Why does Mildred need help when Montag gets home?

In Part 1 of Ray Bradbury's Fahrenheit 451, when Montag gets home after meeting Clarisse for the first time, he finds that his wife, Mildred, is lying motionless in bed. While the narration specifically notes that Mildred is laid out "uncovered and cold, like a body displayed on the lid of a tomb," at first Montag thinks that his wife is just asleep as usual. Then he finds a "small crystal bottle of sleeping-tablets which earlier today had been filled with thirty capsules and which now lay uncapped and empty in the light of the tiny flare." Mildred has overdosed on sleeping pills and needs to have her stomach pumped in order to survive. Montag calls the emergency hospital, and two men come with two machines, one that pumps the stomach, and one that simultaneously empties the body of blood and fills it with "fresh blood and serum". 
The next day, Mildred denies having taken the pills when Montag confronts her about it, saying "What would I want to go and do a silly thing like that for?" She acts as if she doesn't remember anything from the night before, but we as readers know that the overdose probably wasn't an accident. 

When Shmuel has a black eye, what does Bruno think happened?

At the beginning of chapter 14, Bruno visits Shmuel and notices that he has a black eye. When Bruno asks Shmuel how he received the black eye, Shmuel becomes silent and shakes his head. Shmuel does not want to discuss how he received his black eye and tells Bruno that he doesn't want to talk about it. As a naive child, Bruno simply assumes that Shmuel had a conflict with a bully who ended up punching him in the eye. Bruno assumes that there are bullies on the opposite side of the fence and recalls being around bullies back home in Berlin. Bruno experiences the urge to help Shmuel but cannot think of any way to help him, and he understands that Shmuel simply wants to forget about the incident that resulted in his black eye. Despite Shmuel's black eye, Bruno continues to ask him if he can crawl underneath the fence to play, but Shmuel prevents him from doing so.

One afternoon, when Bruno sees Shmuel, he notices that he has a black eye. He is immediately curious, so naturally asks him how he got it. But Shmuel, not wanting to get into trouble, doesn't want to tell him. Bruno also wants to know if he can come round to the other side of the fence and play with Shmuel. For obvious reasons, however, that simply isn't possible.
Bruno's actions underline not just his natural inquisitiveness, but also his total naivety about the concentration camp and what goes on there. His world is still that of an innocent boy who has successfully been inured by his family from the horrors of concentration camp life and the warped ideology that it so starkly illustrates. To him, Shmuel is just another boy, albeit one who always wears striped pajamas. As Bruno has absolutely no understanding of the violence and brutality of the concentration camp, he assumes that Shmuel is being bullied by another boy. That, he reasons, would explain the black eye.

What was the main functions of the Knights Templar?

The Knights Templar, also known long ago as "The Poor Knights of Christ and the Temple of Solomon," were a quasi-military group formed in the early twelfth century by European Christians early in the Crusades. The Knights took their name from their original headquarters, which was in the Temple Mount, near the site of King Solomon’s Temple.
Their original function was to protect Christian pilgrims on their way to the Holy Land. These pilgrims were being harassed and slaughtered by outlaws on the road. During the Crusades, the Knights' functions expanded. Sometimes they accompanied armies into battle, and they are particularly famous for their role in helping the Kingdom of Jerusalem win the Battle of Montgisard.
But they are perhaps most notably known for establishing a financial system that aided pilgrims on their journey. Pilgrims would deposit money or valuables with the Knights, then receive a document stating that value, which they then could redeem in the Holy Land. This protected their assets from outlaws on the road. This was perhaps an early precursor to a banking system.
Once the Crusades were lost by the Christian side early in the thirteenth century, the Knights diminished in importance. Many of the Knights were eventually arrested, and some executed, as European royalty sought control over them.

College Algebra, Chapter 10, 10.3, Section 10.3, Problem 10

Suppose that a die is rolled. Determine the probability of the given event.

a.) The number showing is a two or three.

The probability of showing a two on a die is $\displaystyle P(2) = \frac{1}{6}$. Similarly, the probability of showing a three on a die is also $\displaystyle P(3) = \frac{1}{6}$. Since we have mutually exclusive events, we get

$\displaystyle P(2) + P(3) = \frac{1}{6} + \frac{1}{6} = \frac{2}{6} + \frac{1}{3}$

b.) The number showing is an odd number..

The odd numbers on the sample space $n(S) = \{ 1,2,3,4,5,6 \}$ are $1,3$ and $5$. Thus, the probability of getting an odd number is

$\displaystyle \frac{3}{6} = \frac{1}{2}$

c.) The number showing is a number divisible by 3.

The numbers are divisible by 3 in the sample space is $3$ and $6$. Thus the probability is

$\displaystyle \frac{2}{6} = \frac{1}{3}$

In “Through the Tunnel,” how does Jerry show growing maturity as he prepares for the swim through the tunnel?

Once Jerry sets his mind to swimming through the tunnel like he saw the big boys do, he practices holding his breath and staying under water day after day.  This kind of meticulous practice provides evidence of his growing maturity.  After several days of going to the wild bay to practice, "He did not ask for permission [...] to go to his beach."  Children ask permission and wait for adults to grant it; however, Jerry begins to exercise his new maturity and independence by acting without asking his mother -- as he has in the past -- if he can go to his own beach and not accompany her to their old, "safe beach." 
Further, Jerry is developing the ability to delay gratification of his wishes.  Earlier, he couldn't wait for his mother to purchase the goggles he needed, and he pestered her until she took him, and then snatched them from her hand, like a child.  But now, he thinks, "if he tried, he could [probably] get through the long tunnel, but he was not going to try yet.  A curious, most unchildlike persistence, a controlled impatience, made him wait."  Jerry's growing maturity makes it possible for him to delay gratification of his desires, and he waits to attempt the feat until he is more sure of his ability. 

In Journey to the West by Wu Cheng 'En, what is the summary of the last chapter (Chapter 100), and what is the chapter's surprise ending?

In Chapter 100, the people of Chen Village are devastated when they discover that the four travelers have left. They use the food they have prepared for the travelers as sacrificial offerings, and from then on, yearly sacrifices are made in the Buddhas' honor.
The travelers eventually come to the Watching For the Scriptures Tower and are met by Emperor Taizong. Delighted to see them, the Emperor bids the Tang priest and his three companions follow him back to the palace. At the palace, the Emperor invites the Tang priest to sit in the throne hall; Monkey, Pig, and Friar Sand unpack the scrolls, and the Emperor demands to know how many scriptures there are and how the scriptures were found.
Sanzang (the Tang priest) answers that the Lord Buddha had originally given the travelers "blank, wordless versions" of the scriptures. In order to recover the real ones, the travelers had to hand over their "begging bowl of purple gold" to the two arhats, Ananda and Kasyapa. In all, there are thirty-five scriptures. The Emperor is pleased with Sanzang's words and orders the Protocol Office to hold a thanksgiving banquet in the Eastern Hall.
After the banquet, the four travelers return to the Hongfu Monastery, where they are welcomed by the monks. The next morning, the travelers are formally thanked by the Emperor for managing to retrieve all 5,048 rolls of the 35 scriptures; additionally, the formal words of acknowledgement and thanks for the travelers' accomplishment will be recorded as a "Preface to the Holy Teaching." The Emperor states that the scriptures will be translated for the edification of the Chinese people.
On the advice of Sanzang, the Emperor tasks "the officials of the Hanlin Academy and the Palace Secretariat to copy out the true scriptures" and the Copying Monastery to publish copies for the people. The original scriptures will be stored as "great treasures." Next, the Emperor asks Sanzang to expound upon the scriptures at the Monastery of the Wild Goose Stupa. However, before Sanzang can begin, the Eight Vajrapanis appear to take the four travelers back West.
Back West at the Vulture Peak, the Tathagata gives the four travelers their rewards for having completed their mission successfully. They are each promoted to bureaucratic posts in Heaven. Sanzang is made the Candana-punya Buddha, Sun Wukong is made the Victorious Fighting Buddha, Zhu Wuneng is made the Altar Cleanser, and Sha Wujing is made the Golden Arhat. Meanwhile, the travelers' faithful horse is made a Heavenly Dragon of the Eight Classes of Being. Also, Monkey is allowed to be rid of Guanyin's magic golden band. Now that he is a Buddha, he need no longer wear it on his head.
The chapter ends with all of Heaven paying homage to the Buddhas. If you're looking for the surprise ending, I suspect it is the moment when the four travelers are abruptly taken back to the West by the Eight Vajrapanis and rewarded for their faithful work.

How does Esch describe her love for Manny in Salvage the Bones by Jesmyn Ward? What does it reveal about her character?

Early in the book, Esch says that before Manny, she let other boys have her “girly heart” (as she describes her sexuality) because they wanted it—not because she wanted to give it. “I’d let boys have it because for a moment, I was Psyche or Eurydice or Daphne. I was beloved. But with Manny, it was different; he was so beautiful, and still he chose me, again and again. He wanted my girl heart; I gave him both of them.”
Esch sees her love for Manny as the kind of passionate, all-consuming love portrayed in myths and legends. Later, she says, “I imagine that this is the way Medea felt about Jason when she fell in love, when she knew him; that she looked at him and felt a fire eating up through her rib cage, turning her blood to boil, evaporating hotly out of every inch of her skin.”
This shows the depth of Esch’s feelings for Manny and also shows her intelligence through her connection to the legends of the past, which on the surface, couldn’t be more different from the circumstances of her own life.
When Manny denies he is the father of her baby, Esch’s furious reaction reveals her strength. She doesn’t shrink away, and even as she attacks him physically, she tells him she loves him, which is a brave act of honesty for a young girl or anyone. Manny is not worthy of her love, but the fact that she feels so deeply for him and shows such strength gives us hope that she will be a good mother to her baby.

In short, Esch describes her love for Manny in a strange way, as "certainty" and "as deep as a tree's roots."  This reveals that Esch's character is both passionate and loyal.  

It is the way that all girls who only know one boy move. Centered as if the love that boy feels for them anchors them deep as a tree's roots, holds them still as the oaks, which don't uproot in hurricane wind. Love as certainty.

These words from Esch are the best evidence in regards to her intense love for Manny.  She uses a particular literary device in her description of this passionate love: the simile.  A simile is a comparison using the words "like" or "as."  In this case, Esch's love is compared to "a tree's roots" running deep within the ground.  This kind of love can't be uprooted, even by "hurricane wind."  The description reveals how strong Esch's love for Manny truly is.  Esch's love is not temporary.  It is certain.
Esch also reveals something about love when she talks about her mother "mashing" words together.  Esch "mashes" words together, too.

‘Belove’ when Manny was curling pleasure from me with his fingers in mid-swim in the pit. 

Note that the words "be" and "love" are combined in this quotation.  This is another bit of evidence of Esch's passionate love for Manny.  The irony is that Manny is always desiring sex, but Esch believes love to be much more than sex.  She often laments that Manny "never kisses her the way she has seen him kiss another girl."  Esch desires this kind of passionate kiss from Manny very much.  Thus, even though Esch has had sex with other men, Manny is the only man who Esch truly loves.

He is not the first boy she has been with, but he is the only one she has truly wanted.

What is the theme of "An Occurrence at Owl Creek Bridge" by Ambrose Bierce?

I think there is a main theme about time and how the perception of its passage is fluid. I'm quite certain most people have experienced how time seems to "fly" at certain times and "crawl" at others. The same occurs in this story. In the moments between the officer stepping aside and Farquhar's death, time slows dramatically. Farquhar experiences hours and hours of time in the fractions of seconds that exist before his neck snaps.  
I think another theme is the theme of imagination/ dreams/ illusion vs. reality. When readers first meet Farquhar, we are told that he longs to fight for the Southern cause. He has dreamed up a romanticized version of what war is.  

Circumstances of an imperious nature, which it is unnecessary to relate here, had prevented him from taking service with that gallant army which had fought the disastrous campaigns ending with the fall of Corinth, and he chafed under the inglorious restraint, longing for the release of his energies, the larger life of the soldier, the opportunity for distinction. 

Unfortunately for Farquhar, the reality of war isn't as glorious as he imagines it is. The reality of the situation is that war is dangerous and brutal. Farquhar longs for distinction, but the reality is that no southerner will know what he tried to do. There will be no glory in his success (because he failed), and no one will celebrate his failed attempt because no one knows he went to try and sabotage the bridge. 
The reality vs. non-reality theme continues in other parts of the story, too. The Union scout (reality) presented himself as a southern soldier (illusion). Farquhar imagines the information obtained is genuine only to discover that in reality it was all a trap. Farquhar also imagines a miraculous escape only to wind up dead in real life from hanging. 

Describe the central tenets of Jainism, Buddhism and Hinduism. What similarities can be found among these three religions?

It would be quite presumptuous to think I could do full justice to the details of three major world religions in a single post, but I think I can at least give you some of the broad strokes about their similarities and differences. All three religions are found primarily in India and East Asia, and have existed for at least 2000 years.  All three are very complex and have a variety of different traditions---especially Hinduism, which is probably the most diverse religion in the world. All three religions share the common basic moral values that are found in almost every human culture, such as prohibitions on murder, theft, and fraud. All three religions involve belief in reincarnation and karma in at least some of their sects. In addition, all three religions emphasize meditation and nonviolence as paths to enlightenment.Jainism takes nonviolence particularly seriously, as many Jain are strict vegans who believe that all living things have souls, and seek to minimize their harmful impact on all things, even the plants and the soil. Buddhists and Hindus are also often vegetarians, but a significant number are not.Sexuality is viewed quite differently in Hinduism compared to the other two religions; there is a strong tradition of Hinduism viewing sexuality as an important part of enlightenment (such as the Kama Sutra, which is actually a Hindu sacred text as well as a sex manual). Buddhism and Jainism generally view sexuality as a form of personal indulgence that is to be generally minimized if not avoided altogether. Due to the great diversity of beliefs within these religions, there are many exceptions to both of these broad patterns.Buddhism and Jainism are both more codified than Hinduism. Hinduism has no one particular text or set of laws that all Hindus believe in. Almost all Buddhists follow the Three Practices (virtue, meditation, enlightenment) and the Four Noble Truths (suffering exists, suffering is caused, suffering can be ended, suffering is ended by following the eightfold path).Almost all Jain believe in the Three Jewels (right belief, right knowledge, right conduct), as well as the Five Great Vows. Then we come to the thorny question of how many gods. Buddhists may believe in no god, one god, or many gods. Hindus generally believe in many gods, but often have one god that they believe all other gods come from. Jain generally believe in no gods at all.
http://www.bbc.co.uk/religion/religions/jainism/ataglance/glance.shtml

http://www.religioustolerance.org/buddhism1.htm

http://www.religioustolerance.org/hinduism.htm

What do you understand are Jim's feelings when he first sees Della after her sacrifice?

In O. Henry's ironic short story, Jim and Della are an extremely poor couple who sell their most prized possessions in order to get each other expensive Christmas gifts, which turn out to be worthless. In order to buy Jim a fob for his valuable pocket watch that has been passed down through his family, Della sells her long, beautiful hair to Madame Sofronie for twenty dollars. Later that night, Della waits patiently for her husband to return home and worries that Jim will think she looks ugly without a full head of hair. When Jim arrives home and enters the door, he stares at his wife with a peculiar expression on his face. Soon after Jim sees his wife's haircut, the reader learns that Jim has bought Della an expensive set of combs. One can imagine that Jim is initially astonished and disheartened when he first discovers that Della has cut her hair, because the combs he bought her would be useless. After learning that Della sacrificed her hair to buy an expensive fob that he will not be able to use, Jim silently sits down for their Christmas dinner with a full heart of joy and appreciation for Della's love and sacrifice.

Calculus of a Single Variable, Chapter 9, 9.7, Section 9.7, Problem 29

Taylor series is an example of infinite series derived from the expansion of f(x) about a single point. It is represented by infinite sum of f^n(x) centered at x=c . The general formula for Taylor series is:
f(x) = sum_(n=0)^oo (f^n(c))/(n!) (x-c)^n
or
f(x) =f(c)+f'(c)(x-c) +(f^2(c))/(2!)(x-c)^2 +(f^3(c))/(3!)(x-c)^3 +(f^4(c))/(4!)(x-c)^4 +...
To determine the Taylor polynomial of degree n=4 from the given function f(x)=ln(x) centered at x=2 , we may apply the definition of Taylor series.
We list f^n(x) up to n=4 as:
f(x) = ln(x)
f'(x) = d/(dx)ln(x) =1/x
Apply Power rule for derivative: d/(dx) x^n= n *x^(n-1) .
f^2(x) = d/(dx) 1/x
= d/(dx) x^(-1)
=-1 *x^(-1-1)
=-x^(-2) or -1/x^2
f^3(x)= d/(dx) -x^(-2)
=-1 *d/(dx) x^(-2)
=-1 *(-2x^(-2-1))
=2x^(-3) or 2/x^3
f^4(x)= d/(dx) 2x^(-3)
=2 *d/(dx) x^(-3)
=2 *(-3x^(-3-1))
=-6x^(-4) or -6/x^4
Plug-in x=2 , we get:
f(2) =ln(2)
f'(2)=1/2
f^2(2)=-1/2^2 = -1/4
f^3(2)=2/2^3 =1/4
f^4(2)=-6/2^4 = -3/8
Applying the formula for Taylor series, we get:
sum_(n=0)^4 (f^n(2))/(n!) (x-2)^n
=f(2)+f'(2)(x-2) +(f^2(2))/(2!)(x-2)^2 +(f^3(2))/(3!)(x-2)^3 +(f^4(2))/(4!)(x-2)^4
=ln(2)+1/2(x-2) +(-1/4)/(2!)(x-2)^2 +(1/4)/(3!)(x-2)^3 +(-3/8)/(4!)(x-2)^4
=ln(2)+1/2(x-2) -(1/4)/2(x-2)^2 +(1/4)/6(x-2)^3 -(3/8)/24(x-2)^4
=ln(2)+1/2(x-2) -1/8(x-2)^2 + 1/24(x-2)^3 -1/64(x-2)^4
The Taylor polynomial of degree n=4 for the given function f(x)=ln(x) centered at x=2 will be:
P_4(x)=ln(2)+1/2(x-2) -1/8(x-2)^2 + 1/24(x-2)^3 -1/64(x-2)^4

sum_(n=2)^oo (-1)^n/(nlnn) Determine whether the series converges absolutely or conditionally, or diverges.

To determine the convergence or divergence of the series sum_(n=2)^oo (-1)^n/(nln(n)) , we may apply Alternating Series Test.
In Alternating Series Test, the series sum (-1)^n a_n is convergent if:
1) a_n is monotone and decreasing sequence.
2) lim_(n-gtoo) a_n =0
3) a_ngt=0
For the series sum_(n=2)^oo (-1)^n/(nln(n)) , we have:
a_n = 1/(nln(n)) which is a positive, continuous, and decreasing sequence from N=2.
Note: As "n " increases, the nln(n) increases then 1/(nln(n)) decreases.
Then, we set-up the limit as :
lim_(n-gtoo)1/(nln(n))= 1/oo =0
By alternating series test criteria, the series sum_(n=2)^oo (-1)^n/(nln(n))  converges.
The series sum_(n=2)^oo (-1)^n/(nln(n))  has positive and negative elements. Thus, we must verify if the series converges absolutely or conditionally. Recall:
a) Absolute Convergence:  sum a_n  is absolutely convergent if sum|a_n|   is convergent.  
b) Conditional Convergence:  sum a_n is conditionally convergent if sum|a_n|  is divergent and sum a_n  is convergent.  
We evaluate the sum |a_n| as :
sum_(n=2)^oo |(-1)^n/(nln(n))|=sum_(n=2)^oo 1/(nln(n))
Applying integral test for convergence, we evaluate the series as:
int_2^oo1/(nln(n))dn=lim_(n-gtoo) int_2^t 1/(nln(n))dn
Apply u-substitution: u =ln(n) then du =1/ndn .
int 1/(nln(n))dn =int 1/(ln(n))*1/ndn
                       =int 1/u du
                        =ln|u|
Plug-in u=ln(n) on the indefinite integral ln|u| , we get:
int_2^t 1/(nln(n))dn =ln|ln(n)||_2^t
Applying definite integral formula: F(x)|_a^b = F(b)-F(a) .
ln|ln(n)||_2^t =ln|ln(t)|-ln|ln(2)|
Then, the limit becomes:
lim_(n-gtoo) int_2^t1/(nln(n))dn =lim_(n-gtoo) [ln|ln(t)|-ln|ln(2)|]
                                   =lim_(n-gtoo)ln|ln(t)|-lim_(n-gtoo)ln|ln(2)|
                                   = oo - ln|ln(2 )|
                                   =oo
int_2^oo1/(nln(n))dn=oo implies the series  sum_(n=2)^oo |(-1)^n/(nln(n))| diverges.
 
Conclusion:  
The series sum_(n=2)^oo (-1)^n/(nln(n)) is conditionally convergent sincesum |a_n| as   sum_(n=2)^oo |(-1)^n/(nln(n))| is divergent and sum a_n as sum_(n=2)^oo (-1)^n/(nln(n)) is convergent.

What is the significance of the Russian Roulette?

The title of the book is a reference to scenes in the movie The Deer Hunter starring Robert De Niro. In this movie, De Niro plays a traumatized Vietnam veteran who was forced to play games of Russian Roulette by his Viet Cong captors. Russian Roulette acts as a metaphor for the inescapable and utterly random chaos of war.
One of the lead characters in the book, George, is nicknamed De Niro. He and his friends are obsessed with The Deer Hunter, and identify strongly with the film's damaged, mentally-scarred characters. He also plays Russian Roulette with his friend Bassam on a couple of occasions. More generally, the randomness, violence and death associated with the deadly game comes to epitomise the daily struggle of young men amidst the ruins of war-torn Beirut. Life itself, like Russian Roulette, has become a potentially lethal game of chance in which one can die at any moment. Reckless gunplay is a way for these young men to deal with the horrors of a hopeless, soul-destroying existence in a city wracked by a seemingly endless conflict. 

Single Variable Calculus, Chapter 8, 8.1, Section 8.1, Problem 10

Evaluate $\displaystyle \int \sin^{-1} x dx$
If we let $u = \sin^{-1} x$ and $dv = dx$, then
$\displaystyle du = \frac{1}{\sqrt{1-x^2}} dx$ and $\displaystyle v = \int dx = x$

So,
$\displaystyle \int \sin^{-1} x dx = uv - \int v du = x \sin^{-1} x - \int \frac{x}{\sqrt{1-x^2}} dx$
To evaluate $\displaystyle \int \frac{x}{\sqrt{1-x^2}} dx$ we let $u_1 = 1 - x^2$, then $du_1 = -2xdx$


Then,

$
\begin{equation}
\begin{aligned}
\int \frac{x}{\sqrt{1-x^2}} dx &= \int \frac{\frac{-du_1}{2}}{\sqrt{u_1}} = \frac{-1}{2} \int u_1^{-\frac{1}{2}} du_1 = -\frac{1}{2} \left[ \frac{u_1^{\frac{1}{2}}}{\frac{1}{2}} \right]\\
\\
&= -(u_1)^{\frac{1}{2}} + c = -(1-x^2)^{\frac{1}{2}} + c
\end{aligned}
\end{equation}
$


Therefore,

$
\begin{equation}
\begin{aligned}
\int \sin^{-1} x dx &= x \sin^{-1} x - \left[ -(1-x^2)^{\frac{1}{2}} \right] + c\\
\\
&= x \sin^{-1} x + (1-x^2)^{\frac{1}{2}} + c
\end{aligned}
\end{equation}
$

What does Juliet mean when she says, "Indeed I never shall be satisfied / With Romeo, till I behold him—dead— / Is my poor heart so for a kinsman vexed"?

This particular line of text is probably best understood when it is written out in the line organization that Shakespeare originally wrote.

Indeed, I never shall be satisfied
With Romeo, till I behold him—dead—
Is my poor heart for a kinsman vexed.

These three lines really mess with first time readers, and I definitely have to spend some time with my classes explaining what Juliet is doing here. During Juliet's conversation with her mother in Act 3, Scene 5, Juliet is doing something very difficult with language. She's saying the words that her mother wants to hear; however, Juliet is actually saying something completely different. Juliet's words sound like she wants Romeo dead, and that is what her mother wants to hear, but Juliet is actually professing her love for Romeo. In the above few lines, the dashes are a big key to interpreting the lines. At first glance, the line could read like the following:

Indeed, I never shall be satisfied with Romeo, till I behold him dead.

Lady Capulet hears Juliet saying that holding Romeo's dead body will make her happy; however, that ever so subtle dash/pause makes it possible to read "dead" with the second half of the text. It would read like the following:

Dead is my poor heart for a kinsman vexed.

That has an entirely different meaning. Juliet is essentially saying that her heart is dead over Tybalt's death. The lines could also be interpreted as Juliet saying that she won't be satisfied with Romeo until the two of them have lived a long and loving life, and he dies in her arms. These lines are not the only lines in this scene that have hidden meanings. Juliet asks for the poison so that she may "temper" it and use it against Romeo. Lady Capulet thinks that Juliet wants to fiddle with the poison to make it more effective, but Juliet wants to "temper" it and make it weaker. Juliet ends her tricky speech with the following lines.


Oh, how my heart abhors
To hear him named, and cannot come to him.
To wreak the love I bore my cousin
Upon his body that slaughtered him!



She is saying that she can't stand Romeo's name, which is what her mom wants to hear; however, Juliet can't stand to hear it because she can't be with him. Lady Capulet also hears that Juliet wants to "wreak" the love that she once had for Tybalt upon the man that killed Tybalt. Lady Capulet would think that Juliet wants to take her emotions out on Romeo, but Shakespeare's audience would fully understand by now that Juliet is dropping a huge innuendo about wreaking her love upon Romeo's body.

How did Hooter get the nickname "Hooter"?

Hooter's real name is Brian Melrose, but he does not look like a Brian Melrose, according to the author. He is large and goofy looking and, in Matt's mind, resembles the cartoon character Fred Flintstone. Hooter has a very good heart, and in third grade he took care of a baby owl with a broken wing. He put the owl into a box and hooted at it to keep it company. Eventually, his parents made him give the owl to an animal shelter, but the neighborhood kids had begun to call him "Hooter," and the nickname stuck to him.
Hooter is physically strong, and Matt says that Hooter will be the "strong man" in their Adventure Club because Hooter has more strength and muscles than the other members. At the same time, Matt says that they will turn to Hooter if they need to rescue any baby animals, as this is one of Hooter's talents. Hooter is both strong and caring; he is a gentle giant.

College Algebra, Chapter 9, 9.3, Section 9.3, Problem 48

Determine the sum $\displaystyle 1 - \frac{1}{2} + \frac{1}{4} - \frac{1}{8} + ... - \frac{1}{512}$.

Here the geometric sequence has $a = 1$ and $\displaystyle r = \frac{-1}{2}$, using the formula


$
\begin{equation}
\begin{aligned}

a_n =& ar^{n -1}
\\
\\
512 =& 1(2)^{n -1}
\\
\\
\ln 512 =& \ln 2^{n -1}
\\
\\
n - 1 =& \frac{\ln 512}{\ln 2}
\\
\\
n =& \frac{\ln 512}{\ln 2} + 1
\\
\\
n =& 10

\end{aligned}
\end{equation}
$



From the formula of geometric partial sum


$
\begin{equation}
\begin{aligned}

S_n =& a \frac{1 - r^n}{1 - r}
\\
\\
S_{10} =& 1 \left( \frac{\displaystyle 1 - \left( \frac{-1}{2} \right)^{10} }{\displaystyle 1 - \left( \frac{-1}{2} \right) } \right)
\\
\\
S_{10} =& \frac{1025}{1536}

\end{aligned}
\end{equation}
$

What is a pilgrimage, and does Momaday take one?

A pilgrimage is a spiritual quest, a journey to a place of that has moral or religious significance to the person who embarks on the journey. In The Way to a Rainy Mountain, Momaday embarks on a pilgrimage to his grandmother’s grave, a place he believes will bring him closer to his people and give him a fuller understanding of his place in the world. For a journey to be a pilgrimage, it has to have personal meaning to the journeyer, and it has to help him reach a different level of consciousness. For Momaday, traveling to his grandmother’s’ grave allowed him to return to his spiritual roots and absorb into his conscious memory the collective experience of his ancestors, the Kiowa people. Momaday’s quest is one of self-discovery, in other words. He travels to a place that has historical significance to him in order to feel more connected to his heritage and gain a fuller understanding of his identity.

A pilgrimage is usually a long journey one makes to a religious shrine or other location of deeply spiritual significance: Lourdes, the Wailing Wall, or Kedarnath, for example. Metaphorically, however, a pilgrimage may also be a period of intense inner reflection, wherein one examines values and beliefs, or even represent the progress of a social group over time.
Using paternal, historical, and authorial voices, Momaday constructs the history of the Kiowa Indians in his three-part narrative. Through his juxtaposition of folklore and history with personal memoir, Momaday discovers more about his own heritage and the Kiowa from an anthropological perspective. Even the titles of the book’s three sections evoke the stages of a pilgrimage: they are titled “The Setting Out,” “The Going On,” and “The Closing In,” respectively. The journey Momaday enjoins readers to take is one that will lead them to a new understanding and appreciation of how to perceive the history of an indigenous people. In this way, The Way to Rainy Mountain could be thought of as a pilgrimage.

What point of view does Virginia Woolf use in "The New Dress"?

As a modernist author, Virginia Woolf experimented with literary form, and her use of point-of-view was no exception. In “The New Dress,” Woolf uses a third-person point of view. This point of view can be described as limited since we have access to the thoughts of the main character (Mabel) but not the other characters in the story. 
Woolf’s use of point-of-view, however, is much more complicated than the labels of "third-person" and "limited" might suggest. Woolf was known for her use of free indirect discourse, a narrative style that—although rooted in the third person—provides the degree of unmediated access to a character’s thoughts that we tend to associate with a first-person point of view. Consider the following passage in which Mabel’s own thoughts are presented through the narrator:

“But instead of looking fierce or tragic as Rose Shaw would have done—Rose would have looked like Boadicea—she looked foolish and self-conscious and simpered like a school girl and slouched across the room.”

This description provides us with a sense of Mabel’s own thoughts, and it does so in a stylistically noteworthy way: Woolf’s use of the em-dash draws attention to Mabel’s own thoughts, but it does so without presenting them as her own.
Throughout the story, we have access to Mabel’s own thoughts as they jump from one concern to another. Mabel is highly conscious of her own thought patterns, as she moves from reflections on the English Empire to Shakespeare to the people around her:

“She meant, or she tried to make herself think that she meant, that it was the picture and not her dress, that was old-fashioned.”

We learn not only what Mabel thinks but about her thought process itself. As the story progresses, her thoughts become increasingly fragmented:

“She would go to the London Library to-morrow. She would find some wonderful, helpful, astonishing book, quite by chance, a book by a clergyman, an American no one had ever heard of; or she would walk down the Strand and drop, accidentally, into a hall, where a miner was telling about the life in the pit, and suddenly she would become a new person.”

In these final moments of the story, we have access to Mabel’s stream of consciousness as she moves from highly detailed fantasy to fantasy; in these moments, time and space are replaced by Mabel’s unmediated thoughts.

Which three quotations can show the significance of the ducks in central park?

Holden, in Salinger's The Catcher in the Rye, is very concerned about defending the lives and interests of the innocent. In this case, Holden feels responsible for the ducks during the winter. In chapter 12, Holden asks his cab driver, Horowitz, about the ducks and where they go when the lake is frozen over. Horowitz is confused at such a question and doesn't know how to answer the boy. The ducks' significance to Holden can be seen through the discussion he has with the cab driver in the following:

"The ducks. Do you know, by any chance? I mean does somebody come around in a truck or something and take them away, or do they fly away by themselves—go south or something?" (81-82).

Such a seemingly random question takes the cab driver aback, but it shows that Holden has thought of the innocent little birds before. Based on Holden's distrust for authority figures, he probably also wonders if the city, or any other adults, does anything to help innocent creatures like this each year. In like manner, Holden probably identifies with the ducks and feels as helpless in his own life as he thinks the ducks are in theirs. But then the cab driver brings up the fish in the lake and confuses the conversation further. So, Holden asks the following:

"All right. What do they do, the fish and all, when that whole little lake's a solid block of ice, people skating on it and all?" (82).

Now Holden is concerned about the fish who are trapped in the ice, which is more complicated than the ducks' situation. Horowitz gets frustrated, and the conversation gets more heated. Finally, Horowitz says something that seems to calm Holden down a little bit:

"If you was a fish, Mother Nature'd take care of you, wouldn't she? Right? You don't think them fish just die when it gets to be winter, do ya? (83).

Holden doesn't want to continue the conversation, though, because he says, "I was afraid he was going to crack the damn taxi up or something" (83). What Horowitz says suggests that Holden needs to have faith in Mother Nature and not worry about things that he doesn't have control over. Holden understands the theory, but it doesn't seem to help him remedy his concern. Because of the many traumatic experiences that Holden has had in his life, from his brother Allie's death to the suicide of a classmate, he worries about the lives of the innocent when left unchecked. The ducks, for example, seem helpless and innocent to Holden, just like children are, and that is why they are significant to him.

What is the Analytic of the Sublime by Kant?

This refers to the second book of the first division of Kant's Critique of Judgement. Here, Kant discusses aesthetic judgement and breaks this down into two components: the beautiful and the sublime. Beauty, for Kant, is a pleasurable feeling caused by the perception of an object that everyone ought to recognize. The sublime, on the other hand, is a feeling of pleasure in the superiority of reason over nature, on the one hand, and the displeasure of the imaginative or physical powerlessness in the face of nature. In this way, appreciation of the sublime is a kind of "vibration" between exaltation and dread. It is this quality of displeasure that marks the difference between the sublime and the merely beautiful.

The Analytic of the Sublime is a concept introduced by Immanuel Kant in Critique of Judgment to delineate the nature of beauty as opposed to the nature of the sublime. While they are similar, in the study of Aesthetics, Kant reasons that Beautiful and Sublime are very different concepts.
Kant's explanation of Sublime vs. Beautiful hinges on the lynch pin of human reasoning, making Sublimity something that is beyond the understanding of lesser beings. Beauty is intrinsic, he reasons, and all creatures can find beauty, to an extent. Sublime, however, is something that passes beyond the realm of our understanding—it is not only beautiful, but powerful and mysterious in its incomprehensibility. Because of this, humans alone can experience it because we are the only creatures that have a rationality that knows its own limits. In this way, sublimity is something that is so beautiful and powerful that it breaks through the limits of our understanding and goes to the core of what makes us human—reason.

The Analytic of the Sublime comes from Book Two of Kant's Critique of Judgment. This is a very important work in the field of aesthetics, a branch of philosophy concerned with matters of beauty and artistic taste. In the Analytic of the Sublime, Kant attempts to draw a clear distinction between the beautiful and the sublime. Most people tend to confuse the two, but Kant wants to show that the popular understanding of the sublime is mistaken. Kant's argument is an analytic in that it breaks down the component parts of what constitutes the sublime the better to analyze them.
So what does Kant mean by the sublime? The sublime, unlike the beautiful, has an air of mystery about it, something we can't quite seem to grasp or define. Things that are sublime, like a large black storm cloud or a gigantic mountain, appear too big for us to comprehend. However, on closer inspection, this turns out not to be the case. Our whole concept of sublimity is related to our understanding of absolute freedom—for example, the moral values that, according to Kant, we give to ourselves out of our reasoning faculty—and absolute totality (in simple language, the whole of everything that exists).
The sublime, therefore, is related to our faculty of reason, something unique to humans. As such, it is in us, in our minds' capacity to apprehend truths of reason, rather than in the objects themselves, such as the examples of the storm cloud and the large mountain we looked at earlier. Whenever we feel ourselves overawed by the sublime—being caught in the middle of a violent sea storm, for example—what's actually happening, according to Kant, is that we're getting in touch with those ideas of reason, those ideas of absolute freedom and absolute totality which we as rational human beings all share.

what are archaic words Keats used in ode to autumn

Archaic words or phrases are those that have long-since fallen out of the current vernacular. "Ode to Autumn" is (if you will excuse the pun) ripe with archaic words that serve to illustrate the timelessness of the poems sentiment, as well confound new-comers to poetry of this time period.A quick scan of the poem will reveal the use of the ever popular "Thee", "Thou", "Thy", and "Hath". These words are frequently used in poetry of Keats' time and earlier. In modern English none of these words see any use, but all have modern equivalents.
Both Thee and Thou are archaic forms the the modern word "You", The difference being that Thee is used when referring to the subject of a sentence and Thou is used when referring to the object of a sentence.

Thy is the archaic first person singular form of the word "your". English used to distinguish between the singular and plural versions of the word your. Not featured in this poem is the word "ye", the plural version of thy (we're all familiar with "hear ye, hear ye!")
In addition to these words you can find the words oft, hath, and dost.

Oftis an archaic form of the English word "often" in addition to being archaic it is also a poetic form of the word, meaning you would not normally see this word used out of verse.

Hath is the archaic third person singular form of the modern word "Have"

Dost is the archaic form of the second person singular form of the word "Do"
On top of these common archaic words, Keats uses a few phrases that would be foreign to a modern English speaker:
When Keats refers to "Thatch-eves" in line four of the poem he is referring to the part of the bottom part of a roof that hangs over the sides of a cottage.
In line 5 Keats uses the phrase "cottage-trees" this phrase distinguishes the trees he is talking about as trees that would have grown naturally by a simple village as opposed to trees grown on a large orchard.
In line 32 of the poem Keats refers to a "Garden-croft" this is simply an enclosed garden.
With a clear understanding of these words and phrases it should be a simple matter to understand the rest of the poem.

Archaic words are those that are no longer in common use or have lost their original meaning, yet can still be used to lend a certain historical tone to works of creative writing. There are a number of such examples in "To Autumn." Keats uses them mainly to establish a connection between himself and those writers of the past he so much admires such as Shakespeare and Spenser. The timelessness of the poem's subject matter also makes the use of archaic words legitimate, rather than simply an exercise in affectation or contrivance.

Who hath not seen thee oft amid thy store?

"Thee," "thy," and "thou" crop up quite a lot in "To Autumn." Such archaisms were still quite commonly used by poets in Keats's day, although Wordsworth and Coleridge challenged this convention in their "Lyrical Ballads." Nevertheless, they were not used in everyday speech or normal conversation.

Thou watchest the last oozings hours by hours.

Nowadays, we'd say "You watch..." so this is another example of archaic words, as is the following:

And sometimes like a gleaner thou dost keep...

In current usage we'd say "You do keep," or more commonly, simply "You keep."
https://www.poetryfoundation.org/poems/44484/to-autumn

Single Variable Calculus, Chapter 4, 4.3, Section 4.3, Problem 56

Suppose that all of the functions are twice differentiable and the second derivatives are never 0.

a.) If $f$ and $g$ are concave upward on interval $I$, prove that $f+g$ is concave upward on $I$.
b.) Prove that $g(x) = \left[ f(x) \right]^2$ is concave upward on $I$. Suppose that $f$ is positive and concave upward on $I$.


a.) If both $f$ and $g$ has upward concavity, $f''(x) > 0$ and $g''(x) > 0$ on $I$.
Then, $(f+g)'' = (f'+g')' = f''+g'' > 0$ on $I$.
Therefore, $(f+g)$ has upward concavity at $I$.


b.) If $f$ is positive and has upward concavity on $I$, then $f(x) > 0$ and $f''(x) > 0$

So,

$
\begin{equation}
\begin{aligned}
g'(x) &= 2 f(x) f'(x)\\
\\
g''(x) &= 2 \left[ f(x) f''(x) + f'(x) f'(x) \right]\\
\\
g''(x) &= 2 f(x) f''(x) + 2[f'(x)]^2
\end{aligned}
\end{equation}
$


$f(x)$ and $f''(x)$ are all positive, therefore $g(x)$ has upward concavity at interval $I$.

In Things Fall Apart by Chinua Achebe, would it be right to condemn Umuofia for the killing of Ikemefuna ?

An interesting question! According to the text, Okonkwo was the one who struck the killing blow during Ikemefuna's execution. Prior to Ikemefuna's death, Ogbuefi Ezeudu, a village elder and former warrior of Umuofia, had warned Okonkwo against participating in the boy's execution.
Ogbuefi's reason for discouraging Okonkwo from slaying Ikemefuna was that the young boy looked to Okonkwo as a father figure. In Ogbuefi's eyes, Okonkwo's participation would be dishonorable. Even Obierika later proclaimed that what Okonkwo had done would not "please the Earth. It is the kind of action for which the goddess wipes out whole families."
Yet, despite the fact that two clansmen disapproved of Okonkwo's participation in Ikemefuna's death, the tribal leaders still subscribed to the Oracle's authority in the matter. Ikemefuna was slated to die, regardless of anyone's wishes in the matter. Despite the judgment, there were those who disagreed with the execution of the innocent boy. It appears, though, that the larger community had no choice but to submit to the authority of the Oracle and its tribal leaders.
The text tells us that Nwoye was especially traumatized by Ikemefuna's death, a death he had been powerless to prevent. Additionally, while Nwoye's mother sympathized with Ikemefuna's predicament, she too was powerless to affect a rescue on his behalf. It can be seen from the text that Umuofian society places a great premium on the authority and wisdom of the Oracle and its leaders. As to whether it is right to condemn Umuofia for Ikemefuna's death, we must ask ourselves whether we agree with the Umuofian concept of justice.
In the beginning of the story, a woman from Umuofia was murdered by someone from the Mbaino clan. In response, Umuofia offered two alternatives to Mbaino: either both tribes went to war or a Mbaino young man and virgin girl were given to Umuofia as compensation for the woman's death. Mbaino, anxious to avoid war with the powerful Umuofia, had agreed to the second alternative. The text tells us that this was the "normal course of action," which leads us to conclude that Umuofian society thrived on strict interpretations of entrenched Igbo ethics.
To change the culture, dissent must be allowed. If we disagree with the concept of justice in Umuofia, we may well condemn all of Umuofia for Ikemefuna's death. If, however, we see some value in Umuofian justice, we may interpret Ikemefuna's death as the necessary sacrifice in response to an Umuofian woman's senseless murder. Regardless of our choice, it is plain from the text that there are those in Umuofia who have begun to question the traditions of the clan.

In "Aner Clute" from Spoon River Anthology, what is the real reason she ends up wasting her life going from bar to bar?

She ends up "wasting her life," as you put it, because of one error in judgment that marks her for life.
In the poem, she claims that people asked her the same question you do:

Over and over they used to ask me...
How I happened to lead the life,
And what was the start of it.

Her answer is true to life, but not the real reason why she "[leads] the life":

Well, I told them a silk dress,
And a promise of marriage from a rich man--

This is the story that people expect to hear: a materialistic young woman "loses her virtue" to a rich man who makes "a promise of marriage," but does not come through.
It was, instead, the unfair judgment of others, and their need to mark her as a woman of ill-repute, that make it impossible for her to lead a normal life. She uses the analogy of a boy who steals an apple. Instead of getting sympathy and a brief admonishment, he becomes marked as a thief by every member of society. As a result, he cannot find work and decides to become what everyone believes him to be anyway.
Aner Clute is the same: because everyone wishes to believe that she is a tramp, she becomes one. Her identity is marked by one faulty act committed in her youth.

What is the difference between a servant and a slave, and how does this relate to Chains by Laurie Halse Anderson?

Slaves differ from servants in three important aspects: value, consent, and treatment.
In terms of the value that they are rewarded for their labor, servants are paid for their work, while slaves are not. They are forced to labor for free, and the most that the fortunate among them can expect in return is basic human kindness.
Servants consent to work for their employers but slaves do not. Their labor is both forced and enforced by threats of physical harm and worse. We see this in Chains when Isabel and her sister, Ruth, are originally promised freedom upon the death of their owner, Miss Mary Finch. This promise proves to be worth nothing when a relative of Miss Finch's sells the girls to the Locktons.
Servants are generally treated better than slaves. In Chains, the treatment that Becky, the Locktons' housekeeper, receives from her employers, is practically lavish compared to the treatment that Isabel receives from those very people.

Peter Wood, a professor of history at Duke University, was asked this very same question.  His answer has always surprised me because I always assumed that the difference between a servant and a slave was that a servant could legally choose to quit, while a slave could not do that.  Wood's description of the difference between slaves and servants is quite interesting.  
A servant could be a white person or black person.  Skin color doesn't make a difference.  The defining feature of a servant is that he or she is under contract to work for a certain number of years.  When the contract time runs out, that person is free to leave and seek out another contract if desired.  What I find interesting about Wood's response is that he says owners occasionally treated their servants worse than their slaves because the owner knew that he/she had the servant for a limited time.  In essence, the servant was the equivalent of a rental, while the slave was actual property and needed to be taken care of.  
In Isabel's situation though, Isabel was treated much more poorly as a slave than Becky was treated as a servant. 

Why is each character in "The Rocking-Horse Winner" motivated to acquire money?

The two characters whose motivations we gain insights into are the mother and Paul. The father remains in the shadows, seen through the eyes of the mother, while the uncle and groom simply seem to have a reasonable, healthy enjoyment of betting on the races. The mother, however, has an empty spot in her soul that she tries to fill with money; however, as is almost always the case with inner emptiness, money simply can't fill the void. She is dissatisfied with her husband and, we are told, is incapable of really loving her children. Money becomes her substitute for love, and the house is permeated by the sense that there is never enough, despite the family's comfortable lifestyle.
Paul goes on his endless quest of riding his rocking horse to win money for his mother because he senses her emptiness and wants to make her happy and earn her love and approval. He gives all his winnings to her. He eventually rides himself to death to win money, money that he doesn't want for himself, in the attempt to fill his mother's void.

What type of literary devices does William Shakespeare use within Act 4 and how does it position the reader?

The literary device that is most consistently used throughout act 4 of Romeo and Juliet is dramatic irony. Dramatic irony is when the reader/audience knows something that the characters do not. This device is used all the way through act 4.
In act 4, scene 1, Paris comments about how much Juliet has been weeping for Tybalt's death (4.1.6–15). While this is partially true, the audience knows that Juliet is also weeping for Romeo's banishment. During the entire exchange between Paris and Juliet, the audience knows that Paris's insistence on getting married will only push Juliet further away from him. Paris and Lord Capulet believe that Juliet's wedding to Paris will cheer her up and make her forget her grief for Tybalt. However, the audience knows that the prospect of a wedding only makes Juliet more upset and desperate.
In act 4, scene 2, Lord Capulet is relieved to find Juliet in a better mood and ready to marry Paris. The audience knows that Juliet has actually worked out a way to escape this marriage, but Capulet does not know this.
In act 4, scene 5, the Capulet family discovers that Juliet is "dead." The audience knows that Juliet has actually taken a sleeping potion that makes her have the appearance of being dead, but the Capulet family falls for the trick and has her buried.
Dramatic irony is used throughout act 4 and positions the reader to have additional knowledge of the thoughts and motivations of the main characters. It builds interest in suspense in act 4 and prepares the audience for the play's dramatic outcome.
https://www.folgerdigitaltexts.org/html/Rom.html

How does Wilde use the play The Importance of Being Earnest to satirize the heroic morality of the upper classes?

Oscar Wilde was an avid satirist of what he viewed as the pretensions of upper-class Victorian society. His play The Importance of Being Earnest is not directly about the foibles of that society. Rather, it is about the subterfuge in which the play’s two main protagonists, Jack Worthing and Algernon Moncrieff, engage as a means of cutting loose and avoiding responsibility respectively. While the play is centered upon the difficulties that arise when worlds collide and deceptions become increasingly inconvenient to perpetuate, the setting provides for ample opportunities for Wilde to skewer Victorian social customs, particularly in the persons of Lady Bracknell and Miss Prism.
Much of The Importance of Being Earnest takes place at Manor House, a palatial estate in Hertfordshire, in addition to the opening scenes at Algernon’s London apartment, described in the play’s directions as “luxuriously and artistically furnished.” An early clue as to the upper-class pretensions of Lady Bracknell is offered in the opening dialogue between Algernon and his manservant, Lane, in which the former, anticipating Lady Bracknell’s arrival, asks Lane, “have you got the cucumber sandwiches cut for Lady Bracknell?” Cucumber sandwiches were associated with the upper class and Lady Bracknell’s preference for such an item is intended to convey the sense of snobbishness that Wilde sought to invoke.
Lady Bracknell’s entrance into Algernon’s apartment introduces the audience to the character and her myriad foibles and pretensions. As the play progresses, examples of Wilde’s efforts at satirizing Victorian social customs continue. In responding to her nephew’s statement that he will miss dining with her because he must attend to Bunbury (a nonexistent person Algernon uses to evade unpleasant situations), whose health, he declares, is in decline, Lady Bracknell states,

Well, I must say, Algernon, that I think it is high time that Mr. Bunbury made up his mind whether he was going to live or to die.  This shilly-shallying with the question is absurd.  Nor do I in any way approve of the modern sympathy with invalids.

This cavalier attitude on the part of the wealthy Lady Bracknell toward the lower classes constitutes the playwright’s most scathing commentary on Victorian society. As Lady Bracknell interrogates Jack regarding his suitability to court Gwendolyn, she informs him,

I feel bound to tell you that you are not down on my list of eligible young men, although I have the same list as the dear Duchess of Bolton has.  We work together, in fact.  However, I am quite ready to enter your name, should your answers be what a really affectionate mother requires.

As she continues to question Jack regarding his background, the Lady again injects a certain invective into her views of others:

Lady Bracknell:  [Sternly.]  What are your politics?
Jack: Well, I am afraid I really have none.  I am a Liberal Unionist.
Lady Bracknell:  Oh, they count as Tories.  They dine with us.  Or come in the evening, at any rate.  Now to minor matters.  Are your parents living?
Jack: I have lost both my parents.
Lady Bracknell:  To lose one parent, Mr. Worthing, may be regarded as a misfortune; to lose both looks like carelessness.  Who was your father?  He was evidently a man of some wealth.  Was he born in what the Radical papers call the purple of commerce, or did he rise from the ranks of the aristocracy?

The Importance of Being Earnest is replete with examples of Wilde’s interest in satirizing the morality of the society in which his play takes place. By providing such a prominent place in his play for his most pretentious character (Lady Bracknell), it is made exceedingly evident that Wilde intended for this component of his work to be just as important as the underlying plot regarding Jack’s double life, his romantic intentions toward Gwendolyn, and the revelations regarding Jack and Algernon’s relationship, among other plot points.

What are the rhetorical devices used in "The Piece of String?"

"The Piece of String" is a short story by Guy de Maupassant, in which the author utilizes a number of different rhetorical devices to help convey his point. In the first paragraph, we see asyndeton, a form of parallelism where conjunctions are omitted:

by their hard work, by the weight on the plow which, at the same time, raised the left shoulder and swerved the figure, by the reaping of the wheat which made the knees spread to make a firm "purchase," by all the slow and painful labors of the country.

The use of asyndeton here serves to amplify the intensity of the labor, making the workers' trials seem unending. Like the labor, the sentence seems to draw on and on.
We also see the use of simile to lend vividness to the mental picture the author paints, with the women's blouses "like balloons ready to carry them off." Enumeratio—the listing of numerous details—is also used for this purpose: "that smacked of the stable, the dairy and the dirt heap, hay and sweat."
Another form of parallelism, anaphora, is used to good effect in the story. Anaphora is where the same initial word or words begin a series of sentences or clauses, as "He understood . . . He tried . . . He felt it." The successive strong verbs and similarly structured short sentences help to amplify the starkness of the man's feelings, reflected by the curtness of these statements.

A popular expression asserts that "9-11 changed everything." Is this an accurate reading of American History since 2001?

Clearly the terrorist attacks of 9/11 had profound effects that we are still trying to come to terms with today. It was a moment as important as it was tragic. But it did not, perhaps, change everything, as we often hear. Since the end of the Cold War, the United States had begun to grapple with the problems posed by international terrorism and, particularly by the mid-1990s, the terror network known as Al-Qaeda. The Clinton Administration had witnessed multiple bloody terror attacks, including one on the World Trade Center itself, and disrupting and destroying global terror networks had already become a major focus of US foreign policy by September 11, 2001. Indeed, President Clinton had authorized multiple missions to kill or capture Al-Qaeda leader Osama Bin Laden during his presidency. So perhaps it is more accurate to say that the terror attacks of 9/11 alerted Americans to a reality that they had not previously considered—that their nation was involved in what would become known as a "war on terror." Certainly 9/11 changed much, especially domestically, but many of the forces unleashed by 9/11 were already churning under the surface.
https://2001-2009.state.gov/s/ct/rls/wh/6947.htm

What literary movement is "The Hollow Men" a product of?

"The Hollow Men" by T.S. Eliot is an example of a modernist poem. The poem was published in 1925 at the height of the modernist movement, which included literature, visual art, and film.
Modernism is characterized by a break with Romantic and Victorian traditions. Stream-of-consciousness narration replaced the intrusive voice of a third person omniscient narrator or the italicized thoughts of a speaking character. Modernist literature discussed subjects such as sexuality and violence that were previously avoided in literature. It did not shun vulgarity either.
"The Hollow Men" addresses the alienation and void of moral purpose that many people, particularly returning soldiers, felt after the First World War. In the first stanza, the narrator suggests even the camaraderie that develops in a war zone has not brought comfort or a sense of strength: 

    We are the stuffed men    Leaning together    Headpiece filled with straw. Alas!    Our dried voices, when    We whisper together    Are quiet and meaningless    As wind in dry grass

Calculus of a Single Variable, Chapter 8, 8.3, Section 8.3, Problem 43

Indefinite integrals are written in the form of int f(x) dx = F(x) +C
where: f(x) as the integrand
F(x) as the anti-derivative function
C as the arbitrary constant known as constant of integration
For the given problem int sin(2x)cos(4x) dx or intcos(4x)sin(2x) dx has a integrand in a form of trigonometric function. To evaluate this, we apply the identity:
cos(A)sin(B) =[sin(A+B) -sin(A-B)]/2
The integral becomes:
int cos(4x)sin(2x) dx = int[sin(4x+2x) -sin(4x-2x)]/2dx
Apply the basic properties of integration: int c*f(x) dx= c int f(x) dx .
int [sin(4x+2x) -sin(4x-2x)]/2dx = 1/2int[sin(4x+2x) -sin(4x-2x)]dx
Apply the basic integration property: int (u+v) dx = int (u) dx + int (v) dx .
1/2 *[int sin(4x+2x)dx+int sin(4x-2x)dx]
Then apply u-substitution to be able to apply integration formula for cosine function: int sin(u) du= -cos(u) +C .
For the integral:int sin(4x+2x)dx , we let u = 4x+2x =6x then du= 6 dx or (du)/6 =dx .
int sin(4x+2x)dx=intsin(6x) dx
=intsin(u) *(du)/6
= 1/6 int sin(u)du
=-1/6cos(u) +C
Plug-in u =6x on -1/6 cos(u) +C , we get:
int sin(4x+2x)dx= -1/6 cos(6x) +C
For the integral: intsin(4x-2x)dx , we let u = 4x-2x =2x then du= 2 dx or (du)/2 =dx .
intsin(4x-2x)dx=intsin(2x) dx
=intsin(u) *(du)/2
= 1/2 int sin(u)du
= -1/2cos(u) +C
Plug-in u =2x on -1/2 cos(u) +C , we get:
intsin(4x-2x)dx= -1/2 cos(2x) +C
Combing the results, we get the indefinite integral as:
intcos(4x)sin(2x) dx= 1/2*[ -1/6 cos(6x) -(-1/2 cos(2x))] +C
or -1/12 cos(6x) +1/4 cos(2x) +C

What are some characteristics of the "sublime"?

The sublime is a guiding principle of both Romanticism and its sister movement gothic literature. It draws largely from Edmund Burke's 1757 work, A Philosophical Enquiry into the Origin of Our Ideas of the Sublime and Beautiful. Burke's sublime is drawn from passion and "astonishment," a state in which "the mind is so entirely filled with its object, that it cannot entertain any other." Astonishment, then, according to Burke, is what causes something to become, to us, a sublime object which pushes everything else out of our consciousness. Violent, or forceful, emotions are the key to what makes something sublime. Burke also identifies "terror" as, in fact, "the ruling principle" of the sublime, which gives some indication of why the sublime is as much a commonality in gothic literature as in Romanticism. The sublime can be reached as much—and, indeed, perhaps more—through the sort of terror which overcomes a person entirely, as through astonished awe at the beauty of nature.
The sublime was adapted by the Romantics mainly in terms of its emphasis upon strong emotion. For Wordsworth and other Romantic poets, the sublime in nature represented something so beautiful or awe-inspiring that it provoked strong emotions and therefore became sublime. It is notable, however, that Burke makes a distinction between the sublime and the beautiful. While something can be sublimely beautiful, things may also be sublimely terrifying. Burke also makes a clear distinction between the effects of the sublime—which are overwhelming and "tighten" the fibers of the body—and those of the beautiful, which should relax the beholder to a supreme degree.
For Burke, something is sublime or beautiful not because of what it is in itself, but because of the strength of its effect on the beholder. As such, the idea of the sublime is not objective but entirely subjective.

Single Variable Calculus, Chapter 7, 7.2-2, Section 7.2-2, Problem 8

Express the quantity $\displaystyle \ln (a + b) + \ln(a - b) - 2 \ln c$ as a single at logarithm.


$
\begin{equation}
\begin{aligned}

\ln (a + b) + \ln (a - b) - 2 \ln c =& \ln [(a + b)(a - b)] - 2 \ln c
&& \text{(recall that } \ln x + \ln y = \ln (xy))
\\
\\
\ln (a + b) + \ln (a - b) - 2 \ln c =& \ln [(a + b)(a - b)] - \ln (c)^2
&& \text{(recall that } k \ln x = \ln (x)^k)
\\
\\
\ln (a + b) + \ln (a - b) - 2 \ln c =& \ln \left[ \frac{(a + b)(a - b)}{e^2} \right]
&& \text{(recall that } \ln x - \ln y = \ln \frac{x}{y}
\\
\\
\ln (a + b) + \ln (a - b) - 2 \ln c =& \ln \left(\frac{a^2 - b^2}{c^2} \right)
&&


\end{aligned}
\end{equation}
$

From Rabindranath Tagore's "Lost Jewels," explain the character of Mani, in the light of the statement, "Mani did not understand Bhusan, it is true."

Mani, Bhusan's wife, does not understand her husband's gentle and accommodating nature and mistakes his gentle love for indifference or even greed. According to the schoolmaster who narrates "Lost Jewels," Bhusan is a modern man who treats his wife in too mild a manner. The schoolmaster says, "A man need not necessarily be ugly or poor to be cheated of his wife's love; but he is sure to lose it if he is too gentle." The schoolmaster maintains that a wife who gets gifts too easily from her husband and who does not need to cajole him into doing things for her will not love her husband. 
Mani is a beautiful and pampered woman who enjoys privileges without working for them. As the schoolmaster says:

"She used to get her caresses without asking, her Dacca muslin saris without tears, and her bangles without being able to pride herself on a victory. In this way her woman's nature became atrophied, and with it her love for her husband. She simply accepted things without giving anything in return."

In other words, Mani never has to sacrifice anything for her marriage, and she does not learn to commit to anything or anyone. She leads a very placid life, as she is not worried about her husband's love. She practices efficiency in running the house, and she never has to worry about losing her looks, as she seems to remain young forever. 
As Bhusan does not ask anything from her, Mani does not need to give anything and becomes selfish as a result. As the schoolmaster says of Bhusan:

"His love for his wife was of that kind which has to tread very carefully, and cannot speak out plainly what is in the mind; it is like the attraction of the sun for the earth, which is strong, yet which leaves immense space between them."

Therefore, when Bhusan loses his money and needs credit, he does have the nerve to ask Mani for her jewels, but she suspects that he will, as she doesn't know her husband very well. Instead of sacrificing her jewelry, she is convinced by her cousin to escape wearing it and is never seen again. The gulf that Bhusan leaves open between him and his wife--arising out of his gentleness--makes her suspicious. In that gulf, she inserts suspicion, and she never understands her husband's true goodness and love. 

What major events occur in the story?

One of the most important events in the story is Peyton Farquhar's execution. He's hanged from a bridge by Union soldiers for conspiring to commit an act of sabotage, a very serious crime in wartime. Peyton was lead to commit this capital crime by a man who he believed to be a Souther soldier, who urges him to destroy the bridge in order to hold up the advance of the Union army.
The Southern soldier turns out to be no such thing, of course; he's a Union trooper in disguise. But because Peyton is such a loyal supporter of the Confederacy, he's willing to do whatever it takes to assist the cause, no matter how risky. One could argue that his fateful decision to try and blow up the bridge is the most important event in "An Occurrence at Owl Creek Bridge," as it leads directly to his death by hanging, which is the story's main dramatic focus.

The story's main event is revealed at the end when Peyton Farquhar is hanged "from the timbers of the Owl Creek Bridge." The rest of the story's events are either the reminiscences of Farquhar or his desires expressed as a fantasy, such as the reunion with his wife in the moments before his death.
The story opens with the event of soldiers standing sentry at either end of the bridge while officers oversee the preparations for a hanging. The event that led up to Farquhar's condemnation is replayed: a Union scout in the guise of a Confederate comes to the house, and the fateful conversation between the soldier and Farquhar regarding the bridge takes place.
The event of Farquhar escaping the noose and being fired upon in Owl Creek does not actually take place; it is the detailed fantasy that Farquhar creates to distract himself from the agonizing truth of his imminent execution.

Who is the protagonist?

The protagonist in Thomas Wolfe's short story "The Far and the Near" is the unnamed train engineer. Little is said about him in the few pages of the story. We know that this engineer ran his locomotive daily between two cities. Every afternoon as he passed a certain cottage he blew the train's whistle as a greeting to the woman and her daughter who lived there. He worked for the railroad for over twenty years and never failed to send this greeting to the unnamed women.
The author does not provide much more detail about the engineer's background. We know that he was married and had children. We know that he was impacted greatly by his service as a railroad engineer, including the several tragic occasions when his train had struck people and other vehicles on the tracks.
There are only three characters in the story, the engineer, the woman, and her daughter. As the story is centered almost entirely on the engineer, it is easy to identify him as the protagonist. We, the readers, get to learn about his emotions, thoughts, and observations. The other two characters are merely vehicles to understand the journey of the engineer. The short story is focused on his idealistic vision and his eventual disillusionment. We never really know what the two women actually thought of him, or what they were thinking at all. We only know what the engineer interprets from their actions and behavior.

Why does Charles become a well-known character to the family?

Charles becomes a well-known character to the family because every day, on his return from kindergarten, Laurie delights in sharing Charles's latest exploits with his family. On his first day, for instance, Laurie comes home and tells his parents that Charles was "fresh" to the teacher. As the days go by, Laurie shares even more with his parents about Charles's behavior, telling them about how Charles hit the teacher, yelled loudly, and refused to do exercises.
In addition, for Laurie's parents, Charles's exploits are shocking, given his young age. Laurie's mother, in particular, worries that Charles is a bad influence on her son.
Despite her reservations, Charles's exploits become a source of fascination to Laurie's parents. Each day, they are eager to learn of his latest misdemeanors and, by the third week of kindergarten, Charles has become an "institution" in the household.
What they fail to realize, however, is that Charles is nothing more than a creation of Laurie's. He creates this alter ego so he doesn't have to tell his parents what he has really been up to in kindergarten.

Single Variable Calculus, Chapter 3, 3.4, Section 3.4, Problem 25

a.) Determine the equation of the tangent line to the curve $y = 2x \sin x$ at the point $\displaystyle \left( \frac{\pi}{2}, \pi \right)$


$
\begin{equation}
\begin{aligned}

\qquad y' =& (2x) \frac{d}{dx} (\sin x) + (\sin x) 2 \frac{d}{dx} (x)
&&
\\
\\
\qquad y' =& 2x \cos x + 2 \sin x
&&
\\
\\

\end{aligned}
\end{equation}
$




Let $y' = m_T$ (slope of the tangent line)


$
\begin{equation}
\begin{aligned}


y' = m_T =& 2 \left( \frac{\pi}{2} \right) \cos \left( \frac{\pi }{2} \right) + 2 \sin \left( \frac{\pi}{2} \right)
&& \text{Substitute value of $x$}
\\
\\
m_T =& 2
&&

\end{aligned}
\end{equation}
$


Using Point Slope Form substitute the values of $x, y$ and $m_T$


$
\begin{equation}
\begin{aligned}

y - y_1 =& m (x - x_1)
&&
\\
\\
y - \pi =& 2 \left( x - \frac{\pi}{2} \right)
&&
\\
\\
y - \pi =& 2x - \frac{2 \pi}{2}
&&
\\
\\
y =& 2x - \pi + \pi
&&
\\
\\
y =& 2x
&& \text{Equation of the tangent line at $\large \left( \frac{\pi}{2}, \pi \right)$}

\end{aligned}
\end{equation}
$



b.) Graph the curve and the tangent line in part (a) on the same screen

How much would women and children be paid for the work they did during the Industrial Revolution?

Women and children provided some of the labor in the factories during the Industrial Revolution. Since there were no laws at this time requiring children to attend school, many children worked to help their family make ends meet. There were no minimum wage laws for any workers, so factory owners could pay workers whatever they wanted to pay them. Generally, women and children were paid less than men for the work they did. While some women worked to help their families earn money, other women worked because there were no other viable alternatives for them. Some women were also trying to save money for when they married.
Children were paid very little. For example, it was common for children to work about twelve hours a day or more, six days a week, and be paid one dollar. In one factory in Massachusetts, children were paid between 40 cents and $1.10 for one night’s work. Eventually, there were calls to pass laws to regulate child labor and require kids to attend school.
Women were also paid very little. In some of the factories in New England, women were paid between $3.00 and $3.50 per week. They would work twelve-hour days, six days a week.
Women and children were badly paid for the long hours they worked in very poor working conditions.
https://junior.scholastic.com/pages/content-hubs/real-teens-of-history.html

How does the speaker seek to rejuvenate himself through art in "Sailing to Byzantium" by William Butler Yeats?

The speaker in this poem by W.B. Yeats is, we may infer from the opening line, an old man, concerned that, in his old age, he has become "but a paltry thing." He feels that to be old is to be little more than a "tattered coat upon a stick, unless / Soul clap its hands and sing"—that is, the soul of a person must be stimulated in order to keep that person spiritually alive. It is in pursuit of this goal that the speaker has embarked upon a journey to Byzantium, that "holy city."
Rejuvenation, as such, is not the speaker's goal. He does not wish to be young again, but for the "sages standing in God's holy fire" to gather him "into the artifice of eternity." He speaks of leaving his body and becoming, instead of something shaped like a "natural" creation, something "of hammered gold and gold enamelling," which could then exist as it has always existed, singing "of what is past, or passing, or to come." Through the art of the holy city, then, the speaker seeks to somehow transmutate from a living human being into something immortal in its "artifice," filled with song.
The idea of songs and singing is an interesting concept in this poem. Once he is "out of nature," the speaker still imagines himself "set upon a golden bough to sing," as if a knowledge of everything in the universe, in the past, present and future, might become part of his song, although he is no longer "natural." His soul needs to sing, or else he will be "but a paltry thing." And yet, in the opening stanza of the poem, the birds in the trees, too, are "at their song," and yet they are described as "these dying generations." The poem seems to suggest that, through their singing, even the birds seek to keep themselves from death.

In "Sailing to Byzantium," Yeats sees the creation of art as a possible method of escaping one's natural old age and mortality. The poem begins with a description of a world of life in conflict with the certainty of death. The speaker in the poem muses on the fragility of old age, and much of the poem focuses on ways of reversing, or at least remedying, this fragility. Some of the key lines pertaining to this theme occur in the final stanza. For example, the speaker says he wants to be reborn in "such a form as Grecian goldsmiths make / Of hammered gold and gold enamelling / To keep a drowsy Emperor awake" (27-9). In these lines, the speaker is asserting that artistic creation can sidestep old age and death, and that the artistic creative process has the ability to rejuvenate old age by making one essentially immortal. All in all, Yeats presents art as something timeless, something that can sing "Of what is past, or passing, or to come" (32), and so only by creating and engaging with art can one rejuvenate one's old age and escape one's inevitable mortality. 
https://www.poetryfoundation.org/poems/43291/sailing-to-byzantium

Single Variable Calculus, Chapter 3, 3.3, Section 3.3, Problem 91

Where is the function $f(x) = |x^2-9|$ differentiable? Find a formula for $f'$ and sketch its graph.




Based from the graph, the values of $x$ from $-3 < x < 3$ are flipped or reflected to the $x$-axis.
By using the definition of the absolute value, we can deduce $f(x)$ as


$
f(x) = \left\{
\begin{array}{c}
x^2 - 9 & \text{for} & x \geq 3\\
9-x^2 & \text{for} & -3 < x < 3\\
x^2 - 9 & \text{for} & x < -3
\end{array}\right.
$


Now, we can find the formula for $f'(x)$ by taking the derivative of the Piecewise Function $f(x)$


$
f'(x) = \left\{
\begin{array}{c}
2x & \text{for} & x \geq 3\\
-2x & \text{for} & -3 < x < 3\\
2x & \text{for} & x \leq -3
\end{array}\right.
$





Referring to the graph, we can say that $f(x)$ is differentiable every where except at $x = \pm 3$ because
of jump discontinuity making its limit from and right unequal.

4^(2x-5)=64^(3x) Solve the equation.

To evaluate the given equation 4^(2x-5)=64^(3x) , we may let 64 =4^3 .
The equation becomes:  4^(2x-5)=(4^3)^(3x) .
Apply Law of exponents: (x^n)^m = x^(n*m) .
4^(2x-5)=4^(3*3x)
4^(2x-5)=4^(9x)
Apply the theorem: If b^x=b^y then x=y .
If 4^(2x-5)=4^(9x ) then 2x-5=9x .
Subtract 2x on both sides of the equation 2x-5=9x .
2x-5-2x=9x-2x
-5=7x
Divide both sides by 7 .
(-5)/7=(7x)/7
x = -5/7
Checking: Plug-in x=-5/7 on 4^(2x-5)=64^(3x).
4^(2(-5/7)-5)=?64^(3*(-5/7))
4^((-10)/7-5)=?64^((-15)/7)
4^((-45)/7)=?64^((-15)/7)
4^((-45)/7)=?(4^3)^((-15)/7)
4^((-45)/7)=?4^(3*(-15)/7)
4^((-45)/7)=4^((-45)/7)  TRUE
or
0.000135~~0.000135  TRUE
Thus, the x=-5/7  is the real exact solution of the equation 4^(2x-5)=64^(3x) .

What is current?

I am assuming that your question refers to electric current.
Electric current is motion of electric charges. The electric charges can move when placed in an electric field. That is, in the region of space where there will be electric force acting on the charges.
Electric charges that are free to move, if placed in an electric field, are found in certain materials called conductors. A metal wire is an example of a conductor. A conductor is used to connect an element where current is needed (such as a light bulb) to a battery, a device that produces potential difference (commonly known as voltage, a measure of change of electric field) between its two terminals. Together, a light bulb, a conductor and a battery can be made into the simplest electrical circuit. The flow of the electric charge around the circuit is electric current.
Electric current is measured as the amount of charge that flows through the cross section of a conductor in a unit of time:
I = (Delta q)/(Delta t) . The unit of measurement of the current is Amperes, after the scientist who discovered that the current-carrying wires create magnetic field.
 

Why does the Happy Prince send the ruby to the seamstress?

"The Happy Prince" is a short story written by Oscar Wilde that was published in his collection of stories entitled The Happy Prince and Other Tales in 1888. In the story, the Happy Prince is a statue who is admired by the townspeople. He was once a rich and happy prince who lived in the palace, but now, as a golden statue, he weeps over "all the ugliness and all the misery" of his city.
One day, a swallow lands on the Happy Prince and mistakes his tears for rain. Once they begin talking, the Happy Prince asks Swallow if he will deliver the ruby from his sword to a seamstress. Swallow seems burdened by the request, especially since he has plans to fly to Egypt and enjoy the warm weather with his swallow friends; however, the Happy Prince finally convinces him to help, so Swallow flies away with the ruby.
The Happy Prince chose to deliver the ruby to the seamstress because she was very poor and had a sick son that she could not provide adequate care for. Wilde describes the seamstress as having a "thin and worn" face with "coarse, red hands, all pricked by the needle."
Swallow slips into the "poor house" and places the ruby by the seamstress's thimble, then flies around her sick son to help cool his fever. When Swallow returns to the Happy Prince, he mentions that he now feels warm despite the cold weather. The Happy Prince replies, "That is because you have done a good action."

In the story "Raymond's Run," what is Squeaky's responsibility?

In Toni Cade Bambara's short story "Raymond's Run," Squeaky's main responsibility is to take care of her intellectually disabled older brother, Raymond. In the first paragraph of the short story, Squeaky mentions that her only responsibility is to mind her brother and also says that she is willing to fight anyone who attempts to make fun of Raymond. Squeaky keeps an eye on her brother and makes sure that she walks between him and the road to prevent Raymond from bolting into the middle of the street. She also takes Raymond to the May Day races, where she competes against other girls in her age group and ends up winning first place. While Squeaky is running in the big race, she looks over and sees Raymond running adjacent to her on the other side of the fence. Following the race, Squeaky decides to invest her time in coaching Raymond on how to run; she believes that he can be a competitive athlete.

In Toni Cade Bambara's story "Raymond's Run," Squeaky's family responsibility is to care for her disabled brother, Raymond. Due to Raymond's developmental disabilities he needs constant care to keep him safe and out of trouble. Squeaky takes this responsibility very seriously so that her mother can concentrate on caring for the family home.
Raymond tags along with Squeaky wherever she goes in their Harlem neighborhood. While she practices her breathing and high-stepping, Raymond can be seen prancing along pretending he is driving a carriage. When Raymond runs through the pigeons or into the puddles along the street, Squeaky is quick to correct his actions so that she does not get in trouble at home.
If the other children mock Raymond for his large head or mental deficits, Squeaky quickly comes to his defense by fighting the perpetrator. She is a loyal, caring sister who looks out for her brother's well-being.

What are Antonio's thoughts after he guarantees a pound of his own flesh to Shylock if he does not repay his loan?

In Act I, Scene 3 of Shakespeare’s The Merchant of Venice, Antonio agrees to a preposterous proposal by the sneaky Shylock — that he pledge a pound of his own flesh as a guarantee if he can’t come up with Bassanio’s payment in three months. 

SHYLOCK: “…let the forfeit
Be nominated for an equal pound
Of your fair flesh, to be cut off and taken
In what part of your body pleaseth me.”

Confident he will have no problem securing the necessary amount, Antonio not only pledges a pound of his own flesh, but also states he will have the sum ready in two months.
After Shylock leaves, we see a note of sarcasm from Antonio:

The Hebrew [Shylock] will turn Christian: he grows kind.

Bassanio replies that he does not like the terms of this agreement, even calling Shylock a “villain”. 
Antonio, unfazed by the intense meaning of his deal with Shylock, consoles Bassanio with these words:

Come on: in this there can be no dismay;
My ships come home a month before the day.

Antonio is completely unruffled by Shylock’s severe demand, confident his ships will be prosperous and bear the money Antonio will need to pay back his loan. Even though his own flesh is on the line, Antonio is far calmer about the arrangement than Bassanio, even being so bold as to crack a joke about Shylock.
http://shakespeare.mit.edu/merchant/full.html

https://www.playshakespeare.com/merchant-of-venice/synopsis

Calculus of a Single Variable, Chapter 8, 8.4, Section 8.4, Problem 30

Recall that indefinite integral follows the formula: int f(x) dx = F(x) +C
where: f(x) as the integrand
F(x) as the anti-derivative function
C as the arbitrary constant known as constant of integration
For the given problem int 1/(x^2+5)^(3/2)dx , it resembles one of the formula from integration table. We may apply the integral formula for rational function with roots as:
int 1/(u^2+a^2)^(3/2)du= u/(a^2sqrt(u^2+a^2))+C
By comparing "u^2+a^2 " with "x^2+5 " , we determine the corresponding values as:
u^2=x^2 then u = x and du = dx
a^2 =5 then a = sqrt(5) .
Plug-in the corresponding values on the aforementioned integral formula for rational function with roots, we get:
int 1/(x^2+5)^(3/2)dx =x/(5sqrt(x^2+5))+C

In "The Farmer Refuted" by Alexander Hamilton, what is the most persuasive comment made? What would be another strong title for this text? How can we infer the content of Seabury's text that preceded Hamilton's response? How would the original audience have received this text? Do you think Hamilton responded to Seabury in an appropriate manner? Based on this text, would you classify the American Founding Fathers as heroes or traitors?

There are many persuasive comments in "The Farmer Refuted." Perhaps among the most persuasive is Hamilton's defense of natural law, which he states in the following way:

"Hence, in a state of nature, no man had any moral power to deprive another of his life, limbs, property or liberty; nor the least authority to command, or exact obedience from him; except that which arose from the ties of consanguinity."

This means that man's right to life, liberty, and property come directly from God and cannot be taken away, even by the king. The only instance in which a person can revoke these rights is from a familial tie. Another strong title for this text might be "In Defense of Natural Law," as, in its essence, the document states that humans have inalienable rights, or rights that cannot be taken away and that are given to them by natural law. 
It can be presumed that Seabury called the Congress in Philadelphia illegal, as Hamilton writes, "You, Sir, triumph in the supposed illegality of this body; but, granting your supposition were true, it would be a matter of no real importance." Seabury, who wrote under the pseudonym Farmer, was the Presiding Bishop of the Episcopal Church in America. By contradicting Seabury, Hamilton showed that he was bold and unafraid to take on the powerful. Hamilton insisted that the Congress was legal because, as he wrote, "When human laws contradict or discountenance the means, which are necessary to preserve the essential rights of any society, they defeat the proper end of all laws, and so become null and void." That is, laws that go against natural rights of man do not need to be followed. Seabury's opinion was different in that he thought that the Congress convened in Philadelphia was illegal and that the British king was the ultimate authority who must be heeded in the colonies. 
Loyalists would have perceived Hamilton's treatise as traitorous, while those who supported the American Revolution (which broke out a year after Hamilton wrote this document) would have supported his argument. If you feel that the colonies had the right to disobey a king who went against their interests, then you might support Hamilton and feel that he responded to Seabury in an appropriate manner, using arguments that go back to Locke and Hobbes and the idea of the social contract. If you support this argument, you would also classify the Founding Fathers as heroes who believed in the social contract and therefore rebelled against a king who they felt had violated their natural rights. 

What do others say about Holden? Please give examples.

This is a tricky question because Holden is the narrator of his story, so anything anyone else says about him is filtered through Holden himself as he explains his interactions with the other people. With this fact in mind, here are three examples of what Holden says others say about him.
Holden meets three older women in the Lavender Room, and the blonde that he dances with criticizes his bad language when they talk. According to this blonde woman, Holden uses inappropriate language much too often. She says to him, "Watch your language, if you don't mind" and then later, "I don't like that type language" when Holden says "Chrissakes," and she threatens to stop talking with him if he keeps up his blasphemy.
When Sally and Holden go ice-skating, Holden gets very animated and energetic when speaking with Sally about school and the pointlessness of his experiences at all of his various schools. Twice, Sally asks Holden to stop shouting and to lower his voice, which annoys Holden, who claims that he wasn't raising his voice at all. The fact that Sally says Holden is being loud suggests that he does in fact raise his voice in an aggressive way when he gets worked up about a topic.
When Holden meets up with Luce—his old Student Adviser at Whooton—at the Wicker Bar in New York, they engage in what Luce describes as a "typical Caulfield conversation" about girls and sex. When Luce reveals that he is involved with a woman from Shanghai, he describes the Chinese approach to sex as both "a physical and spiritual experience," which leads Holden to say that he would like to go to China. At this point, Luce describes Holden as having an "immature mind."

Where is Macbeth going when he sees the bloody dagger?

When Macbeth sees the bloody dagger in act 2, scene 1, he is on his way to Duncan's chamber. The purpose of his visit to the chamber is to kill Duncan and take the crown of Scotland for himself.
Just before he sees the dagger, Macbeth is having second thoughts about killing Duncan. Although he wants to be king, he does not want to betray Duncan in such an evil and violent manner. The dagger, however, appears to be pointing the way to Duncan's chamber, and Macbeth interprets this as a sign that he must act before he loses his courage completely:

Words to the heat of deeds too cold breath gives.

We could interpret the dagger, therefore, as a physical manifestation of Macbeth's ambition. Specifically, his desire to be the king of Scotland.
After seeing the dagger and hearing the signal from Lady Macbeth, Macbeth proceeds to Duncan's chamber and kills him.

Describe a character sketch of Gulliver.

Gulliver, as his name implies, is gullible, or easily deceived: he tends to trust too much in appearances. However, he is not witless, as he manages to survive the many perils of his travel.
Gulliver is not an imaginative person but more a recorder of facts. We can trust that he will give us an accurate accounting of what he sees on his travels, but at the same time, he may not understand the implication or deeper meaning of what is going on. This leads to comedy, as he will give straight faced, earnest accountings of ridiculous inventions or rituals he observes, not seeming to understand how ludicrous they are.
Despite all this, Gulliver is a kind-hearted man, even though this trait gets him into trouble. His tendency to surface evaluations, such as thinking the petty and mean Lilliputians must be good because they are tiny and attractive, leads readers to reflect on their own superficial judgments. At the end, Gulliver goes overboard in his love of the Houyhnhnms by coming back to Europe and living in a stable with horses. This is an indication of his moral goodness—he wants European society to behave more rationally and humanely—but also warns us not to go to extremes in our rejection of humanity.

In Henry Lawson's story "The Drover's Wife," what does the wooden shack in which the drover's wife lives with her four children look like?

The wooden shack of the family of the drover is a two-room building, a makeshift construction apparently erected from whatever lumber could be gleaned: "stringy-bark, with split slabs" of wood for flooring in the main room. The kitchen has only a dirt floor. 
Clearly indicative of an impoverished family, this shack, which houses a family of six, is inadequate. When a five-foot black snake slithers under the house into the main living area, the drover's wife is forced to bring her small children out to the kitchen, where parts of this room are unprotected from the wind because of the shabby slab wall through which drafts can come. She makes the children get up onto a large, crudely constructed kitchen table where she has made a bed with the pillows and covers she has quickly snatched from inside. With nowhere for her to lie, the mother sits in a chair during the night.

"The Drover's Wife" is set in the desolate Australian Outback, a dry and Spartan area that seldom sees activity or visitors. The Outback is considered largely inhospitable to Australians due to the harsh climate and lack of amenities. The area is also highly prone to drought, flooding and fires, which makes it an undesirable location in which to live. It is in this inhospitable landscape that the drover's wife and her husband have chosen to build their home, an unimpressive shack in the middle of nowhere. The shack is described as being 19 miles away from any sign of civilization and located on the main road. Wild animals such as snakes and poisonous insects abound, and the characters finding a large snake in their wood pile is the main event that takes place within the short story. The drover's wife must contend with the isolation that comes with not hearing from her husband in six months. Life in the rugged shack is difficult and lonely, and the shack itself serves as a character throughout the story.
As the story progresses, the wooden shack is described as drab and lackluster. There are minimalist structures used to house the cattle, and the drover's wife has dug trenches around the shack to prevent it from flooding. Despite its drab appearance, the shack provides the family with what little protection they can expect against the elements and other natural threats in the bush. Wanderers and dangerous animals alike make occasional appearances, and the shack keeps the drover's wife and her children shielded from them. There is also a porch with wood stored underneath it, and when a snake disappears underneath the porch, the family must wait to flush it out at dawn so they can kill it. In this sense, the shack is both a problem (due to its poor construction and remote location) and a source of protection.  

How did the policiy of containment contribute to tensions during the Cold War?

In 1946, diplomat George Kennan, in his famous "Long Telegram," described the Soviet Union as evil and that it was the United States's duty to confront communism wherever it attempted to grow.  President Harry Truman created a policy called "containment" which used varying degrees of force to stop the spread of communism.  The United States provided aid to rightist guerrillas in the Greek civil war in order to avoid a communist takeover there.  The United States also influenced an election in Italy when it looked like leftists would take over the nation.  The United States spent money on project such as Radio Free Europe in order to carry out a propaganda war against the Soviets.  The United States also used conventional warfare on the Korean peninsula when North Korea invaded South Korea.  All of this created tensions with the Soviet Union because the Soviet Union thought that the United States was spreading its influence all over the world. It sought to spread its influence by sending aid to communist regimes in North Vietnam.  The United States thought that all communism regimes were controlled from the Kremlin, so it sought to stop all leftist movements in the developing world, even at times when it had to support rightist dictators.  

Beginning Algebra With Applications, Chapter 7, 7.1, Section 7.1, Problem 36

Which sum will be zero $P + Q, Q + R,$ or $P + R$?

If we add $P$ and $Q$, we have


$
\begin{equation}
\begin{aligned}

P + Q =& (ax^3 + bx^2 - cx + d) + (-ax^3 - bx^2 + cx - d)
&&
\\
\\
=& (ax^3 - ax^3) + (bx^2- bx^2) + (-cx + cx) + (d-d)
&& \text{Use the commutative and associative properties of addition to rearrange and group like terms.}
\\
\\
=& 0
&& \text{Combine like terms}

\end{aligned}
\end{equation}
$


If we add $Q$ and $R$, we have


$
\begin{equation}
\begin{aligned}

Q + R =& (-ax^3 - bx^2 + cx - d) + (-ax^3 + bx^2 + cx + d)
&&
\\
\\
=& (-ax^3 - ax^3) + (-bx^2 + bx^2) + (cx + cx) + (-d + d)
&& \text{Use the commutative and associative properties of addition to rearrange and group like terms.}
\\
\\
=& -2ax^3 + 2cx
&& \text{ Combine like terms and write the polynomial in descending order.}

\end{aligned}
\end{equation}
$


If we add $P$ and $R$, we have


$
\begin{equation}
\begin{aligned}

P + R =& (ax^3 + bx^2 - cx + d) + (-ax^3 + bx^2 + cx + d)
\\
\\
=& (ax^3 - ax^3) + (bx^2 + bx^2) + (-cx+ cx) + (d + d)
&& \text{Use the commutative and associative properties of addition to rearrange and group like terms.}
\\
\\
=& 2bx^2 + 2d
&& \text{ Combine like terms and write the polynomial in descending order.}


\end{aligned}
\end{equation}
$


So, $P+Q$ has the sum equal to zero.

Calculus of a Single Variable, Chapter 6, 6.3, Section 6.3, Problem 9

The general solution of a differential equation in a form of y' = f(x) can
be evaluated using direct integration. The derivative of y denoted as y' can be written as (dy)/(dx) then y'= f(x) can be expressed as (dy)/(dx)= f(x) .
For the problem yy'=4sin(x) , we may apply y' = (dy)/(dx) to set-up the integration:
y(dy)/(dx)= 4sin(x) .
or y dy = 4 sin(x) dx

Then set-up direct integration on both sides:
inty dy = int 4 sin(x) dx
Integration:
Apply Power Rule integration: int u^n du= u^(n+1)/(n+1) on inty dy .
Note: y is the same as y^1 .
int y dy = y^(1+1)/(1+1)
= y^2/2
Apply the basic integration property: int c*f(x)dx= c int f(x) dx and basic integration formula for sine function: int sin(u) du = -cos(u) +C
int 4 sin(x) dx= 4int sin(x) dx
= -4 cos(x) +C

Then combining the results for the general solution of differential equation:
y^2/2 = -4cos(x)+C
2* [y^2/2] = 2*[-4cos(x)]+C
y^2 =-8cos(x)+C
y = +-sqrt(C-8cosx)

Single Variable Calculus, Chapter 6, 6.3, Section 6.3, Problem 18

Use the shell method to find the volume generated by rotating the region bounded by the curves $y = x^2, y = 2 - x^2$ about the $x = 1$. Sketch the region and a typical shell.








If we use a vertical strips, notice that the distance of the strips from the line $x = 1$ is $1 - x$. If you revolve this distance about $x = 1$, you'll get the circumference $C = 2 \pi (1 - x)$. Also, notice that the height of the strips resembles the height of the cylinder as $H = y_{\text{upper}} - x_{\text{lower}} = 2 - x^2 - (x^2)$. Thus, we have..

$\displaystyle V = \int^b_a C(x) H(x) dx$

In order to get the values of the upper and lower limits, we simply determine the points of intersection of the curves...


$
\begin{equation}
\begin{aligned}

x^2 &= 2 - x^2
\\
2x^2 &= 2
\\
x^2 &= 1
\\
x &= \pm 1

\end{aligned}
\end{equation}
$


Therefore, we have..


$
\begin{equation}
\begin{aligned}

V =& \int^1_{-1} 2 \pi (1 - x) (2 - x^2 - (x^2)) dx
\\
\\
V =& 2 \pi \int^1_{-1} (2 - 2x^2 - 2x + 2x^3) dx
\\
\\
V =& 2 \pi \left[ 2x - \frac{2x^3}{3} - \frac{2x^2}{2} + \frac{2x^4}{4} \right]^1_{-1}
\\
\\
V =& \frac{16 \pi}{3} \text{ cubic units}

\end{aligned}
\end{equation}
$