What are some examples of why you know the narrator is unreliable in the story "The Cask of Amontillado"?

As a first person narrator making what is probably a death bed confession fifty years after the fact, Montresor is telling the story in a way most likely to justify what he has done. We have nobody else's version of the tale with which to compare what Montresor tells us. Therefore, we have to take his word about what happened. This is the word of someone capable of murdering a rival in heinous way by walling him up in a catacomb and leaving him to die, so one has every reason to suspect that this narrator is mentally unstable.
Further, Montresor never specifies what were the "thousand injuries" he claims Fortunato perpetrated against him. That there were so many leads one to believe they must have been small. But if that is true, we wonder why Montresor reacted in such an extreme way.
All of this uncertainty, along with the barbaric nature of the crime, undermines Montresor's reliability as a narrator.

Montresor never mentions even one of the "thousand injuries" that Fortunato has supposedly inflicted upon him: 

The thousand injuries of Fortunato I had borne as I best could, but when he ventured upon insult I vowed revenge. 

Montresor also does not detail what the "insult" was. The reader could simply take Montresor's word for it, but that is an assumption. A narrator establishes himself as a reliable source by providing explanations and reasons for his statements. Montresor never does this with the injuries and insults. 
Montresor also brags about his ability to hide the truth: 

It must be understood that neither by word nor deed had I given Fortunato cause to doubt my good will. 

Montresor proves how he can lie to and manipulate Fortunato. Since he is directly addressing the reader, who's to say he is not being a manipulative narrator as well? 
Some have suggested that Montresor's French name implies that he is new to Italy and therefore, he would have no Italian coat of arms. When Fortunato says he doesn't remember Montresor's coat of arms, this might be a minor insult because Montresor would not have a coat of arms. And note the motto: "Nemo me impune lacessit." This basically means "no one can harm me unpunished." It seems possible that Montresor could have made this up to underscore his feelings of vengeance. We can only guess what else he may have made up. 

Single Variable Calculus, Chapter 3, 3.1, Section 3.1, Problem 28

If $\displaystyle f(x) = \frac{x^2 + 1}{x - 2}$, find $f'(a)$.

Using the definition of the derivative


$
\begin{equation}
\begin{aligned}

f'(a) &= \lim_{h \to 0} \frac{f(a + h) - f(a)}{h}
&& \\
\\
f'(a) &= \lim_{h \to 0} \frac{\displaystyle \frac{(a + h)^2 + 1}{a + h - 2} - \frac{a^2 + 1}{a - 2}}{h}
&& \text{Substitute $f(a + h)$ and $f(a)$}\\
\\
f'(a) &= \lim_{h \to 0} \frac{(a - 2)(a^2 + 2ah + h^2 + 1) - (a^2 + 1)(a + h - 2)}{(h)(a + h -2)(a - 2)}
&& \text{Get the LCD of the numerator and simplify}\\
\\
f'(a) &= \lim_{h \to 0} \frac{a^3 + 2a^2 h + ah^2 +a - 2a^2 - 4ah - 2h^2 - 2 - a^3 - a^2 h +2a^2 - a - h + 2}{(h)(a + h -2)(a - 2)}
&& \text{Expand the equation}\\
\\
f'(a) &= \lim_{h \to 0} \frac{\cancel{a^3} + 2a^2 h + ah^2 + \cancel{a} - \cancel{2a^2} - 4ah - 2h^2 - \cancel{2} - \cancel{a^3} - a^2 h + \cancel{2a^2} - \cancel{a} - h + \cancel{ 2}}{(h)(a + h -2)(a - 2)}
&& \text{Combine like terms}\\
\\
f'(a) &= \lim_{h \to 0} \frac{a^2h + ah^2 - 4ah - 2h^2 - h}{(h)(a + h -2)(a - 2)}
&& \text{Factor the numerator}\\
\\
f'(a) &= \lim_{h \to 0} \frac{\cancel{h}(a^2 + ah - 4 - 2h - 1)}{\cancel{(h)}(a + h - 2)(a - 2)}
&& \text{Cancel out like terms}\\
\\
f'(a) &= \lim_{h \to 0} \left[\frac{a^2 + ah - 4a - 2h - 1}{(a + h - 2)(a - 2)} \right] = \frac{a^2 + a(0) - 4a - 2(0) - 1}{(a + 0 - 2)(a - 2)}
&& \text{Evaluate the limit}

\end{aligned}
\end{equation}
$


$\qquad\fbox{$f'(a) = \displaystyle \frac{a^2 - 4a - 1}{(a - 2)^2}$} $

Why do you think the young lady asked Framton the initial set of questions?

Vera asks Nuttel all the questions because she wishes to set him up for a scare. She knows he is down for a "nerve" cure and so thinks it would be fun to truly frighten the already nervous man. He comes across as a bore, so Vera probably also wants to get rid of him as a guest.
When Vera learns he knows nothing of her aunt or her family or any of the people in the area, she is then free to tell him almost any story she wants and be believed. Because Mr. Nuttel doesn't realize that her aunt's husband and two brothers are alive, Vera makes up a story that they disappeared a year ago and are presumed dead, but she says that her aunt leaves the window (we would call it a French door) open in the hopes they will return. When Mr. Nuttel sees the very much alive threesome coming home, he thinks he is seeing ghosts and flees.

At the beginning of the story, Framton Nuttel arrives at Mrs. Sappleton's home with a letter of introduction and is greeted by her mischievous niece, Vera. Vera initially asks Mr. Nuttel if he knows anyone from around the area and if he is familiar with her aunt, Mrs. Sappleton. Framton responds by telling Vera that he knows absolutely nobody from the area and only knows Mrs. Sappleton's name and address. Vera then begins to tell Mr. Nuttel a made-up story about why her aunt leaves the French window open. The reason Vera initially questions Frampton Nuttel is to understand his background better and discern if he is gullible enough to believe her fanciful ghost story. Vera's inquiries indicate that Mr. Nuttel will be easily deceived and that she can have fun making the neurotic, unfamiliar man lose his nerve when Mr. Sappleton and Ronnie arrive home after hunting. 

How did leaders react to revolutionary ideals in Europe after the French Revolution and the reign of Napoleon?

On the whole, they reacted with absolute horror. The crowned heads of Europe were strongly against the French Revolution from the start, seeing it as an attack on the established order of things. We should always remember when examining this period that most rulers believed themselves to be appointed by God. To topple the monarch was therefore seen, not just as rank treachery, but as a sacrilegious act against the divine order of things. A number of European states responded to what they saw as a dangerous development by declaring war on Revolutionary France. Not surprisingly, one of these was the Holy Roman Empire, ruled by Marie Antoinette's brothers Emperor Joseph II and, after him, Leopold II.
In the subsequent revolutionary wars, French forces swept across neighboring countries, taking large tracts of territory from their monarchist enemies—most notably the Spanish Netherlands. The counter-revolutionary forces were surprised by the ferocity and superior martial spirit of the French and eventually found themselves forced to sue for peace. The intervention on behalf of Louis XVI had been a failure.
If anything, Napoleon was perceived as an even greater danger to European monarchies. The Corsican general's famed military genius gave him an aura of invincibility in his early campaigns, and he was able to rack up a string of impressive victories against opposing forces, most notably when he crushed the Prussian army at Jena in 1809.
Napoleon proceeded to expand French territory considerably, mainly at the expense of Europe's various monarchies. The Holy Roman Empire—into whose ruling family Marie Antoinette had been born—was forcibly dissolved by Napoleon after his victory at the Battle of Austerlitz; it had stood for just over a thousand years, yet Napoleon swept it away and established the Confederation of the Rhine, a deliberately weak and fractured French satellite state.
Despite his enormous successes on the battlefield, Napoleon's grip on power was never completely secure. He had expanded French territory too far, too fast. The remaining European monarchies—Britain, Portugal, Sweden, Spain, Austria, and Russia, as well as a number of German states—formed themselves into the so-called Sixth Coalition which eventually defeated Napoleon at the Battle of Leipzig in 1814. The same powers formed the basis of the Seventh Coalition, which inflicted Napoleon's final defeat a year later at Waterloo.

What is Mead's punishment in "The Pedestrian" by Ray Bradbury?

Mr. Mead is arrested and will be taken to the Psychiatric Center for Research on Regressive Tendencies. 
In the year 2053, Mr. Mead is an odd man. He lives alone, and he likes to take walks at night. Oddest of all, Mr. Mead does not have a "viewing screen" in his house.
The story begins with Mr. Mead exiting his house at eight o'clock at night. His plan is to go on a walk around the neighborhood. His walks are long, too.  

Sometimes he would walk for hours and miles and return only at midnight to his house.

On this particular night, a police car pulls up alongside Mr. Mead. The car begins questioning him about why he is out of his house. The car seems shocked and suspicious of Mr. Mead because Mr. Mead does not have a wife or viewing screen.  

"And you have a viewing screen in your house to see with?"
"No."
"No?" There was a crackling quiet that in itself was an accusation.

To the police and the world of 2053, Mr. Mead's activity is so odd that he must be certifiably insane. The police car assumes he is a danger to himself and the general public; therefore, the police car arrests Mr. Mead and plans to take him to a psychiatric facility.

Why is the Valley of Ashes important to chapter three of The Great Gatsby?

The Valley of Ashes provides a counterpoint to the lavishness of East Egg and West Egg. The Valley of Ashes represents extreme poverty and hopelessness. Those who inhabit the valley are condemned to live their lives there—they do not have the financial means to escape, and their potential is suppressed by the rich who encircle their valley. In the text, Fitzgerald describes the valley as

"a fantastic farm where ashes grow like wheat into ridges and hills and grotesque gardens; where ashes take the forms of houses and chimneys and rising smoke and, finally, with a transcendent effort, of ash-grey men, who move dimly and already crumbling through the powdery air." (26)

The way Fitzgerald describes it evokes an image of a crumbling reality, one that is temporary and one that a slight breeze might disperse into the air, like ashes from a fire. This is a stark contrast to the lavish lifestyles of the nearby rich in East Egg and West Egg. The only way those rich folks see the valley is when they are forced to drive or ride the train through it. The valley represents the decay of the American Dream, the middle class, and the moral and social decay of America post–World War I. Greed and excess are encouraged through the industrialization of America at the expense of the poor and middle classes. The ashes dumped into the valley represent the byproduct of American capitalism—the burning up and away of the people who make up the base of the American economy in order to support the rich and ultra-rich. For all of these reasons, the Valley of Ashes remains one of Fitzgerald's most striking literary symbols. 

In "The Summer of the Beautiful White Horse" by William Saroyan, did John Byro know the boys had his horse?

Using evidence from the text, the reader can find indications that John Byro suspected the boys had his horse in “The Summer of the Beautiful White Horse” by William Saroyan.
John Byro was not part of Aram and Mourad’s Armenian family. He was a lonely man who learned the Armenian language in order to communicate with and relate to the family. One day, after his horse was gone for a month, Byro walked ten miles to visit with Aram’s mother and uncle. He explained that his horse was missing, which rendered his surrey useless. The uncle becomes animated and tells John Byro to pay no mind to his missing horse. If a man walks ten miles just to have coffee and a smoke but brings up his missing horse in conversation, it is a good indication there was more to his visit than just a friendly discussion.

Then another visitor arrived, a farmer named John Byro, an Assyrian who, out of loneliness, had learned to speak Armenian. My mother brought the lonely visitor coffee and tobacco and he rolled a cigarette and sipped and smoked, and then at last, sighing sadly, he said, my white horse which was stolen last month is still gone. I cannot understand it.

Another indication that John Byro knows the boys have his horse arises when the boys meet the man as they are walking with the horse. As he closely examines the horse, he tells the boys the horse they are walking seems to be a twin to his horse. Yet, he never insists the horse is his or turns the boys in for having the horse. Byro understands the family’s honor and knows that once the boys are cornered, they will return his horse, which they do.

I could swear it is the horse that was stolen from me many weeks ago. May I look into its mouth?
Of course, Mourad said.
The farmer looked into the mouth of the horse.
Tooth for tooth, he said. I would swear it is my horse if I didn't know your parents. The fame of your family for honesty is well known to me. Yet the horse is the twin of my horse.

In Swift's Gulliver's Travels, what main difficulty do the Lilliputians face while shifting Gulliver onto a newly prepared vehicle to carry him?

The main problem the Lilliputians face while attempting to move Gulliver from his place on the beach into their city is simply lifting and placing him into the vehicle with which they plan to move him.  They already have impressive machinery to move large objects because they use these to build their nine-foot ships, Gulliver tells us, but actually lifting him into this machine poses a difficulty.  Eventually, eighty poles are erected, to which pulleys are fastened, and some nine hundred of the strongest Lilliputian men are called to hoist Gulliver up by the cords they've tied around him using these pulleys.  It is a process that takes almost three hours, as Gulliver finds out later because he sleeps through the whole production, his wine having been drugged.

Single Variable Calculus, Chapter 2, 2.1, Section 2.1, Problem 6

Suppose that a rock is thrown upward on the planet Mars with a velocity of $10$ m/s, its height in meters $t$ seconds later is given by $10t-1.86t^2$.

a. Find the average velocity over the given time intervals:

(i) [1,2]
(ii) [1,1.5]
(iii) [1,1.1]
(iv) [1,1.01]
(v) [1,1.001]

Average velocity = $\frac{\delta distance}{\delta time} = \frac{y_2 - y_1}{t_2 - t_1}$

$
\begin{equation}
\begin{aligned}

\begin{array}{|c|c|c|c|c|c|}
\hline\\
& t_1(s) & t_2(s) & y_1 (m) = 10t_1 - 1.86 t_1^2 & y_2(m) = 10t_2 - 1.86t_2^2 & V_{ave}(m/s) = \frac{y_2 - y_1}{t_2 - t_1} \\
\hline\\
(i) & 1 & 2 & 8.14 & 12.56 & 4.42 \\
\hline\\
(ii) & 1 & 1.5 & 8.14 & 10.815 & 5.35 \\
\hline\\
(iii) & 1 & 1.1 & 8.14 & 8.7494 & 6.094 \\
\hline\\
(iv) & 1 & 1.01 & 8.14 & 8.2026 & 6.26 \\
\hline\\
(v) & 1 & 1.001 & 8.14 & 8.1463 & 6.3\\
\hline
\end{array}

\end{aligned}
\end{equation}
$


b. Estimate the instantaneous velocity when $t=1$

Therefore, the value of instantaneous velocity when $t = 1$ is approximately equal to $6.3$m/s

What makes "The Village Blacksmith" an inspirational poem?

What makes "The Village Blacksmith" particularly inspiring is the way the man himself goes about his work every day no matter what life throws at him. Being a blacksmith is hard, physical work and requires a lot of strength. That in itself is inspiring. And we're left in no doubt by Longfellow that the blacksmith is a hard worker:

His brow is wet with honest sweat, He earns whate'er he can, And looks the whole world in the face, For he owes not any man.

Not only is he a hardworking man, he's also fiercely independent. He can stand tall and look his fellow men in the eye because he works for himself; he's not reliant on anyone else for his daily bread. In many respects, the village blacksmith is the epitome of the age-old American tradition of rugged individualism. At the same time, he's unmistakably a part of his community, going to church every Sunday and listening to his daughter sing in the choir. As a widowed father he cares deeply for his daughter and venerates the memory of his late wife:

He hears his daughter's voice, Singing in the village choir, And it makes his heart rejoice. It sounds to him like her mother's voice, Singing in Paradise! He needs must think of her once more, How in the grave she lies; And with his hard, rough hand he wipes A tear out of his eyes.

The village blacksmith inspires because he teaches us all a valuable lesson in how to live our lives. Whatever he endures, be it hard work, sorrows, or joys, he still carries on, striving hard to shape his life just as he shapes hot, burning metal on his anvil.
https://www.bartleby.com/102/59.html

Single Variable Calculus, Chapter 3, 3.3, Section 3.3, Problem 54

Find the equation of the tangent line and normal line of the curve $y = (1 + 2x)^2 = 1 + 4x + 4x^2$ at the point $(1,9)$

Required:

Equation of the tangent line and the normal line at $P(1,9)$

Solution:



$
\begin{equation}
\begin{aligned}

\qquad y' = m_T =& \text{Slope of the tangent line}\\
m_N =& \text{Slope of the normal line}
&&
\\
\\
\qquad y' = m_T =& \frac{d}{dx} (1) + 4 \frac{d}{dx} (x) + 4 \frac{d}{dx} (x^2)
&& \text{}
\\
\qquad y' = m_T =& 0 + 4(1) + 4(2x)
&& \text{}
\\
\qquad y' = m_T =& 4 + 8x
&& \text{}
\\
\\
\qquad m_T =& 4 + 8x
&& \text{Substitute value of $x$ which is 1}
\\
\\
\qquad m_T =& 4 + 8 (1)
&& \text{Simplify the equation}
\\
\\
\qquad m_T =& 12
&& \text{}
\\
\\


\end{aligned}
\end{equation}
$


Solving for the equation of the tangent line:



$
\begin{equation}
\begin{aligned}

\qquad y - y_1 =& m_T(x - x_1)
&& \text{Substitute the value of the slope $(m_T)$ and the given point}
\\
\\
\qquad y - 9 =& 12(x - 1)
&& \text{Multiply $12 $ the equation}
\\
\\
\qquad y - 9 =& 12x - 12
&& \text{Add $9$ to each sides}
\\
\\
\qquad y =& 12x - 12 + 9
&& \text{Combine like terms}
\\
\\
\qquad y =& 12x - 3
&& \text{Equation of the tangent line to the curve at $P (1,9)$}


\end{aligned}
\end{equation}
$


Solving for the equation of the normal line


$
\begin{equation}
\begin{aligned}

m_N =& \frac{-1}{m_T}\\
m_N =& \frac{-1}{12}
&&
\\
\\
y- y_1 =& m_N(x - x_1)
&& \text{Substitute the value of the slope $(m_N)$ and the given point}
\\
\\
y - 9 =& \frac{-1}{12} (x - 1)
&& \text{Multiply $\large \frac{-1}{12}$ in the equation}
\\
\\
y - 9 =& \frac{-x + 1}{12}
&& \text{Add $9$ to each sides}
\\
\\
y =& \frac{-x + 1}{12} + 9
&& \text{Get the LCD}
\\
\\
y =& \frac{-x + 1 + 108}{12}
&& \text{Combine like terms}
\\
\\
y =& \frac{-x + 109}{12}
&& \text{Equation of the normal line at $P(1,9)$}

\end{aligned}
\end{equation}
$

Single Variable Calculus, Chapter 7, Review Exercises, Section Review Exercises, Problem 96

Evaluate $\displaystyle \int^{\frac{\pi}{2}}_0 \frac{\cos x}{1 + \sin^2 x} dx$


$
\begin{equation}
\begin{aligned}

\text{If we let } u =& \sin x, \text{ then}
\\
\\
du =& \cos x dx

\end{aligned}
\end{equation}
$


Make sure that the upper and lower limits are also in terms of $u$.

So,


$
\begin{equation}
\begin{aligned}

\int^{\frac{\pi}{2}}_0 \frac{\cos x}{1 + \sin^2 x} =& \int^{\sin \left( \frac{\pi}{2} \right)}_{\sin (0)} \frac{du}{1 + u^2}
\\
\\
=& \int^1_0 \frac{du}{1 + u^2}

\end{aligned}
\end{equation}
$



Recall that


$
\begin{equation}
\begin{aligned}

\frac{d}{dx} (\tan^{-1} (x)) =& \frac{1}{1 + x^2}
\\
\\
=& \left[ \tan^{-1} u \right]^1_0
\\
\\
=& \tan^{-1} (1) - \tan^{-1} (0)
\\
\\
=& \frac{\pi}{4}

\end{aligned}
\end{equation}
$

What are the objectives of the main characters in ruined?

The three leads of the play are Mama Nadi, Josephine, and Sophie. The three women have very different specific objectives that all lead to essentially the same outcome: survival.
Mama Nadi achieves her objective of surviving the conflict in the Congo by running a bar and brothel to the best of her business-like abilities. She maintains a sense of order in her establishment in order to ensure that her customers know what to expect, an objective that protects her financially. Sometimes, Mama Nadi sacrifices her own integrity to make sure that her business is running, but maintaining integrity is a less important objective than survival.
Josephine achieves her objective of survival by using her body as a form of sexual insurance. She looks to please the men in her world as a way to make sure she has a means to a better life. Though attention and ego-boosts appear as if they are important objectives to Josephine, ultimately, they both contribute to her goal of surviving the war.
Sophie is the youngest and least experienced of the three women, and she works towards her objectives with honesty and a naive sense of optimism. She, like Mama Nadi and Josephine, wants a better life, and this life involves a medical operation to repair the effects of her injuries. She also wants to rescue Salima as well as herself, an objective that may not have ever been realistic.

For Mama Nadi, her main goal seems to be to run her business successfully enough that she can feed herself and the young women who work for her. She wants to feel safe and have small creature comforts like chocolates and lipsticks. Josephine, who appears to be the most senior of Mama's girls, seems most interested in being comfortable and maybe even getting out of her situation. Mr. Harari seems interested in taking Josephine with him at one point, and she would obviously like to leave Mama's if possible. Sophie and Salima seem most interested in peace and safety. Both have been the victims of unimaginable violence.
Commander Osembenga's main goal is to squash the rebellion and kill its leader, Jerome Kisembe. Mr. Harari wants safety and comfort, just like Josephine. When he is given an opportunity to escape, he takes it. Fortune wants his wife, Salima, back, but it is too late in her mind for such a reconciliation. Christian, as he tells Mama in the end, wants to settle down and "sleep in the same bed every night." He wants someone to love and someone to love him.

Is "The Black Cat" by Edgar Allan Poe a work of magical realism?

Because the genre of literary magical realism began, at the earliest, in the twentieth century, literary scholars would not place "The Black Cat," published by Edgar Allan Poe in 1843, in that movement.
Magical realism is a type of fiction characterized by a realistic setting that is somehow affected by elements that are magical or supernatural.  The narrator of "The Black Cat" kills Pluto, his first cat, and sometime later, a cat that looks very much like but not identical to Pluto enters his life.  The narrator's perversity turns him against this cat as well, and the narrator ends up accidentally killing his wife when he is aiming his ax at the cat.  He inadvertently walls the cat up with his wife's corpse, but, days later, it makes enough noise to attract the police's attention, and the narrator's crime is revealed.
It is quite plausible that two black cats can look extremely similar except for a single marking, and it is also possible that a cat could survive without food or water for a few days.  While the story may be somewhat implausible, there is nothing magical or supernatural in "The Black Cat," making it a horror story rather than a work of magical realism. 

How is fear created in "The Signal-Man" by Charles Dickens?

Another way that Dickens creates fear in this story is through his use of setting. This is perhaps most evident in the opening paragraphs of the story when the narrator first arrives at the signal box.
You will notice that Dickens does not reveal specific details about the setting to the reader. For example, he does not tell the reader that he is meeting a signalman at his place of work. Instead, Dickens creates a sense of fear and uncertainty by emphasizing the strange sights and sounds of the setting. He compares the setting to a "deep trench," for instance, and highlights the "angry sunset." He also describes the "violent pulsation" caused by a passing train, as well as the dank, dark atmosphere.
By honing in on these details, Dickens creates a setting which evokes fear and uncertainty in the reader while also building tension and suspense ahead of the story's main events.

Dickens creates a sense of fear in a number ways. Here are three.
1. Imagery that evokes desolation, foreboding, and the supernatural
After the narrator has descended the path and joined the signal-man at his station, he describes the place as a "great dungeon." He comments on the "gloomy" red light and the  

"gloomier entrance to a black tunnel, in whose massive architecture there was a barbarous, depressing, and forbidding air. So little sunlight ever found its way to this spot, that it had an earthy, deadly smell; and so much cold wind rushed through it, that it struck chill to me, as if I had left the natural world."

The vivid sensory impressions set the scene. This is the sort of place where the reader can easily imagine seeing a ghost.
The sense of foreboding is furthered by the narrator's first impression of the signal-man himself. For a moment, the narrator says, "a monstrous thought came into my mind…that this was a spirit, not a man."
2. The recounting of uncanny events and deadly episodes
The content of the signal-man's stories is intrinsically disturbing. For instance, when the signal-man reaches out to the dark, mysterious, urgent figure, it suddenly disappears. Then,

"…within ten hours the dead and wounded were brought along through the tunnel over the spot where the figure had stood.”

3. Empathy and fear contagion
Fear is contagious; we tend to become more anxious or frightened when we witness fear in others. More generally, observing distress in others evokes an empathic response. We experience their emotions second-hand. Dickens uses this aspect of human psychology to induce fear in the reader.
For instance, at the beginning of the story, the signal-man reacts to the narrator with great wariness. The narrator is aware of this, noting, "I detected in his eyes some latent fear of me." He wonders if there is an "infection in his mind."
Later, we learn that the signal-man hears the bell ring when no one else can. He believes that it signals the return of the ghost. The reader is left to consider this man's position -- spending long hours, alone in this gloomy place, waiting with anxiety for the bell to ring.
The reader is also influenced by the fearful reactions of the narrator. For example, when he hears the signal-man's story, he mentions the "slow touch of a frozen finger tracing out my spine," and notes that a "disagreeable shudder crept over me."
And when he thinks he sees the ghost he again shares his immediate, involuntary reaction with us:

"I cannot describe the thrill that seized upon me, when, close at the mouth of the tunnel, I saw the appearance of a man, with his left sleeve across his eyes, passionately waving his right arm."

Even the ghost's body language suggests anguish and distress about death:

"It was an action of mourning. I have seen such an attitude in stone figures on tombs."

What are the fundamental principles of leadership? What are the fundamental principles of human resource management applied by organisations wishing to get the best out of their people?

There are a number of approaches to enumerating the fundamental principles of leadership. Some approaches enumerate eight or ten principles while others enumerate five principles. In general, though, there are two essential approaches, and there is a great deal of cross-over between all approaches. One essential approach focuses on ethical and respectful behavior, stressing that the person is never the problem; the situation external to the person is the problem; constructive relationships and leading by example are necessary. The other essential approach focuses on qualifications for leadership, stressing such things as communication skills, decision-making proficiency, taking responsibility, providing information, delegating tasks, flexibility, passing on the vision, and enabling employees.One five-step model for the fundamental principles of leadership developed by the Leadership Challenge relies heavily on the personal qualities of the leader. This five-step model advocates:

Modeling the way things will be, setting the standard for how people will be treated, and identifying small goals that lead to larger objectives.
Inspiring a shared vision of what the company will come to be by using "magnetism and quiet persuasion" to inspire partnership in the vision.
Challenge the status quo by being innovative, experimenting and taking risks.
Enabling employees to act independently by fostering collaboration and team projects, with behavior founded in "trust and human dignity."
Encouraging the heart--the spirit--of employees by recognizing contributions and hard work.

Brad Sugar of Action Coach advocates a different approach, one that is based in what the leader does rather than what the leader is. In his ten-step plan, he advocates:

Know your attributes and strengthen the weak areas.
"Be technically proficient," with a solid understanding of the jobs your employees do.
While striving for company growth, "seek responsibility" and accept responsibility for your errors.
Have the tools and methods for sound decisions.
Set a good example; employees trust what they see.
Care about and look out for the well-fare of your employees.
Communicate, and keep people up-to-date with information.
For success in responsibilities, develop a "sense of accountability, ownership and responsibility" in employees.
Tasks and roles for employee assignment need to be communicated so they are understood; then they need to be "supervised, and accomplished" so employees have success and self-esteem.
Unit your employees as a team to attain a united spirit and the fullest fulfillment of capabilities.

Use your knowledge of heat transfer methods to explain how under floor insulation reduces the loss of heat through the floor. I understand that if the floor of a house is insulated, the floor prevents heat loss or gain. This is thermal insulation. I also understand that this is because the distance between the particles in an insulator is greater than that of a conductor, but I need to put it into a scientific manner. Any information will be appreciated.

There are three methods of heat transfer that come to mind.
The first is conduction. Conduction is when the excited particles of one atom or molecule touch the excited particles in the atoms or molecules of another substance. This is how heat goes from one solid to another, or from single particles to other single particles, in typical usage.
The second is convection. Through convection, energy is transferred in the same way as conduction, but instead of a solid absorbing the energy, a fluid, such as a liquid or gas, absorbs the energy. In addition, the absorption of energy causes the fluid to move about, generating convection currents. These convection currents are common in ovens, the ocean, and even the earth's mantle.
Finally, radiation is a way that heat is transferred. This is when the atoms and molecules of the substance eject energized parts of themselves to increase entropy. Common radiation includes alpha, beta, and gamma decay, which you can learn more about here. This radiation is physical, and can be stopped by hitting other particles.
To conclude, the floor insulation prevents the escape of heat through all of these methods. The floor is a good insulator, as you mentioned, and is resistant to conductive heat loss. The floor separates the heat in the home from the air outside, which slows down the convection currents beneath the flooring. The floor blocks the radiation emitted in the building, sending it back before it can escape.
As far as your question on what in particular makes the flooring a good insulator, there are a few reasons. The first is that the insulation has molecules that are separated from each other with distance. The second is that the insulation has layers of material. Heat transfers from one object to another and across thin films slower than across single materials. Third, the structure of the material may be lattice oriented in a way that increases resistance to heat transfer. This means amorphous materials, like amorphous silicon, will be more resistant than an aligned block of silicon. Even little things, like the Thermal Hall Effect, can make a difference in the insulation a material provides.
https://www.condmatjclub.org/jccm-content/uploads/2015/03/JCCM_MARCH_2015_02.pdf

Why was Holling able to buy the cream puffs so cheaply? Why did his plan go wrong?

The answer to this question can be found in the November chapter. Holling needs to buy the class some cream puffs to make up for the ones that he accidentally tainted with chalk dust, which caused all of the kids to get sick, and they threatened him if he didn't get them some clean cream puffs. The problem is that Holling doesn't have enough money to buy from the baker. Holling attempts to trade labor for the cream puffs, but the baker says that he doesn't need any work done. What the baker needs is somebody who knows Shakespeare.

"What I should really need," he said, "is a boy who knows Shakespeare."

Holling has just started going through works of Shakespeare on his Wednesdays with Mrs. Baker, so Holling announces that he knows Shakespeare. The baker is skeptical, but Holling proves his knowledge by reciting a few passages. The baker is impressed and gives Holling the cream puffs that he needs. Getting the cream puffs cheap is a win for Holling, but it does sort of backfire on Holling. Holling also agrees to be in a Shakespeare production that the baker is putting on, and Holling gets to play Ariel and wear tights with feathers on his butt.

What are the five most significant events in 1776 by David McCollough, not focusing only on the military engagements?

1776 focuses primarily on military events because the author covered political events of the same year in a previous book: John Adams.
The first important event described in the war actually took place in October 1775, in London. King George III gave an important speech to British Parliament in which he promised to crush the rebellion. After that speech, peaceful reconciliation was out of the question.
The second key event happened in March 1776. The Americans put cannons in Dorchester Heights, forcing the British to evacuate Boston. Henry Knox, head of artillery, had dragged the cannons 300 miles from Ticonderoga to Boston.
The third major event, which the author describes as the most important event in the book, was George Washington's escape from Brooklyn in August. Despite being defeated in battle, Washington managed to extricate his weakened army. Had the British managed to trap Washington, the war would have been over.
A fourth significant event was at the end of 1776. The British drove Washington's depleted forces across New Jersey. With Washington on the verge of defeat, the British went into winter quarters. This enabled the Americans to rally and win victories in the Trenton-Princeton campaign. For the second time, the British had allowed Washington to recover and escape.
A final event that unfolded gradually throughout the year was George Washington's development as a field commander. He learned from the mistakes he made and became much more decisive and capable in subsequent years.
These are the five most significant events in 1776.

It is, of course, difficult to point to exclusively non-military events in a book that focuses so much on the Revolutionary War. So there are some events in this answer that are basically military. Still, some are more political in nature. 
The first event actually occurs in October of 1775. After a speech by King George and a lengthy debate in Parliament, with significant dissenting voices, both houses of Parliament voted to approve Lord North's plan to send a large military and naval force to the colonies, then in a state of all-out rebellion. This marked, in many ways, a point of no return in the conflict and was thus a major event. Another occurred in March of 1776, when Washington's capture and fortification of Dorchester Heights forced the British army to abandon the city of Boston. McCullough describes this event as the "first thrilling news of the war" for the rebels (108). 
Another event, of course, was the decision of the Second Continental Congress to declare independence from Great Britain. This decision, reached on July 2, meant that the war would be an "all-out war for an independent America" and was a major turning point described in the book (137). But this occurred even as another crucial event was taking place--the massive invasion of New York by the British army and navy. Finally, the book closes with a speech by King George in 1777. Echoing the debates in Parliament at the beginning of the book, the speech announced that, despite the previous year's events, the Americans had not "recovered from their delusion" (292). 

How did Odysseus end up back in Ithaca sleeping on the beach?

Odysseus reaches Ithaca thanks to the Phaeacians, who listen to his incredible story and decide to help him get back to Ithaca after twenty years of traveling. King Alcinous and Princess Nausicaa give Odysseus a ship and many gifts to take home, and Odysseus sails back to Ithaca safely. He disguises himself as a beggar before proceeding towards the town. He is not shipwrecked and does not sleep on the beach.
The island where Odysseus is shipwrecked and is found in a deep sleep on the beach is not Ithaca but the island of the Phaeacians. Before reaching the island, Odysseus was supposed to be sailing home. Earlier in the story, in fact, Odysseus leaves Calypso with his men in order to return home. However, the god Poseidon sends out a storm which causes Odysseus's ship to sink. In fact, Poseidon is angry because Odysseus previously blinded his son Polyphemus (a cyclops who, in Odysseus's defense, was actually trying to eat him and all his men). Odysseus ends up as the only survivor on the beaches of Scheria, the island of the Phaecians, where Nausicaa finds him sleeping on the beach.
Nausicaa then takes him to the palace, where the Phaeacians listen to his story and decide to help him. Hopefully this clears up any doubts about the two different islands!

which historians (with quotes) support that USA was responsible for increased tensions for the Vietnam war from 1961-1972? similarly which historians (with quotes) agree that USSR was responsible for increased tensions during Vietnam war from 1961-1972

With the exception of the war in Iraq, no other war in American history has divided historians as much as the Vietnam War. You are right that some historians blame the United States for increased tensions during the Vietnam War, while others hold the USSR responsible. Let's begin with historians who blame the United States.
The most widely read historians of this stripe were William J. Duiker, Arthur M. Schlesinger, Jr., Gabriel Kolko, John W. Lewis, David Halberstam, and George McTurnan Kahin. Kahin and Lewis co-wrote The United States in Vietnam, a book highly critical of American war policy in Southeast Asia. In particular, Kahin was a staunch supporter of the Khmer Rouge communist insurgency and strongly condemned South Vietnam's goal of separation from North Vietnam.
Many of the above historians were strongly critical of South Vietnamese president Ngo Dinh Diem and the support he received from the American government and military apparatus. Here are two quotes from Kahin's book The United States in Vietnam:

But to attain and keep the military initiative outside...urban strongholds, the United States has had to resort to warfare of a kind that is destroying the rural Vietnamese society it hopes to deny the Vietcong...Although Washington has declared that the first essential is to give the people security, it feels that this can only be achieved by eradicating the Vietcong from their midst. This social surgery requires military actions in contested areas on a non-selective basis...
The continuing American insistence that the war in the South is simply a case of aggression from the North has led to erroneous conclusions concerning de-escalation.

Meanwhile, historians who largely supported the American role in Southeast Asia during the Vietnam War included Guenter Lewy (who wrote America in Vietnam); Norman Podhoretz (who wrote Why We Were In Vietnam); Harry G. Summers, Jr.; Bruce Palmer, Jr.; and Philip B. Davidson. These historians argued that civilian legislative leaders obstructed American military efforts to contain the North Vietnamese communist insurgency.
As for historians who believed that the USSR was responsible for increased tensions during the Vietnam War, here are a couple of quotes from Thomas J. Christensen:

“Ho Chi Minh was able to exploit Chinese and Soviet jealousies of one another to gain maximum support for his goals in South Vietnam. From 1965 until early 1968, the rivalry between Beijing and Moscow also served to scuttle multiple Soviet-inspired proposals for peace talks between the Vietnamese communists and the United States.”
As early as 1965, 50 percent of Soviet aid to communist countries was going to Vietnam, and 60 percent of this was military aid.

Christensen contends that the Sino-Soviet rivalry in Vietnam led to increased tensions in the Southeast Asian region during the Vietnam War. For more, please refer to the books I mentioned and the links below.
Sources:
1) Historians and the Vietnam War: The Conflict Over Interpretations Continues, George W. Hopkins, Studies in Popular Culture, Vol. 23, No. 2 (October 2000), pp. 99-108
2) Worse Than a Monolith: Alliance Politics and Problems of Coercive Diplomacy by Thomas J. Christensen
https://www.modernamericanpoetry.org/dashboard

What are some actions Jonas does and what can we learn about him from his actions?

Throughout Jonas's training as Receiver of Memory, he realizes that he values personal freedom to make decisions, appreciates situations in life that cause happiness and joy, and gradually becomes jaded with his mundane community, which is focused on safety and conformity.
After learning the truth behind the term "release," Jonas and the Giver devise a plan to change the community for the better. Unfortunately, Jonas is forced to dismiss the plan in order to save Gabriel's life. Jonas makes the difficult decision to escape from the community with Gabe and travel to Elsewhere while simultaneously avoiding the community's search planes. Jonas's decision to flee the community reveals his courage, determination, and selfless nature. Jonas chooses to do the right thing and make the independent decision to leave his family and community behind in order to change his life's trajectory and save Gabriel. The reader learns from Jonas's actions that he is a courageous, independent, confident individual who is willing to take risks to better his life and stand up for what is right.

f(x)=x^2e^(-x) , n=4 Find the n'th Maclaurin polynomial for the function.

Maclaurin series is a special case of Taylor series that is centered at c=0 . The expansion of the function about 0 follows the formula:
f(x)=sum_(n=0)^oo (f^n(0))/(n!) x^n
 or
f(x)= f(0)+(f'(0))/(1!)x+(f^2(0))/(2!)x^2+(f^3(0))/(3!)x^3+(f^4(0))/(4!)x^4 +...
To determine the Maclaurin polynomial of degree n=4 for the given function f(x)=x^2e^(-x) , we may apply the formula for Maclaurin series.
To list f^n(x) up to n=4 , we may apply the following formula:
Product rule for differentiation: d/(dx) (u*v) = u' *v +u*v'
Derivative property: d/(dx) (f+-g+-h) = d/(dx) f +-d/(dx) g+-d/(dx) h
Power rule for differentiation: d/(dx) x^n =n*x^(n-1)
Derivative formula for exponential function: d/(dx) e^u = e^u * (du)/(dx)
f(x)=x^2e^(-x)
Let u =x^2 then u' = 2x
      v = e^(-x)  then v' = e^x*(-1) =-e^(-x)
d/(dx) (x^2e^(-x)) = 2x*e^(-x) + x^2*(-e^(-x))
                        = 2xe^(-x) -x^2e^(-x)
Let: u =x then u' =1
        v = e^(-x)  then v' =-e^(-x)
Note: c = constant value.
d/(dx) c*xe^(-x) = c*d/(dx) xe^(-x)
                     = c*[1*e^x +x * (-e^(-x))]
                      = c*[e^x-xe^(-x)]
                      = ce^x-cxe^(-x)
d/(dx) c*e^(-x) = c*d/(dx) e^(-x)
                  =c*(-e^(-x))
                  =-ce^(-x)
 
f'(x) =d/(dx) (x^2e^(-x))
           = 2xe^(-x) -x^2e^(-x)
f^2(x) = d/(dx) (2xe^(-x) -x^2e^(-x))
            =d/(dx) 2xe^(-x) -d/(dx) x^2e^(-x)
            = [2e^(-x)-2xe^(-x)] - [2xe^(-x) -x^2e^(-x)]
            =2e^(-x)-2xe^(-x) - 2xe^(-x) +x^2e^(-x)
            =2e^(-x)-4xe^(-x) +x^2e^(-x)
f^3(x) = d/(dx) (2e^(-x)-4xe^(-x) +x^2e^(-x))
            =d/(dx) 2e^(-x) -d/(dx) 4xe^(-x)+ d/(dx) x^2e^(-x)
            =[-2e^(-x)] -[4e^(-x)-4xe^(-x)]+ [2xe^(-x) -x^2e^(-x)]
            =- 2e^(-x) -4e^(-x)+4xe^(-x)+ 2xe^(-x) -x^2e^(-x)
             =- 6e^(-x)+6xe^(-x) -x^2e^(-x)
f^4(x) = d/(dx) ( - 6e^(-x)+6xe^(-x) -x^2e^(-x))
          =d/(dx) (-6e^(-x)) + d/(dx) 6xe^(-x)- d/(dx) x^2e^(-x)
         =[ 6e^(-x)]+[6e^(-x)-6xe^(-x)] -[2xe^(-x) -x^2e^(-x)]
         =6e^(-x)+6e^(-x)-6xe^(-x) -2xe^(-x) +x^2e^(-x)
          =12e^(-x)-8xe^(-x) +x^2e^(-x)
Plug-in x=0 for each f^n(x) , we get:
f(0)=0^2e^(-0)
          =0*1
          =0
f'(0)=2*0*e^(-0) -0^2e^(-0)
           =2*0*1 +0*1
           =0
f^2(0)=2e^(-0)-4*0*e^(-0) +0^2e^(-0)
            =2*1 -4*0*1 +0*1
              =2
f^3(0)=- 6e^(-0)+6*0*e^(-0) -0^2e^(-0)
           =-6*1 +6*0*1 +0*1
           =-6
f^4(0)=12e^(-0)-8*0*e^(-0) +0^2e^(-0)
             =12*1 -8*0*1 +0*1
            =12
Note: e^(-0) = e^0 =1 .
Plug-in the values on the formula for Maclaurin series, we get:
sum_(n=0)^4 (f^n(0))/(n!) x^n
      = f(0)+(f'(0))/(1!)x+(f^2(0))/(2!)x^2+(f^3(0))/(3!)x^3+(f^4(0))/(4!)x^4
      = 0+0/(1!)x+2/(2!)x^2+(-6)/(3!)x^3+12/(4!)x^4
      = 0+0/1x+2/2x^2-6/6x^3+12/24x^4
      = 0+0+x^2-x^3+1/2x^4
      = x^2-x^3+1/2x^4
The Maclaurin polynomial of degree n=4 for the given function f(x)=x^2e^(-x) will be:
P(x)=x^2-x^3+1/2x^4

y = arctan(x/2) - 1/(2(x^2+4)) Find the derivative of the function

The derivative of y with respect to is denoted as y' or (dy)/(dx) .
 For the given equation: y = arctan(x/2) -1/(2(x^2+4)) ,
we may apply the basic property of derivative:
d/(dx) (u-v) =d/(dx) (u) - d/(dx)(v)
 
Then the derivative of y will be:
y' = d/(dx)(arctan(x/2) -1/(2(x^2+4)))
y' =d/(dx)(arctan(x/2)) - d/(dx)( 1/(2(x^2+4)))
To find the derivative of the first term: d/(dx)(arctan(x/2)) , recall the basic derivative formula for inverse tangent as:
d/(dx) (arctan(u)) = ((du)/(dx))/(1+u^2)
With u = x/2 and du=(1/2) dx or (du)/(dx) =1/2 , we will have:
d/(dx)(arctan(x/2)) = (1/2) /(1+(x/2)^2)
                           = (1/2) /(1+(x^2/4))
Express the bottom as one fraction:
d/(dx)(arctan(x/2)) = (1/2) /((x^2+4)/4)
Flip the bottom to proceed to multiplication:
d/(dx)(arctan(x/2)) = 1/2*4/(x^2+4)
                          = 4/(2(x^2+4))
                          =2/(x^2+4)
 
For the derivative of the second term: d/(dx)(1/(2(x^2+4))) , we can rewrite it using the basic property of derivative: d/(dx) (c*f(x)) = c* d/(dx) f(x) where c is constant.
d/(dx)(1/(2(x^2+4))) = (1/2) d/(dx)(1/(x^2+4))
Then apply the Quotient Rule for derivative: d/(dx) (u/v)= (u' * v- v'*u)/v^2 on  d/(dx)(1/(2(x^2+4))) .
We let:
u = 1 then    u' = 0
v = x^2+4 then v'=2x
v^2= (x^2+4)^2
Applying the Quotient rule, we get:
d/(dx)(1/(2(x^2+4))), = (0*(x^2+4)-(1)(2x))/(x^2+4)^2
                         =(0-2x)/ (x^2+4)^2
                         =(-2x)/ (x^2+4)^2
 
Then (1/2) * d/(dx)(1/(x^2+4)) =(1/2) * (-2x)/ (x^2+4)^2
                                              = -x/ (x^2+4)^2
 For the complete problem: 
y' =d/(dx)(arctan(x/2)) - d/(dx)( 1/(2(x^2+4)))
y' =2/(x^2+4) + x/ (x^2+4)^2
 

What is a good quote from the book called Farewell to Manzanar?

Here is another good quote from the book Farewell to Manzanar:

Like so many of the women there, Mama never did get used to the latrines. It was a humiliation she just learned to endure: shigata ga nai, this cannot be helped. She would quickly subordinate her own desires to those of the family or the community, because she knew cooperation was the only way to survive (30).

In this excerpt, Jeanne speaks about the ways her mother adapts to life at Manzanar, the relocation camp where the family is forced to live because they are Japanese-Americans during World War II. She writes that her mother adapts an attitude of quiet resilience and accommodation. Mama accepts that nothing can be done except to live in the crowded camp as best she can, and she is guided by her commitment to her family and her community. She suppresses her own needs and wants, even though she desperately wants privacy, in favor of living amiably with others and doing the best she can for her family. The author writes that everyone in Manzanar has inherited these seemingly contradictory traits—accommodation to others and a desire to maintain one's privacy—from living in the crowded country of Japan.

In chapter one, the narrator, Jeanne Wakatsuki, describes the day two FBI agents came to arrest her father. As he left Woody's place on Terminal Island, the men flanked Papa, and "He didn't struggle. There was no point to it. He had become a man without a country."
This quotation is a good one because it establishes the absurdity of the arrests of Japanese American people in the US after the attack on Pearl Harbor and what it meant for them. Jeanne's father was a Japanese immigrant who had built, over the course of thirty-five years, a commercial fishing business, owned two boats, and had children born in America. After the attack on Pearl Harbor he burned a Japanese flag and his identity papers. He wasn't able to become an American citizen because of the US government's policies, and so he literally was a man without a country. He was no longer a citizen of Japan, by choice, yet he was not, legally speaking, an American. His experiences after his arrest and the family's internment offered a tragically diminished life for him from which he never recovered.

Who is the protagonist in The Namesake by Jhumpa Lahiri?

Jhumpa Lahiri's The Namesake fits the description of a bildungsroman, which is a work of literature that tells the story of a protagonist's formative years. The protagonist of The Namesake is Gogol, who eventually changes his name to Nikhil as a way of displaying his own independence from his parents.
The novel begins, as many bildungsromans do, with the story of Gogol's birth. The reader gets to know his parents and other people in Gogol's life while the events in the plotline unfold, focusing on the childhood, adolescence, and early adulthood experiences of Gogol. These descriptions of Gogol's parents and their families provide the reader with a thorough backdrop of cultural information; the reader understands through these details the life into which Gogol emerges on the day he is born. Because the reader has an intimate understanding of Gogol before Gogol himself even appears, the reader feels invested in the development of the hero of the novel. As protagonist, Gogol faces many conflicts and complications throughout the novel that make his life rich and interesting.

Gogul Ganguli is the protagonist in The Namesake.
The entire narrative of The Namesake revolves around Gogul's experiences. Gogul's complex and agonizing search for identity is the basis for the novel. He experiences this struggle emotionally and culturally. We understand the full implications behind Gogol's profound realizations about his own existence, the love he holds for other people, and how he fares in balancing his own needs with his need for others' acceptance. No other character experiences these realities as forcefully as Gogol does. From being so unsettled in the world to finding his place in it, Gogol is the means through which the novel's message emerges.  
Another reason why Gogol is the protagonist is because Lahiri uses him to convey her own experiences. For example, Lahiri struggled with her own name in a way that mirrors Gogol's: "I always felt so embarrassed by my name. . . You feel like you're causing someone pain just by being who you are." Gogol learns a person's identity encompasses both their past and future and the need to accept one's own namesake. Gogol is the vehicle through which Lahiri communicates thematic and personal truths in The Namesake.

In what ways are Marlow and Kurtz considered to be "morally ambiguous" characters, and how does this illuminate the overall meaning of the story?

Marlow and Kurtz reveal a dichotomy in their personalities as they both are depicted as having positive and negative character traits and beliefs, which helps illustrate and support Conrad's view of humanity's inherently wicked nature.
While Marlow is portrayed as a relatively self-conscious man who detests the inefficient, abusive nature of the company and its employees, he is nonetheless fascinated by Kurtz and shares inherent personality traits with the enigmatic character. Marlow is obsessed with traveling deep into the African continent and ends up admiring Kurtz, despite witnessing his wicked nature. Marlow continues his journey even after witnessing the negative effects of imperialism each time he stops at one of the company's stations. Marlow also lies to Kurtz's "intended" and discovers that there is darkness in every human heart. Marlow's questionable decision to continue journeying deep into the Congolese jungle, his admiration for Kurtz, and his dishonest response to Kurtz's intended portray him as a morally ambiguous character.
Likewise, Kurtz is also a morally-ambiguous character, despite his obvious flaws and maniacal nature. Kurtz initially entered the Congolese jungle in hopes of exposing civilization to "savages" and creating a structured, organized society deep in the African continent. Unfortunately, Kurtz becomes a victim of his own inherent primitive nature once he distances himself from civilization. Kurtz's soul becomes corrupted, and he begins ruling as a tyrant and god over the natives. His inherent wickedness flourishes in the uncivilized environment void of rules, laws, and regulations. Kurtz can be considered a morally ambiguous character because he begins his journey into the Congolese jungle with positive intentions only to become a victim of his own inherently wicked nature.
Conrad's depiction of Marlow and Kurtz as both being morally ambiguous people illustrates his negative views of humanity. Conrad's novella portrays humans as inherently wicked beings and challenges the reader's perception of civilization and humanity.

What factors contributed to the decline of the powerful self-reliant Iroquois Indians?

The Iroquois established a unique federation of nations on the American continent that saw great peace and prosperity.  The arrival of English colonists caused the decline of this once prosperous people for a number of reasons. The English brought with them a myriad of diseases for which Native Americans did not have an immunity.  Smallpox, measles, and influenza were particularly devastating to the population of the Iroquois during the Seventeenth Century. In addition to the diseases brought by the English, political and economic uncertainty and turmoil would follow.  The competition for furs between European countries plunged the Iroquois into a number of conflicts that cost the tribes lives on the battlefield.  Death from warfare and disease coupled with unfair treaties with the new American government ultimately led to the demise of the Iroquois.  
https://www.everyculture.com/multi/Ha-La/Iroquois-Confederacy.html

In "Swing Low, Sweet Chariot," who is coming over Jordan to carry the speaker home?

"Swing Low, Sweet Chariot" is an African-American spiritual, a song written in a distinctive style combining Christianity with the slave experience. Spirituals are influenced by African musical traditions. While spirituals were originally monodic (all singers sang a single melody in unison), they have evolved to include intricate choral harmonies. 
"Swing Low, Sweet Chariot" may actually have been written by Wallis Willis, a member of the Choctaw tribe. It was popularized by the Jubilee Singers of Fisk University and became increasingly popular in the 1960s as part of a folk and protest song movement. 
The song is narrated in the first person and takes the form of direct address, with the speaker asking the "chariot" to swing low and "carry me home." The home in question is Heaven. Specifically, the speaker states:

I looked over Jordan, and what did I see...
A band of angels coming after me,

The angels are crossing the Jordan River to take the speaker home.

Which type of EMR is trapped by the greenhouse effect?

Carbon dioxide and other greenhouse gases including methane, nitrous oxide, tropospheric ozone and CFC's are all accumulating in the atmosphere due to human activities. They are the causes of global climate change. 
In an actual greenhouse, its glass panels allow sunlight in, but trap heat energy, preventing it from escaping. This causes the temperature inside a greenhouse to be quite warm.
Greenhouse gases absorb infrared radiation, the electromagnetic radiation that is radiated heat from the sun. As sunlight strikes Earth, some of it is converted to heat which should radiate back into space. However, the greenhouses gases in the atmosphere slow this process down and warm the temperature of the lower atmosphere. This leads to global warming.
Infrared radiation has longer wavelengths than visible light, but shorter wavelengths than microwaves along the electromagnetic spectrum. The shortest wavelengths on the electromagnetic spectrum are gamma rays, followed by X-rays, ultraviolet, visible light, infrared, microwaves, radar, tv, and radio waves which are the longest.
To summarize, the type of EMR trapped by greenhouse gases is called infrared radiation.
 

What's the adage which Old Man Warner shares about the value of keeping the lottery?

The ancient adage which Old Man Warner cites that pertains to the value of retaining the lottery is "Lottery in June, corn be heavy soon."
Old Man Warner, the oldest man in the village, is representative of those people who blindly follow a tradition and find value in this custom because it has lasted. He tells the others to whom he recites the old adage, "There's always been a lottery." Moreover, Warner believes soundly in this ancient rite performed to ensure a good harvest. He adds that without a lottery, the people of his community may soon find themselves eating "stewed chickweed and acorns."
Such a character as Warner cannot be swayed to any other way of thinking. He boasts of living through seventy-seven lotteries, and he considers those residents of other villages who have done away with their lotteries as toying with danger: "Nothing but trouble in that....Pack of young fools." Clearly, Old Man Warner represents those who unthinkingly follow a tradition simply because it is a practice that has been around for many years.

In the first half of the poem, where is the port?

I think what you are asking is "where is the poet" in this poem. In order to answer that, we need to clarify the idea that the poet is not necessarily the actual narrator of the poem. We have no idea where the poet "is" in the poem. However, Whitman gives us a number of clear details to allow us to determine where the narrator of the poem is located.
In line four, the narrator specifically states that they are "sitting" in a "lecture room" of some sort. There is also clear indication that the narrator is not alone in the lecture room, as there is also the "learn'd astronomer," one of the central focuses of the poem, but also "much applause" based on what the astronomer is saying. The first three lines also make it clear that the narrator is listening to some sort of specific lecture, as "proofs," "figures," and "charts and diagrams" are all "ranged out" and "shown" by the astronomer. Finally, Whitman's narrator begins to feel "tired and sick" and leaves the lecture hall to enter into "the mystical moist night-air" late in the poem, which gives the reader the sense that the lecture hall was very stuffy. While it is difficult to tell where the poet, Whitman himself, was when he wrote the first half of the poem, his narrator is clearly situated in a crowded, stuffy lecture room, being subjected to the demystification of the world. The narrator eventually leaves the lecture to return to the natural world and enjoy it for what it is.

What happens during Aunt Alexandra's missionary circle?

Scout’s experience attending her aunt Alexandra’s missionary circle is eye-opening for the young girl. The gathering of women that occurs in Chapter 24 of Harper Lee’s novel To Kill a Mockingbird provides the author’s young precocious narrator an opportunity to observe and comment on the eclectic group gathered in her home. Scout does not initially intend to participate in the discussions that day, but Alexandra invites her into the circle. As Scout explains regarding her aunt’s invitation/summons, this “was a part of her campaign to teach me to be a lady.” The presence of Miss Maudie proves crucial to Scout’s ability to endure the idiosyncrasies of the various personalities present, but the conversations that take place are a challenge.
Throughout To Kill a Mockingbird, Lee observes through the eyes of her young protagonist the prejudices and myriad shortcomings among the town of Maycomb’s citizenry. The issues of racial prejudice and judgmentalism are a constant theme in Lee’s novel, and they are present during the missionary circle’s gathering. Among the more notable occurrences during the gathering involve Mrs. Grace Merriweather, “the most devout lady in Maycomb,” as Scout notes. Mrs. Merriweather dominates much of the discussion, focusing on her experiences in Africa among a tribe called the Mrunas. Mrs. Merriweather was in Africa as part of a church mission to bring Western civilization and Christianity to the impoverished of the continent. It is during Mrs. Merriweather’s discussion of the Mrunas and the poverty she observed that the hypocrisy of these supposedly cultured, educated women is most apparent. Note, in the following passage, the irony apparent in Lee’s narration:

“When Mrs. Merriweather shook her head, her black curls jiggled. ‘Jean Louise,’ she said, ‘you are a fortunate girl. You live in a Christian home with Christian folks in a Christian town. Out there in J. Grimes Everett’s land there’s nothing but sin and squalor.’”

To Kill a Mockingbird depicts racial prejudice and injustice at its most basic. Racism is the novel’s most enduring image. The arrest, trial, and conviction of Tom Robinson, falsely accused of raping a white woman, constitutes Lee’s most damning indictment of the prejudices and narrow-mindedness that dominate the culture she depicts. The population of Maycomb is rife with the kind of racism that repeatedly led to miscarriages of justice and that tarnished the country in which these crimes took place. The most important development that occurs during the missionary circle, then, is the blatant hypocrisy evident in Mrs. Merriweather’s comments regarding Christianity and the destitute tribes of Africa she visited. That the meeting should involve so much discussion of the moral superiority of Christians at the same time these Christian citizens of the American South can so cavalierly countenance a miscarriage of justice involving an innocent black man becomes even more important when the gathering is interrupted by the arrival of Atticus with the news that Tom Robinson was shot and killed. That, and recognition that despite their differences, Aunt Alexandra and Miss Maudie and Scout could find common ground within the atmosphere of hypocrisy, are the most significant developments of the day.

In Chapter 24, Scout attends Aunt Alexandra's missionary circle along with several other ladies from the Maycomb community. Scout is apprehensive about joining the conversation and listens as the ladies discuss J. Grimes Everett's missionary work in Africa. Throughout their conversation, Lee exposes Mrs. Merriweather's ignorance and prejudice towards foreign cultures. Mrs. Merriweather and Mrs. Farrow then discuss how their African American maids are upset about the outcome of Tom Robinson's trial. The ladies criticize their maids' behavior and comment that Jesus would have never gone around grumbling. Mrs. Merriweather then indirectly criticizes Atticus for defending Tom Robinson by saying,

"I tell you there are some good but misguided people in this town. Good, but misguided. Folks in this town who think they're doing right, I mean" (Lee 142).

Miss Maudie is aware of Mrs. Merriweather's subtle criticism of Atticus and says, "His food doesn't stick going down, does it?" (Lee 142). Scout does not fully comprehend why Maudie is so upset but notices that Aunt Alexandra gives her a look of gratitude. Scout is in awe of Alexandra's subtle acknowledgment and realizes that she will soon enter into the world of women. Miss Merriweather then says that the people living in the North are hypocrites for trying to dismiss their prejudice against African Americans. Scout tries to occupy herself and begins to daydream while Miss Merriweather is talking. Suddenly, Atticus arrives home and interrupts the missionary circle to tell Alexandra and Cal that Tom is dead.

What is the significance of the Duke's visitor in the poem and what their presence reveals about the events surrounding the poem (context)?

To his guest the duke, says,

The Count your master's known munificence Is ample warrant that no just pretenseOf mine for dowry will be disallowed;Though his fair daughter's self, as I avowedAt starting, is my object.

Therefore, we can surmise that the person visiting the duke is an emissary for a count whose daughter the duke is pursuing. His reference to her dowry makes it clear that the duke is hoping to marry the count's daughter. In fact, he calls her his "object." He means, of course, his goal, but it is a telling word choice: the narrative makes it obvious that he cares a great deal for objects, things that he can own and control, but he cares less about actual people who have wills of their own that might conflict with his. For example, he is quite proud of the portrait of his "last duchess," but he evidently had her killed when he was unable to control her behavior to his satisfaction. He says, "I gave commands; / Then all [of her] smiles stopped together." He refused to address the behavior that bothered him: that she was made happy by small as well as great things, and she did not appreciate him more than she did any other gift given to her. Because he considers that to be "stooping" (and he will not lower himself).
In fact, the person's visit to the duke, presumably to work out the details of the dowry and nuptials, is what prompts the duke to tell the story of his last duchess in the first place. He is clearly showing this emissary around his home, focusing on the works of art that he possesses, one of which is the portrait of his now deceased wife.

What mixed emotions does Percy feel when he talks to his dad?

In chapter 21, Percy finally meets his father, Poseidon. At Mount Olympus (above Manhattan, of course), Zeus and Poseidon are seated on thrones.
When Percy enters, both gods appear to have been arguing. Percy kneels before Poseidon and is rewarded with a rebuke from Zeus. However, Poseidon maintains that it is only right that Percy acknowledge his own father first.
Upon meeting his father, Percy experiences mixed emotions. He feels great reverence, but he also feels a little intimidated by Poseidon. Above all, Percy feels detached from his father, as Poseidon has been alienated from his son for much of the latter's young life. It is also evident that Percy also feels a desperate need for his father's approval.
As the two finish discussing Kronos, who has proclaimed his own return from the pit, Percy feels a twinge of sadness. Poseidon admits that he is sorry for bequeathing Percy a hero's fate, which is "never anything but tragic." Percy's sadness does not last for long, of course. Poseidon's last words bring a measure of joy to Percy, however.

"You did well, Perseus. Do not misunderstand me. Whatever else you do, know that you are mine. You are a true son of the Sea God."

So, Percy has mixed feelings when he talks to his father: awe, sadness, pride, respect, and finally, a measure of joy.

Intermediate Algebra, Chapter 3, 3.4, Section 3.4, Problem 8

Illustrate the linear inequality $x + y \leq -3$ in two variables.

To graph $x + y \leq -3$ we must graph the boundary line $x + y = -3$ first. To do this, we need to find the
intercepts of the line

$x$-intercept (set $y = 0$):

$
\begin{equation}
\begin{aligned}
x + 0 &= - 3\\
\\
x &= -3
\end{aligned}
\end{equation}
$


$y$-intercept (set $x = 0$):

$
\begin{equation}
\begin{aligned}
0 + y &= - 3\\
\\
y &= - 3
\end{aligned}
\end{equation}
$


Now, by using test point. Let's say point $(-4,-2)$ from the left of the boundary line.

$
\begin{equation}
\begin{aligned}
x + y &\leq - 3\\
\\
-4 + (-2) &\leq -3 \\
\\
-4 - 2 &\leq -3\\
\\
-6 &\leq -3
\end{aligned}
\end{equation}
$


Since the inequality symbol is $\leq$, then the boundary line must be solid.
Moreover, since the test point satisfy the inequality, then we must shade the left
portion of the boundary line. So the graph is,

In Hatchet by Gary Paulsen, what is the most important thing Brian does to survive?

The most important thing that Brian does to survive in Hatchet is develop his mental toughness.
Brian was in a state of panic prior to recognizing the power of mental strength.  He had taken over flying and landing the plane after the pilot suffered a heart attack. The crash landing was in the middle of the wilderness, severely wounding Brian. Hailing from an urban area, Brian had no real idea of what to do.  He found himself struggling for food and shelter, while being victim to animals and natural elements.  All of these realities begin to take a toll on him.  Anxiety settles in, and his survival chances decrease as a result.
Brian has to develop mental strength to confront the challenges that confront him.  Developing this element is the most important thing he does to ensure his survival. One of the first moments where we see this is in Chapter 5.  In the midst of his tension, Brian remembers the instruction of one of his teachers. This helps him establish the mentality needed to survive challenging situations:

Brian had once had an English teacher, a guy named Perpich, who was always talking about being positive, thinking positive, staying on top of things. That's how Perpich had put it—stay positive and stay on top of things. Brian thought of him now—wondered how to stay positive and stay on top of this. All Perpich would say is that I have to get motivated. He was always telling kids to get motivated.

Thinking about Perpich's words triggers the first instance of Brian figuring out how to survive.   Instead of dwelling on all of the things that have gone wrong or everything he does not have, Brian "gets motivated" about what he needs to do.  After thinking about Perpich's teachings, Brian identifies the need for shelter and food, and uses his shirt to keep the "vampires" or mosquitoes off his back. The ending to the chapter shows the value of Perpich's instructions:  "I have to get motivated, he thought, remembering Perpich. Right now I'm all I've got. I have to do something."
When Brian establishes the mental toughness to face down the elements around him, his survival chances increase.  Things begin to fall into place for him.  He gets his first bit of luck when he throws the hatchet against the cave wall, making sparks that allow him to figure out how to create a fire.  From this, Brian figures out how to find food and cook them over the fire.  He enhances his shelter, creating a food shelf and a door to keep out intruders.  Brian develops a toughness that enables him to survive attacks from a moose as well as a tornado.  Brian maximizes his chances for survival by developing mental toughness.  This enables him to endure the natural elements, and invariably triumph over them.

What is the role of management in reducing workplace stress for first responders?

In the effort to reduce workplace stress for first responders, managers must act as counselors, mentors, communicators, administrators, and care supervisors/overseers.
The role of communicator is probably the most important one for managers. Managers must make themselves available to listen to the concerns of first responders and to assure their employees that any negative feelings (fear, grief, anger, and shock) that surface in the line of duty are perfectly natural. In this way, managers act as mentors who provide emotional guidance during local and national disasters. A manager's level-headed response to trauma assures first responders that they too can maintain functionality despite high stress levels.
Managers also play an important administrative role in mitigating stress at the scene of the tragedy or disaster. This administrative role overlaps with the care overseer role. Basically, managers must make available respite areas at the scene of the tragedy, where first responders can rest, eat, or take showers. Before the rescue mission begins, managers should also work to pair experienced first responders with newer emergency workers. This allows managers to monitor stress levels and to reinforce the safety procedures that will protect first responders at the scene of a disaster.
As care overseers, managers must monitor work breaks and put proper hydration regimes in place. Also, some first responders have to be encouraged to rest, despite their reluctance to do so. Additionally, disaster zones are often dangerous places, and managers in their administrative roles must ensure that first responders have adequate security and phone privileges in the event of threats to their lives. A manager who fails to fulfill his/her administrative role properly can contribute to high stress levels among first responders. 
After the crisis, good managers continue to act as mentors, counselors, and administrators. They institute time off from work for highly impacted first responders. Upon the first responder's return to work, an effective manager may choose to assign the first responder to less demanding responsibilities in order to facilitate his/her transition back to work. The manager may also initiate private counseling sessions with the first responder to determine whether continued mentoring assistance is necessary.
To learn more about how managers can act as effective counselors and care overseers, please refer to the links below.
 
https://www.govtech.com/em/training/Beyond-Debriefing-Responders-Emotional-Health.html

How is Madame Loisel greedy?

In “The Necklace” by Guy de Maupassant, it is stated that Madame Loisel “suffered endlessly, feeling herself born for every delicacy and luxury." Even though she comes from a poor family, and is married to a simple clerk who works at the Ministry of Education, she dreams of classy things and is envious of those people who possess these things. For instance, she is greatly disturbed by the possessions of one of her rich friends, whom she refuses to visit on this basis. She is discontented by what she has and is always keen on acquiring what she cannot afford to have. Thus, when her husband, in trying to please her, gets her an invitation to a party at the Ministry of Education, all she can think of is the dress she is to wear at the party. She does not even consider how difficult it must have been for her husband to get them invited to the party. Her actions show that she is a greedy person who is full of herself.
Another example of Madame Loisel’s greed is her inability to choose a simple piece of jewelry from the pieces offered to her by her friend, Madame Forestier. In spite of being shown many pieces, she still asks whether there are more pieces to be seen. The necklace she finally settles on is quite beautiful and when she wears it to the party, makes her the center of all attention. However, she loses this necklace on her way home from the party. She and her husband then have to replace the lost necklace at a cost of about thirty-six thousand francs. Her greed and vanity, therefore, pushes her family into great debt.

What was the reaction by the colonists to the British Troops?

The colonists did not react positively to the British troops that were stationed in the colonies. When the British sent troops to enforce the Proclamation of 1763, the colonists were not happy. The colonists resented this law, which prevented them from moving to the lands the British had gained from the French following the French and Indian War. They were even more upset when they had to provide housing and supplies for these troops.
After the Townshend Acts were passed, which placed new taxes on various items, the British sent troops to Massachusetts. This did not go over well with the colonists, who knew the troops were not being sent there to protect them. The colonists did not view the British troops positively, partially because of how the troops acted. They often were rude and disrespectful to the colonists, and the troops were not known to display high standards of moral behavior.
The presence of British troops in the colonies helped stoke the anti-British flames that were growing in the colonies and eventually led to the start of the Revolutionary War.
https://www.historycentral.com/Revolt/british.html

Why is literature a difficult term to define?

While works we would now consider literature have existed for several thousand years, dating back before the invention of writing, literature being used as a category is relatively recent.
The ancient Greeks had several terms referring to what we now would call literature. Poetry, divided into drama, epic, and lyric sub-genres, was understood as a genre. Prose fiction was not developed until late antiquity. In general, poetry was considered part of the educational discipline of grammar, and taught as part of instruction in reading. Prose, and the art of prose composition, fell under rhetoric. In Latin, similarly, poetry was part of secondary education in "letters." The study of style was equally applied to prose and poetry, and included examples from the poets, Plato, oratory, and history.
Our modern notion of "literature" as something distinct from pedagogical environment and meter (or lack thereof) is essentially Romantic and tries to divide literature from nonliterary texts using somewhat vague criteria of creativity, quality, or style. Such criteria, are, unfortunately, subjective, making defining literature in the modern sense rather problematic.

What is the main point of writing the poem "Ozymandias"?

The overarching theme of the poem "Ozymandias" is the transience of human life and its achievements. Ozymandias was a great Egyptian pharaoh, otherwise known as Ramasses II, who once built a huge statue of himself. But now, due to the passing of several centuries, the statue lies in ruins, reduced to a sad collection of fragments decaying in the desert. However, the pedestal still remains, and the inscription on that pedestal reads as follows:

My name is Ozymandias, king of kings:Look on my works, ye Mighty, and despair!

The inscription is an expression of the pharaoh's monumental arrogance. He genuinely believed that his deeds upon this earth would make him immortal. Yet his great statue lies in ruins, showing that however grand, however important we think we are, we must all one day succumb to the ravages of time.

How is the poem "Anyone Lived in a Pretty How Town" by E.E. Cummings an exploration/commentary of the human condition?

This poem describes two people, "anyone" and "noone," whose names help the reader to understand that, although specific people are discussed by the poet, these people could represent countless others—the protagonist could, indeed, be "anyone." The passage of time is shown in the poem through the references to the seasons ("spring summer autumn winter," "autumn winter spring summer"), while the behavior of the people in the town is the same in all weathers ("sun moon stars rain").
If "anyone" and "noone" are avatars for any two humans, then, the outlook of the poem on the way we exist in the world is rather bleak. While "anyone" and "noone" obviously care deeply for each other—"noone loved him more by more"—the "women and men" around them "cared for anyone not at all"; everything they "sowed" and "reaped" seemingly focused upon their own preoccupations. The suggestion is that the people in this town are too preoccupied with their own lives to consider the feelings of others.
The only people in the town who are exceptions to this rule are the children, who "guessed" at the love between anyone and noone, but this sort of emotional intelligence is lost as they get older ("down they forgot as up they grew"). Beyond the innocence of youth, we "forget to remember" other people and what is important to them.
The cycle of life, meeting and marrying another person, is not restricted to anyone and noone in this poem—"someones married their everyones," and we can assume that these people feel as strongly about each other as noone and anyone do: they "said their nevers they slept their dream." For each couple, their love is of monumental importance, but to others, they are simply people going through the ordinary motions of life ("sleep wake hope and then").
Cummings's colloquial diction when he notes "one day anyone died I guess" underscores the fact that, while "noone stopped to kiss his face," this event was unremarkable for those "busy folk" who then "buried them side by side." Noone and anyone, who lived and breathed for each other, have died, but life in the town continues as normal—the people "reaped their sowing and went their came"—because while "anyone's any was all" to noone, to everyone else, their lives had little impact. What seems deeply important to us and the people we love often does not touch others around us, who are focused on the cyclical progression of their own lives.

What are the similarities between Gretchen and Squeaky?

Gretchen P. Lewis is Squeaky's main competitor at the upcoming May Day races and is also considered a talented runner. Like Squeaky, Gretchen is also confident in her racing abilities. At the beginning of the story, Squeaky mentions that Gretchen has been telling everyone that she will win the first-place medal in the May Day fifty-yard dash. However, Squeaky believes that she will beat Gretchen because she considers herself to be the "fastest thing on two feet."
Squeaky mentions numerous times throughout the story that she is not interested in trading insults with other girls and would much rather fight someone than verbally spar with another person. Similarly, Gretchen is depicted as a rather reserved girl, who is more concerned about her actions than insults. In the scene where Gretchen and her friends approach Squeaky and Raymond on the street, Gretchen is the only person who does not speak. As her friends make rude comments toward Squeaky, Gretchen simply crosses her arms and listens. Gretchen is also a talented runner and is a formidable opponent. When Squeaky arrives at the May Day races, Mr. Pearson mentions that Gretchen should give Squeaky a run for her money. Squeaky also recognizes Gretchen's talent and continually shows her concern about beating Gretchen. After the two girls race, the judges argue over who won. The close finish highlights Gretchen's athletic ability and confirms that she is as good as everyone thought. Also, Squeaky mentions that Gretchen smiles back at her after the race and hopes that Gretchen will be interested in helping coach Raymond. Both girls are serious about running and share a mutual respect for each other. Overall, Squeaky and Gretchen seem to have more in common than one would assume judging by Squeaky's initial point of view.

"The wrinkled sea beneath him crawls": does this line reveal the eagle's proudness?

Though Tennyson never specifically describes the eagle in his poem as proud, one can find aspects of his verse that support this interpretation. When reading the poem, one must remember that Tennyson is part of the Romantic period, and the Romantics glorified nature. The eagle is, of course, one of the more majestic creatures in nature.


Not only are eagles typically considered magnificent birds, but the one in Tennyson's poem is soaring "close to the sun". The sun is, of course, an extremely important part of nature. It is also perched high above us all, almost like a king in the sky. The eagle's closeness to the sun puts him above all else figuratively and literally. Also the phrase "in lonely lands," further helps to elevate the eagle. Not only is he close to the sun, but the land below him is personified as lonely, which one could interrupt as weak compared to the eagle.


When one finally arrives at the line, "The wrinkled sea beneath him crawls," one knows that the eagle is above all else in every sense. The word "crawls" is a word one would ascribe to something weaker. Babies crawl. Those who can't walk crawl. The fact that Tennyson's uses the word "crawls" to describe the powerful sea, further highlights the eagle's strength and superiority. It is from this superiority that one could argue that the eagle is proud. Although Tennyson doesn't outright say the eagle is proud, his writing could support that interpretation.

Finally, the poem's last line could be interrupted as a reinforcement of the eagle's pride. When Tennyson compares the eagle to a thunderbolt, one of the most powerful, and frightening aspects of nature, we see the eagle's power over all below. It is easy to see that something so powerful and majestic could be proud. The fact that, at the poem's beginning, Tennyson chose to humanize the eagle by describing his claws as hands, makes it even more believable that a bird of prey could feel pride, a very human emotion.

Individual readers are going to interpret this line differently. For me personally, no, I do not think "the wrinkled sea beneath him crawls" shows the eagle's pride.
On one hand, the line is very literal. The eagle is a soaring bird with great vision. It is capable of flying quite high with minimal effort. Its vision allows it to scan and spot targets from a great distance away. When you are far away from something, it appears to barely move. Think of a road trip. The trees along the roadside blur past your car, but the mountains in the distance barely appear to move at all. If you've ever had a window seat on an airplane, you've seen the same effect. The plane might be moving hundreds of miles per hour; however, the ground beneath you appears to slowly inch by. This is what the line in the poem is indicating. The eagle is very high up, and the ocean appears to crawl by. Additionally, we know the eagle is high up because the great waves of the ocean appear to be merely wrinkles.
If I'm forced to find additional meaning from the line, I think it shows the eagle acting from a place of privilege. This doesn't automatically equate to pridefulness. Rulers and kings are usually seated at a place of elevation, or they have a castle on the hill. Being higher than someone else usually connotes power and privilege. The eagle is in a powerful and privileged position, which is why it is such an effective predator, but again, that doesn't necessarily mean prideful.

The eagle in Alfred Lord Tennyson's "The Eagle" is undoubtedly a noble figure, and "The wrinkled sea beneath him crawls" can easily be interpreted as a sign of the eagle's pride. The line contributes to an overall image of superior integrity, as the vast and powerful ocean is literally "beneath" the eagle, and it is "wrinkled" and "crawls" more like a small mammal than an immense force of nature. It suggests that the power and dignity (perhaps termed "pride") of the eagle eclipses everything else in the scene.
The other lines in this brief poem contribute to the mood and tone created by the line "The wrinkled sea." The eagle is such a singular being; rather than being a dot in the sky, the sky revolves around him: "Ring'd with the azure world, he stands." Even when the eagle makes his descent, he is not stooping to a lower level, but falling "like a thunderbolt," which is to say, with great natural power. The eagle's sense of presence and command of his surroundings surpasses the enormity of both the ocean and the sky.

Calculus of a Single Variable, Chapter 6, 6.1, Section 6.1, Problem 23

To determine whether the given function is a solution of the given differential equation, we can find the derivative of the function and check if it satisfies the equation.
To find the derivative of y = x^2e^x , use the product rule:
(fg)' = f'g + fg'
Here, f = x^2 and f' = 2x , and g = e^x and g' = e^x .
So y' = 2xe^x + x^2e^x = x(2 + x)e^x .
The left-hand side of the given equation will then be
xy' - 2y =2x^2e^x + x^3e^x- 2x^2e^x = x^3e^x . This is exactly the same as the right-hand side of the given equation, which means y(x) = x^2e^x is a solution.
The function y(x) = x^2e^x is a solution of the given differential equation.

How did the ancient Nubians' and ancient Libyans' environments influence their cultural development in terms of economics, politics, and religion?

Ancient Nubia was located in southern Egypt and northern Sudan and was divided into two parts--Upper Nubia, or Kush, which was the southern portion, and Lower Nubia, the northern portion. The people of ancient Nubia depended on the flooding of the Nile to grow and irrigate their crops. While people in the desert areas of Nubia remained pastoral nomads, Lower Nubia developed one of the first states in the world, which was settled by the so-called A-Group culture (which developed from about 3800 BCE-3100 BCE; they were given this name because their ancient name is not known). Their remains show that they had similar symbols to those of Egyptian kings, and their civilization was strengthened through trading such items as ebony, ivory, gold, and carnelian with Egypt until their civilization was taken over by the Egyptians during the First Dynasty.
Later, around 2000 BCE, the C-Group culture also developed along the Nile, as did the Kerma or Kush culture around 1500 BCE. As the Kush culture grew in power, they extended northward towards Egypt, and the Egyptians built fortifications in response. During the New Kingdom (1550–1069 BCE), Egypt conquered Nubia, which they referred to as Kush. All of the powerful ancient Nubian states developed along the Nile, which provided them with the surplus crops and trade routes to develop governments. Before the Egyptians conquered the Nubians, the Nubian religion was independent of the Egyptians, though little is known about it. After being conquered by the Egyptians, the Nubians developed a religion that borrowed from that of the Egyptians. In addition, some Nubian deities such as Sekhmet may have been introduced from Nubia to the Egyptian religion.
Ancient Libya's borders are not known exactly, but they lie west of the Nile. The land was a desert. Ancient Libya was mainly inhabited by pastoral nomads, the most populous of whom were the Libu. They lived by eating goats and sheep and using the animals' hides for shelter and clothing. They followed a traditional Berber religion before the introduction of Islam, and this ancient religion was notable for its cult of the dead. They also had their own system of deities. Their pastoral nomadic way of life did not result in the growth of a strong government. Instead, their civilization was a collection of tribes led by different kings rather than a unified kingdom. 

Single Variable Calculus, Chapter 4, 4.4, Section 4.4, Problem 42

Determine the formula for a function that has vertical asymptotes $x = 1$ and $x = 3$ and horizontal asymptotes $y = 1$.

The vertical asymptotes must make the denominator of the function 0. So we have,


$
\begin{equation}
\begin{aligned}

(x - 1)(x - 3) =& 0
\\
\\
x^2 - 3x - x + 3 =& 0
\\
\\
x^2 - 4x + 3 =& 0

\end{aligned}
\end{equation}
$


Since we know that the degree of the denominator is 2, we must introduce a variable $x$ in the numerator with degree of 2 to make the horizontal asymptote equal to 1, because to find the horizontal asymptote we need to find the highest degree of $x$ in numerator and denominator. So we have,

$y = x^2$

Hence,

$\displaystyle y = \frac{x^2}{x^2} = 1$

Therefore,

The equation of the function is $\displaystyle f(x) = \frac{x^2}{x^2 + 4x + 3}$ or $\displaystyle f(x) = \frac{x^2}{(x - 1)(x - 3)}$

In the final chapter of Chronicle of a Death Foretold, elaborate on the instances of how Santiago's death could have been prevented and on how it could have been prevented specifically from when his girlfriend's dad gave him the option to stay and hide or run.

In the final chapter of the book, Nahir Miguel warns Santiago Nasar that the Vicario brothers are planning to kill him. The text tells us that Santiago is more perplexed than frightened by the warning.
Nahir Miguel gives Santiago two options: either to hide in the Miguel home or to face the Vicario brothers with a rifle. Despite the warning, Santiago makes no concrete plans to protect himself. Here, we can see that Santiago would have lived had he taken up Nahir Miguel's offer of protection.
Instead, Santiago decides to leave the Miguel home. As he walks past the town square, he receives still more warnings from the townsfolk. Someone shouts at him to go by the old dock instead of heading home. Santiago chooses to ignore the advice. Then, Yamil Shaium yells at Santiago to seek refuge in his store while he looks for his hunting gun (and cartridges). At this time, there are many voices clamoring for Santiago's attention, but he decides to ignore them all.
Because Santiago cannot accept that there is an actual threat to his life, he becomes an open target to his murderers. If he had accepted the offers of protection from Yamil Shaium or Nahir Miguel, he might have succeeded in saving his life.
Going back to before Nahir Miguel's warning, we see that others also warned Santiago about the intentions of the Vicario brothers. For example, Clotilde Armenta gave her own warnings to Santiago. However, her words fell on deaf ears. Clotilde Armenta's husband (Don Rogelio de la Flor) probably voiced the real reason Santiago and many others refused to take the threat to Santiago's life seriously:

"Don't be silly," he said to her. "Those two aren't about to kill anybody, much less someone rich."

Meanwhile, the Vicario brothers did not keep their thirst for vengeance secret. They mentioned their intentions to more than a dozen people.
Just prior to the attack on Santiago, Clotilde Armenta grabbed Pedro Vicario and warned Santiago to run. Although Santiago did run when he finally saw the brothers approaching, he made the mistake of running for the front door. Just a few minutes prior, Placida Linero (Santiago's mother) had locked the door, believing that her son was inside the house. If the front door had not been locked, Santiago might have lived.
So, the above are many of the instances that describe how Santiago's death could have been prevented.

What causes Rainsford to change in the story?

Sanger Rainsford experiences a significant transformation and gains perspective after being hunted by the maniacal General Zaroff throughout Ship-Trap Island for three consecutive days. At the beginning of the story, Rainsford expresses his belief that the world is made up of two classes: "the hunters and the huntees." He believes that it is his inalienable right to exercise his strength and dominance over weaker beings. Rainsford also lacks sympathy for the animals he hunts and tells Whitney that the prey has no understanding of what is going on while they are being hunted.
Unfortunately, Rainsford falls off the yacht and must swim to General Zaroff's nearby island. During his first meal with the general, Rainsford is appalled to learn that Zaroff hunts humans throughout the island for sport. Rainsford ends up becoming Zaroff's prey and is forced to avoid the general and survive on the treacherous island for three consecutive days. As Rainsford is being hunted, he gains perspective and sympathy for the animals he hunts. He experiences the feelings of terror, fear, and anxiety as Zaroff closes in on him with his group of hunting dogs. By the end of the story, Rainsford illustrates his dramatic transformation by telling the general, "I am still a beast at bay...Get ready, General Zaroff." Rainsford's harrowing experience has made him more sympathetic to the animals he hunts and has expanded his perspective on the sport of hunting. Without becoming Zaroff's prey and narrowly surviving his game, Rainsford would have probably remained a callous, insensitive big-game hunter.

The cause of Rainsford's change is that he goes from being the hunter to being the hunted.
At the beginning of the story, Rainsford shows zero care for the animals that he hunts. He feels that the animals are prey and nothing more; they are not thinking and emotional creatures. They operate on nothing more than instinct; therefore, they do not feel fear.  

"You're a big-game hunter, not a philosopher. Who cares how a jaguar feels?"
"Perhaps the jaguar does," observed Whitney.
"Bah! They've no understanding."
"Even so, I rather think they understand one thing—fear. The fear of pain and the fear of death."
"Nonsense," laughed Rainsford.

All that changes after being shipwrecked on General Zaroff's island. Zaroff hunts humans, and he makes Rainsford his prey. Rainsford is appalled at the scenario; however, he has little choice but to run and fight for his survival. Once the hunting begins, Rainsford gets to see, feel, and understand the other side of the hunt. He gains a new respect for the animals that he hunts because he now understands what it feels like to be pursued by a relentless killer that has zero care for how his prey feels. Because he is being hunted by Zaroff, Rainsford now fully understands and empathizes with the animals that he once hunted. That is why the following quote from Rainsford is so important.

"I am still a beast at bay," he said, in a low, hoarse voice.

He does not say that he's a man seeking vengeance or even self-defense. Rainsford labels himself "a beast." He sees himself as an animal, and he is no longer thinking like a human. He's been cornered into a situation in which he absolutely must kill or be killed. That's what happens when an animal is cornered; it will fight harder than it ever has before with no concern for the other aggressor. That is now Rainsford. Gone is the opinion that killing another human being is morally suspect. That change in Rainsford would not have happened without his island experience.

Calculus of a Single Variable, Chapter 2, 2.4, Section 2.4, Problem 79

You need to find the equation of the tangent line to the given curve, at the point (pi/4,1) , using the formula:
f(x) - f(pi/4) = f'(pi/4)(x - pi/4)
You need to notice that f(pi/4) = 1.
You need to evaluate the derivative of the given function, using chain rule, such that:
f'(x) = ((tan x)^2)' => f'(x) = 2tan x*(tan x)'
f'(x) = 2tan x*(1/(cos^2 x))
You need to evaluate f'(x) at x = pi/4 , hence, you need to replace pi/4 for x in equation of derivative:
f'(pi/4) = 2tan (pi/4)*(1/(cos^2 (pi/4)))
f'(pi/4) = 2*1*1/(((sqrt2)/2)^2) => f'(pi/4) = 4
You need to replace the values into equation of tangent line, such that:
f(x) - 1 = 4(x - pi/4) => f(x) = 4x - pi + 1
Hence, evaluating the equation of the tangent line to the given curve, at the given point, yields f(x) = 4x - pi + 1.

Are Dexter's memories of the summer accurate or idealized?

Dexter's memories of the summer are idealized and unrealistic. For example, when he is young and working as a golf caddy, he dreams during the winter of a fantastical summer in which he is a golf champion. In these dreams, he owns a Pierce-Arrow, a very high-end car, and is a well-respected member of the golf club--so well respected, in fact, that he is followed by an adoring crowd who also admire his diving ability with mouths open in wonder. Years later, he also succumbs to a kind of summer fantasy when he meets Judy Jones again and thinks that he can make her be faithful to him. During this time, he is wildly unrealistic about who Judy is and even asks her to marry him, which never happens. He loses his sense of reality and thinks of his relationship with her in the same idealized way he dreamed of becoming a rich golf champion when he was a boy.