f(x)=1/(x+2) Graph the function. State the domain and range.

f(x) = 1/(x+2)
First, determine the vertical asymptote of the rational function. Take note that vertical asymptote refers to the values of x that make the function undefined. Since it is undefined when the denominator is zero, to find the VA, set the denominator equal to zero.
x+2=0
x=-2
Graph this vertical asymptote on the grid. Its graph should be a dashed line. (See attachment.)
Next, determine the horizontal or slant asymptote. To do so, compare degree of the numerator and denominator.
degree of numerator = 0
degree of the denominator = 1
Since the degree of the numerator is less than the degree of the denominator, the asymptote is horizontal, not slant. And its horizontal asymptote is:
y=0
Graph this horizontal asymptote on the grid. Its graph should be a dashed line.(See attachment.)
Next, find the intercepts.
y-intercept:
y=1/(0+2)=1/2
So the y-intercept is (0,1/2) .
x-intercept:
0=1/(x+2)
(x+2)*0=1/(x+2)*(x+2)
0=1
So, the function has no x-intercept.
Also, determine the other points of the function. To do so, assign any values to x, except -2. And solve for the y values.
x=-10 , y=1/(-10+2) = -1/8
x=-7 , y=1/(-7+2)=-1/5
x=-4 ,y=1/(-4+2)=-1/2
x=-1 , y=1/(-1+2)=1
x=1 , y=1/(1+2)=1/3
x=3 , y=1/(3+2)=1/5
x=8 , y=1/(8+2)=1/10
 Then, plot the points (-10,-1/8) , (-7,-1/5) , (-4,-1/2) ,(-1,1) ,   (0,1/2) ,   (1,1/3) ,   (3,1/5) , and (8,1/10).
And connect them.
Therefore, the graph of the function is:

Base on the graph, the domain of the function is (-oo, -2) uu (2,oo) . And its range is (-oo, 0) uu (0, oo) .

May I have a detailed analysis of John Goodbye's poem entitled ''The Uncles'' in terms of language/structure/ themes/imageries/tone?

Language:
The poem reads more like prose than poetry and is a eulogy to the speaker's uncles. It is clear that the poet has done this deliberately. He uses mechanical engineering jargon throughout the poem which signifies the specific particularity of the uncles' trade. They are mechanical engineers who do the hard work of creating engines and other mechanical parts according to clients' specifications. The language indicates how very specific the requirements are. Their measurements have to be correct to the finest detail and the uncles therefore have to be mathematicians to understand exactly what is required and ensure that the requirements are met:

...crossing sevens like émigré intellectuals,measuring in thous and thirty-secondths (scrawledon torn fag-packets); feinting with slide rules,...

The language emphasizes knowledge and mastery of their trade. The poet uses terms such as 'Swarfega kings' and 'émigré intellectuals' to denote the uncles' expertise. Their knowledge is foreign to those not involved in the trade and, therefore, when they use the jargon associated with it, they sound like intellectuals from a different world. In addition, the language exposes the habits they have: they smoke and take tea breaks as if they are something special and, therefore, the tea has to be specially prepared. They work hard and are dedicated. They keep their workspace neat but are always at risk: one uncle lost part of a finger in an accident and, as a result, cannot play the banjo anymore. They are exposed to steel shavings and cuts and have lost some of their hearing because of the continuous noise in the workshop.
It is significant that 'Uncles' is capitalized and repeated throughout the poem, which emphasizes the eulogistic tone. The speaker looks up to these men and obviously has great admiration for their skill and dedication. 
Structure:
The poem has no real structure and is written more in prose format. There is no actual rhyme or rhythm although some alliteration is used. The entire poem depicts the structured disorganisation one finds in an engineering workshop. An outsider would be confused by the array of tools, parts, equipment and other objects seemingly just lying around, but the uncles are organized and know exactly why each object occupies a specific space. The poem is fast-paced and copies the continuous activity found in the workshop. The constant activity is indicated by the use of enjambment and commas which indicate short breaks in between work activities. Full stops are cleverly used to demarcate and emphasize a specific activity.
Theme:
The poem's purpose and theme is clearly to indicate the speaker's respect and appreciation for his uncles. He finds their expertise and dedication to their work commendable and, through this poem, wishes to show that what may seem ordinary and mundane is actually very special.
Imagery:
The poet uses alliteration, as in line 3 where the 's' is repeated: 

Swarfega kings, enseamed with swarf and scobs, skin

The repetition here depicts the constant sound made by electrical cutting tools and equipment in the workshop and is also onomatopoeic. A number of metaphors are also used, such as 'Swarfega kings,' which suggests that the uncles are masters of how to use a cleaning agent, obviously to clean off the grime and grease from their hands and forearms. The metaphor 'Emigre intellectuals' suggests that they are experts from a foreign nation. In 'their chamfered years,' the metaphor implies that their years have been cut away and compares this to their action of cutting away metal. The contrast in the phrase 'mess of order' suggests controlled disorder—that what might seem confusing is actually purposefully set out.
Tone:
The tone is clearly eulogistic throughout. The speaker has the greatest admiration for his uncles, indicated by the use of the capital 'u.' His respect for them and what they do is emphasized when he ends the poem with a last reference to them: 'My Uncles.'

A block of mass m rests on a horizontal table. The block is pulled by a massless rope with a force F at an angle theta . The coefficient of static friction is mu_s=0.60 . The minimum value of the force needed to move the block depends on the angle theta . Calculate what angle theta is needed to move the block with a weight equal to 400 N with the minimum force possible.

The minimum possible force to move the block has to be just equal to the maximum possible value of static friction. (Static friction is the friction force between the table and the block that keeps the block from moving.) The maximum possible value of the magnitude of the static friction is
F_s = mu_sN , where N is the normal force (the force from the table on the block, acting perpendicular to the table.) 
If the horizontal component of the applied force is just equal to the maximum possible static friction, the block will start moving with no acceleration, so from the second Newton's Law, 
Fcos(theta) = mu_sN
The normal force can also be found from the second Newton's Law, considering the components of the forces perpendicular to the table:
-W + Fsin(theta) + N = 0
Here, W is the magnitude of the gravitational force on the block, or weight.
From here, N = W - Fsin(theta)
and Fcos(theta) = mu_s(W - Fsin(theta))
Solving this for F results in
F = (mu_sW)/(cos(theta) + mu_ssin(theta))
To find the minimum value of F, take the derivative with respect to the angle:
(dF)/(d(theta)) = mu_sW*(-sin(theta)+mu_scos(theta))/(cos(theta)+mu_ssin(theta))^2
The derivative is zero when 
mu_s = tan(theta) , which means that the minimal value of the force is reached when
theta = arctan(mu_s) = arctan(0.6) = 31 degrees
The angle of approximately 31 degrees is required to move the block with the minimal force possible.
 
http://hyperphysics.phy-astr.gsu.edu/hbase/N2st.html

The static force opposes the motion of the object, and the maximum value of the static-friction force is proportional to the normal force F_n . The normal force is equal to the vertical component of the force F . Keeping the magnitude of F constant and increasing theta from zero results in an increase in the vertical component of the force and a decrease in F_n ; thus decreasing the maximum static-friction force f_(max) . The object will begin to move if the horizontal component of the force exceeds f_(max) .
Apply Newton's second law to the block and solve for F in terms of theta .
eq. (1) :-> sum F_x=Fcos(theta)-f_s=0
and
eq. (2) :-> sum F_y=F_n+Fsin(theta)-mg=0
The maximum magnitude of force that can be applied before the block slips is:
f_s=f_(s,max)=mu_s*F_n
Now eliminate f_s and F_n in eq. (1) and eq. (2) and solve for F .
You will find that the force as a function of angle is
F(theta)=(mu_smg)/(cos(theta)+mu_ssin(theta))
Now to find the minimum force we must take the derivative and set it equal to zero to find the critical value of theta between 0 and pi/2 .
(dF(theta))/(d theta)=-(mu_smg)(-sin(theta)+mu_scos(theta))/(cos(theta)+mu_ssin(theta))^2=0
This equation is satisfied when the numerator is equal to zero. Therefore:
(dF(theta))/(d theta)=-(mu_smg)(-sin(theta)+mu_scos(theta))=0
(-sin(theta)+mu_scos(theta))=0
Solve for theta .
sin(theta)=mu_scos(theta)
tan(theta)=mu_s
theta=tan^-1(mu_s)+pi*n , n = any integer
Although we only care about solutions between 0 and pi/2 so let n=0 . Then we have one solution which is:
tan^-1(0.6)~~pi/6
F(pi/6)=(mu_smg)/(cos(pi/6)+mu_ssin(pi/6))
F(pi/6)=(240 N)/(sqrt(3)/2+0.6*1/2)~~206 N
Hence at an angle of about pi/6 it only takes about 206 N to move the box, which is the minimum possible value.
https://www.physicstutorials.org/home/mechanics/dynamics/newtons-second-law-of-motion

https://www.themathpage.com/

Calculus of a Single Variable, Chapter 7, 7.6, Section 7.6, Problem 19

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:
M_x=rhoint_a^b 1/2([f(x)]^2-[g(x)]^2)dx
M_y=rhoint_a^bx(f(x)-g(x))dx
The center of mass (barx,bary) is given by:
barx=M_y/m
bary=M_x/m
We are given, y=-x^2+4x+2,y=x+2
Refer to the attached image. The plot of y=-x^2+4x+2 is in red color and the plot of y=x+2 is in blue color. The curves intersect at (0,2) and (3,5) .
Now let's evaluate the area (A) of the region,
A=int_0^3((-x^2+4x+2)-(x+2))dx
A=int_0^3(-x^2+4x+2-x-2)dx
A=int_0^3(-x^2+3x)dx
Using basic integration properties:
A=[-x^3/3+3x^2/2]_0^3
A=[-(3)^3/3+3/2(3)^2]
A=[-9+27/2]
A=9/2
Now let's evaluate the moments about the x- and y-axes using the formulas stated above,
M_x=rhoint_0^3 1/2([-x^2+4x+2)]^2-[x+2]^2)dx
M_x=1/2rhoint_0^3{[(-x^2+4x+2)+(x+2)][(-x^2+4x+2)-(x+2)]}dx
M_x=1/2rhoint_0^3{[-x^2+5x+4][-x^2+3x]}dx
M_x=1/2rhoint_0^3(x^4-3x^3-5x^3+15x^2-4x^2+12x)dx
M_x=1/2rhoint_0^3(x^4-8x^3+11x^2+12x)dx
Evaluate using the basic integration rules:
M_x=1/2rho[x^5/5-8(x^4/4)+11(x^3/3)+12(x^2/2)]_0^3
M_x=1/2rho[x^5/5-2x^4+11/3x^3+6x^2]_0^3
M_x=1/2rho[(3)^5/5-2(3)^4+11/3(3)^3+6(3)^2]
M_x=1/2rho[243/5-162+99+54]
M_x=1/2rho[243/5-9]
M_x=1/2rho[(243-45)/5]
M_x=1/2rho(198/5)
M_x=99/5rho
M_y=rhoint_0^3x((-x^2+4x+2)-(x+2))dx
M_y=rhoint_0^3x(-x^2+4x+2-x-2)dx
M_y=rhoint_0^3x(-x^2+3x)dx
M_y=rhoint_0^3(-x^3+3x^2)dx
M_y=rho[-x^4/4+3(x^3/3)]_0^3
M_y=rho[-x^4/4+x^3]_0^3
M_y=rho[-1/4(3)^4+3^3]
M_y=rho[-1/4(81)+27]
M_y=rho[(-81+108)/4]
M_y=rho(27/4)
M_y=27/4rho
Now evaluate the center of mass by plugging in the values of moments and area as below:
barx=M_y/m=M_y/(rhoA)
barx=(27/4rho)/(rho9/2)
barx=(27/4)(2/9)
barx=3/2
bary=M_x/m=M_x/(rhoA)
bary=(99/5rho)/(rho9/2)
bary=(99/5)(2/9)
bary=22/5
The center of mass (barx,bary) are (3/2,22/5)

Calculus: Early Transcendentals, Chapter 3, 3.2, Section 3.2, Problem 7

g(x)=(1+2x)/(3-4x)
g'(x)=(2(3-4x)-(1+2x)(-4))/(3-4x)^2
g'(x)=10/(3-4x)^2

What do the men do when they seize Daniel?

Hello! Thank you for your question. 
The section that you are asking about is in Chapter 4, where Simon takes Daniel to the synagogue in order to try to seek a glimpse of Jesus of Nazareth. Near the end of the chapter, Daniel attempts to throw a rock at two Roman soldiers when he is grabbed by two men. 
The two men are minor characters and stop Daniel from his attempt at riling up the Romans. Their ultimate goal is to stop him (very possibly saving his life) and to scold him for his joining in with zealots to cause trouble. Seeing as how the Jews at the time were completely under Roman rule, it is understandable that these men would have wanted to prevent any action that would have caused the Romans to impose more harsh control over them. 
 

What is the meaning of the quote “no doors slammed, no carpets took the soft tread of rubber heels” from the short story "There Will Come Soft Rains"?

"There Will Come Soft Rains" follows an automated house in a world where humanity has been destroyed by nuclear war. Bradbury opens this short story with the following passage:

In the living room the voice-clock sang, Tick-tock, seven o'clock, time to get up, time to get up, seven o'clock! as if it were afraid that nobody would. The morning house lay empty. The clock ticked on, repeating and repeating its sounds into the emptiness. Seven-nine, breakfast time, seven-nine!

That is the very first paragraph that opens this story. What, then, does it establish? What we see here is a house continuing to run according to a preset routine, as if it still held human residents. This then is the tension that shapes the story: the house is a work of technology, created to serve a purpose. But in a world without humans, that purpose has now been rendered obsolete.
The quote you are asking about reflects that same tension. It is invoked in the context of that same routine which introduces the story, a routine intended with a family in mind. The house had been created to serve humans, but there are no humans left. The house stands empty, but it still goes on as if it isn't. This is the tragedy of the house itself, even if the house itself is unaware of the tragedy of its own existence.
Through his use of rich descriptive passages, Bradbury is able to depict the aftermath of a nuclear war where humanity has vanished and its technology is all that appears to have survived.

At the beginning of the short story "There Will Come Soft Rains," Bradbury illustrates the everyday automated routines of a technologically advanced smart home, which operates daily functions to make the anonymous family's life easier and more efficient. Despite the automated wake-up call and the impressive breakfast, which is produced by sophisticated mechanisms, the family is eerily absent. Bradbury emphasizes the family's absence by writing, "But no doors slammed, no carpets took the soft tread of rubber heels" (1). While describing the elaborate mechanically-driven morning routine, Bradbury highlights the lack of slamming doors and stampeding feet, which are the typical sounds of an active family getting ready to start their day. As the story progresses, the readers discover that the only thing remaining in the wake of a nuclear blast zone is the technologically advanced smart home, which continues to function despite the fact that the family it caters to has died in the blast.

To understand the meaning of this quote, let's first put it into some context. It is one minute past eight in the morning. In the story, this is the time when parents leave the house to go to work and children leave to go to school. As such, we would expect to read about the slamming of the doors and the tread of rubber heels of the carpet. This would indicate to the reader that people are leaving the house to start their day.
However, in this quote, Bradbury is telling us that these sounds are missing from the house today. The purpose of this is to highlight the silence in the house. He wants the reader to understand that these people, who should be making noise as they get ready for work and school, are not there. He is therefore highlighting the sense of loss.
Looking deeper, Bradbury is also highlighting the darker side of technology. Thanks to the atomic bomb, this family has been eradicated and will never again slam a door nor tread on the carpet. Only their automated house remains, but it has no idea that the family will never return.

Despite the fact that the automated house in Ray Bradbury's short story "There Will Come Soft Rains" has started the day by making announcements and cooking breakfast, there is no sign of humans. In the first paragraph the narrator indicates that "The morning house lay empty" and later that "no doors slammed, no carpets took the soft tread of rubber heels." Instead of describing human characters, the narrator makes the house itself the main character. It is not revealed until well into the story that there has been an atomic blast and that the house is the only one still standing "in a city of rubble and ashes." The humans who inhabited the house, two parents and two children, have been incinerated in the attack, but their silhouettes remain on the charred outside wall on one side of the house, reminiscent of photographs taken in the days after the first atomic bomb was dropped on Hiroshima in 1945.

Calculus: Early Transcendentals, Chapter 4, 4.1, Section 4.1, Problem 35

You need to find the critical points of the function, hence, you need to evaluate the solutions to the equation g'(y) = 0.
You need to evaluate the first derivative, using the quotient rule:
g'(y)= ((y-1)'(y^2-y+1) - (y-1)(y^2-y+1)')/((y^2-y+1)^2)
g'(y)= (y^2-y+1 - (y-1)(2y-1))/((y^2-y+1)^2)
g'(y)= (y^2-y+1 - 2y^2 + 3y - 1))/((y^2-y+1)^2)
g'(y)= (-y^2+2y)/((y^2-y+1)^2)
You need to solve for g'(y) = 0, such that:
-y^2+2y = 0 => y^2 - 2y = 0
Factoring out y yields:
y(y - 2) = 0 => y = 0
y - 2 = 0 => y = 2
Hence, evaluating the critical numbers of the function for g'(y) = 0, yields y = 0 and y = 2.

What are the dangers of ideologies in The Crucible by Arthur Miller?

The danger of ideologies in this text, as in life, is that people adhere to them rigidly and refuse to entertain ideas that contradict or undermine the ideas to which they already hold. For example, Deputy Governor Danforth adheres to his ideology of strict authoritarianism even when it becomes clear to everyone else that he has been mistaken in his estimation both of the accusing girls and in the guilt of the accused. In act 4, he explains why he will neither pardon the convicted nor postpone the scheduled hangings, saying:

While I speak God's law, I will not crack its voice with whimpering. If retaliation is your fear, know this—I should hang ten thousand that dared to rise against the law, and an ocean of salt tears could not melt the resolution of the statutes.

His ideology tells him that maintaining his authority and continuing to appear strong and certain in the law is the most important thing he can do; never mind the fact that several innocent people could die as a result or that almost everyone else is united against his feelings. Danforth makes it clear that the death of others, even thousands of others, is nowhere near as important to him as maintaining his authority and power within the community. This kind of failure to recognize the human collateral of such a choice is the danger of ideology.

Arthur Miller depicts how religious ideologies concerning a strict adherence to the Bible, unwavering obedience to elected authority figures, and oppressive gender roles contribute to the unhinged hysteria surrounding the witch trials, which result in the deaths of numerous innocent citizens. Salem's authority figures are products of a theocracy and believe they were selected by God to do his bidding on earth. Characters like Deputy Governor Danforth, Judge Hathorne, and Reverend Parris are portrayed as callous, selfish authority figures, who are obsessed with power and wish to remain in exalted positions. The prominent ideology in the austere, religious community encourages blind obedience towards authority figures, which contributes to the witch trials as citizens automatically support the court's decisions.
The ideology regarding adherence to Biblical principles also plays a significant role in the witch trials. The citizens genuinely believed in evil spirits, the devil's power, and malevolent witches. Anyone without a sound knowledge of the Bible or a perfect reputation is viewed with suspicion. When John Proctor does not recall each of the Ten Commandments, Reverend Hale says, "Theology, sir, is a fortress; no crack in a fortress may be accounted small" (Miller, 67).
Reverend Hale's comment best describes the community's attitude towards upholding Biblical principles. Since citizens were not able to openly expresses their grievances out of fear that they would tarnish their reputations, resentment builds in the community and many feuds are played out in the corrupt court.
The community's ideologies regarding gender roles are also dangerous and motivate Abigail and her followers to continue acting as officials of the court. In the Puritan community, young women were oppressed and expected to remain quiet and meek, which is in accordance with the Puritan perspective of the Bible. Once Abigail Williams and her followers gain popularity and attain a revered status, they continue to falsely accuse innocent citizens in order to maintain their positions of authority.

Ideologies play an important role in The Crucible.
The characters possessing ideologies, or a set of beliefs that influence decision making, use them to control others and consolidate their own power in Salem. For example, Hathorne and Danforth represent an authoritarian ideology.  They believe that their power should be unquestioned.  They demonstrate this power in the way they summon people to the trials and insist that names are given and that those accused accept their wrongdoing. This authoritarian ideology prevents accepting any conclusion that might challenge their power.  
Another example of the danger of ideologies can be seen in Abigail.  An ideology of emotional manipulation motivates her.  Abigail seeks to increase her power over people in the town.  She does this through deceit and by playing people against one another.  For example, Abigail creates the fear of witches to distract from how she covets John Proctor.  Abigail continues this when she sees that naming names increases her importance in the town.  She uses the ideology of emotional manipulation to consolidate power over the town.  Her ideology proves to be extremely dangerous.
Ideologies motivate Danforth, Hathorne, and Abigail. Others, such as the Putnams and Abigail's friends, follow their example. Ideologies are dangerous in The Crucible because they serve to justify unreasonable control and power over others.

Single Variable Calculus, Chapter 3, 3.3, Section 3.3, Problem 77

Determine the equation of the normal line to the parabola $y = x^2 - 5x + 4$ which is parallel to the line
$x - 3y = 5$


$
\begin{equation}
\begin{aligned}
\text{Given:}&&& \text{Parabola}\quad & &y = x^2-5x+4\\
\phantom{x}&&& \text{Line} \quad & & x - 3y = 5
\end{aligned}
\end{equation}
$


Solving for slope$(m)$ using the equation of the line

$
\begin{equation}
\begin{aligned}
x - 3y &= 5
&& \text{Transpose } x \text{ to the right side}\\
\\
-3y &= 5-x
&& \text{Divide both sides by -3}\\
\\
\frac{-3y}{-3} &= \frac{5-x}{-3}
&& \text{Simplify the equation}\\
\\
y &= \frac{x-5}{3} \quad \text{ or } \quad y = \frac{1}{3}x - \frac{5}{3}
&& \text{By using the general formula of the equation of the line}\\
\\
y &= mx + b
&& \text{Slope}(m) \text{ is the numerical coefficient of }x\\
\\
m & = \frac{1}{3}
\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}
y &= x^2 - 5x + 4\\
\\
y'&= \frac{d}{dx} (x^2) - 5 \frac{d}{dx} (x) = \frac{d}{dx}(4)
&& \text{Derive each term}\\
\\
y'&= 2x - (5) (1) + 0
&& \text{Simplify the equation}\\
\\
y' &= 2x - 5
\end{aligned}
\end{equation}
$


Solving for the equation of the normal line,

$
\begin{equation}
\begin{aligned}
m_N &= \frac{-1}{m}
&& \text{Slope of the normal line is equal to the negative reciprocal to the slope of the line which is } \frac{1}{3}\\
\\
m_N &= \frac{-1}{\frac{1}{3}}\\
\\
m_N &= -3
\end{aligned}
\end{equation}
$


Let $y' = m_N$

$
\begin{equation}
\begin{aligned}
y' & = m_N = 2x - 5
&& \text{Substitute the value of slope}(m_N)\\
\\
-3 & = 2x - 5
&& \text{Add 5 to each sides}\\
\\
2x &= 5 - 3
&& \text{Combine like terms}\\
\\
2x &= 2
&& \text{Divide both sides by 2}\\
\\
\frac{2x}{2} &= \frac{2}{2}
&& \text{Simplify the equation}
\end{aligned}
\end{equation}
$


Using equation of the parabola

$
\begin{equation}
\begin{aligned}
y & = x^2 - 5x + 4
&& \text{Substitute the value of } x\\
\\
y & = (1)^2 - 5(1)+4
&& \text{Simplify the equation}\\
\\
y & = 0
\end{aligned}
\end{equation}
$


Using point slope form

$
\begin{equation}
\begin{aligned}
y - y_1 &= m(x-x_1)
&& \text{Substitute value of } x,y \text{ and slope}(m)\text{ of the line}\\
\\
y - 0 &= \frac{1}{3}
&& \text{Simplify the equation}
\end{aligned}
\end{equation}
$


The equation of the normal line is $\displaystyle y = \frac{x-1}{3}$

What is the parting gift that Ursula's colleagues give her?

In The Rainbow, Ursula Brangwen receives a gift of two poetry books, one by Meredith and the other by Swinburne. The gift is significant, as it is highly symbolic of how Lawrence treats books throughout his body of work. Lawrence is suspicious of the materiality of books. To him, they are simply artifacts or things. To him, it does not matter whether the book is a first edition or has a particularly attractive cover design; only what is written inside matters. The text is the thing. The book is dead, but the text lives and breathes.
The occasion of Ursula's receiving the books is her leaving the school where she has been working as a teacher. In writing this scene, Lawrence is suggesting that the giving of books has become something of a respectable middle-class ritual. Giving books, those material objects made from dead trees, is not about encouraging a love of learning, the spread of knowledge, or even the sheer enjoyment of reading; it is simply a sign of social status. One reads because one wants to appear genteel and learned. It is the appearance that matters. The analogy Lawrence seeks to draw between books as objects and the bourgeoisie is unmistakably clear: everything is just for show and outward respectability.

An example of a Qin reform resulting in greater social organization was the division of China into ________. A. three distinct social classes B. 21 military and labor divisions C. countless feudal estates D. 36 prefectures

The first Emperor of China, Qin Shi Huang, came to power during the Warring States Period. After Duke Xiang asked Shang Yang to carry out his political reforms, the Qin (pronounced Chin) state grew so powerful that it was able to overthrow the other 6 strong warring states. The Qin reforms created “the first centralized, unified, multi-ethnic feudal state in Chinese history—the Qin Dynasty” (Warrior Tours). One of the first steps in centralization and unification was to make sure the Emperor’s power was supreme. To do this, he needed to end the traditionally separate, local divisions in Chinese society that were governed by feudal lords. By dividing China into thirty-six prefectures and appointing his own governors to control each, he was able to reduce the power of the nobility and place all power in his own hands. Thus, a Qin reform that resulted in greater social organization was the division of China into 36 prefectures. 
Although this reform brought a more peaceful life to the Chinese people, Qin Shi Huang was a tyrannical ruler who required endless military service, forced hard labor onto those who didn’t contribute enough to the state, imposed high taxes, and used harsh punishments to eliminate people he thought were against him. The cruel rulership, known as Legalism, under the Qin Dynasty prompted peasant revolts that led to its downfall after only 16 years.
https://www.ancient.eu/Qin_Dynasty/

When was the poem published?

This poem was originally published in 1916 in a collection entitled Mountain Interval; it was the first poem in the book. The poem relies on the symbol of the two roads, diverging in the forest. They represent a choice, really any choice, in a person's life. The narrator, a traveler, examines both roads from his vantage point and knows he must make a decision about which one to take. It is a difficult decision for him because the second road is "just as fair" as the first, and "the passing there / Had worn them really about the same": in other words, just about the same number of people have taken each road. He wishes there were some way that he could take both roads, but he knows that once he picks one, it will never really be possible to take the other one because "way leads on to way." One decision leads to another leads to another, and so on, and one ends up far away from one's original choice.
Ultimately, the narrator says that he will eventually, when he's older, tell people that he took the road that had been "less traveled by" other people, but such a road does not exist in the poem because "both that morning equally lay." This seems to indicate, then, that people like to believe that they have made unique choices even though such unique choices really do not exist. The choices we make may seem quite meaningful, in hindsight especially, though they really are not.

In "Sinners in the Hands of an Angry God," what does Edwards consider essential for salvation?

Jonathan Edwards' famous sermon "Sinners in the Hands of an Angry God" is an excellent example of the revivalist movement in churches during the Great Awakening. Grounded in the dominant theology of the day, the Great Awakening introduced an emotional component to the role of the church, using images and prayers to evoke affective responses from the congregation.
Soteriology, or the question of what we must be saved from and how we are saved, is at the heart of Edwards' sermon. He uses vivid imagery to describe Hell, a literal place of eternal torment for those he terms the Wicked. He further describes that the Wicked are literally held, dangling over the pit, by God. It is only the willpower of God, he asserts, that keeps them from falling into Hell at any given moment. People can work to stay healthy, avoid death, profess the best of intentions, even sit in church every Sunday. 
Ultimately, Edwards points toward a covenant of grace between man and God—the idea that God is the ultimate power, but that God created a covenant with mankind through Jesus Christ. God alone has the power of life over death, redemption over sin.
For Edwards, it is merely at his own whim that God keeps man from the pit at any given moment. In order for the pit to be avoided entirely, man must enter fully into the covenant through the mediation of Christ. Intention, good works toward their fellow men, and sitting in church are not enough. Edwards is calling for full-on conversion. It is not simply the mind which must accept and contemplate a concept of covenant and grace. The heart must be fully devoted to Christ. God's restraint from simply throwing them into Hell is a chance to change. 
https://digitalcommons.unl.edu/cgi/viewcontent.cgi?referer=&httpsredir=1&article=1053&context=etas

How does the story end?

Hoot nicely wraps up just about every conflict. The major thing that concludes is that the construction of the restaurant has been stopped. Roy, Mullet Fingers, and Beatrice successfully prove to everybody that the owls do indeed live there. Additionally, they are able to prove that the construction company intentionally ignored environmental impact studies of the site. Roy and Beatrice have grown close over the course of the story, and the story ends with their friendship securely set. About the only "loose end" that the story leaves is what happens to Mullet Fingers. He has disappeared once again; however, the book ends with a little nod or tribute to him. Readers get to see Roy go out to the secret creek that Mullet Fingers showed him, and Roy attempts to catch a fish. He is unsuccessful, but he vows to keep on trying.

Guess I'll have to come back another day and try again, Roy thought. That's what a real Florida boy would do.

Single Variable Calculus, Chapter 7, 7.6, Section 7.6, Problem 38

If $\tan^{-1} (xy) = 1 + x^2 y$. Find $y'$
If we take the derivative implicity, we have...


$
\begin{equation}
\begin{aligned}
\frac{\frac{d}{dx}(xy)}{1 + (xy)^2} &= 0 + \left[ x^2 \cdot \frac{d}{dy} (y) \frac{dy}{dx} + 2x \cdot y \right]\\
\\
\frac{x \frac{dy}{dx}+y(1)}{1+(xy)^2} &= x^2 \frac{dy}{dx} + 2xy\\
\\
x \frac{dy}{dx} + y &= \left[ 1 + (xy)^2 \right] \left( x^2 \frac{dy}{dx} + 2xy \right)\\
\\
x \frac{dy}{dx} \left[ 1 + (xy)^2 \right] \left( x^2 \frac{dy}{dx} \right) &= y\left( 2x + 2x^3 y^2 - 1\right)\\
\\
\frac{dy}{dx} &= \frac{y\left( 2x + 2x^3 y^2 - 1\right)}{x\left( 1 - x \left[ 1 + (xy)^2 \right] \right)}\\
\\
\frac{dy}{dx} &= \frac{y\left( 2x + 2x^3 y^2 - 1\right)}{x\left( 1 - x - x^3y^2 \right)}
\end{aligned}
\end{equation}
$

Calculus of a Single Variable, Chapter 2, 2.2, Section 2.2, Problem 62

Take the derivative of the function.
y' = sqrt3 -2sin(x)
Set the derivative function equal to zero, since we want to know where x is when the slope is zero.
0 = sqrt3 -2sin(x)
2sin(x)=sqrt3
sin(x)=sqrt(3) /2
We need to find all the angles of x where the y-coordinate of the unit circle equals to \sqrt3 /2 on the domain [0,2pi).
The y-value sqrt3 / 2 will exist in the first and second quadrants of the unit circle.
The angles are:
x=pi/3,(2pi)/3
These two values will give us zero when we substitute them back into the derivative function.
To get the points, plug these two values back to the original function.

y=sqrt3 (pi/3) + 2cos(pi/3)= sqrt3 (pi/3) +1
The first point is: (pi/3, (sqrt3 pi)/3 +1)
y=sqrt3 ((2pi)/3) + 2(cos((2pi)/3))= (2sqrt3 pi) /3 + 2(-1/2)= (2sqrt3 pi) /3-1
The second point is: ((2pi)/3,(2sqrt3 pi) /3-1)

Compare and contrast "Uncle Rock" Gilb, "Christmas, 1970" Castillo, and "We Real Cool" Brooks from Woman Hollering Creek.

The most obvious contrast in these three selections is the format. "Christmas, 1970" is a free-verse poem, "Uncle Rock" is a short story in prose form, and "We Real Cool" is a short but structured poem composed of four couplets.
There are strong similarities, however. Each once can be seen as a cultural commentary on the life of minorities in America. Castillo is Cuban-American, Gilb is half-Mexican in heritage, and Brooks is African-American.
Each of these three writers draws on their differentiated experiences in their writing. In "Christmas, 1970," Castillo implies that this is the characters' first Christmas together in America, and the children are excited to put up the tree, but their mother will just "cry into the new year/ with Lidia and Emerito/ our elderly downstairs neighbors." She seems to be weeping for what they have given up by moving.
In "Uncle Rock," Gilb shows a young Mexican-American boy named Erick, who rarely talks, but watches his mother struggle with her new life in America. She talks about the old days in Mexico, which confuses him because, from what she says about it, it sounds terrible. She wants to find a good man to marry who can help her provide a stable home for Erick. Erick observes many potential suitors pass through the story. Some are rude and behave inappropriately towards his mother, but one takes him to his first baseball game.
Brooks's "We Real Cool" is about a group of young African-American boys playing pool in Chicago. Brooks is well-known for her short pieces depicting the urban poor. She uses "we" constantly in the poem, showing how much of the boys' sense of identity comes from their group identity. The rhythm of the writing and the references within the poem to jazz are a connection to the heavy emphasis on music within Brooks's culture.
In your essay, perhaps you could emphasize the different formats of these three pieces, as well as the three different minority cultures which they represent, while discussing similarities such as figurative language and somewhat auto-biographical cultural commentary.

When talking about the philosophy of idealism, what are some contemporary examples in art education?

While Idealism is a complex philosophical theory with various proponents and many different versions, the version that is most pertinent to the field of art education is the one espoused by Hegel. Hegel, a nineteenth-century German philosopher, published his Aesthetics in 1835, and the first English translation appeared some forty years later—thus the influence of this work went far beyond his native Germany. His philosophy is called "idealistic" because he claimed that ultimate reality was in the mind or spirit (Geisst in German)—it was, in that sense, ideal. Idealism also holds that understanding the self is a key to understanding reality. For Hegel, understanding of the self requires a synthesis between the self and the external world, and art has an important role to play in this synthesis.
In Hegelian aesthetics, the most important function of art is to expose the truth in the material form of art. Beauty arises from this reconciliation of matter and form that only art is capable of. Art—along with religion and philosophy—is one of the three ways in which we can apprehend ultimate reality, so for Hegel, art occupies a much more central position than it did for many of his contemporaries.
Hegel's impact on art education came through figures like the American educator, William Torrey Harris, who was an important figure in art education in the nineteenth century and sought to apply Hegelian principles in art education in various educational institutions. In an address to the National Education Association in 1889, Harris said:

The cultivation of taste, the acquirement of knowledge on the subject of the origin of the idea of beauty (both its historic origins and the philosophical account of its source in human nature), the practice of producing the outlines of the beautiful by the arts of drawing, painting and modeling, the criticism of works of art with a view to discover readily the causes of failure or of success in aesthetic effects.

These were ideas that were clearly influenced by Hegel. Harris, was also influenced by earlier Romantic idealists such as Amos Bronson Alcott and Elizabeth Peabody. Idealism was important for art education because it was a foil for aestheticism. Art was more than something frivolous or something additional to a regular curriculum—it was seen as an important site of self-understanding and moral and political transfiguration.
In the contemporary world, the effect of these strands of thought can be seen most clearly in the educational philosophies of Montessori and Waldorf schools, both of which take art education to be essential to a holistic curriculum.

Compare and contrast Samuel Pepys's style in his diary entries with Jonathan Swift's style in Gulliver's Travels.

A comparison of a section of a description of a place in both Samuel Pepys's diaries and Jonathan Swift's Gulliver's Travels will illustrate differences and likenesses between the two authors' styles.
A section of Pepys's diary, from September 7, 1665, recounting his visit to Swakeley's estate is as follows:

A very pleasant place, bought by him of Sir James Harrington’s lady. He took us up and down with great respect, and showed us all his house and grounds; and it is a place not very moderne in the garden nor house, but the most uniforme in all that ever I saw; and some things to excess. Pretty to see over the screene of the hall (put up by Sir J. Harrington, a Long Parliamentman) the King’s head, and my Lord of Essex on one side, and Fairfax on the other; and upon the other side of the screene, the parson of the parish, and the lord of the manor and his sisters. The window-cases, door-cases, and chimnys of all the house are marble.

A section from Gulliver's account of his time in Lilliput, published in 1726 is below:

At the place where the carriage stopped there stood an ancient temple, esteemed to be the largest in the whole kingdom; which, having been polluted some years before by an unnatural murder, was, according to the zeal of those people, looked upon as profane, and therefore had been applied to common use, and all the ornaments and furniture carried away. In this edifice it was determined I should lodge. The great gate fronting to the north was about four feet high, and almost two feet wide, through which I could easily creep. On each side of the gate was a small window, not above six inches from the ground: into that on the left side, the king’s smith conveyed fourscore and eleven chains, like those that hang to a lady’s watch in Europe, and almost as large, which were locked to my left leg with six-and-thirty padlocks. Over against this temple, on the other side of the great highway, at twenty feet distance, there was a turret at least five feet high.

Although written more than half a century apart, both writers use a similar style, straightforward, simple, and fully in modern English. Both passages should be comprehensible to a twenty-first–century audience in terms of both vocabulary and grammar. Both writers connect clauses through the use of the conjunction "and," and both use semicolons, a form of punctuation not as common in modern times. Pepys, however, uses shorter sentences than Swift and sometimes employs sentence fragments, as one would expect to occur in a private journal. Swift also provides a bit more explanatory background material to orient the reader, fitting the information into clauses within long sentences.
Mostly, however, the styles are similar, as they are secular and straightforward. They are both a precursor to today's journalistic style, attempting to lay out the facts in a clear, objective manner.

Both Samuel Pepys and Jonathan Swift wrote with little embellishment, Pepys from a literal vantage point and Swift from a figurative one. In both Pepys's diary and Swift's Gulliver's Travels, there is little in terms of self-reflection or introspection. Pepys's diary entries are factual and unadorned by comments of a personal nature.
Consider Pepys's diary entry for September 2nd, 1666: this is the account of how the Great Fire of London began and of the damage it inflicted on the city. Pepys wrote that he was alerted to the fire by Jane, one of his maids. The rest of the diary entry for that day consists of a dispassionate account of events as they unfolded. Accordingly, little could be done to save the houses and buildings in the fire's path. Like many Londoners, Pepys took pains to secure important documents and belongings after it became apparent that the fire could not be suppressed.
Upon Pepys's suggestion, the king gave the command to pull down the houses in the fire's path. Sadly, all such efforts to thwart the fire's advance proved futile. Pepys's rapport with King Charles II is contrasted with Swift's uncomfortable detente with the fictional Emperor of Lilliput in the first part of Gulliver's Travels. While the monarch of Pepys's account is largely accommodating and responsive, the monarch of Swift's account must be mollified into action. It is only after Gulliver's compassionate treatment of the six soldiers (who tried to execute him) that the king relaxes his wary stance toward his giant prisoner. He orders Gulliver to be supplied with "a proportionate quantity of bread and wine" and "other victuals" for his sustenance. The emperor also has his tailors design suitable clothing for Gulliver and commissions his "greatest scholars" to teach Gulliver the Lilliputian language.
In Pepys's world, the king is an informed and sympathetic public figure, but in Gulliver's fictional world, a monarch is often arbitrary and impossibly difficult to please. Unlike Pepys, Swift definitely provides a more nuanced view of the English monarch.
It is true that Pepys's world is literal and the events he relates are historical, while Swift's world is fictional. Both Pepys and Swift even utilize linear narratives and largely dispassionate tones in their respective stories. However, there is one important difference: where Pepys's account of life is candid and unadorned with analytical insight, Swift's account of an Englishman's fictional life is satirical in nature.
Swift uses Gulliver's varied experiences to criticize the British government, colonialism, science, and human nature. Read Perceptions of Satire in Gulliver's Travels in order to help you understand what Swift is satirizing in his story. As with Pepys, Swift chooses not to include a running commentary of his personal musings. He merely relates what Gulliver sees and experiences during his travels, leaving us readers to deduce for ourselves the significance of Gulliver's exploits.

Which image in the poem "Sonnet 97" conveys nature's bounty?

In "Sonnet 97" the speaker is lamenting being separated from his beloved. To be apart from her for so long feels like the cold of winter. And yet they first parted during the summer, a time of great beauty and the full flowering of nature's bounty:

Yet this abundant issue seemed to me
But hope of orphans, and unfathered fruit.

"Abundant" means something that exists in large quantities, so the speaker's referring here to the fruits of nature. "Issue" in this particular context means something produced. Here, nature has produced her summer fruits in abundance. But the speaker's not remotely interested in any of that. He's still longing for his beloved; indeed, he's pining for her so much so that, to him, the bounties of nature no longer mean anything:


For summer and his pleasures wait on thee,
And thou away, the very birds are mute.



The pleasures of summer are nothing without the presence of the speaker's love by his side. One season changes imperceptibly into another, yet they might as well all be winter, so terribly sad and bereft is the speaker without his love.
https://www.poetryfoundation.org/poems/45101/sonnet-97-how-like-a-winter-hath-my-absence-been

In chapter 33, what does Risa say the Admiral has done for her?

The answer to this question can be found in the final sentences of chapter 33.

The Admiral was an odd bird, but he'd done something no one else had been able to do for her since she'd left StaHo. He'd given her back her right to exist.

Chapter 33 begins with Risa appearing before the tribunal at the Graveyard. It is their job to figure out what job to give each Unwind. Risa is assigned menial labor. Specifically, she is told that she will be a dishwasher in the camp, and she is not happy about it.

"Well, they always need help in the galley," says Starboard. "Especially after meals."
The girl gives Risa a long, pleading look, perhaps hoping that Risa will come up with something better for herself, but all Risa says is "Fine. Dishwasher. Am I done here?"

As Risa turns to leave, the next Unwind comes in with blood pouring out of his nose. Risa simply reacts to help. She begins questioning the cause of the injury, and she begins physically administering care. Basically, without even knowing it, she exactly follows the steps of a trained medic.

His shirt is caked with dried blood, and both his nostrils have started bleeding fresh.
"What happened to you?"
He looks at her, sees who it is, and says, "Your boyfriend— that's what happened to me. And he's gonna pay."
Risa could ask him a dozen questions about that, but the kid's bleeding all over his shirt, and the first priority is to stop it. He tips his head back.
"No," Risa tells him. "Lean forward, otherwise you'll gag on your own blood."
The kid listens. The tribunal of three come out from behind their desk to see what they can do, but Risa has it under control.
"Pinch it like this," she tells him. "You need to be patient with this kind of thing." She shows the kid exactly how to pinch his nose to stem the flow of blood.

The tribunal is impressed and immediately changes her role from dishwasher to medic. Risa is terrified of the job, but she gains considerable confidence in herself and her skills over the next month. Risa once again has confidence in herself, and she feels more complete because she has a purpose. She finds her role fulfilling and important, and she knows that people depend on her. She is pulling her own weight, and that makes her feel wanted. It makes Risa believe that she truly belongs in the world and that she deserves to live rather than be unwound.

Chapter 33 describes the beginning of Risa's time in the Graveyard, starting with the tribunal all new recruits must go through, in front of the Admiral's particularly trusted proteges. While the tribunal is not impressed with her musical skills, Risa insists that she will do any job she is given, and manages to pass the tribunal on this basis. Risa eventually is assigned galley duty.
However, as she is leaving the tribunal, Risa encounters a boy whose bleeding nose was, he says, caused by Connor. The tribunal notice that Risa seems to know exactly what to do, and determine that Risa should be "immediately promoted from dishwasher to medic." While Risa initially finds it "terrifying" to be performing the duties of a medic without any training, soon she develops a sense of security in herself.
At the end of the chapter, Risa says that the Admiral had "given her back her right to exist."

What has Capulet decided for his daughter, concerning Paris?

When we first meet Paris, he is in talks with Lord Capulet about marrying Juliet. Lord Capulet reminds Paris that Juliet is young and, while girls her age do sometimes marry, it would be better for her health if they waited two more years. He concludes the meeting by emphasizing that Juliet must give her consent to marry, and he, Lady Capulet, and the Nurse all encourage Juliet to look upon Paris with a favorable eye.
After Romeo has killed Tybalt, however, Lord Capulet changes his mind about waiting two years and needing Juliet's consent. Perhaps seeing how dangerous Verona could be for his young daughter, he decides that Juliet and Paris will wed immediately, thus taking her away from the city. When she does not immediately agree, he threatens to disown her. Although this may appear to be the ravings of a cold-hearted father, it seems likely that Lord Capulet is afraid for his daughter's life and shaken after the death of his nephew; he feels that marrying Paris is the best thing for her.

Early in the play, Count Paris approaches Lord Capulet—not for the first time, it seems, as Capulet references what he has "said before" about marrying Juliet. Capulet continues to feel that Juliet is too young to marry, at only thirteen years old. He says, "Let two more summers wither in their pride / Ere we may think her ripe to be a bride" (1.2.10-11). In other words, he wants Paris to wait another two years before asking Juliet to be his wife, as this would bring her to the ripe old age of fifteen. He believes girls who get married too young are "marred" by it. Further, Capulet tells Paris, "woo her, [...] get her heart. / My will to her consent is but a part" (1.2.16-17). He encourages Paris to try to win Juliet's love in the meantime, because his own consent is only one part of what is needed for their marriage to go forward. He says that Juliet's own consent is also needed.

How does Grim demonstrate that he does not trust his grandson initially but then slowly change his mind in Freak the Mighty?

In the beginning of the novel, Max's grandfather, Grim, remarks to his wife, whom Max calls Gram, that Max looks so much "like Him," meaning Maxwell's father. Maxwell notes that his grandfather will never speak his father's name; it is as though it "is too scary to say." Max narrates,

Grim says that night in the kitchen, "...the boy is like him, we'd better watch out: You never know what he might do while we're sleeping. Like--his father did." (Ch. 1)

Thus, Grim tells his wife that it is more than Max's physical resemblance to his father that bothers him; it is also Max's behavior that is similar to his father's. Apparently, he is very worried that Max will turn out like his father.
After Max meets the small boy who is called Freak, they become friends. Coincidentally, Freak's mother, whom he calls Gwen, was once friends with Max's mother. She knew his father, but Gwen will only tell Max that his father made it difficult for his mother to have friends. Later, in Chapter Seven, Freak and Max watch the Fourth of July fireworks; unfortunately, however, while they walk around, they encounter Tony D, a gang leader. Freak boldly calls "Blade," as Tony is known, a "cretin." But as luck would have it, a police car passes them, and Blade runs off.
In Chapter Eight, Max's grandfather gives Max a "pruney" look when he sees Max wet from the pond after he is brought home by the police from where he and Freak watched the fireworks. While they turn over Max to his grandparents, the police (who have given the two friends a ride home) tell Max's grandfather that Max rescued "the poor crippled midget kid."

So Grim listens to the cops and then he gives me this weird look, like, imagine my surprise....(Ch.8)

When Max is dry, his grandmother offers Max some ice cream, but his grandfather interrupts, saying that what Max should have is a cup of coffee. "Real coffee," he adds. After Gram has made this coffee, Grim hands Max the cup. Max narrates,

Grim is handing me coffee in a china cup, from the set they never use. He gives me that cup like it's a really big deal, maybe because I'm not allowed to drink coffee yet, and he's so Grim-like and serious I open my mouth to say what's the big deal...and something happens. (Ch. 8)

Max realizes now that his grandfather is proud of him, and he recognizes that Max is not like his father. Grim beams at Max with pride.

Calculus of a Single Variable, Chapter 7, 7.6, Section 7.6, Problem 26

First lets find the bounds of integration. When looking at the graph the furthest that the lamina is bounded on the y-axis is where the curves interest. Lets find those points.
y+2=y^2
0=(y+1)(y-2)
Therefore the y bounds are y=-1 and y=2. Then we will integrate between the furthest right curve (x=y) and the furthest left curve.
The center of Mass is:
(x_(cm),y_(cm))=(M_y/M, M_x/M)
Where the moments of mass are defined as:
M_x=int int_A rho(x,y)*y dy dx
M_y=int int_A rho(x,y)*x dy dx
The total mass is defined as:
M=int int_A rho(x,y)dy dx
First, lets find the total mass.
M=int^2_-1 [int^(x=y+2)_(x=y^2) rho dx] dy
M=rho int^2_-1 [(y+2)-(y^2)] dy
M=rho [(1/2)y^2+2y-(1/3)y^3]|^2_-1
M=9/2 rho
Now lets find the x moment of mass.
M=int^2_-1 y*[int^(x=y+2)_(x=y^2) rho dx] dy
M=rho int^2_-1 y*[(y+2)-(y^2)] dy
M=rho int^2_-1 (y^2+2y-y^3) dy
M=rho ((1/3)y^3+y^2-(1/4)y^4)|^2_-1
M_x=9/4 rho
Now the y moment of mass.
M=int^2_-1 [int^(x=y+2)_(x=y^2) rho x dx] dy
M=rho/2 int^2_-1 [x^2|^(y+2)_(y^2)] dy
M=rho/2 int^2_-1 (y^2+4y+4-y^4) dy
M=rho/2((1/3)y^3+2y^2+4y-(1/5)y^5)|^2_-1
M_y=36/5 rho
Therefore the center of mass is:
(x_(cm),y_(cm))=(M_y/M, M_x/M)=((36/5 rho)/(9/2 rho),(9/4 rho)/(9/2 rho))=(8/5,1/2)
The moments of inerita or the second moments of the lamina are:
I_x=int int_A rho(x,y)*y^2 dy dx
I_y=int int_A rho(x,y)*x^2 dy dx
I won't solve these integrals step by step since they are very similar to the others, but you will find that:
I_x=63/20 rho
I_y=423/28 rho

Single Variable Calculus, Chapter 2, 2.3, Section 2.3, Problem 47

Given the function $f(x) = \displaystyle \frac{x^2-1}{|x-1|}$

a.) Find $(i) \lim\limits_{x \to 1^+} f(x) \qquad (ii) \lim\limits_{x \to 1^-} f(x)$



$
\begin{equation}
\begin{aligned}
(i) \lim\limits_{x \to 1^+} f(x) & = \lim\limits_{x \to 1^+} \displaystyle\frac{x^2-1}{x-1}\\
& = \lim\limits_{x \to 1^+} \displaystyle\frac{(x+1)\cancel{(x-1)}}{\cancel{(x-1)}}\\
& = \lim\limits_{x \to 1^+} (x+1)\\
& = 1+1\\
& = 2\\

(ii) \lim\limits_{x \to 1^-} f(x) & = \lim\limits_{x \to 1^-} \displaystyle \frac{x^2-1}{-(x-1)}\\
& = \lim\limits_{x \to 1^-} \displaystyle\frac{(x+1)\cancel{(x-1)}}{-\cancel{(x-1)}}\\
& = \lim\limits_{x \to 1^-} - (x+1)\\
& = \lim\limits_{x \to 1^-} -x-1\\
& = -1 - 1\\
& = -2
\end{aligned}
\end{equation}
$


b.)Is the $\lim\limits_{x \to 1} f(x)$ exist?
$\lim\limits_{x \to 1} f(x)$ does not exist because the left and right hand limits are different


c.) Sketch the graph of $f$

Explain why the word "atom" was an appropriate term for Democritus to choose?

Democritus was a pre-Socratic philosopher famous for first proposing that everything was made up of "atoms". The word atom comes from the Greek "atomos" which loosely translates as "indivisible". According to his theory, atoms were the basic constituents of all material things. Democritus suggested that if one attempted to break things down to their most basic elements one would eventually reach a point where there would be an "indivisible" element, an atom. He was a materialist in philosophical terms, and suggested everything was made up of "atoms and the void". Matter and space.
In this sense Democritus is a kind of proto-scientific thinker, and was influential with other famous materialists like the Roman Lucretius, who wrote about the atomic theory in his poem "De rerum natura" (On the Nature of Things).
The atomic theory resurfaced in the modern context with the chemist John Dalton in the early 19th century and became more refined in the late 19th with the discovery of the electron by J.J. Thomson and further developments of atomic physics in the 20th century.
https://en.wikipedia.org/wiki/Atom

Democritus's view was that everything was composed of "atoms," which, he thought, were indivisible particles. The term "atom" comes from the Greek word "tomos," which means "slice" or "section." (Consider the meaning of other words that contain root "tom," such as "tomography.") The prefix "a" indicates negation, or opposite of what follows. (Again, think of some words with Greek roots that begin with "a.") Thus, the term "atom" is an appropriate name for a particle that cannot be broken up into smaller pieces. Democritus' theory stated that there are different kinds of atoms (which form different kinds of matter), that they are in constant motion, and there is empty space between them.
The contemporary atomic theory of matter, confirmed by numerous experiments, agrees with most of these assumptions: matter is in fact composed of atoms, there is empty space between them, and atoms are constantly moving or vibrating. Of course, we know now that an atom is not the smallest constituent of matter, as was once assumed. An atom itself consists mostly of empty space, with nucleus (containing protons and neutrons) in the center and electrons orbiting around it. The electrons, protons and neutrons are called "elementary" particles, which implies that they cannot be broken down further. However, the protons and neutrons are theorized to consist of even smaller pieces, called quarks.
https://en.wikibooks.org/wiki/General_Chemistry/Atomic_Structure/History_of_Atomic_Structure

What does "a score" mean in the poem "Loveliest of Trees, the Cherry Now"?

Now, of my threescore years and ten,Twenty will not come again,And take from seventy springs a score,It only leaves me fifty more.

The word score means twenty. "Score" is not commonly used anymore, but it is not entirely obsolete. In the first line of the stanza quoted above, the poet is estimating that his lifetime should be threescore (sixty) years plus ten, or seventy years. In the second line he reveals that he is now twenty years old; so in the third line, when he says, "And take from seventy springs a score," he means he is mentally deducting twenty years (a score) from his seventy years of life expectancy.
Cherry trees blossom very early in the spring. The poet is calculating that he has fifty springs of life expectancy left. It is a nice way of paying tribute to the beautiful cherry trees. He is thinking only of how many times he can hope to see them in bloom again. Many people will agree with him that the cherry tree is the loveliest of trees. They are not only beautiful, but they are harbingers of spring.
The English poet A. E. Housman, who is remembered for his cycle of poems A Shropshire Lad, was born in 1859 and died in 1936; so he actually lived to be seventy-seven years old, a little longer than he had expected.

When Matt first pulls a gun on Richard Strout, what does he order Strout to do?

In "Killings," by Andre Dubus, Matt is a grieving father whose son, Frank, has been murdered by Richard Strout. The reader learns that Frank has been dating Mary Ann Strout, who was just recently separated from Strout. Frank returns home one night beaten and bruised. He informs his parents that Strout is the one that did it. Soon after, Strout, described as being "too hot-tempered," shoots and kills Frank as he is with Mary Ann and her two sons.
Matt shares with his friend, Willis, that it is difficult for his wife to see Strout out on bail. Matt also informs him that he has a gun that he carries with him. One night, after Strout is leaving his job as a bartender, Matt and Willis are waiting for him near Strout's car. Matt's first directions to Frank are, "Don't talk. Unlock the front and back and get in."

What are some of the products that come from crude oil?

Crude oil is composed of many different kinds of hydrocarbons, and can be broken down or refined to produce a wide spectrum of things. 
The main product of petroleum is gasoline. This is used to fuel engines, and is a volatile mixture of lighter petrochemicals.
The second most common product of crude oil is diesel. Diesel is similar to gasoline, but is heavier and less volatile than it's fuel cousin. Diesel is also used to run engines, but can only be used in special engines designed with the lower volatility in mind.
A significant portion of crude oil is used to make jet fuel, which is similar to diesel in composition but contains a different concentration of sulfur and has different lubrication properties. Neither diesel nor jet fuel will catch fire in the presence of an open flame, but both still contain lots of energy.
Some oil is used to make heating oils for lamps and burners, and is similar to diesel.
Crude oil can be used to make lubrication oils, which do not burn easily and can maintain lubrication at extremely high temperatures. These oils are used in engines, mechanized parts, windmills, and any other type of joint or hinge.
Gas products, such as propane and butane, are extremely volatile and burn easily. These are used in lighters, heaters, grills, and stoves.
Solvents are made with crude oil, and work very well on organic material like rubber and plastic.
Rubbers and plastics are made with crude oil or components of crude oil.
A vast portion of crude oil is used to generate electricity, particularly the liquid fuels and gasses like gasoline, diesel, and propane.

Beginning Algebra With Applications, Chapter 5, 5.4, Section 5.4, Problem 10

Using the slope intercept form, determine the equation of the line that contains the point whose coordinates are $(2,3)$ and has slope of $\displaystyle \frac{-1}{2}$.


$
\begin{equation}
\begin{aligned}

y =& mx+b
&&
\\
y =& \frac{-1}{2}x + b
&& \text{Replace $m$ with } \frac{1}{2}
\\
3 =& \frac{-1}{2} (2) + b
&& \text{Substitute $x = 2$ and $y = 3$}
\\
3 =& -1 + b
&& \text{Solve for } b
\\
\\
4 =& b
&& \text{Add } 1
\\
\\
y =& \frac{-1}{2}x + 4
&& \text{Write the equation of the line by replacing $m$ and $b$ in $y = mx+ b$ by their values}

\end{aligned}
\end{equation}
$

What is the effect of the parallelism in Act 3 Scene 2 (Line 96-97) of Romeo and Juliet?

The parallelism in this interchange between the Nurse and Juliet—"Will you speak well of him that killed your cousin?" / "Shall I speak ill of him that is my husband?"—leads into a monologue from Juliet which explores the issue further, with the same point being revisited again in parallel terms: "Wherefore, villain, didst thou kill my cousin? / That villain cousin would have killed my husband." Juliet uses the identifier "villain" to describe both cousin and husband, because in either situation described, her loyalties are divided: if Romeo, a man from a rival family, kills a member of Juliet's family, Juliet should, theoretically, be bound by honor to hold him in contempt. However, because of the situation between the two families, Juliet equally feels unable to express complete solidarity with the man she loves, because in doing so, she sets herself in opposition to her own family.
The parallelism here, then, has the effect of expressing the difficulties of the situation in which Juliet finds herself. From both angles, the situation looks untenable. Juliet's repetition of the word "villain" suggests she is shuttling between a position in which Romeo is a villain, and a position in which her own family is, and is unable to find a point of compromise between the two. This emphasizes the impossibility of her position, and also the fact that she fully appreciates its difficulty.

This scene takes place just after Juliet's nurse has informed her that Romeo has killed her cousin, Tybalt.  The nurse asks Juliet, "Will you speak well of him that killed your cousin?"  And Juliet's response, "Shall I speak ill of him that is my husband?" echoes the structure of the nurse's initial question.  The effect of this parallelism is that it bluntly exposes the paradox within which Juliet is trapped: how can she feel love for the man who killed her kinsman?  Yet how can she hate the husband that she loves?  Obviously, anyone who murders her beloved cousin in the streets should be her enemy as well, but she is duty-bound to honor and love her husband as she has taken an oath before him, the friar, and God.  How can she do both?  The parallelism, besides emphasizing her impossible position, also shows Juliet's intelligence in that she understands the position she's in. 

In respect to globalization, how has your global perspective been expanded over the past several years, and what has caused that expansion?

Our global perspective has expanded over the years for a variety of reasons. One way that our global perspective has expanded is with the growth of businesses beyond our borders. We are realizing that we must be competitive internationally. This has become painfully clear, as companies have moved jobs overseas to save on labor costs. Workers in some other countries, such as Mexico, China, and India, are paid less than American workers. This has led to jobs being shipped overseas, and/ or American workers having to take pay and benefit cuts. It also means our calls to customer service or technical support centers may not be handled in the United States.
Another example of our expanding global perspective can be seen in the increase in the number of terrorist attacks throughout the world. Many of these recent attacks have occurred in places that normally haven’t experienced these attacks. France, Belgium, and Germany are some countries where these attacks have occurred. These recent attacks have required our government and the American people to be very vigilant because these attacks could occur here in the future. The attacks on September 11, 2001, in New York, Washington, D.C., and Shanksville, Pennsylvania made us realize we are vulnerable to possible terrorist attacks. The recent attacks have reminded us of this vulnerability. Fighting terrorism will take a global effort.
The impact of civil wars in other countries has also expanded our global perspective. We realize these conflicts create issues with refugees who want to come here to escape the strife in their homelands. We need to develop policies about how to handle these refugees. We also need to try to prevent the conditions that often help lead to the outbreak of civil wars. The issue with the Syrian refugees is one we are currently trying to face.
Finally, as we try to take actions to protect our environment, we realize this must be a global effort. Some countries have less restrictive rules regarding pollution. We are trying to work together with other countries to deal with issues such as global warming and pollution control. As the global climate changes, it will have an impact throughout the world. Global cooperation is needed to deal with these issues.
https://www.globaleducation.edu.au/global-education/what-are-global-perspectives.html

How does Conor's relationship with the monster change throughout the course of the narrative in Patrick Ness's A Monster Calls?

At first, Conor believes the monster is merely a vision in a dream; then, he becomes confused about what is real and what is not. Further, he does not understand the meaning of the monster's three tales until he admits the truth about himself, a truth which the monster helps him realize.
When the monster first calls, it appears after the moon passes before Conor's window that looks out upon an old church and its graveyard. Also visible is a large yew tree that transforms into a monstrous human shape:

I have come to get you, Conor O’Malley, the monster said, pushing against the house, shaking the pictures off Conor’s wall, sending books and electronic gadgets and an old stuffed toy rhino tumbling to the floor (Chapter 1).

Conor refuses to believe this monster is nothing more than a dream. After Conor is attacked by the bullies at school, the monster reappears that night at precisely 12:07 a.m. When the monster tells Conor that he wishes to talk with him, Conor says that he will meet him outside so his mother will not be awakened. Conor is amazed that he walks down the stairs when it is only a dream.

“It’s only a dream,” he said again.But what is a dream, Conor O’Malley? the monster said. . . Who is to say that it is not everything else that is the dream? (Chapter 5)

The monster tells Conor that he only appears for matters of life and death; further, he states that he will return to Conor, and he will relate three stories from when he walked before, and they will be scary. Also, after he tells three stories, Conor will tell a story, and it will be the truth--not just any truth, but Conor's truth, the truth of which Conor is afraid. 
Later, the monster returns and relates the first of his tales, a story about a man who thought only about himself. The tale involves a kingdom that experiences hardships, as all the males die but the grandson. Conor does not like this story because the surviving grandson kills his beloved farmer's daughter and blames it on his grandmother, the regent, so he can be king when he becomes old enough.

Conor hesitated, confused. “You said you made sure she was never seen again.”"And so I did. When the villagers lit the flames on the stake to burn her alive, I reached in and saved her" (Chapter 9).

The second tale is about a man punished for his selfishness. He was a minister who preached against cutting down a yew tree for medicinal products, and drove an apothecary away. When his daughters were ill, the minister begged the apothecary cure his daughters. The apothecary refused; consequently, the girls died.
Conor argues that the apothecary should have helped. The monster responds,

He was greedy and rude and bitter, but he was still a healer. The parson, though, what was he? He was nothing. Belief is half of all healing (Chapter 17).

The third tale is about an invisible man. He is not truly invisible, but people no longer pay attention to him until the man finally decides to make people see him.
All of these tales are relevant to Conor's life. The yew tree which transforms into the "monster" gives advice and teaches lessons with his three tales. He wants Conor to come to grips with his mother's terminal condition and stop trying to be "invisible" because, he tells Connor, he must tell the truth:

Belief is half of healing. . . I came to heal you (Chapter 24). 

Conor has thought more of himself and his grief over his mother's approaching death. Rather than meaning to frighten Conor as in their first encounter, the monster becomes an instructor to the boy:

You must tell the truth or you will never leave this nightmare, the monster said, looming dangerously over him now, its voice scarier than Conor had ever heard it. You will be trapped here alone for the rest of your life (Chapter 27).

Finally, Conor admits the truth: that he has wanted to believe that his mother would be cured. The monster tells him that he has not come to heal her, but rather to heal him by encouraging Conor to tell the truth.

And it was for this that the monster came. It must have been. Conor had needed it and his need had somehow called it. And it had come walking. Just for this moment (Chapter 29).

In the final chapter, Conor tells his mother that he does not want her to go. He holds her in understanding until he can let her go.

Who is more bound by convention and who is braver in Hedda Gabler, Hedda, or Thea?

Of the two, Thea is more bound by convention because she adopts (and seems to be fulfilled by) a servile position with regard to Eilert Løvborg. Her intellectual participation in his work can be interpreted as a sort of proto-feminist quality, but Thea is so completely selfless about it and has adapted herself so thoroughly to the role of the female "suffering in the background," that her behavior has little in it that is genuinely progressive. Her devotion to Løvborg constitutes a kind of bravery, but for the modern reader and audience (and the more progressive of Ibsen's own time) it's hard not to see something comical and silly about her actions.
Hedda is unconventional in terms of her skeptical and cynical attitudes about her husband and almost everything else. She is a jaded woman, but from a progressive standpoint one has to admire her, for she is rebelling against a system that keeps women "in their place" and forces them into role-playing, such as that of her own marriage to Tesman. It's a kind of bravery to express her feelings that marriage, female subordination, and the male rivalries and/or bonding she observes are mere tomfoolery, but she still has allowed herself to be locked into a conformist situation. Her suicide is less a brave act than an escape from facing the consequences of her behavior that she should have realized would lead to destruction.
In summary, Thea is the more conventional of the two, and her bravery is mostly of a kind that is required to put up with the nonsense of the roles females were made to play. Hedda is decidedly unconventional, but the bravery she possesses and which enables her to defy convention could have been put to a less destructive purpose.

Why does Alice wish that she could shut up like a telescope?

When Alice says that she wishes she could shut up like a telescope—meaning that she wishes she could be folded down into a very small space, the way a telescope can be folded down to a small size for transportation—she has a very specific reason for saying this. At this point, Alice has spotted a very small door, about the size of a rat hole, and through the hole she can see "beds of bright flowers" and cool fountains. All in all, it looks a very attractive garden, but Alice finds that she cannot even fit her head through the small door. As such, she has no chance of ever reaching the garden. Theoretically, if she could compress herself into a very small space the way a telescope does, she could pass through the door and then unfold herself again in the garden.
Alice, in the end, is unable to find a "book of rules" for telescoping in this fashion, but she does find a bottle with the words "DRINK ME" written on it. Subsequently, she is interested to find that she begins shrinking down to a very tiny size indeed, and she is able to comfortably fit through the door.

Alice is like many children, she gets bored, and is afraid of what becoming an adult will be. In the story Alice in Wonderland, Alice wants to go down the rabbit hole, however she is not able due to her size. She wishes she could shut up like a telescope, because she is referring to telescopes such as the one explorers used during their expeditions. Telescopes could extend and retract in size and could be carried and used when needed. When Alice says that she wants to shut up, she refers to the ability to reduce a telescopes size by collapsing it’s moving parts. She expresses the desire to shrink and grow as easily as she extend or contract a telescope. The simile serves as a reminder that Alice is a child that is scared of becoming an adult, and wishes to remain a child.

What are the intensive, physical, and chemical properties of matter?

Your question could be broken down into two categories: physical versus chemical properties, and intensive versus extensive properties.
Physical properties of matter have to do with features that can be measured and with the material by itself.  Some examples include melting and boiling points, color, density, state of matter at SATP (gas, liquid, solid), odor, conductivity, hardness, etc.  Chemical properties have to do with how the substance interacts with other substances.  Examples include combustibility or reactivity with acids/bases. Notice that the chemical examples require another substance to be present to interact (or not) with the material you are studying.
Extensive and intensive properties are further sub-categories of physical properties.  Intensive properties do not depend on the amount of matter.  Things like hardness, color, odor, and density fit in here.  Extensive properties are dependent on the amount of the material.  This includes things like mass and volume.

What are some chapters in the novel To Kill a Mockingbird in which the theme "the effects of poverty and ignorance" are portrayed?

Many times when people are ignorant, or lacking awareness or knowledge, they do not know how to act or what to say in certain situations. In the setting of the 1930's, people who were poor were much more isolated from the conventional wisdom and manners of their times than they are today; consequently, they would exhibit behavior and say things that demonstrated their ignorance.
In Chapter 3, Scout wants to retaliate against Walter Cunningham, because she was punished by Miss Caroline after she tried to explain why Walter had no lunch, as well as why he would not accept the offer of a quarter. At lunchtime, Jem sees Scout trying to punish Walter due to her scolding from the teacher; he stops her. After learning why Scout has attacked him, Jem graciously invites Walter to their house to eat with them. Then, while they eat, Walter asks for syrup. Scout watches as "Walter poured syrup on his vegetables and meat with a generous hand. He would probably have poured it into his milk glass had I not asked what the sam hill he was doing" (Ch.3). Poor Walter does this because there probably is not enough food for him at home, so by pouring syrup on top of it, he adds calories and feels fuller with less food. Because he has become accustomed to this taste, Walter is ignorant of good manners when he is a guest, and he does not know better than to cover the wholesome taste of the food at the Finches' house.
Of course, no one epitomizes ignorance and poverty more than the Ewells. In their efforts to not fall beneath the level of the black population with the white community, they make a charge against a black man before he can say anything publicly about them. Then, in the courtroom, they both show their ignorance with their poor thinking skills, lack of vocabulary, and lack of social skills. For instance, Bob Ewell does not know the meaning of ambidextrous, nor does he understand the reasoning behind Atticus's questioning him about which hand he uses to sign his name. Later, Atticus has one part of Sheriff Tate's testimony read back to Bob Ewell by the court reporter.

“…which eye her left oh yes that’d make it her right it was her right eye Mr. Finch I remember now she was bunged.” He flipped the page. “Up on that side of the face. Sheriff, please repeat what you said; it was her right eye I said—”

This testimony demonstrates that someone who is left-handed struck Mayella in her right eye, and in his lack of understanding of why Atticus has this testimony read to him, Bob Ewell says that he agrees with Sheriff Tate's testimony. By doing this, in his ignorance, Ewell has unknowingly implicated himself as the source of Mayella's black eye.
Mayella also exemplifies the stultifying effects of poverty when she takes the witness stand. First of all, she is frightened by Atticus. When Judge Taylor asks her, "What are you scared of?” she demonstrates that she has not understood the purpose of Atticus's questioning, although she knows that he is against them.

Mayella says something behind her hands.“What was that?” asked the judge. “Him,” she sobbed, pointing at Atticus. “Mr. Finch?” She nodded vigorously, saying, “Don’t want him doin‘ me like he done Papa, tryin’ to make him out left-handed…”

Her speech causes even little Scout to wonder if she has "good sense." Judge Taylor scratches his head, and he explains to Mayella,

“Mr. Finch has no idea of scaring you,” he growled, “and if he did, I’m here to stop him. That’s one thing I’m sitting up here for. Now you’re a big girl, so you just sit up straight and tell the—tell us what happened to you."

Ironically, in her ignorance of the law, Mayella has no anxiety about lying under oath and accusing poor Tom Robinson of a crime for which he can be put to death.

In Chapter 3, Lee portrays the association between poverty and ignorance in the character of Burris Ewell and his family. Burris comes from a poor family and displays his ignorance through his disrespectful comments directed at Miss Caroline. Burris' father does not value education and does not require his children to attend school. Later on in the chapter, Atticus explains to Scout how Bob Ewell spends most of his money on alcohol instead of feeding his children. The Ewells are a prime example of how Lee incorporates the theme of poverty and ignorance. The Ewell children suffer from their father's inability to maintain a steady job and their lack of moral education results in an ignorant attitude towards others.
In Chapter 15, the Old Sarum bunch attempt to lynch Tom Robinson before the trial. The Old Sarum bunch consists of poor, ignorant farmers. Their ignorance is displayed in their prejudiced views towards African Americans. Fortunately, Atticus and his children prevent them from harming Tom Robinson. The mob's ignorance would have been the catalyst for harming the Finch family in order to lynch Tom Robinson. The mob's socioeconomic status is what brings them together, and violence is perpetuated by their ignorance.

What are some examples of metaphors in "Ozymandias" by Percy Bysshe Shelley?

A metaphor is a comparison that does not use the words "like" or "as." "Ozymandias" is not a sonnet heavy on metaphors, but we can locate a few. For example, the "two vast and trunkless legs" of stone of Ozymandias's statue are a symbol for the futility of human glory. Shelley is metaphorically comparing Ozymandias's quest to be the great king who everyone fears, even other rulers, to the broken statue he has become. Like the statue, Ozymandiass' kingdom is shattered and in ruins, buried in desert sands, as is Ozymandias himself. He is no longer mighty and fearsome but, like his statue, a pathetic reminder of long-lost power.
The "boundless and bare" sands of the desert are also a symbol for the relentless way time buries all human achievement by patiently outlasting the span of human civilization. We can consider how these sands function metaphorically in the mental image this poem creates as well.

The two existing educator answers have already addressed the key things to be aware of in terms of metaphors in this poem. There are few "obvious" metaphors; we do not see the most common metaphorical construction in which something is stated to be something else without literal truth ("the curtain of darkness," "the moon's a balloon"). We can find some examples; "the heart that fed," for example, is a metaphor. The heart did not literally feed but rather it metaphorically sustained. The "hand that mocked," similarly, is a type of rhetorical device known as synecdoche, in which the "hand" does not mean literally the hand alone, but is a representation of the person who owned the hand and who did the "mocking."
In a broader sense, however, the "trunkless legs of stone" and the "shattered visage" which lies "half sunk" in the sand is a metaphorical representation of Ozymandias's hubris. The inscription on the pedestal has become ironic because Ozymandias once expected the mighty to "despair" because his works were so evident and vast, and yet now the "despair" comes only from the fact that the statue is a "Wreck" and "nothing beside remains" of Ozymandias's once great works. The statue, submerged in the desert, is a symbol of pride before a fall, Ozymandias's misplaced belief in his own longevity now sunk in the middle of nowhere, with no indication of what he had to be proud of.

While there are definitely metaphorical components to Shelley's famous sonnet, it should be noted that there are few direct metaphors in the poem.
The "lone and level sands" that "stretch away" can be a metaphor for time. Centuries of time have past, like sands through the hour glass, piling up to bury the memory of Ozymandias's greatness. 
Finally, the description the poem relates of the fallen statue can be taken as a metaphor of the transitory nature of individual human fame and achievement. No matter how important an individual may seem in his day, even a ruling tyrant who subdued many people, his fame and achievement will crash and fade until time erases all but the poorest remnants of the person's former greatness, just as the desert has claimed the dominion of Ozymandias.
Although the poem does not have many overt metaphors, it contains many subtle comparisons that the careful reader can unearth. 

A metaphor directly equates two things which in literal terms are unrelated. There are multiple examples of metaphor in "Ozymandias," not limited to the ones listed below.
The first is found in the first line, "a traveller from an antique land." Normally, we reserve the word "antique" for old objects, specifically ones which can be collected or easily owned. We would not normally apply the term "antique" to a region or country, so this association may be intended to convey something of the speaker's poor, stereotypical, or one-dimensional understanding of the traveller's origin; perhaps he sees the land as "antique" in the same way that popular generalizations of "the Orient" or "the jungles of Africa" do not really represent those places in truth.
Another metaphor is the "sneer of cold command." Command is not literally cold, as in temperature, but cold in terms of human emotion and empathy. The "shattered visage" is described as cruel, dispassionate, and haughty.

What are the advantages and disadvantages of the euro system? Explain.

The euro system has created a large zone within Europe in which various countries all share the same currency.  This single currency system has one major advantage, as well as one major disadvantage.
The major advantage of having a single currency is that it makes trade between countries much easier.  It does this in a number of ways.  Companies that want to trade within the euro zone do not have to exchange currency in order to do so.  This reduces the cost of buying and selling across national borders.  People and companies who want to shop can do so much more easily because they know what the prices offered by suppliers in various countries mean.  Imagine if you are a car manufacturer and you want to compare the price of parts made by suppliers in five different countries.  This requires you to calculate exchange rates, which takes time and therefore costs more money.  With a single currency, you do not have to do this.  In addition, with a single currency, this hypothetical auto maker would not have to worry about changes in the exchange rate.  Since their country and the suppliers’ countries all have the same currency, they know that changes in exchange rates will not change their costs.  In all of these ways, and more, the existence of the euro makes it easier for people and companies in the euro zone to trade with one another, even if they are in different countries.
The major disadvantage of the single currency has to do with the economies of specific countries.  The problem is that you have many countries with very different economies all tied to the same currency.  This makes it impossible for different countries to change their monetary policies to adjust for the needs of their economies.  For example, if Greece is in a recession but other euro zone countries are not, Greece cannot simply implement a looser monetary policy because it does not have its own currency.  Similarly, countries cannot devalue their currency when they are part of the euro zone. This was another problem for Greece in its recent economic crisis.  If it had had its own currency, it could have allowed it to devalue, which would have helped the Greek economy significantly.  When countries with different economies are linked together in a single currency, they can be harmed because they all have to have the same monetary policies and currency values even though it might be better for separate countries to have separate policies.
Thus, the euro system is good for business in general because it makes it cheaper and easier to do business between countries.  However, the euro system’s major disadvantage is that it does not allow different countries to have different policies that fit their respective economies.

Single Variable Calculus, Chapter 5, 5.5, Section 5.5, Problem 46

Find the definite integral $\displaystyle \int^a_0 x \sqrt{a^2 - x^2} dx$

Let $u = a^2 - x^2$, then $du = -2x dx$, so $\displaystyle xdx = \frac{-du}{2}$. When $x = 0, u =a^2$ and when $x = a, u = 0$. Thus,



$
\begin{equation}
\begin{aligned}

\int^a_0 x \sqrt{a^2 - x^2} dx =& \int^a_0 \sqrt{a^2 - x^2} xdx
\\
\\
\int^a_0 x \sqrt{a^2 - x^2} dx =& \int^a_0 \sqrt{u} - \frac{du}{2}
\\
\\
\int^a_0 x \sqrt{a^2 - x^2} dx =& \frac{-1}{2} \int^a_0 u^{\frac{1}{2}} du
\\
\\
\int^a_0 x \sqrt{a^2 - x^2} dx =& \frac{-1}{2} \left[ \frac{u^{\frac{1}{2} + 1}}{\displaystyle \frac{1}{2} + 1} \right]^a_0
\\
\\
\int^a_0 x \sqrt{a^2 - x^2} dx =& \frac{-1}{2} \left[ \frac{u^{\frac{3}{2}}}{\displaystyle \frac{3}{2}} \right]^a_0
\\
\\
\int^a_0 x \sqrt{a^2 - x^2} dx =& \left[ \frac{-1}{\cancel{2}} \cdot \frac{\cancel{2}u^{\frac{3}{2}}}{3} \right]^a_0
\\
\\
\int^a_0 x \sqrt{a^2 - x^2} dx =& \left[ \frac{-u^{\frac{3}{2}}}{3} \right]^a_0
\\
\\
\int^a_0 x \sqrt{a^2 - x^2} dx =& \frac{-a^{\frac{3}{2}}}{3} - \frac{(-0)^{\frac{3}{2}}}{3}
\\
\\
\int^a_0 x \sqrt{a^2 - x^2} dx =& \frac{-a^{\frac{3}{2}}}{3}

\end{aligned}
\end{equation}
$

What about the boardinghouse rules make it hard for Lyddie to have Rachel with her?

Lyddie is a factory girl who works for a corporation. She also stays in a corporation-owned boardinghouse. What all this means is that Lyddie has to adhere to certain rules and social protocols. Earlier in the book, readers learn that Lyddie has to buy new clothes when she first arrives because it just won't do to look like a dirty farm girl. Additionally, Lyddie must attend church.
In chapter 15, Lyddie is reminded of another of the boardinghouse's rules. The women are not allowed to have any men or children at the house with them. This is a problem for Lyddie because her Uncle Judah has just brought Lyddie her sister, Rachel. Lyddie's mother is incapable of caring for Rachel, and Uncle Judah can't do it either. Uncle Judah expects Lyddie to care for Rachel, and that puts Lyddie in a bind. Rachel isn't allowed to stay at the boardinghouse because Lyddie isn't allowed to have children there, and Rachel isn't old enough or strong enough to be a factory employee.

Why did America enter WWII?

One can easily point to the Japanese attack on Pearl Harbor as being the reason why the United States entered World War II. But while this is certainly true, the answer regarding why the country entered the war is more nuanced than simply thanks to the occurrences of a single event.
Even as late as 1940, U.S. President Theodore Roosevelt had told the American people that their "boys are not going to be sent into any foreign wars." However, British Prime Minister Winston Churchill was persistent in asking for U.S. assistance and participation in World War II. Some believe that Roosevelt was taking steps toward bringing the United States into the war even before the bombing at Pearl Harbor.
After the attack, only one congressman opposed the declaration of war. If the attack hadn't been enough to provoke the United States, then Germany's declaration of war against the United States just four days later certainly would have been. 

What are the character traits of Bard?

Bard is a fairly well-developed character even though he enters the story near its end. There are a number of clear character traits and several more that can be inferred from the text. I’ll give you a few examples to get you thinking.
Bard stays until the very end of the battle of Esgaroth. His company has fled and he is down to his last arrow when the thrush finds him and tells him of the dragon’s weakness. This demonstrates that Bard is courageous. He is also proud, which we see as he comes back from the battle, declaring himself to be the slayer of the dragon. He does not, however, seem to be arrogant, since he defers to the Master of the town in the conversation that follows. Roac the crow declares Bard to be trustworthy when he speaks with Thorin regarding the approaching men, telling him to speak with Bard rather than the Master. And we see Bard fulfill that trust when he lays the Arkenstone to rest with Thorin after the battle.
We can infer that Bard is strong, as he draws a large bow, and that he is disciplined, because one needs much practice with such a weapon to become a good shot and captain of a company. You might also call him measured, as he seems to consider his words and actions carefully.
There are more traits to discover, but this should give you a good start.

How well did the United States respond to Cold War threats?

The United States responses to the threats of the Cold War varied from positive to negative. Perhaps the most positive reaction came from the "Sputnik moment."
On Oct. 4, 1957, the Soviet Union launched Sputnik 1, the first Earth-orbiting satellite, into space. Terrified that the United States was falling behind the Soviet Union in technology, the United States Congress swiftly passed the National Defense and Education Act, which increased funding for education, especially in science and engineering, and also passed the National Aeronautics and Space Act, creating NASA. Both of these acts led to great improvements in education and scientific research in the United States, as well as to a golden era of space exploration and scientific advances.
On the other hand, paranoia generated by the Cold War led to the rise of Joseph McCarthy and the Republican-led House Un-American Activities Committee, which, fueled by anti-Soviet paranoia, threatened basic civil liberties in the United States, including creating blacklists of people who were suspected not of actual treason, but simply of ideological sympathy with socialism, who were spied on, fired, and barred from certain jobs.
https://www.history.com/topics/cold-war/joseph-mccarthy

https://www.newyorker.com/tech/annals-of-technology/is-america-facing-another-sputnik-moment

What is a summary of the article "Cognitive Costs of Exposure to Racial Prejudice" by Salvatore & Shelton?

The purpose of this study was to look at how people's cognitive resources were depleted when they were faced with cues about racial prejudice. The examiners had subjects review hiring decisions that were motivated by blatant and ambiguous prejudice and not at all motivated by racial prejudice. The subjects, who were 250 Princeton undergraduates (122 blacks, 128 whites), had to review recent hiring decisions made by a company. The subjects received a resume and job description and had to rate four candidates. They were then asked to start a second experiment during which they were administered a Stroop color-naming test, which measures cognitive impairment.
The results showed that Black subjects experienced significantly more interference effects than did whites in the ambiguous prejudice condition. Whites, on the other hand, experienced more interference than black subjects did in the blatant prejudice condition. The groups had comparable interference in the no-prejudice condition. Black subjects experienced more interference in the ambiguous prejudice condition than in the other two conditions, and white subjects experienced more interference in the blatant-prejudice condition than in the other two conditions.
The results suggested that whites are not as able to handle blatant prejudice as blacks are in the short term (though blacks can develop mental and physical issues as a result of long-term blatant prejudice). Blacks, on the other hand, are more affected by ambiguous prejudice, a level of prejudice that whites may not even register. The effects of this cognitive impairment may be widespread, as there are many ambiguously prejudicial cues in the work world.

This study, published in 2007, took 250 Princeton undergraduates, split almost equally between blacks (122) and whites (128), and studied how their cognitive functioning was impacted by cases of blatant and ambiguous hiring discrimination. In the case of blatant discrimination, a hiring manager recommended hiring an obviously less qualified candidate because he was white (the more qualified candidate was black). In the ambiguous case, the reasons for choosing the less qualified white candidate were not obviously tied to race.
Blacks were less likely to have their cognitive functioning impaired by blatant racism than whites were, probably, the study's authors concluded, because blacks were more used to blatant racism as a reality, and, thus, more psychologically prepared for it. Blacks were more likely than whites, on the other hand, to have their cognitive functioning impaired by ambiguous racism (whites sometimes didn't even register it at all.)
The study concludes that:

Future research should focus on useful interventions that minimize this disruption [caused by racism], so that individuals of all ethnicities can be better equipped to anticipate and cope with prejudice without incurring individual costs.

This research article attempts to address the effect that exposure to prejudice has on an individual’s cognitive development and performance across two races, blacks and whites. It especially looks at the depletion of cognitive resources due to exposure to various kinds of racial prejudice.
Two kinds of prejudice are looked at: blatant and ambiguous.
Blatant/overt prejudice is a hot and direct kind of prejudice. Most groups of people targeted by this kind of prejudice have developed coping strategies over the years. Unlike blatant prejudice, the ambiguous kind is indirect and difficult to put a finger on. Targets of the ambiguous kind of prejudice struggle with coping skills since it is difficult to classify the kind of prejudice being faced. For instance, when faced with blatant sexism, women act in a hostile and engaged manner, whereas ambiguous sexism brings forth anxiety and a lack of action.
The article is based on a study where participants analyze fictional hiring recommendations that either are or are not blatantly or ambiguously inspired by racial prejudices. Afterwards, participants undergo a Stroop (1935) color-naming task so that their cognitive impairment levels can be assessed. The levels of cognitive impairment were analyzed for two racial groups: blacks and whites. Participants consisted of 250 undergraduate students from Princeton University.
Findings
Study results showed the following:
Among whites, blatant prejudice depleted cognitive performance more than ambiguous prejudice, suggesting that this group could be less prepared to dealing with the latter in professional settings. Their black counterparts, on the other hand, appeared better equipped to cope with blatant prejudice.
Blacks are at a higher risk of cognitive impairment as a result of ambiguous prejudice as compared to their white counterparts.
https://equity.ucla.edu/wp-content/uploads/2016/11/Salvatore-Shelton-2007.pdf