What is the main events of this story

The Robe is a 1942 Christian novel by Lloyd Douglas, a Lutheran minister and writer.  The Robe follows the story of Marcellus, an officer of the Roman army who participates in the crucifixion of Jesus Christ. However, he is conflicted because he believes Jesus to be innocent.  
The main events of The Robe include Marcellus winning the robe of Jesus in a dice game among Roman soldiers.  At a gathering of Romans shortly afterward, Marcellus is goaded into wearing the robe, which upsets him deeply and provokes a mental collapse.
Marcellus is later restored to health by touching Jesus's robe. Consequently, he becomes a Christian and retraces Jesus's steps through the Roman province of Judea.  Marcellus's conversion displeases the emperor, Caligula, and Caligula orders Marcellus's execution.  The robe, at Marcellus's request, is ultimately passed on to Simon Peter, an early leader of the Christian church.

Which provision is the heart and soul of the Constitution?

While there are many important sections to the Constitution, I would say that articles one, two, and three make up the heart and soul of the Constitution, as these articles focus on the concept of separation of powers. Article I deals with the legislative branch. This is a very long section that details the structure of Congress. It also explains how long each term of office is for an elected official, the qualifications a candidate must have in order to run for office, and what powers belong to Congress. It also states that any bill raising revenue must start in the House of Representatives.
Article II deals with the executive branch. It explains who can run for President, and what qualifications a person must have in order to run for that office. It outlines the duties and responsibilities of the President. It also explains how a president can be removed from office.
Article III deals with the judicial branch. It explains the role of the various courts and explains what kinds of cases the courts may hear.
These three articles deal with each branch of the government. The branches of the government are a very important part of the Constitution. The concept of separation of powers, a key cornerstone of the Constitution, is clearly evident as a result of these three articles. In my opinion, these articles make up the heart and soul of the Constitution.
http://constitutionus.com/

Describe Pip's first meeting with Miss Havisham.

Pip's first meeting with Miss Havisham is one of the most startling passages in the novel. It is told by different, but intermingled voices, those of the "young" Pip and the "adult" Pip. We see Miss Havisham through both pairs of eyes.
To the young Pip, she is a frightening witchlike creature, living in a darkened room around the the mouldering remains of her wedding cake and still dressed in her yellowing wedding gown.
The "young Pip" can only put this startling woman within the context of a "ghastly waxworks" he has seen. He finds her inhuman and frightening:

Now, waxwork and skeleton seemed to have dark eyes that moved and looked at me. I should have cried out, if I could.

He says of her:

she had a crutch-headed stick on which she leaned, and she looked like the Witch of the place.

We see an example of the "adult Pip" in the following passage:

It was not in the first few moments that I saw all these things, though I saw more of them in the first moments than might be supposed. But I saw that everything within my view which ought to be white, had been white long ago, and had lost its lustre and was faded and yellow.

The adult Pip takes a more reasoned view. In the first sentence quoted above, this Pip, looking back, says he saw more on first seeing Miss Havisham than might be expected. He also generalizes, summarizing, as an adult would, that everything that should have been white was yellow.
In this scene, we are offered much description of the very strange Miss Havisham. As you go through it, you can try to pick out which parts are shown through the eyes of the young Pip and those of the adult Pip.

Miss Havisham is known to be an immensely wealthy woman who leads a secluded life. She has requested for Pip to go and play at her house. Pip lives with his sister and Joe, her husband since he was little. They lead an average life with Joe working as a blacksmith. When the opportunity presents itself, Pip’s sister is upbeat and encourages Pip to proceed as requested. Pip’s fortunes are set to change for the better.
On his first meeting, Pip describes Miss Havisham as a strange lady. Pip is anxious to meet the woman, and everything about the place only adds to his anxiety. Finally, Miss Havisham engages Pip in a short conversation and asks him to play. Pip is unable to comply with the request and opts to remain fixed to his position. Pip realizes that Miss Havisham leads a miserable and lonely life. The meeting is extremely strange, and Pip hopes to take his leave as soon as it is possible. He is, however, forced to play cards with Estella, the cruel young girl.

Why should plastic surgery on teenagers be banned?

Cosmetic surgery amongst teenagers is a controversial trend. In the modern world, the already self-conscious teen is constantly bombarded with images of perceived physical perfection on social media and in movies and television. Teenagers see social media "influencers" with perfect bodies, smooth skin, and flowing hair every time they go online. These influencers are sometimes worshipped for traits that were bestowed upon them by a doctor rather than genetics.
Teens are prone to low self-esteem and self-consciousness simply given the phase of life that they are in. Their bodies are changing and they're experiencing a wave of emotions. They're trying to navigate social intricacies and find where they fit in. Cosmetic plastic surgery may be a means of satisfying someone else's standards rather than their own—thus the concern.
As with most controversial topics, there are also sound arguments to the contrary. According to the US National Library of Medicine National Institutes of Mental Health,there are "psychological studies which have reported a reduced psychological burden in teens undergoing cosmetic surgery." Meaning, some issues related to physical appearance were actually decreased after surgery for some teens.
While some countries have banned cosmetic plastic surgery for those under 18, others have put precautionary measures in place instead. For instance, a teenage patient may be asked to take a few months to think about their decision to have plastic surgery a bit further before going forward. Anyone under 18 (and their legal guardian) should consider the physical risks and psychological ramifications before opting for cosmetic plastic surgery.

In answering this question, we need to make a distinction between plastic surgery carried out for clinical reasons and cosmetic plastic surgery. In some cases, teenagers will need to have reconstructive surgery after serious illnesses such as cancer. As well as being necessary from a clinical standpoint, such surgery can help to build young patients' confidence and self-esteem.
Cosmetic plastic surgery—or aesthetic plastic surgery as it's sometimes known—is more difficult to justify. Growing numbers of young adults are profoundly unhappy with the way they look, especially girls. They're constantly bombarded with images of physical perfection in magazines, in film, on TV, and on social media. These images can have a negative impact on young adults' body image and self-esteem.
Although plastic surgery could provide a respite from feelings of inadequacy, it simply deals with the symptoms rather than the underlying causes of the problem. If society were more accepting of differences in physical appearance and didn't idealize certain facial features and body shapes, then perhaps young adults would feel less pressure to subject themselves to surgical procedures. Allowing young adults to undergo plastic surgery would reinforce rather than challenge society's standards of what's considered beautiful, and this would arguably exacerbate the problem rather than solve it.

Describe the town of Maycomb, Alabama.

Maycomb is a small town in Alabama, right at the heart of the deep south. Scout gives us the impression that this is a place much like any other, where nothing much of interest ever happens. This turns out not the be the case for a number of reasons, but before any of the action of the story gets underway, there certainly doesn't seem anything particularly remarkable about this neck of the woods.
It's notable that Scout says that the Finches only wound up in Maycomb due to a strange quirk of fate. If Andrew Jackson hadn't run the Creeks—a Native-American tribe—up the creek, then Scout's ancestor Simon Finch wouldn't have paddled all the way up the Alabama. Then where would Scout and her family have been? This important piece of family folklore would appear to suggest that Maycomb is not the kind of place where anyone would choose to settle down. It's an out-of-the-way place, a tired old town where people move slowly.
As well as the intense heat, this is largely because there's no need for folks to hurry. They don't have much money, and in any case, there's nowhere to go and nothing much to see. All in all, Maycomb is almost identical to countless other small towns across the length and breadth of Depression-era America.

In Chapter 1, Scout describes her hometown of Maycomb, Alabama. She says that Maycomb was a small, old town where people moved slowly. Scout says that in the summer the weather could become extremely hot to the point that men's stiff collars would wilt by nine in the morning. The ladies of Maycomb were gentle Southern Belles who would bathe at noon and fan themselves on their porches after they took their naps. People were in no hurry because there was nothing to do in Maycomb. Scout also mentions that people had little to no money to spend because of the economic crisis. No much in Maycomb had changed since the Civil War and most of the businesses were situated around the town center. Maycomb is also a rather melancholy town which is a common element of Southern Gothic literature. Since nothing goes on in the small town, most of the attention is focused on the controversial trial of Tom Robinson. 

How does anti-transcendentalism relate to "Rappaccini’s Daughter?"

Transcendentalists believed in the divinity of nature. Many, like Ralph Waldo Emerson, thought that when we are in nature, something very special happens to us. We return to a childlike state of innocence, and, at the same time, we are restored to both reason and faith. Many believed in something called the Oversoul, which was a trinity of sorts consisting of humankind, nature, and God. They thought that connecting with nature would bring us closer to God and help us to understand ourselves better.
In "Rappaccini's Daughter," however, nature is not a good and blessed thing, made by God, with the power to restore and revive us; instead, it is something corrupt and poisonous, made by man, having the power to weaken and destroy us. Hawthorne presents a very different view of what nature can be, especially when meddled with by humans. It becomes destructive and menacing.

How can I write a hook for comparing and contrasting Napoleon and Mr. Jones?

When determining a hook for an essay or article, there are one of many ways to choose from. Some people like to use shocking or dramatic statements to catch a reader's attention. Others like to use impressive quotes from the author that lead right to the thesis statement. And many people like to use a thought-provoking question that grasps the reader's attention by asking him/her to think deeply about the topic before introducing the thesis statement. Any of these strategies are good, but what might be best in a compare/contrast essay is a "would you rather" type of question.
Since the essay will compare the leadership of the farm before and after the revolution, the writer might want to get the reader to think about which leader is better to live under. For example, some would argue that life was better under Mr. Jones rather than Napoleon, because at least the animals were fed and cared for. Under Napoleon's rule, he manipulated and lied to his fellow animals to the point of complete disrespect, starvation, and, ultimately, death. Thus, a good thought-provoking question would ask the reader to consider how he or she would like living under each leader. Asking the hook's question in a "would you rather" framework would be fun and interesting, too. However, if your essay calls for not using the second person "you," then reframe it to fit the assignment. Here are a couple of examples:

Would you rather live under a dictator who is not of your breed or race, but feeds you three meals a day and works you very hard, or serve a dictator of your own race who manipulates you, beats you, kills your friends, and works you even harder each day?
Would it be better to work for a dictator who yells and screams each day, and is tough on his workers, but feeds them every day and keeps them safe and warm; or work for a dictator who promises better working conditions and food, and claims to understand the plight of the workers, but winds up beating, manipulating, and killing the workers to keep control of his leadership position?

You can shape the hook to suit your needs for the thesis and essay to follow, but either way, the above format helps to provide both sides of the Mr. Jones and Napoleon debate, while also applying a fun game at the same time.

How is satire used in "The Devil and Tom Walker"?

Satire is the use of hyperbole, irony, and humor to critique people, institutions, and even social norms. The purpose of satire is to alert people to crucial problems in society and to encourage specific changes.
In The Devil and Tom Walker, Washington Irving uses satire to criticize greedy moneylenders, shrewish women, hypocritical leaders, and biased historians.
Tom's wife is described as "a tall termagant, fierce of temper, loud of tongue, and strong of arm. Her voice was often heard in wordy warfare with her husband." In the 18th century, it was believed that shrewish women exhibited traits antithetical to those expected of a refined woman. When Tom shares the story of his encounter with Old Scratch, Tom's wife demands that he "comply with the black man's terms and secure what would make them wealthy for life." For her part, Tom's wife decides to take things into her own hands when her husband perversely refuses to comply with her demands.
She goes and meets with Old Scratch himself, taking with her "the silver teapot and spoons and every portable article of value." Washington Irving uses situational irony to critique the actions of an overbearing and shrewish wife; her actions reward her with the opposite of what she's hoped for. Instead of reaping great rewards from her efforts, she becomes the victim of Old Scratch and is "never heard of more."
The narrator tells us that "What was her real fate nobody knows, in consequence of so many pretending to know. It is one of those facts that have become confounded by a variety of historians." Here, Washington Irving is critiquing the problem of biased historians corrupting the truth about historical events. In the story, some say Tom's wife had "eloped with the household booty"; still others imagine that Old Scratch had decoyed her into a dismal quagmire." Meanwhile, there are those who support the theory that she had "lost her way among the tangled mazes of the swamp and sunk into some pit or slough." So, there's a variety of stories about the fate of Tom's wife, all suppositions engendered from the imaginations and biased perceptions of various parties.
In the story, Washington Irving also satirizes corrupt moneylenders and hypocritical leaders. Ministers and great men of the colony are portrayed as evil and untrustworthy men. Old Scratch pronounces judgment on these influential men, and they are burned up as firewood in the story: "Since the red men have been exterminated by you white savages, I amuse myself by presiding at the persecutions of quakers and anabaptists; I am the great patron and prompter of slave dealers, and the grand master of the Salem witches." Instead of God presiding over the judgment of these men, the author has the Devil do the honors, an irony.
Later, in the story, the author uses humor and hyperbole to highlight Tom Walker's hypocrisy. After enriching himself at the expense of his clients, Tom becomes religious because he's afraid for his chances in the afterlife: "He became, therefore, all of a sudden, a violent church goer. He prayed loudly and strenuously as if heaven were to be taken by force of lungs. Indeed, one might always tell when he had sinned most during the week, by the clamour of his Sunday devotion." Basically, Tom becomes religious, not for altruistic purposes, but so that he can cheat the Devil out of the bargain he's made with him.
As can be seen, the author uses satire as a sort of social commentary about life in New England in the 18th century.
 
 
 

College Algebra, Chapter 9, 9.1, Section 9.1, Problem 72

Suppose that Helen deposits $\$2000$ at the end of each month into an account that pays $6\%$ interest per year compounded monthly. The amount of interest she has accumulated after $n$ months is given by the sequence.
$\displaystyle A_n = 2000 \left( 1 + \frac{0.024}{12} \right)$

a.) Find the first six terms of the sequence.
b.) Find the amount in the account after 3 years.

a.)

$
\begin{equation}
\begin{aligned}
i && I_1 &= 100 \left( \frac{1.005^{(1)} - 1}{0.005} - (1) \right) = 0\\
\\
ii&& I_2 &= 100 \left( \frac{1.005^{(2)} - 1}{0.005} - (2) \right) = 0.5\\
\\
iii&& I_3 &= 100 \left( \frac{1.005^{(3)} - 1}{0.005} - (3) \right) = 1.50\\
\\
iv&& I_4 &= 100 \left( \frac{1.005^{(4)} - 1}{0.005} - (4) \right) = 3.01\\
\\
v&& I_5 &= 100 \left( \frac{1.005^{(5)} - 1}{0.005} - (5) \right) = 5.03\\
\\
vi&& I_6 &= 100 \left( \frac{1.005^{(6)} - 1}{0.005} - (6) \right) = 7.55\\
\end{aligned}
\end{equation}
$


b.) If $\displaystyle n = 5 \text{years} \times \frac{\text{12 months}}{\text{1 year}} = 60 \text{months}$, then
$\displaystyle I_{60} = 100 \left( \frac{1.005^{(60)} - 1}{0.005} - (60) \right) = \$977$
It shows that the interest has accumulated $\$977$ after $5$ years.

How does the novel end? What is Wiesel's tone?

Night ends with the retreat of the Germans and the liberation of Eliezer and the other prisoners. Wiesel states that among the prisoners there is no real thought of taking revenge. All of them are in a state of starvation, so all anyone wants to do is eat. "Our first thought as free men was to throw ourselves on the provisions." The only thing besides getting bread that "some of the young men" do involves going into the nearby city of Weimar "to sleep with girls."
Wiesel relates that at this point he became seriously ill and spent two weeks in a hospital hovering between life and death. When he recovers enough to stand up, he looks in the mirror and states that "a corpse stared back at me."
His point is that a genocide survivor becomes, in effect, one of the living dead. There is no happiness for him, despite his liberation. Those in this situation typically suffer from what is now known as PTSD (Post Traumatic Stress Disorder), an ongoing condition from which few recover fully, if at all. They also have what is called "survivor's guilt." The inner question of "why did I survive when the others did not?" is unanswerable. Wiesel never sees his mother and sister again after the initial separation of men and women upon arrival at the camp. His father died on the death march as the prisoners were being tranferred west before the advancing Russian army. Night concludes darkly with the absence of any joy or even relief. Instead there is only lasting trauma, numbness, and bafflement at the cruelty and genocide that has been seen by the survivor.

The novel ends with Elie describing how the prisoners' resistance movement defeated the SS officers shortly before American soldiers liberated them from Buchenwald at six o'clock. Elie goes on to describe how the emaciated prisoners could only think of food and not revenge. After Elie gets food poisoning, he recalls looking at his reflection in the mirror and staring directly at a corpse, which is something that he will never forget.
The tone of the ending of the story is somber, melancholy, and pessimistic. Elie's horrific, traumatizing experiences in the German concentration camps have ruined his childhood and dramatically impacted his life. The last scene depicting Elie staring at his emaciated, corpse-like reflection is sobering and dramatic. Elie's melancholy tone reflects how the Holocaust has emotionally, physically, and psychologically damaged him.

I need detail analysis, including short summary of every stanza of Auden's poem 'In Memory of W.B. Yeats'. And also please write a short notes on the following lines as i don't understand their meaning 2. line-17, Lines 18-21, line- 33, The parish of rich women; who is it referring to? , line 34-36, lines 36-40. Line- 47 ' all the dogs of Europe bark': are the dogs here literal or referring to something

Auden wrote this poem shortly after Yeats’s death in 1939, as a tribute to one of the most influential, talented poets in English literature. Divided into three sections, the poem is both a typical elegy (funeral poem) and a meditation on poetry itself.
Section I imagines Yeats on his deathbed, supposing that his great mind faded away. The speaker also suggests that while some will remember the death of this great writer, others will barely notice.
Section II differs from the first in tone, audience, and form. The speaker directly addresses Yeats, chiding him for his flaws and mistakes. This chastising tone could indicate the speaker’s frustration that Yeats was an imperfect man rather than the idealized hero Auden and others imagined Yeats to be. This section also suggests that while Yeats was a fantastic poet, his poems—like all poems—may not have achieved what he desired them to do.
Section 3 returns to the formal style of the first section. However, the repeated quatrains underscore Auden’s purpose: paying respectful tribute to Yeats is important to the speaker. Despite the speaker’s earlier dismissal of poetry’s significance, this section reflects the beauty and necessity of Yeats’s contribution to humanity. The speaker implores Yeats to “teach the free men how to praise” from beyond the grave.

Line 17: The “current of feeling” is his consciousness. He “became his admirers” because his consciousness will survive through their continued study of his work.

Lines 18-21: The news of Yeats’s death will have reached people across the world, many of whom will know little about him. This opens up the possibility that some might remember him not as he actually was but as a footnote in an average day.

Line 33: The speaker is accusing Yeats of womanizing, like many famous men.

Lines 34–41: Many of Yeats’s poems were tied to his home country of Ireland. The speaker suggests that Yeats’s poetry did not fix the turmoil in Ireland that occurred throughout his life. Nevertheless, the poems persist even in Yeats’s absence.

Final Note: The “dogs of Europe” alludes to a famous line from Shakespeare’s Julius Caesar, “let slip the dogs of war.” Remember, this poem was written in 1939, on the cusp of World War II. Auden is referring to the growing hostility among European governments. He mentions this international discord as one of the reasons why poetry like Yeats’s is needed in the world.

How does Marat/Sade contrast and complement the theories of theatre from Aristotle, Artaud, and Brecht?

Marat/Sade is a play about putting on plays in an insane asylum. While there is some history behind this premise, Peter Weiss’s play is more about the theatre itself and the power of theatre to transform audiences. Brecht and Artaud were two important  influences in Peter Brook’s famous staging of the play with the Royal Shakespeare Company in 1964.
Antonin Artaud was a surrealist who developed an approach to theatre called “The Theatre of Cruelty.” His premise was to subvert the conventions of theatre by encouraging a kind of “sensory overload” in the audience through the use of flashing lights, discordant sounds, inaudible or nonsensical dialog and so forth. This is meant to allow the audience to feel the unexpressed emotions of the subconscious.
Bertolt Brecht approached theatre as a way to indoctrinate or educate audiences about Marxist theories of labor and class struggle. Like Artaud, Brecht saw conventional theatre as suspect; however, while Artaud sought to give voice to the subconscious, Brecht subverted theatrical conventions in order to foreground their bourgeois nature and make a space for Marxist discourse. Brecht coined the term “Verfremdungseffekt” (alienation effect) for a series of strategies a playwright could use to subvert the audience’s desire to “believe” the story of the play. Music, for example, is not used to advance or enhance the story of the play but rather to break up the narrative flow and comment on the story.
Brook’s staging of Marat/Sade made use of both techniques. The play-within-a-play structure serves to reinforce the artificiality of the theatrical experience, while the frequent musical numbers serve to interrupt the action of the play. The character of Sade in particular enacts a kind of doubleness; he plays himself in the play-within-a-play, and his debates with Marat can be understood as a commentary on the history of Marat’s assassination as well as a commentary on staging plays in an insane asylum (or by the Royal Shakespeare Company, in the case of Brook). While much of the play is about the nature of “revolution,” the ending, in which the patients/actors are beaten into submission, calls into question whether such change is possible.

Calculus: Early Transcendentals, Chapter 4, 4.3, Section 4.3, Problem 59

When using a graph of f"(x), we follow concavity test:
A a section of function f(x) is concave up when f"(x) > 0.
This means the segment of the graph of f"(x) is above the x-axis.
A a section of function f(x) is concave down when f"(x) < 0.
This means the segment of the graph of f"(x) is below the x-axis.
Using computer algebra system, here is the graph of f(x) = (x^4+x^3+1)/(sqrt(x^2+x+1))



For its second derivative graph:
f"(x) =

The graph of f"(x) intersects the x-axis at x~~ -0.7 and x~~ 0.1.
These will be used as the boundary values to set the intervals of concavity.
These are the final answers.
Concave up: (-oo ,-0.7) and (0.1, +oo )
Concave down: (-0.7, 0.1)

In case you prefer a more accurate data, here is maximize view of the graph of f"(x).


The graph of f"(x) intersects the x-axis at x=-0.64 and x=0.03.
These will be used as the boundary values to set the intervals of concavity.
Concave up: (-oo ,-0.64) and (0.03, +oo )
Concave down: (-0.64, 0.03)

What do you think Beckett's Molloy is saying about the human condition and human nature?

Molloy's recollections make the human condition seem absurd and pointless, and he implies that human nature seeks certainties without finding any. When the novel begins, Molloy writes, "I am in my mother’s room. It’s I who live there now. I don’t know how I got there." He is uncertain even about how he arrived at his current location.
The point of how he passes the time is also uncertain. He hands a man who arrives at his room pages every week. In return, Molloy receives money. He says that when he receives the pages back, "They are marked with signs I don’t understand. Anyway I don’t read them." The marked pages that he doesn't understand or even read are symbols of the way in which he can't understand or even grapple with his reality. Language also is of no use to him in comprehending the world around him; human nature is such that people can't even make sense of the language they read or hear.
Molloy then begins a very long recounting of a directionless journey he goes on, which symbolizes the directionless and pointless nature of human existence. Beckett implies that human nature is unable to make sense of reality; for example, Molloy can't even remember if his lover's name is Ruth or Edith, and he isn't even sure whether his lover is a woman or man. He says, "Perhaps she too was a man, yet another of them." He goes through experiences without making any real sense of them or understanding them in any way. 
The second part of the novel is narrated by Moran, a detective who also has a pointless mission--to find Molloy and write a report. In the end, Moran begins to hear a voice, and he says, "It told me to write the report. Does this mean I am freer now than I was? I do not know." The voice clearly leaves him mentally disordered. He says at the end of the book, "Then I went back into the house and wrote, It is midnight. The rain is beating on the windows. It was not midnight. It was not raining." In other words, everything he writes does not represent reality, and he is not even clear about the nature of reality. The human condition is such that people are on a pointless and incomprehensible journey. 

II Corinthians 12:3-4 is beyond the intellect. How can we know something beyond the intellect without the intellect?

The answer to this question requires an understanding of Epistemology, the study of knowledge, more specifically, how knowledge is defined and taxonomized.  Put simply, how do we “know” things, and what is meant by “knowing”?  Our intellect, by which is meant our ability and capacity for logical assembly of “facts” to reach a “logical” conclusion, is only one way of gaining knowledge, according to philosophers and examiners of epistemology.  The scientific method is the most common and accepted form of “intellect”; it uses data and experimentation to find physical “truths.”  But there are other ways of knowing, such as personal experience, innate beliefs (we know as “true” that mothers love their children), religious dogma, and even “intuition.”  Philosophers such as Emmanuel Kant point out that we all “know” things that we believe to be true without scientific, “intellectual" proof.  Even the truism “Render to Caesar the things that are Caesar’s, and to God the things that are God’s” can be seen as giving credence to the physical world by “scientific reasoning,” but believing in the spiritual, non-physical world by faith.   Corinthians brings this truth to our understanding of religious faith.  Thomas Aquinas in Summa Theologica spent his life trying to clarify for Christians the difference between faith and proof.

What two skills did Widge learn in the orphanage?

Widge learns how to lie and how to wrestle at the orphanage.
In chapter 7, Widge is assigned to transcribe Shakespeare's Hamlet before the playwright can print his play for the public. Our protagonist must answer to Falconer, the man who has been tasked by Simon Bass (Widge's employer) to make sure Widge does what he is told.
However, Widge experiences several challenges during his transcription project. First, the actors speak too fast. Second, Widge has trouble identifying each speaker on the pages of his writing. He tries to use numbers, but it proves too confusing. Last, but not least, Widge becomes so engrossed in the play that he loses his place on the pages of his notebook.
Knowing that he will not have the full play on paper to hand to Falconer, Widge decides to lie to the man. He remembers that he acquired the skill of lying at the orphanage and perfected the skill during his apprenticeship with Dr. Bright. So, when he meets Falconer, Widge tells the man that it was too noisy in the theater to hear everything. He casually mentions that only about fifty lines are missing. In actuality, Widge knows he missed more than that. 
Although a little irritated, Falconer believes Widge's lies. He tells Widge he will have another opportunity to watch a performance of the play and complete his transcription project.
A second skill that Widge learns at the orphanage is self-defense. In chapter 19, Widge tells us that every child in the orphanage learned the skill of catch-as-catch-can wrestling. The phrase "catch-as-catch-can" refers to pinning down one's opponent in any way one can. The winner is the one who manages to hold down an opponent for a period of time.
In catch-as-catch-can wrestling, contestants can grab on to any part of their opponents' bodies. So, when Nick attacks the defenseless Julian, Widge sets upon Nick; he clings on tightly to Nick's legs and does not let go. The skirmish does not last long, however. It is interrupted by Mr. Armin, the boys' teacher.
So, Widge learns two skills at the orphanage: how to lie and how to wrestle.

What are some of the key events that extremely impact Montag and make him such a dynamic character throughout the novel?

There are many events and plot points in Fahrenheit 451 that impact Montag significantly and force him to change. As the novel begins, Montag is an ordinary fireman who mindlessly burns piles of books because he is told to, but that all starts to change when he meets Clarisse, the strange girl next door. A quirky and intellectual young woman, Clarisse questions Montag's beliefs and prompts him to question them himself. They have frequent conversations—and Montag looks forward to these—about many taboo and philosophical subjects. Montag begins to feel intellectual—and, perhaps, romantic—longing for her, and when she disappears, he begins to feel disillusioned with his life.
Another key event that impacts Montag is his wife's suicide attempt. After she wakes up from her sleep caused by the plethora of sleeping pills, she seems to completely deny having tried to kill herself. Her apparent unhappiness makes Montag uneasy, and he then begins to question the foundation of their marriage and, consequently, their life.
One final key event that shapes Montag's character is the suicide of the woman whose house full of books is to be burned. In a defiant act against the firemen and society as a whole, the woman lights herself on fire and goes up in flames along with her books. This causes Montag to further question the value of the books, for if someone was willing to die alongside them, doesn't that suggest them to be entirely invaluable?

Do you agree with the many historians who consider Persia and China to be two of the greatest empires of the ancient world?

I would agree with that view. There were many great empires in the ancient world, and each had their own unique contributions to their regional development and history. We know a lot about the Persians because the Greeks wrote so much about them, and Alexander the Great had many notable interactions with them. This does, however, mean we are left with a largely ethnocentric view of the ancient Persians, whom the Greeks loved to call “barbarians.” China, on the other hand, has an impressive ancient historical record that is often overshadowed because the Far East is often given inadequate attention in Western mainstream education and popular history. Although Persia and China may not be as “famous” as the more popular examples like the Delian League and Roman Empire, they were both massively influential on global history and civilization.
Cyrus the Great established the first Persian Empire, which is also known as the Achaemenid Empire. Cyrus had amazing military prowess, but what made his conquests especially successful was his compassion and ability to demonstrate empathy for the people he conquered. Sicker writes that Cyrus

went out of his way to show particular sensitivity to the religious traditions and practices of the peoples who had become subject to his rule. Rather than characterize his victory as a defeat of the enemy, he portrayed himself as the successor of the national rulers he had displaced, making appropriate gestures of affiliation to their gods. He made it appear that all that had happened was a change of dynasty, with social and economic life being restored to its traditional patterns (Sicker 78-79).

More importantly, the people were able to observe before their very eyes that Cyrus was not just full of empty promises.
The Achaemenid Empire would eventually become the largest empire in ancient history, but would not have accomplished that without the administrative expertise of Darius the Great. Darius created a much-needed centralized government and built an impressive transportation and communication infrastructure, which included an innovative postal system and the implementation of Aramaic as the official language throughout the Empire. Essentially, Cyrus’s unprecedented benevolent leadership and policymaking during his conquests laid the groundwork for Darius to organize and implement an impressively effective system of administration and network throughout Persia’s massive territory.
Persian culture flourished under the Achaemenid Empire. The Persians had a knack for intellectualism and were especially skilled in science and mathematics. They were known for their beautiful libraries, botanical gardens, and sophisticated medical practices. In addition to traditional Babylonian pagan traditions, the Persians also practiced Zoroastrianism—the world’s first monotheistic religion. Their political and cultural influence spread throughout Western Asia, Eastern Europe, and the Indus Valley.
There were other substantial advancements happening farther east. One of the greatest dynasties of ancient Imperial China was the Qin. The Qin government—specifically under the leadership of its first emperor, Qin Shihuang—was both administratively and militarily skilled, which allowed them to conquer Warring States and replace the outdated feudal governments with one centralized state. According to Wright, this success had a lot to do with the Qin's geographic advantages, which “made it easy to defend but very difficult to capture” (Wright 45). In addition, Imperial China’s economy thrived under the Qin. They developed a written language that included means of measurement and currency, allowing them to create a network of roadways and an amazingly productive trade system throughout the empire.
The Qin’s concept of a centralized government also led to the creation of a unified legal code, which gave the emperor supreme power. This Legalist ideology, though very effective at the time, would eventually lead to the demise of the Qin dynasty. Wright notes, “The Qin was undone and overthrown because of the very Legalist ideology that had helped establish it in the first place. In retrospect, it seems that the main contribution of Legalism and the Qin state that applied it was the unification of China and the creation of a structural model for future dynastic governments” (Wright 50). In addition, Qin Shihuang was extremely brutal and despotic (an interesting opposite to Cyrus the Great), which did not necessarily bode well for the dynasty’s survival. Nonetheless, the contributions of the Qin had a significant and lasting impact on Imperial China.
Persia and China, therefore, share many attributes that made their ancient empires successful, most notably their creation of centralized governments and wide expansion of trade routes.
Works cited:
Sicker, M., The pre-Islamic Middle East (Westport, CT: Greenwood Publishing Group, 2000) 71-108. 
Wright, D., The History of China (Westport, CT: Greenwood Publishing Group, 2001): 45-98.

What is the significance of swimming in Life of Pi?

In the novel The Life of Pi, Pi is very close to his uncle, Mamaji, who is in reality just a close family friend but acts as an uncle and teacher to Pi. Mamaji is a champion swimmer and has swam in pools all over the world. In particular, he loves a particular French pool called the Piscine Molitar, from which Pi gets his name. Pi goes to the local pool with Mamaji frequently and learns how to swim. In doing so, he becomes a fairly skilled and strong swimmer, which will be very helpful to him later on.
When the ship he is on is wrecked and sinks, swimming saves Pi’s life. He makes it successfully to the life raft because of his strong swimming ability and is able to start figuring out how to survive the catastrophe. Living at sea, he has to swim many times to save his life and find food, so swimming quickly becomes a vital part of his existence.

Since Pi’s name in the story is derived from a famous swimming pool in which his champion swimmer uncle practiced, it makes sense that swimming is vital to the story. Much of the early exposition in the tale revolves around Pi learning to swim from his uncle and spending vast amounts of time in the pool. He learns and becomes a very capable swimmer thanks to his uncle’s tutelage, which will eventually be vital to his survival.
Obviously, Pi is later shipwrecked with little hope of rescue and only a small life raft on which to survive. There are several times when he has to swim or tread water in order to survive his ordeal, including initially reaching the life raft. His strong swimming skills are extremely beneficial here and help him to survive the harrowing events until he finally reaches land.

In Yann Martel's novel The Life of Pi, swimming is important to the title character because of his uncle. He wasn't his biological uncle, but a good friend of the family's. Pi grew up calling him "Mamaji," which is a combination of the word for uncle and the suffix "ji" which indicates respect and affection. 
Mamaji, whose actual name is Francis Adirubasamy, was a champion swimmer. The reason Pi was named Piscine, which is French for swimming pool, is because of Mamaji's passion for swimming.
As a child, Pi went with Mamaji to the pool three times a week. Pi was his willing apprentice as Mamaji taught him all he knew about swimming. Pi's father loved to hear Mamaji's stories, which always had to do with swimming. For Pi's father, it was a lovely escape from his everyday life. Here is the quote from the book that explains how Pi was named: 

But no swimming pool in Mamaji's eyes matched the glory of the Piscine Molitor. It was the crowning aquatic glory of Paris, indeed, the entire civilized world. "It was a pool the gods would have delighted to swim in. Molitor had the best competitive swimming club in Paris. . . .The showers gushed hot, soothing water. There was a steam room and an exercise room. The outside pool became a skating rink in winter. There was a bar, a cafeteria, a large sunning deck, even two small beaches with real sand. Every bit of tile, brass and wood gleamed. It was—it was. . ." It was the only pool that made Mamaji fall silent. That is how I got my name when I entered this world, a last, unwelcome addition to my family, three years after Ravi: Piscine Molitor Patel." 

The significance of swimming in this novel is not just about how Pi was named, but also sets the stage for how he was able to survive such a shipwreck. His swimming skills were strong, and he had been taught by the greatest swimmer in all of South India for his entire childhood.

In I Know Why the Caged Bird Sings by Maya Angelou, how does Marguerite's relationship with her mother compare to her relationship with "Momma" (her grandmother)?

Marguerite, or "Maya," has a complicated relationship with her grandmother, who she refers to as "Momma." As a child, she often resents the fact that her grandmother is so strict and religious. It is also this super-strict adherence to religious beliefs, however, that allows Maya to find the dignity to rise above the racism and prejudice that she and her family face from the white folks who also live in their town of Stamps. She respects Momma, because she never sinks to the level of the petty white folks and instead tries to act with maturity and dignity. Because Maya often feels hatred toward herself, she needs someone like Momma to influence her to believe in herself and to see herself in  a positive light. Through her respect for Momma, she finds the strength to overcome that self-hatred, and this is an important life lesson for her.
By the time she moves to St. Louis to live with her mother, she has grown a lot as a person and is a young adolescent girl. Still, she is in need of a self-confidence boost, and that is where her mother comes in. Her mother is fun and adventurous, full of spirit, and very independent. Her kindness and passion for life is what really shapes Maya's transition into a teenager. When she feels lost because black people are not allowed to be train conductors, her mother gives her good advice that only a tough, strong woman would have learned: “Can’t Do is like Don’t Care. Neither of them have a home” (258). This means that nothing is impossible, and these phrases should not be in your vocabulary, if you believe in yourself.
In the beginning, however, her and her brother Bailey do not know if they can depend on their mother. Everything involving her is uncertain. They had been sent to live with her unexpectedly, and just as unexpectedly sent back to Stamps. At first, Maya's relationship with her grandmother proves the more solid and stable one. It is only after living with her mother for a few years that she starts to feel that she can depend on her.

What rule does Ralph establish?

In Chapter 2, Ralph, Jack, and Simon return from their first expedition on the island and hold an assembly. After Ralph explains to the group of boys that they are stranded on an uninhabited island, Jack interrupts him and says that they'll need hunters to kill the numerous pigs. Ralph then creates the first rule on the island. Ralph comments that they cannot have everybody speaking at once during the assemblies, so they will take turns holding the conch shell to address the group. Whenever a person is holding the conch shell during a meeting, no one is allowed speak over them. This system of taking turns is both democratic and civil. The conch shell is an important symbol of civility and structure throughout the novel. As the story progresses, Jack begins to speak over others and breaks the rule of not talking when someone is holding the conch during an assembly.

What can I write about in a letter to Jack from Ralph?

Certainly, the timing of the letter would dictate how Ralph would respond. Let's say that the letter-writing occurs after they are rescued—after all, there are no pens, pencils, or paper on the island.
Having had time to digest everything that's happened, it's hard to say what Ralph would write. Perhaps he would remain furious and outraged (particularly at Jack and Roger) for their roles in the deaths of Simon and Piggy. Or, perhaps, in some benevolent epiphany, Ralph would offer forgiveness and end with some kind of wisdom that the beast is in all of us and that we must choose the righteous path rather than succumb to savage instinct. Does Ralph condemn them (personally in the letter and/or to adults in authority), or does he offer understanding? Or is it something else?
Maybe Ralph would use the letter as an attempt to make Jack realize what he'd done. He could write tributes to Simon and Piggy. This would be kind of a guilt trip but also a way to honor Simon and Piggy. He could offer some allegory indicating that Jack's leadership resembled that of a dictator more than a protective leader. If Ralph chose this way of composing a letter, it would be interesting if he still tried to "save" Jack. It would really be a profound and benevolent gesture. Using the guilt trip or allegorical reasoning or some other tactic, maybe Ralph would try to make Jack see the error of his ways. Maybe the letter could be a tool to prevent future (adult) Jack from repeating the sins of Jack the child. It could be a lesson in ethics and reason: another tribute to Simon and Piggy.

If Ralph's going to write a letter to Jack, he needs to have something to say. The best time for that would be after the boys have been rescued and they've both had a chance to cool down and take stock of their experiences on the island. I can't tell you exactly what you should write, but at the very least Ralph would need to call out Jack for his appalling behavior. He wasn't able to do this while they were still on the island; it would've been way too dangerous, and in any case, Jack wouldn't have listened to reason.
As well as challenging Jack's behavior, I think that Ralph would want to understand exactly why Jack did what he did. What was going through his mind when he did all those terrible things? If Jack remains as unpleasant as he was on the island, then it's unlikely that Ralph will get a response. But at the very least he should try to get an answer out of him, as Jack has a lot to answer for.

It would be best to analyze Ralph and Jack's relationship throughout the novel before drafting the letter and take into consideration which stage of the story Ralph would be addressing Jack from. The two characters feel differently about one another as the novel progresses. In the beginning of the novel, Ralph gets along well with Jack. If Ralph was writing a letter to Jack at the beginning of the story, he would probably generously ask for Jack's opinion and help lead the group of boys. Ralph would more than likely have an open mind to Jack's ideas and would appreciate feedback from him.
As the story advances, Jack becomes increasingly jealous of Ralph and attempts to usurp his power. Ralph quickly becomes frustrated and agitated when dealing with Jack. Ralph realizes that Jack is a jealous, polarizing figure who is trying to gain power. If Ralph were to write Jack a letter in the middle of the story, it would be best for Ralph to threaten Jack with punishment for his insubordination. Ralph would have to assert his power by setting clear limits and addressing Jack's negative behavior. Ralph would also benefit from attempting to include Jack in some of his future decisions to appease his thirst for power.
By the end of the novel, Jack is a tyrannical leader who is attempting to hunt and kill Ralph. If Ralph were writing him a letter at the end of the novel, it is possible that Ralph would probably beg for mercy and agree to become a subordinate member of Jack's tribe in order to survive.

What is a précis for the book A Fierce Discontent: The Rise and Fall of the Progressive Movement in America, 1870-1920 by McGerr?

McGerr's A Fierce Discontent: The Rise and Fall of the Progressive Movement in America, 1870-1920 is a study of the Progressive Era. The author tries to make sense of the many impulses and agendas that defined the Progressive Era. He locates the source of the movement in the impulses and anxieties of the middle class at the time and states that:

Progressivism was the way in which these Victorian men and women came to answer the basic questions of life . . . What is the individual? What is the relationship between the individual and society? (xiv).

In other words, Progressivism was led by middle-class people reacting to the excesses of the Gilded Age and trying to determine the extent to the which the individual bore responsibility for his or her society and was connected to the larger society. He traces the ways in which the Victorian middle class took on four specific battles: to change big business, change people, put an end to class conflict, and deal with segregation. The author focuses on both the larger and more apparent political battles the Progressives waged but also the smaller, more domestic questions they wrestled with (such as divorce and gender roles).
The author recognizes the limits of Progressivism, including its unwillingness to totally restructure the economy and its acceptance of segregation. As the author writes, "the Progressives turned to segregation as a way to halt dangerous social conflict" (page 183). In other words, the Progressives saw segregation as a way to protect groups such as African-Americans and Native Americans from destruction.
McGerr's argument is based on a wide range of sources, including both public acts and laws, the writings of private individuals, and cultural sources, such as reporting on sports. The author states that it's important to understand the Progressive Era because it set the stage for the political battles that would be waged for the rest of the 20th century.

Why did the governor's attorneys walk out of the court? How did the judge react to this?

In Chapter 9, the governor's attorneys walked out of the court as a protest. The lead attorney, Tom Harper, had initially asked Judge Ronald Davies to disqualify himself from the case, as he had been appointed by the federal government to preside over the arguments. The governor's attorneys feared the judge would be biased against the state, so their main priority was to get Judge Davies off the case.
Later in the proceedings, Tom Harper asked that Judge Davies dismiss the case altogether, claiming the case involved constitutional issues that would require a three-judge panel to proceed. Judge Davies asserted that the hearing would continue. Tom Harper then read a statement on behalf of all the governor's attorneys. He stated that the governor and the state's military officials would not concede their constitutional power to the federal government and that they reserved the right to administer the affairs of the state according to their best judgement.
After reading the statement, the governor's attorneys vacated the courtroom because they felt the case was stacked against them. Also, they believed the federal government had overstepped its authority, making their walk-out a protest of sorts. For his part, Judge Davies remained unperturbed by the actions of the governor's attorneys. He calmly pounded the gavel and called the court to order.
When the Department of Justice attorneys proclaimed that they were prepared to offer more than a hundred witnesses in support of the order for integration, Judge Davies said the one hundred witnesses would be allowed to have their day in court after the recess.

If you were on the jury in this case, how would you vote on Steve Harmon? Discuss your reasons for coming to this decision.

This is a great question because it is very open ended. As a classroom debate topic, I have students that fall into both guilty and not guilty camps. It is entirely up to you to defend what you think.
I realize that the concept of "innocent until proven guilty" is the place that all jurors are supposed to start, but I believe that's also unrealistic. Steve is on trial. He was caught by law enforcement officers, so there has to be some question as to validity of Steve actually being innocent. His "friends" don't really help out a juror's suspicions. King, Cruz, and Alou are all known thugs in a rough neighborhood, and we find out in chapter 14 that King invited Steve to the drugstore "payday." We also know from chapter 7 that Steve thinks those tough guys in his neighborhood are pretty cool.

I had looked at him and wanted to be tough like him.

Finally, Steve admits that he was at the drugstore looking for some mints. None of this evidence is definitive proof that Steve is guilty of anything, but it doesn't prove his innocence either.
On the other hand, his innocence seems to fit more in line with Steve's personality. He may look up to the thugs in the neighborhood, but when it comes down to it, Steve is quite scared of jail and violence. He's a good kid, and Mr. Sawicki states the same thing. Steve might run with a rough crowd every now and again as a result of where he lives, but Steve is not guilty of being part of a murder.

What point is Thoreau making by telling us he got his shoes fixed and led the huckleberry party on the day he was released?

It shows that he considered spending a night in jail for standing up for his beliefs to be just one of his various activities that week. It wasn’t special or particularly life-changing. He was living at Walden Pond at the time, about a one-mile walk from the downtown part of Concord. He was running an errand in town when Sam Staples stopped him about non-payment of the poll tax. Thoreau went along with what needed to be done; was angry and frustrated when one of his aunts came over from her house across the common in the middle of the night to pay the tax; and was released the next morning to continue his town errands. And that was that. Except, of course, that it wasn’t. When people asked Thoreau why he had allowed himself to be put into jail instead of just paying the bill, he felt the need to write up a lecture about the experience. He delivered it several times in Concord. Eventually he molded it into an essay. He would perhaps be puzzled and surprised today to learn how meaningful and symbolic that single overnight stay in the Middlesex County jail has become to readers and activists in the 20th and 21st centuries.

What was the significance of religion to the ancient Egyptians?

Religion permeated every aspect of ancient Egyptian life. The ancient Egyptians were polytheistic and assumed that different gods had powers specifically relevant to particular aspects of their lives. Different gods were assumed to be patrons of or associated with specific towns or regions as well as with certain aspects of life such as justice or fertility or professions (for example, Thoth was associated with scribes and writing).
The Egyptians had magnificent temples intended as houses for the gods; they acted as the center for a ritual calendar filled with festivals marking important times of the year. The temples and temple scribes were particularly important in religious rituals surrounding death. Pharaohs, the rulers of Egypt, were believed to be quasi-divine and had important ritual as well as civic roles. In addition to temples and state religions, there were types of popular religion or ritual, such as making offerings to the gods to ask for good crops or health. The Egyptians also consulted oracles to find out about the future.
The Egyptian gods were very concerned with Ma'at or harmony. One important element of living a harmonious life was gratitude. Thus gods served to reinforce morality and cultural norms.
The afterlife was quite important in Egyptian religion, and corpses were preserved and mummified so that they would be in good shape for the afterlife; elaborate tombs were built to house the mummies of pharaohs and important nobles. Various funerary goods were buried with people so that they would be well-supplied in their afterlives. 
The soul was judged after death. If it passed the judgment, it would have a happy eternal life in the lands of Osiris, but if it failed, it would be cast to the devourers and perish utterly. Thus much of people's religious behavior was aimed toward pleasing the gods in order to have a happy afterlife. 

In George Orwell's 1984, is the telescreen mandatory? What about in Mr Charrington's antique shop?

Telescreens are mandatory for Outer Party members like Winston and Julia. They are two-way screens, which means that people can be spied on through them. Winston, for example, never knows when someone might be viewing his activities. One morning, in fact, he is scolded by an observer watching from behind the screen for not doing his exercises properly. It is only because of a quirk of architecture in his flat, which has a small alcove, that he feels somewhat safe writing in a journal, away from the screen's view.
Proles are exempt from having screens, as they don't count to the Party. Mr. Charrington has no visible screen in his shop, though we later find out that a surveillance screen is hidden behind a picture in the room Julia and Winston rent from him.
Winston is stunned that O'Brien is able to turn off his telescreen. That act is impossible for Outer Party members. It shows how powerful O'Brien is.

In 1984, the telescreen is mandatory for Party members and, as such, telescreens are installed in the homes and workplaces of these people as well as in public areas. The telescreen is a useful tool for the Party because it enables the constant surveillance of the movements and conversations of Party members. It also acts as an effective deterrent against rebellion and thoughtcrime. 
There are, however, some exceptions to this rule. Proles, for example, are exempt from having a telescreen and this explains why there is no screen in Mr. Charrington's antique shop. Winston notices this when he goes to visit the shop to see about renting the room above in Part One, Chapter Eight.
In addition, Inner Party members, like O'Brien, have a telescreen but are allowed to turn it off for short periods. This is because Inner Party members are the most influential and important people in Oceania's society, and we see this when Winston and Julia go to O'Brien's apartment in Part Two, Chapter Eight.

How are the witches powerful in Macbeth?

The witches are powerful in two important senses. In the first sense—the supernatural sense—they possess evil powers which they can harness to destroy anyone who gets in their way. As well as being evil, the Weird Sisters are rather petty and vindictive. One of them vows to drain the very life out of a sailor simply because his wife wouldn't share her chestnuts.
In natural terms, the witches are powerful in that they mesmerize Macbeth with prospects of earthly power. They successfully plant the seeds of ambition in Macbeth's mind, which act as a catalyst for his subsequent descent into barbarism. Macbeth becomes obsessed with the witches's prophecies, ensuring that the Weird Sisters continue to exert a hold over him right up until the end of the play. When their wicked spell is finally broken, it's too late for Macbeth, and he is slain by a vengeful Macduff.

Though there is disagreement among readers about whether or not the Weird Sisters truly possess the ability to prophesy or influence the future, it is clear they do have some supernatural powers at least. For example, after delivering their predictions to Macbeth and Banquo in Act I, Scene 3, the witches vanish. Obviously, this is not something the average person can do, so it does show us the Weird Sisters have some power. 
Later, the Weird Sisters meet up with Hecate, the ancient Greek goddess of witchcraft and magic, and they discuss how they are going to continue to manipulate Macbeth.  Namely, they will make him feel safe so he lets down his guard and becomes vulnerable. Hecate says, "you all know security / Is mortals' chiefest enemy" (Act III, Scene 5, lines 32-33). She and the witches powerfully manipulate Macbeth so he feels secure, using the apparitions they conjure to do so. They are thus powerful in this way as well.

How successful are the playwrights in going against religion in the play Inherit the Wind written by Jerome Lawrence and Robert E. Lee?

I wouldn't say that Inherit the Wind is anti-religion as such. Rather it is an extended critique of a kind of fundamentalist religious mindset that seeks to tell people how and what they should think. It is not just Bertram Cates who is on trial; it's the whole town and its fundamentalist convictions. The strategy of Lawrence and Lee in critiquing religious fundamentalism is reflected in the character of Henry Drummond, the defense attorney. He gives Matthew Brady sufficient rope on the witness stand, so to speak, giving him ample opportunity to make himself and his literalist interpretation of the Bible look utterly ridiculous.
At the same time, Brady is presented as a generally decent man, albeit hopelessly ignorant when it comes to science and modern learning. It's notable, for example, that he is presented in a much more sympathetic light than the Reverend Brown, who not only opposes Cates but actually condemns anyone who seeks forgiveness for him. Brady, despite his hostility to Cates and his teachings, is still enough of a Christian to remind the congregation of the need for forgiveness.
The play's overall lack of hostility to religion per se can be seen once more towards the end. After Matthew Brady collapses and dies, Drummond is genuinely upset. He also puts the cynical reporter Hornbeck in his place for his animosity towards Brady and religion as a whole.

What are the details in the story that reveal time and space in Great Expectations?

Charles Dickens makes it clear that most of the action of Great Expectations take place in London and Kent. Identifying the locations is generally easy as Dickens specifically provides names of the setting. It is the time of the story that gets a little more difficult to pin down. Dickens does provide a few clues that help us narrow this down though.
In chapter 53, a match is described as being the source of a fire.

He lighted the candle from the flaring match with great deliberation, and dropped the match, and trod it out.

Friction matches were invented in 1826, so we can assume that the action takes place after this year. When Pip leaves London for Sattis House, there is no mention of railroads, which did not come to London until 1837. Perhaps this is an oversight, or it is a deliberate omission because the city did not have a railroad at the time of the story. Another clue occurs in chapter 36 when Mr. Wemmick lists all the bridges along the Thames. He fails to mention the Hungerford Bridge which was built in 1845, so we know for sure that the story takes place before this year. We can, therefore, be sure that the story most likely takes place between 1826 and 1837, and definitely not after 1845.

Maniac Magee visits the West End and the East End. Think about how the two sides of town are similar and different.

Two Mills is a town that is divided into East End and West End. The dividing line is Hector street, and Hector street has an east side and a west side. It's as if there is an "invisible chalk line" right down the middle of the street. What is unfortunate is that the only thing that is different in the east and west parts of town is the race that lives in each area. The East End is for the black people, and the West End is for the white people.

Hector Street was the boundary between the East and West Ends. Or, to put it another way, between the blacks and whites. Not that you never saw a white in the East End or a black in the West End. People did cross the line now and then, especially if they were adults, and it was daylight.

Other than the racial differences, East End and West End are a lot alike. Both sides of town have people who care for Maniac, and both sides of town have people who want nothing to do with Maniac. The socioeconomic status of both sides is similar as well. Two Mills is a fairly run-down and poor town, and the average education level of both sides is similar, too. We are told that Maniac is colorblind when it comes to racial issues, and that is why he simply can't see a difference between the West End and the East End. To Maniac, there aren't any differences.

Maniac Magee was blind. Sort of. [. . .] Maniac kept trying, but he still couldn't see it, this color business. He didn't figure he was white any more than the East Enders were black.

The fictional town of Two Mills, Pennsylvania is segregated along racial lines. The West End is exclusively white; the East End is exclusively black. There's very little in the way of social interaction between the two parts of town. As Maniac Magee is a stranger in town, the racial differences in Two Mills don't mean anything to him, and so he's able to pass back and forth between the West and East End without too much difficulty. He certainly has no hesitation in staying with the Beale family, for example.
Despite a glaringly obvious difference between the two areas, there are also similarities. For one thing, they've both seen better days. Two Mills is a struggling industrial town whose heyday has long since gone. Though separated by race, the West Enders and the East Enders share a fierce pride in their respective communities. They may not have much, but they do have a strong sense of place, which makes a big impression on a homeless orphan like Maniac.

What would be a major turning point in the beginning of Harper Lee's To Kill A Mockingbird?

A turning point, by definition, follows a set of plot points that make up the rising action. As such, there are no turning points at the beginning, as the early section of the novel leads up to turning points specific to a particular character or set of characters, theme, plotline, etc.
The novel's central climax or turning point relating to the theme of good and evil occurs in Chapter 28. Bob Ewell attacks Jem and Scout as they walk home from the Halloween pageant. Boo Radley comes to the children's defense, and Ewell is found dead under an oak tree. Sheriff Tate writes in the official report that Mr. Ewell died by falling on his own knife, however, Boo may have killed Ewell (the novel makes it unclear).
As part of the falling action, Scout recognizes Boo as the man who saved her and Jem. Scout treats him like an old friend in an affectionate and heartfelt moment, greeting him with a "hey, Boo." She walks Boo home and never sees him again, but the experience teaches Scout a valuable lesson. Boo is not the dangerous degenerate that Maycomb society believes him to be. It occurs to Scout that Boo had been the person hiding gifts for herself and Jem in the tree. For Scout, this is a lesson not to accept societal judgments at face value.
Going back to the rising action associated with this theme, the lead up to Boo Radley's true nature being discovered features him leaving presents for the children and folding and fixing Jem's pants after he sneaks into the Radley's yard. In the case of Bob Ewell, his violent nature is featured when Atticus proves that he attacked his own daughter Mayella during the trial. After Atticus humiliates him in court, Bob Ewell publicly threatens him. This provides motivation for Ewell to attack Atticus' children in revenge.

A turning point in a story is the moment the rising action becomes falling action, leading to the story's resolution. The turning point is the most intense moment of the story, also called the climax. In the beginning of Harper Lee's To Kill a Mockingbird, all action is still considered rising action. There are, however, two central plots in To Kill a Mockingbird, and it is in the middle of the book that one plot reaches its turning point, while the other does not reach its turning point until the end.The main plot concerns the children's coming-of-age story. While Scout and Jem reach their greatest points of maturity in different parts of the book, it's not until the very end of the book that Scout, the main protagonist, reaches her greatest point of maturity; therefore, the turning point concerning the children's coming-of-age story does not occur until the end of the book. The second plot concerns Atticus's decision to defend Tom Robinson, a decision that significantly influences the children's maturity.The turning point concerning Atticus's defense of Tom Robinson occurs in Chapter 22, at the trial, the moment Judge Taylor reads the jury's guilty verdict. Prior to that moment, the reader hopes as Jem hopes, which is that all circumstantial evidence Atticus revealed during the trial pointing to Robinson's innocence and Bob Ewell's guilt is enough to convince the jury. The evidence that is most damaging for the Ewells is the fact that Mayella had been bruised in her right eye by a left-handed man standing before her; Robinson is completely crippled in his left arm and hand, whereas Ewell is left-handed. Jem expresses his confidence that Robinson will be acquitted when he says to Reverend Sykes, " ... but don't you fret, we've won it ... . Don't see how any jury could convict on what we heard--" (Ch. 21). Yet, the jury returns with a guilty verdict, sealing Robinson's fate. While Atticus hopes there is a chance at appeal, all action upon hearing the verdict turns to falling action, culminating in the resolution of Robinson being killed attempting to escape prison, desperate to take matters of justice into his own hands. Since all action concerning Robinson's trial turns to falling action the moment we learn the verdict, we know this is the turning point or climax concerning this particular plot line within the story.
https://literarydevices.net/climax/

Calculus of a Single Variable, Chapter 6, 6.4, Section 6.4, Problem 11

Given (x-1)y'+y=x^2-1
when the first order linear ordinary differential equation has the form of
y'+p(x)y=q(x)
then the general solution is,
y(x)=((int e^(int p(x) dx) *q(x)) dx +c)/e^(int p(x) dx)
so,
(x-1)y'+y=x^2-1
=> (x-1)[y' + y/(x-1)] = x^2 -1
=> y'+y/(x-1)= ((x+1)(x-1))/(x-1)
=> y'+y/(x-1)= (x+1) --------(1)

y'+p(x)y=q(x)---------(2)
on comparing both we get,
p(x) = 1/(x-1) and q(x)=(x+1)
so on solving with the above general solution we get:
y(x)=((int e^(int p(x) dx) *q(x)) dx +c)/e^(int p(x) dx)
=((int e^(int (1/(x-1))dx) *(x+1)) dx +c)/e^(int(1/(x-1)) dx)
first we shall solve
e^(int (1/(x-1)) dx)=e^(ln|x-1|) = |x-1|
When x-1<=0 then ln(x-1) is undefined , so
e^(int(1/(x-1)) dx)=x-1
so
proceeding further, we get
y(x) =((int e^(int (1/(x-1))dx) *(x+1)) dx +c)/e^(int(1/(x-1)) dx)
=((int (x-1)*(x+1)) dx +c)/(x-1)
=((int (x^2-1) ) dx +c)/(x-1)
= (x^3/3 -x +c)/(x-1)

y(x)=(x^3/3 -x +c)/(x-1)

How did the Reign of Terror cause the National Convention to be replaced by the Directory?

Robespierre and the Jacobins massively overreached during the Terror. The Terror was getting rapidly out of hand, destroying the lives of many who, by no stretch of the imagination, could reasonably be described as hostile to the Revolution. It seemed to many in the National Convention that no one was safe from the guillotine.
Furthermore, there were tensions within the Committee of Public Safety regarding the future direction of events. Robespierre, for his part, remained utterly convinced of his own unimpeachable integrity as well as the moral purity of the Terror. Other members of the Committee, such as Carnot, resented Robespierre and what they saw as his growing dictatorship. In due course, Robespierre found himself caught in the middle between radicals and moderates. With growing economic problems and public unrest, the difficulties assailing the revolutionary government were increasing by the day.
Also, as the Revolutionary Army continued to chalk up an impressive string of victories, the threat of foreign invasion receded sharply. Under those conditions, it became increasingly difficult for the Jacobins to justify their reign of terror. Inside the National Assembly, the Montagnards, the large mass of deputies who had kept their heads down during the Terror, finally came to life, whipped up into action mainly by men such as Barras, himself a deputy, who convinced many of his colleagues that their names were on a death list drawn up by Robespierre.
Robespierre unwisely confirmed such fears with an ill-judged speech in the Convention on 9 Thermidor (a month in the French Revolutionary calendar). In it, he detailed the existence of growing plots and conspiracies against the regime and spoke of an unnamed group of traitors in the Convention. The instinct for self-preservation among the deputies now kicked in, stiffening their resolve to overthrow Robespierre and his despotic regime. Robespierre's speech was shouted down by a hostile Convention, which accused him of being a tyrant.
Robespierre was finally done in by the narrowness of his political power base. The Jacobin Club and the more radical Communes rallied to his defense, but the Convention had now declared him a tyrant and an outlaw. Crucially, it had the force of arms on its side. Eventually, Robespierre and a number of his most radical followers went to the guillotine. The Committee of Public Safety was replaced by the Directory, a five-man executive which proceeded to carry out its own repressive agenda against opponents on the Left, the so-called White Terror.
https://www.britannica.com/event/Thermidorian-Reaction

Chicanx experiences represent a truth worth knowing and living. It offers us a model for human liberation. Please choose one example from contemporary Chicanx life that we have discussed throughout the course that you believe is a model for human liberation. Present your example (tell us what it is and the context) and how it contributes to a vision of justice and democracy.

The Chicanx movement, along with the very closely related Latinx movement, is a model for liberation in that it arose in opposition to the ostensibly male-dominated culture of the Chicano movement. This movement began in the late 1960s, when activists began to embrace their identity in the face of institutionalized oppression. They rejected the title of "Mexican American" and instead looked to a past that emphasized their history in the American Southwest. The Chicanx movement went beyond this in order to promote a non-gendered approach to liberation. One scholar and activist noted that the Chicano movement was "male-defined . . . sexist, misogynist[ic], and homophob[ic]." It promoted a vision of the family that was centered around men as breadwinners and heads of household. The Chicanx (sometimes "Chicana/o" is used instead) movement was a rejection of all of this, emphasizing that sexism and misogyny intersect with oppression as a result of race and class structures. It also reflected a more fluid understanding of gender, which like race, is a social construct. Today, the term is mostly used among scholars who point to the importance of language as a marker of identity. This term was used by the late Gloria Anzaldúa, whose work on Chicanx identity revolutionized the field, and Rodolfo Acuña, whose book  Occupied America became a staple in identity studies courses even beyond Chicanx reading lists. In short, Chicanx scholarship attempts to incorporate the broadest possible array of identities and experiences to help understand what was once known as Mexican American studies.
https://books.google.com/books?id=y786DwAAQBAJ&pg=PA32&dq=Chicanx&hl=en&sa=X&ved=0ahUKEwjN9aiSy7TYAhVL54MKHRJiCI8Q6AEIRDAF

https://jsri.msu.edu/upload/occasional-papers/oc07.pdf

https://www.colorlines.com/articles/google-recognizes-queer-chicanx-scholar-gloria-anzaldua-new-doodle

The Chicanx Movement is a bold effort, aimed to attack the root of Latin dominator culture; namely, the fact that the default (and all-inclusive) pronoun is the masculine. Though we do not have the same gendering of nouns in the English language, one might compare the Chicanx Movement to the ways we have begun to replace the words Man and Men with human and humans in Western philosophical language ("All Men are created equal," "The Rights of Man," "Man and Superman," etc). 
The movement has not walked an easy path. Much of the world discredits the Chicanx phenomenon as a way for pretentious Americans to subvert the structure of a language that they have no business interfering with. Still, proponents of the movement stubbornly defend its attempts to challenge a form of linguistic imperialism that dates back to 1492. The famous philosopher Ludwig Wittgenstein said "the limits of my language are the limits of my world." By this, he meant that one can only be as empowered as one's language allows themselves to be. And along these same lines, the Chicanx Movement believes that restructuring the gender binary of the Spanish language is the first step toward disempowering the harmful patriarchy. 

The Chicanx movement is a movement for civil rights for Mexican American people. It uses the gender-neutral "Chicanx" to embrace chicanos, chicanas, and people who identity with other genders. There are many examples of the ways in which the Chicanx movement has furthered justice and democracy.
For example, the movement started with the activism of Reies Lopez Tijerina, a Texas-born activist who was referred to as the "Malcolm X of the Chicano Movement." From the mid-1950s to the mid-1970s, he led a grassroots movement to reform land grants in New Mexico that dated back to the Treaty of Guadalupe Hidalgo that ended the Mexican War. He led Chicanos to seek land that had been marked for Anglos by surveyors and that contravened the terms of the treaty. In addition, he fought for the recognition of Chicano/a culture and for economic opportunities for Chicanos/as. He also joined with the 1968 Poor People's Campaign led by Martin Luther King and served as its Chicano leader.
The movement continues today in organizations such as the Southwest Voter Registration Project (see the link below), whose slogan is, "su voto es su voz," or "your voice is your vote." This organization seeks to increase the participation of Latinos/as and other minorities in the democratic process. They host voter registration drives around the nation and, through the Latino Academy, train people for community leadership positions through courses in public speaking, political activism, and other areas. This organization promotes democratic values by seeking to involve all Americans, even those who have historically been disenfranchised, in the process of voting and carrying out community organization projects. There might be other similar organizations or efforts within the movement that have inspired you.
http://svrep.org/about_svrep.php

In "Games at Twilight," what key details suggest that the children use this rhyming game to choose who will be "it".

The best evidence that I can point you toward is the immediacy that the children fall into place and begin playing the rhyming game.  
The children decide that the first game that they all should play is hide-and-seek.  Then there is an argument about who should be it.  If you have ever played the game, you are familiar with this argument.  Mira quickly steps in to intervene, and she starts pushing and shoving kids into a circle of sorts.  While she is doing that, she is yelling "Make a circle, make a circle!'' Once the kids are in that circle, nobody explains anything.  There is no explanation about how the rhyming game works.  The rule about how and when to clap in rhythm is never stated.  Mira simply shouts out "Now clap!"  The children all know exactly what to do, and the children all know exactly when they have been eliminated and are safe from being "it."  That familiarity tells readers that the clapping game to choose a person is something that all of the children know and are used to.  

. . . and every now and then one or the other saw he was safe by the way his hands fell at the crucial moment—palm on palm, or back of hand on palm—and dropped out of the circle with a yell and a jump of relief and jubilation.

Calculus of a Single Variable, Chapter 6, 6.4, Section 6.4, Problem 61

Given equation is y'+y/x=xy^2

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

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

=> -u' +(1/x) u =x

=>u' -(1/x) u = -x so this linear equation is of the form
u' + pu=q
p=-(1/x) , q=-x
so I.F (integrating factor )
= e^(int p dx) = e^(int -(1/x) dx) = e^(-lnx)=1/x

and the general solution is given as
u (I.F)=int q * (I.F) dx +c
=>u (1/x)=int (-x) * (1/x) dx +c
=>u (1/x)=int (-1) dx +c
=>u (1/x)= -x+c
=>u= (c-x)/(1/x) = x(c-x)
but u=1/y
1/y = x(c-x)
y=1/(x(c-x))

is the general solution.

What did President Monroe order Andrew Jackson to do in 1818?

In 1818, President James Monroe ordered General Andrew Jackson to pursue the Seminole Indians deeper into the territory of Florida in what came to be known as the First Seminole War. In autumn of the previous year, Jackson began his attempt to subdue the Seminoles, but this resulted in devastating counterattacks in which the Seminoles destroyed several American settlements.
In March of 1818, President Monroe instructed Jackson to enter Spanish territory to stamp out the Seminole opposition once and for all. Jackson took about 4,000 soldiers, including many allied Native warriors, with him and marched as far as Anhaica (Tallahassee), which he burned to the ground. He then continued on to Micosukee, a native village, which he also thoroughly destroyed.
Monroe argued that taking the fight against the Seminoles into Spanish territory was justified since the Spanish had effectively lost control of the Native inhabitants there. Monroe saw the inability or unwillingness of the Spanish colonial authorities to reign in the Seminoles as a direct threat to American interests. Consequently, he ordered General Jackson to also take the Spanish fort in what later became St. Marks and to occupy the town of Pensacola. These actions helped persuade Spain to cede the territory of Florida to the United States the following year.

Discuss the difference between how conflict-perspective sociologists and functionalist-perspective sociologists view politics and government. Which perspective, in your opinion, gives the most accurate vantage point on politics and government?

The answer to this question lies in the definition of those types of sociology, which you can understand from their names. Functionalist perspective sociologists believe that the government rose as a necessary function and as a servant to society, while conflict theorists propose that the struggle between society and anarchy dictated a need for government.
The functionalist view of government sees it as steering a unified ship. There are external struggles and factors to overcome, but the interior is a cohesive unit. As such, it is performing a servant function, ensuring that order is maintained.
On the other hand, conflict perspective sociologists propose that the society is in inherent struggle; there is conflict between internal groups, and the government is tasked with keeping things in balance as they battle over limited resources. The conflict theorist believes that the difficulties to overcome are internal. In that way, they view government as protecting us from ourselves.

Functionalist-perspective sociologists view government and the political process as a means of ensuring a stable and orderly society, which, in their perspective, means a functional society. This perspective views the state as a means of creating and enforcing the status quo of society, and as such, maintaining order. The state supposedly functions as a cohesive force that unites society in a manner that ensures the most stability, cohesion, and social equilibrium.
Conflict-perspective sociologists understand the state to be a source of concentrated power that maintains order through force and coercion. This perspective recognizes how the state and powerful individuals/companies create and enforce a society, economy, and political system that benefits those in power. As such, any groups of people not within this the top of this power hierarchy must struggle for access to resources and quality of life.
I believe this conflict perspective is much more realistic, as it thoroughly recognizes how every single group of people not within the political and economic elite must engage in serious political and social movements against state and economic oppression. For example, every minority and oppressed group has had to (and most groups still) engage in a prolonged struggle for access to individual and collective liberation.

According to the functionalist perspective, the government plays the role of maintaining law and order in the society. It manages the society as a single unit. It ensures that all groups within the society are able to function in harmony with each other towards the achievement of a collective good. As such, the functionalist perspective is committed to societal order and methods of maintaining the status quo. Social change can only be achieved via consensus.
The conflict perspective, on the other hand, focuses on conflict as a means towards societal change. It states that various groups within a society, be they economic groups, religious groups, ethnic groups etc, are always in competition with each other for the limited resources. The dominant group that often forms the government then has to look for ways of controlling other groups so as to maintain their power. For instance, the ruling class can push for policies that only benefit them, while exploiting the rest. Order in the society is based on the manipulation and control of the people by the dominant groups. The conflict theorists look at the conflicts of interests that exist among different groups of people in a society.
It would appear that both of these viewpoints are important in explaining the role of government in society. This is because a government needs unity among its people for it to be stable. However, in order for it to achieve unity, it must be willing to first address the conflicts that exist among the different groups within the society.
https://philschatz.com/sociology-book/contents/m42918.html

Single Variable Calculus, Chapter 3, 3.6, Section 3.6, Problem 24

Find $\displaystyle \frac{dx}{dy}$ of $y \sec x = x \tan y$ by Implicity Differentiation.
$\displaystyle \frac{d}{dy} (y \sec x) = \frac{d}{dy} (x \tan y) $


$
\begin{equation}
\begin{aligned}
(y) \frac{d}{dy} (\sec x) + (\sec x) \frac{d}{dy} (y) & = (x) \frac{d}{dy} (\tan y) + (\tan y) \frac{d}{dy} (x)\\
\\
(y) (\sec x \tan x) \frac{dx}{dy} + (\sec x)(1) &= (x) (\sec^2y) + \tan y \frac{dx}{dy}\\
\\
y \sec x \tan x \frac{dx}{dy} + \sec x &= x \sec^2 y + \tan y \frac{dx}{dy}\\
\\
y \sec x \tan x \frac{dx}{dy} - \tan y \frac{dx}{dy} &= x \sec^2y - \sec x\\
\\
\frac{dx}{dy} (y \sec x \tan x - \tan x) &= x \sec^2 y - \sec x\\
\\
\frac{\frac{dx}{dy} \cancel{(y \sec x \tan x - \tan x)}}{\cancel{y \sec x \tan x - \tan x}} &= \frac{ x \sec^2 y - \sec x}{y \sec x \tan x - \tan x}\\
\\
\frac{dx}{dy} &= \frac{ x \sec^2 y - \sec x}{y \sec x \tan x - \tan x}
\end{aligned}
\end{equation}
$

College Algebra, Chapter 4, 4.6, Section 4.6, Problem 50

Find the intercepts and asymptotes of the rational function $\displaystyle r(x) = \frac{2x - 4}{x^2 + x - 2}$ and then sketch its graph.

We first factor $r$, so $\displaystyle r(x) = \frac{2 (x - 2)}{(x + 2)(x - 1)}$

The $x$-intercepts are the zeros of the numerator $x = 2$.

To find the $y$-intercept, we set $x = 0$ then

$\displaystyle r(0) = \frac{2 (0 - 2)}{( 0 + 2) (0 -1)} = \frac{2(-2)}{(2)(-1)} = 2$

the $y$-intercept is $2$.

The vertical asymptotes occur where the denominator is , that is, where the function is undefined. Hence the lines $x = -2$ and $x = 1$ are the vertical asymptotes.

We need to know whether $y \to \infty$ or $y \to - \infty$ on each side of each vertical asymptote. We use test values to determine the sign of $y$ for $x$- values near the vertical asymptotes. For instance, as $x \to -2^+$, we use a test value close to and to the right of $-2$ (say $x = -1.9$) to check whether $y$ is positive or negative to the right of $x = -2$.

$\displaystyle y = \frac{2 (-1.9 - 2)}{(-1.9 + 2)(-1.9 - 1)}$ whose sign is $\displaystyle \frac{(-)}{(+)(-)}$ (positive)

So $y \to \infty$ as $x \to -2^+$. On the other hand, as $x \to -2^-$, we use a test value close to and to the left of $-2$ (say $x = -2.1$), to obtain

$\displaystyle y = \frac{2 (-2.1 - 2)}{(-2.1 + 2)(-2.1 - 1)}$ whose sign is $\displaystyle \frac{(-)}{(-)(-)}$ (negative)

So $y \to - \infty$ as $x \to -2^-$. The other entries in the following table are calculated similarly.

$\begin{array}{|c|c|c|c|c|}
\hline\\
\text{As } x \to & -2^+ & -2^- & 1^+ & 1^- \\
\hline\\
\text{The sign of } y = \frac{2(x - 2)}{(x + 2)(x - 1)} & \frac{(-)}{(+)(-)} & \frac{(-)}{(-)(-)} & \frac{(-)}{(+)(+)} & \frac{(-)}{(+)(-)} \\
\hline\\
\text{So } y \to & \infty & - \infty & - \infty & \infty \\
\hline
\end{array} $

Horizontal Asymptote. Since the degree of the numerator is less than the degree of the denominator, then $y = 0$ is the horizontal asymptote.

College Algebra, Chapter 9, 9.2, Section 9.2, Problem 38

Suppose the 12th term of an arithmetic sequence is $32$, and the fifth term is $18$. Find the 20th term.

To find the $n$th term of this sequence, we need to find $a$ and $d$ in the formula

$a_n = a + (n -1) d$

From this formula we get

$a_{12} = a + (12-1) d = a+ 11d$

$a_5 = a + (5-1)d = a + 4d$

Since $a_5 = 18$ and $a_{12} = 32$, we get the two equations



$
\left\{
\begin{equation}
\begin{aligned}

a + 11d =& 32
&& \text{Equation 1}
\\
\\
a + 4d =& 18
&& \text{Equation 2}

\end{aligned}
\end{equation}
\right.
$


We eliminate $a$-term in each equations and solve for $d$



$
\left\{
\begin{equation}
\begin{aligned}

a + 11d =& 32 &&
\\
\\
-a-4d =& -18
&& -1 \times \text{Equation 2}
\\
\\
\end{aligned}
\end{equation}
\right.
$


$
\qquad
\begin{equation}
\begin{aligned}

\hline\\
\\
\\
7d =& 14
&& \text{Add}
\\
\\
d =& \frac{14}{7}
&& \text{Divide by } 7
\\
\\
d =& 2
&&

\end{aligned}
\end{equation}
$


We back-substitute $d =2$ into the first equation and solve for $a$


$
\begin{equation}
\begin{aligned}

a+11(2) =& 32
&& \text{Back-substitute } d=2
\\
\\
a =& 32-22
&& \text{Subtract } 11(2)=22
\\
\\
a =& 10
&&

\end{aligned}
\end{equation}
$


So we get $a=10$ and $d=2$. Thus, the $n$th term of this sequence is $a_n = 10+2(n-1)$

The 20th term is

$a_{20} = 10 + 2(20 - 1) = 48$

Single Variable Calculus, Chapter 6, 6.1, Section 6.1, Problem 4

Determine the area of the shaded region



$
\begin{equation}
\begin{aligned}
A &= \int^{y_2}_{y_1} (x_{\text{right}} - x_{\text{left}}) dy\\
\\
A &= \int^3_0 \left[\left( 2y - y^2\right) - \left( y^2 - 4y \right) \right] dy\\
\\
A &= \int^3_0 \left( -2y^2 + 6y \right) dy\\
\\
A &= \left[ \frac{-2y^3}{3} + \frac{6y^2}{2} \right]^3_0\\
\\
A &= \left[ \frac{-2(3)^3}{3} + \frac{6}{2} (3)^2 \right] - \left[ \frac{-2(0)^3}{3} + \frac{6(0)^2}{2} \right]\\
\\
A &= 9 \text{ units}^2
\end{aligned}
\end{equation}
$

What would happen to the life of a cell if there was no Golgi apparatus?

The golgi apparatus contains vesicles and folded membranes and is involved in cellular transport. It is a packaging organelle. The golgi apparatus packages proteins into vesicles inside of the cell before sending them to their destinations. The golgi apparatus processes proteins for secretions that contain enzymes that attach sugar monomers to proteins. If the golgi apparatus is not present the packaging and transport of materials would cease to happen. So, various substances such as sugar monomers would not be able to be transformed into proper forms for further use. The secretory activities of the cell would also cease to occur. Also, if there is no golgi apparatus, the plasma membrane would be affected because it needs to be able to grow larger for cell division.

How do tsunamis affect the atmosphere?

Tsunamis are known for the great destruction they cause on land. Some recent, devastating tsunamis were observed in Japan and Indonesia. Interestingly, scientists have found that, apart from the lithosphere, our atmosphere is also affected by the tsunamis.
Ionosphere, a layer of atmosphere that lies between 50 and 300 miles (80 and 500 km) above the Earth's surface is primarily affected by the tsunamis. The waves generated by the tsunamis cause ripples in the ionosphere and disturb the electron density in that region of the atmosphere. More specifically, the tsunamis cause gravity waves in the atmosphere and these waves match the horizontal speed of the tsunami (as was observed during the 2011 tsunamis in Japan). The earthquake that caused the 2011 Japan tsunamis also created acoustic and Rayleigh waves that reached the ionosphere. 
An interesting effect of the resulting changes in the ionosphere is the anomalies in GPS data, which may allow the scientists to (someday) detect the tsunami. 
 

How does George Orwell's Animal Farm relate to collectivism?

The economic system that the animals build on the farm is a prime example of collectivism. In political and economic terms, collectivism can be defined as a system whereby the government or the people own the land and the means of production. That's what appears to happen on Manor Farm. According to Old Major's ideology of Animalism, animals must work together to create a better society. All the animals are equal—though in actual fact, some are "more equal than others"—so everything is held in common; there's no private ownership involved.
Animal Farm is a work of satire, and Orwell's treatment of collectivism is suitably satirical. He conveys the impression that, although collectivism's a fine idea in practice, in reality it's completely unworkable. The Soviet Union under Stalin is what Orwell is satirizing here.
Not all the animals on the farm work hard to build this shining new utopia. The ruling pigs are lazy and arrogant, thinking themselves better and smarter than all the other animals. They lord it over the farm, living off the hard work of others. And in any case, the pigs don't even believe in the values of collectivism; they see it as nothing more than an instrument of control. It comes as no surprise when, at the very end of the book, they develop an understanding with neighboring farmers and it becomes impossible to distinguish pigs from humans.

Are there any quotes in Macbeth that discuss trust?

We can also find examples of trust quotes which relate specifically to Macbeth's relationship with The Witches. This relationship is based entirely on trust: that is, Macbeth trusts their every word and treats their prophecies as fact. When he first meets them in act I, scene III, for example, Macbeth's instant trust of The Witches is shown by the following line:

Stay, you imperfect speakers, tell me more.

In other words, although Macbeth knows that these women are witches, he has developed an instant trust towards them.This explains why he wants to know more about what they have to say.
We can find another example of his trust towards The Witches in act III, scene IV, after Macbeth has just seen Banquo's ghost:

I will tomorrow—
And betimes I will—to the weird sisters.
More shall they speak, for now I am bent to know,
By the worst means, the worst.

Here, Macbeth is saying that The Witches hold all the answers. He trusts them so much that he will not make another move without hearing what they have to say.
While these quotes do not explicitly talk about trust, they provide strong indications of how Macbeth feels about The Witches. These quotes make it clear that he trusts them and their every word.

In act 4, scene 3, Macduff encourages Malcolm to fight against Macbeth and regain the title of King of Scotland that is rightfully his. However, Malcolm does not completely trust Macduff and cautiously responds to his comments regarding Scotland under Macbeth's tyrannical reign. Malcolm understands that Macbeth could have easily sent Macduff to spy on him and begins to test Macduff's loyalty. To determine whether or not Macduff is trustworthy, Malcolm tells him that he would be a terrible king because he has numerous vices. Malcolm tells Macduff that he is malicious, greedy, deceitful, and violent, which disturbs Macduff and causes him to lament for his homeland. Macduff's passionate outburst proves to Malcolm that he is trustworthy, and Malcolm ends up enlisting Macduff's help to defeat Macbeth. Malcolm tells Macduff,

Macduff, this noble passion, Child of integrity, hath from my soul Wiped the black scruples, reconciled my thoughts To thy good truth and honor (Shakespeare, 4.3.117-119).

Overall, Malcolm tests Macduff's loyalty by feigning to be an ignorant and wicked king, which elicits a passionate response from Macduff and proves that he is trustworthy and loyal.

Macbeth is all about trust and betrayal. So, here are two major examples of the abuse of trust in the play.
1. At the beginning of the play, king Duncan strips the traitorous Thane of Cawdor of his titles and has him killed because the thane conspired with the Norwegians against Duncan. Duncan was naturally disappointed because he trusted the thane:

There's no art To find the mind's construction in the face: He was a gentleman on whom I builtAn absolute trust.

The King states that one's appearance can be rather deceiving and that although he trusted the thane, he was eventually tricked by him. What is ironic is that king Duncan will put his trust in another man who will betray him just like the thane of Cawdor did. And this man is, of course, Macbeth.
 2. When Macbeth confronts the dilemma of whether to murder king Duncan or not, he goes through the list of reasons why he should not kill the king. One of the most important reasons is because Duncan trusts him:

He's here in double trust; First, as I am his kinsman and his subject, Strong both against the deed; then, as his host, Who should against his murderer shut the door, Not bear the knife myself.

So, Macbeth states that Duncan trusts him for two reasons. First, they are relatives, so killing the king would not only be unacceptable, but sinful as well. Macbeth is also his most loyal subject, so he should support him, not murder him. Second, Duncan will be a guest at Macbeth's home, so, as his host, Macbeth should protect him and make sure that Duncan is safe. Nevertheless, we know that Macbeth will abuse this trust which Duncan has and take advantage of the fact that Duncan is at his home so that he could kill the king.