College Algebra, Chapter 2, 2.4, Section 2.4, Problem 74

Jan and Krix leave Detroit at 2:00 PM and drive at a constant speed, traveling west. They pass Ann Arbor, $40 mi$ from Detroit at 2:50 PM.

a.) Express the distance traveled in terms of the time elapsed?

b.) Draw the graph of the equation in part (a).

c.) What is the slope of this line? What does it represent?



a.) Recall that $\displaystyle V = \frac{d}{t}$, so $d = Vt$


$
\begin{equation}
\begin{aligned}

d =& \frac{40 mi}{50 min} (t)
\\
\\
d =& \frac{4}{5} t

\end{aligned}
\end{equation}
$


b.)








c.) The slope of the line is $\displaystyle \frac{4}{5}$. It represents the constant speed that Jan and Krix exhibits.

What is meant by the expressions "rules of inheritance" and "gender bias"? How do they apply to The Lion, the Witch and the Wardrobe?

"Gender bias" refers to treating people unfairly because they belong to a certain gender; traditionally, women and girls are given less credibility than boys and men (though this type of bias is starting to change).
In The Lion, the Witch, and the Wardrobe, Lucy, the youngest child and a girl, finds Narnia first. After she returns from the magical world that she finds by passing through the wardrobe, the others hardly notice that she was missing. She tells her older siblings, a sister and two brothers, "But I've been away for hours and hours." Her older brother, Edmund, says, "Batty!" He then taps his head and says, "Quite batty." Her sister, Susan, says, "Don't be silly, Lucy.... We've only just come out of that room a moment ago, and you were there then." And Lucy's older brother, Peter, says, "She's not being silly at all...she's just making up a story for fun, aren't you, Lu? And why shouldn't she?" No one believes Lucy, perhaps in part because she is the youngest and a girl, and this situation makes Lucy quite miserable: 

"But Lucy was a very truthful girl and she knew that she was really in the right; and she could not bring herself to say this. The others who thought she was telling a lie, and a silly lie too, made her very unhappy."

Lucy lives in a state of misery because no one believes her, in part because of her gender and in part because of her age. Her siblings consider little girls prone to making up stories. Edmund then enters the wardrobe and sees that Narnia is a reality; only then does he believe Lucy. However, when he leaves Narnia, he lies and tells Susan and Peter that Lucy imagined Narnia to play a cruel trick on Lucy.
The "rules of inheritance" define who can inherit titles and property when someone dies. In The Lion, the Witch and the Wardrobe, the White Queen tells Edmund that she will bring him up to be a prince. She tells him:

"You are to be the Prince and--later on--the King; that is understood. But you must have courtiers and nobles. I will make your brother a Duke and your sisters Duchesses."

In reality, the Queen's election of Edmund to be king goes against traditional laws of inheritance, as the oldest boy, Peter, would be king before Edmund. According to traditional rules of inheritance, boys inherited the throne before girls did, which also shows gender bias.  

College Algebra, Chapter 4, 4.4, Section 4.4, Problem 10

Find all possible rational zeros of $U(x) = 12x^5 + 6x^3 - 2x - 8$ using the rational zeros theorem (don't check to see which actually are zeros).

By the rational zeros theorem, the rational zeros of $U$ are of the form


$
\begin{equation}
\begin{aligned}

\text{possible rational zero of } U =& \frac{\text{factor of constant term}}{\text{factor of leading coefficient}}
\\
\\
=& \frac{\text{factor of 8}}{\text{factor of 12}}

\end{aligned}
\end{equation}
$


The factors of $8$ are $\pm 1, \pm 2, \pm 4, \pm 8$ and the factors of $12$ are $\pm 1, \pm 2, \pm 3, \pm 4, \pm 6, \pm 12$. Thus, the possible rational zeros of $U$ are

$\displaystyle \pm \frac{1}{1}, \pm \frac{2}{1}, \pm \frac{4}{1}, \pm \frac{8}{1}, \pm \frac{1}{2}, \pm \frac{2}{2}, \pm \frac{4}{2}, \pm \frac{8}{2}, \pm \frac{1}{3}, \pm \frac{2}{3}, \pm \frac{4}{3}, \pm \frac{8}{3}, \pm \frac{1}{4}, \pm \frac{2}{4}, \pm \frac{4}{4}, \pm \frac{8}{4}, \pm \frac{1}{6}, \pm \frac{2}{6}, \pm \frac{4}{6}, \pm \frac{8}{6}, \pm \frac{1}{12}, \pm \frac{2}{12}, \pm \frac{4}{12}, \pm \frac{8}{12}$.

Simplifying the fractions and eliminating duplicates, we get

$\displaystyle \pm 1, \pm 2, \pm 4, \pm 8, \pm \frac{1}{2}, \pm \frac{1}{3}, \pm \frac{2}{3}, \pm \frac{4}{3}, \pm \frac{1}{4}, \pm \frac{1}{6}, \pm \frac{1}{12}$.

In "The Open Boat" by Stephen Crane, in which the conflict is man vs. nature, what do the men fear about nature?

The men most fear their own death by Nature, that it does not particularly concern Nature whether they live or die because Nature is going about its own processes and practices. In the first paragraph, for example, the narrator says,

The horizon narrowed and widened, dipped and rose, and at all times its edge was jagged with waves that seemed thrust up in points like rocks.

Nature is brutal. It rocks and jostles the men in the boat with waves that are described as being as treacherous as rocks. The connotation of words like "jagged" and "thrust" is violent and harsh, and this illustrates the men's fear of Nature. It is uncontrollable, and despite their best efforts, they really cannot do much to help themselves. It feels, to them, as though they ride in a "bath-tub" because they are so dwarfed by the sheer enormity and awesomeness of Nature, of the sea, of the waves that are "most wrongfully and barbarously abrupt and tall."
By the end, the correspondent thinks,

Perhaps an individual must consider his own death to be the final act of Nature.

One's death really is just another fact of Nature, just another thing that Nature accomplishes, like trees growing or waves crashing. Finally, the arbitrariness of the oiler's death seems to confirm the validity of this thought and the men's fear. He is the youngest, is in the best shape, and has worked the hardest in the boat to keep everyone alive, and yet he is the one who dies "face downward" in the water.

The story is told mainly through the point of view of the correspondent, who is presumably writing about the experience after the event. What he and the other three men fear is mainly the indifference of nature. Nature cares nothing about them, whether they live or die. If they manage to get through the surf and to the shore, that will be a matter of sheer luck. If the boat is swamped by a big wave and they all drown at sea, that will also be a matter of luck. Nature is infinitely more powerful than these four men. 
The little boat, lifted by each towering sea, and splashed viciously by the crests, made progress that in the absence of sea-weed was not apparent to those in her. She seemed just a wee thing wallowing, miraculously, top-up, at the mercy of five oceans. Occasionally, a great spread of water, like white flames, swarmed into her.
Stephen Crane's main point seems to be that there is no god who has any compassion for human beings. They have to look out for themselves as best they can in this pitiless universe. Crane's short story "The Open Boat" makes the reader feel the imminence of death and the cold, indifference of nature. The boat itself seems to symbolize the fragility of human life.

What three events took place as the story Tuck Everlasting began? What connected them?

Event number one is Mae Tuck beginning her travels to the small town of Treegap.  She only makes the trip once every ten years, and she makes the trip in order to meet her two sons, Miles and Jesse.  
Event number two is Winnie Foster losing her patience and deciding to think about running away.  
Event number three is a strange man arriving at the Foster's front yard.  He claims to be looking for somebody, and he won't elaborate.  
All three of those seemingly disconnected events are indeed connected.  The stranger turns out to be the man in the yellow suit, and he is looking for the Tuck family.  He suspects that they are immortal, and he wants to find out their secret.  The day after meeting the man in the yellow suit is the day that Winnie decides to give running away a small test run.  She goes in the forest, and she meets Jesse Tuck.  Mae Tuck arrives shortly after with Miles, and the three Tucks "kidnap" Winnie.  As the Tucks try to spirit themselves away, they pass the man in the yellow suit.  
I suppose if I had to pick a physical item or person from the story that connects all three events, I would pick the entire Tuck family.  The stranger wants to find this mysterious family, Winnie accidentally discovers the family, and the stranger follows Winnie and the escaping Tucks in order to learn their secret.  

What are the girls alleged to have been doing in the woods? What were they actually doing?

Abigail insistently tells her uncle, the Reverend Parris, that all she and the other girls did in the forest was dance. She says, "Uncle, we did dance, let you tell [the town] I confessed it—and I'll be whipped if I must be. But they're speakin' of witchcraft. Betty's not witched." Abigail knows what horrible trouble she and the other girls will be in if anyone finds out what they were really doing. This is why she threatens the others with a "pointy reckoning" in the middle of the night if they say a word. When Betty wakes up, she reveals that Abigail actually "drank a charm to kill John Proctor's wife." Further, Mrs. Putnam reveals to Reverend Parris that she sent her daughter, Ruth, to Parris's Barbadian slave, Tituba, to conjure the spirits of Mrs. Putnam's other dead children in order to find out who is responsible for their deaths. Despite the fact that "it is a formidable sin to conjure up the dead," as Parris says, Mrs. Putnam feels it is the only way she can find out who "murdered [her] babies." In addition, rumors are running rampant through the town regarding what the girls were doing, and people now assume that Parris's daughter, Betty, has been bewitched. Mrs. Putnam has heard Betty can fly, and she wants to know how high. She says that "Mr. Collins saw her goin' over Ingersoll's barn, and come down light as a bird [...]." Ultimately, there are quite a few different stories going around about what the girls were doing, and none of them seems to contain the full and total truth.

After Meursault arranged for his mother to live in a nursing home why did he visit her so infrequently?

Meursault's infrequent visits to see his mother show how little he has in common with others. He is alienated from other people, including his only family member. Simply put, there is no reason for his not visiting, but this lack of a reason permeates more than his relationships. From his perspective, to visit and not to visit may not seem so different. Meursault has few preferences and sees no reason for differentiating between things that might usually be considered obvious or common sense. This same absence of reason and indifference to social norms also make it impossible for Meursault to answer why he killed a man. The "best" answer might seem obvious to his lawyer, but like with the question of visiting his mother, Meursault is uninterested in attaching himself to any reasons. He is, instead, more focused on the awkwardness of the nursing home patients and the blinding light of the sun.

Meursault is a nihilist. This means that he doesn't believe in anything, be it God, love, or country. It is not surprising, then, that he is so emotionally detached from everyone, including both his girlfriend and his mother. It's not so much that he hates his mother; he simply can't feel anything for her, so utterly indifferent is he to every other human being.
Meursault's cold, unfeeling attitude towards his mother becomes an important element in his murder trial. It soon becomes clear that Meursault is not simply on trial for killing the Arab at the beach, he's also on trial for his nihilism and his total refusal to conform to society's norms and values. It is instructive that Meursault's lack of grief at his mother's funeral is cited as evidence of the threat he poses to society. In the trial it begs the question of what kind of man doesn't cry at the death of his own mother? It is also somewhat telling that Meursault's relationship with his mother is regarded as of greater cultural significance than his murder of the Arab, thus revealing the deeply ingrained racism in French colonial society.

College Algebra, Chapter 1, 1.4, Section 1.4, Problem 60

Find all solutions of the equation $x^2 + 2x + 2 = 0$ and express them in the form $a + bi$.


$
\begin{equation}
\begin{aligned}

x^2 + 2x + 2 =& 0
&& \text{Given}
\\
\\
x^2 + 2x =& -2
&& \text{Subtract } 2
\\
\\
x^2 + 2x + 1 =& -2 + 1
&& \text{Complete the square: add } \left( \frac{2}{2} \right)^2 = 1
\\
\\
(x + 1)^2 =& -1
&& \text{Perfect square}
\\
\\
x + 1 =& \pm \sqrt{-1}
&& \text{Take the square root}
\\
\\
x + 1 =& \pm \sqrt{i^2}
&& \text{Recall that } i^2 = -1
\\
\\
x + 1 =& \pm i
&& \text{Subtract } 1
\\
\\
x =& -1 \pm i
&&
\\
\\
(x + (1 + i))(x + (1 - i)) =& 0
&&

\end{aligned}
\end{equation}
$

How does sexuality play a role in the story?

As the story opens and Frances and Mike walk along, their conversation reveals that this married couple has been in bed together on Saturday night into late Sunday morning. Frances notices Mike looking at another woman and proposes they spend the day together instead of in the company of others. In the midst of her proposal and just after Frances has kissed his ear suggestively in public, Mike looks closely at another woman and notices that "she looked very solid and strong and her belly was flat, like a boy's, under her skirt, and her hips swung boldly because she was a dancer and also because she knew Michael was looking at her." The tacit exchange between Mike and the woman is purely physical, frankly sexual, and entirely fleeting.
Eventually, Mike and Frances speak honestly about his wandering eye. Mike admits "I can't help but look at them. I can't help but want them." He even confesses that he may one day act on his interest. Mike acknowledges that his objectification of women is based purely on their looks and his sexual desires, and this moment of devastating honesty does nothing to temper his appetite nor clear the air in a positive way with Frances.

What is the function of a computer?

While the uses and applications of computers and computer-based technology are nearly endless, the core functions of computers can be placed into four main categories. All of the categories revolve around some aspect of data.
Input—A computer receives and accepts data that is input by a user. More often than not, that is done with a keyboard and mouse, but it could also be done with webcams, other computers, and various data storage devices.  
Storage—A computer can store vast amounts of data in multiple formats.
Processing—This is probably one of the most important functions of a computer. Computers can take input data and process it to give a user the desired information or organization of that information.  
Output—This is the computer's ability to display processed information to a user. A computer can output information through its monitor, speakers, and/ or printer.  

How does Dolly Winthrop influence Eppie and make raising the child easier for Silas in George Eliot's Silas Marner?

Dolly Winthrop coaches Silas Marner on how to care for Eppie, and she strongly urges him to be sure the baby is baptized and receives religious instruction. Gently, she makes suggestions and allows Silas to care for the child on his own. In this way, Eppie will be his "little un" and no one else's.
Nevertheless, Dolly is adamant Silas have Eppie baptized, urging him to talk to Mr. Macey as soon as possible. She explains,

For if the child ever went anyways wrong, and you hadn't done your part by it, Master Marner—'noculation, and everything to save it from harm—it 'ud be a thorn i' your bed for ever o' this side the grave (Chapter XIII).

Silas Marner takes Dolly's advice to heart, and the baby is christened. To love another human being and share in her life provides Silas with a richness he never experienced with his gold. Further, as Eppie's mind grows, Silas's memory also grows.
One day, Dolly warns Silas not to spoil Eppie, but Silas cannot bring himself to make the "soft and safe places" of Eppie "tingle." Dolly suggests Silas put Eppie in the coal hole for a while. This form of punishment becomes ineffective because Eppie thinks the coal hole is fun. As a result, Silas uses patience instead of punishments to raise Eppie. Silas takes her with him when he delivers his linen, and he stops to chat with his customers, who discuss child-rearing with him. Eppie becomes all Silas's hope and joy, and, therefore, raising her is easy for him.

The ring structure of glucose indicates that it is a(an) A. monosaccharide B. disaccharide C. fatty acid D. nucleotide E. amino acid

Monosaccharides contain the elements carbon, hydrogen and oxygen, with twice as many H to O atoms. An example of a monosaccharide is glucose. Monosaccharides are the building blocks of more complex carbohydrates.
Two monosaccharides can join by a covalent bond called a glycosidic linkage to form a disaccharide. An example is sucrose, or table sugar which is formed when the monosaccharides glucose and fructose are chemically joined. When several monosaccharides join by glycosidic linkages, this forms large polymers called polysaccharides including starch and cellulose.
A diagram depicting a monosaccharide can show its carbon skeleton in a linear arrangement. However, in an aqueous solution, the carbon skeleton of sugar can form a ring.
The answer to your question is that the ring structure of glucose indicates that it is a monosaccharide or choice A. If it were a disaccharide, there would be two rings therefore it cannot be answer B. It cannot be choice C as a fatty acid is a long linear skeleton of carbon with mainly Hydrogen atoms attached. The nucleotide in choice D contains either the sugar ribose or deoxyribose attached to a phosphate group and to a nitrogenous base. It is more complex than just a single ring structure. For choice E, amino acids are building blocks of protein and are not found in a ring formation. 
I have included a diagram of glucose to illustrate why choice A is the correct response.
http://www.biotopics.co.uk/as/glucose2.html

Julius Caesar: Act 2 Vocabulary With the following vocabulary terms define the part of speech, give the definition, and use the word in a sentence. augmented ingrafted appertain visage emulation affability augurers

Augmented can be a past-tense verb or an adjective meaning "to add to something or make something greater" OR describing something as having been added to, or made greater. A very modern example can be found in the phrase "augmented reality," which is similar to virtual reality. To write a sentence containing this word, think of something that was made greater, in either size or value, by something else. Then it's a simple matter of writing "X was augmented by x" or "X augmented the experience of x."
Ingrafted is the past participial of the verb "engraft," which is synonymous with the far more commonly used word "graft." So "ingrafted" has the same meaning as the more common "grafted," which describes something that has been inserted or affixed to something else. For example, you've probably heard of skin grafts, a kind of surgery in which skin is transplanted/affixed to a different part of the body. To write a sentence containing this word, think of something you can describe as having attached to something else. For example, "the vines were ingrafted on the side of the building."
Appertain is a verb meaning "to relate, reference, or concern." "Appertaining" might also be synonymous with the phrase "In regards to." One example sentence might be, "I don't see how your story appertains to our conversation." Try to write your own using this same formula.
Visage is a noun meaning "face." In Julius Caesar, the word is used in the following context:

O, then by dayWhere wilt thou find a cavern dark enoughTo mask thy monstrous visage?

So, essentially, Brutus is asking how he will mask his hideous face. For your own sentence, simply try using the word visage where you would usually use the word "face."
Emulation is a noun and is defined as "an attempt to imitate a person or achievement." I'm sure you can think of celebrities who might be trying to emulate each other's careers. Pay attention to usage in your example sentence, as "to emulate" is a verb, while "emulation" is a noun, and your teacher has asked you to define the noun form. One example sentence would be, "Cardi B's emulation of Nicki Minaj has helped her to achieve success."
Affability is the noun form of the adjective "affable," which describes someone who is kind and easygoing. Think of a sentence in which you might use the word friendliness or gentleness (both of which are also noun forms of adjectives), and replace that word with affability instead.
Augurers is the most archaic word in this set that you've been asked to define, meaning that it does not have much modern usage. It is a plural noun that means "oracles," "prophets," or "fortune tellers." Your sample sentence might begin, "The augurers predict," and then finish with a fortune or prophecy.

Precalculus, Chapter 1, 1.3, Section 1.3, Problem 110

Find the equation of the line whose graph is given.







Based from the graph, the intercepts are $(-2,0)$ and $(0,-1)$. Using the formula for slope, $\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}$, we have



$\displaystyle m = \frac{-1-0}{0-(-2)} = \frac{-1}{2}$



The slope is $\displaystyle \frac{-1}{2}$. Now we use point slope form to find the equation




$
\begin{equation}
\begin{aligned}

y - y_1 =& m(x - x_1)
&& \text{Point Slope Form}
\\
y - 0 =& \frac{-1}{2} [x - (-2)]
&& \text{Substitute } m = \frac{-1}{2}, x = -2 \text{ and } y = 0
\\
y =& \frac{-1}{2} x - 1
&& \text{Slope Intercept Form}
\\
\text{or} &
&&
\\
\frac{1}{2} x + y =& -1
&& \text{General Form}

\end{aligned}
\end{equation}
$

A Midsummer Night's Dream- Shakespeare This play focuses on the power of imagination and its ability to overcome, fix, redeem, forgive, love, and write. Find three examples of how imagination either functions or is imagined to function inside the play. Think not only about statements made by Theseus and Puck but about the play produced by the rude mechanicals, Bottom’s experience, the lovers spats, the role of drama, and so on.

This assignment is designed to get students to think about Shakespeare's A Midsummer Night's Dream thematically, which means that as you work on developing your own answer to it. Rather than simply summarizing the play, you are being asked to pull together what the play is saying about how dreaming and imagination affect characters. 
The starting point for such a thematic analysis is actually the very end of the play in which Puck offers the following disclaimer:

Think but this, and all is mended,
That you have but slumber'd here . . .
And this weak and idle theme,
No more yielding but a dream . . .

As you write an essay in response to this prompt, you might want to assert that Puck (and Shakespeare himself) is being disingenuous in disclaiming the power of the imagination. In fact, it is the imagination of the characters (and of people in general) and their ability to picture things as other than they actually are that allows change. 
First, you might discuss the two young lovers. Their problems are straightforward. Hermia loves Lysander but her father wants her to marry Demetrius. Helena loves Demetrius, who is engaged to Hermia. The young women are close friends and this love issue is affecting their friendship. The efforts of the young lovers to straighten out these problems fail in the real world. They are only resolved in the dream world of the forest through the intervention of the fairies, which are imaginary creatures.
The play within the play of the mechanicals about Pyramus and Thisbe also shows the effect of imagination on love. The key element of the plot is that Pyramus's imagining the death of Thisbe to the lion has the real effect of causing him to commit suicide and his suicide causes Thisbe eventually to kill herself. In other words, the death of the two lovers is caused by their imaginations. 
Thus as you work on writing your essay, you should look at how the imagination has real effects within the narrative of the play, leading to positive or negative outcomes for lovers. Finally, you might conclude with returning to Puck's speech and mentioning yet another reality, that of Shakespeare, whose imagination, as it "bodies forth / The forms of things unknown" actually earns real money for him, turning him into a wealthy man. The playgoers spend real money to attend the play, spend real time watching it, and contribute to real salaries for real members of Shakespeare's company.

What is the last thing that Helen Keller remembers before her illness?

It is not precisely clear what is the last thing Keller remembered before her illness. After being ill, she remembers the light getting dimmer and dimmer before going out altogether. Most importantly, however, before getting sick, Helen learned and remembered the word for water. After her illness left her blind and deaf, she would still say the word "wah-wah." As she expresses it:

Even after my illness I remembered one of the words I had learned in these early months. It was the word "water," and I continued to make some sound for that word after all other speech was lost.

It's difficult not to imagine that some dim memory of the word "water" helped trigger her years later to make the connection between the water from the pump running on her hands and the word water Miss Sullivan was writing in her palm, unlocking for Keller the key to language and knowledge.
Since Keller lost her capacity to see and hear at nineteen months, the fleeting sensory memories of seeing and hearing occurred very early in her life. One has to think that in a child whose development is not interrupted, those early memories are obscured by the rush of sensations the toddler continues to experience while learning language. Helen Keller had only a few scraps of those sensations to cling to, but they were helpful to her.

In Iraq, how could the standard of living improve while maintaining good relations with their neighbors and the world community? How can Iraq maximize profits for exports, minimize costs for imports while using environmentally sound practices?

There is no secret to improving the standard of living of the population of Iraq. Ethnic and religious enmities have to be put aside in favor of stabilizing the country politically so that the nation's economy can grow, and there must be a political system free of the kind of corruption endemic to much of the more recently decolonized world.
For many decades, until the U.S. invasion in 2003, Iraq was ruled by the country's minority Sunni population. The majority Shi'a were repressed while their resources were used by the ruling regimes to benefit the Sunni minority. In the meantime, the Kurdish population in the north, as with the Kurdish populations in neighboring Syria, Iran and Turkey, sought independence from Arab dominance. In addition, Iraqi society is riven with tribal and clan rivalries that were largely kept under control when the late and enormously brutal dictator Saddam Hussein was in power.
The invasion of Iraq by the United States removed Saddam Hussein, his family (his two sons were notoriously sadistic), and his tribe from power and attempted to replace it with a democratic system. Democracy in a country in which the majority of people have been repressed by a hostile religious minority (the Sunni-Shi'a divide is the cause of enormous bloodshed throughout much of the Muslim world) may seem like a good idea, but in Iraq it did not work as hoped. Suddenly in power, the majority Shi'a sought to marginalize the now-defeated Sunnis, and the result was civil war, with the added complication of the growth of terrorist organizations like al Qaeda and, now, the Islamic State.
All of this history is given because, when discussing a subject like the standard of living in Iraq, it would folly to pretend that all of these problems did not exist. They do exist, and, until at least some of them are resolved, improving the life of the average Iraqi citizen will remain problematic. This is not to say that there have not been improvements in some areas. The economically (due to vast oil deposits and refining and shipping assets) vital southern region of Iraq has enjoyed some stability, which has allowed for economic growth, which has improved the standard of living for many people. In the north, under the protection of the United States since the 1991 conflict (the United States drove Iraqi military forces out of Kuwait, which it had invaded), the Kurdish population has enjoyed considerable autonomy and, with it, economic growth, peace and stability.
The Kurdish model is important in the context of improved standards of living in at least portions of Iraq. Because Iraqi Kurdistan has been largely peaceful, the Kurdish population there was able to establish functioning political and economic systems. That is the key to Iraq as a whole. It must have political stability provided by a government that enjoys legitimacy among the entirety of the population. It must have an economy open to foreign investment, and it must be as free from corruption as possible. Then, Iraq can better exploit its vast oil and gas reserves, as well as diversify its economy so that it is less dependent upon frequently volatile oil prices.
The key to minimizing costs for imports while maximizing profits from exports, once the above conditions are met, involves establishment of free trade agreements among other nations. If one uses Singapore as a model, enormous economic growth can result from a free trade system free of corruption. If incoming goods are not taxed via tariffs, and if outgoing goods are competitive in terms of quality and price, then the objectives should be met, with the concomitant growth in gross domestic product such practices usually achieve. The key, then, is equitable distribution of revenue and a practical utilization of that revenue for the common good, as in infrastructure improvements.

Why do we remember Gary Paulsen?

I believe that Gary Paulsen is a well-remembered author because he wrote the book Hatchet and its sequels. That book is almost universally loved by younger students. In that book, Paulsen was able to find a lot of relatable common ground with his readers. He has a young protagonist that is under a tremendous amount of emotional turmoil from the very beginning of the book. His parents are no longer together, and many modern readers can relate to that on a personal level.
Paulsen then quickly brings Brian into immediate physical danger through a plane crash in the middle of nowhere. Putting Brian in this kind of survival situation is relatable because most readers have been camping at least once in their lives. Most of my students also admit to having been lost from their parents at one time or another. It might have been for only five minutes, but the experience is almost always traumatic. Paulsen takes that fear and pairs it with the knowledge of camping.
I think the other reason that Paulsen and his books are remembered so well is because he mixes real-world science into the narrative. Whenever I have to teach about light refraction and water, there is always a student that comments on Brian having to adjust for the light bend in order to spear the fish. Paulsen explained a physics concept in a way that makes realistic sense to a ten-year-old. That makes a deep impact on a reader.
Finally, I think Paulsen is remember by many readers because he is a prolific writer. He has written more than two hundred books.

Gary Paulsen is one of the premier writers of young adult literature. During the 1980s and 90s, young adult literature was starting to split into its own category separate from children's and adult literature. For most of the 20th century, young adults were either directed to children's or adult literature with very little appropriate for them outside of classroom readers. Gary Paulsen is part of a group of writers that brought young adult literature into a respectable and available genre with writers such as Natalie Babbitt, Chris Crutcher, and S.E. Hinton.
Paulsen's novels include:
Hatchet: A thirteen-year-old boy must survive in the wilderness following a plane crash and deal with his parents' recent divorce.
Brian's Winter: A sequel to Hatchet.
Dogsong: On a thousand mile journey on dogsled through the arctic tundra, an Inuit boy seeks to find himself while struggling with tradition and modernity.
The River: This book also follows Brian, of Hatchet, as psychologists task him to recreate a similar survival situation to study the effects that wilderness survivalism has on a person's psychology.
Aside from these books, Paulsen has written more than 200 books and won the Margaret Edmunds award from the American Library Association for his contributions in young adult literature. Paulsen has also won the Newbery Award three times for The Winter Room, Hatchet, and Dogsong.
Also, Gary Paulsen is still alive and writing at 78 years old, so we don't need to remember him yet.

Look at the words in the following three phrases and transcribe all the underlined sounds. How many different pronunciations do you end up with? a). ( ough). ' a rough- coated dough-faced ploughman' b) (th). ' don't bother both your brothers' c) (o) ' to do and to go '

This is an interesting language learning assignment. English is strange in that the same series of letters can represent different phonemes (language sounds). In the case of a), you end up with three different sounds from the same four letters. "Ough" can sound like "uff", "oh", and "ow", respectively.
The phonemes associated with "th" in phrase b) include both a hard and soft sound, with the soft "th" letting through a bit more air between the tongue and top teeth. The words "bother" and "brothers" have the harder consonant blend, and the word "both" has the more aspirated sound.
In phrase c), you again have two different phonemes derived from the letter "o". In the words "to", "do", and the second "to", the phoneme is "oo". In the word "go", the phoneme is "oh".
This can be very hard to figure out without hearing a real person say the words. The Cambridge Dictionary website (as well as many other dictionary websites) has a small red speaker icon next to the definitions of words that will play the correct pronunciation of that word when pressed. I've included the link below.
https://dictionary.cambridge.org/us/dictionary/

Why do people toast the Boy Who Lived?

In the first volume of this series, we are able to see back to the beginning of Harry Potter's life among muggles (non-magical people). For his safety, he is placed with his muggle relatives by leaders in the magical community at Hogwarts. The book mentions that, at this time, "people meeting in secret all over the country were holding up their glasses and saying in hushed voices: 'To Harry Potter—the boy who lived!'" This is because the infant Harry Potter recently survived an attack by Voldemort, one of the most powerful and sinister wizards in the world at the time. Harry's parents, along with scores of other witches and wizards, were killed by Voldemort. Yet Harry survived and in fact injured Voldemort in some way.
We understand from the story that Voldemort has been accruing followers and power, with dark, murderous intentions. He is a force to be reckoned with and poses a terrible threat to innocent people, magical and muggle alike. The fact that a baby was able to thwart his seemingly unprecedented power gives people hope that Voldemort is conquerable—that there are means that may be used to defeat him. People "all over the country" toast Harry and his survival because it shows there is hope for regaining peace in the midst of Voldemort's campaign of murder and chaos. 

The initial velocity is 0 km/hr , the final velocity is 24 km/hr and the time is 3 s what is the acceleration?

Take note that acceleration is the rate of change of velocity with respect to time. So to solve it, take the difference between the initial and final velocity. Then, divide it by time it took for the velocity to change from its initial to final value.
a= (Delta v)/(Delta t)
a= (v_f - v_i)/(Delta t)
a=(24 (km)/(hr) - 0(km)/(hr))/(3s)
a= (24 (km)/(hr))/(3s)
In order for the unit to be consistent, change the time from seconds to hours.
a= (24 (km)/(hr))/(3s* (1hr)/(3600s))
a= (24 (km)/(hr))/(1/1200hr)
a = 28 800 (km)/(hr^2)
Therefore, the acceleration is 28800 km//hr^2 .

How does the scaffold in The Scarlet Letter bring greater meaning to the message, and does how the symbol further Hawthorne's purpose?

Hawthorne's employment of the three scaffold scenes in The Scarlet Letter is a brilliant structuring device; it not only frames the narrative, but it also directs the readers' attention to the essential themes of the novel. This symbol furthers Hawthorne's purpose, as it incites feelings of isolation in the characters.
In all three of the scaffold scenes, the main characters are present, but their arrangement concerning the scaffold differs. These arrangements are significant in meaning and in developing themes.
In the first scaffold scene, before a condemning crowd, Hester stands alone in her ignominy with the scarlet letter on her breast and her living symbol of her sin, Pearl, clutched to this breast. Accosted with the harsh Puritan judgments of the crowd, such as the woman who declares that she has "brought shame upon us all, and ought to die" (Ch.2), Hester is isolated from society. Nevertheless, she courageously bears her isolation. This illustrates the theme of conflict between individual and society.
In the second scaffold scene, which is in the middle of the novel and is seven years after the first scene, the Reverend Arthur Dimmesdale stands alone on the scaffold in the dark of night. Tortured by his guilt and remorse that he lacked the courage to confess his sin years ago, he stands on the scaffold to admit to God his sin. When Hester and Pearl approach on their way home from the governor's mansion, the minister asks them to join him on the scaffold. 

"Come up hither, Hester, thou and Little Pearl. . . . Ye have both been here before, but I was not with you. Come up hither once again, and we will stand all three together." (Ch.12)

But when Pearl asks the minister if he will stand with her mother and her tomorrow, the minister replies, "Nay; not so, my little Pearl. . . . I shall, indeed, stand with thy mother and thee one other day, but not to-morrow!" (Ch.12) Ironically, the minister implies Judgment Day, but he does, in fact, stand with them one day before the Puritan community. Lurking in the shadows is Roger Chillingworth who acts as physician to the minister, and only Hester realizes that Chillingworth means to harm him. However, the minister "yields himself to the physician." (Ch.12) The theme represented here is ambiguity—some know of Dimmesdale's guilt while others do not.
In the third scaffold scene, there are parallels to that of the first scene. The townspeople meet in the marketplace and Hester is again rejected by "her fellow-creatures" while Reverend Dimmesdale is still revered as a saint. However, before he dies, Dimmesdale feels that he must confess. He calls Hester and Pearl up to the scaffold on which he has taken a position. At that moment old Chillingworth hurries forward to "snatch back his victim from what he sought to do." But the minister repulses him.

"Ha, tempter! Methinks thou art too late! . . . Thy power is not what it was! With God's help, I shall escape thee now!" (Ch.23)

Hester helps the minister ascend the steps to the scaffold with Pearl's hand clasped in his. Chillingworth knows that his victim has escaped him. For the minister confesses his sin and reveals the imprint of "the ghastly miracle" upon his chest, stunning the crowd. He asks Pearl if now she will kiss him since he has confessed and she does. Then the minister dies his "death of triumphant ignominy before the people."(Ch.23) This scene furthers the themes of innocence, guilt, and sin.

One of the messages with which Hawthorne leaves readers comes in the final chapter of the book, "Conclusion." The narrator says, "'Be true! Be true! Be true! Show freely to the world, if not your worst, yet some trait whereby the worst may be inferred!'" In other words, then, we are all sinners—something else the narrator claims in this chapter—and we have a duty to be honest about that sinfulness. When we try to pretend as though we are without sin, we run the risk of committing further sin, as Dimmesdale does.
When he cannot admit his sinfulness, and stand on the scaffold with Hester, he adds sin on top of sin. When the other women in the town judge her—saying that the letter should be branded on her forehead or that she should be executed for what she's done—they add new sin on top of old.
The scaffold is the symbol of the admittance of sinfulness, and if everyone in the town were honest, they'd have to accept their own place on it. Instead, they lie to cover up their own sinful natures—a nature that each person shares with everyone else.

At the beginning of The Scarlet Letter, Hester Prynne and her illegitimate child, Pearl, stand on the scaffold in Boston so they can be public objects of scorn. Hawthorne writes, "The very ideal of ignominy was embodied and made manifest in this contrivance of wood and iron" (33). In other words, the scaffold is meant to shame people because it holds the gaze of the person on the scaffold forward so the offender's eyes must meet the crowd's. The scaffold enhances the idea that Hester and her child are outcasts, as they are held aloft from everyone else as sinners. 
At the end of the book, as the Reverend Dimmesdale is dying, he asks Hester and Pearl to help him ascend the scaffold, which he once feared. Hawthorne writes that as Dimmesdale ascends the scaffold, the crowd would not have thought it strange "had he ascended before their eyes . . . fading at last into the light of heaven" (140). Dimmesdale sacrifices himself on his death bed by telling the truth—that he is Pearl's father and a sinner—and the scaffold at this point acquires a symbolism that is similar to the cross on which Jesus Christ was crucified. Hawthorne's message is that Hester, Pearl, and Dimmesdale are saintly, while the crowd that crucified them is evil. The striking symbol of the cross reinforces Hawthorne's message that in Puritan society, those who are outcasts are truly saints while those who cast them out are sinners. 

Why would Beatty make Montag burn his own house?

Beatty wants to punish Montag for the transgression of owning books. As he says to Montag when they arrive at his house and the firemen start breaking windows as a prelude to burning it,

"For everyone nowadays knows, absolutely is certain, that nothing will ever happen to me. Others die, I go on. There are no consequences and no responsibilities. Except that there are. But let's not talk about them, eh? By the time the consequences catch up with you, it's too late, isn't it, Montag?"

Beatty feels he has given Montag chances to reform and that Montag has not taken them. Beatty is a smart, angry man who has a sadistic streak, and he wants to rub in Montag's face the fact that a fireman is not allowed to own books. He therefore mocks and jeers at Montag, trying to show him the futility and powerlessness of his frail paper volumes against the destructive force of the fireman's flames.
Beatty's sadism—his desire to punish Montag and make him suffer acutely—comes out when he says to Montag,

"I want you to do this job all by your lonesome, Montag. Not with kerosene and a match, but piecework, with a flamethrower. Your house, your clean-up."

Montag ultimately decides that Beatty provoked him by arming him with a flamethrower and having him burn his house because Beatty had a death wish and hoped for Montag to kill him:

Beatty had wanted to die. He had just stood there, not really trying to save himself, just stood there, joking, needling, thought Montag . . .

Toward the beginning of the novel, Captain Beatty informs Montag that firemen are allowed to possess a book for twenty-four hours before they burn it on their own. However, if the fireman does not burn the book after twenty-four hours, the firemen are called to burn it for him. The policy of having the curious fireman burn the book himself indicates that the fireman has eradicated his intellectual pursuits and fully supports the government institution. Likewise, Captain Beatty wants Montag to burn his own house as a gesture of Montag's compliance and acceptance of the government's stance on censoring books. Captain Beatty might also want Montag to destroy his own house because of the psychological impact it would have on Montag. By burning his own home, Montag is acknowledging that he alone was the cause of the destruction, initially by reading novels and then by actually torching his home.

What are some adjectives to describe Raymond from Raymond's Run?

Squeaky's intellectually disabled older brother, Raymond, is depicted as an enthusiastic boy. He has a lively personality and follows his sister wherever she goes. Squeaky mentions that she has to keep an eye on him at all times and makes sure that he walks on the inside of the sidewalks—he has a tendency to run out into traffic or act like he is a circus performer on the curb. Raymond's behaviors during his walks with Squeaky depict him as a reckless, spontaneous person. Raymond is also portrayed as an imaginative, carefree boy who does not worry about obeying rules and just focuses on enjoying himself. The fact that Squeaky must constantly supervise and protect her brother illustrates that he is a dependent person who relies on his sister's help. Raymond's ability to keep pace with Squeaky while she is training and racing indicate that he is also athletic and energetic, which influences her decision to help him train.

Squeaky refers to her older brother, Raymond, as "not quite right," which could probably be referred to as developmental disabled. His disability does not define him, though; he has many other attributes. Another adjective to describe Raymond is imaginative, as he likes to picture himself as a circus performer. He is sometimes messy because he likes to slosh around in the gutter, and these actions mean he is also playful. Sometimes, he is also impulsive, as he likes to dash into the middle of Broadway and scare the pigeons. Raymond can be immature at times, as he still likes to play on the swings. Raymond is also more competitive and athletic than his sister, Squeaky, realizes, as he imitates her and runs the May Day race along with her.

How can you put Martin Luther King's "I Have a Dream" speech into perspective with the Declaration of Independence?

These two documents are among the most famous (and arguably the best) expressions of the ideals of American liberty. Perhaps the best way to put the speech into perspective with respect to the Declaration of Independence is to consider the ways that King himself references the Declaration. Early in the speech, King observes that the United States was founded on an ideal of liberty that can be traced to the Declaration and the Constitution. He compares these documents to a "promissory note":

When the architects of our republic wrote the magnificent words of the Constitution and the Declaration of Independence, they were signing a promissory note to which every American was to fall heir. This note was the promise that all men, yes, black men as white men, would be guaranteed the unalienable rights of life, liberty, and the pursuit of happiness.

Unfortunately, King says, the nation has "defaulted" on this "promissory note" inasmuch as it has denied the rights to life, liberty, and the pursuit of happiness to its African American citizens. King frames the civil rights movement as an attempt to "cash the check" that was made out to all American citizens. In other words, he calls on the United States to make good on the promises it made in its founding documents and to live up to its ideals. In the most famous (extemporaneous) section of his speech, he says that his "dream" is that the nation will "rise up and live out the true meaning of its creed" that "all men are created equal." So aside from King's astonishing oratorical skills, the famous "I Have a Dream" speech is in many ways remarkable for its insistence that the nation live up to the ideals its founders claimed as its basis.
https://teachingamericanhistory.org/library/document/i-have-a-dream/

Why did the Americans think it was a good idea to invite the Japanese to a neutral island and demonstrate the power of the atomic bomb?

That's an interesting question! Due to the toll in human lives, the Allied powers were desperate to end the war as quickly as possible. At the time, the Japanese military had perpetrated atrocities all across Asia, with no end in sight. I won't go into Japanese war crimes in my answer, but perhaps you may be interested in the links below:
Japanese War Crimes from the United States Inter-agency Working Group (IWG)
Statistics of Japanese Democide
Here is a A Cross-Section of Japanese War Crimes, including the Bataan Death March, The Bangka Island Massacre of Australian army nurses, the murder and cannibalism of American pilots, and similar other crimes.
The scientists who worked on the atomic bomb believed that a bomb demonstration on a deserted island could convince Japan to surrender. So, why were they opposed to immediately dropping the bombs on a Japanese city? First, some feared that the atomic bomb would fail to do enough damage and would further embolden Japan in its imperialistic ambitions. Also, the scientists feared that the use of nuclear weapons could set off an arms race and result in the threat of a future nuclear war.
So, these are the two main reasons for why some experts wanted a bomb demonstration. Despite their recommendations, the Scientific Panel that advised the United States Secretary of War made two opposing recommendations:
1) That the United States should not perform a bomb demonstration for the United Nations. Instead, it should quietly inform its allies about its intentions to use the weapon.
2) Since the panel could not propose any other way of ending the war, they concluded that there was "no acceptable alternative... [other than] direct military use" of the atomic bomb.
In the end, the atomic bombs were used, first on Hiroshima, then on Nagasaki days later.
For more, please refer to the links provided.
https://thebulletin.org/2016/08/why-the-united-states-did-not-demonstrate-the-bombs-power-ahead-of-hiroshima/

https://www.nps.gov/articles/trumanatomicbomb.htm

What is the resolution?

This answer is not as straightforward as I would like it to be. The resolution depends on which version of the text that you are asking about. The original text of Hiroshima has four chapters. Hersey added chapter five 40 years later, and it briefly explores the six characters’ lives in the years after the bomb. Some of the characters do quite well, while others have long standing health issues as a result of radiation sickness.
If we are looking at Hersey's original text, the resolution is a bit more open-ended. Readers are told that each of the six characters are attempting to get on the road to recovery. It is a difficult road, fraught with health concerns and the deaths of friends and family members. Near the end of the chapter, readers get a paragraph that tells us that a year has passed since the bomb has dropped. Its opening sentence is a good resolution summary. The main characters have indeed survived the bomb, but their lives have been utterly destroyed.

A year after the bomb was dropped, Miss Sasaki was a cripple; Mrs. Nakamura was destitute; Father Kleinsorge was back in the hospital; Dr. Sasaki was not capable of the work he once could do; Dr. Fuji had lost the thirty-room hospital it took him many years to acquire, and had no prospects of rebuilding it; Mr. Tanimoto’s church had been ruined and he no longer had his exceptional vitality.

How would you describe the Garden of Death in "The Canterville Ghost" by Oscar Wilde?

The Garden of Death is featured in Chapter Five of "The Canterville Ghost," when the ghost tells Virginia Otis of his strong desire to leave Canterville Chase and to sleep forever. 
Though the ghost has not been to the Garden, he has a strong impression of its appearance and atmosphere. It exists beyond the "pine-woods," for example, and is guarded by a "yew tree" which protects the sleepers with its long branches. Inside, the grass is "long and deep" and the earth is "soft" and "brown." The Garden is also decorated with "hemlock flower" and filled with the sound of the nightingale's song.
According to the ghost, there is no sense of time nor place inside the Garden. Furthermore, there exists no today nor tomorrow; no life nor death. The Garden is simply a place of peace where the dead can sleep forever, without fear of ever being disturbed.

Single Variable Calculus, Chapter 2, 2.3, Section 2.3, Problem 10

a.) Determine what is wrong in the equation $\displaystyle \frac{x^2+x-6}{x-2} = x+3$

The function in the left side is defined for all values of $x$ except for $x=2$. However, the function on the right side is
on every values of $x$

b.) Prove that the equations $\lim\limits_{x \rightarrow 2} \displaystyle \frac{x^2+x-6}{x-2} = \lim\limits_{x \rightarrow 2} (x+3)$ is correct.


$
\begin{equation}
\begin{aligned}
\lim\limits_{x \rightarrow 2} \displaystyle \frac{x^2+x-6}{x-2} & = \lim\limits_{x \rightarrow 2} \displaystyle \frac{(x+3)\cancel{(x-2)}}{\cancel{x-2}} & & \text{(By Factoring)}\\
\lim\limits_{x \rightarrow 2} \displaystyle \frac{x^2+x-6}{x-2} & = \lim\limits_{x \rightarrow 2} \displaystyle (x+3)
\end{aligned}
\end{equation}
$

How old is India?

The answer to this question depends on what you mean by India. Geologically speaking, the Indian Craton formed when it broke away from Pangea during the Jurassic Period about 160 million years ago and then separated from Gondwana 125 million years ago.
The first human inhabitants of what is now India arrived around about 75,000 years ago, although this claim has been disputed. Concrete archaeological evidence suggests that humans certainly were in the region as early as 30,000 years ago. These were likely migratory stone age hunter-gatherers. The earliest known permanent settlements date to about 9,000 years ago at the Bhimbetka rock shelters, which feature some of the best preserved cave paintings of the period.
Around 2500 BCE, the first civilizations were founded there with the establishment of the Indus River Civilization. This civilization built some of the earliest known cities in the world. It thrived until around the end of the Bronze Age around 1500 BCE.
The modern state of India dates to 1947 when India won its independence from Great Britain. It was partitioned that year into the two independent states of India and Pakistan (Pakistan was later partitioned into the two nations of Bangladesh and Pakistan).

Archeologists have found human remains in India dating back to approximately 30,000 years ago.  In that time, India was not an established country.  Rather, various groups of people settled in or traveled through the area that is now India.
The Indus Valley Civilization was established during the Bronze Age.  It was located in western India, and also in Pakistan.  Hinduism and the caste system were established around 500 BC.  In the centuries that followed, various empires and kingdoms ruled the region.  The name India was first used by Lucian around 200 AD.  The word was derived from "Indus."
India was a colony of Great Britain for many years.  The nation of India gained its independence from Britain in 1947, two years after the end of World War II.  The official name of the nation is the Republic of India.
 

Why doesn't Fortunato want the narrator to go to Luchesi?

Fortunato does not want Montresor, the narrator, to go to Luchesi to get an evaluation of the rare cask of Amontillado for a couple of reasons. First of all, it is reasonable to assume that Fortunato possesses quite a lot of arrogance regarding his own abilities as a connoisseur of wine. He clearly considers himself superior to Luchesi in this regard, as he asserts that "Luchesi knows nothing about wines, nothing at all." Therefore, one reason that Fortunato doesn't want the narrator to ask Luchesi about the Amontillado is that it feeds his ego to be the arbiter of the sherry's quality.
Another reason Fortunato doesn't want Montresor to ask Luchesi to taste the Amontillado is because, as the narrator observes, Fortunato "liked to drink good wine." It is reasonable to assume, then, that Fortunato really would like to drink a first-rate sherry and doesn't want to pass up this rare opportunity.

Fortunato says that he does not want Montresor, the narrator, to go to the other wine expert in town, Luchesi, because "Luchesi cannot tell Amontillado from Sherry." In other words, then, Fortunato says that Luchesi's expertise in wine is not as good as his own. This is why he says he does not want Montresor to go and request help from Luchesi.  
However, Montresor knows that Fortunato will not be able to resist gloating over Montresor's having been tricked into purchasing a great quantity of wine that cannot possibly be the rare amontillado. Even now, Fortunato says, "You have been imposed upon." Fortunato is sure that Montresor has been taken advantage of, and Montresor knows that Fortunato's pride in his connoisseurship in wine is his one "weak point." Fortunato's pride will compel him to follow Montresor into his niter-encrusted vaults, despite his bad cold and cough, so that he can revel in both his own discernment as well as Montresor's bad judgment.

Calculus of a Single Variable, Chapter 7, 7.2, Section 7.2, Problem 25

For the region bounded by y=1/x ,y=0 , x=1 and x=3 and revolved about the x-axis, we may apply Disk method. For the Disk method, we consider a perpendicular rectangular strip with the axis of revolution.
As shown on the attached image, the thickness of the rectangular strip is "dx" with a vertical orientation perpendicular to the x-axis (axis of revolution).
We follow the formula for the Disk method:V = int_a^b A(x) dx where disk base area is A= pi r^2 with.
Note: r = length of the rectangular strip. We may apply r = y_(above)-y_(below).
Then r = f(x)= 1/x-0
r =1/x
The boundary values of x is a=1 to b=3 .
Plug-in the f(x) and the boundary values to integral formula, we get:
V = int_1^3 pi (1/x)^2 dx
V = int_1^3 pi 1/x^2 dx
Apply basic integration property: intc*f(x) dx = c int f(x) dx .
V = pi int_1^3 1/x^2 dx
Apply Law of Exponent: 1/x^n =x^(-n) and Power rule for integration: int x^n dy= x^(n+1)/(n+1) .
V = pi int_1^3 x^(-2) dx
V = pi*x^((-2+1))/((-2+1)) |_1^3
V = pi*x^(-1)/(-1) |_1^3
V = pi*-1/x |_1^3 or -pi/x|_1^3
Apply definite integration formula: int_a^b f(y) dy= F(b)-F(a) .
V = (-pi/3) - (-pi/1)
V = -pi/3+pi
V = 2pi/3

According to line 2, with what activities are people preoccupied?

William Wordsworth's "The World Is Too Much With Us" laments the disconnect between humanity and the natural world that surrounds it. The poem begins in the following way:

The world is too much with us; late and soon, Getting and spending, we lay waste our powers;— Little we see in Nature that is ours; We have given our hearts away, a sordid boon!

Line two focuses on two related ideas: "Getting and spending" and "lay[ing] waste our powers." While one can make an educated guess that "getting and spending" refer to aspects of materialism within society, the third and fourth lines help to clarify this. Wordsworth expands by saying that there is "little in Nature that is ours," thus adding another level to our obsession with material goods. The idea of possession and ownership is central to the "[g]etting and spending" established on line two, but line three expands to show that our misdirected obsession with owning is such that nature—something that people should feel a connection to—has been rejected and replaced with a desire for material goods. Due to all of the getting, spending, and rejecting of nature, "we lay waste our powers," meaning that we sacrifice the good that we are capable of, all in the name of ownership of things.

Who is Jonas?

In The Giver, Jonas is the protagonist. In the beginning of the story, Jonas is anticipating the Ceremony of Twelve, during which time the Committee of Elders will determine Jonas's assignment. After studying and observing Jonas, they will determine how Jonas can best serve his community. Jonas is careful with his language, thoughtful, brave, and possesses some characteristics that many others do not. For example, while most in his community have dark eyes, Jonas has light eyes. Jonas also discovers that he can see in color, which is a unique gift because most in his community do not see color.
At his Ceremony of Twelve, it is announced by one of the Elders that Jonas is chosen to be the Receiver of Memory. The Elder shares that the Receiver of Memory must have three qualities: intelligence, integrity, and courage. In addition to these qualities, Jonas has the "Capacity to See Beyond."

Jonas is the protagonist in the novel The Giver. He is a perceptive eleven-year-old boy who is chosen to be the Receiver of Memory for his community when he turns twelve. At the start of the novel, he is empathetic; but after his training, his empathetic nature is further developed into strong emotional intelligence. He cares about people and becomes highly aware of the suffering of those around him.

Who are the antagonists and protagonists in "The Adventure of the Speckled Band"?

Sherlock Holmes is usually considered the protagonist in any of his stories. Helen Stoner comes to him for help because she fears her life is in danger. The prime suspect is her stepfather Dr. Grimesby Roylott. The author, Sir Arthur Conan Doyle, has Dr. Roylott put in an appearance at 221B Baker Street shortly after Helen leaves. This meeting between Holmes and Roylott is necessary to establish that Dr. Roylott is Holmes' opponent, or the antagonist. The violent and half-mad Roylott establishes the conflict during his short appearance at Holmes' residence.

“I will go when I have said my say. Don't you dare to meddle with my affairs. I know that Miss Stoner has been here. I traced her! I am a dangerous man to fall foul of! See here.” He stepped swiftly forward, seized the poker, and bent it into a curve with his huge brown hands.

Dr. Roylott does not appear in the story again until after he has been bitten by his own poisonous snake and is found sitting dead in his room. But his existence as a threat has been established, and it hovers like a black cloud over Stoke Moran. He seems fully capable of killing Holmes and Watson if he found them snooping around inside his house. No doubt he would have a number of guns to choose from on a country estate. When his body is discovered it shows that Holmes has been victorious in their conflict. In the very last paragraph of the story he accepts responsibility for Roylott's death.

"Some of the blows of my cane came home and roused its snakish temper, so that it flew upon the first person it saw. In this way I am no doubt indirectly responsible for Dr. Grimesby Roylott's death, and I cannot say that it is likely to weigh very heavily upon my conscience.”

There is only one protagonist and one antagonist. Dr. Watson accompanies Holmes because he is the narrator and has to observe everything from the first appearance of Helen Stoner at 221B Baker Street. But Holmes is the protagonist and Roylott the antagonist. Helen Stoner might be called "the bone of contention" or "the MacGuffin." 
 

I need help with an essay on The Namesake. I am trying to figure out how to explain how relationships between member of different generations relate to a large idea of the novel. I am so confused on what to focus on or where to begin. Any help will be appreciated.

Jhumpa Lahiri's The Namesake is a coming-of-age novel about Gogol (Nikhil) Ganguli as he struggles to come to terms with his cultural heritage and his name. This is related to his relationship with his parents, who are from India and immigrated to Boston soon after they were married and before Gogol was born.
The novel begins before Gogol's birth and the omniscient narrator reveals Ashima's and Ashoke's thoughts. We hear about their background in India and how they met: their parents arranged their marriage. The couple moves to Boston for Ashoke's job as a professor. At first, Ashima is very lonely and has trouble adjusting to American ways. Ashoke's transition is a bit easier since he has a community of coworkers and a job to occupy his time. When Gogol is born, Ashima's primary role is to rear her son. In the novel's first chapter, Gogol is born in an American hospital. The hospital demands the parents name him before they take him home, but Ashima and Ashoke are waiting for word from an elder relative in India, as is their tradition. They never receive the letter, so Ashoke decides to name him Gogol, after a Russian author. Gogol is special to Ashoke because he was reading a collection of Gogol's stories on a train when the train crashed, killing most of the passengers. He feels that Gogol's book saved his life; he names his son Gogol because, as he tells him later, the name reminds him "of everything that followed" the accident (124). 
Much of Gogol's conflict as he grows up has to do with this name. He does not understand why his parents would name him something so strange. It is not even an Indian name. When he begins school, his parents tell the school his name will be Nikhil. At first, Gogol does not want to go by this new name since he is accustomed to being Gogol at home. As he grows up, though, he realizes how odd "Gogol" is and eventually legally changes his name to Nikhil. As a teen and young adult, Gogol distances himself from his parents. He becomes involved with a young American woman named Maxine and spends all his time with her and her parents, who are much more laidback and less traditional than Gogol's parents. Even after Ashoke tells Gogol about the significance of his name, he cannot quite understand why his dad wants to commemorate a tragedy through his son. 
However, a turning point occurs when Ashoke suddenly dies while in Ohio working. Gogol has been out of touch with his family, but he is responsible for identifying his dad's body and cleaning out his apartment. He is struck by grief and finally realizes the significance of his father to his life. This causes him to break ties with Maxine and to reunite with his family, embracing his background of Indian traditions more enthusiastically. 
The central conflicts in the novel are Gogol's struggle to embrace his name and his struggle to relate with his parents and their traditions. His name comes from his parents, the members of the older generation, so it is inherently connected to the generational conflict in The Namesake. 

Calculus of a Single Variable, Chapter 5, 5.6, Section 5.6, Problem 72

This function is defined on [-1, 1] and is continuously differentiable on (-1, 1). Its derivative is
f'(x) = 1/sqrt(1 - x^2) - 2/(1 + x^2).
Let's solve the equation f'(x) = 0:
1/sqrt(1 - x^2) = 2/(1 + x^2), both sides are non-negative, hence it may be squared:
1/(1 - x^2) = 4/(1 + x^2)^2, which is equivalent to
1 + 2x^2 + (x^2)^2 = 4 - 4x^2, or (x^2)^2 + 6x^2 - 3 = 0.
This gives us x^2 = -3 +- sqrt(9 + 3), it must be non-negative so only "+" is suitable.
Thus x^2 = -3 + sqrt(12) = sqrt(3)(2 - sqrt(3)) which is lt1, and x_(1,2) = +-sqrt(sqrt(3)(2 - sqrt(3))) approx +-0.68.
Now consider the sign of f'(x). Near x=+-1 it tends to +oo and therefore is positive, at x=0 it is negative. Therefore f(x) increases from -1 to -sqrt(sqrt(3)(2 - sqrt(3))), decreases from -sqrt(sqrt(3)(2 - sqrt(3))) to +sqrt(sqrt(3)(2 - sqrt(3))) and increases again from +sqrt(sqrt(3)(2 - sqrt(3))) to 1.
The answer: f(-1) is a local one-sided minimum, f(1) is a local one-sided maximum, f(-sqrt(sqrt(3)(2 - sqrt(3)))) is a local maximum and f(sqrt(sqrt(3)(2 - sqrt(3)))) is a local minimum.

What were the different subjects that Helen learned during the first year of her education? Describe her learning process.

After Helen learns the words for things, having had Miss Sullivan spell them into her hand, Helen's teacher then uses squares of cardboard and punches the braille spelling of the word into one of the squares. Helen takes the cardboard squares and pins them to the object for which they stand. Naturally, she has trouble with abstract concepts since there is nothing to touch in those cases. One day, though, Helen strings beads in a pattern of two of one kind, then three of another kind. When she makes an error in this pattern, Miss Sullivan corrects her, and Helen restrings the beads. Then as Helen tries to figure out if she is stringing the beads correctly, Miss Sullivan touches her forehead and spells out in Helen's hand the word "think." This abstract concept is the first that Helen learns.
Whenever Miss Sullivan talks with Helen, she spells into the girl's hand. When Helen responds, sometimes she does not know the right word or idiom that will convey her thoughts, so her teacher supplies her with the new words and urges her to continue in their conversation even if she cannot keep up her part of the dialogue. Helen writes in her autobiography that this process goes on for several years because, being deaf, she cannot hear the idiomatic expressions that are in constant use in even the simplest conversations and are picked up unconsciously by children who can hear. She explains to her readers,

The little hearing child learns these from constant repetition and imitation. The conversation he hears in his home stimulates his mind and suggests topics and calls forth the spontaneous expression of his own thoughts. This natural exchange of ideas is denied to the deaf child. My teacher, realizing this, determined to supply the kinds of stimulus I lacked (Chapter 7).

Repeating to Helen as much of what she hears as possible, Miss Sullivan even demonstrates how Helen can be part of the conversation by spelling out what she wants to say into her teacher's hand. But, Helen is reluctant to partake in conversations with others, and for a long time, she searches for words that are appropriate for the occasions in which she finds herself.
When Miss Sullivan takes Helen to the Perkins Institute for the Blind in Boston, Helen is surprised to learn that all the children cannot see either. They spell out words in her hands just as her teacher has, and Helen is delighted. One day the students go to Bunker Hill, and Helen has her first history lesson. The following day she rides on a steamer to Plymouth and visits the area where the Pilgrims landed. Helen states that she acquires a little model of Plymouth Rock with the embossed numbers "1620" on it. She delights in holding this memento as "[I] turned over in my mind all that I knew about the wonderful story of the Pilgrims" (Chapter 9). 

Why would the playwright choose to use Puritanism as a backdrop for a comment on hysteria in The Crucible?

Arthur Miller likely chose the Salem Witch Trials of 1692 in order to comment on the hysteria created by the McCarthy hearings of the 1950s because they have several elements in common. First, both populations feared an enemy they could not identify by sight: anyone could be a witch, according to the Puritans, and anyone could be a Communist. It was simply impossible to look at someone and know their motives and allegiances. Moreover, both populations feared terrible and immediate personal harm from these antagonists; both felt that their community's security was at risk as a result of their presence. In both communities, then, paranoia led to hysteria, and people began to turn on their neighbors. In the Salem Witch Trials, the testimony of children was used to condemn innocent men and women to death, and during the Red Scare, the testimony of schoolchildren might be enough to get a teacher believed to have Communist sympathies fired. Finally, during both episodes in American history, it was not enough to simply confess to wrongdoing; the convicted had to name names of other guilty parties in order to be considered credible. Though no one was put to death as a result of the McCarthy hearings, the rampant hysteria created an environment of fear that matched, in many ways, the emotional environment created by the girls' accusations in The Crucible.

What kept Pi alive?

If you are referencing The Life of Pi, there are a number of arguments that can be made about how Pi survived. One of the most cogent is his faith. As a student of religion, he makes connections to his spiritual life in his moments of deepest anguish. Further, his religion helps him understand the suffering he is experiencing.
Another possibility is his deep empathy. Because Pi is so attuned to the thoughts, feelings, and experiences of his "animalistic" fellow passengers, he is able to befriend, care for, and even at times control the "tiger," Richard Parker. In no other realistic circumstance could a young boy essentially tame a wild, predatory cat—one who fights a shark and wins, one who is starving and emaciated and ravenous, one who looks at Pi like he is food. But because of Pi's immense capacity for understanding and empathy, he is able to overcome this barrier. His relationship with Richard Parker is what ultimately saves him.

What are some examples of when Hamlet acts insane?

Hamlet is experiencing some personal conflict as a result of the information he gets from his father (the ghost) that his uncle is a murderer.  His father wants to be avenged, and Hamlet wants to comply, but Hamlet is a complicated soul.  Just killing his uncle is not his style.  His mother married his uncle, a fact that makes him very angry.  He's conflicted about killing his uncle.
While Hamlet is trying to figure things out, he behaves in a very strange manner the many people would consider crazy.  To some people, the first sign of his insanity is seeing and speaking to ghosts.  Even if you accept that, there are other instances of Hamlet behaving irrationally and rudely.
One example is Hamlet’s behavior toward Ophelia.  By all accounts Ophelia is a sweet girl, and Hamlet was sweet on her.  Whatever the extent of the relationship, Hamlet’s treatment of Ophelia is beyond harsh.  It is uncalled for.

HAMLET
You should not have believed me; for virtue cannotso inoculate our old stock but we shall relish ofit: I loved you not.
OPHELIA
I was the more deceived.
HAMLET
Get thee to a nunnery: why wouldst thou be abreeder of sinners? I am myself indifferent honest;but yet I could accuse me of such things that itwere better my mother had not borne me … (Act 3, Scene 1)

Hamlet’s harsh and crude treatment of Ophelia is nothing compared to what he does to her father.  He kills him, more or less accidentally, and then when his uncle tries to get Hamlet to tell them where the body is, Hamlet uses it as another opportunity to prove that he is crazy. 

KING CLAUDIUS
Now, Hamlet, where's Polonius?
HAMLET
At supper.
KING CLAUDIUS
At supper! where?
HAMLET
Not where he eats, but where he is eaten … (Act 4, Scene 3) 

It’s funny in a completely morbid way.  Hamlet doesn’t want anyone to guess his intentions regarding his uncle, so he wants to make everyone think he is crazy.  He tells his friends Rosencrantz and Guidenstern that he knows " a hawk from a handsaw," and he is wily enough to avoid his uncle's plot to murder him.
 
 

In The Boy in the Striped Pajamas by John Boyne, how many children live in the hut with Shmuel?

In Chapter 12, Shmuel tells Bruno about his experience leaving his home in Poland. Shmuel explains to Bruno that the first hut his family was forced to stay in was only one room. He goes on to tell Bruno that he lived there with his mother, father, brother, as well as another family that had "sons." Shmuel then tells Bruno that one of the sons was named Luka, and he used to beat him up. Bruno shakes his head to contradict Shmuel because he doesn't believe that two families could live in one hut, but Shmuel insists that he is being honest. Shmuel then says that there were eleven people living in the hut together. Using this information one can figure out that Shmuel was living with six other children in one hut before they were sent away to live in Auschwitz. Shmuel does not give any information regarding how many children he lives with in Auschwitz, but the reader does learn that Shmuel's mother was taken away from them. Shmuel currently lives with his brother, Josef, and his Papa in a hut at Auschwitz.

College Algebra, Chapter 4, Chapter Review, Section Review, Problem 26

Find the quotient and remainder of the rational function $\displaystyle P(x) = \frac{x^3 + 2x^2 - 10}{x + 3}$



If we let $Q(x)$ and $R(x)$ be the functions of the quotient and the remainder, then by applying long division







Thus, $Q(x) = x^2 - x + 3$ and $R(x) = -19$.

In Marigolds what is the meaning or significance of this passage: "We children, of course, we were only vaguely aware of the extent of our poverty. Having no radios, few newspapers, and no magazines, we were somewhat unaware of the world, outside our community."

Understanding the setting of a story is important because the setting shapes the mood and tone. By knowing the setting, the reader can vividly picture where the story is taking place. The story "Marigolds" introduces the setting in the first few paragraphs when the narrator says she grew up during the Great Depression. The mood and tone of this story is gloomy and melancholy. While describing the setting of her childhood, the narrator describes that her most vivid memory of her childhood was dust.
"When I think of the hometown of my youth, all that I seem to remember is dust—the brown, crumbly dust of late summer—arid, sterile dust that gets into the eyes and makes them water, gets into the throat and between the toes of bare brown feet."
The narrator continues describing her childhood by stating, "we children, of course, were only vaguely aware of the extent of our poverty. Having no radios, few newspapers, and no magazines, we were somewhat unaware of the world outside our community." Because the narrator was a child during the Great Depression, she was rarely able to experience things and places outside of her community. By stating "...vaguely aware of the extent of our poverty," the narrator explains how she and the children in her community were unaware of their poverty because they had known no other way of living other than in poverty. They had no other lifestyle to compare to their own. Without access to media, the children had little knowledge about places and events beyond their community.
The narrator continues to describe their impoverished setting by comparing it to living in a cage. This imagery allows the reader to visualize the narrator's limitations and the depravity caused by the Great Depression. Due to her lack of experience, the narrator is naive to the severity of her living situation.

Please summarize the book Companion to Spanish Colonial Art at the Denver Art Museum by Donna Pierce.

Almost the entire western half of the United States used to be a Spanish colony, although it was not as well developed as Spanish colonies in Central and South America. This geography gives Denver a unique advantage for art collection: while the city itself was not founded by Spanish colonizers, it nevertheless is about dead center of the former colony. As such, it has brought in a great deal of unique art, which is the subject of Donna Pierce's book.
The Companion contextualizes many of the famous pieces in this collection. It helps viewers to better understand the artist's life, works, time period, and location. For those who are unfamiliar with many aspects of Spanish colonial art, or even art history in the first place, the Companion discusses styles, transitions, themes, and use of light or color.
The book is set up to approach artistic movements rather than time periods. Over one hundred different pieces are referenced, some from the Spanish colonization of the southwestern US and some from other parts of the (much larger) Spanish Empire.

If you're like me, when you hear "Spanish Colonial art," the first city you think of is not Denver.
Shows what we know: the Denver Art Museum is home to one of the biggest and most comprehensive Spanish Colonial art collections in the world.
Donna Pierce's book Companion to Spanish Colonial Art at the Denver Art Museum is a guide to the museum's collection, which began in 1936 and now contains over three thousand objects from all across South America, Central America, and the American Southwest.
As the collection's curator, Pierce knows her stuff. Rather than presenting a chronological timeline of the collection's highlights and dropping a string of dates, she organizes her book by theme. The dawn of global trade and its influence on art figures prominently into the collection, for example. Pierce uses this thematic structure to provide context for the sculptures, silver, furniture, ceramics, jewelry, paintings, and other objects of art that make up the museum's collection.
http://mayercenter.denverartmuseum.org/Publications.htm

Donna Pierce’s book Companion to Spanish Colonial Art at the Denver Art Museum focuses on the museum’s collection of Spanish art. This collection began in 1936. It now contains over 3,000 objects and is regarded as the finest collection of Spanish art in the United States. The Spanish Colonial galleries at this museum contain paintings, furniture, silver, and decorative art.
This book is the first book to focus solely on this museum’s Spanish Colonial collection. This book is organized by theme, and it has pictures of over one hundred items from Spanish America and the southwestern part of the United States. Various subjects are covered in this book including native traditions, church art, everyday-life art, and the styles of the region.

Donna Pierce’s book Companion to Spanish Colonial Art at the Denver Art Museum is a guide to the museum’s extensive collection of Spanish colonial art, spanning works from Spanish America and the southwestern United States. Pierce was the former curator of this art collection. The museum initiated the collection in 1936, and it has since grown to include more than 3,000 pieces, arguably the most comprehensive collection of artworks of this era and region.
Pierce’s book features photographs of more than 100 objects, including paintings, sculpture, furniture, silver, and other decorative arts. Rather than being arranged chronologically, the volume organizes artworks thematically. Pierce illustrates the continuity of native traditions, despite Spanish colonial dominance. She features church and mission art, showing the religious influence of Spain along with native features. The book also discusses hybrid art forms, regional artistic styles, and art that emerged from aspects of everyday life.
Companion to Spanish Colonial Art also discusses cultural interaction beyond just Spanish colonists and Native American people. For example, the book discusses the use of folding screens used as room dividers, which is a decorative style borrowed from Asian culture. The screen featured in the book (Garden Party on the Terrace of a Country Home) is the only screen of its kind in an American museum.

College Algebra, Chapter 2, Review Exercises, Section Review Exercises, Problem 54

Chris is hired by an accounting firm at a salary of $\$60,000$ per year. Three years later his annual salary has increased to $\$70,000$. Assume that his salary increases linearly.
a.) Find an equation that relates his annual salary $s$ and the number of years $t$ that he has worked for the firm.

$
\begin{equation}
\begin{aligned}
s &= \left( \frac{70,500-60,000}{3} \right)t + 60,000\\
\\
s &= 3500 t + 60,000
\end{aligned}
\end{equation}
$


b.) What do the slope and the $s$-intercept of his salary equation represent?
The slope 3500 represents the annual increase of Chris salary and the $s$-intercept is the salary offered to Chris for the first year.

c.) What will his salary be after 12 years with the firm?

$
\begin{equation}
\begin{aligned}
\text{when } t &= 12\\
\\
s &= 3500(12) + 60,000\\
\\
s &= 102,000
\end{aligned}
\end{equation}
$

After 12 years, Chris salary will be $\$102,000$

College Algebra, Chapter 7, 7.1, Section 7.1, Problem 44

Find the complete solution of the system

$
\left\{
\begin{array}{ccccc}
3x & + y & & = & 2 \\
-4x & + 3y & + z & = & 4 \\
2x & + 5y & + z & = & 0
\end{array}
\right.
$


We transform the system into row-echelon form

$\left[ \begin{array}{cccc}
3 & 1 & 0 & 2 \\
-4 & 3 & 1 & 4 \\
2 & 5 & 1 & 0
\end{array} \right]$

$\displaystyle \frac{1}{3} R_1$

$\left[ \begin{array}{cccc}

1 & \displaystyle \frac{1}{3} & 0 & \displaystyle \frac{2}{3} \\
-4 & 3 & 1 & 4 \\
2 & 5 & 1 & 0
\end{array} \right]$

$\displaystyle R_2 + 4 R_1 \to R_2$

$\left[ \begin{array}{cccc}
1 & \displaystyle \frac{1}{3} & 0 & \displaystyle \frac{2}{3} \\
0 & \displaystyle \frac{13}{3} & 1 & \displaystyle \frac{20}{3} \\
2 & 5 & 1 & 0
\end{array} \right]$

$\displaystyle R_3 - 2 R_1 \to R_3$

$\left[ \begin{array}{cccc}
1 & \displaystyle \frac{1}{3} & 0 & \displaystyle \frac{2}{3} \\
0 & \displaystyle \frac{13}{3} & 1 & \displaystyle \frac{20}{3} \\
0 & \displaystyle \frac{13}{3} & 1 & \displaystyle \frac{-4}{3}
\end{array} \right]$

$\displaystyle \frac{3}{13} R_2$

$\left[ \begin{array}{cccc}
1 & \displaystyle \frac{1}{3} & 0 & \displaystyle \frac{2}{3} \\
0 & 1 & \displaystyle \frac{3}{13} & \displaystyle \frac{20}{13} \\
0 & \displaystyle \frac{13}{3} & 1 & \displaystyle \frac{-4}{3}
\end{array} \right]$

$\displaystyle R_3 - \frac{13}{3} R_2 \to R_3$

$\left[ \begin{array}{cccc}
1 & \displaystyle \frac{1}{3} & 0 & \displaystyle \frac{2}{3} \\
0 & 1 & \displaystyle \frac{3}{13} & \displaystyle \frac{20}{13} \\
0 & 0 & 0 & -8
\end{array} \right]$

$\displaystyle \frac{-1}{8} R_3$

$\left[ \begin{array}{cccc}
1 & \displaystyle \frac{1}{3} & 0 & \displaystyle \frac{2}{3} \\
0 & 1 & \displaystyle \frac{3}{13} & \displaystyle \frac{20}{13} \\
0 & 0 & 0 & 1
\end{array} \right]$

This last matrix is in row-echelon form, so we stop the Gaussian Elimination Process. Now if we translate the last row back into equation form, we get $0x + 0y + 0z = 1$ or $0 = 1$, which is false. This means that the system has no solution or it is inconsistent.

f(x)=sin(3x) ,c=0 Use the definition of Taylor series to find the Taylor series, centered at c for the function.

Taylor series is an example of infinite series derived from the expansion of f(x) about a single point. It is represented by infinite sum of f^n(x) centered at x=c . The general formula for Taylor series is:
f(x) = sum_(n=0)^oo (f^n(c))/(n!) (x-c)^n
or
f(x) =f(c)+f'(c)(x-c) +(f^2(c))/(2!)(x-c)^2 +(f^3(c))/(3!)(x-c)^3 +(f^4(c))/(4!)(x-c)^4 +...
To apply the definition of Taylor series for the given function f(x) = sin(3x) , we list f^n(x) using  the derivative formula for trigonometric function: d/(dx) sin(u) = cos(u) *(du)/(dx) and d/(dx) cos(u)= -sin(u)*(du)/(dx) .
Let u = 3x then (du)/(dx) =3 .
f(x) =sin(3x)
f'(x) = d/(dx) sin(3x)
           = cos(3x)*3
           =3cos(3x)
f^2(x) = d/(dx) 3cos(3x)
            =3 d/(dx) cos(3x)
            =3*( -sin(3x)*3)
            =-9sin(3x)
f^3(x) = d/(dx)-9sin(3x)
            = -9 d/(dx)sin(3x)
             =-9 * cos(3x)*3
           = -27cos(3x)
f^4(x) = d/(dx) -27cos(3x)
            =-27*d/(dx) cos(3x)
            = -27 * (-sin(3x)*3)
            =81 sin(3x)
 f^5(x) = d/(dx) 81sin(3x)
            =81*d/(dx) sin(3x)
            = 81* (cos(3x)*3)
            =243cos(3x)
 Plug-in x=0 on each f^n(x) , we get:
 f(0) =sin(3*0)
         =sin(0)
         =0
 f'(0)= 3cos(3*0)
           =3cos(0)
           = 3*1
           =3  
 f^2(0)= -9sin(3*0)
           =-9sin(0)
            =-9 *0
            =0
 f^3(0)= -27cos(3*0)
            =-27 cos(0)
             =-27*1
            =-27
 f^4(0)= 81sin(3*0)
            =81sin(0)
            =81*0
             =0
 f^5(0)= 243cos(3*0)
            =243cos(0)
             =243*1
             =243
 Plug-in the values on the formula for Taylor series, we get:
 sin(3x) = sum_(n=0)^oo (f^n(0))/(n!) (x-0)^n
 =sum_(n=0)^oo (f^n(0))/(n!) x^n
 =f(0)+f'(0)x +(f'^2(0))/(2!)x^2 +(f^3(0))/(3!)x^3 +(f^4(0))/(4!)x^4 +(f^4(0))/(4!)x^4 +...
=0+3x +0/(2!)x^2 +(-27)/(3!)x^3 + 0/(4!)x^4 +243/(5!)x^5+...
=0+3x +0/2x^2 +(-27)/6x^3 + 0/24x^4 +243/120x^5+...
=0+3x +0 -9/2x^3 + 0 +81/40x^5+...
=3x -9/2x^3 +81/40x^5+...
The Taylor series for the given function f(x)=sin(3x) centered at c=0 will be:
sin(3x) =3x -9/2x^3 +81/40x^5+...

Why did Henry VIII create his own church? What country was he king of?

Henry VIII was the king of England. Throughout the early part of Henry's reign, England was part of an undivided Western Christendom. There was one single Church, and the Pope stood at its head. However, in the early sixteenth century, things changed rapidly. A number of people became dissatisfied with the Church and its teachings and wanted to reform it. They became known as Protestants, and the Protestants began a very important period of history called the Reformation.
Henry did not have much time for the Reformation, at least not initially. He was always quite conservative when it came to religious beliefs. However, he was a king, and he jealously guarded his throne against any kind of threat, whether it was from an English aristocrat, a foreign prince, or a Pope.
Henry wanted to divorce his first wife, Catherine of Aragon, and marry his mistress, Anne Boleyn. The Church would not permit divorce, however, no matter how hard Henry tried to bend the rules. As a result, Henry angrily broke off all relations with Rome and declared himself Supreme Governor of the Church of England. With other changes happening in Europe, the Reformation was now in full swing. Where once there had been one church, now there were several. The European continent was bitterly divided between Protestants and Catholics.
As well as being free to divorce Catherine of Aragon and marry Anne Boleyn, Henry was now able to get his hands on the Catholic Church's extensive land and property holdings throughout his kingdom. These were very valuable, and Henry gladly seized them, selling them off to his supporters for huge sums.
Creating a separate church and making himself its head was mainly a political act on Henry's part. It gave him greater freedom to do what he wanted and greatly increased his wealth and power.

Describe the development of early atomic theory, including contributions from Dalton, Thomson, Rutherford, Bohr, and Schrödinger.

Human understanding of atomic theory has developed vastly, thanks to the contributions of several scientists whose work spanned the early 1800s through the 1920s. The work of Dalton, Thomson, Rutherford, Bohr, and Schrödinger occurred over a short period, and their discoveries advanced atomic theory rapidly. Below is a brief summary of each of their contributions to atomic theory.
 
John Dalton
John Dalton was a scientist in the 1800s. Simply, he was the first to describe atoms and their properties. His contribution to atomic theory consisted of five main tenets (1805): 

All matter is composed of small particles called atoms.
Atoms are the smallest unit of matter; Matter cannot be broken down into units smaller than atoms; Atoms are indestructible.
There are different kinds of atoms; atoms of the same kind of element are identical to each other. Atoms of the same element are identical in mass and size and have the same properties.
In chemical reactions, atoms are rearranged, combined, or separated.
Compounds are formed when two or more different kinds of atoms join together.

 
J.J. Thomson
J.J. Thomson was a scientist who lived from the mid 19th century until the mid-20th century. Around the turn of the century, he was the first to discover sub-atomic particles: he is credited with the discovery of the electron. Thomson's discovery led to related discoveries around isotopes and radioactivity.
 
Ernest Rutherford
Shortly after Thomson's discovery of the electron, Ernest Rutherford discovered a concentration of mass within the center of an atom, which he called the nucleus. His famous Gold Foil Experiment in 1909 showed that atoms were composed of a nucleus surrounded by electrons. His discovery added to atomic theory by describing the atom more accurately as a conglomerate of several subatomic particles.
 
Niels Bohr
Niels Bohr was an active scientist around the same period as Rutherford. They worked together on a model to describe the structure of the sub-atomic particles of an atom. The Rutherford-Bohr model, or simply the Bohr model (1913), describes the atom's structure as similar to a solar system. The nucleus is in the center and smaller particles such as electrons circularly orbit around it. Bohr's model is seen as a precursor to current quantum theory.
 
Erwin Schrödinger
Erwin Schrödinger created several equations that advanced the understanding of atomic theory on a quantum level. Early in his career, he described the movement of an electron as a wave-function. In quantum mechanics, Schrödinger's equation (1926) is a physics description that describes quantum behavior in relation to time. Schrödinger's description of atomic structure, the wave mechanical model, describes electron position within orbitals, not orbits. This conceptualization of atomic structure posits that electrons do not orbit in circles as Bohr suggested, but rather in a much more complex manner. Schrödinger's work was at the forefront of a sea change moment in scientific history when atomic understanding was advancing into the quantum realm.
 
http://abyss.uoregon.edu/~js/21st_century_science/lectures/lec05.html

What is the significance of Mr. Peterson's knowledge of "The Gold-Bug" story in Avi's The Man Who Was Poe?

In Avi's The Man Who Was Poe, the fact that Mr. Peterson has read Edgar Allan Poe's short story "The Gold-Bug" shows us that Mr. Peterson is well-acquainted with who the author is and his abilities.  Poe is gifted with the skills of observation and critical thinking that allow him to solve complex mysteries as well as to write them. Hence, as soon as Mr. Peterson finds out who Poe really is, Mr. Peterson begins worrying about his plans with Mr. Rachett being foiled, and the two partners in crime take further actions that make it more difficult for Poe and Edmund to find Edmund's sister. "The Gold-Bug" was an award-winning short story Edgar Allan Poe submitted for a contest in 1843. The mystery thriller depicts a search for pirated gold, and the clues to the gold's whereabouts are hidden in an elaborately coded message that must be deciphered. The hunt for gold parallels the theft of gold that serves as Mr. Rachett and Mr. Peterson's motive for kidnapping and murder. Mr. Rachett and Mr. Peterson apparently felt so inspired by Poe's story of gold theft that they decided to imitate Poe by communicating with each other in the code Poe developed for his own secret message within his short story. Mr. Rachett and Mr. Peterson felt that their plans were going splendidly until the day Poe poses as a "private investigator from the Lowell Insurance Company" and shows up at the Providence Bank, the bank from which the gold was stolen (p. 75). After Mr. Peterson, a clerk at the bank, shows Poe, calling himself Mr. Grey, around the vault, he receives a message from Mr. Prachett warning him that Mr. Grey is really Poe. Knowing how clever Poe is and fearing that he has figured everything out, Mr. Rachett and Mr. Peterson make plans to leave the city, taking Edmund's sister with them.

int_0^1 e^(-x^2) dx Use a power series to approximate the value of the integral with an error of less than 0.0001.

From the table of power series, we have:
e^x = sum_(n=0)^oo x^n/n!
     = 1+x+x^2/(2!)+x^3/(3!)+x^4/(4!)+x^5/(5!)+ ...
 To apply this on the given integral int_0^1 e^(-x^2)dx ,
we replace the "x " with "-x^2 ".
e^(-x^2)= sum_(n=0)^oo (-x^2)^n/(n!)  
          =sum_(n=0)^oo ((-1)^n*x^(2n))/(n!)
          = 1/(0!) -x^2/(1!)+x^4/(2!) - x^6/(3!) +x^8/4!-x^(10)/(5!)+x^(12)/(6!) -...
          = 1 -x^2 +x^4/2-x^6/6 +x^8/24-x^(10)/120+x^(12)/(6!)- ...
The integral becomes:
int_0^1 e^(-x^2)dx =int_0^1 [1 -x^2 +x^4/2-x^6/6 +x^8/24-x^(10)/120+x^(12)/720-...]dx
To determine the indefinite integral, we integrate each term using Power Rule for integration: int x^ndx =x^(n+1)/(n+1) .
int_0^1 [1 -x^2 +x^4/2-x^6/6 +x^8/24-x^(10)/120+x^(12)/720-...]dx
=[x-x^3/3 +x^5/(2*5)-x^7/(6*7) +x^9/(24*9)-x^(11)/(120*11)+x^(13)/(720*13)-...]|_0^1
=[x-x^3/3 +x^5/10-x^7/42+x^9/216-x^(11)/1320+x^(13)/9360-...]|_0^1
Apply definite integral formula: F(x)|_a^b = F(b) - F(a) .
F(1) = 1-1^3/3 +1^5/10-1^7/42+1^9/216-1^(11)/1320+1^(13)/9360- ...
         = 1 -1/3 +1/10-1/42 +1/216-1/1320+1/9360- ...
F(0) = 0-0^3/3 +0^5/10-0^7/42+0^9/216-0^(11)/1320+0^(13)/9360- ...
          = 0 -0 +0 -0 +0-0+0- ...      
All the terms are 0 then F(0)= 0 .
We can stop at 7th term (1/9360 ~~0.0001068) since we only need error less than 0.0001.
Then,
 F(1)-F(0)=[1 -1/3 +1/10-1/42 +1/216-1/1320+1/9360] -[0]
                      = 0.7468360343
Thus, the approximation of the integral will be:
int _0^1 e^(-x^2)dx ~~0.7468

Single Variable Calculus, Chapter 3, 3.4, Section 3.4, Problem 17

Show that $\displaystyle \frac{d}{dx} (\csc x) = - \csc x \cot x $

Get the reciprocal of $\csc x$

$\csc x = \displaystyle \frac{1}{\sin x}$

Use the Quotient Rule to derive $\displaystyle \frac{1}{\sin x}$


$
\begin{equation}
\begin{aligned}


\frac{d}{dx} (\csc x) =& \frac{\displaystyle \sin x \frac{d}{dx} (1) - \left[ 1 \frac{d}{dx} (\sin x) \right]}{(\sin x)^2}
&& \text{}
\\
\\
\frac{d}{dx} (\csc x) =& \frac{\sin x (0) - (\cos x)}{\sin ^2 x }
&& \text{Simplify the equation}
\\
\\
\frac{d}{dx} (\csc x) =& \frac{- \cos x}{\sin ^2 x}
&& \text{Factor out $\displaystyle \frac{-1}{\sin x}$ and $\displaystyle \frac{\cos x}{\sin x}$}
\\
\\
\frac{d}{dx} (\csc x) =& - \left( \frac{1}{\sin x} \right) \left( \frac{\cos x}{\sin x}\right)
&& \text{Get their identities}
\\
\\
\frac{d}{dx} (\csc x) =& - \csc x \cot x
&& \text{}


\end{aligned}
\end{equation}
$

College Algebra, Chapter 9, 9.3, Section 9.3, Problem 46

Determine the partial sum $S_n$ of the geometric sequence that satisfies $\displaystyle a_2 = 0.12, a_5 = 0.00096$ and $n=4$.

Since this sequence is geometric, its $n$th term is given by the formula $a_n = ar^{n -1}$. Thus,

$a_2 = ar^{2-1} = ar$

$a_5 = ar^{5-1} = ar^4$

From the values we are given for these two terms, we get the following system of equations


$
\left\{
\begin{equation}
\begin{aligned}

0.12 =& ar
\\
0.00096 =& ar^4

\end{aligned}
\end{equation}
\right.
$


We solve this system by dividing.


$
\begin{equation}
\begin{aligned}

\frac{ar^4}{ar} =& \frac{0.00096}{0.12}
&&
\\
\\
r^3 =& 0.008
&& \text{Simplify}
\\
\\
r =& 0.2
&& \text{Take the cube root of each side}

\end{aligned}
\end{equation}
$


Substituting for $r$ in the first equation $ar = 0.12$, gives


$
\begin{equation}
\begin{aligned}

0.12 =& a(0.2)
\\
\\
a =& \frac{0.12}{0.2}
\qquad \text{Divide by } 0.2
\\
\\
a =& \frac{3}{5}
\\
\\
a =& 0.6

\end{aligned}
\end{equation}
$


Then using the formula for partial sum


$
\begin{equation}
\begin{aligned}

S_n =& a \frac{1 - r^n}{1-r}
\\
\\
S_4 =& 0.6 \left( \frac{1-0.2^4}{1-0.2} \right)
\\
\\
S_4 =& 0.7488

\end{aligned}
\end{equation}
$

Explain the festivals celebrated by the Franks and others in the annex.

Despite being forced to hide in the annex, the Franks and the others there are able to celebrate a number of holidays.
One of the more significant festivals that they celebrate is Hanukkah. Hanukkah is an eight-day Jewish holiday celebrated in late November or December. It commemorates a miracle that occurred after the war with the Greeks in the Second Century BCE when the Jews rededicated the Temple in Jerusalem. It is normally celebrated with food, song, and the lighting of a nine-candled candelabra called a menorah. The Franks managed to bring a menorah with them to the annex. Usually, the candles are allowed to burn all the way down. However, the Franks only light them for a few moments in order to avoid drawing attention. Still, they are happy to be able to celebrate this holiday.
They also celebrate St. Nicholas Day. Celebrated on December 6, this festival is typically associated with gift-giving and feasting. Although it is a Christian holiday, the Franks, like most of their Dutch neighbors, still celebrate St. Nicholas Day in 1943. Even though they do not have much in the way of presents to give, Anne gives everyone in the annex a poem. They also decorate their home as best they can considering their limited supplies.
All this goes to show that the Franks and the other residents of the secret annex do their best to try to carry on as normal, even given their dangerous and clearly abnormal circumstances.