What laws have limited Americans’ (or certain groups’) freedoms?

American freedom has been checked by certain events in history. In 1798, John Adams signed The Sedition Act, which made it illegal to speak out against the government or print criticisms of the administration. The act aimed to remove anti-Federalist sentiment from the press. While this act was repealed before Adams left office, it damaged the Federalist party and made John Adams appear paranoid to voters.  
During the Civil War, Lincoln suspended the writ of habeas corpus, meaning the Federal government did not need to have a reason to jail someone, only a suspicion that the person was engaged in anti-government activities. Lincoln also instituted martial law to keep Maryland in the Union.  
In 1917, Woodrow Wilson brought back the Sedition Act and also created the Espionage Act. Wilson's Postmaster General A. Mitchell Palmer created a system where international mail was highly scrutinized and made it illegal to speak out against the war, the draft, or war industries. The most notable person arrested in this sting was Eugene V. Debs, who ran on the Socialist ticket for president in 1916.  
In 2001, George W. Bush signed the Homeland Security Act into law. This Act allows the government to access cell phone records and internet searches to put people on terrorist watch lists. So far, the Act is controversial among privacy advocates and has sparked debate about cell phone and internet rights.

y' + y/x = xsqrt(y) Solve the Bernoulli differential equation.

Bernoulli equation has form y'+P(x)y=Q(x)y^alpha. We can convert any such equation into linear equation differential equation by using substitution z=y^(1-alpha). To learn more about this method of solving Bernoulli equation check out the links below.
We will show a somewhat different method which can also be used for solving linear equations.
y'+y/x=x sqrt(y)
Make substitution y=uv => y'=u'v+uv'
u'v+uv'+(uv)/x=x sqrt(uv) 
v(u'+u/x)+uv'=x sqrt(uv)                                                                (1)
Let us now assume that the expression in brackets equals zero (we can choose almost anything instead of zero, but this makes the calculation easier) in order to calculate u.
u'+u/x=0
u'=-u/x
(du)/u=-dx/x
Integrating both sides yields
ln u=-ln x
ln u=ln x^-1
u=x^-1
Plugging that into (1) gives
x^-1 v'=x sqrt(x^-1 v)
Now we multiply by x to get only v' on the left hand side. 
v'=x^2x^(-1/2)sqrt v
v'=x^(3/2)sqrt v
(dv)/sqrt v=x^(3/2)dx
Integrating the above equation gives us
2sqrt v=(2x^(5/2)+C)/5
Divide by 2 and square the whole equation in order to get v.
v=(x^5+2Cx^(5/2)+C^2)/25
Now we just plug the obtained u and v into the substitution to get the final result.
y=x^-1 cdot (x^5+2Cx^(5/2)+C^2)/25  
y=(x^5+2Cx^(5/2)+C^2)/(25x)  lArr The general solution. 
http://mathworld.wolfram.com/BernoulliDifferentialEquation.html

https://en.wikipedia.org/wiki/Bernoulli_differential_equation

What is Glamis?

In William Shakespeare's tragic play Macbeth, the titular character is referred to as the "Thane of Glamis" from the very outset. This is a reference to a specific location in Scotland. Glamis is the name of the area that Shakespeare's Macbeth rules, and it is located in the eastern part of Scotland in the county of Angus. While Shakespeare situates his King Macbeth in Glamis Castle, the real life Macbeth didn't have any ties to it. However, the castle does have ties to other famous people, as it was the childhood home of Queen Elizabeth II, the Queen Mother.In Macbeth, Shakespeare uses the name of real people and places from history, like Glamis and Macbeth, but he plays with the true history of them. His version of Macbeth is far more sensational than that of the real Macbeth, and Shakespeare populates his Scotland with far more supernatural elements (although the real Glamis Castle is said to be one of the most haunted places in Scotland). It is the site of the murder of King Malcolm II (which probably inspired Shakespeare to situate the murder of Duncan here as well). Situating his play in specific locations that his audience would be familiar with presents a much more attractive, believable tale.
https://theculturetrip.com/europe/united-kingdom/scotland/articles/a-tour-of-macbeths-scotland-in-13-places/

What is the masterpiece in "The Last Leaf" by O. Henry?

In "the Last Leaf," the masterpiece is essentially Behrman's final, grand artistic endeavor. In the text, we learn the old painter, despite being a failed artist, has always envisioned creating a piece of art that will distinguish him as a noted practitioner of his craft. He never quite succeeds in fulfilling his goal, however, and as time progresses, he becomes a distinctly cantankerous and ill-tempered fellow.
Behrman is not a man without heart, though. When he learns his neighbor, Johnsy, is dying, Behrman sets out to paint his life's masterpiece. Johnsy is depressed and suffers from a deep malaise that is as physical as it is psychological. She believes she won't live out the remainder of her life and is content to die as soon as possible. Johnsy tells her companion, Sue, that when the last leaf on the ivy vine falls off, she'll be ready to die. Sue doesn't want Johnsy to continue in this morbid state of mind. She pulls down the blinds of the window in Johnsy's room, but knows this is only a temporary fix.
When Johnsy demands to have a look at the ivy vine, Sue has to humor her. When Sue pulls up the blinds, both are surprised to see the last leaf still hanging on the vine. In due time, the last leaf inspires Johnsy to snap out of her depression. She decides to live and to live as fully as she can. It is only later when Sue discovers the truth that both women realize what a true masterpiece Behrman had really painted. When the last leaf fell off the ivy vine, Behrman had braved the cold rain and snow to paint a replacement leaf on the vine. Because of his selfless action, Behrman contracts pneumonia, which eventually costs him his life. Yet, his very realistic portrayal of a leaf is responsible for saving a young woman's life.
Essentially, Behrman finally realizes his dream of creating a real masterpiece, and his final work is a testament to the greatness of his artistry.

Single Variable Calculus, Chapter 2, 2.2, Section 2.2, Problem 41

Estimate the equations by graphing all the vertical asymptotes of the curve $y = \tan (2 \sin x) \quad -\pi \leq x \leq \pi$. Then find the exact equation of these asymptotes.



To find the exact equation of the asymptotes, we know that the tangent function has vertical asymptotes at $\displaystyle x = \frac{\pi}{2} + n \pi$, where $n$ is an integer and $n$ $\pi$ for its multiple cycles. So,



$
\begin{equation}
\begin{aligned}

2 \sin x & = \frac{\pi}{2} + n \pi\\

\sin x =& \frac{\pi}{4} + \frac{n \pi}{2} ; \quad \text{ for } -\pi < x < \pi, \\

\sin x =& \frac{\pi}{4}\\

x =& \sin ^ {-1} \left[\frac{\pi }{4}\right] = 0.9033

\end{aligned}
\end{equation}
$


The other value of $x$ is obtained from taking the supplementary angle

$\displaystyle x = \pi - \sin^{-1} \left[\frac{\pi}{4}\right]$

$x = 2.2383$

Therefore, the value of the asymptotes are exactly $x = \pm 0.9033 \text{ and } x = \pm 2.2383$

What are the conflicts in Editha?

In William Dean Howells's short story "Editha," the titular character Editha is a woman who has fallen prey to sensationalist war propaganda. As a result, she glorifies and romanticizes war, calling it a "cause so high and noble," and does not fully understand its consequences.
The main conflict of the story is that Editha pushes George Gearson, her fiancé, to enlist and fight in the Spanish-American War. Unlike Editha, George does not believe that war is glorious or a part of God's plan. His father lost an arm in the Civil War and his mother, Mrs. Gearson, has always been very anti-war as a result. However, George eventually does as Editha wishes, and he is killed almost immediately after he is sent off to battle. As she promised to do if anything happened to George, Editha goes to visit his mother. Mrs. Gearson lets Editha know how foolish she was for not thinking of the possibility that George would die, and that she has no sympathy for her.
To make matters worse, it seems that Editha doesn't really change her ways. With one word from another woman that she hardly knows, Editha feels justified and is right back to her blindly patriotic, pro-war ways, beginning to "live again in the ideal."

How does ethics limit the natural sciences?

Development of various technologies affect people and the environment in a lot of way. For instance, in the biomedical field (biosciences), the development of drugs require testing on animals and humans before they are considered viable treatment options. In biotechnology, companies might need to expand and take up land, necessitating deforestation to acquire more lot for expansion. These simple considerations all deal with ethics. Biomedical scientists cannot just give an untested drug to a person to see what happens, or lie to the person about possible side effects. Land cannot just be bought regardless of its effect on the environment or communities for a laboratory to be expanded.
Ethics consists of a set of values and beliefs long believed and accepted by a culture or in the case of some universally accepted by most of the world's population - for example, murder is not acceptable. Obviously, science is not immune to any ethical questions such as whether murder is acceptable, but in the biosciences, ethics usually deals with testing technologies and drugs on humans.
A more recent issue would be the CRISPR/Cas9 system. The system was discovered and developed to be a highly efficient genome editing tool. Ideally, as long as the sequence is known, any sequence of DNA can be edited and any mutation can be introduced. In an ideal world, this is perfect. This means that genetic diseases can now be cured by simply utilizing the technology. However, the system is not perfectly studied yet, and off-site effects are not yet completely documented. Without ethics standing in the way, a scientist could use this system without any further test say on an embryo predicted to have an illness - or maybe even introduce a very rare illness - to see if it works. You can even get an adult, introduce an engineered CRISPR/Cas9 that will change the color of his eyes. However, that is not the case. This is not considered ethical - or at the very least, is considered a grey area in the field. Not fully understanding yet the consequences of the technique makes it very iffy to try on a human subject. 
The same is the case for novel treatment procedures. In the instance that a scientist notices that formulation A kills a certain form of bacteria similar to one that infects humans, he cannot simply jump ahead and give formulation A to everyone with that infection. He has to study it, elucidate it's properties, cross-reaction with other drugs, and then go through the different phases of clinical trials - and each of those clinical trials are tightly regulated by an ethics board to ensure that fabrication of data isn't done (this is another ethical concern in the sciences, but not one that is related to limiting the natural sciences).
In all these cases, ethics is limiting the progress of science in a way that it slows it down. Testing the CRISPR technology straight to humans will directly reveal the effects it has on humans, if any. However, questions like 'which humans do we use as guinea pigs?' or 'what if the test subject dies?' arise and this is where ethics comes in. 
The natural sciences allow human technology to progress - to make life easier, and to cure diseases. While it can be argued that the existence of rules based on ethics - norms and beliefs of a culture - can hinder and slow down the process of discovery, it can also be argued that ignoring these rules will be counterproductive as you will be, in a sense, sacrificing a few (although in a utilitarian sense, the good of the many is still the priority). 
The ethical concerns and issues in science are very complicated. Some scientists may have the tendency to skirt these ethical regulations because their priority is discovery (again, fabrication of data and making up stuff is not what I'm talking about here, but tests that would otherwise seem be considered unethical due to involvement of human test subjects). This is why in every funding agency and research regulatory boards, an ethical committee exists - to ensure than everything is done according to universal ethical principles.
To end this, I'd like to talk about Barry Marshall. He was studying H. pylori and suggested that it causes ulcers. No one in the scientific community believed that a bacteria can survive in the extreme environment in stomach acids (no proof then, so it wasn't their fault). Marshall thought it was possible, and so ingested the bacteria - after a few days, he got ulcer and proved it was caused by a bacterial agent. He goes on to win the nobel prize for this discovery. This was not an ethical move by today's standards. However, had he not done that, it might have taken a few years to understand the disease.
In the end, we see that there is a complicated relationship between ethics and scientific discovery - particularly the speed by which discoveries are made (another example is during the dark ages, when religion blocked scientific discovery, while different it is an example of the effect of a wide-spread norm). However, it should be kept in mind that the sciences work for the betterment of the world, and as humans, we all subscribe to some universal ethical 'law,' and since science is a human endeavor, it might sometimes be necessary for it to abide by these too - otherwise, it might lead to chaos.

What are some examples of word choice that convey the setting of this story?

In the first sentence, the narrator tells us that we are at the "shore" and that the "young English boy" and his mother are on "holiday."  Thus, we can begin to ascertain that the setting of the story is the seaside, and mother and son have gone to the beach for a vacation.  Later, when Jerry is trying to fit in with the older boys who are able to swim through the tunnel in the rock at the wild bay, the narrator tells us that the boys were "of that coast," and Jerry tries to throw all the French he knows at them in an attempt to keep their attention on him.  These are good clues that the setting is, more specifically, the French Riviera, a popular beach locale for British vacationers.  Moreover, the narrator draws a distinction between Jerry's mother's "safe beach" and the "wild bay" he prefers to go to because he seems to be growing up and desiring more independence than he used to. 

What are the historical significance, background, and evolution of the words to the song Maple Leaf Rag by Scott Joplin?

When examining the lyrics to Scott Joplin's classic ragtime composition Maple Leaf Rag, it is important to keep in mind that the lyrics were written some time after the 1899 publication of Joplin's original music, and not by Joplin. Rather, the lyrics were penned by Sydney Brown. Brown's lyrics, which were added with or without--probably the latter--Joplin's consent by his first publisher, John Stark, who had acquired the rights to Maple Leaf Rag and with whom Joplin had an ongoing feud, were noticeably racist and perpetuated negative stereotypes of African Americans. 
Ragtime was a product of late-nineteenth-century America and, more specifically, of the American South. As with blues and jazz, to which ragtime was a precursor, this musical genre was unique to the African American community, in particular those in St. Louis and Sedalia, Missouri. The origins of ragtime, then, cannot be separated from the racial hostilities and institution of racial segregation that continued to plague the South for decades after the end of the Civil War. And, in contrast to some other ragtime composers, Joplin eschewed music that catered to the lowest common denominator of white American society. The publication by Stark of Brown's lyrics, consequently, do not reflect upon Joplin, but upon the racism endemic to society during the latter's life. Ray Argyle, in his history of ragtime and of Joplin's role in popularizing it, Scott Joplin and the Age of Ragtime, quotes the American Federation of Musicians' 1901 declaration that "swore to play no ragtime and to do all in their power to counteract the pernicious influence...of the Negro school." (p. 36) Such was the atmosphere in which Brown penned the lyrics to Joplin's composition.
The lyrics to Maple Leaf Rag are replete with negative imagery illuminating the racial prejudices of the time:

I came from ole Virginy from the county AcomacI have no wealth to speak of 'cept de clothes upon my backI can do the country hoe-down I can buck and wing to show downAnd while I'm in the notion, just step back and watch my motion
Oh go 'way man, I can hypnotize dis nationI can shake the earth's foundation wit' the Maple Leaf Rag
..
The men were struck wit' jealousy, the razors 'gan to flashBut de ladies gathered 'round me for I'd surely made a mash
The finest belle, she sent a boy to call a coach and fourWe rode around a season 'till we both were lost to reason....

Note the use of phrases like "de clothes," "I can buck and wing," "I can hypnotize  this nation," and "I can shake the earth's foundation wit' the Maple Leaf Rag." Brown's lyrics tell of a poor African American walking into a presumably upper-class white dance and scandalizing the attendees. Among the pernicious stereotypes of African American men was that they were sex-crazed predators who targeted white women. When the singer suggests that he can "shake the earth's foundation," he is playing to the fears of many caucasians that blacks were innately threatening not only to the status quo but to the sanctity of white women. The reaction of the men in the ballroom further perpetuates the myth of the ever-threatening African American and, of particular note, of the white man's need to castrate the black man who will otherwise rape white women with wanton abandon.
Sydney Brown's lyrics for Scott Joplin's composition are rarely heard for the simple reason that they do not improve the music and are highly offensive. They represented a bastardization of Joplin's music while also illuminating the blatant racism of the era in which both the original composition and the lyrics were written.
http://www.perfessorbill.com/lyrics/lymaple.htm

What are the advantages and disadvantages of interpersonal communication?

Interpersonal communication is the exchange of information between people. This is not just limited to verbal communication but instead includes body language and facial expressions as well as textual communications and other interactions that are mediated by technology in some way. The advantages of interpersonal communication are immense.
Interactions are predicated on the exchange of information over time, and so interpersonal communication facilitates many facets of human behavior, and all facets of human social behavior. Unfortunately, not all of this behavior is pleasant to experience, and so interpersonal communication's downsides emerge when coercive, violent, or harmful means are used to affect how information passes between two people.
This fact is essential to understanding the ways that interfering with someone's idea of truth through violent or coercive interpersonal communication is such a traumatizing form of abuse and highlights how bad the downsides of interpersonal communication can be.

Textbook writers define "interpersonal communication" as "the nonverbal interaction between two or more interdependent people" (see citation below).
The term "interdependent" is important because social scientists want to distinguish interpersonal communication from impersonal communication.
Consider, for example, this scenario: You make a purchase at a supermarket and interact with the clerk in a rote, automatic way -- treating her as an "it" instead of as a "you." Is that interpersonal communication? Not according to scholars like Martin Buber. It's impersonal, so it doesn't count.
Interpersonal communication includes face-to-face communication, but it can also include other forms of communication, like instant messaging, exchanging email messages, and "talking" via online chat rooms. What's important is that each communicator responds to the other as a "you," not as an "it."
Interpersonal communication can serve many advantageous purposes. It allows us to influence the behavior, attitudes, and opinions of others. It allows for more effective, efficient cooperation, and can help us forge or maintain a social bond. It can help us learn, and relate to the problems or situations that other individuals face. Interpersonal information can help us negotiate, ask for help, offer aid, ask forgiveness, apologize, or achieve reconciliation. We may also use interpersonal communication in order to relax and play.
When psychologists and other social scientists talk about the disadvantages of interpersonal communication, they are usually thinking in terms of the harm that can arise from conflict and emotional turmoil.
For instance, in the academic volume, The Dark Side of Interpersonal Communication, researchers talk about the ways that interpersonal communication can lead to negative outcomes. These range from bad moods to actual harm (psychological or physical). Examples include:
the communication of complaints and criticism
bullying
teasing
the communication of threats
domestic abuse
 
The definition and clarifications about face-to-face and other forms of interpersonal communication are from:
Beebe et al. 2010. Interpersonal Communication: Relating to Others, Fifth Canadian edition. Pearson. (Chapter 1, p. 4).
http://wps.prenhall.com/ca_ab_beebe_intercomm_4/48/12319/3153764.cw/-/3153765/index.html

http://www.pearsoncanada.ca/media/highered-showcase/multi-product-showcase/devito-ch01.pdf

https://books.google.com/books?id=yYvaoG0lR6sC&printsec=frontcover&dq=dark+side+of+interpersonal+communication&hl=en&sa=X&ved=0ahUKEwjC1sS769DPAhUBW2MKHd1MDkwQ6AEIJzAA

Interpersonal communication is the face-to-face exchange of thoughts and feelings between people.  This form of communication is advantageous to building strong relationships with others.  Interpersonal communication allows others to feel close and connected.  When speaking face-to-face, you are able to observe the other person’s body language and tone of voice, both valuable clues to the true meaning of the message.  Interpersonal communication is the desired method to discuss issues that are highly sensitive. 
On the other hand, interpersonal communication takes time, something that most people have little of in this day and age.  It is quicker to send a text or email if you only need to share basic information that is impersonal in nature.  Interpersonal communication is also limited by geography.  It is not always feasible to speak face-to-face with everyone you need to communication with during the day.  Although once the most desired method of communication, interpersonal communication is being used less frequently due to the technology now available to everyone. 

Calculus of a Single Variable, Chapter 7, 7.4, Section 7.4, Problem 12

The arc length of a function of x, f(x), over an interval is determined by the formula below:
L=int_a^bsqrt(1+((dy)/(dx))^2)dx
So using the function given, let us first find (dy)/(dx):
d/(dx)(ln(cos(x)))=(1/(cos(x)))*(-sin(x))=-(sin(x))/(cos(x))=-tan(x)
We can now substitute this into our formula above:
L=int_a^bsqrt(1+((dy)/(dx))^2)dx=L=int_0^(pi/3)sqrt(1+(-tan(x))^2)dx
Which can then be simplified to:
L=int_0^(pi/3)sqrt(1+tan^2(x))dx=int_0^(pi/3)sqrt(sec^2(x))dx=int_0^(pi/3)sec(x)dx
Then you find the definite integral as you normally would. (Using the method shown on the link below, you can find the integral of sec(x).)
L=int_0^(pi/3)sec(x)dx=ln|sec(x)+tan(x)|_0^(pi/3)
L=ln(sec(pi/3)+tan(pi/3))-ln(sec(0)+tan(0))=ln(2+sqrt(3))-ln(1+0)
L=ln(2+sqrt(3))-ln(1)=ln(2+sqrt(3))~~1.32
So the exact value of the arc length of the graph of the function over the given interval is ln(2+sqrt(3))
which is approximately 1.32.

Imagine the world economy is made up of two economies, a small home economy and a large foreign economy. What would be the effect on the home economy if there were an increase in foreign income when exchange rates are floating? And if there were an increase in foreign money supply when exchange rates are fixed?

Because the home economy is small relative to the foreign economy, we can safely assume that changes at home will not significantly affect the state of the foreign market. This is called a "small open economy" model.If foreign income increases, its demand for goods will increase, and this includes goods that are imported from the home economy. Therefore demand for home goods will increase, resulting in money flows from outside.These money flows will increase demand for our currency, which since the exchange rate is floating will rise in value. This will reduce money flowing in as exports and increase money flowing out as imports. When equilibrium is reached, both exports and imports should have increased, increasing our GDP but not changing our balance of trade.An increase in the foreign money supply will cause inflation in the foreign economy, and also increase money flows into the home economy. Between both the increased exports and the foreign inflation, the home currency will have even more pressure to increase in value. But since the exchange rate is fixed, this can't happen. So the currency will remain undervalued.Instead, the home economy will begin accumulating foreign reserves, and will begin to experience a trade surplus and a current account surplus. This will make the home balance sheet stronger, which may seem desirable (some economists think it is desirable in some cases), but carries four large downsides:First, it pulls reserves from other countries, who may not be able to sustain their current account deficits indefinitely. If their deficit collapses, so must our surplus.Second, it can trigger inflation in the local economy, which monetary policy may be insufficient to control.Third, it means exchanging real goods for nothing more than paper, gradually reducing the real wealth of the home country.Fourth, it introduces inefficiencies into the global trade system that reduce wealth for everyone, similar to a tariff or quota.
https://budgeting.thenest.com/mean-currency-undervalued-32198.html

Who was King Louis 16?

Louis XVI was king of France from 1775 to 1792. His power as king was gradually weakened after the French Revolution began in 1789. Three years later the monarchy was abolished, and Louis was imprisoned and executed for treason in January 1793.
It was ironic that Louis XVI was the king during whose reign the Revolution occurred, since his tenure by the standards of absolute monarchy was mild and relatively liberal. He supported the Americans during the War of Independence and sent armies, the navy, armaments and supplies, and huge amounts of cash to America to aid the cause of Independence and defeat France's perpetual enemy, Great Britain. The money spent by France drove the country massively into debt and was one of the factors that brought on the Revolution in 1789.
At first Louis and his queen, Marie-Antoinette, daughter of Maria Theresa of Austria and brother of the current Holy Roman Emperor Joseph II, appeared to cooperate with the revolutionary movement and agreed that reform of the system was necessary. Though Louis was well meaning, both he and his consort were clueless as to what the people really wanted or needed. When they tried in June of 1791 to escape across the border into Germany, they were arrested and brought back to Paris. From this point on, in spite of Louis' acceptance of the Constitution in September of that year, the royal couple were viewed as traitors and enemies. The situation became worse for them when Austria and Prussia declared war on Revolutionary France in 1792. The monarchy was abolished in September of that year, and Louis XVI was executed by beheading in early 1793, with Marie-Antoinette killed later in the same year.

What are some main things that I might have missed in TKAM? There are several things I didn't pick up on such as how the story is about love. Could you name any more?

I assume that you picked up on how the story of the trial of Tom Robinson offers a commentary about racism and how various people join in with it, or oppose it (openly or quietly).  
I also assume you noticed that with the Boo Radley plotline, TKAM addresses the matter of people who don't fit in to society, the rumors and fear that surround them, and how they may in fact be gentle souls.
Here are a few things I didn't fully appreciate the first time I read the story.
Childhood. One reason TKAM is so entertaining is that it is told from the point of view of a young child.  Much of the fun in the story comes from Scout's descriptions of the games, legends, and value system that she, Jem, and Dill share as children.  Also, her description of the first day of kindergarten is not to be missed.
Much of the humor in the story comes from the fact that Scout, though she is the narrator, doesn't understand what is going on in certain scenes.  One notable one is the scene where Jem lies and tells his father that the kids have been playing strip poker.  
Scout's innocence and cluelessness become poignant in the scene where Atticus is guarding the jail, and Scout barges in to the middle of a hostile mob and begins chattering away.
Coming-of-age. TKAM can be read as a coming of age story, not about Scout, but about her older brother Jem.  In the course of the book, Jem goes from being a nine-year-old firmly planted in childhood, to a moody almost-13-year-old who is coming to grips with the world around him.  Early in the book, he figures out that Boo Radley has been reaching out to him and Scout, though Scout does not realize this.  
Later, we see Jem lose his innocence when he is sure that Tom Robinson will be acquitted, but instead the jury find him guilty.  The morning after the trial, Miss Maudie debriefs this shock with Jem, and she "promotes" him to the adult world by giving him, for the first time, a full-sized piece of cake instead of a small cake in a patty-pan.  Atticus also talks Jem through his dismay that the law could allow such an unjust thing to happen.
Often, we have to read between the lines to see the struggles and changes that Jem is going through, because these are described from Scout's point of view.
Southern values and culture.  Though TKAM offers a devastating condemnation of racism in the culture of the 1930s South, it does not portray the culture as wholly bad.   We see the racism in the trial, and the snobbery in Aunt Alexandra and her circle of ladies.  We see the gossip, personified in Miss Stephanie Crawford.  But we also see some good Southern values in Miss Maudie, who "had an acid tongue in her head," but was unfailingly kind to the children, was an avid gardener, and who faced the burning down of her house and yard without even a hint of dismay.  We see dignity, formality and never-failing politeness in many adult characters, but especially in Atticus.  And we see the horrible old Mrs. Dubose, who is a snob and a racist but who is determined to break her morphine addiction before she dies.  Atticus calls her "the bravest person I ever knew." 
Parenting.  Read through the book, paying attention to all the good things Atticus does as a parent.  Notice how he expects the children to respect him, Calpurnia, and other adults (such as Aunt Alexandra), even when he does not agree with them.  Yet he has unique parenting values that do not match perfectly with the values of his family and society, and sometimes he has to fight a bit to pass these on to his children (e.g. when Aunt Alexandra comes to live with them).  Notice too the subtle ways he tries to prepare the children for the jeers they will face when Tom Robinson comes to trial.  
In a sense, everything Atticus does is for the sake of living with integrity in front of his children.  Atticus sends Jem to read to Mrs. Dubose so Jem can see an example of bravery.  He is a crack shot, but he shoots a gun exactly once in the book, because he does not want his children to learn that violence is something to be proud of.  At the end of the book, Atticus can barely stand to cover up the way that Bob Ewell died:

"Sometimes I think I'm a total failure as a parent, but I'm all they've got.  ... if I connived at something like this, frankly I couldn't meet [Jem's] eye, and the day I can't do that, I'll know I've lost him.  I don't want to lose him and Scout, because they're all I've got." 

 

In Hoot, how does the setting in each chapter impact the plot?

The book Hoot is fairly simple in terms of setting.  The story takes place in a small Florida town, and within that town a few locations become repeated setting locations.  Those locations are Roy's home, school, the school bus, and the construction site for the new pancake house.  
Chapter 1 takes place on the school bus.  It's an effective location to introduce readers to Roy and Dana.  It also allows the author to have Dana smash Roy's face against a window and see a strange running boy.  
Chapter 2 begins on the bus.  Readers get a repeat of Dana's bullying, but this time Roy punches Dana in the face in order to chase after the boy.  The chase moves onto a golf course, and Roy is hit in the head with a golf ball. The story picks up at school.  The return to school is important because readers are introduced to Beatrice Leap, who is strangely protective of the mysterious running boy.  
Chapter 3 has two settings.  The first is Roy's house. All this does is introduce readers to his parents.  The second location is the construction site.  It will become a key location as the story continues.  In this chapter, it only introduces readers to the fact that there is ongoing vandalism there.
Chapter 4 is mainly at the construction site.  Delinko falls asleep in his squad car, which is important because it allows his car to be vandalized.  
Chapter 5's setting is near the construction site.  The impact on plot at this location is that Roy finally gets to meet the mysterious boy.  His name is Mullet Fingers.  
Chapter 6 is all over the place.  Parts of it are at Roy's home.  Other parts at the police station, Roy's school, the golf course, and the construction site area.  In terms of plot, not much actually happens during this chapter.  The police station is important because Delinko is confined to desk duty for a month.  The construction site is important because Roy is attempting to bring Mullet Fingers some shoes, but instead his bike gets stolen by Beatrice.
Chapter 7's key location is a junkyard.  It's important to the plot because it gives Beatrice the privacy to tell Roy that Mullet Fingers is her brother and that's why she is so protective of him.
Chapter 8 returns to the construction site because readers are told that Curly is trying to secure the site against further vandalism.  He does this by bringing in four Rottweilers.  
Chapter 9 is basically a straight continuation of chapter 8.  Most of the action takes place at the construction site.  All of the dogs have run off because snakes have been found on the property.  The plot result is that Chuck is further enraged and orders bulldozing to begin immediately.  
Chapter 10's setting is en route to the construction site.  Along the way, Beatrice tells Roy a bit more about Mullet Fingers and her family situation.  Once at the construction site, an important plot detail is finally revealed.  Mullet Fingers is trying to stop construction in order to protect some owls.  
Chapter 11 continues at the construction site.  In terms of plot, the most important thing that happens here during this chapter is that Mullet Fingers is not doing well after getting bit by one of the dogs.  He's in such bad shape that Roy and Beatrice are forced to take him to the hospital.  
Chapter 12 is at a new location for the story.  It takes place at the hospital.  Mullet Fingers tells the hospital that he is Roy, and Roy's parents are contacted and come to the hospital.  This forces Mullet Fingers to flee, and Roy is left trying to explain his way out of the situation.  
Chapter 13 is back at Roy's house.  The most important plot point for this chapter is that Roy explains almost the entire situation to his dad.  His dad says that he'll help look into the situation, but readers aren't sure anything will actually come of it.  
Chapter 14 takes place at an old shipwrecked stone-crab boat.  This again is one of those chapters where not much actually happens, but it’s a critical chapter in terms of character development.  Roy and Mullet Fingers spend most of the time talking to each other about the construction and the owls, and the result is that the two boys bond and become closer friends.
Chapter 15 is a chase sequence.  It begins at Dana’s house and ends at the construction site.  Roy successfully lures Dana to the site, and Dana winds up getting arrested and accused of being the vandal.  This removes the Dana conflict for the remainder of the book.
The bulk of chapter 16 takes place at Roy’s house.  He hears about Dana’s arrest.  His father gives him some advice on where to look for legal documentation that can stop the construction project.  It appears that Roy’s father has been giving the matter some serious thought, and it looks like Roy just might wind up being successful in trying to stop the construction.  
Chapter 17 has two key locations.  The first is the police station.  This location is important to the plot because it shows readers that Delinko doesn’t believe that Dana is the vandal.  The other location is the construction site. Curly is told by Chuck that the groundbreaking ceremony will begin on Wednesday.  This will force Beatrice, Roy, and Mullet Fingers to do some fast thinking and acting.  
Chapter 18 begins at the construction site.  The importance of the location is that Delinko finally realizes that there are owls present.  The chapter then moves to school, and readers are told that Roy brainstorms a way to stop the construction.  Finally, back at the junkyard, Mullet Fingers listens to Roy’s plan.  It isn’t clear if Mullet Fingers will work the plan or not.  
Chapter 19 is mostly at the construction site.  Nothing happens other than Chuck and the other important construction people showing up for the groundbreaking ceremony.  
Chapter 20 is at the construction site.  This is the climax of the plot.  The owl evidence is presented.  Chuck is enraged, and the crowd begins to support the heroic efforts of Roy, Beatrice, and Mullet Fingers.  
Chapter 21 is the falling action and takes place at Roy’s house.  It’s during this chapter that Roy gives a reporter the legal documentation that proves that the construction company intentionally overlooked the presence of the owls.  This leads to the conclusion: Chuck is forced to resign and the pancake company attempts to clean up their image by donating a bunch of money.  Roy is glad to be in Florida and readers are presented with a nice tidy wrap-up to the story. 

Does wealth inequality leads to racism and discrimination? Why?

This is a complicated question—one that academics and policymakers alike have struggled to comprehend. Does economic inequality lead to racial discrimination? Or is it the other way around? (Is is the chicken or the egg?) Or are they simply problems that go hand in hand, without one causing the other?
It depends on who you ask. Bernie Sanders famously called wealth inequality and racism "parallel problems." Others see the two problems as being so interconnected that they've collapsed two terms into a single phrase: the "racial wealth gap."
Let's look at the numbers. According to a study published last year and frequently cited in literature on the topic, 10.9% of white households earn incomes below the federal poverty line. Latino households come in at 23.5% and black households at 26.1%. The study shows that minority households (especially African-American) fall far behind white households in nearly every way you can measure wealth: they earn less, they're underemployed, they have less access to education, healthcare, and credit, and they don't own as many homes or businesses as their white counterparts.
Looking at this information, you could see another argument: what if it's racism that causes wealth inequality, not the other way around? Ta-Nehisi Coates has written extensively on the topic of black poverty, and he's been a strong advocate for reparations for African-Americans whose ancestors were slaves. In Coates's view, it's the history of slavery that's given white people a distinct economic advantage over black people. Slavery, after all, was a way for white people to get richer while using the free manpower of their black slaves. The USA has a debt to pay to the families of those slaves, Coates argues. Especially because even now, so many years after slavery was abolished, black people have never recovered from the deficit. 
Race and wealth are correlated, clearly. But whether or not one causes another isn't easily measured. If you're writing an essay on this topic, I'd suggest looking at the following resources, and at Coates's argument for reparations to address the racial wealth gap.
 
 
https://www.theatlantic.com/politics/archive/2016/02/why-we-write/459909/

https://www.weforum.org/agenda/2013/09/the-problem-with-wealth-inequality/

Single Variable Calculus, Chapter 3, 3.7, Section 3.7, Problem 32

The equation $\displaystyle \frac{dP}{dt} = r_0 \left( 1 - \frac{P(t)}{p_c} \right)P(t) - \beta P(t)$ represents the rate of change of the fish population present in the fish pond.

$
\begin{equation}
\begin{aligned}
\text{where }& r_0 \text{ is the birth rate of the fish.}\\
& P_c \text{ is the maximum population that the pond can sustain.}\\
& \beta \text{ is the percentage of the population that is harvested.}
\end{aligned}
\end{equation}
$


a.) At what value $\displaystyle\frac{dP}{dt}$ corresponds to a stable population?
b.) Find the stable population level. Suppose that a pond can sustain 10,000 fish, the birth rate is 4%, and the harvesting rate is 4%.
c.) What happens if $\beta$ is raised to 5%.

a.) If the population is stable, then rate of change is neither decreasing nor increasing, that is, $\displaystyle \frac{dP}{dt} = 0$


$
\begin{equation}
\begin{aligned}
\frac{dP}{dt} = 0 &= r_0 \left( 1 - \frac{P(t)}{p_c} \right)P(t) - \beta P(t)\\
\\
\beta \cancel{P(t)} &= r_0 \left( 1 - \frac{P(t)}{p_c} \right)\cancel{P(t)}\\
\\
\beta & = r_0 \left( 1 - \frac{P(t)}{p_c} \right)
\end{aligned}
\end{equation}
$


b.) $\displaystyle \frac{dP}{dt} = 0$, for the condition of population stability.
From part(a),

$
\begin{equation}
\begin{aligned}
\beta & = r_0 \left( 1 - \frac{P(t)}{p_c} \right) && \text{where } r_0 = \frac{5}{100}, \quad P_c = 10,000, \quad \beta = \frac{4}{100}\\
\\
\frac{4}{\cancel{100}} &= \frac{5}{\cancel{100}} \left( 1 - \frac{P(t)}{10,000} \right)\\
\\
\frac{4}{5} &= 1 - \frac{P(t)}{10,000}\\
\\
P(t) & = \left( 1 - \frac{4}{5} \right) 10,000\\
\\
P(t) &= 2,000
\end{aligned}
\end{equation}
$


c.) If $\displaystyle\beta = \frac{5}{100}$, from part (a)


$
\begin{equation}
\begin{aligned}
\cancel{\frac{5}{100}} &= \cancel{\frac{5}{100}} \left( 1 - \frac{P(t)}{10,000}\right)\\
\\
1 &= 1 - \frac{P(t)}{10,000}\\
\\
P(t) &= (1-1) (10,000)\\
\\
P(t) &= 0
\end{aligned}
\end{equation}
$

Intermediate Algebra, Chapter 3, 3.3, Section 3.3, Problem 66

Determine an equation of the line passing through the points $\displaystyle \left( \frac{3}{4}, \frac{8}{3} \right)$ and $\displaystyle \left( \frac{2}{5}, \frac{2}{3} \right)$.

(a) Write the equation in standard form.

Using the Slope Formula,

$\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{\displaystyle \frac{2}{3} - \frac{8}{3}}{\displaystyle \frac{2}{5} - \frac{3}{4}} = \frac{\displaystyle - \frac{6}{3}}{\displaystyle - \frac{7}{20}} = - \frac{6}{3} \cdot - \frac{20}{7} = \frac{40}{7}$

Using Point Slope Form, where $m = \displaystyle \frac{40}{7}$ and $(x_1,y_1) = \displaystyle \left( \frac{3}{4}, \frac{8}{3} \right)$



$
\begin{equation}
\begin{aligned}

y - y_1 =& m(x - x_1)
&& \text{Point Slope Form}
\\
\\
y - \frac{8}{3} =& \frac{40}{7} \left( x - \frac{3}{4} \right)
&& \text{Substitute } x = \frac{3}{4}, y = \frac{8}{3} \text{ and } m = \frac{40}{7}
\\
\\
y - \frac{8}{3} =& \frac{40}{7}x - \frac{30}{7}
&& \text{Distributive Property}
\\
\\
21y - 56 =& 120x - 90
&& \text{Multiply each side by $21$}
\\
\\
-120x + 21y =& -90 + 56
&& \text{Subtract each side by $(120x - 56)$}
\\
\\
-120x + 21y =& -34
&& \text{Standard Form}
\\
\text{or} &
&&
\\
120x - 21y =& 34
&&

\end{aligned}
\end{equation}
$



(b) Write the equation in slope-intercept form.


$
\begin{equation}
\begin{aligned}

-120x + 21y =& -34
&& \text{Standard Form}
\\
\\
21y =& 120x - 34
&& \text{Add each side by $120x$}
\\
\\
y =& \frac{120}{21}x - \frac{34}{21}
&& \text{Divide each side by $21$}
\\
\\
y =& \frac{40}{7}x - \frac{34}{21}
&& \text{Slope Intercept Form}

\end{aligned}
\end{equation}
$

How did early civilizations deal with democracy? What were its major limitations? Is democracy compatible with running an empire?

Democracy was a very rare phenomenon in antiquity. Most of the great empires, such as the Egyptian, Mesopotamian, and Persian ones, were actually monarchies, often theocratic in nature. The two ancient civilizations that experimented with democratic governments had only limited success with the experiments.
The first major democracy, and one that has very much influenced the subsequent growth of this form of political organization was that of Athens. Strikingly, it was a direct democracy in which all citizens could participate by speaking in the Assembly and voting directly on laws. Many of the important positions in Athens were selected by lot to prevent corruption. What made this workable is that there were fewer than 50,000 citizens in Athens, and normal attendance at the Assembly was probably around 10,000. Membership in the Assembly was restricted to males over the age of 18 with Athenian parents or grandparents. Women, slaves, and metics (resident aliens) who constituted the actual majority of the population, could not vote.
The so-called Athenian Empire began as the Delian League, an alliance among Greek city-states against Persia's efforts to conquer Greece. After the defeat of the Persians, Athens, although internally a democracy, behaved increasingly tyrannically in the Delian League, looting its treasury to rebuild the Acropolis and treating other members as subordinate, behavior that soon led to the Peloponnesian Wars. Thucydides argues that democracy led somewhat inevitably to tyrannical behavior, as demagogues like Clean would inflame nativist and oppressive tendencies to maintain their power and popularity. As the "Athenian Empire" lasted only 50 years, we can say that the Athenian democracy did not display much competency in imperial rule.
Rome also began as a small Republic, but its administrative mechanisms were not really adequate to the task of running the empire it almost accidentally acquired after the Punic Wars. Rather than extending a republican form of government to conquered territories, it tended to send provincial governors who acted as absolute rulers. In certain ways, the necessity of administering an empire led to the collapse of the Republic and the beginning of monarchial rule. 

College Algebra, Chapter 5, 5.5, Section 5.5, Problem 30

The pH reading of a glass of liquid is given. Determine the hydrogen ion concentration of the liquid.

(a) Beer: pH = $4.6$

(b) Water: pH = $7.3$



Recall that pH scale is represented as

pH = $- \log [H^+]$ where $H^+ =$ hydrogen ion concentration measured in moles per liter (M)

a.) Beer:


$
\begin{equation}
\begin{aligned}

4.6 =& - \log [H^+]
&& \text{Multiply each side by } -1
\\
\\
-4.6 =& \log [H^+]
&& \text{Take antilog of each side}
\\
\\
10^{-4.6} =& H^+
&& \text{Solve for the hydrogen ion concentration } H^+
\\
\\
H^+ =& 2.51 \times 10^{-5} M

\end{aligned}
\end{equation}
$


b.) Water:


$
\begin{equation}
\begin{aligned}

7.3 =& - \log [H^+]
&& \text{Multiply each side by } -1
\\
\\
-7.3 =& \log [H^+]
&& \text{Take antilog on each side}
\\
\\
10^{-7.3} =& H^+
&& \text{Solve for the hydrogen ion concentration } H^+
\\
\\
H^+ =& 5.01 \times 10^{-8} M

\end{aligned}
\end{equation}
$

How do court decisions shape Constitutional interpretation of the relationship between the national and state governments in the U.S.?

Supreme Court cases have shaped the constitutional relationship between the national government and the state governments. This is a power that is granted to the Supreme Court in the Constitution. These decisions have influenced the balance of power between the national government and the state governments.
In 1803, in the case of Marbury v Madison, the Supreme Court ruled that the Constitution is the supreme law of the land. The ruling also gave the courts the power of judicial review, which is used to determine if a law is constitutional.
In 1819, in the case of McCulloch v Maryland, the Supreme Court ruled that a loose view of the Constitution is acceptable. This increased the power of the federal government by allowing the federal government to do things that were not specifically mentioned in the Constitution.
There were a few other rulings that increased the power of the national government. In 1824, in the case of Gibbons v Ogden, the Supreme Court ruled that the federal government is responsible for controlling interstate trade. In 1937, in the case of National Labor Relations Board v Jones and Laughlin Steel Corp., the Supreme Court ruled that the federal government could regulate products within a national marketplace.
Various Supreme Court rulings have increased the power of the federal government.

Name three figures from the Renaissance.

One key figure from the Renaissance would be Johann Gutenberg. He invented movable type, which allowed books to be printed quickly and thus made them more affordable. Gutenberg's invention also allowed many languages, such as French and English, to be seen in print by the masses, thus making them the language of choice for legal documents. This led to the rise of nationalism in Europe during the Renaissance. Gutenberg's printing press made learning more available which was one of the key points of the period.
Another key figure would be Martin Luther, who in 1517 spoke out against the Catholic Church. Luther saw the Papacy as being corrupt and he wanted a return to the original church as was had by the earliest Christians. Thanks to Luther, Protestants splintered off into various religious sects as people had the courage to interpret the Bible differently.
Another key figure is Christopher Columbus. Columbus, a sailor from Genoa, postulated that it would be easier for Spain to reach the valuable spice trade by sailing west instead of sending trade caravans east. While Columbus did not meet his goal, he did discover the island of Hispaniola. From here, Spain developed a large New World empire. The riches of Spain would be squandered in European wars, but Spain's achievement would inspire other powers to get in on the New World colonial race.

Distinguish between utilitarianism and formalism.

Formalism places emphasis on the act itself to determine whether it is right or wrong. Utilitarianism places emphasis on the situation arising from the act to determine whether the act is acceptable. Thus, utilitarianism is based on the maxim: "The end justifies the means."
Formalism is based on absolute values and dictates that for an action to be considered ethical it has to be morally sound or consistent. For instance, in the Bill of Rights, the rights of individuals are inalienable and should not be curtailed.
Utilitarianism is based on relative values assessed in situational contexts. Thus, the "wrong" thing can be done for the right reasons or if the typical "unethical" act results in higher benefits. For instance, one may be forced to lie in order to save a suspected thief from a lynch mob. In such a situation, the act of lying is considered unethical, but it might be the only way to save the suspect’s life and allow for due process.
https://www.investopedia.com/terms/u/utilitarianism.asp

This distinction is one found most commonly in business ethics.
Utilitarianism is an ethical doctrine that is based on the ethical theory of John Stuart Mill who, in turn, was influenced by the hedonistic ethics of Jeremy Bentham. According to utilitarianism, an action is good insofar as it maximizes good consequences or a good outcome. For example, if a utilitarian were asked to choose between an action that injured five people versus one that injured ten, the utilitarian would always choose the action that results in five people injured since this the best outcome. This, at least, is simple act utilitarianism.
Formalism, on the other hand, focuses on the rules that are right. Formalism is akin to deontological ethics associated with Immanuel Kant in that it places value on principles and rules rather than outcomes. If a wrong action results in fewer people being injured (to use the example from the previous paragraph), the formalist would not choose it. The outcome has no moral significance.

I need help writing an essay in response to the following prompt: B. The Post-Cold War era (1991-present) presents greater danger to the national security of the United States than did the era of the Cold War. The Cold War nuclear threat was obviously a high-level threat, but by the 1960s (after the Cuban missile crisis) the United States and the Soviet Union constructed a relationship which remained hostile but realistic and in which the purposeful use of nuclear weapons was highly unlikely. In contrast, the United States faces a world of many dangers, from hostile and growing competitors like China and Iran to very flexible and violent terrorist and criminal organizations that do not align with the world's national borders. The threat of a terrorist organization obtaining and using a nuclear weapons is more likely than was the launch of a thousand nuclear weapons by the Soviet Union. Explain your answer and be sure to address both sides, discussing why you support one and oppose the other. Be specific and cite any sources you use; do not take quotes directly from any source without proper punctuation and citations.

In writing an essay on this topic, you will need to talk about the wide range of current threats to national security. In order to succeed in this assignment, you might want to break it down into several sections:
Introduction: Your main thesis should center around the fact that it is much harder to defend against a wide variety of threats from multiple types of entities than a single known threat.
Transition: You then should have a transition paragraph in which you discuss some of the major types of security hazards of the post-Cold War era. The main body of your essay should address each type of threat in a separate section.
Rogue States: You might begin by talking about rogue states, especially North Korea, and how by being outside the framework of international law and diplomacy they are a potential threat to US security.
Russia: Putin's Russia may be no less dangerous than the Soviet Union as it still has a nuclear arsenal and is moving towards a rhetoric of extreme nationalism and xenophobia.
China: Here you might discuss the simmering conflicts in the South China Sea and the Nine-Dashed Line territorial claims of China.
Failed States: The next major security threat you might discuss are the failed states such as Syria, Libya, Somalia and Yemen and associated fragile states and discuss how they destabilize regions and increase the threat of terrorism and refugee crises. 
Terrorism and Cyberterrorism: In this section you would discuss how modern technology allows a relatively small group of people to pose major threats to national security by acts of terrorism and cyberterrorism.
Conclusion: You should argue that the sheer variety of current threats makes for a greater national security risk than did the better understood and more limited threats of the Cold War. 

Single Variable Calculus, Chapter 3, 3.9, Section 3.9, Problem 10

Check the Linear Approximation $\displaystyle \frac{1}{\sqrt{4 - x}} \approx \frac{1}{2} + \frac{1}{16} x$ at $****$. Then determine the values of $x$ for which the Linear Approximation is accurate to within $0.1$.

Let $\displaystyle f(x) = \frac{1}{(1 + 2x)^4} x$

Using the Linear Approximation/Tangent Line Approximation

$L(x) = f(a) + f'(a)(x - a)$


$
\begin{equation}
\begin{aligned}

f(a) = f(0) =& \frac{1}{\sqrt{4 - 0}}
\\
\\
f(0) =& \frac{1}{\sqrt{4}}
\\
\\
f(0) =& \frac{1}{2}
\\
\\
f'(a) = f'(0) =& \frac{d}{dx} \left[ \frac{1 }{(4 - x)^{\frac{1}{2}}} \right]
\\
\\
f'(0) =& \frac{\displaystyle (4 - x)^{\frac{1}{2}} \frac{d}{dx} (1) - (1) \frac{d}{dx} (4 - x)^{\frac{1}{2}} }{[(4 x)^{\frac{1}{2}}]^2}
\\
\\
f'(0) =& \frac{\displaystyle (4 - x)^{\frac{1}{2}} (0) - \frac{1}{2} (4 - x)^{\frac{-1}{2}} \frac{d}{dx} (4 - x) }{4 - x}
\\
\\
f'(0) =& \frac{\displaystyle \frac{1}{2} (4 - x)^{\frac{-1}{2}}}{4 -x}
\\
\\
f'(0) =& \frac{1}{2(4 - x)^{\frac{1}{2}} (4 - x)}
\\
\\
f'(0) =& \frac{1}{2(4 - x)^{\frac{3}{2}}}
\\
\\
f'(0) =& \frac{ 1}{2(4 - 0)^{\frac{3}{2}}}
\\
\\
f'(0) =& \frac{1}{2 [(4)^{\frac{1}{2}}]^3z}
\\
\\
f'(0) =& \frac{1}{2 (2)^3}
\\
\\
f'(0) =& \frac{1}{2 (8)}
\\
\\
f'(0) =& \frac{1}{16}
\\
\\
L(x) =& \frac{1}{2} + \frac{1}{16} (x - 0)
\\
\\
L(x) =& \frac{1}{2} + \frac{1}{16 }x

\end{aligned}
\end{equation}
$


So

$\displaystyle \frac{1}{\sqrt{4 - x}} \approx \frac{1}{2} + \frac{1}{6} x$

Accuracy to within $0.1$ means that the function should differ by less than $0.1$

$\displaystyle \left| \left( \frac{1}{2} + \frac{1}{16 } x \right) \right| < 0.1$

Equivalently, we could write

$\displaystyle \frac{1}{\sqrt{4 - x}} - 0.1 < \frac{1}{2} + \frac{1}{16} x < \frac{1}{\sqrt{4 - x}} + 0.1$







This says that the Linear Approximation should lie between the curves obtained by shifting the curve $\displaystyle y = \frac{1}{\sqrt{4 - x}}$ upward and downward by $0.1$. The graph shows the tangent line $\displaystyle y = \frac{1}{2} + \frac{1}{16} x$ intersecting the lower curve $\displaystyle y = \frac{1}{\sqrt{4 - x}} - 0.1$ at A and B. We can estimate the $x$-coordinate of A which is $-3.91$ and the $x$-coordinate of B is $2.14$.

Thus, referring to the graph the approximation

$\displaystyle y = \frac{1}{\sqrt{4 - x}} \approx \frac{1}{2} + \frac{1}{16} x$

is accurate to within $0.1$ when $-3.91 < x < 2.14$

How is Buck different from other Southland dogs Spitz has known?

Buck is smarter and more determined than other dogs from the South. In chapter three, London writes about Spitz's surprise at Buck:

...for of the many Southland dogs he had known, not one had shown up worthily in camp and on trail. They were all too soft, dying under the toil, the frost, and starvation. Buck was the exception. He alone endured and prospered, matching the husky in strength, savagery, and cunning.

While in some respects Buck's background as a pet puts him at a disadvantage (for instance, his paws are not as tough as the other dogs', to the point where he must wear improvised moccasins for protection), in other respects it gives him an edge. When it comes time for the final showdown with Spitz, Buck's strength and fury are no a match for the more experienced dog. Instead, the factor that allows Buck to defeat Spitz is his "imagination"; Buck can fight with his head as well as by instinct. He is able to trick Spitz into defending against a charge when in at the last moment Buck turns and breaks his foreleg. It's clear that Buck is the superior dog.

Spitz is the undisputed alpha dog of the trail. He's used to getting his own way and never being challenged for dominance or control. So when Buck comes along it's a bit of a shock to the system. Spitz feels his supremacy threatened by this upstart newcomer and his enormous strength and bravery. He tries to put Buck in his place by brutally attacking him, tearing his flesh to the bone. But all he gets for his troubles is a good whipping from Francois. From now on, it's war between the two dogs.
What is especially puzzling for Spitz is that Buck is the first Southland dog who's ever shown any kind of strength or fortitude. All the other Southland dogs he's ever come across were way too soft; they never had what it took to withstand the privations of life on the trail. But Buck is different: he matches Spitz in strength, savagery, and cunning. That makes him a serious threat to Spitz's previously unchallenged authority.

List one myth told by Jem about Boo Radley's behavior.

The people in Maycomb County have plenty of tales to tell about Boo Radley in To Kill a Mockingbird. Since the Radley family doesn't typically follow many of the unwritten rules that most of society follows like going to church on Sundays and keeping their doors and shutters open when the weather is nice, the family is often a topic of conversation. Boo is often to blame for certain misgivings or pitfalls in the community. For example, "When people’s azaleas froze in a cold snap, it was because he had breathed on them."
In chapter 1, Jem is educating Dill on the unfortunate qualities and characteristics of Boo Radley, and he has many tales of his own to share. For example, to explain why Boo never leaves the house, Jem believes that Boo is kept chained to his bed. Jem also shares that Boo has blood-stained hands because he eats raw cats and squirrels. In addition, Boo has, "a long jagged scar that ran across his face; what teeth he had were yellow and rotten; his eyes popped, and he drooled most of the time."

Who is the character "Job" that Rebekka references when hallucinating about the women on the ship?

In the story, "Job" is an allusion to the character of Job in the Bible. In the Book of Job, God takes up Satan's challenge and inundates Job with great tragedy, as a means of testing his faith and loyalty. Accordingly, Job's cattle, children, and servants all fall victim to nature's wrath or the murderous intentions of marauders. In addition to all this suffering, God also plagues Job with painful sores all over his body.
In the midst of his trials, Job's three friends, Bildad, Eliphaz, and Zophar, visit him. They try to comfort him but only succeed in making things worse. All three agree that Job must have been guilty of enough evil in his past to have deserved such suffering. They lecture him in self-righteous indignation about wickedness, sin, and the wrath of God. In the end, Job characterizes his friends as "miserable comforters."
The  biblical allusion to Job characterizes Rebekka's suffering in Chapter 7. In the chapter, Rebekka is delirious from smallpox, and she awaits the return of Florens and the blacksmith, in the hopes that the latter might save her. Meanwhile, her friends come to soothe her, but it is only her imagination: "...like all ghostly presences, they were interested only in themselves." Yet, Rebekka maintains that she welcomes the distraction of even these past spirits; she equates them with Job's friends and muses that their meaningless chatter demonstrates the "true value of Job's comforters."
Like Job's friends, the ghostly spirits in Rebekka's imagination "comfort" her. They distract her from her suffering and turn her thoughts away from herself. Like Job, Rebekka longs for God's attention and blessings again; she has no need to be reminded of her weakness, vulnerability, and ignorance. Yet, she concludes that, in the midst of her great trial, "false comfort" is better than none.

In Beowulf, what is the significance of the line, "...out from the marsh, from the foot of misty hills and bogs..."?

The line you've chosen from Beowulf is a great example of the caesura, an important structural element in both Beowulf and Old English poetry as a whole. The caesura is a midline pause used throughout Beowulf, and it provides the poetry with an integral rhythm and structure that improves the flow of the verse. In this particular line, the caesura is important because the rhythm it creates heightens the sense of suspense. In the section of the poem that this line occurs in, Grendel is coming out of the wilderness with violent, murderous intent. The caesura here is vital because it creates a suspenseful atmosphere that perfectly mirrors the oncoming monster. Thus, we see that the caesura is important not only because it promotes rhythm throughout the poetic verse, but also because it makes the overall attempt to tell the story more effective. 

How is the concept of human relationships explored in the poem "Lullaby" by W.H. Auden?

"Lullaby" is an interesting poem in its sheer universality; it represents a relationship most of us recognize, while at the same time rejecting the traditional trappings of love poetry in its acknowledgement that neither the speaker nor his beloved are perfect. The universal sentiments Auden expresses are even more significant because Auden himself was a gay man whose love poetry was to and about other men, yet the point this poem makes is that all human relationships are, at their core, about the same things.
The speaker describes himself as "faithless" while his lover is "mortal, guilty," and yet, in the eyes of the speaker, "entirely beautiful." He knows that this is not reality, but to him it is immaterial. The second stanza incorporates "supernatural" elements and philosophical questions of "soul and body," describing the way "universal hope and love" make knowledge of a beloved's faults drop away. This poem, in particular, focuses on an island in time, "this night," when the lovers need not think of "the cost" of their faults or infidelities; rather, they must treasure each "whisper," "thought," "kiss" and "look," as being the more important truths.
"Beauty, midnight, vision dies," begins the final stanza of the poem: all ephemeral things eventually come to an end, including the beauty of the beloved, the fleeting moment in time described by this poem, and the vision of the lover. Ultimately, however, this is not important, because the nature of human relationships is that "every human love" will forgive faults and guilt in the lover, knowing that this is simply how people are.

What is an example of personification in "The Lady or the Tiger?" by Frank R. Stockton?

As the previous educator answer states, the amphitheater which the king builds in this story is personified as an "agent" which delivers justice. More than this, even the king's own "exuberant and barbaric fancy" is personified as something so powerful as to be almost separate from the king himself, capable of "asserting itself."
Later in the text, we can find other examples. The "doleful iron bells" which ring out in the arena, for example, are personified in that they themselves are not literally "doleful"—they are not capable of feeling this kind of emotion—but the writer ascribes that emotion to them, rather than to the person hearing their sound. The same applies later to the "gay brass bells" which elicit an opposite emotion in the listener.
Towards the end of the story, the human heart is also personified, imagined as something which can lead its possessor "through devious mazes of passion." In this example, the heart represents the whole person, making it an example of synecdoche also. Synecdoche is when one part of something is used to represent the whole thing.

One example of personification in "The Lady, or the Tiger?" by Frank R. Stockton is the following:


This vast amphitheater. . . was an agent of poetic justice, in which crime was punished, or virtue rewarded, by the decrees of an impartial and incorruptible chance.

The amphitheater itself is described as a person who can exercise judgment and bring about justice, so an inanimate object is personified (that is, made into a living being). In this example, the amphitheater becomes the agent of justice, rather than the king, which suggests the king does not really accept responsibility for the terrible system of justice he established. Instead, the building itself, with its constantly changing doors containing a maiden on one side and a tiger on the other, becomes the instrument of justice. The personification in this story is a deliberate choice the author makes to emphasize the way in which the king absolves himself of blame for the barbaric system he has established.

When Doodle finally walks, Brother waltzed Aunt Nicey around the room for a brief, joyful moment. Look at the line. What happens to end their joyful dance? Symbolically, what is interesting about this supposedly light-hearted moment?

The waltz of the brother and Aunt Nicey foreshadows the future of the brother.
After Doodle demonstrates that he can walk, the family rejoices in Doodle's success, and Aunt Nicey dances with the brother. However, Aunt Nicey steps on the brother's toes with her heavy shoes, hurting him "so badly" that the brother feels he is "crippled for life." This reaction is a reminder of the attitude toward disabilities that prevails in this family that has kept little Doodle in a back room and built a casket for him when he was an infant in expectation of his death. When he does not die, the brother tries to force Doodle to learn to walk and not be "crippled" because he is embarrassed to have a brother who cannot walk.
After Doodle's death, the brother becomes crippled from the limitations of his heart and mind that would forcibly demand that Doodle act "normally." In his crippled state, much of the beauty in life seems to have disappeared for the brother. In the exposition of his narrative, for instance, he states that the bleeding tree is gone, and in its place stands a grindstone, often a symbol of continuous and monotonous hard labor. Now, he adds, "if an oriole sings in the elm, its song seems to die up in the leaves, a silvery dust." In other words, with the death of Doodle, the beauty in the brother's life has disappeared. He now is spiritually "crippled for life," limited in his ability to enjoy life and see beauty in it as did Doodle.

Where did the kidnappers take the boy in "The Ransom of Red Chief" by O. Henry?

In “The Ransom of Red Chief,” the two kidnappers take the little boy to a cave on a mountain. We are not told much more about the place where they take him.
According to the narrator, this story takes place in Alabama, near to a small town called Summit. The two men, one of whom is narrator (we find out later his name is Sam) and the other of whom is named Bill, pick out the target of their kidnap plot. They then prepare the place where they will take the kidnapped boy. Here is what the narrator tells us about the place:

About two miles from Summit was a little mountain, covered with a dense cedar brake. On the rear elevation of this mountain was a cave. There we stored provisions.

After they store the provisions, they go into town to kidnap the boy. He puts up quite a fight, but they eventually get him into their buggy. At that point, the narrator says,

We took him up to the cave, and I hitched the horse in the cedar brake.

From this, we can see that the two kidnappers take “Red Chief” up to a cave on a small wooded mountain about two miles from the town where the boy lives.

What is the structure of a tentacle?

A tentacle is unique in that “structure” is a word not often used in reference to this special aspect of biology. That is to say, tentacles are without a skeletal structure and are organs. Several species have tentacles, including squids, octopuses, snails, jellyfish, coral polyps, and even a mole (the star-nosed mole, to be precise). Tentacles are composed mainly of muscle tissue and are used for both movement and object manipulation (think here of an octopus escaping from a jar) as well as sensory perception (taste, smell, feel). The movement aspect and the sensory aspect of a tentacle varies based on the animal in question. In other words, some animals (e.g., the star-nosed mole) use their tentacle primarily for enhanced sensory perception, others use them primarily for movement and manipulation, and others have a combination of both at play.
https://governmentshutdown.noaa.gov/

When was the first house made?

The first house might not have been much of a "house" as we would regard it today, but rather as a gathering place. Australopithecus humans probably used tree canopies to get out of the rain. Archaeologists have discovered a large meeting hall in Nice, France that could have been used for a house, but they doubt that early humans used it for this purpose. It dates from about 400,000 years ago. Some of the earliest examples of houses come from the Mezhirich people of Ukraine from 15,000 years ago, who built houses on the steppe in village communities in order to hunt animals better. Still, they do not see the trappings of "home" here. The first "houses" that archeologists accept as such come from the Natufians from the Middle East. These dwellings date from about 12,000 years ago. These houses are seen as semi-permanent shelters and not just protection against the elements.
http://nautil.us/issue/8/home/in-search-of-the-first-human-home

Do you think Dexter knew his engagement to Irene would not last? What clues does the text provide?

If Judy Jones had not reappeared in Dexter's life on the night of the University Club dance, it is likely that he would have married Irene Scheerer and had the children he imagined hearing her call to in their future. Until Judy reappears, Dexter likely did not think about his engagement to Irene ending. She is "popular," "great," "sweet," and "honorable," and Dexter has a good relationship with her parents. Irene offers Dexter "a sense of solidity" that he accepts, knowing it would never rival the passion he feels for Judy Jones. Irene is destined to be his second choice, and because of Judy's unpredictability, Dexter was willing to settle for Irene.
Dexter never regrets discarding Irene for another interlude with Judy and ultimately feels unmoved by Irene's grief, but this does not suggest that he knew his engagement would not last. If Judy had not returned to his life, albeit briefly, Dexter would have done what everyone expected and married Irene.

A girl from a similar background, Irene, who possesses none of Judy’s beauty or vivacity, is far from Dexter’s ideal mate, as illustrated by the following excerpt: “Irene would be no more than a curtain spread behind him...a voice calling to children.’’ Being described only in piecemeal—a hand, a curtain, a voice—further dehumanizes Irene. Although the images connected with her evoke comfort and domesticity, they pale in comparison to the grand passion Dexter imagines he could have with Judy. One could argue that perhaps Irene was never fully human in Dexter’s eyes, but only a possession to be collected and then discarded at his earliest convenience.
Fitzgerald’s use of colors and seasons in his story further places Irene and Dexter in opposition. Irene, soft-spoken and easy going in nature, could be likened to Spring, while Dexter, cold and melancholic, is the embodiment of Winter.  

What are the pros and cons of using antibacterial soaps?

Antibacterial soap has risen in popularity since the 1980's. It comes in many forms, but most commonly comes in liquid soap with the added ingredient of triclosan, which is an antibacterial and antifungal agent. Handwashing is widely recognized as the most effective method of preventing the spread of disease. Washing with antibacterial soap has pros and cons, The benefits of antibacterial soap are: 
Washing with soap and water removes some bacteria, but bacteria grow quickly and multiply. Antibacterial products remove more bacteria. 
Antibacterial soaps and products are important for use when caring for patients who have weakened immune systems. They don't have the basic defenses against harmful bacteria that a healthy person does, and therefore they are much more susceptible to disease. Using antibacterial products around such persons can help keep them from getting sick. 
The cons or reasons why using antibacterial soap is not beneficial, are: 
The Food and Drug Administration (FDA) recently said that there isn't enough evidence to prove that antibacterial soaps are better at stopping the spread of disease than regular soap and water. 
Manufacturers of antibacterial products have been asked to provide proof that their products do not cause any harmful effects over long periods of time, and they haven't been able to do so. Some studies conducted with animals have suggested links to skin cancer.
Manufacturers have also not been able to prove that their products have more efficacy than the use of plain soap and water. They have recently recommended that consumers stick to the use of plain soap and water for handwashing. 
Triclosan may cause bacteria to become more resistant. According to the FDA's consumer update from September 2016:

"In addition, laboratory studies have raised the possibility that triclosan contributes to making bacteria resistant to antibiotics. Some data shows this resistance may have a significant impact on the effectiveness of medical treatments, such as antibiotics. The FDA and the Environmental Protection Agency (EPA) have been closely collaborating on scientific and regulatory issues related to triclosan. This joint effort will help to ensure government-wide consistency in the regulation of this chemical. The two agencies are reviewing the effects of triclosan from two different perspectives." 
https://www.fda.gov/consumers/consumer-updates/5-things-know-about-triclosan

https://www.fda.gov/consumers/consumer-updates/antibacterial-soap-you-can-skip-it-use-plain-soap-and-water

https://www.unitypoint.org/blankchildrens/article.aspx?id=68ac1797-834f-409c-947b-4df322b04380

How would you respond to the assertion that, before the Europeans colonized Africa, the continent had no literature?

I would say that that assertion is completely false.
When we think of literature, we often fail to realize that our understanding of it is rooted in Western ideas of learning and storytelling—that is, stories and verse written and transmitted to the masses through print. Though it is true that certain Asian cultures also had writing—paper was, in fact, invented in China around 100 BC—the act of telling stories and recording them for posterity is deemed a Western tradition.
Epic narratives, fables, and other tales did exist among other peoples on other continents, however, including Africa. Let's consider how this tradition existed in West Africa, for example.
Sunjata, a tale told among the Mandingo people (from what is now Mali), is one of the best-known African epics. The story was passed down by generations of griots since the thirteenth century. A 'griot' is similar to the troubadour of medieval Europe in that he was skilled in oral performance, reciting histories as epic poems or narratives. The griot differed from the troubadour in the sense that he remained rooted to his tribe and community, while the troubadour traveled from place to place transmitting poems and tales. Also, the troubadour's main function was to entertain. Storytelling was often accompanied with music. On the other hand, the griot's main function is "to preserve, record, and transmit the history of their people" (Hill 35). Finally, griots still exist in some West African communities, whereas troubadours ceased to exist after the invention of the printing press around 1440.
Sunjata is similar to the French and English courtly romances told during the same period. Sunjata was a real person. He was a Mandingo warrior-king who led a revolt against Ghana, a declining empire, in 1200 CE. Ultimately, he united Mali's twelve kingdoms, creating one of the most powerful empires the continent has ever known.
Though this tale is rooted in history, it is regarded as literature because every griot who has told the tale through the ages has improvised its details. There are, in fact, four published versions of the epic and all of them are different. Moreover, as with all epic tales, there are mythical elements to Sunjata. For example, our hero is born crippled and, from birth, is threatened by mortal enemies. The antagonist in the epic is an evil sorcerer king named Sumanguru, or "Soumaoro Kante" in other accounts. Ultimately, Sunjata defeats Sumanguru by attacking his protective life force, a crowing white cock, with a magical counterforce, "a cockspur in a poisoned weapon (arrow or gun)" (Hill 36). 
This narrative deals with some of literature's ageless themes: good vs. evil, heroism, justice vs. injustice, and overcoming adversity. In terms of form, it follows the patterns we see in other literary traditions. There are characters, including a protagonist (main character) and an antagonist (an enemy, or someone who works against the protagonist). There is also a fixed setting and a plot which introduces a situation, brings that situation to a climax, and then provides a clear conclusion/resolution. 
Thus, Sunjata, like Western narratives, is a work of literature. The only difference is that griots did not write it down until very recently.
Source: Hill, Patricia Liggins. Call and Response: The Riverside Anthology of the African American Literary Tradition. Boston and New York: Houghton Mifflin Company. 1998. Print.

How does the title “Contents of the Dead Man’s Pocket” contribute to the story’s suspense?

In the title, the words "dead man's pocket" create suspense. As we begin reading, we wonder whether the protagonist will survive his adventure. This sense of uncertainty creates suspense. Our curiosity is piqued, and we are motivated to continue reading.
The author continues the suspense by having the protagonist's wife attend the matinee alone. Apparently, Tom cannot accompany his wife, because he has work to do. As a result, the stage has been set for his possible "demise." We begin to question how, when, and where he will meet his final end, if, indeed, he is destined to.
Our curiosity moves us to read further. We discover that an important piece of paper has flown out the window. The figures on the paper represent almost two months of work for Tom. If Tom fails to retrieve the paper, it will take him two months to reproduce the calculations.
The author then has Tom climb out onto the ledge. He gives further harrowing details once Tom is outside. Accordingly, the ledge is about as wide as the length of Tom's shoe. Accordingly, Tom must move sideways. The author then tells us how far up Tom really is:

He saw, in that instant, the Loew's theater sign, blocks ahead past Fiftieth Street; the miles of traffic signals, all green now; the lights of cars and street lamps; countless neon signs; and the moving black dots of people. And a violent instantaneous explosion of absolute terror roared through him. For a motionless instant he saw himself externally—bent practically double, balanced on this narrow ledge, nearly half his body projecting out above the street far below—and he began to tremble violently, panic flaring through his mind and muscles, and he felt the blood rush from the surface of his skin.

In the passage above, the author uses tactile and auditory imagery to give us an idea of Tom's terror. Again, the title is foremost in our minds as we read. In the end, however, Tom survives. However, his harrowing experience is described in clear detail by the author. The words "dead man" certainly contribute suspense to the story.

Why would you send August to school if you knew people were going to make fun of him?

Besides his facial deformities and hearing problems, Auggie had no real learning disabilities. His mom was his homeschool teacher and felt that she wasn't qualified to continue teaching him. Auggie's parents knew their son had potential, and in order for Auggie to continue to thrive academically, he needed a school environment. This new school environment would also give Auggie a look into the real world. Even though other students at the school would most likely make fun of Auggie, his parents knew they had no other choice if Auggie was going to be successful later on in life.
I think the bigger picture came into play for Auggie's parents. They knew they couldn't continue to protect and shelter Auggie for the rest of his life. Encouraging and supporting Auggie needed to be their role. Auggie knew how much his parents loved and cared for him, which gave him the strength to start middle school.

This question could be thought of from different perspectives, all with a different response.
As a parent- Auggie was homeschooled. While his mother is very intelligent she realizes she cannot continue his education forever. He needs to learn from experts in each subject area. Also, education is not just expanding tour mental capacities but, also your emotional and social capacities. Auggie needed to learn how to cope with what he will experience on a day to day basis in the real world. He will be judged daily and he needed the tools to deal with how to handle everyday situations and gain acceptance for himself.
Other parents- As an other parent, you would want August to attend school. This is all part of your own children learning acceptance. The realization that everyone is different and that is what makes up "wonder"ful is an excellent and difficult life lesson. Especially for middle schoolers, whom tend to want to conform and blend in. You would also be able to teach your children what to do in a bullying situation and encourage them to act in an appropriate and caring method.

What a great question! The story takes place at a perfect time in Auggie's life for him to experience the world as any other 5th grader would. While his parents struggled initially with this decision, they knew it would be best for him. They knew that it wouldn't be an easy road for their son but came to the realization that they can't shield him from the public forever. Auggie is very intelligent and has a wonderful sense of humor. It would be a shame to not let others see who he truly is beyond his scars.
We all know that making and keeping friends is a hard task. Auggie's parents knew deep down that there would be those who would love him for who he is and not judge him based upon what he looks like. The world is a big place. Leaving our comfort zone can be scary however necessary to know where we belong, let others see our strengths, and find those who will be there when we show weakness.

Preparation is one of the main reasons a parent would send August to school knowing that he would be made fun of. Preparation is key in order to successfully complete any task, and it is the same with the task of growing up. The reality is that August lives in the world that we all do, with people who will be kind and people who won't be. At the end of the day each person has to develop their own mechanism for dealing with both types of people. The only way August would develop these skills is by interacting with his peers. School therefore became a place to learn both academic and social life skills that will prepare him for his future. The hope is that with each encounter, whether positive or negative, will help to prepare him for the next one.

It is hard for a parent who has a student with a disability. I think that it's important to realize that even though a child has a disability, it shouldn't keep that student from being treated like any other kid their age. No matter where you talented child people are going to see them, and they may or may not talk or make fun of them. That shouldn't keep someone from trying to live a normal life. 
 
I think the end goal is to make sure that the student feels supported and loved no matter what. Surround the child with supportive and loving people. building the student up when the world is tearing them down. I think it's important that even though the student might look like their peers it doesn't mean they should be treating them any different. I think this, in turn, helps students without disabilities learn acceptance and support of those who are "different" than them. 

One of the hardest things for a student with disabilities to feel is normal. As the parent of a child with challenges, you want your child to feel as normal and accepted as possible. Augie's parents wanted the same thing for him. No matter where you take your child, no matter where they might go, there will always be people who will stare, who will judge without taking the time to know, and who will make your child feel less than normal. So, you do the best you can as a parent to make that normal as normal as possible for your child. 
You also cannot shield your child from the world forever—this, too, is a rather difficult proposition for parents. How do you help create that safe normal for your child? You can't. All you can do is support your child, be there for him or her when it gets rough, and keep telling them that they are worthy, they are loved, and they are normal—just like Augie. 

int (x^2+6x+4)/(x^4+8x^2 + 16) dx Use partial fractions to find the indefinite integral

int (x^2+6x+4)/(x^4+8x^2+16)dx
To solve using partial fraction method, the denominator of the integrand should be factored.
(x^2+6x+4)/(x^4+8x^2+16) = (x^2+6x+4) / (x^2+4)^2
If the factor in the denominator is quadratic and repeating, the partial fraction of this factor is (A_1x+B_1)/(ax^2+bx+c)+(A_2x+B_2)/(ax^2+bx+c)^2 + ... +(A_nx+B_n)/(ax^2+bx+C)^n .
So expressing the integrand as sum of fractions, it becomes:
(x^2+6x+4) / (x^2+4)^2=(Ax+B)/(x^2+4) + (Cx+D)/(x^2+4)^2
To solve for the values of A, B, C and D, multiply both sides by the LCD.
(x^2+4)^2 * (x^2+6x+4) / (x^2+4)^2=((Ax+B)/(x^2+4) + (Cx+D)/(x^2+4)^2) * (x^2+4)^2
x^2+6x+4=(Ax + B)(x^2+4) + Cx + D
x^2+6x + 4 = Ax^3 + 4Ax + Bx^2 + 4B + Cx + D
At the right side, group together the terms with same power of x.
x^2+6x+4 =Ax^3 + Bx^2 + (4Ax + Cx) + (4B + D)
x^2+6x+4=Ax^3 + Bx^2 + (4A+C)x + (4B + D)
Notice that the right side has a degree of 3. So express the polynomial at the left side with a degree of 3.
0x^3+x^2+6x+4=Ax^3 + Bx^2 + (4A+C)x + (4B + D)
In order that the two polynomials to be equal, the coefficients and the constant should be the same.
So set the coefficient of  x^3 at the left side equal to the coefficient of  x^3 at the right side.
0=A
Also, set the coefficient of x^2at the left side equal to the coefficient of x^2 at the right side.
1=B
Set the coefficient of x at the left side equal to the coefficient of x at the right side too.
6=4A + C       (Let this be EQ1.)
And set the constant at the left side equal to the constant at the right side.
4=4B+D       (Let this be EQ2.)
Since the values of A and B are known already, plug-in them to equation 1 and 2 to get the values of C and D.
Plug-in A=0 to EQ1 to get the value of C.
6=4(0) +C
6=C
And, plug-in B = 1 to EQ2 to get the value of D.
4=4(1)+D
4=4+D
0=D
So the partial fraction decomposition of the integrand is:
int (x^2+6x+4)/(x^4+8x^2+16)dx
= int(x^2+6x+4) / (x^2+4)^2dx
=int (1/(x^2+4) + (6x)/(x^2+4)^2)dx
Expressing it as sum of two integrals, it becomes:
= int 1/(x^2+4)dx + int (6x)/(x^2+4)^2 dx
= int 1/(x^2+4)dx + 6int (x)/(x^2+4)^2 dx
For the first integral, apply the formula int 1/(u^2+a^2) du = 1/a tan^(-1) (u/a) + C .

u = x
du = dx
a=2

For the second integral, apply the formula int u^n du = u^(n+1)/(n+1)+C .

u = x^2+4
du = 2x dx

So the result of each integral is:
= int 1/(x^2+4)dx + 6int (x^2+4)^(-2) *xdx
= int 1/(x^2+4)dx + 3int (x^2+4)^(-2) *2xdx
= 1/2 tan^(-1)(x/2) + 3*(x^2+4)^(-1)/(-1)+C
= 1/2 tan^(-1)(x/2) - 3(x^2+4)^(-1)+C
= 1/2 tan^(-1)(x/2) - 3/(x^2+4)+C
 
Therefore, int (x^2+6x+4)/(x^4+8x^2+16)dx= 1/2 tan^(-1)(x/2) - 3/(x^2+4)+C .

What is a summary of Dark Money by Jane Mayer?

In Dark Money, investigative journalist Jane Mayer digs deep into the story of campaign finance in America. Her 2016 exposé works to undermine the popular belief that increasingly powerful conservative forces in the United States have their origins in a broad-based grassroots rejection of an oversized, intrusive federal government. Instead, she argues, the rise of the “radical right” has at its heart a network of billionaire donors whose libertarian values guide their donations—and protect their bottom lines. In particular, Mayer throws a spotlight on the political contributions of Charles and David Koch, whose collection of charitable foundations, think tanks, and conservative advocacy groups (which together Mayer terms the “Kochtopus”) gives them almost unprecedented control over the Republican Party. Their system works to change public policy on multiple levels: candidates choose their positions carefully to curry favor with the Koch brothers, research institutes disseminate studies that support Koch-friendly conclusions, and youth initiatives help create what Mayer calls conservative and libertarian “beachheads” at educational institutions. Because campaign finance laws permit corporate donations that lack transparency (a right protected by the Citizens United ruling), the exact influence the Koch brothers and billionaires like them have on policy in the United States is difficult to calculate. Dark Money works to parse the complicated financial ties and interests that Mayer argues threaten the very foundation of democracy in America.

What is a quote from the book about the setting?

The novel Hatchet by Gary Paulsen is set in the Canadian wilderness.
After a plane crash, Brian is stranded in the wilderness, alone and terrified. The wilderness plays a very important role throughout the novel, as it pushes Brian to learn to survive. The only thing which Brian carries with him is a hatchet that his mother gave him.
Throughout the novel, Brian grows, develops his survival skills, and learns to work with wood, crafting weapons in order to hunt and fish. He quickly learns that self-pity has no place in the wilderness.
The wilderness is not some beautiful landscape to admire. It is dangerous and mistakes can be fatal. Often it is presented in stark contrast with the city, to which Brian is accustomed. Brian must learn to live in this new reality which is so unfamiliar for him. In the following quote, Brian reflects on how the wilderness forces you to be sharp and on your feet at all times. In the city, on the other hand, mistakes can more easily be rectified.

Small mistakes could turn into disasters, funny little mistakes could snowball so that while you were still smiling at the humor you could find yourself looking at death. In the city if he made a mistake usually there was a way to rectify it, make it all right. Now it was different.

Single Variable Calculus, Chapter 3, 3.7, Section 3.7, Problem 21

$
\begin{equation}
\begin{aligned}
\text{a.) } PV &= C\\
\\
V &= \frac{C}{P}\\
\\
\frac{dV}{dP} &= \frac{P \frac{d}{dP}(C) - (C) \cdot \frac{d}{dP} (P) }{P^2}\\
\\
\frac{dV}{dP} &= \frac{P(0) - (C) (1)}{P^2}\\
\\
\frac{dV}{dP} &= \frac{-C}{P^2}
\end{aligned}
\end{equation}
$


b.) When a gas is steadily compressed at constant temperature, the volume and the pressure inversely proportional to each other(as what Boyle's Law stated). From part(a), we know that the change in volume is proportional to $\displaystyle \frac{1}{P^2}$. At the end of 10 minutes, the pressure of the gas must be higher, making $\displaystyle \frac{dV}{dP} = \frac{1}{P^2}$ lower. Therefore, we can conclude that the volume is decreasing more rapidly at the beginning.

c.) Isothermal compressibility is denoted as $\displaystyle \beta = \frac{-1}{V} \frac{dV}{dP}$; but $\displaystyle \frac{dV}{dP} = \frac{-C}{P^2}$ and $\displaystyle V = \frac{C}{P}$ so,


$
\begin{equation}
\begin{aligned}
\beta &= \frac{-1}{\frac{C}{P}} \left( \frac{-C}{P^2}\right)\\
\\
\beta &= -\frac{\cancel{P}}{\cancel{C}} \left( \frac{-\cancel{C}}{P^{\cancel{2}}} \right)\\
\\
\beta &= \frac{1}{P}
\end{aligned}
\end{equation}
$

What is an analysis of the poetic devices used in "London" by William Blake?

The first two lines of "London" feature repetition, a literary device Blake uses several times in this poem. The word "charter’d," meaning "mapped," is repeated, showing that the city is mapped out in a way that is characteristic of urban life. This type of restriction is in contrast to the freedom of the countryside. In the next two lines, the word "mark" is repeated three times as a means of emphasizing the way in which the polluted city marks its inhabitants. In the following stanza, the word "cry" is repeated (and "cry" also appears in the third stanza), as is the word "every." The repetition of the word "cry" emphasizes the suffering of both adults and children in London. The repetition of the word "every" is a form of anaphora, which is the repetition of a word at the beginning of phrases that follow each other, and it serves to emphasize how this suffering characterizes everyone the poet sees in the city. Many phrases in this stanza also start with "in," another example of an anaphora. 
In the third stanza, the words "Church" and "Palace" are synecdoches--the substitution of part of something for its whole. For example, "Church" stands for religion, while "Palace" stands for the monarchy. Both of these institutions are oblivious to the cries of the people around them.
In the last stanza, the phrase "Marriage hearse" is a kind of oxymoron, or a joining of contrasts. The idea behind this phrase is that the infant is born to a mother who is a prostitute and curses her newborn child. The child's birth is both a marriage, or the result of a sexual union, and a death sentence, as the woman has a plague. Therefore, even birth brings with it the taint of death in "London." 

Calculus of a Single Variable, Chapter 6, 6.4, Section 6.4, Problem 57

Given 3(y-4x^2)dx + xdy = 0
=> 3y - 12x^2 +xdy/dx=0
=> ( 3y - 12x^2)/x +dy/dx=0
=> 3y/x - 12x +dy/dx=0
=> y'+(3/x)y=12x
when the first order linear ordinary differential equation has the form of
y'+p(x)y=q(x)
then the general solution is ,
y(x)=((int e^(int p(x) dx) *q(x)) dx +c)/ e^(int p(x) dx)
so,
y'+(3/x)y=12x--------(1)
y'+p(x)y=q(x)---------(2)
on comparing both we get,
p(x) = (3/x) and q(x)=12x
so on solving with the above general solution we get:
y(x)=((int e^(int p(x) dx) *q(x)) dx +c)/ e^(int p(x) dx)
=(int e^(int (3/x) dx) *((12x)) dx +c)/e^(int (3/x) dx)
first we shall solve
e^(int (3/x) dx)=e^(ln(x^3))=x^3
so proceeding further, we get
y(x) =(int e^(int (3/x) dx) *((12x)) dx +c)/e^(int (3/x) dx)
=(int x^3 *((12x)) dx +c)/x^3
=(int 12x^4 dx +c)/x^3
=(12x^5/5 +c ) /x^3
so y=(12x^5/5 +c )/x^3

What are two differences between the Republican and Democratic parties that may have an ethical impact on the American people?

The differences between the Democratic and Republican parties may have an ethical impact on the American people. In general, Republicans generally want fewer government regulations and interventions and view them as restricting freedom, while Democrats view these government actions as protective and enforcing equality.
Two specific differences between the Republican and Democratic parties right now have to do with trade and immigration. Under the Republican Administration, trade revenue recently has gone up with the repeal of regulations and ethically these actions will benefit Americans by reducing costs and creating jobs. Democrats point out that reducing government regulation of trade could cause safety issues and customer harm. Similarly, the Republicans have eased regulations on the oil industry, which drove down costs to consumers, while Democrats are concerned about the long-term environmental impacts of these decisions.
Immigration also impacts Americans because we are a nation of immigrants. The Republican Administration has sought to impose more restrictions on legal immigration and to heavily restrict illegal immigration, both arguably to benefit jobs and taxpayer outlays for American citizens, as well as increase security through more stringent vetting of immigrants. The Democrats, on the other hand, view the immigration problem as more complex with various tiers of immigrants who deserve more or less consideration for legal status. They also deny that immigrants pose a higher security threat than citizens. The recent moves to curtail immigration also sometimes appeared to be based on questionable motives such as the immigrant's country of origin or religion, which would be unethical.
Since both parties seem to have competing and polarized worldviews, any action by one party will likely raise ethical questions both positive and negative. A dynamic and ever-adapting balance between Republicans and Democrats such as we have now, with their complementary approaches to social order, seems to be the best, though imperfect, solution in a complex society.

Republicans and Democrats differ in views on many prominent issues, and the ethics of whether abortion should be legal or not has been highly polarizing since the Supreme Court ruled it a fundamental right in 1973. Republicans tend to staunchly oppose abortion (this stance is called pro-life), while Democrats tend to advocate that abortion remain accessible to all women (this stance is called pro-choice). Many pro-life individuals feel that human life begins at the point of conception, which would make abortion highly unethical, akin to murder. Many pro-choice individuals, regardless of whether they consider abortion palatable or not, feel that a pregnant woman has the right to decide the fate of the fetus in her womb. Pro-choice advocates often believe that life begins when a child is born, as opposed to at conception, which affects how they ethically view the abortion procedure.
Republicans and Democrats also differ dramatically in views on immigration, which can be considered an ethical issue since immigration policies directly impact people's lives and livelihoods. Republican immigration policies tend to be more restrictive than the policies of Democrats, which is demonstrated through the current administration's travel ban on immigration from certain countries and through President Trump's campaign promise of building a wall between the US and Mexico. The Obama administration's DACA (Deferred Action for Childhood Arrivals) policy, which extends grace towards undocumented individuals already in the country, is currently being phased out by the Trump administration and is a notable example of a Democratic president's work in immigration.
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