces two enemies: Norway and a rebellion led by the Scottish traitor to the throne, Macdonwald. Both enemies are essentially overcome on the battlefield. First, Macbeth and Banquo fight the rebels, led by Macdonwald. The injured captain tells Duncan that

brave Macbeth (for well he deserves that name)
Disdaining Fortune, with his brandished steel [...]
carved out his passage
Till he faced the slave [and]
unseamed him from the nave to th' chops" (Act I, Scene 2, lines 18-24).

He paints a vivid mental picture of Macbeth, slashing through a thicket of bodies to forge a path to Macdonwald, and, once he reached the leader, Macbeth thrust his sword through the man's stomach and ripped him open all the way up to his jaw.
Then, the captain explains, just as Macbeth and Banquo were turning away from their victory over the rebels, the Norwegian king saw his opportunity to attack while they were tired. The king then brought a fresh army, and even though Macbeth and Banquo were clearly alarmed by the prospect of another battle, "they doubly redoubled strokes upon the foe" and won (Act I, Scene 2, line 42). Scotland, then, really owes its safety to the bravery of its champions on the battlefield.

What were the Opium Wars?

The First Opium War was a conflict between Britain and China—at that time ruled by the Qing dynasty—over questions of trade and sovereignty. It took place between 1839 and 1842. At the height of the opium trade through China, mainly facilitated by British merchants, many Chinese people were addicted; in an attempt to crack down on this, the Chinese government burned a huge quantity of opium. This created a hostile environment in which some British sailors killed a Chinese man. The British government objected to the Chinese trying British subjects in their courts, and war soon broke out. The war moved quickly, ending in the British capture of Nanking, and the Chinese were forced to cede Hong Kong to British powers.
The Second Opium War, fought between Britain and France against China, was fought from 1856–1860 and was essentially declared by Britain, and joined by France, as an excuse to try and extend trading permissions in China. By the end of the war, in which the European powers wreaked considerable destruction on Chinese ports, the Beijing Convention ceded many more trading ports and privileges to France and Britain.

In the poem "Snaps," how does Espaillat use conventional scenes and images to reveal them as oppressive settings in gendered identity?

In "Snaps," Espaillat starts with a series of snapshots of a girl that symbolize the way in which she presented one reality to the camera while harboring a different reality. The conventional scene of her as a child, "neatly dressed...in your white middy," presents the image of the perfect girl, who, dressed in white, radiates innocence. In the next snapshot, the girl appears in a conventional pose as a "nice girl with ankles crossed, hands in your lap's small bounded nest." In the metaphor in this line, the girl's lap is a nest, conveying the idea that women's sexuality is contained. 
Capturing these oppressive images, however, the camera catches the "strain/behind its ease," meaning behind the ease of the girl's "obedient pose." The way in which the camera catches the girl's secret ideas is compared, through a simile, to a situation "as if a passage in some plain old book opened into an unexpected place." In other words, the camera captures something unexpected. The tone of this stanza represents a shift from a feeling of oppression to a feeling of openness and exploration. 
The poet uses the girl's body language as a symbol of the girl's defiance, including "the sharp tilt of jaw" and the "small thrust of hip and shoulder." These subtle body movements and gestures represent the girl's hidden defiance. In the last stanza and the last line of the penultimate stanza, the poet refers to "something sleeping" in the girl that is now flashing the poet "a sign," many years later, of the girl's eventual rebellion. The "something" is a personification and a metaphor of the ways in which the girl will eventually go against the oppressive gender identity she was raised with.