Single Variable Calculus, Chapter 3, 3.2, Section 3.2, Problem 48

a.) Suppose that $g(x) = \displaystyle x^{\frac{2}{3}}$, show that $g'(0)$ does not exist.

Using the definition of derivative


$
\begin{equation}
\begin{aligned}

\qquad g'(x) =& \lim_{h \to 0} \frac{g(x + h) - g(x)}{h}
&&
\\
\\
\qquad g'(x) =& \lim_{h \to 0} \frac{(x + h)^{\frac{2}{3}} - (x)^{\frac{2}{3}}}{h}
&& \text{Substitute $g(x + h)$ and $g(x)$}
\\
\\
\qquad g'(x) =& \lim_{h \to 0} \frac{(x + h)^{\frac{2}{3}} - (x)^{\frac{2}{3}}}{h} \cdot \frac{(x + h)^{\frac{4}{3}} + (x)^{\frac{2}{3}} + (x + h)^{\frac{2}{3}} + (x)^{\frac{4}{3}}}{(x + h)^{\frac{4}{3}} + (x)^{\frac{2}{3}} + (x + h)^{\frac{2}{3}} + (x)^{\frac{4}{3}}}
&& \text{Multiply both numerator and denominator by $[(x + h)^{\frac{4}{3}} + (x)^{\frac{2}{3}} (x + h)^{\frac{2}{3}} + (x)^{\frac{4}{3}}]$. Recall that $(a^3 - b^3) = (a - b)(a^2 + ab + b^2)$}
\\
\\
\qquad g'(x) =& \lim_{h \to 0} \frac{(x + h)^2 - \cancel{(x)^{\frac{2}{3}} (x +h)^{\frac{4}{3}}} + \cancel{(x)^{\frac{2}{3}} (x +h)^{\frac{4}{3}}} - \cancel{(x)^{\frac{4}{3}}(x + h)^{\frac{2}{3}}} + \cancel{(x)^{\frac{4}{3}}(x + h)^{\frac{2}{3}}} - x^2}{(h)[(x + h)^{\frac{4}{3}} + (x)^{\frac{2}{3}} (x + h)^{\frac{2}{3}} + (x)^{\frac{4}{3}}]}
&& \text{Combine like terms}
\\
\\
\qquad g'(x) =& \lim_{h \to 0} \frac{(x + h)^2 - x^2}{(h)[(x + h)^{\frac{4}{3}} + (x)^{\frac{2}{3}} (x + h)^{\frac{2}{3}} + (x)^{\frac{4}{3}}]}
&& \text{Expand the equation}
\\
\\
\qquad g'(x) =& \lim_{h \to 0} \frac{\cancel{x^2} + 2xh + h^2 - \cancel{x^2}}{(h)[(x + h)^{\frac{4}{3}} + (x)^{\frac{2}{3}} (x + h)^{\frac{2}{3}} + (x)^{\frac{4}{3}}]}
&& \text{Combine like terms}
\\
\\
\qquad g'(x) =& \lim_{h \to 0} \frac{2xh + h^2}{(h)[(x + h)^{\frac{4}{3}} + (x)^{\frac{2}{3}} (x + h)^{\frac{2}{3}} + (x)^{\frac{4}{3}}]}
&& \text{Factor the numerator}
\\
\\
\qquad g'(x) =& \lim_{h \to 0} \frac{\cancel{h} (2x + h)}{\cancel{(h)}[(x + h)^{\frac{4}{3}} + (x)^{\frac{2}{3}} (x + h)^{\frac{2}{3}} + (x)^{\frac{4}{3}}]}
&& \text{Cancel out like terms}
\\
\\
\qquad g'(x) =& \lim_{h \to 0} \left[ \frac{2x + h}{(x + h)^{\frac{4}{3}} + (x)^{\frac{2}{3}} (x + h)^{\frac{2}{3}} + (x)^{\frac{4}{3}}} \right] = \frac{2x + 0}{(x + 0)^{\frac{4}{3}} + (x)^{\frac{2}{3}} (x + 0)^{\frac{2}{3}} + (x)^{\frac{4}{3}}} = \frac{2x}{(x)^{\frac{4}{3}} + (x)^{\frac{2}{3}}(x)^{\frac{2}{3}} + (x)^{\frac{4}{3}}} = \frac{2x}{(x)^{\frac{4}{3}} + (x)^{\frac{4}{3}} + (x)^{\frac{4}{3}}}
&& \text{Evaluate the limit}
\\
\\
\qquad g'(x) =& \frac{2x}{3(x)^{\frac{4}{3}}}
&& \text{Factor the denominator}
\\
\\
\qquad g'(x) =& \frac{2 \cancel{x}}{3\cancel{(x)} (x)^{\frac{1}{3}}}
&& \text{Cancel out like terms}
\\
\\
\qquad g'(x) =& \frac{2}{3(x)^{\frac{1}{3}}}
&& \text{Substitute $x$ which is zero}
\\
\\
\qquad g'(0) =& \frac{2}{3(0)^{\frac{1}{3}}}
&& && \text{Simplify the equation}
\\
\\
\qquad g'(0) =& \frac{2}{0}
&&

\end{aligned}
\end{equation}
$


The function does not exist because the denominator is zero.

b.) Suppose that $a \neq 0$, find $g'(a)$.

Using the definition of derivative


$
\begin{equation}
\begin{aligned}

\qquad f'(a) =& \lim_{x \to a} \frac{f(x) - f(a)}{x - a}
&&
\\
\\
\qquad f'(a) =& \lim_{x \to a} \frac{(x)^{\frac{2}{3}} - (a)^{\frac{2}{3}}}{x - a}
&& \text{Substitute $f(x)$ and $f(a)$}
\\
\\
\qquad f'(a) =& \lim_{x \to a} \frac{ (x)^{\frac{2}{3}} - (a)^{\frac{2}{3}} }{x - a} \cdot \frac{ (x)^{\frac{4}{3}} + (ax)^{\frac{2}{3}} + (a)^{\frac{4}{3}} }{(x)^{\frac{4}{3}} + (ax)^{\frac{2}{3}} + (a)^{\frac{4}{3}}}
&& \text{Multiply both numerator and denominator by $[(x)^{\frac{4}{3}} + (ax)^{\frac{2}{3}} + (a)^{\frac{4}{3}}]$. Recall that $(a^3 - b^3) = (a - b)(a^2 + ab + b^2)$}
\\
\\
\qquad f'(a) =& \lim_{x \to a} \frac{ x^2 - \cancel{(a)^{\frac{2}{3}} (x)^{\frac{4}{3}}} + \cancel{(a)^{\frac{2}{3}} (x)^{\frac{4}{3}}} - \cancel{(a)^{\frac{4}{3}} (x)^{\frac{2}{3}}} + \cancel{(a)^{\frac{4}{3}} (x)^{\frac{2}{3}}} - a^2 }{(x - a)[(x)^{\frac{4}{3}} + (ax)^{\frac{2}{3}} + (a)^{\frac{4}{3}}]}
&& \text{Combine like terms}
\\
\\
\qquad f'(a) =& \lim_{x \to a} \frac{x^2 -a^2}{(x - a) [(x)^{\frac{4}{3}} + (ax)^{\frac{2}{3}} + (a)^{\frac{4}{3}}]}
&& \text{Factor the numerator}
\\
\\
\qquad f'(a) =& \lim_{x \to a} \frac{\cancel{(x - a)} ( x + a)}{\cancel{(x - a)} [(x)^{\frac{4}{3}} + (ax)^{\frac{2}{3}} + (a)^{\frac{4}{3}}]}
&& \text{Cancel out like terms}
\\
\\
\qquad f'(a) =& \lim_{x \to a} \left[ \frac{x + a }{(x)^{\frac{4}{3}} + (ax)^{\frac{2}{3}} + (a)^{\frac{4}{3}}} \right] = \frac{a + a}{(a)^{\frac{4}{3}} + (a \cdot a)^{\frac{2}{3}} + (a)^{\frac{4}{3}}} = \frac{2a}{(a)^{\frac{4}{3}} + (a)^{\frac{4}{3}} +(a)^{\frac{4}{3}}}
&& \text{Evaluate the limit}
\\
\\
f'(a) =& \frac{2a}{3(a)^{\frac{4}{3}}}
&& \text{Factor the denominator}
\\
\\
f'(a) =& \frac{2\cancel{a}}{3\cancel{(a)}(a)^{\frac{1}{3}}}
&& \text{Cancel out like terms}
\\
\\
f'(a) =& \frac{2}{3(a)^{\frac{1}{3}}} \text{ or } \frac{2}{3 \sqrt[3]{a}}


\end{aligned}
\end{equation}
$


c.) Prove that $y = \displaystyle x^{\frac{2}{3}}$ has a vertical tangent line at $(0, 0)$

If the function has a vertical tangent line at $x = 0, \lim\limits_{x \to 0} f'(x) = \infty$

Given that, $f'(x) = \displaystyle \frac{2}{3(x)^{\frac{1}{3}}}$

Suppose that we substitute a value closer to 0 from the left and the right of the limit of $f'(x)$, let's say $x = -0.0000001$ and $x = 0.0000001$


$
\begin{equation}
\begin{aligned}

& \lim_{x \to 0^-} \frac{2}{3 \sqrt[3]{-0.0000001}} = -143.629
\\
\\
& \lim_{x \to 0^+} \frac{2}{3 \sqrt[3]{0.0000001}} = 143.629

\end{aligned}
\end{equation}
$


This means that where $x$ gets closer and closer to from the left, the value of the limit approaches a very large negative number. On the other hand, as $x$ gets closer and closer to from the right, the value of the limit approaches a very large positive number. The tangent lines with these values become steeper and steeper as $x$ approaches until such time that the tangent line becomes a vertical line @ $x = 0$.

what is the purpose of dystopian literature like in the giver

Science fiction literature allows the author the freedom to ask, “What if?” These authors are free to hold a funhouse mirror up to society and present what is possible or a warning. Dystopian literature such as Lois Lowry’s 1993 young adult novel The Giver falls in to the category of a warning.
Jonas, Lowry’s protagonist, is selected to inherit the position of Receiver of Memory, the person who stores all the memories of the time before Sameness. His society has taken away pain and suffering by converting to "Sameness," a plan that has also eliminated emotional depth from their lives. What on the surface appears to be a utopia is slowly revealed to be a dystopia. Through the establishment of this dystopian society, Lowry can warn her readers about the danger of attempting societal equality by eliminating part of what makes us human.

What were the major supporting arguments?

In 1963, author Rachel Carson published the controversial and highly influential book Silent Spring.  At the time, she was called upon to testify in court about the findings and observations laid out in her book.  This book would become the groundwork for a massive environmental movement which recognized the dangers of chemicals used in agriculture around the world. During this time, she was dying of cancer, birds were not raising their own chicks, and animals were born with horrific defects. The culprit? Pesticides, particularly one known as DDT, a toxic chemical which she argued not only poisoned the bugs that were eating the plants, but also the environment and humans as well.
Carson was a scientist and a citizen, and few authors have captured the imagination and the attention of the public as she did. In Silent Spring, she argues that these toxins make their way into the very fiber of the plants that we eat, into the animals which eat them, into the soil, and into the air, spreading massive amounts of harmful chemicals across the earth and causing long-term devastation the likes of which this planet had never seen.
Although Carson was not religious, she argued that humans had a moral responsibility to coexist with nature and to protect it from human selfishness. She posed a moral question that spurred the ideals behind modern ecology: “By acquiescing in an act that causes such suffering to a living creature, who among us is not diminished as a human being?” Within this question was a call to action, a call to accept our responsibility and do away with our arrogance.  In essence, she wanted people to understand that they were minuscule in the design of the universe, but, through their actions, they could cause lasting effects that would ripple into the future.
Carson used the aftermath of the nuclear bombings and played upon the emotions of the era in her book.  If we are aware of the effects of radiation and seek to protect people from its power, she argued, “How then, can we be indifferent to the same effect in chemicals that we disseminate widely in our environment?” In her investigations and through her observations, she learned that corporations were lying about the effects of their products to consumers; she knew she needed to share this knowledge with the world. She argued that humans should not attempt to control nature in the name of progress, tampering with such a delicate balance would irrevocably damage it.  She was correct, of course.  Through these arguments, she was able to open the public’s eyes to the harsh realities and effects of big business.

Where was Napoleon from?

Napoleon was born on the island of Corsica in the Mediterranean Sea. A year before his birth, the Genoese Republic had ceded sovereign rights over the island to France. The Genoese had ruled over Corsica since the mid-sixteenth century, but due mainly to a forty year war with a growing Corsican resistance movement, the decision was made to sell the island. The Corsicans, then as now, had a fiercely independent streak and no more wanted to be controlled by the French than they had been by the Genoese. However, the French proved militarily more effective than the Genoese and ruthlessly crushed the nascent Corsican republic.
Even so, the spirit of Corsican independence lived on and was never entirely extinguished in the years ahead as the island passed between the ownership of Britain, Spain, and then back to a restored French monarchy after the fall of Napoleon. The man himself had been an ardent Corsican nationalist in his youth, speaking both Corsican and Italian before he learned how to speak French—with a marked Corsican accent he never lost. Yet when he became emperor, Napoleon neglected his native island, which once more faded back into the obscurity from which it had all too briefly been liberated by the escapades of its most famous son.

What qualities does a creature born in the North have? Why?

You must be referring to the Prince of Morocco's speech in Act 2, Scene 1, in which he says,

Bring me the fairest creature northward born,
Where Phoebus' fire scarce thaws the icicles,
And let us make incision for your love
To prove whose blood is reddest, his or mine.

In this scene, the Prince of Morocco has come to woo Portia.  He comes knowing that he is at a disadvantage among her suitors, because he is dark-skinned.  This reflects the value, sadly held at the time, that dark skin is less attractive than light skin.  
Thus the first words out of the Prince's mouth are to ask Portia not to pre-judge him because of his "complexion,/The shadowed livery of the burnished sun."  Then he speaks the lines above, pointing out that his blood is as red as any fair-skinned suitor's.  He later goes on to say that he is considered attractive in his home country. 
So, the quality of a "creature northward born" which the Prince is addressing, is that of being fair-skinned.  
Not coincidentally, "fair" in Shakespearean English could also mean beautiful, as in "fair weather."  
So the Prince is invoking the idea of a rival suitor who is extremely "fair" (i.e. handsome), but also very fair-skinned, coming from a place where the sun's fire can scarcely melt the icicles.  This conjures up a mental image of someone who is very, very pale, as if after a long winter.  

Provide evidence for why Friar Laurence did what he did.

Friar Laurence is a pivotal character in Romeo and Juliet, and without him, much of the plot of the play could not move forward. In addition to marrying the star-crossed lovers, the friar is also the procurer of the sleeping potion that leads, through a series of unexpected events, to Romeo and Juliet's deaths. Friar Laurence means the lovers no ill will, but his attempts to help them, shrouded in lies and secrecy as they are, enable tragedy to occur.
One might not expect a religious man like the friar to trade in subterfuge, but he seems to have a moral outlook that accounts for sometimes doing seemingly suspect things for good reasons. In agreeing to marry Romeo and Juliet in act 2, Friar Laurence hopes to see the feuding Capulets and Montagues make peace as a result of their union. When the two are wed, their problems do not end, however. By act 3, Romeo has been exiled from Verona for killing Tybalt, and Juliet is set to marry Paris against her will. Friar Laurence steps in once again to aid the lovers.
As pressure to marry Paris mounts in act 4, Juliet confesses to Friar Laurence that she will kill herself if her parents force her to go through with it; at seeing her draw a dagger, the friar quickly devises a plan:

Juliet:
Give me some present counsel, or, behold,'Twixt my extremes and me this bloody knifeShall play the umpire, arbitrating thatWhich the commission of thy years and artCould to no issue of true honor bring.Be not so long to speak. I long to dieIf what thou speak’st speak not of remedy.
Friar Laurence:
Hold, daughter. I do spy a kind of hope,Which craves as desperate an executionAs that is desperate which we would prevent.If, rather than to marry County Paris,Thou hast the strength of will to slay thyself,Then is it likely thou wilt undertakeA thing like death to chide away this shame,That copest with death himself to ’scape from it.An if thou darest, I’ll give thee remedy. (4.1.63–78)

Once again, the friar acts out of a worthy impulse—to save the life of Juliet and prevent her from the grievous act of suicide—but his solution is fraught with danger. Romeo and Juliet are impulsive in their behavior throughout the play, and they often act without foresight. Unfortunately, Friar Laurence is not so different. He devises a plan far too quickly, and his secretive maneuvers to aid the two lovers lead to a tangle of lies and confusion.
The friar concocts a sleeping potion to make Juliet appear as though she has died, thus preventing her from marrying Paris and allowing Romeo the opportunity to spirit her away. The message that Friar Laurence sends to inform Romeo of the plan does not reach him, however; the bearer of the missive, a fellow friar, is delayed. Romeo receives news only of the deception—that Juliet has died—and is not aware of the sleeping potion and his intended part in the plan. As a result, Romeo returns to Verona, mistakes Juliet for dead, and poisons himself. Upon waking, Juliet finds her lover dead and kills herself in turn.
Friar Laurence does not account for the potential for confusion and chance in his schemes, and whether it be carelessness or pride that prevents him from seeing these critical flaws, his plans do more harm than good. While the families do make amends at the play's end, as the friar had hoped, there is a tragic cost of life that Friar Laurence has played an unintentional but undeniable part in. He sought to save the life of a despondent Juliet by reuniting her with Romeo, but his interference ultimately could only unite them both in death.

After Romeo instantly falls in love with Juliet after seeing her at the Capulet ball, he expresses his emotions to her in the famous balcony scene. In act 2, scene 3, Romeo visits Friar Lawrence's cell, and the friar can immediately tell that Romeo has been up all night. Friar Lawrence initially thinks that Romeo has been with Rosaline all night but is astonished to learn that Romeo no longer has feelings for her and is instead attracted to his family's enemy. After Friar Lawrence criticizes Romeo for his capricious nature and fleeting emotions, he agrees to secretly marry Romeo and Juliet. Friar Lawrence justifies his decision to marry Romeo and Juliet by saying,


Thy love did read by rote, that could not spell. But come, young waverer, come, go with me, In one respect I’ll thy assistant be, For this alliance may so happy prove To turn your households' rancor to pure love (Shakespeare, 2.3.88-92).


Essentially, Friar Lawrence agrees to marry Romeo and Juliet because he thinks their marriage can possibly bring an end to their families' longstanding feud.

What left Bryan with nothing and made him want to die?

In Hatchet, Brian experiences many moments where he is reduced to tears. He is alone, scared, and hungry. After a brief moment of crying, Brian is usually able to focus and determine what next step he needs to take. Upon hearing the sound of a plane, Brian envisions what his rescue will look like. He sees the plane landing on the water, the pilot amazed that Brian is still alive. But when the sound of the plane starts to fade, and Brian realizes it is leaving, he experiences a new level of despair. He is convinced that they "will not return." That night, he lets his fire go out and he doesn't eat. He falls to his side, where he lays "wishing for death." However, when morning comes, Brian finds himself changed. He smiles at his mistakes and realizes, "he would not let death in again."

Calculus of a Single Variable, Chapter 7, 7.6, Section 7.6, Problem 13

For an irregularly shaped planar lamina of uniform density (rho) , bounded by graphs y=f(x),y=g(x) and a<=x<=b ,the mass (m) of this region is given by,
m=rhoint_a^b[f(x)-g(x)]dx
m=rhoA ,where A is the area of the region.
The moments about the x and y-axes are given by the formula,
M_x=rhoint_a^b1/2([f(x)]^2-[g(x)]^2)dx
M_y=rhoint_a^bx(f(x)-g(x))dx
The coordinates of the center of mass (barx,bary) are given by,
barx=M_y/m
bary=M_x/m
We are given y=1/2x,y=0,x=2
The attached image shows the region bounded by the functions and the limits of integration,
Let's evaluate the area of the region,
A=int_0^2x/2dx
Evaluate the integral by applying power rule,
A=[1/2(x^2/2)]_0^2
A=1/4[2^2-0^2]
A=1/4(4)
A=1
Now let's evaluate the moments about the x and y-axes,
M_x=rhoint_0^2 1/2(x/2)^2dx
M_x=rhoint_0^2 1/2(x^2/4)dx
M_x=rho/8int_0^2x^2dx
Apply the power rule,
M_x=rho/8[x^3/3]_0^2
M_x=rho/8[1/3(2)^3]
M_x=rho/8(8/3)
M_x=rho/3
M_y=rhoint_0^2x(x/2)dx
M_y=rho/2int_0^2x^2dx
Apply power rule,
M_y=rho/2[x^3/3]_0^2
M_y=rho/2[1/3(2)^3]
M_y=rho/2[8/3]
M_y=4/3rho
Now let's find the coordinates of the center of mass,
barx=M_y/m=M_y/(rhoA)
barx=(4/3rho)/(rho(1))
barx=4/3
bary=M_x/m=M_x/(rhoA)
bary=(rho/3)/(rho(1))
bary=1/3
The coordinates of the center of mass are (4/3,1/3)

Calculus of a Single Variable, Chapter 3, 3.4, Section 3.4, Problem 10

y=(-3x^5+40x^3+135x)/270
differentiating
y'=1/270(-15x^4+120x^2+135)
differentiating again,
y''=1/270(-60x^3+240x)
y''=-60/270(x^3-4x)
y''=-60/270x(x+2)(x-2)
In order to determine the concavity , determine when y''=0,
So y''=0 for x=0 , x=-2 and x=2
Now test for concavity in the intervals (-oo ,-2) , (-2,0) , (0,2) and (2,oo )
Now let us plug in the test values x=-3 , -1 , 1 and 3
y''(-3) =-60/270(-3)(-1)(-5)=10/3
y''(-1)=-60/270(-1)(1)(-3)=-2/3
y''(1)=-60/270(1)(3)(-1)=2/3
y''(3)=-60/270(3)(5)(1)=-10/3
Since y''(-3) and y''(1) are positive ,so the graph is concave upward in the interval (-oo ,-2) and ((0,2)
y''(-1) and y''(3) are negative , so the graph is concave downward in the interval (-2.0) and (2,oo )

What are the similarities and differences between behavioral deviance and the possession of involuntarily acquired, undesirable physical characteristics? Do these generalizations apply to all societies at all times?

Behavioral deviance refers to actions voluntarily performed by individuals; these actions often inspire societal disgust, condemnation, and disapproval. For example, acts of behavioral deviance can include acts of sadomasochistic sex, animal torture, and bestiality. Such behavioral deviance perpetrates suffering on others; because of this, they invite the moral condemnation of the larger public.
On the other hand, involuntarily acquired, undesirable physical characteristics are only considered deviant based upon individual perception and biases. For example, someone can be born with a physical anomaly that causes him to be excluded from most social interactions. Claudio Vieira de Oliveira was born with an upside-down head due to a congenital anomaly. He did not choose to be born with such a disability. While many people admire his courage and perseverance in the face of his disability, others may react with disgust and horror at what they consider his deviant physical characteristics.
So, those with undesirable physical characteristics (for example, those who are extremely obese, deformed, or crippled in some way) are often subjected to ridicule, harassment, condemnation, and scorn. Those with such characteristics are labeled deviant not because of their abusive behavior towards others but because of the public's perception of their physical appearances.
Both behavioral deviance and the possession of involuntarily acquired, undesirable physical characteristics are similar in that both often result in negative attitudes from the larger public. Someone with a bad hump might be viewed as inept and untrustworthy as well as socially deviant. At the same time, possession of certain physical features may indicate a predilection for certain deviant beliefs, which in turn can cause the larger public to react in distrust and fear. For example, people who look like they might practice Islam may invite greater scrutiny from society, whether they are actually Muslims or not.
After the 9/11 attacks, a Time poll found the majority of Americans (61%) was against building a mosque two blocks from Ground Zero. These Americans feared the mosque project would not be a gesture of reconciliation, but rather a monument to Muslim hegemony. Fully 70% of Americans felt the mosque would be an insult to the victims of 9/11 (from Erich Goode's Deviant Behavior). So, any Muslim politician or dignitary who spoke in support of the mosque invited public condemnation and anger. Basically, an involuntarily acquired physical characteristic (looking Muslim) can inspire the same attitudes engendered by those who commit acts of atrocity (the deviant behavior exhibited by members of ISIS, for example).
As for your last question, these generalizations don't apply to all societies at all times. For example, marijuana use has been legalized for those 21 and older in Colorado, and consumption is permitted in the same way that alcohol consumption is authorized in the state. Still, there have been and still are people who consider the public consumption of marijuana to be deviant behavior.
Similarly, white supremacy, genocide, and torture have at different times and by different groups of people been viewed as acceptable. Today, most people do not believe so. For example, many Americans believe waterboarding terrorists is an unacceptable practice. Other Americans believe torture is permissible if many lives can be saved as a result of it. For more examples, please refer to the links below.
Source: Deviant Behavior by Erich Goode.
http://www-fp.pearsonhighered.com/assets/hip/us/hip_us_pearsonhighered/samplechapter/0205748074.pdf

Calculus and Its Applications, Chapter 1, 1.6, Section 1.6, Problem 116

Differentiate $\displaystyle f(t) = (t^5 + 3) \cdot \left( \frac{t^3 - 1}{t^3 + 1} \right)$

If we simplify the function first before we take the derivative, we get

$
\begin{equation}
\begin{aligned}
f(t) &= \frac{t^8 - t^5 + 3t^3 - 3}{t^3 + 1}
\end{aligned}
\end{equation}
$


Now, by applying Quotient Rule,

$
\begin{equation}
\begin{aligned}
f'(t) &= \frac{(t^3 + 1) \cdot \frac{d}{dt} \left( t^8 - t^5 + 3t^3 - 3 \right) - \left( t^8 - t^5 + 3t^3 - 3 \right) \cdot \frac{d}{dt} (t^3 + 1)}{(t^3 + 1)^2}\\
\\
f'(t) &= \frac{(t^3 + 1)\left( 8t^7 - 5t^4 + 9t^2 \right) - \left( t^8 - t^5 + 3t^3 - 3 \right) (3t^2) }{(t^3 + 1)^2}\\
\\
f'(t) &= \frac{8t^{10} - 5t^7 + 9t^5 + 8t^7 - 5t^4 + 9t^2 - 3t^{10} + 3t^7 - 9t^5 + 9t^2 }{(t^3 + 1)^2}\\
\\
f'(t) &= \frac{5t^{10} + 6t^7 - 5t^4 + 18t^2}{(t^3 + 1)^2}
\end{aligned}
\end{equation}
$

Calculus: Early Transcendentals, Chapter 7, 7.4, Section 7.4, Problem 23

Integrated int10/[(x-1)(x^2+9)]dx
Solve for the variables A, B, and, C using the method of partial fractions.
10/[(x-1)(x^2+9)]=A/(x-1)+(Bx+C)/(x^2+9)
10=A(x^2+9)+(Bx+C)(x-1)
10=Ax^2+9A+Bx^2+Cx-Bx-C
10=(A+B)x^2+(C-B)x+(9A-C)
Equate coefficients and solve for A, B, and C.
0=A+B
A=-B

0=C-B
0=C+A

10=9A-C
0=A+C
10=10A
A=1
C=-1
B=-1

int10/[(x-1)(x^2+9)]dx=int[1/(x-1)+(-1x-1)/(x^2+9)]dx
=int1/(x-1)dx-intx/(x^2+9)dx-int1/(x^2+9)dx
The first integral matches the formint(du)/u=ln|u|+C
int1/(x-1)=ln|x-1|+C

Integrate the second integral using u-substitution.
Let u=x^2+9
(du)/dx=2x
dx=(du)/(2x)
-intx/(x^2+1)dx=-x/u*(du)/(2x)=-1/2ln|u|+C=-1/2ln|x^2+9|+C

The third integral matches the form int(dx)/(x^2+a^2)=1/atan^-1(x/a)+C
=-int1/(x^2+9)dx=-1/3tan^-1(x/3)+C


=int1/(x-1)dx-intx/(x^2+9)dx-int1/(x^2+9)dx
=ln|x-1|-1/2ln(x^2+9)-1/3tan^-1(x/3)+C

The final answer is:
=ln|x-1|-1/2ln(x^2+9)-1/3tan^-1(x/3)+C

Tessio is told to make a call and tell Barzini to "start on his way." In the previous scene, Barzini is on his way to the meeting with Michael. Are these events happening serially or at the same time from different vantage points in The Godfather?

To respond to the questions after my answer, keep in mind that Michael Corleone's plan is to coordinate all over New York and eliminate his enemies. He cannot bring them together because they would be too suspicious. So, here is how it goes down:


Brazini is shot, then an hour later his assassin calls Michael Coreleone and informs him that Brazini is dead. Hagen is then told to tell Tessio to phone Brazini (even though Brazini has already been shot and killed). But Tessio thinks he is alive because the plan is for Brazini to meet Tessio and Michael and work out new business arrangements. Of course, Michael keeps this plan so that Tessio will not suspect anything. After Tessio hangs up, he says that he hopes Mike (Corleone) will give Brazini and him a good deal. At this point, then, Tessio suspects nothing because he thinks Brazini is coming. Instead, however, he is met by three hitmen and taken away. Before he goes, Tessio asks Hagen if he can get him off, but Tom says he cannot. Tessio then says to tell Michael "It was just business. I always liked Mike."
 
To answer your questions:1. About Tessio: he would have no way of knowing that Brazini has been hit because that murder occurs in another part of the city and no one is going to call him at the Corleone house, for sure. 2. Hagen never kills anyone. Moreover, no one will kill Tessio at the Coreleone house where there are women present or the Corleones could easily be implicated. Instead, then, they take him away so that the body can more easily and anonymously be disposed of.
 
Also, Neri knew that Brazini would be by the cathedral because previous arrangements had all been made by Michael Corleone. (Neri works for Michael as a hitman.) It makes sense for Corleone to hit his enemies one at a time in different places at different times. Otherwise, the men would be too suspicious. Also, the police may not connect all the crimes to Corleone if they occur all over NYC, thinking different dons are ordering hits rather than just Michael.

In Mario Puzo's novel The Godfather, the killing of Barzini and the killing of Tessio are not simultaneous; they are sequential. 
When Tessio is told "Michael is ready for you now," Neri, who has posed as a policeman in order to give Barzini's driver a ticket so that he could be standing right outside of the car, has already shot and killed Don Brazini outside of St. Patrick's Cathedral, where the baptism has taken place. After Neri kills Brazini, he darts through the crowd and jumps into a car around the corner. In the car he changes out of the uniform and puts on an overcoat. The car soon stops and Neri hops into another vehicle while the first car with the uniform and .38 pistol will be disposed of.

An hour later he is in the mall on Long Beach and talking to Michael Corleone. (Book 9, chapter 31)

The next scene involves Tessio, who is waiting in the kitchen of the old Don's house. Tom Hagen comes into this kitchen and tells Tessio, "Mike is ready for you now." This statement indicates that Michael has received the phone call from Neri, who has made it to Long Beach. So this action takes place at least an hour later.
Hagen adds, "You better make your call to Barzini and tell him to start on his way" only to make Tessio believe that all is going as he has planned so that he will not suspect anything.

In the film, to the best of my recollection, Tom Hagen is not at the baptism. He is depicted in the very immediate aftermath of the baptism/slaughter at the Corleone estate where he informs Tessio that he and Michael are aware of his, Tessio's, betrayal. It can, therefore, be inferred that Tom was not at the baptism, as the sequence of events would not allow for him to be at both places at once. It is then that Tessio inquires of Tom as to whether Tom can talk Michael out of having Tessio killed for his betrayal or, as Tessio puts it, "for old time's sake."
My recollection of the novel is that the series of events that comprise the film's climactic sequence similarly occur somewhat simultaneously, but not completely.
I hope that this helps. If you have the time, the screenplay to The Godfather is available at the following site.

Great answer. So just to be clear - Tessio calls Barzini, Barzini sets out for the meeting, Neri shoots him, the Tessio killed. Correct?
Is that order the same in the novel (just not during the baptism)?
 
Thank you!
 
 

The question does not specify whether Mario Puzo's novel The Godfather or the film based upon that novel with a screenplay co-written by Puzo is the source from which the answer is to be drawn. For purposes of discussion, the following answer presumes the latter.
The scenes at issue occur concurrently in the film. Francis Ford Coppola's vision for this series of scenes as spelled out in available drafts of the screenplay and in the final product clearly depict simultaneous developments occurring at the Corleone family estate, at the church at which Michael Corleone is standing as godfather to his sister Connie's baby, and at the various locations around New York City and Las Vegas where the murder of Moe Green takes place. Coppola structured this sequence deliberately for maximum dramatic effect to emphasize the contrast between the solemnity of the religious service against the systematic slaughter of Michael's enemies among the Five Families of New York's Mafia, as well as the murder of Moe Green in distant Las Vegas, the latter illuminating the reach of the Corleone family's financial interests and abilities to protect or advance those interests.
The scenes with Tessio bookend this climactic sequence of events to emphasize the fate that befalls one of the late Vito Corleone's most trusted lieutenants, the caporegime who betrays Vito's successor, the young, newly established godfather, Michael Corleone.

Who is "The Raven" addressed to?

If "The Raven" is addressed specifically to anyone, it would be to people such as Poe himself whose mental world inhabits a region that's a mixture of fact and dream, of the world and a fantasy that partakes of both heaven and hell.
The speaker is a man who, probably like Poe himself and perhaps most other writers and artists in general, lives primarily in the night. While studying, pondering at midnight instead of sleeping, the raven intrudes upon him from the realm of dreams. He is already reveling in "fantastic terrors," and moreover seems in a trance-like state, repeating the strangely musical words over and over again. The raven initially offers hope. The speaker has been utterly alone in his murmuring form of insomnia; the visitor appears at the door and speaks to him, but only, of course, with the now-famous answer "nevermore."
Those to whom Poe addresses the poem are the ones who themselves feel they can answer nothing, beyond that cryptic word, to their own existential questions. The fate of the "lost Lenore," and a possible reunion with her is unknown. The fate of the speaker's own psyche is unknown as well, except for his conviction that it will be perpetually in darkness:

And my soul from out that shadow that lies floating on the floor,
Shall be lifted--Nevermore!

As always in Poe, the mere sound of the words has an importance that rivals their meaning. The reader is caught in a web of music, a jingling sound that in the hands of a lesser poet might descend into doggerel. So finally I would suggest that the verses are directed to the reader susceptible to this kind of extra-linguistic feature of Poe, to a kind of musical mesmerism that seeks to soothe and terrify in the same moment.

The poem "The Raven" is itself not addressed to anyone in particular; it does not contain any instances of apostrophe, nor does it address the raven directly. Rather, its narrator seems to be telling an anecdote to an unknown audience in the fashion of a "fireside story" or supernatural tale. The narrator tells of "once upon a midnight dreary," beginning his tale in traditional storytelling format and setting it in "the bleak December," which lends to the gloomy atmosphere.
The narrator does, however, relate how he addressed the raven--when it was an unknown presence "tapping at [his] chamber door," the narrator addresses him as "Sir...or Madam," but found "darkness there and nothing more." The narrator then brings himself to question whether the presence might be Lenore, his lost love, until eventually "there stepped a stately Raven" into his sight. At this point, the narrator addresses the Raven directly: "Tell me what they lordly name is," receiving the much-quoted answer, "Nevermore."

What are the rules in The Giver with page numbers?

There are a plethora of rules that Jonas and the other citizens must follow. Again, page numbers will vary given the edition of the book that you're looking at so the rules will be listed by chapter:

Chapter One
Pilots cannot fly over the community.
A public apology must be issued if a disruption is caused to the normal, everyday schedule.
Family must have two "tellings": Telling of feelings at night and sharing of dreams in the morning.
Precision of language must be used at all times
Each family unit may only have two children, one boy and one girl.
The third time someone breaks a rule, they will be released to Elsewhere.
You cannot have strong feelings; you must rationalize your feelings.
Those who cannot perform as they should are released.
Children are grouped according to their age.

Chapter Two
The names of new children must be kept secret until the Naming ceremony.
Children are not allowed to ride bikes before they become nines.
Children cannot have comfort objects once they become eights.
All ceremonies take place in December.
The rules are decided by the Elders.
The Ceremony of twelve is when everyone learns of their profession.

Chapter Three
Objects cannot be removed from the recreation area.
Snacks cannot be hoarded.
Girls under nine must keep their hair tied in ribbons at all times.

Chapter Four
You cannot brag.
You cannot be rude.
Community members cannot look upon one another's nakedness.
To receive assignment as a twelve, one must complete all volunteer hours.
Eights have the freedom of choice and begin their volunteer hours.
Birthmothers must bear children for three years. They can't see the children they give birth to. After the three years, they have to work in physical labor until they're released.
Children cannot attend ceremonies of release.

Chapter Five
Stirrings must be reported so treatment can be given.

Chapter Six
Children must wear coats with buttons on the back before they are sevens.
If you aren't healthy or grown enough as an infant, you're released from the community.
You cannot get emotionally attached to a child
Tens get haircuts.
Elevens get new clothes.
If you don't like your assigned job you can apply to go to Elsewhere.

Chapter Seven
During the ceremony of twelves, everyone must line up in the order of the numbers they were given at birth.

Chapter Eight
The community only has one Receiver at a time.
The current Receiver trains his replacement.

Chapter Nine
The failed Receiver's name can never be spoken in the community or used for a baby.
Only the Receiver and Receiver in trainer are exempt from the rule of Rudeness and can ask anyone any questions they want.
Jonas cannot share his training with anyone or share his dreams anymore.
Jonas can't apply for medication if he is injured while training.
Jonas can't asked to be released.
Jonas is allowed to lie.

Chapter Ten
All doors in the community cannot have locks except for The Giver's home.

Chapter Thirteen
Jonas may apply for a spouse but he must hide things like books from his family.
You cannot touch another community member.

Chapter Fourteen
Jonas cannot share or transmit his memories with anyone but the Giver.

Chapter Eighteen
Jonas cannot asked to be released as the Receiver.

Chapter Nineteen
All ceremonies are recorded in the Hall of Records.

The page numbers that the rules are located on are going to vary depending upon the copy/edition of the book which you own. Thus, to make this answer as consistent as possible, I will provide an outline of the rules according to the chapter that they take place in:
Chapter 1:
Planes may not fly over the Community. 
Precision of language must be used to prevent any sort of confusion. It is necessary to say exactly what one means.
Every family unit must have two children (one male, one female).
The third time someone violates a rule, he or she will be brought before the Department of Justice and released from the Community.
Chapter 2:
The Naming List, which lists out the names of the new children in the Community, is to be kept secret. 
Bicycle riding is not permitted until one becomes a Nine. 
Comfort objects are to be confiscated when one become an Eight.
Chapter 3:
Objects are not to be removed or taken home from the Recreational Center.
Chapter 4:
One should not brag about one's own accomplishments.
Volunteer hours must be completed in order to receive one's assignment as a Twelve.
Eights are given the freedom of choice. 
Members of the Community may not look at each other naked, with the exception being the elderly and new children.
Chapter 5:
Stirrings are to be treated with the consumption of morning medicine, and Stirrings are to be reported so that treatment may take place.
Chapter 6:
Fours, Fives, and Sixes are to wear jackets that button in the back.
Sevens are to wear jackets that button in the front.
Elevens are to transition into clothing appropriate for their adolescent bodies.
One may, technically speaking, request to be released to go Elsewhere.
Chapter 10:
Doors must not be locked within the Community (with the exception of The Giver's door).

y_1 = x^2 - 6x , y_2 = 0 Set up the definite integral that gives the area of the region

Let us first find the bounds of integration i.e. the points where the two points intersect each other. To do that we need to solve the following system of equations.
y=x^2-6
y=0
Substituting the second equation into the first yields
x^2-6=0
x^2=6
x_(1,2)=pm sqrt6
If we now look at the image below, we see that the whole region is below x-axis. This means that the integral will be negative so to calculate the area we need to put the minus sign in front of the integral (we could also put the integral in absolute value or we could simply switch lower and upper bounds with each other).
A=-int_-sqrt6^sqrt6 (x^2-6)dx   
Let us now calculate the area of the region.
A=-(x^3/3-6x)|_-sqrt6^sqrt6=-((6sqrt6)/3-6sqrt6+(6sqrt6)/3-6sqrt6)=8sqrt6
Therefore, the area of the region bounded by the parabola y_1=x^2-6 and the line y_2=0 is 8sqrt6.                                                                                    

How does the hero deed at Weathertop constitute mortal combat?

The battle at Weathertop is an episode that occurs in J.R.R. Tolkien’s The Fellowship of the Ring. Weathertop is a hill midway between The Shire and Rivendell, where the hobbits stop for a night’s rest. During the night, the Nazgul find the hobbits and recognize Frodo as the ring-bearer. Frodo has a desperate skirmish with the Nazgul king during which he is wounded by a cursed Nazgul blade. Soon Aragorn emerges to save the hobbits.
Though Frodo and Aragorn both act heroically, it is Frodo who puts the most on the line to keep the ring from the Nazgul. As the evil blade pierces Frodo’s shoulder, Frodo manages to slash the Nazgul’s cloak with his own sword. Frodo’s wound is grievous, but he proves that, in the heat of battle, he is able to face and land a blow against one of the most powerful and evil creatures in Middle Earth.
The skirmish between Frodo and the Nazgul could be described as “mortal combat” insofar as Frodo fights for his life and for the quest to destroy the ring. To be fair, the same cannot be said for the Nazgul, a powerful and possibly immortal being. As a hobbit, Frodo is accustomed to a safe and comfortable life, which makes his bravery at Weathertop all the more remarkable.

Tolkien, J.R.R. - The Fellowship of the Ring. New York: Del Rey; Reissue edition (August 12, 1986)
https://thefairytaletraveler.com/2015/05/14/real-inspirations-for-middle-earth/

Beginning Algebra With Applications, Chapter 5, 5.2, Section 5.2, Problem 116

Graph $3x-2y=-6$ using a graphing device. Verify that the graph has the correct $x-$ and $y$-intercepts.







$x$-intercept:


$
\begin{equation}
\begin{aligned}

3x-2y=& -6
&& \text{Given equation}
\\
3x-2(0) =& -6
&& \text{To find the $x$-intercept, let } y = 0
\\
3x =& -6
&& \text{Divide by } 3
\\
x =& -2
&&

\end{aligned}
\end{equation}
$


The $x$-intercept is $(-2,0)$

$y$-intercept:


$
\begin{equation}
\begin{aligned}

3x-2y=& -6
&& \text{Given equation}
\\
3(0)-2y=& -6
&& \text{To find the $y$-intercept, let } x=0
\\
-2y =& -6
&& \text{Divide by } -2
\\
y =& 3
&&

\end{aligned}
\end{equation}
$



The $y$-intercept is $(0,3)$

Nationalism, Imperialism and Alliances: Discuss the goals of European nationalism and "new imperialism" in the late nineteenth century. Identify the various alliances among nations. How did the alliance system in Europe in the early 1900s develop from nationalism and imperialism? Discuss the debate among allies on the necessity to declare war provoked by the assassination of Archduke Ferdinand. What nations or leaders do you think bear the responsibility for the outbreak of WWI?

Many books could be written on just one of these questions, so this answer does not claim to be comprehensive. The first critical point to be made is on the shift to imperialism. During the middle of the nineteenth century, the last major European nation states, including Italy and Germany, were consolidated into unified entities. This played a major role in expanding their economic power and influence, as they sought to challenge the more established states, France and Britain, for global power and colonies.
After Germany in particular had established a national economy, it began to look beyond its borders for new markets, raw materials, and trading opportunities. By the latter decades of the nineteenth century, the “scramble for Africa” was in full swing, as the European powers competed for control over the resource-rich continent. These factors encouraged the development of alliances. France and Russia, later to be joined by Britain, formed the entente. Germany, meanwhile, had a dual alliance with Austria-Hungary and was seeking to develop its economic and trading interests into the Middle East via the Ottoman Empire. Under these conditions, it was only a matter of time before war broke out.
Britain, which controlled the largest empire in the world, could not accept Germany’s efforts to obtain “a place in the sun.” This was summed up by British diplomat Eyre Crow, who declared in his famous memorandum of January 1907 that Germany was attempting to dominate Europe, and that Britain could not make concessions.
Precisely who was responsible for the war in 1914 is a contentious issue. The German historian Fritz Fischer carried out groundbreaking work in the 1960s to show that planning for war in Berlin was meticulous and the conflict was desired. But an argument can be made that this was true in all countries. After Germany gave Austria-Hungary a blank cheque to confront Serbia, Russia saw an opportunity to expand its power in the Balkans. France could not tolerate a strengthened German neighbor and was bound to Russia in an alliance. Although Britain claimed it entered the war to defend the independence of Belgium, this seems less credible when you consider that it ruled as the colonial power over a huge empire, including India, large swathes of Africa, and even Ireland. None of these countries were free or independent.
The question of imperialism is crucial to an understanding of this period. Lenin’s 1916 work, Imperialism, the Highest Stage of Capitalism, deals with this question from a Marxist perspective. Liberals also took up the question of imperialism, an example of which was the British writer J.A. Hobson’s 1902 work, Imperialism: A Study.
The outbreak of the war in 1914 is also a vast area of study. It should be looked at in connection with a growing frequency of conflicts over the years prior to 1914, such as the series of crises over Morocco, the Balkan wars of 1912–13, and the race for naval supremacy between Britain and Germany. The assassination of Franz Ferdinand and the conflict it triggered did not come out of the blue.
Regarding nationalism, the unifications of Germany and Italy are key topics, as is the turn in France, Germany, and many other countries in the decades before the war to a more aggressive, militarist nationalism.
https://archive.org/details/imperialismastu00goog

https://www.britannica.com/biography/Eyre-Crowe

https://www.marxists.org/archive/lenin/works/1916/imp-hsc/

What were the circumstances each great power faced in developing a military during World War I?

The great powers of World War I all faced unique challenges and circumstances when mobilizing their militaries during the conflict.
Germany
On August 2, 1914, Germany began officially mobilizing for war. At the time the country had a sizable standing army and pool of reserves, numbering at 4.5 million soldiers. However, active recruitment soon swelled those numbers considerably as young German men eagerly enlisted. From the start Germany expected the war to be brief, telling its soldiers that they would be home by Christmas. As a result, the country did not make serious adjustments to its economy to support its military for a prolonged conflict. This led to severe food shortages both for soldiers at the front and the populace back in Germany.
Austria-Hungary
Austria-Hungary had been developing strategies for an offensive long before the outbreak of hostilities. However, the empire's military was not prepared for the modern weapons of the era and suffered heavy losses early on. The commanders and war planners were still using tactics of the previous century, which resulted in high casualties in the face of machine guns, heavy artillery, and poison gas. Overall, the Austro-Hungarian military was woefully underdeveloped. It lacked a proper military budget, and its technology was antiquated compared to its opponents. Being a multi-ethnic fighting force, it also faced the challenge of coordinating operations between units in multiple languages.
Italy
Italy's army was vastly outnumbered by those of Germany and Austria-Hungary. The country was never able to compete in terms of numbers or leadership with its foes. It mostly fought along its northern border in the Austrian Alps. Losses were heavy, numbering in the hundreds of thousands. Before the war, Italy had been in a defensive alliance with Austria-Hungary and Germany. Therefore, the country had never developed much of a plan for fighting against these nations. There was little money for waging the war. The fight essentially destroyed the economy of the nation which was never able to adequately supply its army as a result.
Great Britain
The British army was relatively small compared to the other European powers that fought in World War I. This is because they never drafted soldiers. Rather they relied entirely on volunteers to form their fighting forces. The British military was relatively well equipped though. They had a booming economy prior to the war and were consequently able to keep their fighting forces well supplied with the latest in military technology. Great Britain also had the largest and most advanced navy of its day. However, the quick mobilization process meant that many officers had little or no actual combat experience, and coordination between various units was often unorganized.
France
France had been practicing conscription for years before the start of the war. Therefore, it had a large army, but not a professional one. France also had large colonies in Africa and Asia whose populations helped augment its forces. France relied heavily on fixed fortifications to keep the German advance at bay. This proved disastrous as the German army easily outflanked them by attacking by way of Belgium. During the war, the French readily adapted to using new technology, especially the machine gun, the armored tank, and long-range artillery.
Russia
Russia had the largest army at the start of the war with nearly six million troops ready for combat. That number was quickly doubled once hostilities began. Despite these large numbers the Russians were poorly equipped and technologically outmatched by the German army. Military and political leadership was greatly divided and unorganized as well. This led to massive losses. When the tsar was overthrown in 1917, Russia surrendered and left the war.
The United States
The United States' military contribution to the war was relatively small in terms of personnel. When it entered the war, the expeditionary army numbered just over 200,000. The country drafted an additional four million soldiers. However, a successful economy meant that American soldiers were well equipped with ample supplies and the latest in wartime technology. Moving soldiers and supplies across the Atlantic did prove time-consuming and risky and slowed resupply.

What is an inscribed angle, and how do I solve them in geometry?

In addition to Steveschoen's answer:
(1) The measure of an inscribed angle is 1/2 the measure of its intercepted arc. (In the diagram, 1/2 the measure of arc AC.)
(2) Inscribed angles intercepting the same or congruent arcs are congruent. (In the diagram, choose any point X not on arc AC; the measure of angle AXC is the same as the measure of angle B.)
(3) Tangent-chord angles are closely related as their measure is also 1/2 the intercepted arc.

Inscribed angles are angles inside circles where the vertex is "on the circle", as in the attachment, the angle in red. The green angle is called a central angle.As for solving them, that would depend upon the problem. I can tell you that the measure of the inscribed angle is half the measure of the central angle. So, for instance, if the central angle was 60 degrees, the inscribed angle would be 30 degrees (1/2 * 60). Then, the opposite way, if the inscribed angle was 25 degrees, the central angle would be 50 degrees (2 * 25).

What do others say about Jonas in The Giver?

The best place to look for information about what other community members say about Jonas is chapter 8. This is the chapter in which Jonas is "selected" to be the next Receiver of Memory.

In a firm, commanding voice she announced, "Jonas has been selected to be our next Receiver of Memory." 

Jonas doesn't understand what exactly this means or involves, but the elders describe to him why he has been selected. They give a brief rundown of the key personality traits that they have observed Jonas displaying over the course of his life. 

Jonas was identified as a possible Receiver many years ago. We have observed him meticulously. There were no dreams of uncertainty.
He has shown all of the qualities that a Receiver must have.

The elders name and describe five key traits that Jonas has. They say that Jonas has wisdom, courage, intelligence, and integrity. The fifth characteristic that Jonas has is the "Capacity to See Beyond." This is the trait that the elders do not understand, but the current Receiver says that Jonas has this trait.

Suppose there is a bill to increase the tax on cigarettes by $1 per pack coupled with an income tax cut of $500. Suppose a person smokes an average of 500 packs of cigarettes per year—and would thus face a tax increase of about $500 per year from the cigarette tax at the person’s current level of consumption. The income tax measure would increase the person’s after-tax income by $500. Would the combined measures be likely to have any effect on the person’s consumption of cigarettes? Why or why not?

First, the answer to this question is subjective. Those measures might cause a person to smoke less, but those combined measures might also cause a person to smoke more. Both can be equally defended.
You could also defend a null hypothesis, meaning that no change would occur in the packs consumed per year. This is what I would personally defend. 500 packs per year is a lot of smoking. That's 1.4 packs per day. The average consumption is 1 pack, so the smoker in this example is already considered a heavier smoker than normal. In my opinion, the cost (or savings difference) is likely so negligible that a person's level of cigarette consumption probably wouldn't change.
What I also don't know is what this hypothetical person's annual income is in the first place. Additionally, I don't know what their current debt situation is. If his/her car and house are both paid off, and they make $250,000 per year, I don't think a $500 change either way is going to matter.
Furthermore, it is conceivably possible that this person stops smoking cigarettes cold turkey for reasons other than the cost of keeping the habit or the savings from quitting the habit. Smoking is detrimental to health. The person might scale back from 500 packs per year to zero packs per year in order to hopefully live longer or avoid the various cancers that accompany cigarette usage.
http://healthsurvey.hscic.gov.uk/data-visualisation/data-visualisation/explore-the-trends/smoking/adult/median-smoking.aspx

Many peer-reviewed studies have found that increasing sales taxes on cigarettes decreases smoking among both children and adults, particularly young adults (see the link below from Tobacco Free Kids and the source below). For example, a 2012 report by the Surgeon General called "Preventing Tobacco Use Among Youth and Young Adults" stated that a 10% increase in cigarette prices results in a 3%–5% decrease in the consumption of cigarettes. It is true, however, that adults are more resistant to price increases in cigarettes than younger people are, so if this person is older, they may be less likely to give up smoking. In addition, younger people in particular are tuning to vaping nicotine, so if this person is a younger person, they may start vaping instead of smoking.
In addition, according to the link below from Market Watch, more than 44% of Americans do not pay income taxes, as their take-home pay is too low, or they are not working. Therefore, a tax reduction may not affect them.
Source:
HHS, Preventing Tobacco Use Among Youth and Young Adults: A Report of the Surgeon General, 2012, http://www.surgeongeneral.gov/library/reports/preventing-youth-tobacco-use/full-report.pdf.
https://www.marketwatch.com/story/81-million-americans-wont-pay-any-federal-income-taxes-this-year-heres-why-2018-04-16

https://www.tobaccofreekids.org/assets/factsheets/0146.pdf

There is a problem in missing assumptions of the question, namely that the effect of changes in cigarette prices affects all demographics equally. That actually isn't the case. In general, cigarette taxes reduce smoking in the young and the economically disadvantaged, but have little effect on middle-aged smokers in higher economic brackets. Thus this answer needs to be parsed in terms of demographics.
For people with middle class incomes, the effect is likely to be negligible, with the decision of whether to continue smoking determined by other issues such as the availability of smoking cessation programs and personal choice. According to the CDC, people below the poverty level are twice as likely to be smokers as those living above the poverty line. Education is also a crucial factor, with only 3 percent of people with postgraduate degrees smoking but 24 percent of high school dropouts smoking. Thus, even though taxation is unlikely to change the smoking behavior of the well-educated and affluent, that population is already unlikely to smoke.
For people living in poverty, the income tax cut would be irrelevant, as over 80 percent of people with incomes under $50,000 have no tax liabilities. Since the income tax cut would have no effect on them, the increased cigarette prices would result either in reduced smoking or increased black market cigarette purchases.
https://money.cnn.com/2013/08/29/pf/taxes/who-doesnt-pay-federal-income-taxes/

https://www.cdc.gov/tobacco/data_statistics/fact_sheets/adult_data/cig_smoking/

Single Variable Calculus, Chapter 4, 4.7, Section 4.7, Problem 30

A Norman window has the shape of a rectangle surrounded by a semicircle. If the perimeter of the window is 30ft, find the dimensions of the window so that the greatest possible amount of light is admitted.




Let $P$ and $S$ be the perimeter and surface area of the window.

$
\begin{equation}
\begin{aligned}
P &= x + 2y + \frac{2\pi r}{2} = x + 2y + \pi r\\
\\
\text{since } r &= \frac{x}{2}\\
\\
P &= x + 2y + \pi \frac{x}{2} = x + x \frac{\pi}{2} + 2y
\end{aligned}
\end{equation}
$


Also, the Surface Area of the window is...

$
\begin{equation}
\begin{aligned}
s &= xy + \frac{\pi r^2}{2}; \quad r = \frac{x}{2}\\
\\
s &= xy + \frac{\pi \left( \frac{x}{2} \right)^2}{2} = xy + \frac{\pi x^2}{8}
\end{aligned}
\end{equation}
$


We have, $\displaystyle P = x + x \frac{\pi}{2} + 2y = 30$

Solving for $y$

$
\begin{equation}
\begin{aligned}
2y &= 30 - \left( \frac{2x + x \pi}{2} \right)\\
\\
y &= \frac{30 - \left( \frac{2x + x \pi}{2} \right) }{2} = \frac{60-2x+x\pi}{4}
\end{aligned}
\end{equation}
$


Substituting the value of $y$ to the equation of the Surface Area...
$\displaystyle s = x \left( \frac{60-2x-\pi x}{4} \right) + \frac{\pi x^2}{8} = \frac{60x-2x^2-\pi x^2}{4} + \frac{\pi x ^2}{8}$
Taking the derivative with respect to $x$, we have...

$
\begin{equation}
\begin{aligned}
s' &= \frac{60-4x - 2 \pi x}{4} + \frac{2 \pi x}{8}\\
\\
\text{when } s' &= 0 \\
\\
0 &= \frac{60-4x-2\pi x}{4} + \frac{2\pi x}{8}\\
\\
0 &= \frac{120-8x-4 \pi x + 2 \pi x}{8}\\
\\
0 &= 120-8x - 4\pi x + 2 \pi x\\
\\
0 &= 120 - 8x - 2 \pi x\\
\\
2 \pi x + 8x &= 120\\
\\
2x(\pi + 4) &= 120\\
\\
x &= \frac{60}{(\pi + 4)}\text{ft}
\end{aligned}
\end{equation}
$

so when, $\displaystyle x = \frac{60}{(\pi + 4)}$
$\displaystyle r = \frac{x}{2} = \frac{ \left( \frac{60}{\pi + 4}\right)}{2} = \frac{30}{(\pi + 4)}$ft

and,

$
\begin{equation}
\begin{aligned}
y &= \frac{60 - 2 \left( \frac{60}{\pi + 4} \right) - \left( \frac{60}{\pi + 4} \right) \pi}{4}\\
\\
y &= 4.20 \text{ft}
\end{aligned}
\end{equation}
$


Therefore, the greatest possible amount of height will be admitted if the area of the window is...

$
\begin{equation}
\begin{aligned}
s &= xy + \frac{\pi x^2}{8}\\
\\
s &= \left( \frac{60}{(\pi + 4)} \right) (4.20) + \frac{\pi \left( \frac{60}{\pi + 4} \right)^2}{8}\\
\\

\end{aligned}
\end{equation}\\
\boxed{s = 63\text{ft}^2}
$

In "To Build a Fire," how does the man in the story allow his pride to interfere with his survival?

In "To Build a Fire," the primary reason for the man's death is not the cold itself or the lack of a fire, although these are the most direct and empirical reasons. The real reason is his pride, in that he never should have been out alone in the first place. 
We can immediately see elements of pride—or at least naive confidence—in the man's character. He is mentioned as being new to this country, and so to him, 50 degrees below zero is just a number; he fails to understand the way in which this mere number will affect the nature of life itself. 
As the man reflects on his journey, he frequently thinks back to "the old man from Sulphur Creek," who we may assume from context clues was a wise and helpful person who learned the practical rules of life in the Yukon. One such memory implicates pride as the primary character's weakness.

The man had been very serious when he said that no man should travel alone in that country after 50 below zero. Well, here he was; he had had the accident; he was alone; and he had saved himself. Those old men were rather womanish, he thought.

Following his turn of bad luck, the primary character begins to think on how the old man might have actually been right, and indeed, his last words are "you were right, old fellow, you were right." In retrospect, it seems like a ridiculous thing to have taken pride in, when the presence of another person probably would have saved the man's life. Furthermore, there was never any real reason given for the character to have been traveling alone; it seems as though he may have simply done it to prove that he could. 

College Algebra, Chapter 3, Review Exercises, Section Review Exercises, Problem 80

If $\displaystyle T(x) = \frac{1}{\sqrt{1+\sqrt{x}}}$ find functions $f, g,$ and $h$ such that $f \circ g \circ h = T$.
$T = f(g(h(x)))$
The formula says that, first, take the square root and add 1. Then, take the square root and lastly the result is the divisor of 1. So we let
$h(x) = 1 + \sqrt{x}, \quad g(x) = \sqrt{x} \quad$ and $\quad \displaystyle f(x) = \frac{1}{x}$
Then, by checking

$
\begin{equation}
\begin{aligned}
f(g(h(x))) &= f(g(1+\sqrt{x}))\\
\\
&= f\left(\sqrt{1+\sqrt{x}}\right)\\
\\
&= \frac{1}{\sqrt{1+\sqrt{x}}}
\end{aligned}
\end{equation}
$

How does the organization of the poem shape what the poem says?

Let's start with a simple overview of what the poem says. The narrator is dying, people have gathered around, and the entire room is a peaceful place to be. Unfortunately, a fly enters the room and interrupts the peaceful dying process.
The poem itself is organized and structured to highlight this peaceful atmosphere that gets annoyingly interrupted. The poem is composed of four stanzas of four lines each that are very tightly organized. The lines are written in a perfect iambic rhythm. This means that the syllables alternate from unstressed to stressed throughout each line. I'll use the first line of the second stanza to illustrate. The stressed syllables will be in bold.

The Eyes / around /- had wrung / them dry -

Additionally, lines 1 and 3 of each stanza are tetrameter, and lines 2 and 4 of each stanza are trimeter. This very regular rhythm and meter gives the poem a very singsong feel to it. It's peaceful and it flows well. It perfectly matches a romanticized idea of somebody peacefully going to their death with loved ones nearby.
But remember, the peaceful death is interrupted by an annoying fly. Dickinson's format mirrors this by placing a bunch of dashes in the poem. These dashes force the reader to pause in inconvenient locations, and the flow of the verse is thrown off just like the smooth and peaceful death is inconveniently interrupted by a buzzing fly.

What is ATP and how does it function? What would happen if we did not have ATP?

ATP is short for adenosine triphosphate. It is the universal unit of energy used by biological cells, and it is produced in the mitochondria.  When a cell needs energy, it gets it from ATP.  The name itself tells a great deal about the structure of ATP.  A single ATP is composed of three parts.  The first part is a base.  In this case, the base is adenine.  The second part of the molecule is a sugar.  The sugar is a ribose.  The third part of the ATP molecule is a phosphate chain.  As the name implies, ATP contains three phosphates.  
The phosphate bonds are important because it is the phosphate bonds that carry a lot of potential energy.  When a cell needs energy, a phosphate is removed from the chain. When the bond breaks, the potential energy is released.  Some of my students have a hard time understanding how something "breaking" can release energy.  I illustrate it by stretching a rubber band until it breaks.  The potential energy of the stretched rubber band releases a lot of kinetic and sound energy when the rubber band snaps.  It's a decent analogy for how breaking the ATP molecule into an ADP molecule releases energy. 
I'm not sure which direction to go with the second part of the question.  "What would happen if we did not have ATP."  The short, simple answer is we would die.  Without ATP, cells wouldn't have their "energy currency" and would die.  All living things are made of cells, and as their cells die, the organism dies.  
On the flip side, if ATP never did exist, but life did manage to begin and exist anyway, I would have to say that life must be using some other form of molecular energy.  Then we would be studying that amazing molecule instead of ATP.  
http://www.chm.bris.ac.uk/motm/atp/atp1.htm

What are the metaphors in the story by Ray Bradbury "There Will Come Soft Rains"?

The breakfast stove churns out a lovely breakfast for the people who are no longer there, and a while later, it disposes of the food, which has been left uneaten. The narrator says that "hot water whirled them down a metal throat which digested and flushed them away," and the dishes are dropped into the washer. The pipes in the sink, perhaps a garbage disposal, are compared, via metaphor, to a metal throat. With the inhabitants of the house gone, no longer able to swallow down their breakfast, the house's metaphorical throat replaces their own.
Later, the house itself is compared to an old unmarried woman as a result of its "mechanical paranoia," the way it responds to various critters that have approached it since its humans were, evidently, vaporized. The narrator describes the house's "old-maidenly preoccupation with self-protection" in this way. Further, after the old family dog returns to the home, emaciated and decrepit now, the house begins to make pancakes, torturing the poor beast with the delicious scent. The dog, we are told, begins to froth at the mouth, and "its eyes turned to fire." The animal runs around in circles, biting itself, and finally dies in the parlor. The dog's eyes are metaphorically described as turning to fire, perhaps because the animal's longing for the food the house produces is so strong that it seems to consume his entire being.
Next, the clean-up mice that come out of the walls are referred to as "regiments," comparing them to the military, probably because they are so well-ordered and efficient and single-minded in their maintenance of the home. Still later, the attic of the house is compared via metaphor to a "brain," as the machinery that keeps the house functioning seems to be housed there. As a result of this fire, the house shudders, "oak bone on bone," its beams and rafters compared to the bones that make up a human skeleton.

The house, which continues to function after its inhabitants have been vaporized in a nuclear holocaust, is described in personifying metaphors, such as "it had shut up its windows and drawn shades in an old maidenly preoccupation with self-protection."  On the day the story begins, the house "quivered at each sound, the house did."  After a period of continuing to function mechanically, the narrator describes the house as becoming more and more sensitized to its isolation and reacting fearfully, like an old woman on her own.
The impending metaphoric death of the house begins with the line "At ten o'clock the house began to die."  Somewhere, sighing, a pump shrugged to a stop."  Though the house is fully mechanized and programmed for the family's needs, this is metaphoric language since houses do not actually live, nor do pumps signal their indifference or resignation. 
At the story's end, a single wall stands to witness the house's destruction.  Its repetition of the date deepens the poignancy of the fact that no one is left to hear or respond to the advance of time.

Bradbury uses a number of metaphors in this short story. When describing the house, for example, Bradbury compares it to an "altar," and likens its many appliances, like the cleaning robot-mice, to "attendants." Similarly, he describes the house's attempt to keep intruders out as a religious ritual which goes on "senselessly" and "uselessly." This religious metaphor reinforces the idea of constancy. The house will not stop its functions, even though the family members are all dead and never coming back.
In addition, when describing how the house drops any dust and debris down some tubes into the cellar, Bradbury compares this action to an "evil Baal." Baal is a demon, so by making this comparison Bradbury highlights the house's constant need to remove itself of dirt. It views dirt as an unwelcome guest and removes it as soon as it is discovered. 
Metaphors are, therefore, important in helping Bradbury  bring the house to life while highlighting its various functions. In doing so, he warns the reader that technology can be as equally destructive as it can be helpful. 

the gods have gone away
 

Ray Bradbury's short story "There Will Come Soft Rains," is filled with figurative language. The most prevalent form of figurative language in this story is personification, followed by simile. There are a few metaphors in this story, as well. Metaphors compare two unlike things without using like or as, which distinguishes them from similes. 
One of the metaphors compares the house to a great altar. Here is the quote: 

"The house was an altar with ten thousand attendants, big, small, servicing, attending, in choirs. But the gods had gone away, and the ritual of the religion continued senselessly, uselessly." 

The inhabitants of the house are compared to gods in this metaphor. They are the ones who have gone away. The rituals of the house are compared to religious rituals. Religious rituals are man's attempt to gain access to a god or gods. The house cooks breakfast, gives announcements, prepares baths and entertainment. It is all useless, however, without the family to receive the service. The attendants can't access the gods. The altar, or house, remains empty.  
Another metaphor occurs when the house catches on fire. The house is designed to spray a green chemical to stop fires when they are detected. A metaphor is used to describe this: "Now there were twenty snakes whipping over the floor, killing the fire with a clear cold venom of green froth."
The snakes are the hoses which spout the green fire retardant. The chemical is compared to venom, as it attacks the fire, much as a snake attacks an enemy.  

What would Rousseau and Bossuet say about each other’s arguments? (Obviously they would disagree, but what might they say about the other’s lines of reasoning? For example, what would Bossuet think of the idea of equality? What would Rousseau think about royal authority and why? Is there any place where they might agree on something?)

Bossuet was a theorist of divine right monarchy. He believed that the only proper form of government was one that was divinely ordained. Given the nature of the relationship between God and man he saw in Scriptures, he thought a monarch, accountable to none but God, was the only such government. The monarch would be the sovereign—that is, he would represent and embody all the people. The people, on the other hand, would be given order and safety, which Bossuet thought were unattainable in a government where the people had a voice or a claim on liberties. Rousseau, of course, would have disagreed with most of this. He thought that mankind was inherently free but had been repressed by modern states and societies. As he said in The Social Contract:

Man is born free, and is everywhere in chains.

Rousseau, then, thought the only form of government was one which created the maximum possible freedom for its people. He thus advocated something fairly close to a direct democracy, in which the people would come together regularly to express what he called "the general will." So his conception of the foundation of government was radically different from that of Bossuet, who would have strongly objected to his democratic beliefs. But Rousseau thought that the general will commanded absolute obedience from the people, and in this he was not unlike Bossuet, as well as other thinkers like Bodin and Filmer. He believed in an absolute sovereign that had to be obeyed, but for him the sovereign was the people rather than a monarch.
http://www.iupui.edu/~histwhs/H114.dir/H114.webreader/H114.read.a.Bossuet.html

What does Paul do instead of going to Luis's funeral?

Instead of going to Luis's funeral, Paul goes out into his backyard dressed in just his blue suit. He does not put on a shirt, shoes, or socks. 
In his backyard, he makes his way toward the gray wall. There, he wedges his hands into the space between the wall and the sod. Paul then begins to pull up the sod, revealing a rectangular patch of white sugar sand. The patch is about two feet long and three feet wide.
Paul then scraps off the sand from the upside-down piece of sod. He puts the sand in piles on either side of the rectangular patch. Next, he begins scooping up big handfuls of sand from the patch itself, eventually reaching down into the dirt. Paul knows that this dirt is important; it is the land the tangerine trees grow in, at least, when the land is not covered with a layer of sand and landscaped over.
Paul makes a hole in the dirt, flings his glasses away, and cries his tears into it. He cries for Luis and the loss of the man he never really knew. After a time, Luis stands up, brushes himself off, and retrieves his glasses. He then puts the sand and sod back into place. On the way back into his house, he throws his suit into the garbage. Paul feels that his ritual has been a cathartic one, and he is satisfied that he has properly mourned Luis's death.

Glencoe Algebra 2, Chapter 2, 2.3, Section 2.3, Problem 72

-3x-y+7=0
=> -3x-y= -7
=> 3x+y = 7
=> y = 7-3x
=> y = -3x+7

Single Variable Calculus, Chapter 6, 6.1, Section 6.1, Problem 32

Evaluate $\displaystyle \int^4_0 |\sqrt{x + 2} - x| dx$ and interpret it as the area of a region. Sketch the region.

The integral can be interpreted as the area between the curves $y = \sqrt{x + 2}$ and $y = x$ in the region from $x = 0$ to $x = 4$








Notice that the orientation of the area differs at the point of intersection. To evaluate it, we can divide the area in to two sub region. $A_1$ be the area to the left of point of intersection. While $A_2$ be the area to the right of the point of intersection. So by using vertical strips


$
\begin{equation}
\begin{aligned}

A_1 =& \int^2_0 [\sqrt{x + 2} - x] dx
\\
\\
A_1 =& \left[ \frac{(x + 2)^{\frac{3}{2}}}{\displaystyle \frac{3}{2}} - \frac{x^2}{2} \right] ^2_0
\\
\\
A_1 =& 1.4477 \text{ square units}

\end{aligned}
\end{equation}
$


Then,


$
\begin{equation}
\begin{aligned}

A_2 =& \int^4 _2 [x - \sqrt{x + 2}] dx
\\
\\
A_2 =& \left[ \frac{x^2}{2} - \frac{(x + 2)^{\frac{3}{32}}}{\displaystyle \frac{3}{2}} \right]
\\
\\
A_2 =& 1.5354 \text{ square units}

\end{aligned}
\end{equation}
$


Therefore, the total area is $A_1 + A_2 = 2.9831$ square units

Why was Helen initially unable to ask her teacher questions?

Historians consider the relationship between Anne Sullivan and Helen Keller to have been one of the most heartwarming and miraculous of all time. What Sullivan accomplished in teaching Keller was an extraordinary achievement due to the many gaps that needed to bridged in order to establish an ability to communicate. Not only was Sullivan teaching a student that was both blind and deaf, but was a teacher that was blind herself, rendering Keller unable to even communicate with visual gestures. Keller lived out a frustrating existence in a world of absolute darkness and silence. Sullivan used a painstaking and inventive method of teaching by spelling words in the palm of Keller's hand. Eventually, Keller was able to contextualize water with the word being spelled on her palm, and was finally able to use her sense of touch to ask questions.

Helen Keller is initially unable to ask Miss Sullivan questions because she has no way to communicate. Miss Sullivan has been brought in to try to bridge the gap between Helen's world of darkness and soundlessness and the rest of society.
Helen can only react to the presence of the mysterious woman who hugs her and gives her a doll. She doesn't know who Miss Sullivan is or why she is there. As Helen puts it, she is in a dense fog and doesn't realize she is near the safe harbor that Miss Sullivan represents.
When Miss Sullivan spells the word doll in her hand while Helen is holding her new doll, Helen can't make the connection between the letters and the object. She goes to her mother in delight and shows her the letters, but she has no idea what they mean. It is only after Helen understands, later, that what Miss Sullivan is spelling in her hand means "water" that a new world opens to her, and she has a means to ask her teacher questions.

In "The Monkey's Paw" by W.W. Jacobs, how would you describe the appearance of the monkey's paw?

The monkey’s paw is a disembodied mummified monkey’s paw.
The monkey’s paw is a talisman that supposedly had a spell put on it by a fakir in India.  You can wish on it, and your wish will come true.  It just won’t come true in the way you intended.  Sergeant-major Morris, who brings the Whites the paw, explains that the person who last had the paw wished for death after using it.
The sergeant-major describes the paw as ordinary.

"To look at," said the sergeant-major, fumbling in his pocket, "it's just an ordinary little paw, dried to a mummy."

Basically, someone cut the paw off a monkey, and over time it has been mummified.  The Whites seem to find its appearance disturbing even though Morris describes it as ordinary.  However, due to the spell it now has magical powers.
The monkey’s paw may make the Whites feel disturbed because of the way Morris describes its powers, rather than how it looks.  He makes it seem scary.  Let’s face it, parts of monkeys are a little gross anyway.
After throwing the monkey's paw into the fire, Morris warned the Whites to leave it alone.  They were curious though.  They ended up making a wish, as a lark.

Mr. White took the paw from his pocket and eyed it dubiously. "I don't know what to wish for, and that's a fact," he said slowly. "It seems to me I've got all I want."
  "If you only cleared the house, you'd be quite happy, wouldn't you?" said Herbert, with his hand on his shoulder. "Well, wish for two hundred pounds, then; that'll just do it."

They would later regret making this wish, because the Whites found out why the last person wished for death.  The Whites got their first wish in the worst way, when they got the money but their son was killed.  Then, Mrs. White wished him back to life.  Her husband used the last wish to reverse that wish.

How did the American people feel about the government during the Great Depression? What did they think the federal government should do to help?

The Great Depression, which lasted from 1929 to 1939, was the worst economic crisis in world history. During the worst point of the Great Depression, about 1933, more than half of all Americans were unemployed. Herbert Hoover, who became U.S. president in 1929, presided over the stock market crash that began the crisis and its worst years. During his presidency, many people felt fear, desperation, and hopelessness, as they lost their jobs and homes and saw their savings disappear. It's important to remember that at this time in American history, safety net programs such as unemployment insurance, government-sponsored health insurance programs like Medicare and Medicaid, food stamps, and social security did not exist. Hoover did not initially grasp the seriousness of the situation, and, as a conservative, he believed in limited government and that it was not the government's role to, in effect, directly rescue people experiencing the economic crisis. In fact, in a 1930 speech, he declared, "Prosperity cannot be restored by raids upon the public Treasury." As a result of this seeming indifference, people found him to be cold and uncaring about the despair that was gripping much of the country, and, in 1932, he was soundly defeated by Democrat Franklin D. Roosevelt, who promised a series of progressive reforms and direct relief programs he called the "New Deal." Roosevelt, a highly effective communicator, also took to the new medium of radio to speak directly to the American people about the problems facing the nation and his proposed responses, which went a long way toward easing fear and restoring hope to the nation.
https://books.google.com/books?id=UAjls3YykzgC&pg=PA232&lpg=PA232&dq=Prosperity+cannot+be+restored+by+raids+upon+the+public+Treasury.%22&source=bl&ots=dMtR6s69ah&sig=M3zAVvoybHfcVacPKj_ylJtdEbU&hl=en&sa=X&ved=0ahUKEwiow8CZy7LaAhXKxlQKHWSdB60Q6AEIVzAG

What do the villagers think of Min's work?

In the novel, villagers like Tree Ear believe that Min's work is the finest in the region and possibly in all of 12th century Korea.
As a master potter in the village of Ch'ulp'o, Min produces enviable creations of exquisite celadon ware. This gray-green celadon ware is prized by collectors from as far away as China. Because of its strategic location, Ch'ulp'o does a robust business in ceramics trade. Situated on the shores of the Western Sea, Ch'ulp'o has access to sea routes leading north and to China. The iron-rich soil in Ch'ulp'o greatly supports the production of celadon. Because of the twin advantages of soil and location, potters in Ch'ulp'o have plenty of work.
Over the years, the wealthy come to Ch'ulp'o to purchase celadon pieces for both the royal court and the Buddhist temples. In turn, the potters eventually become a prosperous group of artisans. Their work is highly revered by all the villagers, and Min's most of all.

Why does Prospero decide to show mercy to his enemies? Do you think Prospero had planned to forgive them from the beginning?

Prospero appears to experience quite a transformation throughout the play. Initially, he's bent on revenge against those responsible for his enforced exile. The arrival of his foes on the island presents him, then, with a golden opportunity to exact vengeance. Even here though there are hints of Prospero's later mercy. He expresses sincere concern for the welfare for those on board ship:

But are they, Ariel, safe? (Act I Scene ii).

At the same time, however, Prospero plays with his enemies like a cat with a bird in its claws, giving them the impression that he will have his revenge, even if it means that innocent men like Gonzalo end up suffering. Prospero wants to keep the shipwrecked men guessing as to what he will do to them. After being imprisoned by Prospero in a grove, Alonso, Antonio, and Sebastian are terrified at what they believe will happen to them, as Ariel points out:

The king, His brother, and yours, abide all three distracted, And the remainder mourning over them, Brimful of sorrow and dismay. (Act V Scene i).

But Prospero has made his point and orders their release. There's a sense that this was indeed his plan all along, as all his actions seem so calculated. Yet his mercy, such as it is, doesn't strike one as being particularly sincere. For one thing, he still openly hates Antonio:

For you, most wicked sir, whom to call brother Would even infect my mouth, I do forgive Thy rankest fault, all of them, and require My dukedom of thee, which perforce, I know, Thou must restore. (Act V Scene i).

But Prospero is not a vindictive man—or not very, at any rate. He wants to be restored to his dukedom, and once he's assured of that, then he has no further need of either magic or vengeance.

How do animals and plants live in fast-flowing water?

Animals, such as fish, amphibians, mammals, and insects have a variety of adaptations that let them exist in swift moving water. 
Fast moving water tends to be colder than slow water; some of it originates as snow melt on the sides of mountains, for example. For this, animals in fast water tend to be more cold resistant. This is why you do not see fish like freshwater trout in equatorial regions. These animals struggle and die in slow, warm water.
Fast moving water means that if the animal or plant wants to stay put, it must resist the flow. Fish tend to be far more muscular and lean in these places, while insects like stoneflies, mayflies, and other larvae have ways to secure themselves to rocks and plants while growing. Plants develop strong root systems, and algae hold fast in rocky crevices in the river.
Some animals have to adapt their reproductive systems as well. Because finding a mate is difficult in the sweeping waters, breeding tends to happen all at one time. As an example, salmon have runs, where thousands of fish all swim upriver at once to breed, can dramatically alter the surrounding ecology of the river. Insects like mayflies have hatches, where hundreds of thousands of flies swarm into the air at once to breed and lay eggs.
Other adaptations include slow metabolisms, smaller overall sizes, and fast movement speed.
In the oceans, animals depend on currents in the water to live. Animals like jellyfish and plankton use currents to move around from one place to another, while others rely on currents to bring them nutrients they need to live. These currents also prevent the ocean from stagnating, and stir nutrients and gasses around to the same effect as stirring a compost heap.
Other animals, such as squid, whales, and even salmon, rely upon ocean currents to complete migration events for seasonal breeding, feeding, and other activities.
http://www.adfg.alaska.gov/index.cfm?adfg=wildlifenews.view_article&articles_id=407

Water flows at different speeds along different parts of a river's length.  The plants and animals that live in the fast-flowing stretches are specially adapted to life there.   Some cling to rocks or live under stones so that they are not swept away.

In "The Road Not Taken," what does the speaker mean by "fair" in the first line?

The narrator says in the second stanza of the poem that after looking at the first road, he decides to take the second, as it's "just as fair." By "fair," the narrator could mean "good" and "attractive." In other words, the second path through the woods is just as welcoming and enticing as the first road. However, the narrator could also mean that taking the second road is just as right or as good a choice as taking the first road. In other words, choosing the second path is as right a choice as choosing the first path.
The narrator also chooses the second path because it is "grassy and wanted wear," meaning that the grass is growing long on the second path and it seems as though fewer people have traveled along it. Though the narrator claims he or she wants to return to the first path on another day, the narrator knows that one step often leads to another and that he or she may never return to the first path. 

The word “fair” comes at the beginning of the second stanza of “The Road Not Taken.” In the first stanza, the narrator sees two roads or paths ahead. He’s deciding which one to take. He looks down the length of the one that has been used more often, “Then took the other, just as fair.” Here the word means attractive, beautiful, nice, and maybe even favorable or promising. Although we get the impression that one of the roads is well worn and the other one has grass growing over it in neglect, the narrator spends the second stanza and half of the third assuring us (or himself) that in reality, the two routes are equal in appearance and in sustained foot traffic. His use of the word “fair” plays into this façade, since it can also mean average or impartial.
https://www.poetryfoundation.org/poems/44272/the-road-not-taken

What do you really think caused the narrator to confess?

I think it is his guilt that causes the narrator to confess. In the end, he has gotten away with the murder. The police are fooled by his calm and confident demeanor, and they "chatted pleasantly, and smiled." Suddenly, though, the narrator "grew very pale" and he begins to talk more quickly. He feels that he is gasping for breath and gesticulating violently; he says, "I foamed—I raved—I swore!" In reality, he does none of these things, and they are all taking place within his imagination as the men just keep sitting there. The narrator hears a sound he has heard before: "a low, dull, quick sound—much such a sound as a watch makes when enveloped in cotton." He thinks this sound is the old man's heartbeat still beating underneath the floorboards, but we know that this is not possible. The heartbeat the narrator hears must be his own, and it would be racing, thumping loudly if he were feeling guilty for the murder he has committed. Therefore, I believe it is the narrator's guilt that compels him to confess because a) he was just about to get away with the murder, and b) his quickened heartbeat could indicate a guilty conscience.

Why does Bradbury use so many allusions in "The Veldt"?

“The Veldt” by Ray Bradbury demonstrates the author’s talent for exploring how contemporary trends could play out in future scenarios. This story in particular shows an understanding of how technology can dehumanize people and interfere with psychological and moral development.
The allusions to children’s literature, such as Peter Pan, Green Mansions, and Alice in Wonderland, evoke classic, beloved fantasy worlds and a child’s wish for adventure. The references to these idyllic, old-fashioned worlds then provide a stark contrast with a rogue virtual reality device that takes its cues from the negative aspects of the mind. The Wendy and Peter of Bradbury’s story have created a Neverland, but it’s one based on predators and death, signaling that the classic stories have darker themes running beneath their carefree surfaces.
The children have become addicted to the technology, and George, their father, admits to his wife with emphasis, “They live for the nursery.” Lydia in turn asks George to call in a psychologist, not a technician, to look at the nursery, because the problem isn’t mechanical, it’s mental. The children’s psychological development has been captured by a technology which increasingly traps the family.
David, the psychologist, notes this is a situation about feelings, not facts. The problem can’t be solved by logic or mechanics; it’s a matter of the heart and conscience. He offers a succinct diagnosis, placing responsibility on George and Lydia:

“You’ve let this room and this house replace you and your wife in your children’s affections.”

George and Lydia want to move the family out of the house to get a fresh start. But the nursery, fueled by Peter and Wendy’s dark thoughts, has other plans.
The macabre ending brings the literary allusions to their darkest conclusions. As the Peter in J. M. Barrie’s work states, “To die will be an awfully big adventure.” The Peter and Wendy in Bradbury’s story get their wish to live for the nursery, to hold mad tea parties, and to never grow up, but it comes at the price of their parent’s lives.

In "The Veldt" Ray Bradbury uses a number of literary allusions, many of them related to Peter Pan. Most of the other allusions in the story are also taken from famous children's books, and there's a valid reason for this, as we shall see later on.
The Hadley family and their children, Peter and Wendy—note the allusion to Peter Pan and Wendy Darling—live in a futuristic automated home packed with machines that do everything for them. The children spend all their time in a virtual reality nursery which allows them to inhabit their own fantasy world.
As the story opens, the children are experiencing life on the African veldt. Prior to this, their vivid imaginations had conjured up characters from famous fairy tales and children's stories such as Alice, from Alice in Wonderland, The Mock Turtle, Aladdin, and Dr. Doolittle.
What Bradbury is doing with all these allusions is to highlight the stark contrast between the innocent fantasy world the children have left behind and the harsh, sun-baked animal kingdom, red in tooth and claw, that they now permanently inhabit. Without the existence of proper boundaries in this dystopian world of technological child-rearing, the children's imaginations have run wild, dwelling unhealthily on scenes of savagery and death. The line between reality and virtual reality has become dangerously blurred, as Mr. and Mrs. Hadley will discover to their cost later on.

How female roles influence Yasha in The Magician of Lublin?

The women in Yasha's life are a source of both pleasure and pain, and their influence upon him is perhaps the principal element that drives the plot of The Magician of Lublin.
Yasha uses and manipulates women, though he seems to do so without guile and, at first, without much awareness that his behavior is wrong. Nor is there any real deception in the way he acts, since each woman seems to know he's involved with other girls and, before Yasha's failed burglary brings everything to a head, apparently forgives him. Esther, his wife, suffers in her loneliness at home while he goes on tour. Magda, his assistant in his performances, is madly in love with him, as are Zeftel and Emilia. His future plans are dominated by Emilia, though he realizes he also has feelings for her daughter, Halina. This, as well as being a latent source of guilt to Yasha because she wants him to convert to Christianity, results in Yasha's failed burglary attempt, for he needs money to take Emilia and her daughter to Italy.
Magda's suicide is then the immediate trigger for Yasha's withdrawal from the secular and basically hedonistic life he's led. He has an epiphany that he's betrayed all the women in his world, and instead of pulling himself together and seeking medical attention for his injured foot, he wanders into the Warsaw night and resigns himself to death. His career as a magician and his interest in earthly life are over. From this point he commits himself to the religion of his own people, though in a bizarre way, becoming a holy man isolated in a tiny brick chamber built for him in his home town of Lublin. His decision to do so is almost more akin to that of a Hindu who renounces the material world and becomes a samana, like Hermann Hesse's Siddhartha, than to that of the devout in Judaism.
His guilt about women has made him take this final step, but he is drawn back to Lublin by the presence there of his wife Esther, ultimately the most important of all the female figures in the story. Yet the novel closes with his reading, in his isolated tiny house, a letter from Emilia. Thus Esther and Emilia are the final influences upon him, the former representing the world of Judaism to which he has returned, and the latter the outside, wordly milieu he has rejected. It is an inconclusive ending, leaving open the ultimate question of whether the course Yasha has taken is "right" or "wrong."

what is the tone in Huntress?

The tone of H.D.'s poem "Huntress" is confident and aggressive, as one might expect of a poem narrated by a speaker who is on the hunt. The huntress describes the quick pace of the hunt and uses vivid imagery to illustrate the huntresses (there seem to be more than one of them, since the speaker uses the first person plural pronouns "we" and "us"). The poem opens with the huntress inviting an unknown subject to join the hunt. She writes,

Come, blunt your spear with us,our pace is hotand our bare heelsin the heel-prints—we stand tense—do you see—are you already beatenby the chase? (1-7)

The huntress explains that the "pace is hot" and that they "stand tense." These phrases depict the typical actions of a hunter: they must chase their prey and they must sometimes wait quietly and observe. The huntress asks the invited party whether or not he or she can keep up: "are you already beaten / by the chase?" 
The next two stanzas confidently detail the actions of the huntress's party. They "lead the pace" (8), which shows that they are experienced and self-assured. Their "feet cut into the crust [of the earth] / as with spears" (13-14). This is a somewhat violent image that likens the huntresses' feet to a weapon. They also "broke the clod with [their] heels" in a similar image in line 17. Next, the speaker addresses a series of questions to the unknown subject, basically asking whether that subject will be able to stay on the level of the other huntresses. 
Finally, in the last stanza, the speaker writes,

Spring up—sway forward—follow the quickest one,aye, though you leave the trailand drop exhausted at our feet. (24-27)

The speaker tells the subject to "follow the quickest one" and try to keep up with their pace, but imagines the subject will "drop exhausted at [their] feet." The huntress is confident in her abilities, and though she is welcoming another to join her party, she also feels that her skills are probably superior to this mysterious subject. 
 

In The Hobbit what important feature on Thror's map does Gandalf point out to Thorin?

The most important feature on Thror's map that Gandalf points out to Thorin is the secret passage to the Lower Halls of Erebor.
When Gandalf first shows Thorin the map, the latter is skeptical. He believes that Smaug may already know about the secret entrance. Gandalf replies that the dragon may have knowledge of the passage, but there is little likelihood he can make use of it. 
It turns out that the passage is relatively small in size: it is only five feet high and only admits three people walking abreast at any one time. Gandalf points out that it is impossible for the dragon to crawl into a hole of that size. He then reminds Thorin that he also has the key to the secret door, which Gandalf gives to him for safekeeping.
For his part, Thorin is encouraged that the dwarves now have a surreptitious way to enter the ancient dwarf realm of Mount Erebor.

In "By the waters of Babylon," what does John's discovery about the gods make him realize?

Obviously, John's discovery makes him revise his religious beliefs. The ancients were neither "gods nor demons" but men. Religious edicts can no longer be justified on the basis of their divinity, and John clearly intends to violate some of the old laws. In the last paragraph of the story, he notes the city's name, and indicates his intention to take others into the city. In the first paragraph of the story, we're told that such actions have been "most strictly forbidden."
But John's realizations extend beyond the immediate theological implications. When he thought the ancients were gods, he regarded their achievements as beyond the reach of human beings. For instance, consider what he says about his dream—the dream where he witnesses a busy New York street at night:

"As I looked upon them and their magic, I felt like a child—but little more, it seemed to me, and they would pull down the moon from the sky.  I saw them with wisdom beyond wisdom and knowledge beyond knowledge. And yet not all they did was well done—even I could see that—their wisdom could not but grow until all was peace."

He perceived imperfection in the gods, but nevertheless believed they possessed "wisdom beyond wisdom." Their intellectual and technological feats appeared to be unattainable by mortals.
After his discovery, John indicates his intention to study the writings of the ancients and use this knowledge to advance society. ("We must build again.") He now believes it is possible to achieve some of the feats of the ancients. In fact, he even thinks it is possible to improve on their record—to follow in their footsteps without making the same mistakes. This is supported by John's analysis of what the ancients might have done wrong:

"[I]t is better that truth come little by little. I have learned that, being a priest. Perhaps, in the old days, they ate knowledge too fast."