How does Elizabeth feel about Mr. Darcy?

The greater part of "Pride and Prejudice" showcases the relationship Elizabeth has with Mr. Darcy. At the beginning of the novel, Darcy arrives and sulks in a corner at a party that Elizabeth is also attending. Elizabeth does taking a liking to Darcy due to his looks. However; when she is sitting in the rafters taking a break from dancing, she hears a shocking remark from Darcy.
“She is tolerable; but not handsome enough to tempt me; and I am in no humour at present to give consequence to young ladies who are slighted by other men. You had better return to your partner and enjoy her smiles, for you are wasting your time with me.” Mr. Darcy
Once Elizabeth hears Mr. Darcy's distate, she fast takes a harsh opinion. This opinion is heightened when she discovers Darcy's interference with George Wickham and his breakup of Jane's courtship with Mr. Bingley.
This feeling does not last forever as Mr. Darcy tries to propose to Elizabeth. To be expected, Elizabeth brashly strikes down the proposal and accuses Mr. Darcy of everything she has been a witness of. Mr. Darcy takes it like a man and delivers Elizabeth a letter that changes everything. The letter is his account of everything that she had accused him of. Elizabeth comes to realize that she may have been wrong.
She takes a trip with her aunt and uncle to visit Pemberly, which is Darcy's estate. There, she realizes her true feelings for Darcy but cannot truly come to terms with them. Her feelings do reach a climax when she discovers later that Mr. Darcy saved her sister, Lydia, from a terrible disgrace. For indeed, Mr. Darcy ensured that marriage occurred for Lydia and Jane.
Elizabeth is able to admit her true feelings of love for Darcy at the end of the novel.
Elizabeth, feeling all the more than common awkwardness and anxiety of his situation, now forced herself to speak; and immediately, though not very fluently, gave him to understand that her sentiments had undergone so material a change since the period to which he alluded, as to make her receive with gratitude and pleasure his present assurances. The happiness which this reply produced was such as he had probably never felt before, and he expressed himself on the occasion as sensibly and as warmly as a man violently in love can be supposed to do. The Narrator
Further reading:
https://austenprose.com/pride-and-prejudice-quotes-quips-by-chapter/pride-and-prejudice-quotes-quips-chapters-57-61/

For most of the book, Elizabeth does not like Mr. Darcy at all, but this changes as she begins to learn more about him.
When she first sees Mr. Darcy, Elizabeth thinks he looks very severe and unfriendly, and once he insults her when talking to Mr. Bingley, she is offended.

She is tolerable, but not handsome enough to tempt me; and I am in no humor at present to give consequence to young ladies who are slighted by other men. You had better return to your partner and enjoy her smiles, for you are wasting your time with me.

As the story goes on, she perceives all his actions toward her as trying to make fun of her or upset her. He stares at her constantly and she thinks he is looking for fault in her. He sits near her and she wonders why he can't just leave her alone.
When Mr. Darcy snubs Mr. Wickham, Elizabeth thinks that Mr. Darcy must not like Mr. Wickham because he disapproves of him just as much as he disapproves of her.
This all changes after he proposes to her.
At first, she tries to understand his behavior and what would make him propose to her when she was so sure he disliked her as much as she disliked him.
The letter he gives to her explains all the issues she brought up when she rejected his proposal. He tells her about what happened between Wickham and his sister and he owns up to being involved in taking Bingley away from Hertfordshire.
As she starts to reexamine his behavior, she becomes unsure of what kind of man he could be. But once she meets him again in Derbyshire at Pemberley, her opinion slowly starts to change. She sees how he is with his sister and how at ease he is when he is in his own environment.
The ultimate test comes when she comes to find out that he helped save Lydia from ruin by making sure Mr. Wickham married her. She also suspects that he had a role in why Mr. Bingley comes back to Hertfordshire and proposes to her older sister, Jane, after Darcy's advice had torn them apart before.
And by the time he proposes to her a second time, Elizabeth realizes her feelings for him have completely changed and acknowledges that she now loves him.

Single Variable Calculus, Chapter 2, 2.3, Section 2.3, Problem 4

Determine the $\lim\limits_{x \rightarrow 2} \displaystyle \frac{2x^2+1}{x^2+6x-4}$ and justify each step by indicating the appropriate limit law(s).


$
\begin{equation}
\begin{aligned}
\lim\limits_{x \rightarrow 2} \quad \displaystyle \frac{2x^2+1}{x^2+6x-4} &= \displaystyle \frac{\lim\limits_{x \rightarrow 2} (2x^2+1)}
{\lim\limits_{x \rightarrow 2} (x^2+6x-4)}
&& \text{(Quotient Law)}\\
\lim\limits_{x \rightarrow 2} \quad \displaystyle \frac{2x^2+1}{x^2+6x-4} &= \displaystyle \frac{2\lim\limits_{x \rightarrow 2} x^2 + \lim\limits_{x \rightarrow 2} 1}
{\lim\limits_{x \rightarrow 2}x^2+6\lim\limits_{x \rightarrow 2}x-\lim\limits_{x \rightarrow 2}4}
&& \text{(Sum, Difference and Constant Law)}\\
\lim\limits_{x \rightarrow 2} \quad \displaystyle \frac{2x^2+1}{x^2+6x-4} &= \displaystyle \frac{2(2)^2+1}{(2)^2+6(2)-4}
&& \text{(Constant, Special Limit and Power Special Limit Law.)}
\end{aligned}
\end{equation}\\
\boxed{ \lim\limits_{x \rightarrow 2} \quad \displaystyle \frac{2x^2+1}{x^2+6x-4} = \displaystyle \frac{3}{4}}
$

In "Dead Poets Society," how is the relationship between man and women portrayed?

I assume your question is regarding the 1989 film and not the recent stage production. Because there are very few female characters in Dead Poets Society, the best way to answer this question is to contrast the relationship between two couples. Knox, one of the boys at the school, courts a girl named Chris. Their relationship can be contrasted with Mr. Perry and his wife, the parents of Neil, who is a major character. Chris is an example of how the boys at the school view women in general. She is pretty and mysterious and, for most of the film, apparently unattainable. Knox pursues her because he has a very romanticized view of love. Eventually Chris condescends to kiss Knox, but we never learn whether this leads to a real relationship. By contrast, the relationship between Mr. and Mrs. Perry is far less idealistic. Mr. Perry is very controlling of his wife, and she finds herself caught between obeying her authoritarian husband and wanting to support the son she loves. In these very brief scenes, we see how toxic a loveless marriage can be.

Who was Olympe de Gouges?

Olympe de Gouges was a feminist—often called the first feminist—and social activist who came to prominence during the French Revolution. Born in a small town in Southern France, she moved with her daughter to Paris after her husband passed away. It was there that she changed her name from Marie Gouze to the name by which she's known today. At that time in French society, there weren't many career opportunities for women. Nevertheless, Gouges managed to establish herself as a woman of letters, an intellectual who actively participated in the often intense political debates of the day. She proved herself a gifted writer, publishing plays, novels, and of course political articles. Such literary activity was very rare for a woman in that era; once again, Gouges had shown herself ahead of her time.
For a woman as politically involved as Gouges, the French Revolution was inevitably an event of great significance. She wholeheartedly supported the Revolution, but quickly established herself as a forthright critic of its treatment of women. Despite its rhetoric of liberty and equality, the various stages of the Revolution systematically excluded women from public life. Olympe de Gouges's feminist ideas found their most systematic expression in her Declaration of Women's and Female Citizens' Rights. Here, Gouges used her exceptional literary talents to argue for the complete emancipation of women and the unconditional equality of the sexes.
Not surprisingly, Gouges's ideas were hugely controversial, challenging as they did the entrenched prejudices of even the most radical of male revolutionaries. She soon earned a large number of enemies on account of her vocal activism, which found expression not just in her campaign for women's rights, but also in her call to abolish slavery and the death penalty. It was the latter that led her to oppose the death sentence passed on Louis XVI.
Gouges continued to throw herself into political activity with ever greater passion and resolve. She was a supporter of the Girondin faction in the National Convention, which put her at odds with the more radical Jacobins. Despite the growing danger and violence of French political life, Gouges pressed on with her work, fearlessly attacking leading Jacobin figures such as Marat and Robespierre. After the fall of the Girondins, Olympe de Gouges was arrested on a trumped-up charge. The Reign of Terror was just beginning, and opponents of the new Jacobin regime were being rounded up and, in many cases, sent to the guillotine. Gouges defended herself with great courage at her subsequent trial, but she never stood a chance of acquittal; her execution was a foregone conclusion. And so she went to the guillotine on 3rd November, 1793, at the age of 45, convicted of sedition and the patently false charge of wanting to restore the monarchy.
https://www.britannica.com/biography/Olympe-de-Gouges

Explain the primary function of the branches of the federal government.

The primary function of each branch of federal government is to restrain the other two branches if necessary. The goal is to prevent tyrannical government, which is a cruel or oppressive government that asserts power over its people in an unfair fashion. A division of power, more formally known as a separation of powers, is designed to create a system of checks and balances to ensure that no one branch has too much power.
The idea for a separation of powers through three branches of government can be traced back to Montesquieu, a French judge and philosopher. In The Spirit of Laws, Montesquieu suggested that the executive, legislative, and judicial functions of a government should be shared between three separate branches to prevent overreaching power and protect personal liberty.
In the United States, the federal government is split into three separate branches of government.

The legislative branch proposes laws
The executive branch carries out and enforces laws
The judicial branch evaluates laws and interprets their meaning

Each branch can respond to, or change, the actions of another branch of government. For example, the legislative branch (Congress) can create laws, but the head of the executive branch (the U.S. President) can choose to sign or veto (not sign) those laws. The Justices of the U.S. Supreme Court, which are part of the judicial branch, can evaluate any law, deem it unconstitutional, and overturn it.
By performing their primary function of "checking" the power of other branches, each individual branch of the federal government helps to protect the rights and liberty of U.S. citizens.

Las funciones de las ramas del gobierno federal son mantener el orden en el país con lo que son las leyes impuestas por este.
Entre estas ramas se encuentran el poder legislativo, el ejecutivo y el judicial, de las cuales cada una tiene sus propios aportes en las leyes.
El poder legislativo: Es la entidad como el congreso, que inicia y crea las diferentes leyes para el país.
El poder ejecutivo: Es la entidad como el Presidente, el Vicepresidente o el Gabinete, los cuales son los que hacen cumplir las leyes creadas por el poder legislativo.
El poder judicial: Es la entidad como la corte suprema, el cual está encargado de impartir las leyes impuestas por los otros poderes y que se haga justicia a partir de esta.

The United States government is based on two basic principles: separation of powers and checks and balances. Separation of powers means that the powers and responsibilities of the government are divided between three branches of government: the executive branch, the legislative branch, and the judicial branch. In addition, each of these branches has certain "checks" over the other branches to ensure that no one branch of government has too much power (this is the concept of checks and balances).
The Executive Branch is responsible for carrying out the laws of the United States. It is composed of the president, the vice president, the president's cabinet (which acts as the president's advisers), and various agencies such as the Central Intelligence Agency and the Environmental Protection Agency (which help the President enforce and carry out laws). The President also serves as commander in chief of the armed forces.
The legislative branch makes laws. It is synonymous with Congress, which is made up of the Senate and the House of Representatives. States send representatives to Congress in order to make laws, and Congress has special responsibilities, such as passing laws to raise revenue (taxation) and having the power to declare war.
Finally, the judicial branch interprets the laws passed by Congress. This branch of government is composed of the Supreme Court, which is appointed by the president, and lower federal courts. Whenever there is disagreement about what a law means, the Supreme Court can hear cases and appeals in order to interpret it.

Where is the following quote from Homer's The Odyssey located? "I am Laertes' son Odysseus. Men hold me formidable for guile in peace and war: this fame has gone abroad to the sky's rim."

This quote is taken from Book IX, lines 7-9; Odysseus acknowledges that he is widely known by mortals and gods both, and he is admired and respected for his intelligence and many skills.
At this point Odysseus is the only remaining member of the contingency that he took to Troy. He has spent eighteen days at sea after parting from Calypso and heads toward Scheria, the island of the Phaeacians. But, Poseidon, who hates Odysseus because of what he has done to his son the Cyclops, has been angered at the help the other gods have given Odysseus. So, he creates a maelstrom that nearly drags Odysseus under the sea. Fortunately, he is rescued again by the goddess Ino.  Odysseus continues until he finds a river where he can swim into its waters. He walks onto the shore and rests in a covered area.
The next day, the Phaeacian Princess Nausica discovers Odysseus while she and her handmaidens wait for their clothes to dry. She provides him clothes and has Odysseus walk alone to the palace and instructs him on what to say when he arrives.
Book IX, then, relates the time that Odysseus is a guest of the Phaeacian king and queen, Alcinous and Arete. Alcinous calls an assembly that votes to provide their foreign guest with a ship so that he can return home.
Later, there is a feast and games in honor of the guest, but when Odysseus hears a bard sing of the "quarrel" between Odysseus and Achilles at Troy, he is overcome with sorrow, and he weeps. Nevertheless, at dinner Odysseus asks the bard to sing his song again about Odysseus at Troy, and once again, he cries. So, King Alcinous has the music stopped. Further, after the celebratory games, he asks Odysseus to reveal his identity. Odysseus does, and then he is asked to reveal where he is from and where he wants to go. He begins,

 "I am Laertes's son Odysseus. Men hold me formidable for guile in peace and war: this fame has gone abroad to the sky's rim."

Watch a movie based on the life of a challenged or differently-abled person. Prepare a review of the movie highlighting the challenges and the qualities or methods that helped the person overcome the difficulties faced by him or her. Also comment on the challenges it must have posed to the actor who played the character and the portrayal.

Jim Sheridan's 1989 film My Left Foot stars Daniel Day-Lewis as the real-life Irish author Christy Brown. Christy Brown was a painter and writer who was born with cerebral palsy. As a child, Christy Brown is entirely unable to walk. Throughout the film, Christy is able to master the use of his left foot, using it to carry out many daily duties and, eventually, write and paint.
Part of what makes My Left Foot a fantastic film is the insurmountable performance of Daniel Day-Lewis. Committing every physical fiber of his being to the role, there is not a moment of screen time in which Day-Lewis's performance is not astoundingly believable.
While the film offers an empathetic glance at the difficulties that pervaded the life of Christy Brown, there is never a moment of condescension or pity. In Sheridan's film—and in Day-Lewis's performance—Brown is a man wholly worth admiring. The film never plays the role of a soapy melodrama; there is a tremendous amount of humor in the film to balance out the tragedy, and when tragedy strikes, it is played out naturally and convincingly.

Radio (2003) is a biographical sport drama based upon the story of Harold Jones, a football coach at T.L. Hanna High School (played by Ed Harris), and a young man with an intellectual disability named James Robert "Radio" Kennedy. The young man, played by Cuba Gooding Jr., not only demonstrates the challenges faces a young man with intellectual difficulty, but the compounding barriers that existed because of the stereotypes and resistance he faced from the community when the coach decided to include him as a helper on the team.
This film is set in South Carolina, where high school football is heralded as king in the southern culture. The football coach finds his team harassing Radio and punishes his team; subsequently, he seeks to find out more about Radio's background and learns that his father had passed away. The coach decides to have him help on the football team, which then turns into tutoring him as well. Radio becomes more involved in the high school, whereas previously he had been pushing a shopping cart around the town alone. Radio loves the school, and the school mates and teachers move towards acceptance. However, there is clear resistance from the fathers of the football players who claim that a charity case takes away from the coaching that their sons deserve. Radio demonstrates some extraordinary talents, and some of his misunderstandings are portrayed humorously in this film.
One scene illuminates a little known fact about people with mental disabilities when Radio is arrested. In the movie, Radio was delivering Christmas presents when he was questioned by the police officer as to how he obtained the gifts. Not knowing what to say, and not communicating his answers well, the police officer assumed that he had stolen the presents and placed him under arrest. Many people are unaware that individuals with intellectual disabilities cannot communicate well when questioned by police officers, and often leading questions causes a higher arrest rate of innocent people with intellectual disabilities.
This inspiring story demonstrates the power of inclusion and acceptance as life changing elements for individuals with exceptional abilities, as well as for the communities that open their arms to help others, even when not directly benefited themselves. The powerful quote, "But the truth is, we're not the ones been teaching Radio, he is the one been teaching us," sheds light on the sometimes not so popular belief in this town that individuals who are seen as outside the 'norm' can contribute to society in unique and beautiful ways.
For more information check out these links:
https://www.imdb.com/title/tt0316465/?ref_=fn_al_tt_1
https://en.wikipedia.org/wiki/Radio_(2003_film)

David Lynch's The Elephant Man (1980) is a biopic of Joseph Merrick, the nineteenth-century British man who suffered from extreme facial and bodily deformity. Modern researchers (several years after the release of the film) concluded that Merrick probably suffered from a condition called Proteus syndrome. John Hurt, who plays the title role, wears realistic makeup to convey the look of Merrick's face, which appears to have huge tumors growing on it. Hurt's performance is excellent. You might wish to see if there are any accounts by Hurt, or by other actors who have played similar roles, about the challenge of acting with this type of heavy makeup. Also, try to compare the actor's struggle to that of Merrick himself and see how the key scenes in the film show Merrick interacting with non-disabled people.
Unfortunately, in my view, one cannot offer the same praise to the film overall as to Hurt's performance. It is shot in the same eerie black and white as Lynch's earlier film Eraserhead, and the atmosphere and themes of the two films are similar. However, as Roger Ebert pointed out when The Elephant Man was first released, the script is at fault for portraying Merrick in an inconsistent and even somewhat exploitative way. The attitude of the doctor, played by Anthony Hopkins, is curious and is oddly inconsistent as well. You might want to ask whether this can be attributed simply to "character development" or whether the changes are too extreme and seem to be done simply to make the film as melodramatic as possible.
Perhaps the film's worst flaw, as Ebert pointed out, is the opening dream sequence involving Merrick's mother. It is in keeping with Lynch's surreal horror-film approach seen in all his work but is in extremely bad taste, to say the least. The film's close, by contrast, is poignant and tragic. Merrick, in his bed, asphyxiates himself by lying down full length, something he has never been able to do because the weight of his massive head leaning back will crush his windpipe. Why, one asks, has he decided it's time to end it all, at this particular moment in time?

Why is the Fourteenth Amendment important?

The Fourteenth Amendment is important because it recognizes the citizenship rights of African Americans. Essentially, the amendment grants legal and voting rights to all African Americans.
The Fourteenth Amendment is made up of five sections. The first section grants citizenship rights to anyone born or naturalized in the United States. It also specifies that no citizen can be deprived of "life, liberty, or property" without due process.
The second section guarantees all males (who are at least twenty-one years of age) voting rights. It also states that the government must count "the whole number of persons in each state" to assign representation to Congress. In other words, both white and African American populations must be counted.
The third section states that no one can be elected to office if they participated in "insurrection or rebellion" against the government. After the Civil War, this section prevented Confederate soldiers or politicians from holding elected office.
The fourth section guarantees that the government will pay all its debts. This section was especially significant after the Civil War. It specifically stated that no state should pay any debts incurred as a result of "insurrection or rebellion." Furthermore, any slave-owner who lost slaves would not be reimbursed for their loss. The fourth section of the Fourteenth Amendment stated that claims for these two types of debts would be held "illegal and void." 
The fifth section proclaims that Congress has every power to enforce the specifications of the Fourteenth Amendment.
The Fourteenth Amendment is important because of its citizenship, due process, and equal protection clauses.
https://www.history.com/topics/black-history/fourteenth-amendment

A funnel in the shape of the cone has a radius of 5 in and a height of 20 in. Find the volume of the cone in centimetres cubed if 1 inch ^3=16.39cm^3.

Given that a funnel is in the shape of a cone with
radius = r= 5 inch
height = h= 20 inch
We know that the volume of the cone is given by the formula:
Volume=V=\frac{1}{3}\pi r^2 h
i.e. V=\frac{1}{3}\pi (5^2)(20)
        =\frac{1}{3}\pi(25)(20)
         =523.598 inch^3
However, we are asked to find the volume in cm^3.
1inch^3=16.39cm^3
Therefore, we have to convert the obtained result from inch^3 to cm^3 .
Hence ,
Volume of the funnel  = 523.598\times 16.39 cm^3
                                =8581.78\ cm^3
The volume of the funnel is 8581.78\ cm^3 .

Who is Crooks in Steinbeck's Of Mice and Men?

Crooks is the black stable-hand on the ranch who gets his nickname from his crooked back. Unlike the white workers on the ranch, Crooks is forced to live by himself in a small room attached to the barn because he is black and the farm is segregated. Crooks suffers from racial discrimination and is a sympathetic character who is extremely lonely and ostracized.
In chapter four, Lennie visits his room and Crooks initially displays the corrosive effects of loneliness and discrimination when he purposely upsets Lennie by talking about George leaving him. Crooks also reveals his loneliness by lamenting his difficult situation on the farm and expressing his desire to be treated like he was equal. When Candy and Lennie initially talk about their dream of owning their own homestead, Crooks mentions that it is impossible. Once Candy comments on how close the men are to reaching their dream, Crooks becomes drawn to the dream and offers to help on their homestead for free. Shortly after dreaming about a better future, Curley's wife enters the barn and threatens to have Crooks lynched after he tells her to leave. Overall, Crooks is a sympathetic character who illustrates the difficulties of being a black stable-hand on a segregated farm during the Great Depression.

Crooks is an African-American stable hand who lives by himself, isolated from the other ranch hands, in the harness room. Crooks was born in California, where his father had a chicken ranch. Though he grew up playing with white children, his father liked to maintain his distance from white families, as he knew that they would treat him in discriminatory ways. Crooks is used to being the only African-American person around, including on the ranch. He is called Crooks because he is crippled and has a crooked spine. Steinbeck describes Crooks as "a proud, aloof man."
After years of experiencing racial discrimination, he keeps away from others and expects that they will treat him in the same way. He is lonely and occupies himself reading books because he can't play horseshoes with the other men. Lennie befriends Crooks one day when the rest of the men are in town, and while Crooks is at first unfriendly, Lennie's simple manner wins Crooks over. Crooks becomes excited about Lennie's dream of owning his own land one day.

What quotes in The Crucible show that Reverend Parris mentions hell a lot in his sermons?

In Act I, when Thomas Putnam accuses John Proctor of hardly ever coming to Sabbath day services, Proctor retorts,

I have trouble enough without I come five mile to hear [Parris] preach only hellfire and bloody damnation.  Take it to heart, Mr. Parris.  There are many others who stay away from church these days because you hardly ever mention God any more.

Proctor defends his decision not to come to the meetinghouse on Sunday mornings because, he seems to say, life is hard enough without having to travel a significant distance only to hear a preacher who seems so negative, who inspires fear rather than hope or love, who speaks of the tortures of hell without at least tempering it with references to the pleasures of heaven.
Rebecca Nurse confirms John's point to an extent, saying, "It's somewhat true; there are many that quail to bring their children--."  We can assume that she was going to finish her sentence with "to Sabbath day service" or the like before Parris interrupted her.  He claims that he does not preach for the benefit of children because it is not children who are "unmindful of their obligations toward this ministry."  Thus, it sounds as though Reverend Parris feels that many in his parish do not treat him or his office with the respect that they should, and so he uses Sunday service as an opportunity to remind them that hell awaits if their failure continues.  

In The Orphan Master's Son, does Johnson offer something similar to what appears in a more straightforward ethnography like those written by Fernea and Turnbull? Can you see a relationship between Johnson's project and those of Fernea and Turnbull? If so, what?

An ethnography is a rich qualitative study of a culture that aims to provide "thick description"--that is, a detailed account of everyday life in that culture. The aim of the anthropologist or other author of the ethnography is not only to describe the culture but also to understand it and how its people provide "webs of meaning," or the meanings they make of their experiences.
Fernea and Turnbull, in accounts such as Guests of the Sheik, provide a detailed account of life in an Iraqi village in the 1950s. Elizabeth Fernea lives as the local women do. For example, she learns that although she would like to go to the market and live independently as a western woman does, she is not allowed to do so (page 12). By living this type of life, she comes to understand the way local women feel in their everyday existences and comes to know their intimate details, such as that "A woman's jewelry is her insurance against disaster" (page 33). Only by living among the local people does she come to understand these realities.
Similarly, while Johnson's The Orphan Master's Son is a novel, Johnson also provides these types of ethnographic details about life in North Korea. In describing Jun Do's youth, for example, the author writes, "And then in the year Juche 85, the floods came. Three weeks of rain, yet the loudspeakers said nothing of terraces collapsing, earth dams giving, villages cascading into one another" (page 8). The relationship between Johnson's narrative and a more traditional ethnography is that Johnson provides details about the everyday lives of the people in North Korea, including the famines they face, the political repression they are subject to, and their lack of awareness of what happens outside their country. The similarity between his novel and more traditional ethnography is that they both try to convey the ways in which people construct meaning and understand their realities and they both use cultural relativism, which is when someone tries to understand another culture on its own terms.

Single Variable Calculus, Chapter 3, 3.2, Section 3.2, Problem 47

Suppose that $f(x) = \sqrt[3]{x}$, find $f'(x), f''(x), f'''(x)$ and $f^4(x)$. Graph $f, f', f''$ and $f'''$ on a common screen. Are the graphs consistent with the geometric interpretations of these derivatives?

a.) Let $a \neq 0$, use the definition of derivative $\displaystyle f'(a) = \lim\limits_{x \to a} \frac{f(x) - f(a)}{x - a}$ to find $f'(a)$.

Using the definition of derivative


$
\begin{equation}
\begin{aligned}


\qquad f'(a) =& \lim_{x \to a} \frac{\sqrt[3]{x} - \sqrt[3]{a}}{x - a} \cdot \frac{\sqrt[3]{x^2} + \sqrt[3]{ax} + \sqrt[3]{a^2}}{\sqrt[3]{x^2} + \sqrt[3]{ax} + \sqrt[3]{a^2}}
&& \text{Multiply both numerator and denominator by $\sqrt[3]{x^2} + \sqrt[3]{ax} + \sqrt[3]{a^2}$}
\\
\\
\qquad f'(a) =& \lim_{x \to a} \frac{x + \cancel{\sqrt[3]{ax^2}} + \cancel{\sqrt[3]{a^2x}} - \cancel{\sqrt[3]{ax^2}} + \cancel{\sqrt[3]{a^2x}} - a}{(x - a)(\sqrt[3]{x^2} + \sqrt[3]{ax} + \sqrt[3]{a^2})}
&& \text{Combine like terms}
\\
\\
\qquad f'(a) =& \lim_{x \to a} \frac{\cancel{x - a}}{\cancel{(x - a)}(\sqrt[3]{x^2} + \sqrt[3]{ax} + \sqrt[3]{a^2}) }
&& \text{Cancel out like terms}
\\
\\
\qquad f'(a) =& \lim_{x \to a} \left( \frac{1}{\sqrt[3]{x^2} + \sqrt[3]{ax} + \sqrt[3]{a^2}} \right) = \frac{1}{\sqrt[3]{a^2} + \sqrt[3]{(a)(a)} + \sqrt[3]{a^2}}
&& \text{Evaluate the limit}
\\
\\
f'(a) =& \frac{1}{\sqrt[3]{a^2} + \sqrt[3]{a^2} + \sqrt[3]{a^2}}
&& \text{Combine like terms}
\\
\\
f'(a) =& \frac{1}{3 \sqrt[3]{a^2}} \text{ or } \frac{1}{3(a)^{\frac{2}{3}}}
&&

\end{aligned}
\end{equation}
$



b.) Prove that $f'(0)$ does not exist

Using $f'(a)$ in part (a)


$
\begin{equation}
\begin{aligned}

f'(a) =& \frac{1}{3 \sqrt[3]{a^2}}
\\
\\
f'(0) =& \frac{1}{3 \sqrt[3]{(0)^2}}
\\
\\
f'(0) =& \frac{1}{3(0)} = \frac{1}{0}

\end{aligned}
\end{equation}
$


Therefore, $f'(0)$ does not exist because denominator is zero.

c.) Prove that $y = \sqrt[3]{x}$ has a vertical tangent line at $(0,0)$

If the function has a vertical tangent line at $x = 0, \lim_{x \to 0} f'(x) = \infty$

Given that $f'(x) = \displaystyle \frac{1}{3 \sqrt[3]{x^2}}$

Suppose that we substitute a value closer to from left and right to the limit of $f'(x)$. Let's say $x = -0.00001$ and $x = 0.000001$


$
\begin{equation}
\begin{aligned}

& \lim_{x \to 0^-} \frac{1}{3\sqrt[3]{(-0.00001)^2}} = 2154.43
\\
\\
& \lim_{x \to 0^+} \frac{1}{3 \sqrt[3]{(0.0000001)^2}} = 46415.89

\end{aligned}
\end{equation}
$


This means that where $x$ gets closer and closer to , the value of limit approached a very large number. The tangent line with these values become steeper and steeper as $x \to 0$ until such time that the tangent line becomes a vertical line at $x = 0$.

What is the meaning of the line "I do not ask the wounded person how he feels, I myself become the wounded person" from Walt Whitman's "Song of Myself"?

This amazing insight from Walt Whitman is an encapsulation of his philosophy – that we are not so much individuals as “leaves of grass”; superficially we appear to be individual, unique beings, but in a larger sense, we are each part of the whole, and we share the condition of being “human” – we are "each other" in the larger, cosmic sense.  Here, he differentiates between empathizing the pain of another, and actually “sharing the experience” itself.  It is difficult to paraphrase this difference in words more succinct, more viable, than Whitman’s own.  Whitman’s ability to empathize goes beyond mere imagining what an experience might be to another – he negates the, to his mind, separateness of individuality, and steps, not “into the shoes” of the wounded person, but into the wholeness that is the human species.  His experiences in the Civil War gave him this anguished and anguishing insight.

What is the context of Byron's "When We Two Parted"?

The context of Byron's "When We Two Parted" is the dissolution of a relationship between two people.
It is not difficult to imagine Byron writing this poem from a personalized context. Byron had many affairs and experienced many relationships begin and end. As a result, the poem's context is the disintegration of a love affair. 
While Byron writes from personal experience, the way he constructs the poem's emotional landscape makes it relatable to anyone who has fallen in and out of love. For example, the context of the first two stanzas is a dying relationship. What used to be love and passion is now shrouded in "silence and tears." Byron skillfully suggests that relationships do not die when two people leave. Rather, there are elements that show emotional distance before the actual breakup. He communicates this dynamic in lines like "half broken-hearted/ To sever for years." Byron's imagery of "pale grew thy cheek" and "Colder thy kiss" suggests people part begin to part before they actually do. Byron speaks of "the warning" signs that show a relationship has run its course. These markers indicate love's death. They take place when "vows are all broken" and when a person's name illuminates "shame" where love once was.
The context of regret is illuminated in the final two stanzas. Byron experiences "a shudder" to the question of "Why wert thou so dear?" The questioning of why or how we could have loved someone is another stage of the process of love dying. Realizing this does not bring happiness, but rather "rue." It is a "silence" that accompanies how we "grieve" when someone so positive is now the source of so much hurt. Byron suggests there are no winners when love dies. The poem's closing context is a mourning and cavernous remorse at what once was.
The highly emotional context of "When We Two Parted" is part of its effectiveness. Its primacy on personal experience is what makes it Romantic. Byron's own personal context is able to generate an emotional field we walk through, surveying his pain and our own.

What are some significant quotes in Fahrenheit 451 by Ray Bradbury, that show the meaning of the title "The Hearth and the Salamander"?

Part One is entitled "The Hearth and the Salamander," which are two symbols that represent Montag's life as a fireman. A hearth is the brick stone in front of a fireplace and is traditionally a symbol of the home, which corresponds to Montag's life as a fireman. Montag's occupation as a fireman takes precedence in his life, and he enjoys the sensation of burning books. Bradbury illustrates how burning novels for a living affects Montag by writing,

"Montag grinned the fierce grin of all men singed and driven back by flame. He knew that when he returned to the firehouse, he might wink at himself, a minstrel man, burntcorked, in the mirror. Later, going to sleep, he would feel the fiery smile still gripped by his face muscles, in the dark. It never went away, that smile, it never ever went away, as long as he remembered" (1).

Essentially, Montag's job as a fireman encompasses his entire life, which extends to his home and influences his personality. Therefore, the hearth, which relates to fire and the home environment, is the dominant image in Montag's life at the beginning of the novel.
The salamander in the title of Part One relates to the symbol on Montag's uniform and is the name of their firetruck. The salamander also symbolically represents Montag's life as a fireman. In ancient times, it was believed that salamanders were mythical creatures that could survive in fire. There are several images of the salamander depicted in Part One. Bradbury writes,

"He [Montag] stood in the hall of his house, putting on his badge with the orange salamander burning across it" (8).

Aside from being etched in the logo of the firemen's uniforms, the salamander is also the name of their firetruck. On their way back to the station, Bradbury writes,

"They sat there looking out of the front of the great salamander as they turned a corner and went silently on" (19).

Overall, both the hearth and the salamander are significant images that symbolically represent the way that fire dominates Montag's professional and personal life at the beginning of the novel.

In The Scarlet Letter, what was an example of Hester Prynne's penance?

Hester does penance for her sin by simply remaining in the colony in the first place. She could simply leave, go home or go elsewhere in the colonies, and begin life anew with her daughter, but she chooses to remain. 

Here, she said to herself, had been the scene of her guilt, and here should be the scene of her earthly punishment; and so perchance, the torture of her daily shame would at length purge her soul, and work out another purity than that which she had lost; more saint-like, because the result of martyrdom.

Hester hopes that, by remaining in Boston, the process of atonement through the torture of her shame and public punishment and humiliation will be more complete, so she will acquire a certain kind of purity as a result. She's conscious it is her choice to stay, and she does so with intention and purpose. She feels her daily shame in this place will eventually wipe clean the sin from her soul, and though she can never be innocent of sin again, her choice to remain will bring her a different kind of clarity and goodness.

What is the purpose of Gay's memoir, Hunger: A Memoir of (My) Body?

In her memoir, Hunger: A Memoir of (My) Body, Roxane Gay tells the story of her life as a way of exploring complicated issues like self-image, food, desire, sexual assault, trauma, and our public and private lives. There's not one purpose to this book: it's a multifaceted work. But we can talk a bit about Gay's messages and what she accomplishes in sharing them with a wide audience.
One of the key events in Hunger is the brutal rape that Gay suffers through as a 12-year-old girl. This experience will shape the rest of her life, both in the immediate aftermath and through adulthood. As a young woman, recovering from the assault, we see how rape often causes victims to feel deep shame, fear, and self-loathing. The teenage Gay retreats from the close relationship she previously had with her parents: she doesn't tell them what happened to her, so they can't help her. As time goes on, the shame that she feels erodes her self-confidence:

Hating myself became as natural as breathing. Those boys treated me like nothing so I became nothing.

And she turns to food for comfort and protection. Feeling that it was, at least in part, her own fault that she was "chosen" by the boys who raped her, she decides that being less attractive will prevent history repeating itself.

I ate and ate and ate in the hopes that if I made myself big, my body would be safe. I buried the girl I was because she ran into all kinds of trouble. I tried to erase every memory of her, but she is still there, somewhere... I was trapped in my body, one that I barely recognized or understood, but at least I was safe.

Clearly, one of Gay's objectives is to draw a clear line between rape (or traumatic experiences in general) and the instinct to protect oneself. Not every victim of a crime ends up obese, as Gay did. But in her personal case, she's showing how being fat (that's the author's preferred word to describe herself) is a direct result of the trauma she experienced at the age of 12.
Another purpose of Gay's memoir is to explain what it's like to be fat in a culture that values thinness, physical beauty, and self-control. The world is hostile to fat people, she writes, giving examples from her struggles with dating to the flight attendants who eye her large body as she steps onto a plane. 
Hunger, Gay says, is just a form of desire. One of the objectives of her memoir is to create empathy in the reader: to make her audience consider the ways in which we are all the same. We are all "hungry" in some way, according to Gay. Her book encourages the reader to look around at the world in a different way, assuming that we don't know what kind of trauma any one person has been through, or how it affects his or her current life.

In the Declaration of Independence, when it uses the word "he," who is being referred to?

The "he" is George III, King of Great Britain at the time. Jefferson references him in the sentences that immediately precede the list of grievances.
Historians interpret George III's life and reign in wildly different ways. It is no longer in fashion to see him as either a mad incompetent or a terrible tyrant, but there are many older biographies that present him in that fashion. He is still probably best known to laypeople as Mad King George, due to the mysterious illness that affected him in his older years and eventually left him unable to serve as king. His illness served as the basis for a play by Alan Bennett, The Madness of George III, which in turn served as the basis for the well-regarded 1994 film The Madness of King George.
Contemporary historians take a more balanced view, and pay as much attention to the successes of George III's reign against France as they do to his role in losing the American colonies.
Why did Jefferson spend so much time referring to George III? It was part of his rhetorical strategy. The Declaration of Independence is rightly renowned for its rhetorical flourish, and the section summarizing the "abuses" of the king is one of the highlights of the text. Jefferson uses repetition (more formally, parallel structure and anaphora) to summarize the colonists' grievances. He also draws on the common and recognizable theme of tyranny to create sympathy for his cause. (In reality, some of the grievances Jefferson lays at the feet of George III could have been attributed to Parliament as well.)
https://www.archives.gov/founding-docs/declaration-transcript

Why did Auggie's dad not want him to wear masks?

In the book Wonder, Auggie has a facial deformity that is very difficult for other people to understand. They react in various ways as soon as they see him that make him feel uncomfortable. Auggie found that be wearing an astronaut's helmet, he could eliminate the intial reaction that people had to his face and he felt more normal. He began to use this 'mask' as a crutch by wearing it constantly.
His father took the helmet and threw it away without telling him much like parents do when a child refuses to give up a childhood security blanket. He realized that without his help, Auggie would be unlikely to give up the mask and start facing the world as his himself on his own.
His dad finally tells him the truth at the end of the book that he "couldn't stand seeing that thing cover your face anymore" and that he loves "this face of yours, Auggie, completely and passionately. And it kind of broke my heart that you were always covering it up." Auggie's dad shows here that he did what he did to give him the confidence he needs to be himself in the world.

In the chapter called "Costumes," Auggie explains that when he was little, he wore a kind of mask—an astronaut helmet—wherever he went. He used this type of disguise to hide his face, which is marked by a deformity. When Auggie was very young, he did not want people to stare at him, and wearing the helmet, even in the summer, allowed him to hide his face. The helmet also allowed him to isolate himself to some degree from the rest of the world. Auggie wore the helmet constantly until he was about seven and had eye surgery, and, following his surgery, he couldn't find the helmet anymore.
It turns out that his dad thew out the helmet without telling Auggie. At the end of the book, his dad tells Auggie, "I couldn't stand seeing that thing cover your face anymore." He goes on to explain, "I love this face of yours, Auggie, completely and passionately. And it kind of broke my heart that you were always covering it up." While Auggie hates his own deformed face, his father loves his son's face. Auggie's dad found it depressing when his son kept wearing the helmet to cover his face, as he loves his son's face and wants his son to feel confident about himself and his looks. By throwing away the helmet, Auggie's dad was attempting to make his son rely less on hiding and instead face the world. He wanted his son to learn to accept the way he looks and to show his face to the world.

Is Raymond a static or dynamic character in "Raymond's Run"?

Raymond is a static character.  
A static character is a character that doesn't go through any kind of inner change (or changes very little). Readers don't see any character growth or development in static characters.  
I believe that Raymond is a static character. He is mentally disabled in some way, but the story doesn't give specifics on that. His disability serves as a way to show why Squeaky is so protective of her older brother. It's clear that she loves him, and he loves her in return. By the end of the story, it is Squeaky's opinion of Raymond that has changed.  After witnessing him run, she now sees the potential in Raymond.  Raymond, on the other hand, doesn't have an epiphany about Squeaky. She is the same little sister that she always has been. He loves her dearly, and he supports her unashamedly.

Raymond is hollering from the swings cause he knows I’m about to do my thing . . . 

Readers also get to see that Raymond loves running "with" Squeaky.

And on the other side of the fence is Raymond with his arms down to his side and the palms tucked up behind him, running in his very own style, and it’s the first time I ever saw that and I almost stop to watch my brother Raymond on his first run.

I realize that Squeaky says that is Raymond's "first run," but I've always gotten the impression that Raymond's run that day may have just been the first that Squeaky finally noticed. Raymond runs because Squeaky runs, and it's his way of bonding with his sister. I don't believe that is new emotional ground for Raymond, which is why I believe that he is a static character.

Compare how both poets present their main subject in "Sonnet 130" and "Ozymandias."

Both poems use a central conceit—the idealization or aggrandizement of the human form—to make a point about art and humanity, although their tones are very different. Shakespeare is reacting against (or even satirizing) a tendency in poetry to use hyperbole to idealize female beauty; he contrasts the idealized language used to describe women with the truth about his lover (culminating with the hilarious “And in some perfumes is there more delight / Than in the breath that from my mistress reeks.”). Shakespeare’s poem is funny, but concludes with a serious sentiment: “And yet, by heaven, I think my love as rare / As any she belied with false compare.”
Shelley’s poem is not funny. Here, it is the ancient King, Ozymandias, who has idealized himself by creating a giant statue of himself. Whereas Shakespeare’s point is to poke fun at poetic hyperbole, Ozymandias truly does believe in his own greatness: “My name is Ozymandias, King of Kings; / Look on my Works, ye Mighty, and despair!” Even though the ruined sculpture retains some of the grandeur of the king, Shelley’s point is that even the great works of Ozmandias will erased by time—even something as colossal as the statue.
Both poems make a point about the relationship of art to truth. The difference is in attitude. Shakespeare recognizes that poetry can never capture what he values in his lover; his poem succeeds because it rejects any artistic attempt to describe her beauty. Ozymandias, on the other hand, seeks to make the statue into a kind of permanent symbol of his omnipotence; it is as if he would command art to be faithful in the same way he commands his sculptor. Shelley, with Shakespeare, recognizes the impossibility of that goal; in Shelley’s case, the poem ends on an almost existential note: “‘Nothing beside remains. Round the decay / Of that colossal Wreck, boundless and bare / The lone and level sands stretch far away.’”

Shakespeare's "Sonnet 130" and Shelley's "Ozymandias" deal with different subjects, yet use a similar conceit to convey their themes.
"Sonnet 130" is a romantic ode, and the subject is the beauty of the speaker's paramour. The opening line, "My mistress' eyes," begins the description, and the rest of the poem is a list of subsequent attributes. Ozymandias, on the other hand, is political in nature. The speaker recounts the description of a statue he heard about while traveling; it is the fallen statue of a king with an intimidating epigraph.
The conceit or primary literary device of both poems is a central image: a human idol. Shelley presents his statue in the form of a literary postcard, a ruined statue recounted from a faraway land. Shakespeare generates the image of an idealized beauty that his lover, ironically, does not live up to.
Both poems use the central image to create irony. Shakespeare's list of hyperbolized beauty traits (coral red lips, breasts as white as snow) serves to illustrate how ludicrous such expectations are of female beauty. Similarly, Shelley's fallen statue underscores the hubris of the king unwilling to acknowledge the inevitability of his own demise.

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

Charlie Marlow can be considered a morally ambiguous character insofar as he understands the difference between moral and immoral behavior but does not necessarily take a moral stand when one is warranted. He understands that when he is dispatched to Africa to put a stop to Kurtz's megalomania, it is because the Company wants their ivory, not because Kurtz's behavior in ways unrelated to commerce is a problem. Marlow confesses in the first chapter that "the conquest of the earth" is redeemed by "the idea only." He recognizes that the conquest consists of "taking it away from those who have a different complexion or slightly flatter noses than ourselves." Marlow's slow pursuit of and eventual meeting with Kurtz reveals his understanding that what Europe has been doing to Africa and Africans in the colonial period only appears to help Africa by bringing technology, when in fact what it is doing is deleterious to the continent and its native people. However, Marlow does not act decisively in trying to right any moral wrongs. He merely observes and does the Company's bidding, and he is in that way complicit in the exploitation.
It is challenging to think of Kurtz as a morally ambiguous character. His writing "exterminate all the brutes!" and the symbolic painting he makes suggest that he considers himself and European culture superior to the people of Africa; he appears to understand fully that, instead of bringing civilization and enlightenment to Africa, Europe is plundering it. He is a willing participant in this system, and when he goes rogue, it is only to set himself up as a god to be worshipped. In this way, he is a living, solitary symbol of Europe's rapaciousness and, ironically, feels no sense of obligation to the continent that created him.
Overall, the novel is a strong indictment of colonialism as well as man's embrace of inhumanity, and Conrad brings specificity to his argument by creating Kurtz as a charismatic character that Marlow has a hard time fully condemning.

Marlow's story is meant to shed light on imperialism and the true nature of what Europeans refer to as civilization. Marlow begins his story by mentioning that Europe was at one time a dark, primitive place and challenges conceptions that Europeans are morally and intellectually superior by saying, "strength is just an accident arising from the weakness of others" (1.12). This ambiguity between civilization and savagery is also reflected in the characters of Marlow and Kurtz. Both men hail from relatively wealthy families, are obsessive individuals, lose touch with reality, and are attracted to the primitive nature of the Africans. While Marlow is portrayed as a relatively positive, civilized character, a close examination reveals inconsistencies in his behavior and beliefs. Marlow has a negative perception of women, does not openly oppose the Company's brutal treatment of slaves, lies to Kurtz's Intended, and mentions several times that he wishes to experience life as a Native. During his discussion with the manager, Marlow mentions that he is "getting savage," an intriguing and enigmatic statement. He also wonders why he does not "go ashore for a howl and a dance" when he listens to the natives' ritual. His love/hate relationship with Kurtz is also ambiguous and makes the reader question his true feelings about Kurtz. Similar to Marlow, Kurtz is also a morally ambiguous character. Initially, Kurtz is depicted as a talented, articulate ivory trader, who is admired for his success throughout the Company. Kurtz began his journey into the heart of darkness with the intention of bringing civilization to the natives while simultaneously becoming wealthy in the ivory industry. However, Kurtz descends into savagery after discovering that the natives perceive him as a god. Kurtz becomes corrupted by his supreme power and influence over the natives and essentially transforms into a greedy, maniacal tyrant. Despite Kurtz's depravity, Marlow interprets his last words as recognition for his crimes. Marlow ends up sympathizing with Kurtz, which again presents his ambiguous feelings.
Overall, both characters' moral ambiguity mimics Conrad's argument concerning civilization and savagery. While Europe is depicted as being the epitome of civilization, the Company's inefficient, destructive nature reveals its true makeup. Likewise, both Marlow and Kurtz's complexity demonstrates their propensity to act civil and savage at various times. Marlow's perception of Kurtz also clouds the reader's portrayal of the enigmatic figure and creates a dichotomy between his positive and negative traits. Similar to how the reader interprets Marlow and Kurtz's character, Conrad's story challenges the reader's perception of civilization, imperialism, and nature.

What is the meaning behind the quotation, "I’ve heard you to be a sensible man, Mr. Hale. I hope you will leave some of it in Salem" in The Crucible?

John Proctor hopes Reverend Hale's arrival will end the hysteria about witches, but it doesn't because things have progressed too far.
This comment is about the witch trials causing mayhem in Salem. The hysteria over witches is unreasonable. Reverend Hale is supposed to be an expert. The witch trials are a "beloved errand" for him. Proctor hopes Hale can end the girls' accusations of witchcraft on innocent people.
John Proctor certainly does not believe in witches.

Giles Corey: He don’t believe in witches.
Proctor, to Hale: I never spoke on witches one way or the other. Will you come, Giles?
Giles: No — no, John, I think not. I have some few queer questions of my own to ask this fellow.

The witch trials are a result of a group of girls who claim to have been attacked by witches, who in reality are just townspeople. Since the town fears witches, they believe the girls. The girls' ringleader is Abigail Williams, who has a specific reason to get back at John Proctor because he spurned her after they had an affair.
When Hale arrives, he brings with him his expertise and a bunch of books.

Parris, delighted: Mr. Hale! Oh! it’s good to see you again!Taking some books: My, they’re heavy!Hale, setting down his books: They must be; they are weighted with authority.

For a group of supposedly God-fearing people, the people of Salem go from normal to crazy pretty quickly. Hale, the supposed expert on witches, is unable to derail the insanity. By the time the trials are over, many innocent people will have died as a result of them.

Single Variable Calculus, Chapter 8, 8.1, Section 8.1, Problem 52

Use the formula $\displaystyle \int x^n e^x dx = x^n e^x - n \int x^{n-1} e^x dx$ to find $\displaystyle \int x^4 e^x dx$


$
\begin{equation}
\begin{aligned}
\int x^4 e^x dx &= x^4 e^x - 4 \int x^3 e^x dx\\
\\
&= x^4 e^x - 4 \left( x^3 e^x - 3 \int x^2 e^x dx \right)\\
\\
&= x^4 e^x - 4x^3 e^x + 12 \left( x^2 e^x - 2 \int x e^x dx \right) \\
\\
&= x^4 e^x - 4x^3 e^x + 12 x^2 e^x - 24 \left( xe^x - \int x^0 e^x dx \right)\\
\\
&= x^4 e^x - 4x^3 e^x + 12x^2 e^x - 24 xe^x + 24 e^x + c\\
\\
&= e^x \left( x^4 - 4x^3 + 12 x^2 - 24 x + 24 \right) + c
\end{aligned}
\end{equation}
$

How far should the government intrude on the free market choice?

The only possible answer to this is “to some extent.”  It is impossible to specify a rule that would tell us exactly how much the government should intervene in all cases.
Essentially everyone but the most committed libertarian would want the government to intervene in the free market in some cases.  If there is no intervention, then businesses could sell heroin and cocaine to children.  They could produce child pornography.  You could argue that even slavery would be legal if the government did not intervene at all in the free market.  Hardly anyone would want that.
On the other hand, essentially everyone would agree that we need to limit the degree to which the government can intervene.  Few of us would want the government to tell us that we could not eat meat, for example, or that we could only buy a certain amount of gas each month.  Few of us would want the government to tell us how big our TVs could be or how many hours per day we would be allowed to watch TV.  Practically everyone would agree that there need to be some limits on government intervention.
Thus, it is clear that we have to have some government intervention, but not too much.  Therein lies the issue.  How much is “too much” in any given case?  Let’s look at the issue of food.  Presumably it is okay for the government to say that our food has to be safe.  But how far can they go in defining what is safe? Most people would say that the government could ban foods that would poison us right away.  But what about foods like sugar that are bad for us in the long term but are not going to harm us very much in the short term?  Could the government actually tell us we can’t have food that it deems unhealthy?  Where do we draw this line?
This problem arises in practically every area you can think of.  We want some government intervention, but we do not want too much.  The issue is that not everyone agrees on what is too much.

How does "The Hollow Men" by T. S. Eliot reflect the reality of humanity in the early twentieth century, and is the meaning of the poem still applicable to the twenty-first century?

"The Hollow Men" emerged out of the aftermath of World War I. It can be seen as a paradigm example of modernism in that it reflects a cultural environment in which all the old certainties have been destroyed. Deprived of all the old moral, aesthetic, and political certainties by this cataclysmic conflict, Western humanity has been hollowed out, no longer able to draw on centuries of cultural achievement for its values and principles.
The contemporary relevance of the poem lies in the fact that, in the current climate, many of the certainties that formed the bedrock of Western civilization during the Cold War appear to be under serious threat. In this era of fake news and populism, the values of liberal democracy, the rule of law, and internationalism are under sustained assault from a variety of sources. Once again, Western humanity finds itself hollowed out, deprived of all the old certainties by massive upheaval (in this case the 2008 financial crisis and its aftermath, whose damaging consequences are still being felt to this day).

"The Hollow Men" is largely a poem of despair, decrying the emptiness felt by many in the early twentieth century following the terrible destruction of World War I and as fascism and state communism began to rise. Eliot repeatedly compares men to scarecrows, suggesting a disconnect from the heroic way in which they might try to frame themselves and the way they actually are.
We can understand the modern era in terms of people reacting against the terrors of war, industrial society, and the failed promises of the political systems that dominated the world. In contrast, post-modernism is often discussed as people adjusting to this. For example, there is a general understanding that politicians and corporations are corrupt but little expectation of truth or purity.
In this framework, we can see Eliot's poem as a modern lament for the hollowness of the world and these themes as setting the stage for the world we live in now. I would say "The Hollow Men" very much applies to the present day, but that it's meaning and tone will read differently in the different context we live in. I think few would really argue that world systems live up to the ideals they espouse, so i think framing the world and its leaders as hollow is still a compelling depiction.

"The Hollow Men" reflects a society that is filled with meaninglessness and symbols that have ceased to signify anything. One of the two epigraphs of the poem refers to the death of Kurtz in Conrad's Heart of Darkness. Kurtz is a revered figure in Conrad's novel until the main character, Marlow, finds out that Kurtz is a fraud; Kurtz therefore stands for the meaninglessness of life and of its spiritual deadness.
The beginning of the 20th century was marked by the loss of belief in established ideas and by widespread disillusionment, particularly after the death and destruction caused by World War I. Countries were divided by a belief in western-style democracies, a belief in Fascism, and a belief in Communism, but all systems resulted in war and in destruction. In the face of this wide scale destruction, it was hard for people to sustain their faith and hope.
Eliot reflects people's disillusionment with the hollow men in his poem. These men have a "headpiece stuffed with straw"--in other words, their heads are stuffed with nothing but straw. These men are so hollow, so desiccated in their ideas, that they seem to not be able to enter "death's dream kingdom." Their life does not end with a traditional death; instead, it seems as if death characterizes their hollow lives as they exist in a barren "cactus land." The cactus is a symbol of their spiritual desiccation. Their lives are drained of meaning; they are dry and without sustenance. Instead, they wander as if in a "valley of dying stars." They have no stars to guide their journeys but instead live without guidance and without hope.
Some might argue that the meaning of the poem still applies today, though you have to figure out your own take. Is today's world filled with meaninglessness and with "hollow men" without substance, or do people today find some sort of meaning in their lives and some kinds of hope?

Which British politician agreed with Sam Adams and the other revolutionaries regarding their grievances with the British Parliament's imposition of duties and other acts on the American Colonies?

The politician you're thinking of is Edmund Burke. He was born in Ireland (it's important to remember that at this time Ireland was under British rule; Northern Ireland still is) and moved to London after he gave up on his law studies. He was brought up in a religiously mixed house. He was a practicing Anglican and his sister was a Roman Catholic. In most households at this time, this would have been a strong point of contention. But perhaps it informs the type of pragmatism that Burke brought to the British Parliament when he was elected in 1765. He knew firsthand what British rule looked like. Perhaps that's why he sided with Sam Adams and his compatriots as they petitioned King George III and the Parliament for redress of their grievances. Originally the American Colonies had no desire to be a separate country. They were, after all, loyal British subjects. However, as the Parliament demanded that the Colonists pay for, and perhaps not unreasonably so, the French and Indian War (what the British termed the Seven Years War), things turned sour. American colonists, particularly those who were well off, didn't like the idea of paying additional taxes for their general welfare. Burke saw that the Parliament was being inflexible when it came to the imposition of taxes or duties.American colonists called for a seat in Parliament and Burke thought that more flexibility by Parliament would help maintain a positive relationship with the king's subjects across the Atlantic, but it was not to be. 
http://americainclass.org/sources/makingrevolution/war/text1/burkereconspeech.pdf

http://www.bbc.co.uk/history/historic_figures/burke_edmund.shtml

Single Variable Calculus, Chapter 5, 5.2, Section 5.2, Problem 8

Suppose that $f(x)$ is an increasing function. Estimate $\displaystyle \int^9_3 f(x) dx$ using three equal sub-intervals with (a) right end points, (b) left end points and (c) midpoints. What can you say about your estimates?


$
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
\\
3 & -3.4\\
4 & -2.1\\
5 & -0.6\\
6 & 0.3\\
7 & 0.9\\
8 & 1.4\\
9 & 1.8\\
\hline
\end{array}
$


a.) The width of each rectangle is..

$\displaystyle \Delta = \frac{9 - 3}{ 3} = 2$

So, we can evaluate the area at right end points (starting from $x = 5$)

$
\begin{array}{|c|c|}
\hline\\
x & f(x) \\
5 & -0.6 \\
7 & 0.9 \\
9 & 1.8\\
\hline
\end{array}
$

Now, the total area of the rectangle is..

$2 [-0.6 + 0.9 + 1.8] = 4.2$

b.) By evaluating the area at the left end point (starting from $x = 3$)

$
\begin{array}{|c|c|}
\hline\\
x & f(x) \\
3 & -3.4 \\
5 & -0.6 \\
7 & 0.9\\
\hline
\end{array}
$

Now, the total area of the rectangle is..

$2[-3.4 - 0.6 + 0.9] = -6.2$

c.) At midpoint (starting from $x = 4$)

$
\begin{array}{|c|c|}
\hline\\
x & f(x) \\
4 & -2.1 \\
6 & 0.3 \\
8 & 1.4\\
\hline
\end{array}
$

The total area of the rectangle is

$2 [-2.1 + 0.3 + 1.4] = -0.8$

We can say that our estimates is neither over estimates nor under estimate. Although $f(x)$ is increasing, its value started from negative and changes to positive.

College Algebra, Chapter 3, 3.7, Section 3.7, Problem 8

The graph of $f$ is given below. Determine whether $f$ is one-to-one.







By using horizontal line test, the line intersects the graph more than once. Thus, the function is not a one-to-one function.

Why did Napoleon overthrow the Directory?

The Directory was a five-man committee that took power in France after the fall of Robespierre. Its immediate aim was to restore some semblance of order to a country wracked by the widespread chaos and bloodshed of the Terror. Although initially quite successful, the Directory soon ran into serious difficulties. Conflicts continued apace, with large parts of the country in open rebellion against the government in Paris. The economic problems bequeathed by the Jacobins spiraled out of control—unemployment and inflation soared. France was on the brink of bankruptcy. All the ingredients for another Revolution seemed at hand.
Meanwhile, Napoleon was continuing to prove himself a highly skillful general on the battlefield. His military successes merely served to confirm Napoleon's egomaniacal tendencies, his implacable belief in his own ability. France was rapidly degenerating into chaos, and Napoleon passionately believed that he, and he alone, was the man to restore order and stability.
Fortunately for Napoleon, many in the upper echelons of French politics felt the same way. Behind the scenes, Napoleon and his allies set to work by trying to ease him into power. A fictitious Jacobin plot was fabricated to provide a pretext for Napoleon to take control. Unfortunately, the plot did not go according to plan. Napoleon's allies squabbled among themselves, and when the Corsican general lost patience and tried to force the issue, he was sent packing by an angry, restive Council of Elders.
Enter Napoleon's brother Lucien to save the day. He harangued the soldiers guarding the Assembly, convincing them that there were traitors inside in the pay of England, hell-bent on assassinating Napoleon. After a long search, a sufficient number of deputies was found to authorize the establishment of a triumvirate, a government consisting of three Consuls, one of whom would be Napoleon. This was an attempt to try and give the coup (for that is essentially what it was) some degree of legitimacy. However, there is little doubt that the new regime was formed more or less at the point of a bayonet.
Although power was formally split between three men, there was little doubt as to who was really in charge. The two other Consuls, the Abbe Sieyés and Ducos seriously underestimated Napoleon. As he continued to rack up an impressive string of military victories, he steadily began to consolidate his dominant position within the Consulate until he became First Consul, with full executive power, in December 1799. Napoleon's power further increased until, in 1804, he consolidated his position by crowning himself Emperor.
https://www.ngv.vic.gov.au/napoleon/revolution-to-empire/the-rise-of-napoleon.html

What are Henry Thoreau's views of transcendalism?

Henry David Thoreau was a Transcendentalist. He believed in both the power of nature and the power of the individual. These ideas can be seen in one of his most famous works, Walden.

We must learn to reawaken and keep ourselves awake, not by mechanical aids, but by an infinite expectation of the dawn, which does not forsake us in our soundest sleep.

Here, Thoreau speaks of the power of nature. It is through nature's power that we, as human beings, are able to become spirituality awake (transcend human limitations). Through nature, we learn to elevate our lives through a "conscious endeavor" with nature itself. Thoreau speaks of his desire to no longer live like the "ant" ("meanly"), "fritted away by detail." What he means by this is that the ant lives in the details of life only. It is only when we, mankind, turn away from the "details" of life that we are actually able to live.
"Simplicity, simplicity, simplicity" is Thoreau's mantra. By living simply, one is able to pay far more attention to the nature around oneself. By engrossing oneself in nature, one is able to succeed in life. Thoreau was able to do this by moving to a small cabin in the woods. This change in lifestyle and pace of life allowed him to simplify and to pay attention to the most important things in life, changing the "atmosphere and medium" through which we look at life. By simplifying life, Thoreau was able to pay attention to only the "essential facts of life."
Therefore, Thoreau looked at Transcendentalism as a way of life. Through Transcendentalism, one (he) is able to depend upon one's own individualism and imagination to transcend one's own accepted limitations. By depending upon one's self, as Thoreau illustrates in Walden, one is able to find one's own wisdom, not the wisdom of the multitudes (because what works for one does not necessarily work for another).

y = 2 , y = 4-x^2/4 Set up and evaluate the integral that gives the volume of the solid formed by revolving the region about the x-axis.

For the region bounded by  y=2 and y =4-x^2/4 revolved  about the x-axis, we may  apply Washer method for the integral application for the volume of a solid.
As shown on the attached image, we are using vertical rectangular strip that is perpendicular to the x-axis (axis of revolution) with a thickness of "dx" . In line with this, we will consider the formula for the Washer Method as:
V = pi int_a^b [(f(x))^2-(g(x))^2]dx
where f(x) as function of the outer radius, R
        g(x) as a function of the inner radius, r
For each radius, we follow the y_(above) - y_(below) , we have y_(below)=0 since it a distance between the axis of rotation and each boundary graph.
For the inner radius, we have: g(x) =2-0=2
For the outer radius, we have: f(x) =(4-x^2/4 )-0=4-x^2/4
 
To determine the boundary values of x, we equate the two values of y's:
4-x^2/4 =2
-x^2/4 =2-4
-x^2/4 =-2
(-4)(-x^2/4 ) =(-4)(-2)
x^2=8   then  x= +-sqrt(8)  or  +2sqrt(2) and -2sqrt(2)
Then, boundary values of x: a=-2sqrt(2) and b=2sqrt(2) .
 Plug-in the values in the formula V = pi int_a^b( (f(x))^2 -(g(x))^2) dx , we get:
V =pi int_(-2sqrt(2))^(2sqrt(2)) [(4-x^2/4)^2 -2^2]dx .
 
Expand using the FOIL method on: (4-x^2/4)^2 = (4-x^2/4)(4-x^2/4)= 16-2x^2+x^4/16 and 2^2=4 .
The integral becomes:
V =pi int_(-2sqrt(2))^(2sqrt(2)) [16-2x^2+x^4/16 -4]dx
V =pi int_(-2sqrt(2))^(2sqrt(2)) [12-2x^2+x^4/16 ]dx
Apply basic integration property: int (u+-v+-w)dx = int (u)dx+-int (v)dx+-int(w)dx  to be able to integrate them separately using Power rule for integration:  int x^n dx = x^(n+1)/(n+1) .
V =pi *[int_(-2sqrt(2))^(2sqrt(2))(12) dx -int_(-2sqrt(2))^(2sqrt(2)) (2x^2) dx + int_(-2sqrt(2))^(2sqrt(2)) (x^4/16)dx]
V =pi *[12x-2 *x^3/3+1/16*x^5/5 ]|_(-2sqrt(2))^(2sqrt(2))
V =pi *[12x-(2x^3)/3+x^5/80 ]|_(-2sqrt(2))^(2sqrt(2))
Apply the definite integral formula: int _a^b f(x) dx = F(b) - F(a) .
V =pi *[12(2sqrt(2))-(2(2sqrt(2))^3)/3+(2sqrt(2))^5/80 ]-pi *[12(-2sqrt(2))-(2(-2sqrt(2))^3)/3+(-2sqrt(2))^5/80 ]
V =pi *[24sqrt(2)-(32sqrt(2))/3+(8sqrt(2))/5 ] -pi *[-24sqrt(2)+(32sqrt(2))/3-(8sqrt(2))/5 ]
V =(224sqrt(2)pi)/15 -(-224sqrt(2)pi)/15
V =(224sqrt(2)pi)/15 +(224sqrt(2)pi)/15
V =(448sqrt(2)pi)/15 or 132.69 (approximated value)

How does Miss Peregrine's Home for Peculiar Children by Ransom Riggs relate to the Holocaust?

The novel alternates between realistic and fantasy worlds in conveying the way that Jacob learns about the Second World War, when the Nazis killed and persecuted millions of Jews, along with gay people, Romanis, and others. Jacob’s Grandpa Portman is a Holocaust survivor. As a child, he had lived in Poland but was evacuated to Wales. During the war, many children were sent away from their homes on the Continent to England and other countries, and many English children were sent away from the urban centers to the countryside.
In the novel, the Holocaust is personified as a group of monsters called the Hollowgast. Much of the novel involves Jacob’s deciphering which aspects of his grandfather’s statements and memories are based in fact and which are products of his imagination. For example, Grandpa tells Jacob to go to the home in Wales and find the hawk; it turns out that the administrator was named Miss Peregrine, which is a type of falcon, a bird closely related to the hawk. He was also fearful that the monsters would return, and Jacob starts to see them in his dreams. When Jacob finally gets to the school, he realizes that some of Grandpa’s apparent imaginings are true: Miss Peregrine can turn into a bird, the Hollowgast monsters have embodied forms, and Jacob can travel back in time to the 1940s. These kinds of physical manifestations become real because this is a fantasy novel, but the kinds of danger that Jacob faces are those that actually occurred during the war.

Two ways that Miss Peregrine's Home for Peculiar Children can relate to the Holocaust is in its treatment of persecution and its display of people who feel compelled to take action in the face of injustice.
The persecution of the peculiars is one way the novel connects to the Holocaust.  The syndrigast, or people who are "peculiar," are viewed with hostility.  They are not like everyone else.  Their difference is what causes others to hunt them down and kill them.  This is similar to the way that Nazis saw Jewish people.  They sought to capture and kill them.  The peculiars must flee to different areas to avoid capture, a sad parallel to what Jewish people had to do during the Holocaust.  
Another connection to the Holocaust is how the novel shows responses to human suffering.  Both Jacob and his grandfather make conscious choices to fight for people who are suffering.  Jacob's grandfather committed himself against the Nazis and to fighting monsters.  For his part, Jacob resolves to help the peculiars.  In both settings, people are taking action against injustice.  Jacob and his grandfather could have chosen to do nothing.  Yet, they feel compelled to act. This shows a clear connection to the Holocaust time period.  Even though the Nazis killed many people, there were some who stood up for the rights of others. For example, Johanna Eck was a German who hid Jewish people in her home.  Suzanne Spaak left her life of wealth and privilege to join the Underground.  Like Jacob and his grandfather, they undertook great risk to do what they felt was right. 

In Harry Potter and the Deathly Hallows by J.K. Rowling, is there any mythological story behind each of the Deathly Hallows?

The Deathly Hallows are three magical objects central to the plot of the Harry Potter series, especially the last book. Though the Hallows are real, physical objects in the story, they are surrounded in myth and mystery. Something which is hallow is holy or sacred, and while it's an unusual form of the term, a sacred or holy object could be described as a hallow. To call these three magical items--a wand, a stone, and a cloak--the Deathly Hallows tips us off to the fact that they are related to death and are sacred for that reason.
The story behind the Deathly Hallows goes something like this:
Three brothers were traveling through some woods when they came to a river too deep to cross by wading through. Luckily, the three brothers were wizards and easily conjured up a bridge. Death (personified) was angry that he had been cheated out of three souls, so he appeared to the brothers. Death congratulated the brothers on having outwitted him and offered them each gifts of their own choosing. 
The first brother, who loved to duel, asked for a wand more powerful than any other. Death grabbed a branch from a nearby elder tree and transformed it into a wand.
The second brother, who was arrogant, wanted to humiliate Death and so asked to have the power to bring back the dead. Death grabbed a stone from the riverbank and enchanted it for the brother.
The third brother, the smartest of the bunch, asked for the power to walk free from this encounter with Death unable to follow him. Death gave him his own cloak, which granted the brother invisibility.
The three brothers then crossed the bridge and went on their ways with their gifts. The first brother made it into a town and challenged another man to a duel. Of course, his wand was the most powerful in existence and he won. He then boasted and dared anyone to try and take the wand from him. While he slept that night, someone crept into his room, slit his throat, and took the wand. Death had outsmarted the first brother and given him the key to his own death.
The second brother made it all the way to his own home before trying to use his enchanted stone. He turned it over three times in his hand, and before him appeared the figure of his dead fiancee. Though he could see her, he could not touch or speak to her. The second brother was so distressed that he killed himself, joining his long-gone love, the first brother, and Death.
The third brother enjoyed his gift for many years. The cloak gave him the power to remain invisible to Death, and only when he was ready to go did he take it off and bestow it upon his son. The third brother greeted Death like an old friend and finally went with him.
 
That is the bulk of the story, but we learn from Harry's friend Ron that there is a little more to it. Ron and lots of other wizard children grew up hearing this story as a bedtime story or folk tale. Though it is somewhat ambiguous, we are lead to believe that the Tale of the Three Brothers actually happened when it is revealed that the Hallows are real items. It is implied that the invisibility cloak Harry received anonymously during his first year at Hogwarts was the hereditary gift of the third brother.
With regards to the conflict of the seventh book, it is believed that any one person who owned all three of the Deathly Hallows would become a Master of Death. Owning the wand, the cloak, and the stone would make someone an essentially unstoppable force. As such, Voldemort wants to get his hands on the Deathly Hallows and fulfill his dream of immortality.
https://harrypotter.fandom.com/wiki/Deathly_Hallows

What are at least two traits of Hazel Grace?

Let's start with a few obvious and simple character traits for Hazel.  Hazel is a sixteen year old female with cancer, but she doesn’t let the cancer define and rule her life.  Yes, it causes her to act certain ways, but she also doesn’t wallow in her own world of depression due to knowing that she is dying.  One character trait that I deeply appreciate about Hazel is just how selfless she is.  She is very self-conscious about her impact on other people, and she doesn’t want to be a burden in life or in death. One of her biggest concerns is how much her death will hurt her mom, and Hazel wants to minimize that.  

There is only one thing in this world shittier than biting it from cancer when you're sixteen, and that's having a kid who bites it from cancer.

In addition to being a selfless and loving character, Hazel is also a very confident girl.  She simply doesn’t care what the world thinks.  She doesn’t try to “be cool” and follow trends.  She is confident in herself and her self-image.  Her short pixie haircut is a reflection of that attitude.  Hazel doesn’t try to hide this attitude and confidence from other characters either.  In chapter three, Hazel bluntly tells her mother that she simply doesn’t care to try to fit in with everything.  

"I take quite a lot of pride in not knowing what's cool."

I would be remiss if I didn’t say that another of Hazel's character traits is her bravery.  She’s dying from cancer, but she doesn’t wallow in fear and self pity.  She embraces the life that she has, and she is constantly working to make the best of a bad situation.  Given the same situation, I hope that I could be as positive and brave as Hazel.

Hazel Grace Lancaster, the protagonist of The Fault in Our Stars, is presented as a relatable yet profound character who is negotiating her relationship with life, death, and cancer. We gather that Hazel is intelligent, or at least very self-motivated, as she is already enrolled in college courses at the age of sixteen. Hazel is also very mature, but sadness ages a person in certain ways. Hazels' sense of self-awareness and morality is surprising to many people who meet her. For example, Augustus' parents are surprised when Hazel explains that she is a vegetarian because she wants to minimize the amount of suffering she causes in the world. I think that Hazel could also be described as brave. She is not afraid to speak up when she disagrees with someone and had the courage to go all the way to Amsterdam to meet her favorite author. 

Explain how the author develops the theme that home is a joyful and safe place with evidence from the text.

In "The Ambitious Guest" the family shown living in the isolated house is a picture of happiness: a mother and father, young girl and small child, and elderly grandmother. It's meant as a straightforward depiction without irony, without any dark secret as might be expected from a Hawthorne story if we know his work. The house is open to strangers, who walk right in and are accepted with warmth. The inclusion of the guest does nothing to disrupt this picture, as he bonds with them immediately and finds that they sympathize with his wish to achieve one great thing and then die. The young man does not seem to value life itself—which is unusual—but only the quality of being remembered for an act or acts accomplished in life.
The ultimate message of the story, however, is that not only is the process of life the guest does not value ephemeral; it is random as well. No one could know that the avalanche would strike the very spot they ran to for safety, and spare the house they thought would be destroyed. It's arguable that by this outcome Hawthorne meant to convey that "ambition"—the seeking of something beyond the comfort and security of what we have—is the thing that kills us. But his theme seems an even darker one: that whatever human beings plan and secure for themselves—a supposedly safe home, clothes for burial as the grandmother has, an idea for accomplishment like that of the ambitious guest—all of this can come crashing to ruin at any moment, and regardless of our will to survive and achieve, there is nothing we can do to prevent such a random outcome.

The author of the short story “The Ambitious Guest” starts by explaining the location of the home. The home is situated in a “cold dangerous spot” near a steep mountain. It is in the Notch of the White Hills which is referred to as the “bleakest spot of all New England,” with a weather that is exceedingly cold in the winter and has a sharp wind throughout the year. Yet, the interior of the house is safe and happy. The hearth in the house has a roaring fire that expels any cold, and the people of the house even laugh at each other’s jokes in spite of the scary sound made outside by rolling stones.
Indeed, the parents, children, and grandmother are each defined, using various adjectives, as being very happy: the parents’ faces have a “sober gladness,” the oldest girl is “the image of happiness,” and the grandmother is the “image of happiness grown old.” The house doubles up as a tavern, where lodgers only pay for food and accommodation. When a young male traveler enters the house, he says, “Ah, this fire is the right thing, especially when there is such a pleasant circle around it.” The author builds the theme that the house is a joyful and safe place by contrasting its warm interior with the cold exterior.

What was Neely Crenshaw's philosophy in Bleachers by John Grisham?

Neely Crenshaw is obsessed with the divide between his current life as an ordinary real estate salesman whose wife has left him and his "past life" as a football captain and star adored by the entire town of Messina. His philosophy prior to his career-ending injury during a college game was that of an athlete: complete belief in the glory of the game, a misplaced sense that being a champion is eternal, and a willingness to win at all costs.
Back then, Crenshaw was trapped in his own hero's complex, one that set him at odds with the severe techniques of Coach Eddie Rake. After his career is over, Crenshaw seems to be paralyzed by his faded fame and the fear that the people of Messina resent him for never "making it big." This internal conflict serves as one of the major points of the novel, and is perhaps best described by one of Crenshaw's fellow players:

You count the years until you get a varsity jersey, then you’re a hero, an idol, a cocky bastard because in this town you can do no wrong. You win and win and you’re the king of your own little world, then poof, it’s gone. You play your last game and everybody cries. You can’t believe it’s over. Then another team comes right behind you and you’re forgotten.

summarize the advantages of computers/software and the use of computer technology in investigations, summarize the disadvantages to law enforcement with respect to the advancements of computers, research a case where the computer was used to aid in the commission of a crime, research a case where the use of the computer was beneficial to the prosecution in a criminal case, and provide a final conclusion/paragraph that addresses your subjective opinion as to whether these technologies, in an overall sense, are of benefit or a hindrance to law enforcement efforts.

Computers, software, and other digital technologies have revolutionized the ways in which we investigate crime. Technologies such as biometrics, body-worn cameras, and crime mapping and analysis software have provided both support and accountability to officers on the ground, while forensic technologies such as laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS), alternative light photography, high-speed ballistics photography, 3D forensic facial reconstruction, magnetic fingerprinting and automated identification (AFIS), and link analysis software for forensic accountants have greatly aided scientists in the compilation of evidence key to securing convictions.

Unfortunately, updates in technologies are not one-sided, and criminals and criminal groups have also benefitted from advancements in computers, software, and other systems. According to the FBI’s Crime Complaint Center, total Internet crime complaints have risen from 262,813 in 2013 to 298,728 in 2016, with losses ranging from $781.80M in 2013 to $1.4B in 2016. Identity theft complaints have also risen dramatically (100K to 400K since 2001). Technologies have afforded criminals new avenues to conduct familiar crimes such as identity theft, credit card fraud, and vehicular theft, while also creating new opportunities for crimes like “sextortion” (threatening to share compromising sexual photos of victims unless they meet certain demands), synthetic identity theft (creating an entirely new identity), credit card skimming, and illegal “dark web” internet marketplace transactions for sex, drugs, weapons, and murder.

One such case of computer use and criminal activity involves Justin Larson, a 30-year-old computer scientist who used encrypted communications to distribute drugs. After deeply researching drug classifications and how to distribute them illegally through digital means, Larson connected to a Chinese fentanyl dealer over the dark web, where he communicated via a sophisticated messaging system. Essentially, whenever Larson communicated with his supplier, he would type his message (a) in an encrypted platform that would (b) generate a self-destructing link, and then (c) send the link to the supplier through encrypted web-based e-mail systems, after which (d) the message would be destroyed.

In order for forensic investigators to piece together the digital evidence for Larson’s case, they needed to perform a range of detailed forensic digital investigations on Larson’s mobile devices and work with web-based e-mail providers to find people connected to Larson. Investigators determined that his girlfriend was signing for and accepting packages that had been shipped from a Chinese distributor and delivered via TNT, a private commercial carrier. On January 25, 2017, Larson was convicted of conspiracy to distribute narcotics; five counts of possessions or attempted possession of a controlled substance and controlled substance analogue with intent to distribute; one count of possession with intent to distribute; and one count of distribution of a controlled substance. He was sentenced to life in prison.

As you can see from Larson’s case above, the advancement of technology has created the opportunity for even the smallest criminal to interface with global criminal organizations. However, at the core of all these criminal activities is still a human element. While technologies may provide additional tools to disguise this fact, at the end of the day, there’s still a human behind the wheel, and human beings are particularly fallible. With crime, all it takes is one screwup, and you have compromised your security. Law enforcement operates with a much wider margin of error.

Instead of asking the question of whether technologies are a benefit or a hindrance to law enforcement, the smarter question might be how law enforcement can use the newly freed resources technologies provide to better intervene in at-risk populations, and hopefully reduce the development of criminal onset.
https://www.encyclopedia.com/science-and-technology/computers-and-electrical-engineering/computers-and-computing/computer-crime

https://www.policeforum.org/assets/ChangingNatureofCrime.pdf

What is one significant similarity and one difference between Mr. Marroner in "Turned" and Mr. Hammond in "The Stranger," and how would you relate them to terms of theme, major conflict, setting, plot, and narrative mode?

One major similarity between Mr. Hammond and Mr. Marroner is that they both claim to love their wives deeply. However, Mr. Hammond is faithful to his wife, who he prefers to see as innocent and naive, while Mr. Marroner cheats on his wife, whose strength and purpose he admires.
Mr. Hammond loves his wife. He's so excited to see her upon her return that he's convinced everyone else watching the ship is also excited to see her. Yet he thinks of her as naive and needing him to help her. For example, he thinks that if he was on the ship, he'd bring her tea and watch her drink it, rather than a servant doing so. When it's revealed that she had a great time on her trip and that she was popular on the ship, he starts to become suspicious. He doesn't like that she has a life outside of him and one that he can't control. By the time he finds out that she was alone with a young man who died, he has already decided that she can't be trusted and ruminates that the rest of their marriage is ruined because they'll never really be alone again.
Mr. Marroner loves his wife. He writes her letters to tell her he misses her and when he returns home to find her gone, he's helpless. Unlike Mr. Hammond, though, Mr. Marroner appreciates that his wife is strong, intelligent, and has a full life. In one of the letters that he writes her, he says that he's glad she wouldn't be ruined if he were to die. He's glad that she's strong enough to go on and live. However, her strength is the very thing that allows her to leave him when she finds out he's impregnated their young housekeeper.
Mr. Hammond is not confident in the love of his wife. He thinks that "he had the feeling that he was holding something that was never quite his. Something too delicate, too precious, that would fly away once he let go." This is expressed in his anxiety over her every action. Mr. Marroner, on the other hand, is completely secure. He's able to stay away for months, blatantly cheat on her, and promise to support the woman whom he impregnated. When he arrives at the house she's moved to, he thinks "she would forgive him—she must forgive him. He would humble himself; he would tell her of his honest remorse—his absolute determination to be a different man." His confidence in their marriage is what allows him to pretend to others that everything is fine even when Mrs. Marroner is clearly gone and not intending to return home.
The major conflict in both stories is the reaction of one spouse to the behavior of another. Mr. Hammond is a passive character who hasn't done anything, while Mr. Marroner is an active character who did change the course of the story. By cheating on his wife, he set the events of the story in motion. Mr. Hammond, on the other hand, just waits to speak to his wife and then fumes over what he's learned and his suspicions about her behavior.
Mr. Marroner's confidence in his wife allows him to leave her home for months at a time. Mr. Hammond, on the other hand, wants to follow his wife to another part of the ship while she says goodbye to the doctor she met onboard. Despite their differences, their love for their wives creates a kind of need for both men. Even though he is suspicious of her, Mr. Hammond doesn't indicate a desire to leave his wife. Mr. Marroner continues to pretend his marriage is okay in public and then tracks down his wife and approaches her to try to get forgiveness for his actions.
Mr. Marroner is less sympathetic than Mr. Hammond because he chose to cheat on his wife. When he tracks her down, it's clear that she has moved on and has no intention of taking him back. The very traits he admired in her are the ones that will allow her to prosper without him. Mr. Hammond, on the other hand, doesn't seem to manage well without his wife for any length of time. The anxiety within him as he waits to see her against is almost palpable. He calms himself only by assuring himself that she's there and not ill.
While the themes of both stories focus on marriage, "The Stranger" is thematically more about the obsession that one spouse has for another while "Turned" is more about betrayal. Mr. Hammond is so focused on his wife that he can't see anyone else or conceive of anyone not being excited about her homecoming. Once they're reunited, the idea of her even going a few steps away is clearly one he doesn't want to entertain. Mr. Marroner, on the other hand, actively betrays his wife despite his avowed love for her. While he does think at the end that he'll be a different man for her, there's no evidence that he'd be capable of doing so.
One major difference between the stories is that "The Stranger" is told from the perspective of Mr. Hammond. The reader can't have any idea what kind of feeling his wife has for him or what she's done on her voyage. The reader is forced to share his anxiety and worry about their marriage and whether he'll keep her. In "Turned" though, the narrator is omniscient and knows the thoughts and feelings of the three primary characters. The reader can be sure as soon as Mr. Marroner gets home to an empty house that he isn't going to reunite with his wife. The reader understands her resolve from the beginning of the story when she realizes who has actually wronged her—her husband.

Intermediate Algebra, Chapter 2, 2.3, Section 2.3, Problem 50

Sheryl Zavertnik won $\$60,000$ on a slot machine in Las Vegas. She invested part of the money at $2\%$ simple
interest and the rest at $3\%$. In one year, she earned a total of $\$1,600$ in interest. How much was invested at each rate?

Step 1: Read the problem, we are asked to find the amount invested on each rate.
Step 2 : Assign the variable. Then organize the information in the table.
Let $x = $ amount invested in $2\%$ interest rate
Then, $60,000 - x= $ amount invested in $3\%$ interest rate


$
\begin{array}{|c|c|c|c|c|c|}
\hline
& \rm{Principal} & \cdot & \text{Interest Rate} & = & \rm{Interest} \\
\hline
2\% & x & \cdot & 0.02 & = & 0.02x \\
\hline
3\% & 60,000 - x & \cdot & 0.03 & = & 0.03(60,000 - x) \\
\hline
\end{array}
$


The total interest earned is equal to the sum of the interests at each rate.

Step 3: Write an equation from the last column of the table
$0.02x + 0.03(60,000 - x) = 1,600$

Step 4: Solve

$
\begin{equation}
\begin{aligned}
0.02x + 1,800 - 0.03x &= 1,600\\
\\
-0.01x + 1,800 &= 1,600 \\
\\
-0.01x &= -200\\
\\
x &= 20,000
\end{aligned}
\end{equation}
$


Then by substitution,
$60,000 - x = 60,000 - 20,000 = 40,000$

Step 5: State the answer
In other words, the amount invested in $2\%$ and $3\%$ interest rate is $\$20,000$ and $\$40,000$ respectively.

What do you think is the cause of the tragedy in Doctor Faustus?

In Christopher Marlowe’s play, much as in a Greek tragedy, Faustus is brought down by a fatal flaw. There is an element of his character that is destined to clash with the proper workings of the universe. Even if he did many good works that offset the likelihood of a tragic end, he would not escape his fate.
A difference in the Renaissance interpretation of tragedy, however, is that Faustus does almost nothing to counteract the probability of a downfall. By aligning himself with Mephistopheles, he takes on the role of Lucifer the fallen angel: he believes that he can be greater than God. Beyond mere pride, this is heresy. Faustus imagines there is a sort of temporary, play-acting kind of damnation from which he will extricate himself because of the contract’s terms. He underestimates the totality of evil to which he has consigned his immortal soul.

The tragedy that befalls Doctor Faustus is ultimately caused by what the ancient Greeks called hubris, or overweening pride. Faustus is profoundly dissatisfied with life. He's an exceptionally intelligent man, a polymath with a genuine hunger for knowledge. Yet he feels frustrated with the limits of mere human knowledge; he wants to do more; he wants to have magic powers. This gaping void at the heart of Faustus's intellectual life makes him vulnerable to corruption by the devil. So desperate is Faustus to practice the black arts that he agrees to sell his immortal soul to Lucifer in exchange for twenty-four years of Mephistopheles's service.
Faustus's pride will simply not allow him to accept that he's just a human being, with all the necessary limitations that that involves. By engaging in sorcery he hopes to turn himself into some kind of super-human, almost a god. And though he knows what he's doing is fundamentally wrong, he still does it anyway. His overweening pride, his hubris, is too strong for him to turn back and repent of his sins. A man of great intelligence has overreached himself, and the consequences for his immortal soul are catastrophic in the extreme.