What is the setting of chapter 1 and what is odd about it?

The setting of chapter 1 isn't entirely one exact place. The chapter contains a little bit of detail regarding the town of Treegap, the "touch-me-not" house, a road, and a wood:

On the left stood the first house, a square and solid cottage with a touch-me-not appearance, surrounded by grass cut painfully to the quick and enclosed by a capable iron fence some four feet high which clearly said, "Move on—we don't want you here." So the road went humbly by and made its way, past cottages more and more frequent but less and less forbidding, into the village. But the village doesn't matter, except for the jailhouse and the gallows. The first house only is important; the first house, the road, and the wood.

There really isn't anything strange about the town of Treegap. The "touch-me-not" cottage is a bit strange in the fact that it doesn't present itself as welcoming, but the real strangeness is found in the road and wood. Readers are told that the Foster family owns the wood; however, they show next to zero interest in it:

In any case, the wood, being on top—except, of course, for its roots—was owned bud and bough by the Fosters in the touch-me-not cottage, and if they never went there, if they never wandered in among the trees, well, that was their affair.

Readers finally get a clue as to the strangeness of the wood in the final paragraph of chapter 1. We are told that the cows absolutely do not go through the wood. Instead, they have made a path that goes around the wood. It's as if there is something odd or foreboding in the wood that should be avoided at all costs:

In the end, however, it was the cows who were responsible for the wood's isolation, and the cows, through some wisdom they were not wise enough to know that they possessed, were very wise indeed. If they had made their road through the wood instead of around it, then the people would have followed the road. The people would have noticed the giant ash tree at the center of the wood, and then, in time, they'd have noticed the little spring bubbling up among its roots in spite of the pebbles piled there to conceal it. And that would have been a disaster so immense that this weary old earth, owned or not to its fiery core, would have trembled on its axis like a beetle on a pin.

Readers will eventually learn that the tree marks the location of a very special spring that grants eternal life to anybody that drinks from it. The setting of the first chapter is strange because readers are told that animals know better than to go there.

What proves that there is strong feminism in "Raymond's Run"?

Feminism can be defined as the political and social movements that champion the rights of women, promote equality of sexes in a patriarchal society, and support female empowerment. In Toni Cade Bambara's short story, the protagonist, Hazel Elizabeth Deborah "Squeaky" Parker, is depicted as a strong, talented female character with high aspirations. Hazel's mindset, confidence, and personality embody the feminist ideology and illustrate female empowerment.
Squeaky is the fastest person in her age group and never backs down from a challenge. She does not fear any boy or girl and confidently believes that she will take home the first-place medal at the May Day races. Squeaky's main competitor is also a female, who is new to the neighborhood and known as a talented athlete. Squeaky demonstrates her talent by winning first place and reveals her leadership skills by committing to coaching her differently abled brother, Raymond. Squeaky's role as a strong, confident female is aligned with the feminist agenda, which promotes equality among sexes and female empowerment.

What is the significance of juxtaposing Miss Maudie’s house fire with the first snow day in Maycomb in To Kill a Mockingbird?

In chapter 8, Harper Lee juxtaposes the coldest weather Maycomb has experienced since 1885 with Miss Maudie's house fire to foreshadow the upcoming division and conflict among the citizens regarding the Tom Robinson trial. The extremely cold weather and the fire are both destructive natural forces that serve as a portent to the hazardous effects of racism that will negatively influence the community and cause conflict throughout the pleasant, small town. As the Tom Robinson trial approaches, citizens begin to bicker with one another, and they criticize Atticus for defending a black man. During the trial, Maycomb's overt prejudice is exposed, and this prejudice is ultimately responsible for the death of an innocent man. The children also lose their childhood innocence after witnessing racial injustice firsthand. Then, Bob Ewell seeks revenge by attempting to murder Jem and Scout. Overall, Harper Lee's juxtaposition in chapter 8 foreshadows the harmful effects of racism in the typically pleasant quiet town of Maycomb and hints at the upcoming conflict in the community regarding the Tom Robinson trial.

The unusual juxtaposition of fire and snow is significant because it hints at the many conflicts to come. Fire and snow are antithetical forces: they cannot coexist; one must prevail over the other. Yet both are equally destructive in their own way, and their unique combination seems to point towards some kind of trouble, the kind of which Maycomb has never really seen before.
Such unprecedented weather—the first snowfall anyone in town can remember—acts as a portent for the trial of Tom Robinson and the incredibly bitter divisions it will generate. As snow is rare in Maycomb, so too will be the conflicts surrounding the forthcoming trial be exceptional. There's always been conflict in the town, to be sure, but nothing quite like what's about to happen.
When Scout sees the snow, she thinks the world's ending. She's not far wrong, because her carefree innocent life is about to change forever. Fire traditionally represents Hell, so combined with the unseasonal snowfall, we can see why Scout thinks that the world is coming to an end.

In "Marriage is a Private Affair" by Chinua Achebe, how do we see children raised by extremely strict parents becoming rebellious?

The issue here is complicated by cultural context. The studies of authoritarian parenting done in the United States are situated within a sophisticated modern society, and focus on middle class Caucasians among whom arranged marriages are regarded as very alien and excessively authoritarian. The Ibo society of Nigeria portrayed by Achebe is not the United States in the twenty-first century and different cultural norms apply.
The key distinction Achebe is making is between traditional village life and an urban life that is postcolonial, having adapted many of the values of British society. The young couple in the story is part of a transitional population with ties to both worlds, educated and sophisticated, but still with emotional connections to the traditions of extended family and village culture.
Nnaemeka's father is not portrayed as overly controlling in terms of Nigerian village society, and in fact the reactions of the villagers show his ideas and behaviors to be relatively normal, even if his continued refusal to accept Nene eventually appears overly stubborn. Nnaemeka is not really a rebel or juvenile delinquent, but simply a young man in love who desires his father's approval for his marriage. While he does marry the woman of his choice, and reacts to his father's authority by standing his ground, he is not rebellious in the sense of being driven to anti-social behavior out of resentment of authority. 
The story, in fact, ends with reconciliation due to the loving persistence of Nene. It is the father, not the son, who has maintained the rift, and even the father is eventually reconciled to the marriage by the existence of grandchildren. Overall, the arc of the story suggests that the title is ironic. Although marriage might on the surface appear private, in fact, it does involve the whole village and extended family. The story therefore is not simply, as it would be if set in modern Britain or the United States among middle class families, one of personal choices or rebellions but rather one about a clash of traditional Ibo and modern postcolonial Nigerian culture. 

How did the narrator attempt to open an account?

The narrator attempted to open an account secretly.
Upon entering the bank, the narrator asked to speak to the manager privately. Because of the narrator's nervous agitation and air of secrecy, the manager assumed that he was dealing with a private detective. After questioning him, however, the manager discovered that the narrator merely wanted to open an account.
For his part, the manager assumed that the narrator was, at the very least, a relatively wealthy man. After all, the latter's cautious manner seemed to suggest it. Upon discovering that the narrator wanted to deposit a mere fifty-six dollars into his new account, the manager dropped his previously ingratiating manner.
Unceremoniously, the manager referred the narrator back to the accountant. By this time greatly embarrassed, the narrator unwittingly stepped into the safe. Coldly, the manager ordered the narrator to vacate the room.
The accountant then assisted the narrator in depositing his money. Immediately after, the narrator requested a withdrawal. The accountant told the latter to fill out a withdrawal slip. Because of his nervousness, the narrator asked to withdraw all of the funds he had just deposited.
In the end, the narrator had little choice but to leave with all of the money he had just deposited. Because of his extreme nervousness, the unfortunate narrator had attempted to open an account secretly.

What works or figures influenced Thomas Paine's own ideas and writing?

In writing The Rights of Man, Paine was actually inspired by a contemporary whose ideas opposed Paine's own: Edmund Burke, best remembered today for his philosophy of the sublime and strong opposition of the French Revolution. In The Rights of Man, Paine sought to refute Burke's argument. The subject of the rights of people to rebel against their governments was a contentious one at the time, and Burke himself was writing amid a groundswell of approval for the revolution that had been stirred up by the popular preacher and mathematician Richard Price. Other figures who wrote against Burke's pamphlet included Mary Wollstonecraft (author of A Vindication of the Rights of Women) and William Godwin. This period was marked by lively debate and came to be known as the Revolution Controversy, with thinkers on both sides of the debate producing pamphlets and collections of essays in order to propagate their points of view.
Wollstonecraft had heard Price give numerous sermons on the topic of revolution and the supposed connection between the French Revolution and the Glorious Revolution that had taken place in England the century before. Price's ideas are generally believed to have been the primary influence on all the key liberal thinkers of the Revolution Controversy. Paine, however, had also been inspired by his own observations in France. He strongly believed that the revolution was justified and that men were born free and equal and must oppose and reject any government that did not also take this view.

What is Zhu Bajie's new title for his efforts in Xuanzang?

Zhu Bajie's new title is Altar Cleanser.
He is given this title by the Tathagata. Accordingly, Zhu Bajie once served as Marshal Tien Peng, a water god in the River of Heaven. He was an illustrious warrior. However, his reign as a river god ended after he flirted with an immortal maiden at the Heavenly Peach Banquet.
Because of his indiscreet behavior, Zhu Bajie was sentenced to be reborn as a beast. Then, after his conversion to Buddhism, he zealously guarded Xuanzang as the holy monk made his journey west. Upon hearing that he has been given the title of Altar Cleanser, Zhu Bajie becomes visibly upset. He questions why he has been given such scant honors when the holy monk and Sun Wukong have both been made Buddhas.
The Tathagata responds by reminding Zhu Bajie that he is still lazy and has a voracious appetite. As a result, Zhu Bajie has not purified his soul enough to ascend to greater honors. The Tathagata contends that Zhu Bajie should be happy with his new position, since it will accord him plenty to eat.

What is a summary of the documentary "Harold Shipman, Doctor Death" (Serial Killer Documentary)? What are the main points?

This video is about Dr. Harold "Fred" Shipman, dubbed "Doctor Death," who the video describes as "one of the world's most prolific serial killers." The video starts with an English investigator (named Stan Egerton) who starts looking into a forgery case in Hyde, England, regarding a will for an 81-year-old woman named Mrs. Grundy. The deceased's daughter, a solicitor, found out that Dr. Shipman had deceived her mother by telling her mother that she was signing an authorization for a survey, not a will. Dr. Shipman had been the target of an earlier secret investigation about the large number of deaths he had certified, but the investigation was inconclusive. There were other people with suspicions in the community, including the local undertaker and a local taxi driver. 
The video goes back to Dr. Shipman's history at school, including his former rugby playing and the death of his mother to cancer when Fred was 17. Some believe this "early introduction to morphine and death had a lasting effect on Fred." His reaction to his mother's death was bizarre at the time, as he reported that he had gone for a run in the rain in response. He developed a dependence on a highly addictive pain killer in the 1970s and went to court for obtaining drugs by deception and was fined 600 pounds. He obtained the drug by forging prescriptions and oversubscribing, but he underwent treatment and kicked his dependence. He worked at a group medical practice and then took his 3,000 patients to his own practice so that he could "enjoy his secret indulgence--murder," as the video says. 
The investigation into Mrs. Grundy's death found that she was killed by an injection of morphine. Detectives began to uncover a pattern of many women dying at home, dressed in day clothes, shortly after seeing Dr. Shipman. The doctor's computer files showed that he had taken out records or added records to cover up his deadly acts. He had often recorded deaths before they actually happened. The community was in shock as the investigation proceeded and many bodies of the deceased were exhumed. Shipman killed many people for what was described as "paltry sums," but he killed one, Bianka Pomfret, to inherit a great deal of money. Her body, when exhumed, was found to contain a large quantity of morphine, and the police accused Dr. Shipman of the murders of many former patients. 
The video also describes the great lengths Dr. Shipman went to so that he could obtain morphine, including killing the father of one patient who questioned the doctor's treatment of his son. People posit that Dr. Shipman simply killed patients because he no longer wanted to care for them--for no other reason. 

What is the form of the sonnet?

Sonnet 55 uses the form and structure that is now called the "Shakespearean" sonnet because of Shakespeare's use of it throughout his sonnet cycle. It differs from the Petrarchan sonnet form that was more commonly used at the time of Sonnet 55's writing. As with all sonnets, the poem has fourteen lines. However, its rhyme scheme differs from that of Petrarchan sonnets in a way which helps Shakespeare set up and execute the argument of the sonnet and then bring it to a conclusion in the closing two lines.
The rhyme scheme of the Shakespearean sonnet is ABAB CDCD EFEF GG. The rhyme scheme of a Petrarchan sonnet, by contrast, is ABBAABBA CDECDE. There are other sonnet types (see the link below). But perhaps the reason Shakespeare chose the form he did (which is named after him, but which he did not actually invent himself) is that it is a more appropriate vehicle for the points he wished to convey. In Sonnet 55, we can see how the structure with a rhyming couplet as the final two lines, using a different rhyme from all that have preceded it, helps isolate the "moral," or point, of the sonnet by emphasizing these lines:

So, till the Judgement that yourself arise,
You live in this, and dwell in lovers’ eyes.

College Algebra, Chapter 5, 5.4, Section 5.4, Problem 30

Solve the equation $e^{2x} - e^x - 6 = 0$

$
\begin{equation}
\begin{aligned}
e^{2x} - e^x - 6 &= 0\\
\\
(e^x - 3)(e^x + 2) &= 0 && \text{Using trial and error}
\end{aligned}
\end{equation}
$

Solve for $x$

$
\begin{equation}
\begin{aligned}
e^x - 3 &= 0 &&& e^x + 2 &= 0\\
\\
e^x &= 3 &&\text{Add }3& e^x &= -2 && \text{Subtract 2}\\
\\
\ln e^x &= \ln 3 &&\text{Take $\ln$ of each side}& \ln e^x &= \ln(-2) && \text{Take $\ln$ of each side}\\
\\
x &= \ln3 &&\text{Property of $\ln$}& x &= \ln(-2) && \text{Property of $\ln$}
\end{aligned}
\end{equation}
$

The solution to the given equation is only $x = \ln 3$, since $\ln (-2)$ is undefined.

How does literary criticism in Margaret Atwood's "Happy Endings" parallel the social rebellion present in story?

The Atwood "story" does several things at once. 
It is a guide of sorts, a kind of lesson to aspiring writers about how plot works, and about how stories end. Her point, given at the end of the piece, is that plot is simply a "what and a what and a what," a series of empty events with interchangeable details and characters. The only true ending, as she says, is that "John and Mary die."
The examples she uses, the story of John and Mary in all its permutations, lays out in a purposely schematic way the sexual politics of John and Mary's relationship. Mary either allows herself to be used by John because she hopes he will marry her (story B) or because she feels sorry for him (C), but in each case Mary is frustrated because John cannot meet her needs. Neither John nor Mary is very clear on what their real needs might be, and it is ironic and tragic that neither John's ability to act nor Mary's more limited ability to get what she wants leads to any fulfillment. In fact, B and C both end in suicide or murder. Atwood's point is that no matter how you switch around events, the outcome (the lack of emotional connection, or of essential freedom to be ones' self) remains the same.
If we understand this story to be about "social rebellion," then the thing it is revolting against is (I suppose) the petty concern for "plot" and "happy endings" that fiction writers and everyday people are so obsessed with. The details of plot make no difference: it doesn't matter in the end whether John is young or old, or if real estate values go up or down.
Atwood's final line points a way out of this dilemma: in trying "how" and "why," she is calling for action to make real change (the "how") and analysis to understand our current situation (the "why"). She suggests that the true purpose of fiction may be to effect change in these ways.

a_n=(-2/3)^n Determine whether the sequence with the given n'th term is monotonic and whether it is bounded.

a_n=(-2/3)^n=(-1)^n(2/3)^n={(-(2/3)^n if n=2k-1),((2/3)^n if n=2k):}
This tells us that odd-numbered terms are negative, while even-numbered terms are positive. Since the terms alternate in sign, the sequence is alternating. In other words, the sequence is not monotonic.
All terms of the sequence are in [-2/3,4/9].
This is because -(2/3)^n< -(2/3)^(n+1), forall n in NN  and lim_(n to infty)-(2/3)^n=0
Also, (2/3)^n>(2/3)^n, forall n in NN and lim_(n to infty)(2/3)^n=0
Clearly -2/3 is the smallest term of the sequence and 4/9 is the greatest.
Therefore, the sequence is bounded.
The image below shows the first 20 terms of the sequence. We can see that the sequence is also convergent even though it is not monotonical                             

What did Timothy suspect about the island that he didn't tell Phillip at first?

I believe that this question is asking about events in chapter seven. Phillip and Timothy have finally gotten themselves ashore on a small, deserted island. Timothy leaves to scout out the island and find a suitable location for shelter. When Timothy returns, he tells Phillip that the island is quite small, but it has some positives to it. Phillip is suspicious, though, that Timothy isn't giving him all of the information.

"You are worried about something, Timothy.  Please tell me the truth. I'm old enough to know."

Timothy then confides to Phillip that they are likely in an area known as the "Devil's Mouth." It is an area of ocean and islands that is not frequented by ships. It is a dangerous area for ships because of the numerous sharp coral banks. Timothy says that it's a large "U-shaped ting." The small cay that they are on is one of many small cays that is contained within the ring of coral. The coral prevents ships from getting close, so Phillip and Timothy now have almost no chance of being spotted by a passing ship.

Discuss the historical background of the story.

"The Last Class" is set in Alsace, a region between France and Germany that has been fiercely contested between the two nations for years. This was especially true during the Franco-Prussian War, which was a major victory for Prussia used as a pretext for creating a unified Germany under the Prussian rulers. The war took place in 1870, and the story is set a little while after the conflict. As part of the treaty that ended the war, Germany received Alsace, which had been under French control.
This is why, when Frantz goes to school at the beginning of the story, he learns that French is no longer to be taught at his school. Instead, the teacher, Monsieur Hamel, says that the German government has mandated that students may only learn in German. This, of course, is a very distressing occurrence for the students. Frantz is very upset, largely because this news has so visibly affected his teacher. By the end of the story, Hamel can only shout "Vive La France" to his students, and the future is very uncertain. So the story explores the effects of big geopolitical events on ordinary people. Readers may be aware that Alsace was reclaimed by France after World War I.
https://www.commonlit.org/texts/the-last-class-the-story-of-a-little-alsatian

Explain this quote that Nick says to Gatsby. What does he mean by this? "'They're a rotten crowd,' I shouted across the lawn. 'You're worth the whole damn bunch put together'"

It is clear throughout the novel that Nick comes to view Gatsby as a man with noble character. Nick gets sucked into and enthralled by the world that Gatsby lives in, and also comes to understand his fascination and obsession with that world; Gatsby has come by his fame and fortune by "humble beginnings" in Nick's eyes. He wasn't born into a wealthy family, but was a fortunate recipient and thankful patron of the life he lived.
Nick also realizes throughout the novel that none of Gatsby's aura of golden living was for himself, but for love. Gatsby is humble, generous, welcoming, and vulnerable to Nick. Although he is a part of this "rotten" social circle, Gatsby is vastly different than Tom and Daisy and their own obsessions of wealth, appearance, and shallow friendships. Gatsby can never truly fit in with the crowd of old money, taught class and arrogance, and selfishness. He was born into a poor family, an army man, and had to work his way into the whirlwind of a society he now belongs.
Understanding all of this, we can see why Nick views Gatsby as "worth" more than "the whole bunch"; Gatsby has morals, character, and a conscience compared to his constituents. Nick sees his good heart and his vulnerable soul as opposed to the hollow and counterfeit individuals he surrounds himself with.

This remark shows that Nick has been entranced by the "world of Gatsby". This scene occurs in Chapter 8. Nick and Gatsby had just had a long talk about Gatsby's past history. Gatsby did not feel worthy of Daisy because she was of a high social status, and he was not. Nick hates this. He hates this because he does not feel fondness toward the ultra-rich, famous, but empty people who populate Gatsby's parties.
He comes to the conclusion that Gatsby is worth all of the so-called "friends" who flit around him, leeching off of his money, drinks, music, food, and excesses. This is said the last time before he is killed. By this point, Nick's character has developed. He has already made his judgments about the other varying characters in the book. He has particularly made up his mind about the upper-class people, Daisy and Tom. Since the beginning of the story, Nick has become more vocal about his opinions.
Before this quote, we were aware at just how much Nick treasured his relationship with Gatsby, but not how Gatsby feels about Nick. In this instance, he smilingly shows Nick just how much his relationship with Nick means to him.
He has finally realized what "true worth" really is. To Nick, true worth isn't the money, the big homes, the parties, the cars, the food and drink...but the individual's soul and spirit determine his or her true worth.

Among other things, the statement shows just how much Nick has been sucked into Gatsby's world, like so many others before him. Previously, there'd always been an air of detachment about Nick, a sense that he was somehow above the fray of Gatsby's strange, exciting world. Yet even he has succumbed to its charms, drawn in by a combination of Jay's charisma and the fundamental decency of his character.
By complete contrast, Nick utterly rejects the world of Tom, Daisy, and Jordan and the shallow, vacuous phoniness it represents. He respects Gatsby all the more because he's not really one of them. Gatsby is an outsider: someone who'll never be accepted by the old money elite of East Egg. And for Nick, that's something to admire. Although Gatsby may mix socially with such people, and although he clearly aspires to be accepted by them, he still retains some integrity.
The key word in Nick's statement is "worth." Gatsby may not have been born with a silver spoon in his mouth; he may have derived his phenomenal wealth from the proceeds of organized crime; yet for all that he's still worth a whole lot more than all the Toms and Daisys of this world put together. Nick has changed because, thanks to his relationship with Gatsby and his negative experience of running with the East Egg crowd, he's finally realized where the true worth of someone really lies.

Calculus of a Single Variable, Chapter 5, 5.7, Section 5.7, Problem 42

Recall that int f(x) dx = F(x) +C where:
f(x) as the integrand function
F(x) as the antiderivative of f(x)
C as the constant of integration..
For the given problem, the integral: int x/sqrt(9+8x^2-x^4)dx
does not yet resemble any formula from table of integrals.

To evaluate this, we are to apply u-substitution by letting:
u = x^2 then u^2 = x^4 and du = 2x dx or (du)/2 = x dx .
Then the integral becomes:
int x/sqrt(9+8x^2-x^4)dx =int x dx/sqrt(9+8x^2-x^4)
=int ((du)/2)/sqrt(9+8u-u^4)
Apply the basic property of integration: int c f(x) dx = c int f(x) dx to factor out 1/2 .
int ((du)/2)/sqrt(9+8u-u^4) = 1/2int (du)/sqrt(9+8u-u^4)
The integral does not yet resembles any integration formula.
For further step, we apply completing the square on the part: 9+8u-u^2 .
Completing the square:
Factoring out -1 from 9+8u-u^2 becomes: (-1)(-9-8u^2 +u^2) or -(u^2 -8u-9) .
u^2 -8u-9 resembles ax^2 +bx+c where:
a=1 , b= -8 and c=9 .
To complete the square we add and subtract (-b/(2a))^2 .
Plug-in the value of a=1 and b=-8 in (-b/(2a))^2 :
(-b/(2a))^2 =(-(-8)/(2*1))^2
=(8/2)^2
=4^2
=16.
Adding and subtracting -16 inside the ():
-(u^2 -8u-9) =-(u^2 -8u-9+16-16)
To move out "-9" and "-16" outside the (), we distribute the negative sign or (-1).
-(u^2 -8u-9+16-16) =-(u^2 -8u-9+16) +(-1)(-9)+ (-1)(-16)
=-(u^2 -8u-9+16) +9+ 16
=-(u^2 -8u-9+16) +25
Factor out the perfect square trinomial: u^2 -8u+16 = (u-4)^2
-(u^2 -8u+16) + 16 = -(u-4)^2+25
Then it shows that 9+8u-u^4 =-(u-4)^2+25
=25-(u-4)^2
= 5^2 -(u-4)^2
Then,
1/2 int (du)/sqrt(9+8u-u^4)= 1/2int (du)/sqrt(5^2-(u-4)^2)
The integral part resembles the basic integration formula for inverse sine function:
int (du)/sqrt(a^2-u^2)= arcsin(u/a)+C
Applying the formula, we get:
1/2int (du)/sqrt(5^2-(u-4)^2) =1/2 arcsin ((u-4)/5) +C
Plug-in u =x^2 for the final answer:
int x/sqrt(9+8x^2-x^4)dx =1/2 arcsin ((x^2-4)/5) +C

In Thomas Paine's Common Sense: Why are Paine's reasons and rhetoric significant?

Thomas Paine wanted the message of "Common Sense" to be very accessible to his audience, the people of the American colonies. He was contracted to convince as many people as possible that separation from Britain was the right decision at that time.
Paine relied heavily on appeals to logic.  In the quotation below, he anticipated an opposing argument and refuted it.

"I have heard it asserted by some, that as America hath flourished under her former connection with Great Britain, that the same connection is necessary towards her future happiness, and will always have the same effect. Nothing can be more fallacious than this kind of argument. We may as well assert, that because a child has thrived upon milk, that it is never to have meat; or that the first twenty years of our lives is to become a precedent for the next twenty."

Paine's point is that the past practices of Britain may have enabled the colonies to "flourish," but he argues that there is no indication that a continued relationship will continue to yield the same result.  His use of a simple analogy about child rearing would be readily understandable by the masses.
Paine also refutes the claim that Britain should continue to rule the colonies because the people of the colonies are of English descent.  His claim,

"Not one third of the inhabitants, even of this province, are of English descent"

would ring true to people of the colonies in 1776 because there had been an influx of immigrants from all over Europe: Holland, France, Germany, etc. 
Paine doesn't miss  opportunities to appeal to emotion. For example, to those who would say that "Britain is the parent country," Paine counters, "Then the more shame upon her conduct. Even brutes do not devour their young."  
By keeping his message consistent, appealing to both logic and emotion, and using examples and analogies that would be resonant with his audience, Paine built his reputation as the pamphleteer of the American Revolution.
 
 
 
http://www.njhistoryroundtables.org/documents/CommonSense.pdf

Should a legal system based upon the Bible include private property rights?

The Bible is pro-private property rights. There are many passages that support this. Accordingly, all Governments — throughout the world, nationally, and locally — should protect private property rights. God knows that personal ownership of private property is fundamental to every individual’s ability to express his best possible self as a reflection of his being created in God’s image (I will unpack that idea in this study). In addition, private property rights are fundamental to personal and national fruitfulness (we will see examples of this in what follows also). So read on, my friend, and learn more about how you can justify such beliefs based upon what God has said in His Word.

This is most definitely a personal opinion question. Different people are going to feel quite strongly about various answers. Some people are going to emphatically favor this type of legal system while others are going to emphatically be against it. My recommendation is to pick whichever argument you feel more passionately about. Your reader will "hear" that passion. My other recommendation is to consider who your reader is. Is he/she likely to want one answer over the other. If that is the case, then consider giving your reader the information he/she wants.
Regardless of how you answer this question, it is a persuasive argument. A strong thesis is needed, and then at a minimum three pieces of support. If an argument only has a single piece of supporting evidence, the argument doesn't come across that forcefully.
Personally, I would argue in favor of a legal system that is based on biblical teachings and includes laws about private property rights. I think arguments could be made that many other legal rights systems are based on biblical principles; therefore, the private property rights should be as well. Otherwise, it appears that certain things are being singled out to be biblical, while others are not. I think this will lead to more problems than anything else. Additionally, being based on something doesn't mean it is following every single aspect of it in a word-for-word fashion. Let's use book to movie adaptations for a parallel comparison. There are plenty of times that a movie states that it is based upon a book. Readers always notice the changes that are made, in order to adapt that book into a movie. The movie isn't exactly like the book anymore; it's based on the book. The core of the story is still there, but certain things were changed to work best in a new medium. Laws about property rights can work the same way. They can be based on biblical principles, but they can be adapted to modern day societal norms.

How does O.Henry create a balance between foreshadowing and surprise in "After Twenty Years."?

In "After Twenty Years," O. Henry molds his main characters with a certain anonymity that provides some foreshadowing while at the same time providing for the surprise ending.
Foreshadowing
In the exposition of the story in which two old friends have agreed to meet twenty years after their parting ways, the first character who is introduced is simply referred to as the "policeman." Also, since this policeman, an officer of the law who patrols a certain neighborhood, is a familiar personage to readers of O. Henry's time, there is nothing about him which would lead these readers to think that he has a primary role in the narrative. His routine questioning of the man waiting for his old friend in the doorway arouses no suspicions, either, but it does provide subtle foreshadowing as the man's lighting of his cigar reveals a "little white scar near his right eyebrow" and a large diamond as a scarfpin. Another very subtle hint of what is to come are some words said by this stranger:

"We figured that in twenty years each of us ought to have our destiny worked out and our fortunes made, whatever they were going to be."

Surprise Ending
Since the policeman on the beat seems insignificant, with the later appearance of "a tall man in a long overcoat" who goes directly to the man in the doorway, readers may well assume that he is Jimmy, the stranger's old friend for whom he has been waiting, especially because he asks, "Is that you, Bob?" But, when this tall man steps under the bright lights of a drug store as the two walk along arm-in-arm, the old friend suddenly stops, removes his arm, and says, "You're not Jimmy Wells," the narrative is then set up for the surprise ending. For, Patrolman Jimmy Wells has sent a plainclothes policeman to meet 'Silky Bob' and to give Jimmy's letter to his old friend, explaining why he has not met him.
 
 

Single Variable Calculus, Chapter 7, 7.2-2, Section 7.2-2, Problem 82

Determine the area of the region bounded by the curve $\displaystyle y = \frac{2}{x-2}$, $x$-axis, $x = -4$ and $x = -1$.

By using vertical strips,

$
\begin{equation}
\begin{aligned}
A &= \int^{-1}_{-4} \left( y_{\text{upper}} - y_{\text{lower}} \right)\\
\\
A &= \int^{-1}_{-4} \left(0 - \left( \frac{2}{x-2} \right) \right) dx\\
\\
A &= \int^{-1}_{-4} \frac{-2}{x-2} dx
\end{aligned}
\end{equation}
$

Let $u = x- 2$
$du = dx$

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

$
\begin{equation}
\begin{aligned}
A &= -2 \int^{-1-2}_{-4-2} \left( \frac{1}{u} \right) du\\
\\
A &= - 2 \int^{-3}_{-6} \frac{du}{u}\\
\\
A &= -2 [\ln u]^{-3}_{-6}\\
\\
A &= -2 [\ln(-3)-\ln(-6)]
\end{aligned}
\end{equation}
$

We can't evaluate the area since $\ln$ of negative number doesn't exist. However, since the function is reflected about $x = 2$ its area is equal to the rgion bounded by the curve, $x$-axis and the lines $x = 5$ and $x = 8$. $A = 1.3863$ square units.

In some scenes, the dialogue for several characters is written as play dialogue. Why is this?

This novel, perhaps more than any others written by Fitzgerald, closely parallels his own life as he struggled to make ends meet, despite being one of the highest paid authors in the country. The financial collapse came at the end of a decadent period in history, and that is portrayed in the novel as well. This stylistic approach described in the question is done to show that the main characters, Anthony and Gloria, feel like their lives are playing out separate from them. They're waiting for an inheritance that will make their lives easier, but it is slow in coming, and yet they still want to continue the extravagant lifestyle they had when they first got together. The reality of poverty begins to wear away at them, making them cynical and depressed. Writing some scenes of dialogue in the style of a stage play underscores the surreal feeling that Anthony and Gloria both have about their situation: they feel like they are "performing" in front of their friends and social acquaintances as a couple that has plenty of money and is happy and carefree, but in reality they're destitute and unhappy.

What are some negative qualities that Frankenstein's creature possesses?

The Creature is extremely vindictive. He is born and then abandoned, and he is reviled by all he meets for his ugliness. He feels he has been given an unfair hand by fate and by the humans too shocked by his appearance to give him a chance. As the Creature famously tells his creator, "If I cannot inspire love, I will cause fear." This is the credo by which he lives the rest of his life.
The Creature lashes out at the world for its rejection of him. When he realizes William is Victor's brother, he kills him, then frames the innocent Justine for the crime, allowing her to be executed with no remorse. In this way, the Creature has let the world's cruelty toward him infect his interactions with other people; he becomes the very thing he so hates.
In addition to this, the Creature takes sadistic pleasure in hurting Victor. He rejoices that the pain inflicted upon him has been returned to the one responsible for his alienation and suffering.

In all honesty, the creation possesses the same negative qualities that human beings have. He can get incredibly angry and resentful, even destructive, when he's been treated poorly. For example, when his overture of friendship has been rejected by the DeLaceys and he learns that they are moving far away because of their fear of him, he burns their house down. Further, after he's been shot by the hunter for saving the little girl from drowning, he attempts to kidnap William Frankenstein, Victor's youngest brother, in order to educate the child and raise the child as his friend. He does desperately want a companion, but it is selfish to kidnap a person in an attempt to create one. Moreover, the creature then kills William when the child calls him mean names, and he rejoices in his ability to create pain and fear in his creator. The happiness he feels when he thinks of the pain he can cause another person is certainly a negative quality as well.

What larger, universal truth is presented in Golding's Lord of the Flies through the themes of power, the personal price of conformity, and the monster that lies within human nature?

The universal truth presented by Golding through these themes is a sobering one. It is that mankind, despite what we might like to believe, is not fundamentally good. Rather, we are fundamentally evil, and left totally to our own devices, without some kind of institution to regulate us, we are always subject to reverting to our base instincts, what Sigmund Freud called the "id," that will overcome whatever sense of morality that exists within us. There is much in the novel that supports this pessimistic view.
As for the theme of power, we can see that as the novel goes on, the basis for power is contested and indeed changes over time. At first, the boys seek to replicate, at least somewhat, the order that existed at their school. Piggy and Ralph, in their attempts to establish this order, base their efforts on reason and intellect, which Piggy, in many ways, represents. The conch, for example, becomes an emblem of power, one which summons the boys to the beach. When asked where the "man" who blew the "trumpet" had gone, Ralph answers that "there's no man with a trumpet. Only me" (25). Later, he lifts the conch to assert his qualifications to be leader, saying "seems to me we ought to have a chief to decide things" (28). Jack, on the other hand, bases his authority on his leadership of the chorus, which gives him, as Golding describes it, a sort of "offhand authority," a point he makes explicit before losing the election for "chief" to Ralph (26). Ralph and Piggy continue to appeal to reason, rationality, and legitimate authority as a basis for power throughout the book, but Jack begins to appeal to baser instincts--his ability to hunt, exemplified by the pig he killed, and his ability as a hunter to protect the "littluns" from the supposed "beast" on the island.
Eventually Jack declares his "independence" from the power represented by the conch, and we see that many of his band, most of whom have not left his side since the days he served as their leader in the choir, continue to follow him more or less blindly. Jack is charismatic and he appeals, like demagogues do, to the baser instincts of the boys, both their fears and the fun of the hunt. Whereas Ralph attempts to maintain order, Jack wants the boys to embrace disorder, and they follow him, conforming despite the fact that his leadership more or less abandons the idea that they will ever be rescued. But his flouting of the rules appeals to some of the other kids, who take to him when he whoops, "[b]ollocks to the rules! We’re strong—we hunt! If there’s a beast, we’ll hunt it down!" (130). This line demonstrates Jack's contempt for authority as well as his appeal to the fears of the other boys, who conform to his vision and to his leadership.
As the book advances, it becomes clear that there is no "beast." In fact, this is Golding's major theme--the "beast" is the inherent evil that lies within people, unleashed in this story by the absence of adults, structure, and rationality. Simon (who is later killed by the boys) actually makes this point fairly early in the book, when the boys are debating the existence of the beast:  "What I mean is. . . maybe it’s only us" (126). As it turns out, he is right. Jack is not protecting the boys from anything, he is in fact representative of the beast itself. The death of Piggy (and Simon) at the hands of Jack and his followers demonstrates the power of evil to overcome rationality, intellect, and human decency. 

In Monster by Walter Dean Myers, what do the two flashback scenes in which Steve learns of Nesbitt's murder suggest about his emotions at the time? What conclusions can you draw about his probable guilt or innocence?

In the first chapter of Monster, the narrator, Steve, mentions that, to him, being in jail is like being in a movie—one of the old ones that are difficult to follow. In fact, Steve decides to journal about his trial as if it were a movie, and the title he chooses is "Monster," since that’s what the prosecutor is calling him; this gives readers their first real glimpse of who Steve might be.

Just like in a real film, the author of Monster, Walter Dean Myers, chooses to give us further clues as to who Steve is as a person, his interior character traits. During two of these cutscenes, Steve learns that Aguinaldo Nesbitt has been murdered, and it is in the description of Steve’s reaction to this that we can infer more about Steve’s emotional state.

In the first flashback, Steve overhears two women discussing the shooting. Steve begins to walk, then trot, finally breaking into a run until the camera pans the neighborhood, and we can no longer see him. Steve is literally running away from the news of Nesbitt’s death. Clearly he is afraid, but whether this fear comes from guilt is still unclear.
In the second flashback, Steve is watching the news, and the recent shooting is the current hot topic. Jerry changes the channel, seemingly unfazed. Steve, however, is described as staring fish-faced—in other words, eyes bulging, mouth gaping. These are sure signs of fear and maybe even some guilt.

But is Steve guilty? Is he the monster the prosecution would have the jury believe him to be? It’s hard to say. On the one hand, we know Steve hung out with a pretty rough crowd; in chapter fourteen, he is even asked to be a lookout for the heist Nesbitt dies on, and Steve was there: “I walked in a drugstore to look for some mints and then I walked out,” he writes in his journal. But whether he was also acting as a lookout, we don’t know.

Conversely, Steve is portrayed as a good kid; his teacher testifies describing him as bright and compassionate, and he is terrified of jail and the violent men inside. Whether he is truly guilty and whether these flashbacks offer proof of this or not is ambiguous. One thing is for certain: at his core, Steve is just a scared kid, struggling to figure out who he really is.

In the first flashback scene, Steve overhears two women speaking about the murder of Aguinaldo Nesbitt. Steve then walks through the crowd of people, and begins to sprint away as the camera pans out. Steve running away from the scene suggests that he feels guilty about his involvement in the crime and is trying to escape from the reality of the situation. In the second flashback scene, Steve is watching the news and listens as the newscaster says that two armed men robbed and killed Aguinaldo Nesbitt. Jerry then picks up the remote and changes the channel. Steve Harmon's mouth is wide open and is in absolute shock after hearing about the tragedy. Two weeks later, Steve watches the news and learns that Richard "Bobo" Evans was arrested for robbery and murder. The camera then cuts to Steve's room, where he is lying on his bed with his eyes open. When he hears a knock on the door, Steve does not even react. Steve's emotions after learning about the crime suggest that he was involved because he is extremely worried and afraid. When Steve overhears the women talking about the crime, he runs away out of fear. After learning that the store owner was murdered during the robbery, Steve is shocked. His emotions reveal his fear and anxiety about being arrested for his involvement in the robbery. Steve's reactions suggest that he was involved and is guilty of participating in the robbery and murder of Aguinaldo Nesbitt.

Can you explain Robert I. Moore's idea of a "persecuting society"? Specifically, how might Moore's theory relate to the United States today regarding gender and sexuality?

In the preface to the second edition of The Formation of a Persecuting Society, Robert I. (R.I.) Moore notes that his study of systemic persecution of certain categories of individuals should in no way be interpreted as suggesting is a focused study of a specific period of time and that extrapolations based upon his findings should be applied with caution. He also warns against interpreting his findings as constituting an indictment of "the Church" relative to other institutions and prejudices, writing that "the Church was not the sole, or even the principle agent of persecution." Moore's point, then, was that the phenomenon of institutional or systemic persecution was not limited to any one institution, such as the Church, or to any one government, people, or culture. And therein lies the enduring problem of persecution: it survives the passage of time and crosses borders. It could be said to be a part of the human condition, and therein lies the tragedy.
One of the principle advantages of Moore's revised edition of The Formation of a Persecuting Society is its expanded examination of the application of his principles or findings to contemporary society, if only briefly, a particularly interesting extension given the continued persecution of some of the same groups discussed in the context of medieval Europe: Jews and homosexuals. Such groups, as well as lepers and heretics (the latter once considered a bygone category of persecuted individual but now revitalized in the age of Islamist terrorism) were the principle groups targeted for persecution in Moore's study. Jews and homosexuals remain persecuted groups today, though homosexuals (and, increasingly, transgender individuals) gradually but steadily gain acceptance in mainstream societies. In the case of Jews, there has been a resurgence of anti-Semitism in Europe and, of particular note, across the United States as well, a particularly disturbing development in light of the role the United States has historically played in providing a safe haven for persecuted groups, including Jews.
Moore's central thesis is that the persecution of select categories of humanity cannot be considered as a series of isolated incidents but rather should be regarded as part of a much broader societal propensity to identify and isolate specific groups for any number of reasons specific to each group (e.g., Jews and the crucifixion; lepers and the fear of contagion, etc.). Applying that thesis to perceptions of homosexuality, or sexuality in general, in the United States, one could logically make the argument that the phenomenon of persecution of homosexuals (and, today, transgender individuals) fits into the model Moore identified in his study of the Middle Ages. The same often irrational designation of certain groups as undesirable and appropriate targets for discrimination exists today around the world, including in the United States, as it existed hundreds of years ago in Europe. The thought processes that delegitimize or dehumanize certain categories of individual continue to be prevalent. Moore's thesis can be applied, although it is up to the individual to weigh carefully the validity of that application given the scale of discrepancies between the Middle Ages and today.

Describe why the discovery of America was one of the most important events in history , according to Adam smith .

In Wealth of Nations, economist Adam Smith foretells of the coming of globalization.  In the book, he describes how Western Europe has benefited from receiving the raw materials of North America, such as its precious metals, agricultural commodities, and timber.  However, to Smith, this is not enough to change the world.  He then goes on to describe how the discovery of America has changed the economies in Poland and Hungary, two central European nations that did not have a direct colonization role in the New World.  Smith describes how trade networks connect Western Europe with Central and Eastern Europe and how it seems that people everywhere covet goods that were in some way produced in America, such as chocolate.  In order to receive these goods, people in Eastern and Central Europe have to improve their own industrial capacities in order to fully participate in the global trade.  With the discovery of America, everyone who trades with the colonizers prosper.  This expanding of markets was indeed world-changing.  
http://www.let.rug.nl/usa/documents/1776-1785/adam-smith-from-the-wealth-of-nations-1776-of-colonies.php

int (x^3 - 6x - 20)/(x + 5) dx Find the indefinite integral.

The answer given by gsarora17 will simplify to x^3/3-(5x^2)/2+19x-115ln|x+5|+C
A direct method to this result is to simplify the integrand by long division or synthetic division and then integrating term by term:
int (x^3-6x-20)/(x+5)dx=int [ x^2-5x+19 - 115/(x+5)]dx
=x^3/3-(5x^2)/2+19x-115ln|x+5|+C as above.

int(x^3-6x-20)/(x+5)dx
Let's evaluate the integral by applying integral substitution,
Let u=x+5, =>x=u-5
du=dx
int(x^3-6x-20)/(x+5)dx=int((u-5)^3-6(u-5)-20)/udu 
=int((u^3-5^3-3u^2*5+3u*5^2)-6u+30-20)/udu
=int(u^3-125-15u^2+75u-6u+10)/udu
=int(u^3-15u^2+69u-115)/udu
=int(u^2-15u+69-115/u)du
Now apply the sum rule,
=intu^2du-int15udu-int115/udu+int69du
=intu^2du-int15udu-115int(du)/u+69intdu
Use the following common integrals,
intx^ndx=x^(n+1)/(n+1)
and int1/xdx=ln(|x|)
=u^3/3-15u^2/2-115ln|u|+69u
Substitute back u=x+5,
=(x+5)^3/3-15/2(x+5)^2-115ln|x+5|+69(x+5)
Add a constant C to the solution,
=(x+5)^3/3-15/2(x+5)^2+69(x+5)-115ln|x+5|+C
 

What is the summary of the plot of the Gospel of Matthew, including the beginning, the middle, and the end?

The Gospel of Matthew follows many of the ancient traditions of the biography of the holy man, a subgenre of the encomium. The traditional elements of the genre, as set out in Menander Rhetor and other rhetoricians of the period, include distinguished ancestry, miraculous signs at birth, evidence of precocious childhood, and famous deeds and sayings. 
The Gospel of Matthew derives its materials from two sources, the Gospel of Mark and a collection of the sayings of Jesus sometimes called "Q". Some of this material was shaped into typical rhetorical forms such as the chreia ( a short narrative followed by a moral maxim). 
The Gospel of Matthew begins with an extended genealogy tracing Jesus' ancestry back to Abraham and then describes his miraculous conception and the events surrounding his birth. The central section begins with Jesus' encounter with John the Baptist, focuses on the ministry of Jesus, and incorporates many of his sayings and teachings. The central section ends with a description of the Last Supper and the trial and death of Jesus. The final section addresses the Resurrection of Jesus and foundation of Christianity as Jesus instructs his apostles to go out to evangelize the world.

What is a summary of The Selection by Kiera Cass?

The Selection is the first installment in The Selection Series by Kiera Cass. The novel can be categorized under the young-adult, dystopian, romance categories and can be compared with both The Bachelor and Cinderella.
In the distant future, war has given rise to the kingdom of Illéa, a society divided into eight castes. The novel begins with the protagonist, America Singer, receiving a letter indicating she is a candidate in the upcoming Selection, a contest in which thirty-five girls must compete for the affection of the Royal Prince. Though most view the Selection as an opportunity of a lifetime, America has no desire to be a participant and despises having to leave everything she knows and love behind to fight for a prince and title she doesn't even want. However, everything changes once America finally meet Prince Maxon, including her priorities, plans, and purpose.

How did the Ku Klux Klan define Americanism?

One would hope that the Ku Klux Klan did not define "Americanism" per se, as a whole. But unfortunately it did represent that part of Americanism that has, from the beginning 400 years ago, been defined by a wish to oppress non-white people and to keep them in a position subordinate to the whites in perpetuity.
The positive thing about American society is that in spite of this endemic racism, genuine progress has been made in stages over the centuries. Many scholars believe that it would have been better for African Americans if the Revolution of 1775–1783 had not succeeded. This is a complex issue, given that the British at times made efforts to free the enslaved people if they would fight for the Crown. However, in the aftermath of the successful war for independence, all of the northern states passed gradual abolition laws, and the Northwest Ordinance provided for the exclusion of slavery from the Northwest Territory. So progress of a kind was made, decades before the abolitionist movement got into full swing and the Civil War did liberate the enslaved people as a whole.
Though the defeated South, the former Confederacy, accepted the abolition of slavery, it is tragic that they refused to allow the integration of African Americans into society and that they passed the oppressive Jim Crow laws creating the segregated world that lasted for nearly another century. The Ku Klux Klan was in the vanguard of "enforcing" this oppressive situation, carrying out raids to persecute and terrify the freed people. The blazing cross was a perversion of Christianity but also symbolic of Americans' hypocritical use of religion through the ages to justify not only slavery but other forms of exploitation. The actions of this terrorist group were, in fact, the essence of that aspect of America or Americanism which had deliberately submerged non-whites in the social hierarchy, first through slavery and then through laws disallowing them from living together and in equal status with the whites.
As bad as America has been in this regard, and still is in terms of institutionalized racism, ongoing police brutality, and barely disguised appeals to racist attitudes in the public from the highest levels of government, things have still changed for the better. These positive changes are a form of "Americanism" as well. So the Ku Klux Klan defined only the worst of what America was or still is.

Describe the relationship between Sebastian and Antonio in Twelfth Night.

Antonio looks after Sebastian.  He really cares about Sebastian, and wants to protect him.  This is why he stays in Illyria even though his legal history is such that he really should not be seen around there.
Antonio seems to think that since he rescued Sebastian from the shipwreck he should continue to look after him.

SEBASTIAN
O good Antonio, forgive me your trouble.
ANTONIO
If you will not murder me for my love, let me beyour servant.
SEBASTIAN
If you will not undo what you have done, that is,kill him whom you have recovered, desire it not. … (Act 2, Scene 1)

Antonio gives Sebastian his purse to hold.  They agree to meet up later.  It is all fairly innocent except there is the one problem.  Antonio is a wanted man in Illyria. 
Sebastian ends up in the same place as his twin sister, by chance, having no idea that she is alive or that she is pretending to be a man.  When Cesario/Viola is dueling with Sir Andrew, Antonio steps in.  He feels that helping Sebastian is the right thing to do, since Sebastian is his friend.  Then he gets arrested for his past deeds.
Antonio asks Sebastian for his purse.  Cesario refuses.  Antonio is very upset.  He has been an excellent friend to Sebastian, and in his time of need, Sebastian turns on him and refuses to give him his own money!  Cesario/Viola is confused, offering to give what little money he/she has.

ANTONIO
I must entreat of you some of that money.
VIOLA
What money, sir?...
ANTONIO
Will you deny me now?
Is't possible that my deserts to youCan lack persuasion? … (Act 3, Scene 4)

In the end, they get it straightened out that these two are twins, and that Antonio actually gave his purse to one twin and asked for it back from the other.  However, he was still able to offer a valuable service to Viola when he intervened for her in the duel, thinking he was helping Sebastian.  Therefore, he was a friend to both twins.

How has recent research changed our view of the origins, migration, and diversification of the Native Americans who were the first to settle the Western Hemisphere?

From the 1930s through the 1990s, the most commonly accepted theory for the peopling of the Americas was the Clovis-First Model. This theory was based on projectile points found near Clovis, New Mexico, that had suggested a widespread Clovis culture across North America. It also suggested that these were the first inhabitants of the continent, having arrived about 11,000 years ago after an opening in the glaciers occurred. In recent years, the Clovis-First Model has been challenged by a number of new findings.
In 1997, radiocarbon dating at an archaeological discovery in Monte Verde, Chile, dates human occupation in the area to about 14,500 years ago, much older than the Clovis model. This alone essentially debunked the older theories.
One newer theory is known as the Coastal Route Theory. It suggests that the earliest peoples to come to the Americas did not wait for the glaciers to melt. Rather, they traveled south along an ice-free route along the Pacific Coast. Since sea levels were lower during the ice age, the route they would have taken is now underwater, making archaeological research nearly impossible. However, geological evidence does exist to show that such a route was possible. It is highly plausible that migrants used this route to enter the continent prior to the melting of the glaciers. However, it remains just a theory.
Perhaps some of the most intriguing new research involves the study of genetics. This new research shows how different native populations diverged and merged over the last 15,000 years. One interesting new finding is that the native populations of the Amazon share certain genetic markers with the native peoples of New Guinea and Australia, suggesting a common ancestry. Just how this information affects the origin theories of the early inhabitants of the hemisphere is not yet clear.
As more information and research technologies emerge, we will likely learn more about the first people in the Americas. What we are repeatedly discovering is that people came to the Americas earlier than previously thought and perhaps from more than one origin.
https://www.nps.gov/bela/learn/historyculture/other-migration-theories.htm

In Canto 18 of Dante's Inferno, why is the priest in hell?

Dante explores the numerous circles of Hell in this story, in each of which a different sin is relegated. Throughout the story we have seen the punishments for a number of terrible sins, and in Canto 18, we come to the area where fraud is punished. The eighth circle of Hell, one of the worst, holds the eternal punishment for sinners guilty of fraud.
Within this circle is the priest, normally considered a holy man, and Dante is shocked to find a clergy member here in Hell. However, this gets to the heart of sin—that anyone can fall deeply into it. The priest is guilty of defrauding his congregation, and this is what Dante wants to comment on in the Catholic Church. He is angered at the amount of deception in the church and wants to condemn it in this work.

Dante’s 18th Canto in this work explores the eighth circle of Hell, where those who sinned by fraud are sent after death. He has the circle divided into three groups for various types of fraud and their associated punishment. It is in this circle that he comes across a priest.
Dante is criticizing the Catholic Church for their fraud and their attempts to take advantage of and mislead their parishioners. The priest in Hell is guilty of having defrauded his laypeople and led them astray. It is one of the vilest things, according to Dante, to defraud someone in some way, and it is worse for the church to defraud its followers. The eighth circle is second to last, showing how despicable and villainous the priest is.

Dante writes about the eighth circle in the eighteenth canto of his Inferno. Here those who sinned by deception are cursed to stride continuously in horrible conditions, whipped by a demon to keep moving. Dante recognizes four people within this circle, but none of them is identified specifically as a priest. However, he does mention that there are shades covered in excrement so that they cannot be recognized as either priest or lay-person.
One such shade is Alessio Interminei of Lucca, a member of Dante's despised Guelph party. Throughout the cantos, Dante makes his disdain for the Church known, and this canto is another reminder. The particular ravine that Alessio resides in is filled with sewage, perhaps implying that clerics belong in the gutter. This is also a place for flatterers and liars, euphemistically surrounded by their own waste. Dante seems to be telling us that he believes that what is said by this Guelph aristocrat—as well as by Church leaders—is only as good as their own feces.

Canto 18 is about those who have been condemned to hell for fraud. There isn't an obvious priest character in this section—I think you may be referring to Alessio of Lucca, whom Dante says is so covered in grime that it was difficult to tell "if he were clerk [a priest] or layman." In fact, Dante identifies him as Alessio of Lucca. Very little is known of this character, except that he was a member of the Guelph Party, who supported the Pope as opposed to the Holy Roman Empire.
In this canto, Dante identifies his sin as that of flattery. Alessio himself confesses that he was unable to stop himself from expressing flatteries, with the result that he has "sunk low" because of this behavior. Presumably, Alessio was known at the time of writing as a notorious flatterer; this reputation has not survived him except through this text, but evidently Dante viewed flattery as a behavior to be frowned upon.

What are characteristics of Helen Keller?

There are a lot of different characteristics that could be used to describe Helen Keller. She was an amazing woman, but if I had to pick a single trait for her, I would say that Helen Keller was tenacious. She simply refused to give up on anything. Most people would say that she was dealt a difficult hand in life, but Keller never let it stop her from achieving her hopes and dreams. She exhibited great perseverance throughout her life. I don't want to say that Keller was never discouraged or depressed, but she never let herself wallow in self-pity.

My work was practice, practice, practice. Discouragement and weariness cast me down frequently; but the next moment the thought that I should soon be at home and show my loved ones what I had accomplished spurred me on, and I eagerly looked forward to their pleasure in my achievement.

In order for her to accomplish all that she did, she had to be more than tirelessly persistent. She was also intelligent. She had to be, in order to learn all that she learned as well as figure out how best to use the skills that she had and navigate around in a world that is not very accommodating for somebody who is Deaf and Blind.

From an early age, Helen Keller displayed a very determined nature. Although this took the form of willfulness early in her life, it, along with her willingness to persevere despite her disabilities, proved a positive asset later, when she began her education and throughout the rest of her life. Determination, perseverance, unshakable self-confidence, as well as the courage to not only pursue but also realize what many considered unthinkable goals at that time were definitely key aspects of her personality.
In addition, Helen was also highly intelligent, inquisitive, intuitive, and empathetic. Once she acquired an education—although she could have simply reveled in this accomplishment—Helen’s visionary ambitions stretched far beyond herself. She used her knowledge and experience to help other people with disabilities gain equal access to education and equal status as members of society.

When in Gulliver's Travels by Swift does Gulliver realize that travel was his "fortune to do"?

Gulliver tells us that it is his "Fortune" to travel after he has gone to study at Emanuel College in Cambridge (from age fourteen to seventeen) as well as after he has been apprenticed to Mr. James Bates for four years.  Therefore, we can understand him to be about twenty-one years old when he is making decisions to learn as much as he possibly can about the kinds of knowledge most needed for those who undertake voyages.  However, what he says is that he has "always believed" that it would be his fortune to travel at some time or another, and so he must have actually had this realization at a very young age, so young that he cannot remember a time before it because he says now that he's always known it.

What is the tone of "The Appointment in Samarra" by W. Somerset Maugham?

The famed English poet W. Somerset Maugham wrote this interesting version of this, said to be an ancient Mesopotamian fable or folktale. The tone is fascinating because it is deceptively simple and somewhat misleading because of the point of view. The author clearly indicates the point of view with the centered line that begins the fable: "The speaker is Death."
Death relates the story of the Baghdad merchant who sends his servant to the marketplace, and the servant recounts his frightening experience there, seeing Death. Death is a woman, and the servant says that Death jostled him and "made a threatening gesture." The servant asks the merchant to lend him a horse so he can ride to Samarra, to escape Death's plans for him. Death then says the merchant went to the marketplace and "saw me in the crowd" and asked about the incident:

Then the merchant went down to the marketplace and he saw me standing in the crowd and he came to me and said, Why did you make a threatening gesture to my servant when you saw him this morning?

This sentence offers perhaps the most important clue as to the tone of this short piece of writing. Death, the speaker, has an omniscient viewpoint and begins in what seems to be the third person but here abruptly switches to a first person narrative. In the final line, the story's surprise and irony are revealed—that Death was not threatening the servant, but merely reacting with surprise to see him in Baghdad, because she had an appointment with the servant "tonight in Samarra."
But even though the switch to a first person perspective and the revelation of the appointment reveal Death's all-powerful perspective and control over human fate, there is a slightly confusing conundrum here. If Death is in control of the servant's fate, why is she not able to predict the servant's actions as well? This suggests Death is not quite all-powerful after all, yet it also suggests that the fate of death, referred to as an "appointment," is inescapable and final.
The story is therefore slightly confusing and mysterious, despite its simplicity and brevity. Its tone feels very straightforward, but the information revealed is ultimately very somber and ominous.

Which measure of central tendency is the most appropriate to use/report for nominal, interval and ratio measurements?

Nominal data refers to data that can be grouped into named categories. For instance, the gender of students enrolled for a given course in a given university. The best measure of central tendency to use for this kind of data is the mode. This is because the data is non-continuous.
Interval and ratio data are both continuous, hence mathematical operations can be performed on them. For interval data, the order of the values and the exact differences between them is known, e.g. temperatures of students in a class. The best measure of central tendency for reporting interval data is the mean (when the data is not skewed) or the median (when the data is skewed). Ratio data has, in addition to interval data’s properties, a clearly defined absolute zero, for instance, height data. The best measure of central tendency to use for ratio data is the mean (for non-skewed data) and the median (for skewed data).
The mean is found by summing up all the values in the data set and dividing this total sum by the number of values.
The median is the value of the middle item in a data set whose items have been arranged in order of size.
The mode is the most frequently occurring item in a data set.
https://statistics.laerd.com/statistical-guides/measures-central-tendency-mean-mode-median.php

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3157145/

Calculus of a Single Variable, Chapter 3, 3.2, Section 3.2, Problem 46

You need to find out if the mean value theorem can be applied to the the given function, hence you need to verify if the function is continuous on [0,pi] and differentiable on (0,pi), and it is, since all trigonometric functions are continuous and differentiable on the interval.
Since the mean value theorem can be applied, then there is a point c in (0,pi), such that:
f(pi) - f(0) = f'(c)(pi-0)
You need to evaluate f(pi) and f(0):
f(pi) = cos pi + tan pi => f(pi) =-1 + 0 = -1
f(0) = cos 0 + tan 0 => f(0) = 1 + 0 = 1
You need to determine f'(c):
f'(c) = -sin c + 1/(cos^2 c)
Replacing the found values in equation f(pi) - f(0) = f'(c)(pi-0) yields:
-1-1 = pi*(1/(cos^2 c) - sin c)
-2 = pi*(1/(cos^2 c) - sin c)
Replace 1 - sin^2 c for cos^2 c :
-2 = pi*(1/(1 - sin^2 c) - sin c)
You need to use the substitution sin c = v:
-2 = pi*(1/(1 - v^2) - v) => -2 = pi(1 - v + v^3)/(1 - v^2)
2v^2 - 2 = pi - pi*v + pi*v^3
pi*v^3 - 2v^2 - pi*v + pi + 2 = 0
Since there is no solution to the given equation pi*v^3 - 2v^2 - pi*v + pi + 2 = 0 , then there is no valid value of c in (0,pi), such as f'(c) = 0 and the mean value theorem cannot be applied.

The density of water is 1000 kg/m3. What does this mean?

Hello!
Density is a quantitative physical characteristics of a substance or more or less stable mixture. When we take some piece or quantity of a substance, it has mass and volume. The mass divided by volume is called density, and it depends on substance only (remains the same for different pieces of the same substance).
Different substances have different density. The density of water is about 1000 (kg)/m^3, or 1 g/(cm^3). This means that every cubical meter of water weighs about 1000 kg, every half of a cubical meter weighs 500 kg and so on. So if we know what the substance is, we can compute its weight given a mass, and vice versa.
That said, density of a substance may change with temperature and pressure, sometimes significantly.

Can we say India is a democratic country? Give one example.

Yes, we can say that India is a democratic country. A former and highly prized colony of the British Empire—India was considered “the jewel in the crown” of the empire—Independent India adopted a parliamentary system of government modeled on that of the British. Part III of India’s constitution, which is far more voluminous than that of the United States, specifies the rights of the country’s citizens, including such fundamental concerns as speech, assembly, and religion. Section 19 of this provision reads as follows:

19. Protection of certain rights regarding freedom of speech, etc:
All citizens shall have the right to freedom of speech and expression;
• Freedom of expression b. to assemble peaceably and without arms;
• Freedom of assembly c. to form associations or unions or co-operative societies;
• Freedom of association
• Right to join trade unions
• Freedom of movement d. to move freely throughout the territory of India; e. to reside and settle in any part of the territory of India; . . .

India’s constitution establishes an office of the president and a bicameral parliamentary structure (the Council of States and the House of the People are the two chambers). It also delineates divisions of authority between branches of government. The citizenry votes for members of Parliament, and an electoral college casts ballots for the president. A prime minister is elected from the majority party in Parliament and is responsible for most of the day-to-day duties of a chief executive. In short, India is a democracy. Political representation reflects the will of the electorate.
An example of India as a functioning democracy occurs with every national election. These take place at least every five years. While India is not without its problems, including political corruption, its electoral processes are widely perceived as legitimate, and the country is considered the world’s largest democracy by virtue of its enormous population (1.3 billion).

India gained its independence from England in 1947 and adopted its constitution in 1950. It is the kind of democracy known as a “parliamentary democracy.” A parliamentary democracy differs from a presidential democracy in that its executive (usually a prime minister) is chosen from its legislative branch.
Obviously, in a democracy, voters select their political leaders. In India, there is universal suffrage for citizens above 18 years of age (meaning every citizen who is at least 18 can vote). The people vote for the representatives that make up the lower house of the legislative branch, called the Lok Sabha. The Lok Sabha then selects the Prime Minister, who is the head of the government.
India also elects its own state representatives, who then vote for the members of their national upper legislative body, the Rajya Sabha,
Finally, India has multiple political parties that offer voters different political ideologies to choose from.
So India is indeed a democracy, although it has been criticized for failing to adequately achieve the democratic goals of reduced poverty and illiteracy.
 
https://www.infoplease.com/encyclopedia/arts/visual/american-canadian/indiana-robert

Who is the Greek mythology figure that comments on love and the relationships between women and men in "The Wasteland" (section three)? Which part of his representation is significant? Why?

The figure from Ancient Greek mythology who makes an appearance in section three, "The Fire Sermon," of T.S. Eliot's The Wasteland is the prophet Tiresias, a character who appears in Homer's The Odyssey and several Greek dramas as well. Tiresias has both male and female features and, though he is blind, he has the ability to see into the future. Tiresias is the speaker of section three, which primarily focuses on sexual relationships between men and women, as well as homosexual relationships.
That Tiresias is the one commenting on love and relationships between men and women is particularly significant because of the prophet's ambiguous gender. The description of Tiresias in the poem combines traditionally male and female attributes:

I Tiresias, though blind, throbbing between two lives,
Old man with wrinkled female breasts, can see.

This description, along with Tiresias's ability to see the future, would seem to give the prophet the unique authority to comment on the experiences of both men and women.

In To Kill a Mockingbird, what are some literary devices used from chapter 12 to chapter 24?

Remember that literary devices include not only figures of speech, but also techniques such as the use of imagery, allusion, and irony. Fortunately, Harper Lee is a master of all of the above, and To Kill a Mockingbird has ample examples of them on practically every page. Chapter 12 is the beginning of the second part of the book. This is when Calpurnia takes Jem and Scout to her church because Atticus is gone. Lula, a member of Cal's church, notices the children coming and is described through metaphorical imagery as follows:

She was bullet-headed with strange almond-shaped eyes, straight nose, and an Indian-bow mouth. (119)

With such visual imagery, the reader can picture the shape of Lula's head, eyes, nose, and mouth by drawing upon words and phrases that they understand in the world around them. For example, bullets and almonds have a similar shape, very much like an Indian's bow. Hence, not only does Lee use imagery and metaphors to describe this character, but she also applies allusion to real-world visual images to get the description across to the reader. Other examples of literary devices can be found in the list below.
Chapter 13 - "As a result the town remained the same size for a hundred years, an island in a patchwork sea of cotton fields and timberland" (131). (This is metaphorical imagery comparing the town to an island in the middle of a "sea," not of water, but of cotton fields.)
Chapter 14 - "Punk, punk, punk, her needle broke the taut circle. She stopped, and pulled the cloth tighter: punk-punk-punk. She was furious" (137). ("Punk" is used as onomatopoeia: auditory imagery.)
Chapter 15 - "We had a week of peace together. After that, little, it seemed. A nightmare was upon us" (144). (This is metaphorical foreshadowing: Future life events surrounding the night before the trial are being referred to as a nightmare.)
Chapter 16 - "'Mr. Cunningham's basically a good man,' he said, 'he just has his blind spots along with the rest of us'" (157). ("Blind spots" are metaphors for not being able to see incorrect beliefs within ourselves.)
Chapter 17 - "The varmints had a lean time of it, for the Ewells gave the dump a thorough gleaning every day, and the fruits of their industry . . . made the plot of ground around the cabin look like the playhouse of an insane child" (170). (This is a simile comparing the Ewell home to a playhouse of an insane child.)
Chapter 18 - "Apparently Mayella's recital had given her confidence, but it was not her father's brash kind: there was something stealthy about hers, like a steady-eyed cat with a twitchy tail" (181). (This is also a simile: Mayella's testimony is compared to a cat while using the word "like".)
Chapter 19 - "Mayella Ewell must have been the loneliest person in the world. She was even lonelier than Boo Radley" (191). (This is an allusion referring to someone that the audience knows: Boo Radley.)
Chapter 20 - "One more thing, gentlemen, before I quit. Thomas Jefferson once said that all men are created equal . . ." (205). (This is an allusion referring to someone that the audience and the jury know: Thomas Jefferson.)
Chapter 21 - "If Mr. Finch don't wear you out, I will--get in that house, sir!" (207). (The dialect here is used to further characterization of Calpurnia.)
Chapter 22 - "'Just looka yonder,' he pointed. 'Every one of 'em oughta be ridin' broomsticks. Aunt Rachel already does'" (217). (This is an allusion to witches.)
Chapter 23 - "Jem, see if you can stand in Bob Ewell's shoes a minute" (218). (This is a metaphorical idiom.)
Chapter 24 - "Mrs. Merriweather played her voice like an organ; every word she said received its full measure" (230). (This is a simile comparing the woman's voice to singing and reading music.)

This sounds like a daunting question, but Harper Lee’s language is so rich that the literary devices are not too difficult to discover. I’ll try to get you started with a couple, and you can continue from there.
Allusion is a literary device used often in To Kill a Mockingbird. This is a reference by the author to another subject. It could be a reference to a literary work or an event in history. It is up to the reader to have the background knowledge to understand the allusion. For example, in chapter 12, the author references the Bible as she talks about the mischief Jem got into one time at church. She says, “until someone investigated and brought forth Eunice Ann saying she didn’t want to play Shadrach any more—Jem Finch said she wouldn’t get burnt if she had enough faith, but it was hot down there.” This refers to the story in the Bible of Shadrach, Meshach, and Abednego and the fiery furnace. The author is alluding to this story.
Another literary device is imagery. The author uses this at the beginning of chapter 13 as she lets us know that Aunt Alexandra is here to stay. “I heard the suitcase hit the bedroom floor with a thump. The sound had a dull permanence about it.” She gives us both the word “thump” and the idea that a sound can be permanent, and these contribute to the reader’s sense that this is no ordinary visit by their aunt.
It might help you to have a list of literary devices handy as you skim the book for them. A helpful website is linked below.
Lee, Harper. To Kill a Mockingbird. (Soft Cover). Perennial, 1961.

How does Celia's character change and mature during the course of the novel?

I believe that the best indicator of Celia Bowen's maturation and overall change is her relationship with her father, Hector Bowen, which evolves over the course of the novel. Throughout the novel, Hector Bowen proves to be a hard and demanding task master. He demands a lot from Celia, and he is not happy with anything less than her best. His expectations of her abilities are high, and he withholds praise frequently. When he first begins training Celia, she tries very hard to live up to the unrealistic expectations. She wants to please her father; however, as the novel progresses, Celia's love and compassion for other people begins to outweigh her desire to be the hardened magician that her father would like her to become. She learns that the end goal of the circus and her battle with Marco is that one of them will die. Celia is unwilling to bring the competition to that gruesome conclusion, so she actively begins looking for a way to circumvent the rules of the competition. She is confident enough in herself and her abilities to defy her father's wishes and the rules of the game. This allows her to find a way to live on with Marco and keep the circus and everybody involved alive. 

How is industrialism and economic/social change addressed in The Importance of Being Earnest? How does it affect individual life?

Industrialism is not central to the plot of The Importance of Being Earnest by Oscar Wilde. The Industrial Revolution is reflected most clearly in the play in the presence of the railway. Although aristocrats in earlier centuries tended to gather in London for the "season" and the retreat to country houses in the summer, railroads are the enabling technology for Jack's rapid movements from city to country.
The Miss Prism subplot also relies on technology. First, of course, the infant Jack was left by accident in a handbag at Victoria Station. Next, the sort of novel she is described as writing is associated with "railway stalls," which sold cheap popular novels (often on themes of romance or crime). In Wilde's time, they were disparaged as lowbrow fiction and criticized as exemplars and causes of cultural decline.
Another common trope found in the novel, parodied in Algernon's "Bunburying," is the notion of the countryside as pastoral, traditional, and morally good and the city as associated with decadence and vice.
Much of the social anxiety readers see in Lady Bracknell and her daughter is the result of the rise of a wealthy industrial class. This meant that money was no longer the exclusive property of the landed aristocracy, and thus the insistence in the play on such things as addresses, manners, and relatives is a way of distinguishing class despite the spread of wealth. The inversion of hierarchy, where Lane becomes an arbiter and model of morality, also addresses the same social anxiety.
Perhaps the greatest social change seen in the play is the decline of the practical role of the aristocracy and its descent into frivolity and quest for status. The traditional "country squire" had been a farmer. He would be responsible for managing large amounts of land and an agricultural workforce. He would often serve as a magistrate, act as a patron to the parish church, offer reading lessons, and generally be a crucial part of village life. In Wilde's play, readers see an aristocracy living off rents or invested funds, unmoored from local country duties, living essentially trivial lives, pursuing pleasure and prestige but not really having a greater purpose in life.

In the epic poem Beowulf, how do Beowulf's heroic qualities affect the story?

In the epic poem Beowulf, Beowulf's heroic qualities are essential to the progression of the plot. His heroism sets up the major battle scenes and conflicts of the poem.
Near the start of the poem, Beowulf has heard that the monster Grendel is terrorizing Hrothgar's kingdom. Grendel is angered by the sounds of celebration in the mead hall at night and goes to the hall to kill and eat the men who are feasting there. This continues for some time, and no one seems able to stop it. Beowulf decides to go to Hrothgar's kingdom with his own men to try to defeat the beast. Beowulf is granted permission by Hrothgar and eventually succeeds in killing Grendel. This choice, to cross the sea and go to a foreign kingdom to help a king he does not even know personally only to put himself in physical danger to fight the monster, shows Beowulf's heroism: he puts his life on the line to save others.
Later, Beowulf travels to the monster's cave to kill Grendel's mother, who has continued to stalk the kingdom to avenge her son's death. Beowulf is brave: he decides to go to the monster's home turf, so to speak, and take her on. He is helped by a magical sword, and Beowulf does defeat the beast. This ushers in a period of peace for Hrothgar's kingdom. 
Later, at the climax of the poem, Beowulf is an old king whose people are being threatened by a dragon. Even though he is old and somewhat out of practice, our hero puts himself on the line again to save his people. He is mortally wounded in the fight, but one of his men steps up and kills the dragon. Beowulf's heroism is celebrated by his men, who build him a monument and an impressive funeral pyre. 
In conclusion, Beowulf's heroism moves the plot along and sets up the major conflicts/battles in the poem. His heroism is also a key feature of epic poetry, which helps to define Beowulf as such.

What is a democratic republic?

A democratic republic is another name for a representative democracy. The United States, Japan, and most countries in Europe fit this bill. As opposed to direct democracy, which has only ever existed once, in Ancient Athens, and which requires the entire populace to participate in all decision making on an almost daily basis, representative democracies (republics) delegate the daily details of governance to officials elected by the populace at large.
In a democratic republic, or representative democracy, the will of the people gets expressed through elections, and those representatives that get elected are entrusted by the voters to govern in a way that is consistent with the wants, needs and ideals of that representatives' constituents. This system is far more practical than direct democracy, for by delegating daily governance to elected representatives and a meritocratic body of technocrats, the general population can go about its daily business, thus creating a vibrant, diversified economy. 
Ironically, the most repressive regimes in the world often call themselves democratic republics, meaning that they actually put the words "democratic republic" in the name of their country, whereas as legitimate republics mostly do not. Whenever you read about a country called "The Democratic Republic of...." be wary. The Democratic Republic of the Congo, for example, is rife with corruption, state sanctioned violence against civilians, and is in almost perpetual civil war. Likewise, North Korea, the most totalitarian state in the world, calls itself the "Democratic Republic of Korea," whereas South Korea, which is actually is a democratic republic, is simply called the Republic of Korea. 
The best way to find out if a country is actually a democratic republic is to see if it holds free and fair elections, where the results are monitored and opposition parties are free to campaign without limitations or intimidation. A real democratic republic will often have numerous parties vying for power, and perhaps most importantly, it will have a history of peaceful transitions of power between rival parties.
Finally, true democratic republics have civilian oversight of the military. This last part is crucial because even legitimate democratic republics are not immune from military coups, and the ability of a republic to keep its military separate from its political leadership is crucial to maintaining the integrity of both. That is why in many democratic republics, such as the United States, members of the military are forbidden from publicly expressing their political preferences. 

A democratic republic is a nation which functions as both a democracy and a republic, incorporating elements of philosophies of government. In a democracy ("people's rule") all people participate in the decision-making process by casting a vote. In a republic, the people elect representatives to participate in decision-making for them. Both forms of government have had some differences over time and throughout space, especially when it comes to who was considered a "person" or full citizen under the government. 
In the modern sense, a democratic republic is a nation where all citizens participate in decision making, but the administration and implementation of these decisions falls into the hands of elected officials. Unfortunately, the term "democratic republic" has been adopted by a number of totalitarian states including the Democratic People's Republic of Korea, also called North Korea. Though the DPRK holds elections for public office, including Supreme Leader, there is only one political party in the nation and often only one candidate appears on the ballot. This is not a true example of a democratic republic because it offers only the illusion of democratic or republic government.
https://www.britannica.com/topic/democracy

https://www.britannica.com/topic/republic-government

Single Variable Calculus, Chapter 3, 3.1, Section 3.1, Problem 18

a.) Determine the equation of the tangent line to the graph of $y=g(x)$ at $x = 5$ $\text{ if } g(5) = -3 \text{ and } g'(5) =4$




b.) Suppose that the tangent line to $y = f(x)$ at $(4,3)$ passes through the point $(0,2)$. Find $f(4)$ and $f'(4)$






$\text{a.) }$ Using point slope form


$y - y_1 = m(x-x_1)$

Recall from the definition that the derivative of the function is equal to the slope so,



$
\begin{equation}
\begin{aligned}
m &= g'(5) = 4\\
y-(-3) &= 4(x-5)\\
y+3 &= 4x-20\\
y &= 4x - 20 - 3\\
y &= 4x-23
\end{aligned}
\end{equation}
$


$\text{b.) }$ The line passes through the points $(4,3)$ and $(0,2)$ so we can use two
point form to determine the equation of the line.



$
\begin{equation}
\begin{aligned}
y - y_1 &= \frac{y_2-y_1}{x_2-x_1} (x-x_1)\\
y-3 &= \left( \frac{2-3}{0-4} \right) (x-4)\\
y-3 &= \frac{1}{4} (x-4)\\
y-3 &= \frac{x}{4}-1\\
y &= \frac{x}{4}+2\\
f(x) &= \frac{x}{4}+2\\
f(4) &= \frac{4}{4} +2 = 1+2 = 3\\
f(4) &= 3
\end{aligned}
\end{equation}
$



From the definition,



$
\begin{equation}
\begin{aligned}
f'(x) &= \lim\limits_{h \to 0} \frac{f(x+h)-f(x)}{h}\\
f'(x) &= \lim\limits_{h \to 0} \frac{\frac{x+h}{4}+2 - \left[\frac{x}{4}+2\right]}{h}\\
f'(x) &= \lim\limits_{h \to 0} \frac{\cancel{\frac{x}{4}}+\frac{h}{4}+\cancel{2}-\cancel{\frac{x}{4}}+\cancel{2}}{h} \\
f'(x) &= \lim\limits_{h \to 0} \frac{\cancel{h}}{4\cancel{h}}\\
f'(x) &= \lim\limits_{h \to 0} \left(\frac{1}{4}\right)\\
f'(x) &= \frac{1}{4}\\
f'(4) &= \frac{1}{4}
\end{aligned}
\end{equation}
$

In chapter 20 of Candide, can you explain what does Martin think about God and why?

Martin the scholar believes that God has cruelly abandoned the world. He thinks this because, wherever you look, men are always at each other's throats and killing each other. This unshakable conviction is confirmed by the events that he and Candide witness on the high seas. En route to Bordeaux, the two men watch a particularly intense sea battle. One of the ships sinks, and the entire crew perishes. By recognizing one of his stolen jewel sheep floating in the water, Candide is able to identify the ship as belonging to the cruel slave-owner Vanderdendur.
Candide claims that Vanderdendur's death shows that there's some justice in the world after all; this wicked man got what was coming to him. But Martin disagrees. It wasn't just Vanderdendur who went down with the ship but his crew as well. This is why Martin thinks that God has effectively abandoned his creation. The innocent are punished alongside the guilty, the good with the evil.

were Ignossi and twala brother each other?

As the group of travelers approaches the land of the Kukuana, they are met by a group of locals led by Infadoos, son of Kafa, and Scragga, son of the reigning King of the Kukuanas, Twala.
Infadoos’s father, Kafa was a King. When he died, the kingship was passed on to Imotu, who was Infadoos’s half-brother. However, Imotu had a twin brother who was secretly kept alive by their mother, in spite of their traditions—according to the customs of the Kukuana people, the weaker one of the twins must die. The weaker twin was called Twala.
According to Infadoos, when Imotu was King, there came a famine upon the people. At this time, Imotu already had a three-year-old son by his favorite wife. The boy was called Ignosi. The people complained because of the ravaging famine. Gagool, the wise and terrible woman, took advantage of the situation to introduce Twala as the people’s new King. Upon being proclaimed as King, Twala murdered his twin brother Imotu and took over the kingship. Imotu’s wife and son, Ignosi, ran away never to be seen again.
Therefore, Infadoos, Imotu, and Twala are all brothers. Twala would be Ignosi’s uncle.

Fortunato is hesitant to follow Montresor into the vaults. Why do you think Poe included this detail?

The classic horror short story "The Cask of Amontillado" by Edgar Allan Poe tells of a man named Montresor, who plots elaborate vengeance on someone he supposes is an enemy. His motivation is summed up in the first sentence: "When he ventured upon insult I vowed revenge." Sane people might possibly want to repay insult, but not with murder. Montresor prepares a far chamber in his family vaults with the tools and materials he needs, makes sure that his servants will be gone from the house, and then comes up with a story about a hidden case of Amontillado, a type of sherry wine, to lure Fortunato to his doom. He knows that Fortunato considers himself a wine connoisseur, would scorn the opinion of Luchresi, and would offer his own services as a tester.
When they meet at the carnival, Montresor converses with Fortunato so skillfully that it is Fortunato's suggestion that they immediately go to the vaults. Montresor cleverly protests, but not too much. At the empty house, Montresor obtains two torches, and he and Fortunato pass through numerous rooms before they come to the archway leading to the vaults and a winding stairway that takes them downward.
At this point, when they have reached the damp ground of the catacombs, Fortunato hesitates. There are three reasons for this. Firstly, he is already drunk. He sways uncomfortably on his feet, and when he looks at his host, Montresor observes that his eyes are "two filmy orbs that distilled the rheum of intoxication." Fortunato also sees white streaks of niter upon the otherwise dark walls. Montresor calls it "white web-work." This may be creepy-looking, and it is also unhealthy. Finally, Fortunato has a severe fit of coughing that renders him unable to move or speak for several minutes.
Again Montresor pretends to persuade him to retreat. Fortunato would have done well to listen, although by this point it is probably already too late for him to save himself. Instead, he insists on continuing. Even the niter heavy upon the walls and the heaps of skeletons that they pass do not deter him, and finally he is chained up by Montresor and left in the vaults.

In “The Cask of Amontillado,” Fortunato’s initial hesitation lends verisimilitude to the story and prevents Montresor from gaining his victory with unconvincing ease. Most importantly, it gives Montresor the occasion to display his cunning in the use of reverse psychology. Instead of insisting that Fortunato should accompany him and trying to pressure him into doing so, Montresor refers to their mutual acquaintance Luchresi, whose reputation as a connoisseur of wine rivals Fortunato’s own. This appeal to Fortunato’s vanity proves entirely successful, and he insists on proceeding, while Montresor increases his resolution by raising objections.
There is no doubt that Montresor, brooding on his revenge, will have considered the nature of Fortunato’s last thoughts as he dies slowly in the catacombs. The reflection of how easily he could have escaped and how simple it was for Montresor to dupe him into continuing regardless of any objections will only lend additional bitterness to his end. This, of course, will make the revenge all the sweeter and more complete in Montresor’s eyes.

From the beginning of the story, Montresor makes it clear that he considers himself the injured party. We never learn the exact insults and indignities that he so strongly feels Fortunato has imposed on him, but there is no doubt that he wants the reader to know that he is superior to his rival.
Montresor knows the other man well enough to understand his weaknesses and prey upon them. Fortunato cannot resist the fine wine that Montresor offers him. His gluttonous nature is one thing Montresor has counted on—and correctly so.
When they pause partway down, Fortunato has a nasty coughing fit, and his future killer feigns concern. Despite the threat to his health that the damp underground way presents, the man is determined to drink the prized wine. Montresor is again establishing his superiority by showing how well he has anticipated his rival's moves, while the other is clueless as to what Montresor is up to.

After Montresor and Fortunato descend into the catacombs, we see Fortunato hesitate before entering because of a fit of coughing.  Poe included this for two reasons.  One, it shows the reader Fortunato's weakness, his lungs.  Second, it helps foreshadow the ending of the text.  By pointing out the "white webwork which gleams from [the] cavern walls" and showing Fortunato's reaction when being around the niter for only a short time, the reader can surmise that further exposure to this mold will contribute to the downfall of Fortunato and is a key part to Montresor's diabolical plan.

Fortunato follows Montresor down a long, winding staircase to the Montresor family catacombs. Fortunato then hesitates for a few minutes before entering into the vaults because the niter on the walls gives him a coughing fit. As Montresor remembers it, the scene unfolds as follows:

"It is farther on," said I; "but observe the white web-work which gleams from these cavern walls."
He turned towards me, and looked into my eves with two filmy orbs that distilled the rheum of intoxication.
"Nitre?" he asked, at length.
"Nitre," I replied. "How long have you had that cough?"
"Ugh! ugh! ugh! --ugh! ugh! ugh! --ugh! ugh! ugh! --ugh! ugh! ugh! --ugh! ugh! ugh!"
My poor friend found it impossible to reply for many minutes.

Poe includes this detail to show how weak Fortunato's lungs are. It is dangerous for him to be breathing the bad air in the catacombs. One can imagine that once Montresor walls him up, he will be coughing; thus suffering terribly, with nobody to hear him or help him.
However, the detail serves an even more diabolical purpose for Poe, for it shows how sadistic Montresor's plan is. Montresor says early on that he wants Fortunato to suffer from the revenge Montresor exacts on him. Montresor has seemingly thought of every detail that will increase his enemy's pain.