Calculus: Early Transcendentals, Chapter 3, 3.1, Section 3.1, Problem 39

The differential of a polynomial term like Ax^n is nAx^(n-1)
If f(x)=x^4-2x^3+x^2
then f'(x)=(4)(1)x^(4-1)-(3)(2)x^(3-1)+(2)(1)x^(2-1)
Completing the basic math we get f'(x)=4x^3-6x^2+2x
Looking at the graphs of the original function (black) and it's derivative (blue), we see:

For X values less than 0, the slope of the original function (black) is negative (as x values increase towards 0 from the left, the function decreases in value), therefore it's derivative (blue) is negative.
From x=0 to x=0.5, the slope of the original function becomes positive (the value of the function rises as x increases), therefore the derivative (blue) is positive for this duration.
From x=0.5 to x=1, the slope of the original function (black) is again negative as shown by the derivative (blue) again being below the x axis.
For x values above 1, the original function again has a positive slope, resulting in a positive derivative.

Do dogs lay eggs?

Dogs do not lay eggs. In fact, dogs, like humans, are members of the mammal animal classification. In order for an animal to be classified as a mammal, they must* possess the following traits:
Have hair or fur
Give birth to live young
Drink milk from their mother
Are warm blooded
Are vertebrates
Because dogs are mammals, they do not lay eggs. They, (like us humans!) have all the characteristics of a mammal including giving birth to live young.
*It is important to note that the duck billed platypus, as well as a couple species of ant eaters, lay eggs even though they are mammals.

Dogs do not lay eggs. Instead, they are classified as mammals and give birth to live young. When females become sexually mature, they can become pregnant. They have an estrous cycle, whereby reproductive hormones cause changes that can lead to pregnancy.
Their reproductive cycle lasts from two to four weeks. Female dogs reach puberty between eight and eighteen months, depending on the breed. The hormone estrogen stimulates eggs to be released from ovaries, and if males mate with females during the period known as estrus, the females can become pregnant. Like all mammals, they have internal fertilization of their eggs.
After estrus, a period, known as diestrus, occurs, whether the dog is pregnant or not. At this time, the hormone progesterone is high.
The gestational period for canines is approximately 63 days, and the embryos develop in the uterus during this time. Dogs can have up to six puppies; however, this number can vary somewhat, depending on the breed.
Once the puppies are born, the females are capable of supplying nourishment to their young via their mammary glands, which can produce milk.
I have attached a link to an article about the anatomy of the reproductive system in dogs with an illustration of the female anatomy.
https://www.petcoach.co/article/anatomy-and-function-of-the-reproductive-system-in-dogs/

Where do you believe this lottery is taking place? Based on the outcome of the story, what do you think the author is saying about the people?

I believe the lottery in this story is taking place in a small town in the northeast United States.
Some of this is based on explicit statements, like the way Jackson calls the place a "village." This refers to small settlements. Some of this is based on the names of the characters in the story. The names are either English (Summers, Graves) or French (Delacroix) in origin. This fits the New England area. Some, like Hutchinson, were actual names from Puritan history. New England is one of the few places in the United States where historical traditions are well enough established to support a ritual like the lottery, which is old enough to have sayings and superstitions about it.
Based on the outcome of this story, I believe Jackson is saying people can follow social pressure and established traditions too far--that they are willing to kill or die to follow them.
 

Calculus: Early Transcendentals, Chapter 4, 4.2, Section 4.2, Problem 14

Mean Value Theorem states a function f(x) that the satisfies the following hypotheses:
1. a function f(x) that is continuous on the closed interval [a,b]
2. differentiable on the open interval (a,b)

Then there is a number “c” such that a ltcltb and
f'(c) =(f(b)-f(a))/(b-a)
or f(b) – f(a) = f’(c) (b-a).
Mean Value Theorem indicates that at least one number “c” will exists within the said function. To be able to solve the value of “c”, we consider the special case of Mean Value theorem where we assumed f(a)= f(b) (Rolle’s Theorem).

A. For the given function f(x) = e ^(-x) with closed interval [0,2], we solve first for the endpoints.
Plug-in x= 0 in f(x)=e^(-x) :
f(0) = e^(-0)
=e^(0)
=1
First endpoint: (a, f(a)) = (0,1)

Plug-in x= 2 in f(x)=e^(-x):
f(0) = e^(-2)
= (1)/(e^ (2)) or 0.135335
then (b, f(b)) = (2,(1)/(e^(2)) )
Second endpoint: (b, f(b)) = (2,(1)/(e^(2)) )
Law of Exponent: x^(-n) = (1)/(x^(n))
B. Solve for the slope of the secant line using the formula:
f'(c) = (f(b)-f(a))/(b-a)
Plug-in the two endpoints:
f'(c) = ((1)/(e^(2))-1)/(2-0)
f'(c) = ((1)/(e^(2))-1)/(2)
f'(c) = (1)/(2e^(2)) - (1)/(2) or -0.432332358
C. Solve for the derivative function f'(x).
f'(x) = e^(-x) * (-1 dx)
= -e^(-x) dx
D. Solve for (c, f(c))
Recall the slope of the tangent line = f'(c).
Equate the answers from part B and C:
((1)/(e^(2))-1)/(2) = -e^(-x)
((1)/(e^(2))-1)/(2)= -(1)/(e^(x))
Multiply both sides by -1:
(((1)/(e^(2))-1)/(2))*(-1) = ((-1)/(e^(x))*(-1)
(1-(1)/(e^(2)))/(2)= (1)/(e^(x))
Cross-multiply to isolate e^(x) :
e^(x) = (2)/(1-(1)/(e^(2)))
Take LN from both sides:
ln(e^(x)) = ln ((2)/(1-(1)/(e^(2))))
x = ln(2) - ln(1-(1)/(e^(2)))
x = ln(2) - ln((e^(2)-(1))/(e^(2)))
x = ln(2) - (ln(e^(2)-1)-ln(e^(2)))
x = ln(2) - ln(e^(2)-1) + ln(e^(2))
x = ln(2) - ln(e^(2)-1) + ln(e^(2))
x = ln((2)/(e^(2)-1)) + 2
or x= 0.8385606384 rounded off to c= x =0.8386.
Solve for f(c):
Plug-in x=0.8386 in f(x) = e^(-x)
f(0.8386) = e^(-0.8386)
= 0.4323
Then (c, f(c)) =( 0.8386 , 0.4323)
E. Find tangent line equation.
slope of tangent line = f'(c) =-0.4323
point (c, f(c)) =( 0.8386 , 0.4323)
It shows that secant line and tangent line are parallel.
Using the formula: y=mx+b to solve for b.
0.4323 = (-0.4323) *(0.8386) +b
0.4323 =-0.3625 +b
0.4323 +0.3625 = -0.3625 +0.3625 +b
b=0.7948
Tangent line equation: y = -0.4323x +0.7948
Please see the attached file for the graph.
Blue line is the secant line using the two endpoints: (a, f(a)) and (b, f(b)).
Green line is the tangent line using line equation: y = -0.4323x +0.7948.
Red curve is the graph of f(x) = e^(-x) .

How does Hemingway's "code hero" connect to his story "Hills Like White Elephants"?

Hemingway's code hero is a man who could be identified as a man's man.  He likes to drink, have affairs with women, engage in physical activities such as hunting or fishing.  He is stoic and courageous in the face of danger, and handles the challenges of the world with grace and dignity.  The American in the short story "Hills Like White Elephants" shows some of the characteristics of this stock character.  This story is almost entirely a dialogue between a girl named Jig and the American.  It is told from an objective point of view, so what we know about the male character comes primarily from this conversation and a few descriptive details provided about the setting.  In this conversation we learn that the couple has been together for a while.  Their relationship has consisted of trying new drinks and traveling around Europe, and having a "fine time." 
The American is clearly knowledgeable about drinks, because the girl defers to his judgment several times when they order.  He also speaks Spanish and interprets for the girl the waitress's words.  He is clearly the dominant figure in the relationship, in his pressing Jig to have an abortion and her ultimate submission to his will. 
His actions portray the typical Hemingway hero--a drinker, a lover, and a man who does not want to be tied down.  The American exemplifies the attitudes of  of the Lost Generation about which Hemingway often wrote. After WW1, many of these young people seemed to reject the values of their parents and to have no sense of purpose and see no real meaning in life.  
However, even though the man may be the typical macho Hemingway hero, he does not come across as courageous, or acting with dignity and grace.  In his obvious desire to avoid any type of commitment to his lover, he chooses death over life, bachelorhood over family, and hedonism over love.  He says none of the words that Jig wants to him to say about marriage and family.  He seems callous and insensitive to Jig, and even though he offers to accompany her when she has the abortion, this offer seems self-serving and cowardly.  

Who is Baldeo in The Tiger in the Tunnel by Ruskin Bond?

Baldeo is the main character in this great and terribly sad short story. He is a married man and a father of two children. He has a daughter and a 12-year-old son named Tembu.
Baldeo and his family are not wealthy, and they live near a forest in India. Baldeo provides for his family in two ways. He works their small rice field but is forced to supplement the remainder of the family's income by working for the railroad. He is one of the line's watchmen, and his job is to make sure that the railway track through a nearby tunnel stays clear. There is also a signal lamp that he tends to.
Baldeo is a hard working man, as evidenced by the long hours he puts in to ensure that his family has enough to eat. We also know that he cares deeply for the safety of his son. That is why Baldeo doesn't have Tembu accompany him to check the tunnel and the lamp. Baldeo knows that the jungle can be a dangerous place, and he has been hearing stories of a man-eating tiger. I believe that it also has to be said that Baldeo is quite brave. He knows that the tiger has him cornered; however, Baldeo doesn't panic. Instead, he bravely squares off against the tiger, knowing there is little chance for winning.

In short, Baldeo is the main character in The Tiger in the Tunnel.  He lives in a village just outside of a jungle in India.  Even though Baldeo has a small plot of land in order to grow rice and other plants, he still needs to support his family further; therefore, he works as a watchman for the railroad.  Baldeo’s main job is to keep the signal lamp lit (and keep the tunnel free of obstacles) so that the train can safely make it through the tunnel and deliver the mail.  In order to do this job, Baldeo needs to take shelter in a little hut by the tunnel.  Baldeo is very skilled with his one weapon: an axe. Unfortunately, one night a tiger appears.  Even though Baldeo is able to dodge the tiger for a while (and even partially sever its leg), Baldeo’s axe gets embedded in bone, which renders the weapon useless.  With no weapon to speak of, Baldeo is killed by the tiger.  Baldeo’s job is then passed down to his son, Tembu.

What would the advantage be for early Israelites to create and follow a monotheistic, messianic, law-based tradition rather than one of the other religions practiced in the region at the time? Frame your answer in terms of a response to the conditions of the times.

As the previous answer suggests, we have to take religious belief seriously when answering questions like this. In other words, we have no reason to believe that many Israelites did not earnestly and sincerely believe in their monotheistic faith. The question also seems to assume that monotheism is somehow more "developed" than polytheistic faiths, which will surely evolve themselves over time. But with these caveats, it could be argued that monotheism carried certain advantages for a people, or at least their elites. There are advantages, for example, to a "law-based" religion because such a faith is based on texts. Knowledge of these texts, attainable through literacy, might allow access to cultural capital not possible in religions that do not emphasize texts. Another argument might be that monotheistic faiths are not as divided among cults that might contribute to political instability. This, however, must be qualified by pointing out that even monotheistic faiths experience serious divisions—as the emergence of Jesus or the divisions between Shia and Sunni in Islam have demonstrated. But beyond these considerations, it is difficult to say that there were significant advantages—independent of theology—to monotheism. 
https://books.google.com/books?id=JBPZ3wfYEF0C&pg=PA69&lpg=PA69&dq=advantages+of+monotheism+anthropology&source=bl&ots=wNHqp19cVX&sig=P3sgv9qx5aCfUhYUV7I8TRq_om0&hl=en&sa=X&ved=0ahUKEwiBvoqOn5DUAhUJ0YMKHd01CUsQ6AEIQDAE

The reasons for the emergence of a monotheistic religion that supplanted (for some) earlier, polytheistic religions cannot be derived without at least some reference to the Bible, specifically the Hebrew Bible. Judaism as a monotheistic religion has its origins in the first five books of the Hebrew Bible, which comprise the Torah, and the origins of the Hebrew Bible are subject to considerable discussion. Some forms of monotheism did precede the emergence of Judaism; ancient Egypt practiced a form of monotheism known as Atenism, referring to the God Aten. Atenism, however, was not fully monotheistic, as it did not reject the notion of other gods per se but elevated the sun-disk god Aten to the place of primacy. Written histories were few and far between at the time, and the Bible is a principal source for the history of Judaism. In his Histories, Tacitus wrote of the origins of the Jews who populated the region the Romans called Palestine:

"It is said that the Jews are refugees from Crete, who settled on the confines of Libya at the time when Saturn was forcibly deposed by Jupitor...while there are many who think the Jews an Ethiopian stock, driven to migrate by their fear and dislike of King Cepheus. Another tradition makes them Assyrian refugees, who, lacking lands of their own, occupied a district of Egypt, and later took to building cities of their own and tilling the Hebrew territory and the frontier-land of Syria."

Later, Tacitus describes the beliefs of the Jews as follows:

"The Jews acknowledge one god only, of whom they have a purely spiritual conception. They think it imperious to make images of gods in human shape out of perishable materials. Their god is almighty and inimitable, without beginning and without end. They therefore set up no statues in their temples, or even in their cities, refusing this homage both to their own kings and to the Roman emperors."

Tacitus, as a more thorough reading of his writings reveals, was no admirer of the Jews. As a Roman senator, his loyalties were to the polytheistic empire that he served, and the Jews were viewed in a less than benign light. This suggests that the advantages that accrued from converting to Judaism in the period weren't always obvious; converts often faced the antipathy of adherents to other religions, like Tacitus. 
The question of what advantage was to be derived from adherence to a monotheistic religion is a bit problematic. It ignores the importance of the Torah to Judaism and instead assumes a more mercenary motivation behind the development of the theological aspects of the religion. Assuming one rejects the Hebrew Bible as untrue, one can suggest that the origins of Judaism as a monotheistic religion lay in rejection of polytheism out of some notion of moral, racial superiority. Or one can accept the Hebrew Bible as a legitimate source of historical information, which would lead one down a much more empathetic path. Remember that in the Bible, God commands Abraham to travel to a specific region for the purpose of establishing a home for His people. As told in the King James Version of the Book of Genesis (12:1-3):

"Now the Lord had said unto Abraham, Get thee out of they country, and from the kindred, and from they father's house, unto a land that I will whew thee:
"And I will make of thee a great nation, and I will bless these, and make they name grew; and thou shalt be a blessing."

If one takes the Bible literally, and many do, then a monotheistic Judaism was not created by people for their own advantage but rather born because God commanded it. Another history, the veracity of which is open to interpretation, is that of Flavius Josephus, a Roman-Jewish historian writing in the first century AD, who wrote the following with respect to God's covenant with Abraham:





"Now Abram...at the command of God went into Canaan, and therein he dwelt himself, and left it to his posterity.... [H]e determined to renew and to change the opinion all men happened then to have concerning God; for he was the first that ventured to publish this notion, That there was but one God, the Creator of the universe; and that, as to other [gods], if they contributed any thing to the happiness of men, that each of them afforded it only according to his appointment, and not by their own power." 

Jewish law is ancient and inseparable from the Hebrew Bible. We could make the case that there were few to no advantages to Israelites in the development of a monotheistic, law-abiding religion. Indeed, given the long history of anti-Semitism (known as "the oldest hatred" of humanity), it is highly questionable whether any advantage accrued to the Jews as a result of their adoption of a monotheistic religion. The argument, given the history of the last several thousand years, could be advanced that the Israelites would have been better off following blindly in the footsteps of others rather than going on a separate path. That, however, would have required a rejection of the notion of a covenant between one God and Abraham.
If one has to make a case for the advantages of a conversion to Judaism in the time period, it could be argued that a significant advantage accruing to the Israelites by virtue of their adoption of a monotheistic, law-based tradition would be their presumed success in securing their place in the universe. The covenant entered into between God and Abraham would cement the Israelites' advantage in defeating their enemies and establishing a permanent homeland in the territory specified by God. In the Book of Genesis (15:18), the Bible states that God promised to Abraham and his followers a substantial expanse of land:

"In the same day the Lord made a covenant with Abraham, saying, Unto thy seed have I given this land, from the river of Egypt unto the great river, the river Eurphrates:"

This covenant would be reaffirmed over the years, as when God addressed Moses, specifying the boundaries in which His people would live in peace. [Book of Numbers (34:1-13)]. By adopting, or accepting, the monotheistic religion that would become known as Judaism, the Israelites would be able to assert themselves among myriad enemy tribes and kingdoms secure in the knowledge that victory would be theirs. From a theological perspective, this is pretty significant, and it remains a religious foundation for many orthodox Jews today, even though many acknowledge the practical impossibility of any such development absent a major and highly visible sign from God that would be accepted by all those who stood in the way of the Israelites' determination to build a homeland within the boundaries specified by God.
By adopting a monotheistic religion, the Israelites would determine the word of God to be final; this would legitimize the Israelites' struggle for a homeland where they would be free from persecution. This, then, could be the principal advantage of a monotheistic religion.
http://classics.mit.edu/Tacitus/histories.html

https://www.jewishvirtuallibrary.org/timeline-for-the-history-of-judaism

Single Variable Calculus, Chapter 3, 3.2, Section 3.2, Problem 18

Find the derivative of $\displaystyle f(x) = mx + b$ using the definition and the domain of its derivative.


$
\begin{equation}
\begin{aligned}

\qquad f'(x) &= \lim_{h \to 0} \frac{f(x + h) - f(x)}{h}
&&
\\
\\
\qquad f'(x) &= \lim_{h \to 0} \frac{m (x + h) + b - (mx + b)}{h}
&& \text{Substitute $f(x + h)$ and $f(x)$}
\\
\\
\qquad f'(x) &= \lim_{h \to 0} \frac{\cancel{mx} + mh + \cancel{b} - \cancel{mx} - \cancel{b}}{h}
&& \text{Combine like terms}
\\
\\
\qquad f'(x) &= \lim_{h \to 0} \frac{m \cancel{h}}{\cancel{h}}
&& \text{Cancel out like terms}

\end{aligned}
\end{equation}
$


$\qquad \fbox{$f'(x) = m$}$

Both $f(x)$ and $f'(x)$ are linear functions that extend on every number. Therefore, their domain is $(-\infty, \infty)$

What is Squeaky's full name in "Raymond's Run"?

Squeaky's full name is Hazel Elizabeth Deborah Parker. 
Readers are able to read her full name a total of three times during the story. The first time is when Squeaky is registering for her race. She speaks to Mr. Pearson, and he calls her "Squeaky" as he hands her the race number and pins. Squeaky is not happy about Mr. Pearson calling her that, so she corrects him by saying her full name.  

“Well, Squeaky,” he says, checking my name off the list and handing me number seven and two pins. And I’m thinking he’s got no right to call me Squeaky, if I can’t call him Beanstalk.
“Hazel Elizabeth Deborah Parker,” I correct him and tell him to write it down on his board.

Mr. Pearson quickly repeats her name and asks Squeaky a follow-up question.  
The final time readers see Squeaky's full name is after her race. The race between Squeaky and Gretchen is very close. The race officials have to take a few extra minutes to confirm who really won the race. After a bit of deliberation, the winner is announced. Squeaky won the race, and the announcer says her full name to the crowd.  

But of course everyone thinks I’m jumping up and down because the men on the loudspeaker have finally gotten themselves together and compared notes and are announcing “In first place — Miss Hazel Elizabeth Deborah Parker.”

How is sexual orientation a continuum?

Jean Liedloff's definition of continuum states that human beings require some form of natural experience to attain the most favorable physical, mental, and emotional progress. Natural experience is based on activities that have been dictated by the evolution process.
Based on Liedloff's interpretation, sexual orientation is a continuum, in that it's defined by the experiences and the environment that an individual is exposed to. A person can be straight because he or she grew up in a heterosexual family and was constantly showered with love from both the mum and dad. Alternatively, a person may be attracted to another from the same sex because it gives him or her the highest form of satisfaction. In other words, sexual orientation is a continuum because it contributes toa person's existence.
http://www.continuum-concept.org/cc_defined.html

Sexual orientation can be viewed as a continuum because people's preferences can lie on a continuous spectrum between exclusively heterosexual and exclusively homosexual. Understanding sexuality as a continuum is useful because it acknowledges that people can experience attraction to different genders in varying amounts, and allows for the fluidity of sexuality that some people can experience. Fluidity of sexuality refers to the concept that people's attraction to certain genders can fluctuate throughout their lifetimes based on changing feelings or circumstances.
Alfred Kinsey's studies of sexuality were significant in developing this concept because Kinsey acknowledged that bisexual people could be attracted to different genders to varying degrees. The Kinsey scale is an example of a sexual continuum; it ranks people's level of attraction to different genders by asking them to assess themselves on a scale from 0 to 6, with 0 being exclusively heterosexual and 6 being exclusively homosexual. Scholars have added more nuance and room for fluidity to Kinsey's scale since his studies in the 1940s, but his work was formative to the modern understanding of sexuality as a continuum.
http://www.fullerton.edu/universityblues/gay_lesbian/sexuality_continuum.htm

Who does Howard save at the end of Skippy Dies? Is it Carl? Is Ruprecht still with Lori when the school burns down?

The questions you are asking are purposely left unanswered; however, I will try to explain as much as I can about what you are asking.  First, we are not told the exact student that Mr. Howard Fallon (the history teacher) saves.  Mr. Fallon simply “raced back into the burning building and rescued a trapped student.”  Yes, the student certainly could be Carl.  The importance of the happening is not the particular student, but that both he/she and Mr. Fallon are recovering and that Mr. Fallon has behaved heroically.  Next, we learn about the status of Ruprecht and Lori only at the end of the book and are not told about their exact status as the school burns down.  In an earlier chapter, we learn that Lori is singing into her cell phone on the night of the concert (to try an experimental performance) and Ruprecht is backstage.  The call is eventually dropped which we can assume is because the school is burning down at the time.  Later, Ruprecht shows up at Lori’s window and throws pebbles to get her attention.  This is when they begin talking.  Again, we are not told exactly when the school was burning down.  We learn that it has burned down from a Christmas bulletin talked about later.  The school could have been burning down when Lori was singing on the phone and Ruprecht was backstage.  The school could have been burning down when Ruprecht was en route to Lori’s house.  The school could have been burning down after Ruprecht already arrived at Lori’s house.  The reader cannot be sure; however, what is important is that both Ruprecht and Lori surive.

Questions about the book called " The Awakening" 1.identify the novel's point of view and discuss the effect of any significant shifts in narrative voice. In other words, when does the protagonists point of view change within the novel and why is it important ? 2. Explore the significance of the setting of the text. How does the setting impact the overall themes and character development of the narrative? 3.identify one major theme that you discover and support that theme with evidence from text. 4. Select four quotations from the text that illustrate each of the following: mood, tone, symbolism, and figurative languague. What is their significance to the meaning of the work as a whole.

The Awakening is told from a third-person omniscient point of view. It is tempting to say that it is limited omniscient because the narrator spends so much time detailing Edna's thoughts and feelings, but the narrator does offer the thoughts and feelings of other characters at times.
The settings, New Orleans and Grand Isle, are of import, in part, because Edna is an outsider here. She is not used to the Creole way of life, which is something made painfully transparent to her when a salacious novel makes its way through Grand Isle society. The Creole men and women read it openly while Edna feels she must hide it when it is her turn. Edna's outsider status gives her even more to contemplate. It further distances her outward life, and the way in which she must conform in order to retain social acceptance, from her inner life, the way in which she would like to behave and the choices she would prefer to make: the two are often at odds. The individual is almost always at odds with society (in novels at least), and Edna is no exception.
One major theme of this text is that the price of freedom from social rules is alienation. We see this in the end, especially, when Robert refuses to stay with Edna in any relationship other than a marriage. She simply wants them to be together as lovers, not with her as his wife/possession, and he cannot stomach living so outside of the norm. Should Edna, a married woman, simply remain married to Leonce and yet sleep with Robert openly, the social repercussions would be catastrophic: Edna and Robert would be utterly shunned. Consider, as well, Madamoiselle Reisz: she lives outside the rules—she never married, she has devoted her life to her music—and she is only really invited to be the entertainment at parties, never as a simple guest. Her alienation is likely the result of her failure to behave, in more ways than one, in a manner that is considered to be socially appropriate.
In Chapter IX, the narrator writes of Edna, "But the very passions themselves were aroused within her soul, swaying it, lashing it, as the waves daily beat upon her splendid body." This is a good example of mood and tone. In terms of mood, the words are exciting but dangerous at the same time: "aroused" and "passions" vs. "lashing" and "beat." We sense that there is danger to be found in this awakening of passions. Further, this language is somewhat sympathetic toward Edna: an indication of tone. She seems like an unwitting victim to her passions, something she cannot control. In Chapter X, the waves "coiled back [into the water] like slow, white serpents." This is a simile, an example of figurative language, that compares the waves to snakes: a comparison that might conjure up images of the devil in the garden of Eden, a symbol of temptation, just as the sea tempts Edna. Birds, especially caged birds are often used symbolically for Edna in the text as well; so that would be a great place to start to look for symbolism quotations—see in the final scene: "A bird with a broken wing was beating the air above, reeling, fluttering, circling, disabled down, down to the water." Quotations like these help us to come to themes regarding the oppression to be found in strictly regimented gender roles, or, specifically, when women are oppressed.

Why does Atticus not bring a chair for the stranger in the room? Who might this stranger be?

Chapter 28 of To Kill a Mockingbird is quite an exciting chapter. It is in this chapter that Scout and Jem are attacked in the darkness by Bob Ewell on their way home from the schoolhouse. A man intervenes on their behalf and carries Jem home. Soon after, Dr. Reynolds and Heck Tate arrive at the Finch home. Suggesting that everybody take a seat, Atticus proceeds to get another chair from the living room. All of the adults in the room are seated with the exception of one.
Scout believes that Atticus knows "the ways of country people," so it does not strike her as particularly odd that a man is left standing. She assumes that the man prefers to stay where he is. Eventually, Scout tells her story of what happened. As she identifies the man standing as the one that must have intervened in the scuffle, she looks up at his face and says, "Hey, Boo." The man without a chair is Boo Radley, their reclusive neighbor. Atticus knows that Boo would prefer to go unnoticed, so he does not offer him a chair. After a while, the men move out onto the front porch to talk. Picking up on her father's clues, Scout leads Boo to a chair on the porch that is in "deep shadow."

During the Revolutionary War, the British switched to a southern strategy that ultimately failed. Why did the British move the fighting to the South?

There were several reasons why the British moved the fighting to the South in the Revolutionary War. One of the reasons was that British were not experiencing success in the North. The British had lost the Battle of Saratoga and had failed to cut the New England colonies off from the rest of the colonies.
Another reason for moving the fighting to the South is that the British had to defend all areas of the colonies. While the colonists did not have to win in all areas, the British had to be sure that they did not lose any of the thirteen colonies.
The British also moved the fighting to the South because more loyalists lived there. The British hoped they would get more support and a warmer welcome in the areas where many loyalists lived.
The British had some initial successes after moving the fighting to the South. They won battles at Charleston, Savannah, and Camden. However, the colonial strategy of using guerilla warfare techniques and avoiding large battles eventually wore down the British.
The British surrendered after the Battle of Yorktown.

Single Variable Calculus, Chapter 2, 2.3, Section 2.3, Problem 55

Assume $\displaystyle \lim \limits_{x \to 1} \frac{f(x) - 8}{x- 1} = 10$, Find $\lim \limits_{x \to 1} f(x)$


$
\begin{equation}
\begin{aligned}
& \lim \limits_{x \to 1} \frac{f(x) - 8}{x - 1} = 10
\qquad
\Longrightarrow
\qquad
\frac{\lim \limits_{x \to 1} [f(x) - 8]}{\lim \limits_{x \to 1}(x-1)} = 10
\qquad
\text{(Multiplying $\lim \limits_{x \to 1} (x - 1)$ to both sides of the equation)}\\


& \frac{\lim \limits_{x \to 1} [f(x) - 8]}{\cancel{\lim \limits_{x \to 1}(x-1)}}
\cdot
\cancel{\lim \limits_{x \to 1}(x-1)}
= 10 \cdot \lim \limits_{x \to 1}(x-1)\\

& \lim \limits_{x \to 1} [f(x) - 8] = 10 \cdot \lim \limits_{x \to 1}(x-1)\\

& \lim \limits_{x \to 1}f(x) - \lim \limits_{x \to 1} 8 = 10 \cdot \lim \limits_{x \to 1} (x-1)\\

& \lim \limits_{x \to 1} f(x) - 8 = 10 \cdot (1-1)\\

& \lim \limits_{x \to 1} f(x) = 0 +8 = 8\\

& \lim \limits_{x \to 1} f(x) = 8

\end{aligned}
\end{equation}
$

What is the difference between diffusion and osmosis?

Diffusion and osmosis are both examples of passive transport. Passive transport does not require any energy to happen. It is a natural process that moves materials from an area of higher concentration to an area of lower concentration. The differences in concentration of materials is called a concentration gradient, and substances naturally move down (higher to lower) the gradient.  For example, when you put a drop of food coloring in a glass of water, the food coloring will begin moving from where there is a high concentration of food coloring to where there is a lower concentration of food coloring.  This will occur until equilibrium is reached and the food coloring is evenly spread out.  Osmosis and diffusion both work passively based on a concentration gradient. 
A difference between osmosis and diffusion is that diffusion can occur in any mixture (with or without a semipermeable membrane), but osmosis always occurs across a semipermeable membrane.
Another key difference is that osmosis is only the movement of water across the membrane. 
When I teach this concept to my students, I stress that osmosis is the diffusion of water.  I also like to say that all osmosis is diffusion, but not all diffusion is osmosis.  
https://socratic.org/questions/why-is-osmosis-a-unique-form-of-diffusion

https://www.thoughtco.com/difference-between-osmosis-and-diffusion-609191

A pulsed laser fires a 1000 MW pulse that has a 200 ns duration at a small object that has a mass equal to 10.0 mg and is suspended by a fine fiber that is 4.00 cm long. If the radiation is completely absorbed by the object, what is the maximum angle of deflection of this pendulum?

The attached diagram shows the displacement of the pendulum bob, through an angle theta, as a consequence of the complete absorption of the incident radiation. Now use conservation of mechanical energy.
Delta K +Delta U=0
(K_f-K_i)+(U_f-U_i)=0
In this case, set the initial potential energy of the pendulum to zero and since the final state of the pendulum comes to a complete stop, K_f=U_i=0 .
-K_i+U_f=0
U_f=K_i
mgh=p_i^2/(2m)
mgL(1-cos(theta))=p_i^2/(2m)
Solve for theta .
eq. (1) :-> theta=cos^-1(1-P_i^2/(2m^2gL))
Now use conservation of momentum between the laser and the initial momentum of the pendulum, p_i .
p_i=p_(laser)
Use the momentum relation for light. Then relate energy to the laser power P .
p_i=E_(laser)/c=(P delta t)/c
Now substitute for p_i in eq. (1) .
theta=cos^-1(1-(P^2(Delta t)^2)/(2m^2c^2gL))
Substitute numerical values and evaluate theta .
theta=cos^-1(1-((1000 MW)^2(200 ns)^2)/(2(10.0 mg)^2(2.998*10^8 m/s)^2(9.81 m/s^2)(0.0400 m)))=6.10^@
https://en.wikipedia.org/wiki/Photon

https://www.physicsclassroom.com/class/energy/Lesson-2/Analysis-of-Situations-in-Which-Mechanical-Energy

Single Variable Calculus, Chapter 4, 4.4, Section 4.4, Problem 38

Determine the horizontal and vertical asymptotes of the curve $\displaystyle F(x) = \frac{x - 9}{\sqrt{4x^2 + 3x + 2}}$

Solving for the vertical asymptotes

We set the denominator equal to zero

$4x^2 + 3x + 2 = 0$

Using the discriminant of $ax^2 + bx + c$ which is $\Delta = b^2 - 4ac$.

(If $\Delta < 0$, then the equation $ax^2 + bx + c = 0$ has no real solution.)


$
\begin{equation}
\begin{aligned}

\Delta =& (3)^2 - 4 (4)(2)
\\
\\
\Delta =& 9 - 32
\\
\\
\Delta =& -23

\end{aligned}
\end{equation}
$


But $-23 < 0$

So $4x^2 + 3x + 2 = 0$ has no real solution.

Therefore,

$F(x)$ has no vertical asymptotes

Solving for the horizontal asymptotes

In the function $\displaystyle F(x) = \frac{x - 9}{\sqrt{4x^2 + 3x + 2}}$ we remove everything except the biggest exponents of $x$ found in the numerator an denominator.

So we have


$
\begin{equation}
\begin{aligned}

F(x) =& \frac{x}{\pm \sqrt{4x^2}} \qquad \text{where $F(x) = y$}
\\
\\
y =& \frac{\cancel{x}}{\pm 2 \cancel{x}}
\\
\\
y =& \pm \frac{1}{2}

\end{aligned}
\end{equation}
$



Thus, the horizontal asymptotes are $\displaystyle y = \frac{1}{2}$ and $\displaystyle y = \frac{-1}{2}$

Therefore,

The function $F(x)$ has no vertical asymptotes and have horizontal asymptote which is $\displaystyle y = \frac{1}{2}$ and $\displaystyle y = \frac{-1}{2}$

Single Variable Calculus, Chapter 2, 2.4, Section 2.4, Problem 30

Show that the statement $\lim \limits_{x \to 3} (x^2 + x - 4) = 8$ is correct using the $\epsilon, \delta$ definition of limit.

From the definition of the limit
$\text{if } \quad 0 < |x - a| < \delta \quad \text{ then } \quad |f(x) - L| < \varepsilon$

if $0 < | x - 3 | < \delta$ then $|(x^2 + x - 4 ) - 8 | < \epsilon$

$|(x^2 + x - 4) - 8| < \epsilon \quad \Longrightarrow \quad |x^2 + x - 12| < \epsilon$

To associate $|x^2 + x -12|$ to $|x - 3|$ we can factor and rewrite $|x^2 + x -12|$ to $|(x + 4 )(x - 3)|$ to obtain from the definition

if $0 < | x - 3| < \delta$ then $|(x + 4 )(x - 3)| < \epsilon$

We must find a positive constant $C$ such that $|x + 4 | < C$, so $|x + 4| |x - 3| < C | x - 3|$

From the definition, we obtain

$C | x - 3 | < \epsilon$

$|x - 3| < \frac{\epsilon}{C}$

Again from the definition, we obtain

$\displaystyle \delta = \frac{\epsilon}{C}$

Since we are interested only in values of $x$ that are close to $3$, we assume that $x$ is within a distance $1$ from $3$, that is, $|x - 3| < 1$. Then $2 < x < 4$, so $6 < x + 4 < 8$

Thus, we have $| x + 4 | < 8$ and from there we obtain the value of $C = 8$

But we have two restrictions on $|x - 3|$, namely

$\displaystyle |x - 3|< 1$ and $\displaystyle |x - 3| < \frac{\epsilon}{C} = \frac{\epsilon}{8}$

Therefore, in order for both inequalities to be satisfied, we take $\delta$ to be smaller to $1$ and $\displaystyle \frac{\epsilon}{8}$. The notation for this is $\displaystyle \delta = \text{ min } \left\{1, \frac{\epsilon}{8}\right\}$

How did the American Revolution function as a civil war?

The Revolutionary War functioned as a civil war in the sense that opinions on the war split families in the colonies. Benjamin Franklin was an ardent Patriot; one of his sons was a Loyalist. This was but one example of many where loyalties divided families and would continue to divide families after the war was over. People had varying reasons for wanting to stay with Britain. Some people saw Parliament as correct and paid their taxes. Others disagreed with Parliament but did not want to risk losing British trade.
Others feared what a new government would look like; though they disliked the way they were currently being governed, they did not want to risk change. Others did not want to risk being taken over by Spanish or French interests in the New World. After the war, the victorious Patriots treated the Loyalists as traitors; many were blackballed from political life or otherwise harassed. Some Loyalists even moved north into Canada, though this was a minority.
The Revolutionary War functioned as an ideological civil war as well. According to the Patriots, before the war they were not treated as Britons with natural rights but rather as an enemy being occupied in time of war. While Loyalists claimed that Parliament had a right to restore order, Patriots claimed that there were limits to Parliament's ruling power when Parliament decided to make laws without colonial consent.
This ideological split made people reexamine what it meant to be governed and what their privileges and obligations would be to that government. This civil war would still be debated after the new nation won its independence in 1783. It would be as divisive as the physical war that preceded it.

As the question implies, the American Revolution was not a simple war for independence from Great Britain—in fact, the war included a fierce conflict between those colonists who supported British rule and those who fought against that rule. As many studies of the conflict have shown, throughout the colonies there were significant numbers of Loyalists who either fought for the British or, in less violent ways, supported Britain's rule. In the southern colonies, which tended to be more conservative than northern colonies, Loyalists may have outnumbered Rebels in many areas. Throughout the colonies, as much as 30% of white colonists most likely supported Britain either directly or indirectly.
Although Loyalists came from all levels of society, many tended to be from the upper property owning stratum—those who had wealth, land, and, most importantly, positions dependent upon the ruling country. In his Origin & Progress of the American Rebellion, Peter Oliver, who was a judge during the Boston Massacre trial, began his (Loyalist) history of the Revolution by noting that

But for a Colony, which had been nursed in its Infancy, with the most tender Care & Attention; which had been indulged with every Gratification that the most forward [that is, badly disciplined] Child could wish for. . . . (Origin, p. 3)

Typically, Loyalists such as Oliver viewed the Revolution as a struggle between a wayward headstrong child against a benevolent father. Throughout the Revolution, the struggle was often characterized as almost a family dispute, albeit a violent one. Oliver, and others of his class, preferred not to see the rebellion as a civil war—that is, a dispute founded on ideas—but as an unaccountable betrayal of the parent-child relationship.
Although violence between Loyalists and Rebels varied greatly during the Revolution, most historians conclude that some level of conflict between citizens was constant during the war and was perhaps greatest in the Carolinas where atrocities occurred almost routinely between the farming and land-owning classes, especially in the later years of the struggle.
After the British surrendered at Yorktown, many Loyalists, as many as 150,000, fled the country. Many fled to Canada and a lesser number to Great Britain. The sad fact is that many, including Peter Oliver, never recovered from the loss of what they believed was their birthright—a successful colony of Great Britain.
http://courses.missouristate.edu/ftmiller/Documents/POliver.htm

In some ways, the Revolutionary War can be viewed as a civil war. British citizens were pitted against British citizens. There were people, called loyalists, who believed we should stay with Great Britain. These people felt the British government was justified in its actions. They also felt that there might be chaos if we broke away from the British. In some cases, people depended on the British for their jobs. If the British left, they would lose their jobs. The Patriots supported breaking from Great Britain. They believed that the British were violating our rights and not treating us fairly. There were many instances where the loyalists were harassed for supporting the British. At times, loyalists faced violence or angry mobs because of their support of the British government.
In some cases, the Revolutionary War split family members. There were times when family members fought on opposite sides of the conflict. In some cases, brothers fought against brothers, such as the Goforth brothers at the Battle of Kings Mountain. Benjamin Franklin’s son supported the British and was basically disowned by his father.
Finally, the Revolutionary War can be viewed as a civil war because the British colonists were fighting against the British government. The colonists felt they no longer could support Great Britain and be ruled by them. Thus, they fought for their independence.
http://americainclass.org/sources/makingrevolution/rebellion/text1/text1.htm

Why is Meg the most suitable person to go to Camazotz?

When Charles Wallace is left behind on Camazotz under the power of the evil IT, Meg realizes that she is the most suitable person to try to retrieve him and bring him back home. This is because she knows him better than anyone else and also because she has been to Camazotz. Her father has been gone so long that he and Charles Wallace don't really know each other anymore. Calvin only recently became involved with the Murry family, so he hasn't had enough time to get to know Charles Wallace all that well either. Meg, therefore, is the one person left with knowledge of Camzotz who is close to Charles Wallace. Charles Wallace also understands her well. If anyone is going to be able to break through IT's mind control to reach the real Charles Wallace, Meg has the best chance. As she says:

it has to be me. It can't be anyone else. I don't understand Charles, but he understands me. I'm the one who's closest to him. Father's been away for so long, since Charles Wallace was a baby. They don't know each other. And Calvin's only known Charles for such a little time.

What is the tone of "The Most Dangerous Game" by Richard Connell?

There is a menacing tone to "The Most Dangerous Game."
Connell's use of dark foreshadowing with the exotic setting, the strange occurrences, and bizarre characters introduced in the exposition quickly puts readers "on edge," as they fear what will happen next. This element of danger is immediately introduced as Rainsford and Whitney travel to hunt jaguar; then, when Rainsford falls overboard and must swim for a long time before finding any shoreline, there is clearly a forbidding tone. Later, Rainsford's frightening encounter with the massive Ivan, whose tongue has been cut out is, indeed, disconcerting. The greatest menace is presented in the form of the owner of the chateau, "a lofty structure with pointed towers plunging upward into the gloom." This man is the Russian General Zaroff, whose "dead black eyes" do not change as he calmly speaks of his bizarre penchant for hunting "the most dangerous game."
After Rainsford becomes Zaroff's prey, there is great tension and the dark, forbidding tone of the narrative heightens. Certainly, the story's exploration of fear and death generates a menacing tone to the fast-paced action of this work.

How does the writer use indirect characterization to develop the conflict between mother and daughter in "Two Kinds"?

Indirect characterization is characterization that requires a reader to infer traits of a character based on how that character acts, thinks, and talks to other characters, and how other characters respond to the character in question.
This question specifically asks about traits that propel the mother/daughter conflict forward, so it is probably best to begin looking at the text around the point when Jing-mei decides that she will no longer respond positively to her mother's attempts to make Jing-mei into a prodigy.

I won't let her change me, I promised myself. I won't be what I'm not.

This quote doesn't explicitly tell readers that Jing-mei is rebellious and willful, but it indirectly points readers toward that analysis. We see Jing-mei deciding that she is going to go her own way, regardless of what her mother thinks. As the conflict between mother and daughter continues, Jing-mei digs in harder and deeper, and this shows that she is also stubborn, resilient, and able to persevere through adversity. You could probably make the case that Jing-mei is also selfish. All of those traits propel the conflict to its climax, where Jing-mei screams out that she doesn't want to be her mother's daughter anymore:

"Then I wish I weren't your daughter, I wish you weren't my mother," I shouted.

When an author uses direct characterization, they explicitly tell the reader what qualities or traits a character has. When an author uses indirect characterization, they tell us how the character behaves, speaks, or thinks so that we can infer their qualities for ourselves.
The narrator, Jing-mei, never tells us that her mother was a believer in the American dream, but she does say that Suyuan believed that a person could be anything they wanted to be in America. Suyuan, through her daughter's descriptions, is characterized as a woman who wholeheartedly believes that, with hard work, a person can do anything in America, and her daughter is no exception to this rule. Suyuan has complete faith in her daughter's ability to be the best...at something. At first, Jing-mei is "just as excited" as her mother, but her self-esteem begins to deteriorate as she fails more and more of her mother's tests of her aptitude. She says that seeing her mother's "disappointed face" over and over forces "something inside [her]...to die." Suyuan continues to pressure Jing-mei, forcing her to take up the piano, but, by now, Jing-mei is becoming defiant. She says that she is determined "not to be anybody different" from who she feels she is. After her disastrous talent show debut, Suyuan's face tells her daughter that "she had lost everything," and Jing-mei "felt the same way." The more Suyuan pushes—out of love, though it doesn't feel that way—the more Jing-mei resists, and their conflict escalates quickly.

Indirect characterization is accomplished by describing what the character says and does.
Jing-mei and her mother are in a conflict because the mother wants Jing-mei to become a prodigy. She eventually decides that she wants Jing-mei to be a pianist, and so she dictates a schedule of lessons and practice. When Jing-mei rebels and asks, "Why don't you like me the way I am? . . . I can't play the piano," Jing-mei's mother slaps her and calls her ungrateful.
Jing-mei subverts her mother's will by not trying very hard in her lessons and taking advantage of the fact that her teacher is too deaf to hear missed notes. She plays in rhythm because that's all he can hear, but she doesn't practice the notes.
Ultimately, Jing-mei tells her mother, "I'm not going to play anymore." When her mother attempts to force her by pulling her to the piano and lifting her onto the bench, they have an argument that ends after Jing-mei tells her that she wishes she (Jing-mei) were dead, like the children her mother left behind in China. This ugly outburst ends the argument, and the subject of piano lessons is tabled.

The setting of the story is very limited; it is confined largely to a room, staircase, and front door. How does this limitation help to express the theme or big idea of the story? In other words, why is the setting so limited?

Arguably, every aspect of "The Story of An Hour" is minimal and short-lived. First, there is no overuse of language or stylistic devices. As the title suggests, the story itself is quite short. Also, a quick look at all the other short-lived and minimally described elements of this story lets us know that Chopin is writing for something other than mere literary entertainment. She wants to make a point.
Short-lived elements (regarding Louise Mallard):
her happiness : she only gets to experience it while she thought her husband died.
her dreams: they surfaced as soon as she felt that she was finally free.
her hopes: same as her dreams.
her life: she is relatively young.
Minimally-described things:
her emotions: we only see the phrase, "yet, she loved him," but when did she?
the home: like your question states, minimal description is provided.
the husband: we only know that his name is Brent and that he is a relatively decent man.
her family: we know very little of her background or upbringing.
her history: we know she is a married, middle class woman but not much else.
her condition: we also know that she suffers from a heart condition, but we are not aware to what extent this is a dangerous thing for her.
All this said, it is arguable that the details of these things are minutia compared to the real problem of the story: Louise is a depressed and unhappy woman living in a time when women had limited, if any, rights in society. As such, a woman's only way to happiness was through the fortune of making a "good" (a.k.a financially stable) marriage.
Yet, the moral of this story still shows that not even having that benefit is enough to satisfy an individual's loneliness and sadness over an underachieved life. That is the point Chopin is trying to make: How can we not see, as a society, that women are as much individuals as men are. Who ever dictated that a gender is not human enough to feel, want, and desire without limits? Mirroring society through her story, Chopin makes a clear and concise point about equality. The rest of the details really do not matter in the wide scheme of things.
Therefore, in order to bring out this very unfortunate reality, Kate Chopin mutes any distracting element from the story and consistently focuses on the theme of inequality the best way she can: succinctly, subtlety, but still manages to get straight to the point.

The strict limitations of the setting mirror the strict limitations placed on women during the Victorian era, the time in which Louise Mallard lives.  As Louise mentally processes the fact that her husband is dead, the first words she speaks aloud are "'free, free, free!'"  Though the joy she feels is a "monstrous" one, she feels it nonetheless.  She knows that her husband loved her, and she feels that she, at times, loved him.  However, most tellingly, she reflects on the idea that

There would be no one to live for her during those coming years; she would live for herself.  There would be no powerful will bending hers in that blind persistence with which men and women believe they have a right to impose a private will upon a fellow-creature. A kind intention or a cruel intention made the act seem no less a crime as she looked upon it in that brief moment of illumination.

She seems to have felt trapped in her marriage.  Perhaps she never wanted to marry at all and was forced to as a result of societal expectation.  Perhaps she didn't want to marry Brently but had to because there was no good, socially-acceptable reason to refuse him.  Whatever the case, her marriage seems to have made her feel that she could not live for herself, that she must always give way to whatever her husband wanted, because that is what marriage demanded of Victorian women.  They were forced to live relatively small lives. 
Likewise, the setting is small, and it parallels the figurative "smallness" of Louise's life.  She has been confined, restricted, and almost the first thing she does after learning of her husband's death is to open the window and look outside, as though his death has liberated her from confinement; she notices the birds and the trees and the clouds now.  One of the main themes of the story, about the confinement marriage posed to women during this era (even when the marriage was a loving one), is further expressed by the story's setting.

A velocity selector has a magnetic field that has a magnitude equal to 0.28 T and is perpendicular to an electric field that has a magnitude equal to 0.46 MV/m. What must the speed of a particle be for that particle to pass through the velocity selector undeflected? What kinetic energy must electrons have in order to pass through the velocity selector undeflected?

Assume, for these electrons, their motion is from left to right through the velocity selector and the electric field is upward. This means the electric force is downward and hence then the magnetic force must be upward and the magnetic field into the page. We can apply the condition for transnational equilibrium to relate v to E and B. Then use the definition of kinetic energy to find the energies of the electrons that pass through the velocity selector undeflected.
https://www.britannica.com/science/Lorentz-force

Single Variable Calculus, Chapter 7, 7.1, Section 7.1, Problem 16

Suppose that $f(x)$ is your height at age $x$. Determine whether it is one to one.
We know that a person's height remains constant after a certain age, so there are more than two years at which a person has the same height. Thus, $f(x)$ is not a one to one

Calculus of a Single Variable, Chapter 5, 5.6, Section 5.6, Problem 69

To find the relative extrema of a function, we may apply the First derivative test on a open interval before and after x=c. It states:
a) f'(x) gt0 from the left and f'(x)lt0 from right of x=c then there is local maximum at x=c
b)f'(x) lt0 from the left and f'(x)gt0 from right of x=c then there is local minimum at x=c .
* A sign change of f'(x) from left and right of x=c will indicate a possible relative extrema (local minima/local maxima). If f'(x) has the same sign on both sides of x=c then there is inflection point at x=c .
For the given function:f(x) = arcsec(x)-x , we have the first derivative:
f'(x) =1/(sqrt(x^2)sqrt(x^2-1) )-1 .
Equate f'(x) =0 to solve for x=c :
1/(sqrt(x^2)sqrt(x^2-1) )-1 = 0
Multiply both sides by sqrt(x^2)sqrt(x^2-1) to get 1 -sqrt(x^2)sqrt(x^2-1) = 0
Move sqrt(x^2)sqrt(x^2-1) to the other side to get 1 = sqrt(x^2)sqrt(x^2-1)
Square both sides: 1 =x^2 *(x^2-1)
Expand: 1=x^4-x^2 or x^4-x^2-1=0
Apply Quadratic formula: x= +-sqrt((1+sqrt(5))/2)
x= +1.27, -1.27 as the critical values of f(x) .
For the critical value x= 1.27, it shows that:
f'(1.1) = 0.98 which positive on the left of x=1.27
f'(1.5) =-0.40 which is negative on the right of x=1.27
then it follows that x=1.27 is the location of the local maximum

For the critical value x= -1.27 , it shows that:
f'(-1.5) =-0.40 which is negative on the left of x=-1.27
f'(-1.1) = 0.98 which positive on the right of x=-1.27
then it follows that x=-1.27 is the location of the local minimum.

With the given function: f(x)=arcsec(x)-x , then
Local maximum: f(1.27) = -0.60579
Local minimum: f(-1.27) = 3.74738

Please see the attach file for the graph of
f(x) =arcsec(x)-x

Provide a detailed study guide of the story "The Village Saint" by Bessie Head including the themes, analysis of characters, and important passages.

The themes of "The Village Saint" are feminine power and emotional (psychological) masks. In fact, the phrase "reality is not what it seems" perfectly sums up the main theme of the story.
Mma-Mompati hides an intractable and selfish nature behind a facade of grace, nobility, and warmth. She presides over her village as the resident "holy woman," her "polished etiquette" and "professional smile" the hallmarks of her benign solicitude. While her husband, Rra-Mompati, presides over tribal affairs, Mma-Mompati reigns as the chief comforter and wise woman of her village. We are told that she manages to keep up her "saintly" facade for twenty-six years, which begs the question: can we ever really claim perfect knowledge of anyone?
Today, psychologists would say that Mma-Mompati shows signs of narcissistic personality disorder. People who suffer from this disorder are invariably self-centered, manipulative, and demanding individuals. They have a great need for praise and the constant attention of others. A main trait shared by those with narcissistic personality disorder is apathy or a lack of empathy. In the story, Bessie Head hints at Mma-Mompati's hidden apathy

She had a professional smile and a professional frown of concern for everything, just like the priests.

Mma-Mompati has so perfected a persona of benignity that her natural egocentric self stays hidden from others. The only evidence for her duplicity is her ubiquitous "professional" smile and frown, which she never fails to lavish on others at opportune moments. In reality, Mma-Mompati lacks a true appreciation for others' concerns; her "holy woman" persona is actually just a means of gaining the attention, praise, and adulation she craves.
Because no one is the wiser regarding Mma-Mompati's true nature, the whole village is thrown into a state of universal indignation when Rra-Mompati leaves her for another woman. No one can understand how Rra-Mompati could leave such an angelic woman. Mma-Mompati's assiduous charm makes it difficult for Rra-Mompati to convince his fellow villagers of the truth. Often, the narcissist's greatest weapon is her carefully-crafted persona which may be impervious to all but the most persistent observer. So, a retiring husband who is accustomed to being overshadowed by his wife may find it almost impossible to break the spell she has cast over others.
It is only when Mompati (their son) marries that Mma-Mompati's true nature is exposed. Mma-Mompati's enemy is Mary Pule, a "thin, wilting willowy dreamy girl with a plaintive, tremulous voice." Mary Pule, however, shows herself to be Mma-Mompati's equal in every way. Like Mma-Mompati, Mary has perfected the art of the emotional mask. Her disarming exterior hides an iron will, every bit as tenacious as that of her mother-in-law's. It is Mary who effectively stops Mma-Mompati from taking huge cuts from Mompati's paychecks.
The text tells us that Mompati finds peace after handing over his paychecks to Mary (instead of to Mma-Mompati). The older lady is furious when she discovers that her control over her son has been broken by the "plaintive little wretch" she despises. Notice that Mary does not react to Mma-Mompati's explosive rage. Instead, she portrays herself as a persecuted daughter-in-law, telling the villagers weepy stories about "misery and torture" at the hands of a cruel mother-in-law.
In the Mompatis' patriarchal culture, women like Mma-Mompati and Mary Pule have found ways to wield power without appearing to undermine the positions of men. Through manipulation and emotional power-plays, women target the vulnerabilities of men to gain an advantage. Even during courtship, a woman like Mary Pule retains control by first identifying male vulnerabilities and then engaging in behavior that creates the illusion of male agency. Bessie Head's story effectively redefines the meaning of power.
https://www.psychologytoday.com/us/conditions/narcissistic-personality-disorder

Based on Chapters 5-9 of Ian Haney López's Dog Whistle Politics: How Coded Racial Appeals Have Reinvented Racism and Wrecked the Middle Class: According to the author, what led to and fueled the creation of the Tea Party? What are the "four hatreds," according to Haney Lopez, that motivated the Tea Party?

According to the author, the Tea Party was not motivated by outright racism but by the coded racial hatreds contained in dog whistle politics. While members of the Tea Party denied being motivated by racism, they were, the author points out, "united in their hostility towards Obama" (page 150) because they did not feel that Obama could possibly represent them. This rejection of the idea that Obama could be President motivated their continuing the falsehood that Obama was not born in the U.S.--the so-called "birther" movement.
The Tea Party was motived, the author suggests, by the following "four hatreds (page 152):"
Welfare: The Tea Partiers see welfare as taking money away from hardworking white people and giving it to the undeserving poor (who are, in their minds, nonwhite).
Immigration by undocumented people: The Tea Party sees immigrants, particularly brown immigrants, as taking money away from white taxpayers and causing crime.
Arab Muslims: Tea Partiers regard Arab Muslims as the enemy within the nation.
Obama himself: The Tea Party regards Obama as the incarnation of the hatreds and fears they feel about welfare, undocumented immigrants, and Arab Muslims and therefore as the devil incarnate.
The author states that dog whistle politics explains the contradictions of the Tea Party philosophy. For example, they hate entitlement programs such as welfare, which they link to nonwhites, but they support government entitlement programs such as Medicare and Social Security, which they feel benefit white people. 

How did Timothy protect Phillip from the storm?

In Chapter 15, a large storm washes over the island. The wind blows over the hut in which Phillip and Timothy live, and Timothy protects Phillip by covering Phillip's body with his own. They spend two hours that way, as the storm blows over them with lashing rains and strong winds. The storm is so harsh that they can barely breathe.
As the sea begins to come up the beach, Timothy brings Phillip to the palm trees on the rise for shelter. Timothy ties Phillip and himself to the tree. Water laps against their ankles and feet, and Timothy continues to protect Phillip with his body against the driving wind. They remain that way for about an hour, until the wind dies down and they can untie themselves from the tree. When the eye of the storm passes over and the winds pick up again, worse than ever, Timothy again ties Phillip to the tree and protects the boy with his body. Several large waves pass over them, and, in the end, the storm kills Timothy while Phillip survives. Timothy gives his life to protect Phillip. 

Using examples from the story, how could the sacrifice of the nightingale be treated as unnecessary?

In The Nightingale and The Rose, the nightingale sacrifices her life for the student that she hears from the window. The student is upset because he wants to ask a girl to a dance and she desires a red rose. However, the student doesn’t have any red roses in his garden, meaning he wouldn’t be able to invite the “love of his life.” The nightingale takes it upon herself to produce a red rose for this student, and sacrifices her own well-being to create this red rose. It is unfortunate this should happen, though, because as soon as the student finds the rose and brings it to his “love,” she rejects him because someone else had brought her some real jewels which “cost far more than flowers.” Because of this materialistic view of the world, the nightingale’s sacrifice could be treated as unnecessary. Even though she made the biggest sacrifice she could (her own life), the outcome is still the same (whether or not the student goes to the dance with the professor’s daughter). The existence of the red rose does not change the course of the student’s life as the nightingale had hoped it would.

In "The Nightingale and the Rose," it can be argued that the nightingale's sacrifice was unnecessary because the red rose (which she dies for) does not bring about the student's happiness. At the beginning of the story, for example, the girl tells the student that she will dance with him if he brings her a red rose. Having fallen in love, the student dedicates himself to this pursuit. By the end of the story, however, the girl has completely changed her mind about the student because she has met the Chamberlain's rich nephew and he has won her over by giving her some jewels as a gift. The need for the rose is, thus, negated because the girl has already found another boy to dance with.

f(x,y) = 2ln(x/y) Determine whether the function is homogenous and if it is, determine its degree

A function f(x, y) is called homogenous (homogeneous) of degree n, if for any x, y we have f(tx, ty) = t^n f(x, y).
The given function is homogenous of degree 0, because
f(tx, ty) = 2ln((tx)/(ty)) = 2ln(x/y) = f(x, y) = t^0 f(x,y).
The difficulty is that this function is not defined for all x and y. The above equality is true for all x and y for which it has sense.

Given
f(x,y)=2ln(x/y)
if the function has to be homogenous then it has to be of the form
f(tx,ty)=t^n f(x,y)
so,
f(tx,ty)=2ln((tx)/(ty))= 2ln(x/y) as , on cancelling t .
so the function is of the form f(tx,ty)=t^n f(x,y) and the degree is n=0

Precalculus, Chapter 1, Review Exercises, Section Review Exercises, Problem 24

Determine the center and radius of the circle $x^2 + y^2 + 4x - 4y - 1 = 0$. Graph the circle. Find the intercepts, if any.

We complete the square in both $x$ and $y$ to put the equation in standard form


$
\begin{equation}
\begin{aligned}

x^2 + y^2 + 4x - 4y - 1 =& 0
&& \text{Given equation}
\\
(x^2 + 4x) + (y^2 - 4y) =& 1
&& \text{Group the equation in terms of $x$ and $y$. And put the consistent on the right side of the equation}
\\
(x^2 + 4x + 4) + (y^2 - 4y + 4) =& 1 + 4 + 4
&& \text{Complete the square: add } \left( \frac{4}{2} \right)^2 = 4 \text{ and } \left( \frac{4}{2} \right)^2 = 4 \text{ on both sides of the equation}
\\
(x + 2)^2 + (y - 2)^2 =& 9
&& \text{Factor}

\end{aligned}
\end{equation}
$


We recognize this equation as the standard form of the equation of a circle with $r=3$ and center $(-2,2)$







To find the $x$-intercepts, we let $y = 0$. Then


$
\begin{equation}
\begin{aligned}

& (x + 2)^2 + (y-2)^2 = 9
&&
\\
& (x + 2)^2 + (0-2)^2 = 9
&& y = 0
\\
& (x + 2)^2 + 4 = 9
&& \text{Simplify}
\\
& (x + 2)^2 = 5
&& \text{Apply the Square Root Method}
\\
& x + 2 = \pm \sqrt{5}
&& \text{Solve for } x
\\
& x = -2 \pm \sqrt{5}
&&

\end{aligned}
\end{equation}
$


The $x$-intercepts are $-2 + \sqrt{5}$ and $-2- \sqrt{5}$.

To find the $y$-intercepts, we let $x = 0$. Then


$
\begin{equation}
\begin{aligned}

& (x + 2)^2 + (y-2)^2 = 9
&& \text{Given equation}
\\
& (0 + 2)^2 + (y-2)^2 = 9
&& x = 0
\\
& 4 + (y - 2)^2 = 9
&& \text{Simplify}
\\
& (y-2)^2 = 5
&& \text{Apply the Square Root Method}
\\
& y - 2 = \pm \sqrt{5}
&& \text{Solve for } y
\\
& y = 2 \pm \sqrt{5}
&&

\end{aligned}
\end{equation}
$


The $y$-intercepts are $2 + \sqrt{5}$ and $2 - \sqrt{5}$.

How did the Spanish impact the culture of the Caribbean?

Most European countries have had some kind of impact on the development of the America, particularly those which were the most active during the "discovery" of the Americas. The Spanish conquistadors who first came into contact with indigenous peoples would define the way the Americas were seen in Europe as well as how the natives saw Europeans. As different islands and territories were made into colonies by Spain, the Spanish brought their culture to the Americas. They brought traditional European clothing and mannerisms, their language, and even their standards of education. Spain sought to "civilize" the indigenous people, often sending Spanish families to the Americas to educate the natives. This usually included converting them to Catholicism and giving them Spanish last names, the legacy of which can still be seen today. Along with this, the Spanish left a mark on the ethnicity of the Caribbean; white Spaniards began to marry and otherwise mix with the indigenous peoples, giving rise to people with mixed Spanish-indigenous blood (mestizos). Many inhabitants of the Americas today are of this mixed-blood descent, creating a unique ethnicity separate from "wholly indigenous" or "wholly European." Many aspects of Caribbean culture are adapted from this early Spanish influence, from the food of the region to the different Spanish dialects spoken throughout.

Discuss the impact of the northern nomad peoples upon Chinese society in the late Tang and Song eras. Be specific.

The most important nomadic peoples to play an important role in Chinese history during the later Tang and Song dynasties were the Uyghurs, Liao (Khitans), and Jurchens.
The Uyghurs are a Turkic speaking people who, in the middle of the eighth century, formed their own powerful state, the Uyghur Khaganate. In 756, the Tang emperor asked the Uyghurs to help him to suppress the An Lu Shan rebellion, and the Uyghur horsemen agreed; they took part in the decisive battles and looted the capital, Luoyang. The Tang Empire had to send them tens of thousands of rolls of silk as a tribute in return. However, in the middle of the ninth century, the Uyghur state collapsed because of defeats at the hands of the Siberian Kyrgyz nomads (in 840) as well as the Tang forces (in 843).
The Liao or Khitan empire was a sinicized nomadic empire that came to include parts of Northern China during the decline of the Tang empire and the ensuing political fragmentation of the middle of the tenth century. The Khitans used the Tang model to organize their state and bureaucracy while striving to preserve their nomadic customs and military effectiveness. In the early eleventh century, the Liao emperor Shengzong defeated the Song army and forced the Chinese government to pay him a large yearly tribute in silk and silver.
In the early twelfth century, the Jurchens destroyed the Liao Empire and founded their own Jin dynasty. Many Khitans moved to Central Asia, where they defeated the Seljuks and formed their own Western Liao empire (the Kara Khitai state), which in 1216 succumbed to Mongol attack. Meanwhile, the Jurchen sinicized the nomadic Jin Empire, which gradually came to include all of Northern China. The Song dynasty retained control only over Southern China.
The Jurchen emperor Shizong received a Chinese education, but he also promoted the development of Jurchen culture and learning. In 1164 he concluded a peace treaty with the Southern Song dynasty. While in 1207 Jurchens successfully defeated a Song invasion, they could not protect their country from Mongol attack from the North (1211–1234). In 1234, the Mongol armies conquered the Jurchen state.

How is education presented in Hard Times?

Education in Hard Times is often presented as little more than rote learning and the transmission of facts. In the notorious figure of Mr. Gradgrind, we have the epitome of Victorian utilitarianism with regards to the education of children. What matters more than anything else for him is that knowledge must have utility value, which is to say it serves some practical purpose. In such a rigid ideology there is no place for imagination or creativity. Mr. Gradgrind didn't become such a wealthy entrepreneur by studying poetry or art; he made his own way in the world by the understanding of cold, hard facts.
He lacks the imagination to understand that education can be broad and deep, allowing different children to develop their unique talents in their own individual ways. In common with most adults of the time, Mr. Gradgrind regards children as miniature adults. Their minds must be molded into the appropriate shape to prepare them for the outside world, the world of facts.
Yet Sissy Jupe's understanding of what constitutes a horse is arguably more practical than one gleaned from a precise definition learned by rote, the kind you'd find in a dictionary. Sissy knows what horses are because she has experience of them. She doesn't need to define a horse; she just needs to see one, hear one, ride one, or pet and stroke one. In other words, meaning is derived from how we engage in the real world around us, not through defining words and concepts with precision in advance as Mr. Gradgrind would have us do.

What are some quotes with symbolistic imagery in them from Fahrenheit 451 toward the end of the book relating to social conformity?

In the book's final scene, the men gather around a fire for warmth and cooking, as human beings have done for thousands of years.  Though it is a significant departure from how fire is used earlier in the novel, fire is used here as a means of organizing the men and ensuring their survival.  The image of the men silently watching the ritual of the bacon cooking is a reflection of social conformity: people gathering to share a meal.
As Granger, Montag and the other men break camp and begin their hike north, the men fall back to allow Montag to take the lead.  The fact that they have tacitly chosen Montag to lead them is another symbol and an image of social conformity. The men are free to think and act independently, yet they choose to stay together and allow a single man to lead them.  As they walk on, Montag rehearses in his mind what words he will later say to these men who look to him for guidance.

Beginning Algebra With Applications, Chapter 5, 5.4, Section 5.4, Problem 42

Determine the equation of the line through the points whose coordinates are $(-6,-13)$ and $(6,-1)$.

Using the Slope Formula with $(x_1, y_1) = (-6,-13)$ and $(x_2, y_2) = (6,-1)$

$\displaystyle m = \frac{-1-(-13)}{6-(-6)} = \frac{12}{12} = 1$

The slope of the line is $1$.

Using the point slope formula with $\displaystyle m = 1$ and $(x_1, y_1) = (-6,-13)$


$
\begin{equation}
\begin{aligned}

y - y_1 =& m(x - x_1)
&&
\\
y-(-13) =& 1[x - (-6)]
&& \text{Substitute } m = 1, (x_1, y_1) = (-6,-13)
\\
y+13 =& x+6
&& \text{Apply Distributive Property}
\\
y =& x-7
&& \text{Write the slope-intercept form}

\end{aligned}
\end{equation}
$

A talented young engineer (named Alex) at a well-respected medical supply company has been asked to subject one of their products (P) to a final series of safety tests before the company submits P to government regulators to inspect before the company puts P on the market. Alex has been given one week to complete these tests and submit a report to the company with the results. Ordinarily, one week would be plenty of time, but Alex is especially busy this week with matters both professional and personal. As such, Alex thinks about asking for the assignment to be given to someone else, but Alex realizes that this action would not look great. Alex is hoping for a promotion in the coming year. Alex accepts the task, and tries to fit in the safety tests when possible. However, by the time the end of the week comes around, Alex still has not finished half of the required tests. Alex considers asking for an extension but decides against doing so (there’s that potential promotion to think about). Alex thinks, “I’ve done some of the tests and P was safe in those. Further, I’ve spoken to people who were involved in earlier series of tests and others who were involved in the construction of P, and they were pretty confident that P is safe as it is. I’m up against a deadline here. Anyway, the government regulators will give P a look before allowing us to sell P, so I’ve got a bit of a safety net. I’m going to pretend that I did the last several tests (by filling in the report with numbers that we could reasonably expect to show up). Then I’ll sign the report, submit it tomorrow, and that will be that.” This is just what Alex does. Luckily, P turns out to be quite safe. It passes the government inspection without issue and goes on the market soon thereafter. Alex even gets the promotion later that year. Why would John Stuart Mill think that Alex almost certainly acted wrongly in this case, even though things seem to have “gone fine”?

In On Liberty, John Stuart Mill wrote that an individual was allowed to do harm to himself or herself but not to others. He believed that government and authority over others should exist only to prevent individuals from doing harm to others. 
While an individual can, he believed, choose to harm himself or herself, a person does not exist in isolation. Therefore, harm done to oneself (in this case, Alex's lie that he completed all the necessary safety tests) can in fact hurt others. Therefore, while the product seems to be safe, it may have defects down the line that have not yet been discovered. Therefore, Alex's decision to lie about having carried out the safety tests may eventually hurt other people. His lie has the capacity to harm others and not just himself. Accordingly, he violates John Stuart Mill's "harm principle."
In addition, Mill considered acts of harm possible from omission, not just commission. In other words, an individual can do harm by not doing something, not just by doing something. If an individual saw a fire and did not report it or try to put it out, for example, he or she would be violating the harm principle. Therefore, even though Alex does not commit a wrong by his actions, his inability to finish the safety tests is an act of omission that violates the harm principle according to John Stuart Mill. 

What makes "Salvation" by Langston Hughes nonfiction?

"Salvation" by Langston Hughes is a short essay and a chapter of his memoir, entitled The Big Sea. By definition, memoir and essay are both nonfiction forms. A memoir is similar to an autobiography in that it has the writer remembering moments from his life and relaying those to the audience. Hughes is most famous for his poetry, but "Salvation," as a personal essay is definitely a nonfiction text.
The essay is told in first person, as Hughes begins by saying, "I was saved by sin when I was going on thirteen. But not really saved. It happened like this." We can tell from the start that he is going to tell an autobiographical story about his salvation, or his lack thereof. From there, Hughes tells about an experience he had at church as a child. His aunt told him that he would see Jesus and be saved. When he saw Jesus, he would go to the altar and be welcomed by the church community as one of their own. In brief, Hughes never sees Jesus, but he thinks the other children who go to the altar, claiming to have seen Him, are lying. He decides he should lie, too, and be done with the charade. He is welcomed and celebrated as the other children are, but when he goes home that night, he cries in bed because he didn't see Jesus, and further, "now I didn't believe there was a Jesus anymore, since he didn't come to help me." 
The essay reads like a short story told in the first person, but is based on Hughes's personal experience. He makes a very intimate confession at the end of the story about his own faith at that time in his life. Therefore, this text is nonfiction. 

Identify the location where Buddhism originated, and give a brief account of its diffusion and current global spatial distribution.

Buddhism originated in India and is believed to have developed from the teachings of Siddhartha Gautama (born approximately 563 BCE) in Kapilavatthu near the border with Nepal. Gautama spent his life in Bihar and Uttar Pradash in eastern India. 
During the third century BCE, the Mauryan leader Ashoka converted to Buddhism and helped spread the faith by encouraging monks to travel to neighboring lands. In this manner, the faith spread from India to Sri Lanka, Burma, central Asia, Bhutan, Nepal, Tibet, China, Korea, and Japan. After Muslims entered India in the 11th century CE, Buddhism largely disappeared from India, though some historians believe it was in part absorbed into Hinduism. 
The estimates of the number of practicing Buddhists today range from 488 million to 525 million people, representing approximately 7%-8% of the world's population. China has the greatest number of Buddhists, with 244 million Buddhists. Thailand has about 64 million Buddhists, and Japan has about 45 million Buddhists. The other countries with great number of Buddhists are in Asia, including Cambodia, Laos, Sri Lanka, Bhutan, and Taiwan, among others. 

Romeo and Juliet is the most to blame for the bad choices include evidence

Romeo and Juliet both make impulsive, bad decisions that end with each of them committing suicide.
First, Romeo shows his impulsive nature when he says,

O, she doth teach the torches to burn bright! It seems she hangs upon the cheek of night Like a rich jewel in an Ethiope’s ear; Beauty too rich for use, for earth too dear! So shows a snowy dove trooping with crows, As yonder lady o’er her fellows shows. The measure done, I’ll watch her place of stand, And, touching hers, make blessed my rude hand. Did my heart love till now? forswear it, sight! For I ne’er saw true beauty till this night. (act 1, scene 5)

Here he is proclaiming his love for Juliet, whom he just met—right after wallowing in his sadness over his unrequited love for Rosaline. He changes his mind quickly and doesn't think things through.
Later, Juliet shows her impulsive nature when she talks about marrying Romeo. Even though she knows they are moving too fast, she is caught up in her love, or infatuation, for him.

Three words, dear Romeo, and good night indeed. If that thy bent of love be honourable, Thy purpose marriage, send me word to-morrow, By one that I’ll procure to come to thee, Where and what time thou wilt perform the rite; And all my fortunes at thy foot I’ll lay And follow thee my lord throughout the world. (act 2, scene 2)

Even though it was a decision made for love, getting married so quickly without the support of their families was the first bad decision that both Romeo and Juliet made.
Later, when Romeo thinks Juliet is dead, he says,

And shake the yoke of inauspicious stars From this world-wearied flesh. Eyes, look your last! Arms, take your last embrace! and, lips, O you The doors of breath, seal with a righteous kiss A dateless bargain to engrossing death! Come, bitter conduct, come, unsavoury guide! Thou desperate pilot, now at once run on The dashing rocks thy sea-sick weary bark! Here’s to my love! [Drinks] O true apothecary! Thy drugs are quick. Thus with a kiss I die. (act 5, scene 3)

Again his impulsive and impatient nature drive him to make an awful decision to end his own life. Instead of asking someone to help, asking someone what happened, or finding someone to console him, he impulsively decides he cannot go on living.
When Juliet wakes and realizes that Romeo is dead, she says,

What’s here? a cup, closed in my true love’s hand? Poison, I see, hath been his timeless end: O churl! drunk all, and left no friendly drop To help me after? I will kiss thy lips; Haply some poison yet doth hang on them, To make die with a restorative. (act 5, scene 3)

Here, Juliet also acts impulsively. Similar to Romeo, she doesn't reach out for help. She instead makes a rash decision and tragically ends her own life.

What is the resolution in Romeo and Juliet?

The resolution of the play comes when Prince Escalus arrives at the scene of Romeo's and Juliet's deaths. He confirms that Friar Lawrence has told the truth about the relationship between the two young people, and he reads of Romeo's plan to come to Juliet's tomb and drink poison so that he could remain with her in death. The Prince addresses Lords Capulet and Montague, pointing out how their hatred for one another killed the very people they love the most: their children. Capulet and Montague finally put their feud behind them, and Montague even offers to "raise [Juliet's] statue in pure gold," leading Capulet to allow Romeo to be buried with Juliet. The Prince has the final word in the play, symbolizing the return to order and the end of the chaos that was caused by families' mutual hatred. It is "glooming," but at least it is "peace." Justice will now rule, and "Some shall be pardoned, and some punished" for their roles in the sad tale of Romeo and Juliet.

Thanks to the prologue at the beginning of the play, the audience knows that Romeo and Juliet will die, but the fact that neither Romeo nor Juliet knows makes the resolution of the play all the more touching and tragic.
At the end of Shakespeare's tragedy Romeo and Juliet, Romeo mistakenly receives a message that Juliet has died, and the friar's message about her plan to fake her death does not reach him. Romeo is so grief-stricken he decides that he must die as well. When Romeo arrives at the tomb where the Capulets have placed Juliet, the audience knows that Juliet is actually alive, but Romeo does not. He swallows the poison he bought for this purpose and dies moments before Juliet regains consciousness. She sees his dead body upon waking, and she is so overwhelmed with the loss of Romeo that she kills herself with Romeo's dagger. Moments later, the Capulets and Montague arrive with the Prince.
The young lovers of Verona die needlessly, an event which leads their warring families to resolve their problems. The Capulets and Montagues even go as far as to agree to erect statues of their children in Verona to mark the new peace.

If there is a solution of chloroform and alcohol, each in proportion of 50 ml and 50 ml to form a solution of 100 ml, then which one is the solvent and why?

Chloroform is a chemical with the formula CHCl3.  It is a clear liquid and is commonly used as a solvent in organic chemistry.  Alcohol is a generic term for any alcohol but is probably most commonly used as a shorthand for ethyl alcohol (CH3CH2OH).  It is also a clear liquid that is a common solvent in chemistry.  If we mix 50 mL of each of the two chemicals, then we have an equal mixture of both.  The two liquids are miscible with each other and will combine to form a homogeneous mixture.  Since the two are present in equal proportions, we would say that the solvent system is a 1:1 mixture of chloroform and ethanol.  Since they are equal neither of them gets precedence over the other.
https://www.thoughtco.com/definition-of-solvent-604651

What did John Rawls consider a well-ordered society?

John Rawls's seminal work, A Theory Justice (1971), returned political philosophy to many of its founding questions about the nature of freedom, justice, and fairness found in Plato and Aristotle. Rawls here attempts to answer the question: what makes for a just society? This is a question that ultimately comes down to the distribution of both political rights and economic goods.
A well-ordered society for Rawls is one in which all citizens are treated equally under the law and which promotes individual liberty to the extent that it does not infringe on the well-being of others. Rawls carefully navigates a debate still prevalent in political discourse today, that between equality of opportunity and equality of outcomes. Rawls doesn't fall on one side of this debate, he attempts to seek a compromise. Rawls thinks that a well-ordered society should guarantee equality of opportunity but also thinks it should be governed according to what he calls "The Difference Principle." The Difference Principle puts a check on capitalist institutions by sanctioning economic activity that doesn't benefit the poorest members of society.
To summarize, a well-ordered (and just) society is governed by two principles:
1) The Greatest Equal Liberty Principle: "First: each person is to have an equal right to the most extensive basic liberty compatible with a similar liberty for others." (Rawls 1999, p. 266)
2) The Difference Principle: "Social and economic inequalities are to be arranged so that they are both: (a) to the greatest benefit of the least advantaged, consistent with the just savings principle, and (b) attached to offices and positions open to all under conditions of fair equality of opportunity." (Rawls 1999, p. 266)
You may be asking, how is this just society established? To answer this question Rawls employs insights from social contract theory. Rawls asks us to consider what principles society would be governed by if the citizens choosing those principles were unaware of their race, gender, economic background, and the other unique life experiences that often enter political deliberation. This encompasses what Rawls refers to as "the original position." Under this veil of ignorance, Rawls argues that citizens will agree upon principles of justice that seek to promote the enhancement of each and every member of the political community. Immanuel Kant's influence is acutely felt here. According to Kant, only that which is "universalizable" can be considered ethical.
Students interested in Rawls's work should also look at the works of political philosophy this book inspired such as Nozick's Anarchy, State, and Utopia and MacIntyre's After Virtue.
References:
Rawls, J. (1999). A theory of justice. Cambridge: The Belknap Press of Harvard University Press.
https://plato.stanford.edu/entries/rawls/

In his classic work of political philosophy A Theory of Justice, John Rawls elaborates his architecture for a just and well-ordered society, which combines elements of Locke's contract theory, Mill's utilitarianism, and the ethical concepts of Kant. Two founding principles serves as its cornerstones, the "Greatest Equal Liberty Principle" and the "Difference Principle."
The former principle states that each person is entitled to an equal right to the most extensive total system of basic liberties and that this system must apply to all. The latter principle states that social and economic inequalities must require that the greatest benefits are allotted to the most disadvantaged and that all offices and opportunties must be open under conditions of fair equality.
Rawls believes that these principles can naturally be derived from two hypothetical constructs. The first, called the "original position," is that of citizens selecting the principles of a just society. They must make these selections behind the second construct, the "veil of ignorance," which prevents the citizens from having any knowledge of their gender, race, or religion or any awareness of advantages they may possess such as wealth, intelligence, and talent.
Such a blind selection process, Rawls theorizes, would guarantee that citizens would naturally choose the best outcomes for those who would be most disadvantaged by the allotment of natural gifts, since this could ultimately be their position.
In sum, Rawls's A Theory of Justice states that the most well-ordered society is that which provides equal rights to all citizens, the opportunity for equal access to all positions, and the most favorable outcomes accorded to the most disadvantaged.

Rawls considered a well-ordered society to be one in which each individual had an equal opportunity to live a good life, and to have basic liberties, irrespective of the conditions of their birth. All social institutions must be structured in such a way as to ensure that everyone has equal access to them, though Rawls did believe that individuals should be able to excel (and profit materially from their success). In short, Rawls believed that a society founded on justice would be set up to be fair. Laws would be transparent, equitable, and aimed toward promoting justice. Government structures would be equally accessible to all people. While Rawls eschewed engaging in the specifics of how this society would actually be implemented or governed, the gist of his theory of society (as laid out in his landmark work A Theory of Justice) was that society should be ordered in a way that promoted equality and best cared for the least fortunate segments of the society.
https://plato.stanford.edu/entries/rawls/

What is a summary of chapter 5 in The Twenty-One Balloons?

The chapter begins with the Professor being "gently awakened" after four or five hours of sleep. The man insists that the Professor get out of the sun. The Professor has no idea what is happening. He knows that the man isn't a native, and the professor doesn't believe he is a fellow explorer either. It turns out this man is Mr. F, and he confirms for the Professor that he did indeed crash on Krakatoa. Mr. F is excited to know that the Professor believed the island to be uninhabited, because that is by design by the people living on the island.

"This is Krakatoa, all right," he said. "And we who live here are most pleased that the rest of the world is still convinced that Krakatoa is uninhabited. Hurry up, put on your clothes."

Mr. F is quite excited to have a guest on the island, and he quickly ushers the Professor into his tour of the mountain and the mines. The island quakes with magma movement, and the Professor is amazed that anybody can actually live there. He is even more amazed by the diamond mines. As the chapter nears its conclusion, Mr. F admits that he planned to shoot down the Professor's balloon in order to keep Krakatoa's inhabitants a secret. Now that the Professor knows the truth, Mr. F says that he will have to stay on the island forever; however, it shouldn't be a problem after the Professor learns of all of the wonders on the island.

"You have seen our diamond mines, that is, you have seen one of them; there are many other unexplored plots of ground around the base of the mountain where the earth doesn't ever move. Do you understand now why you will have to remain our permanent guest?"

At the beginning of Chapter five, The Professor is awakened by a queerly-dressed gentleman who is kneeling over him. The Professor has a nasty sunburn, and the strange gentleman, Mr. F., offers him a suit similar to his own. It turns out The Professor is now on Krakatoa, an island that he had thought to be uninhabited. Mr. F is glad to hear this belief and tells The Professor that the residents of the island intentionally surrounded their beautiful city with plant growth and underbrush in order to give the illusion to passing ships that nobody lives on the island.
The two men travel to the volcano, which, as it turns out, contains a large number of diamond mines. Mr. F. reveals that he was sent with a handgun to ensure that The Professor landed on the island, and now that The Professor has seen the secrets of the diamond mines, he is no longer allowed to leave. Mr. F. continues to tell The Professor about the island, claiming that the diamonds are so valuable that they are essentially worthless, and if they were to be sold abroad, the entire diamond market would crash due to the sheer volume of diamonds.

int x^2/(x-1) dx Find the indefinite integral

intx^2/(x-1)dx
Rewrite the integral as ,
intx^2/(x-1)dx=int(x^2-1+1)/(x-1)dx
=int((x^2-1)/(x-1)+1/(x-1))dx
=int(((x+1)(x-1))/(x-1)+1/(x-1))dx
=int(x+1+1/(x-1))dx
apply the sum rule,
=intxdx+int1dx+int1/(x-1)dx
Apply the power rule and standard integral intdx/x=ln|x|
=(x^(1+1)/(1+1))+x+int1/(x-1)dx
Apply integral substitution u=(x-1) for int1/(x-1)dx
du=dx
int1/(x-1)dx=int(du)/u
=ln(u)
substitute backu=(x-1),
=ln|x-1|
So the final integration and adding a constant C to the solution yields,
=x^2/2+x+ln|x-1|+C

How does the relationship between Virgil and Dante change throughout Inferno?

I would argue that the relationship between Dante and Virgil doesn't change that much over the course of The Inferno. When Virgil first appears in canto 1, he offers to help Dante, who has been stalled by the she-wolf blocking his path to the hill (Heaven). Virgil tells him that he knows another way; it involves traveling through all of the circles of Hell, but Virgil promises to be Dante's guide and companion.
As Virgil leads Dante through the vestibule of Hell in canto 3 and all of the nine circles that follow, he repeatedly prepares Dante for what he is about to see and protects him from those who question his presence (since he is not dead nor damned yet). Virgil tells Charon, for example, that it is not his place to question what God has deemed necessary. Dante faints repeatedly, overcome by his fear and disgust, and Virgil supports him and helps him move on to the next level.
Finally, in the last ring of the ninth circle, the poets see Satan and the three worst traitors of history—Judas, Brutus, and Cassius—each placed in one of Satan's three mouths. To exit Hell they must literally climb Satan's giant hairy body. Virgil actually carries Dante on his back, symbolizing not only that a sinner must overcome Satan and sin to get to Purgatory or Heaven but also that most sinners need assistance in their quest. As he has done all along, Virgil helps Dante complete his journey through Hell and allows him to move on to purgatory in the next part of The Divine Comedy.

Calculus of a Single Variable, Chapter 3, 3.2, Section 3.2, Problem 4

You need to notice that the given function is continuous on [-1,1] and differentiable on (-1,1), since it is a polynomial function.
You need to verify if f(-1)=f(1), hence, you need to evaluate the values of function at x = 0 and x = 1.
f(-1) = sqrt(2 - root(3)((-1)^2))^3 = 1
f(1) = sqrt(2 - root(3)((1)^2))^3 = 1
Since f(-1)=f(1) = 1 and the function is continuous and differentiable on the given interval, the Rolle's theorem may be applied, hence, there is a point c in (-1,1) , such that:
f'(c)(1+1) = 0
You need to find the derivative of the function, using chain rule:
f'(c) = (sqrt(2 - root(3)(c^2))^3)
f'(c) = (3/2)(2 - c^(2/3))^(3/2-1)*(2 - c^(2/3))'
f'(c) = (3/2)(-2/3)*c^(2/3-1)*(2 - c^(2/3))^(1/2)

f'(c) = -c^(-1/3)*(2 - c^(2/3))^(1/2)
f'(c) = -(sqrt(2 - c^(2/3)))/(root(3) c)
Replacing the found values in equation 2f'(c) = 0 yields:
-2(sqrt(2 - c^(2/3)))/(root(3) c)) = 0 => sqrt(2 - c^(2/3)))/(root(3) c) = 0
Raise to 2rd power both sides:
(2 - c^(2/3)) = 0 => c^(2/3) = 2 => c = 2^(3/2) => c = 2sqrt2
Notice that c =2sqrt2 does not belong to (-1,1).
Hence, applying Rolle's theorem to the given function yields that there is no values of c in(-1,1), such that f'(c) = 0 .

See attachments below

Hello!
1. Let us start from the first question, as it is the most straightforward.


(a) As we see, when x approaches positive infinity, f(x) approaches -2.


(b) As x approaches negative infinity, f(x) approaches 2.


(d) As x approaches 3 from any side, f(x) approaches negative infinity, -\infty.
(e) The vertical asymptotes can be found at x=1 and x=3 (finite values of x where f tends to infinity). The horizontal asymptotes can be found at y=2 and y=-2 (the limits of f on infinity, if it exists exist).


2. To determine the limit, multiply and divide the given expression by sqrt(x^2+cx)+sqrt(x^2+dx). The numerator will become (x^2+cx)-(x^2+dx)=x(c-d).
Now divide both numerator and denominator by x and obtain the following:
(c-d)/(sqrt(1+c/|x|)+sqrt(1+d/|x|)).
Now, we are able to let x-gt\infty, and we get the following:
(c-d)/(sqrt(1+0)+sqrt(1+0))=(c-d)/2.
This is the answer.
3. To get the vertical asymptote x=4, put (x-4) into the denominator, as it will give infinity at x=4. To get the vertical asymptote x=6, multiply the denominator by (x-6).
To balance these factors and get the horizontal asymptote y=4, we need the limit of f at infinity to be equal to 4. Place 4x^2 into the numerator:
f(x)=(4x^2)/((x-4)(x-6)).
It is an answer (there are many others possible).

Why did George Washington feel that citizens should give their loyalty to the nation as a whole?

George Washington's (1732 - 1799) early experiences as commanding general of the Continental Army directly exposed him to the brittle unity and inefficiency created by competing state governments, each jealous of the other and focused on their own benefit and survival over that of the nation as a whole.
Based on these early experiences, Washington realized that the United States would be a frail nation in the absence of national unity and that the inter-state jealousies he'd previously witnessed might again manifest themselves if there was not a collective sense among the citizenry that was not split by regional and partisan considerations.
This focus on national togetherness was a recurrent theme in Washington's public life. His proclamation designating November 26, 1789 as the first Thanksgiving was intended to promote that national unity he sought to inspire.
In his farewell address of 1796, Washington offered a final reminder of his appeal for a sense of union transcending regionalism:

Citizens, by birth or choice, of a common country, that country has a right to concentrate your affections. The name of American, which belongs to you in your national capacity, must always exalt the just pride of patriotism more than any appellation derived from local discriminations.
https://www.history.org/almanack/life/politics/farewell_address.cfm

https://www.whitehouse.gov/about-the-white-house/presidents/george-washington/

George Washington believed that citizens should give their loyalty to the country as a whole. George Washington understood that if people were loyal only to their state or region, problems would develop. He believed that people needed to understand that in a country there are going to be times when actions that are good for the country as a whole may actually harm a state or a region. He knew that decisions had to be made in the best interest of the country.
George Washington also feared what would happen if people made decisions based only on the interests of a state or a region. He believed this would lead to constant squabbles and would slow the progress of the country. He believed this could threaten the existence of the United States if people were more focused on their state or their region instead of being focused on the country as a whole. The success of the country depended on a wider, national view of events.