How does the story "The Bet" end?

The climax of "The Bet" is reached when the banker reads the letter in which the lawyer renounces the two million roubles he was entitled to receive for spending fifteen years in solitary confinement. The banker is humiliated because he was seriously planning to murder his prisoner in order to get out of paying the money. Then, true to his word, the lawyer disappears. There are witnesses to prove that he escaped voluntarily, and the banker keeps the letter locked in his fireproof safe as evidence that he was not responsible for the lawyer's disappearance. 

Next morning the watchmen ran in with pale faces, and told him they had seen the man who lived in the lodge climb out of the window into the garden, go to the gate, and disappear. The banker went at once with the servants to the lodge and made sure of the flight of his prisoner. To avoid arousing unnecessary talk, he took from the table the writing in which the millions were renounced, and when he got home locked it up in the fireproof safe.

The bet has had a strong effect on the characters of both men. Fifteen years of solitude during which the lawyer spent much time reading and meditating have turned him into a sort of holy man and prophet. These same fifteen years, during which the banker was losing most of his fortune and becoming gradually more anxious about having to pay his stubborn prisoner two million roubles, have made the banker lose his self-confidence and even his own self-respect. The moral of Anton Chekhov's story might have been drawn from the New Testament. In the "Sermon on the Mount" in Matthew 6, Jesus says:

19 Lay not up for yourselves treasures upon earth, where moth and rust doth corrupt, and where thieves break through and steal:20 But lay up for yourselves treasures in heaven, where neither moth nor rust doth corrupt, and where thieves do not break through nor steal:21 For where your treasure is, there will your heart be also.

Precalculus, Chapter 6, 6.5, Section 6.5, Problem 27

The trigonometric form of a nonzero complex number is
r*(cos theta +i*sin theta),
where rgt0 is the absolute value of a number and theta in [0,2pi).
Here r=sqrt(9+3)=sqrt(12)=2sqrt(3) and theta=arctan(sqrt(3)/3)=pi/6.

The answer: 3+sqrt(3)i=2sqrt(3)(cos(pi/6)+i*sin(pi/6)).

Calculus and Its Applications, Chapter 1, 1.3, Section 1.3, Problem 10

For the function $\displaystyle f(x) = 2x + 3$
(a) Determine the simplified form of the difference quotient
(b) Complete the table.

a.) For $\displaystyle f(x) = 2x + 3$
$\displaystyle f(x + h) = 2(x + h) + 3 = 2x + 2h + 3$
Then,

$
\begin{equation}
\begin{aligned}
f(x + h) - f(x) &= 2x + 2h + 3 - (2x + 3)\\
\\
&= 2x + 2h + 3 - 2x - 3 \\
\\
&= 2h
\end{aligned}
\end{equation}
$


Thus,
$\displaystyle \frac{f(x + h) - f(x)}{h} = \frac{2h}{h} = 2$

b.)


$
\begin{array}{|c|c|c|}
\hline
x & h & \displaystyle \frac{f(x+h)-f(x)}{h} \\
\hline
5 & 2 & 2 \\
\hline
5 & 1 & 2 \\
\hline
5 & 0.1 & 2 \\
\hline
5 & 0.01 & 2 \\
\hline
\end{array}
$

College Algebra, Chapter 5, 5.5, Section 5.5, Problem 36

In 1994, the Northridge, California earthquake had a magnitude of 6.8 on the Richter scale. A year later, a 7.2-magnitude earthquake struck Kobe, Japan. Determine how many times more intense was the Kobe earthquake than the Northridge earthquake.



Recall that the Richter Scale is defined as

$\displaystyle M = \log \frac{I}{S}$

where

$M$ = magnitude of the earthquake

$I$ = intensity of the earthquake

$S$ = intensity of a standard earthquake

For Kobe, Japan


$
\begin{equation}
\begin{aligned}

M_1 =& \log \frac{I_1}{S}
\\
\\
10^{M_1} =& \frac{I_1}{S}
\\
\\
S =& \frac{I_1}{10^{M_1}}
\qquad \text{Equation 1}

\end{aligned}
\end{equation}
$


For Northridge,


$
\begin{equation}
\begin{aligned}

M_2 =& \log \frac{I_2}{S}
\\
\\
10^{M_2} =& \frac{I_2}{S}
\\
\\
S =& \frac{I_2}{10^{M_2}}
\qquad \text{Equation 2}

\end{aligned}
\end{equation}
$


By using equations 1 and 2


$
\begin{equation}
\begin{aligned}

\frac{I_1}{10^{M_1}} =& \frac{I_2}{10^{M_2}}
&& \text{Multiply each side by } 10^{M_1}
\\
\\
I_1 =& \frac{10^{M_1}}{10^{M_2}} I_2
&& \text{Substitute given}
\\
\\
I_1 =& \frac{10^{7.2}}{10^{6.8}} I_2
&& \text{Evaluate}
\\
\\
I_1 =& 2.51 I_2 \text{ or } 2.50 I_2

\end{aligned}
\end{equation}
$



It shows that the earthquake had struck in Kobe, Japan is $2.50$ more intense than the earthquake that hit Northridge.

What is a plot summary of Crime and Punishment?

Crime and Punishment by Fyodor Dostoyevsky is the story of a young man who decides to kill a pawnbroker in order to take her money and ends up killing her sister as well. He then suffers guilt over what he's done until he confesses to the crime and is sent to jail in Siberia.
The story takes place in Saint Petersburg, Russia and concerns Rodion Raskolnikov, who was once a student but now lives poor and without much income. He convinces himself that he can murder Alyona Ivanovna, a mean pawnbroker, in order to steal her money and do good for society—and himself—with it. In the process, he kills her sister, who walks in on the crime scene. He doesn't even get away with the money, only stealing a few things.
While he got away without being seen, Raskolnikov suffers the effects of his conscience. He worries constantly that he'll be caught and tries to hide the evidence of his crime. He becomes ill from his guilt, acting increasingly suspiciously. He meets Sonya, a virtuous prostitute and the daughter of a man he helped with the money he stole.
The detective in charge of the case, Porfiry, suspects Raskolnikov but has no evidence. When another man confesses to the crime, Raskolnikov thinks he may have gotten away with it again—but there's no reprieve from his guilt. This is when he confesses to Sonya. The confession is overheard by a man obsessed with Raskolnikov's sister, Dunya. The man says he may someday this information against Raskolnikov.
Sonya urges Raskolnikov to confess. His sister's obsessive suitor kills himself after realizing he can never be with Dunya, freeing Raskolnikov from the fear that he will expose him. He considers not telling the police the truth, but he ultimately decides that Sonya is right and that confession is the right thing to do.
Raskolnikov is sentenced to eight years in prison in Siberia. Sonya accompanies him and helps him heal his wounded moral character. His mother dies in illness and shame in light of his actions. His sister, Dunya, marries his friend.

Why did axel not want to go on the trip?

Journey to the Center of the Earth is a novel by Jules Verne, originally published in French in the year 1864. The story is narrated by Axel Lidenbrock, a young man who lives in Hamburg, Germany with his uncle Otto Lidenbrock, a professor of mineralogy.
Axel assists Otto with his experiments, and definitely takes after his uncle in terms of having a scientific mind. As he says himself:

I will admit that I devoured geological science with great relish; I had mineralogist’s blood in my veins, and never felt bored in the company of my precious pebbles.

When Otto finds a manuscript written in Icelandic runes in a shop, he takes it home, and a separate piece of parchment with a message jumbled in a runic code falls out. Axel, almost by accident, figures out how to decode its secret message before Otto does. Axel reads it and finds that the message describes a way to travel in order to reach the center of the earth. Knowing immediately that his Uncle will want to take this journey, he says the following:

‘No! I’m not going to tell my uncle. It would be terrible if he got to know about such a journey. He’d just want to have a go himself. Nothing would stop a geologist of such determination. He would leave anyway, against all obstacles, whatever the cost. And he’d take me with him, and we wouldn’t come back. Never. Not nohow!

Later on, after Axel eventually gives in and tells his uncle how to read the code, and Otto declares that they're going to go on this journey, Axel tries to reason with him, saying:

All right, I accept that this Saknussemm wrote the message, but does it necessarily follow that he actually carried out the journey? Couldn’t the old parchment just be a practical joke?’

And so, we see that Axel does not want to try to go to the center of the earth because he doesn't fully believe that the feat is possible, and thinks that they would die trying.
(Note that any quotes I used in this answer may be slightly different from the ones in your own copy of the book, as there are multiple different English translations of Journey to the Center of the Earth.)

What is the leader of the caravan's key trait in The Alchemist?

The caravan leader's main character trait is his incredible patience. As part of his job as a camel driver, he regularly needs to traverse vast distances across the harshest of deserts. And to do this successfully, he needs to have extraordinary reserves of patience. As with many people that Santiago meets on his travels, the caravan leader imparts numerous pearls of wisdom, derived from years of experience. The caravan leader lives in the moment, something that protects him from fear. As fear can only be fear of the future, the camel driver, by living in the here and now, is inured against it.
The camel driver's patience comes in handy when leading his vast convoy through the desert. As well as Santiago, there are many other people accompanying him on the potentially perilous journey across the burning sands. Although the caravan leader is a Muslim, he recognizes that the members of his convoy profess many different faiths, and so he encourages them to pray to whichever deity it is that they choose to worship. The caravan leader's patience leads to tolerance, which in turn makes it more likely that everyone will work together to make a success of the journey.

Calculus: Early Transcendentals, Chapter 2, 2.3, Section 2.3, Problem 27

lim_(x->0) (4 - sqrt(x))/(16x - x^2)
sol:
lim_(x->0) (4 - sqrt(x))/(x(16 - x))
=> lim_(x->0) (4 - sqrt(x))/(x(4^2 - (sqrt(x))^2))
=> lim_(x->0) (1)/(x(4 + (sqrt(x))))
as x-> 0
and now let us check whether
lim_(x->0^-) ((1)/(x(4 + (sqrt(x))))) is equal tolim_(x->0^+) ((1)/(x(4 + (sqrt(x)))))
so,
lim_(x->0^-) ((1)/(x(4 + (sqrt(x)))))
= (1/0^-) = -oo
and
lim_(x->0^+) ((1)/(x(4 + (sqrt(x)))))
= 1/0^+ = +oo ,
As ,lim_(x->0^-) ((1)/(x(4 + (sqrt(x))))) != lim_(x->0^+) ((1)/(x(4 + (sqrt(x)))))
so limit doesnt exist

What is the theme of "The Yellow Wallpaper" by Charlotte Perkins Gilman? Does it have a motif of creativity vs. insanity?

"The Yellow Wallpaper" by Charlotte Perkins Gilman is a quasi-autobiographical story about a rest cure prescribed for what was diagnosed in her period as a "nervous disorder". The protagonist of the story is portrayed as undergoing such a cure and going slowly insane over the course of the story. As we read it, though, we begin to understand that the so-called cure resembles something like the solitary confinement of prisoners or sensory deprivation, something we now understand as more likely to result in than to cure mental disorders.
The main theme of the story is the tension between the active creative role of the artist or writer and the passivity expected and limited opportunities available for women in Gilman's period. As the protagonist is confined, her creativity manifests itself in creating a story born in hallucination rather than one crafted in words. Thus we are led to understand that the creative imagination when thwarted in its need to create may escape into insanity. 
Shakespeare famously stated 

... the poet’s pen ... gives to airy nothing
A local habitation and a name.

Gilman argues that the creative urge, when deprived of its outlet in artistic creation, will turn to madness. 

What contributed to the rapid industrialization of America?

Technology was a factor that contributed to the rapid industrialization of America.
In the period following the Civil War, technology played a very large role in the industrialization of America.  For example, the technology behind the Bessemer process contributed to rapid economic growth.  The Bessemer process helped to produce vast quantities of steel in an inexpensive manner. This steel became an invaluable resource in industrialization. Technology in the form of transportation helped to economically transform America, as well.  The development of the Transcontinental Railroad unified the nation through the railways.  The result was that goods could be easily transported across America and this helped to facilitate industrialization in America.
Another technological advancement that helped to industrialize the nation was in Henry Ford's embrace of the assembly line.  This method increased production of automobiles while maximizing efficiency.  Finally, Edison's invention of the light bulb was another example of how technology contributed to American industrialization.  With the light bulb, industrialization growth could take place at any given time.  Industrial expansion was no longer limited by sun light.  
These technological advancements were critical in the rapid transformation of the nation from farms to factories.   As a result, economic growth advanced at a very rapid rate and helped to catapult America into a dominant industrial power.

How does Anna's meeting her second husband affect her intellectual growth in "The Leap"?

In "The Leap," Anna's mother meets her second husband while recovering in hospital from her accident as part of the Flying Avalons. He is a doctor, and he is called in to look at her mother's arm, which was broken during her fall.
At this point in the story, Anna's mother is unable to read and write. Being stuck in the hospital, however, she becomes so bored that she decides to learn, and it is the doctor who teaches her. According to Anna, he grades her first exercises in return for hearing the stories of her adventures as part of the Flying Avalons. The doctor also buys Anna's mother her first book, a sign of his commitment to her education.
So, Anna's mother and the doctor not only fall in love, but he contributes to her intellectual development by teaching her the important skills of reading and writing.

Anna Avalon of the Flying Avalons was illiterate when she goes to the hospital to be treated for her injuries resulting from her burns and broken arm in the fall under the circus tent. There, Anna met a doctor who taught her to read, and new worlds opened for her.
Acting as narrator, Anna's daughter states that during her mother's stay in the hospital, she and her physician husband exchanged "one form of flight for another." That is, her father offered Anna the metaphoric flight from the darkness of illiteracy through a world of books and the ability to write and express herself more proficiently. In trade, Anna offered her husband the "flight" of imaginary travels throughout the world as she related her experiences in the world's cities.
Since learning to read, Anna has not been "without a book." When blindness befalls her, her inability to read has been a difficulty she can only overcome with the help of another. Her daughter, whose life she once saved from their burning house, has returned to care for and read to her:

I came home to read to my mother, to read out loud, to read long into the dark if I must, to read all night.

There is no doubt that Anna Avalon is the richer for having met her husband who fostered her intellectual growth, a growth which continues even after she loses her sight.

Why did Peter Brook’s production of The Mahabharata offend some critics and audiences?

Peter Brook released his production of the Hindu epic in the U.S., although the French restaged it multiple times. Brook was already a well established master of contemporary theater whose work drew on multicultural sources. For the first time, however, he completely re-interpreted an established, foundational work of an Asian culture.
Both the script and production, as well as Brook's explanations, drew criticism. He seemed almost unaware that the idea of appropriation existed, justifying his choices by referring to his extensive knowledge gained by travel.
The script was developed by a French writer with little direct input from Indian professionals. The basic decision to condense multiple volumes into a shorter work was also problematic, though some complained it was bad theater because it was too long, running 8 to 11 hours.
Frank Rich in the New York York Times (October 19, 1987) found fault with the oversimplified content in combination with overcomplicated staging, as performed in New York. He thought that the essential importance, which was primarily its "moral substance" had been boiled down to superficial sermons and homilies that Western audiences might digest, and could not capture any "enigmatic Hindu concept." The idea of universalism he also found forced, as complexity was "watered down to knock international audiences over the head." On the production itself, he was the harshest, calling the techniques a "smorgasbord of Oriental stagecraft."
https://www.nytimes.com/1987/10/19/theater/stage-from-brook-the-mahabharata.html

The main criticism leveled against Peter Brook's 1985 production of The Mahabharata is that it was culturally appropriative and orientalist.
The play, written by Jean-Claude Carriere, a Frenchman, and staged by Brook, an Englishman, takes for its source material the Sanskrit epic of the same name. Critics of the play found its treatment of Indian myth to be reductive and offensive, while others, including the New York Times review from the time, praised Brook for making the stories accessible across cultures.
Cultural appropriation is a sociological concept defined as a dominant culture adopting elements of a minority culture. It's easy to see why one might accuse Brook of cultural appropriation for his portrayal of Indian culture that was designed for a Western audience and told through his Western lens.

When Stanley is leaving, do the other boys at camp show guilt for their earlier actions towards him?

In Chapter 48 of Louis Sachar's Holes, Stanley and Zero see the other campers for the first time since their harrowing ordeal as Stanley's lawyers free Stanley from the camp and assure him that there will be an investigation into how it was being run and that Zero will be safe. Most of the boys from Group D—Armpit, Squid, Magnet, Zigzag and Twitch, but not X-Ray, who remains in the other room—express excitement that Stanley and Zero survived the desert, a feat they didn't believe to be possible. They are also congratulatory rather than resentful that Stanley is being released, which is a far cry from how they would have behaved when Stanley first arrived at camp, which implies a degree of unspoken remorse. The only one of the boys to explicitly express guilt and ask forgiveness, however, is Zigzag, who says, "Sorry about... you know." Stanley forgives him with a simple, "It's cool."

int cot^4(theta) d theta Use integration tables to find the indefinite integral.

Indefinite integral follows the formula: int f(x) dx = F(x)+C
where:
f(x) as the integrand function
F(x) as the antiderivative of f(x)
C as constant of integration.
 The given integral problem: int cot^4(theta) d theta resembles one of the formulas from the integration table. It follows the integration formula for cotangent function as :
int cot^n(x) dx = - (cot^((n-1))(x))/(n-1) - int cot^((n-2)) (x) dx .
Applying the formula, we get:
int cot^4(theta) d theta =- (cot^((4-1))(theta))/(4-1) - int cot^((4-2)) (theta) d theta
                  =- (cot^3(theta))/3 - int cot^2(theta) d theta
 To further evaluate the integral part:  int cot^2(theta) d theta  we may apply  trigonometric identity: cot^2(theta) =csc^2(theta) -1 .
int cot^2(theta) d theta =int [csc^2(theta) -1] d theta
Apply basic integration property: int (u-v) dx = int (u) dx - int (v) dx.
int [csc^2(theta) -1] d theta =int csc^2(theta) d theta - int 1 d theta
                                     = -cot(theta) - theta +C
Note: From basic integration property: int dx = x  then int 1 d theta = int d theta = theta .
From the integration table for trigonometric function, we have int csc^2(x) dx = - cot(x)  then int csc^2(theta) d theta=-cot(theta ).
applying int [cot^2(theta)] d theta=-cot(theta) - theta +C , we get the complete indefinite integral as:
int cot^4(theta) d theta =- (cot^3(theta))/3 - int cot^2(theta) d theta
                           =- (cot^3(theta))/3 -(-cot(theta) - theta) +C
                          =- (cot^3(theta))/3 + cot(theta) + theta +C

Melissa Sordino is the protagonist in "Speak" by Laurie Halse Anderson. Imagine you were to go through Melinda's trash. What might you find and why?

What an interesting assignment! This particular project may help us chart Melinda's emotional growth as the story progresses.
One of the first items we may find in Melinda's trash is the piece of paper with the word "tree" on it. If you recall, Melinda isn't too excited about her art assignment. Since she already knows how to draw a tree, Melinda doesn't think that the assignment will be beneficial or educational in any way. Look for her to throw away the scrap of paper as soon as she can.
The next item we may find in Melinda's trash is one of her mother's kitchen counter notes. This one says "Pizza, 555-4892. Small tip this time." Melinda admits that it's a family practice to communicate with notes; however, the notes are impersonal, and it is obvious that Melinda feels the lack of authentic discourse within the family circle. Her frustrated "What else is there to say?" speaks volumes about her feelings of alienation.
Another item we may find in Melinda's trash is the pom-pom Heather handed her before the Homecoming pep rally. Melinda isn't especially enthused about the rally, but she goes along to please Heather. Sadly, she finds that her friends and classmates are less than understanding about her actions at Kyle Rodger's party the previous summer. For her part, Melinda is too emotionally drained to explain why she called the police. The pom pom represents a school community that has essentially turned its back on her, and it is also a reminder that she will never be like her cheerleader classmates, the Girls Who Have It All. Hence, the pom pom would likely end up in her trash.
The next items that may possibly end up in Melinda's trash are various drawings of trees. You may recall our protagonist's art assignment. Melinda is completely frustrated with her inability to create meaningful art. Her frustration stems from her repressed emotions, but she has difficulty understanding this until later in the story. Her trash bin would likely contain discarded drawings of trees.
Another item we may find in Melinda's trash is the results of a personality assessment test on Job Day. Melinda's test results declare that she should consider careers in forestry, firefighting, communications, and mortuary science. Of course, none of these interest her, and the results seem to be a distressing judgment about her potential in the future. Hence, we may find the results of this assessment test in Melinda's trash.
Yet other items we may find in Melinda's trash are all the calendars she bled on. During her winter break, Melinda finds herself working at her father's office. She is tasked with putting all the calendars into envelopes, sealing them, and then putting mailing labels on them. When the sharp edge of an envelope cuts her tongue as she licks it, Melinda bleeds onto some of the calendars. Her father is furious, so these calendars would probably end up in the trash, whether Melinda discards them at the office or in her own trash bin at home.
As the story progresses, Melinda's grades continue to drop. Her spring semester grades show her failing a few of her classes and getting D grades for the others. The only class she excels in is Art, where she receives an A. It may be conceivable to find Melinda's report card in the trash, as her failing grades are a devastating reminder that her life is falling apart.
Hope this helps! See if you can find the last three items on your own.

Calculus of a Single Variable, Chapter 9, 9.2, Section 9.2, Problem 9

sum_(n=1)^oo n/(n+1)
To verify if this infinite series diverges, apply the Divergent Test.
In the Divergence Test, it states that if the limit of a_n is not zero, or does not exist, then the sum diverges.

lim_(n->oo) a_n != 0 or lim_(n->oo) = DNE

:. sum a_n diverges

So, taking the limit of a_n as n approaches infinity yields:
lim_(n->oo) a_n
=lim_(n->oo) n/(n+1)
=lim_(n->oo) n/(n(1+1/n))
=lim_(n->oo) 1/(1+1/n)
=1/(1+0)
=1
Since the result is not equal to zero, therefore, the series is divergent.

What do Simon and Rosh have in common? How are they different?

Simon and Rosh are both extremely driven by their personal beliefs. Simon is one of Jesus's twelve disciples, often titled "Simon the Zealot." It's important to note this because there were two disciples named Simon—Simon Peter, who walked on water with Jesus, and Simon, known as the Zealot. This story includes the character of Simon the Zealot.
Zealots refer to early (first-century) Jewish people who were seeking to overthrow the Roman government. They were rebel leaders who believed that the Roman government was encouraging people to stray away from God. They were so passionate about their beliefs that they were willing to do just about anything, including acts of violence, to overthrow the new political leaders.
Simon the Zealot, however, was passionate but not violent in his pursuit of political and religious change. He was striving for freedom from Rome, but his goal was to act in love, like Jesus taught, rather than through violent acts. Because he met Jesus, he no longer believed that violence was the answer. He realized that his faith, as an Israelite, was changing because of Jesus's teachings. His beliefs were radically changed because of his relationship with Jesus. Daniel, however, still wants to use violence to aim for revolution. He wants to seek revenge for the horrible acts that the Romans committed that affected his family and friends. After meeting Jesus, Simon works for love and peace. His zealousness, or passion, is turned toward spreading God's love and grace.
Rosh, too, is a leader, but he leads a group of rebels. For a while, when Daniel ran away from his master, Rosh cared for his needs. Daniel views Rosh as a good man at the start of the story, just as he views Simon the Zealot as a good man. As time goes on, though, Daniel realizes that Rosh's violent pursuit of freedom is not what he agrees with. He sees how selfish Rosh's pursuit is, especially when Rosh refuses to help free Joel from the Romans. His selfishness contrasts greatly with Simon the Zealot's love (that he adopted from Jesus's teachings).
While both leaders greatly impact the story, sometimes seek to help others, and are pursuing freedom from Roman rule, Rosh always pursues this freedom through violent rebellion. Simon the Zealot may have once thought that violence was the answer but realizes that love is the true answer when he meets and follows Jesus. Daniel, the protagonist of the story, agrees with Simon Zealot that love is the path to true freedom by the end of the novel.

Calculus: Early Transcendentals, Chapter 1, 1.6, Section 1.6, Problem 26

Determine a formula for the inverse function $\displaystyle y= \frac{e^x}{1 + 2e^x}$

To find the inverse of $f$, we must first write
$\displaystyle y = \frac{e^x}{1 + 2e^x}$
Then we solve this equation for $x$

$
\begin{equation}
\begin{aligned}
y ( 1 + 2e^x) &= e^x\\
\\
y + 2e^x y &= e^x\\
\\
2e^x y - e^x &= - y\\
\\
e^x(2y - 1) &= -y\\
\\
e^x &= \frac{-y}{2y - 1}\\
\\
\ln e^x &= \ln \left[ \frac{-y}{2y - 1} \right]\\
\\
x &= \ln \left[ \frac{-y}{2y - 1} \right]
\end{aligned}
\end{equation}
$


Finally, we interchange $x$ and $y$:
$\displaystyle y = \ln \left[ \frac{-x}{2x - 1} \right]$

Therefore, the inverse function is
$\displaystyle f^{-1}(x) = \ln \left[ \frac{-x}{2x - 1} \right]$

For an assignment for English, what visual representation can I make for the story of Macbeth? The visual representation needs to be of a symbol that is not obvious in the story. This is supposed to be a visual essay with a thesis.

In terms of an "obvious" symbol, I imagine you are being advised to avoid using the dagger Macbeth sees before him or superficial representations such as castles or Highland landscapes, which might represent the setting but do not represent the core of the story. Personally, I would argue that the best symbol you could use to represent Macbeth visually would be blood.
Blood recurs throughout the story as a motif, and it has multiple meanings. Blood as a representation of guilt—the "blood on my hands" concept—pervades the story, both before and after the actual murder is completed. When Macbeth is mustering the courage to kill Duncan, he imagines a dagger before him that represents the instrument with which he will commit the murder, but, more importantly, as he contemplates the deed, he begins to see "on thy blade and dudgeon gouts of blood." Macbeth determines that although the dagger is not real, "it is the bloody business" of the murder that is making the dagger appear to him. Blood is a symbol offered to Macbeth within the play by his own "heat-oppressed brain," and it symbolizes guilt.
Later, when he has killed Duncan, Macbeth questions whether "all great Neptune's ocean" could "wash this blood / Clean from my hand?" He feels sure that the evidence of his guilt, as represented by the blood, is so obvious that it will indeed stain all it touches: if he were to touch the sea, it would turn red.
At first, Lady Macbeth tells him he is being ridiculous, saying that although her hands, too, are "of your colour," her heart is not "white" as Macbeth's heart is. Later in the play, however, we see the symbol of blood rise again; when Lady Macbeth succumbs to her guilt and begins to go mad, she muses while sleepwalking, "who would have thought the old man to have had so much blood in him?" The blood here seems to represent not only Duncan's literal blood, but the following question: who would have thought that murdering him would create such an endless ocean of guilt? Lady Macbeth echoes her husband's earlier plaint when she says, "will these hands ne'er be clean?"
At the end of the play, when Macduff and Macbeth are about to fight to the death, Macduff rightly calls Macbeth "thou bloodier villain / Than terms can give thee out!" It is as if he is recognizing the extent to which Macbeth's guilt has been painted upon him in the form of blood, both literally and metaphorically.

What is the difference between race and ethnicity?

There are few situations where word choice matters more than in discussions of race and ethnicity.
Most people associate race with biology and ethnicity with culture. It's important to stress the culture and language part of it. Ethnicity isn't just a question of affiliation; it's also a question of choice. It's also a question of group membership. And it's usually associated with a geographic region. It's also often confused or conflated with nationality, but that's not the same thing.
Today people identify with ethnicity positively because they see themselves as being part of that group. People can't just simply say, "Well, I want to become a member of that race." You either are or are not a member of that race. Whereas, if you wanted to look at ethnicity based on culture, you could learn a language, you can learn customs - there are things that you can learn so that you could belong to that group. 
In summary, race refers to physical characteristics, like skin color or hair texture and ethnicity refers to cultural characteristics that are not always visible, like language and religion.

Even though ethnicity and race have similarities with regard to the notion of common ancestry, they have differences in various ways. Only few among us could correctly state the differentiation between race and ethnicity. This is due to the fact that we tend to group them into the same type of definition. Even though the dictionary could show that these two terms are similar, they are in fact different. The definition relating to ethnicity and race is linked respectively to sociological and biological factors. Ethnicity refers to cultural factors such as language, ancestry, regional culture and nationality. Race on the other hand is defined as that which states an individual's physical characteristics like bone structure, texture, hair color, skin color, and so on.
 
The primary difference between race and ethnicity is that while race is fundamentally unitary—meaning you could have only a single race, you could have several ethnicities. One could ethnically identify as Polish and Irish, however one has to be either white or black. The predominant differentiation between race and ethnicity is that race is hierarchical and imposed socially. Inequality is ingrained within the system.  One could have no control over the race. This is how one is being identified by others. A strong difference between ethnicity and race is that race tends to be institutionalized in a manner which has major social impacts on the members of various groups.
 
Another difference is that around the world and throughout history there have been ferocious conflicts among ethnic groups. However in most of the countries, majority of the ethnic groups would peacefully get along well. In comparison to ethnic conflicts, prejudice in the name of race continues to be an issue around the world. Yet another differentiation is that while ethnicity could be mimicked or changed by means of beliefs and choices; race cannot be changed. Ethnicity provides us the opportunity to alter since we could end up rejecting our own and could grab another. One could advance from one region to another and absorb customs, actions and beliefs for identifying with that particular ethnicity. However one would not be able to do that with race. Ethnicity could be hidden or displayed, based on personal choices; however racial identities would be on display always.

Both race and ethnicity are social constructions. However, the latter is a connection forged on one's sense of belonging to a particular country (i.e., nationality), as well as a shared language, cultural traditions, and ancestral lineage. Groups of people may live within the same borders but may not share a common ethnic identity. Ethnic difference exists in presumably homogeneous countries, such as China.
Race is an idea of human difference born out of a group's shared physical traits (e.g., hair color, eye color, skin color) and ancestral lineage. Biologically, there is no such thing as race. Our physical differences developed as a result of adaptation and natural selection. For example, Northern Europeans with blond hair and blue eyes developed these traits so that their bodies could absorb Vitamin D from sunlight more efficiently, due to the lack of direct sunlight in countries such as Germany or Denmark. However, the natives of these countries are still, like all human beings, descended from a common ancestor in prehistoric Central Africa: Mitochondrial Eve, the veritable mother of the entire human race.
In the eighteenth century, pseudosciences emerged which helped to establish the idea of separate races based on certain physical traits, such as skull size (e.g., craniometry). Notions of the "inferior" intelligence and character of some groups (e.g., Africans) versus the "superior" intelligence and character of other groups (e.g., Europeans) emerged at this time, as did the designation of European peoples as "Caucasian," a moniker based on the belief that all European peoples originated in the Caucasus. 
Genetically, we can identify ethnicity. Race is a bit trickier. With the popularity of genetic testing, people are finding that their lineages are a bit more complicated than they may have believed. For example, people who appear to be primarily of African descent sometimes find, through DNA testing, that they have more ancestors from European countries than from African ones. Famously, the historian and genealogist Henry Louis Gates, Jr. discovered this truth about himself through genetic testing. 
Now, one would think that a man who discovers that more than half of his ancestry is European would identify as such. Yet, the fact remains that Gates appears to be a black man. The assumption of one's race is based mainly on appearance —not origins or genetic lineage. Ethnicity can help to determine race, but it is not a decisive factor.

Can I have a detailed analysis of Jennings's poems "Poem in Winter" and "Fishermen" in terms of language/structure/tone/ imagery/symbols?

Jennings's 15-line poem "Poem in Winter" uses winter snow as a symbol to stand for the simple hopes of children as they look for "auguries." Using simple language, she compares their hopes to adult hopes, as adults wait "behind a pane of glass." The pane is a metaphor representing the way in which adults protect themselves from the world. She also uses alliteration in lines such as "falling of flakes" to create a lyrical tone. The image of children waiting for the snow to fall evokes the idea that children are ready to experience the world in a way adults are not, as they hide behind glass.
Jennings's "Fishermen" is also simple in its language and also evokes a tone of peace and patience. In this poem of three stanzas (the first composed of seven lines and the second two composed of six lines), fishermen sit patiently by the river and exult in the uncertainty of their catch, not caring if they catch a fish or not. The fishermen are compared to boys who have no patience and often draw up empty nets. The poem uses a number of images, including that of the fish once they are caught, "so solid and on the bank and still." This line uses alliteration, or the repetition of the initial sounds of words, to create a lyrical and peaceful feel ("future frogs" in the third stanza is also an example of alliteration).The poem also uses a metaphor in which the fish are compared to "inquiries in the river." While swimming around, the fish represent promises and questions that are not yet answered.

How does Douglass's perspective change over My Bondage and My Freedom in chapter 17 (XVII: The Last Flogging)? How does this perspective carry over to "What to the Slave Is the Fourth of July?"

In chapter 17 of Frederick Douglass's memoir, he describes an incident wherein, feeling bolstered by a "magic root" given to him by a kind friend, Sandy, he meets in the woods, he returns to Covey, a man who has abused him in the past. Douglass does not really believe in the power of the root, but his time in the woods with Sandy and his wife has made him feel connected to his other "brother in bondage," and it is in this spirit that he decides to resist when Covey, a white man, attempts to hurt him again. Where previously, a word from Covey could have made Douglass "tremble like a leaf in a storm," now he feels suddenly imbued with spirit, forgetting that he is black and Covey is white and experiencing the two of them, for the first time, as simply two men. It is evident, too, that Covey is afraid that he will not be able to win the battle, as he calls to various others for help and, ultimately, Douglass is able to overcome him. This has the effect of breaking Covey's hold over Douglass, but more importantly,


this battle with Mr. Covey,—undignified as it was, and as I fear my narration of it is—was the turning point in my "life as a slave." It rekindled in my breast the smouldering embers of liberty; it brought up my Baltimore dreams, and revived a sense of my own manhood. I was a changed being after that fight. I was nothing before; I WAS A MAN NOW. It recalled to life my crushed self-respect and my self-confidence, and inspired me with a renewed determination to be A FREEMAN.


Douglass is reminded that he is, indeed, a man and not a piece of property, and moreover, a man as strong as any white man. After this fight, Covey does not take Douglass to the authorities, which Douglass infers is because of embarrassment on Covey's part—he does not want others to know that he has been unable to control a black youth, who most would think "inferior." But to Douglass, this fight serves as a reminder that those who want their freedom must strike the first blow.

In "What to the Slave is the Fourth of July?" we see Douglass continue to use this understanding to power his rhetoric. First, he discusses the fact that, in order to gain their freedom, white Americans were forced to strike a blow against the home country, because "oppression makes a wise man mad." Douglass appreciates and approves of the behavior of the Founding Fathers, but questions why those in the audience would "drag a man in fetters into the grand illuminated temple of liberty." Now with a strong belief in his own worthiness as a man, and in the right of the oppressed to seek liberty, Douglass feels it is hypocritical to expect "the negro" to feel in any way part of the Fourth of July celebrations. On the contrary, he feels that it is pure hypocrisy to celebrate a free nation and yet continue to oppress a significant black population within that nation.

Douglass argues that, in the way slaves are punished for severe crimes, there is already an acknowledgement that slaves are men, rather than animals or property:


There are seventy-two crimes in the State of Virginia, which, if committed by a black man, (no matter how ignorant he be), subject him to the punishment of death; while only two of the same crimes will subject a white man to the like punishment. What is this but the acknowledgement that the slave is a moral, intellectual and responsible being? The manhood of the slave is conceded. It is admitted in the fact that Southern statute books are covered with enactments forbidding, under severe fines and penalties, the teaching of the slave to read or to write. When you can point to any such laws, in reference to the beasts of the field, then I may consent to argue the manhood of the slave. When the dogs in your streets, when the fowls of the air, when the cattle on your hills, when the fish of the sea, and the reptiles that crawl, shall be unable to distinguish the slave from a brute, then will I argue with you that the slave is a man!


In affirming "the equal manhood of the Negro race," Douglass enumerates the many ordinary pursuits a slave takes on in his or her lifetime as an example of how ridiculous it is to expect slaves to "prove that we are men." And yet, America has already declared that to enslave a man is wrong, yet maintains slavery on the pretense that black slaves are not men. Douglass's position points out the inherent hypocrisy in the system. His rhetoric—"it is not light that is needed, but fire; it is not the gentle shower, but thunder"—emphasizes his strength of conviction and the spirit of self-belief which first dawned upon Douglass on the day he fought with Covey, as detailed in his memoir.

Critically discuss how Douglass’s Narrative might be read as a meditation on the multiple meanings of freedom.

Frederick Douglass has a deeper understanding of freedom than the simple manumission of slaves. Throughout the Narrative, Douglass links the formal freedom of slaves with a fuller, deeper, more spiritual sense of freedom that elevates the soul and allows free men and women to reconnect with their suppressed humanity.
Douglass sets out in painstaking detail his many, and often brutal, experiences of slavery. However, his personal testimony is not just a litany of woes; Douglass is anxious to inspire those fellow African Americans still enslaved. To that end, he must give them hope, however remote a prospect it may seem. Each experience, then, must reveal that his spirit cannot be broken, no matter how hard slavers try to destroy him. He may not have had legal freedom throughout his enslavement, but he still retained his inner, spiritual freedom. Ironically, his slave masters lack this freedom while still holding the whip. Their souls have been corrupted by active participation in the "peculiar institution." They are forced to cling to a willful distortion of Christianity in order to justify slavery and their involvement in it.
Douglass's notion of freedom is not abstract; indeed, he is intensely suspicious of the highly abstract concept of freedom upon which the United States was founded. The reason for this is that it coexists with the brutality of slavery, the ultimate negation of liberty. Douglass understands freedom in concrete, practical terms. In the Narrative, he proffers a number of routes to achieving it, such as escaping to a Northern city, for example. Life is far from rosy up there, especially for a black man, but it is still much better than toiling away on a Southern plantation.
Douglass also values education as a means to achieve freedom. By learning to read and write, he has been given a glimpse of freedom. However, this knowledge can be a curse as well as a blessing. It makes him all the more frustrated because, despite his newfound knowledge, he still cannot escape. It takes an act of violence against Mr. Covey, his slave master, to give him the confidence fully to attain freedom. In doing so, he begins to realize his humanity.
The idea of freedom emerging from the Narrative has a number of components, all of them practical: education, community solidarity among African Americans, alliances with white abolitionists, and a strong sense of rebellion. Yet, all these elements are ultimately a means to an end. The end is to allow African Americans to get in touch with and share an underlying humanity from which they have been systematically excluded for so long.

Despite Watergate, did Richard Nixon's presidency start the Republican ascendency of the following period? Why and how did this happen?

Despite Watergate, Nixon established the Republican ascendancy that followed him. Nixon claimed to represent what he called the "Silent Majority," by which he meant the conservative white Americans who had not benefited from the liberal policies of Kennedy and Johnson. By the time of Nixon's election in 1968, many white Americans felt left out and disregarded by the federal government. They felt that policies such as Johnson's War on Poverty were not aimed at helping them, and they also resented federal regulations and were eager to see them repealed or rolled back. In addition, growing inflation and the sense that Vietnam was going to be a lost cause made them eager for a stronger America, militarily and economically.
Although Carter, a Democrat, won the election in 1976, Republicans after Nixon, including Reagan and the Bushes, won office using many of Nixon's strategies and building on his appeal to the white voters who felt that the federal government had abandoned them and had jettisoned the idea of a strong America. For example, Reagan's 1984 promise that "it's morning in America again" was designed to restore American voters' faith that the U.S. could be an economic and military powerhouse, as it had been in years past. Nixon and his Republican successors established the idea that Democrats were associated with international and economic weakness, while Republicans could bolster the economy and the American military. 

When told in essay writing to write an essay with no less than 450 words, how do I know when it is 450 words or less? This is for taking the WAEC, so it's for their marking scheme.

Standardized tests can be so hard! Especially when they are taken on paper rather than computer, estimating your word count can be difficult. The WAEC does require your essay to be a minimum of 450 words, and any words above that number do not influence your score in any way. So how do you figure out how many words you have written without wasting valuable time counting each word?
Generally speaking, one single spaced, hand-written page comes to about 100 words. Since everyone’s handwriting is different, though, you could count the number of words on three or four of your pages during your test prep in order to give yourself an idea of how many words are on your hand-written pages. If you don’t have time to do that (if you are taking the test very soon), you can count the number of words on the first five lines of your essay and divide that number by five (to get the average number of words per line). Then take the average number of words per line and multiply it by the number of lines in your essay.
This second option may still take too long if you are doing it during the examination. I recommend trying to figure out about how many words you write on a page before you go in to take the test, and then using that number to estimate the word count of your essay. If you do write about 100 words per page, then you know you need four and a half or five pages to make the 450-word minimum.
I’ve included a link to the WAEC Online webpage below. Good luck!

How does Boyle's The Tortilla Curtain explore what it is to be an American? What questions are raised about immigration and national security?

In The Tortilla Curtain, to be American means to be overcome with fear regarding the reality of immigration.  Boyle raises significant questions about whether this insecure mindset towards immigration can effectively address it.
Boyle uses the Mossbachers as representative of the modern American identity regarding immigration.  Inside the comfortable world of Arroyo Blanco Estates, immigration is spoken about in positive terms. Boyle shows that people like the Mossbachers hold an abstract approach that is rooted in the "not in my backyard" approach.  As long as the issue of immigration is away from them, it is viewed as an acceptable aspect of American life.
Boyle shows that when challenges arise, American identity takes a fearful approach towards immigration.  The Mossbachers abandon liberal optimism and embrace a darker approach to immigration when economic and social issues present themselves.  They view immigration as a threat to their lifestyle and their world.  The Mossbachers accept nativist generalizations about immigrants such as "the more you give them the more they want, the more of them there are" or "they were ubiquitous, prolific as rabbits," and "they were death for business" as truth.  Boyle suggests that when economic and social interests are threatened, American identity becomes inwardly drawn, retreating to fear about immigration.  No better is such pessimism shown than in the community's desire to build the wall. When Kyra and Delaney accept the need for the fence to wall off the community, it is clear that it is more psychological than anything else: “This is a community . . . an exclusive private highly desirable location. And what do you think’s going to happen to property values if your filthy coyotes start attacking children.” 
Boyle shows how the desire to build the wall around Arroyo Blanco Estates reflects something deeper about American identity.  The wall is rooted in the desire to keep immigrants out.  However, it also reflects a desire to stop the world's changing dynamics.  The community's residents cannot accept the reality of a changing world:

... All Delaney’s neighbors could talk about, back and forth and on and on as if it were the key to all existence, was gates….To be erected at the main entrance and manned by a twenty-four-hour guard to keep out those very gangbangers, taggers and carjackers they’d come here to escape.

American identity is depicted as a flight from a changing world.  Rather than seek to understand it, American identity is shown to run from it.  Boyle views the Mossbachers as part of the growing demographic incapable of effectively dealing with a changing America.  It is an America that looks, behaves, and expresses itself differently than it did in the past.  Struggling to adapt to this difference is another part of how Boyle sees American identity in the modern setting.
The Tortilla Curtain raises questions about immigration and national security. One centers on the role of wealth.  Boyle's depiction of the Rincons and the Mossbachers is a tale of two different realities.  The consolidation of economic wealth in the world of Arroyo Blanco Estates is a stark contrast to the world that Candido and America experience.  Even though both couples live in America, they experience two different realities. The natural question is why there is such an intense consolidation of wealth in the richest country in the world.  Certainly, there can be more effective ways of reaching people who have come to America.  There must be paths to successfully integrate new arrivals into our national tapestry and economic workforce.  Instead of reaching out and attempting to bring in people like Candido and America, who want to be a part of the nation, Boyle shows the America of Arroyo Blanco Estates trying to wall itself off to protect "property values." The issue of economic marginalization is a part of the immigrant experience in The Tortilla Curtain.  
Boyle shows how the people of the Arroyo Blanco Estates hold prejudicial attitudes towards those who have entered the country.  These discriminatory beliefs can connect to national security.  Candido and America have no other hope than to find their own piece of the American dream in "El Norte." However, Boyle shows that the rejection they face at the hands of the people like the ones who live in the Arroyo Blanco Estates could have a profound impact on national security.  Being seen as "rabbits" or "death for business" takes a toll.  Over time, people filled with hope about America might become disenchanted with it. As a result of being seen as "the other" or as an "outsider," such individuals might embrace criminal activity, and actions that could harm national security.  
Boyle argues that the inwardly drawn approach of building a wall does not solve the challenges that immigration poses.  No wall can prevent the wildfire that threatens the Arroyo Blanco Estates community or can offset the mudslide that causes Candido to save Delaney.  Boyle argues that we must embrace solutions that emphasize outreach and an inclusion of voices in order to effectively address issues of national security arising from immigration. The story shows how inward approaches that underscore fear will not work. A real threat to national security can be seen when Delaney takes a gun to find Candido.  When citizens walk around with guns looking for people like a hunter would for prey, national security is threatened.  Such a reality is an extension of the inward approach to immigration.  Boyle shows that accepting fearful and demonizing approaches to immigration could harm national security.   

Why did they have to move?

If you are referring to why Abilene Tucker and her father, Gideon, have to move, I can answer that question.
Both have to move to accommodate Gideon's job change. The text tells us that Gideon is hired for a summer railroad job in Iowa. Since he cannot not take his daughter with him, Gideon arranges for a preacher named Pastor Shady Howard to stand in as Abilene's guardian.
Abilene relates that she travels by train to meet the preacher in the town of Manifest and that she has little with her. Her most prized possession among her meager belongings is Gideon's compass.
Abilene's first meeting with Pastor Shady Howard is nothing like what she had envisioned. This is because Pastor Shady does not resemble the image of a typical preacher in Abilene's mind. He is dressed somewhat shabbily and exhibits strange behavior for a supposed man of the cloth. In time, Abilene comes to learn the truth about her father (his real name is Jinx) and how he was convinced that he would "jinx" her life if he didn't leave her.

What is a detailed analysis of the poem "Sons Departing" by John Cassidy in terms of language, structure, themes, imagery, and symbols?

Language: Cassidy's use of language in "Sons, Departing" is most notable in the way he chooses to have the narrator describe the setting. In the second stanza, for example, Cassidy chose to use the phrase "miles of empty air" as a more creative way to say that the sky stretched forever on the horizon. He found unique ways to make our minds picture things we see almost every day, like the "torn clouds" in the second stanza (a phrase used to describe the clouds that are drifting apart).
Structure: The structure of the poem as a whole, the stanzas, and the individual lines are what gives this poem its flow. It moves at a steady pace, mirroring the steadiness of the sons' "retreating footfalls"—yet it's not so slow that we grow tired. Because each stanza is a complete sentence, and because Cassidy makes use of enjambment (the continuation of a sentence, without a pause, from one line to the next), we're able to move with each stanza's action as it happens and pause at the end to reflect.
Themes: This poem has themes of loss, of life, of growing up. The themes are different for the narrator and the characters (father and sons, respectively). For the narrator, he's losing his boys. It's an inevitable loss that happens as his children grow older, but that doesn't mean he's ready or prepared for them to leave as he admires their journey in one direction: the future. The boys and the sea represent the theme of life, the openness and uncertainty (yet excitement) of the future.
Imagery: Cassidy's images are very strong. Instead of simply describing the waves in the second stanza as foamy or small or large, he says, "the sea its irregular / runs and spatters of white." We know what he's talking about, we can visualize it, and his phrasing evokes the image more strongly than a simple "the waves were different sizes and foamy." We see this type of language and imagery (which often go hand in hand) throughout the poem but most notably at the end.
The final line reads, "their walk was one-dimensional, and final." Cassidy chose to use "one-dimensional" and "final" to describe his sons going off on their own. He could have chosen to say "they walked in the opposite direction for good," but he worded it in a way that was easier to picture and felt more profound, as if the end of one journey and the beginning of another.
Symbols: The biggest symbol in this poem is the sea, as it can tie in to a number of things the speaker and the sons may be feeling. For the speaker, the uncertainty of the sea and the empty air could symbolize the fear and uneasiness he feels for his sons as they depart into the world. It could symbolize the broad emptiness within him, as they would have been a big part of his life and now they're seemingly disappearing.
For the sons, it could symbolize life itself. What's ahead of them is as uncertain as the waves but as open as the horizon and the sky. They can go and do and be whatever they want; it's an exciting journey.

Structure: The poem consists of five quatrains (four-line stanzas). The four lines are each comprised of a single sentence (this technique is called enjambment) spoken in the past tense and beginning with the plural pronoun "they" to observe the young men. The form is free verse, meaning there is no regular meter or rhyme scheme.
Language: Cassidy intersperses descriptions of the natural world (see below in imagery) with that of the depersonalization that results from entering the larger world.  The hedges are "clipped privets" and the young men who are first described as just clearing the top of the hedges with hair "blond with sunlight" resolve, in the final stanza, to "sunlit points" as they fade into the distance.
Themes: John Cassidy's "Sons, Departing" speaks to loss and separation and the pain parents feel as their grown children leave their daily care.  The speaker observes at least two young men taking leave, presumably, of their seaside home.  Their destination is unknown--it could be war or the larger world generally.
Imagery: The poem relies heavily on natural imagery; examples by stanza, quoted, are:
"hedges," "sunlight," "flowers"
"sea," "air," "sky," clouds"
"privets" (hedge)
"gulls," "wind"
"sunlit," "random patterns of the sea"
The natural imagery contrasts with the "clipped privets" and the straight line of the young men's path.
Symbols: The young men head toward a distant sea that perhaps symbolizes the profundity of the separation the observer feels as the young men depart. The observation that the young men don't look back and the last line, "their walk was one-dimensional and final," deepen the pathos of the idea that an irrevocable line has been crossed.

What are the names of the slaves in Oliver Optic's Rich and Humble, published in 1863?

There are no slaves explicitly mentioned in Rich and Humble, Or, The Mission of Bertha Grant: A Story for Young People by Oliver Optic. Considering the book was published in 1863 and is set in New York, this is not terribly surprising. Slavery was abolished in the state of New York by that time. However, the book does make mention of servants in the employment of Bertha's father, Mr. Grant. The following are those who are named:
Ben - The boatman is a former sailor and a constant presence in Bertha's life. Notably, he suspects and then discovers that Richard, Bertha's brother, stole ten dollars from her to gamble with.
Mrs. Green - Mrs. Green is the housekeeper. She taught Bertha how to make dresses and helps care for Noddy after his fall. 
John - His position is not explicitly named, but he is responsible for providing the horses used to pull a boat out of a river. Presumably, his name is the origin for a pseudonym that Richard uses earlier in the story. 

What mood does the first chapter of Dickens' A Tale of Two Cities set?

The first chapter of A Tale of Two Cities begins with one of the most immortal opening phrases in English literature: "It was the best of times, it was the worst of times..." The opening paragraph goes on to refer to an "epoch" of both faith and "incredulity," of hope and despair. The opening chapter goes on to evoke such paradoxes in order to describe an era where powerful forces that historians and social scientists would later describe as "structural" would tear the lives of the people of London and Paris apart. This was an era of extreme wealth and extreme poverty. Dickens does mention a number of differences between France and England, especially as relates to religion and criminal justice, but the social problems that plague both countries are described as very serious and pervasive, all the more so since they exist alongside wealth and privilege. In short, the first chapter strongly suggests that conflict is imminent, yet the characters in the story carry on unaware:

Thus did the year one thousand seven hundred and seventy-five conduct their Greatnesses, and myriads of small creatures—the creatures of this chronicle among the rest—along the roads that lay before them.
https://www.owleyes.org/text/tale-of-two-cities/read/chapter-i-the-period

From Section II, we infer that Farquhar, almost literally the only character, was lured or even entrapped into an attempt to blow up Owl Creek Bridge. Which event foreshadowed that Farquhar was being lured or entrapped?

In part II of the story, the narrator describes a recent evening when a "gray-clad soldier" rode up to the Farquhars' home. Confederate soldiers wore gray uniforms during the Civil War, while Union soldiers wore navy blue; thus, Farquhar assumes that the man he is speaking to is a fellow supporter of the Confederacy and fights for the south. When Farquhar requests news of the front, the soldier informs him that the Northern soldiers are repairing the railroads, transportation lines which are vital to their war effort. The soldier mentions the Owl Creek Bridge, some thirty miles away from Farquhar's home, and he describes the scarcity of its guards. Farquhar then asks,

Suppose a man [...] should elude the picket post and perhaps get the better of the sentinel, [...] what could he accomplish?

He wants to know what harm he could do to the Union effort. We can imagine, then, that he will take the soldier's hint to set fire to the bridge in order to disrupt the Union war efforts. Finally, after the soldier drinks the water brought to him by Mrs. Farquhar, he takes his leave. The narrator, in the final sentence of part II, informs us that the soldier "was a Federal scout." In other words, he is not a Confederate soldier but works for the Union army. In this way, he lures Farquhar into committing the crime for which he is hanged.

Calculus of a Single Variable, Chapter 3, 3.3, Section 3.3, Problem 18

Given: f(x)=x^2+6x+10
Find the critical values for x by setting the first derivative of the function equal to zero and solving for the x value(s).
f'(x)=2x+6=0
f'(x)=2x=-6
x=-3
The critical value for the first derivative is x=-3
If f'(x)>0, the function will increase in the interval.
If f'(x)<0, the function will decrease in the interval.
Choose a value for x that is less than -3.
f'(-4)=-2 Since f'(-4)<0 the function is decreasing in the interval (-oo,-3).
Choose a value for x that is greater than 0.
f'(0)=6 Since f'(0)>0 the function is increasing in the interval (-3, oo).
Because the function changed direction from decreasing to increasing a relative minimum will occur at x=-3. The relative minimum is the point (-3, 1).

One of the things that Swift examined critically in Gulliver's Travels is the government's role in education. Where in the book does it talk about the government's role in education? What does it mean that the portrayal of education in Gulliver's Travels mirrors the debate over the issue today, as it centers around inequality and barriers to keep the wealthy and the elite dominant and prevent anyone from challenging that dominance?

When Gulliver is among the Lilliputians, he learns about their system of education. Swift writes, "parents are the last of all others to be trusted with the education of their own children." Parents must deliver their children, both boys and girls, to state-run nurseries when the children are 20 months old. There, the children are trained to occupy roles that are similar to those of their parents. In other words, the sons of the wealthy receive a particular form of education, and sons of the merchants receive another form of education (girls' education is different). Only the children of laborers do not attend school. 
State-run education is still a very important topic today and one that is fiercely debated. Some critics argue that American education perpetuates inequality, as the system of education among the Lilliputians does, because children of wealthier families generally go to schools with better resources and get better educations than do children of less well-to-do families. Therefore, the way in which Swift satirizes education in Gulliver's Travels mirrors the modern debate over the way in which our school system prevents social mobility and keeps the elite in a dominant position. 

What advantage does the tesseract have?

A tesseract is a wrinkle in space and time that allows the Murry children, like their father before them, to leap over great distances in the space-time continuum. As Mrs. Whatsit explains it, if you wrinkle up the cloth of a skirt, an ant can travel across it much faster. Likewise, by using wrinkles in time, Mrs. Whatsit, Who and Which can almost instantly arrive at other planets. Tessering, or using a tesseract, allowed Mr. Murry to get quickly to the planet Camazotz, and it allows Meg, Charles Wallace and Calvin to follow him there and save him from the power of IT. It also allows all of them to return to earth in the blink of an eye. This fortunate feature makes space travel possible for humans.

In the letter to his old pal, what concerns does Jimmy express?

In a letter to his old friend, Jimmy expresses a few concerns. First, he no longer wants or needs the tools of his old trade. His chief concern is that the tools go to someone he can trust. This is why he wants his old friend to meet him; Jimmy doesn't want his tools to get into the wrong hands. Ironically, he doesn't want other criminals to profit from his tools, only his chosen inheritor (who is presumably a thief as well).
Jimmy also has another concern: he no longer wants to continue with his old life because he is getting married. He is in love and writes that he will get married to the "best girl on earth" in two weeks. It is likely that Jimmy does not want his new wife to come across the tools of his old trade. So, Jimmy wants to rid himself of his tools before the wedding day.
Also, Jimmy wants to move west and doesn't want any memories of his old life to follow him. With the tools gone, he will have made a clean break of it. He can then begin afresh, with his future before him.

Why is Jimmy Valentine pardoned?

Jimmy Valentine is pardoned because he has many important friends and connections on the outside. The last sentence of the first paragraph of the story indicates this important fact.

When a man with as many friends on the outside as Jimmy Valentine had is received in the “stir” it is hardly worth while to cut his hair.

Jimmy is characterized throughout "A Retrieved Reformation" as young, intelligent, good-looking, well-dressed, and popular. Everybody, including the Warden, likes him. The name Jimmy, rather than Jim or James, is intended to suggest likeability and popularity. The last name of Valentine suggests affection. Jimmy has "many friends on the outside" because of his winning personality. Since he is very successful in his profession as a safecracker, he is generous with his money. No doubt he contributes handsomely to the right politicians in the days when graft and corruption were so commonplace.
At the same time that Jimmy is portrayed as successful, there are some indications that he may be too successful. Too many people know about him and talk about him. He seems to be in danger of becoming a hardened criminal who keeps getting arrested and spending more and more time behind bars. One indication is contained in the first words Mike Dolan, an apparent cog in a big politician machine, says to him.

“Sorry we couldn't make it sooner, Jimmy, me boy,” said Mike. “But we had that protest from Springfield to buck against, and the governor nearly balked. Feeling all right?”

Jimmy has been incarcerated much longer than he had expected. This must have given him time to think about his future.

He had served nearly ten months of a four year sentence. He had expected to stay only about three months, at the longest. 

Jimmy knows he is in danger of losing all his "friends on the outside" if he keeps getting busted for bank jobs. They will want to forget they ever knew him. He has become too successful, too notorious. When he commits three safecracking jobs right after being released from state prison:

Ben Price investigated the scenes of the robberies, and was heard to remark:


“That's Dandy Jim Valentine's autograph. He's resumed business. Look at that combination knob—jerked out as easy as pulling up a radish in wet weather. He's got the only clamps that can do it. And look how clean those tumblers were punched out! Jimmy never has to drill but one hole. Yes, I guess I want Mr. Valentine. He'll do his bit next time without any short-time or clemency foolishness.”

Jimmy is smart enough to move to an entirely new territory of operations. In Elmore, Arkansas, he falls in love at first sight with Annabel Adams and decides to reform. But she is only the catalyst. He had been sensing the need for a change since spending ten sobering months in prison. He seemed indifferent to the Warden's lecture at the time of his release, but he was really thinking along the same lines as the Warden, who liked him and gave him this sincere parting advice:

“Now, Valentine,” said the warden, “you'll go out in the morning. Brace up, and make a man of yourself. You're not a bad fellow at heart. Stop cracking safes, and live straight.”

Jimmy was beginning to realize that honesty is the best policy, that crime does not pay. A man with all his superior assets--intelligence, skills, good looks, winning personality--can do better by going straight than by following the downward path of a recidivist. His success in Elmore proves it. He is soon engaged to the most beautiful girl in town and has become a prosperous leading citizen.

How does Beatty discover Montag's green bullet?

To answer this question, take a look at Part Three of the novel. During a confrontation between Beatty and Montag, Montag is wearing the green bullet, the two-way communication device that enables him to talk to Faber.
Beatty has no idea that Montag is wearing this device. As the confrontation intensifies, however, Beatty strikes Montag on the head, causing Montag to stumble backward and for the green bullet to fall out of his ear and onto the ground. 
Beatty picks up the bullet and grins. At first, he thinks it might be a seashell radio but then he places it half into his ear and realizes that there is another person, Faber, on the other end.  Beatty confiscates the device (by placing it into his pocket) and tells Montag that he will use the bullet to trace Faber's whereabouts. This threat to Faber is one of the reasons why Montag kills Beatty. 

At the beginning of Part Three, Beatty commands Montag to burn his home and gives him a flamethrower. After Montag torches his home, Beatty tells him that he is under arrest. Beatty then explains to Montag that his wife and her friends called an alarm on him. As Beatty is speaking, Faber yells into Montag's ear to get away. Beatty then strikes Montag on his head, and the green bullet falls out of his ear onto the sidewalk. Faber's voice can faintly be heard yelling for Montag to leave as Beatty walks over and picks up the green bullet. Beatty then turns it off and puts it into his pocket. Beatty looks at Montag and tells him that he saw the green bullet in his ear when Montag tilted his head. Beatty mentions that initially, he thought it was a Seashell radio, but when Montag "turned clever" he began to wonder. Beatty then tells Montag that he will trace the green bullet back to its owner.

Single Variable Calculus, Chapter 7, 7.2-1, Section 7.2-1, Problem 52

Prove that the function $y = Ae^{-x} + Bx e^{-x}$ satisfies the differential equation $y'' + 2y' + y = 0$.


$
\begin{equation}
\begin{aligned}

\text{if } y =& Ae^{-x} + Bx e^{-x}, \text{ then by using Product Rule}
\\
\\
y' =& Ae^{-x} (-1) + B [xe^{-x} (-1) + (1) e^{-x}]
\\
\\
y' =& -Ae^{-x} + Be^{-x} (-x + 1)

\end{aligned}
\end{equation}
$


Again, by using Product Rule


$
\begin{equation}
\begin{aligned}

y'' =& -Ae^{-x} (-1) + B [e^{-x} (-1) + e^{-x} (-1) (-x + 1)]
\\
\\
y'' =& Ae^{-x} + Be^{-x} [-1 + x - 1]
\\
\\
y'' =&Ae^{-x} + Be^{-x} [-2 + x]

\end{aligned}
\end{equation}
$


Therefore,


$
\begin{equation}
\begin{aligned}

& y'' + 2y' + y = 0
\\
\\
& [Ae^{-x} + Be^{-x} (-2 + x)] + 2 [-Ae^{-x} + Be^{-x} (-x + 1)] + [Ae^{-x} + Bxe^{-x}] = 0
\\
\\
& Ae^{-x} - 2Be^{-x} + Bxe^{-x} - 2Ae^{-x} - 2Bxe^{-x} + 2Be^{-x} + Ae^{-x} + Bxe^{-x} = 0
\\
\\
& 0 = 0

\end{aligned}
\end{equation}
$

Who was the first president of the United States?

The first President of the United States was George Washington.  He served as General and Commander-in-Chief of the Continental Army during the American Revolutionary War.  He was elected to the Presidency by the Electoral College twice, in 1789 and 1792.  On April 30, 1789, he was officially sworn in to his first term as President.
It is important to note that, strictly speaking, there could be no "President of the United States" prior to the ratification of the U.S. Constitution in 1788, which supplanted the Articles of Confederation and created the "United States" as we understand the term today.  The Articles of Confederation represented a minimalist governing compact amongst the thirteen colonies in existence at the time, all of which were under British rule.
During the Revolutionary War, a national governing body - the Continental Congress - was convened in response to Britain's 'Intolerable Acts" toward the colonies.  The first President of the First Continental Congress was Peyton Randolph, elected by his fellow Congressional delegates in 1774.  Cyrus Griffin was the final President of the Continental Congress prior to the enactment of the Constitution and the election of George Washington as the true first "President of the United States."

The first president of the United States was George Washington. Washington was an extremely popular figure because of his character, reputation, and service in the American Revolutionary War. 
In the election of 1788, he was the unanimous first choice of all the members of the Electoral College. Since the country did not have political parties like we have today, there was no nominating process like we see in modern presidential elections. However, there were two general sides—the Federalist side and the Anti-Federalist side. Washington's sympathy was with the Federalist side, and over ninety percent of the electors selected via the popular vote were also Federalists.
Washington was elected again in 1792. Once again, he was the unanimous first choice of all the members of the Electoral College. By this time, the two major parties of the early American republic, the Federalist Party and the Democratic-Republican Party, had started to take form. However, there was still no party nominating process like we know today, and historians consider both sides to have "nominated" Washington for president. The Federalists, whose electors once again received over 90% of the popular vote, backed John Adams for vice-president. The Democratic-Republican electors backed New York's governor, George Clinton.
Washington refused to seek a third term. In his Farewell Address, he urged Americans not to be seduced by the factionalism of political parties. It was a warning his fellow citizens did not heed.
https://avalon.law.yale.edu/18th_century/washing.asp

What are the effects of Tom's decision to go after the yellow paper?

When the yellow sheet on which Tom has recorded all the information he has gathered on "four long Saturday afternoons" and countless hours during evenings at the public library and home, Tom Benecke is incredulous:

It was hard for him to understand that he actually had to abandon it—it was ridiculous—and he began to curse.

Tom finds it difficult to realize that of all his papers this yellow sheet has to be the one to have floated out his window almost as though in insult. He stands and considers the situation. It will take him two months to duplicate all the information recorded on this yellow sheet. If he does not submit his fresh ideas on ways to display groceries on Monday, they will not be in time for the spring displays, and he will lose the promise of advancement in his company. 
Because he desires professional advancement more than anything else, it is not long before Tom impulsively goes out the window to retrieve his yellow sheet. When he reaches the paper on the narrow ledge of the high apartment building, Tom bends to pick it up. As he leans carefully, Tom sees beneath him and realizes how dangerously high up he is:

And a violent instantaneous explosion of absolute terror roared through him . . . he began to tremble violently, panic flaring through his mind and muscles, and he felt the blood rush from the surface of his skin.

Considering what would happen if he falls, Tom realizes he must fight against his panic and place one foot before the other until he reaches his window:

He didn't know how many dozens of tiny sidling steps he had taken, his chest, belly, and face pressed to the wall; but he knew the slender hold he was keeping on his mind and body was going to break.

Trying desperately to reign in his terror, Tom moves slowly along the ledge as he holds the retrieved paper between his teeth. He concentrates on putting one foot before the other until his hands grope nothing but space and he slips at his window. Tom reaches desperately for something on which to hold, but his hands feel only space. As he starts to fall, Tom's wrists strike the window sill and are knocked off. When he begins to lose his balance, he does the following:

he flung his arms forward, his hands smashing against the window casing on either side; and—his body moving backward—his fingers clutched the narrow wood stripping of the upper pane.

For a brief moment, Tom hangs between life and death. But he manages to pull himself up, and he looks through the closed glass at his living room and the comfort and safety he has left behind. When he notices his reflection in the glass, Tom takes the yellow sheet out of his mouth, crumbles it, and puts it into his pocket. Then, he assesses the situation in which he finds himself. Tom knows that his wife will not return for four hours; he also knows that he cannot stay on the ledge that long. Pondering the reality that his life would be wasted if he were to die now, Tom rethinks his values.
Forming a plan, Tom summons all his strength and shoots his arm forward toward the glass, shouting his wife's name. Swinging his fist, he breaks through the glass; he then falls forward into the room. Although he feels the "triumph" of success, Tom does not lie on the floor as he has promised himself if he should make it back into the apartment. Instead, he picks up the broken glass. Distractedly, he unfolds the yellow sheet for which he has risked his life. Now it has lost its importance. Tom places it on his desk with only a pencil to hold it down. Hurriedly, Tom grabs his coat, hoping to catch his wife at the movies. When he throws open the apartment door, the draft lifts the yellow sheet, and it again blows out the broken window. This time Tom just laughs at the absurdity of his obsession with his yellow sheet when his marriage is what matters.

Which "antique land" and whose statue does Shelley refer to in "Ozymandias"?

It isn't specified exactly which "antique land" is being referred to in the poem. In this particular context "antique" simply means "ancient," as in ancient Egypt, Greece, or Rome. It's possible that the traveler mentioned in the opening line has just come back from Egypt, which is where he saw the ruins of Ozymandias's statue decaying in the sand.
Ozymandias is an alternative name for Ramses II, an Egyptian pharaoh. He believed himself to be a great ruler, so great in fact that he was certain his name and all his earthly achievements would live on forever, inspiring awe in each succeeding generation. But he was profoundly mistaken. He is not just long-dead but also long-forgotten. The last remnants of his earthly rule lie crumbling in the desert. Ozymandias was so arrogant, so blind to reality, that he was unable to see that everything in this world is transient and will one day fade away.
https://www.poetryfoundation.org/poems/46565/ozymandias

What are a couple of Jack's character traits in the novel Lord of the Flies?

Jack has several character traits that make him the main antagonist of Lord of the Flies. He is portrayed as vicious and arrogant from the start of the book, but when he receives the admiration of the other boys for his hunting prowess, it only inflates his already large ego. Jack becomes obsessed with hunting (even going so far as to threaten the other boys) because he recognizes that it impresses the younger children.
Jack's ambition and lust for power are also an important part of his character. The boys view Ralph as their leader, a fact that causes friction between him and Jack. Many of the things Jack does throughout the book are to position himself as the leader of the boys instead of Ralph.
Another important character trait for Jack is jealousy of Ralph tied up in his own insecurities. When the boys choose Ralph as their leader, it is clearly an affront to Jack, and his jealousy leads him to commit many of the heinous acts he performs later in the book.

Jack is a jealous, violent individual who craves power and eventually usurps it from Ralph throughout the novel. He is also a skilled hunter who voices his displeasure about maintaining a signal fire, building shelters, and following rules. He is a selfish individual who continually argues with Piggy and neglects the littluns. Jack values barbarism over civilization and quits Ralph's group in order to start his own tribe at the other end of the island. Jack is also a tyrannical leader who encourages violence and savagery. As leader of this tribe, Jack manipulates the boys' fear by promulgating the belief in the beast and promoting violence. Jack leads his group of savages on several hunting expeditions, neglects the need for a signal fire, and punishes individuals who do not follow his commands. The threat of violence deters any dissenters and Jack eventually commands his hunters to kill Ralph. 

Single Variable Calculus, Chapter 3, 3.1, Section 3.1, Problem 50

The graph below shows how the temperature $T$ affects the maximum sustainable swimming
speed $S$ of Coho Salmon.



a.) State the meaning of the derivative $S'(T)$ and its corresponding units.



b.) Estimate the values $S'(15)$ and $S'(25)$ and interpret them.








$\quad$ a.) The meaning of the derivative of $S'(T)$ is the rate at which the speed of Coho Salmon
varies with respect to temperature; its unit is $\displaystyle \frac{cm}{s^2}$



$\quad$ b.) Based from the graph,



$\qquad\displaystyle S'(15) \approx 0.375 \frac{cm}{s^2}$



$\qquad\displaystyle S'(25) \approx -0.4 \frac{cm}{s^2}$



$\quad$These values represents the acceleration of the salmon with respect to the temperature, the acceleration
of the salmon increases up to $20^\circ\rm{C}$. However, the acceleration starts to decrease beyond $20^\circ\rm{C}$

I need help developing a thesis for "Ode to the West Wind."

When developing a thesis statement about a poem, you may be asked to focus on the development of a theme, or you may be asked to analyze how the poet uses specific techniques to create a theme or meaning in the work. 
When writing about Percy Shelley's "Ode to the West Wind," it's first important to know what an ode is; an ode is a lyric poem (a lyric poem is usually in first person, expressing the speaker's emotions) that typically celebrates the subject of the poem, in this case "the West Wind." Starting with this premise, we can read through the poem and try to discover what the speaker admires or enjoys about the wind and test whether the tone of the speaker matches up with what we would expect in an ode.
The first section of the ode depicts the dark power of the west wind. It is described as an autumn wind that drives dead leaves "to their dark wintry bed" (6), "Each like a corpse within its grave" (8) for the fall and winter, until the spring wind breathes life into the world again. Shelley speaks to the west wind in apostrophe, a direct address to an entity that is either not human or not present to reply to the poet. The poet addresses the wind as "Wild Spirit" and as "Destroyer and preserver" (13–14). The poet seems to admire the power of the wind, even though its job is to sweep death across the landscape.
The second section of the ode continues along the same thematic lines. The wind is again described as associated with the dying leaves of autumn. The wind is addressed as "Thou dirge / of the dying year" (23–24). The speaker ends this section by entreating the wind to "hear" him (28). The first two parts invoke and describe the wind.
In Part III, the speaker varies his imagery and depicts the changing of summer to fall. Therefore, we see more description of the "blue Mediterranean" and "sea-blooms" (30, 36). When those dreamy summer environments sense the west wind approaching, though, they "grow gray with fear, / And tremble and despoil themselves" (38–39). The wind destroys, but its awesome power cannot be denied.
Section IV sees the speaker put himself into the position of the leaf that might be carried by the west wind. The speaker becomes subject to the power, and here his admiration for the wind becomes most clear: he aspires to be "tameless, swift, and proud" like the wind (53). This section represents the most significant shift in the poem because the poet involves himself and his wishes, intertwining them with the powers of the wind that he describes.
This sentiment continues in Part V, where the speaker asks,

Be thou, Spirit fierce, 
My spirit! Be thou me, impetuous one! (58–59)

He wants his "dead thoughts" (60) to be swept away, across the world, like the dead leaves of fall. He wants to be free of the old and to be reborn. He ends the poem by saying that "Spring [cannot] be far behind" when we hear the the west wind (67). Again, the speaker admires the power of the west wind, wants it to help him begin again, and looks forward to the rebirth of spring.

Discuss the notion of the plot being the soul of the tragedy in Greek tragedies.

It looks like you would like to discuss Aristotle's notion of the plot as the "soul of tragedy" in Greek theater. To aid our understanding of this notion, we'll turn to Aristotle's Poetics.
In his treatise, Aristotle proclaims that plot is the "soul of tragedy" and that character must stand in second place. To Aristotle, tragedy involves action. This is because tragedy is really an imitation of life, which consists of human action.
He asserts that every good tragedy must have six parts, and these are plot, character, diction, thought, spectacle, and song. Additionally, since tragedy involves action, the plot must constitute the chief focus of the play. It is through plot, after all, that the actions of the principal characters are displayed.
Thus, Aristotle contends that "without action there cannot be a tragedy; there may be without character." He then goes on to describe how a good plot should be structured so as to achieve the maximum effect upon the audience. To Aristotle, a plot is a thing of precision: it must have a clear beginning, middle, and end. The unity of plot is of great importance: any beautiful piece of work must be undoubtedly perspicuous (or clearly outlined).
Aristotle criticizes the "episodic" plot, where actions succeed each other in no particular sequence. Essentially, an episodic plot contains episodes (or chapters) that don't present a harmonious whole, with a clearly defined beginning, middle, and end. The progression of the story may not be linear, so to speak, and there is no "natural continuity" between episodes. Aristotle maintains that the plot must follow a logical "cause and effect" sequence in order to create the deepest impression on the audience. Since tragedies imitate actions that inspire both fear and pity, they must follow a complex plan.
Aristotle explains this clearly in his treatise. He tells us that a good tragedy should not be about a good man who experiences adversity. Such a story merely shocks us; it doesn't evoke both pity and fear. Similarly, a good tragedy never shows an evil man moving from adversity to prosperity. Again, such a story evokes neither fear nor pity.
Aristotle also contends that the downfall of a villain falls into the same category: sure, it's satisfying in a moral sense, but it hardly inspires both pity and fear. Aristotle then tells us what a perfect plot entails: it should outline the story of a man (who isn't necessarily a virtuous character) and whose downfall is caused not by vice but by a "frailty" of sorts. Aristotle contends that it would be even better for this character to come from a "renowned and prosperous" background. He then gives us the examples of Orestes, Oedipus, Alcmaeon, and others.
So, to Aristotle, the plot is the "soul of tragedy" because it is the principle part of the play. Without plot or action, there can be no story to tell. So, plot must reign supreme over the other aspects of a play.
http://classics.mit.edu/Aristotle/poetics.html

Who is Munshi Premchand?

Munshi Premchand (1880 – 1936) was a renowned Indian writer whose works include numerous short stories, more than a dozen novels, essays and literary translations. He was born as Dhanpat Rai, but later took up the pen name Premchand. His father was called Ajaib Rai, a post office clerk. His mother, Anandi Devi, died when he was eight years old. His father then remarried. However, Premchand was not close to his stepmother.
Premchand started his studies at seven years of age at a Madrasa in Lalpur. Here, he learned Urdu and Persian. He later joined the Queen College of Benares where he sat for his matriculation exam which he passed with a second division. However, he was unable to pursue further studies since he had lost his father during the same span of time. He started his career as a tuition teacher then moved on to the position of assistant teacher a few years later. He also started writing fiction. His first novel was called “Asrar e Ma’abid”. It talked about corruption in the temple. Later, around 1905, he met the editor of a magazine called “Zamana”, for which he wrote many articles and stories in the following years.
He took up a variety of positions and continued to write in Urdu and Hindi. Around 1921, Premchand quit his job to focus on his writing. Up until his death in 1936, he focused on his literary career, except for a few job stints that he used to improve his financial situation.
For a more detailed analysis of Munshi Premchand’s life, please refer to the attached reference article.
https://www.thefamouspeople.com/profiles/munshi-premchand-101.php

What is the setting in the book When the Legends Die?

When the Legends Die is a novel written by Hal Borland that tells the story of Thomas Black Bull’s life. Thomas Black Bull is a Ute Native American from Southwest Colorado. He travels throughout his life, so the setting also changes throughout the novel. However, it is primarily focused on the American Southwest in the early part of the twentieth century. The novel begins in Pagosa, but Thomas Black Bull and his family must soon flee to the wilderness, where they live off the land. From there, the setting changes back to the Ute Indian Reservation, then moves throughout the Southwestern United States as Thomas travels with a rodeo to Colorado, New Mexico, Texas, and Oklahoma. At the end of the novel, Thomas returns to his roots, where he lives in the wilderness again.

The setting of When the Legends Die is the western United States, in particular Colorado. The main character, Thomas Black Bull, is a member of the Ute Native American tribe. The novel has Thomas living in the small town of Pagosa. He also lives in the wilderness (sometimes with both parents, sometimes with just his mother, and sometimes completely alone) and at a Native American reservation school.
Just as Legends has its setting in a number of specific locations, the protagonist of the novel goes through some name changes. He is given the name Little Black Bull at birth by his parents. When a white minister baptizes him, he is given the name Thomas Black Bull. Nearing his teenage years, he renames himself Bear's Brother and later, while popular on the rodeo circuit, his fans nickname him Killer Tom.
In short, in When the Legends Die, a change in setting often signals a change in name/identity for the protagonist.

Why did the three men decide to go on a boating experience?

The three men decided to go on a boating experience because they believed that they were overworked and needed rest.
Chapter 1 begins with J., the narrator, discussing how he is prone to many dangerous diseases. His hypochondriac tendencies, however, escape him. Meanwhile, his friends, George and William Harris, are equally adamant that they suffer their share of debilitating illnesses.
In the end, all three decide that a change of scenery would refresh their minds and invigorate their health. However, they initially disagree about where they will vacation. J. suggests that George pick a quiet "old world spot," far from the "madding crowd." William then suggests a sea trip, but J. disagrees. He argues that a sea trip is only a good choice when one has a few months to spare. Since they only have a week, a sea trip would be a disaster.
The three men then argue about the disadvantages of a sea trip. In the end, George suggests a trip up the river. Finally, the three men agree that this is what they will do for rest and relaxation.

Why did Luis join a gang?

Like a lot of young kids growing up in a poor inner-city area, Luis finds himself systematically excluded from society, held down by a culture of discrimination and low expectations. In such a grim environment, street gangs provide a kind of surrogate family with a sense of belonging. Luis grows up surrounded by these gangs in all corners of the neighborhood. They're full of tough, scary men with tattoos who always seem to command fear and respect. Luis wants to be just like them; he wants the respect he doesn't get from society as a young Hispanic male; he wants to be a part of something. Then again, Luis doesn't really have much choice in the matter. As a poor barrio kid with little in the way of an education, there's always been the expectation that Luis will get involved in gang activity sooner or later. Otherwise, there's a serious danger that he might end up being seriously beaten or even killed.

How does The Crucible explore the importance of truth, justice, and integrity?

In Arthur Miller's allegorical play The Crucible, he examines the themes of truth, justice, and integrity through different characters and their reactions to the witch trials that have upset and ruined the entire community. While characters such as John Proctor, Francis, Rebecca Nurse, and Giles Corey represent truth, justice, and integrity, Salem's authority figures and Abigail Williams represent the complete opposite.
In act 3, John Proctor brings Mary Warren into town in an attempt to undermine Abigail's authority and end the witch trials. Francis Nurse and Giles Corey also support Proctor's cause and argue for justice and truth. When Proctor hands over a petition signed by community members vouching for Rebecca Nurse and Martha Corey, Deputy Governor Danforth illustrates that he is not concerned with truth or justice by telling Francis Nurse

No, old man, you have not hurt these people if they are of good conscience. But you must understand, sir, that a person is either with this court or he must be counted against it, there be no road between.

Deputy Governor Danforth and Judge Hathorne are only concerned about maintaining their positions of authority and influence over the community. They consider anyone questioning the proceedings as a threat and refuse to recognize the truth. Giles Corey then informs Danforth that he has a signed disposition from a community member claiming that Thomas Putnam is using the witch trials as a land grab. When Giles refuses to disclose the identity of the person who overheard Thomas Putnam speaking to his daughter about the land, Danforth attempts to misuse truth and justice by telling Giles

Old man, if your informant tells the truth let him come here openly like a decent man. But if he hide in anonymity I must know why. Now sir, the government and central church demand of you the name of him who reported Mr. Thomas Putnam a common murderer.

In contrast to Deputy Governor Danforth and Judge Hathorne, John Proctor publicly ruins his valuable reputation by finally admitting that he slept with Abigail, in the hopes that his testimony will undermine her authority. John Proctor demonstrates his integrity and honesty by telling Salem's authority figures

I have known her, sir. I have known her.

In act 4, John Proctor ends up tearing his false confession and becomes a martyr by accepting his fate. John Proctor realizes that his death could possibly spark a riot similar to the one that took place in the town of Andover and disband Salem's corrupt court. Before John is led to the gallows, he says,

You have made your magic now, for now I do think I see some shred of goodness in John Proctor. Not enough to weave a banner with, but white enough to keep it from such dogs[...]Give them no tear! Tears pleasure them! Show honor now, show a stony heart and sink them with it!

Overall, Miller depicts how certain characters exercise honesty, argue for justice, and display integrity, while Salem's corrupt authority figures and Abigail Williams are only concerned with maintaining power and influence in the community.

Describe Feld's attitude toward Miriam and Max in the Bernard Malamud short story "The First Seven Years."

Bernard Malamud's short story "The First Seven Years,"  is about a middle-aged Jewish man named Feld who must come to grips with his daughter Miriam's independence. Feld wishes for his daughter to get a college education, which Miriam does not want to pursue. Failing that, he wants her to date and possibly marry a young man named Max.
Malamud reveals Feld's attitude toward Max in the story's first paragraph:

Neither the shifting white blur outside nor the sudden deep remembrance of the snowy Polish village where he had wasted his youth could turn his thoughts from Max the college boy (a constant visitor in his mind since early that morning when Feld saw him trudging through the snowdrifts on his way to school), whom he so much respected because of the sacrifices he had made throughout the years—in winter or direst heat—to further his education.

Obviously, Feld feels a certain admiration toward Max. Like himself, Max knows the value of a good education. Feld believes he would be a good match for his daughter Miriam, and a good provider.
We see Feld's thoughts about Miriam a little later, when he thinks about trying to set the two up on a date:

Or suppose Miriam, who harped so often on independence, blew up in anger and shouted at him for his meddling?

Feld is showing some frustration with his daughter over her independent nature, and it is apparent that he is also frustrating her with his attempts to influence her behavior. But Feld also has a certain respect for his daughter, or he wouldn't be worried about her reaction. 
In the end, Feld's judgment will be proven wrong, as Max and Miriam turn out to be uninterested in each other. His attitude toward Miriam changes to one of acceptance when he allows his assistant Sobel, a man he thinks is beneath her, to pursue a relationship with her.