Why does Yep feel like an outsider?

Yep feels like an outsider for lots of reasons. For one thing, as a Chinese American he does not feel completely accepted in society. No matter where he goes or what he does, he never seems to fit in anywhere. Yep was raised in a predominantly black neighborhood; at the same time, he is too American to fit easily into Chinatown and too Chinese to fit in anywhere else. There is also the inevitable generation gap between himself and his hardworking immigrant parents. Yep's parents spend every hour that God sends running a grocery store, which leaves little time for them to devote to their son. Because Yep cannot speak Chinese, he is unable to connect with his grandmother, Marie Lee, who leads a traditional Chinese lifestyle. It is no wonder that Yep feels like such an outsider.

What was Samson Occom's point of view in From a Short Narrative of My Life?

Samson Occom uses the first person point of view in his story.
The first person point of view lends immediacy to our reading experience. In the narrative, Occom speaks earnestly about his faith in God and his strong desire to educate the Native children entrusted to his care. He also relates with strong emotion his dismay at the treatment he received from the Church.

Now you See what difference they made between me and other missionaries; they gave me 180 Pounds for 12 years Service, which they gave for one years Services in another Mission, — In my Service (I speak like a fool, but I am Constrained) I was my own Interpreter. I both a School master and Minister to the Indians, yea I was their Ear, Eye & Hand, as Well as Mouth. . . what can be the Reason that they used me after this manner?

In the above quote, Occom tells us that he "speaks like a fool." He does not claim to be wiser than the Church leaders, and his humility is apparent. However, his distress is clear; he questions how the religious authorities could have treated a fellow Christian with such shameful disregard. The grave disparity in pay causes Occom great pain. 
He voices his anguish at being blamed for being "extravagant." His narrative is filled with earnest, powerful sentiments:

I Can’t Conceive how these gentlemen would have me Live. I am ready to (forgive) their Ignorance, and I would wish they had Changed Circumstances with me but one month, that they may know, by experience what my Case really was; but I am now fully convinced, that it was not Ignorance.

Through the first person point of view, Occom is able to focus our attention on the injustices he endured as an Indian missionary.
https://literarydevices.net/point-of-view/

Calculus of a Single Variable, Chapter 3, 3.1, Section 3.1, Problem 22

Given: f(x)=2x^3-6x,[0, 3]
Find the critical values for x by setting the derivative equal to zero and solving for the x value(s).
f'(x)=6x^2-6=0
6(x^2-1)=0
6(x+1)(x-1)=0
x=-1, x=1
The critical values for x are x=1 and x=-1. Plug in the critical value(s) and the endpoints of the interval into f(x). Because x=-1 is not in the interval [0, 3], it is not necessary to plug in the x=-1
f(x)=2x^3-6x
f(0)=2(0)^3-6(0)=0
f(1)=2(1)^3-6(1)=-4
f(3)=2(3)^2-6(3)=36
Examine the f(x) values to determine the absolute extrema.
The absolute minimum value is the point (1, -4).
The absolute maximum value is the point (3, 36).

Single Variable Calculus, Chapter 8, 8.2, Section 8.2, Problem 36

Determine the integral $\displaystyle \int \frac{\sin \Phi}{\cos^3 \Phi} d \Phi$


$
\begin{equation}
\begin{aligned}

\int \frac{\sin \Phi}{\cos^3 \Phi} d \Phi =& \int \frac{1}{\cos^3 \Phi} \sin \Phi d \Phi

\end{aligned}
\end{equation}
$


Let $u = \cos \Phi$, then $du = - \sin \Phi d \Phi$, so $\sin \Phi d \Phi = -du$. Thus


$
\begin{equation}
\begin{aligned}

\int \frac{1}{\cos^3 \Phi} \sin \Phi d \Phi =& \int \frac{1}{u^3} \cdot -du
\\
\\
\int \frac{1}{\cos^3 \Phi} \sin \Phi d \Phi =& - \int \frac{1}{u^3} du
\\
\\
\int \frac{1}{\cos^3 \Phi} \sin \Phi d \Phi =& - \int u^{-3} du
\\
\\
\int \frac{1}{\cos^3 \Phi} \sin \Phi d \Phi =& \frac{-u^{-3 + 1}}{-3 + 1} + c
\\
\\
\int \frac{1}{\cos^3 \Phi} \sin \Phi d \Phi =& \frac{-u^{-2}}{-2} + c
\\
\\
\int \frac{1}{\cos^3 \Phi} \sin \Phi d \Phi =& \frac{u^{-2}}{2} + c
\\
\\
\int \frac{1}{\cos^3 \Phi} \sin \Phi d \Phi =& \frac{1}{2u^2} + c
\\
\\
\int \frac{1}{\cos^3 \Phi} \sin \Phi d \Phi =& \frac{1}{2 (\cos \Phi)^2} + c
\\
\\
\int \frac{1}{\cos^3 \Phi} \sin \Phi d \Phi =& \frac{1}{2 \cos^2 \Phi} + c
\\
\\
\int \frac{1}{\cos^3 \Phi} \sin \Phi d \Phi =& \frac{1}{2} \sec^2 \Phi + c


\end{aligned}
\end{equation}
$


then


$
\begin{equation}
\begin{aligned}

\int \sec^3 x dx =& \int udv
\\
\\
\int \sec^3 x dx =& uv - \int v du
\\
\\
\int \sec^3 x dx =& \sec x \tan x - \int \tan x \cdot \sec x \tan x dx
\\
\\
\int \sec^3 x dx =& \sec x \tan x - \int \sec x \tan^2 x dx
\qquad \text{Apply Trigonometric Identity } \sec^2 x = \tan^2 x + 1
\\
\\
\int \sec^3 x dx =& \sec x \tan x - \int \sec x (\sec^2 x - 1) dx
\\
\\
\int \sec^3 x dx =& \sec x \tan x - \int (\sec^3 x - \sec x) dx
\\
\\
\int \sec^3 x dx =& \sec x \tan x - \int \sec^2 x dx + \int \sec x dx
\qquad \text{Combine like terms}


\end{aligned}
\end{equation}
$




$
\begin{equation}
\begin{aligned}

\int \sec^3 x dx + \int \sec^2 x dx =& \sec x \tan x + \int \sec x dx
\\
\\
2 \int \sec^3 x dx =& \sec x \tan x + \int \sec x dx
\\
\\
2 \int \sec^3 x dx =& \sec x \tan x + \ln (\sec x + \tan x) + c
\\
\\
\int \sec^3 x dx =& \frac{\sec x \tan x + \ln (\sec x + \tan x)}{2} + c


\end{aligned}
\end{equation}
$


@ 2nd term

$\int \sec x dx = \ln (\sec x + \tan x) + c$

Combine the results of the integration term by term


$
\begin{equation}
\begin{aligned}

\int \tan^2 x \sec x dx =& \frac{\sec x \tan x + \ln(\sec x + \tan x)}{2} - \ln (\sec x + \tan x) + c
\\
\\
\int \tan^2 x \sec x dx =& \frac{\sec x \tan x + \ln(\sec x + \tan x) - 2 \ln (\sec x + \tan x)}{2} + c
\\
\\
\int \tan^2 x \sec x dx =& \frac{\sec x \tan x - \ln (\sec x + \tan x)}{2} + c
\\
\\
\text{ or} &
\\
\\
\int \tan^2 x \sec x dx =& \frac{1}{2} (\sec x \tan x - \ln (\sec x + \tan x)) + c


\end{aligned}
\end{equation}
$

Why do Connie and her mother clash?

Connie's mother has a tendency to compare Connie to her older sister, June, and that comparison seems to manifest with Connie being considered inferior.  In the story's first paragraph, Connie's mother asks why Connie cannot keep her room clean like June does, and why she uses stinky hair spray even though June does not.
Connie's vanity is also a sore spot between mother and daughter.  Connie is fond of looking at herself in the mirror, and her mother criticizes her for it, asking "you think you're so pretty?" Connie believes that her mother is jealous of her beauty because she was once beautiful but "now her looks were gone."
On the fateful day of her aunt's barbecue, Connie opts to stay home and wash her hair to let it dry in the sun all day.  When she rolls her eyes at her mother in response to the invitation to go to the barbecue, her mother sharply responds, "stay home alone, then."
Generally speaking, Connie is a typically rebellious teenager who is testing boundaries, and her mother is a parent struggling with the transition. 

In Warriors Don't Cry by Melba Pattillo Beals, what were some problems the characters faced? What were the solutions to the problems?

The main problem that the nine black students face is the resistance of the white students to their presences at the high school. Melba Pattillo Beals names some of her enemies: a boy named Andy and a girl named Sammy Jo Parker, who takes part in an interview with The New York Times in which she says that she suspects that the black students are being paid by the NAACP to attend Central High.
The students contend with the general problem of the white segregationists not understanding that they are not conspiracists but simply fellow teenagers who want to attend a quality school. However, the most pervasive problem is the daily violence to which the black students are subjected. Melba describes instances in which her life is threatened, including an attempt by a group of white girls to set her on fire while she is using a bathroom stall. Worse, many of the white teachers and administrators are unsympathetic to the fears expressed by Melba and the other students and even accuse them of imagining the violent harassment. Thus, the students have to contend with these problems on their own.
To help her maintain her mental strength, Melba depends greatly on her mother and grandmother. She also finds solace in her faith in God and reads about the non-violent civil disobedience of Mahatma Gandhi.

Some specific problems Melba faces throughout the book all trace to the prevailing racist attitude in Little Rock.
Melba is unable to enter the school on her first scheduled day. On her first day at school with the other students, she has to be escorted secretly from the building to avoid an angry mob outside; she even overhears an adult in the principal’s office suggest that one of the students he offered up to appease the mob. After that, Melba has a personal escort Danny, a member of the 101st Airborne Division. Danny saves Melba twice from potentially life-threatening situations. The first of these is a stick of dynamite that is hurled down the stairs at Melba. The second is when Melba gets an unidentified acidic chemical splashed in her eyes. These severe instances of bullying are extreme examples of how the racist attitudes of the city impacted Melba’s daily life.
She also receives little support from the adult teachers. On top of this, Melba has to deal with threats of violence at her home.

In Warriors Don't Cry, the main problem that Melba and the other members of the Little Rock Nine faced was integrating Central High School in 1957-1958. Some of the white students at the school harassed the Little Rock Nine, while others even assaulted them or threw objects at them. In the face of danger, pressure, and harassment, the Little Rock Nine had to get through the school year by employing different solutions. Melba Pattillo, the author of the book, survived by imagining that she was a warrior doing battle in the school. She steeled herself for violence and attacks each day; she could not respond with violence, but she did respond with constant vigilance and mental toughness. The other students handled the violence and harassment in different ways; for example, Minnijean Brown dropped a tray loaded with chili on some students and then was expelled from school for calling some girls "white trash." The other students lasted out the year, and then the school closed rather than integrate.

College Algebra, Chapter 4, 4.4, Section 4.4, Problem 78

Determine all rational zeros of the polynomial $P(x) = 2x^4 + 15x^3 + 31x^2 + 20x + 4$ and then find the irrational zeros, if any. Whenever appropriate, use the Rational Zeros Theorem, the Upper and Lower Bounds Theorem, Descartes' Rule of Signs, the quadratic formula or other factoring techniques.


So, $\displaystyle \frac{-1}{2}$ is a zero and $\displaystyle P(x) = \left( x + \frac{1}{2} \right) \left( 2x^3 + 14x^2 + 24x + 8 \right)$. We continue by factoring the quotient, the possible rational zeros of $P$ are $\displaystyle \pm \frac{1}{2}, \pm 1, \pm 2, \pm 4, \pm 8$ we check again the negative candidates first, beginning with the smallest.
Using Synthetic Division,


So $-2$ is a zero and $\displaystyle P(x) = \left(x + \frac{1}{2} \right) (x+2) (2x^2 + 10x + 4)$. We now factor the quotient using quadratic formula.

$
\begin{equation}
\begin{aligned}
x &= \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\
\\
x &= \frac{-10 \pm \sqrt{(10)^2 - 4(2)(4)}}{2(2)}\\
\\
x &= \frac{-5\pm\sqrt{17}}{2}
\end{aligned}
\end{equation}
$

Therefore, $\displaystyle P(x) = \left( x + \frac{1}{2} \right) (x + 2)\left( x + \frac{5+\sqrt{17}}{2}\right) \left( x + \frac{5-\sqrt{17}}{2}\right)$

In Hamlet, how does the text confront the reader or audience with scenes of violence? How do violent scenes contribute to the meaning of the play?

In Shakespeare's Hamlet, the two scenes of violence that occur in full view of the audience are Hamlet's accidental killing of Polonius in act 3, scene 4 and the violent climax of the play in act 5, scene 2.
Other acts of violence relevant to the plot occur out of sight of the audience, as they do in the Ancient Greek plays of Aeschylus, Sophocles, and Euripides. The violence is reported—often in the most horrific and graphic detail—by a messenger or a secondary character who observed the violence, or, less often, by a participant in the violence.
In an unusual variation, the ghost of Hamlet's father describes his own death to Hamlet in act 1, scene 5.

GHOST. Sleeping within my orchard,My custom always of the afternoon,(65)Upon my secure hour thy uncle stole,With juice of cursed hebenon in a vial,And in the porches of my ears did pourThe leperous distilment, whose effectHolds such an enmity with blood of man(70)That, swift as quicksilver, it courses throughThe natural gates and alleys of the body,And, with a sudden vigour, it doth possetAnd curd, like eager droppings into milk,The thin and wholesome blood. So did it mine;(75)And a most instant tetter bark'd about,Most lazar-like, with vile and loathsome crustAll my smooth body.Thus was I, sleeping, by a brother's handOf life, of crown, of queen, at once dispatch'd... (1.5.64-80)

Hamlet's killing of Polonius in act 3, scene 4, although shocking in its unexpectedness, suddenness, and violence, is actually hidden from the audience's view.

GERTRUDE. What wilt thou do? Thou wilt not murder me?Help, help, ho!
POLONIUS. (Behind the arras) What, ho! help, help, help!
HAMLET. (Drawing) How now! a rat? Dead, for a ducat, dead!

Makes a pass through the arras

POLONIUS. (Behind the arras) O, I am slain!

Falls and dies. (3.4.23-27)
The audience sees Hamlet thrust his dagger or sword through the curtain behind which Polonius is eavesdropping on Hamlet's conversation with his mother and sees Polonius fall to the floor from behind the curtain.
Throughout the play, Hamlet has done nothing but talk about taking revenge on Claudius for murdering Hamlet's father. Hamlet even had an opportunity to kill Claudius outright in act 3, scene 3, when Claudius was on his knees praying for forgiveness for the murder, but Hamlet talked himself out of killing Claudius. In this scene with his mother, however, Hamlet takes instant, decisive action against a person who he only thinks might be Claudius.
The effect of this scene is that the audience sees Hamlet act in a way that is totally inconsistent with his previous actions—or, rather, his total inaction—and shows the audience a part of Hamlet's character they haven't seen before.
The violent deaths of Rosencrantz and Guildenstern in Hamlet's place in England are mentioned only in passing by Hamlet at the beginning of act 5, scene 2. Hamlet is much less concerned about their deaths than he is about telling Horatio how clever he was to rewrite the letter that Claudius sent with them to King Edward of England requesting that "not to stay the grinding of the axe, / My head should be struck off" (5.2.25-26).

HORATIO. So Guildenstern and Rosencrantz go to't.
HAMLET. Why, man, they did make love to this employment!They are not near my conscience; their defeatDoes by their own insinuation grow. (5.2.61-63)

So much for the deaths of Rosencrantz and Guildenstern. It was their own fault.
Gertrude interrupts Claudius and Laertes while they're plotting Hamlet's death to report Ophelia's death to them. Although Ophelia's death isn't particularly violent, it's nonetheless distressing (or seemingly so) to those three characters and hardens Laertes's vengeful heart even further towards Hamlet.
Ophelia's death resolves a lingering question for the audience as to what happened to Ophelia after her "mad scene" (Act 4, Scene 5) and also avoids having Ophelia as the only major character (other than Horatio) left alive at the end of the play.
The final scene of Hamlet is the only truly violent scene that the audience observes. The scene serves to resolve all the loose ends of the plot and avenges all the real and imagined wrongs that the remaining characters need to avenge.
Although Hamlet didn't intend to avenge his father's death on his mother, Gertrude, she's justly rewarded for possibly participating in the plot against Hamlet's father and for her "incestuous" marriage to Claudius. Some Shakespeare scholars suggest that Gertrude might even have known that the goblet of wine intended for Hamlet was poisoned, and she drank it herself to spare Hamlet's life or to take her own life out of guilt for what she's done.
Hamlet avenges his father's death by (finally) killing Claudius. Laertes avenges Hamlet's killing of his father, Polonius, and avenges his sister, Ophelia, for whose madness and death Laertes blames Hamlet.
It remains only for Horatio to report to Fortinbras all the violence relevant to the plot, after the play is over.

HORATIO. ... So shall you hearOf carnal, bloody and unnatural acts;Of accidental judgments, casual slaughters;Of deaths put on by cunning and forced cause;And, in this upshot, purposes mistookFall'n on the inventors' heads. All this can ITruly deliver. (5.2.395-401)

There are numerous examples of violence throughout Hamlet. However, it is best to concentrate on those which have the greatest degree of dramatic significance for the play as a whole. Let us start off with one that takes place before the play even starts: the murder of King Hamlet, the protagonist's father. This is arguably the most important act of violence in the text: it sets the tone for all subsequent events in the play and provides Hamlet with the prime motivating factor for his actions (or lack thereof). The murder of Hamlet's father is the foundational act of violence that leads directly or indirectly to all other acts of violence in the play.
In act 1, scene 5, the ghost of Hamlet's father appears to him and tells him how he really died. Hamlet, like everyone else, assumed that his father had died after being bitten by a poisonous snake. In reality, Claudius crept up on him while he was sleeping in the orchard and poured poison down his ear. Additionally, Claudius seduced King Hamlet's queen, Gertrude:

Ay, that incestuous, that adulterate beast,
With witchcraft of his wit, with traitorous gifts—
O wicked wit and gifts, that have the power
So to seduce!—won to his shameful lust
The will of my most seeming-virtuous queen.

Hamlet's fraught relationship with his mother will be an important theme running throughout the rest of the play. The ghost is firmly establishing in Hamlet's mind an intimate link between Claudius' act of murder and Gertrude's adultery.
 
Gertrude, unwittingly perhaps, always seems to be related to violence. Indeed, for Hamlet, her betrayal of his father and subsequent marriage to Claudius is an act of violence against honor, dignity, and all that is decent.
 
Gertrude is in the thick of things again in act 3, scene 4. She gets into a blazing row with Hamlet, who lets fly with a volley of vicious personal abuse against his mother. As expected, it revolves around his detestation of Gertrude for marrying his father's murderer. Hamlet's verbal violence spills over into physical violence as he stabs and kills Polonius, who had been hiding behind a curtain to eavesdrop on Hamlet's conversation. At this stage in the play, whether we believe that Hamlet's madness is real or feigned, there is no doubt that whatever is going on in that mind of his is having deadly repercussions.
 
Murder is not the only kind of violence which has significance in the play. Take Ophelia's suicide, for example. At least, most people conclude that she committed suicide. The Church refuses to bury her in hallowed ground, a sure sign that she actually did kill herself. At the very least, Ophelia does not really care whether she lives or dies because she is so psychologically damaged by the twin tragedies of Hamlet's rejection and the death of her father, Polonius. It is significant that a relatively passive character in the play shows more resolution in enduring "the slings and arrows of outrageous fortune" than Hamlet himself, even though it did lead to her death.
 
The act of violence that the whole play leads up to—Hamlet's revenge upon Claudius in act 5, scene 2—turns out to be much less dramatic than we expect. One quick swig of poison and it is all over. However, there is still some significance to this particular act of violence, nonetheless. Claudius's death allows King Hamlet to be avenged and serves as a neat instance of poetic justice. Just as he poisoned his brother and (inadvertently) his wife, so too has he poisoned himself.
 
Hamlet had a number of oppurtunities to kill Claudius. In this scene he stabs him, but it is not enough to kill him. It is important for the overall dramatic structure of the play that Claudius ends up dying in the same way as his brother. Thus, the ambiguity of violence in Hamlet is revealed. It can be terrible, brutal, and unjust. Yet, just like fire, it can purge and destroy. 

How were the Americans justified for the acquisitions of Texas and Mexico between 1845 and 1848?

It is a matter of perspective whether the United States was justified in taking Texas and other lands from Mexico in the 1840s. The Mexican government never officially recognized Texas as an independent country, and they did not think the United States should annex Texas. The Mexicans also felt the United States illegally moved its military into Mexican land between the Nueces and Rio Grande Rivers. Therefore, the Mexicans did not feel the United States was justified in the actions that led to the Mexican-American War and, eventually, the Mexican Cession.
From the American perspective, the United States felt it should expand from the Atlantic Ocean to the Pacific Ocean. The Americans knew that the people of Texas wanted to join the United States. Many Americans had gone to live in Texas and wanted to be part of the United States. Therefore, the United States felt justified in annexing Texas.
The United States also was interested in gaining land from Mexico. The Americans wanted to spread their culture and way of life to new lands. The Americans also wanted to settle lands west of the Mississippi River. The Americans believed that by expanding to lands controlled by Mexico, the Americans would be able to more quickly settle and develop these areas. Thus, the Americans believed, in the name of progress, that it was acceptable and justifiable to settle these areas that Mexico had controlled.
https://www.u-s-history.com/pages/h302.html

Will Isabel ever find Ruth?

The answer to this question is going to change depending on each reader's opinion of Isabel and the ending of Chains.  Throughout the novel, Isabel works extremely hard to make sure that she and Ruth stay together.  Isabel is even willing to take a beating for Ruth, so readers are likely to believe that Isabel will do anything in her power to stay close to Ruth.  Unfortunately, Isabel and Ruth are slaves.  Their fate is subject to the will of their owners, and Madam Lockton is not a kind and loving owner.  She is every bit as violent and conniving as her husband.  In an effort to hurt Isabel, Madam Lockton gets rid of Ruth. She tells Isabel that she sold Ruth.  In chapter 43, readers discover that Madam Lockton did not actually sell Ruth.  She could not find a buyer, so Madam Lockton sent Ruth to her property in Charleston. 

"Brat," Madam spat. "Couldn't find a buyer. Had to ship her down to Charleston. I shall tell the estate manager to get rid of her, toss her in the swamp. Her death will be on your head, you insolent fool."

At this point, Isabel is supremely motivated to escape the Lockton household.  She successfully does this, rescues Curzon, and escapes the city.  That is when the novel ends.  The exact fate of both Isabel and Ruth is left completely open. I do think, however, that the story ends in a way that is meant to suggest that Isabel will track down and free Ruth.  Based on her tenacity, intelligence, and strength of will demonstrated throughout the story, I do believe that Isabel will fight "like a lion" and find Ruth.  

Calculus of a Single Variable, Chapter 5, 5.7, Section 5.7, Problem 7

Indefinite integral are written in the form of int f(x) dx = F(x) +C
where: f(x) as the integrand
F(x) as the anti-derivative function
C as the arbitrary constant known as constant of integration

In the given problem: int t/sqrt(1-t^4)dt , we follow: int f(t)dt =F(t) +C.
The problem can be rewritten as:
int (t *dt)/sqrt(1^2-(t^2)^2)

This resembles the basic integration formula for inverse sine function:
int (du)/sqrt(a^2-u^2) = arcsin(u/a) +C
Using u-substitution, we let u = t^2 then du = 2t*dt or (du)/2= t*dt .
Note: a^2 = 1 then a = 1
The indefinite integral will be:
int (t *dt)/sqrt(1^2-(t^2)^2)=int ((du)/2)/sqrt(1^2-(u)^2)
Applying the basic property of integration: int c*f(x)dx = c int f(x) dx , we get:
(1/2) int (du)/sqrt(1^2-u^2)
Applying the basic integral formula for inverse sine function:
(1/2) int (du)/sqrt(1^2-u^2)=1/2arcsin(u/1) +C
=1/2arcsin(u)+C
Plug-in u=t^2 in 1/2arcsin(u) +C to express the indefinite intergral in terms of int f(t)dt=F(t)+C :
int t/sqrt(1-t^4)dt =1/2arcsin(t^2) +C

In Macbeth, is Macbeth a victim or aggressor?

Both.  It does seem as though, in the beginning, the Weird Sisters plan to manipulate Macbeth.  When they meet in Act 1, scene 1, they chant, "Fair is foul and foul is fair / Hover through the fog and filthy air" (1.1.12-13).  They appear to imply that they are going to make good things seem bad and bad things seem good, and this is designed to trick Macbeth into believing that something is good when it will really lead to his ruin.  In this sense, then, he is a victim.
On the other hand, once Macbeth's terrible ambition is sparked by the Weird Sisters' "prophecies," he becomes an aggressor.  He not only murders the king, Duncan, but he also plans the murder of his former best friend, Banquo, as well as Banquo's young son, and Macduff's innocent wife, children, and servants.  Once Macbeth starts on his path of destruction, he continues to become worse and worse, changing from a somewhat sympathetic figure to an awful and ruthless tyrant. 

Why does Nag hide in the bathroom in "Rikki-Tikki-Tavi"?

Nag hides in the bathroom in order to ambush and kill the man of the house.  
By this point in the story, Rikki-tikki has proven that he is a threat to Nag, Nagaina, and their eggs. He killed Karait and successfully dodged an attack from behind. Both instances show Rikki-tikki is a threatening, quick predator. Nag and Nagaina need a way to get rid of Rikki-tikki. Their plan involves killing the people in the house. They both believe that the threat that Rikki-tikki is to them will go away once the people are killed. Nagaina believes Rikki-tikki will be easier to hunt with no people around.

"Go in quietly, and remember that the big man who killed Karait is the first one to bite. Then come out and tell me, and we will hunt for Rikki-tikki together."

Nag believes that Rikki-tikki will simply leave of his own volition if the house is devoid of people.  

"I will kill the big man and his wife, and the child if I can, and come away quietly. Then the bungalow will be empty, and Rikki-tikki will go."

Either way, Nag and Nagaina agree that the man needs to be killed first. Nag's plan is to ambush the man in the bathroom because the man is not likely to be carrying a defensive weapon there.  

Now, when Karait was killed, the big man had a stick. He may have that stick still, but when he comes in to bathe in the morning he will not have a stick. I shall wait here 'till he comes.

Describe O'Connor's style in "A Good Man is Hard to Find." What sort of diction does she use? What effect does it have on her rhetoric?

O’Connor’s style is often described as Southern regionalism/realism. Her stories are often categorized somewhere between the Southern Gothic and contemporary genres. Her plain style is infused with images of Southern culture and hints of dialect, but her descriptions tend to be matter-of-fact.
The diction O’Connor uses throughout the story could be described as a mixture of both ordinary and distinct. Words like “aloose” and “dontcha” in the first few paragraphs are examples of slang, for instance.
This adds to the realism of the story, but it also makes O’Connor’s rhetoric accessible to a wide range of readers. Considering that common themes across her writing include grace and redemption, it makes sense that O’Connor would employ a realistic style in order to spread her message broadly.

O'Connor uses comic diction and an ordinary style through most of this story. She tells it through the eyes (up until the very end, after her death) of the grandmother, who does not have a sophisticated mind or vocabulary. As we listen to the story, the effect of the style is to lull us into thinking this is a comic tale about a typical Southern family heading out on a 1950s road trip vacation. The events are completely ordinary: family squabbling, stopping for lunch. The effect of this is to make it all the more shocking when the mood changes after the car lands in the ditch on the deserted road, and the Misfit and his gang appear. The sudden switch to horror genre and death disorients us as readers, just as it disorients the family and the grandmother. Like her, we are groping to understand what is going on in "real time," with no time to adjust as the commonplace world turns upside down.

Describe the major features of a biome.

The term "biome" refers to a zone that contains lifeforms that share a set of common characteristics as a result of living and developing in similar climates and environments. The same biomes can be found across continents as long as the different regions share the same environmental characteristics. A single biome can contain a number of different habitats and ecosystems. Therefore, it is important not to confuse biomes with these two other terms. Simply put, an ecosystem refers to any system, large or small, in which living and non-living things interact with each other. A habitat is a physical space in which living things exist.
Biomes are categorized in different ways by different researchers, but generally, seven major terrestrial biomes are recognized (see NASA source below). These are shrubland, tundra, rainforest, desert, temperate deciduous forest, coniferous forest, and grassland. There are also aquatic biomes, such as shallow seas and intercoastal zones. Species that inhabit a particular biome may vary in many respects, but they will likely share certain features which enable them to live there. It is possible to divide large biomes into smaller sub-biomes or micro-biomes, such as deciduous forest and lowland tropical rainforest. Even the human gut and digestive tract, which hosts many different bacteria, can be considered a micro-biome.
http://www.theglobaleducationproject.org/earth/global-ecology.php

In what year was "The Ghosts" written?

"The Ghosts" is a short story included in a collection of short stories by Edward Plunkett, who published under the name Lord Dunsany. The collection, The Sword of Welleran and Other Stories, was the third book published by Lord Dunsany and was published in October of 1908. Lord Dunsany's most well-known and influential works were published in a time frame between 1905 to 1919, and in this time frame he wrote many stories in what is now considered the fantasy genre, although the genre did not exist in his time. Some of the short stories in The Sword of Welleran refer back to Lord Dunsany's creation of various gods and creatures first appearing in his two previous books, The Gods of Pegāna and Time and the Gods. Lord Dunsany's creation of the fantasy genre would later influence writers who are now considered pinnacles of the fantasy genre, such as J. R. R. Tolkien, Ursula K. Le Guin, and H. P. Lovecraft.

What are examples of metaphor, simile, foreshadowing, and personification in "The Most Dangerous Game"?

Like most pieces of literature, Richard Connell's tale of adventure, "The Most Dangerous Game," contains elements of foreshadowing and figures of speech such as metaphor, simile and personification. There are three good examples of foreshadowing in the beginning of the story. Foreshadowing is when there are hints and clues about what will happen later in a story. First, the fact that the island which the yacht passes seems to have a sinister reputation and is labeled "Ship-Trap Island" foreshadows the fact that the owner of the island is sociopathic murderer who hunts men. Second, the discussion between Rainsford and Whitney on board the yacht over whether animals feel fear and pain foreshadows Rainsford's later experience on the island when he is a "beast at bay." Third, the pistol shot which causes Rainsford to fall off the yacht foreshadows the future hunt between Rainsford and Zaroff.
Metaphors abound in the text of the story. A metaphor is a comparison of two unlike things. One of the most important metaphors which reoccurs is Rainsford and Zaroff being compared to various types of animals. The hunting of men is also compared to a "game" by Zaroff. The following metaphors are in order as they appear in the story:
"Outdoor chess!" Zaroff compares the future hunt of Rainsford to the board game which requires mental skill. 
"He was in a picture with a frame of water, and his operations, clearly, must take place within that frame." The island is compared to a picture within a frame.
"I have played the fox, now I must play the cat of the fable."
"Even so zealous a hunter as General Zaroff could not trace him there, he told himself; only the devil himself could follow that complicated trail through the jungle after dark." Rainsford compares Zaroff to the devil. A fitting comparison because Zaroff does indeed track down Rainsford.
"The Cossack was the cat; he was the mouse."
"Following the trail with the sureness of a bloodhound came General Zaroff."
"Even as he touched it, the general sensed his danger and leaped back with the agility of an ape."
Connell also employs several similes in the weaving of his story. A simile uses like or as to make a comparison between two unlike things or ideas. Again, these are in the order they appear in the text:
"The revolver pointed as rigidly as if the giant were a statue."
"'They indicate a channel,' he said, 'where there's none: giant rocks with razor edges crouch like a sea monster with wide-open jaws.'"
"He flattened himself down on the limb, and through a screen of leaves almost as thick as a tapestry, he watched."
"Rainsford's impulse was to hurl himself down like a panther, but he saw the general's right hand held something metallic—a small automatic pistol."
"Rainsford did not want to believe what his reason told him was true, but the truth was as evident as the sun that had now pushed through the morning mists."
"He tried to wrench it back, but the muck sucked viciously at his foot as if it were a giant leech."
Personification is when human qualities are given to a non-human subject:
"The sensuous drowsiness of the night was on him."
"...on three sides of it cliffs dived down to where the sea licked greedy lips in the shadows."
"An apprehensive night crawled slowly by like a wounded snake." Not only does this sentence contain personification, it also has a simile.
"Across a cove he could see the gloomy gray stone of the chateau."

What does Fitzgerald suggest about the American Dream through his depiction of Jay Gatsby and Nick Caraway?

Fitzgerald portrays the vain pursuit of the American Dream by depicting the corruption of Gatsby's soul and Nick Carraway's jaded perception of the upper class. Jay Gatsby compromises his morals, fails to develop meaningful relationships with others, alters his identity, and is blinded by Daisy's beauty in his pursuit of the American Dream. Gatsby becomes corrupted by wealth after deciding to enter the bootlegging business. After achieving financial success, Gatsby's pursuit of happiness is not over, and he attempts to recreate his past with Daisy. Gatsby believes that he can purchase happiness and eventually dies a lonely, unhappy man. He fails to develop relationships with genuine people and is attracted to Daisy's toxic personality and lifestyle. Aside from his father and Nick Carraway, none of his associates or apparent friends attend his funeral.
Nick Carraway decides to move back home after witnessing the true nature of the superficial elite. Nick is disgusted by the lying, cheating, immoral nature of East and West Egg citizens. He witnesses their chaotic, superficial lives firsthand and chronicles the demise of Jay Gatsby. Nick Carraway gives up on his dream of attaining wealth in the bond industry and chooses to live a comfortable lifestyle in the Midwest.

int sin(-7x)cos(6x) dx Find the indefinite integral

Indefinite integrals are written in the form of int f(x) dx = F(x) +C
 where: f(x) as the integrand
           F(x) as the anti-derivative function 
           C  as the arbitrary constant known as constant of integration
For the given problem int sin(-7x)cos(6x) dx or intcos(6x)sin(-7x) dx   has a integrand in a form of trigonometric function. To evaluate this, we apply the identity:
cos(A)sin(B) =[sin(A+B) -sin(A-B)]/2
The integral becomes:
intcos(6x)sin(-7x) dx = int[sin(6x+(-7x)) -sin(6x-(-7x))]/2dx
                                          = int[sin(6x-7x) -sin(6x+7x)]/2dx
 Apply the basic properties of integration: int c*f(x) dx= c int f(x) dx .
int[sin(6x-7x) -sin(6x+7x)]/2dx= 1/2int[sin(6x-7x) -sin(6x+7x)]dx
 Apply the basic integration property: int (u+v) dx = int (u) dx + int (v) dx .
1/2 *[int (sin(6x-7x))dx - int sin(6x+7x)dx]
Then apply u-substitution to be able to apply integration formula for cosine function: int sin(u) du=-cos(u) +C .
For the integral: intsin(6x-7x)dx , we let u = 6x-7x=-x then du= - dx or (-1)du =dx .
intsin(6x-7x)dx=intsin(-x) dx
                                 =intsin(u) *(-1)du
                                 =(-1) int sin(u)du
                                 =(-1)(-cos(u) )+C  
                                 =cos(u) +C
Plug-in u =-x on cos(u) +C , we get:
intsin(6x-7x)dx= cos(-x) +C
For the integral: intsin(6x+7x)dx , we let u = 6x+7x=13x then du= 13 dx or (du)/13 =dx .
intsin(6x+7x)dx=intsin(13x) dx
                                  =intsin(u) *(du)/13
                                  = 1/13 int sin(u)du
                                  = 1/13( -cos(u))+C or -1/13cos(u) +C
Plug-in u =13x on -1/13 cos(u) +C , we get:
intsin(6x+7x)dx= -1/13 cos(13x) +C
Combing the results, we get the indefinite integral as:
intsin(-7x)cos(6x) dx= 1/2*[ cos(-x) -(-1/13 cos(13x))] +C
or   1/2 cos(-x) +1/26 cos(13x) +C
Since cosine is an even function,  cos(-x) = cos(x) , so we get:
intsin(-7x) cos(6x)dx=1/2 cos(x) +1/26 cos(13x) +C

What motive did Theo Theodorakis have to murder Sam Westing?

Sam Westing is not actually murdered by anybody, but the guests of the Sunset Towers are not privy to that information. They all believe that he is dead, and they believe that one of them is guilty. The 15th clue really drives home the idea that Westing is dead and one of the tenants is guilty.

And time is running out. Hurry, find the name before the one who took my life takes another.

Theo's motive is essentially the same as everybody else's motive. The Westing fortune is large, and having that money would be a huge blessing in Theo's life. The idea of Theo committing murder to gain a lot of money for himself is completely absurd. When Theo was asked his "position," he wrote down "brother." He sees himself as second. Chris is more important, and Theo sees himself as the brother. Chris is not Theo's brother. Theo is Chris's brother. If I had to come up with a reason for Theo to kill Westing, it would be to obtain money that would be used to care for his brother and family. That's not unrealistic. Readers find out in chapter 8 that Theo plans to give half of his $10,000 to his parents and half to his friend.

First, the money. They signed their names to the check; half would go into Doug Hoo’s savings account; half would go to Theo’s parents.

No one actually kills Sam Westing; he fakes his own death in order to be closer to his family. But most of the characters playing the Westing game have some kind of motive to murder him.
Theo's possible motive for killing Sam Westing would be the same as just about everyone else's: money. Theo is quite a selfless character, though, someone utterly devoted to the welfare of his family. If he did get his hands on the money, he wouldn't spend it on himself; he would put it towards providing medical care for his disabled brother Chris. Theo will do pretty much anything to help out his family. After all, this is a guy who willingly walks away from a partial scholarship so that his folks can pay for Chris's treatment. So it's not beyond the bounds of possibility that he would take the fateful step of killing Sam Westing.

What are the advantages of reducing air resistance on a car?

There is one main advantage to reducing air resistance on a car.  The advantage is that this reduces the amount of drag on the car, thereby reducing the amount of fuel that is needed to drive the car at any particular speed and for any particular distance.
When a car is driven, it converts the chemical energy in its fuel into kinetic energy (motion).  However, not all of the chemical energy in the fuel converts to kinetic energy.  Instead, some is lost to heat and some to sound.  The heat and the sound are caused by friction.  One source of friction is air resistance.
If we reduce the amount of air resistance on the car, less of the chemical energy will be converted into heat and sound.  This is beneficial because, when we drive a car, we want as much of the chemical energy as possible to be converted into kinetic energy.  We do not want to waste our fuel making heat and noise.  By reducing the amount of air resistance, we improve the efficiency of our fuel usage.  We increase the distance that we can drive on any given amount of fuel.  This is very useful for car owners (and for society as well since it means that we waste less of our resources).

Single Variable Calculus, Chapter 2, 2.4, Section 2.4, Problem 10

Find a number $\delta$ by using a graph such that if $5 < x < 5 + \delta \quad$ then $\displaystyle \quad \frac{x^2}{\sqrt{x-5}} > 100$


We can determine the value of $\delta$ by getting the point of intersection of the curve and the line $y=100$. As shown in the graph:






$
\begin{equation}
\begin{aligned}
\frac{x^2}{\sqrt{x-5}} & = 100\\
x^2 &= 100\sqrt{x-5}\\
x^2 - 100 \sqrt{x-5} & = 0\\
\end{aligned}
\end{equation}
$

Solving for $x$,
$\quad x = 5.0659$


Hence, the value of $\delta$ is...


$
\quad
\begin{equation}
\begin{aligned}
5 + \delta & \leq x \\
\delta & \leq x - 5\\
\delta & \leq 5.0659 -5\\
\delta & \leq 0.0659
\end{aligned}
\end{equation}
$

How are the core values of integrity, honesty, loyalty, and moderation presented in Shakespeare's Richard III?

Of the values listed—integrity, honesty, loyalty, and moderation—the protagonist, Richard himself, exhibits none. What's more, he tells us in his opening soliloquy that he isn't going to: "I am determined to prove a villain / And hate the idle pleasures of these days."
Throughout most of the play, characters that do exhibit these values either do so at their peril, or do so in warped ways. For example, Queen Margaret is savagely honest in her appraisal of almost everyone else in the play, including Richard, but her honesty comes from bitterness, and she is far from honest about herself and her own actions. Buckingham exhibits loyalty to Richard almost to the end, but this is in expectation of riches and lands as rewards, and he abandons Richard when it becomes clear he has fallen from favor with the newly made king.
It's left to the highly idealized figure of Henry Richmond, the eventual historical Henry VII, to display integrity and moderation. Shakespeare deliberately contrasts Richmond and Richard's orations to their troops to show that Richmond is a paragon of knighthood, invading the kingdom only to bring law, order, and justice back to the land, while Richard is as bloodthirsty and duplicitous as ever. As virtually all scholars observe, Henry Richmond had to be portrayed in this way, since his ascension to the throne had to be seen as legitimate. He becomes the first Tudor king, father of Henry VIII, and thus grandfather to the reigning monarch, Elizabeth I.

What were two movements that emerged in American society during the 1830s and 1840s that dealt with the connection between Evangelical Protestantism and the reform movements? What were the movements trying to accomplish and how did they go about it?

One movement with explicit connections to Evangelical Protestantism was the abolitionist movement. While the issue of slavery divided most of the main Protestant denominations, Evangelicals were at the vanguard of the movement in the North. Quakers had long opposed slavery, frequently petitioning the federal government against the institution and advocating emancipation in Northern states. William Lloyd Garrison, perhaps the most vocal abolitionist other than Frederick Douglass, was motivated in large part by his belief that slavery was a sin that could not be tolerated by American Christians. Others like the Grimké sisters and Wendell Phillips were also motivated by their religious beliefs, as were two men who attempted to launch slave revolts in Virginia—Nat Turner and later John Brown.
Evangelicals also railed against the evils of alcohol in what was known as the temperance movement. Across the nation, Evangelical preachers railed against the evils of alcohol, which they painted as a great source of evil in American society. Lyman Beecher, the founder of the American Temperance Society, was a Presbyterian minister who spent much of his life preaching against alcohol from the pulpit. In town after town in the North, especially the Northeast and Ohio, congregations took "teetotal pledges" to avoid all alcohol.
In general, Evangelicalism, which arose with the Second Great Awakening, helped spark all of the major reform movements, including abolition and temperance, in the 1830s. People began to envision a society shaped by Christian virtue and to believe that sins could be purged from society.
http://nationalhumanitiescenter.org/tserve/nineteen/nkeyinfo/amabrel.htm

https://ohiohistorycentral.org/w/Lyman_Beecher

How is pneumonia described in the story?

In "The Last Leaf," pneumonia is personified in different ways. First, O'Henry refers to pneumonia as "a cold, unseen stranger." This stranger "stalked" about Greenwich Village and laid his "icy fingers" on his victims. The disease is also compared to a "ravager." O'Henry also says that pneumonia is not chivalrous because he attacks a little woman, meaning Johnsy. Pneumonia is also called "the red-fisted, short-breathed old duffer." 
These images make the reader call to mind a ruthless and revolting old man who wheezes, who is cold at heart, and who has fingers made of ice. By personifying the disease, O'Henry makes Johnsy's opponent seem real and makes the reader want to rally behind Johnsy in her fight against pneumonia. It is only hope and faith that will be able to help Johnsy defeat this enemy, and until she has something to believe in (which turns out to be the last leaf clinging to the ivy vine on the brick wall outside her window), she can't begin to defeat her opponent, pneumonia. 

In the story, pneumonia is personified as a bold "ravager" who stalks a community unawares and smites his victims "by scores." The author tells us that Mr. Pneumonia is a "red-fisted, short-breathed old duffer." 
Based on the author's description, Mr. Pneumonia can be compared to the Grim Reaper, which is the personification of death. In the story, pneumonia acts like the Grim Reaper. He is a mercurial killer in that his choice of victim seems arbitrary.
Mr. Pneumonia's latest victim is Johnsy, whom the author describes as a "mite of a little woman with blood thinned by California zephyrs." Interestingly, it is another "old duffer" who comes to Johnsy's rescue; to placate Mr. Pneumonia, Mr. Behrman (an aging artist who lives in Johnsy and Sue's building) offers himself up in Johnsy's place.
Johnsy, discouraged by the turn her life has taken, tells Sue that she will soon die when the last leaf falls off the vine outside her window. However, the leaf never falls off, even after a powerful storm. Encouraged by the leaf's will to live, Johnsy soon recovers. Later, she discovers that Mr. Behrman spent long hours outside painting the last leaf on the vine. The leaf was a masterpiece, so realistic that Johnsy was none the wiser. Mr. Behrman's sacrifice was an unselfish act of love.

sum_(n=1)^oo 1/(9n^2+3n-2) Find the sum of the convergent series.

sum_(n=1)^oo1/(9n^2+3n-2)
Let's rewrite the n'th term of the sequence as,
a_n=1/(9n^2+3n-2)
=1/(9n^2+6n-3n-2)
=1/(3n(3n+2)-1(3n+2))
=1/((3n+2)(3n-1))
Now let's carry out partial fraction decomposition,
1/((3n+2)(3n-1))=A/(3n+2)+B/(3n-1) 
Multiply the above equation by LCD,
1=A(3n-1)+B(3n+2)
1=3An-A+3Bn+2B
1=(3A+3B)n-A+2B
Equating the coefficients of the like terms,
3A+3B=0    -----------------(1)
-A+2B=1  ------------------(2)
From equation 1,
3A=-3B
A=-B
Substitute A in equation 2,
-(-B)+2B=1
B+2B=1
3B=1
B=1/3
A=-1/3
a_n=(-1/3)/(3n+2)+(1/3)/(3n-1)
a_n=1/(3(3n-1))-1/(3(3n+2))
Now we can write down the n'th partial sum of the series as:
S_n=(1/(3(3-1))-1/(3(3+2)))+(1/(3(3*2-1))-1/(3(3*2+2)))+..........+(1/(3(3n-1))-1/(3(3n+2)))
S_n=(1/6-1/15)+(1/15-1/24)+.........+(1/(3(3n-1))-1/(3(3n+2)))
S_n=(1/6-1/(3(3n+2)))
sum_(n=1)^oo1/(9n^2+3n-2)=lim_(n->oo)S_n
=lim_(n->oo)(1/6-1/(3(3n+2)))
=1/6

Why do the rest of the actors run off when Bottom reappears?

The events you are referring to take place in Act III, scene I of A Midsummer's Night Dream. When Bottom reappears, his head has been turned into that of an ass by the mischievous fairy Puck, who loves to play tricks. This startles Bottom's companions and they run away. Puck then aims to follow the other actors into the woods to frighten them even further by transforming into various scary forms, such as a headless bear, a hog a fire, and many others.  
Bottom does not know that he now has the head of a donkey. His companion Snout returns briefly and tells him that his head has been transformed, but Bottom takes this as an attempt to trick him and scare him. There is quite a play on the word "ass," which obviously has an ironic meaning. Bottom does not understand what Snout is trying to tell him and replies that Snout is acting like an ass–– when actually Bottom is the "real" ass! 

SNOUT: O bottom, thou art changed! What do I see on thee?
BOTTOM: What do you see? You see an ass head of your own, do you?

When Snout leaves, Bottom remains in the woods and starts to sing to prove his bravery, believing that his friends are only trying to make "an ass" of him. 

BOTTOM: I see their knavery: this is to make an ass of me, to fright me if they could. But I will not stir from this place, do what they can. I will walk up and down here and I will sing, that they shall hear I am not afraid.

In what respect is the title of "The Guest" ironic?

The title of "The Guest" is ironic because the Arab (to whom the title applies) is not really a guest at all; he is a prisoner. The description of the Arab demonstrates his status: he is in the company of a policeman called Balducci, for example, and his hands are bound. Balducci has escorted him as far as Daru's school and now expects Daru to complete the Arab's journey to the police headquarters in Tinguit.
Moreover, the title "The Guest" implies that the Arab is a welcome visitor. While Daru treats the Arab with kindness by offering him food and a bed to sleep in, it is quite clear that his guest is, in fact, very unwelcome. Daru demonstrates this feeling through his complaints to Balducci and, in doing so, reveals another sense of irony.

What did Atticus do after supper that Jem and Scout thought was peculiar?

Atticus is normally a creature of habit, so when he breaks his routine, Scout and Jem immediately sense there's something up. Why on earth does Atticus need that extension cord and the lightbulb? And where he is going at this hour? Earlier on, the children were curious as to why Atticus was standing outside the house talking to Heck Tate and some other men. Again, this was unusual, and they immediately realized that something was up.
Curiosity eventually gets the better of Scout and Jem—as it often does—and so they head out after dark to find out what's going on. They find Atticus sitting outside the jail house, reading a newspaper by the lightbulb he brought with him. (Ah, so that's what it was for!) But it's still unclear as to why he's sitting there in the first place. It soon becomes apparent that Heck Tate's had word of a Lynch-mob ready to descend on the jailhouse to mete out summary justice to Tom Robinson. Naturally, Atticus doesn't want that to happen, so he's going to do whatever he can to stop his client from being killed. Yet it turns out to be Scout who actually prevents this from happening.

In chapter 15 of To Kill a Mockingbird, Atticus does something that Scout and Jem find interesting. After finishing supper, Atticus enters the living room with an extension cord attached to a light bulb. He tells the children, "You folks'll be in bed when I come back, so I'll say goodnight now." As Atticus is leaving, Jem notices that he takes the car. The children find this interesting as well.
Later, the children sneak out to see what Atticus is doing. They find him sitting in a chair and reading a newspaper in front of the jail. The extension cord is hanging from the building, and he is reading by the lamp's light. Feeling that everything is fine, they start to leave—but then they notice a line of cars approaching. A group of men get out of the cars with the intent of lynching Tom Robinson. It is Scout who causes them to turn away.

Precalculus, Chapter 10, 10.1, Section 10.1, Problem 17

The given slope is m = -1 .
Take note that if the slope of the line is given, to determine the angle of inclination, apply the formula:
tan theta = m
where theta is the angle measured counterclockwise from the positive x-axis going to the right of the line. And its range of values is from 0 to 180 degree only (0^o lt= theta lt=180^o) .
Plugging in the value of m, the formula becomes:
tan theta = -1
Then, take the inverse of tangent to isolate theta.
theta =tan ^(-1)
theta = -pi/4 rad =-45^o
Take note that when the computed value is negative, to get value of angle of inclination in the interval 0^o lt= thetalt=180^o , add 180 degree (pi rad).
theta = -pi/4 + pi = (3pi)/4 rad
theta = -45^o + 180^o = 135^o
Therefore, in radians, the angle of inclination is (3pi)/4 rad. And in degree, the angle of inclination is 135^o .

College Algebra, Chapter 1, 1.5, Section 1.5, Problem 60

Find all real solutions of the equation $\displaystyle \sqrt{1 + \sqrt{x + \sqrt{2x +1}}} = \sqrt{5 + \sqrt{x}}$


$
\begin{equation}
\begin{aligned}

\sqrt{1 + \sqrt{x + \sqrt{2x +1}}} =& \sqrt{5 + \sqrt{x}}
&& \text{Given}
\\
\\
1 + \sqrt{x + \sqrt{2x + 1}} =& 5 + \sqrt{x}
&& \text{Square both sides}
\\
\\
\sqrt{x + \sqrt{2x + 1}} =& 4 + \sqrt{x}
&& \text{Subtract } 1
\\
\\
x + \sqrt{2x + 1} =& 16 + 8 \sqrt{x} + x
&& \text{Square both sides}
\\
\\
\sqrt{2x + 1} =& 16 + 8 \sqrt{x}
&& \text{Cancel out } x
\\
\\
2x + 1 =& 256 + 256 \sqrt{x} + 64x
&& \text{Square both sides}
\\
\\
256 \sqrt{x} + 62x + 255 =& 0
&& \text{Combine like terms}
\\
\\
256 \sqrt{x} + 62 (\sqrt{x})^2 + 255 =& 0
&& \text{If we let } w = \sqrt{x}
\\
\\
256w + 62w^2 + 255 =& 0
&& \text{Subtract } 255
\\
\\
62w^2 + 256 w =& -255
&& \text{Divide both sides by } 62
\\
\\
w^2 + \frac{256}{62} w + \frac{16384}{3844} =& \frac{-255}{62} + \frac{16384}{3844}
&& \text{Complete the square: add } \left( \frac{\displaystyle \frac{256}{62}}{2} \right)^2 = \frac{16384}{3844}
\\
\\
\left( w + \frac{128}{62} \right)^2 =& \frac{287}{1922}
&& \text{Perfect Square}
\\
\\
w + \frac{128}{62} =& \pm \sqrt{\frac{287}{1922}}
&& \text{Take the square root}
\\
\\
w =& \frac{-128}{62} \pm \frac{\sqrt{287}}{31 \sqrt{2}}
&& \text{Subtract } \frac{128}{62} \text{ and simplify}
\\
\\
w =& \frac{-128 + \sqrt{574}}{62} \text{ and } w = \frac{-128 - \sqrt{574}}{62}
&& \text{Solve for } w
\\
\\
\sqrt{x} =& \frac{-128 + \sqrt{574}}{62} \text{ and } \sqrt{x} = \frac{-128 - \sqrt{574}}{62}
&& \text{Substitute } w = \sqrt{x}
\\
\\
x =& \left( \frac{-128 + \sqrt{574}}{62} \right)^2 \text{ and } x = \left( \frac{-128 - \sqrt{574}}{62} \right)^2
&& \text{Solve for } x


\end{aligned}
\end{equation}
$

They also served who only stand and wait. How does Milton arrive at the above conclusion?

The line you have included in the question is the final line of Milton's "When I Consider How My Light Is Spent (On His Blindness)," so in order to realize how Milton reaches that conclusion, we will need to analyze the poem from beginning to end.
The poem is best divided into two major sections. In the first part of the poem, the speaker begins,

When I consider how my light is spent,
Ere half my days, in this dark world and wide,
And that one Talent which is death to hide
Lodged with me useless, though my Soul more bent
To serve therewith my Maker, and present
My true account, lest he returning chide;
“Doth God exact day-labour, light denied?”
I fondly ask (1–8).

Milton began going blind, and he expresses here how worried he is that he will not be able to use "that one Talent" that he thinks can best serve his God. The first couple of lines see Milton reflecting on his gradually waning vision; because of his worsening blindness, he feels increasingly more in the "dark world." His gift (his poetry) is now useless to him, he feels, since he cannot read (or write or revise his writing). He feels he has used his talent to honor God, and now he is not sure how he can do that any more.

The response he gets leads to the conclusion in the final line:


But patience, to prevent
That murmur, soon replies, “God doth not need
Either man’s work or his own gifts; who best
Bear his mild yoke, they serve him best. His state
Is Kingly. Thousands at his bidding speed
And post o’er Land and Ocean without rest:
They also serve who only stand and wait.” (8-14)



The voice that "replies" to Milton is, presumably, an inner voice that reminds him that there are other ways to serve God. The voice tells him that God does not need or demand a believer's work. One only needs to submit to God's "mild yoke." He says that many serve God by moving "o'er Land and Ocean without rest." However, a person can still serve God by simply patiently obeying and quietly following God's word. This helps Milton feel that he is still able to worship the deity even though he will no longer praise him through his writing.

Calculus of a Single Variable, Chapter 9, 9.3, Section 9.3, Problem 29

Recall that the integral test is applicable if f is positive and decreasing function on the infinite interval [k, oo) where kgt= 1 and a_n=f(x) . Then the series sum_(n=1)^oo a_n converges if and only if the improper integral int_1^oo f(x) dx converges. If the integral diverges then the series also diverges.
For the given series sum_(n=1)^oo 1/n^3 , the a_n = 1/n^3 then applying a_n=f(x) , we consider:
f(x) = 1/x^3 . The function is positive and as x at the denominator side gets larger, the function value decreases. Therefore, we may determine the convergence of the improper integral as:
int_1^oo 1/x^3 = lim_(t-gtoo)int_1^t 1/x^3 dx
Apply the Law of exponent: 1/x^m = x^(-m) .
lim_(t-gtoo)int_1^t 1/x^3 dx =lim_(t-gtoo)int_1^t x^(-3) dx
Apply Power rule for integration: int x^n dx = x^(n+1)/(n+1).
lim_(t-gtoo)int_1^t 1/x^3 dx =lim_(t-gtoo)[ x^(-3+1)/(-3+1)]|_1^t
=lim_(t-gtoo)[ x^(-2)/(-2)]|_1^t
=lim_(t-gtoo)[ -1/(2x^2)]|_1^t
Apply the definite integral formula: F(x)|_a^b = F(b)-F(a) .
lim_(t-gtoo)[ -1/(2x^2)]|_1^t=lim_(t-gtoo)[-1/(2*t^2) -(-1/(2*1^2))]
=lim_(t-gtoo)[ -1/(2t^2)-(-1/2)]
=lim_(t-gtoo)[-1/(2t^2)+1/2]
= 1/2 .
Note: lim_(t-gtoo) 1/2 =1/2 and lim_(t-gtoo)1/(2t^2) = 1/oo or 0
The integral int_1^oo 1/x^3 is convergent therefore the series sum_(n=1)^oo 1/n^3 must also be convergent.

What are some quotes about family in The Catcher in the Rye?

The Catcher in the Rye is full of quotes about family. Here are three to start, with a little information about each of them.
The very first sentences of the novel are about family:

If you really want to hear about it, the first thing you'll probably want to know is where I was born, an what my lousy childhood was like, and how my parents were occupied and all before they had me, and all that David Copperfield kind of crap, but I don't feel like going into it, if you want to know the truth. In the first place, that stuff bores me, and in the second place, my parents would have about two hemorrhages apiece if I told anything pretty personal about them. They're quite touchy about anything like that, especially my father.

This passage reveals Holden's attitude towards his own early life, or at least, it reveals how Holden feels about talking about his childhood. Here as well the reader can find some interesting information about how Holden perceives his parents and their protectiveness of their privacy.
Later in the novel, in part 5, Holden mentions his brother:

He's dead now. He got leukemia and died when we were up in Maine, on July 18, 1946. You'd have liked him. He was two years younger than I was, but he was about fifty times as intelligent. He was terrifically intelligent. His teachers were always writing letters to my mother, telling her what a pleasure it was having a boy like Allie in their class. And they weren't just shooting the crap. They really meant it. But it wasn't just that he was the most intelligent member in the family. He was also the nicest, in lots of ways.

This passage is also revealing as Holden is somehow simultaneously open and honest about a very sensitive family tragedy, while he is cagey about his family at the same time. He doesn't describe the not-nice behaviors in any detail, but the reader knows that they exist.
This passage about family can be found in part 15:

My father's quite wealthy, though. I don't know how much he makes––he's never discussed that stuff with me––but I imagine quite a lot. He's a corporation lawyer. Those boys really haul it in. Another reason I know he's quite well off, he's always investing money in shows on Broadway. They always flop, though, and it drives my mother crazy when he does it. She hasn't felt too healthy since my brother Allie died. She's very nervous. That's another reason why I hated like hell for her to know I got the ax again.

Holden is clear here about his guilt and his sense of responsibility for his mother's happiness, but he is less clear about how he feels about his father and his father's career. This lack of transparency makes for some interesting opportunities for literary analysis as the reader can go in a lot of different directions with the evidence here.

Why is the story called "Dusk"?

What a great question. I believe the short story "Dusk," by Saki has its title for a two-fold reason. The setting is around 6:30 on a March evening in Hyde Park: dusk. But more importantly, I believe Saki is commenting on our inability to actually see others.
The protagonist, Norman Gortsby, is a cynical man who reckons himself perceptive, aware of the plight and motives of other people. He enjoys sitting in Hyde Park at dusk watching the people go and come. He presumes those who leave have places to go while those who come are defeated in some way.
He immediately thinks an old man sitting near him one of these defeated people, yet the old man gets up and leaves. When a young man sits next to him, indeed sounding defeated, Norman asks him what is wrong, and the young man tells him that he has forgotten which hotel he was staying in when he left to buy soap and that now he is stuck in a strange city with nowhere to sleep. He hopes some kind stranger will help him out so that he can sleep in a safer place.
Though the story sounds convincing, Norman, cynical as usual, is convinced that the young man is a clever panhandler trying to trick strangers into giving him money that he will never repay. When the young man cannot produce his bar of soap, Norman feels justified in his judgment and the young man leaves. But when Norman notices a small cake of soap on the ground near the bench, he feels terrible for having not seen the truth about this young man's honesty, tracks him down, and loans him some money. Feeling good about this faith-restoring encounter, Norman returns to his bench only to find the old man whom he had earlier presumed was defeated searching for his lost cake of soap. Ironically, Norman's enlightenment has only served to darken his outlook.
Dusk can represent a number of things symbolically, but in this case I think it represents not only Norman's inability to fully see the truth in either of the men, but also his dim, cynical outlook on life, which is only reinforced by the young panhandler's swindle that left Norman defeated. Saki is telling us to be careful whom we trust, but he's also telling us that trusting can give us a kind of joy that cynicism cannot. We are faced with a choice. Either we darken our hearts a little as we learn through experience not to trust other people, or we choose not to see so that we can believe in others. Either way, the outlook is dim, and we are always in the dusk.

In the novel Three Men in a Boat, Jerome was medically ill. Do you agree?

No, the character-narrator of the book, J., is not medically ill. He may be a hypochondriac, though, and he may just believe that he is sick. Or at least, J. has a quick inclination to become sick when this possibility is suggested to him.
In the first chapter, J. shares the story of his trip to the British Museum as a way of illustrating his approach to life. Here he consults the medical reference book and quickly believes that he is afflicted with almost all of the diseases described in it. Is this even possible in real life? Of course not. As usual, J. overreacts, or he misinterprets information and experiences that come his way. This early story quickly unveils to us some of the personality quirks of this character. He also tells it in a humorous way, setting the stage for many more odd encounters and humorous situations to come. Three Men in a Boat is full of such scenes. It makes for enjoyable reading.

Calculus: Early Transcendentals, Chapter 7, 7.4, Section 7.4, Problem 8

int ((3t-2)/(t+1)) dt
sol:
let t+1 = u
=> t= u-1
=> dt =du
int ((3t-2)/(t+1)) dt
= int ((3(u-1)-2)/(u)) du
= int ((3u-3-2)/(u)) du
= int (3u-5/u) du
= int (3- (5/u)) du
= int 3 du - int (5/u) du
= 3u - 5*ln(u)
= 3*(t+1)- 5*ln(t+1) +C
:)

Why does Darry now hate Paul Holden?

Paul Holden is Darry's former friend and Soc member, the first to challenge Darry at the start of the rumble. Pony mentions that Paul had played halfback on Darry's football team and used to be close with his oldest brother. Unlike Darry, whose parents died in a tragic accident and who was forced to abandon his dreams of playing college football in order to raise Pony and Soda, Paul was fortunate and had the opportunity to enroll in college.
As the two boys stare each other down, Pony notices that Paul views Darry with hate, contempt, and pity. Darry hates and envies Paul because he was given certain advantages and opportunities in life. While Paul continued to play football and earn a college education, Darry was forced to work two jobs and struggles to make ends meet. Darry also hates the fact that he is representing the Greasers, which Pony understands is a source of shame. Overall, Darry is jealous of Paul's fortunate life and resents the fact that Paul was given so many opportunities while he was forced to work to support himself and his family and abandon his dreams.

At the rumble between the Socs and the greasers, Darry steps forward to start the fighting, saying "I'll take on anyone." When Paul Holden responds to Darry's challenge, Ponyboy hears Soda react with surprise and perhaps dismay, and Ponyboy recognizes Paul as Darry's old friend from his football days. According to Ponyboy, they hate each other now, despite sharing history and good times in the past: "[t]hey hate each other because one has to work for a living and the other comes from the West Side."
Ponyboy blames their hatred on the differences in their positions in society, which have nothing to do with them as people. In the time since Darry and Paul were friends, a lot has happened to Darry; he lost his parents and took on the responsibility of his younger brothers, and so much of his potential to do more with his life was lost. Paul, on the other hand, seems to have enjoyed the privilege of his position and attended college, something that may have interested Darry once. Darry's hatred of Paul may come from a feeling of envy and resentment that Paul might not even appreciate everything that he has.

Does Dimitri marry Katerina?

Having seduced Katerina—or Katusha, to use the diminutive by which she's known—Prince Dmitri wishes to atone for his sins. When Katusha is sent to a Siberian penal colony after being convicted of murder, Dmitri becomes ever more determined to change, to affect a deep spiritual transformation within his soul. To this end, he tries his best to help Katusha, following her to Siberia and pulling strings to make sure that she's housed with the political prisoners, well away from the serial criminals who try to take advantage of her.
Moreover, Dmitri wants to marry Katusha, but it's all for the wrong reasons. Dmitri doesn't truly love Katusha; he simply wants to cleanse his soul. Marrying Katusha will be a means to a selfish end, nothing more. For her part, Katusha isn't interested. If she's going to marry, then it will be for love. So she declines Dmitri's proposal, opting instead to stay with Valdemar Símonson, a political prisoner whom she meets in Siberia.

The word “ring-giver” is an example of a kenning. What are some other examples of kennings in Beowulf?

In relation to Anglo-Saxon literature, a "kenning" can be defined as a metaphorical phrase or compound word used to name a person, place, or thing. Kennings abound in Beowulf; the poem's four-beat alliterative lines allow for a huge variety of them to be used. As well as "ring-giver," we have "battle-sweat" meaning blood. And in his brutal epic encounter with Grendel's Mother, Beowulf does indeed shed a fair amount of battle-sweat. Another one is "sail road" meaning the sea. If you think about it, a sail road is exactly what the sea is to Anglo-Saxon warriors like Beowulf. They routinely set sail upon the high seas to trade, fight battles, and explore new lands.
"Sleep of the sword" is a particular favorite of mine. You won't be surprised to discover that it means "death." Notice how two concepts have been yoked together: the sleep of death and the method used to bring it about. Like "battle-sweat" and "sail road," "sleep of the sword" provides us with a glimpse into Anglo-Saxon culture, where death, especially to brave and noble warriors, often came at the end of a sword.

Kennings are compound metaphors common in literature derived from Old Norse linguistic traditions. Functionally they appear may appear frivolous or unnecessarily abstract, but are intended to provide imagery and dexterity to the poet in order to avoid repeating words or to improve the narrative creativity of the work. "Ring-giver" is intended to emphasize the role of a king or leader as a benefactor and source of reward for good service, rings (or torcs, a type of collar or necklace) being a form of jewelry that often conferred status.
Kennings are found throughout "Beowulf" and comprise a significant portion of the text, both in narrative illustration and word count. "Ring-giver" is found on line 1102, and others in this portion of the text include "hate-bites" on 1122, referring to wounds, and "battle-light" on 1142, referring to a sword. 
http://www.heorot.dk/beowulf-rede-text.html