Single Variable Calculus, Chapter 2, 2.3, Section 2.3, Problem 54

Suppose $r$ is a rational function, show that $\lim \limits_{x \to a} R(x) = R(a)$ for every number $a$ in the domain of $r$

Let $P(x)$ be a rational function



$
\begin{equation}
\begin{aligned}

R(x) =& \frac{P(x)}{Q(x)} &&; \text{ Suppose that $Q(x) \neq 0$}\\
\\
R(a) =& = \frac{P(a)}{Q(a)}\\
\\
\lim \limits_{x \to a} R(x) =& \frac{\lim \limits_{x \to a} P(x)}{\lim \limits_{x \to a} Q(x)} &&; \text{ Suppose that $\lim \limits_{x \to a} Q(x) \neq 0$
(applying the limit law)} \\
\\
\lim \limits_{x \to a} R(x) =& \frac{P(a)}{Q(a)}
\\
.: \lim \limits_{x \to a} R(x) = R(a)


\end{aligned}
\end{equation}
$

Where does Katniss live within District 12?

Katniss and her family live in the section of District 12 known as the Seam.  
In chapter one, Katniss gives readers background information about herself, her family, District 12, and their house.  She informs readers that District 12 is a mining district, and the Seam is where many of the miners live.  Katniss further clarifies her house's location by telling readers that it is on the outer edges of the Seam.  She says that she only has to go through a few gates to reach a run down field called the Meadow.  

Our house is almost at the edge of the Seam. I only have to pass a few gates to reach the scruffy field called the Meadow. Separating the Meadow from the woods, in fact enclosing all of District 12, is a high chain-link fence topped with barbed wire loops.

The Meadow is important because it borders the forest.  Between the two is a chain link fence that is meant to keep predators out and the people of District 12 in.  Katniss ignores this rule because she goes outside of the fence in order to hunt for food for her family.

Most of the Peacekeepers turn a blind eye to the few of us who hunt because they’re as hungry for fresh meat as anybody is.  

Glencoe Algebra 2, Chapter 2, 2.6, Section 2.6, Problem 60

A linear inequality describes an area of the coordinate plane that has a boundary line. Every point in that region is a solution of the inequality. In simpler speak, a linear inequality is just everything on ONE side of a line on a graph.
There are a couple ways to determine whether the point (0,0) lies in the region described by the inequality, y < 2x + 3.
You could graph the inequality on a coordinate plane. However, the easiest way is by using substitution.
To do this take the x and y values from the ordered pair and substitute them into the inequality. Remember an ordered pair is always written (x,y). In this case x = 0 and y = 0.
STEPS:
0 < 2(0) + 3 0 is substituted for both the x and y values.
0 < 3 Next, simplify the expression on the right using the order of operations (multiplication first, then addition).
Since 0 < 3 is a true statement, the ordered pair (0,0) satisfies the inequality, y < 2x + 3.

What vision upsets Macbeth the most?

The visions you’re referring to are those that are given to Macbeth by the three witches in Act IV. Following the prophecy the witches gave him at the beginning of the play, Macbeth is anxious to know what the conclusion will be, given that his wife has been having second thoughts. He seeks them out to “answer me / To what I ask you.” They respond by providing three speakers from their cauldron, and Macbeth sees their messages as a boon to his cause. He is told to beware the Thane of Fife (Macduff), that none of woman born shall harm him, and that he will not be defeated until Birnam Wood marches to high Dusninane Hill.
Assuming these are all good tidings, and interpreting his victory as sure, Macbeth is in high spirits until the end of his meeting with the three hags: a line of kings, with the ghost of Banquo following. Macbeth is clearly appalled at the vision, for it serves to bolster the witches’ original prophecy for Banquo from Act I: “Thou shalt get kings, though thou be none.” After Macbeth’s short reign, the witches are affirming that it will be Banquo’s heirs and not Macbeth’s that will become the rulers of Scotland.
As Macbeth has no children, and Banquo’s son Fleance is in hiding somewhere in the wilderness of Scotland, Macbeth knows that this is the vision that is most likely to come true. Little does he know, the witches have told no lies, and he should be equally afraid of the three earlier prophecies as well!

Arguably, in act 4, scene 1, the vision which upsets Macbeth the most is the final one in which he sees a long line of Banquo's sons who are all kings of Scotland. This is shown clearly by Macbeth's physical and emotional reactions. As he watches Banquo's sons walk by, for example, Macbeth talks about how this vision "sears" his eyeballs.
In addition, Macbeth verbally attacks the witches for showing him such a vision:

Filthy hags!
Why do you show me this?

Watching this vision is so painful to Macbeth that he shouts, "I'll see no more" and calls it a "horrible sight."
What this shows is that, for Macbeth, the thought of losing his crown to Banquo's son is the one thing he fears the most at this point. As you will remember, Fleance escapes Macbeth's henchmen earlier in the play, meaning that there is a possibility that this vision could come true.

How do tourists make their tourism choices and what are the factors that influence those choices?

First, different types of tourists are influenced by different factors. A well-educated elderly couple spending a summer traveling around Europe may have very different motivations than a college student on spring break in Florida. People with young children will obviously prioritize locations that have activities and facilities geared towards family travel, while the elderly or disabled may be concerned about accessibility.
The single most important factor influencing destination choice is recommendations from friends or family. This effect is amplified by social media, on which people often share vacation photographs and anecdotes.
Price is an important factor, too, with sales or special offers sometimes motivating people considering a specific destination to decide to visit it; someone who is reluctant to visit a given hotel at $250/night might decide a $150/night special makes that hotel affordable. 
Often, people enjoy visiting places they have seen or read about, with Jane Austen fans deciding to visit Brighton or people who enjoyed the Lord of the Rings films visiting New Zealand to see the stunning scenery they enjoyed in the film. History enthusiasts will visit scenes of famous battles or other historical events, while on a more poignant note, Jews might visit the remains of Nazi concentration camps or Holocaust memorials, and many relatives of fallen soldiers or civilians may visit war memorials or the 9/11 memorial as part of exploring their own roots.

Calculus and Its Applications, Chapter 1, 1.6, Section 1.6, Problem 48

Differentiate $\displaystyle f(t) = \frac{3t^2 + 2t - 1}{-t^2 + 4t +1}$
By applying Long Division, we have



Thus,
$\displaystyle f(t) = -3 + \frac{14t + 2}{-t^2 + 4t + 1}$
Then, by taking the derivative using Quotient Rule, we obtain

$
\begin{equation}
\begin{aligned}
f'(t) &= \frac{d}{dt} (-3) + \frac{d}{dt} \left( \frac{14t + 2}{-t^2 + 4t + 1} \right)\\
\\
f'(t) &= 0 + \frac{(-t^2 + 4t + 1) \cdot \frac{d}{dt} (14t + 2) - (14t + 2) \cdot \frac{d}{dt}(-t^2 + 4t + 1) }{(-t^2 + 4t + 1)^2}\\
\\
f'(t) &= \frac{(-t^2 + 4t + 1)(14) - (14t + 2)( -2t + 4)}{(-t^2 + 4t + 1)^2}\\
\\
f'(t) &= \frac{-14t^2 + 56t + 14 - \left[ -28t^2 + 56t - 4t + 8 \right]}{(-t^2 +4t + )^2}\\
\\
&= \frac{-14t^2 + 56t + 14 + 28t^2 - 56t + 4t - 8 }{(-t^2 + 4t + 1)^2}\
\\
&= \frac{14t^2 + 4t + 6}{(-t^2 + 4t + 1)^2} \quad \text{ or } \quad \frac{2(7t^2 + 2t + 3)}{\left[ (-1) (t^2 - 4t - 1)\right]^2}\\
\\
&= \frac{2(7t^2 + 2t + 3)}{(-1)^2(t^2 - 4t - 1)^2}\\
\\
&= \frac{2(7t^2 + 2t + 3)}{t^2 - 4t - 1}

\end{aligned}
\end{equation}
$

Beginning Algebra With Applications, Chapter 3, 3.3, Section 3.3, Problem 140

Evaluate $\displaystyle \frac{3}{8}(16 - 8c) - 9 \geq \frac{3}{5}(10c - 15) + 7$

$
\begin{equation}
\begin{aligned}
\frac{3}{8} (16) - \frac{3}{8} (8c) - 9 &\geq \frac{3}{5}(10c) - \frac{3}{5} (15) + 7 && \text{Use the Distributive Property to remove the parenthesis}\\
\\
6 - 3c - 9 &\geq 6c - 9 + 7 && \text{Simplify}\\
\\
-3c - 6c &\geq - 9 + 7 - 6 + 9 && \text{Group terms}\\
\\
-9c &\geq 1 && \text{Combine like terms}\\
\\
\frac{-9c}{-9} &\geq \frac{1}{-9} && \text{Divide each side by -9}\\
\\
c &\leq -\frac{1}{9} && \text{Remember that if you divide or multiply numbers ,the inequality symbol reverses}
\end{aligned}
\end{equation}
$

Describe one strength of one of the three branches of government.

In the United States, there are three branches of government. Each branch of government has certain strengths. The strength of Congress is that it makes laws. Many of these laws also deal with spending money. This gives Congress a great deal of power and influence.
One of the strengths of the executive branch is that the president has many opportunities to get his message to the American people. The president can have news conferences to explain his thinking or his actions. The president’s press secretary holds daily meetings with the press to answer questions about decisions the president has made or actions the president has taken. The president gives a yearly State of the Union speech where he can lay out his plans for the country. This speech is televised nationally and is held with all members of Congress present. The president can also go on national television during times of crisis or emergencies to talk to the American people. No other government official has the number of options and opportunities to get his or her message to the American people. Any comment that the president makes usually gets coverage by the press.
One of the strengths of the judicial branch is the power of judicial review. The Supreme Court has the power to review laws and actions to determine whether they are constitutional. This power forces Congress to consider how the Supreme Court might view a proposed law. The same is true for an executive order that the president might issue. If it was thought that a law or executive action might be declared unconstitutional, it might influence what the final version of the law or executive action would be.
http://www.pbs.org/tpt/constitution-usa-peter-sagal/we-the-people/separation-of-powers/

https://www.thoughtco.com/separation-of-powers-3322394

The great strength of having three branches of government, the executive, legislative, and judicial, is that, when they work correctly, they provide checks on each other, preventing one person or small group of people from amassing too much power. The president must defer to Congress and the courts, Congress to the courts and the president, the courts to Congress and the president.
But this question asks for one strength of one branch of government. One strength of the legislative branch is its ability to pass laws. Because the legislators –– members of Congress and Senators –– are elected democratically by the citizens of the country, the laws they make, ideally, represent the will of the governed.  Also, because Congress crafts these laws, it has the power to shape how the government spends its tax dollars. Through its policies, Congress can redistribute wealth upward or downward for the larger good. It can pass legislation that will help the country to prosper and can create laws that protect the weaker from the stronger. However, it does all this knowing that the judicial branch can review its laws to ensure that they fall within the confines of the Constitution. The president also has the power to veto any bill, though Congress can override the veto. 

In this answer, I will provide one strength for each of the branches of the United States government.  Those three branches are the legislative branch (Congress), the executive branch (headed by the president), and the judicial branch (headed by the Supreme Court).
The major strength of Congress is its ability to make laws.  No law can be proposed, let alone passed, without the consent of Congress.  This means that Congress has the sole authority, for example, to impose taxes and to allocate money for spending.  Presidents may have big plans and important proposals, but only Congress has the power to make these plans into actual laws.
A major power of the president (and, therefore, of the executive branch) is what Theodore Roosevelt called the “bully pulpit.”  The president is the most famous political figure in the nation. He (or someday she) can command the attention of the public.  The public does not really pay much attention when, for example, Paul Ryan gives a speech about proposed policies, but it does pay more attention when the president speaks.  This gives the president more power to persuade the people than anyone else in our system.
The major power of the Supreme Court is the power of judicial review.  This means that the judicial branch gets to decide what laws are and are not constitutional.  For example, the Supreme Court changed the way our political campaigns are financed when it struck down campaign finance laws in the Citizens United case that was decided in 2010.  The Court also has done things like making segregated schools illegal (Brown, 1954) and declaring that states cannot ban all abortions (Roe, 1973).  The ability to say what the Constitution means gives the judicial branch a great deal of power.
https://www.oyez.org/cases/2008/08-205

How would you describe the dualism in Winston Smith's personality in Orwell's 1984?

Winston Smith grew up with one sets of norms for the first eleven years of his life and then moved to another. In his early life, though economically deprived and always hungry, he lived in a family with his little sister and a mother who loved him dearly and was willing to sacrifice for him. After his sister and mother disappeared, he was raised as an outer Party member. As an adult Party member when we first meet him, he is filled with fear, hate, and violent fantasies. He holds others, such as the Parsons and the proles, in contempt, and he loathes the Party. He wants to rape and harm Julia. This second personality is a product of the Party.
When Winston meets and falls in love with Julia, he develops his humane, loving side. He wants to sacrifice for Julia, and he comes to see the fat, old prole who hangs laundry outside his window as a beautiful human being. He remembers and dreams more and more about his mother as Julia triggers memories of the love he experienced as a child and which is still buried inside him. He finds too that humanity resides in the simple rituals of two people who love each other doing ordinary things together, such as drinking tea and talking.
The new person Winston has become, however, is anathema to the Party. The Party can't tolerate him being loyal and loving to another human being. It can't bear him being happy, because his happiness means it doesn't have total power over him. It wants him in a complete state of abject loyalty to Big Brother. When he is arrested, the Party, though O'Brien, uses torture to try to eradicate every vestige of humanity from Winston, so that he is nothing more than an empty shell.
Winston represents, therefore, two very different beings: the ever fearful, ever angry creature the Party has wrought and the caring, compassionate self brought forth from being loved by his mother and Julia. The Party almost wholly destroys him but never fully eradicates the loving self, because in the moments before he dies, he remembers a happy time playing a game of Snakes and Ladders with his mother, a memory completely divorced from anything to do with the Party or Big Brother.

Dualism is a feature of Winston's personality and we see strong evidence of this in Part One, when Winston is battling between conformity and rebellion against the Party. The fact that Winston purchases the diary, for example, (and risks being imprisoned) suggests that he desperately wants to make a stand against the Party's oppressive regime. This is further reinforced by his writing of the phrase, "DOWN WITH BIG BROTHER," over and over.
By Chapter Two, however, Winston's internal need to conform takes over. He realises that writing in the diary is an intensely risky business:

And in front of him there lay not death but annihilation. The diary would be reduced to ashes and himself to vapour.

Winston's fatalistic attitude contrasts strongly with his desire to rebel and to build a future in which the Party no longer exists. It creates an internal sense of conflict within Winston and it is this conflict which drives the plot of Part One. 

Single Variable Calculus, Chapter 7, 7.8, Section 7.8, Problem 66

Estimate the value of the $\displaystyle \lim_{x \to 0} \frac{5^x - 4^x}{3^x - 2^x}$ by using its graph. Then use L'Hospital's Rule to find the exact value.




Based from the graph the value of the limit as $x$ approaches 0 is $y \approx 0.52$. Now by using L'Hospital's Rule...

$
\begin{equation}
\begin{aligned}
\lim_{x \to 0} \frac{5^x - 4^x}{3^x - 2^x} &= \lim_{x \to 0} \frac{5^x (\ln 5) - 4^x (\ln 4)}{3^x(\ln 3)- 2^x(\ln 2)}\\
\\
&= \frac{5^0 (\ln 5) - 4^0 (\ln 4)}{3^0 (\ln 3) - 2^0 (\ln 2)} = \frac{\ln 5 - \ln 4}{\ln 3 - \ln 2}
\end{aligned}
\end{equation}
$


By applying the Laws of Logarithm, we have...
$\displaystyle = \frac{\ln \frac{5}{4}}{\ln \frac{3}{2}}$

Suppose that $f(x) = 2x \sin x$ and $g(x) = \sec x - 1$

What is surprising to the signalman when the narrator calls to him in "The Signal-Man"? Why?

When the narrator calls to the signalman, the man has something "remarkable in his manner. . . His attitude was one of such expectation and watchfulness," as though he is wary of the narrator. It is as though he has seen the narrator before and is afraid of him.
Once the narrator descends and talks with the signalman, the man reveals to the narrator that his calling down from above has reminded the signal-man of an apparition he has seen before because the narrator called out the very words of the apparition. Hearing this in such a dismal, dark, and lonely place, the narrator wonders if the signalman himself is not some sort of apparition. Nevertheless, the narrator establishes a relationship with the strange man, who describes his job to him. Further, the man confides in him that he has seen a man covering his eyes and his right arm who waves violently and calls out, "For God's sake, clear the way!" 
Shortly after this conversation, the narrator sees what seems to be an apparition at the opening of the tunnel. The man stands with his arm over his eyes; he waves desperately at the mouth of the tunnel. After he runs to the signal box, he is informed that the signalman has been killed by a train that morning. Eerily, just as the signalman described his apparition, a man covered his eyes to prevent himself from seeing the train run over the signalman.
The narrator asks the men around the opening of the tunnel what has happened. "Signalman killed this morning, sir," one replies. "Not the man I know?" the narrator asks fearfully. When he is brought to the poor, dead man, the narrator asks how his death has occurred, and the men describe exactly what has happened to the signal-man. It is eerily familiar to the narrator.
"What did you say?" the narrator asks the engineer. He replies, "I said, 'Below there! Look out! Look out! For God's sake, clear the way!"
Shaken, the narrator realizes what occurred is exactly like what the ghostly apparition has done as described by the signalman.

In “A Rose for Emily” by William Faulkner, who is ultimately responsible for the death of Homer Barron?

Miss Emily Grierson is responsible for the death of Homer Barron in William Faulkner's classic short story "A Rose for Emily." Miss Emily is depicted as a tortured soul, who grew up under her father's authoritative guardianship. After her father passes away, she initially refuses to acknowledge his death and rarely leaves her home. Once Homer Barron arrives in Jefferson, he begins courting Miss Emily and the entire town disapproves of their relationship, because they feel Miss Emily is dating below her social class. The community members also mention that Homer likes men and overhear him saying that he was not a marrying man. Miss Emily then purchases arsenic from a local pharmacy and refuses to give the pharmacist a reason for her purchase. After Miss Emily purchases the arsenic, Homer Barron is never seen or heard from again. Miss Emily's arsenic purchase coupled with Homer Barron's disappearance implies that she murdered him. There is ample evidence to suggest Miss Emily is mentally ill and capable of murdering Homer Barron. The fact that Miss Emily's gray hair is on the pillow next to Homer's skeleton also implies that she was engaging in necrophilia. One could also argue that Miss Emily's father is indirectly responsible for Homer Barron's death. If he would have allowed Emily to date local men, socialize with her neighbors, and had not been such an oppressive force in her life, she may have developed into a sane, rational woman, who would not be capable of murdering anyone.

Readers are left to assume that the arsenic that Miss Emily Grierson bought from the druggist is the agent that killed Homer Barron, her erstwhile gentleman companion, whom the narrator and others assumed to have been her fiancé. After Emily bought an engraved toilet set and nightshirt that were obviously for Homer Barron and no wedding was held, Homer Barron disappeared. It is apparent that he had not planned to marry her, and because of her social standing, Emily could not allow her reputation to be compromised in that way, since she had been seen publicly so often in Homer Barron's company. Since Homer Barron's decomposed body was found in Emily Grierson's home, it seems that it could only have been her who killed him. She had the means (arsenic), the motive (shame at being rejected), and opportunity (as he was a frequent visitor).

What does Scrooge think has caused Marley's ghost to appear?

Initially, Scrooge believes that the appearance of Marley's ghost is a result of indigestion. However, once the ghost has gotten Scrooge to take the first steps toward understanding that the ghost is indeed "real," Scrooge begins to think of other reasons as to why it has appeared.
As he continues to talk with Marley's ghost, it says, “I am here to-night to warn you, that you have yet a chance and hope of escaping my fate. A chance and hope of my procuring, Ebenezer.” To which Scrooge replies "You were always a good friend to me . . . Thank’ee!”
Here Scrooge discerns another reason for the presence: his old friendship with Marley. In this moment, Marley's desire to help out his old friend has caused the ghost to appear. However, when the ghost tells him about the three spirits yet to come, "Scrooge’s countenance fell almost as low as the Ghost’s had done." Scrooge's understanding begins to shift again. This is no kind act of friendship; this is something more. However, Scrooge's new understanding holds for only a brief moment, as in stave 2 Scrooge's perspective again shifts as his mind again attempts to rationalize the ghost away.

Scrooge went to bed again, and thought, and thought, and thought it over and over and over, and could make nothing of it. The more he thought, the more perplexed he was; and the more he endeavoured not to think, the more he thought.
Marley’s Ghost bothered him exceedingly. Every time he resolved within himself, after mature inquiry, that it was all a dream, his mind flew back again, like a strong spring released, to its first position, and presented the same problem to be worked all through, “Was it a dream or not?”

Here Scrooge again has trouble believing that the ghost has even appeared at all, in some ways returning to his initial belief that the vision was all the result of indigestion. However, this perspective is soon obliterated once and for all as Scrooge meets the first of the three spirits and revisits his own past.
 

Scrooge thinks that Marley's ghost is merely the result of some indigestion. He says,

"You may be an undigested bit of beef, a blot of mustard, a crumb of cheese, a fragment of an underdone potato. There's more of gravy than of grave about you, whatever you are!"

Scrooge believes that he might have eaten something not entirely fresh, something that is now wreaking havoc with his senses, and that this explains what he evidently believes is a hallucination of sorts. In his final sentence above, he actually uses a pretty clever pun to explain this view. The words gravy and grave obviously sound a lot alike, and Scrooge employs some (surprisingly) witty wordplay when he suggests that Marley's ghost is more likely the result of something Scrooge ate (like a gravy) rather than the result of Marley actually being dead (as in, in a grave). His choice to use two words that sound so much alike produces the humor. However, he is soon made to believe his senses.

Single Variable Calculus, Chapter 3, 3.1, Section 3.1, Problem 23

a.) Suppose that $\displaystyle F(x) = \frac{5x}{ 1 + x^2}$, find $F'(2)$ and use it to find an equation of the tangent line to the curve $\displaystyle y = \frac{5x}{1 + x^2}$ at the point $(2,2)$

Using the definition of the derivative of a function $F$ at a number $a$, denoted by $F'(a)$, is

$\qquad \displaystyle \qquad F'(a) = \lim_{h \to 0} \frac{F(a + h) - F(a)}{h}$

We have,


$
\begin{equation}
\begin{aligned}

\qquad F'(a) =& \lim \limits_{h \to 0} \frac{\displaystyle \frac{5(a + h)}{1 + (a + h)^2} - \frac{5a}{1+ a^2}}{h}
&& \text{Substitute $F'(a + h)$ and $F(a)$}\\
\\
\qquad F'(a) =& \lim \limits_{h \to 0} \frac{(5a + 5h)(1 + a^2)- 5 a[1 + (a + h)^2]}{(h)(1 + a^2)[1 + (a + h)^2]}
&& \text{Get the LCD of the numerator}\\
\\
\qquad F'(a) =& \lim \limits_{h \to 0} \frac{5a + 5a^3 + 5h + 5a^2 h - 5a (a^2 + 2ah + h^2 + 1)}{(h)(1 + a^2)[1 + (a + h)^2]}
&& \text{Expand the equation}
\\
\qquad F'(a) =& \lim \limits_{h \to 0} \frac{\cancel{5a} + \cancel{5a^3} + 5h + 5a^2 h - \cancel{5a} - \cancel{5a^3} - 10a^2 h - 5ah^2}{(h)(1 + a^2)[1 + (a + h)^2]}
&& \text{Combine like terms and simplify}\\
\\
\qquad F'(a) =& \lim \limits_{h \to 0} \frac{5h - 5a^2 h - 5ah^2}{(h)(1 + a^2)[1 + (a+ h)^2]}
&& \text{Factor the numerator}\\
\\
\qquad F'(a) =& \lim \limits_{h \to 0} \frac{\cancel{h}(5 - 5a^2 - 5ah)}{\cancel{(h)}(1 + a^2)[1 + (a + h)^2]}
&& \text{Cancel out like terms}\\
\\
\qquad F'(a) =& \lim \limits_{h \to 0} \frac{5 - 5a^2 - 5ah}{(1 + a^2)[1 + (a + h)^2]} = \frac{5 - 5a^2 - 5a(0)}{1 + (a + 0)^2}
&& \text{Evaluate the limit}\\
\\
\qquad F'(a) =& \frac{5 - 5a^2}{(1 + a^2)^2}
&& \text{Substitute the value of $(a)$}\\
\\
\qquad F'(2) =& \frac{5 - 5(2)^2}{(1 + (2)^2)^2}
&& \text{Simplify}

\end{aligned}
\end{equation}
$



$\qquad \fbox{$F'(2) \displaystyle = \frac{-15}{25} = \frac{-3}{5}$} \qquad$
Slope of the tangent line at $(2,2)$

Using Point Slope Form where the tangent line $y = F(x)$ at $(a, F(a))$


$
\begin{equation}
\begin{aligned}

y - F(a) =& F'(a) (x -a)\\
&& \\
\\

y =& \frac{-3x + 6}{5} + 2
&& \text{Substitute the value of $a, F(a)$ and $F'(a)$}\\
\\

y =& \frac{-3x + 6 + 10}{5}
&& \text{Combine like terms}


\end{aligned}
\end{equation}
$


$\qquad \fbox{$ y = \displaystyle \frac{ -3x + 16}{5}$} \qquad$ Equation of the tangent line at $(2,2)$

b.) Draw a graph of the curve and the tangent line on the same screen.

What bothers Claudius and Gertrude about Hamlet's dress?

A grief-stricken Hamlet is moping around Elsinore, still mourning the death of his father. In keeping with tradition, he is wearing black. Claudius isn't too happy that Hamlet hasn't been able to get over his loss and move on. For one thing, Hamlet's sad demeanor acts as a constant reminder of Claudius's villainous act. Hamlet doesn't know it yet, but his father was murdered by Claudius, and so it's not surprising that Claudius doesn't want to be reminded of this inconvenient fact. He then proceeds to give Hamlet a patronizing lecture, telling him that, although it's awfully sweet of him to show such grief over his father's death, he needs to move on, man up, and start acting like a prince:

Tis sweet and commendable in your nature, Hamlet, / To give these mourning duties to your father: / But, you must know, your father lost a father; / That father lost, lost his, and the survivor bound / In filial obligation for some term To do obsequious sorrow. But to persever / In obstinate condolement is a course / Of impious stubbornness; 'tis unmanly grief (act 1, scene 2).

Gertrude is also a little unnerved by Hamlet's black clothing and equally black demeanor. She too is reminded of her late husband. Though her advice to Hamlet is couched in much gentler, softer language than that of Claudius, her message is pretty much the same:

Good Hamlet, cast thy nighted color off, / And let thine eye look like a friend on Denmark. / Do not forever with thy vailèd lids / Seek for thy noble father in the dust: Thou know’st ’tis common; all that lives must die, / Passing through nature to eternity (act 1, scene 2).

Precalculus, Chapter 6, 6.4, Section 6.4, Problem 40

You need to use the formula of dot product to find the angle between two vectors, u = u_x*i + u_y*j, v = v_x*i + v_y*j , such that:
u*v = |u|*|v|*cos(theta)
The angle between the vectors u and v is theta.
cos theta = (u*v)/(|u|*|v|)
First, you need to evaluate the product of the vectors u and v, such that:
u*v = u_x*v_x + u_y*v_y
u*v = cos(pi/4)*cos(pi/2) + sin(pi/4)*sin(pi/2)
u*v = cos(pi/2-pi/4) = sin pi/4 = sqrt2/2
You need to evaluate the magnitudes |u| and |v|, such that:
|u|= sqrt(cos^2(pi/4) + sin^2(pi/4)) => |u|= sqrt(1) =>|u|= 1
|v|= sqrt(cos^2(pi/2) + sin^2(pi/2)) => |v|= sqrt(1) =>|v|= 1
cos theta = (sqrt2/2)/(1*1) => cos theta = sqrt2/2 => theta = pi/4
Hence, the cosine of the angle between the vectors u and v is cos theta = sqrt2/2 , so, theta = pi/4.

why were george and lennie going to the ranch

After reading chapter one, we find that George and Lennie are headed to the new ranch for a couple of reasons. The first reason is because Lennie got in trouble at their previous ranch. More specifically, Lennie has a fascination with soft things and wanted to touch a woman's soft dress. Unaware of Lennie's disability, the woman thought that he was trying to hurt or even rape her, so George and Lennie were required to flee that ranch. They obtained work permits and proceeded to find work in Soledad on the new ranch.
The second reason they are headed to the ranch is because they must work to earn money to achieve their dream. Both George and Lennie have a dream of owning their own ranch someday where Lennie can tend to the rabbits. This current ranch will provide them with a place to live while they save their money to one day buy their own piece of land.

To answer this question, take a look at Chapter One when we meet George and Lennie on their way to the new ranch. From their conversation, we learn that they were forced to leave their previous ranch because Lennie got into trouble. Specifically, Lennie wanted to stroke a girl's dress because it felt soft. However, she believed that he was trying to rape or hurt her, which resulted in George and Lennie having to flee the ranch and find work elsewhere.
Another reason for going to the ranch is financial. George and Lennie have a dream of owning their own ranch and must save up enough money if they are to make this dream a reality. The new ranch, therefore, will provide them a living while they get the money together to buy a place of their own.

Precalculus, Chapter 9, 9.4, Section 9.4, Problem 17

You need to use mathematical induction to prove the formula for every positive integer n, hence, you need to perform the two steps of the method, such that:
Step 1: Basis: Show that the statement P(n) hold for n = 1, such that:
1 = 1(1+1)/2 => 1 = 1*2/2 => 1=1
Step 2: Inductive step: Show that if P(k) holds, then also P(k + 1) holds:
P(k): 1 + 2 + .. + k = (k(k+1))/2 holds
P(k+1): 1 + 2 + ... + k + (k+1) = ((k+1)(k+2))/2
You need to use induction hypothesis that P(k) holds, hence, you need to re-write the left side, such that:
(k(k+1))/2 + k + 1 = ((k+1)(k+2))/2
k(k+1) + 2k + 2 = k^2 + 2k + k + 2
k^2 + k + 2k + 2 = k^2 + 2k + k + 2
Notice that P(k+1) holds.
Hence, since both the basis and the inductive step have been verified, by mathematical induction, the statement P(n): 1 + 2 + 3 + ... + n = (n(n+1))/2 holds for all positive integers n.

Give three examples of Decius using flattery to get Caesar to the Capitol.

Decius advises Brutus that he is quite sure he can "o'ersway" Caesar, even if he has "resolved" not to come to the Capitol. He says that flattery is generally effective in persuading Caesar:

But when I tell him he hates flatterers,He says he does, being then most flattered.

Later, when Caesar asks Decius to tell the senators that he "will not come today," Decius calls him "Most mighty Caesar," beginning to wear him down with flattering epithets. Later, Decius offers a reinterpretation of Calpurnia's dream which paints Caesar as a font of goodness: "from you great Rome shall suck / Reviving blood." Caesar is, indeed, swayed by this argument; he allows Decius to convince him that the vision of a statue spouting blood could actually be a positive sign.
Finally, Decius appeals to Caesar's desire for general approval and praise by telling him that the senate has decided "to give this day a crown to mighty Caesar." If Caesar does not come to the Capitol, Decius says, they might change their minds.

Single Variable Calculus, Chapter 1, 1.3, Section 1.3, Problem 61

(a) Suppose you have $g(x) = 2x+1$ and $h(x) = 4x^2 + 4x +7$, find a function $f$ such that $f o g = h$.

In order to obtain the equation of $f(x)$, we must consider first that the highest degree of the function $h$ is 2 and the highest degree of $g$ is 1, then the function $f(x$) must have the highest degree of 2 also.

Let $f(x) = Ax^2 + Bx + C$ where $A, B, C$ are constant


$
\begin{equation}
\begin{aligned}

f \circ g(x) &= f(g(x))\\
f(2x + 1) &= Ax^2 + Bx + C\\
f(2x + 1) &= A(2x + 1)^2 + B(2x + 1)+ C\\
f \circ g & = 4Ax^2 + 4Ax + A + 2Bx + B + C\\

\end{aligned}
\end{equation}
$


To obtain $f \circ g = h$

$f \circ g = h$


$
\begin{equation}
\begin{aligned}

4Ax^2 + 4Ax + A + 2Bx + B + C &= 4x^2 + 4x + 7\\

\end{aligned}
\end{equation}
$


To solve the value of $A$


$
\begin{equation}
\begin{aligned}

\frac{\cancel{4}A\cancel{x^2}}{\cancel{4}\cancel{x^2}} &= \frac{\cancel{4x^2}}{\cancel{4x^2}}\\
A &= 1

\end{aligned}
\end{equation}
$


To solve the value of $B$


$
\begin{equation}
\begin{aligned}

4Ax + 2Bx &= 4x\\
4(1)x + 2Bx &= 4x\\
4x + 2Bx &= 4x\\
2Bx &= 4x - 4x\\
\frac{\cancel{2}B\cancel{x}}{\cancel{2}\cancel{x}} &= \frac{0}{2x}\\
B &= 0

\end{aligned}
\end{equation}
$


To solve the value of $C$


$
\begin{equation}
\begin{aligned}

A + B + C &= 7\\
1 + 0 + C &= 7\\
C &= 7 - 1\\
C &= 6

\end{aligned}
\end{equation}
$


Substitute values of $A, B$ & $C$ to the function $f(x) = Ax^2 + Bx + C$

$f(x) = (1)(x^2) + (0)(x) + 6$

$\fbox{$f(x) = x^2 + 6$}$

(b) Assume that $f(x) = 3x + 5$ and $h(x) = 3x^2 + 3x + 2$, find a function $g$ such that $f \circ g = h$
In order to obtain function $g(x)$, we must know that the highest degree of $h$ is 2 and the higest degree of $f$ is 1, then $g$ must have the highest degree which is 2.
Let $g(x) = Ax^2 + Bx + C$ where $A, B,$ and $C$ are constant then


$
\begin{equation}
\begin{aligned}

f \circ g (x) =& f(g(x))\\
f(Ax^2 + Bx + C) =& 3x + 5\\
f \circ g =& 3Ax^2 + 3Bx + 3C + 5\\
\text { To obtain } f \circ g =& h\\
3Ax^2 + 3Bx + 3C + 5 =& 3x^2 + 3x + 2\\
\end{aligned}
\end{equation}
$


Solving for the value of $A, B, C$


$
\begin{equation}
\begin{aligned}

\frac{\cancel{3} A \cancel{x^2}}{\cancel{3}\cancel{x^2}} =& \frac{\cancel{3x^2}}{\cancel{3x^2}}\\
A =& 1\\
\\
\frac{\cancel{3}B \cancel{x}}{\cancel{3x}} =& \frac{\cancel{3x}}{\cancel{3x}}\\
B =& 1\\
\\
3C + 5 =& 2\\
3C =& 2-5\\
\frac{3C}{3} =& \frac{-3}{3}\\
C =& -1
\end{aligned}
\end{equation}
$


Substitute the value $A, B, C$ to function $g(x) = Ax^2 + Bx + C$

$g(x) = (1)(x^2) + (1)(x) + (-1)$
$\fbox{$g(x) = x^2 + x - 1$}$

If it takes 50 mL of 0.05M HCL to neutralize 345 mL of Mg(OH)2 solution, what is the concentration of the Mg(OH)2 solution?

First, write the unbalanced equation:
Mg (OH)_2 + H Cl = Mg Cl_2 + H_2 O.
It is simple to balance it:
Mg (OH)_2 + 2H Cl = Mg Cl_2 + 2H_2 O
(give the coefficient 2 to H Cl to balance 2 Cl at the right side, then give the coefficient 2 to H_2 O to balance O, and we are done).
Thus one mole of Mg (OH)_2 requires two moles of H Cl to be neutralized.
Next, there are 0.05 (mol)/L * 50*10^(-3) L = 2.5*10^-3 mol  of  H Cl  in  H Cl solution, therefore there are twice less moles of Mg (OH)_2, 1.25*10^-3 mol. This gives the molarity (molar concentration) of Mg (OH)_2 to be equal to  (1.25*10^-3 mol)/(345 mL) = (1.25 mol)/(345 L) approx 0.0036 M.  This is the answer.

What were the features of Lincoln's plan of Reconstruction?

Following the Union victory in the American Civil War, there were several plans for reconstruction. President Lincoln's Ten Percent Plan was far different from the one put in place under President Andrew Johnson.
The Ten Percent Plan intended to reunite the country by weakening the Confederate states and reunify the nation through reconstruction rather than harshly punish the Confederate states for the costly war. To establish a new state government in the Union, ten percent of the state's prewar voters needed to take an oath of loyalty.
After completing this step, states could begin the process of electing delegates to draft a new state constitution and start rebuilding. All Confederates were eligible for a full pardon except for high-ranking military and party members. Lincoln's compromise would protect the property of all citizens living in Confederate states, with the exception of slaves.
The plan, which wasn't supported by Congress, didn't promote the rights of former slaves. But, it did require states to recognize the end of slavery.
https://worldhistoryproject.org/1863/12/8/lincoln-attempts-reconstruction-with-the-ten-percent-plan

https://www.britannica.com/event/Reconstruction-United-States-history

Abraham Lincoln developed his own plan of Reconstruction. It was often referred to as the Ten Percent Plan. President Lincoln was thinking of Reconstruction before the Civil War had ended. He issued his plan in December 1863.
His plan had several features. Once ten percent of the voters of a state would take an oath of loyalty to the United States, they would be able to form a new state government. They would adopt a state constitution that banned slavery. President Lincoln was also willing to offer amnesty to all white southerners who agreed to be loyal to the United States. However, this didn’t include the former leaders of the Confederacy. President Lincoln also encouraged the southern states to give more freedoms to the former slaves. However, since this wasn’t required in his plan, states were under no obligation to do this.
President Lincoln believed that Reconstruction should not be unduly harsh on the South. President Lincoln knew the country needed to reunite. He believed a harsh plan would make unity more difficult. His plan reflected these ideas.
https://www.history.com/this-day-in-history/lincoln-issues-proclamation-of-amnesty-and-reconstruction

https://www.u-s-history.com/pages/h177.html

Single Variable Calculus, Chapter 3, 3.3, Section 3.3, Problem 24

Determine $Y(u) = (u^{-2} + u^{-3})(u^5 - 2u^2)$


$
\begin{equation}
\begin{aligned}

y(u) =& (u^{-2} + u^{-3})(u^5 - 2u^2)
&& \text{Expand the equation}
\\
\\
y(u) =& (u^{-2 + 5} + u^{-3 + 5} - 2u^{-2 + 2} - 2u^{-3 + 2})
&& \text{Simplify the equation}
\\
\\
y(u) =& u^3 + u^2 - 2u^0 - 2u^{-1}
&& \text{Apply Power Rule}
\\
\\
y'(u) =& \frac{d}{du} (u^3) + \frac{d}{du} (u^2) - 2 \frac{d}{du} (u^-1) - \frac{d}{du} (2)
&&
\\
\\
y'(u) =& 3u^2 + 2u - (2)(-1)(u^{-2}) - 0
&& \text{Simplify the equation}
\\
\\
y'(u) =& 3u^2 + 2u + 2u^{-2}

\end{aligned}
\end{equation}
$

What do Mary’s geraniums symbolize?

This is open to interpretation, and Mary's geraniums are actually mentioned only twice in the story. However, if we think about what Mary represents in a wider context, we can infer from that what her geraniums may symbolize.
When the Doctor first sees Mary's geraniums, he is surprised that they are still blooming despite the fact that geraniums do not typically stay in flower in the winter. He asks her what she has done to keep the flowers alive, and remarks that every time he passes the house, it is always full of flowers. Mary doesn't answer his question, but she does immediately pluck one of the best geraniums and offer it to the doctor. The geraniums, then, represent the outcome of Mary's nurturing nature and her tenacity. Because Mary is an endless reserve of comfort and sustenance to her family, she is able to represent this physically by filling the house with the flowers which represent this sustenance and keep the house beautiful. Mary's dedication does not flag, even when others might be tempted to leave off tending to their charges for a time (as in winter). Mary's dedication does not know seasons, but flowers all year.
Later in the story, Rosicky notices that Mary had "a big red geranium in bloom for Christmas." This has been given to her by Doctor Ed from Omaha, and the flower reminds Rosicky "of plants he had seen in England." Like Rosicky, then, the geranium is not necessarily a plant native to the land in which they are now living. It reminds him of other countries and other times. But just as the geranium is able to flower under Mary's care in this new country, so the Rosicky family, transplanted from elsewhere, will eventually set down roots and flower if they stick together. The flourishing of Mary's geraniums, then can be said to symbolize the flourishing of the wider family, born out of dedication and unity.

What is an analysis of "America" by Allen Ginsberg?

The poem "America" by Allen Ginsberg is a simultaneously painful and sardonic cry for what he feels is America's betrayal of its citizens. Allen Ginsberg was one of the pillar figures of the Beat Generation, which arose in the early 1950's streets of New York. The Beat movement is difficult to define succinctly since it refers to both a small, connected group of authors as well as a widespread feeling of anger and apathy that was spreading to many American youths in the post-war era. This poem, "America", was written in 1956; just one year after Ginsberg's first reading of his most well-known work, "Howl". Ginsberg and the Beat movement gained a lot of popularity after the debut of "Howl", and Ginsberg now thought it was time to address America head-on.


"America I've given you all and now I'm nothing"

The first line of the poem makes it clear Ginsberg feels as though the relationship he shares with his home country is unfair or uneven. Ginsberg states that although he has given all of himself away, he has gotten nothing in return. This is Ginsberg's chance to demand answers and change for several of the country's wrongdoings and shortcomings. While Ginsberg makes several serious, straightforward accusations, he also employs a heavy use of irony and sarcasm while speaking to America. He speaks of war crimes and social injustice, but also complains that he wants to buy what he needs from the supermarkets with his "good looks". Ginsberg does this in order to convey the disorienting, tumultuous task of identifying as an American.
Even while Ginsberg makes demands for justice on behalf of the displaced and disenfranchised, it is clear that he does not feel sure of himself or his message. This is crescendoed in the final line of the first stanza, in which he states

"It occurs to me that I am America.I'm talking to myself again."

Along with a large population of Americans at the time, Ginsberg felt unsure of his place in his country and its plans. He felt genuine anger and desire for justice for so many of America's actions, yet still knew that he himself was made from America, and he himself still is America, no matter how much he dislikes it. Towards the end of the poem Ginsberg presents an excerpt of what could be internal dialogue that plagues him and fellow Americans.

"America its them bad Russians.
Them Russians them Russians and them Chinamen. And them Russians.
The Russia wants to eat us alive. The Russia’s power mad. She wants to take our cars from out our garages.
Her wants to grab Chicago. Her needs a Red Reader’s Digest. Her wants our auto plants in Siberia. Him big bureaucracy running our fillingstations.
That no good. Ugh. Him make Indians learn read. Him need big black n******. Hah. Her make us all work sixteen hours a day. Help."

The short, choppy way in which the sentences are written sound like an individual losing his mind, punctuated by a short, exhausted plea for help from the madness. The poem is presented in a stream of consciousness format, and thus evokes feelings of urgency and rawness. Ginsberg cared about his country and the well-being of its citizens deeply, he just also felt as though it was driving him insane. The poem "America" runs parallel to many of the themes prevalent in other works that came from the Beat Movement. The youth of America felt as though their country was spinning out of control, and leaving its most vulnerable citizens behind. The country was the most powerful force in the world, yet many felt not a force for good. That's why Ginsberg closes his poem with a statement of independence; declaring that no matter the wrongs done to him and others around him, he's not stopping.

"America I'm putting my queer shoulder to the wheel"

Explore the links below to hear a live reading of Ginsberg's "America", as well as a short video which pairs his reading with images of America at the time. Be sure to pay attention to the emotions you hear in Ginsberg's voice, and the emotions you feel as you hear the words and imagine the scenes presented; it's the most important part of reading Ginsberg's poetry.

"America" by Allen Ginsberg might be described as a protest rant or outcry against perceived social, political, and personal injustice in the United States. Ginsberg was part of the Beat Generation of writers and artists, who embraced jazz music, African American culture, drug use, leftist politics, and sexual liberation. Among others, the "Beats" included Ginsberg, Jack Kerouac, and William Burroughs. Ginsberg's membership in this "fraternity" is made evident by his reference to Burroughs in Tangiers in this poem.
The poem is perhaps best analyzed from an historical and cultural perspective. It was written in 1956 during the McCarthy era and the Cold War. Ginsberg is "raging" against political and social injustice in America. He references (among other things) "the Wobblies" (an international labor union), Trotskyites, the atom bomb, Marx, Tom Mooney, Spanish Loyalists, the Scottsboro Boys, and Sacco and Vanzetti. In doing so, he is positioning himself as left-leaning politically, against racial injustice, and against America's militarism. The poem also decries rampant capitalism through Ginsberg's laments about his own financial status as an artist and attacks on American corporate greed. The poem ends with "America I'm putting my queer shoulder to the wheel," a statement about Ginsberg's sexuality (a controversial issue for the 1950s) and his determination to impact American society through his writing, which is exactly what he is doing in the poem.
The poem is structured as a series of questions, which echoes Langston Hughes's poem "Let America Be America Again."

What is a critical analysis of the poem "O What is That Sound"?

W.H. Auden’s “O What is That Sound” is a ballad in which two narrators—presumably married—converse about a troupe of soldiers that is coming toward their home. The poem was published in the early 1930s, a time of growing civil unrest and military strategizing as Europe marched ever closer toward World War II.
Each stanza follows a question-and-answer format with an ABAB rhyme scheme throughout. The first line of each stanza begins with “O,” which indicates a sense of urgency or confusion. The repetition in the poem emphasizes this tone and establishes a sing-song rhythm that mimics the “drumming, drumming” mentioned in the first stanza.
A shift occurs at the end of the seventh stanza with the line “And now they are running.” While earlier descriptions of the “scarlet soldiers” have been rather rational and unconcerned, the second narrator, who has been answering the other’s questions, seems surprised by this detail. Noticing for the first time that the soldiers seem headed directly for their home, the second narrator is distressed.
The last two stanzas of the poem have a frightened, suspenseful tone that suggests something violent is about to happen to the narrators: the soldiers’ “boots are heavy on the floor” and “eyes are burning.” The imagery of burning eyes suggests anger or destruction, which is directed toward at least one of the narrators.
Therefore, Auden is commenting on the destructive, violent nature of war that invades even the most provincial places—along with the persecution it includes. Considering that WWI had ended shortly before the poem’s publication and that WWII came shortly after (Hitler became chancellor of Germany in 1933), Auden’s poem has an almost prophetic mood.

How does Lincoln's Second Inaugural Address show that his views have changed since his First Inaugural Address?

President Lincoln’s second inaugural address showed that his views had changed from when he gave his first inaugural address. When President Lincoln first took office, our country was splitting apart. Several states had left the Union already, and there was concern additional states could leave. As a result, President Lincoln had to make it very clear that he had no intention of ending slavery where it already existed. If he came out and said he was against slavery and wanted to end it, more states might have left the Union. He might also have lost the support of some people in the North who were not against slavery but were in favor of saving the Union.
In his second inaugural address, President Lincoln made it very clear that he opposed slavery. He made it clear that the Civil War was about the issue of slavery, which he considered to be an evil institution. He believed it was our duty to solve the slavery issue. By this time, it was clear the North would win the war. This allowed President Lincoln to use this address to try to heal the wounds the Civil War had caused and to focus on reuniting the country.
http://www.let.rug.nl/usa/presidents/abraham-lincoln/first-inaugural-address-1861.php

https://www.ourdocuments.gov/doc.php?flash=false&doc=38

Who founded Islam?

The Prophet Muhammad was the founder of Islam. Muhammad was a merchant who was born in and lived in Mecca, a commercial hub on the Arabian peninsula. He worked along the many trade routes that traversed the region and became wealthy in the process. As he entered middle age, the Archangel Gabriel appeared to him and commanded him to recite a series of revelations that he made to him. These became the foundation of the Qur'an, and the basic truth that was revealed was that there was no God other than Allah, a departure from the polytheism practiced throughout much of the region. Muhammad was forced to leave Mecca due to the unpopularity of his message with many of the wealthy merchants in that city, and went to Medinah in 622, a journey known as the hijrah. He returned triumphantly a few years later as his preaching had popularized his message to the point where even Mecca's elites had embraced it. After his death, Islam spread along trade routes and through Arab military expansion through the Middle East, North Africa, and the old Byzantine Empire.
https://www.metmuseum.org/learn/educators/curriculum-resources/art-of-the-islamic-world/unit-one/the-prophet-muhammad-and-the-origins-of-islam

https://www.metmuseum.org/toah/hd/isla/hd_isla.htm

The religion of Islam was not founded by any individual person; it is a religion of God, Allah, in Arabic. Contrary to popular belief that Muhammad is the founder of Islam, Muhammad was merely a 40-year-old man (570-632 AD) whom Allah chose to represent and spread the religion. When Allah chose Muhammad, he became a messenger and prophet of Allah. In Islam, the holy book known as, the Quran, is a book of guidance written by Allah and dictated to Muhammad through visits from the Angel Gabriel, Jibreel in Arabic. Muhammad memorized the dictations, (he was illiterate), and understood the meaning. Thus, he began spreading Islam to his close family members and friends, then to the community for the next twenty-three years until his death at the age of 63. Muslims believe that the principles and teachings of Islam predate Muhammad, as the Quran states, “He [Allah] has sent down upon you [O’ Muhammad] the book of truth, confirming what was before it. And He [Allah] revealed the Torah and the Gospel.”

According to Islamic tradition, the founder of the religion was the prophet Mohammad, who was born in Mecca in 570 C.E. When Mohammad was at the age of 40, Allah (the name of God in Islam) revealed himself to Mohammad as the one true God, and, through the Angel Gabriel, delivered the teachings that would become the Islamic holy book known as the Qu'ran. The Qu'ran defines Islam as the religion of the one true God, it outlines the rules and requirements for behavior and describes the conditions that would bring about the end of the world and the Apocalypse. In the Saudi Peninsula of Mohammad's day, the monotheistic Judaism and Christianity were well established, and there were many followers of ancient polytheistic traditions. Islam took hold because of Mohammad's military and political prowess, and remains a dominant world religion to this day. Mohammad died in 632 C.E.

A Complicated Kindness is roughly structured along the lines of the bildungsroman. How would you examine the novel’s approach to this genre in a five paragraph essay?

This is an exciting topic, one that suggests many different ways of approach and methods of organization.
Because your instructor specified that you should write “at least 5 paragraphs,” you’re free to write more—assuming your thoughts and your chosen method of organizing them require more than five paragraphs.
I suggest that before you create your outline for this essay you spend some time getting familiar with the bildungsroman as a genre. What is it? What are the most famous examples of it? What are some non-examples—that is, what distinguishes a bildungsroman from any other novel? If you have notes on the bildungsroman genre from class or from your course textbook, refer to those as well.
A good place to start to get a general understanding of a literary term is an encyclopedia entry. Here’s a good one on the bildungsroman.
Then, once you’re comfortable with the basic idea, dig a little deeper: refer to an encyclopedia of literary terms, or a reference on critical literary theory. This one and this one are a few entries from trusted texts, just to get you started.
While you’re researching, you might try searching your school’s database of literary journals to see if other students, authors, or literary critics have already explored the idea you’re about to explore, namely how A Complicated Kindness fits with the genre of the bildungsroman. Try searching with key terms like the book’s title and the word “bildungsroman.” The point here is of course not to copy what other people have said, but to sift through their ideas, weigh them, and perhaps allow them to shape your own perspective. It’s completely okay to skip this extra step. When it comes to writing about literature, there is plenty of joy and value in forming ideas solely on your own.
As you discover exactly what a bildungsroman is, you’ll come across many examples of novels that meet their criteria. Now, I doubt you have time to read those novels, but I bet you have time to read summaries of them, so you can get a better idea of how a bildungsroman unfolds. To find a summary of a particular novel, just type its title into the search bar here on our site.
My advice next is to take a very close look at the essay instructions. You don’t want to accidentally oversimplify them. Your instructor has already stated that the novel does basically follow the pattern of a bildungsroman. Notice, then, that your goal here is not to answer the simple question, “Is the novel a bildungsroman?” Rather, your goal is to answer the question, “How does the novel’s approach compare with that of a bildungsroman?” In other words, what aspects of this book are like a bildungsroman and in what way exactly?
By now as you’ve researched the bildungsroman you’ve made yourself a list of its key aspects. (What are they? Some sources list just two or three aspects to define a bildungsroman, some list more, and—at the risk of overwhelming you—I’ll share that this instructor lists eighteen key aspects of a bildungsroman.)
You might choose to organize your essay around those aspects. Let’s say that, according to your understanding, a bildungsroman must have three certain aspects (let’s call them A, B, and C), probably has another certain aspect (let’s call it D), and never has another certain aspect (let’s call that one E). So, in between your introduction and conclusion you can have five paragraphs: one for each of those aspects (A, B, C, D, and E), and in each paragraph, you can discuss how A Complicated Kindness does or does not exhibit that particular aspect.
Or, you might choose to organize your ideas by brainstorming a list of the most important, more pervasive qualities of A Complicated Kindness, and then spend a paragraph on each of those qualities, explaining how each is or isn’t characteristic of the bildungsroman. For example, an important quality of this novel is how Nomi grows as a person (which is definitely a typical quality in a bildungsroman), and another is how the novel's humor is quite dark (which is a quality that has very little to do with the bildungsroman).
Regardless of how you decide to organize your thoughts, the success of your essay will hinge on how well you illustrate the qualities that you do see in A Complicated Kindness. For example, it would be effective to write that Nomi is a sensitive person who actively reaches for answers and self-growth, as evidenced by her attempt to uncover the truth about her mother, Trudie, and Trudie’s involvement with Mr. Quiring. (There's your cue to discuss the situation, bringing in relevant quotes from the novel that illustrate Nomi's thirst for knowledge.) But, it would be ineffective to write that Nomi is sensitive and that she cares about what happened to her family in the past. Why? It’s too vague. You’re trying to claim that the novel aligns somewhat with the qualities of a bildungsroman, so throughout your body paragraphs, point to the precise people, events, and statements that back up your claim.
Remember to sandwich your discussion with an introduction and a conclusion, good places to tie your ideas together and say why they’re worth the reader’s consideration.
Good luck, and let us know if you have other questions!
https://www.britannica.com/art/bildungsroman

https://www.oxfordreference.com/view/10.1093/oi/authority.20110803095505632

As your instructor wants your work organized into a five paragraph essay, your major focus in completing this assignment should be clarity of structure, in which each paragraph has a strong single focus.
Introduction: In your first, introductory paragraph you should define the Bildungsroman, or apprenticeship novel. This is a genre focused on the coming of age of a protagonist, usually focusing on the protagonist's psychological development. Although it usually has some sort of plot structure, its emphasis is more on the protagonist's thoughts and feelings than on action.
Paragraph 2: The protagonist Nomi Nickel, a sensitive and rebellious young teenage girl, is a typical protagonist of the Bildungsroman in both her age and her rebellion against her environment. Thus your first body paragraph should focus on how the character fits the genre.
Paragraph 3: The second body paragraph should focus on the second crucial issue for whether a novel fits this genre: the degree to which the character evolves. Since she moves from stages of acceptance of her community, through rebellion to qualified acceptance, she fits the criteria for a protagonist in the genre.
Paragraph 4: Explore the novel's use of the psychological, another aspect of the genre. We encounter many instances of self-reflection by the character such as her speculation that:

It’s hard to grieve in a town where everything that happens is God’s will. It’s hard to know what to do with your emptiness when you’re not supposed to have emptiness.

Paragraph 5: This should summarize how your evidence points to the novel fitting within the genre. 
 
 

What does Orwell's vision of the future look like in the book 1984?

There are many aspects to Orwell's vision of the future in his famous novel. The basic outlines can be summarized as follows, with the proviso that in a relatively brief answer such as this, any description of the 1984 world must be simplified to an extent.
We are told early on that the story is taking place in a world where a nuclear war has occurred, for there is a reference to the time early in Winston's memory "when the atomic bomb fell on Colchester." The actual details beyond that are not given, but the world has been reorganized into three "superstates": Oceania, which we are led to believe includes the British Isles, the United States, and the rest of the Americas, and possibly the other English-speaking parts of the world such as Australia; Eurasia, which includes the continent of Europe including the former Soviet Union and possibly the Middle East; and Eastasia, which would be China, Japan, Southeast Asia, and most of the Pacific islands, presumably. The world is in a continuous state of war, usually with one superstate in alliance with another against the third one.
All three super-states apparently have the same dictatorial, totalitarian system of government. Freedom of speech is suppressed, and even freedom of thought is dangerous because the assumption is that the secret police, called the Thought Police, have the ability to find out what people are thinking and arrest them for anti-government ideas even if the offending person has not actually committed an overt crime. The social hierarchy consists of three strata or levels. At the top is the Inner Party, the elite government managerial class who have the highest standard of living and actually "run things," creating "policy" and systematically feeding lies to the public and directing the falsification of historical records.
The group just below them is the Outer Party, to which Winston, Julia, and most of the other characters in the story belong. These people, though Party members, have no say in how the state is run and are basically low-level but skilled functionaries who carry out the tasks assigned by the Inner Party bosses. In some sense they are a futuristic version of the middle class—people with technical skills but without authority, like the non-managerial employees of a business.
And the third, lowest level of the hierarchy are the proles, the working-class people who make up approximately 70% of the population. The system is supposed to be a form of socialism, but the Party are taught to despise the proles, and even to consider them "not human beings." At the very pinnacle of this structure is Big Brother, the "Leader," a kind of futuristic Stalin or Hitler who may in fact not even be a real person but merely a symbol of absolute authority personified. His huge picture is posted everywhere, made to look as if the eyes are following one at all times. The population is under constant surveillance through "telescreens," TV screens which are placed everywhere and have the ability both to transmit and to receive, so that people are being watched at all times. Private life has come to an end.
Bombs are falling on London all the time, because of the perpetual state of war Oceania is in with one or the other of the rival super-states. But no "progress" one way or the other ever occurs in this warfare. We are given to understand that although the use of atomic bombs was at least partly what resulted in this post-cataclysmic world, only "conventional" bombs are now dropped, and appear to do no significant damage. The endless war is a psychological mechanism to keep the population in a state of fear and terror. The general condition of life in Oceania, and presumably the other superstates, is one of privation. Food is scanty and poor, Outer Party members must wear uniforms (specifically overalls, which traditionally are the clothing of British working-class people, though Party members are taught to despise the working class), their clothing and housing is in bad condition, and there is no freedom of social interaction. Though the society is atheistic, it is also sexually puritanical. Winston and Julia, in merely having a relationship without being married, are committing a crime. The end result is that they are arrested and tortured into a "re-educated" state, not entirely because Winston has had "heretical" thoughts which he has recorded in a diary, but because he and Julia have defied the Party simply through their act of loving each other.
This is the nightmare future Orwell has imagined. It is a projection into the future of things that were already happening in the first half of the twentieth century in both the Soviet Union and Nazi Germany. A government has taken control that purports to be socialistic, but the actual aim of the leaders is unlimited and absolute power for themselves. When Winston is being tortured and "re-educated," O'Brien makes it clear that the old ideas about equality and a workers' states are a sham, intended to dupe the population into thinking the leaders support them. An important part of this dystopian world is the Party's manipulation of language, the creation of a new, scaled-down English called Newspeak in which words are constantly being "destroyed" in order to limit people's ability even to think anti-government ideas, in so much as thought is dependent on words. It's not necessary to dwell on the fact that although Orwell's predictions have not come true, even thirty-four years after the year in which his novel is supposed to take place—some elements of them can be seen in real life today. It is anybody's guess if the complete prophesy will be fulfilled in the near or distant future.

What does Marmee say before Beth dies?

There isn't any mention in the novel of Marmee saying anything in particular before Beth dies, although the novel does state that, in her final days and hours, Beth "clung to the hand that had led her all her life." Both Marmee and Beth's father accompany her as she dies, and Alcott makes a particular point of stating that dying utterances or last words to a dying person are rarely as momentous as they are in books. For Beth, "the tide went out easily" and without fanfare, and she dies cradled on her mother's bosom. The last words actually addressed to Beth in the book are from Jo, who has watched over Beth closely throughout her final illness. Jo promises she will try very hard to keep going after Beth's death, and not be too sad, knowing she is going to a better place.

What two lines in her poem "On the Death of George Whitefield" concurs with the egalitarian nature of the great awakening and offers a partial explanation for her love of Whitefield?

In her elegy to the Reverend George Whitefield, African-American poet Phillis Wheatley expresses her admiration for the Anglican minister and laments his passing.  Lines five and six communicate, as you say, "the egalitarian nature of the Great Awakening."

"Thy sermons in unequalled accents flowed,
And every bosom with devotion glowed;"

Wheatley observes that Whitefield had no equal in the pulpit and that everyone who heard his sermons was devoted to him and God.  The Great Awakening, a religious revival movement in the American colonies which Whitefield was involved in the 1740's, sought to bring all people to the church; this egalitarian spirit was much different than the exclusionary stance the Puritans had taken in earlier years in the northern colonies.
It may well be that Phillis Wheatley, a slave in a Boston home, was especially impressed by a man who welcomed African-American slaves into the church and preached that God did not discriminate.  Some credit Whitefield with establishing African-American Christianity.

Calculus: Early Transcendentals, Chapter 6, 6.1, Section 6.1, Problem 23

y=cos(x) , y=sin(2x) , x=0 , x=pi/2
Refer the attached image, y=cos(x) is plotted in red color and y=sin(2x) is plotted in blue color.
From graph,
cos(x) is above sin(2x) from 0 to pi/6
sin(2x) is above cos(x) fron pi6 to pi/2
Area of the region enclosed by the given curves A=int_0^(pi/6)(cos(x)-sin(2x))dx+int_(pi/6)^(pi/2)((sin(2x)-cos(x))dx
A=[sin(x)-(-cos(2x)/2)]_0^(pi/6)+[-cos(2x)/2-sin(x)]_(pi/6)^(pi/2)
A=[sin(x)+cos(2x)/2]_0^(pi/6)+[-cos(2x)/2-sin(x)]_(pi/6)^(pi/2)
A=(sin(pi/6)+cos(pi/3)/2)-(sin(0)+cos(0)/2)+(-cos(pi)/2-sin(pi/2))-(-cos(pi/3)/2-sin(pi/6))
A=(1/2+1/4)-(0+1/2)+(1/2-1)-(-1/4-1/2)
A=1/4-1/2+1/4+1/2
A=1/2

Who and what is the protagonist and antagonist in the play "The Weir," by Conor McPherson?

Though this play, which includes people in a bar telling supernatural stories, does not involve a traditional protagonist or antagonist, the first three men in the bar—Jack, Brendan, and Jim—might be considered the protagonists. They anticipate the arrival of Valerie, a woman arriving in Sligo from Dublin, and they criticize their friend, Finbar, for escorting Valerie (as Finbar is married). When Valerie arrives in the pub, they vie for her attention and establish themselves as local experts, telling Valerie about the "faery" road that goes under the house that she has bought from Finbar.
Jack, Brendan, and Jim establish Valerie as the antagonist, as she is new to town. However, after they tell traditional Irish tales of ghosts and the supernatural, Valerie contributes her own tale about the death of her daughter from drowning. Her sad tale turns the men's attitudes toward her from distrust and sexual tension to sympathy and connection. In this sense, Valerie is the antagonist because she counters the men's banter and traditional ghost stories with a tale of deep emotion and sorrow. In the process, she turns their attitudes from ones that men traditionally have of women (competition) to a deeper human connection. The antagonist in the play could also be considered the force of the supernatural or fate, which controls the characters in each of the stories and is superior to them and their desires. 

What are plate boundaries?

This question almost certainly refers to the boundaries between lithospheric plates, also called tectonic plates. The outermost, solid part of the Earth is called the lithosphere. Large regions of the lithosphere are now known to move relative to one another, sliding on top of the asthenosphere, the layer beneath the lithosphere. The asthenosphere is the upper part of the Earth’s mantle and is described as “plastic,” meaning that even though it is solid, it deforms easily, allowing the plates of the lithosphere to slide on top of it.
Lithospheric plates are large, often millions of square miles. Most of North America is on one plate, for example. Based on the movement of these plates, the continents of the Earth previously all came together and moved apart again.
Lithospheric plates do not move fast—only one or a few centimeters in a year—but they do not all move in the same direction, so interesting things occur at the boundaries, the edges where two plates are in contact. Consider the boundary between two plates that are moving toward one another. This is called a convergent boundary. Something has to happen to the rock from the two sides that is being pushed together. What happens is that either one side subducts—passes beneath the other down into the Earth’s mantle—or else the rock gets pushed together, thickening and moving upward, forming a mountain range. The Alps and the Himalayas were formed this way.
If the two plates are moving apart, molten rock from the mantle wells upward to fill in the gap between them. This is called a divergent boundary. Plates can also move past one another in opposite directions. This is a transform boundary. The San Andreas fault system is an example where the Pacific plate is moving northwest while the adjacent North American plate is moving southeast. This relative motion cases frequent earthquakes as the rocks at the boundary catch on one another and then slip, catching up with the movement of their respective plates.

What would be a thesis statement about how Macbeth's soliloquies help readers see him in a better light?

A soliloquy occurs when a character speaks his thoughts aloud when the other characters are absent. Only the audience gets to hear what he is thinking.
Macbeth's seven soliloquies help us to understand his thought processes and his inner conflicts. The soliloquies are key to adding dimension to his character. If we only saw him from the outside, we might think of him as nothing more that a sociopathic killer from the start. Knowing his thoughts helps us to understand that he begins with a conscience. Through his soliloquies we track how he becomes dehumanized over time as his path of bloodshed continues.
We learn, for instance, in Macbeth's first soliloquy in act 1, scene 7, that he realizes and dreads the risks of killing Duncan. He wishes it could all end cleanly, with just this one death. However, he understands that once he starts down this road, it is likely to get bloodier and bloodier: he knows in his heart that Duncan's death won't be the end. He knows the bloodshed will come back to haunt him in this life as well as the afterlife. As he says:

Bloody instructions, which, being taught, return
To plague th' inventor

He shows himself to be human in his consideration of how wrong it is to betray Duncan. Duncan will be a guest under his roof: Macbeth, as his host, is supposed to protect him. Further, Duncan has been a good and just king who doesn't deserve to die.We also learn that ambition drives him to contemplate this path. Ambition is his only motivation: he doesn't enjoy violence and is heartsick at the idea of killing a beloved king. He has nothing ("no spur") against Duncan personally. We learn from his own thoughts that too much ambition is his great flaw. He states:


I have no spur
To prick the sides of my intent, but only
Vaulting ambition.

As we move to his soliloquy in act 3, scene 1, we see some of the changes that have come over Macbeth. Gone are the qualms and worries about killing a good man. Macbeth in this soliloquy rationalizes to himself killing Banquo. Banquo was once his good friend and does not deserve to die, but Macbeth has hardened inside and doesn't think about that. He doesn't care about his friend at all, but only about himself. He sees Banquo as a threat, because Banquo heard the witches' prophecy and might betray him.Macbeth is consumed with anger that he took all the risks of killing Duncan, but according to the witches' prophecy, it is Banquo's heirs who will inherit the throne. Macbeth says:


They [the witches] hailed him father to a line of kings.
Upon my head they placed a fruitless crown
And put a barren scepter in my grip.

Being king is not the be all and end all that Macbeth imagined, and now he lashes out coldly in anger against his friend. He has lost the capacity for trust and friendship. His evil deeds have made him evil. We know this because of the way he speaks his thoughts aloud, full of anger and hate.In act five, scene five, Macbeth gives another soliloquy. By now, near the end of the play, he is devoid of fear and feeling. In this soliloquy, he reacts to the death of his wife by saying, indifferently, that she would have died anyway:

She should have died hereafter.

Then he expresses his complete disillusionment with life. He has killed a good king, along with many other innocent people, and plunged his country into war, but it is all, as far he is concerned, for nothing. His evildoing has made life meaningless for him. He says he merely goes through the motions of living day to day, and it doesn't matter to him if he lives or dies:



Tomorrow, and tomorrow, and tomorrow,
Creeps in this petty pace from day to day
To the last syllable of recorded time,
And all our yesterdays have lighted fools
The way to dusty death. Out, out, brief candle!
Life’s but a walking shadow, a poor player
That struts and frets his hour upon the stage
And then is heard no more. It is a tale
Told by an idiot, full of sound and fury,
Signifying nothing.


In the end, he is nothing. His ambitions were not worth the price.Possible theses could be something like what follows:We learn through the soliloquies that getting what he wants through evil means has left Macbeth alone, barren, and empty, only a shell of a human being. Without the soliloquies, we wouldn't understand how dehumanized he has become.Macbeth's soliloquies give us a window into his soul that shows that evil acts turn a person evil. Shakespeare, through the soliloquies, is showing that a person isn't born evil but becomes evil through the decisions he makes.

Why does Oedipus believe that Teiresias can provide him information on the death of Laius?

Before Teiresias appears in Thebes at Oedipus's request, Creon returns from the oracle of Delphi, to which Oedipus had sent him to find out why Thebes is suffering so much. The ancient Greeks believed that Apollo was the god of prophecy and that he was the original source of the responses the Delphic oracle would offer to those who came to her with questions. It is she who tells Creon that the reason for the suffering in Thebes is that the murderer of Laius, the former king, was never found and prosecuted. Oedipus, then, decides to launch a full investigation of the crime. However, he doesn't really know how to begin; luckily, the Chorus offers him a suggestion: "For the quest, 'twere well, methinks / That Phoebus, who proposed the riddle, himself / Should give the answer—who the murderer was."
In other words, they believe that, since Apollo (Phoebus) was responsible for the oracle's message, asking someone else with the gift of prophecy, who would also be favored by Apollo, might be a good start. The chorus says, "if any man sees eye to eye / With our lord Phoebus, 'tis our prophet, lord / Teiresias." Therefore, Oedipus doesn't call Teiresias just because he is a prophet, but also because his ability to see the future and interpret omens would have come from Apollo, the same god who compelled the oracle to tell Creon what to do. If any god can help them, it is Apollo, and since Teiresias is Apollo's mouthpiece, so to speak, Oedipus calls for him.

The play Oedipus Rex was written by the Greek playwright Sophocles, who appears, from the limited available biographical evidence, to have been a conventionally pious man of his period. Both Sophocles and his audience would have believed in divination, the possibility of certain expert seers or oracles knowing the will of the gods and being able to interpret various signs to learn of things normally outside human knowledge.
Teiresias is a seer, dedicated to the service of Apollo, the god of prophecy. The gods have granted him the gift of prophecy, including a limited ability to see both past and future. Thus Oedipus asks him about the death of Laius because of his skill at prophecy. As Tiresias does, in fact, correctly identify the murderer, Oedipus was correct in asking him but misguided in not immediately believing his answer. In all of the plays in which he appears, Tiresias' answers to questions are always correct, although sometimes difficult to interpret at first. 

9/(x^2-6x+9)=(3x)/(x^2-3x) Solve the equation by cross multiplying. Check for extraneous solutions.

Cross-multiplication is applicable when have two fractions or rational expressions equated to each other.  It is method wherein we multiply the denominator towards the numerator on the other side. This will helps to simplifying the equation by getting rid of the fraction form on each side.
For a given equation:  a/b=c/d where b and are nonzero, we may cross-multiply to simplify it as:  a*d = c*b .
Applying cross-multiplication on the given equation 9/(x^2-6x+9)=(3x)/(x^2-3x) , we get:
9*(x^2-3x)=(3x)*(x^2-6x+9)
Apply distribution property.
9x^2-27x=3x^3-18x^2+27x
Subtract 9x^2 from both sides of the equation.
9x^2-27x-9x^2=3x^3-18x^2+27x-9x^2
-27x=3x^3-27x^2+27x
Add 27x  on both sides of the equation.
-27x+27x=3x^3-27x^2+27x+27x
0=3x^3-27x^2+54x
or 3x^3-27x^2+54x=0
Factor out the greatest common factor (GCF) 3x .
(3x)(x^2-9x+18)=0
Apply x^2-9x+18= (x-3)(x-6) , we get:
3x(x-3)(x-6)=0
Apply zero-factor property to solve for x by equating each factor to 0 .
3x=0
(3x)/3 =0
x=0
 
x-3=0
x-3+3=0+3
x=3
 
x-6=0
x-6+6=0+6
x=6
Possible values of x=0,3,6 .
To check for extraneous solution, plug-in each x on 9/(x^2-6x+9)=(3x)/(x^2-3x) .
Note: Any value divided by 0 results to undefined value.
An undefined result implies the x value is an extraneous solution.
Let x=0  on 9/(x^2-6x+9)=(3x)/(x^2-3x) .
9/(0^2-6*0+9)=?(3*0)/(0^2-3*0)
9/(0-0+9)=?0/(0-0)
9/9=?0/0
1=? undefined   FALSE
Let x=3  on 9/(x^2-6x+9)=(3x)/(x^2-3x) .
9/(3^2-6*3+9)=?(3*3)/(3^2-3*3)
9/(9-18+9)=?9/(9-9)
9/0=?9/0
undefined=? undefined   FALSE
Let x=6  on 9/(6^2-6x+9)=(3x)/(x^2-3x) .
9/(6^2-6*6+9)=?(3*6)/(6^2-3*6)
9/(36-36+9)=?9/(36-18)
9/9=?18/18
1=1             TRUE
 
Therefore, the x=0 and x=3 are the extraneous solutions.
The x=6 is the real exact solution of the given equation 9/(x^2-6x+9)=(3x)/(x^2-3x) .

Intermediate Algebra, Chapter 4, 4.1, Section 4.1, Problem 28

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

& 3x - y = 10 \\
& 2x + 5y = 1

\end{aligned}
\end{equation}
$ by substitution. If the system is inconsistent or has dependent equations.

We solve for $y$ in equation 1


$
\begin{equation}
\begin{aligned}

& 3x - y = 10
&& \text{Given equation}
\\
& -y = -3x + 10
&& \text{Subtract each side by $3x$}
\\
& y = 3x - 10
&& \text{Multiply each side by $-1$}

\end{aligned}
\end{equation}
$


Since equation 1 is solved for $y$, we substitute $3x - 10$ for $y$ in equation 2.


$
\begin{equation}
\begin{aligned}

2x + 5 (3x - 10) =& 1
&& \text{Substitute $y =3x - 10$}
\\
2x + 15x - 50 =& 1
&& \text{Distributive Property}
\\
17x - 50 =& 1
&& \text{Combine like terms}
\\
17x =& 51
&& \text{Add each side by $50$}
\\
x =& 3
&& \text{Divide each side by $17$}

\end{aligned}
\end{equation}
$


We found $x$. Now we solve for $y$ in equation 1.


$
\begin{equation}
\begin{aligned}

y =& 3(3) - 10
&& \text{Substitute } x = 3
\\
y =& 9 - 10
&& \text{Multiply}
\\
y =& -1
&& \text{Subtract}

\end{aligned}
\end{equation}
$

What are chapter summaries for The Innocents Abroad by Mark Twain?

The Preface introduces Twain's work as "travel-writing," while humorously separating it from "solemn scientific" writing, "attractive" though that might be. He explains that portions of his writing will be reproduced from letters he had written to the "Daily Alta California, of San Francisco," the "New York Tribune" and the "New York Herald," noting that all had given "the necessary permission." Chapter 1 introduces the advent of a new and unusual excursion advertised and "chatted" about across America in "newspapers" and by "firesides." It was that of taking a "royal holiday" on a "gigantic scale" on a "steamship" to explore "beyond the broad ocean in many a strange clime and in many a land renowned in history!" Twain tells how "this brave conception" was to allow participants to "hob−nob with nobility and hold friendly converse with kings and princes, grand moguls, and the anointed lords of mighty empires!" He explains how "every household in the land" was "longing" to be one of the "one hundred and fifty" passengers on this extravaganza excursion to "the Crimea, Greece, and intermediate points of interest." To entice his readers, Twain adds the advertisement, dated 1867, in full to display to advantage the lure of the excursion. In testimony to the effectiveness of the advertisement, he tells how he hurried to the treasurer's office to deposit his 10 percent fee, being delighted that he could still acquire a stateroom. Twain's ironic wit is on display when he says that upon giving references of his character, he chose names of those who knew him least: he chose "all the people of high standing [he] could think of in the community who would be least likely to know anything about [him]."After an announcement that the "Plymouth Collection of Hymns [a Puritan hymn book] would be used on board the ship," Twain's ironic wit is further evident: "I then paid the balance of my passage money." The simple positioning of this sentence ironically implies a causal connection between the hymn book choice and his payment. This is ironic because he implies, by suggestion of cause and effect, that no right thinking person could care about the selection of a hymn book as a reason to expend money on the excursion. He carries the irony further with a Calvinistic allusion to "being 'select.'"

   Shortly a supplementary program was issued which set forth that the Plymouth Collection of Hymns would be used on board the ship. I then paid the balance of my passage money.   I was provided with a receipt and duly and officially accepted as an excursionist. There was happiness in that but it was tame compared to the novelty of being "select."

Twain then enumerates celebrities who were enrolled to go but who cancelled due to various urgent matters. He ends by saying that, although the excursion now traveled without celebrities, like the Reverend Henry Ward Beecher and Lieutenant General Sherman, they still had the "'battery of guns' from the Navy Department" with which to salute royalty. The accompanying letter of introduction from the "Secretary of the Navy," as it was extended to "General Sherman and party," may have left them to their own devices (as Sherman was called to the American plains during "the Indian war") with the "courts and camps" of Europe, but with the "seductive" itinerary including Gibraltar, Paris, Jerusalem, and Bermuda still in tact, he and the others were nonetheless happy. As he says, "What did we care?"
http://twain.lib.virginia.edu/innocent/iahompag.html

College Algebra, Chapter 4, 4.2, Section 4.2, Problem 84

Suppose that a cardboard box has a square base, with each edge of the base has length $x$ inches. The total length of all 12 edges of the box is 144in.
a.) Show that the volume of the box is given by the function $V(x) = 2x^2 ( 18 - x)$
b.) What is the domain of $V$? (Use the fact that length and volume must be positive.)
c.) Draw a graph of the function $V$ and use it to estimate the maximum volume for such a box.


a.) Recall that the formula for the perimeter of the box with square base with edge $x$ is $P = 8x + 4y$. Solving for $y$, we have

$
\begin{equation}
\begin{aligned}
144 &= 8x + 4y && \text{Divide both sides by 4} \\
\\
36 &= 2x + y\\
\\
y &= 36 - 2x
\end{aligned}
\end{equation}
$

Recall that the volume of the box is $V = x^2 y$

$
\begin{equation}
\begin{aligned}
V &= x^2 (36 - 2x)\\
\\
V &= 2x^2 (18 -x)
\end{aligned}
\end{equation}
$


b.) If $V$ can never be a negative value, then the domain of $V$ is $(-\infty, 18]$
c.)


Based from the graph, the maximum volume is approximately $1730 \text{ in}^3$

Historians such as Suzanne Lebsock have been interested in the extent to which southern women’s access to property gave them freedom and autonomy. Looking at Petersburg women of different classes and races, evaluate how much freedom they had in the household, in general decision making, and in their sexual behavior. How does their freedom and position compare with that of Helen Jewett or the young women who worked in textile mills in New England? Reference: The Free Women of Petersburg by Suzanne LesbocK

In the Introduction to her book, Lebsock writes, "Women in Petersburg experienced increasing autonomy, autonomy in the sense of freedom from utter dependence on men" (page xv). In Petersburg, Virginia in the nineteenth century, fewer women decided to marry, more women worked, and some married women were able to have separate estates that their husbands could not own. This loophole was developed so that women could maintain property even if their husbands went into debt, as many did in the panics and economic turbulence of the nineteenth century. As the author points out, women were not allowed this freedom because of feminism, but this freedom allowed women to develop autonomy. 
Women in Petersburg who were wealthy had more sexual choice and power. For example, only 28.6% of the wealthiest widows in the town married, while 72.7% of the poorest did (27). This shows that while people were beginning to desire companionate marriage (a marriage based on love and respect), women did not feel that marriage often offered them this chance. Therefore, if they could support themselves, they did not choose marriage. In addition, women's growing power within the family is suggested by the declining birth rate. At the beginning of the 19th century, the typical white woman had 7 or 8 children, but this number fell to 3 to 4 by the close of the century (50). In addition, although women controlled less than a third of the property in Petersburg, one third of them established separate estates for their daughters (78). This statistic shows that they valued the power and freedom that separate estates could offer to their daughters.
Free black women also possessed a great deal of autonomy. In Petersburg, one half of the free black households were headed by women from 1800 to 1860 (89). While black women struggled with poverty and discrimination, they held 40-50% of the property among free blacks (90). The author writes that free black women experienced less inequality between the sexes than did white women.
Young women in New England who worked in mills were still subject to patriarchal rules. They often lived in boarding houses, where their hours were strictly controlled. In the late 1830s and 1840s, financial depression made their situation even more desperate, and they were often forced to work two looms at a time (see the source in the link below). In addition, they generally earned far less than men. Helen Jewett was a Maine-born prostitute who was killed in New York City in the 1830s (when she was in her early 20s). Her accused killer was acquitted. The mill girls of New England and figures such as Helen Jewett had less autonomy than the women in Petersburg who were able to inherit estates. 
http://www.newenglandhistoricalsociety.com/sarah-bagley-avenges-new-england-mill-girls/

What did aunt Polly want Tom to do on a Sunday

As a respectable, God-fearing woman, Aunt Polly wants Tom to attend Sunday school and church. But for Tom, it's all a bit of a bore. He doesn't like being told what to do, especially if it involves sitting still for long periods of time when he could be out having fun.
However, after Tom racks up an impressive collection of bible tickets in return for trading all the spoils he earned from his whitewashing scam, Sunday school suddenly becomes more interesting. Because now Tom is about to be awarded the prize of a Bible. This is his reward for supposedly memorizing lots of the good book's verses. But Tom being Tom, he didn't put in the necessary hard work; he obtained all this Bible tickets purely by fraud. So when Judge Thatcher calls on Tom to display his extensive knowledge of Scripture in front of the whole congregation, the mischievous young scamp makes a complete fool of himself.

Tom Sawyer has a particular hatred for Sunday school and everything about it. He has a far from unblemished Sunday school record, and he especially dislikes having to put on his special Sunday school outfit and dress for the occasion. Tom's cousin, Mary, is "fond of" Sunday school, as is Sid, but Tom is seen "snarling" at the prospect.
After Sunday school is over, Tom has to attend church itself with his Aunt Polly and his cousins. Polly makes sure that Tom is kept close to the aisle, in order to try and make him pay attention—she seems to think that if he is allowed to sit anywhere near the open window, the sight of the summery scenes outside will distract his attention from what is going on in the church. It is evident that Tom's nature is opposed to sitting still, and he especially doesn't like having to sit still at church while wearing his Sunday best.

What types of mystery stories did Edgar Allan Poe create?

Edgar Allan Poe's mystery stories broke new ground because of his imaginative plot lines.  Three of his stories are widely regarded to be the first American detective fictions: "The Murders in the Rue Morgue," "The Mystery of Marie Roget," and "The Purloined Letter," and feature a gifted amateur detective, C. Auguste Dupin. "The Murders in the Rue Morgue" was sensational because of its murderer: a razor-wielding orangutan.  Dupin is able to solve this, and the other two crimes, through his formidable intelligence, empathy, and his use of what Poe called "ratiocination," a technique of reasoning.
Other Poe mysteries, "The Gold Bug," "Thou Art the Man," and "The Man of the Crowd" introduced staples of modern detective fiction including the use of surveillance, code-breaking, and forcing a suspect's confession.
Sir Arthur Conan Doyle, British author of the Sherlock Holmes mysteries, called Poe's work "a model for all time."
 
 

American writer, editor and critic Edgar Allen Poe (1809-1849) gained worldwide fame as a short story writer and poet. Well-educated, much of his writing made allusions to Classical Mythology and touched upon themes of horror, loss, revenge, and reasoning. His mystery stories are famous for not only being clever and engrossing, but also for inventing the first "consulting detective" in fiction, C. Auguste Dupin. The mysteries range from the mundane, as in "The Purloined Letter," to the savage and grotesque, as in "Murders in the Rue Morgue" and "The Mystery of Marie Roget." Other mystery stories include "The Gold Bug," centered on breaking a cipher, and "The Man in the Crowd," where one man "shadows" another throughout the city.

Calculus of a Single Variable, Chapter 6, 6.3, Section 6.3, Problem 13

For the given problem: yln(x)-xy'=0 , we can evaluate this by applying variable separable differential equation in which we express it in a form of f(y) dy = f(x)dx .
to able to apply direct integration: int f(y) dy = int f(x)dx .
Rearranging the problem:
yln(x)-xy'=0
yln(x)=xy' or xy' = y ln(x)
(xy')/(yx) = (y ln(x))/(yx)
(y') /y = ln(x)/x
Applying direct integration, we denote y' = (dy)/(dx) :
int (y') /y = int ln(x)/x
int 1 /y (dy)/(dx) = int ln(x)/x
int 1 /y (dy)= int ln(x)/x dx

For the left side, we apply the basic integration formula for logarithm: int (du)/u = ln|u|+C
int 1 /y (dy) = ln|y|
For the right side, we apply u-substitution by letting u= ln(x) then du = 1/x dx .
int ln(x)/x dx=int udu
Applying the Power Rule for integration : int x^n= x^(n+1)/(n+1)+C .
int udu=u^(1+1)/(1+1)+C
=u^2/2+C
Plug-in u = ln(x) in u^2/2+C , we get:
int ln(x)/x dx =(ln(x))^2/2+C
Combining the results, we get the general solution for differential equation (yln(x)-xy'=0) as:
ln|y|=(ln|x|)^2/2+C

The general solution: ln|y|=(ln|x|)^2/2+C can be expressed as:
y = C_1e^((ln|x|)^2/2)+C .

Challenge: Construct as many Kennings (Old English Poetry, for example in Beowulf, 'Oar-Steed' means Ship) for the following words, in their current form (Imperative); 'Compose', 'Seek', 'Dream' and 'Imagine'.

Remembering that kennings offer a visual or sensory description of a word's meaning, I can offer some suggestions for thinking about the words you list, but very much want to emphasize that these are simply to offer guidance: you need to use these as a starting point for developing your own kennings.
So let's think about what the command "compose" means: one meaning is to write something: what image comes into your mind when you think about composing or writing an essay or a poem? Do you think about paper and a pen? Do you think about words flowing in black ink across a white page? A kenning would involve this type of imagery. To compose could be to "page-ink." I am sure you can come up with other images. Could you think up an image that would picture composing on a computer?
Likewise, what does "seek" conjure in your mind: to search for something? To head out on an adventure? Is it searching for a treasure? Could you call it "treasure hunt?"
I will do a little bit more to give you the idea: remember, just think about what concrete pictures the word forms in your mind to create a kenning.
OK, "dream." What do you think about--what picture arises-- when you read the word dream? Ghostly images? Weird images? Could you call a dream a "weird-picture" or a "jumble picture?" Do the same for imagine. What visual picture comes into your mind when you think about the word? Do you think about how the world could be better, brighter, more colorful? Do you build castles in the clouds?How could that become a kenning?  When you imagine do you "Castle-paint?"  Again, I am sure you can come up with more and better ideas.

How should I describe Ludwig Wittgenstein's contributions of meaning as use, the language game, and the private language? Please use examples to illustrate the idea.

What Wittgenstein is challenging is the dominant notion in contemporary philosophy that meaning can be reduced to propositions, that there is some underlying logic to our language which it is somehow the business of the philosopher to discover. To a large extent, this was Wittgenstein's position in his earlier work, most notably in the Tractatus. However, he subsequently abandoned that position to argue for meaning as being intimately bound up with how we use ordinary language in our daily lives.
Let us take a brief example from Wittgenstein to illustrate the point. Although we can define a tree, for instance, for the purposes of scientific classification or compiling a dictionary, that definition is itself dependent on how we have already been using the word "tree" in our everyday language. In other words, we do not know what a tree is only because we read about it in a science book or a dictionary, we know about it because we have direct experience of trees and have been able to share that experience with others by way of language.
According to Wittgenstein, this approach is the exact opposite of how many philosophers have traditionally looked at the matter. They seek to establish a logical definition of something, but the object in question is already being experienced, talked about, and understood. They have things the wrong way round, and the resulting confusion helps to explain why there are so many seemingly unsolvable problems in philosophy. Concepts do not need to be clearly defined in order to be meaningful.
The later Wittgenstein, then, sees most of the problems of philosophy as being related to a misunderstanding and misuse of language. Meaning is not something that can be crystallised into a neat propositional structure by speculative philosophers. Instead, we need to look at how language is used in the many different human discourses or language games, as Wittgenstein calls them.
Each language game has its own unwritten rules. However, these rules are themselves determined over time by custom and usage. They are not set down in advance. We learn the rules simply by playing the game and by participating in each specific discourse. There are many different language games, and each one has different rules. The language game of, say, theology, will be completely different from the language game of science; the language game of engineering will be different from the language game played by high school students and so on.
Although there is a bewildering array of different language games, they all have one thing in common: they are public. This is to say that their meaning is one that can be shared by others. Otherwise, it would not be possible for players in each language game to communicate with each other in any meaningful sense. In fact, language games would not even be possible in the first place.
That being the case, there can be no such thing as a private language. For language to have any kind of meaning, it needs to be communicated and shared. Even if my friend and I are the only two people in the world who understand each other, there still needs to be some way of communicating between ourselves. In other words, although our language game would only consist of two players, it would still need to be public, it would still need to be shared, and it would still be based on certain rules derived from usage over time.
https://plato.stanford.edu/entries/wittgenstein/