g(t) = t^2*2^t Find the derivative of the function

The derivative of a function f at a point x is denoted as  y' = f'(x)
There are basic properties and formula we can apply to simplify a function such as the  Product Rule provides the formula:
d/dx(u*v) = u' *v + u * v'
 For the problem:g(t) = t^2* 2^t we let :
u = t^2  
v = 2^t
Now we want to find the derivative of each function.
Recall the power rule for derivatives:d/dx(u^n)=n*u^(n-1) du/dx  
So, for u = t^2 , 
u' = 2t
Recall that for differentiating exponential functions: 
d/dx(a^u) =a^u* ln(a)*du/dx  where  a!=1 .
With the function v = 2^t , we get v' = 2^t*ln(2) *1 = 2^tln(2)
We now have:
u = t^2
u' = 2t
v=2^t
v' =2^tln(2)
Then following the Product Rule:d/(dx)(u*v) = u' *v + u * v', we get:
g'(t) = 2t*2^t + t^2* 2^tln(2)
g'(t) = t2^(t+1) + t^2 2^tln(2 )  
 
 
 
 
 

Calculus of a Single Variable, Chapter 10, 10.3, Section 10.3, Problem 31

Parametric curve (x(t),y(t)) has a horizontal tangent if its slope dy/dx is zero, i.e when dy/dt=0 and dx/dt!=0
Curve has a vertical tangent line, if its slope approaches infinity i.e dx/dt=0
and dy/dt!=0
Given parametric equations are:
x=t+4
y=t^3-3t
dx/dt=1
dy/dt=3t^2-3
For Horizontal tangents,
dy/dt=0
3t^2-3=0
=>3t^2=3
=>t^2=1
=>t=+-1
Corresponding points on the curve can be found by plugging in the values of t in the equations,
For t=1,
x_1=1+4=5
y_1=1^3-3(1)=-2
For t=-1,
x_2=-1+4=3
y_2=(-1)^3-3(-1)=2
Horizontal tangents are at the points (5,-2) and (3,2)
For vertical tangents,
dx/dt=0
However dx/dt=1!=0
So the curve has no vertical tangents.

Who comes to visit Brutus in his backyard what do these individuals want?

Act II, scene I begins with Brutus pacing up and down his yard, questioning his reasons for assassinating Caesar. He has no personal vendetta against Caesar, but seems convinced that he must kill him for the sake of the people. He is interrupted by his servant Lucius who tells him that Cassius has arrived with a group of men with “half their faces buried in their cloaks.”
Cassius introduces them as Trebonius, Decius Brutus, Casca, Cinna and Metellus Cimber. As fellow conspirators, they have come to plot the assassination of Julius Caesar.
Before they begin their discussion, Cassius wants them all to swear on an oath. Brutus, however, declines, saying

No, not an oath: if not the face of men,The sufferance of our souls, the time's abuse,—If these be motives weak, break off betimes,And every man hence to his idle bed;

They start their discussion by debating whether they should bring Cicero on board. The five men think it would be a good idea:

O, let us have him, for his silver hairsWill purchase us a good opinion

Again Brutus declines:

For he will never follow any thingThat other men begin.

Next they debate whether they should kill Anthony as well. Brutus agrees that Anthony could cause them problems, but thinks “our course will seem too bloody.”
Finally, Decius offers to bring Caesar to the capitol where the assassination will take place.

Let me work;For I can give his humour the true bent,And I will bring him to the Capitol.

However, Cassius says they will all go to meet him. They will meet again the next day at the “eighth hour.”

In Act Two, Scene 1, Cassius and the other senators conspiring against Julius Caesar arrive at Brutus's home wearing cloaks that cover their faces. The conspirators visiting Brutus's home include Cassius, Casca, Decius, Cinna, Metellus, and Trebonius. Cassius proceeds to introduce the senators conspiring against Caesar to Brutus, who politely shakes their hands. When Cassius suggests that the senators swear an oath, Brutus argues that there is no need for an oath because they are justified in carrying out the necessary task. The senators then discuss whether or not they should include Cicero in their plan to assassinate Julius Caesar, but Brutus decides against it. Cassius then suggests that they also kill Mark Antony, but Brutus argues that the Roman populace will think they are too bloody. After Decius tells the conspirators that he will convince Caesar to visit the Senate, Brutus reminds the senators to appear happy, and the conspirators go their separate ways.

Explain the title of the story "The Open Window."

The title seems to emphasize the importance of the open window in the story. It also sets a somewhat ominous tone. It suggests that something or other is going to cause trouble from the outside. Something is going to have to come in through that open window or the title wouldn't have been used for the story.
Vera takes advantage of the fact that there is a big French window standing wide open rather late on a not very warm day. The fact that Mr. Sappleton wore his white waterproof coat when he went hunting shows that the weather is overcast and threatening to rain. Vera gets Framton Nuttel's attention focused on the open window when she tells him her ghost story. The mischievous girl knows that her aunt will be sitting and looking towards the open window while she waits for her men to return for tea. 
The open window plays a prominent role in the story. It creates a reason to explain that the hunters are accustomed to leaving and departing through that window, so Framton will understand that the "ghosts" are heading straight towards him rather than entering through a side-door or backdoor in their wet clothes and muddy boots. 
The title focuses the reader's attention on the open window and gives it special and perhaps ominous significance. It dominates the setting in which the entire story takes place. Readers will remember the sight which caused Framton Nuttel to panic and flee from the house.

In the deepening twilight three figures were walking across the lawn towards the window, they all carried guns under their arms, and one of them was additionally burdened with a white coat hung over his shoulders. A tired brown spaniel kept close at their heels. Noiselessly they neared the house, and then a hoarse young voice chanted out of the dusk: "I said, Bertie, why do you bound?"

 

What factors contributed to the passage of the Civil Rights Acts of 1964 and 1965?

The passage of the Civil Rights Act of 1964 and the Voting Rights Act of 1965 were very important accomplishments of the civil rights movement. The Civil Rights Act of 1964 was something that had been proposed by President Kennedy prior to his death in 1963. However, President Kennedy didn’t help many people get elected to office in 1960, and they weren’t willing to stick their neck out on what was considered to be a very controversial bill at that time. When President Kennedy was assassinated, this changed the dynamics for this bill.
President Johnson used the assassination of President Kennedy to help get support for this bill. He told Congress the passage of this bill was a way to honor the legacy of the fallen leader. President Johnson knew President Kennedy wanted this bill passed. President Johnson had helped other elected officials in the past with programs they had wanted, and he was able to call in some favors to get this bill passed.
The nonviolent protests also helped bring about the passage of this bill. People were able to watch on television how nonviolent protesters were treated in Birmingham in 1963. They were able to see how the nine kids that tried to attend high school at Central High School in Little Rock were being treated. These events helped to sway public opinion in favor of passing this law.
The Voting Rights Act was also passed as a result of how the police treated the marchers who were protesting the lack of African-American registered voters. When people watched on television, they saw the brutal methods that the police used against the nonviolent marchers who were attempting to march from Selma to Montgomery. President Johnson was also infuriated. This led to the passage of the Voting Rights Act of 1965.
Both of these laws were major accomplishments for those who believed change could occur through the use of nonviolent methods.
https://www.history.com/topics/black-history/civil-rights-act

https://www.history.com/topics/black-history/voting-rights-act

https://www.voanews.com/usa/non-violence-was-key-civil-rights-movement

What are choices and freedoms Meursault has in The Stranger?

Throughout Camus's The Stranger the themes of choices and freedom remain pervasive. The protagonist Meursault maintains an absurdist point of view on life, feeling very minimally affected by the events of his life. His indifference allows him to exercise his free will in strange ways; when offered a potential promotion opportunity at work, Meursault simply, and indifferently, reflects,

I didn't care much one way or the other . . . I answered that one never changed his way of life; one life was as good as another, and my present one suited me quite well.

Meursault has the choice of accepting or denying the promotion, yet he neither specifically accepts nor denies it. He offers a careless response that either choice would suit him as equally well as the other.
Later, Meursault gets involved with his temperamental neighbor Raymond, whom Meursault continuously hangs around simply because Raymond demands his company and assistance. Meursault is a sort of yes-man who often goes along with what people say simply because he doesn't have a strong reason not to. He gets involved with the lovely Marie because she is interested in him, and because he feels as though he might as well go with the flow. Meursault is a free man who simply moves along somewhat lifelessly with the currents of life.

Beginning Algebra With Applications, Chapter 8, 8.1, Section 8.1, Problem 2

Explain why the statement is true.

a. The terms of the binomial $3x-6$ have common factor.

The common factor of $3x-6$ is $3$. So $3x-6 = 3(x - 2)$.

b. The expression $3x^2 + 15$ is not in factored form.

The factored form is $3x^2 + 15 = 3(x^2 + 5)$ and the common factor is $3$.

c. $5y - 7$ is a factor of $y(5y - 7)$.

The expanded form of the expression $y(5y-7)$ is $5y^2 - 7y$. That's why $5y-7$ is the factor.

What are three distinctions that underlie social science?

There is no universally accepted list of "three distinctions that underlie social science" among social scientists. The only place I've seen that specific phrase used is in the context of course materials about criminal justice research (see link below). There, it is used in the context of discussing the different forms that social science research can take. I'll frame my answer with that in mind, but what I say applies to social science in general.
1. Nomothetic versus idiographic explanation
One distinction that underlies different types of research concerns explanation. Some research is aimed at explaining a general category of phenomena. The goal is to make generalizations that apply to a wide range of cases -- to uncover general principles or laws.  This is called nomothetic explanation. An example would be attempting to explain how early childhood stress contributes to the development of poor self-regulation skills. The researcher looks for an explanation that applies to a whole class of cases (e.g., children growing up in poverty in the United States). Nobody expects the single factor (childhood stress) to explain entirely why any specific individual develops poor regulation skills. Rather, researchers are looking for a general pattern that tends to hold across a wide range of individuals.
By contrast, idiographic explanations are aimed at understanding unique causal pathways and contingencies. They are concerned with individual cases.
For instance, how did a particular child, George, end up with poor self-regulation skills? Researchers aren't looking for answers that apply to all children, or even all kids in a certain category. They want to know what unique combination of circumstances and factors led him to develop the way he did. Research with this sort of explanation as a goal often takes the form of in-depth case studies.
2. Types of reasoning used: Inductive and deductive
Some social scientists like to talk as if inductive and deductive reasoning are inverse operations. You might read about inductive being "bottom up" reasoning and deductive being "top down" reasoning. The idea is that inductive reasoning starts by looking an individual case, the details of the data, and then making guesses or inferences about patterns and causation. You go from the specific to the general. Then "deductive reasoning" is presented as being the opposite of this, because you start with a generalization you take to be true, and then determine what specific conclusions necessarily follow from it.
The problem with this characterization is that it misses what "deductive" and "inductive" really means according to the formal study of logic and the philosophy of science. What's crucial isn't "top down" versus "bottom up," but reasoning that involves reaching conclusions that follow with logical certainty versus reasoning that involves conclusions that are merely probable. Reasoning from a syllogism like "All animals have DNA; humans are animals; therefore, all humans have DNA" is deductive. If the premises are true, then the conclusion must be true. With inductive reasoning, you don't have the conclusion nailed down as logically true. It's just likely.
So all social scientists make regular use of inductive reasoning. It's what everyone uses all the time -- whenever we make inferences that aren't, strictly speaking, guaranteed to follow by virtue of logic. But having said that, you can make some distinctions between research that pays explicit attention to deductive reasoning, and research that sticks mostly to inductive reasoning. For instance, when social scientists engage in controlled hypothesis testing (like conducting experiments), they often make use of the principles of deductive reasoning. They may try to come up with predictions that follow necessarily from their hypotheses, and then set up conditions to test those predictions.
3. Types of data used - qualitative versus quantitative
Another important distinction is the type of data that social scientists collect. Quantitative data are more likely to be collected when using a more deductive, hypothesis-testing approach. Researchers using quantitative data start by defining exactly what they will measure and how they will measure it. The aim is to record information numerically or make observations that can be sorted into discrete classes (like yes/no categories). A quantitative approach to data might, for instance, measure a child's self-regulation skills in terms of how many minutes he or she managed to avoid eating a forbidden treat.
A lot can get lost when you measure only quantitative data, so some social science research emphasizes qualitative data instead. Qualitative is non-numerical; it's the descriptive information you might gather by interviewing people with open-ended questions, or observing them and recording your subjective impressions of what's going on. Case studies -- in-depth analyses of individuals -- often make use of qualitative data.
https://www.academia.edu/7460058/Quantitative_vs._Qualitative_Research_in_Social_Science

https://www.coursehero.com/file/14632528/Chapter3/

https://www.thoughtco.com/nomothetic-3026355

What are some similarities between Harper Lee's and Scout Finch's childhoods?

It is widely understood that Harper Lee based the character of Scout Finch largely around herself, so it would certainly stand to reason that they would have similar experiences in their respective childhoods.
Both were raised in Alabama, but perhaps the similarity that stands out the most between the two is that both Lee's and Scout's fathers were attorneys who defended black men, something considered extraordinarily controversial at the time. It can be inferred from this that the character of Atticus Finch is most likely heavily based upon Lee's real father.
In fact, Harper Lee's father once defended nine black men who were accused of raping two white women. Though there was medical evidence of innocence, all but one of the men were sentenced to death. This event shares striking similarities with the trial in the novel.

Harper Lee based the character of Scout on herself, so many of Scout's childhood experiences reflect similar ones in Harper Lee's own past. For example, the friendship between Scout and Dill was inspired by Harper Lee's friendship with the writer Truman Capote, whose physical description in real life resembles Dill closely. Also, Harper Lee's father was an attorney like Atticus Finch, so it is likely that family discussions around court cases involving black men like the ones at the Finch home were also inspired by real-life conversations. During the 1930s, when Harper Lee would have been a child, having been born in 1926, a real trial was underway concerning the accusation by two white women of rape by a group of young black men. The Scottsboro Trials, as they are remembered, parallel many of the details of Tom Robinson's trial in the novel.

Calculus of a Single Variable, Chapter 9, 9.2, Section 9.2, Problem 34

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

In the novel Lord of the Flies, describe the "beast" that appears to come out of the sea.

Although being on the island without adult supervision is initially an awfully big adventure for the boys, delight soon turns to fear. Here they are, stuck on a remote desert island without any immediate prospect of being rescued. Under the circumstances, it's no wonder that fear takes over. But like a lot of fear, it's completely misplaced. There is no beast on the island, but because the boys are young, immature, and superstitious, they genuinely believe that there is one.
Despite Jack's initial skepticism, he encourages the other boys to believe in the existence of the beast as he knows that this will consolidate his power over them. If the boys are in the constant grip of fear, then they'll look to Jack to be their savior, knowing just how wild and reckless he is. As the old saying goes, it takes a thief to catch a thief; and most of the boys on the island, in looking to Jack for protection, believe that they need a beast to catch a beast.

In Chapter 5, Ralph holds an assembly to discuss why the boys are not following through with the tasks agreed upon during the meetings. He then begins to address the existence of the "beast." Ralph, Jack, and Piggy firmly believe that the "beast" does not exist. Then, a littlun named Percival mentions that the "beast" lives and comes out of the sea. Percival does not go into detail about the "beast" because he passes out after commenting that it lives in the sea. The boys then begin to argue about its identity before Jack and his hunters decide to leave the meeting. While Piggy attempts to rationalize its existence by thinking scientifically, only Simon understands its true identity. The "beast" in the water is only a figment of the boys' imagination. It represents the inner fears that they feel on the uninhabited island at night. The true nature of the "beast" is the inherent wickedness in each individual. It is a not a tangible being, but rather a symbol of their inherent evil. 

College Algebra, Chapter 3, 3.7, Section 3.7, Problem 82

Suppose that a car dealership advertises a $\$ 15 \%$ discount on all its new cars. In addition, the manufacturer offers a $\$1000$ rebate on the purchase of a new car. Let $x$ represent the sticker price of the car.

a.) Suppose only the $15 \%$ discount applies. Find a function $f$ that models the purchase price of the car as a function of the price $x$.

b.) Suppose only the $\$ 1000$ rebate applies. Find a function $g$ that models the purchase price of the car as a function of the price $x$.

c.) Find a formula for $H = f \circ g$.

d.) Find $H^{-1}$. What does $H^{-1}$ represent?

e.) Find $H^{-1} (13, 000)$. What does your answer represent?



a.) The purchase price of the car is equal to the difference of the regular price of the car and the discounted price. Thus,

$f(x) = x - 0.15x = 0.85x$

b.) If only $\$ 1000$ rebate applies, then

$g(x) = x - 1000$

c.)


$
\begin{equation}
\begin{aligned}

H = f \circ g = f(g(x)) =& f(x - 1000) = 0.85 (x - 1000)
\\
\\
H(x) =& 0.85 (x - 1000)

\end{aligned}
\end{equation}
$


d.) To find for $H^{-1}$, we set $y = H(x)$


$
\begin{equation}
\begin{aligned}

y =& 0.85(x - 1000)
&& \text{Solve for $x$; divide both sides by } 0.85
\\
\\
\frac{y}{0.85} =& x - 1000
&& \text{Add } 1000
\\
\\
x =& \frac{y}{0.85} + 1000
&& \text{Interchange $x$ and $y$}
\\
\\
y =& \frac{x}{0.85} + 1000
&&

\end{aligned}
\end{equation}
$


Thus, $\displaystyle H^{-1} (x) = \frac{x}{0.85} + 1000$

If $H(x)$ represents the over all discounted price of the car, then $H^{-1} (x)$ represents the original price of the car, without discounts and rebates.

e.)


$
\begin{equation}
\begin{aligned}

H^{-1} (13,000) =& \frac{13,000}{0.85} + 1000
\\
\\
=& \$ 16,294.12

\end{aligned}
\end{equation}
$


It shows that when the discounted price of the car is $\$ 13,000$, its original price is $\$ 16, 294.12$.

When did the astrologer usually starts his day’s business?

The astrologer usually begins his day's business at noon or midday, as the story goes.
According to the text, the astrologer is always punctual; this means that, at exactly the same time each day, customers can expect to find him sitting underneath the huge tamarind tree at Town Hall Park. There, he will have his paraphernalia spread out before him: a square piece of cloth with mystic charts on it, a notebook, a stack of palmyra writing, and a dozen cowrie shells.
The astrologer will be wearing his usual saffron-colored turban, and his forehead will be smeared with sacred ash and vermilion. The text tells us that large groups of people will pass by the astrologer's station throughout the day. Perhaps, the astrologer begins his work at midday because that's when the crowds begin to swell.
From the story, we learn that the astrologer is efficient in how he conducts his business. Because of his experience, he can decipher each customer's concerns within five minutes of their initial meeting. Then, after ten minutes of his customer speaking, the astrologer will be prepared with his diagnosis and answers to anxious questions. He is always careful to present a respectful attitude, regardless of each customer's foibles and predilections. The astrologer is a clever businessman and usually earns enough money for his daily upkeep by nightfall each day.

"An Astrologer's Day," the titular story of a collection R. K. Narayan published in 1947, begins with an explanation of the astrologer's daily schedule. This is the first line of the story:

Punctually at midday he opened his bag and spread out his professional equipment. . . .

So the answer to your question is "midday," or noon. It seems a little late for a person to be starting his daily work, doesn't it? But Narayan continues to offer details of the astrologer's schedule and the circumstances of his professional life throughout the story. For instance, he describes the crowds that surround the astrologer. He sits, with his tools spread out before him, amid other vendors on a street that runs through a large park:

A surging crowd was always moving up and down this narrow road morning till night. . . .

The crowd will be there through the night, Narayan writes, and we can assume that's why the astrologer doesn't start working until noon.
Also, the story reveals, the astrologer's schedule depends on having enough light to see and to do business. The area where the astrologer works is not illuminated by municipal lighting, so the vendors are partly dependent on each other for light sources:

The nuts vendor blew out his flare and rose to go home. This was a signal for the astrologer to bundle up too, since it left him in darkness except for a little shaft of green light which strayed in from somewhere and touched the ground before him.

College Algebra, Chapter 8, 8.4, Section 8.4, Problem 34

Complete the square to determine whether the equation represents an ellipse, a parabola, a hyperbola, or a degenerate conic. If the graph is an ellipse, find the center, foci, vertices and lengths of the major and minor axes. If it is a parabola, find the vertex, focus and directrix. If it is a hyperbola, find the center, foci, vertices and asymptotes. Sketch the graph of the equation. If the equation has no graph, explain why.


$
\begin{equation}
\begin{aligned}

x^2 + 4y^2 + 20x - 40y + 300 =& 0
&& \text{Subtract } 300
\\
\\
x^2 + 4y^2 + 20x - 40y =& -300
&& \text{Factor and group terms}
\\
\\
(x^2 + 20x + \quad) + 4 (y^2 - 10y + \quad) =& -300
&& \text{Complete the square: add } \left( \frac{20}{2} \right)^2 = 100 \text{ or both sides and } \left( \frac{-10}{2} \right)^2 = 25 \text{ on the left and $100$ on the right}
\\
\\
(x^2 + 20x + 100) + 4(y^2 - 10y + 25) =& -300 + 100 + 100
&& \text{Perfect square}
\\
\\
(x + 10)^2 + 4(y - 5)^2 =& -100
&& \text{Divide both sides by } -100
\\
\\
\frac{-(x + 10)^2}{100} - \frac{(y - 5)^2}{100} =& 1
&&

\end{aligned}
\end{equation}
$


We can see that the equation has no solution since the sum of the squares can never be a negative value. Thus, the equation is a degenerate conic and it has no graph.

Calculus of a Single Variable, Chapter 5, 5.8, Section 5.8, Problem 44

Indefinite integral are written in the form of int f(x) dx = F(x) +C
where: f(x) as the integrand
F(x) as the anti-derivative function
C as the arbitrary constant known as constant of integration
For the given problem: int sec^2(3x)dx , the integrand function: f(x)=sec^2(3x) is in a form of trigonometric function.
To solve for the indefinite integral, we may apply the basic integration formula for secant function:
int sec^2(u)du=tan(u)+C
We may apply u-substitution when by letting:
u= 3x then du =3 dx or (du)/3 = dx .
Plug-in the values of u =3x and dx= (du)/3 , we get:
int sec^2(3x)dx =int sec^2(u)*(du)/3
=int (sec^2(u))/3du
Apply basic integration property: int c*f(x)dx= c int f(x)dx .
int (sec^2(u))/3du =(1/3)int sec^2(u)du
Then following the integral formula for secant, we get:
(1/3)int sec^2(u)du= 1/3tan(u)+C
Plug-in u =3x to solve for the indefinite integral F(x):
int sec^2(3x)dx=1/3tan(3x)+C

How does the author build tension?

The author builds tension in several ways. 
She begins by introducing a conflict early in the story. Accordingly, riots have erupted outside the city. The perpetrators of the riots are "people of another color." The conflict between two distinct racial groups spills over into the suburbs, where burglaries are becoming the norm. 
Next, the author divulges that trusted members who are "people of another color" are the only ones employed by homeowners in the area. Gordimer fractures the subversive group further into "trusted" and "untrusted" categories. Now, the "trusted" category of housemaids and gardeners are pitted against the "untrustworthy" in their racial group. So, there are different levels of conflict in the story. 
Another way Gordimer builds tension is by using sound and visual imagery to describe the prevailing anxieties in the characters' lives. For example, homeowners in vulnerable suburban areas must live with hi-tech alarms that often increase the tension in their lives.

The alarm was often answered-it seemed-by other burglar alarms, in other houses, that had been triggered by pet cats or nibbling mice. The alarms called to one another across the gardens in shrills and bleats and wails that everyone soon became accustomed to, so that the din roused the inhabitants of the suburb no more than the croak of frogs and musical grating of cicadas' legs. 

Also, desperate homeowners are shown to resort to extreme measures to protect themselves. These extreme measures lend a claustrophobic, threatening intensity to the story. This is another way the author builds tension.

...there was the low-cost option of pieces of broken glass embedded in cement along the top of walls, there were iron grilles ending in lance-points, there were attempts at reconciling the aesthetics of prison architecture with the Spanish Villa style (spikes painted pink) and with the plaster urns of neoclassical facades (twelve-inch pikes finned like zigzags of lightning and painted pure white).
 

Why does Conrad delay the real-time appearance of Kurtz?

When Joseph Conrad wrote Heart of Darkness, his scathing indictment of European imperialism and the exploitation of indigenous peoples it entailed, he clearly hoped to illuminate to the extent possible the physical and emotional toll exacted on conqueror and conquered alike of those practices. The character of Kurtz, a figure of almost mythological proportions as Conrad’s narrative progresses, finally makes his appearance near the end of Heart of Darkness because Conrad wanted first to illustrate the depths of depravity, racism, and greed that created Kurtz.
As Conrad’s protagonist, Marlow, embarks on his journey into the interior of the Congolese jungle, he encounters individuals along the way who progressively stoke his interest in and eventual obsession with the mysterious station agent. This interest in Kurtz, however, needs time to incubate. Marlow initially displays a distinct lack of interest in Kurtz, evident in the following conversation he has with the accountant:

One day he remarked, without lifting his head, "In the interior you will no doubt meet Mr. Kurtz." On my asking who Mr. Kurtz was, he said he was a first-class agent; and seeing my disappointment at this information, he added slowly, laying down his pen, "He is a very remarkable person."

This lack of interest in Kurtz continues as the extraordinarily productive agent continues to be the subject of admiring conversation while Marlow’s boat works its way down the river. Note in the following passage Marlow’s growing disdain for what he believes to be an increasingly ubiquitous, if unseen, presence:

There were rumors that a very important station was in jeopardy, and its chief, Mr. Kurtz, was ill. Hoped it was not true. Mr. Kurtz was... I felt weary and irritable. Hang Kurtz, I thought.

As Marlow proceeds on his journey, however, his initial lack of interest in Kurtz grows into a sense of fascination and obsession. This fascination with the figure of Kurtz is a product of the surrealistic and horrific stories Marlow hears and the scenes he personally observes. The deeper into the jungle his boat takes him, the darker and more mentally exhausting the experience. At one point, Marlow is told of another European, a Swede, who joined with innumerable others to seek fortune at the expense of the land and the peoples who inhabit this forbidding terrain:

"It is funny what some people will do for a few francs a month. I wonder what becomes of that kind when it goes upcountry?" I said to him I expected to see that soon. 'So-o-o!' he exclaimed. He shuffled athwart, keeping one eye ahead vigilantly. "Don't be too sure," he continued. "The other day I took up a man who hanged himself on the road. He was a Swede, too." "Hanged himself! Why, in God's name?" I cried. He kept on looking out watchfully. "Who knows? The sun too much for him, or the country perhaps."

Combine these tales of the mental toll taken on those who come to exploit the region’s riches with the soul-deadening appearances of the native Africans forced into brutal labor under dismal conditions and the prospect of encountering a fellow European at the end of line, who, it is revealed, has come to view himself as a god among savages, becomes too much to ignore. Kurtz is a rising star in the Company, so proficient is he at accumulating ivory on behalf of his employer, but one who has grown in stature at the expense of his own sanity. The only way Conrad could methodically illustrate Kurtz’s road to madness was through the observations and education of Marlow, the man who will become caretaker of Kurtz’s legacy. Heart of Darkness is not about Kurtz; rather, it is about the journey of a British seaman who comes to understand while traversing a long river into the Congolese jungle how morally corrupting is the policy of colonialism.

Describe how Earth's rotation affects a pendulum.

In an inertial frame of reference, it doesn't. If it's an ideal pendulum, the pendulum goes on swinging exactly as it did before. Even realistic pendulums are only slightly distorted by the effect of friction and air resistance. But we are standing on the Earth, which is not an inertial frame of reference. The rotation of the Earth under the pendulum makes the pendulum appear to change direction from our frame of reference. An apparent force (or "fictitious force") emerges, the Coriolis force, which is not a fundamental force like gravity, but a result of using a rotating frame of reference. This force is proportional to the velocity of the pendulum and the rotation of the Earth, and acts in a direction perpendicular to the pendulum's motion.This force is very small, because the Earth's rotation is not very fast (2pi radians per day by definition). But it can be measured, and if you leave a good pendulum swinging back and forth over the course of a day and mark its movements you can see how the motion will precess around in a circle.

College Algebra, Chapter 4, 4.2, Section 4.2, Problem 40

Factor the polynomial $P(x) = x^6 - 2x^3 + 1$ and use the factored form to find the zeros. Then sketch the graph.
Since the function has an even degree of 4 and a positive leading coefficient, its end behaviour is $y \rightarrow \infty \text{ as } x \rightarrow -\infty \text{ and } y \rightarrow \infty \text{ as } x \rightarrow \infty$. To find the $x$ intercepts (or zeros), we set $y = 0$.


$
\begin{equation}
\begin{aligned}
0 &= x^6 - 2x^3 + 1\\
\\
0 &= w^2 - 2w + 1 && \text{Let } w = x^3\\
\\
0 &= (w-1)^2 && \text{Perfect Square} \\
\\
w &= 1 && \text{Substitute} w = x^3\\
\\
x^3 &= 1
\end{aligned}
\end{equation}
$



Thus, the $x$-intercept are $x = 1$

How does Achilles act in the Underworld?

Achilles's shade in the underworld is virtually identical to Achilles the mortal warrior. He's a proud, surly character completely at odds with his surroundings. Even though he's by far the most important shade in the underworld, he still hates the place with a passion. Odysseus is surprised that such a great hero, someone who achieved such remarkable feats of bravery on the field of battle, could possibly be so utterly miserable. But Achilles has seen heroism and its consequences from both sides, and so has a much deeper understanding of what it entails than the mortal Odysseus. Almost uniquely among the veritable cast of thousands in The Odyssey, Achilles challenges the dominant notion of heroism and its allied notion of glory. There's nothing glorious about Hades for Achilles, for as he tells Odysseus:

By god, I'd rather slave on earth for another man—some dirt-poor tenant farmer who scrapes to keep alive—than rule down here over all the breathless dead.

Achilles is dead by the time the action of the Odyssey takes place. Odysseus therefore meets Achilles when he visits the underworld. Just as he was when he was alive, Achilles is moody and brooding. He tells Odysseus that it is terrible to be a shade in the land of the dead. Even a revered ghost like him finds no solace in his fame. Achilles tells Odysseus that it is better to be a nobody, even a landless peasant, in the land of the living than a famous hero among the dead.
When we knew him in the Iliad, Achilles was a gloomy and ill-tempered teenager. Little has changed now that he is dead, other than that he does not boast like before. Gone are his pride and arrogance. Perhaps death has given him perspective that fame and glory are not the achievements that should be coveted most. Even though Odysseus does his best to cheer up Achilles, the dead warrior acts as despondent as in the Iliad when Agamemnon takes away Briseis, his war prize. Only now, instead of being angry, Achilles has resigned himself to being in this sorry state for all eternity.

Odysseus' meeting with Achilles in the Underworld is perhaps my favorite part of The Odyssey, as it's one of the most thought-provoking moments in the poem. When Odysseus meets Achilles during his visit to the Underworld, the ghost of Achilles tells the king of Ithaca that death is terrible. In fact, Achilles says, he would rather be a living, breathing, normal person than a famous but dead hero. 
This moment is intriguing because Achilles specifically chose a short but glorious life in favor of a long but unremarkable one. Getting what he wished for, Achilles became renowned as the greatest warrior who ever lived, but he also died on the battlefield at Troy. As such, it would appear that Achilles regrets his decision, and that he specifically regrets his decision to value fame and glory over all else. Thus, when Odysseus sees Achilles in the Underworld, the ghostly warrior seems to question the whole enterprise of yearning for a mythological reputation. This notion seems to undermine the whole point of epic poetry (which essentially celebrates the larger-than-life deeds of heroes), and so it serves as a surprisingly subversive philosophical point. Perhaps, Homer seems to suggest, it would be better to avoid idealizing the blustering heroes of The Iliad and The Odyssey, as the life of epic poetry is not as glamorous as it seems.

Why did the Liberal landslide of 1906 catch people by surprise? What were the Liberal issues that attracted voters to the Liberals? Why? Did the issues have anything in common, or was it an accidental convergence of unrelated issues that led to Liberal victory?

The main issue at the 1906 General Election was free trade. The governing coalition of Conservatives and Liberal Unionists was split down the middle by the issue. Some argued for free trade, but others like Joseph Chamberlain favored protectionism, or Tariff Reform as it was called. The Liberals were able to exploit divisions in the governing coalition, maintaining a consistent position on the issue of free trade. They argued that free trade would keep prices low, especially for basic goods such as bread. This proved to be a particularly attractive measure for the working poor and lower middle-classes.
The Conservatives had been in power for quite some time, and inevitably many thought that it was time for a change. Although free trade was the main issue during the election campaign, it was not the only one. There was a general sense that the country was facing a number of pressing problems which urgently needed to be addressed, and that the Unionist coalition had neither the energy nor the ability to deal with them.
The Unionists had benefited greatly from patriotism during the height of the Boer War. But the aftermath had revealed some uncomfortable truths about the conflict. The use of concentration camps by the British to house Boer civilians was hugely controversial, especially among the educated middle-classes. And the appalling physical condition of many British Army recruits highlighted the terrible effects of urban poverty and undernourishment.
The Liberals were able to win their landslide by successfully building a coalition of different interest groups—labor unions, working people, Non-Conformists, educated professionals—that proved unbeatable. On almost all the major issues, whether it was free trade, the Boer War, or national education policy, the Liberals were able to appeal to a much wider base of support than the Unionists.
Though different in some respects, the various issues highlighted during the 1906 campaign all had one thing in common—they struck a chord with each and every sector of the Liberal Party. The Party had been a rather unstable coalition of interests for a number of years, and it was this very instability which had ensured Tory dominance in government. Yet the key issues of the 1906 campaign came together fortuitously for the Liberals, allowing them—temporarily at least—to reunite the disparate elements of their coalition to form a united front against a different kind of coalition—the Unionist coalition—that had become even more fractious and unstable than the Liberals had been in the recent past.

How would you explain the poem "The Gardener" by Robert Louis Stevenson?

"The Gardener" by Robert Louis Stevenson is a poem from the collection A Child's Garden of Verses. It is written for an audience of children. The narrator of the poem is a young boy. We can tell that he is of the upper middle or upper classes as his family can afford a large garden, a gardener, and a cook. 
The young boy wants to live in the moment and play and seems quite disappointed that the gardener is focused on his job and does not want to chat or play. Although Stevenson does not put it in these terms, we can see this as an example of a certain type of entitlement or privilege of a young, well-off boy whose perspective is quite narrowly limited to his own desire to be entertained. The boy resents the rules and necessities of the adult world.
The poem is organized into five quatrains rhymed AABB. The meter of the poem is iambic tetrameter. Generically, it is a "carpe diem" poem, arguing for enjoying the nice weather before the winter. As with the traditional carpe diem poem, which urges a woman to yield to sexual advances of a lover because life is short, the arguments appear on the surface plausible until one thinks about real consequences. Just as the young maidens who yielded up their virtue risked social ostracism, diseases, and pregnancy, so the gardener, if he stops working to play or leaves the shed unlocked so that the tools might get damaged or stolen, risks losing his job and livelihood. The gardener, after all, is not a spoiled rich child but a hardworking man in economically precarious circumstances (servants were not well paid in this period). Thus while a child reading the poem might sympathize with the narrator, as adults we can see that the actual situation is not simply one of adults being boring but of adults having responsibilities and of actions having consequences.

"The Gardener" is written from the point of view of a child regarding a serious and somber gardener. The gardener does not talk as he works, and he makes the child stay on the walk rather than treading in the flowers. As soon as he has finished his work, the gardener locks the door to the garden so that the child cannot play there. The child sees the gardener working behind the currant row, where only the cook is allowed to gather currants (a kind of berry) for cooking. The gardener appears serious. In the third stanza, the gardener devotes himself to digging flowers and cutting hay without any inclination to speak or play. In the last two stanzas, the child rebukes the gardener for being so serious. The child says that in the winter, the gardener must put down his barrow, when everything has stopped growing. Therefore, the gardener should enjoy the summer and spend time playing with the child. This poem is in part about how children regard adults as far too serious and also about the way in which adults might heed children's advice to play more when they can. 

In The Brief Wondrous Life of Oscar Wao by Junot Diaz, what is the relationship like between Lola and Max?

Lola is the sister of Oscar, the main character in The Brief and Wondrous Life of Oscar Wao. Lola is Oscar's older sister and, as such, she is very protective of him. This behavior is a stark contrast to the way she interacts with other characters in the story, including the minor character of her ex-boyfriend, Max.
At the beginning of the narrative, Lola announces that she broke up with her boyfriend Max at the same time that she chose to drop out of school. Although she does not go into detail about the breakup, it is the beginning of a self-destructive period for her character. Soon after the breakup, she sleeps with the father of one of her classmates for $2,000. Lola's conflicted feelings about Max become evident after his death. Max is killed in a jaywalking accident and Lola gives the $2,000 to his family to help them after the loss.
Despite his relatively minor role in the story, Lola's relationship with Max gives the reader significant insight into her character. When Lola breaks down on a plane after Max's death, her facade of strength is momentarily broken, revealing the vulnerability underneath.

In the book Johnny Tremain, what metaphor does the author use to describe Percy's brigade?

As the other educator wrote, Percy's brigade is compared to a dragon as it marches toward Concord from Boston. This metaphor calls out several elements. First of all, it evokes the image of a long train on the move. Percy's brigade is made up of over seven hundred infantry soldiers, and it would have stretched on for quite some distance. Dragons are also a symbol of the English. Therefore, it is a fitting metaphor. Dragons represent the strength of Great Britain. The English army was a highly disciplined fighting machine. In order to be effective, each individual soldier was trained to act as just one small part of a larger fighting unit. By comparing Percy's soldiers to one singular beast, Esther Forbes is highlighting the discipline and unified fighting strength of the British soldiers.

After the battle had begun between the rebels and British forces, Percy's brigade marches to Lexington and Concord from Boston. The author writes, "the heavy dragon marched on its thousands of feet," and, later, she describes the brigade as "this great scarlet dragon" (page 224). She uses the metaphor of a dragon to describe Percy's brigade. Johnny Tremain notes the force and perfection of the brigade as they pass--the way in which every button is sewed onto their uniforms properly and every buckle is in the right place. Every box of cartridges holds just the right number of cartridges, and every musket also has a bayonet. Every horse has four shoes. The army, clad in scarlet, looks so powerful and perfect that Johnny is afraid about what they will do to the "untrained, half-armed farmers" (page 224) who are defending Lexington and Concord. 

A molecule of roughly spherical shape has a mass of 6.10 x 10-25 kg and a diameter of 0.70 nm. The uncertainty in the measured position of the molecule is equal to the molecular diameter. What is the minimum uncertainty in the speed of this molecule? (h = 6.626 x 10^34 J • s) The issue is there seems to be a similar question that is asking for just the minimum speed not the minimum uncertainty in the speed and those are clearly different because I found two answer keys with those different questions and different answers. For minimum speed it should be .2 m/s For minimum uncertainty in speed choices are A) 78 m/s B) 7.8 m/s C) .78 m/s

I asked the professor .7759 is correct

Hello!
This problem is similar to the previous. The uncertainty principle states that both position and velocity of a particle cannot be measured exactly. Mathematically,
Delta p*Delta x gt= bar h/2,
where p is for impulse (momentum), which is equal to m*v, mass by velocity, and x is the position. Correspondingly, Delta p means uncertainty of measuring momentum and Delta x  means uncertainty of measuring position. Obviously Delta p = m*Delta v.
bar h is the so-called reduced Planck's constant, h/(2 pi). Therefore the minimum uncertainty in the speed is
Delta v = h/(4pi)*1/(m*Delta x).
All quantities are given, so the numerical result is
Delta v approx (6.626*10^(-34))/(4*3.14)*1/(6.10*10^(-25)*0.7*10^(-9)) =(6.626)/(4*3.14*6.10*0.7) approx0.1235 (m/s).
I took into account that nano- means 10^(-9).
To obtain the result you want one should "forget" to divide by 2pi, then it would be about 0.7759 m/s, C. But I'm almost sure about the values.
The second question, about the minimum speed, requires a separate consideration.

Single Variable Calculus, Chapter 2, 2.5, Section 2.5, Problem 3

(a) Given the graph of $f$, state the numbers at which $f$ is discontinuous and explain why.










Referring to the graph of $f$, the graph is discontinuous at number -4 because $f(-4)$ is not defined. Also, the function is discontinuous at -2 and 2 because
the left and right hand limits are different. Lastly, the graph is discontinuous at number 4 because of infinite discontinuity.

(b) Determine whether $f$ is continuous from the right, or from the left, or neither from the numbers stated in part (a)

Referring to the graph, the function is continuous from left at $x = -2$ and $x=-4$.
Also, the function is continuous from right at $x = 2$ and $x = 4$

What symptoms does Henry show?

Henry comes back from the war a different man. While before he was talkative and full of fun energy, now he spends most of his time alone and quiet. Also, he is restless and jumpy. These changes in Henry’s character are described by the narrator of the story, who is also Henry’s baby brother, Lyman. In fact, Henry changes so much that his family worries about his state of mind. They think that he should see a doctor, but are not decided about what medical facility they should take him to, as the reservation does not have Native American doctors.
The story starts with a description, given by Lyman, of Henry’s life before he left for the war. From this description, the reader learns that Henry was a normal, easygoing Native American man who loved to have fun. For instance, when Lyman and Henry see a red convertible during a trip in town, the brothers decide to use up all their savings, which they’ve carried with them, to purchase the car. Afterward, the two take trips to all kinds of places in the car and have lots of fun too. The Henry after the war rarely laughs, and when he does, it “sounds more like he is choking.” He is strung up and cannot relax no matter how much he tries to. A description is given of how he sits on his chair: “he sits in his chair, gripping the armrests with all his might as if the chair itself is moving at a high speed.” Since Lyman remembers how much his brother loved the car, he tries to use it to “bring back the old Henry.” However, his trick fails, as he loses his brother in the end.

Under what situations can Congress conduct investigations and delegate authority to administrative agencies?

According to the House of Representatives website, the Constitution does not outline specific powers of investigation for Congress, but instead notes:

“All legislative Powers herein granted shall be vested in a Congress of the United States, which shall consist of a Senate and House of Representatives” (Article I, section 1).

In other words, Congress has the legislative power to pursue investigations as it sees fit. This is why there are congressional hearings for everything from jaywalking to opioid abuse to elections. Congress has the right to form committees, with investigations typically falling under the purview of a particular committee. The House Oversight Committee for example, which is a standing committee that has existed since the early 1800s, investigates how federal dollars are spent by recipients. Special committees may also be convened from time to time, such as the Special Committee to Investigate Pearl Harbor or the Special Committee to Investigate 9/11.
When it comes to administrative delegation, things become a little more complicated. The Supreme Court has wrestled with Congressional delegation powers for hundreds of years, with one of the more recent examples being the SCOTUS rulings on the Affordable Care Act, a.k.a Obamacare. The 2012 rulings determined that the individual mandate for healthcare was, in fact, constitutional due to Congress' power to make laws regarding taxation. Because Congress passed the ACA into law, which was within their purview, the SCOTUS affirmed Congress's power regarding taxation.
In short, when Congress feels out of its depth, that its resources will be insufficient, or that an issue has created a conflict within the legislative body, it has the power to delegate authority to outside agencies.

What do you think "The Gift of the Magi," written a century ago, has to say about our consumer society today?

I would argue that “The Gift of the Magi,” by O. Henry, can suggest to us that our consumer society is too focused on material things. It suggests that we should be less materialistic and more interested in our human relationships.
In this story, Della and Jim have very little money. They are so poor that they cannot afford to buy one another Christmas presents. However, each wants the other to have something material. Jim wants Della to have the combs for her hair while she wants him to have a fob for his beloved watch. Jim sells his watch to get the combs while Della sells her hair to get the fob. Neither of them, therefore, ends up able to use what the other gives them. Even so, they are very happy because they realize how much they love one another and how much more important their love is than their material possessions.
We can say that this story is telling us that we are too materialistic. We want all sorts of material things. We care more, arguably, about these material goods than we care about the people around us. “The Gift of the Magi” can suggest to us that we in modern society should change our priorities. It can suggest that we should be like Jim and Della after they exchange their presents. We should realize that the relationships we have with other people are much more important than any of the material goods we are so eager to acquire.

What is the summary of chapters 20 and 21 in Monkey by Wu Ch'eng-en?

In Chapter 20 of Monkey, the prince hears from his mother that the king hasn't been himself for the past three years. The Prince returns to the priest Tripitaka and enlists Monkey to retrieve his drowned father. Monkey coerces Pigsy into assisting him. Pigsy collects the King from the Dragon. In Chapter 21, Monkey and Pigsy take the resuscitated King back to Crow-cock to displace, capture and punish the imposter king. They discover that the imposter had been sent there three years ago as retribution for a crime committed by the true king.
In Chapter 20, during an emotional reunion, the prince's mother confesses that she has for three years wondered about the nature of her husband (his father, the King) who seemed, three years ago, to have suddenly changed so much. Having Tripitaka's story about an imposter king confirmed, the prince returns to him and requests Monkey's assistance in rescuing the true king from his underwater grave. Monkey--who displays his magical powers for the prince--tricks Pigsy into coming along to help by promising him full possession of treasure "worth more than an army of ten thousand men."
After Monkey provides the prince with plenty of game to fulfill the hunt he earlier told the imposter king he was going on (without game, the king might accuse and imprison him), then, when Monkey and Pigsy arrive at the banana-plant and find the well under a "slab of stone," Pigsy is lowered into the well by Monkey's magically stretched cudgel. After more of Monkey's trickery, Pigsy consents to dive down to find the "treasure," which is really the drowned king. On the other side of a guarded under-water portal, Pigsy talks to the "Dragon King of the Well" in his "Crystal Palace."
Pigsy refuses to carry the king--who has been preserved for three years by the Dragon King through a magical pearl--out of his death chamber (because he won't be paid a fee), but the Dragon ejects the king's body along with Pigsy and, upon the Dragon's removing the magical "water-fending pearls," the gate to the Crystal Palace vanishes. Monkey forces Pigsy to bring up the body, which, as Monkey confirms, has been for three years wonderfully preserved by the magical pearl. They return to the temple "to show him to Tripitaka." Pigsy, feeling "very ill-used" by Monkey "thought of a plan to revenge himself," which will make things worse for Monkey later when Tripitaka, tricked by Pigsy, gives Monkey a "head-ache spell."
In Chapter 21, despite the feud Pigsy carries on against Monkey, Tripitaka supervises while Monkey--with the power of Lao Tzu's "Nine Times Sublimated Life Restoring Elixir" from the "Trayaśimstra Courtyard of the heavenly palace of Quit Grief" in the "thirty-third heaven"--restores the king through the breath of life. 

Monkey stepped forward, and putting his wide mouth against the Emperor’s lips he blew hard into [the king's] throat.

The three, Monkey, Tripitaka and vengeful Pigsy (with Sandy also), take the true king, now called the "Emperor," on his journey back to Crow-cock. After an emotional entrance to the city (without the "five hundred priests in gorgeous procession, blowing conches"), the false king questions their papers and motives, though they are saved by Monkey's magic and by the prince of Crow-cock who speaks for them. Monkey now has his chance to triumphantly disclose that they have with them the true king and that the one on the throne is an imposter!

I raised him from the dead and restored him to life without hurt or harm. He earnestly begged to be admitted to our faith, and act as carrier on the road, to join with us in our quest and journey to the Western Land. The false king who sits on the throne is that foul magician; he that now carries our load is Crow-cock’s rightful king!

A battle ensues between Monkey and the shape-shifting wizard imposter, who turns himself into the image of Tripitaka. With the help of deities Monkey magically summons, he avoids slaying his priest master and pursues the imposter to the clouds, where a second recitation of the "head-ache spell" separates the imposter from the real Tripitaka. Just as Monkey is about to victoriously end the fight, Bodhisattva Manjuśrī appears commanding Monkey to stop. In a magic mirror Bodhisattva shows that the false king and wizard is really Bodhisattva Manjuśrī’s lion, which he rides upon.
Bodhisattva reveals that the true king had three years ago thrown a disguised Bodhisattva (disguised as a begging priest) into the river to die, but Bodhisattva had then been rescued by "a guardian spirit" after three nights. When he afterward complained to Buddha about what the king had done, Buddha sent the lion as a wizard to replace the king and throw the king in the well for three years as retribution. Monkey, now satisfied with the reason for the imposter's role and that the imposter never hurt anyone (including the king's wives), allows Bodhisattva to take the lion and leave.

‘Very well then,’ said Monkey. ‘Take him away. If you had not come just in time, he’d have been dead by now.’ Manjuśrī then recited a spell and said, ‘Creature, back to your true shape and look sharp about it!’ ... [Bodhisattva] Manjuśrī, putting down the lotus that he carried in his hand, harnessed the lion, mounted him and rode away over the clouds.

[Image: Wu Cheng'en (Ch'êng-ên) (United States public domain).]
https://www.britannica.com/biography/Wu-Chengen

Describe Charles Darwin's theory of evolution by natural selection.

Charles Darwin (1809-1892) first proposed the idea of evolution, which says that species of living things change over time. Darwin focused on the effect that environmental conditions have on the makeup of a population and the characteristics of individuals, which we call natural selection. Natural selection is not the only mechanism of evolution; biologists today recognize that another effect, genetic drift, also results in changes in a population or species over time.
An important thing to remember about natural selection is that individuals do not adapt; a population or species does. Individuals can be more or less successful under the existing environmental conditions. "Success" in natural selection is all about reproduction. The most successful individual is the one that has the most progeny. Some individuals will not only survive, but attract mates, be fit enough to reproduce, and produce maximum numbers of progeny. Others may produce only a few progeny, may barely survive but without the surplus of energy needed to reproduce, or may die before reaching reproductive age.
Offspring of the most successful individuals will be over-represented in the next generation. Assuming that the successful parents passed on some of all of the traits that made them successful, these offspring will continue to be more successful than their contemporaries, and will in turn be over-represented in the next generation. Over succeeding generations, the population as a whole includes more and more individuals who have the "successful" traits, and, as a whole, the population comes to resemble those individuals.
Today we know a great deal about genetics, DNA, and the mechanisms by which traits are inherited, which Darwin did not. But he did know that offspring tend to resemble their parents, which was enough for him to elucidate his theory.
Two things that are necessary for natural selection are (1) diversity or variation within a population and (2) some environmental condition that favors one trait or set of traits over another.
https://www.biography.com/scientist/charles-darwin

How does the poet use allusion in this poem?

Byron uses allusion in this poem to create a sense of place and to generate an understanding of whose side God is on in the battle. He references "the blue waves" in "deep Galilee," which the reader would understand as a reference to the Galilee where Jesus was born. The Biblical allusions continue in the third stanza when the poet describes how "the Angel of Death . . . breathed in the face of the foe," a striking image which suggests that the "foes" are subjected to the power of God acting upon them.
The final stanza demonstrates the most consistent use of allusion, with the poet referencing several notable "heathen" cultures from the Old Testament who suffer at the hands of God (whom they disavowed): the worshippers of Baal and the Gentiles (non-Jews, people who were not the promised children of God) were "melted like snow" in the eyes of God, who did not smile upon them. The widows of Ashur, also, are set wailing in pain. Ashur was an East Semitic god, another opponent of the Lord whose power is clearly nothing compared to his.

How do I solve for X and Y when Y = log_3(6) and X = log_6(5)? The question asks me to express log_3(10) in terms of Y and X. What do they mean when they say "express"?

Hello!
"Express" something in terms of X and Y means to find an expression (formula, rule) that gives this "something" as a result of operations on X and Y. The example of a formula is  X+2Y.
Denote the number in question  log_3(10)  as Z.
Then we need to "solve for Z", not "solve for X and Y".
To do this, we need some properties of logarithms:
log_a(b*c) = log_a(b) + log_a(c),  (logarithm of a product)
log_a(b/c) = log_a(b) - log_a(c),  (logarithm of a quotient)
log_a(a) = 1,
log_b(a) = (log_c(a))/(log_c(b))  (change of a base),
log_a(b) = 1/(log_b(a))   (a consequence of change of a base).
Then we can state that:
log_3(10) = log_3(2*5) =   (log of a product)
= log_3(2) + log_3(5) = log_3(6/3) + log_3(5)   (log of a quotient). Also I am rewriting 2 as 6/3 since 2 = 6/3
=log_3(6) - log_3(3) + log_3(5) =   (change of a base)
= Y - 1 + (log_6(5))/(log_6(3)) = Y - 1 + X*log_3(6) =   
= Y - 1 + X*Y.
This is the expression we need.
http://dl.uncw.edu/digilib/Mathematics/Algebra/mat111hb/EandL/logprop/logprop.html

Old Man Fat keeps threatening Chee with the government man in town. "Who" is the government man, and why would he have any power over Chee?

From the story, the "government man" quite possibly refers to the state authorities (who are usually backed by the courts in cases involving domestic conflicts). Old Man Fat is saying that government officials have the jurisdiction to decide who Chee's daughter lives with, and he's warning Chee against taking his daughter by force. Old Man Fat's implication is that Chee could be arrested or prosecuted if he tries to get his own way.
Chee knows that the authorities in his own tribe would side with Old Man Fat, and his father-in-law knows this as well. After all, the tradition has always been that a daughter belongs to her mother's people. Because of this, Chee feels that he has little hope of getting his daughter back no matter which authorities decide his case.

He would have to give his daughter up if the case were brought before the Headman of Little Canyon, and certainly he would have no better chance before a strange white man in town.

In the end, Chee comes up with a novel way to change his father-in-law's mind. He plants two fields: a large one, filled with corn, pumpkins, and squash, and a smaller one, filled with onions, carrots, and chili peppers. At the end of the summer, he reaps a bountiful harvest and ties bulging packs of food across two pack ponies to take to his in-laws. When he sees Old Man Fat again, he notices that the older man has lost some of his previous cockiness.
Apparently, the trading post has closed, and Chee's in-laws are now struggling financially. The story ends with Chee unloading a winter's worth of food in his in-laws' home; with the food, he manages to reclaim his daughter from her grandparents.

How did Gulliver land on the beaches of the strange new land?

In Gulliver’s Travels by Jonathan Swift, Gulliver begins his story with a little about his background. He was the middle boy of five sons and was taken in as an apprentice to a London surgeon. With money Gulliver received from his father during his apprenticeship, he studied navigation. The surgeon he apprenticed for introduced him to Captain Pannel, who allowed Gulliver to accompany his crew on voyages. Eventually, Gulliver married and gained an offer to journey on the Antelope to the South Sea.
On this journey, the ship was overtaken by a storm and driven into rocks. Gulliver swam to the nearest shore. There, he found no houses or inhabitants. Feeling exhausted, he opted to stop for the night and sleep in a patch of grass. When he woke up, he found his legs and arms tied to the land. He saw tiny creatures measuring about half a foot in height. Dozens of others surrounded him. This kicked off his adventures in the land of Lilliput. It was on Lilliput that his adventures with the tiny Lilliputians began.

Who is Scout describing in the quote "he was the most boring child I had ever met"?

Scout is referring to Francis, one of her distant relatives. He's not distant enough as far as she's concerned, given that he's such a frightful bore. Francis is Aunt Alexandra's grandson, and he has clearly been spending a lot of time round his granny because he's picked up on her disapproval of Atticus's representing Tom Robinson in court. When Atticus takes his children to Finch's Landing, Scout's not exactly thrilled to see Francis there. She's even less thrilled when Francis starts taunting her. Not only does he call her good friend Dill a "runt," for good measure he also says that Atticus is a "n****r lover" on account of his agreeing to be Tom Robinson's defense attorney.
Scout doesn't take this lying down. She curses Francis and proceeds to give him a well-deserved pasting. She's so mad at him that she has to be pulled off by members of the family. The whole episode illustrates once again just how hard it is for Scout to control her temper. It also shows us that she won't tolerate insults against the people she cares about most.

Who are the characters in Oliver Optic's Rich and Humble?

There are a number of characters in Rich and Humble, including Bertha, Richard, Mr. Grant, Mr. Grayle, and Mr. Sherwood. Each of them has an impact on Bertha at some point during the story.
Bertha is the protagonist of the story. After her home and her family are taken from her by Mr. Grayle, she sets out to prove their innocence and reclaim her home and fortune. She is honorable, dignified, intelligent, and kind. She's very loyal to her family and believes in her father's innocence. Through her actions, the family is able to regain their former wealth.
Richard is Bertha's brother. He's a trial to the entire family. He drinks, creates problems, and can't be trusted. He's reckless—even at the end of the book, he isn't reformed. 
Mr. Franklin Grant is a loving father who mourns his deceased wife. He goes to jail for fraud, even though he is innocent. When Mr. Grayle accuses him of fraud, he gives him the deed to Woodhill while he raises the money to pay him back—even though he isn't obliged to. He does it so others won't question his honor.
Mr. Samuel Grayle is the man who frames Mr. Grant and takes over Woodhill, the Grants' home. He blames Mr. Grant for a deal that went bad and accuses him of fraud. When Mr. Grant gives him the bill to Woodhill as collateral, he sends the police to arrest Mr. Grant and takes possession of the estate.
Noddy Nodderson is an orphan who lives in the Hollow. He takes care of himself but is wild, disreputable, and prone to trouble. 
Master Charley is the young child at Blue Hill, where Bertha works as a governess. He is a difficult and spoiled child.
Mrs. Byron is the mistress of Blue Hill and Master Charley's mother. She fires Bertha when she discovers that her last name is Grant, not Loring, and that her father is in jail for fraud.
Peter is the head groom at Blue Hill. He offers Bertha a place to stay when she loses her job as a governess. 
Mr. Sherwood is Mr. Grant's clerk. He sleeps at the office in New York City and has proof of Mr. Grant's innocence. He tells Bertha he's waiting to get the evidence before the court and staying in the office to protect it all in the meantime.

College Algebra, Chapter 9, 9.5, Section 9.5, Problem 6

Prove that the formula $\displaystyle 1^2 + 2^2 + 3^2 + ... + n^2 = \frac{n (n + 1)(2n + 1)}{6}$ is true for all natural numbers $n$.

By using mathematical induction,


Let $P(n)$ denote the statement $\displaystyle 1^2 + 2^2 + 3^2 + ... + n^2 = \frac{n (n + 1)(2n + 1)}{6}$

So, $\displaystyle P(1) = \frac{4 (1 + 1)(2(1) + 1)}{6} = \frac{(2)(3)}{6} = \frac{6}{6} = 1$. Thus, we prove the first principle of the mathematical induction.

More over, assuming that $P(k)$ is true, then $\displaystyle 1^2 + 2^2 + 3^2 + ... k^2 = \frac{k (k + 1)(2k + 1)}{6}$

Now, by showing $P(k + 1)$, we have


$
\begin{equation}
\begin{aligned}

1^2 + 2^2 + 3^2 + ... k^2 + (k + 1)^2 =& \frac{(k + 1) [(k + 1) + 1][2 (k + 1) + 1]}{6}
\\
\\
1^2 + 2^2 + 3^2 + ... k^2 + (k + 1)^2 =& \frac{(k + 1)(k + 2)(2k + 3)}{6}
\\
\\
1^2 + 2^2 + 3^2 + ... k^2 + (k + 1)^2 =& \frac{(k^2 + 3k + 2) (2k + 3)}{6}
\\
\\
1^2 + 2^2 + 3^2 + ... k^2 + (k + 1)^2 =& \frac{2k^3 + 6k^2 + 4k + 3k^2 + 9k + 6}{6}
\\
\\
1^2 + 2^2 + 3^2 + ... k^2 + (k + 1)^2 =& \frac{2k^3 + 9k^2 + 13k + 6}{6}
\\
\\
1^2 + 2^2 + 3^2 + ... k^2 + (k + 1)^2 =& \frac{1}{3} k^3 + \frac{3}{2} k^2 + \frac{13}{6} k + 1

\end{aligned}
\end{equation}
$


We start with the left side and use the induction hypothesis to obtain the right side of the equation:


$
\begin{equation}
\begin{aligned}

=& [1^2 + 2^2 + 3^2 + k^2] + [(k + 1)^2]
&& \text{Group the first $k$ terms}
\\
\\
=& \frac{k (k + 1)(2k + 1)}{6} + (k + 1)^2
&& \text{Induction hypothesis}
\\
\\
=& \frac{2k^3 + 3k^2 + k}{6} + k^2 + 2k + 1
&& \text{Expand}
\\
\\
=& \frac{1}{3} k^3 + \frac{1}{2} k^2 + \frac{1}{6} k + k^2 + 2k + 1
&&
\\
\\
=& \frac{1}{3} k^3 + \frac{3}{2} k^2 + \frac{13}{6} k + 1

\end{aligned}
\end{equation}
$


Thus, $P(k+1)$ follows from $P(k)$, and this completes the induction step.

Calculus: Early Transcendentals, Chapter 4, 4.3, Section 4.3, Problem 21

Using First Derivative Test, we follow:
f'(a) >0 and f'(b) <0 in the interval a f'(a) <0 and f'(b) >0 in the interval aNote:
When f'(x) >0 or f'(x) = positive value then function f(x) is increasing or has a positive slope of tangent line (slant line going up).
When f'(x)< 0 or f'(x) = negative value then function f(x) is decreasing or has a negative slope of tangent line (slant line going down).
Applying power rule derivative on f(x) = x^(1/2) -x^(1/4):
f'(x)=(1/2)x^(1/2-1) -(1/4)x^(1/4-1)
f'(x)=(1/2)x^(-1/2) -(1/4)x^(-3/4)
f'(x)=(1/(2x^(1/2))) *((2x^(1/4))/(2x^(1/4)))-1/(4x^(3/4))
f'(x)=(2x^(1/4) -1)/(4x^(3/4))
Let f'(x)=0:
(2x^(1/4) -1)/(4x^(3/4))=0
2x^(1/4) -1=0*(4x^(3/4))
2x^(1/4) -1=0
2x^(1/4) = 1
x^(1/4) = 1/2
(x^(1/4))^4 = (1/2)^4
x=1/(16)or 0.0625
Table:
x 0.04 0.0625 0.08
f'(x) -0.295 0 0.106
f(x) decreasing increasing
It shows f'(0.04) <0 and f'(0.08)> 0 then local minimum point occurs at x=1/(16) or 0.0625.
As for Second Derivative Test, a critical point at x=c such that f'(c) =0 and f"(c) is continuous around the region of x=c follows:
f"(c) >0 then local maximum occurs at x=c.
f"(c) <0 then local minimum occurs at x=c
Applying power rule on f'(x)=(1/2)x^(-1/2) -(1/4)x^(-3/4) :
f"(x) =(-1/2)(1/2)x^(-1/2-1) -(-3/4)(1/4)x^(-3/4-1)
=(-1/4) x^(-3/2) +3/(16) x^(-7/4)
=-1/(4x^(3/2)) +3/(16x^(7/4))
Plug-in x=1/(16) in f"(x)=-1/(4x^(3/2)) +3/(16x^(7/4)).
f"(1/(16) )= 8 positive value
Continuation....
For the actual local minimum value of f, we plug-in x= 1/(16) in f(x)=x^(1/2)-x^(1/4) :
f(1/(16)) =(1/(16))^(1/2)-(1/(16))^(1/4)
f(1/(16)) = 1/4- 1/2
f(1/(16))= -1/4 or -0.25
or f"(1/(16) )> 0 then local minimum occurs at x=1/(16)
First derivative test will do if the second derivative function is not easy to derived.
Second derivative test will be easier if f"(x) is solvable with few steps.
This way we can plug-in critical value x=c directly on f"(x) to check of the local extrema is maximum or minimum.

What role does social convention play in Wuthering Heights?

Social convention plays a major antagonistic role in Wuthering Heights. Catherine Earnshaw is, by nature, a wild personality. She loves being outdoors, playing rough, and being rather nasty. However, once she starts approaching adulthood, social conventions play a bigger role in her life. She is tempted by high society, represented in the genteel character of Edgar Linton. She begins wearing fine clothes, putting on airs to appear more imperious and polite, and staying indoors, away from Heathcliff, a boy who is closer than a brother or even a lover to her.
Catherine's turning to high society is seen as a betrayal of Heathcliff and her own nature. It could be argued that her obeying social conventions eventually leads to her death. She makes herself ill, unable to commit to Heathcliff or Edgar fully. She wants social privilege, but she is far more drawn to the wild freedom of her girlhood, of which she mourns her loss to Nelly. These two opposing forces are never reconciled within her heart, and in the end, the conflict destroys her.
Heathcliff, by contrast, either disobeys social conventions or bends them to his whim. He comes back from his absence as a wealthy man. He appears to have tempered his bad moods with the behavior of a gentleman. However, deep down, he is still vengeful and uses social conventions to carry out his plans. He marries Isabella and forces Catherine the younger to marry his son in order to gain control of Thrushcross Grange. He wheedles control of Wuthering Heights away from Hindley by loaning him large amounts of money for his drinking and gambling addictions.

A common theme of Romantic literature is the defying of social convention. As a brooding, Byronic hero, Heathcliff presents a fundamental challenge to society and the values it embodies. He is all about emotion, passion, and following your heart. These are the very things that society demands must be kept in constant check for the sake of propriety, especially in the case of women. For a man to act according to the dictates of his heart is one thing, but for a woman it's a different matter entirely. Social convention regards female emotions as inherently dangerous, required at all times to be subjected to the restraining influence of a husband within the respectable bounds of marriage.
The tension between what the heart wants and what society demands runs right throughout the story. Catherine finds herself torn between the two imperatives, and it's never completely clear which one she will eventually choose to follow. That she finally plumps for social convention by marrying the wealthy and gentle Edgar may disappoint more than a few readers, but given the prevailing standards of the time, it's an entirely understandable choice.

Social convention dictates that Catherine Earnshaw make as advantageous a marriage as possible. She is expected to marry a man as wealthy and as far up the class ladder as she can. Therefore, when the wealthy and distinguished Edgar Linton falls in love with her and starts to pay suit, she is expected to respond. Her alcoholic brother Hindley cleans up his act when Linton comes to call, knowing the marriage would raise the family's status. Catherine herself is not in love with Linton, but she encourages him to propose because she wants the wealth and prestige that marriage to him would bring.
When he actually proposes, however, Catherine comes to Nelly Dean in a state of anguish. She knows convention says she must marry Linton—handsome, rich, and a gentleman—but in her heart she loves Heathcliff.
Nelly tells her she should not marry Linton if she does not love him. Catherine responds that she cannot marry Heathcliff, much as she would like to, because he has been too far "degraded" by Hindley. Again, social convention raises its head. Catherine simply can't envision herself married to an impoverished farm hand—which is what Heathcliff has become—no matter how much she loves him. As Heathcliff will tell Catherine as she is dying, she brought her death on herself by violating her own heart in marrying Linton.

What do you think is Gabriel’s purpose in the play?

The character of Gabriel is analogous to that of the wise fool in Shakespeare's plays, providing a kind of commentary on events and other characters in the play. Gabriel's disabilities, stemming from his cognitive impairment caused by a war injury, cause him to engage in rambling speeches about his relationship to the angels. In the Bible, when the angel Gabriel blows his trumpet, he's indicating the return of the Lord to earth. This is a common trope used in gospel songs. And in Fences, Gabriel sees himself in the role of his namesake, telling us how he's waiting for St. Peter to call upon him to open the gates of heaven.
Troy exploits Gabriel, but his disabled brother is unable to comprehend this. However, in the guise of the angel, Gabriel warns of judgement day and says that Troy's name is in St. Peter's book. Despite his chronic disability, Gabriel is still able to provide the audience with a wise commentary on his brother's unacceptable behavior, which points ominously towards the fate of his soul.

How is the New Deal similar or different from progressivism?

In their own different ways, both the Progressive movement and the New Deal had a profound impact upon American politics and society. Radical reform was at the heart of Progressivism, and to some extent the policies enacted under the New Deal built upon this legacy. Yet, there were differences. Progressivism was more concerned with formal, rather than substantive change. Its main focus was on the remedy of existing abuses within American democracy and the capitalist system. For example, in the early twentieth-century, the heyday of Progressivism, a raft of legislation was passed by Congress that dealt with such issues as child labor, food safety standards, and greater participation in the democratic process.
The Progressive movement never sought to challenge the fundamentals of American society as such; instead it expressed a keen desire that the prevailing social and economic systems should operate more fairly, more efficiently. It had a high moral tone, which opponents found grating and at times self-righteous. In many respects, Prohibition was the most famous—or infamous—fruit of Progressivism, representing as it did a policy steeped in an explicitly moralistic worldview that embraced virtually every aspect of public policy.
The New Deal, on the other hand, was concerned with the practical economic goal of getting the country back to work after almost four years of the Great Depression. To achieve this goal, it wasn't enough to enact reforms as the Progressives had done; it was further necessary to devote substantial sums of tax dollars to stimulate the economy and create much-needed jobs for the millions of unemployed.
The advocates of Progressivism had inspired the passing of the Sixteenth Amendment, which for the first time allowed Congress to levy a federal income tax. But it took the New Deal to take this reform and use it for the kind of massive government intervention in running the economy thought necessary to end the Depression. If the Progressive movement changed the existing rules on how things should be done, the New Deal changed them in relation to what should be done.

Calculus of a Single Variable, Chapter 9, 9.6, Section 9.6, Problem 39

To apply Root test on a series sum a_n , we determine the limit as:
lim_(n-gtoo) root(n)(|a_n|)= L
or
lim_(n-gtoo) |a_n|^(1/n)= L
Then, we follow the conditions:
a) Llt1 then the series is absolutely convergent.
b) Lgt1 then the series is divergent.
c) L=1 or does not exist then the test is inconclusive. The series may be divergent, conditionally convergent, or absolutely convergent.
In order to apply Root Test in determining the convergence or divergence of the series sum_(n=1)^oo ((3n+2)/(n+3))^n , we let: a_n =((3n+2)/(n+3))^n.
We set-up the limit as:
lim_(n-gtoo) |((3n+2)/(n+3))^n|^(1/n) =lim_(n-gtoo) (((3n+2)/(n+3))^n)^(1/n)
Apply the Law of Exponents: (x^n)^m= x^(n*m) .
lim_(n-gtoo) (((3n+2)/(n+3))^n)^(1/n) =lim_(n-gtoo) ((3n+2)/(n+3))^(n*1/n)
=lim_(n-gtoo) ((3n+2)/(n+3))^(n/n)
=lim_(n-gtoo) ((3n+2)/(n+3))^1
=lim_(n-gtoo) (3n+2)/(n+3)
To evaluate the limit lim_(n-gtoo) (3n+2)/(n+3) , we divide each term by the highest denominator power: n .
lim_(n-gtoo) (3n+2)/(n+3)=lim_(n-gtoo)((3n)/n+2/n)/(n/n+3/n)
=lim_(n-gtoo) (3+2/n)/(1+3/n)
Apply the limit property: lim_(x-gta)[(f(x))/(g(x))] =(lim_(x-gta) f(x))/(lim_(x-gta) g(x)).

lim_(n-gtoo) (3+2/n)/(1+3/n) =(lim_(n-gtoo) (3+2/n))/(lim_(n-gtoo)(1+3/n))
= (3+2/oo)/(1+3/oo)
= (3+0)/(1+0)
=3/1
=3
The limit value L = 3 satisfies the condition: Lgt1 since 3gt1 .
Conclusion: The series sum_(n=1)^oo ((3n+2)/(n+3))^n is divergent.

int_0^4 x/sqrt(3+2x) dx Use integration tables to evaluate the definite integral.

 To evaluate the given integral problem:  int_0^4 x/sqrt(3+2x)dx , we determine first the indefinite integral function F(x). From the table of indefinite integrals, we may consider the formula for integrals with roots as:
int u/sqrt(u+-a) du = 2/3(u-+2a)sqrt(u+-a)+C
 Take note that we have "+ " sign inside the square root on int_0^4 x/sqrt(3+2x)dx  then  we will follow: 
int u/sqrt(u+a) du = 2/3(u-2a)sqrt(u+a) +C.
 We may let a = 3 and u = 2x  or x= u/2
For the derivative of u, we get du = 2 dx or (du)/2 = dx .
Plug-in the values: u = 2x or x=u/2 ,and (du)/2 = dx , we get:
int_0^4 x/sqrt(3+2x)dx =int_0^4 (u/2)/sqrt(3+u)* (du)/2
                        =int_0^4 (u du)/(4sqrt(3+u))
 Apply the basic properties of integration: int c*f(x) dx= c int f(x) dx .
int_0^4 (u du)/(4sqrt(3+u)) =1/4 int_0^4 (u du)/sqrt(3+u)
Apply the aforementioned integral formula from the table of integrals, we get:
1/4 int_0^4 (u du)/sqrt(3+u) =1/4*[2/3(u-2(3))sqrt(u+3)]|_0^4
                 =1/4*[2/3(u-6)sqrt(u+3)]|_0^4
                 =2/12(u-6)sqrt(u+3)|_0^4
                 =1/6(u-6)sqrt(u+3)] |_0^4or((u-6)sqrt(u+3))/6|_0^4
Plug-in u = 2x on((u-6)sqrt(u+3))/6 +C , we get:
int_0^4 x/sqrt(3+2x)dx =((2x-6)sqrt(2x+3))/6|_0^4
Apply definite integral formula: F(x)|_a^b = F(b) - F(a) .
((2x-6)sqrt(2x+3))/6|_0^4 =((2(4)-6)sqrt(2(4)+3))/6-((2(0)-6)sqrt(2(0)+3))/6
=((8-6)sqrt(8+3))/6- ((0-6)sqrt(0+3))/6
=(2*sqrt(11))/6- (-6sqrt(3))/6
= sqrt(11)/3-(-sqrt(3))
= sqrt(11)/3+sqrt(3)
= (sqrt(11)+3sqrt(3))/3 or 2.84 (approximated value).

Who is Alma?

There are actually two Almas in The Book of Mormon: Alma, a father, and Alma the Younger, who is his son. Both live on the American continent around 100-70 BCE as prophets and government leaders. The first Alma starts out as a priest for a wicked king named Noah. After another prophet, named Abinadi, preaches against King Noah, Alma escapes the palace and starts preaching the gospel of Jesus Christ in exile. He later rises to become a high priest for a good king named Mosiah.
Alma the Younger, however, starts out as a rebellious young adult who not only disagrees with his father's religious beliefs about a Savior who will come to redeem mankind, but he outwardly disgraces him and the church. In fact, Alma the Younger becomes friends with King Mosiah's three sons and they strongly persecute members of the Christian church. Not only that, they start to lead members away from the church while also behaving poorly and harassing others.
A beautiful story of redemption unfolds as Alma the Younger sees an angel who puts him in a coma for three days. During that time, Alma the Younger suffers sadness, sorrow, and pain for his sins. He sees Jesus Christ in a vision and decides to repent and to change his life for the better. He comes out of the coma with a repentant heart and does everything he can to make amends for the wrongs he committed in the past. Later in his life, he leaves a government position as a judge to serve a mission to preach the gospel of Jesus Christ.
Alma the Younger's conversion story is found in chapter 36 of The Book of Alma, of course found within The Book of Mormon.

College Algebra, Chapter 4, 4.4, Section 4.4, Problem 60

The polynomial $P(x) = -x^4 + 10x^2 + 8x - 8$.

a.) Find all the real zeros of $P$

The leading coefficient of $P$ is $-1$, so all rational zeros are integers. They are divisors of constant term $-8$. Thus, the possible zeros are

$\displaystyle \pm 1, \pm 2, \pm 4, \pm 8$

Using Synthetic Division







We find that $1, 2, 4$ and $-1$ are not zeros but that $-2$ is zero and that $P$ factors as

$\displaystyle -x^4 + 10x^2 + 8x - 8 = (x + 2)\left( -x^3 + 2x^2 + 6x - 4 \right)$

We now factor the quotient $-x^3 + 2x^2 + 6x - 4$. Its possible zeros are

$\pm 1, \pm 2, \pm 4$

Using Synthetic Division







We find that $-2$ is a zero and that $P$ factors as

$\displaystyle -x^4 + 10x^2 + 8x - 8 = (x + 2) (x + 2) (-x^2 + 4x - 2)$

We now factor the quotient $-x^2 + 4x - 2$ using Quadratic Formula, we get


$
\begin{equation}
\begin{aligned}

x =& \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\\
\\
x =& \frac{-4 \pm \sqrt{(4)^2 - 4(-1)(-2)}}{2 (-1)}
\\
\\
x =& 2 \pm \sqrt{2}


\end{aligned}
\end{equation}
$


The zeros of $P$ are $-2, 2 + \sqrt{2}$ and $2 - \sqrt{2}$.

b.) Sketch the graph of $P$

What does Scout do that impresses Aunt Alexandra?

Aunt Alexandra, who always wants things to be her own way, is not too approving of Scout, who Alexandra's opinion is not ladylike. This should not come as a surprise because Scout is quite a tomboy and Aunt Alexandra has "boarding school manners."
Here is a quote by Aunt Alexandra which shows just that:

Jem's growing up now and you are too," she said to me. "We decided that it would be best for you to have some feminine influence.

However, Scout eventually realizes that being a lady is not too bad as she begins to admire her aunt's politeness toward other women, even the ones she does not like. Scout takes this as an example. As she says at the end of chapter 24, "If Aunt Alexandra could be a lady at a time like this, so could I."
To win Aunt Alexandra's favor, Scout decides to dress up as a Southern belle, a stereotype signifying women of decent manners. She even goes on to participate in the missionary circle, where women gather around to talk about God and religion.

Throughout the majority of the novel, Scout has a difficult relationship with her aunt, and the two continually antagonize each another. However, Scout attempts to impress her aunt by dressing up as a Southern belle and participating in the missionary circle with the other local ladies.
Scout, who is a natural tomboy, absolutely hates wearing dresses and participating in social events but does so in chapter 24 to impress her aunt. At the beginning of the chapter, Scout waits patiently in the kitchen and asks Calpurnia if she can help in any way. Calpurnia then allows Scout to carry in a rather heavy silver coffee pitcher on a tray into the living room, where the ladies are having casual conversations. When Scout brings the coffee pitcher in on the tray, she mentions,

My journey was successful: Aunt Alexandra smiled brilliantly (Lee, 233).

Overall, Scout impresses her aunt by wearing a dress and participating in her missionary circle with the other local ladies.

What were the conditions that were present in India in the 1920's that allowed Gandhi and Nehru to rise to prominence as nationalists?

Indian resentment towards British control was one of the major conditions that fueled the rise of nationalist leaders such as Gandhi and Nehru.
In the 1920s, many Indians were angry at how the British were treating them.  One source of discontent was the lack of acknowledgement of Indian sacrifice during World War I.  Indian servicemen fulfilled their duty in fighting for their parent nation, Britain.  However, after the war, Britain's actions failed to recognize such sacrifice. Britain showed dismissiveness and disdain towards the Indian demand for greater autonomy in taxation and political self-determination.  This began to fuel resentment and the ascension of nationalist leaders like Gandhi and Nehru. 
In the 1920s, British actions justified nationalism as a viable response.  The "Quit India" campaign intensified with events such as the Amritsar Massacre, when British forces opened fire on unarmed civilians. Leaders like Gandhi and Nehru began to call for demonstrations against British rule.  Gandhi was particularly effective with his insistence on nonviolent civil disobedience.  He made Indians believe that the struggle for independence was more spiritual than political.  Being able to make the call for nationalism a moral one cast the British as evil and unjust. Through Gandhi's example, Indians viewed opposing the British as an ethical imperative.  Nehru's focus was equally effective, but focused on the political aspect.  He helped to form the Indian National Congress. This political party's sole priority was the independence of India.  Gandhi's call for moral action and Nehru's political organization fueled their their rise as nationalist leaders in 1920s India.
https://www.nationalarchives.gov.uk/education/empire/g3/cs3/background.htm

How do people get invited to Gatsby’s parties?

Generally speaking, you don't need a formal invitation to attend one of Gatsby's legendary parties. Word of mouth spreads like wildfire, and the next thing you know, dozens of pleasure-seeking party animals have descended on Gatsby's opulent West Egg fun palace like a swarm of hedonistic locusts, determined to have themselves a ball. Certain special people like Nick do receive formal invitations, but for the vast majority it's unnecessary. It's pretty much open house chez Gatsby; people just turn up, avail themselves of their host's lavish hospitality, and have a great time.
It's instructive that most people seem not to know who Gatsby is or what he even looks like. Their mysterious host moves unobtrusively amidst the heaving throng of drunken flappers and sundry freeloaders. But they're not there to see him; they're there to be seen. Rocking up at one of Gatsby's shindigs is deemed essential for anyone who's anyone in that neck of the woods.
Although Gatsby's guests are more than happy to help themselves to his food and drink his champagne, they're not so keen on turning up at their host's funeral. This demonstrates their true values—or lack of them—their shallowness and utter vacuity. There's just no social cachet or prestige in paying your last respects to someone you never really knew in the first place.

How are social distinctions identified? How are gender roles portrayed?

Malcolm Gladwell's purpose in writing Blink was to expound on a trait of human intelligence that he believes can improve decision-making, namely rapid cognition. Thus he does not focus on social distinctions or gender roles primarily; he wants to elucidate a skill that all human beings share. However, within the course of his discussion, he does elude to social distinctions and gender roles.
As a mixed-race person himself, Gladwell comments on racial issues several times in the book. In chapter 3 he discusses the Implicit Association Test (IAT) at length, pointing out that many people in American society carry racial prejudices against blacks, whether they know it or not. He was distressed to find that the IAT revealed that he himself had "pro-white associations." In chapter 6, he relates a story of four white policemen who were involved in a police shooting of a black unarmed man in the Bronx in 1999. Gladwell does not simply blame the shooting on racism but seeks to understand it as an example of a "mind-reading failure." Also in chapter 3, Gladwell relates the story of a successful used car salesman who states, "You cannot prejudge people in this business." The man succeeded because he was unwilling to use the customer's perceived social class as a marker for how he would treat them. From these examples and others, readers sense that Gladwell wants to downplay the importance of social class and race.
Gladwell also asserts the effectiveness of women in professional roles. In chapter 5 he describes going to lunch with two women who owned a professional food-tasting company. In the conclusion, he relates the story of a woman trombone player who had to go to court to receive her rightful position as lead trombone in a symphony orchestra. From these and other examples, it is clear that Gladwell supports women's ability to pursue careers in business and music based on their abilities, not on their gender.

Prove that the old man is thefatalistic hero of the story

First let's define what it means to be fatalistic. Basically, fatalism is the belief that we have little control over future events. It is also the belief that we can do little to change what fate determines for us. So, a person who is fatalistic is a person who believes that he must resign himself to the inevitable.
In the story, the old man makes no move to continue on his journey, despite the narrator's warning that the enemy is approaching. While the narrator watches the bridge anxiously for the enemy's advance, the old man seems content to talk about his animals. He tells the narrator that he left his farm only because he was told to do so.
The old man divulges that he has no relatives and that the animals he left behind were his only family. He talks about the animals with love and great emotion. Although the narrator tells him that there are trucks up the road that will take him to Barcelona, the old man makes no effort to move in that direction; he proclaims that he knows no one in Barcelona.
At the end of the story, the narrator again urges the old man to move on. For his part, the old man stands up but appears too weak to make the journey to the trucks on foot. He sits back down and mumbles that he has only been taking care of his animals. So, the old man is fatalistic because he has resigned himself to whatever fate will befall him. He accepts that he can do nothing else to save himself, and his actions demonstrate his belief that it is futile to struggle against the inevitable.

The theme of "In This Strange Labyrinth How Shall I Turn" seems to be love. However, the end is leaving me a bit confused. In the last two lines of the poem, is the speaker deciding to walk down the path of love regardless of the perceived risks?

Well . . . it's the opposite of this, really. What Mary Wroth is saying is that if we can just trust to love, we won't need to worry about choosing a "way" within the labyrinth of life, because love will guide us through the maze using its "thread." The left way and the right way, which Wroth's speaker is tempted and troubled by in this poem, are not really love—one of them leaves the traveler suspicious, while the other seems to be more lust than love ("burn"). The speaker is in a quandary because every route looks uncertain and dangerous, and standing still seems even more impossible.
Ultimately, however, the speaker doesn't have to make a decision of her own. Like in the Classical Greek story of Theseus and Ariadne—wherein Ariadne traced the correct path through King Minos's labyrinth with thread, so that Theseus could get back out after having killed the Minotaur—there is a thread leading the speaker through this labyrinth, too. All she needs to do is find it, hold onto it, and believe that this is the way of love marked out for her. She knows this is the best thing to do; her impulses "move" toward it, and she must only listen.

In "In This Strange Labyrinth How Shall I Turn?," Mary Wroth discusses the complicated nature of love, and the last two lines have a lot of meaning.
In this sonnet, Wroth is referencing Greek mythology, and understanding these references might help clarify these last lines. The labyrinth plays an important role in the myth of Theseus and the minotaur. In this myth, King Minos hides the minotaur, a half-man–half-bull monster, in the large maze referred to as the labyrinth. When his son is killed by the bull that fathered the minotaur, King Minos demands that seven young men and women must be sacrifices to the minotaur every year—a bit like the Hunger Games. Theseus is one of the young men sent to the minotaur, and he believes he will finally be able to defeat this monster. When he falls in love with Princess Ariadne, King Minos's daughter, she promises to help him. Ariadne gives Theseus thread to wind through the labyrinth so he can find his way out again. He manages to kill the minotaur and find his way out with Ariadne's thread.
When Wroth references taking "the thread of love," she is alluding to Ariadne's thread. The speaker is indeed deciding to follow love regardless of the consequences that have been considered throughout the sonnet. But the story of Ariadne's thread is a hopeful one which works out for the lovers in the end, making this ending more hopeful and optimistic than it might at first appear.

Calculus of a Single Variable, Chapter 8, 8.4, Section 8.4, Problem 21

Given to solve ,
int 1/sqrt(16-x^2) dx
using the Trig substitutions
for sqrt(a-bx^2)
x= sqrt(a/b) sin(u)
so for ,
int 1/sqrt(16-x^2) dx --------(1)
so , x can be
x= sqrt(16/1) sin(u)
= 4sin(u)
=> dx = 4cos(u) du
so,for (1) we get
int 1/sqrt(16-(4sin(u))^2) (4cos(u) du)
=int (4cos(u))/sqrt(16-16(sin(u))^2) du
= int (4cos(u))/(4sqrt(1-sin^2(u))) du
= int (4cos(u))/(4sqrt(cos^2(u))) du
= int (4cos(u))/(4cos(u)) du
= int (1) du
= u+c
but x= 4sin(u)
=> x/4 = sin(u)
=> u = arcsin(x/4)
so ,
=> u+c
= arcsin(x/4)+c
so ,
int 1/sqrt(16-x^2) dx = arcsin(x/4)+c

In Shakespeare's Othello, why does Iago feel that he should have Cassio's job?

At the beginning of the first scene in Shakespeare's Othello, Iago is complaining bitterly to Roderigo that Othello has chosen someone other than Iago to be his lieutenant, his second-in-command.
Iago tells Roderigo that he had arranged for well-placed Venetian citizens ("three great ones of the city") to speak to Othello on his behalf. Othello wouldn't see them, Iago says. Othello made overblown excuses to avoid seeing them and told them that he has already chosen a lieutenant: Michael Cassio.
Iago provides information about his own qualifications for the position by explaining Cassio's shortcomings to Roderigo.
Iago says that Cassio is a Florentine, not a Venetian, implying that Cassio has mixed loyalties to Othello and Venice.
Iago considers his own military experience far superior to Cassio's. Iago says that Cassio has no experience commanding men on the field of battle and implies that Cassio can't even control his own wife.
Cassio is schooled ("a great arithmetician"), whereas Iago is not. Iago mocks his schooling and military training as being limited to a theoretical study of Roman military exploits—"the bookish theoric, / Where in the toga'd consuls can propose / As masterly as he."
Iago says that Cassio talks a good game, militarily, but has no experience to back it up.
In contrast, Othello has seen Iago's military skills firsthand, in battles at Rhodes and in Cypress, as well as other campaigns in Christian and non-Christian countries alike. Even though Iago has much more training and experience than Cassio, Othello chose Cassio, whom Iago calls the bookkeeper ("this contercaster"), implying that he knows nothing but debits and credits.
Iago finds himself stuck, seemingly forever, as "his Moorship's ancient": Othello's ensign and flag-bearer.
Iago seems to be resigned to Othello's decision and to the current state of affairs in the military.

IAGO. Why, there's no remedy. 'Tis the curse of service,Preferment goes by letter and affection,And not by old gradation, where each secondStood heir to the first. (1.1.34–38)

However, Iago is by no means as accepting of the situation as he says.

RODERIGO. I would not follow him then.
IAGO. O, sir, content you.I follow him to serve my turn upon him... (1.1.41–43)

In time, Iago will take revenge on Cassio and Othello for Othello's choice of Cassio as his lieutenant.

Many scholars consider Iago to be one of Shakespeare's most raw and sinister portrayals of evil, and one of the things that make him so terrifying is that we, as the audience, never really get a convincing reason as to why he does the things that he does. If he only had a lust for power, that would be one thing. Men doing terrible things for positions of power, such as Hamlet's Claudius and Macbeth's titular character, is not at all a foreign concept in Shakespeare's works. However, such is not the case with Iago. His desire for higher office seems distantly secondary to his pure, venomous, and often humorously unexplained hatred for Othello. Iago has been Othello's battle companion and friend for many years, always maintaining a facade of honesty and integrity. Perhaps he feels that his efforts are being overlooked by Othello due to his passing over Iago for the promotion to lieutenant, in favor of Cassio. After all, Iago claims that he certainly has more battle experience than Cassio. Another explanation could be that this perceived slight makes Iago paranoid that Othello does not trust him as much as he thinks. Perhaps Iago's facade of honesty is not at convincing as he had previously been certain. Whatever the case, it is this event that finally sets Iago actively against Othello and creates the action of the play.

First, as Iago explains to Roderigo, he has had more experience than Cassio on the battlefield. Iago says that he has fought and proven his worth:

At Rhodes, at Cyprus, and on other grounds
Christian and heathen

Second, Iago believes he should get the job not only on the basis of his experience, but on the basis of seniority. He believes he should have been next in line and was unfairly jumped over. As he tells Roderigo, he plans to get revenge for how he has been treated.
We don't know if what Iago says is true or not, but it is amply clear from the play that Iago has a huge chip on his shoulder. There is no doubt he is smart, clever, and able to lay a trap, given how he deceives the people around him, most of whom are hardly stupid. Somewhere along the way, however, in some deep way, he seems to have felt his talents and worth were overlooked. He carries a deep-seated anger and sense of injury within him, and it comes out in what the poet Coleridge called "motiveless malignancy," or a desire for spite that seems disproportionate. We know, too, that he is racist. He can't seem to get over the fact that Othello, a black man, is his commander and the spouse of a beautiful white woman, and this contributes to his sense of injury.

Iago is a very difficult character to understand, because although he spends lots of time talking to the audience, he never makes it very clear what his motivation is for doing anything. (Indeed, the poet and critic Samuel Taylor Coleridge refers to Iago's nature as "motiveless malignity," which is to say that he is evil and destructive for no apparent reason.) We know that Iago considers himself worthy of the lieutenant's post: "I know my price, I am worth no worse a place." We know that he considers Cassio incompetent for the position because Cassio "never set a squadron in the field" and "mere prattle without practice / Is all his soldiership." We don't know for a fact what Iago thinks his qualifications are, but we can infer from what he says about Cassio that Iago's battlefield experience makes him more qualified for the position in his own eyes.

Iago is a complex and duplicitous character. That means we can never fully trust what he says, even when he is speaking a soliloquy. Part of his belief that he deserved the promotion is grounded in his own sense of entitlement.
He does, however, give a clear account of why he thinks he is better qualified than Cassio in the first scene of the play. 
The first and most explicit reason why he believes that he deserves the promotion is that he is senior to Cassio and has been serving longer. Next, Cassio is a Florentine rather than a Venetian. Also, Cassio is a "bookish theoric" rather than someone who has substantial battleground experience. Iago mentions that he has served in far more places than Cassio and had given proof of his skill as a soldier in that service while Cassio is basically untried. 
Finally, Iago believes in the value of an older tradition "where each second / Stood heir to the first" and he does not feel Othello should simply have the right to choose his own lieutenant "by letter and affection."