Precalculus, Chapter 3, 3.3, Section 3.3, Problem 45

Since all of the terms are being multiplied inside the ln, that means to expand them, one must rewrite them as added.
Therefore,
Given
lnxyz^2
Then,
lnxyz^2=lnx+lny+2lnz

In what ways has Holling tried to bring peace to his world

Probably the best place to look for support on how Holling tries to bring peace to his world is to look at the relationship between Holling and his sister, Heather. Through most of the book, Heather is quite antagonistic to Holling.  n her defense, she is antagonistic to just about everybody. I have to give Holling a lot of credit because no matter how mean or snarky Heather is to him, Holling never reciprocates it back to her. He wants to have a good relationship with his sister. He needs it actually because deep down Holling knows that he'll never have a great relationship with either of his parents.  
Holling begins to thaw Heather's icy exterior and harsh attitude toward him when he saves her from being hit by the bus. His actions were more reflex than conscious thought to save her and their relationship, but his actions do give Heather a wake up call about the fact that her brother loves her deeply enough to risk his own life. 
Heather will eventually run away from home, and she will get stranded far away. It isn't Mr. or Mrs. Hoodhood that rescues her. It's Holling. His father actually refuses to help, and Holling takes the situation into his own hands. He wants his sister back, and he's willing to do whatever it takes to get her back. The book ends with their warring relationship finally at peace. 

"Holling," she said. "I was so afraid I wouldn't find you."
"I was standing right here, Heather," I said.  "I'll always be standing right here." 

 

What is the suitcase a symbol for in Bud, Not Buddy?

In Bud, Not Buddy the suitcase is a symbol of who Bud is. It represents all he has in the world, his past, present and hopefully future. The items in the suitcase (the rocks, blanket, picture of his mother and flyers of this "father") all represent what he is trying to get to in his life. Throughout the book Bud is searching for his "father" relying on the clues left by his mother that reside in that suitcase. It represents security and a connection to "home." Without the suitcase, Bud is lost and without it he will never be able to find that closure that he needs on this journey that he is on. Looking back on the moment he was about to jump the train out of Hooverville he clutches onto the flyer in his hand not willing to let go and lose any part of who he is.

In Bud, Not Buddy, the suitcase, or what is inside of it, is symbolic of Bud's family and his search for identity. The reader meets Bud when he is ten years old and living at the Home, an orphanage.The only connection Bud has with his past is contained within the suitcase: it contains a blanket, rocks that are written upon, flyers of Herman Calloway and his band, and a picture of his Momma. As the story progresses, Bud leaves a foster family and ends up traveling in search of his father, who he mistakenly assumes is Herman Calloway.
During this journey to find his family, Bud carries the suitcase, his most prized possession. However, it is what is inside the suitcase that is priceless, and it confirms his identity to his grandfather, Herman Calloway. When Calloway sees the rocks, the flyers, and the picture of his daughter, Bud's heritage is revealed. After this revelation, Bud realizes he has finally found his family and his home. At the end of the novel, he can finally unpack the suitcase, which had been exchanged for a saxophone case earlier. He spreads the blanket on his bed and tacks the picture of his mother on the wall. He is home. Bud has matured, and the saxophone case with the saxophone, his future, is proof.

Bud's suitcase symbolizes his transient lifestyle as he travels from Flint, Michigan to Grand Rapids in search of his father, as well as everything that Bud considers important in life. Bud carries a blanket, an old tobacco bag with rocks inside, flyers depicting Herman Calloway's performances, extra clothes, and an envelope with his mother's picture inside. These items have particular significance to Bud and represent his connection to his family and past. The items inside the suitcase also contain Bud's memories, which comfort him through difficult experiences and guide him towards Herman Calloway, who lives in Grand Rapids, Michigan. Throughout the novel, Bud carries his suitcase everywhere he goes and never leaves it behind. Bud's suitcase is essentially an extension of himself, because it contains his dearest memories. Overall, Bud's suitcase symbolizes his lifestyle and everything that he considers important in life.

Why did Maya lie on the witness stand?

Maya lies on the witness stand because of events that led up to her rape by Mr. Freeman. Mr. Freeman had molested her multiple times leading up to her rape (Chapter 11). When asked by the prosecutor if there had been previous incidents of sexual assault, Maya feels as though she is caught in a trap. She does not want to lie, but she also does not want to admit to the previous incidents. She fears that if she admits to them, she will be seen as a "bad girl." She also fears rejection by her family, who took her to the hospital and stood by her throughout the ordeal. She is afraid that they will feel betrayed because she did not tell them about the previous incidents of abuse.
After she lies on the stand and Mr. Freeman is released and then beaten to death, Maya feels immense amounts of guilt. She feels that her lie resulted in the death of a man who, despite his abuse of her, she viewed as a father figure. Her family never discusses the incident, and this only serves to intensify her guilt.

Why do you think Paulson chose to use Brian's third limited point of view rather than either Brian's first person point of view or a third person objective point of view?

Paulson's choice of a third limited point of view for Hatchet succeeds on several levels. Yet this choice poses two distinct questions. Why not the first person, and why not the third person objective? 
The power in this book is the capacity for the reader to feel akin to Brian's situation and actions; to feel as closely tied to Brian in this moment as possible. This makes the reader feel as though they are trapped in the Canadian wilderness, having to tackle the unknown challenges of each grueling day. Were the story written from the third person objective point of view, none of Brian's thoughts or feelings would be transmitted in the narrative. Especially considering the absence of dialogue in this book, that would utterly deaden the empathy the reader feels for Brian. When the book describes Brian's fear, anger, and doubt, the reader can feel it too, is further drawn into the story. 
If Brian's thoughts and feelings are so important, why not just use the first person point of view? The reader does not read from Brian's direct thoughts and experiences, but watches him and his struggles in the third-person. Though it seems contradictory, this point of view also instills more empathy in the reader than if it were a first-person point of view. If Brian were telling the story, the reader would feel as though they are Brian, and Brian is in charge. Looking at Brian as a separate entity heightens his loneliness, his isolation, and creates a tension for young readers: they are their own person, simply watching Brian, and they cannot help him. 
In a way, the method of third-person limited point of view in this book is an exercise in moderation. The author gives insight into Brian's thoughts and feelings, but not enough insight to see the bigger picture, including any clear sign that Brian will eventually be saved. The author's point of view gives enough information to feel drawn in but not so much information that the reader feels detached and knowledgeable about this story. Just as Brian suffers and wonders what will happen, so too must the reader. 

using act 1 scene 3 write about how Shakespeare presents witchcraft and the supernatural include Macbeth's reactions and how Shakespeare presents witchcraft and the supernatural in the play as a whole

Our first impression of the witches, as with anything in Shakespeare or in drama overall, depends partly on acting, directing, lighting, production design, and the other elements of stagecraft. The words Shakespeare gives to the witches are at first a bit more comical than frightening, though most productions of the play do not emphasize this. The sing-song manner in which the witches speak, and the eccentric things they say, create an oddly humorous tone, as in:

Her husband's to Aleppo gone, master o' th' Tiger;
But in a sieve I'll thither sail,
And like a rat without a tail,
I'll do, I'll do, and I'll do.

And:

Here I have a pilot's thumb,
Wrecked as homeward he did come.

It is only when Macbeth and Banquo appear on the scene that things take a much darker turn, as the witches hail Macbeth successively as Thane of Glamis, Thane of Cawdor, and King of Scotland. Macbeth's reaction is famously described by Banquo:

Good sir, why do you start and seem to fear
Things that do sound so fair?

Macbeth seems to know already, even at this point, that he cannot trust himself and that he is possibly going to embark on a killing spree. If not, there would be no reason for him to react in the way Banquo notices. The strange, puzzling message spoken by the witches to Banquo increases the generally creepy implications of the prophecy:

First Witch: Lesser than Macbeth and greater.
Second Witch: Not so happy, yet much happier.
Third Witch: Thou shalt get kings, though thou be none.
So all hail, Macbeth and Banquo!

The prediction concerning Banquo relates to the belief (which was current in Shakespeare's time) that Banquo was an ancestor of the Stuarts, the ruling dynasty in England (as they continued to be in Scotland) after the death of Elizabeth I. The witches, therefore, are immediately shown to have valid knowledge of the future. Any comical impression would become more subdued at this point. But the tension between humor and horror exists in each appearance of the witches and their encounters with Macbeth. That he deliberately goes back to them to consult them later in the play shows how strongly he's being driven on by their prophecies, unable to save himself and to break free of the horrible chain of wrongdoing that has fettered him.
Yet the additonal manifestations of the supernatural in Macbeth are, in my view, far more terrible and frightening than the witches. Banquo's ghost, when it appears, throws Macbeth into a state of hysteria. The ghost's face is so mangled and horrifying that Macbeth says it "would appall the devil" as he answers Lady Macbeth's charge that he, Macbeth, is a coward and her questioning of his manliness. Since no one except Macbeth sees the ghost, it's possible that it is, as Lady Macbeth asserts, merely a hallucination:

This is the very painting of your fear! This is the air-drawn dagger you said led you to Duncan!

Shakespeare's theme here, and throughout the play as a whole, concerns illusion versus reality. Earlier, when Macbeth is preparing to murder Duncan, he soliloquizes about the "dagger" that appears to him out of nowhere, to which Lady Macbeth alludes in the banquet scene. He wonders himself if it is real or just a "dagger of the mind, proceeding from the heat-oppressed brain." The underlying point Shakespeare makes could be that what we consider the supernatural, in general, is actually a projection of human thought and intention. If so, however—that is, if we are to make a purely naturalistic interpretation of Macbeth—one has to ask why more than one person at times can see or hear the supposedly hallucinatory things, as Macbeth and Banquo both do with the witches. It could be mass hysteria, though this interpretation is probably a case of overthinking the situation.
An interesting additional point is that when Macbeth has been transferred to other genres, the witches or their equivalents are more frightening than in the play itself, I would argue. This is true in Kurosawa's samurai version of the story, Throne of Blood, and in Verdi's operatic version. In the latter, music is the dominant means of conveying emotion and meaning. In Throne of Blood, the witches are represented by a solitary, androgynous figure who quietly, almost robotically, sings its prophecy to Ishizu (Macbeth) and Miki (Banquo) in a manner more cryptic and eerie than that of Shakespeare's witches in any production of Macbeth I have seen. The essence of Shakespeare's poetry is that it conveys multiple meanings and implications, and many different interpretations are thus possible concerning the witches, and the supernatural in general, in Macbeth.

The witches in 1.3 are full of mischief and quick to exact revenge on those that they think have wronged them somehow. When the witches first appear, one of them says she has been off killing pigs, while another says she intends to torment a sailor because his wife refused to share her food with her.
When Banquo and Macbeth arrive, the audience learns that the witches are ugly, as Banquo comments on their skinny lips and their "beards" (1.3.48). Banquo and Macbeth have no idea where the witches have come from or where they go, but suggest that perhaps they came from a bubble in the earth and that they vanish into the wind (1.3.80-85).
Banquo and Macbeth are startled and suspicious about what the witches have to tell them, although the prophecy eventually causes Macbeth to allow his own ambition to run wild. When Macbeth has his first proof of the prophecy, he exclaims

This supernatural soliciting Cannot be ill, cannot be good. If ill, Why hath it given me earnest of success Commencing in a truth? (1.3.142-146).


The witches don't actually force Macbeth to do anything. Macbeth hears their words and then takes action on his own. He does play out their prophecy, but it is by his own hand and not through any action of theirs. These supernatural beings are creepy, ugly, and mysterious, but it is through Macbeth's own faults that he becomes a murdering tyrant.
https://www.folgerdigitaltexts.org/html/Mac.html

College Algebra, Chapter 4, 4.1, Section 4.1, Problem 76

Suppose that a rain gutter is formed by bending up the sides of a 30 inch wide rectangular metal sheet as shown in the figure below.

"Please refer to the figure in the book"

a.) Find the function that models the cross sectional area of the gutter in terms of $x$.

b.) Find the value of $x$ that maximizes the cross sectional area of the gutter in terms of $x$.

c.) What is the maximum cross sectional area of the gutter?

a.) By observation, the cross sectional area of the gutter is $A = x(30 - 2x)$

$A = 30x - 2x^2$

b.) The cross sectional area is a quadratic function with $a = -2$ and $b = 30$. Thus, its maximum value occurs when

$\displaystyle x = \frac{-b}{2a} = \frac{-30}{2(-2)} = \frac{30}{4} = \frac{15}{2} $ inches

c.) Therefore, the maximum value of area is

$\displaystyle A = 30x - 2x^2 = 30 \left( \frac{15}{2} \right) - 2 \left( \frac{15}{2} \right)^2 = \frac{225}{2} \text{ in}^2$

Which two characters are vividly described through their physical appearances in Geoffrey Chaucer's "The General Prologue"?

In many ways, Chaucer was a master of description, and he brought many of his characters to life in "The General Prologue." Chaucer described two characters who deserve special attention: the Wife of Bath and the Miller.
The Wife of Bath is one of Chaucer's most memorable characters, if only because the prologue to her tale delves into a remarkable feminist discourse, but we also get a picture of her early on in "The General Prologue." Chaucer describes her in vivid fashion, noting she is "gap-toothed" (20), full-figured (24), and that her face is "bold," "fair, and red of hue (10). All in all, Chaucer describes a physical appearance that matches the Wife's vivacious, unapologetic personality, and it's easy to envision her based on his description. 
The Miller is a similarly memorable character, and his tale is one of the bawdiest in The Canterbury Tales. Chaucer describes the Miller as "a chunky fellow, broad of build" (5) with a red beard (8) and a hairy wart on his nose (10-12). Based on this description, readers picture a coarse, tough fellow with something of a rude streak.
In considering these descriptions, it's important to recognize Chaucer is describing his characters in strikingly realistic tones. Rather than idealizing his characters, he makes them look and act like real, normal people. This sense of realism is one of the reasons Chaucer's work has remained influential for hundreds of years.
https://www.owleyes.org/text/canterbury-tales/read/the-miller

https://www.owleyes.org/text/canterbury-tales/read/the-wife-of-bath/root-218788-1

Calculus of a Single Variable, Chapter 9, 9.1, Section 9.1, Problem 22

a_n=6+2/n^2
To find the limit of a sequence, let n approach infinity.
lim_(n->oo) a_n
=lim_(n->oo) (6 + 2/n^2)
=lim_(n->oo) 6 + lim_(n->oo) 2/n^2
Take note that a limit of a constant is equal to itself lim_(x->c) a = a.
Also, if a function is in the form a/x^m , where m is any positive number, its limit as x approaches infinity is zero lim_(x->oo) a/x^m =0
lim_(n->oo) 6 + lim_(n->oo) 2/n^2
= 6 + 0
=6
Therefore, the sequence's limit is 6.

What are two types of cervical carcinomas?

The most common types of cervical carcinomas are squamous cell carcinoma and adenocarcinoma. In the majority of cases (70 percent or more), the malignant cells are classified as squamous cell carcinomas. In the cervix, they line the outer surface. Normal squamous cells have a thin and flat appearance. It is worth noting that cancerous cells can have an abnormal appearance. Their unchecked proliferation also results in an abnormal accumulation of mutations.
In about 10 to 20 percent of cases, the cells are classified as adenocarcinomas. This type of carcinoma affects mucus-producing cells. In the cervix, they line the cervical canal. These cells are normally column-shaped. There are other types of cervical carcinomas, but these two make up the majority of cervical cancer cases.
https://about-cancer.cancerresearchuk.org/about-cancer/cervical-cancer/stages-types-grades/types-and-grades

https://www.nccc-online.org/hpvcervical-cancer/cervical-cancer-overview/

What is radical, new, or innovative in D. F. McKenzie’s description of bibliography as "a sociology of texts"?

McKenzie opened up bibliography as a field by incorporating what he called the "social processes" of how texts are produced and disseminated. He argued that the way texts are produced and distributed—and which texts are printed and reprinted—documents larger changes in a society and that these texts, in turn, influence social change. He allowed the field of bibliography to open in new ways to encompass how economic, social, and political factors impact publishing and how publishing exerts an influence over them. 
McKenzie looked at how various social forces determined what format a book or text appeared in and how it was distributed through a culture. He studied why certain texts were written or produced, why they were rewritten and reproduced in particular ways, and why some books were allowed to quietly fade into obscurity. He was innovative in asserting that book publishing—and republishing—does not occur in a vacuum divorced from other cultural influences. It is not simply the "best" or the most marketable books that get printed or reprinted, but the books that reflect, reproduce, and reinforce certain perceived social needs. As a case in point, McKenzie examined how the production of two texts in New Zealand, the 1835 Declaration of Independence and 1840 Treaty of Waitangi, helped authorize the transfer of sovereign power from the Maori to the British. 
McKenzie was also an innovator in other forms of media; he integrated film, music, and video into the the field of bibliography.

Single Variable Calculus, Chapter 7, 7.2-2, Section 7.2-2, Problem 76

Determine the volume of solid obtained by rotating the region under the curve $\displaystyle y = \frac{1}{x^2+1}$ from 0 to 3 about the $y$-axis.

By using vertical strips, and applying the shell method, notice that the strips have distance from $y$-axis as $x$ and if you rotate this length about $y$-axis, you'll get a circumference of $c = 2\pi x$. Also, the height of the strips resembles the height of the cylinder as $\displaystyle H = y_{\text{upper}} - y_{\text{lower}} = \frac{1}{x^2+1} - 0 = \frac{1}{x^2+1}$. Theus,



$
\begin{equation}
\begin{aligned}

V &= \int^3_0 c(x) H (x) dx
\\
\\
V &= \int^3_0 3(2 \pi x) \left( \frac{1}{x^2+1} \right) dx

\end{aligned}
\end{equation}
$



Let $u = x^2 + 1$, then

$du = 2x dx$

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



$
\begin{equation}
\begin{aligned}

V &= \pi \int^{(3)^2+1}_{(0)^2 +1} \frac{1}{u} du
\\
\\
V &= \pi \int^{10}_1 \frac{du}{u}
\\
\\
V &= \pi [ \ln u]^{10}_{1}
\\
\\
V &= \pi [\ln10-\ln1]
\\
\\
V &= \pi \ln(10) \text{ cubic units}

\end{aligned}
\end{equation}
$

Describe the characteristics of the English colonies in the Chesapeake region, the Carolinas, the Middle Colonies (Pennsylvania, New York, New Jersey, and Delaware), and New England prior to 1700.

The Chesapeake region was noted for its tobacco production. The region used slaves and indentured servitude prior to 1700; though by the end of the period, it was starting to phase out indentured servants and would use only slaves. The region was also known for malaria outbreaks in the fall that would periodically decimate the population of rich and poor alike. Successful plantation owners owned thousands of acres and many slaves in order to produce tobacco. The planters controlled the economy and political life of the region.
The Middle Colonies were noted for their diversity and large successful farms. Pennsylvania was established by Quakers and was tolerant of other religious groups; the region experienced an influx of German immigrants by the end of the period. New York City was noted for its trade. Its religious and cultural diversity were due to its being a Dutch colony at first. New York was one of the first places in the New World that welcomed Jewish immigrants. Though the colonies had slavery, they were not as dependent on them as the Chesapeake and Southern colonies.
The Carolinas produced indigo, rice, and tobacco, though cotton was starting to become important by the end of the period. The Carolinas used slavery due to a shortage of indentured servants and the fact that chattel slavery could be owned indefinitely along with their offspring. These colonies were also more sparsely populated than other colonies.
New England would be established by English families seeking freedom to practice their Calvinist religion away from persecution by the Church of England. Due to poor soil and cold climate, these people would turn to small farms, logging, whaling, fishing, and trade for their commerce. The English families had many children to support labor needs. The meetinghouse and the church were the most important buildings in the close-knit communities of New England. Though some had slaves, they were treated as luxury items, and slavery would end in this region before the American Revolution.

The New England colonies were colonies in which the economy depended mainly on manufacturing and trade. While there was some farming that occurred, it was mainly subsistence farming. The soil was rocky, and the climate was cooler than in other regions. Thus, the growing season was also shorter. With forests and rivers nearby, and with excellent ports, manufacturing and trade were important economic activities. Slavery existed, but it was in a limited fashion. Many Puritans lived in most of the New England colonies. While they freely practiced their religion, other religions weren’t tolerated. The only exception to this was in the colony of Rhode Island, which had religious toleration.
The middle colonies had a mixture of economic activity. Colonies such as New York and New Jersey had more manufacturing than farming. Colonies such as Pennsylvania and Delaware had more farming. The middle colonies were known as the breadbasket colonies because a lot of grain was grown there. There was religious tolerance throughout the middle colonies, especially in Pennsylvania and Delaware. The middle colonies had more slaves than the New England colonies had but fewer slaves than the southern colonies had.
The Chesapeake Colonies and the Carolinas had many slaves, as farming was very important in both places. The Chesapeake Colonies were known for growing tobacco while the Carolinas grew indigo, rice, and cotton. The climate in both regions was very suitable for farming. The climate was very mild. Additionally, the soil was very fertile. Slaves were used extensively in both regions to help with the farming. Most people in the southern colonies followed the teachings of the Church of England.

The economy of the Chesapeake, particularly Virginia, was based on agriculture, including the cultivation of tobacco and cotton, and the colony began importing slaves in 1619. A pyramidal social hierarchy developed in which white planters were at the top and white indentured servants and slaves were at the bottom. After Bacon's Rebellion in 1676, the white planters decided to increasingly rely on slavery rather than indentured servitude, given the restive class of white indentured servants who resented the rich elite. The system of slavery became increasingly harsh over time. The Carolinas were founded by settlers from Barbados and were involved in raising indigo, rice, cotton, and other crops. They brought with them a harsh form of slavery. Both the Chesapeake and the Carolinas were largely Anglican in religion.
The middle Colonies, particularly Pennsylvania (which was founded as a Quaker colony), and New York (founded originally by the Dutch, who permitted Jews and other religious minorities to enter), practiced religious tolerance. Their agriculture was based on cultivating crops such as wheat and other grains, and they had far fewer slaves than the deep south. 
The New England colonies were originally founded as theocracies and places for the Puritans, who faced persecution in England, to practice their religion freely. They were, however, largely intolerant of other religions, save in Rhode Island, a colony based on religious tolerance. The settlers arrived as families and lived in planned communities ruled by the church and the family. As the soil was rocky, New England had far fewer slaves than in the north and ran small industries, built ships, and ran small farms. The New England colonies emphasized the importance of literacy (to read the Bible) and had early forms of primary public schools. They also had some of the first colleges, including Harvard, founded in 1636. 

What happened when the war on the Eastern Front ended in World War I?

The decision by the Soviet Union to pull out of World War I was a decision that concerned the Allies. The Soviet Union signed the Treaty of Brest-Litovsk in 1918. The fighting against Germany in the Soviet Union would stop. The Soviet Union gave up a significant amount of land. Finland, Ukraine, and Georgia became independent. The Soviet Union gave Germany and Austria-Hungary land in Poland, Latvia, Lithuania, and Estonia.
This treaty also impacted the Allies. Since Russia was one of the Allied Powers, the departure of Russia from fighting in World War I allowed Germany to concentrate its fighting on the Western Front. Germany was able to move troops from the Eastern Front to the Western Front. This gave Germany a better chance of winning the war.
Fortunately, the United States had joined the war and helped the Allies. The Central Powers were eventually defeated, and the Treaty of Brest-Litovsk was nullified by the terms of the Versailles Treaty.
https://www.history.com/topics/world-war-i/treaties-of-brest-litovsk

https://www.historytoday.com/archive/months-past/treaty-brest-litovsk

Why do you think Maniac wants Grayson to talk about his past? Why do you think Grayson finally agrees to tell his story?

The text doesn't flat out say why Maniac is so interested in Grayson's past, so feel free to state what you think and support it. I think in general Maniac wants to hear about Grayson's past because Maniac is a nice, caring kid that likes to learn about other people. As Maniac learns about them, he finds ways to invest in them and help them. Grayson isn't the only character that Maniac does this with either. Piper, Russell, and Mars Bar all benefit from Maniac's investment in them. Maniac seems to naturally want to help people, and he can't help Grayson if Maniac doesn't know anything about him.
At the end of chapter 24, Maniac asks Grayson for a bedtime story, and Grayson claims that he doesn't know any stories. Maniac doesn't believe it and asks Grayson what he wanted to be when he grew up. Grayson answers, and that gives Maniac a little doorway into Grayson's past. The next chapter has Maniac pestering Grayson about his past baseball career.

After a story like that, Maniac couldn't just stay behind, so he tagged along when Grayson went back to work. He helped the old man raise a new fence around the children's petting farmyard.

I believe that Maniac is truly interested in the stories. I think Grayson initially tells about his past in order to appease Maniac or get Maniac to stop bugging him about it. I also think that Grayson is finally happy to be able to tell his stories to somebody that genuinely cares about the stories and him. It feels good for him to talk about the past.

Why does Rainsford choose to confront Zaroff in the end of "The Most Dangerous Game" rather than simply ambush him? What does this reveal about his personality?

There is no direct answer to this question, but using inference, we can speculate as to why Rainsford chooses his big finale at the end of the story.
Rainsford is prideful about hunting, which shows the control he holds over seemingly helpless animals. He knows he can outsmart and overpower them with his guns and years of experience. This hubris becomes apparent when he talks to Whitney about the concept of the hunter versus the huntee.
However, the power dynamic shifts when Rainsford arrives at Zaroff's home and is given a life or death proposition. Now Zaroff is the proud hunter in control and Rainsford is a helpless huntee, but Rainford doesn't let his nerves get the best of him and sets out to use his expertise against Zaroff.
Rainsford tries a few tricks in the jungle, but it's clear he's not fooling anyone. While his booby-traps do work to some extent, they don't work on Zaroff. Rainsford quickly realizes he is way in over his head. He needs to get on a level playing field with Zaroff, and he knows it won't happen in the jungle.
In the end, Rainsford waiting for Zaroff in his bedroom is the ultimate irony. Zaroff starts hunting humans because he wants to be outsmarted. He wants to hunt something that can challenge him, and Rainsford is literally everything he asks for. Zaroff gets what he wants.
However, Rainsford and Zaroff don't see eye to eye when the rules are laid out, and Rainsford realizes this could never be a fair match because Zaroff has his gun. Rainsford finally sees what Whitney was talking about. Irony reigns again. By waiting in Zaroff's bedroom, Rainsford is turning the tables back to his advantage, but he is also leveling the playing field. Rainsford is making them fight it out like animals in the wild removing the hunter/huntee paradigm. The best man, or animal, will win. There are no tricks and what would have been murder turns into self-defense. It could be conceivable that Rainsford's heart wouldn't let him kill a human the same way he would kill an animal. It seems the heart of the answer lies in the fact that Rainford's perspective on hunting changes when he becomes the huntee. Maybe it's his pride. Maybe it's his heart. Maybe it's simply his competitive nature oozing out of his angry body.
In the end, Rainsford's choices reveal he is a prideful, competitive man who is not one to give up easily. He fought for his life and refused to let Zaroff win. His competitive nature and steady hands show he is a strong, courageous person who would literally fight to the death if it meant keeping his life. However, his pride, just like Zaroff, got him into this mess in the first place. It seems it was pride that led him into the bedroom to stalk his prey and become the ultimate hunter.

That's a good question.  There isn't any textual evidence that directly tells readers why Rainsford doesn't simply shoot Zaroff in the back from a concealed location.  I think one possible reason is pride.  Rainsford wants Zaroff to know that he has been beaten.  Rainsford also wants Zaroff to know that Rainsford beat him.  If Rainsford took a sneaky shot at Zaroff, Zaroff wouldn't know that he had been beaten by Rainsford.  Zaroff would just be dead.  Rainsford is a popular hunter.  His skills have made him famous, and he still finds hunting normal animals thrilling. On the other hand, Zaroff pompously claims that he has grown bored with hunting the most dangerous animals in the world.  In a way, Zaroff seems to be claiming that he is a far better hunter than Rainsford because animals are not a challenge anymore.  By showing himself, Rainsford essentially says, "See, I knew you weren't better than me."  
Perhaps another reason has nothing to do with pride.  Perhaps Rainsford simply wants Zaroff to know what it feels like to be the prey.  Rainsford has been hunted to within an inch of his life, and nothing was fun about it.  Zaroff thinks it is great fun because he is not the one being hunted.  Rainsford's motivation might be just wanting Zaroff to feel what it's like to have the tables turned.  
A third possible reason deals with Rainsford's general character.  Rainsford is a reasonably moral man.  Zaroff presents a fairly logical explanation as to why hunting humans is acceptable.  Rainsford isn't even intrigued in the slightest.  He's appalled from the very beginning, and he calls Zaroff a murderer.  

"Hunting? Great Guns, General Zaroff, what you speak of is murder."

I think Rainsford's morality just won't let him shoot a man in the back.  That's why he confronts Zaroff instead of ambushing him.  

Single Variable Calculus, Chapter 7, 7.8, Section 7.8, Problem 56

Determine the $\displaystyle \lim_{x \to \infty} \left( 1+ \frac{a}{x} \right)^{bx}$. Use L'Hospital's Rule where appropriate. Use some Elementary method if posible. If L'Hospitals Rule doesn't apply. Explain why.

We can rewrite the limit as...
$\displaystyle \lim_{x \to \infty} \left( 1 + \frac{a}{x} \right) = \lim_{x \to \infty} \left( 1 + \frac{1}{\frac{x}{a}}\right)^{ba\left(\frac{x}{a} \right)}$
If we let $\displaystyle u = \frac{x}{a}$, then...


$\displaystyle \lim_{x \to \infty} \left( 1 + \frac{1}{u}\right)^{ba u} = \lim_{x \to \infty} \left[ \left( 1 + \frac{1}{u} \right)^u \right]^{ab}$

Recall that $\displaystyle \lim_{x \to \infty} \left( 1 + \frac{1}{x} \right)^x = e$

$
\begin{equation}
\begin{aligned}
\lim_{x \to \infty} \left[ \left( 1 + \frac{1}{u} \right)^u\right]^{ab} &= [e]^{ab}\\
\\
&= e^{ab}
\end{aligned}
\end{equation}
$

How does George Wilson represent that the Valley of Ashes is a place where citizens who can never achieve the American dream reside?

George Wilson is a hard working man trying to run his own business who can't get ahead because he is treated as a piece of trash by people like Tom Buchanan. Tom jerks him around and pretends to have a car to sell him so that he can have an excuse to come to and to telephone the garage—all so that he can make arrangements to sleep with George's wife. George might as well be part of ashes he lives near for all the humanity Tom assigns him.
People like George can't get out of the Valley of Ashes because men like Tom, with inherited wealth on their side, manipulate them. Tom not only sleeps with Myrtle under George's nose but he is able to manipulate George into killing Gatsby by convincing him that Gatsby was the one who ran over Myrtle.
The deck is stacked against men like George, who don't realize that the American Dream is not meant for people like them.

George Wilson is the perfect symbol for the downside of the American Dream. He runs a fairly unsuccessful garage in the Valley of Ashes, a place whose residents seem to be unable to get on in life, who only live there because they have no place else to go. George certainly can't keep his wife, Myrtle, in a style to which she wants to become accustomed, hence her affair with Tom Buchanan, which provides her with an entree into a world of wealth, glamour and opulence, one far removed from the general air of boredom and hopelessness in the Valley of Ashes.
Amid all the wild parties, the glamorous fashions and ostentatious displays of wealth, it's important to bear in mind when reading The Great Gatsby that far more Americans in the 1920s lived like George Wilson than Gatsby, Tom, or Daisy Buchanan. George and his neighborhood, the Valley of Ashes, represent the forgotten men and women of the American Dream in the Roaring Twenties –– ordinary, decent, hard-working people, generally anonymous and chronically unable to escape from a life of toil and thwarted ambition.

Discuss the motif of nature in Julio Cortazar's "Meeting."

In Meeting, the motif of nature highlights the themes of revolution and the transcending character of Luis/Fidel, one of the chief revolutionaries of the Cuban Revolution. The story begins with a quote from one of Che Guevara's works, in which the hero contemplates suicide as he leans against a tree trunk. Meeting itself is an appropriation of Che's retelling of Fidel Castro's independence war against Cuban president Fulgencio Batista, which culminated in 1959. 
The motif of nature is epitomized in the forbidding terrain of the Sierra Maestra mountain ranges, where Castro and Che make their last desperate stand against Batista. In late 1956, Che, Castro, and eighty revolutionaries had approached the Sierra Maestra mountains from the region of Playa Las Coloradas; however, they were ambushed by Batista's soldiers before they could get very far, and fewer than twenty of the revolutionaries survived. The survivors broke up into smaller groups and took refuge in the Sierra Maestra mountains. In Cortazar's story, Fidel/Luis is separated from Che (the narrator of the story) and some of the other surviving guerrillas. Che is worried because he does not know Luis/Fidel, Pablo, and Lucas's fate.
In the mountain region, Che tells us that he and his fellow revolutionaries have to contend with excruciating hunger, swampy terrain, and vermin. Nature becomes a nemesis, a symbol of the oppressive Batista regime. Meanwhile, the tree (another nature motif that is present at the beginning of the story) reappears later in the story. The narrator tells us that he has a vision about Luis/Fidel beside a tree, surrounded by his fellow revolutionaries. In the vision, Luis takes off his face as if it were a mask and bids his peers to put it on their own faces. One by one, the soldiers resist Luis's invitation to do so. The narrator, Che, then speculates what would happen to the guerrilla movement if Luis dies. 
He comes to the conclusion that all of them would continue the fight but that none of them could do it with Luis's "face." The tree against which Luis/Fidel leans in the midst of mountain terrain reinforces the image of Luis/Fidel as a god-like revolutionary figure. The Gautama Buddha himself was said to have attained enlightenment under the shade of the Bodhi tree. Here, the nature motif supports the theme of revolutionary fervor and Marxist enlightenment.
In the story, Cortazar views Luis/Fidel as a savior of sorts. The tree motif appears several times in the story. The narrator likens the war to Mozart's "death flourish" in the first movement of the Hunt quartet. He imagines that the rhythm of this "death flourish" intertwines with the branches of a tree; indeed, the rhythm becomes the tree itself, separating into branches and stems in a harmony of purpose. The narrator revels in the order of such a musical arrangement. It mimics the order that is in nature.
The narrator hopes that the war effort will usher in the same order, politically and socially. Historically, this doesn't happen; after the victories of the Cuban Revolution, Fidel Castro set himself up as a dictator in place of Batista. However, in the story, Cortazar highlights his own conversion to the Marxist revolutionary cause. In Cortazar's retelling of Che's narrative, Luis/Fidel is the messianic revolutionary figure. It is fitting that the tree motif appears again towards the end of the story. This time, Luis is leaning against the trunk of a tree as he and the narrator discuss the future and everything they have endured since they reached the Sierra Maestra mountain range.

What type of character is Mr. Thomas? Flat, Static, Round, Dynamic?

Mr. Thomas is a flat character in "The Destructors" by Graham Greene because he has only one or two personality traits, which are not altered in course of the narrative.
In this story that is set post-World War II, Mr. Thomas represents the older generation of Great Britain and its past tradition. His house stands alone in its neighborhood since the others have been destroyed during bombings. With its two-hundred-year-old spiraling staircase and wainscoting, this house is representative of the British upper class since it was designed by Sir Christopher Wren, the architect of the famous St. Paul's Cathedral.
When Trevor (T.) takes over as the leader of the gang, the group becomes nihilistic, finding destruction as their form of creation since they have lived around it. T. wants nothing to be left of the house; he believes the old order of Britain has failed and should be replaced. As the boys tear the house down from the interior, their act of destruction is creative because it is so cleverly done that the exterior remains standing until the lorry (truck) to which they have secretly tied the wooden struts pulls it down. When Mr. Thomas (Old Misery), who has been away on holiday, sees the end of his beautiful home he sobs. This sad, old snobbish man, in his powerlessness, now feels the terrible effects of the physical and moral destruction of war.

Why does Tree-ear suppose Min touched the clay with his eyes closed?

Tree-ear closely watches Min at work. As part of the process of making pottery, Min needs to drain the clay. This is because water needs to be mixed in with the clay and then poured through a sieve until all the pebbles and other impurities are removed. All of this takes a very long time, and this step must be repeated multiple times to achieve the right consistency of clay.
Tree-ear notices that when Min feels the clay, he closes his eyes. He supposes that this is because the right consistency of clay must be felt, rather than seen. Feeling the clay allows Min to appreciate the difference in the clay as it is poured through the sieve. As part of his apprenticeship in Min's workshop, Tree-ear tries to copy his master. But because Tree-ear is so inexperienced, it takes him quite a long time to get the process right.

How does Lysander fall in love with Hermia?

Egeus, Hermia's father, speaks to Theseus in act 1, scene 1, asking him to forbid Lysander to marry Hermia. According to Egeus, Hermia has fallen in love with this young man because Lysander bewitched her. Egeus outlines all the ways Lysander has wooed his daughter. Hermia says she considers Lysander, not her father, a god.
As for Lysander, we get much less of an explanation, though the many ways he has sought Hermia testify to a man besotted and lovesick. Lysander states of Hermia:

My love is more than his [Egeus's].

Lysander also implies he loves Hermia because she is "beauteous," or beautiful.
Helena offers more insights, saying that Lysander loves Hermia for her eyes, her voice, and her fairness. But she also notes that love is like an irrational child. It doesn't need a logical reason to love. Once a person decides to love someone, he or she turns all the beloved's features into beauties. Helena states:

Things base and vile, holding no quantity,
Love can transpose to form and dignity.
Love looks not with the eyes but with the mind.
And therefore is winged Cupid painted blind.
Nor hath Love’s mind of any judgment taste—
Wings and no eyes figure unheedy haste.

Lysander's largely unexplained love for Hermia thus perfectly fits the play's theme of love as a form of lunacy or madness, a way of being that is without rational basis.

Lysander and Hermia are in love before the play begins, so we do not get to see their courtship. But we can infer from what they say about each other that they are typical young people in love, drawn to each other by physical attraction and an idealized version of what the beloved one is.
They are suited to each other by class and status, which is what Lysander emphasizes in the beginning of the play when Hermia's father openly prefers Demetrius to him as Hermia's suitor, so, again, we can assume they had many opportunities to see and appreciate each other on social and court occasions.
Through the magical twists and turns of A Midsummer Night's Dream, we can believe that they are restored to what is perhaps a more mature love by the end of the play . . . unlike Helena and Demetrius, who are together only because the love potion was never removed from Demetrius's eyes.

y = 4x^2 , x = 0 , y =4 Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis.

We can use a shell method when a bounded region represented by a rectangular strip is parallel to the axis of revolution. It forms an infinite number of thin hollow pipes or “representative cylinders”.
 In this method, we follow the formula: V = int_a^b  (length * height * thickness)
or V = int_a^b 2pi* radius*height*thickness
For the bounded region, as shown on the attached image, the rectangular strip is parallel to x-axis (axis of rotation). We can let:
r=y
h =f(x) or h=x_2 - x_1
The x_2 will be based on the equation y =4x^2 rearranged into x= sqrt(y/4)  or x =sqrt(y)/2
h =sqrt(y)/2-0
h=sqrt(y)/2
For boundary values, we have y_1=0 to y_2=4 (based from the boundary line).
Plug-in the values:
 V = int_a^b 2pi*radius*height*thickness, we get:
V = int_0^4 2pi*y*sqrt(y)/2*dy
V = int_0^4 2pi*y*y^(1/2)/2*dy
V = int_0^4 piy^(3/2)dy
Apply basic integration property: intc*f(x) dx = c int f(x) dx.
V = pi int_0^4 y^(3/2)dy
Apply power rule for integration: int y^n dy= y^(n+1)/(n+1).
V = pi *(y^(3/2+1))/((3/2+1))|_0^4
V = pi *(y^(5/2))/((5/2))|_0^4
V = pi *y^(5/2)*2/5|_0^4
V = (2pi y^(5/2))/5|_0^4
Apply definite integration formula: int_a^b f(y) dy= F(b)-F(a) .
V = (2pi (4)^(5/2))/5-(2pi (0)^(5/2))/5
V = (64pi)/5 -0 V = (64pi)/5  or 40.21 (approximated value)

What is the relationship of a man and land as depicted in the story "How Much Land Does a Man Need?"

Land is depicted in the story as primarily a source of wealth. The grasping peasant, Pahom, becomes obsessed with the ownership of land and the wealth and social status it will bring. In the process, he loses sight of land as a place to call home, to set down roots. He no longer has the kind of mystical kinship to the soil advocated so strongly by Tolstoy. In his desire to acquire as much land as he can get his hands on, Pahom comes to regard the ground beneath his feet as an object, an economic commodity, something to be exploited for all it's worth.
The Bashkirs have a much healthier, more traditional attitude towards land, and so have no hesitation in allowing Pahom to take as much as he can traverse by foot in a single day. In their naivety they are wise, and Tolstoy insinuates that Pahom should adopt the same attitude. Sadly for him he does not, and in his headlong pursuit of landed wealth, Pahom loses not just his soul but also his life. How much land does a man need? Just enough to bury a coffin. Tragically, greed and materialism had taken over Pahom's life so completely that he was only able to reestablish his lost contact with the soil in death.

What is an example of the connection between sex and politics in the Roman Empire?

There is no more notorious example than that of Valeria Messalina, typically just called "Messalina," the third wife of Emperor Claudius. She, too, was of royal blood. She was the great grand-niece of the lauded Emperor Augustus and cousin to the notorious Emperors Nero and Caligula.
Messalina was rumored to have been so promiscuous that she held a competition with a prostitute at a Roman bordello. She wagered that she could manage to have sex all night, outlasting the prostitute. It is said that Messalina won the competition. 
Historians, now understanding the sexism that existed in Ancient Rome, suspect that Messalina, though probably adulterous, was probably not as promiscuous as historical records claim. She was a powerful woman who was directly and ruthlessly involved in politics, even causing her husband Claudius to condemn numerous senators to death. The reason for this is said to have been their refusal of her sexual advances, but one cannot be certain.
As is true today, when women assert their political power in ways that the patriarchy does not like, their characters are smeared or simplified by one transgression.
https://www.britannica.com/biography/Messalina-Valeria

College Algebra, Chapter 2, 2.5, Section 2.5, Problem 36

Suppose that the stopping distance $D$ of a car after the breaches have been applied varies directly as the square of the speed $s$. A certain car travelling at $\displaystyle 50 \frac{\text{mi}}{\text{h}}$ can stop in 240 ft. What is the maximum speed it can be travelling if it needs to stop in 160ft?

$
\begin{equation}
\begin{aligned}
D &= ks ^2 && \text{Model}\\
\\
240 \text{ft} \times \frac{1 \text{mile}}{5280 \text{ft}} &= k \left( 50 \frac{\text{mi}}{\text{h}} \right)^2 && \text{Substitute the given and convert ft into miles}\\
\\
\frac{1}{22} \text{mi} &= k \left(2500 \frac{\text{mi}^2}{\text{h}^2} \right) && \text{Simplify}\\
\\
k &= \frac{\frac{1}{22}\text{mi}}{2500 \frac{\text{mi}^2}{\text{h}^2}}\\
\\
k &= \frac{1}{55000} \frac{\text{h}^2}{\text{mi}}
\end{aligned}
\end{equation}
$


Then if,

$
\begin{equation}
\begin{aligned}
D &= 160 \text{ft},\\
\\
D &= ks^2\\
\\
160 \text{ft} \times \frac{1 \text{mile}}{5280 \text{ft}} &= \frac{1}{55000} \frac{\text{h}^2}{\text{mi}} (s^2) && \text{Solve for }s \\
\\
\frac{1}{33} \text{mi} &= \frac{1}{55000} \frac{\text{h}^2}{\text{mi}} (s^2)\\
\\
s^2 &= \frac{55000}{33} \frac{\text{mi}^2}{\text{h}^2} && \text{Take the square root}\\
\\
s &= \frac{50\sqrt{6}}{3} \frac{\text{mi}}{\text{h}}
\end{aligned}
\end{equation}
$


It shows that if the car needs to stop in 160ft. Its speed must be a maximum of $\displaystyle \frac{50\sqrt{6}}{3} \frac{\text{mi}}{\text{h}}$

Why did French Prime Minister Joseph Caillaux spend two years in prison during World War I?

Joseph Caillaux had served as Prime Minister of France for only seven months. Despite his short tenure of office, he proved to be a hugely controversial figure. In particular, he was strongly criticized for his pro-German foreign policy, which large sections of public and political opinion felt was not in the Republic's best interests. To make matters worse, it emerged that Caillaux had been conducting clandestine negotiations with the German government behind the back of Fallières, president of France. The ensuing scandal forced Caillaux from office.
Yet even after his resignation, Caillaux continued to be a figure of public controversy. When the First World War broke out, he was a leading advocate of a peaceful settlement with Germany. This earned him the undying hostility of many, who accused him of being, at best, a defeatist, and at worst, a traitor. In 1918, Caillaux was arrested and charged with high treason. After a lengthy delay he was sentenced to three years' imprisonment, but with time served he was released. He was also banished from French territory for five years and deprived of his civil rights for ten years.

Why was the theater closed in 1642?

The English Civil War had begun earlier in 1642, so many people began to feel going to the theater was purely frivolous at such a time. Further, the rise of Puritanism had already begun to chip away at theater attendance because Puritans considered such forms of entertainment to be corrupting influences. Puritans rose to power in the British Parliament in 1642, giving them the power to shut down all theaters. Puritans even began to demolish those theaters, just to be sure they could not be used. In the meantime, anyone caught going to a theatrical production could actually be fined. The war not only affected the theater, but it forever changed the way the English monarchy and Parliament would function.

What did the authors find in the second stage of the analysis when linking attitudes across these three groups (i.e., pro, mid, and con) to police use of force (i.e., coercion) behavior? Terrill, W., Pauline III, E. A., & Manning, P. K. (2003). POLICE CULTURE AND COERCION. Criminology, 41(4), 1003-1034.

Terrill, Pauline, and Manning found that there were some notable consistencies of thought across all three groups of police officers concerning use of force in policing. In the second stage of analysis, the authors established three distinct groupings of "pro," "mid," and "con" to distinguish attitudes among police officers regarding use of verbal and physical force when interacting with the public. The authors found all three groups had the highest agreement among the use of verbal force, while there were many variations of thought among groups regarding when it is acceptable to us physical for force when interacting with an individual.
The pro-culture groups were certainly the most willing to use verbal and physical force against an individual and also most closely aligned with a culture of policing in general. This finding by the authors certainly draws a correlation between the fundamental function and culture of police and the institution of policing and state violence, coercion, and oppression. Those who were more adamantly against using violent coercion and physical force against individuals were found to be less aligned with the general culture of policing and the police as a state institution.

The researchers created a three-level (trichotomized) set of attitudes in contrast to most previous analyses that had established a dichotomy between attitudes for and against traditional views of police culture. In addition to “pro” and “con,” they included those falling in the middle, or mid-range.
For the pro group, they concluded that the officers would be more likely to frequently display coercive authority through their behavior; such display could include aggression and the violation of citizen rights. The con-culture group had two clusters that had some variation in attitudinal intensity, views toward citizens, and to some extent, views toward their supervisors. Still, both clusters’ approach to policing was nonaggressive in that they did not support the crime-fighting role or violating citizens’ due process. The mid-range group, also having two clusters, did not reject an aggressive approach but favored its use on a selective basis. Overall, they had positive views of citizens and supervisors and toward following procedural guidelines.
Because "force" includes verbal commands, they found the highest amount of agreement among all three groups regarding approval of verbal force—over 30% in all groups. Regarding physical force, the pro and mid classification officers were very similar, with only the con group significantly different. Over 50% of officers associated the detainee's level of resistance with decisions to use force. There was consistency among different police departments, with differences often pertaining to the number of officers present on scene.
https://www.researchgate.net/publication/227617486_Police_Culture_and_Coercion

In the second stage of the analysis, the authors looked at whether there was empirical evidence to back up the contrast in attitudes among the three groups of police officers (pro, meaning those officers who were favorable toward traditional police culture), mid (meaning those officers who were in the middle), and con (meaning those officers who were negative toward traditional police culture). After conducting an ANOVA analysis, the authors found that the means of Cluster 1 of the con group differed significantly with the clusters of the pro-group for 7 out of the 10 attitudinal dimensions when compared to Cluster 3, 7 out of the 10 dimensions when compared to Cluster 5, and 5 out of the 10 dimensions when compared to Cluster 7. Cluster 6 of the con group differed from the three pro-groups in eight out of ten dimensions. The authors found that clusters from the mid-group shared attitudes with both the con and pro-groups. You can find the results on page 1017 of the research study.
The authors found that the officers in the pro-culture group most closely agreed with elements of traditional police culture, including distrust of citizens, aggressive policing techniques, and selective law enforcement, while the con group contained two clusters that held the opposite views (trust of citizens, less aggressive techniques, and protection of due process rights). The mid group endorsed views that were in the middle. You might consider the meaning of the evidence the authors found—that there are significant differences in the attitudes of these three groups of officers. 

Precalculus, Chapter 1, Review Exercises, Section Review Exercises, Problem 36

Determine the equation of the line perpendicular to the line $3x - y = -4$ and containing the point $(-2,4)$. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer.

We know that if the two lines are perpendicular, the product of their slopes is $-1$. We write the equation $3x - y = -4$ in slope intercept form to find the slope.


$
\begin{equation}
\begin{aligned}

3x - y =& -4
\\
-y =& -3x - 4
\\
y =& 3x + 4

\end{aligned}
\end{equation}
$


The slope is $3$. The slope of the other line is $\displaystyle \frac{-1}{3}$.

Using Point Slope Form,


$
\begin{equation}
\begin{aligned}

y - y_1 =& m (x - x_1)
&&
\\
\\
y - 4 =& \frac{-1}{3} [x - (-2)]
&& \text{Substitute } m = \frac{-1}{3}, x = -2 \text{ and } y = 4
\\
\\
y =& \frac{-1}{3}x - \frac{2}{3} + 4
&& \text{Simplify}
\\
y =& \frac{-1}{3}x + \frac{10}{3}
&& \text{Slope Intercept Form}
\\
x + 3y =& 10
&& \text{General Form}

\end{aligned}
\end{equation}
$

How could the third estate lower high taxes?

The reason the Third Estate faced high taxes was that they lacked the legal privileges that the First and Second Estate had under the Bourbon monarchy. The clergy and the nobility were essentially exempt from most taxes. So in order to reduce the tax burden on themselves, the people of the Third Estate needed to enact taxes on the other two estates. A series of ministers under Louis XVI had attempted to make this happen, but these efforts were consistently voted down by the ultra-conservative Parlement of Paris, which was dominated by nobles. When the fiscal crisis of 1789 forced Louis to summon the Estates-General, a meeting of representatives from each of the three estates, the Third Estate delegates realized that their efforts to enact more equitable taxation would be defeated. This is why they formed the National Assembly and forced (aided by the constant threat of crowd violence) Louis to accept a series of reforms establishing a constitutional monarchy. Key to those reforms was the elimination of tax privileges that favored the nobility and the clergy. So as it turned out, the only way to establish more equitable taxation was through a fundamental alteration of the social and political order in France. This alteration marked the outbreak of the French Revolution, one of the most cataclysmic events in Western history.
https://www.history.com/topics/france/french-revolution

In "Young Goodman Brown," what accessory does Goodman Brown's wife wear?

Young Goodman Brown's wife, Faith, wears "pink ribbons [in] her cap," and because they are mentioned so many times throughout the story, this is a clue that they have some symbolic significance. They are mentioned in the very first paragraph when Faith is introduced. Soon after, Faith blesses her husband as he's about to go off into the woods, and she is described as having her "pink ribbons." After Goodman Brown has left home,

he looked back and saw the head of Faith still peeping after him, with a melancholy air, in spite of her pink ribbons.

As Brown travels deeper and deeper into the woods, he thinks that he hears his wife's voice, "uttering lamentations." He panics and lets out a "cry of grief, rage, and terror," spotting a "pink ribbon" which is "caught on the branch of a tree." The fifth and final reference to the pink ribbons occurs after Brown has returned home and "he spied the head of Faith, with the pink ribbons, gazing anxiously forth [...]."
Given the ribbons' color—pink—they seem representative of a lack of maturity, of innocence. This interpretation fits with her name and personality as well: "faith" seems to imply grace, innocence, optimism. These are all things that Brown seems to associate with his wife, and so finding her ribbon in the forest seems to signify a loss of both innocence and Brown's Faith, both in terms of his wife and in terms of his Christian faith. By the time he returns to town, he's become "A stern, a sad, a darkly meditative, a distrustful, if not a desperate man [...]." For the remainder of his life, "he shrank from the bosom of Faith."

Describe the settlements in the Carolinas. What were the differences between the Carolinas and the Chesapeake?

In the seventeenth century there were essentially two major settlements in the Carolinas, which were granted by King Charles II to a group of eight noblemen known as the "Lords Proprietors" between 1663 and 1665. In the beginning, there was actually no North and South Carolina—the colony was simply known as "Carolina." The two settlements mentioned earlier were Charles Town in the modern South Carolina Low Country and the Albemarle region in northeastern North Carolina. Charles Town has been described as a "colony of a colony" because it was founded by settlers from the sugar island of Barbados. These settlers came because of land pressure on that small island, and, finding the region unsuitable for sugar cultivation, they began to trade in Indian slaves, which they sent to Barbados and other places throughout the British colonies. This trade was eventually replaced as a major source of income by rice, which was grown on massive plantations throughout the Low Country. South Carolina planters imported African slaves to cultivate the plant, and so, to an even greater degree than the Chesapeake, South Carolina became a slave society. As for early North Carolina, the first settlers in the Albemarle region were from Virginia. Most were religious dissenters and former indentured servants who sought to escape the increasingly stratified society in Virginia. Over time, more settlers came, even settling further west and southward, in modern-day New Bern. Conflict with Native peoples led to the Tuscarora War, which opened the interior for settlement in the second decade of the eighteenth century, but the colony really only took off in terms of population with the settlement of thousands of Scots-Irish people and Germans from Pennsylvania and Virginia. Over time, the northeast of North Carolina came to resemble the Chesapeake, with planters cultivating tobacco with slave labor. The area around Wilmington resembled the Low Country, with some rice plantations along with indigo, "Sea Island" cotton, and naval stores. Overall, North Carolina's plantation economy, along with the social stratification that accompanied it in South Carolina and Virginia, remained only modestly developed in the years leading up to the Revolution.
https://www.ncpedia.org/lords-proprietors

Calculus of a Single Variable, Chapter 7, 7.3, Section 7.3, Problem 19

We can use a shell method when a bounded region represented by rectangular strip is parallel to the axis of revolution. It forms of infinite number of thin hollow pipes or “representative cylinders”.
In this method, we follow the formula: V = int_a^b (length * height * thickness)
or V = int_a^b 2pi* radius*height*thickness
For the bounded region, as shown on the attached image, the rectangular strip is parallel to x-axis (axis of rotation). We can let:
r=y
h =f(x) or h=x_2 - x_1
The x_1 will be based from the boundary line x=0.
The x_2 will be base on the equation y =x^3 rearranged into x= root(3)(y)
h = root(3)(y)-0
h=root(3)(y)
For boundary values, we have y_1=0 to y_2=8 (based from the boundary line).
Plug-in the values on
V = int_a^b 2pi *radius*height*thickness, , we get:
V =int_0^8 2pi y*root(3)y*dy
Apply basic integration property: intc*f(x) dx = c int f(x) dx.
V = 2pi int_0^8 y* root(3)(y)dy
Apply Law of Exponent: root(n)(y^m)=y^(m/n) then root(n)(y)= y^(1/3)and y^n*y^m = y^(n+m)
V = 2pi int_0^8 y y^(1/3)dy
V = 2pi int_0^8 y^(1/3+1)dy
V = 2pi int_0^8 y^(4/3)dy
Apply power rule for integration: int y^n dy= y^(n+1)/(n+1).
V = 2pi y^(4/3+1)/(4/3+1) |_0^8
V = 2pi y^(7/3)/(7/3) |_0^8
V = 2pi y^(7/3)*(3/7) |_0^8
V = (6pi y^(7/3))/7 |_0^8
Apply definite integration formula: int_a^b f(y) dy= F(b)-F(a).
V = (6pi (8)^(7/3))/7 -(6pi (0)^(4/3))/7
V =(768pi)/7-0
V =(768pi)/7 or 344.68 (approximated value).

How is language being used in a figurative manner in the poem "They Flee from Me" by Sir Thomas Wyatt?

The most obvious metaphor that governs the poem "They Flee from Me" by Thomas Wyatt is the comparison of women (or lovers) to animals, and perhaps more specifically to deer.  In this unrequited love poem, the speaker--obviously a male--describes how women who formerly slept with him willingly now run away from him, much like deer who venture close to a human bearing food and later flee.  Here taking bread becomes a euphemism for sex.  Words such as "gentle," "tame," "meek", "wild," "range," apply both to women and to deer.  
The first stanza speaks of women (or deer) in the plural, but the second clarifies  the fact that this poem is really about one specific lover.  Here we have sultry imagery describing the woman who initiates the relationship with the speaker.  

When her loose gown from her shoulders did fall,
And she caught in her arms long and small . . .

She asks the speaker "Dear heart, how like you this?" The words "dear" and  "heart" are particularly effective here because they serve as puns.  "Dear" and "heart" are homophones for "deer" and "hart," respectively.  These puns reinforce the deer metaphor and tie the woman's seduction of the speaker to the first stanza by giving a specific example of how he was "stalk[ed]." Somewhat ironically, it is the woman who is the aggressor, the stalker, while the man is her willing victim.
In the last stanza, specific word choices indicate the woman's rejection of the speaker and his resulting bitterness.  His "gentleness" is now unappreciated.  She has moved on to "newfangledness," quite possibly suggesting new lovers. The word "kindly" is ironic in referring to how he feels she has treated him, and the speaker closes with wondering what she now deserves.  

College Algebra, Chapter 2, 2.3, Section 2.3, Problem 60

Find the solutions of the inequality $0.5x^2 + 0.875 x \leq 0.25$ by drawing appropriate graphs. State each answer correct to two decimal places.


Based from the graph, the solutions are approximately
$\displaystyle -2 \leq x \leq \frac{1}{4}$

By using algebra,

$
\begin{equation}
\begin{aligned}
0.5 x^2 + 0.875x &\leq 0.25 \\
\\
0.5x^2 + 0.875 x - 0.25 &\leq 0 && \text{Subtract } 0.25\\
\\
x^2 + \frac{7}{4}x - \frac{1}{2} &\leq 0 && \text{Divide both sides by } 0.5\\
\\
(x+2) \left( x - \frac{1}{4} \right) &\leq 0 && \text{Factor out}

\end{aligned}
\end{equation}
$


The factors on the left hand side are $x+2$ and $x - \frac{1}{4}$. These factors are zero when $x$ is -2 and $\frac{1}{4}$, respectively. These factors divide the number line into intervals.
$(-\infty, -2]\left[ -2, \frac{1}{4} \right]\left[ \frac{1}{4}, \infty \right)$
Let's test the numbers at the intervals,



Thus, the solution set is...
$\displaystyle -2 \leq x \leq \frac{1}{4}$

Calculus of a Single Variable, Chapter 2, 2.2, Section 2.2, Problem 61

We will need to take the derivative of the function and set the derivative equal to zero.
y' = 1+cos(x)
0 = 1+cos(x)
cos(x)= -1
The value of x is the angle where we have a point on the unit circle with an x coordinate value of -1.
The domain given exists from [0,2 pi) .
The only value that the unit circle will have a (-1,0) point is when the angle is pi radians, or 180 degrees.
We can work our way backward and find that in both radians and degrees ,respectively:
cos(pi)=cos(180) = -1
Therefore, the value of x in radians where we have a slope of zero is:
x=pi
Substitute this angle back to the original function to find the point.
y=x+sin(x)
y=pi+sin(pi)
The value of sine at pi radians or 180 degrees is 0.
y=pi+0= pi
The exact point existent on the given domain would be:
(pi,pi)

Explain the various kinds of research that scientists do to answer a question or solve a problem.

Research, broadly speaking, is the process of gathering and analyzing data to answer problems, understand a concept, or discover something. It is something done that can solve an existing problem, understand and explore an idea, and/or make arguments grounded on facts. In science and scientific research, there are two broad categories: applied or basic.
Basic research refers to the kind of research that primarily aims to understand a concept. It involves experimentation and analysis of data obtained from experiments involving the understanding of mechanism and working of certain things. For instance, understanding the mechanism by which DNA is replicated is considered basic research - or basic science. In short, it aims to understand the fundamentals of a discipline.
Applied research refers to the kind of research that has direct effects to human life. The main thrust of applied research is the progress and development of technologies that will make life easier. For instance, drug discovery researches and research involving engineering are considered research.
In brief, basic research contributed to the increase of knowledge, while applied research aims to solve a given problem. These research categories, however, are in no way exclusive. Most scientists are involved in both. Understanding how two proteins interact with each other is considered a basic form of research. Creating drugs that will interfere with these two proteins - like those involved in cancer - can be considered applied research as it solves the problem of cancer. It can also be referred to as translational research - bridging the basic sciences and the applied sciences.
Aside from these broad categories, research can be qualitative or quantitative. Qualitative research is descriptive and aims to explain things, while quantitative aims to quantify something. For instance, qualitative basic research can include understanding and describing the interaction between proteins, while quantitative basic research could be quantifying the strength of these interactions, or for instance, quantifying how much of a drug would have enough of an effect to disrupt these interactions. In a clinical research, another broad type of research that may be classified as applied research, qualitative would simply be looking at the relationship between two factors - i.e. exercising more increases brain activity - and quantitative would be measuring the magnitude of these effects, and using statistical tools to describe them.
---In summary,
To solve a problem, scientists do applied research. Drug discovery is a form of applied research as one tried to treat or cure a diseases. Most engineering researches are also applied researches as one tries to develop and improve existing technology. To answer questions and understand the fundamental principles underlying certain concepts, scientists do basic science. Identifying and understanding proteins involved in a disease is a kind of question a basic scientist answers. In general, these do fields often intersect with each other as the fundamental understanding of nature will often result to a technology that betters human life - or a problem usually warrants understanding of a basic concept.
https://documents.uow.edu.au/content/groups/public/@web/@commerce/documents/doc/uow012042.pdf

sum_(n=0)^oo (2n)!(x/3)^n Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval.)

For the power series sum_(n=0)^oo (2n)!(x/3)^n , we may apply Ratio Test.
In Ratio test, we determine the limit as:
lim_(n-gtoo)|a_(n+1)/a_n| = L
or
lim_(n-gtoo)|a_(n+1)*1/a_n| = L
 Then ,we follow the conditions:
a) L lt1 then the series converges absolutely.
b) Lgt1 then the series diverges.
c) L=1 or does not exist  then the test is inconclusive.The series may be divergent, conditionally convergent, or absolutely convergent.
The given power series sum_(n=0)^oo (2n)!(x/3)^n has:
a_n =(2n)!(x/3)^n
Then,
1/a_n=1/((2n)!)(3/x)^n
      =1/((2n)!)(3^n/x^n)
      =3^n/((2n)!x^n)
a_(n+1) =(2(n+1))!(x/3)^(n+1)
            = (2n+2)!x^(n+1)/3^(n+1)
            = (2n+2)(2n+1)((2n)!) x^n*x/(3^n*3)
             =((2n+2)(2n+1)((2n)!) * x^n*x)/(3^n*3)
Applying the Ratio test on the power series, we set-up the limit as:
lim_(n-gtoo) |((2n+2)(2n+1)((2n)!) * x^n*x)/(3^n*3)3^n/((2n)!x^n)|
Cancel out common factors: x^n , (2n)! , and 3^n .
lim_(n-gtoo) |((2n+2)(2n+1)*x)/3|
Evaluate the limit.
lim_(n-gtoo) |((2n+2)(2n+1)*x)/3| = |x/3|lim_(n-gtoo) |(2n+2)(2n+1)|
                                            = |x/3|* oo
                                            = oo
The limit value L= oo satisfies Lgt 1 for all x . 
Therefore,  the power series sum_(n=0)^oo (2n)!(x/3)^n diverges for all x based from the Ratio test criteria:  Lgt1 then the series diverges.
There is no interval for convergence.
Note: The radius of convergence is 0 . The x=0 satisfy the convergence at points where (2n)!(x/3)^n=0 .

Could any of the characters in The Crucible have done more to end the hysteria in Salem?

Reverend Hale could certainly have done a lot more to end the hysteria. As both a man of God and an expert in witchcraft he should've been able to see straight away that there was no foundation to Abigail Williams' lies and false accusations. Although he did intervene to try and halt the court proceedings, by that time it was too late. The hysteria had already got completely out of control and no one was in a position to stop it, no matter how hard they tried.
Danforth, as the most senior judge in the Salem witch trials, could've put a stop to the hysteria early on by ruling that there was insufficient evidence to determine that anyone was guilty of witchcraft. But for largely selfish reasons he chose not to. An incredibly vain man, he was so puffed up by the enormous power and prestige that the trial brought him, so enamored of being the center of attention, that he wanted the proceedings to continue for as long as possible. Instead of trying to get at the truth and deliver justice for the accused Danforth abused his authority, his exalted position as judge to send innocent people to their deaths.

Abigail Williams could have brought the hysteria to an end; after all, she is the one who started it by threatening the other girls into silence and perpetuating it by implicating more and more people for her own selfish motives.
Mary Warren and the other girls could have come clean to the Salem authorities and informed them of Abigail's threats. If they had presented a united front against her instead of shrinking in fear, lives could have been saved.
If he had behaved as a leader of his congregation instead of becoming preoccupied about holding onto his job, Reverend Parris could have saved lives. His willful blindness about Abigail's machinations and his own daughter's involvement in witchcraft, as well as his eagerness to take down political enemies like the Nurses, Coreys, and Proctors, prevents him from putting a stop to the hysteria.
Hathorne and Danforth, as the magistrates with the power to levy judgment and punishment, could have suspended the trials until more investigation was conducted. By allowing spectral evidence and not looking more closely at the accusers and their possible motivations, the two magistrates are ultimately responsible for letting the hysteria destroy a community.

There are several characters who play a significant role in the spread of hysteria and other characters with important information that could have ended the witchcraft hysteria in Salem. One could argue that John Proctor's hesitance to reveal Abigail Williams's true nature results in the spread of hysteria and the arrest of numerous innocent citizens. In act 2, John's wife urges him to travel to Salem immediately and expose Abigail. However, Proctor hesitates because he does not want to ruin his reputation and has a hard time believing that the citizens actually trust the young girls in court.
Mary Warren is another character who knew that Abigail was lying. Instead of telling the authorities about Abigail's malevolent intentions, Mary Warren ends up following Abigail's orders and adds to the hysteria.
Reverend Hale is another character who could have stopped the spread of hysteria but quickly assumed that the accusations were true instead of immediately examining the characters of Abigail and her followers. Instead of questioning the source of the accusations, Reverend Hale initially believes that the girls are not lying and becomes suspicious of the citizens accused of witchcraft.

Many of the named characters in the play The Crucible are based upon actual historical records and people who were actually involved in the events portrayed. Certainly, any number of these people could have acted in ways to shift the course of events. For example, Abigail Williams could have chosen not to spread lies or to manipulate the other girls into following her lead. Justice Danforth could have chosen not to believe the girls' fantastical stories (referred to in court proceedings as "spectral evidence") over the accused. The Reverend Hale could have chosen to remain involved in the trials, instead of walking away in frustration; his attempts to be a voice of reason put him at odds with the judges and court magistrates, who had various political reasons for wanting rebellious people like John Proctor to be silenced.
Any number of townspeople could have refused to believe the accusations of witchcraft, instead of being willing to believe that witchcraft was behind any number of occurrences, from Betty Parris' strange afflictions, to the other things described (cows' milk drying up, children falling ill, etc.). Being able to accuse others of witchcraft effectively meant that community members could bring about the ostracization and ruination of their neighbors without ample evidence or proof, because the environment was so superstitious and supportive of these witchcraft rumors.

What are examples of things that hinder interaction among groups?

There are many different ways to classify people into "groups." You can, for instance, separate people by gender, by religion, by race, or by a number of other different subsets or preferences, such as "does the person like vegetables?"
Once people are separated into different groups, they often tend to stay within that group for reasons such as lack of conflict and having things in common. If you love a TV show, and you have a group of friends who also love that TV show, what reason do you have to try to separate?
Similarly, many people choose to remain in cohorts of their biology. Many people choose to befriend people of similar races, genders, hair colors, ages, etc. This is associative, because people assume that people who look the same will, in some facet, also behave the same. By remaining with people who are like you, you will limit potential conflicts of interest.
The issue there is that you will never grow. Meeting and learning about other groups of people is a valuable piece of education that gives you incredible human qualities such as empathy and understanding. If you are of one religion, you will likely be attracted to others who also practice that religion. But if you only talk to people in your religion, you will never learn about other religions and other beliefs.
There is a difference between trying to convert people of other groups, and interacting with people of other groups. If you are a female and you only communicate with males in order to convince them that females are the best, you have not developed a meaningful relationship outside of your group. However, if you try to learn from your male friend about his experiences in life and how they differ from yours as a female, you will become a more wholesome individual.
Many people are afraid of being "wrong," or of having a difference of opinion with another person. That is why groups do not often attempt to extend their hands to people of other groups. However, if you make the effort to become a more educated person by learning about the experiences of other people with other opinions, you will grow as a person considerably more than you would if you limited yourself to being surrounded by people who are exactly like you.

History provides several examples of factors that may hinder or delay interaction between groups of people. One example that is becoming less and less of a factor in our modern day and age is geographical features such as oceans, mountains, and deserts. Historically, these features created natural boundaries, as it was difficult for people without sufficient technology to move across or through them. These boundaries often led to the creation of significantly different cultures on either side of them.
In some cases, this happened even when there was little actual distance between the groups. For example, while Japan is now a unified country, it was once made up of dozens of independent fiefs, each with their own unique attributes, because of the many mountains and bodies of water breaking up the Japanese islands. Similarly, the cultures on either side of the Himalayas are measurably distinct, despite having relatively little mileage between them. 
However, with the rise of the internet and other tools of globalization, these physical boundaries are less and less of a barrier to interaction. It is now possible for someone to communicate not only with a person on the other side of the mountains, but on the other side of the world. Now, barriers to interaction tend to be more cultural, such as language or political differences. 

In The Cay by Theodore Taylor, what is the Germans' motivation for blowing up the oil tankers?

At the beginning of The Cay, Phillip is on the island of Curacao, a Dutch island off Venezuela. In early 1942, Germans blow up the oil refinery on Aruba, the neighboring island. Then they blow up six tankers that bring oil to the refinery on Curacao (page 10). The oil is used to make kerosene, diesel, and gasoline. German subs really did destroy the Lagos oil refinery in Aruba in 1942 because this oil refinery was used to fuel Allied ships. By blowing it up, the Germans hoped to disrupt Allied shipping in the Caribbean. The Germans also actually blew up oil tankers in the region (see the link below) with the same goal of disrupting Allied shipping in the area. Later, Phillip is on a British tanker that is sadly torpedoed by a German submarine. 
https://willemsubmerged.wordpress.com/2009/01/13/pedernales-the-phoenix-of-aruba/

Who was Thomas Hobbes?

Thomas Hobbes of Malmesbury (1588 – 1679) was an English political philosopher. He is distinguished by an attitude of rationalism and materialism. He thinks that most human and natural phenomena can be explained rationally and scientifically.
Although Hobbes was a prolific author who wrote treatises on many different subjects, including physics, optics, and rhetoric, his most influential work was the Leviathan, a work that set forth the seminal "social contract" theory of government authority. This theory argues that people cede a degree of personal liberty to governments in exchange for safety and security. 
Hobbes famously stated that life in a state of nature was "solitary, poor, nasty, brutish and short" and that the natural state of humanity was perpetual war. He thus advocated strong, even authoritarian, government, as necessary to restrain the naturally chaotic and selfish impulses of humanity. 

College Algebra, Chapter 1, 1.2, Section 1.2, Problem 6

Find formulas for $r$ and $t$, suppose that $d = rt$.

if $d = rt$, then


$
\begin{array}{cccccc}
\text{if} & d = rt, & \text{then} & \text{if} & d = rt, & \text{then} \\
& d = rt & \text{divide $t$ on both sides of the equation } & & d = rt & \text{divide $r$ on both sides} \\
& \displaystyle \frac{d}{dt} = \frac{r \cancel{t}}{\cancel{t}} & \text{solve for } r & & \displaystyle \frac{d}{r} = \frac{\cancel{r} t}{\cancel{r}} & \text{solve for } t \\
& \displaystyle r = \frac{d}{y} & & & \displaystyle t = \frac{d}{r} &
\end{array}
$

Why do Rebecca Nurse and Giles Corey's fates affect John Proctor powerfully?

John Proctor has a lot of respect, admiration, and liking for both Rebecca Nurse and Giles Corey. They all share varying degrees of dislike for Reverend Parris and are initially suspicious that the girls are behaving disingenuously when they make their accusations.
When Rebecca Nurse chooses execution instead of giving a false confession to save her life, John admires her deep faith and personal integrity. Rebecca will not commit the sin of lying or turning her back on her religion because she cares more about her eternal life than her earthly one. When John is considering a false confession to save his own life, he ultimately finds he cannot do it, but he refuses to think of himself as being on the same moral plane as her. He knows he is flawed, while he sees no fault in her.  
John's feelings about Giles Corey are similar. Giles will neither enter a plea nor give up the name of the person who heard Putnam tell his daughter to accuse George Jacobs because Giles believes that to do so would lend credibility or legitimacy to the trials. By remaining silent he takes a moral stand, and like Rebecca, Giles will not give a false confession to save himself from execution.
Though he is younger than them and has two children and a pregnant wife, John's ultimate decision is to emulate their behavior, perhaps finding in it some personal redemption.  

In the 19th century, how was women's mental illness viewed by society?

In the 19th century, women's mental illness was not considered a serious issue, as Charlotte Perkins Gilman's "The Yellow Wallpaper" demonstrates. Doctors, rather than analyzing female patients' mental symptoms, simply prescribed a "rest cure." Like the narrator in Gilman's story, women were expected to heal, simply by resting. As the story reveals, however, the cure could prove far more detrimental than beneficial, and it is no coincidence that Gilman's narrator goes mad.
Gilman explains her motivation for penning the short story in her expository text, "Why I Wrote the Yellow Wallpaper." In it, she explains that the account is based largely on personal experience. "I went home and obeyed [the rest cure] for three months," she writes, "and came so near the borderline of utter mental ruin that I could see over."
Hence, she wrote the story largely to spread awareness about the true results of the rest cure. Moreover, after reading "The Yellow Wallpaper," her physician ceased prescribing the treatment.

How has The BFG's life changed by the end of the novel?

The BFG tells Sophie early in the novel that he has been around for so long that he does not remember how he came to be.  He guesses that he simply appeared around the same time that the earth was created.  We learn at the beginning of the novel that his life has been the same for a very long time; he catches dreams, eats disgusting snozzcumbers, and watches glumly as the other giants go off to kidnap and gobble up local children.  He seems somewhat lonely and not particularly happy, but it has been this way for so long that he doesn't seem to be able to imagine any other way of life.
However, things start to change when Sophie enters his life.  She introduces him to new ideas and makes him realize that his life could actually be better.  These changes start out small.  When The BFG tells Sophie how much he hates eating snozzcumbers, she asks him if he really NEEDS to eat it.  He replies, "You do unless you is wanting to become so thin you will be disappearing into a thick ear."  He seems to believe that snozzcumbers are literally the only alternative to eating "human beans".  Sophie opens his eyes, though, by telling him, "We don't have to eat snozzcumbers.  In the fields around our village there are all sorts of lovely vegetables like cauliflowers and carrots."  
These changes become more dramatic when Sophie decides that they simply must do something to stop the giants from guzzling up children.  The BFG has never let a human being see him before because he was convinced that they would lock him away or hurt him, but Sophie convinces him to walk right up to the Queen's window and introduce himself.  She also convinces him to stand up to the other giants, which is something he has always been too afraid to do on his own.  
By the end of the book, The BFG has completely embraced an entirely new way of life.  He is considered a hero by many leaders of foreign countries - is even given an elephant, his most precious desire, by the Ruler of India!  The Queen of England has built him a house fit for a giant right next to her castle, and a small cottage right next door for Sophie.  The BFG even learns how to read and write, and we find out at the end of the novel that he is actually the author of the novel itself!  Nearly everything about The BFG's life has changed, and it appears that he will continue living a very happy life for a very long time. 

Use your ideas about factors that affect thinking, decision making, and memory to draw conclusions about cognition and what it means to be a person. Include brain-based factors.

There are several brain-based factors that influence the way we make decisions and think about things. Scientists have begun to isolate brain areas involved in different types of decisions using patients who have suffered injuries to one section of their brains. For example, scientists have found that the front part of the frontal lobe is involved in decisions that involve abstract reasoning, as this region of the brain controls planning, organization, and the so-called "executive functions" (the ability to decide on and execute a task). Decisions that involve concrete reasoning involve the back of the frontal lobe. Other decisions that involve integrating visual information are processed through the parietal lobe, which processes sensory information. When part of the brain is involved in a decision, it shows increased activity in the neurons in that region. Memory is processed in an area of the brain called the limbic system, which includes the amygdala, hippocampus, and other structures. Damage to the hippocampus, for example, can result in anterograde amnesia, or the inability of people to form new memories.
This means that cognition and many of the qualities we associate with being human are, in reality, based on the firing of neurons in different parts of the brain. The sense we make of these cognitive functions is in part what makes us human and adds to our individuality.
https://human-memory.net/parts-of-the-brain/

How does The City of Ember meet requirements of a dystopia?

The City of Ember, written by Jeanne DuPrau, illustrates a dystopian society. This is done by DuPrau's use of setting, situations, and character mentality. The setting takes place underground. The power grid and food supply are constantly questioned. The lights flicker and often and blackouts are common. This is dystopic because everyone lives in fear that the power will eventually go out for good. The food supply has dwindled over the years, with certain foods becoming nonexistent. This reduction and loss of food leave characters in fear as well.
Many of the situations depicted in the novel can also be defined as dystopian. No one is able to exert free will when it comes to their occupation. Jobs are drawn from a hat on the last day of school. The outside of the town is considered off-limits, yet some people go there to seek out a better life. Some of those who leave come back insane, which is another reason that inspires fear. Lastly, the timeline for the city is only two hundred years. The city has been going for 240 years, and the population is fearful that the end could come at any time.
One final example of the novel's dystopian characterization is the fear the characters live in. In one event, Doon finds that the mayor has been hoarding and eating the limited food supply. Doon and Lina (the main protagonists) try to warn the other characters about this, and they are threatened by the mayor with their lives.
Most poignantly, the characters live in actual darkness, both physically and mentally—living in fear that the city they reside in may go dark at any time and not knowing they reside in an underground city meant as a way to escape impending doom (it is not told what this disaster is), instead of a city meant to sustain life for generations on end.

What are two things that happen when Victor is out to sea?

After Victor has traveled the British Isles with his friend, Henry Clerval, for some months, he goes off by himself, having decided to occupy a remote island on which to make the female creature he has promised to his original creation.  As he labors, he finds himself repulsed by the work he does to make this female.  Upon reconsidering his promise to his creature, Victor destroys the female, and the creature then threatens to be with Victor on his wedding night since Victor has determined to deprive him of a female companion of his own. 
Before Victor can go to rejoin Henry, he sets out in a small boat, going about four miles from shore.  In the darkness of the water at night, he "took advantage of the moment of darkness and cast [his] basket [of laboratory equipment] into the sea [...]."  In other words, Victor gets rid of all the chemical instruments he would to make another creature.  He begins to feel so much better, liberated and refreshed, that he actually lies down and falls asleep.  Evidently, during this time, the creature finds Henry and strangles him, so that when Victor's boat washes up on shore again, he will be accused of the murder.

Why did the planters of Virginia turn to chattel slavery?

Most of the original laborers of the Virginia colony were indentured servants. Indentured servitude served as a method for less wealthy people in England to fund their settlement in the New World. Essentially, indentured servants would sign up to work for the Virginia Company, or other estate owners, for seven years in return for passage to the new world and, often, shares in the company. These laborers were necessary to complete the backbreaking work in the tobacco fields necessary to fund the colonial enterprise.
However, by the end of the seventeenth century, there was a shortage of indentured servants. To fill the labor gap, more and more enslaved Africans were brought to the region to work the tobacco fields. There had been slaves in Virginia since 1619. However, for most of the century, indentured servants were considered more skilled and profitable than slaves.
By 1700, the shortage of people in England signing up to be indentured servants was causing their price to rise dramatically. Additionally, the tobacco industry had grown substantially. There just were not enough laborers to keep up with demand. At the same time, African slaves were coming down in price as the trade grew into a major transatlantic venture. It simply became more profitable for planters to use Africans as their main source of labor. While an indentured servant had a limited term of employment and would need to be replaced after his or her term was over, a slave would work for their entire life. They also could have children born into slavery, which meant that they became a self-sustaining source of labor.
African slaves were also treated much more poorly and were often worked much harder than indentured servants were. Feelings of racial superiority played into this. A slave owner usually had fewer qualms about mistreating and overworking a slave than a fellow Englishman. All this led to the rapid growth of slavery in Virginia. In 1670, there were about 2,000 slaves in Virginia. That number grew to 100,000 by 1750.
http://www.u.arizona.edu/~marietta/349_information.htm

https://guides.loc.gov/american-women-law

In the book How to Read Literature Like a Professor, which quotes refer to the book Frankenstein?

Foster uses such a variety of works—from novels to poetry to plays—in his analyses that most works aren't referenced repeatedly. However, there are so many ways that you could tie various chapters of focus into the plot and themes of Frankenstein. Here are some ideas:
1. Chapter 1: Every Trip is a Quest (Except When It's Not): Both Victor and the monster make several trips in the book, and in each case, they are searching for something. Consider Victor's travels to Ingolstadt. It is here that he becomes passionate about the sciences, which will lead to his creation of the monster. Also consider when the monster removes himself from the close physical proximity of Victor and places himself in the woods close to the DeLacey family. It is here that he grows abundantly in knowledge and desires to be part of a family like the one he observes. In several instances in the book, the characters are really on a quest for self-knowledge when they embark on a trip.
2. Chapter 6: The Bible: There are several Biblical parallels in Frankenstein. The creature can be likened to Adam, the first man. He wants Victor to create a female (Eve) for him. Does that make Victor God? Not exactly, but in his creation of life, he does assume a god-like position, which he then abandons completely. Perhaps this is why the monster finds solace in Paradise Lost.
3. Chapter 11: Violence: The creature commits numerous murders in the novel, the first being William Frankenstein (directly), which is then blamed on Justine. One could argue that he is indirectly responsible for her murder as well. Through William, we see the symbolic death of innocence that Victor's creation has caused. Does he, then, as the creator, bear the ultimate responsibility since he has given no moral leadership to the creature? That's a great debate.
There are other chapters where it is easy to tie in Frankenstein as well. It's a great piece to analyze, as it is so rich in character development and plot complications.

There are actually a few references to Frankenstein in the book. In Chapter 21, Marked for Greatness, the author discusses physical deformities as symbols for inner dysfunction or moral turpitude (depravity).
He discusses Mary Shelley's monster from a historical perspective; the atrocious figure of the monster explores nineteenth-century fears about the unholy alliance between science and supernatural quackery.

Thanks to Hollywood, the monster looks like Boris Karloff or Lon Chaney and intimidates us by its sheer physical menace. But in the novel, it's the idea of the monster that is frightening, or perhaps it’s really the idea of the man, the scientist-sorcerer, forging an unholy alliance with dark knowledge that scares us. The monster represents, among other things, forbidden insights, a modern pact with the devil, the result of science without ethics.

In fact, the dubious science of galvanism was the central premise that gave birth to Frankenstein, the monster. In Chapter 21, the author also introduces the hypothesis that Frankenstein unwittingly represents the ugly parts in all of us that we would rather keep hidden from public view.

Romanticism gave us the notion, rampant throughout the nineteenth century and still with us in the twenty-first, of the dual nature of humanity, that in each of us, no matter how well made or socially groomed, a monstrous Other exists.
What they share with Shelley’s monster is the implication that within each of us, no matter how civilized, lurk elements that we’d really prefer not to acknowledge – the exact opposite of The Hunchback of Notre Dame or “Beauty and the Beast,” where a hideous outer form hides the beauty of the inner person.

In the above quotes, the author makes the point that, when a writer takes the trouble to clothe a character with significant physical anomalies, he "probably means something by it," and we should try to understand the inherent symbolism behind his actions.