In "The Lottery," what is the significance of Tessie's final scream? What aspect of the lottery does she explicitly challenge?

"It isn't fair, it isn't right," Mrs. Hutchinson screamed, and then they were upon her.

The above is Tessie's final scream and the final line of the story.
Tessie challenges the lottery as, in her opinion, conducted unfairly in this particular instance.
She decides the procedure used is unfair once she is chosen as the human sacrifice. If somebody else had been chosen under the same set of circumstances, presumably she would not have protested and simply returned to her dishes after helping to kill the person.
Tessie is the type of person who supports cruel institutions or traditions because she doesn't believe they could ever hurt her. She is perfectly willing to go along with terrible things happening to other people as long as she is exempted from the suffering. But the moment it happens to her, suddenly, it's a problem and unfair.
The significance of Tessie's final scream is to show that protesting an unjust system is pointless once you're the target. By that time, it's too late. You need to stand up for other people and call out a practice as wrong on general principle ahead of time in order to be able to save yourself from it.

When Tessie Hutchinson hears that her husband, Bill, has drawn the slip of paper that means someone in his family will be sacrificed in the next round of the drawing, Tessie protests to the officials, saying "you didn't give him time enough to take any paper he wanted. I saw you. It wasn't fair!"
Tessie tries to avoid drawing but is reminded that "daughters draw with their husband's families." Again, Tessie complains that this is unfair, insisting that "Don and Eva . . . take their chance." Once she has drawn her slip from the box, Tessie's husband has to pry the slip of paper from her clenched hand. 
As the villagers surround her with their stones, Tessie first says, then screams, "It isn't fair!  It isn't right!" and then the others begin pelting her.  Tessie openly challenges the legitimacy of the lottery, while others are silently complicit or speak only in low voices that other communities "have already quit lotteries."
 

If there is irony in the story, how does it affect our understanding? Is the theme ambiguous because of the irony? Explain how the irony functions in the story.

There is a great deal of dramatic irony in this story. Dramatic irony is created when the audience, or reader, knows something that one or more characters do not. In this story, we, of course, know of Montresor's plot against Fortunato. We don't know exactly what Montresor is planning to do, but we do know that he is plotting to effect Fortunato's "immolation," or complete destruction. Therefore, we watch, with building tension, as Montresor ensnares his victim, manipulating Fortunato into walking right into a deadly trap.
Despite the fact that Montresor insists that he must "punish [his adversary] with impunity," that the revenge will be incomplete, even void, if he must endure some consequence of it, there is evidence to suggest that he hasn't avoided consequence: that guilt has remained with him since the murder. He says in the final lines that it has been one "half of a century" since he took his revenge, and so it seems likely that he is now an old man, perhaps even confessing his sins to a priest on his deathbed. In the second sentence of the story, he addresses his auditor, describing the listener as one which "so well know[s] the nature of [Montresor's] soul." This provides further evidence that he might be speaking to a priest, someone to whom he has confessed for some time, someone who would understand him better than most. Thus, if Montresor has actually been carrying this guilt around for fifty years, it would seem that he has not escaped punishment and that his conscience has actually punished him for it—if he feels the need to confess it, then it must be weighing on him. Therefore, there is another dramatic irony at work here: Montresor believes that he got away with murder and that his revenge was really effective, but if we infer that he has carried his guilt with him for a half century, then we know something he doesn't: that his revenge, by his definition, was not complete.
We might, then, understand the story's theme to be that one cannot harm another person, no matter how justified it may seem, without burdening one's conscience; or, we might understand the theme to be that revenge injures the avenger as much as the avenged. However, if you do not believe that Montresor feels guilty for his crime, then this would eliminate this particular irony and change the theme as well.

Intermediate Algebra, Chapter 1, 1.1, Section 1.1, Problem 96

Simplify $8 + 7 \leq 3.5$. Then tell whether the resulting statement is true or false.


$
\begin{equation}
\begin{aligned}

& 8 + 7 \leq 3.5 \\
& 15 \leq 15

\end{aligned}
\end{equation}
$


The statement is true.

From Articles I–VII of the US Constitution, what are five examples of violations of popular sovereignty, political equality, political liberty, justice and/or democracy?

Breaches of the 1st Amendment would include the following: 
The government adopting a national religion
The government forcing you to practice a religion 
The government preventing you from practicing your religion of choice, so long as no one is being injured and no laws are being violated
The government preventing you from speaking your mind, so long as it isn't endangering those around you
The government preventing you from peacefully assembling
Breaches of the 3rd Amendment would include the following: 
The government, through an act of Congress or Executive action, mandating that you must allow soldiers to occupy your residence and feed them
Breaches of the 4th Amendment would include the following:
The government (i.e. representatives of the government, police, etc.) taking your property or rummaging through your personal belongings without probable cause
The government (i.e. representatives of the government, police, etc.) detaining you for no reason
Breaches of the 5th Amendment would include the following:
The government making you give testimony that would hurt your own defense in a legal case
The government retrying you for a case where you've already been found innocent
The government taking your things without going through a legal process to do so
The government taking your things for public use without compensating you for the seizure
https://www.law.cornell.edu/constitution/first_amendment

In the book The Art of Racing in the Rain, what are the turning points or significant events that affect the development of the plot?

When a reader talks about "turning points and significant events" he or she is speaking specifically about plot development.  The plot of a story is comprised of six different parts:  the exposition, the inciting incident (or conflict), the rising action, the climax, the falling action, and the resolution.  The Art of Racing in the Rain is a perfect novel to speak about these plot points as "turning points and significant events."
In the exposition, the reader learns about our narrator, Enzo, who is a dog.  Even though the crux of the story centers around Denny (the race car driver and Enzo's owner), Enzo's thoughts as narrator are very important. It is not long before Enzo begins to run into serious issues that affect the humans around him.  As Eve (Denny's wife) gets sick and begins to die of cancer, we have experienced the inciting incident or conflict of the book. Immediately, we enter the rising action as Eve's parents take Zoe (Denny's child) from Denny.  The tension rises as the trial looms.  Denny visits Zoe on weekends, and Enzo listens instinctively. Throughout all of the rising action, we learn all about Enzo's thoughts about humans.  Enzo's dreams continue when he sleeps during the trial.  Enzo dreams that he participates in the trial (with the help of a voice synthesizer) and helps everything turn out okay.  The climax (which is sometimes called the "turning point") of the story is the end of the trial when Annika recounts the events, Denny is freed, and Zoe is given back to her dad. During the falling action, we learn of Enzo's hip troubles and other issues that prove he is getting old.  It is not a surprise when Enzo dies in Denny's arms, promising to come back as a human.  The resolution of the story happens when Denny gives a very young fan an autograph.  The young fan's name is Enzo.  The reader infers, of course, that Enzo's dream of becoming "a man" has come true.

What does Petronius's satire of Trimalchio say about the integration of Roman freedmen in society?

At the time when Petronius wrote The Satyricon, the population of freedmen in Rome was relatively large, even more so in the Italian peninsula as a whole. They were given the same level of citizenship as free-born Romans but were seldom accepted as equals, being widely considered as vulgar parvenus who had acquired manumission by good luck. As such, their social status as freedmen was seen as really no different from that of slaves in that both groups were ultimately dependent upon the whims of masters.
There was an additional reason for the general contempt of society towards freedmen. Roman society traditionally derived its wealth and stability from agriculture. Despite the notable expansion of trade and commerce, the ownership of land, especially farmland, still enjoyed an elevated social status in the eyes of most Romans, particularly among the aristocracy. Freedmen, however, being less class-conscious, had no compunction in getting their hands dirty, making as much money as they could in the vulgar world of trade and business.
Trimalchio is the epitome of the nouveau riche freedman whose dazzling wealth acts as a standing insult to the Roman upper classes. He is unapologetically brash, throwing lavish parties and adorning the walls of his house with vulgar paintings depicting himself and his journey from slave to wealthy arriviste.
Yet Petronius is much too good of a writer, much too subtle in his biting description of Roman society in all its hypocrisy, to engage in one-dimensional snobbery. His characterization of Trimalchio, and by extension of freedmen in general, is a good deal more ambiguous than we might expect. Trimalchio has bought his way into the upper echelons of Roman society, though without being fully accepted. Nevertheless, he still imbibes the general air of decadence breathed greedily by the Roman elite, so there is a rude kind of equality at work.
There is a difference, though, between Trimalchio and his noble acquaintances and dinner guests. And this difference is crucial for an understanding of the portrayal of freedmen in The Satyricon. Trimalchio is who he is, unabashedly so. He doesn't pretend to be anything other than a freedman, albeit an enormously wealthy one who loves to flaunt his riches at every available opportunity. But this makes him considerably more honest, and more recognizably human, than the old money nobility who hypocritically wax lyrical about the virtue of the simple life of the Roman noble while at the same time throwing themselves into a pit of utter debauchery at the drop of a hat.

What are some quotes about Victor's determination?

From a young age Victor Frankenstein's determination was apparent; as he begins describing himself in chapter two, he admits that his temper was "sometimes violent," that his "passions [were] vehement" and that "it was the secrets of heaven and earth that I desired to learn."
When Frankenstein arrives at university in Ingolstadt he quickly surmises that he will transcend what his professors are describing as achievements in science, and he "will pioneer a new way, explore unknown powers, and unfold to the world the deepest mysteries of creation."
As Frankenstein narrows his scientific interest to breaking through the bonds of life and death, he becomes pale and emaciated because of his obsessive work in his laboratory. He does unspeakable things to living animals and digs up graves for the materials he needs.  As he describes his experiments in retrospect, he is horrified at the lengths to which he went, losing "all soul or sensation but for this one pursuit."  He neglects his parents, his friends, and the beauty of the verdant summer as he comes closer and closer to the moment in November when the creature first opens its eyes.
 

Why are vessels more efficient in the transportation of water than tracheids?

The vessels of the xylem are more efficient than the tracheids in water conduction due to the presence of perforations in them. These perforations allow for the continuous flow of water into the xylem vessels. In comparison, tracheids are not perforated.
The xylem tracheids are long, narrow, tubelike cells. The walls of tracheids are thick and hard. Their main functions include the conduction of water and the provision of mechanical support to the body of the plant. The tracheids have no perforation plates and are thus not perforated cells.
In comparison, the xylem vessels are perforated cells and have a comparatively larger diameter than the tracheids. The walls of vessels are less thick when compared to those of the tracheids. The different members of xylem vessels are interconnected through porous plates, known as perforation plates, and are thus capable of transporting water more easily when compared to tracheids.
Hope this helps.

Calculus: Early Transcendentals, Chapter 7, 7.1, Section 7.1, Problem 23

You need to solve the integral int_0^(1/2) (x) cos (pi*x) dx , hence, you need to use substitution pi*x = t => pi*dx = dt => dx = (dt)/(pi)
int x*cos (pi*x) dx = 1/(pi^2) int t*cos t
You need to use the integration by parts for int t*cos t such that:
int udv = uv - int vdu
u = t => du = dt
dv =cos t=>v =sin t
int t*cos t = t*sin t- int sin t dt
1/(pi^2) int t*cos t = 1/(pi^2)(t*sin t +cos t) + c
Replacing back the variable yields:
int x*cos (pi*x) dx = 1/(pi^2)(pi*x*sin(pi*x) +cos (pi*x)) + c
Using the fundamental theorem of calculus, yields:
int_0^(1/2) (x)cos (pi*x) dx = 1/(pi^2)(pi*(1/2)*sin(pi/2) +cos (pi/2) - 0*sin 0 - cos 0)
int_0^(1/2) (x)cos (pi*x) dx = 1/(pi^2)(pi/2 - 1)
Hence, evaluating the integral, using integration by parts, yields int_0^(1/2) (x)cos (pi*x) dx = 1/(pi^2)(pi/2 - 1).

What is an example of foreshadowing in "The Necklace"?

An example of foreshadowing in "The Necklace" has to do with the necklace itself. One day, Mathilde's husband brings home an invitation to "an evening reception at the Ministerial Mansion." Once Mathilde buys a new dress for the event, she decides to take her husband's suggestion and borrow a necklace. Her friend, Mme. Forestier, immediately agrees to loan a "superb diamond necklace" in a "black satin box" to Mathilde.
After a glorious evening, Mathilde and her husband return home and notice that she no longer has the necklace. After much searching, they take the black box to the jeweler whose name was inside the box in the hopes of finding a similar necklace. The jeweler looks at his records and says, "I didn't sell that necklace madame. I only supplied the box." Mathilde and her husband have to borrow a large sum of money to replace the necklace. After ten years, Mathilde sees Mme. Forestier and decides to tell her the truth about the necklace. When Mme. Forestier hears that her necklace was replaced with another, she informs Mathilde that her necklace was a fake, and only worth about five hundred francs.
The foreshadowing occurs when we see that Mme. Forestier easily agrees to loan the necklace, and the jeweler states that he only supplied the box. These are clues that the necklace was not as valuable as Mathilde and her husband believed.

One of the twins happily asks John if Linda is dead. What does John do to the child?

After a date with Lenina that ends with John shoving her and forcing her to hide in a bathroom, John is notified by phone that his mother has overdosed on soma. Soma is a drug that people take every day, as encouraged by the World Controllers. This tragedy marks the end of Linda and John's enjoyment of the decadent world they find themselves in. When John arrives at the hospital, he is horrified to find his mother in a soma-stupor. It becomes clear that she is dying and he collapses to grieve at her bedside, recalling his childhood memories of her. This visceral reaction causes the nurses in the ward to believe that John has gone mad and worry that he will disturb a group of Delta twins who are there on a death tour. The children observe John's grief with distant curiosity before coming into the room to disturb him.
As John continues to cry over his mother's near-lifeless body, the children crowd around him to observe her death as if it is a spectacle for their entertainment. John is repulsed by the fact that they are eating eclairs, seemingly unaffected by the death and suffering that surrounds them. This is, in fact, the purpose of the death training that is used to condition the fear of death out of all citizens from a young age. One of the twins remarks that he thinks Linda is fat, which offends an already unstable John. Adding to his anger, Linda talks about Popé in her sleep. When one of the twins casually asks, "Is she dead?" after Linda has been silent for a while, John shoves him to the ground in a violent display that further shocks everyone in the ward. John's reaction is the result of all the anger that began accumulating on his date with Lenina. In a literary sense, it is the culmination of his growing distaste for society and its decadence as well as the apathy it instills. The child is merely a scapegoat for John's disgust with society in general, a construct he feels powerless to overcome.

What are your thoughts on the Obama Administration's decision to allow oil and gas exploration in the Arctic? What are the drawbacks to your position?

I am not sure of your opinion on this issue, so I will try to show you both sides of the argument and let you make your own decision. First, look at the positive aspects of this. There is projected to be 34 billion barrels of crude in the Chukchi region, over half of it less than 200 feet deep. By 2040, analysts project shale oil will not be enough to power the American economy; other sources will be needed.
Now, for the negatives. I am biased in my opinion, so this list may cloud your judgment. First, greater availability of oil will lead to less desire to develop alternate sources of energy, such as hydroelectric and solar. Global warming is becoming a worldwide issue, and America uses more oil than any other country — developing oil reserves is not a good example for nations that America criticizes for their pollution. Next, it's cold in Chukchi and supply lines are hard to create. While workers can be enticed with higher salaries, it would become more difficult to supply these workers with what they need given the current state of roads in the region. The region is also ecologically delicate in ways biologists are just starting to realize fully. The region is home to saltwater fish that are an important part of the world's food supply and ecosystem. Any potential spill would take a gargantuan effort to clean up — perhaps even larger than the Deepwater Horizon Spill of 2010.
I have enclosed an article that lists both the positives and negatives of America's Arctic drilling program. For your paper, I would take a side, and then argue the side I chose, then point out the drawbacks of my side, whether or not I decide to drill. You should also, however, make sure you point out that your side is correct in that its positives outweigh the negatives.
https://investmentu.com/shell-oil-pros-cons-arctic-drilling-why-start-now/

College Algebra, Chapter 1, 1.5, Section 1.5, Problem 74

Solve the equation $\sqrt{x} + a \sqrt[3]{x} + b \sqrt[6]{x} + ab = 0$. Suppose that $a$ and $b$ are positive real number.


$
\begin{equation}
\begin{aligned}

\sqrt{x} + a \sqrt[3]{x} + b \sqrt[6]{x} + ab =& 0
&& \text{Given}
\\
\\
(\sqrt{x} + a \sqrt[3]{x}) +(b \sqrt[6]{x} + ab) =& 0
&& \text{Group terms}
\\
\\
\sqrt[3]{x} (\sqrt[6]{x} + a) + b (\sqrt[6]{x} + a) =& 0
&& \text{Factor out } \sqrt[3]{x} \text{ and } b
\\
\\
(\sqrt[3]{x} + b)(\sqrt[6]{x} + a) =& 0
&& \text{Factor out } \sqrt[3]{x} + b
\\
\\
\sqrt[3]{x} + b =& 0 \text{ and } \sqrt[6]{x} + a = 0
&& \text{Zero Product Property}
\\\
\\
x =& (-b)^3 \text{ and } x = (-a)^6
&& \text{Solve for } x
\\
\\
x =& -b^3 \text{ and } x = a^6
&&


\end{aligned}
\end{equation}
$

Homer was a Greek poet; he probably lived around 700 B.C. Is that a compound or simple sentence?

Although this sentence does not use any of the “FANBOYS” coordinating conjunctions, it is nevertheless a compound sentence. This is because the semicolon can take the place of a coordinating conjunction.
In a typical compound sentence, there are two independent clauses which are linked by a coordinating conjunction. For example, Sentence #6 in the screenshot you attached is clearly a compound sentence. It uses the coordinating conjunction “and” to imply Achilles’ anger was related to the fact that he only had one real friend. Sentence #1, about which you are asking, does not have a coordinating conjunction.
Even so, it is still a compound sentence. Compound sentences (as you can see in the link below) can be constructed using a semicolon instead of a coordinating conjunction. In Sentence 1, we have two independent clauses that could each form a standalone sentence. These two sentences are combined with a semicolon, which implies that the two clauses are related in some way. Because a compound sentence can be made using two independent clauses and a semicolon, the sentence you have given us here is a compound sentence.

What is one response to the end of "Harrison Bergeron" by Kurt Vonnegut?

On one hand, when Harrison breaks free from his handicaps, it is a liberating moment. When he removes the dancer's handicaps and they embrace in a romantic display of dancing and grace, it is a triumphant moment. 
On the other hand, when Harrison breaks free, he names himself emperor and selects his empress. He doesn't speak on behalf of other people who have been handicapped. He doesn't inspire a rebellion or an uprising. He only talks about himself: 

"I am the Emperor!" cried Harrison. "Do you hear? I am the Emperor! Everybody must do what I say at once!" He stamped his foot and the studio shook.

Knowing that Harrison has been fighting the oppression of the Handicapper General, it is disheartening to see him assert himself as a tyrant. He doesn't say anything about changing the way society is governed. He just immediately becomes obsessed with power. 
So, when he and his empress are killed, it is tragic. But given the selfish way he deals with his brief freedom, it doesn't seem as though his society has lost a righteous savior. Harrison wastes his opportunity and because of everyone else's handicaps, he is quickly forgotten. 

Calculus of a Single Variable, Chapter 9, 9.2, Section 9.2, Problem 42

Recall that infinite series converge to a single finite value S if the limit of the partial sum S_n as n approaches oo converges to S . We follow it in a formula:
lim_(n-gtoo) S_n=sum_(n=1)^oo a_n = S .
To evaluate the sum_(n=0)^oo 3^n/1000 , we may express it in a form:
sum_(n=0)^oo 1/1000 * 3^n .
This resembles form of geometric series with an index shift: sum_(n=0)^oo a*r^n .
By comparing "1/1000 * 3^n " with "a*r^n ", we determine the corresponding values: a = 1/1000 and r = 3 .
The convergence test for the geometric series follows the conditions:
a) If |r|lt1 or -1 ltrlt 1 then the geometric series converges to sum_(n=0)^oo a*r^n =sum_(n=1)^oo a*r^(n-1)= a/(1-r) .
b) If |r|gt=1 then the geometric series diverges.
The r=3 from the given infinite series falls within the condition |r|gt=1 since |3|gt=1 . Therefore, we may conclude that sum_(n=0)^oo 3^n/1000 is a divergent series.

What is legislation?

Legislation can simply be understood as the law enacted by a body empowered to do so. This means that before a law can come in place, it must be from recognized body empowered by the constitution to do so. Using Nigeria as a case study,  before a new law emerge, it must pass some readings,referendum and then on the final stage the president will have to append his signature. It is the source of law that most people are familiar with. It can be rightly regarded as the main source of law. In present day Nigeria,legislation for the Federation is made by the National Assembly.As this is backed up by the provision of S. 4 (1) of the 1999 Constitution of the Federal republic of Nigeria (as amended) which provides:
The legislative powers of the Federal Republic of Nigeria shall be vested in a National Assembly for the Federation, which shall consist of a Senate and a House of Representatives.
Legislation could either be Acts, Ordinances, Decrees, Edicts and laws. Acts are laws made by the central legislature during a democracy. Ordinances are laws made by the central legislature before 1st Oct, 1954 (when federalism was introduced). On the other hand, decrees are federal laws made in a military regime, edicts are state laws in a military regime while laws are state laws in a democracy.
Before legislation can be enacted in a democracy, it has to pass through some procedures as provided for in the Constitution. On the other hand, in the case of A.G.F vs. Guardian Newspaper Ltd and Ors it was decided by the courts that all it takes for a decree to be enacted is the valid signature of the military Head of State.
All federal legislation till 31st January 1990 in Nigeria were consolidated in the Laws of the Federation of Nigeria 1990. (L.F.N 1990). It was revised in 2002 and is now published as L.F.N 2004.
One of the types of legislation is delegated legislation.

Legislation technically refers to the making and enacting of laws. An example of legislation would be an act of Congress. Today, most people use the words "law" and "legislation" almost interchangeably. This was not always the case. The 20th century libertarian philosopher Hayek, for example, made a clear and important distinction between law and legislation, one foundational to his classical liberal philosophy.
For Hayek, law means common law, judge-made law that establishes legal precedents. In making their decisions, judges are discovering and giving voice to long-standing community principles handed down through successive generations. By doing so, they are creating a general framework of rules, one that allows for the maximum exercise of individual liberty. As this framework is general, it does not impose a specific way of life on anyone; it simply enables each individual to maximize his/her own liberty while respecting that of others. We can then see why Hayek regards common law as playing a vital role in strengthening the operation of the free market economy he so highly values.
Legislation is a completely different matter entirely. Unlike law, it is created for a specific purpose; it does not arise spontaneously over time. If law provides a broad framework, legislation hands down a detailed social blueprint. It is designed largely to allow those in power to carry out policy programs usually involving the enormous expansion of the state. This gives those in positions of authority huge power and largely unchecked power at that. Human nature being what it is, if you give someone a lot of unchecked power, odds are at some point they will abuse it; this is what Hayek fears most of all.
Legislation imposes itself upon society, unlike common law whose roots are buried deep within society. The separation of legislation from any real foundation in society means that it is often used for programs of massive social engineering by governments, programs which tend not to correspond with the views of the vast majority. (A good example would be the enactment of many of the Great Society programs under President Johnson in the 1960s). In other words, legislation imposes a certain way of life on people, effectively telling them how to live their lives. Legislation gains credence and authority relatively quickly; it would take common law centuries to arrive at a similar social prescription. It is no wonder, says Hayek, that governments with radical agendas, such as Hitler's Third Reich or the USSR under Stalin, saw legislation as an essential tool in carrying out their revolutionary plans.
We can illustrate Hayek's point with a hypothetical example. Let us say that Congress voted to reintroduce slavery. Could that act of Congress really be described as law? Hayek says no. Though it would be a formally enacted piece of legislation, it would not have the status of law in his eyes or the eyes of most other people. Law for Hayek is something that transcends; it is an expression of a higher morality to which we all must adhere if we are to live in a free society that respects our uniqueness as individuals and allows us to pursue our own happiness. An act of Congress reintroducing slavery clearly would not fall under this category. For reasons already discussed, legislation is a serious threat to a free society whose establishment and preservation are the most important components of Hayek's entire social, economic, and political philosophy.

Calculus and Its Applications, Chapter 1, 1.6, Section 1.6, Problem 8

Take the derivative of $y = (4 \sqrt{x} + 3 )x^3$: first, use the Product Rule; then,
by multiplying the expression before differentiating. Compare your results as a check.
By using Product Rule,

$
\begin{equation}
\begin{aligned}
y' = \frac{d}{dx} \left[ (4\sqrt{x} + 3) x^3 \right] &= (4\sqrt{x} + 3) \cdot \frac{d}{dx} (x^3) + x^3 \cdot \frac{d}{dx} (4 \sqrt{x} + 3)\\
\\
&= (4 \sqrt{x} + 3)(3x^2) + x^3 \left( \frac{4}{2\sqrt{x}} \right)\\
\\
&= \left( 4x^{\frac{1}{2}} + 3 \right) (3x^2) + x^3 \left( \frac{2}{x^{\frac{1}{2}}} \right)\\
\\
&= 12x^{\frac{5}{2}} + 9x^2 + 2x^{\frac{5}{2}}\\
\\
&= 14x^{\frac{5}{2}} + 9x^2
\end{aligned}
\end{equation}
$


By multiplying the expression first,

$
\begin{equation}
\begin{aligned}
y = (4 \sqrt{x} + 3)x^3 = \left( 4x^{\frac{1}{2}} + 3 \right) x^3 = 4x^{\frac{7}{2}} + 3x^3 \\
\\
y' &= \frac{d}{dx} \left[ 4x^{\frac{7}{2}} + 3x^3 \right] = 4 \cdot \frac{7}{2} x^{\frac{7}{2} - 1} + 3 \cdot 3 x^{3 - 1}\\
\\
&= 14x^{\frac{5}{2}} + 9x^2 \text{ or } 14\sqrt{x^5} + 9x^2
\end{aligned}
\end{equation}
$


Both results agree.

How does Tris change as the story progresses? Is she a reliable narrator?

In the story, Tris sheds her shy, awkward image for a warrior persona in the space of a short period. Although the transformation is impressive, Tris’s account of her experiences demonstrates just how difficult her adjustment has been. Upon leaving Abnegation, our heroine is thrust into a terrifying world populated by bullying peers, formidable authority figures, and a shadow government that seeks her demise. In this new world, she must also process the unfamiliar new feelings that Tobias awakens in her and endure numerous trials that test her psychological resilience. To her surprise, our heroine learns that the fear simulations reinforce her divergence, a trait that propels her to decisive action on behalf of her beleaguered city.
As for whether Tris is a reliable narrator, it is evident that her objectivity is sometimes questionable. For example, Tris resents Tobias for "throwing knives" at her and scolding her at "every opportunity" during training. However, it is evident that Tris’s perspective has been skewed by her naïveté and ignorance. It is only after Tris learns about the murder of Tori's brother that she begins to understand the rationale behind Tobias’s austerity.

In "How to Talk to Girls at Parties," what do you think Vic sees at the end of the story that upset him so much?

In the short story by Neil Gaiman, "How to Talk to Girls at Parties," the first-person narrator, Enn, retells the events that took place thirty years earlier at a party in London.
Enn's inexperience with girls at the age of fifteen is evident; he always ends up in the kitchen "listening to somebody's mum going on about politics or poetry or something" (para 6) while his friend, Vic, always gets the girl.
From the onset of the story, Gaiman foreshadows the strange turn of events that will take place that night. The neighborhood where the party takes place is located in a "grimy maze" of backstreets. Rusty cars and dirty shops sell "alien spices" and pornographic magazines (para 12). This is not the type of place young boys would usually go to a party to talk to girls.
Furthermore, Gaiman uses irony when Vic tells Enn that talking to girls is easy:"'They're just girls," said Vic. "They don't come from another planet'" (para 16). As we find out at the end of the story, these are not just girls, and, more than likely, they did come from another planet.
When Vic runs away from Stella, Gaiman purposely leaves Vic's sentence unfinished, "She wasn't a—"
So, what did upset Vic so much that he threw up and cried like a little boy? What corrupted his innocence? Perhaps as aliens, the girls also had other alien characteristics that were not of the typical female gender. Whatever Vic discovered about Stella while he was with her terrified him because she was not a normal female.
Therefore, ironically, perhaps Enn did not learn to talk to girls at parties that evening, but instead he held a conversation with beings most definitely not girls.

Throughout the story "How to Talk to Girls at Parties," there's a hint that the women at the party are not exactly women— or even human. This idea is foreshadowed early in the story and then the narrator, Enn, explains his run-in with these non-human "women" at the party. This is why we can guess as to what Vic means when he says, "She wasn't a—"
In the story, Enn explains his trouble talking to girls. He says that while Vic could get away with not actually talking to girls because he's good looking, Enn "did not know what to say to girls." The entire story is Enn trying to talk to girls. The first girl he speaks to is named "Wain Wain" and oddly says after a long speech, "Soon I must return to Wain, and tell her all I have seen. All my impressions of the place of yours." The next girl he speaks to calls herself a tourist and that on her last tour she "went to sun, and we swam in sunfire pools with the whales." Finally, the last girl Enn speaks to at the party is named Triolet and she calls herself a poem. She says about her people,

There are places that we are welcomed. . . and places where we are regarded as a noxious weed, or as a disease, something immediately to be quarantined and elimated. But where does contagion end and art begin?

After Triolet recites a poem in Enn's ear, Vic comes into the kitchen in a panic and says they need to leave. When they leave, Enn looks back and sees Stella, who is staring at them. Enn's description of Stella is interesting and explains these non-women:

Her clothes were in disarray, and there was makeup smudged across her face, and her eye—
You wouldn't want to make a universe angry. I bet an angry universe would look at you with eyes like that.

All of these clues lead to only one conclusion: Stella, who Vic was with upstairs, was not human. This frightens him so much that he ends up "sobbing in the street, as unselfconsciously and heartbreakingly as a little boy."

What is the central idea (thesis) of Desert Solitaire by Edward Abbey?

In writing Desert Solitaire, Abbey places his work alongside other major texts of the environmental literature movement. Most important is Henry David Thoreau's Walden, published in 1854, which documents that writer's experience living in voluntary poverty in a small, remote cabin. Like Thoreau, Abbey is both humorous and cantankerous, with a wide-ranging intellect. The stories in Desert Solitaire describe adventures during his time in the canyonlands, and he argues for the fragility of nature, man's requisite humility when approaching wildness, and his affinity for rural life and self-sustainability.
Abbey documents the steady and nefarious creep of civilization into the wilderness, which he lampoons in "Havasu," noting how the local natives have decided against allowing the Department of the Interior to bulldoze a road right up to their spectacular waterfalls. There is value in being remote, in being hard to reach, suggests Abbey. Easy access is not always a good thing.
In his introduction, Abbey writes this:

Do not jump into your automobile next June and rush out to the canyon country hoping to see some of that which I have attempted to evoke in these pages. In the first place you can't see anything from a car; you've got to get out of that goddamned contraption and walk, better yet crawl, on hands and knees, over the sandstone and through the thornbush and cactus. When traces of blood begin to mark your trail you'll see something. Maybe. Probably not.

Rather than encouraging readers to live vicariously through Abbey's adventures, he advocates a lifestyle that gets you out of your comfort zone, stripped of pretense and ready to learn, experience, and risk. Central to his book is this appeal. Live richly, fight comfort, learn as much as you can. In this way, his central idea echoes the work of Thoreau (and others). In wildness is your salvation, if you have the guts to face it.

Desert Solitaire by Edward Abbey is not really a book with a singular thesis, but a series of meditations about the Great Basin desert and his experiences as a ranger in Arches National Park outside Moab, Utah. Over the course of the book, Abbey reflects extensively on wilderness and displays several consistent attitudes about it, but does so in an exploratory manner rather than by linear argument.
His first major point is that the wilderness is the spiritual home of people in North America. Notably, he believes that if we destroy our wilderness areas or stop visiting and preserving them, we destroy something at the center of our own spirit, saying:

A civilization which destroys what little remains of the wild, the spare, the original, is cutting itself off from its origins and betraying the principle of civilization itself.

He believes that wilderness and the flora and fauna inhabiting it have intrinsic worth to the human spirit. 
One of the most well-known and characteristic sections of the book is his description of a trip down Colorado River and his meditations on the Glen Canyon dam, and the vast destruction it wrought on the river ecosystem and the irreplaceable remains of the Anasazi, who created stunning cliff dwellings before Europeans settled the region. He sees the dam as showing the government complicit with the forces of urbanization and corporate greed, stealing a magnificent heritage of natural beauty that should belong to everyone and destroying it to profit a limited number of people, something he considers unambiguously evil. 
In his evocation of the beauty of the high desert, Abbey argues that we ourselves are part of nature, and that to destroy our environment or other species within it, we ultimately destroy ourselves, both in terms of our spirit and eventually our survival, as our ranching and dam building degrades our environment. 

In The Outsiders, why doesn't Cherry want to see Dally again?

In this novel by S. E. Hinton, two different social groups of adolescents are at odds with one another: The Socs, who come from wealthy families, do well in school and are expected to become productive, influential members of society; and the Greasers, from poorer families, who don't have strong family role models and who tend to be rebellious and do poorly in school. Cherry is with the Greasers, Dally or Dallas is with the Socs. When the two meet there is immediate tension and Dallas flirts with her, while Cherry is rude and insulting. To complicate matters, Dally's younger friend Ponyboy has a crush on Cherry.
In the film version by Francis Ford Coppola, Dally is played by Matt Dillon and Cherry by Diane Lane. In the scene being discussed, Cherry yells at Dally and he mocks being offended, but seems to know that she likes him. After Dally walks off, and Cherry is standing with Ponyboy, she states firmly, "I hope I never see Dallas Winston again!" After a pause she roll her eyes and says more softly, with a frustrated air, "If I do, I'll probably fall in love with him." She walks off, and Ponyboy looks dejected. This dialogue is slightly changed from the book (Cherry says  "I could fall in love with Dallas Winston... I hope I never see him again, or I will.", but even more effective.
Dally and Cherry come from different worlds, but there is a sense of the forbidden in their attraction to one another. Dally is more reckless and exploits this attraction by flirting; Cherry is more hesitant even though it's clear she is interested in him.

How can I make a title for the best feature of a cellphone?

Coming up with titles is hard.  I actually never wrote titles for my papers in high school or college until after everything else was done.  I needed the inspiration of all of the other stuff to come up with a decent title.  Based on the question, it sounds like that part is done already.  I do not know what cellphone or cellphone feature that the question has in mind, so I'll have to be a bit broad.  
When coming up with a title, you want the title to apply to the topic, not be mundane, and shorter is better than longer because it's generally easier to remember.  
My favorite feature of my cellphone is the camera.  I know that's not exciting, but I have three little kids, so the camera gets used a lot.  It's a camera but it doesn't have a cool title name.  I'm kind of partial to "The Time Capture Device."  It sounds way more scientific than "camera," but the problem is that it is longer than the actual name.  Maybe "Photo Cannon" is better.  
Regardless of the feature that you are trying to provide a title for, don't be afraid to be silly with the title.  I've often found that starting out with silly names often leads to titles that are quite creative.   

Who was Amir in The Kite Runner by Khaled Hosseini most like in A Thousand Splendid Suns? Tariq or Rasheed?

Khaled Hosseini's The Kite Runner follows the story of Amir, a Pashtun boy living in Kabul who loves to kite fight with Hassan, the Hazara son of Amir's father's servant. After an older bully by the name of Assef attempts to attack Amir, Hassan intervenes on Amir's behalf. Assef vows to get revenge, and he does--by beating and raping Hassan in an alleyway after one of the kite fights. Amir witnesses this event and yet does nothing to stop it. To alleviate the guilt he feels when he sees Hassan, Amir sets Hassan up to make it look like Hassan has stolen from Amir's father. 
Thus, I would argue that Amir is more like Rasheed from A Thousand Splendid Suns than Tariq. In this novel, Rasheed is a complicated figure who possesses both great love for his son and expresses great cruelty toward the women in his life. Like Amir, Rasheed commits a terrible act of deception; he sets up Laila (his future wife) by hiring a man to falsely inform her of her true love's death--a manipulative gesture which leads to their marriage. Amir does not possess the simplicity or purity of Tariq, who largely appears as a romantic figure. 

Why would Christmas presents provoke tears from Bailey and Maya?

As children living in Stamps, Arkansas with their grandmother, Maya and Bailey cried during Christmas after receiving gifts from their estranged parents. Maya recalls receiving a photograph from her father and a tea set, along with a doll from her mother, who lives in Long Beach, California. Instead of appreciating the gifts sent from her parents, Maya becomes depressed and begins to cry. When Maya walks out back, she also finds her brother in tears. Maya had told herself that their parents were dead in order to explain why she and Bailey were shipped off to Arkansas to live with their grandmother. The gifts confirm that both of their parents are alive and forces Maya and Bailey to ask the difficult question concerning why their parents no longer wanted them around. Maya wonders if she and Bailey did something wrong that motivated their parents to abandon them and is overwhelmed with feelings of inadequacy and loneliness. Essentially, the Christmas gifts the children receive bring up negative feelings and remind them that their parents did not want them for some unknown reason.

What is the setting of "Raymond's Run"?

The setting of the short story "Raymond's Run" is Manhattan in New York. Manhattan contains a lot of people, but the area itself isn't that large; however, that's still a fairly broad location. In the sixth paragraph of the story, Squeaky narrows down the setting location. She tells readers that she lives in Harlem. Harlem is located just north of Central Park and just southwest of Yankee Stadium. I believe that the story takes place on the western edge of Harlem because Squeaky mentions two specific streets. She mentions Amsterdam Avenue and Broadway. As for the time setting, nothing specific is given to readers. The original publication date of the story is 1971, and the story is likely taking place around that date. Readers do know that the story is taking place during the months of April and May because Squeaky is running in the annual May Day races (May Day is May 1st).

A line passes through the point (10,-2) and forms with the axes a triangle of area of 9 sq units. Find the equation of the line.

Hello!
Denote the slope of this line as m. The vertical line (which has an undefined slope) doesn't suit us, so we'll not miss a solution. Horizontal line with m=0 doesn't suit also, so we can divide by m.
The equation of such a line is y = m*(x-10) - 2. The triangle formed with this line and the axes is a right one (because the axes are perpendicular to each other). So its area is 1/2 * |OX| * |OY|, where O is the origin, X is the x-intercept of the line and Y is the y-intercept.
The y-intercept is y(0) = -10m-2. The x-intercept is the x for which y= m*(x-10) - 2=0, so it is 2/m+10.
Thus our equation for m becomes
1/2 |(-10m-2)*(2/m+10)| = 9.
It is the same as |(5m+1)*(1/m+5)| = 9/2, or |1/m (5m+1)^2| = 9/2.
If we suppose m is positive, then it becomes
(5m+1)^2 = 9/2 m, or 25m^2+10m+1=9/2 m, or 25m^2+11/2 m +1=0, or 50m^2+11m+2=0. This equation has no solutions.
Well, what about negative m's? The equation becomes (5m+1)^2 = -9/2 m, or 25m^2+10m+1=-9/2 m, or 25m^2+29/2 m +1=0, or 50m^2+29m+2=0.
The discriminant is D = 29^2-4*50*2 = 29^2 - 20^2 = 9*49, so sqrt(D)=3*7=21. The solutions are (-29+-21)/100, m_1 = -50/100=-1/2, m_2 = -8/100 = -2/25. And both are negative as supposed.
Uff. There are two possible equations, y=-1/2(x-10)-2=-1/2x+3 and y=-2/25(x-10)-2=-2/25 x-6/5.
 

In "The Minister's Black Veil," why do the villagers bury Mr. Hooper without removing the veil?

When the Reverend Mr. Clark sits by Father Hooper's deathbed, Mr. Clark asks Father Hooper to allow him to remove the veil from Father Hooper's face so that he can meet eternity without it.  Father Hooper, however, is horrified by this idea, and he shrieks, "'Never! [...].  On earth, never!'"  It is clear that Father Hooper wishes never to have the veil removed, and this may be one reason that his parishioners do not remove it.
Further, everyone gathered at Father Hooper's deathbed still seems to fear the mysterious veil.  Mr. Clark even suggests that it signifies some terrible sin Father Hooper had committed.  However, Father Hooper asks, 

"Why do you tremble at me alone? [....] Tremble also at each other!  Have men avoided me, and women shown no pity, and children screamed and fled, only for my black veil?  What, but the mystery which it obscurely typifies, has made this piece of crape so awful?  When the friend shows his inmost heart to his friend; the lover to his best beloved; when man does not vainly shrink from the eye of his Creator, loathsomely treasuring up the secret of his sin; then deem me a monster, for the symbol beneath which I have lived, and die!  I look around me, and, lo! on every visage a Black Veil!"

It seems to be, in part, this "mystery" that Father Hooper describes that so terrifies the people.  They seem always to have had an obscure idea of what the veil symbolizes -- that each of us has secret sins that we attempt to hide from each other, ourselves, and even God -- but no one wants to admit that they might understand because that would be tantamount to admitting that one has these secret sins on one's soul, and what everyone wants the most is to hide this very fact.  If, in truth, these people really do have even a vague understanding of the veil's meaning, then they would not want to remove it after Father Hooper has died because it is a meaningful and accurate symbol; if, on the other hand, they really don't have a concept of the veil's meaning, then they would not want to remove it because it is such a mystery, and we fear mysteries.

int (5x-2) / (x-2)^2 dx Use partial fractions to find the indefinite integral

int(5x-2)/(x-2)^2dx
Let's use partial fraction decomposition on the integrand,
(5x-2)/(x-2)^2=A/(x-2)+B/(x-2)^2
5x-2=A(x-2)+B
5x-2=Ax-2A+B
comparing the coefficients of the like terms,
A=5
-2A+B=-2
Plug in the value of A in the above equation,
-2(5)+B=-2
-10+B=-2
B=-2+10
B=8
So now int(5x-2)/(x-2)^2dx=int(5/(x-2)+8/(x-2)^2)dx
Now apply the sum rule,
=int5/(x-2)dx+int8/(x-2)^2dx
Take the constant's out,
=5int1/(x-2)dx+8int1/(x-2)^2dx
Now let's evaluate each of the above two integrals separately,
int1/(x-2)dx
Apply integral substitution u=x-2
=>du=dx
=int1/udu
Use the common integral :int1/xdx=ln|x|
=ln|u|
Substitute back u=x-2
=ln|x-2|
Now evaluate the second integral,
int1/(x-2)^2dx
Apply integral substitution:v=x-2
dv=dx
=int1/v^2dv
=intv^(-2)dv
Apply the power rule,
=v^(-2+1)/(-2+1)
=-v^(-1)
=-1/v
Substitute back v=x-2
=-1/(x-2)
:.int(5x-2)/(x-2)^2dx=5ln|x-2|+8(-1/(x-2))
Add a constant C to the solution,
=5ln|x-2|-8/(x-2)+C

What is unusual about the point of view in "The Wrong Category" by Ruth Rendell?

Author Ruth Rendell was a master of writing mystery stories.  In her collection of short stories entitled A Fever Tree and Other Stories, she includes a story called "The Wrong Category." This story is interesting because the author seems to lead the reader right to the identity of the killer, only to completely change their mind right at the end.
Throughout the story, we follow Barry, an awkward, ugly little man who has taken to haunting the locations of several murders. His mother hates him going out at night to these spots, but he seems to enjoy visiting them. It would seem that we are reading the story through the perspective of the actual murderer!
Everything, it appears, would hint at Barry being the culprit of the murders; he fits the profile, he likes to visit (or revisit) the locations where the murders occurred, and he picks up a girl at the bar who fits the profile of the murdered girls.  In fact, he takes her to a location and suggests that this would be the perfect spot to commit another murder.  She runs, and he chases her.  
It would be obvious that Barry were the murderer, except for a few small details.  For example, was he simply trying to help her when she ran away from him at the murder spot? Why would he tell his victim and give her a chance to get away?  Perhaps he has simply realized something about the pattern of the criminal by taking up the hobby of following the murders.
As we can see, this unusual point of view is simply one ingenious device that the author uses to lead us in the wrong direction.  We only see what Barry is doing, so we naturally think everything he does is suspicious, which leads us to draw the conclusion that he must be the murderer.  The outcome of the story seems completely obvious.  We have a limited perspective, however, which leaves the author room to completely surprise us right at the end with some information that we never considered.  Rendell is a true master of mystery.

Analyze the poem as a yearning for individualism and knowledge, rather than focusing on its undercurrents of insensitivity and misogyny.

Many scholars and readers have noted that Tennyson's "Ulysses" exhibits strong undercurrents of misogyny and general male insensitivity. This point is perfectly valid, as the Ulysses in the poem shows a remarkable disregard for the needs of his wife, son, and loyal subjects. Be that as it may, the poem is also significant in its examination of individualism and the thirst for knowledge. Indeed, one could accurately say that the poem argues for the centrality of the individual's need to learn and discover.
In remembering his past deeds, Ulysses notes, "always roaming with a hungry heart / Much have I seen and known" (12-13), thus suggesting that he has always yearned for the freedom to learn through travel. Indeed, by the end of the first stanza, the aged king asserts that he is "yearning in desire / To follow knowledge like a sinking star, / Beyond the utmost bound of human thought" (30-32). This individualistic desire to learn about the world through adventure becomes the focus of the poem, and it is the primary driving force that motivates Ulysses to finally leave home and set off on a new journey. As such, it's hardly surprising that, toward the end of the poem, Ulysses promises "To sail beyond the sunset, and the baths / Of all the western stars, until I die" (60-61). In short, though the Ulysses in the poem is decidedly misogynistic in his rejection of his wife and family, he also displays an admirable individualism, as his decision to leave ultimately affirms the importance of individual exploration and the search for knowledge. 
https://www.poetryfoundation.org/poems/45392/ulysses

Specific detail is often what makes writing immediate and real, yet Dickinson does not state what causes the “great pain.” Why does she leave out this detail?

While specific detail can make writing more vivid, it can also make it difficult for readers to relate when the detail described is completely outside of his or her experience. Much of Dickinson's writing draws upon the events of her own life, but here we might argue that the vagueness of the reference helps to make the poem more universal, allowing the reader to bring their own experience to bear in its interpretation. Dickinson does not refer to "my great pain," but instead describes a universal aftermath to pain, in general, and therefore pain as it is specific to each reader.
There are other details in the poem which are more specific and which help the reader to appreciate what the poem conveys. The aftermath of pain is described as "the Hour of lead," which, if survived, is remembered "as Freezing persons recollect the Snow." The language in the final stanza is suggestive of emotional numbness (leadenness), emphasized further by the imagery of "freezing persons" falling into "chill––then Stupor––then the letting go," which seems to allude to hypothermia. A sensory field is, therefore, created. Meanwhile, the generic articles applied throughout the poem to "the Nerves," "the stiff Heart," "the Feet" allow the reader to imagine their own nerves, hearts, and feet ("mechanical," again suggestive of numbness) in this situation.

What does "thy bones are marrowless, thy blood is cold" mean in Macbeth?

This particular quote is from Act 3, Scene 4. Macbeth and Lady Macbeth are entertaining dinner guests, and Banquo's ghost decides to crash the party. Macbeth is quite capable of seeing the ghost, but nobody else sees the ghost. That doesn't stop Macbeth from talking to the ghost and telling it to go away. Macbeth knows it is a ghost and not the real Banquo because Banquo is dead. The quote in the question is what Macbeth says to the ghost near the end of the scene. He is telling Banquo's ghost to go away and return to the grave. Macbeth is basically saying that the ghost has no place at the dinner or in the world of the living because it is not living. Macbeth's proof that the ghost is not living is the fact that it does not have bones filled with marrow nor does it have warm blood. Macbeth's conversation with the ghost ends with Macbeth challenging the ghost to come back in any other form. If the ghost does that, Macbeth says that he won't be afraid. Finally, Macbeth challenges the ghost to come back in actual, real living format for a duel.

"What man dare, I dare.
Approach thou like the rugged Russian bear,
The armed rhinoceros, or th' Hyrcan tiger;
Take any shape but that, and my firm nerves
Shall never tremble. Or be alive again,
And dare me to the desert with thy sword.
If trembling I inhabit then, protest me
The baby of a girl. Hence, horrible shadow!
Unreal mockery, hence!"

 

What are the theme topics of the poem "Still I Rise?"

The predominant theme in this inspiring poem is pride. The speaker is clearly proud of her identity and expresses this by conveying her positive self-esteem in various ways throughout the poem. For example, she states in stanza two

I walk like I've got oil wells
Pumping in my living room.

This is an affirmative declaration in which the speaker asserts that she walks like someone with great wealth, which means she holds an upright posture and does not slouch out of embarrassment or shame. She walks with dignity, proud of her identity. She is confident and assertive. The allusion to someone with great wealth is confirmed in stanza five when the speaker says the following:


’Cause I laugh like I've got gold mines
Diggin’ in my own backyard.



The wealth the speaker alludes to is not material but symbolic. She is a gold mine or an oil well—her wealth lies in her personhood. Her identity is what enriches her and makes her proud. She is proud of who she is, and those who cannot deal with the manner in which she carries or expresses herself have only themselves to blame. In stanza seven, the speaker further accentuates her positive attitude by asking her obviously prejudiced listener if it comes as a surprise that


...I dance like I've got diamonds
At the meeting of my thighs?



Further confirmation of the speaker's positive self-regard lies in the use of phrases such as "my sassiness" (line 5), "my haughtiness" (line 17), and "my sexiness" (line 25). Her direct address is deliberate and questions the listener's bigotry. The most forceful of the speaker's statements in this regard is her proclamation "I rise," which is repeated throughout the poem like a mantra.



This bold declaration introduces another theme: resilience. The speaker emphasizes how willful and determined she is to resist all prejudice against her. Irrespective of what her persecutors do, she has the power to resolutely withstand their discrimination and intolerance. She asserts in stanza one, for example, that even though they may demonize her history and tread on her, she will rise. In stanza six she proclaims that though those who hate her may criticize her, stare her down, or even kill her, she would, in spite of their evil, still rise.



In effect, the speaker is expressing great courage, which is another theme. Her outspoken and determined resistance against others' narrow-minded prejudice is an affirmative stance that she is determined to take. She will, in spite of their best efforts to break her, stand up and rise proudly. The speaker concludes by courageously expressing the fact that she will leave behind all terror and fear. Her purpose is to fulfill her destiny in a bright and certain future by giving hope to those who have been enslaved and to inspire them to realize their dreams.

Maya Angelou's poem "Still I Rise" explores many themes, primarily looking at the idea of oppression, specifically oppression based on her race. Angelou often tackles the theme of race in her writing and this can be seen throughout the stanza's in this poem. She uses the concept of oppression versus wealth.
For example in the fifth and seventh stanzas of the poem


Does my haughtiness offend you?
Don't you take it awful hard
’Cause I laugh like I've got gold mines
Diggin’ in my own backyard


Does my sexiness upset you?
Does it come as a surprise

That I dance like I've got diamonds
At the meeting of my thighs?

At the time this was written things like oil and gold were of utmost importance, and by referencing the ownership of them she is expressing that she will rise past the oppression.
When mentioning the idea that she holds herself up as if she has the status of someone who is built and "made" from diamonds and she will not be made to follow directions or obey, she will dance!

Angelou also use of words like sexiness or haughtiness shows an abundance of confidence. Which can be construed as a blow at those who were oppressing them, the white males of time who were self righteous, or the reader may see it as Angelou's overconfidence to outweigh the oppression handed to slaves and African Americans.

Maya Angelou's defiant, triumphant poem "Still I Rise" primarily explores the theme of oppression based on race and gender. The speaker of the poem directly addresses her oppressor as "you" and responds to the attempts to oppress her and her people with the refrain "I'll rise." She refuses to be kept down or put in her place.
The first stanza ties the poem to history:

You may write me down in history
With your bitter, twisted lies,
You may trod me in the very dirt
But still, like dust, I'll rise.

The reference to the writing of history seems to imply that the oppression the speaker is responding to is not just personal but societal, part of a long line of disenfranchisement based on skin color.

The theme of gender comes into the poem explicitly in the second and seventh stanzas, in which the speaker discusses her "sassiness" and "sexiness," both traits that women, and especially black women and other women of color, have historically been punished for.

No matter what happens or what is thrown at Maya Angelou, she will always rise. The theme of "Still I Rise" is really about self respect, and confidence. In the poem, she reveals how she will overcome anything with her self-esteem. She shows how nothing can get her down.

There are various themes present in this short poem, and the themes are all closely tied together and related to one another. There is a theme of oppression that allows the speaker of the poem to discuss the themes of strength, determination, and resilience in the face of that oppression.
The first stanza of the poem already alerts readers to the speaker's determination to not be put down by oppression. The first few lines illustrate the oppression that is present, and the final line of the stanza is the speaker fighting back.

You may write me down in history
With your bitter, twisted lies,
You may trod me in the very dirt
But still, like dust, I'll rise.

The speaker does a great job of reminding readers of oppression and the fact that the speaker will not be discouraged.


You may shoot me with your words,
You may cut me with your eyes,
You may kill me with your hatefulness,
But still, like air, I’ll rise.



The speaker's unceasing drive to stand in the face of difficulties is best illustrated by the poem's repetition of "I rise" or "I'll rise."

The most important themes in literature are sometimes formed when a death takes place. In the book Wuthering Heights, do you think this statement is true? Provide 3 reasons supporting your argument and provide a theme that comes from the death.

Death is certainly an important thematic element in Wuthering Heights. The first death to play an important role is the death of Mr. Earnshaw. Once Earnshaw is no longer present to protect Heathcliff, Heathcliff becomes the target of Hindley's abuse. This physical and emotional abuse hardens Heathcliff and leads to the eventual revenge plot that carries the weight of the second half of the novel.
A second death that plays an important part of the story is Catherine's. Heathcliff's confrontation with her before her passing leads to further distress on his part. He demands that she haunt him, and she seemingly does. He wanders the moors and becomes even more entrenched in his plans for revenge against Hindley and the Lintons.
While other deaths continue to move the plot forward in different ways, it is Heathcliff's death at the end of the novel that finally completes the cycle of revenge that starts many years before. Having completed his revenge and become the sole possessor of the Grange and the Heights, Heathcliff dies after suffering from melancholy and anorexia. He is buried next to Catherine and finally finds a semblance of peace.

Death absolutely provides thematic material in Wuthering Heights. First, the father's death early in the story leads to the theme of abuse and how abuse and neglect draw Cathy and Heathcliff into a very close bond. Second, Cathy's death has a shattering effect on Heathcliff, and third, even if he does not love as deeply, Linton mourns Cathy's demise and never remarries, showing that death changes lives.
An important theme arises from Cathy's death. The novel is metaphysical, meaning it posits, or argues for, another world beyond the material. Cathy believes that after she dies she will be flung on the moors because she doesn't belong in heaven: nature is her true home and where she longs to be. In the novel, Cathy and Heathcliff might be separated in life by her dying, but the intimation in the novel is that their love is so deep and their souls so tightly intertwined that they will be together after death: a love like theirs cannot be killed. 

What is the significance of the scene when Phoebe gives Holden his hunting hat back in The Catcher in the Rye?

Holden's bright red hunting hat is a vivid expression of his unique personality. In common with most young adults, he wants to proclaim his individuality, and wearing the big old hunting hat allows him to do precisely that. He wants to stand out from the crowd, to look completely different from others of his age. And to Holden, the bright red hunting hat is a sign of his authenticity, setting him apart from all the "phonies" by which he's constantly surrounded. Most important of all, the hat is a kind of comfort blanket, something that Holden feels gives him protection from a world he neither likes nor understands.
In giving the hat to Phoebe towards the end of the book, Holden is showing his concern for her well-being. He is offering his sister a symbol of childhood and the relative safety and security that it embodies. Holden is concerned at the potentially difficult transition to young adulthood that Phoebe may encounter. His own experiences in this regard form the basis of the entire book, and the last thing he wants is for Phoebe to have to go through a similar upheaval.
But he needn't worry. She's already much more mature than Holden in most respects, so she really doesn't need his hat. Throwing the floppy red hunting hat back at her brother is Phoebe's way of telling Holden that she's going to be just fine.

Would Reconstruction have turned out much differently if Lincoln had not been assassinated, or were the problems between the North and the South too much for any one leader to overcome?

I believe that Reconstruction would have turned out much differently had Lincoln not been assassinated. It is true that cultural differences existed between whites in the North and the South, but, except for the slavery issue, the two groups were not that different. Many white Northerners had supported slavery: abolition was not a universally held principle in Northern states before the war, though after the war the North unified around extending rights and freedoms, such as the vote, to blacks.
Where Reconstruction took a hit without Lincoln was in race relations. Lincoln and the early Reconstructionists wanted to create a more racially equal society in the South. They wanted the former slaves to have a fair chance to integrate in the South with the vote and with educational and economic opportunities.
Unfortunately, after Lincoln was assassinated, Andrew Johnson, the new president and a Democrat, took a harsher view towards black rights. For example, he left it up to the states to decide whether they wanted to grant blacks the vote. Further, because many Southern leaders thought Johnson supported them, they instituted what were called Black Codes, binding blacks to work on farms without being able to quit, a situation that outraged Northerners as slavery under a different guise.
Because of Johnson, Southern whites were able to create a rigid white/black caste system which alienated Northerners, and more importantly, made life much more frightening and difficult for blacks. While the same might have happened under Lincoln or thereafter, the likelihood is that all blacks would have started their freed lives with the vote and greater protection so that they would have had more equality with Southern whites.

Why does Cholly Breedlove rape Pecola?

As the previous educators have mentioned, Cholly's rape of Pecola is directly tied to the trauma that he experienced during his first sexual experience with Darlene. What was supposed to have been a healthy exploration of sexuality in the context of a community cookout—that is, a circumstance in which Cholly should have felt safe and comfortable—turned into an instance in which he was reminded of the omnipresence of white supremacy.
Ironically, Cholly doesn't feel anger toward the white men who disrupt him (or, at least, he doesn't think he does); however, he feels, or projects, his anger onto Darlene—ignoring how she, too, is being humiliated in this instance. Cholly can't bring himself to feel anger toward the white men, realizing how futile that emotion would be. He projects it onto Darlene because, within the white supremacist and patriarchal social structure in which he must exist, she is the only person who is "lower" than he.
His marriage to Pauline, which began with tenderness, has soured into a violent and contentious arrangement. Shortly before he rapes his daughter, Cholly watches her washing dishes at the sink. Pecola makes a small but meaningful gesture when she scratches the back of her leg with her big toe. Cholly watches her and is reminded of how Pauline once made a similar gesture when she was younger and they were in love.
Cholly's decision to rape his daughter results from a moment in which memories of love and tenderness are confused with memories of humiliation and trauma. Cholly never learned how to love and only understands sexuality in the contexts of humiliation and dominance. One could say the same about Pauline, whose experience of giving birth to Pecola occurred in the context of being observed by medical students. Their instructor, a doctor, pointed out how Pauline and other black women are like horses in terms of their supposed ability to give birth with ease. He says this in the midst of Pauline's typical experience of immense pain.

Cholly's never fully developed as a sexual being. This is mainly because he associates sex with violence and humiliation on account of his traumatic first sexual experience. None of this can in anyway excuse what he does to Pecola, but it does at least provide us with a possible explanation as to why he acts as he does.
Since that first sexual encounter, Cholly's never felt fully in control of this life. This is probably why he drinks so much; it's his way of finding solace in a harsh, unlivable world which has always seemed to pass him by. Despite this, Cholly still feels the need to impose himself on the world around him, to have at least some small measure of control over his life. That's why he singles out Pecola for sexual abuse. He knows that she will never laugh at him, or humiliate him, or do anything to take the whip hand away from him. She is an easy target, someone who will give him back something of the power and control that was taken away from him during his first sexual experience.

In Toni Morrison’s The Bluest Eye, Cholly Breedlove is an angry, psychologically disturbed man who takes out his rage on those who are less powerful than he.
This is traced to Cholly’s first sexual experience with Darlene, when two white men interrupted the young couple and laughed as they watched the couple have intercourse. This encounter forever cements Cholly’s perception of sex as a form of conquest and a source of shame.
Cholly’s alcoholism, as it is portrayed in the novel, doesn’t help him deal with the angst he has about his past, but rather exacerbates his rage. Pecola is the most vulnerable person to which Cholly has access. He knows she will neither fight back nor be believed if she told others about his abuse. Cholly possibly uses sexual violence to feel powerful because of his feelings of impotence in life.

sum_(n=1)^oo n/(n^4+1) Confirm that the Integral Test can be applied to the series. Then use the Integral Test to determine the convergence or divergence of the series.

sum_(n=1)^oon/(n^4+1)
The integral test is applicable if f is positive, continuous and decreasing function on infinite interval [k,oo) where k>=1 and a_n=f(x) . Then the series sum_(n=1)^ooa_n  converges or diverges if and only if the improper integral int_1^oof(x)dx converges or diverges.
For the given series a_n=n/(n^4+1)
Consider f(x)=x/(x^4+1)
Refer to the attached graph of the function. From the graph we can observe that the function is positive , continuous and decreasing on the interval [1,oo)
We can determine whether function is decreasing, also ,by finding the derivative f'(x) such that f'(x)<0 for x>=1 .
We can apply integral test , since the function satisfies the conditions for the integral test.
Now let's determine whether the corresponding improper integral int_1^oox/(x^4+1)dx converges or diverges.
int_1^oox/(x^4+1)dx=lim_(b->oo)int_1^bx/(x^4+1)dx
Let's first evaluate the indefinite integral intx/(x^4+1)dx
Apply integral substitution:u=x^2
=>du=2xdx
intx/(x^4+1)dx=int1/(u^2+1)(du)/2
Take the constant out and use common integral:int1/(x^2+1)dx=arctan(x)+C
=1/2arctan(u)+C
Substitute back u=x^2
=1/2arctan(x^2)+C
int_1^oox/(x^4+1)dx=lim_(b->oo)[1/2arctan(x^2)]_1^b
=lim_(b->oo)[1/2arctan(b^2)]-[1/2arctan(1^2)]
=lim_(b->oo)[1/2arctan(b^2)]-[1/2arctan(1)]
=lim_(b->oo)[1/2arctan(b^2)]-[1/2(pi/4)]
=lim_(b->oo)[1/2arctan(b^2)]-pi/8
=1/2lim_(b->oo)arctan(b^2)-pi/8
Now lim_(b->oo)(b^2)=oo
=1/2(pi/2)-pi/8 [by applying the common limit:lim_(u->oo)arctan(u)=pi/2 ]
=pi/4-pi/8 
=pi/8
Since the integral int_1^oox/(x^4+1)dx converges, we conclude from the integral test that the series converges.

How does Chinua Achebe, through his novel Things Fall Apart, counter the imperialist stereotypes of Africa as an uncivilized continent?

In An Image of Africa, Achebe talks at length about the grotesque and inaccurate African caricatures that inhabit the margins of Western literature and exist only to justify the condescending white narrative of the "uncivilized" continent of Africa:

Heart of Darkness projects the image of Africa as "the other world," the antithesis of Europe and therefore of civilization, a place where man's vaunted intelligence and refinement are finally mocked by triumphant bestiality (1614).

Chinua Achebe's Things Fall Apart was written in part to counteract poisonous Eurocentric depictions of Africa as a "dark" continent. Indeed, by centering the novel on the traditional warrior Okonkwo and casting white settlers as an invasive force, Achebe subverts Eurocentric expectations. One interesting section that shows that the white settlers have displaced traditional Umuofian values occurs when Okonkwo and Obierika discuss a land dispute. The white settlers installed a European judicial model in Umuofia and, in doing so, have completely upset the customs of the people. When Okonkwo asks if the white man understands Umofian culture, Obierika responds in a pointed fashion,

How can he when he does not even speak our tongue? But he says that our customs are bad. . . He has put a knife on the things that held us together and we have fallen apart (176).

Here, Achebe gives readers an often marginalized perspective. White settlers believe (perhaps sincerely) that they help "uncivilized" Africans by applying their own model of justice. Achebe shows the side often disregarded or overlooked by Western literature: he shows that this "fair and balanced" approach by white judges tosses aside decades of Umuofian customs.
Perhaps the most interesting and foreboding passage of the novel comes at the very end. After spending the majority of the novel in the native perspective, Achebe shifts the narrative focus to the white District Commissioner. The novel ends as he ponders how to work Okonkwo's story into his own book:

The story of this man who had killed a messenger and hanged himself would make interesting reading. One could almost write a whole chapter on him. Perhaps not a whole chapter but a reasonable paragraph at any rate. . . He had already chosen the title of the book, after much thought: The Pacification of the Primitive Tribes of the Lower Niger (208-9).

The ironic part here, of course, is that much more than a paragraph has already been written about Okonkwo. The arrogant District Commissioner wants to appropriate only the section that he finds interesting about Okonkwo and weave this into his own Eurocentric vision of Africa. Even the working title of his book reveals that he considers the people of the region to be monolithic, a group defined by their "primitive" nature and destined to be "pacified" by white settlers.
Thus, by writing the novel from the typically overlooked perspective of a traditional tribal man in Nigeria, Achebe subverts Western ideas about the region.
I took the passage from An Image of Africa from The Norton Anthology of Theory and Criticism, 2nd ed.

Precalculus, Chapter 6, 6.5, Section 6.5, Problem 36

You need to go from trigonometric form in standard form of the complex number, hence, you just need to simplify it replacing the values of trigonometric functions for cos (5pi/12) and sin (5pi/12) , such that:
z = 6(cos (5pi/12) + i*sin (5pi/12))
cos(5pi/12) = cos (6pi/12 - pi/12) = cos(pi/2 - pi/12) = sin(pi/12)
sin(pi/12) = sin((pi/6)/2) = sqrt((1 - cos(pi/6))/2)
sin(pi/12) = (sqrt(2 - sqrt3))/2
sin(5pi/12) = cos(pi/12) = (sqrt(2 + sqrt3))/2
z = 6((sqrt(2 - sqrt3))/2 + i*(sqrt(2 + sqrt3))/2)
z = 3(sqrt(2 - sqrt3) + i*(sqrt(2 + sqrt3)))
Hence, the standard form of the given complex number is z = 3(sqrt(2 - sqrt3) + i*(sqrt(2 + sqrt3))).

I read that interference happens for "monochromatic light" so does interference occur with white light even though it consists of many wavelengths?

Sure it does!
The reason we say it happens with monochromatic light is the formulas work well with monochromatic light. The interference bands are dependent on the wavelength of light passing through the slits. If you have a range of wavelengths passing through the slits, you will have a range of interference patterns, and the formulas you use would have a third variable.
Rainbows are similar to white light interference patterns. In a rainbow, white light passes through droplets of water acting as prisms, splitting the light into it's component colors. When white light passes through a slit, the interference patterns are all shifted slightly depending on the individual wavelength considered to be passing through.
Lets say you have a slit some distance from a wall, and lights are passing through it. Say you shine a red light through, and on the far wall you get a space 1 cm wide between the bands. Then, you swap the red bulb in your light with a green one, and repeat the experiment. Now, the bands are a different distance apart, say 1.07 cm. What do you think would happen if you shone both at the same time? You would see the two wavelengths produce their two spectral patterns. White light is just a wide range of visible lights, so this theory would extend there.

Calculus: Early Transcendentals, Chapter 3, 3.1, Section 3.1, Problem 22

Differentiate the function $y = \sqrt{x}(x - 1)$


$
\begin{equation}
\begin{aligned}
\text{We have } y &= x^{\frac{1}{2}} (x - 1)\\
\\
y &= x^{\frac{1}{2} + 1} - x^{\frac{1}{2}} = x^{\frac{3}{2}} - x^{\frac{1}{2}}
\end{aligned}
\end{equation}
$


So,

$
\begin{equation}
\begin{aligned}
\frac{dy}{dx} &= \frac{d}{dx} \left( x^{\frac{3}{2}} - x^{\frac{1}{2}} \right)\\
\\
&= \frac{d}{dx} \left( x^{\frac{3}{2}} \right) - \frac{d}{dx} \left( x^{\frac{1}{2}} \right)\\
\\
&= \frac{3}{2} \cdot x^{\frac{3}{2} - 1} - \frac{1}{2} x^{\frac{1}{2} - 1}\\
\\
&= \frac{3}{2} x^{\frac{1}{2}} - \frac{1}{2} x^{-\frac{1}{2}}\\
\\
\text{or}\\
\\
&= \frac{3}{2} \sqrt{x} - \frac{1}{2\sqrt{x}}
\end{aligned}
\end{equation}
$

College Algebra, Chapter 9, 9.3, Section 9.3, Problem 38

Suppose the first term of a geometric sequence is $3$ and the third term is $\displaystyle \frac{4}{3}$. Find the fifth term.

Since this equation is geometric, its $n$th term is given by the formula $a_n = ar^{n-1}$. Thus,

$a_1 = ar^{1-1} = a$

$a_3 = ar^{3-1} = ar^2$

From the values we are given for these two terms, we get the following system of equations:


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

3 =& a
\\
\frac{4}{3} =& ar^2

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



We solve this system by substituting $a = 3$ into the second equation


$
\begin{equation}
\begin{aligned}

\frac{4}{3} =& 3r^2
&& \text{Substitute } a = 3
\\
\\
\frac{4}{9} =& r^2
&& \text{Multiply both sides by } \frac{1}{3}
\\
\\
r =& \frac{2}{3}
&&

\end{aligned}
\end{equation}
$


It follows that the $n$th term of this sequence is

$\displaystyle a_n = 3 \left( \frac{2}{3} \right)^{n-1}$

Thus, the fifth term is

$\displaystyle a_5 = 3 \left( \frac{2}{3} \right)^{5-1} = 3 \left( \frac{2}{3} \right)^4 = \frac{16}{27}$

What does Elena want to be when she grows up?

In "American History" by Judith Ortiz Cofer, Elena wants to be a teacher when she grows up.
Having to move from Puerto Rico to America with her family was somewhat traumatic for Elena. The city of Paterson, New Jersey isn't kind to her. Her nickname at school is Skinny Bones, she isn't allowed to take advanced classes even though she has good grades because her first language isn't English, and she dreams of Puerto Rico and what life would be like there. The other people from Puerto Rico who live in her building often speak of going back to Puerto Rico to retire.
When she daydreams about her past and future, Elena thinks that "As for me, I was going to go to college and become a teacher." She is always focused on the future until she falls for Eugene and makes a connection with him. That's the first time she says her thoughts move from the future to the present.

What does Luke Stevens bring to Lyddie?

The answer to this question can be found in chapter 14. This chapter begins by narrating about the increased pace of the factory and how the various girls are responding to it. Several are not able to keep up. Lyddie is able to keep up; however, she is asked to train a new girl, Brigid. Lyddie is not happy about it, and Diana keeps pressuring everybody to sign the petition. Lyddie is averse to signing it, because she doesn't want to lose her job and her income. Money is extremely important to Lyddie. That's why the letter that Luke brings is such an important part of Lyddie's character development. The letter is from Ezekiel, the runaway slave that Lyddie helped earlier in the novel. The letter explains that he was able to escape to Canada largely in part because of the money she gave him. Included with the letter is money, with interest, to repay Lyddie's loan to him. Lyddie realizes how much she has changed. She once gave away her entire savings to a stranger, and she now struggles with sending her own mother a single dollar.

Luke Stevens is a former neighbor of Lyddie. Luke's family is Quaker, and they drive Lyddie to her work at Cutler's Tavern and Baker's Mill. Their great kindness towards Lyddie stands in stark contrast to how she is subsequently treated at her various jobs. So when Luke turns up at the factory one day, Lyddie is very pleased to see him indeed, though initially she doesn't recognize him. Luke gives Lyddie a package and tells her that all is well with her brother Charlie.
Inside the package is a letter from Ezekiel Freeman, the runaway slave that Lyddie once helped to escape. Ezekiel says that he's safely made his way to Canada and is now a free man. He was able to escape thanks to help from Luke's family—as Quakers strongly opposed to slavery—and Lyddie, who gave him the money she received from selling a calf. As a token of gratitude to Lyddie, Ezekiel encloses a bank draft for the sum of fifty dollars.

College Algebra, Exercise P, Exercise P.4, Section Exercise P.4, Problem 72

Simplify the expression $\displaystyle \left( \frac{xy^{-2}z^{-3}}{x^2y^3z^{-4}} \right)^{-3}$ and eliminate any negative exponents.

$
\begin{equation}
\begin{aligned}
\left( \frac{xy^{-2}z^{-3}}{x^2y^3z^{-4}} \right)^{-3} &= \left( \frac{x^2y^3 z^{-4}}{xy^{-2}z^{-3}} \right)^{3} && \text{Law: } \left( \frac{a}{b} \right)^{-n} = \left( \frac{b}{a} \right)^n\\
\\
&= \frac{(x^2)^3(y^3)^3(z^{-4})^3}{x^3(y^{-2})^3(z^{-3})^3} && \text{Law: } (ab)^n = a^nb^n\\
\\
&= \frac{x^6 y^9 z^{-12}}{x^3y^{-6}z^{-9}} && \text{Law: } \frac{a^m}{a^n} = a^{m-n}\\
\\
&= x^{6-3} y^{9-(-6)} z^{-12-(-9)} && \text{Simplify}\\
\\
&= x^3 y^{15} z^{-3} && \text{Definition of negative exponent } a^{-n} = \frac{1}{a^n}\\
\\
&= \frac{x^3y^{15}}{z^3}
\end{aligned}
\end{equation}
$

75 ml of a solution of HNO3 (0.0125 M) are added to 130 ml of a solution of Be(OH)2 (0.0240 M). Calculate the ph of the final solution and the volume of HCl or Mg(OH)2 to add to neutralize the obtained (final) solution. The concentration of the acid or base for the neutralization is 0.075.

This is a classic acid/base chemistry question.  First let's find the total number of moles of protons and hydroxide ions that will be present in the reaction.  First, we multiply the molarity of HNO3 (nitric acid) by the volume:
(0.0125 moles / L) * 0.075 L = 0.0009375 moles of H+
Now let's do the same thing to find the moles of hydroxide (OH-) present.  Each mole of Be(OH)2 will produce 2 moles of OH- so we need to multiply by 2:
(0.0240 moles / L) * 0.130 L * 2 = 0.00624 moles of OH-
Since the H+ will react with OH- to produce H2O, we need to see which species in present in a greater amount.  There are more moles of hydroxide present than protons, so we can subtract the numbers to find out what the excess amount of hydroxide remaining is:
0.00624 - 0.0009375 = 0.0053025 moles of OH- remaining.
We can divide the moles of hydroxide by the total volume of solution present to find the concentration of hydroxide.  The total volume of the solution is 130 mL + 75 mL = 205 mL
0.0053025 moles / 205 mL = 0.0259 M
We can convert the molarity of hydroxide ions into a pOH value by taking the negative log of the concentration via the equation below:
pOH = -log[OH-] = -log(0.0259) = 1.59
Since pH + pOH = 14, that means that we subtract the pOH from 14 to find the pH:
pH = 14 - pOH = 14 - 1.59 = 12.41
So the pH of the solution is 12.41.  The amount of a 0.075 M solution of HCl needed to add to neutralize the hydroxide is calculated below:
0.0053025 moles * (1 L / 0.075 moles) = 0.0707 L = 70.7 mL
So 70.7 mL of HCl solution would be required to neutralize the resulting solution.

Examine some of the cultural, economic, and political changes, and the reasons for these changes, in America in the late nineteenth and early twentieth century.

The period spanning the turn of the century witnessed extraordinary change in the United States. Much of this change can be attributed to the advent of industrial capitalism. This development, which focused at first on the manufacture of capital goods, led to the rise of massive corporations and trusts, such as Carnegie Steel and Standard Oil, that used innovative techniques to seize almost total control of their respective markets. Other firms producing consumer goods, including tobacco, sugar, beef, and other industries, followed suit, and by the turn of the century, the American economy was controlled by an increasingly small, but extraordinarily powerful, group of businessmen and corporations. Economically, this development accompanied the growth of a large working class that became increasingly restive as they perceived a growing gap between their earnings and those of business leaders. Another major political, cultural, and social change was the influx of millions of immigrants during the period. These "new" immigrants came from eastern and southern Europe, as well as Asia, and they came mostly seeking economic opportunity. They settled largely in urban neighborhoods, and this, combined with internal migrations, caused cities to grow rapidly in size. The urbanization of America during this period was one of its major social trends, and one that ushered in a host of new concerns that social reformers began to target. Politics was dominated by business interests, but farmers (through the Populist movement) and workers (through labor unions) increasingly sought to assert themselves politically. African-Americans were stripped of the limited political gains made during Reconstruction, and by the end of the nineteenth century, almost none could vote in the South, which established Jim Crow segregation laws to maintain white supremacy.
http://www.digitalhistory.uh.edu/era.cfm?eraid=9

What is the major conflict John Proctor faces in Act III regarding saving his wife ?

In Act III, Proctor has come to the court to argue that Abigail and the other girls are lying when they accuse others of witchcraft and pretending when they behave as though they've been bewitched.  He wants to prove his wife, and the wives of his friends, innocent, but, to do so, he will have to offer some proof that Abigail has other motives than to cleanse the community of evil.  The court's position is that God is speaking through the girls, and so compelling evidence is required to prove that this is not the case, and that Abigail is, in fact, manipulating the judges and community in order to get rid of Elizabeth Proctor.  However, in order to prove his wife's innocence and his former mistress's guilt, John will have to reveal to the world that he cheated on his wife and slept with Abigail.  He does not want to have to do this because he is deeply ashamed of his conduct and realizes the importance of reputation (this information will tarnish his reputation quite a bit).  Thus, he is conflicted about confessing the truth and saving his wife because he does not want to have to reveal his misconduct.

Intermediate Algebra, Chapter 4, 4.2, Section 4.2, Problem 36

Solve the system of equations $\begin{equation}
\begin{aligned}

x + 3 + z =& 2 \\
4x + y + 2z =& -4 \\
5x + 2y + 3z =& -2

\end{aligned}
\end{equation}
$. If the system is inconsistent or has dependent equations, say so.


$
\begin{equation}
\begin{aligned}

-2x - 6y - 2z =& -4
&& -2 \times \text{ Equation 1}
\\
4x + y + 2z =& -4
&& \text{Equation 2}
\\
\hline

\end{aligned}
\end{equation}
$




$
\begin{equation}
\begin{aligned}

2x - 5y \phantom{+2z} =& -8
&& \text{Add}

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

-3x - 9y - 3z =& -6
&& -3 \times \text{ Equation 1}
\\
5x + 2y + 3z =& -2
&& \text{Equation 3}
\\
\hline

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

2x - 7y \phantom{+3z} =& -8
&& \text{Add}

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

2x - 5y =& -8
&& \text{New Equation 2}
\\
2x -7y =& -8
&& \text{New Equation 3}

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

2x - 5y =& -8
&&
\\
-2x + 7y =& 8
&& -1 \times \text{ New Equation 3}
\\
\hline

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

\phantom{2x + } 2y =& 0
&& \text{Add}
\\
y =& 0
&& \text{Divide each side by $2$}

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

2x - 5(0) =& -8
&& \text{Substitute } y = 0 \text{ in New Equation 2}
\\
2x =& -8
&& \text{Multiply}
\\
\\
x =& -4
&& \text{Divide each side by $2$}

\end{aligned}
\end{equation}
$




$
\begin{equation}
\begin{aligned}

-4 + 3(0) + z =& 2
&& \text{Substitute } x = -4 \text{ and } y = 0 \text{ in Equation 1}
\\
-4 + 0 + z =& 2
&& \text{Multiply}
\\
z =& 6
&& \text{Add each side by $4$}

\end{aligned}
\end{equation}
$


The ordered triple is $\displaystyle \left( -4,0,6 \right)$.

College Algebra, Chapter 5, 5.4, Section 5.4, Problem 56

Find the value of $x$ to make the statement $(\log x)^3 = 3 \log x$

$
\begin{equation}
\begin{aligned}
(\log x)^3 &= 3 \log x\\
\\
(\log x)(\log x)(\log x) &= 3 \log x && \text{Expand } (\log x)^3\\
\\
\frac{\left( \cancel{\log x} \right) (\log x) (\log x)}{\cancel{\log x}} &= \frac{3 \cancel{\log x}}{\cancel{\log x }} && \text{Divide by } \log x\\
\\
(\log x)(\log x) &= 3 && \text{Cancel out like terms}\\
\\
(\log x)^2 &= 3 && \text{Simplify}\\
\\
\log x &= \sqrt{3} && \text{Take the square root of each side}\\
\\
10^{\log x} &= 10^{\sqrt{3}} && \text{Raise 10 to each side}\\
\\
x &= 10^{\sqrt{3}}
\end{aligned}
\end{equation}
$

Then by checking,

$
\begin{equation}
\begin{aligned}
\left(\log 10^{\sqrt{3}}\right)^3 &= 3 \log 10^{\sqrt{3}}\\
\\
5.1962 &= 5.1962
\end{aligned}
\end{equation}
$

In what ways might Vedantic Hinduism’s vision of Brahman and Non-duality help some of the world’s problems today (e.g., crime, conflicts and war, economic issues, environmental problems)?

The Vedas are the recorded revelations of the earliest thinkers who were at one in mind and soul with the essence of the cosmos and the essential truths of the cosmos. Their thoughts and teachings on these essential truths were recorded by the sage Vyasa hundreds of years later in book form known now as the four Vedas.
The Brahmana are the exposition sections in each of the four Vedas. Each of the four Vedas is comprised of four parts: hymns (Samhita), prose exposition (Brahmana), appendices, and the concluding theological discussions (Upanishads, or vedanta). The Brahmana are followed by the vedanta, which provide theological discussion of the Vedantic idea of Brahman (Encyclopedia Britannica).
Brahman is the name of the essential cosmological force and origin of the Vedantic truths. This essential origin and truth, this Brahman, is described as "impersonal, transcendent reality. . . the divine ground of being" (Vedanta Society). Brahman is said to have a formless, impersonal existence of purity and perfection as well as a personal existence, taking a human form as and when needed, such as in the persons of Sri Krishna (3220 B.C.) and Jesus.
Vedantic non-dualism asserts an impersonal, formless nature for Brahman. Non-dualism further asserts that the essence of the individual human soul is identical to the essence of Brahman—"The universe of beings and things is merely an appearance of Brahman in time and space. The individual soul and Brahman are absolutely non-different"—and that destructive tendencies ("bondage") stem from human ignorance of this truth while peaceful, harmonious tendencies ("liberation") stem from unfettered communion with Brahman (Johnson and McGee).
An extensive application by humankind of these precepts to today's problems may result in significant changes in action, perception and outcomes since, according to the Vedantic idea of Brahman non-duality, the problems today originate in our ignorance of the true nature of our souls. Brahmanic oneness in humankind may result in some of the following changes:
Economic: greed would be liberated from human actions resulting in the cessation of economic oppression and deprivation; those in want and need would want and need in oppression and deprivation no longer.
Environmental: ecological degradation would cease since the degradation of ecosystems, in forms such as deforestation, ocean pollution, and encroaching carbon footprints, is motivated by greed and ignorance.
War and Crime: peaceful and harmonious feelings would prevail so that impulses toward the building up of relationships and toward implementing solutions of fairness would dominate.
https://vedanta.org/what-is-vedanta/

Who is Mr. Hiram Otis?

Hiram Otis, patriarch of the Otis family, is presented by Wilde as being the quintessential American. Direct, outspoken, and down-to-earth, Mr. Otis has no time for anything that smacks of flim-flam. And flim-flam is precisely what he thinks this whole Canterville ghost business really is. Hiram is a resolutely practical man, who finds the whole notion of the supernatural to be so much nonsense.
Wilde uses the character of Mr. Otis to comic effect, highlighting the culture clash between the United States and old Europe. Otis is fiercely proud of his country's democratic heritage, which stands in stark contrast to the rigidly hierarchical class structure of British society, dominated as it is by an aristocratic elite. An illustration of this comes when Otis refuses to accept the Canterville jewels. Otis understands the importance of the jewels to the dignity of the English aristocracy, but as a firm believer in the values of republican simplicity, he cannot accept them. To him, they symbolize an effete, pleasure-loving aristocracy which is alien to traditional American values.

Mr. Hiram Otis is the father of the American family that rents Canterville Hall in England. Like the rest of his family, he is completely American. He definitely does not believe in ghosts, and when Sir Simon leaves a bloodstain by the fireplace, Mr. Otis is all for scrubbing it out using Paragon laundry detergent. Even when it becomes clear there is a ghost in the house, Mr. Otis is not afraid of it.
When his daughter Virginia wants to marry an English aristocrat, Mr. Otis is unimpressed. He also objects to her receiving the Canterville jewels as her reward for helping Sir Simon to his final rest. Aristocracy and jewels go against his sense of rugged democratic principles and the ideals of American simplicity. However, in the end, he gives in.

Calculus: Early Transcendentals, Chapter 4, Review, Section Review, Problem 3

You need to evaluate the local absolute extrema of the function, hence, you need to find the zeroes of the equation f'(x) = 0.
You need to evaluate the derivative using the quotient rule:
f'(x) = ((3x - 4)'(x^2+1) - (3x - 4)(x^2+1)')/((x^2+1)^2)
f'(x) = (3(x^2+1) - (3x - 4)(2x))/((x^2+1)^2)
f'(x) = (3x^2 + 3 - 6x^2 + 8x)/((x^2+1)^2)
f'(x) = (-3x^2 + 3 + 8x)/((x^2+1)^2)
You need to solve for x the equation f'(x) =0:
(-3x^2 + 3 + 8x)/((x^2+1)^2) = 0 => -3x^2 + 3 + 8x = 0
3x^2 - 8x - 3 = 0 => x_(1,2) = (8+-sqrt(64 + 36))/6
x_(1,2) = (8+-sqrt(100))/6 => x_(1,2) = (8+-10)/6
x_1 = 3 ; x_2 = -1/3
You need to evaluate the function at critical points:
f(3) = (3*3 - 4)/(3^2+1) => f(3) = (5)/(10) => f(3) = 1/2
f(-1/3) = (3*(-1/3) - 4)/((-1/3)^2+1) => f(-1/3) = (-5)/(10/9) => f(-1/3) = -9/2
You need to evaluate the function at the end points of interval:
f(-2) = (3*(-2) - 4)/((-2)^2+1) =>f(-2) = (-6 - 4)/(4+1)= > f(-2) = -2
f(2) = (3*2 - 4)/(2^2+1) => f(2) = 2/5
Hence, the absolute maximum of the function, on the interval [-2,2], is 1/2 and it occurs at x = 3 and the absolute minimum of the function is -9/2 and it occurs at x = -1/3.

How can I research two historical people or organizations and contrast their lives and purpose in honor of Black History Month?

The best way to begin this research is to google each option given by your teacher, and then read a little about each to find the two persons you would like to write about.
Once you determine the subjects of your research, it becomes important to determine the questions you will ask about those subjects to find out what you will write about. Luckily, your teacher provided several of those questions, making your job much easier.
You may decide to read a little more online to get to know your subjects generally, but it soon becomes important to make it to the library to search for books on your two subjects.
Armed with the questions from your teacher, as well as others you have decided are important, gather the information from books you have obtained from the library and begin to develop a narrative for each person that answers your questions, as well as the questions your teacher provided.
With that information, begin to compare and contrast your two historical persons, and formulate this into your research paper.

The good news is that your instructor gave you many options from which to choose. Now, you have to narrow your choices.
First, Google each name on your list. Google often provides a Wikipedia entry first (Wikipedia is helpful for basic information about backgrounds and is usually correct about that information), which will tell you who each person is and why they mattered. You should select a person whose background coincides with your own interests. For example, if you are interested in feminism, you might want to select a group that includes Shirley Chisholm and Audre Lorde. If you are interested in science, you might choose a group with Dorothy Vaughan, et al. The movie Hidden Figures was about those three women. While you should not use the movie as research (the movie makes some things up, as filmmakers often do), you can use films to help you generate interest, to help you understand something about the time period in which events occurred, and to start off your process of asking questions.
After you have decided on which figures to cover, go to the library and select some texts (e.g., biographies, historical texts) to ensure that you are factually correct when you talk about events, each person's actions, and the socio-political contexts in which they did their work. Be sure to make a parenthetical note showing the page numbers on which you get your information, as well as the author's name. It would look something like this: (Lewis 28). You should also make a list of each book from which you source information, including the author, title, publisher, publishing location, the year of publication, and the type of source (e.g., web, print). You will need this information for your bibliography.
Because your instructor wants a log of your research, take careful notes. Each note-taking session should be dated. Write down interesting facts, as well as the key details that your instructor requires. Find out what the adults in your life know about these people. If they do not know anything at all, mention that, too. Think about why that may be. As you learn more about each figure, think about what else you would like to know. Write down those questions.
In regard to events, your instructor seems to be asking you to record the key events that occurred during the historical figures' lifetimes. However, you may want to confirm that before moving forward with the project.
I hope this helps. Happy researching!