College Algebra, Chapter 2, 2.2, Section 2.2, Problem 4

a.) If a graph is symmetric with respect to the $x$-axis and $(a,b)$ is on the graph, then $\left(\underline{\phantom{x}a\phantom{x}}, \underline{\phantom{x}-b\phantom{x}}\right)$ is also on the graph
b.) If a graph is symmetric with respect to the $y$-axis and $(a,b)$ is on the graph, then $\left(\underline{\phantom{x}-a\phantom{x}}, \underline{\phantom{x}b\phantom{x}}\right)$ is also on the graph
c.) If a graph is symmetric with respect to the origin and $(a,b)$ is on the graph, then $\left(\underline{\phantom{x}-a\phantom{x}}, \underline{\phantom{x}-b\phantom{x}}\right)$ is also on the graph

Why did Mrs. Daugherty become excited after she noticed Dough carrying a copy of Jane Eyre?

It isn't Mrs. Daugherty who's excited at seeing a copy of Jane Eyre in Doug's back pocket; it's actually Mrs. Windermere. Different adults seem to have different reactions to seeing Doug carrying this book around. Mr. Loeffler commiserates with Doug; he had to read the book when he was in high school and he hated it. Fortunately for him, he got appendicitis in the middle of reading the book, so had to stay off school for three weeks. When Mrs. Daugherty sees the book, she simply asks Doug whether he likes reading. "It's complicated," comes the reply.
For her part, Mrs. Windermere is most impressed with Doug's reading matter. He comes round to her house delivering ice cream; it's then that she notices the book in his back pocket. She invites Doug into her book-lined study where she shows him a first edition of Jane Eyre. Mrs. Windermere is very enthusiastic about the book, describing it as one of the world's great stories.

What is a balanced chemical equation for iron oxide reacting with carbon monoxide that produces atomic iron and carbon dioxide?

Hello! Most likely, it is iron (III) oxide, Fe_2 O_3. Carbon monoxide is identified as CO, and carbon dioxide is identified asCO_2.
The unbalanced reaction is Fe_2 O_3 + CO -> Fe + CO_2. To balance it, place undetermined coefficients before each molecule and find them:
a_1 * Fe_2 O_3 + a_2 * CO = a_3 * Fe + a_4 * CO_2.
The quantities of each atom on both sides must be the same. There are three types of atoms in this reaction: Fe, C, and O. For Fe atoms, we have 2a_1 = a_3, for C atoms, we have a_2 = a_4, and for O atoms we have 3a_1 + a_2 = 2a_4.
Substitute a_4 = a_2 from the second equation to the third and obtain 3a_1 + a_2 = 2a_2 or a_1 = 1/3 a_2. Substitute this into the first equation and obtain 2/3 a_2 = a_3.
All coefficients must be natural numbers, so the smallest value for a_2 is 3. Then, we get a_3 = 2/3 a_2 = 2, a_1 = 1/3 a_2 = 1, and a_4 = a_2 = 3.
The balanced reaction is as follows:
Fe_2 O_3 + 3 CO -> 2 Fe + 3 CO_2.
http://www.chm.bris.ac.uk/motm/co/coh.htm

Single Variable Calculus, Chapter 8, 8.1, Section 8.1, Problem 12

Evaluate $\displaystyle \int p^5 \ln p dp$
If we let $u = \ln p$ and $dv = p^5 d_p$, then
$\displaystyle du = \frac{d_p}{p} \text{ and } v = \int p^5 d_p = \frac{p^6}{6}$

So,

$
\begin{equation}
\begin{aligned}
\int p^5 \ln p d_p &= uv - \int v du = \frac{p^6}{6} \ln p - \int \frac{p^6}{6} \left( \frac{d_p}{} \right)\\
\\
&= \frac{p^6}{6} \ln p - \frac{1}{6} \int p^6 d_p\\
\\
&= \frac{p^6}{6} \ln p - \frac{1}{6} \left[ \frac{p^6}{6} \right] + c\\
\\
&= \frac{p^6}{6} \left[ \ln p - \frac{1}{6} \right] + c
\end{aligned}
\end{equation}
$

What are some things he can see from the vents in his room?

In the story, Luke must hide in the attic, as he is an illegal third child. The attic doubles as his bedroom and playroom. In fact, it is the only room in the house that can keep Luke safely hidden.
For his part, Luke despises the attic. There are no windows there, which means that he gets few glimpses into the outside world. So, Luke is very excited when he discovers that there are vents in the attic roof, one at each end.
From one of the vents, Luke can see a small strip of road and the cornfield beyond. The other vent faces the backyard. From this second vent, Luke is able to see the woods near the house. He is shocked when he looks through this second vent: the acres and acres of land that were once filled with trees are being cleared.
Construction crews are everywhere; from his vantage point, Luke can see bulldozers, backhoes, and trucks. Luke eventually discovers that new houses will be built on the cleared land.
On another occasion, Luke is able to watch his father and two brothers (Matthew and Mark) load the family hogs onto the livestock trailer. Sometimes, Luke also gets to watch his brothers climb onto the school bus in the mornings. After the new houses are completed, Luke is able to spy on his new neighbors. This is how he discovers Jen, another third child in the neighborhood.
The vents basically allow Luke glimpses into the outside world.

What is the exposition of the story "Rikki-Tikki-Tavi?"

In terms of literature and standard plot charts, the exposition (or introduction) is a literary device that is used to introduce background information about events, settings, and characters to readers.
The exposition for "Rikki-Tikki-Tavi" is quick and straightforward. Readers are introduced to Rikki-Tikki as the main character that fought a war across many rooms of the big bungalow in Segowlee cantonment. We are also told that other animals in the area helped him out during the fighting. One of them is a tailorbird, and the other is a muskrat. It is an interesting exposition because it is a bit of a flashback. We are being told about things that Rikki-Tikki did before we are told about how Rikki-Tikki became involved with the house, its occupants, and other animals in the first place. 

This is the story of the great war that Rikki-tikki-tavi fought single-handed, through the bath-rooms of the big bungalow in Segowlee cantonment.

That information containing the details of the story does eventually get to readers, but it begins in the third paragraph.

One day, a high summer flood washed him out of the burrow where he lived with his father and mother, and carried him, kicking and clucking, down a roadside ditch.

College Algebra, Chapter 4, 4.4, Section 4.4, Problem 86

Prove that the polynomial $P(x) = x^{50}-5x^{25}+x^2-1$ does not have any rational zeros.
Since the leading coefficient is $1$, any rational zero must be a divisor of the constant term $-1$. So the possible rational zeros are $\pm 1$. We test each of these possibilities


$
\begin{equation}
\begin{aligned}
P(1) &= (1)^{50}- 5(1)^{25} + (1)^2 - 1\\
\\
P(1) &= -4\\
\\
P(1) &= (-1)^{50} -5 (-1)^{25}+ (-1)^2 - 1\\
\\
P(1) &= 6
\end{aligned}
\end{equation}
$


By lower and upper bounds theorem, $-1$ is the lower bound $1$ is the upper bound for the zeros. Since neither $-1$ nor $1$ is a zerom all the real zero lie between these numbers.

the three predictions made by the witches for banquo

In Act One, Scene 3, Macbeth and Banquo meet the Three Witches on the heath as the men are traveling to the king's court at Forres. Both men are surprised at the appearance of the witches and listen carefully as the witches give them their prophecies. The witches initially address Macbeth as the Thane of Glamis, the Thane of Cawdor, and future King of Scotland. After hearing Macbeth's favorable prophecies, Banquo asks the witches to elaborate on his future. The first witch tells Banquo that he will be lesser than Macbeth but greater than him. The second witch tells Banquo that he is not as happy as Macbeth, yet is much happier than him. The third witch tells Banquo that his descendants will be kings, even though he will never sit on the throne. Banquo's first two prophecies are considered paradoxes, which are statements that contradict themselves yet seem to have a hidden truth in them.

What is the universe made of?

The universe is made up of the following three components:
1) Matter (or baryonic matter): 4.6%
2) Dark Matter: 24%
3) Dark Energy: 71.4%
The baryonic matter is the matter that we are familiar with, the matter that is made up of atoms (which are further made up of neutrons, protons, and electrons). Metals, objects, animals, plants, and our bodies are all examples of baryonic matter.
For most of human history, baryonic matter was thought to be the only constituent of the universe. It was only recently when scientists found that there are other constituents of the universe as well. In fact, baryonic matter is the smallest constituent of the universe (in terms of mass).
Our current understanding of the universe suggests that most of the universe is made up of matter that we cannot see (dark matter) and energy that behaves in a manner that is opposite to that of gravity (dark energy). In fact, the dark energy is the principal constituent of the universe and explains the observed accelerated expansion of our universe.
More details about the various constituents of the universe can be found at the reference link. Hope this helps.
https://map.gsfc.nasa.gov/universe/uni_matter.html

Single Variable Calculus, Chapter 7, 7.2-2, Section 7.2-2, Problem 50

Find $\displaystyle \frac{d^9}{dx^9} (x^8 \ln x)$.


$
\begin{equation}
\begin{aligned}

& \text{if } f(x) = x^8 \ln x, \text{ then by using Product Rule.. }
\\
\\
& \frac{d}{dx} = x^8 \left( \frac{1}{x} \right) + 8x^7 \ln x
\\
\\
& \frac{d}{dx} = x^7 + 8x^7 \ln x


\end{aligned}
\end{equation}
$


Again, by using Product Rule..


$
\begin{equation}
\begin{aligned}

\frac{d^2}{dx^2} =& x^7 \left[ 8 \left( \frac{1}{x} \right) \right] + 7x^6 (1 + 8 \ln x)
\\
\\
\frac{d^2}{dx^2} =& 8x^6 + 7x^6 + 56x^6 \ln x
\\
\\
\frac{d^2}{dx^2} =& 15x^6 + 56x^6 \ln x

\end{aligned}
\end{equation}
$


Again, by using Product Rule..


$
\begin{equation}
\begin{aligned}

\frac{d^3}{dx^3} =& x^6 \left[ 56 \left( \frac{1}{x} \right) \right] + 6x^5 (15 + 56 \ln x)
\\
\\
\frac{d^3}{dx^3} =& 56x^5 + 90 x^5 + 336 x^5 \ln x
\\
\\
\frac{d^3}{dx^3} =& 146 x^5 + 336 x^5 \ln x

\end{aligned}
\end{equation}
$


From these pattern, we can see that if you differentiate the $x^8$ nine times, the term will go to 0 since at the 8th time, the term is already a constant and we know that the derivative of a constant is 0. Thus, we can disregard the first term. Also, the second term is similar to the first term except that it is multiplied by 8 and the power is one less.

Now, after taking the derivative 7 times we get..

$\displaystyle \frac{d^7}{dx^7} = 8! \left( \ln (x) + \left( \frac{1}{x} \right) (x) \right) + \text{ constant}$

Therefore, the ninth domain is


$
\begin{equation}
\begin{aligned}

\frac{d^9}{dx^9} =& 8! \left( \frac{\displaystyle \frac{d}{dx} (x)}{x} \right) = 8! \left( \frac{1}{x} \right)
\\
\\
\frac{d^9}{dx^9} =& \frac{8!}{x}

\end{aligned}
\end{equation}
$

Who was Amelia Earhart?

Amelia Earhart was an American aviator, and she accomplished a great deal in the field of aviation. She is best known for being the first woman to fly alone across the Atlantic Ocean: On May 20, 1932, she left Newfoundland, Canada and arrived a day later in Londonderry, Northern Ireland. She also was the first person to fly alone from Hawaii to the mainland of the United States, which occurred in 1935.
As a young woman, she did various things that didn’t fit the image of a woman for that time period. She played basketball and also took a course in auto repair. She did go to college for a period of time, but she was really interested in flying. She passed her flying test in December 1921.
Amelia Earhart’s career is filled with many firsts for a woman. In addition to the accomplishments mentioned above, she was the first woman to fly alone over 14,000 feet, as well as the the first woman to receive the Distinguished Flying Cross. She also was the first woman to fly alone, nonstop, across the United States. This flight began in Los Angeles, California and ended nineteen hours later in Newark, New Jersey.
Unfortunately, her plane was lost over the Pacific Ocean as she was trying to fly around the world in 1937. There are many theories regarding her disappearance, but the United States government claims that her plane crashed into the Pacific Ocean.
https://www.history.com/topics/exploration/amelia-earhart

Single Variable Calculus, Chapter 1, 1.3, Section 1.3, Problem 29

Find the functions $f+g, f-g, f \cdot g,$ and $f/g$ and their domains

$f(x) = x^3 + 2x^2, \qquad g(x) = 3x^2-1$


$
\begin{equation}
\begin{aligned}

@ f+g\\
f+g =& f(x)+g(x) && \text{ Substitute the given values of the function $f(x)$ and $g(x)$}\\
f + g=& x^3+2x^2+3x^2-1 && \text{ Combine like terms }
\end{aligned}
\end{equation}
$


$\boxed{f + g = x^3+5x^2-1 } $

$\boxed{\text{ The domain of this function is :} (-\infty,\infty)}$



$
\begin{equation}
\begin{aligned}
@f-g\\
f-g =& f(x)-g(x) && \text{ Substitute the given values of the function $f(x)$ and $g(x)$}\\
f-g =& x^3+2x^2-(3x^2-1) && \text{ Simplify the equation}\\
f-g =& x^3+2x^2-3x^2+1 && \text{ Combine like terms}
\end{aligned}
\end{equation}
$


$\boxed{f-g = x^3-x^2+1}$

$\boxed{\text{ The domain of this function is :} (-\infty,\infty)}$



$
\begin{equation}
\begin{aligned}
@f \cdot g\\
f \cdot g =& f(x).g(x) && \text{ Substitute the given values of the function $f(x)$ and $g(x)$}\\

f \cdot g =& (x^3+2x^2)(3x^2-1) && \text{ Using FOIL method}
\end{aligned}
\end{equation}
$


$\boxed{ f \cdot g = 3x^5 + 6x^4 - x^3 - 2x^2}$
$\boxed{\text{ The domain of this function is :} (-\infty,\infty)}$


$
\begin{equation}
\begin{aligned}

@f/g\\
f/g =& f(x)/g(x) && \text{ Substitute the given values of the function $f(x)$ and $g(x)$}\\



\end{aligned}
\end{equation}
$


$\displaystyle f/g = \frac{x^3+2x^2}{3x^2-1}$
$\boxed{\text{ The domain of this function is :} (-\infty, -\sqrt{\frac{1}{3}}) \bigcup(-\sqrt{\frac{1}{3}},\sqrt{\frac{1}{3}}) \bigcup (\sqrt{\frac{1}{3}},\infty)}$

Can you find the passages in which Orwell tries to develop an answer to his central question? How does he use repetition to signpost these meditations?

If the central question Orwell poses is what to do about imperialism, it is in the paragraph in which it suddenly dawns on him that he will have to shoot the elephant regardless of whether it makes sense or not that he develops an answer: the system has to go. If he had earlier thought the British Raj was an "unbreakable tyranny," he now realizes it is hollow. Imperialism is "futile," as he puts it, because the system itself becomes the tyrant of the so-called masters, as well of the subjugated natives.
In this passage, Orwell us the word "hollow" twice, first to describe the emptiness of the British rule in Asia, and then to describe what happens to the individual who participates in the system: he becomes dehumanized, a sort of "dummy" playing a preset role. The narrator also repeats the words "two thousand," which emphasizes the force of the faceless mass that is the "natives," supposedly powerless but exercising great force in their numbers, bending the so-called masters to their will. Another repetition is the word "watch" or "watching," which emphasizes the pressure of the natives' gaze. "Shoot the elephant" is also repeated, a sign that this act has become a performance, as is almost everything the sahibs or rulers do. All the repetitions suggest this is simply one in a repeated set of shows the British put on in an attempt to assert a futile control.

Why does Lennie want to leave the farm?

When Curley first meets Lennie and George, he begins questioning the two men and George answers for Lennie, knowing that Lennie is unintelligent and might say something inaccurate or inappropriate. Curley then notices that Lennie is not answering any of his questions and becomes hostile towards the two men. George is forced to defend his friend and warns Lennie to avoid Curley at all costs after Curley leaves the bunkhouse. George also tells Lennie that Curley will cause them trouble before Candy elaborates on Curley's pugnacious personality. When Curley's wife enters the bunkhouse looking for her husband, Lennie admires her and smiles in her direction. After Curly's wife leaves, George refers to her as "jail bait" and warns Lennie to never speak to her. Lennie responds by saying,

"I don't like this place, George. This ain't no good place. I wanna get outa here...Le's go, George. Le's get outa here. It's mean here."

Lennie clearly feels threatened being at the ranch and fears that he will make a tragic mistake. After experiencing Curley's antagonistic nature and being told that he must avoid Curley's wife, Lennie does not feel safe being on the farm, which is why he wants to leave immediately.

y = 9-x^2 , y = 0 Find b such that the line y = b divides the region bounded by the graphs of the equations into two regions of equal area.

Given ,
y = 9-x^2 , y = 0
first let us find the total area of the bounded by the curves.
so we shall proceed as follows
as given ,
y = 9-x^2 , y = 0
=> 9-x^2=0
=> x^2 -9 =0
=> (x-3)(x+3)=0
so x=+-3
 
the the area of the region is = int _-3 ^3 (9-x^2 -0) dx
=[9x-x^3/3] _-3 ^3
= [27-9]-[-27+9]
=18-(-18) = 36
So now we have  to find the horizonal line that splits the region into two regions with area 18
as when the line y=b intersects the curve y=9-x^2 then the ared bounded is 18,so
let us solve this as follows
first we shall find the intersecting points
as ,
9-x^2=b
x^2= 9-b
x=+-sqrt(9-b)
so the area bound by these curves y=b and y=9-x^2 is as follows
A= int _-sqrt(9-b) ^sqrt(9-b) (9-x^2-b)dx = 18
=> int _-sqrt(9-b) ^sqrt(9-b)(9-x^2-b)dx=18
=> [-bx +9x-x^3/3]_-sqrt(9-b) ^sqrt(9-b)
=>[x(9-b)-x^3/3]_-sqrt(9-b) ^sqrt(9-b)
=>[((sqrt(9-b))*(9-b))-[(sqrt(9-b))^(3)]/3 ]-[((-sqrt(9-b))*(9-b))-[(-sqrt(9-b))^(3)]/3]
=>[(9-b)^(3/2) - ((9-b)^(3/2))/3]-[-(9-b)^(3/2)-(-((9-b)^(3/2))/3)]
=>[(2/3)[9-b]^(3/2)]-[-(9-b)^(3/2)+((9-b)^(3/2))/3]
=>(2/3)[9-b]^(3/2) -[-(2/3)[9-b]^(3/2)]
=(4/3)[9-b]^(3/2)
but we know half the Area of the region between y=9-x^2,y=0 curves =18
so now ,
(4/3)[9-b]^(3/2)=18
 
let t= 9-b
=> t^(3/2)= 18*3/4
=> t=(27/2)^(2/3)
=> 9-b= 9/(root3 (4))
 
=> b= 9-9/(root3 (4))
 
=9(1-1/(root3 (4))) = 3.330
 
so b= 3.330

Considering the dangerous journey Rainsford overcomes in the story, what do you think he has learned?

As the question stated, this is an opinion based question. The author does not explicitly tell readers what Rainsford did and did not learn from his experience with Zaroff.  The answer could go a few different ways.  
1.  Rainsford learned nothing.  Rainsford is an experienced hunter that tells his colleague in the beginning of the story that prey animals have no feelings.  They do not experience fear or anything similar.  As prey, Rainsford felt fear, but he still doesn't believe that animals experience the same feeling.  He believes this because he still considers humans different from the prey species that he normally hunts.  Readers know that Rainsford considers humans different because he admits that he believes humans are the only animals capable of reasoning.  Despite his experience with Zaroff, Rainsford still feels that humans are different from animals, and animals experience no fear.  
2. Rainsford now has learned that the animals that he hunts experience fear.  The fact is interesting to Rainsford, but he still continues to be an avid hunter; however, he now has more respect and compassion for the animals that he hunts and kills.
3. Rainsford learns that hunted animals experience fear.  Because of this knowledge, Rainsford gives up hunting completely.   
4. Rainsford is so thrilled from his experience with Zaroff that he decides he wants more of the experience.  He has learned that Zaroff was correct and the ultimate hunting thrill is hunting humans.  Rainsford takes over the island and continues to use it in the same way that Zaroff used the island.  Rainsford now becomes a hunter of men. 

Calculus: Early Transcendentals, Chapter 6, 6.5, Section 6.5, Problem 4

Find average value of t/sqrt(3+t^2)
over [1,3]
1/(3-1) int_1^3 t/sqrt(3+t^2) dt
We will solve this integral using u substitution.
Let u = 3+t^2
du = 2t dt
(du) / 2 = t dt
Substitute the u and du into the equation.
1/(3-1) int (1/2)(du)/sqrt(u)
1/4 *2sqrt(u)
1/2 sqrt(3+t^2)
evaluate the limits 3 and 1
1/2 (sqrt(12) - sqrt(4))
1/2 (sqrt(12) - 2)

Determine a fourth-degree Taylor polynomial matching the function e^x at x_0=1 .

The formula for the Taylor polynomial of degree n centered at x_0 , approximating a function f(x) possessing n derivatives at x_0 , is given by
p_n(x)=f(x_0)+f'(x_0)(x-x_0)+f''(x_0)/(2!)(x-x_0)^2+f'''(x_0)/(3!)(x-x_0)^3+...
p_n(x)=sum_(j=0)^n (f^((j))(x_0))/(j!) (x-x_0)^j
For f(x)=e^x, f^((j))(2)=e^2 for all j .
Therefore to fourth order in x about the point x_0=2
e^x~~p_4(x)=e^2+e^2(x-2)+e^2/2(x-2)^2+e^2/(3!)(x-2)^3+e^2/(4!)(x-2)^4
Notice the graph below. The function p_4(x)~~e^x (red) the most at x=2 . It will become more and more approximate to e^x the higher order the approximation.
http://mathworld.wolfram.com/TaylorSeries.html

How did Sufism affect Muslim politics during the Medieval period?

Sufism developed as an aesthetic movement in the 8th and 9th centuries in Iran, Iraq, Syria, and Egypt. Its adherents were committed to a life of poverty and to meditation. During the Seljuk Turk Dynasty, Sufis became organized into fraternities and built lodges, called khānaqāh, in Persian, that functioned as hospice centers for Sufi travelers and centers of meditation and retreat. These lodges were often located next to schools, called madrasas, or mosques.
The sultans who ruled during this era had taken over without religious legitimacy, and their connection to Sufism provided them with religious authority. Sufis, long connected with the community, were able to help the sultans gain legitimacy with the populations over which they ruled. Sufism, guided by the philosophy of Ibn al-Arabi (1165–1240), focused on the ethical dimensions of being what Ibn al-Arabi called a "perfect man." Sufis were tolerant of a range of religious practices, including wandering dervishes, and their ethical and religious practices provided a great deal of stability and legitimacy for rulers in India, southeast Asia, and sub-Saharan Africa.
 
 

The empirical formula of a compound of molecular mass 120 is CH2O. What is the molecular formula of the compound?

The empirical formula of a compound is the lowest whole-number ratio of atoms in the compound. The molecular formula gives the actual number of each type of atom in a molecule. For example, the compound N_2O_2 has the empirical formula NO.
The molar mass of a compound is a whole-number multiple of its empirical formula mass. 
Let's start by finding the empirical formula mass of this compound:
CH_2O = C + (2)H + O = 12.0 + 2(1.0) + 16.0= 30 grams per mole
We can find the factor by which the molecular formula is larger than the empirical formula by comparing the two masses. Divide the actual molar mass of the compound by the empirical formula mass:
120/30 = 4
Since the molar mass of the compound is four times the empirical formula mass, the molecular formula is four times the empirical formula:
4(CH_2O) = C_4H_8O_2
The linked video provides a detailed explanation and some more examples of this process. 

Is there any other variable that shows an upside of A.D.H.D, other than creativity?

I have a son who has attention deficit (hyperactive) disorder (ADHD), so unsurprisingly, I have done a great deal of reading about it.  While I do think that as with autism, there is a spectrum that makes generalization difficult, I do see how there are some benefits to ADHD. 
It is important to understand that ADHD is somewhat misnamed, since many people who have it can and do pay attention to things. It is just that their attention is somewhat uneven.  And in fact, many people who have ADHD tend to hyper-focus on what interests them, and this can be a powerful advantage. There is a down side to this, of course, since responsible adults need to focus on many things they would rather not, like washing dishes or paying bills.  Generally, though, hyper-focus is often behind the accomplishments of people with ADHD, who double down on projects they are enthusiastic about.
Other advantages stem from the "hunter/gatherer" school of thought regarding ADHD.  From an evolutionary perspective, people who didn't sit still very long were far more likely to live and succeed well enough to pass on their genes.  Moving one's camp frequently and acting unpredictably were advantages in many ways against one's foes.  Also, the person with ADHD tends to not have as many sensory filters, so everything just pours in, sounds, sights, smells, touches, and tastes.  Such a person is in close touch with the environment, very alert in many ways, perhaps better able to track game or forage for food than those who did not have ADHD. While it may not be obvious that this remains an advantage in today's world, I think in many ways it must be.  Soldiers are helped by it, certainly.  An organization that needs some micromanaging would be well-served by this quality. Staying safe in a high-crime area requires this kind of alertness.  And I would rather go on a nature walk with my son than anyone else I know.  He doesn't miss a thing, and thus, neither do I. 
Our genetic diversity exists for a reason, to roll the genetic die to see what works and what doesn't. If we were all alike, we would lose a great deal more than we would gain.  The qualities of ADHD have disadvantages, to be sure, but creativity, hyper-focus, unpredictability, and high awareness are qualities that can be used to great advantage.  
 
https://childmind.org/article/hyperfocus-the-flip-side-of-adhd/

https://www.healthline.com/health/adhd/evolution

Why did Faber kill Mrs. Garden?

Faber killed Mrs. Garden because he feared that she would expose his spy activities.
In the book, Faber is a German spy working on behalf of the Axis forces. He disguises his spy activities by working as a railway clerk by day. At night, he retires quietly to his rented room in Mrs. Garden's home. For her part, Mrs. Garden is a lonely widow who has her eyes on Faber as a love interest.
One night, she decides to visit Faber in his room in order to seduce him. Deep at work transmitting information to German authorities, Faber is unprepared for his landlady's entrance into his room. Since his radio transmitter and code books are out in plain sight, Faber decides to kill Mrs. Garden.
When she swoops in for a kiss, Faber stabs her in the back with his stiletto knife. Eventually, he uses the stiletto to slash her throat. After killing Mrs. Garden, Faber leaves the house for a new location.

Calculus: Early Transcendentals, Chapter 7, 7.1, Section 7.1, Problem 18

2∫(-2excos(2x))dx+2exsin(2x)-1excos(2x)=2(-2∫1excos(2x)dx)+2exsin(2x)-1excos(2x)
Use integration by parts:
int (u)dv = uv-intvdu

Let u = cos(2x) and dv = dx/e^x
Then,
du = -2sin2xdx
v = int(e^-x)dx = -1/e^x

Thus,
int (1/e^xcos(2x))dx =(cos(2x)⋅(-1/e^x)−int((-1/e^x)⋅(-2sin(2x))dx))=(-int(2/e^xsin(2x)dx-1/e^xcos(2x)))
Use the constant multiple rule
-int(2/e^xsin(2x)dx-1/e^xcos(2x))=-(2int(1/e^xsin(2x)dx)-1/e^xcos(2x))
Use integration by parts again for the first part
Let u=sin(2x) and dv=dx/e^x
Then,
du = 2cos(2x)dx and v = int(e^-x)dx = -1/e^-x
Integral becomes

-2int(1/e^xsin(2x)dx-1/e^xcos(2x))=-2(sin(2x)(-1/e^x)-int((-1/e^x)2cos(2x)dx))
-1/e^xcos(2x)=-2(-int((-2/e^xcos(2x))dx-1/e^xsin(2x)))-1/e^xcos(2x)
Apply constant multiple rule
2int((-2/e^xcos(2x))dx)+2/e^xsin(2x)-1/e^xcos(2x)=2(-2int(1/e^xcos(2x)dx))+2/e^xsin(2x)-1/e^xcos(2x)
Simplify
int(1/e^xcos(2x))dx=1/(5e^x)(2sin(2x)-cos(2x))+C

Why do we call the calendar we use today the Gregorian Calendar?

The Gregorian calendar was the idea of Pope Gregory XIII.  The calendar was named after Pope Gregory XIII.  The calendar's initial introduction occurred in the 16th century, in the year 1582.  Prior to the adoption of the Gregorian calendar, European nations used the Julian calendar.  This calendar was introduced under Julius Caesar.  This calendar had certain errors.  For example, a miscalculation caused the calendar to not be consistently aligned with the seasons.
Pope Gregory XIII thought that it was important for Easter to be at around the same time every year.  The Council of Nicea had occurred in the springtime, and it was recorded that Easter had taken place close to this event.  
The Gregorian calendar was first adopted in Catholic nations.  Predominantly Protestant nations were slower to adopt the Gregorian calendar, though they did so eventually.  When Great Britain adopted the Gregorian calendar in 1752, eleven calendar days were lost. 
 
http://galileo.rice.edu/chron/gregorian.html

https://www.history.com/news/6-things-you-may-not-know-about-the-gregorian-calendar

Describe a hardship faced by the English settlers.

Early English settlers to the New World faced a variety of hardships. Among the harshest hardships were the various diseases that decimated the settlements. One of the main reasons the Jamestown settlement failed was that the English used the brackish, salty water of the James River for their drinking water. The water carried all sorts of parasites and other organisms, and it also caused dysentery, an infection of the intestines that causes bloody diarrhea and dehydration. Malaria and yellow fever spread by mosquitos prevalent in the marshy countryside also wiped out many settlers. Finally, the English also suffered from illnesses such as smallpox and typhoid fever, both diseases brought over with them during their voyages from Europe that also plagued their countrymen back home.

The English settlers faced many hardships. One hardship some of the settlers faced was the lack of food. When the settlers arrived, they did not know the condition of the land on which they settled. They did not know what crops would be likely to grow and what crops would likely fail. They also were uncertain about the climate. They did not know how harsh the winters could be in the North or how long the growing season would last. As a result, lack of food was an issue for some of the English settlers.
Fortunately, some of the settlers became friends with some of the Native American tribes. These tribes helped the English settlers by showing them what crops to grow and where to grow them. This helped to alleviate some of the issues regarding the lack of food.
Lack of food was one hardship some of the English settlers faced.
http://nationalhumanitiescenter.org/pds/amerbegin/settlement/text2/text2read.htm

College Algebra, Chapter 3, 3.1, Section 3.1, Problem 72

Due to the curvature of the Earth, the maximum distance $D$ that you can see from the top of a tall building or from an airplane at height $h$ is given by the function $D(h) = \sqrt{2rh + h^2}$, where $r = 3960$mi is the radius of the Earth and $D$ and $h$ are measured in miles.
a.) Find $D(0.1)$ and $D(0.2)$
For $D(0.1)$,

$
\begin{equation}
\begin{aligned}
D(0.1) &= \sqrt{2(3960 \text{mi})(0.1 \text{mi}) + (0.1\text{mi})^2} && \text{Replace } h \text{ by } 0.1\\
\\
&= 28.14 \text{mi}
\end{aligned}
\end{equation}
$


For $D(0.2)$,

$
\begin{equation}
\begin{aligned}
D(0.2) &= \sqrt{2(3960 \text{mi})(0.2 \text{mi}) + (0.2\text{mi})^2} && \text{Replace } h \text{ by } 0.1\\
\\
&= 39.8 \text{mi}
\end{aligned}
\end{equation}
$


b.) How far can you see from the observation deck of Toronto's CN Tower, 1135ft above the ground?

$
\begin{equation}
\begin{aligned}
D(h) &= \sqrt{2rh + h^2}\\
\\
D(1135\text{ft}) &= \sqrt{22(3960 \text{mi})\left(1135\cancel{\text{ft}}\right) \left( \frac{1\text{mi}}{5280\cancel{\text{ft}}} \right) + \left[ \left(1135 \cancel{\text{ft}} \right) \left( \frac{1\text{mi}}{5280\cancel{\text{ft}}} \right) \right]^2 }\\
\\
&= 41.26 \text{mi}
\end{aligned}
\end{equation}
$


You can see $41.26 \text{mi}$ from the observation deck of Toronto's CN Tower that is 1135ft above the ground.

c.) Commercial Aircraft fly at an altitude of about 7mi. How far can the pilot see?

$
\begin{equation}
\begin{aligned}
D (h) &= \sqrt{2rh + h^2}\\
\\
D(7\text{mi}) &= \sqrt{2(3960 \text{mi})(7 \text{mi}) + (7\text{mi})^2}\\
\\
&= 235.56 \text{mi}
\end{aligned}
\end{equation}
$


The pilot will see 235.56mi from an altitude of 7mi.

To what extent did President Reagan's Foreign policy initiatives represent a radical change from other administrations since the 1960s?

Ronald Reagan's foreign policy was, in some sense, a change to a less conciliatory policy toward the Soviet Union than had been seen from previous administrations going back to the 1960s. The change was especially apparent if one compared Reagan with his immediate predecessor, Jimmy Carter.
Reagan made no secret of his belief that Communism was an absolute evil and that he wished to actively combat Communism and the influence of the Soviet Union on the world stage. He accelerated the arms race and did not attempt to be conciliatory toward Mikhail Gorbachev in negotiations with him. Carter's stance had been anti-Soviet as well, but in a reactive mode, rather than the more direct and aggressive manner Reagan was to show. For instance, Carter denounced the Soviets strongly after their invasion of Afghanistan, but before this, his speeches and overall attitude not only toward the Soviets but others had been relatively mild, and had suggested that getting along with countries governed by other systems was a better course than confronting them openly.
In the Middle East, Reagan was a direct supporter of Israel. He was also a realist, pulling the Marines from Lebanon when, after the bombing in October 1983 of the US base, he realized the US position there was unsustainable. Carter had attempted to deal with the Israeli and Arab sides of the conflict on an equal basis. His critics claimed that it was Carter's alleged "softness" that led to the Iranian Revolution in 1979. The situation of the US hostages was resolved when they were released after Reagan took office. Reagan's supporters attributed this to the greater realism of his negotiating team and the stronger stance they took.

What is the poem "Let No Charitable Hope" saying?

The speaker of the poem has reached a stage in her life where she's able to reflect with some measure of wisdom on her experiences. She's now arrived at the conclusion that she's all alone in the world, and there's no point in getting hopeful about changing a condition into which she was born and in which she will die. As a woman, she also feels isolated in a male dominated society—even though she's no longer an "antelope," that is to say, prey to men's desires. Whatever enjoyment she gets out of life takes quite some effort, like getting blood from a stone. It's the only reminder of her humanity in a world in which she's all alone. Hers has been a life without fear. Each year brings with it the promise of hope, but it's really just an elaborate disguise, a mask at once "outrageous and austere." All the speaker can do is respond with a sarcastic, world-weary laugh.

f(x)=cosx Prove that the Maclaurin series for the function converges to the function for all x

Maclaurin series is a special case of Taylor series which is centered at c=0 . We follow the formula:
f(x)=sum_(n=0)^oo (f^n(0))/(n!)x^n
or
f(x) = f(0)+ f'(0)x +(f^2(0))/(2!)x^2 +(f^3(0))/(3!)x^3 +(f^4(0))/(4!)x^4 +...
To list the f^n(x) , we may apply derivative formula for trigonometric functions: 
d/(dx) sin(x) = cos(x) and d/(dx)cos(x) = -sin(x).
f(x)=cos(x)
f'(x)=d/(dx)cos(x) = -sin(x)
f^2(x)=d/(dx) -sin(x) = -cos(x)
f^3(x)=d/(dx) -cos(x)= - (-sin(x))= sin(x)
f^4(x)=d/(dx)d/(dx) sin(x) = cos(x)
Plug-in  x=0 , we get:
f(0)=cos(0) =1
f'(0) = -sin(0)=0
f^2(0) = -cos(0)=-1
f^3(0)=sin(0)=0
f^4(0)= cos(0) =1
Note: cos(0)= 1 and sin(0)=0 .
Plug-in the f^n(0) values on the formula for Maclaurin series, we get:
cos(x) =sum_(n=0)^oo (f^n(0))/(n!)x^n
              =1 +0*x+(-1)/(2!)x^2+(0)/(3!)x^3+(1)/(4!)x^4+...
               =1 +0-1/2x^2+0/6x^3 +1/24x^4+...
              =1 +0-1/2x^2+0 +1/24x^4+...
               =1 -1/2x^2 +1/24x^4+...
                = sum_(n=0)^oo ((-1)^n x^(2n))/((2n)!)
To determine the interval of convergence, we apply Ratio test.
In ratio test, we determine a limit as lim_(n-gtoo)| a_(n+1)/a_n| =L where a_n!=0 for all ngt=N .
The series sum a_n is a convergent series when L lt1 .
From the Maclaurin series of cos(x) as sum_(n=0)^oo ((-1)^n x^(2n))/((2n)!) , we have:
a_n= ((-1)^n x^(2n))/((2n)!) then 1/a_n=((2n)!) /((-1)^n x^(2n))
Then, a_(n+1) =(-1)^(n+1) x^(2(n+1))/((2(n+1))!)
                      =(-1)^(n+1) x^(2n+2)/((2n+2)!)
                      =(-1)^n*(-1)^1 (x^(2n)*x^2)/((2n+2)(2n+1)(2n)!)
                      = ((-1)^n*(-1)x^(2n)*x^2)/((2n+2)(2n+1)(2n)!)
We set up the limit lim_(n-gtoo)| a_(n+1)/a_n| as:
lim_(n-gtoo) |a_(n+1)/a_n| =lim_(n-gtoo) |a_(n+1) * 1/a_n |
=lim_(n-gtoo) |((-1)^n*(-1)^1* x^(2n)*x^2)/((2n+2)(2n+1)(2n)!)*((2n)!) /((-1)^n x^(2n))|
Cancel out common factors: (-1)^n, (2n)!, and x^(2n) , the limit becomes;
lim_(n-gtoo) |(-x^2)/((2n+2)(2n+1))|
Evaluate the limit.
lim_(n-gtoo) |- x^2/((2n+2)(2n+1))|=|-x^2/2| lim_(n-gtoo) 1/((2n+2)(2n+1))
                                           =|-x^2/2|*1/ oo
                                           =|-x^2/2|*0
                                            =0
The L=0 satisfy the Llt1 for every x .
Therefore, Maclaurin series of cos(x) as sum_(n=0)^oo (-1)^n x^(2n)/((2n)!) converges for all x.
Interval of convergence: -ooltxltoo .

Calculus: Early Transcendentals, Chapter 7, 7.4, Section 7.4, Problem 19

You need to use partial fraction decomposition, such that:
(x^2+1)/((x-3)(x-2)^2) = a/(x-3) + b/(x-2) + c/((x-2)^2)
x^2+1 = a(x-2)^2 + b(x-2)(x-3) + c(x-3)
x^2+1 = ax^2 - 4ax + 4a + bx^2 - 5bx + 6b + cx - 3c
Group the terms:
x^2+1 = x^2(a+b) + x(-4a-5b+c) + 4a + 6b - 3c
a + b = 1 => a = 1-b
-4a-5b+c = 0 => c = 4a+5b
6b - 3c = 1 => 6b - 3(4a+5b) = 1 => -9b - 12a = 1
-9b - 12(1-b) = 1 => 3b - 12 = 1 => 3b = 13 => b = 13/3
a = -10/3
c = -40/3 + 65/3 => c = 25/3
(x^2+1)/((x-3)(x-2)^2) = -10/(3(x-3)) + 13/(3(x-2)) + 25/(3(x-2)^2)
Taking integral both sides yields:
int (x^2+1)/((x-3)(x-2)^2) dx = int -10/(3(x-3)) dx + int 13/(3(x-2)) dx + int 25/(3(x-2)^2)dx
int (x^2+1)/((x-3)(x-2)^2) dx = -10/3*ln|x-3| + 13/3ln|x-2| - 25/(3(x-2)) + c
Hence, evaluating the give integral yields int (x^2+1)/((x-3)(x-2)^2) dx = -10/3*ln|x-3| + 13/3ln|x-2| - 25/(3(x-2)) + c.

College Algebra, Chapter 4, 4.4, Section 4.4, Problem 28

Determine all rational zeros of the polynomial $P(x) = x^4 - x^3 - 23x^2 - 3x + 90$, and write the polynomial in factored form.

The leading coefficient of $P$ is $1$, so all the rational zeros are integers. They are divisors of the constant term $90$. Thus, the possible candidates are

$\pm 1, \pm 2, \pm 3, \pm 5, \pm 6, \pm 9, \pm 10, \pm 15, \pm 18, \pm 30, \pm 45, \pm 90$

Using Synthetic Division







We find that $1$ and $3$ are not zeros but that $2$ is a zero and that $P$ factors as

$x^4 - x^3 - 23x^2 - 3x + 90 = (x - 2)(x^3 + x^2 - 21x - 45)$

We now factor the quotient $x^3 + x^2 - 21x - 45$. Its possible zeros are the divisors of $-45$, namely

$\pm 1, \pm 3, \pm 5, \pm 9, \pm 15, \pm 45 $

Using Synthetic Division







We find that $-3$ is a zero and that $P$ factors as

$x^4 - x^3 - 23x^2 - 3x + 90 = (x - 2)(x + 3)(x^2 - 2x - 15)$

We now factor $x^2 - 2x - 15$ using trial and error, so

$x^4 - x^3 - 23x^2 - 3x + 90 = (x - 2)(x + 3)(x + 3)(x - 5)$

The zeros of $P$ are $2, 5$ and $-3$.

McDougal Littell Algebra 2, Chapter 3, 3.2, Section 3.2, Problem 44

The equations 3x - 6y = 20 and -11x + 10y = 5 have to be solved.
From 3x - 6y = 20
3x = 20 + 6y
x = 20/3 + 2y
Substitute in -11x + 10y = 5
-11*(20/3 + 2y) + 10y = 5
-220/3 - 22y + 10y = 5
12y = -235/3
y = -235/36
x = 20/3 + -470/36 = -115/18
The solution of the equations is x = -115/18 and y = -235/36

what were the Assyrians greatest achievements?

The Assyrians were a Semitic group of people who lived in Northern Mesopotamia near the rivers Tigris and Euphrates. They ruled various great empires during their time. The Assyrian empire is viewed as one of the greatest of the Mesopotamian empires due to its military strength and size. The following are some of the greatest achievements of the Assyrian people:
Military strength
The Assyrians were known for their military strategies. They were one of the first Mesopotamian empires to introduce the use of iron weapons. They were particularly good at siege warfare and had creative methods of breaking through the city fortifications of their enemies. They also used siege engines that were built with battering rams at the bases.
Library of Ashurbanipal
The last King of the Neo-Assyrian Empire, who went by the name Ashurbanipal, built a library in ancient Nineveh. The library housed thousands of clay tablets that contained the history of various regions in and around Assyria. Texts such as the Epic of Gilgamesh and the Code of Hammurabi were found in this library.
Technological inventions
The Assyrians developed paved roads, indoor plumbing, a sexagesimal system of keeping time, and the use of locks and keys.
https://www.ancient.eu/Assyrian_Warfare/

The Assyrians are credited with a great many achievements through their timeline. They had practical inventions, like locks and keys, paved roads, use of iron, plumbing, flushing toilets, and the sexagesimal clock (the beginnings of the way we tell time today). The Assyrians also brought about the use of the first guitar, first libraries, first magnifying glass, and the first postal system.
In addition, Assyria contributed invaluable ideas to the world, such as the concept of imperial administration, "of dividing the land into territories administered by local governors who report to the central authority, the King of Assyria" ("Brief History of Assyrians"). Assyria brought high civilization to the people groups living in the empire.
Perhaps the greatest achievement credited to the Assyrians is the founding of the first university, where theology, philosophy and medicine were taught. This was the School of Nisibis. Their statutes would be used as inspiration for the first Italian university.
Literature was also an important contribution by the Assyrians, who systematically translated Greek texts into Assyrian. The subjects included religion, science, philosophy, and medicine. A great medical textbook on ophthalmology, written by Hunayn ibn-Ishaq in 950 A.D. would remain an definitive source up to 1800.
http://www.aina.org/brief.html

How does Schlosser explore irony in Chapter 4 of Fast Food Nation, titled "Success," through his focus on Dave Feamster's Little Caesars' franchise and the concluding spokespeople (especially Reeve) at the sales seminar?

Eric Schlosser’s Fast Food Nation: What the All-American Meal is Doing to the World is a carefully researched examination of the fast food industry from its birth in Southern California during the late-1930s to the present. Schlosser’s book was not intended to praise the founding and growth of this industry, and it does not. While the author is balanced in his description of the individuals and companies that comprise this massive industry, the point of his study is to assess the effects of the fast food industry on the economy, culture, and health of the societies in which McDonald’s, Carl’s Jr., Little Caesars, Subway, and many others have profited. His conclusion is decidedly negative.
Chapter 4 of Fast Food Nation is titled “Success.” Schlosser adopted this chapter title from the name of a large conference to which one of his subjects, Dave Feamster, takes some of his employees. “Success” is a motivational production featuring famous people from politics, sports and business who rally masses of attendees to feel better about themselves and adopt a more positive attitude towards their endeavors. Feamster, a generous and modest former professional hockey player, has wagered his future on the Little Caesars franchises he has gone into debt to purchase in the city of Pueblo, Colorado. This chapter also provided background into the mechanics and risks associated with the franchise business. While Feamster’s debt was very modest in comparison to today’s franchise fees—in effect, the cost to businesspeople of building and operating a fast food restaurant under the corporate umbrella of McDonalds, Little Caesars, and the rest—those fees have increased exponentially over the years. Consequently, the ability of individuals to purchase franchises has left most out of the competition, which is ironic given the vision of the industry's founders.
Feamster lives modestly and treats his employees well. He and his family survive, but they are far from wealthy and, for all his hard work in building his business, his future is increasingly threatened by the encroachment of franchises from Papa Johns, which is a newer entrant into the market in Pueblo.
The irony in Chapter 4 of Fast Food Nation, then, can be found in the precarious nature of the franchisee’s existence against the backdrop of an enormously profitable industry. Whether Dave Feamster is representative of franchise licensees overall is not addressed. Suffice to say that the financial burden of buying a franchise from the large fast food companies depresses the quality of life of all those involved, from the heavily-indebted business owner to the consumer whose health is ultimately jeopardized by excessive consumption of fast food to the taxpayer whose premiums are increased to compensate for the vast number of low-income consumers of foods high in fats and cholesterol who develop diabetes and other obesity-related ailments.
The most significant irony in this chapter, however, involves the appearance at the “Success” convention of the late actor Christopher Reeve. Reeve had been paralyzed in a horse riding accident and was now confined to a wheelchair and could only breathe with the aid of machines. Reeve’s appearance at the convention is ironic because his brief remarks deviate substantially both intellectually and emotionally from all that preceded his appearance and all that followed. The focus of Reeve’s comments was the imperative of maintaining the proper priorities in life and not sacrificing what is seriously important—family and friends—to the all-consuming pursuit of material wealth. Schlosser concludes Chapter 4 with the following passage:

“Men and women up and down the aisles wipe away tears, touched not only by what this famous man has been through but also by a sudden awareness of something hollow about their own lives, something gnawing and unfulfilled.
“Moments after Reeve is wheeled off the stage, Jack Groppel, the next speaker, walks up to the microphone and starts his pitch, ‘Tell me friends, in your lifetime, have you ever been on a diet?’”

Christopher Reeve, in his brief remarks, touched the hearts of those in attendance, but he represented a minor deviation from the convention’s theme of financial success.

The title of Chapter 4, "Success," is ironic, as fast-food franchisees are less and less successful. While people who owned early McDonald's franchises were often successful, current-day franchisees are struggling, including people like Dave Feamster. For example, Schlosser cites a professor who has shown that about 38% of franchise businesses fail after four to five years, compared to about 6% of independent businesses. Feamster, a former NHL player, works hard and makes a respectable living as the owner of Little Caesars' franchises. However, other franchisees struggle, in part because fast food chains put competing restaurants close to each other to get a larger slice of the market. The people who work at fast food restaurants really struggle to get by because they earn so little. At the end of the chapter, the author quotes Christopher Reeve, who gives a motivational speech at the sales seminar. He reminds his audience that there is more to life than money--which is ironic because the entire franchise industry and its employees are focused mainly on money. 

What was the effect of World War I on art?

World War I was such a traumatic event for Europeans that it shook the foundations upon which Western culture and civilization were based. People who witnessed the horrors of the conflict struggled to accept that the world was a rational place ruled by a just and caring God. Equally, they witnessed how science and technology had been harnessed to kill other people. So the art and literature of the postwar era reflected the disillusionment of many people, especially intellectuals. This took several forms. Some, like German artist Otto Dix, produced works that depicted the horrors of war in grisly detail. Others, like Pablo Picasso, rejected artistic (and by implication, political and social) conventions through abstract imagery and forms. Still others, like Dadaists, took the subversion of the traditional to extremes, producing absurdist paintings, sculptures, and poetry devoid of discernible meaning. Marcel Duchamp, for example, submitted a urinal turned upside down to an artistic society as a piece entitled Fountain. In a world where humans had slaughtered one another wholesale for no apparent reason, the conventions and rules of Western society no longer seemed worthy of attention by artists.
https://www.cnn.com/2014/10/30/opinion/merjian-art-modern-wwi/index.html

In Call Of The Wild, when Buck had to work for Charles and Hal, did he ever gain weight again?

In chapter 5, Buck is sold to Hal and Charles. They are arrogant, proud, incompetent owners that nearly kill him as they embark on a dangerous journey. Hal, Charles, and Mercedes initially pack too much luggage on the sled and are reluctant to remove any items. Instead, they add too many dogs to the team and do not properly ration their food and water. As a result, the dogs are overfed before they begin to starve. As their journey continues, the completely exhausted, starving dogs begin to die, and Buck loses a considerable amount of weight. Under Hal and Charles's ownership, Buck no longer looks like the healthy, strong dog he once was and almost dies during the journey. As spring arrives, the ice becomes thinner, and Buck refuses to lead the pack over thin ice, which prompts a severe beating from Hal. Fortunately, John Thorton witnesses the beating and threatens to kill Hal if he touches Buck again. After the incompetent, ignorant owners leave Buck behind with John Thorton, they fall into the river, and Thorton nurses Buck back to health. It takes Buck a considerable amount of time to regain his strength, but he eventually gains weight and returns to his previous exemplary condition. Buck thrives under Thorton's ownership and ends up performing legendary feats that become folklore in the Yukon Territory.

What is the thesis of the essay "Sister Flowers"? What does Mrs. Flowers represent to Ms. Angelou? What are the lessons about living that Mrs. Flowers coveys to Angelou? What senses are used and how is the method of organization revealed in the essay? How does Angelou imply that race was a fact of life in her town?

1. The premise in this essay concerns the value of using one's potential to achieve even more than one believes one is able to. It is evident from Mrs. Flowers's interaction with Marguerite (the speaker) that she wants her to add an extra element to what she has been achieving (in spite of the fact that she clearly displays superior talents already). 
2. Mrs. Flowers is the epitome of "what a human being should be." To Marguerite she is the ideal that she herself is striving toward. The text clearly illustrates the admiration and respect she has for Mrs. Flowers. The fact that Mrs. Flowers pays attention to her inspires her even more.
3. Mrs. Flowers teaches the speaker to not take for granted what she has and just accept that she is okay because she has such unique abilities. She teaches her that she should strive for better.
4. Sight: "She was thin..." "...printed voile dresses and flowered hats..."
Smell: "The odors in the house surprised me." "The sweet scent of vanilla..."
Taste: "...if I hadn't had to swallow, it would have been a dream come true."
Hearing: "I heard poetry for the first time in my life." "Her sounds began cascading gently."
Touch: "...the rough crumbs scratched the inside of my jaws."
5. "She was our side’s answer to the richest white woman in town."
"Our side" is an obvious reference to the fact that there were different sections in the community and that they were separated. In terms of the time setting, the poem was written at a time when communities were segregated according to their race. Blacks and whites lived apart from each other in clearly defined, separate communities, and often laws governed such divisions.

How does Poe create suspense in "The Pit and the Pendulum"?

One way that Poe creates suspense from the very beginning is by giving us an unreliable narrator to narrate the events. He opens the narrative by telling us that he himself doesn't fully trust his senses:

I was sick—sick unto death with that long agony; and when they at length unbound me, and I was permitted to sit, I felt that my senses were leaving me.

If the narrator himself doesn't feel that he has full control of his senses and faculties, how can we be sure of the details that follow? How will he portray the events?
Suspense is further generated by the setting. Part of the narrator's torture is that his punishment is hidden in darkness:

At length, with a wild desperation at heart, I quickly unclosed my eyes. My worst thoughts, then, were confirmed. The blackness of eternal night encompassed me. I struggled for breath. The intensity of the darkness seemed to oppress and stifle me. The atmosphere was intolerably close.

The unknown terrors that lay waiting for the narrator in the darkness increase his sense of panic, and therefore, the reader's as well. Darkness is often symbolic of evil, and this sense of foreboding danger intensifies as the narrator attempts to navigate his dark surroundings.
Thus, the narrator's reaction to his torture increases suspense. Perspiration bursts from every pore. His eyes strain for hope. He thrusts his arms wildly in all directions.
And then, of course, there is the method of torture itself. A swinging pendulum that ends in a sharp blade which descends ever closer to the narrator, with potentially disastrous results, creates a building sense of terror. The pendulum descends slowly, allowing the narrator much time to consider his gruesome end and time for the reader's anticipation to build, as well.
Poe masterfully crafts a language that furthers an eerie tone, utilizing words such as "relentlessly," "unspeakable," "devoured," "struggled," and "annihilated"—and weaving this language throughout the story to increase the story's suspense.

Edgar Allen Poe was the first writer to use many horrific archetypes, or universal themes or mental images, in his stories. To create suspense in "The Pit and the Pendulum," he uses numerous archetypes that inspire a sense of terror, including helpless captivity, darkness, torture, rats, imminent death, and a deep almost bottomless pit.

To further heighten the suspense, Poe creates an acutely sinister atmosphere and draws out the narrator's encounters with each of these fearful things. For instance, when the narrator's sentence is pronounced, he is in a candle-lit room faced by black-robed judges, and the narrator is "sick unto death with that long agony" of not knowing his fate and fearing the worst. When he awakens in utter darkness, Poe draws out the feeling of horror by having him measure the length of his dungeon, and then increases the suspense by having him almost fall into the pit. When he is bound to the wooden framework and the pendulum descends, it inches its way down in agonizing slowness, further creating suspense. Finally, when the narrator escapes the pendulum, he is not simply cast into the pit, but is slowly, slowly forced towards it by the hot enclosing walls.

So Poe creates suspense by using what are now considered classic horror archetypes, by his description of the terrible environment of the dungeon, and by drawing out the narrator's danger by various means with intense, excruciating slowness.

Poe creates suspense, in part, by using a first person narrator. This means that the narrator is a participant in the action and that he uses the first person pronoun, "I." The first person narrator can really only tell us what he's aware of and what he knows to be true, as opposed to a third person narrator who might be able to tell us what all the other characters are thinking and feeling. Because the narrator's perception is limited by darkness and his experience is limited by solitude, he can only tells us as much as he knows, and that is not too much. This creates suspense. Further, the narrator loses consciousness more than once, and we are as clueless as he is as to what he will find when he awakens. Moreover, the narrator talks about being in Toledo, and given his trial, judgment, and torture, we might ascertain that he is being held by the Spanish Inquisition, and this would create suspense as well because we know how ruinous and deadly it was.

I think that a big part of the suspense in "The Pit and Pendulum" comes from two sources.  
The first is the unknown. The reader has no idea why the protagonist has been arrested and sentenced. The opening paragraphs have him in and out of conscious thought all while hallucinating. We don't know who he is or what he has done to deserve punishment. Once he is in his cell, the unknown continues. It's too dark to see anything, so the protagonist (and reader) has no idea where he is. After he successfully evades the pit, the protagonist must face the pendulum. There is always a sense of "what could possibly come next?" That's suspenseful reading.  
The second source for suspense is the protagonist's solitude. Being alone in an unknown place is scary. Having to suffer alone is scary. If the narrator had a cellmate, then readers might hope the two could at least help each other cope. That isn't an option for the protagonist, though. He must go about his torture alone. He's only dependent on himself, which I believe makes the story more suspenseful.

Single Variable Calculus, Chapter 3, 3.3, Section 3.3, Problem 56

Find the equation of the tangent line and normal line of the curve $\displaystyle y = \frac{\sqrt{x}}{x + 1}$ at the point $(4,0.4)$


Required:

Equation of the tangent line and the normal line at $P(4,0.4)$

Solution:


$
\begin{equation}
\begin{aligned}

\qquad y' = m_T =& \frac{(x + 1) \displaystyle \frac{d}{dx} (x^{\frac{1}{2}}) - \left[ (x^{\frac{1}{2}}) \frac{d}{dx} (x + 1) \right] }{(x + 1)^2}
&& \text{Using Quotient Rule}
\\
\\
\\
\qquad y' = m_T =& \frac{(x + 1) \displaystyle \left[ \frac{1}{2 (x^{\frac{1}{2}})} \right] - (x^{\frac{1}{2}})(1)}{(x + 1)^2}
&& \text{Simplify the equation}
\\
\\
\\
\qquad y' = m_T =& \frac{\displaystyle \frac{x + 1}{2 (x^{\frac{1}{2}})} - (x^{\frac{1}{2}})}{(x + 1)^2}
&& \text{Get the LCD}
\\
\\
\\
\qquad y' = m_T =& \frac{\displaystyle \frac{x + 1 - 2x}{2(x^{\frac{1}{2}})}}{(x + 1)^2}
&& \text{Combine like terms}
\\
\\
\\
\qquad y' = m_T =& \frac{-x + 1}{2 \sqrt{x} (x + 1)^2}
&& \text{}
\\
\\
\\
\qquad m_T =& \frac{-x + 1}{2 \sqrt{x} (x + 1)^2}
&& \text{Substitute the value of $x$}
\\
\\
\\
\qquad m_T =& \frac{-4 + 1}{2 \sqrt{4} (4 + 1)^2}
&& \text{Simplify the equation}
\\
\\
\\
\qquad m_T =& \frac{-3}{100}
&& \text{}
\\


\end{aligned}
\end{equation}
$



Solving for the equation of the tangent line:


$
\begin{equation}
\begin{aligned}

\qquad y - y_1 =& m_T(x - x_1)
&& \text{Substitute the value of the slope $(m_T)$ and the given point}
\\
\\
\qquad y - 0.4=& \frac{-3}{100} (x - 4)
&& \text{Multiply $\large \frac{-3}{100}$ in the equation}
\\
\\
\qquad y - 0.4 =& \frac{-3x + 12}{100}
&& \text{Add $0.4$ to each sides}
\\
\\
\qquad y =& \frac{-3x + 12}{100} + 0.4
&& \text{Simplify the equation}
\\
\\
\qquad y =& \frac{-3x + 12 + 40}{100}
&& \text{Combine like terms}
\\
\\
\qquad y =& \frac{-3x + 52}{100}
&& \text{Equation of the tangent line to the curve at $P (4,0.4)$}


\end{aligned}
\end{equation}
$


Solving for the equation of the normal line


$
\begin{equation}
\begin{aligned}

m_N =& \frac{-1}{m_T}
&&
\\
\\
m_N =& \frac{-1}{\displaystyle \frac{3}{100}}
&&
\\
\\
m_N =& \frac{100}{3}
&&
\\
\\
y - y_1 =& m_N (x - x_1)
&& \text{Substitute the value of slope $(m_N)$ and the given point}
\\
\\
y - 0.4 =& \frac{100}{3} (x - 4)
&& \text{Multiply $\large \frac{100}{3}$ to the equation}
\\
\\
y - 0.4 =& \frac{100 x - 400}{3}
&& \text{Add 0.4 to each sides}
\\
\\
y =& \frac{100x - 400}{3} +0.4
&& \text{Simplify the equation}
\\
\\
y =& \frac{100 - 400 + 1.2}{3}
&& \text{Combine like terms}
\\
\\
y =& \frac{100x - 398.8}{3}
&& \text{Equation of the normal line at $P(4,0.4)$}

\end{aligned}
\end{equation}
$

What was the main objective of the Berlin Conference?

In late 1884, Otto von Bismarck, the imperial chancellor, and architect of the German Empire convened a meeting between representatives of fourteen European States to negotiate geographical fragmentation of Africa for their patrons. The Berlin Conference, as the meeting came to be called, offered European powers the opportunity to lay claim on parts of Africa's vast continent rich with minerals and markets. While European powers had explored Africa for decades prior to the conference, the objective of the conference was to cement the spheres of influence for the European powers amidst growing competition.
 
European powers had conducted exploration of various parts of Africa and an insatiable need for resources such as silver, gold, and bronze among others, and a demand for more market fueled intense competition among these states. As a consequence, there arose a need for each European power to carve out part of Africa and exercise their influence. This desire was the motivation behind Otto von Bismarck's call for the conference because he wanted to safeguard the interest of Germany as well as play European interest against each other. Berlin Conference objective of expanding European spheres of influence over Africa was achieved after three months of negotiations. Among the major players, the French curved West Africa for themselves, Belgians acquired the vast Congo and the British took control of East and Southern Africa while Germany took control over four colonies and Portugal two colonies in Southern Africa and one colony in West Africa.
 
Further reading
de Blij, H. J., & Muller, P. O. (2003). Geography: Realms, regions, and concepts (11th ed., pp. 298-300). Hoboken, NJ: Wiley.

The main objective of the Berlin Conference (1884-85) was to codify and legalize the European colonization of Africa. For a number of years, the European powers had been involved in what became known as "The Scramble for Africa." As the name suggests, the process of European colonialism had developed in a somewhat improvised, haphazard fashion, without much in the way of planning or foresight. One serious consequence of this approach was that the colonial powers often became bogged down in petty disputes with each other over territory. There was a real danger that these skirmishes could flare up into out-and-out war.
It was therefore thought necessary by Bismarck, who convened the Berlin Conference, to establish European colonies in Africa on a more formal legal and diplomatic basis. That way any territorial disputes could, it was thought, be amicably resolved, without resorting to conflict. However, Bismarck's motives weren't completely disinterested. Germany was a relative latecomer to European colonization and was becoming increasingly aggressive and expansionist. But as German territory in Africa was still dwarfed by that belonging to Britain and France, Bismarck wanted to make sure that German gains would be protected from potential incursion by the other European powers.
https://www.oxfordreference.com/view/10.1093/acref/9780195337709.001.0001/acref-9780195337709-e-0467

Can you provide an analysis for the story "The Bestseller?"

O. Henry's 1909 short story "The Bestseller" is an amusing tale that explores themes of social class, romance, popular literature, and the American character.
The story's title is a double entendre. The narrator and John Pescud have a conversation about the merits (or lack thereof) of bestselling novels of the day; there is, at the same time, the ironic parallel to Pescud's pursuit of Jesse Allyn—as he is the "best seller" of himself to Jesse's father. Pescud's prowess as a salesman creates a comfortable life and home for himself and Jesse. He is the epitome of an American success story as he begins life in modest circumstances and is able to work his way up into a higher social class through his efforts and a strategic, though genuinely loving, marriage. In a sense, he "saves" Jesse and her father from the crumbling remains of their former prominence in the American South.
O. Henry also takes critical aim at formulaic romantic bestsellers that feature a heroic American character who is able to impress and save highborn Europeans from various threats, and he does so through Pescud's clever wordplay and the farcical situations he describes to the narrator.

Shakespeare begins the play with two secret acts. What is the deception and the effect that these deceptions have on the tone of the play?

One of the secret acts is the marriage between Othello and Desdemona. The two marry in such a way because Desdemona's father, a senator, would never want her to marry a foreigner and a black man like Othello, even though Othello is an important figure in Venice.
While Desdemona's deception of her father is not meant to be malicious, it does have consequences which reverberate throughout the play. Desdemona's father warns Othello that Desdemona's willingness to deceive her own father means she'll have no qualms deceiving a husband, and Othello comes to deeply suspect Desdemona of infidelity even on the slimmest and most trivial evidence, in large part because of this deception.
Another secret act in the opening of the play is how Iago and Brabantio get Desdemona's father out of bed. They cry out, "Thieves!" This is a small deception, but it does set up something important about Iago—he is never what he seems and is willing to use lies to get people to act as he desires.

The play opens with Iago and Roderigo conspiratorially discussing the Moor, in darkness; the tone of the opening scene, in which Iago declares that "in following the Moor, I follow but myself," sets the tone for a play characterized by Iago's duplicity and self-interest and deeds conducted in shadows and secrecy. Ostensibly, Iago is annoyed that Cassio has been made Othello's lieutenant, and Iago only his "ancient" ("I had rather been his hangman," says Cassio). He feels that he was deceived in this matter, and therefore declares "I am not what I am"—a note to the audience that his motives will never be transparent—and sets himself to lowering Othello in social position, as he feels him to be "puffed up."
Next, Roderigo and Iago call out Brabantio under false pretenses—"Thieves, thieves!"—so that they can tell him that his daughter, Desdemona, is currently "making the beast with two backs" with Othello. This second part does turn out to be true, but the audience knows that Iago is calling Brabantio's attention to it not truly out of concern for Brabantio but out of a desire to lower Othello in the estimation of the nobleman.
The contrast between the first and second scene sets the tone for Iago's duplicitous behavior throughout the play, as we here see him declaring his devotion to Othello and fury at Brabantio for having accosted him—although we of course know that it was Iago who sent Brabantio to do this. Iago, we see from the beginning, cannot be trusted. Indeed, perhaps his comment that he does everything in his own self-interest is his only true statement in the play.

Beginning Algebra With Applications, Chapter 3, 3.2, Section 3.2, Problem 128

Solve $\displaystyle \frac{1}{5} d = \frac{1}{2}d + 3$ and check.


$
\begin{equation}
\begin{aligned}

\frac{1}{5} d =& \frac{1}{2}d + 3
&& \text{Given equation}
\\
\\
\frac{1}{5}d - \frac{1}{2}d =& 3
&& \text{Subtract } \frac{1}{2}d
\\
\\
\frac{-3}{10} d =& 3
&& \text{Simplify}
\\
\\
\frac{-10}{3} \left( \frac{-3}{10} d \right) =& 3 \left( \frac{-10}{3} \right)
&& \text{Multiply both sides by } \frac{-10}{3}
\\
\\
d =& -10
&&

\end{aligned}
\end{equation}
$


Checking:


$
\begin{equation}
\begin{aligned}

\frac{1}{5} (-10) =& \frac{1}{2} (-10) + 3
&& \text{Substitute } d = -10
\\
\\
\frac{-10}{5} =& \frac{-10}{2} + 3
&& \text{Simplify}
\\
\\
-2 =& -2
&&

\end{aligned}
\end{equation}
$

Single Variable Calculus, Chapter 3, 3.3, Section 3.3, Problem 33

Differentiate $\displaystyle y = \frac{t^2 + 2}{t^4 - 3t^2 + 1}$



$
\begin{equation}
\begin{aligned}

y' =& \frac{(t^4 -3t^2 + 1) \displaystyle \frac{d}{dx} (t^2 + 2) - \left[ (t^2 + 2) \frac{d}{dx} (t^4 - 3t^2 + 1) \right]}{(t^4 - 3t^2 + 1)^2}
&& \text{Apply Quotient Rule}
\\
\\
y' =& \frac{(t^4 - 3t^2 + 1)(2t) - [(t^2 + 2)(4t^3 - 6t)]}{(t^4 - 3t^2 + 1)^2}
&& \text{Expand the equation}
\\
\\
y' =& \frac{2t^5 - \cancel{6t^3} + 2t - 4t^5 + \cancel{6t^3} - 8t^3 + 12t}{(t^4 - 3t^2 + 1)^2}
&& \text{Combine like terms}
\\
\\
y' =& \frac{-2t^5 - 8t^3 + 14t}{(t^4 - 3t^2 + 1)^2}
&& \text{}
\\
\\

\end{aligned}
\end{equation}
$

What is the summary of William Blake's "Introduction" to Songs of Experience?

Since William Blake's Songs of Experience are best understood when compared to the corresponding Songs of Innocence, one should first read Introduction to Songs of Innocence before attempting a cogent summary of Introduction to Songs of Experience. The poem that introduces the first set of poems describes a fictional meeting with a child who requests the poet to first sing and then record in words his "songs of happy chear [sic]." Thus Blake introduces the first set of verses by describing them as "happy songs every child may joy to hear."
As he introduces the second set of poems, however, the poet isn't as clear about their purpose. Instead of responding to the request of a child, the poet gives a command to the reader to hear what the poet has to say. Instead of a cheerful piper, the writer of this section's poems presents himself as one who transcends time and was present at the Fall of man in the Garden of Eden. Just as the Creator called the "lapsed Soul" into renewed light, so the poet's songs in this section will offer a call to salvation. Thus the poet pleads, "O Earth O Earth return!" and "turn away no more."
However, it's important to understand that Blake isn't referring to the Fall as a fall from innocence into sin but from imagination and insight to the use of physical sight alone. To restore mankind to its ideal state, it will be necessary to look at the world not just through the optimistic simplicity of childhood, but through the mature understanding of one who can recognize both evil and good in the world. In "The Marriage of Heaven and Hell," Blake writes, "Without Contraries is no progression. Attraction and Repulsion, Reason and Energy, Love and Hate, are necessary to Human existence." Blake wants his Songs of Experience to provide the "Contraries" to the Songs of Innocence that will help readers progress toward a more imaginative and creative state of existence—the renewal and awakening the Introduction speaks of.
https://www.poetryfoundation.org/poems/43666/introduction-to-the-songs-of-experience

William Blake's "Introduction to Songs of Experience" exists as a "sister" poem to his "Introduction to Songs of Innocence." When looking at the poems together, one should notice the maturity to later "Experience" poems possesses over the earlier "Innocence" poems.
The poem in question calls for the reader to pay attention to him immediately: "Hear the voice of the Bard!" This attention is demanded based upon the "fact" the Bard knows of the past, present, and future. The poet goes on to declare that the reader should listen because the Bard has "walk'd among the ancient trees" and "heard the Holy Word" (meaning God has spoken to him while in the Garden of Eden).
In the second stanza, the speaker calls out for the reader, who has "fallen" from the light of God to give up the materialism of the earthly world ("the starry pole"). The third stanza calls out to the Earth, assumedly in the same position as man ("it," nature personified, has also turned from God).
The final stanza addresses both man and nature, both who the Bard calls out to "turn away no more." Yet, the speaker understands that both will still turn from God because both are too "slumberous" (weary, stubborn, or tainted) to do so.
In the end, the poem speaks to both man's and the earth's turning from God. The poem acts as a warning against turning from God, although the poet (in his mature experience) realizes that some, if not most, will be unable to do so.

College Algebra, Chapter 5, 5.4, Section 5.4, Problem 74

Suppose that a woman wants to invest $\$ 4000$ in an account that pays $9.75 \%$ per year, compounded semiannually. How long a time period should she choose to save an amount of $\$ 5000$?



Recall that the formula for interest compounded $n$ times per year is..

$\displaystyle A(t) = P \left( 1 + \frac{r}{n} \right)^{nt} $

So if the interest is compounded semiannually, then $n = 2$


$
\begin{equation}
\begin{aligned}

5000 =& 4000 \left( 1 + \frac{0.0975}{2} \right)^{(2) t}
\\
\\
\frac{5000}{4000} =& \left( 1 + \frac{0.0975}{2} \right)^{2t}
\\
\\
\ln \left( \frac{5}{4} \right) =& \ln \left( 1 + \frac{0.0975}{2} \right)^{2t}
\\
\\
\ln \left( \frac{5}{4} \right) =& 2t \ln \left( 1 + \frac{0.0975}{2} \right)
\\
\\
\frac{\displaystyle \ln \left( \frac{5}{4} \right) }{\displaystyle 2 \ln \left( 1 + \frac{0.0975}{2} \right)} =& t
\\
\\
t =& 2.34 \text{ years}
\\
\\
t =& 2 \text{ years} + 0.34 \text{ years} \left( \frac{12 \text{ months}}{1 \text{ year}} \right)
\\
\\
t =& 2 \text{ years} + 4.08 \text{ months}


\end{aligned}
\end{equation}
$


It shows that the woman will save an amount of $\$ 5000$ if the period is approximately $2$ years and $5$ months.

Precalculus, Chapter 5, 5.3, Section 5.3, Problem 45

y= sin ((pix)/2) + 1
Before we solve for the x-intercepts, let's determine the period of this function.
Take note that if a trigonometric function has a form y= Asin(Bx + C) + D, its period is:
P e r i o d = (2pi)/B
If we plug-in the value of B, we will get:
P e r i o d = (2pi)/(pi/2) = ((2pi)/1)/(pi/2)=(2pi)/1* 2/pi=4
Hence, the period of the given function is 4.
Let's solve now the x-intercepts. To solve, set y=0.
y= sin ((pix)/2) + 1
0=sin((pix)/2) + 1
-1= sin ((pix)/2)
Take note that sine has a value of -1 at an angle (3pi)/2 .
(3pi)/2 = (pix)/2
Then, isolate the x.
(3pi)/2*2/pi = (pix)/2*2/pi
3=x
Since the period of the function is 4, therefore the x-intercepts are:
x= 3 + 4n
where n is any integer.

What were some ways in which Helen enjoyed the feel of sound?

Though Helen could no longer hear after she became deaf, she could feel the vibrations of sound.  She loved to placed her hands on an object or living thing as it was making a sound.  Helen had lost her memory of words and could not hear herself speak.  Despite these difficulties, she still made audible noises and placed her hands on her own neck to feel the vibrations caused by the sounds.  Doing this fascinated Helen.  In her autobiography, The Story of My Life, Helen described how she enjoyed the feeling of sound:

I was pleased with anything that made a noise, and liked to feel the cat purr and the dog bark. I also liked to keep my hand on a singer's throat, or on a piano when it was being played (Chapter XIII).

This fascination with sound led Helen to seek instruction in speaking.  She had heard of deaf people who learned how to talk, and Helen desired this for herself.  With Miss Sullivan's assistance, Helen sought the help of Miss Sarah Fuller.
 

http://responsesystemspanel.whs.mil/Public/docs/meetings/Sub_Committee/20140225_CSS/Materials_Presenters/07_RiskFactors_Mann_Hanson_Thornton_2010.pdf Please write a summary of the article from the link on top.

This article is entitled "Assessing Risk for Sexual Recidivism: Some Proposals on the Nature of Psychologically Meaningful Risk Factors," and it appeared in the journal Sexual Abuse: A Journal of Research and Treatment in 2010. Its authors, Ruth Mann, Karl Hanson, and David Thornton, argue that in assessing and reducing the risk of recidivism (committing the crime again) among sex offenders, it is important to identify what factors in the individual post the highest risk for recidivism. They recommend the use of what they call "third generation" intervention tools and procedures. These measure factors that are the most relevant to an individual offender. They are especially interested in identifying "psychologically meaningful risk factors," like individual predilections and behavioral patterns, to inform intervention. For example, someone who is likely to gravitate toward environments where drugs are used might be more likely to become a recidivist—there is a causal link between drug abuse and sexual offenses among convicted sex offenders. The demonstration of sexual preoccupation in a sexual offender would be another such factor. If these factors can be reliably determined, interventions can be planned and tailored to the needs of individuals.

How did the transcontinental railroad further the industrial revolution?

The transcontinental railroad furthered the growth of the Industrial Revolution. Industries had been expanding as Americans moved westward toward the Mississippi River. Once people moved beyond the Mississippi River, businesses grew even more. The building of the transcontinental railroad furthered the growth of American industries. The construction of the transcontinental railroad meant that industries had to provide the products and materials needed for building the railroad. More steel was needed for the tracks, and eventually, more railroad cars and engines were needed.
With the building of the transcontinental railroad, people began to move further west than in the past. These people needed products so they could live in these areas to which they were moving. Businesses needed to grow to meet the increasing demand for products. As a result, businesses expanded westward. New factories were built in the West to make products for the people who were moving and living there.
The transcontinental railroad significantly impacted the growth of the Industrial Revolution.
https://indrevproject123.wordpress.com/2013/01/18/building-of-the-transcontinental-railroad/

https://www.ushistory.org/us/25b.asp

What were the economic consequences of the English Revolution?

There were economic consequences of the English Revolution, called the Glorious Revolution, of 1688.One consequence was that the power of British monarchy was weakened. For example, the British Parliament got control over the levying of taxes. The Parliament also was able to have influence over royal secession, have a say in declaring war, and have influence over political appointments.Great Britain was also changed financially. Because the wars that Great Britain had fought had cost so much money, Parliament began to examine the royal expenses much more closely than it had done in the past. Key financial institutions, such as the Bank of England, also formed.The war ended a monopoly that the Royal African Company had over the trading of slaves. This allowed slavery to grow as a result of the revolution. It was ironic that while this war was designed to give the British people more freedom, it also led to more slavery for some people.This revolution also impacted the British colonies in North America. The colonists began to think that they should eventually have more freedom in the colonies. They heard about the constitutional reforms that were made in Great Britain as a result of the Glorious Revolution. They also knew this was a popular uprising. In Boston, in 1689, the people revolted against the governor of the Dominion of New England. The people were unhappy that the British government had more control as a result of changes made by James II in 1686. The colony returned to the previous form of government, which was run by the Puritans. Another rebellion occurred in New York. After a series of events that led to the death of a prominent person in the revolt, Jacob Leisler, a representative assembly was created. There also was a revolt in Maryland that led to a new government being established. While the colonists were able to make some changes as a result of these revolutions, the British still wanted to maintain a firm grip on their colonies. This would eventually lead to policies that the colonists strongly opposed. As a result of these policies and other incidents, the Revolutionary War, which had a significant financial impact on the British, began in 1776.The English Revolution had economic consequences that were felt throughout the British Empire.
http://www.bbc.co.uk/history/british/civil_war_revolution/glorious_revolution_01.shtml

https://historyofmassachusetts.org/how-did-glorious-revolution-affect-colonies/

https://m.landofthebrave.info/glorious-revolution.htm

Single Variable Calculus, Chapter 4, 4.5, Section 4.5, Problem 16

Use the guidelines of curve sketching to sketch the curve. $\displaystyle y =1 + \frac{1}{x} + \frac{1}{x^2}$

The guidelines of Curve Sketching
A. Domain.
We know that $f(x)$ is a rational function that is defined everywhere except for the value of $x$ that would make its denominator equal to 0. In our case, $x=0$. Therefore, the domain is $(-\infty,0)\bigcup(0,\infty)$

B. Intercepts.
We don't have $y$-intercept since zero is not included in the domain of $f$.
Solving for $x$-intercept, when $y = 0$
$\displaystyle 0 = \frac{x^2 + x + 1}{x^2}$
$0 = x^2 + x + 1$

We have no real solution for this. Hence, there is no $x$-intercept.

C. Symmetry.
The function is not symmetric in either $y$-axis or origin.

D. Asymptotes.
For vertical asymptotes, we set the denominator equal to 0, that is $x^2 = 0$ therefore, $x = 0$ is our vertical asymptote.
For horizontal asymptotes, we divide the coefficient of the highest degree of the numerator and denominator to obtain $\displaystyle y= \frac{1}{1} = 1$


E. Intervals of Increase or Decrease.
If we take the derivative of $f(x)$, by using Quotient Rule.
$\displaystyle f'(x) = \frac{x^2(2x+1)-(x^2+x+1)(2x)}{(x^2)^2} = \frac{-2-x}{x^3}$
When $f'(x) = 0$,
$\displaystyle 0 = \frac{-2-x}{x^3}$
We have, $x = -2$ as our critical number
If we divide the interval, we can determine the intervals of increase or decrease,

$
\begin{array}{|c|c|c|}
\hline\\
\text{Interval} & f'(x) & f\\
\hline\\
x < - 2 & - & \text{decreasing on } (-\infty, -2)\\
\hline\\
x > -2 & + & \text{increasing on } (-2, \infty)\\
\hline
\end{array}
$



F. Local Maximum and Minimum Values.
Since $f'(x)$ changes from negative to positive at $x = -2$ , $\displaystyle f(-2) = \frac{3}{4}$ is a local minimum.

G. Concavity and Points of Inflection.

$
\begin{equation}
\begin{aligned}
\text{if } f'(x) &= \frac{-2-x}{x^3}, \text{ then}\\
\\
f''(x) &= \frac{x^3 ( - 1) - ( - 2 - x ) (3x^2)}{(x^3)^2}
\end{aligned}
\end{equation}
$


Which can be simplified as, $\displaystyle f''(x) = \frac{2(x+3)}{x^4}$
When $f''(x) = 0$
$0 = 2 ( x+3)\\
x + 3 = 0$
The inflection is at $x = -3$
If we divide the interval, we can determine the concavity as,

$
\begin{array}{|c|c|c|}
\hline\\
\text{Interval} & f''(x) & \text{Concavity}\\
\hline\\
x < - 3 & - & \text{Downward}\\
\hline\\
x > -3 & + & \text{Upward}\\
\hline
\end{array}
$



H. Sketch the Graph.

A certain full year course has 20 online quizzes spread through the course. The quizzes are optional in the sense that if a student does any of the quizzes, then quizzes count for 10% of the student’s grade, with each quiz counting for 1/2 mark, but for a student who does no quizzes, that 10% is reallocated to other work. Each quiz has 5 multiple choice questions, and the quizzes are marked on a Pass/Fail basis: if a student answers at least 3 of the 5 questions correctly, the student gets the 1/2 mark for that quiz. Otherwise, the student gets 0 for that quiz. Students are allowed 2 attempts at each quiz, with the higher mark counting, so as long as a student gets at least 3 questions right on at least one attempt, the student gets the 1/2 mark for that quiz. Each question on each quiz tests a different concept from the course material. For each of these concepts, the quiz database contains a set of 4 different questions. When a quiz attempt is initiated, the computer randomly selects one of 4 questions for each of the 5 concepts being tested. Each question in the quiz database has 5 answer choices. Tony took this course during the year which ended in April. He decided to have the grading scheme without a quiz component apply for him. However, he wanted to see what the quiz questions were like, so each time a quiz was available, he initiated a quiz attempt. He didn’t answer any of the questions, and did not submit the quiz. Tony didn’t realize that when the quiz window closes, the computer automatically submits any unsubmitted quiz that has been initiated. All 20 of Tony’s quizzes were submitted. As far as the Professor is concerned, Tony did attempt the quizzes and therefore his final grade was calculated with 0 out of 10 as his quiz mark. Tony has been arguing with the Professor about this. Tony maintains that by never answering any quiz question, it was clear that his intention was not to do quizzes and therefore not have a quiz component in his grade. The Professor has decided to compromise with Tony, in the following way. He will reopen all the quiz windows for Tony, to give him his second attempt at each quiz. Tony will receive 1/2 mark for quizzes for each quiz that he gets at least 3 questions right on. Tony needs a quiz mark of at least 4 out of 10 to improve his grade to a pass. The Professor has made it clear that he will not bump Tony’s mark if he’s close – Tony must pass at least 8 of the 20 quizzes in order to receive a passing grade in the course. Tony is about to sit down at his laptop and do the 20 quizzes. The professor has forgotten that Tony can see his original quiz attempts, including being able to see which was the correct answer for each question. For each quiz question, Tony will look at his original attempt at that quiz on his phone, to see if it is a repeat question. If it is, he will select what he knows is the right answer choice. For any question that is not a repeat question, Tony will randomly choose one of the 5 answer choices, because he has forgotten what little he did know about the course material. (a) Consider any one question on any one quiz. What is the probability that Tony will answer the question correctly? (b) Consider any one of the 20 quizzes. What is the probability that Tony will answer at least 3 of the 5 questions correctly and earn the 1/2 mark for that quiz? (Express your answer exactly, which should be a number with 5 decimal places.) (c) What is the probability that Tony will pass at least 8 of the 20 quizzes? Hint: To answer this, you should be thinking about the number of quizzes that Tony passes, not the value of his “quiz mark” – and certainly not the number of quiz questions he answers correctly. Note: Your answer should be expressed to 4 decimal places. The answer should be as precise as possible, but you should definitely use the easiest method available to calculate that number.

(a) For each question, Tony knows the answer 25% of the time and is forced to guess 75% of the time. His probability of guessing correctly is 20% (1 in 5.)
So the probability that Tony gets a particular question correct on any given quiz is .25(1)+.75(.2)=0.4  (We multiply the probability of having seen the problem by the probability of getting it right; 1/4 of the time he has seen the problem and is guaranteed to get it right and 3/4 of the time he will not have seen the problem and must guess.)
(b) For a given quiz, consisting of 5 questions, we can determine the probability that Tony gets at least 3 questions correct. This is the sum of the probabilities that he gets 3 correct, 4 correct, and 5 correct.
Each of these is a binomial probability, where the probability of a success (getting an answer correct) is 0.4 and the total number of trials is 5:
P(3 correct)=_5C_3 (.4)^3(.6)^2=.2304 P(4 correct)=_5C_4 (.4)^4(.6)=.0768 P(5 correct)=_5C_5 (.4)^5=.01024
So the probability of getting at least 3 correct is .2304+.0768+.01024=.31744
(c) To find the probability that Tony passes at least 8 of the quizzes we recognize that this is also a binomial probability. The probability of success (passing the quiz) is .31744 and the number of trials is 20. The answer is the sum of P(8)+P(9)+...+P(20).
Computationally easier is to find the complement and subtract from 1: 1-[P(0)+P(1)+...+P(7)]
So we have:
1-(0.68256^20+20(.31744)(.68256)^19+_20C_2(.31744)^2(.68256)^18+...
...+_20C_7(.31744)^7(.68256)^13)~~.2836161405
So the probability that Tony passes at least 8 of the quizzes is about 0.2836
(Of course the easiest way to compute this is using technology if allowed. On a TI-83/84 graphing calculator we take 1- binomcdf(20,.31744,7) .)
http://mathworld.wolfram.com/BinomialDistribution.html

College Algebra, Chapter 7, 7.2, Section 7.2, Problem 18

Solve the matrix equation $5(X - C) = D$ for the unknown matrix $X$, where

We solve for $X$


$
\begin{equation}
\begin{aligned}

5(X - C) =& D
&& \text{Given equation}
\\
\\
5X - 5C =& D
&& \text{Distributive Properties of Scalar Multiplication}
\\
\\
5X =& D + 5C
&& \text{Add the matrix $5C$ to each side}
\\
\\
X =& \frac{1}{5} (D + 5C)
&& \text{Multiply each side by the scalar } \frac{1}{5}

\end{aligned}
\end{equation}
$


So,


$
\begin{equation}
\begin{aligned}

X =& \frac{1}{5} \left( \left[ \begin{array}{cc}
10 & 20 \\
30 & 20 \\
10 & 0
\end{array} \right] + 5 \left[ \begin{array}{cc}
2 & 3 \\
1 & 0 \\
0 & 2
\end{array} \right] \right)

&& \text{Substitute the matrices $D$ and $C$}
\\
\\
X =& \frac{1}{5} \left( \left[ \begin{array}{cc}
10 & 20 \\
30 & 20 \\
10 & 0
\end{array} \right] + \left[ \begin{array}{cc}
10 & 15 \\
5 & 0 \\
0 & 10
\end{array} \right] \right)
&& \text{Simplify matrix } C
\\
\\
X =& \frac{1}{5} \left[ \begin{array}{cc}
20 & 35 \\
35 & 20 \\
10 & 10
\end{array} \right]
&& \text{Add matrices}
\\
\\
X =& \left[ \begin{array}{cc}
\displaystyle \frac{20}{5} & \displaystyle \frac{35}{5} \\
\displaystyle \frac{35}{5} & \displaystyle \frac{20}{5} \\
\displaystyle \frac{10}{5} & \displaystyle \frac{10}{5}
\end{array} \right]
&& \text{Multiply the scalar } \frac{1}{5}
\\
\\
X =& \left[ \begin{array}{cc}
4 & 7 \\
7 & 4 \\
2 & 2
\end{array} \right]
&&

\end{aligned}
\end{equation}
$

what does Tennessee mean when he yells ''Euchred, old man!''?

"To euchre" is a verb meaning to cheat or swindle. So you might hear someone say that they'd been "euchred" out of several thousand dollars by a con artist, for example. Euchre is also the name of a card game. During a game of Euchre, if your opponent fails to win three tricks after having made the trump, then they are said to be euchred.
As Tennessee is a notorious gambler and card player, this is what he means when he shakes hands with his partner during his trial; he's effectively been euchred, or trumped by the legal system. But then, Tennessee has himself euchred lots of folk in the past, including his own partner. Unfortunately for him, his euchring days are well and truly over. He's euchred one man too many and is now on trial for his life. The clumsy attempt by Tennessee's partner to bribe the judge hearing his case simply makes him all the more determined to sentence Tennessee to death by hanging, which he does.

Beginning Algebra With Applications, Chapter 5, 5.3, Section 5.3, Problem 44

Graph $\displaystyle y = \frac{3}{4} x + 1$ by using the slope and $y$-intercept.

$y$-intercept:


$
\begin{equation}
\begin{aligned}

y =& \frac{3}{4} x + 1
&& \text{Given equation}
\\
y =& \frac{3}{4} (0) + 1
&& \text{To find the $y$-intercept, let } x = 0
\\
y =& 1
&&

\end{aligned}
\end{equation}
$


The $y$-intercept is $(0,1)$


$
\begin{equation}
\begin{aligned}

m =& \frac{\text{change in } y}{\text{change in } x}
\\
\\
m =& \frac{3}{4}

\end{aligned}
\end{equation}
$


Beginning at the $y$-intercept, move to the right 4 units and then up 3 units.







$(4, 4)$ are the coordinates of a second point on the graph.

Draw a line through $(0,1)$ and $(4, 4)$

Single Variable Calculus, Chapter 2, 2.2, Section 2.2, Problem 21

Estimate the value of the $\displaystyle \lim \limits_{x \to 0} \frac{\sqrt{x + 4} - 2}{x}$ by using a table of values.



Let the values of $x$ be...

$
\begin{equation}
\begin{aligned}


\begin{array}{|c|c|}
\hline\\
x & f(x) \\
\hline\\
-0.1 & 0.251582 \\
-0.01 & 0.250156 \\
-0.001 & 0.250016 \\
-0.0001 & 0.250001 \\
-0.00001 & 0.25 \\
0.00001 & 0.249999 \\
0.0001 & 0.249998 \\
0.001 & 0.249984 \\
0.01 & 0.249844 \\
0.1 & 0.248457\\
\hline
\end{array}

\end{aligned}
\end{equation}
$



The table shows that as $x$ approaches 0 from both directions the
value of the limit approaches 0.25 or $\displaystyle \frac{1}{4}$.


$
\begin{equation}
\begin{aligned}

\displaystyle \lim \limits_{x \to 0} \frac{\sqrt{x + 4} - 2}{x} =& \frac{\sqrt{.000001 +4} - 2}{.000001} = \frac{1}{4}\\

\end{aligned}
\end{equation}
$

Describe the living conditions of slaves transported by ships as a part of the transatlantic slave trade. Did slavery have a role in the growth of racism? What were the main factors in the abolition of the slave trade in the United States?

The living conditions for slaves were about as inhumane as one could imagine. Because the Africans were regarded as cargo, they were packed in the bottoms of ships as such. No considerations were made for pregnant women who gave birth on the ships, or, quite simply, for people who would need to use the bathroom. As a result, for weeks, human beings were forced to lie in their own blood, feces, urine, and vomit, as some of those transported became ill due to illness or from being overwhelmed by the smells.
Slaves were packed very tightly into the bottoms of ships. The goal of the traders was to fit as many bodies in as possible. Mere inches of space separated one captured individual from another. More space was allowed only in instances in which a slave committed suicide by jumping off of a ship, or when those who had become too ill to be sold were forced overboard.
Every few days, slaves would be brought out onto the deck of the ship. Here, they would get exposure to sunlight and were allowed to breathe fresh air. Traders would get buckets of freshwater and throw the water onto the slaves. This was a feeble effort at maintaining hygiene. They were allowed small amounts of food (e.g., manioc, fish) and water to drink.
Slavery certainly had a role in the development of racism. Arguably, if Europeans had simply admitted that they captured Africans out of economic necessity (attempts to enslave Native Americans had failed over the long-term, and white indentured servitude was deemed less economically viable), perhaps some future troubles could have been avoided. It was the need to justify the act of enslavement which caused the racial tensions and hatred that remain prevalent today.
Racism had developed as a pseudo-science in the eighteenth century. Those who studied anthropology and biology began measuring skulls to determine differences between groups of people. It was assumed that the skulls of those of African descent showed evidence of poor mental development. With this, many whites came to believe that blacks deserved enslavement because they were deemed mentally inferior to whites.
Of course, not every white person believed this. There were some who believed that slavery was morally wrong and inhumane. A few even went as far to try to have it abolished, which was the purpose of the abolitionist movement.
It would be incorrect to think that the movement was popular. Though slavery did not exist in the North after the early nineteenth century (New Jersey was the last to abolish it in 1804), Northerners were not exactly more enlightened in their views on race. The popularity of minstrel shows in Northern cities in the 1830s and 1840s is proof of that. 
It would also be incorrect to think that everyone who detested slavery viewed blacks as equals. This was also true of some abolitionists. One of the causes of the rift between Frederick Douglass and William Lloyd Garrison was Garrison's stubborn need to use Douglass as a symbol of his cause instead of viewing Douglass as a peer in the movement.
The slave trade was abolished in the United States in 1807. Great Britain followed suit, abolishing its trade a year later. Other Western nations would continue to perpetuate the trade, including Spain. 
The assumption among some members of Congress was that the abolition of the trade would lead to the eventual discontinuation of slavery in the South. This proved to be untrue. Slavery would not end in the United States until President Lincoln delivered the Emancipation Proclamation in 1863. Until then, to whet its appetite for more slaves, traders and planters forced the breeding of slaves, often raping black women themselves to force pregnancy. Also, free blacks from the North were sometimes kidnapped and brought to the South to be sold.

What is the central theme of poem "The Microscope" by Maxine Kumin?

This is an interesting poem which tells the story of Anton Leeuwenhoek, a scientific pioneer, in a misleadingly simplistic, almost childlike style which masks the profundity of its central idea. Leeuwenhoek, the poet says, sold "pincushions, cloth, and such," an occupation which he neglected in order to begin grinding lenses for a microscope. Possessed by the spirit of scientific inquiry, Leeuwenhoek spends his time examining everything he can think of under his lenses, everything from fish scales to his own blood to bugs so small they are hidden within a water drop. The irony here is that the scientist is making extensive and important scientific advancements, but the townsfolk aren't interested in this. They are only interested in why their store is not open, to provide them with their day-to-day necessities. Irritated by the scientist's deviation from the quotidian, they accuse him of being crazy, saying that he should be shipped off to Spain and calling him "dope." As the final line of the poem says, however, it is because of this man, striving for discovery in the face of public disapproval and mockery, that we "got the microscope."
The central idea of the poem, then, is that all science, when it is first developed, seems "crazy" to those who are interested only in what is immediately relevant to them. It is only the great innovators and geniuses—who can continue to work despite the disapproval of those around them—who actually advance our world.

"The Microscope" suggests that innovation requires genius, and that a genius is rarely understood by his contemporaries. It was necessary for Anton Leeuwenhoek to neglect the quotidian details of his life as a shopkeeper (his "dry goods gathered dust") to pursue his passion for devising a machine that would enable him to examine the unseen, minute details of the natural world. Innovators are not understood or appreciated until their efforts are proven to be of use; in fact, the speaker observes that Anton was called "dumpkof" by those unimaginative observers who were more interested in the practicalities of life: "pincushions, cloth, and such." These manufactured, prosaic items contrast with the exoticism of Nature's "mosquitoes’ wings" and "spiders’ spinning gear." The irony is that his work led him to be considered a pioneer of the very practical science of microbiology.

y=10/(x+7)-5 Graph the function. State the domain and range.

The given function y = 10/(x+7)-5 is the same as:
y =10/(x+7)-5(x+7)/(x+7)
y=10/(x+7)-(5x+35)/(x+7)
y=(10-(5x+35))/(x+7)
y=(10-5x-35)/(x+7)
y = (-5x-25)/(x+7)
To be able to graph the rational function y = (-5x-25)/(x+7) , we solve for possible asymptotes.
Vertical asymptote exists at x=a that will satisfy D(x)=0 on a rational function f(x)= (N(x))/(D(x)) . To solve for the vertical asymptote, we equate the expression at denominator side to 0 and solve for x .
In y =(-5x-25)/(x+7) , the D(x)=x+7 .
Then, D(x) =0  will be:
x+7=0
x+7-7=0-7
x=-7
The vertical asymptote exists at x=-7 .
To determine the horizontal asymptote for a given function: f(x) = (ax^n+...)/(bx^m+...) , we follow the conditions:
when n lt m     horizontal asymptote: y=0
        n=m     horizontal asymptote: y =a/b
        ngtm       horizontal asymptote: NONE
In y =(-5x-25)/(x+7) , the leading terms are ax^n=-5x or -5x^1 and bx^m=x or 1x^1 . The values n =1 and m=1 satisfy the condition: n=m . Then, horizontal asymptote  exists at y=-5/1 or y =-5 .
To solve for possible y-intercept, we plug-in x=0 and solve for y .
y =(-5*0-25)/(0+7)
y =(-25)/7
y = -25/7 or -3.571  (approximated value)
Then, y-intercept is located at a point (0, -3.571) .
To solve for possible x-intercept, we plug-in y=0 and solve for x .
0 =(-5x-25)/(x+7)
0*(x+7) =(-5x-25)/(x+7)*(x+7)
0 =-5x-25
0+5x=-5x-25+5x
5x=-25
(5x)/5=(-25)/5
x=-5
Then, x-intercept is located at a point (-5,0).
Solve for additional points as needed to sketch the graph.
When x=3, the y = (-5*3-25)/(3+7)=-40/10=-4. point: (3,-4)
When  x=-6 , the y = (-5(-6)-25)/(-6+7)=5/1=5 . point: (-6,5)
When x=-9 , the y =(-5(-9)-25)/(-9+7)=20/(-2)=-10 . point: (-9,-10)
When x=-12 , the y = (-5(-12)-25)/(-12+7)=35/(-5)=-7 . point: (-12,-7)
 
As shown on the graph attached, the domain: (-oo, -7)uu(-7,oo) and range: (-oo,-5)uu(-5,oo) . 
The domain of the function is based on the possible values of x. The x=-7 excluded due to the vertical asymptote.
The range of the function is based on the possible values of y . The y=-5 is excluded due to the horizontal asymptote. 

What is the importance of doublethink to the Party's control of the citizens of Oceania?

Doublethink is a form of "reality control" in which people accept two ideas, even when these ideas are contradictory.  For the majority of the novel, for instance, Oceania is at war with Eurasia but, suddenly, during Hate Week, the Party declares that it is fighting against Eastasia and always has been.
You will notice from the text that nobody questions this sudden change, even though they can remember the war against Eurasia. This is why the Party is so successful in maintaining control: it manipulates the popular understanding and perception of the past and the people of Oceania willingly accept it because they have been brainwashed to do so. On a practical level, this means that the Party can do as it pleases, safe in the knowledge that nobody will ever question its actions. 
This is, perhaps, best summed up in the following quote from Emmanuel Goldstein from Part Two, Chapter Nine:

"For the secret of rulership is to combine a belief in one’s own infallibility with the power to learn from past mistakes."