How is poverty discussed in Evicted by Matthew Desmond?

Poverty is the depressing motif that runs right throughout Matthew Desmond's Evicted. As the author is at pains to point out, poverty isn't simply the result of evictions and homelessness, but increasingly its cause. If the very poorest in society can't get Federal help—and over three-quarters of those entitled can't—then they will have no choice but to shell out a considerable proportion of their limited income on keeping a roof over their heads.
The picture given to us by the book is of a vicious cycle of evictions, poverty, criminality, and low expectations, in which too many people are trapped, and from they find it almost impossible to escape. The overriding problem isn't simply one of lax or ineffective regulation—though that is still a concern—it's that poverty in relation to the broken property market is profitable for too many people. Slum landlords such as Sherrena and trailer park owners like Tobin can make a fortune out of poor tenants, safe in the knowledge that their steady stream of clients have nowhere else to go. Moving companies and hauliers can also earn considerable amounts from the never-ending cycle of evictions. There's money to be made in poverty, and unless that fundamental problem is addressed, suggests Desmond, the situation is likely to get worse.

Poverty is a major theme in Evicted by Matthew Desmond. Nearly all of the individuals Desmond speaks with are struggling with poverty. Some of the individuals in the story who are not impoverished, like Sherrena, actually depend on the poverty of others to make money. Sherrena has a successful real estate business because most of her tenants are below the poverty line. Landlords can charge these impoverished individuals high rent—comparable even to the rents in much nicer parts of the city—but are under no pressure to keep the buildings in good condition because they know their tenants are desperate for any place to live. Many of the individuals in Evicted have criminal records or prior evictions, which means they are effectively shut out from the housing market in the nicer parts of the city. Desmond also discusses how the current welfare system makes it difficult for those living in poverty to get back on their feet. Welfare checks typically end up being less than $700, and about 70% of that $700 must go to rent. It is extremely difficult for those living in poverty to save up enough money to actually get on their feet, especially considering that individuals who save over $2,000 are no longer eligible for welfare. Many of the characters Desmond speaks with also suffer from other costly problems such as drug addiction, which makes it difficult for them to afford enough rent to stay in one place for long. Desmond also points out that it is very difficult for people living in poverty to pursue the educational certificates and degrees that are often touted as a path to financial success. Attending classes becomes a practical impossibility when people must balance erratic work schedules with constant evictions and moves.

What were the consequences of Lydia Bennet and George Wickham's relationship in Pride and Prejudice? How did Lydia's obligation to get married contribute to it?

Lydia and Wickham's elopement generates much of the drama in Jane Austen's Pride and Prejudice because their relationship profoundly affects all the principal characters. Lydia's irresponsible behavior — and the fact that she and Wickham do not initially marry — tarnishes the reputation of the other Bennet sisters and potentially damages their prospects of marrying well. As Mr. Collins states following the elopement:

The death of your [Mr. Bennet's] daughter would have been a blessing in comparison of this... They agree with me in apprehending that this false step in one daughter will be injurious to the fortunes of all the others; for who, as Lady Catherine herself condescendingly says, will connect themselves with such a family?

Lydia and Wickham's elopement catalyzes both the Bennet family and Mr. Darcy into action to try and find Lydia, assess the situation, and hopefully orchestrate a marriage to preserve the family's social dignity as much as possible. After Darcy's intervention, Lydia realizes she is indeed "obligated" to marry Wickham, which helps reduce the scandal of their elopement. At the time, young women only left home with a man if they were married, so Lydia's behavior was considered shameful. Formalizing the union minimized the damage to the Bennet family's social standing, and freed Elizabeth, Jane, and the younger sisters from scathing criticism of their association with Lydia. As Elizabeth states before she learns of Wickham and Lydia's marriage: "Our importance, our respectability in the world must be affected by the wild volatility, the assurance and disdain of all restraint which mark Lydia's character."
Interestingly, it is precisely this crisis that draws Darcy and Elizabeth closer together; he singlehandedly goes to London, finds the couple, and compels them to marry, all of which he does out of love for Elizabeth. When she discovers this through Lydia's inadvertent admission and her Aunt Gardiner's letter, Elizabeth realizes Darcy is a selfless man. Thus, a significant consequence of Lydia and Wickham's relationship is that it facilitates the romance between Darcy and Elizabeth.

Please describe the role of prison in reducing recidivism in the mentally ill. You may use this article: http://law.loyno.edu/sites/law.loyno.edu/files/Cummings-FI-PSL.pdf

This article argues that putting the mentally ill in prison is ineffective, costly, and fails to reduce recidivism because it overlooks the underlying problem: the convict’s mental illness.
The article focuses on the impact of so-called “specialty courts,” like drug courts, domestic violence courts, and mental illness courts, to create individual solutions for defendants with particular types of problems. The use of these courts focuses on rehabilitating a convicted defendant rather than merely punishing them. The article then focuses on the state of Louisiana, which has one of the highest prison populations per capita and barely uses mental health courts.
The article discusses how the criminal justice system fails to help those with mental illnesses and how this failure ends up costing the taxpayers of America. By failing to help those with mental illnesses overcome their condition and by simply punishing them for the crimes they commit, the system fails to solve the issue of recidivism.

Calculate the electric field above a ring of charge of radius R and charge density lambda at a point P centered on the axis of the ring.

In general, the contribution to the total electric field E from an infinitesimal piece of charge dE is
dE=(k*dq)/r^2
The total field is then calculated by integrating over all the charge:
E=int(k*dq)/r^2
Where k=1/(4pi epsilon_0) and r is the distance from dq to the point P . 
For this problem, if the point P is a distance z above the ring then we can set up a triangle to get a relationship between z and the distance r.
r^2=z^2+R^2
The vector dE pointing at point P from a chunk of charge, can be broken up into two components, one in the radial direction and one in the vertical direction.
dE=dE_r+dE_z
When considering the total electric field contribution from the ring, the radial contribution of every piece of charge will sum to zero and only the z contribution will be left due to the symmetry of the ring.
dE_z=dE*cos(phi)=dE*(z/r)=(k*dq)/r^2*(z/r)
E_z=int(k*dq)/r^2 *(z/r)
E_z=int (k*z*dq)/r^3
lambda is the piece of charge divided by a piece of length along the ring.
lambda=(dq)/(dl)
From the fact that r*theta is equal to the arc length around a circle we can say that
dl=R*d(theta)
Therefore,
E_z=int (k*z*lambda dl)/r^3
E_z=int (k*z*lambda R d(theta))/r^3
Now substitute for r and integrate theta from [0,2pi] .
E_z=int_0^(2pi) (k*z*lambda R d(theta))/(sqrt(z^2+R^2))^3
E_z=(k*z*lambda R)/(sqrt(z^2+R^2))^3 int_0^(2pi) d(theta)
E_z=(2pi k*z*lambda*R )/(sqrt(z^2+R^2))^3
Therefore the electric field at point P is entirely in the z -direction with magnitude:
E_z=(z*lambda*R)/(2epsilon_0(sqrt(z^2+R^2))^3)
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elelin.html

When does John destroy his wife's dairy?

Throughout the short story, the narrator portrays her husband as rather callous and insensitive to her serious mental condition, and he continually makes decisions that exacerbate her mental illness. One such decision her husband makes is that she is not allowed to write in her diary. John believes that it is imperative that his wife do nothing at all in order to get as much rest as she can. However, John fails to see that socializing, exercise, and mental stimulation is needed to cure his wife's severe depression and impending psychosis. The narrator continues to write throughout the majority of the short story but is continually interrupted by her husband and his sister's presence. The narrator also mentions that she feels too exhausted at times to write in her diary. Overall, the narrator never explicitly states when or if her husband takes her diary. As far as the reader knows, the narrator always possesses the diary and simply hides it from her husband. As the narrator's mental illness worsens, she completely stops writing on her own and becomes infatuated with the figures inside the wallpaper.

How were white people dealing with Native Americans at the end of the Indian wars as opposed to at the beginning, as told in Bury my Heart at Wounded Knee?

Bury my Heart at Wounded Knee by Dee Brown starts off by looking at the Indian wars of the East that took place before 1850.  Many of those looked like open wars of extermination and subjugation.  He also talks about Andrew Jackson's Indian policy of creating an Indian territory.  The army was in charge of protecting white rights above native rights.  Contrast this with the end of the book, the Wounded Knee Massacre.  The governmental bureaucracy took a more active role with the Department of Indian Affairs.  There was no an attempt to "pacify" the natives and drive them onto the reservations by destroying their way of life, mainly the pursuit of the buffalo across the open plains.  The goal was to assimilate the natives the best way the government knew how--to turn them into farmers.  It was only when the natives started acting in non-white ways on the Pine Ridge and Rosebud Reservations with the Ghost Dance did the massacre take place.  To Brown, the attitude of whites turned from conqueror of the wilderness to a more paternalistic, high-handed view that they alone knew what was best for the Native Americans.  

y = 25arcsin(x/5) -xsqrt(25-x^2) Find the derivative of the function

y=25arcsin(x/5) - xsqrt(25-x^2)
Before taking the derivative, express the radical in exponent form.
y=25arcsin(x/5) - x(25-x^2)^(1/2)
To get y', take the derivative of each term.
y' = d/dx[25arcsin(x/5)] - d/dx[x(25-x^2)^(1/2)]
y' = 25d/dx[arcsin(x/5)] - d/dx[x(25-x^2)^(1/2)]
Take note that the derivative formula of arcsine is d/dx[arcsin(u)] = 1/sqrt(1-u^2)*(du)/dx .
Applying that formula, y' will become:
y'=25* 1/sqrt(1-(x/5)^2) *d/dx(x/5) - d/dx[x(25-x^2)^(1/2)]
y'=25* 1/sqrt(1-(x/5)^2) *1/5 - d/dx[x(25-x^2)^(1/2)]
y'=25* 1/sqrt(1- x^2/25)*1/5 - d/dx[x(25-x^2)^(1/2)]
y'=25* 1/((1/5)sqrt(25- x^2))*1/5 - d/dx[x(25-x^2)^(1/2)]
y'=25/sqrt(25-x^2) -d/dx[x(25-x^2)^(1/2)]
To take the derivative of the second term, apply the product rule d/dx(u*v) = u*(dv)/dx + v*(du)/dx .
Applying this, the y' will be:
y'=25/sqrt(25-x^2) - [x*d/dx((25-x^2)^(1/2)) + (25-x^2)^(1/2)*d/dx(x)]
Also, use the derivative formula d/dx(u^n) = n*u^(n-1)*(du)/dx .
y'=25/sqrt(25-x^2) - [x*1/2*(25-x^2)^(-1/2)*d/dx(25-x^2) + (25-x^2)^(1/2)*1]
y'=25/sqrt(25-x^2) - [x*1/2*(25-x^2)^(-1/2)*(-2x) + (25-x^2)^(1/2)*1]
y'=25/sqrt(25-x^2) - [-x^2(25-x^2)^(-1/2) + (25-x^2)^(1/2)]
Then, express this with positive exponent only.
y'=25/sqrt(25-x^2) - [-x^2/(25-x^2)^(1/2) + (25-x^2)^(1/2)]
Also, convert the fractional exponent to radical form.
y'=25/sqrt(25-x^2) - [-x^2/sqrt(25-x^2) + sqrt(25-x^2)]
So the derivative of the function simplifies to:
y'=25/sqrt(25-x^2) +x^2/sqrt(25-x^2) - sqrt(25-x^2)
y'= (x^2+25)/sqrt(25 - x^2) - sqrt(25-x^2)
y'= (x^2+25)/sqrt(25 - x^2) - sqrt(25-x^2)/1* sqrt(25-x^2)/sqrt(25-x^2)
y'= (x^2+25)/sqrt(25 - x^2)-(25-x^2)/sqrt(25-x^2)
y'= (x^2+25 - (25-x^2))/sqrt(25-x^2)
y'=(2x^2)/sqrt(25-x^2)
 
Therefore, the derivative of the function is  y'=(2x^2)/sqrt(25-x^2) .

What were the significant outcomes of the War of 1812 on the United States?

There were significant outcomes for the United States as a result of the War of 1812. One major impact was that it showed that the United States could hold its own if it fought against a major world power. While there was no land that changed hands as a result of the war, the perception of many Americans was that the country had defeated Great Britain, especially after the crushing victory at New Orleans. The war showed that the United States would stand up for its beliefs and fight for them if necessary. The United States was upset that the British interfered with its trade and impressed its sailors.
Another outcome was that it brought a period of political harmony and a sense of national pride to the United States. The Federalist Party disappeared at the end of the war, in part because they were opposed to the war, and people in the country began to believe they could accomplish many things that they might have doubted before. The Era of Good Feelings arrived with the election of 1816. There was only one political party, the Democratic-Republican Party, so most people were on the same page politically. The development of the American System helped American industries to grow and led to improvements in American transportation with the building of new roads, canals, and railroads. The United States became more active in foreign affairs as Florida became American controlled land (a result of a treaty with Spain). The United States also issued the Monroe Doctrine, which told European countries to stay out of the Americas.
https://www.battlefields.org/learn/articles/outcomes-war-1812

The War of 1812 is considered a forgotten war in American history because no property changed hands between the United States and Britain.  The most important thing to come out of the War of 1812 was an increased sense of American nationalism.  Having defeated the most powerful empire during the war, Americans were proud of their nation.  There were more open displays of patriotism after the war.  When word leaked that the Federalists wished to take the Northeast out of the Union in the secessionist movement during the Hartford Convention, most of America turned against the party, signaling its end.  This led to the dominance of the Democratic-Republicans.  While the party did not speak with one voice, there was little of the political fighting that took place during the election of 1800.  
Another key aspect of the war was that the British hold over the Great Lakes region was finally broken.  British forts were used as resupply stations for Native Americans who harassed settlements in the region, though British meddling was a clear violation of the Treaty of Paris of 1783.  After the war, the British left, and the native tribes were left to the mercy of an onrush of Americans.  Within twenty years of the war ending, Native American resistance in the Midwest had largely been broken.  Americans also dropped any serious plans to invade Canada, especially since they were so soundly defeated in this endeavor during the early stages of the war.  

In Wise Blood by Flannery O'Connor, how and why does Hazel Motes create the Church Without Christ?

Flannery O’Connor’s first novel, Wise Blood, was published in 1952. Wise Blood explores themes of religion, belief, and doubt. The protagonist, Hazel Motes, was raised deeply religious as the grandson of a traveling preacher. At the age of 12, he even hoped to one day become a preacher. He grew up struggling with doubts about his faith, however, and becomes an avowed atheist upon returning home from World War II.
Hazel is a complex character because he considers himself anti-religious, yet he constantly contemplates theological matters. This paradox is at the center of this novel. Hazel comes up with the idea for his own anti-God ministry when he meets Asa Hawks, a blind street preacher, and his daughter. Hazel’s Church Without Christ is an answer to the Hawks’ ministry—to preach a new church, “the church of truth without Jesus Christ Crucified.” Hazel develops an obsession with Asa, which is later revealed as stemming from Hazel’s desire to be saved.
Hazel’s unsure and often contradictory preaching is unsuccessful in drawing followers to his Church Without Christ. Relating to themes of the commodification of religion, Hazel’s is the only church in the story that does not seek a profit. By the end of the novel, Hazel reveals that he has been inflicting harm on himself, wearing barbed wire under his shirt. His Church Without Christ has not helped him heal the wounds of guilt and has not led to the redemption Hazel craved.     

From "Nature" by Ralph Waldo Emerson: According to Emerson, how are we connected to nature, and why is that significant? Why does an adult not see nature as they did as a child?

According to Emerson's "Nature," we are all connected to nature most truly when we are alone. The "heavenly bodies," in particular, are what connect us to the sublime, because they represent something which is both continually present and also inaccessible, like God. The significance of nature to us, therefore, is that if we open our mind to it and to its beauty, we are equally opening our mind to the presence of God and of something beyond ourselves. Wise men, according to Emerson, do not "extort [Nature]'s secret" and therefore lose their curiosity about it. The wisest of us will accept that Nature's very mystery represents its closeness to God, and the fact that it can bring us closer to perfection.
This is part of why "few adult persons can see nature." Emerson indicates that only the poet, "he whose eye can integrate all the parts," can see nature as a complete landscape. Most people, in observing nature, can only appreciate superficial parts, appreciating nature through "the eye" only. By contrast, nature "shines into the eye and heart of the child." Nature is, to a child, not simply something to be looked at and experienced with the senses, but something which affects them deeply and without effort.
Emerson suggests that children have a particular "spirit of infancy" which allows them to experience the true delight of nature, whereas adults are unable to accept nature as the constant balm it can be, being too concerned with their "real sorrows." Because children have fewer sorrows and concerns, they are able to connect to nature more fully, enjoying its "cordial." Emerson regrets that others are not able to enjoy the "perfect exhilaration" of being one with nature, entering the woods and finding "perpetual youth." The woods are described as the home of God, his "plantations," in whose tranquillity a man who is open to nature can become one with it, "part or particle of God." The true joy of nature is that it "always wears the colors of the spirit," in that a man "laboring under calamity" will experience the same scene differently to another man who is happy.

In the following scenarios, use the framework for identifying business/legal issues to identify, explain and provide a solution for each: Example 1: A delivery driver is completing his daily route and is approaching an intersection which allows him the right of way on a green light. He must suddenly brake for a pedestrian who walked out in front of his truck and proceeded to walk across the street against a red light. The delivery truck driver fails to stop in time and hits the pedestrian causing serious personal injuries. Example 2: A delivery driver is completing his daily route and is approaching an intersection which signals a red light for him to stop. He does so, but when the light turns green, the vehicle ahead of him does not proceed. The delivery truck driver becomes agitated and accelerates, hitting the vehicle ahead of him, causing personal injury to the driver of that vehicle. Example 3: A delivery driver is completing his daily route and during a severe snow storm, his truck slides off the road and hits a corner store causing severe property damage and injuring an employee.

The legal issues that each of these examples raise is responsibility for the accident and the resulting liability that responsibility entails. The cause of the accident is one of the key factors in tort law.
The first example has a pedestrian who was jaywalking. Without having a right of way, the jaywalking pedestrian is the one who caused the accident, and they will be the one responsible for covering any losses and injuries resulting from the accident, including their own.
The second example involves a truck driver who got angry and deliberately caused a car accident. Because it was a deliberate act, the truck driver was responsible and will be liable for any injuries that were caused. Additionally, because the accident was deliberate, the truck driver might even be made to pay punitive damages—damages that go above and beyond compensating the injured parties and are made to punish especially bad actors for egregious conduct.
While the first scenarios are fairly straightforward, the third example is complex and would be very fact intensive to determine who was at fault. Drivers are responsible for driving reasonably safely in the situations they find themselves, including inclement weather. If the truck driver was driving in a way that would have been safe for sunny and clear conditions but unsafe for snowy conditions, then the driver would be responsible for the accident and would be liable.

What does Spitz do to Buck during the attack?

Spitz deeply resents Buck, seeing him as a threat to his dominant position in the pack. Buck is a strong, hardworking dog, so it's not hard to see why Spitz should come to regard him as such a dangerous rival. One night, when Buck goes to try and get some food, he finds his space occupied by Spitz. Tensions have been building between the two alpha dogs for some time, and as they circle each other threateningly, it seems that a full-blown fight is imminent.
But just when it looks like the fur's about ready to fly, the camp is suddenly invaded by a pack of half-starved huskies, crazed with hunger. Three of them attack Buck, wounding him badly, but not before he sinks his own fangs into one of their jugulars. As if this isn't bad enough, Buck's also being attacked by the treacherous Spitz, shamelessly stealing an opportunity amidst all the confusion to grab him by the throat. This shows just how much Spitz really hates Buck. Instead of standing alongside his fellow trail dog to see off the pack of wild, crazy huskies, he uses their vicious attack as a cover for attacking his rival.

How does Scout show courage in the lynch mob scene?

In chapter 15, Atticus travels to the Maycomb jailhouse to wait outside of Tom Robinson's cell as a precaution to prevent any disgruntled citizens from harming Tom before the trial. Scout initially demonstrates courage and loyalty by following her brother as he sneaks out of the home during bedtime. Despite knowing that her aunt and father will disapprove of their actions, Scout refuses to allow her brother to go downtown alone and tells Jem,

"Then I’m goin‘ with you. If you say no you’re not, I’m goin’ anyway, hear?" (Lee, 150).

Scout, Jem, and Dill end up finding Atticus sitting outside of the Maycomb jailhouse calmly reading a newspaper. Suddenly, several cars arrive from the Meridian highway and a group of men quickly surrounds Atticus. As the children watch from their hiding spot across the street, Scout gets curious and demonstrates her courage by running out into the group of men when she overhears Atticus ask one of them a question. Everyone is astonished at Scout's presence, and she is completely unaware that she has run into the middle of a lynch mob that is willing to harm Atticus in order to murder Tom Robinson. Jem and Dill follow Scout out of their hiding spot, and Atticus tells Jem to go home. When Jem refuses to leave his father, one of the members of the mob grabs Jem. Scout once again demonstrates her courage by kicking the man in the groin and saying, "Don’t you touch him!" (Lee, 154).
Scout also reveals her courage by attempting to have a pleasant, casual conversation with Walter Cunningham during the extremely awkward, dangerous situation. Fortunately, Scout succeeds in getting Walter Cunningham's attention, and he politely speaks to her before telling the mob to leave. Despite the fact that Scout is unaware of the dangerous situation she enters outside of the Maycomb jailhouse, she demonstrates her courage by running out into the middle of the group of men, kicking a stranger in defense of her brother, and striking up a conversation with Walter Cunningham during an uncomfortable, awkward situation.

Is Duncan honest?

The problem with King Duncan, as Shakespeare presents him, is that he is actually too honest and trusting. He has no suspicions of Macbeth and his ambitions at all, and Duncan agrees amiably to being hosted in the castle where he meets his doom. Perhaps he should have paid more attention to his own comment after the original Thane of Cawdor has been executed:

There's no art
To find the mind's construction in the face
He was a gentleman on whom I built
An absolute trust.

Is he honest in naming his son Malcolm as his heir? Yes, because it's important to remember that at this time in Scotland, the crown did not descend automatically from father to son. Duncan is asserting the claims of his firstborn, as he has a right to do, but ultimately, in this warrior society, it will be the strongest who either persuades or murders his way to the throne.

Calculus of a Single Variable, Chapter 6, 6.4, Section 6.4, Problem 12

Given y'+3y=e^(3x)
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'+3y=e^(3x)--------(1)
y'+p(x)y=q(x)---------(2)
on comparing both we get,
p(x) = 3 and q(x)=e^(3x)
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 dx) *(e^(3x))) dx +c)/e^(int 3 dx)
first we shall solve
e^(int 3 dx)=e^(3x)
so
proceeding further, we get
y(x) =((int e^(int 3 dx) *(e^(3x))) dx +c)/e^(int 3 dx)
=((int e^(3x) *(e^(3x))) dx +c)/e^(3x)
=((int e^(6x) ) dx +c)/e^(3x)
= (e^(6x)/6 +c)/e^(3x)
=(e^(6x)/6 +c)*e^(-3x)
so y(x)=(e^(6x)/6 +c)*e^(-3x)

What was the outcome of the court case Plessy v. Ferguson?

In the case of Plessy v Ferguson (1896) the Supreme Court controversially upheld the constitutionality of racial segregation laws. It was held by the plaintiff and his lawyers that racial segregation under the Jim Crow laws was in violation of the Fourteenth Amendment's equal protection clause, which prohibited states from denying anyone equal protection under the law. The Fourteenth Amendment had been passed during Reconstruction and was designed to outlaw the kind of racial discrimination embedded in the law before and during the Civil War.
In Plessy, the plaintiff argued that the provision of separate accommodation for railroad passengers on racial grounds was in breach of the equal protection clause. The Court, however, disagreed, holding in a 7-to-1 majority that, so long as the relevant facilities were "separate, but equal," then there was nothing unconstitutional about such measures. In reality, of course, railroad accommodation for African Americans was anything but equal.
Yet the Court overlooked the substantive issue of social equality and concentrated instead on the matter of legal equality. As the Fourteenth Amendment was concerned with legal equality, the Court held there was nothing in the provision of separate accommodation for non-whites that violated that equality. If the races wished to remain separate, that was no concern of the Court. This was a social, not a legal issue and, as such, beyond the law's remit. Courts of law should not be in the business of forcing people of different races to mix.
The Supreme Court's ruling in Plessy set back the cause of civil rights for decades. All kinds of facilities in the South remained completely segregated along racial lines—not just trains, but buses, schools, restaurants, bars, beaches, even drinking fountains. It wasn't until over half a century later, in Brown v Board of Education (1954) that the Court overruled its early decision in Plessy and finally dismantled the legal apparatus of segregation.

Intermediate Algebra, Chapter 2, 2.3, Section 2.3, Problem 8

Translate the verbal phrase "the product of 6 and a number, decreased by 14" into a mathematical expression. Use $x$ to represent the unknown number.

The expression is $6x - 14$.

What is Kit's opinion of each member of the Cruff family?

There were three members of the Cruff family. Kit first observed "a shabby, dour-looking man and wife" and their young daughter (The Witch of Blackbird Pond, Chapter 1). Kit thought that Goodman Cruff was a "cowed shadow of a husband" (Chapter 2). He was timid and hardly spoke a word, even when his wife treated their daughter cruelly. Kit realized that he did care for his daughter despite his apparent indifference. Goodwife Cruff was suspicious and Kit thought of her as a cold person. She treated Kit with contempt. Kit was sometimes frightened of Goodwife Cruff, who was frequently unkind to Prudence, her daughter. Kit thought that Goodwife Cruff was a gossip when she saw her with a small crowd of women in Wethersfield. She found her to be a serious woman and an overly strict mother.
Kit was very fond of Prudence Cruff, the young daughter. She found the child to be kind, intelligent, and pleasant to be around. Kit thought that Prudence was like

a young fawn that had wandered near the house one morning.  It had drawn nearer... quivering with eagerness at the food Mercy set out, yet tensed to spring at the slightest warning (Chapter 11).

Beyond Prudence's frail body and timid appearance, Kit discovered an eager child who wanted to learn and be loved. Kit came to treasure the time she spent teaching Prudence how to read.

How did President Jackson solve problems?

President Andrew Jackson dealt with the problems faced during his presidency in different ways, but generally by asserting the power of the executive office. He perceived the presence of Native Americans in the Southwest (today's Southeast) as a problem, and he "solved" it by urging his allies in Congress to pass an Indian Removal Act that empowered states to begin making treaties to remove these peoples. When the Supreme Court ruled this law unconstitutional, Jackson ignored the decision and urged the states—particularly Georgia—to begin to open Indian lands to settlement. In the nullification crisis of 1832–1833, Jackson used his powers again, threatening military action against South Carolina if it followed up on its threats of secession. When his opponents brought the Second Bank of the United States up for recharter, Jackson vetoed the bill rechartering it, and then, in an effort to "kill" the bank, had funds removed from it and disbursed to "pet" banks chartered by the states. So Jackson faced problems—real and perceived—with sometimes forceful action that went beyond the previous accepted limits on executive powers.
https://millercenter.org/president/jackson

Based on this chapter 4 (Evaluating How the NYPD Handles Crime Victims Judgements based on statistical performance Measures) in the textbook "The New York City Police Department The impact of its policies and practices", does NYPD treat victims well? Explain why or why not? and Would you change anything? If so, what. If not, why not? Address costs as well.

If one draws one's opinion regarding the manner in which crime victims are routinely treated by the New York City Police Department from Andrew Karmen's essay titled "How the NYPD Handles Crime Victims: Judgments Based on Statistical Performance Measures," then the department has substantial room for improvement.
Karmen's essay, the fourth chapter in the volume titled The New York City Police Department: The Impact of Its Policies and Practices, takes a cynical view of the police department's performance with respect to victims of crime. While Karmen notes the declining rates of crime in New York and in many other major cities, he spends considerable effort arguing that the crime statistics for New York are unreliable due to political pressures to present the city as safer than it actually is. Police officers, Karmen states, citing police department whistleblowers and others, are regularly pressured to report crimes as less serious than is actually the case. The drop in crime, to the extent it existed, was less due, Karmen argues, to police department procedures than to other factors having nothing to do with those procedures.
A byproduct of this pattern of activity is the deficient manner in which crime victims have been handled. Too often, crime victims are not treated as cordially and seriously as their situations warrant. Their victimization is treated as a cold, anonymous development that leaves them with little sense of a successful resolution to their ordeals. As a way of improving the situation of crime victims, Karmen makes several recommendations:
Make the reporting system more "victim friendly";
Arrive on the scene of emergency calls as soon as possible;
Solve the crime;
Recover and return stolen property.
These recommendations are eminently logical. They are also, for the most part, irrelevant. New York City has a population of eight-and-a-half million people. It is a densely-populated metropolis with a tremendous amount of ethnic diversity. The city's police department is stretched thin and faces the daunting task of making life-and-death decisions on a daily basis. To cavalierly suggest that the department should "solve the crime" and "recover and return stolen property" as a way of improving the treatment of crime victims is a little fanciful. The number of crimes committed on a daily basis, even after a marked decline in the rate of crime, is too high to expect more than a marginal improvement in the rate at which crimes like burglary and assault are resolved. Additionally, recovering stolen property is relatively easy if the criminal is captured in the act of the crime, or if a tip from an anonymous citizen leads to a hidden cache of stolen goods. Otherwise, it is almost impossible to ensure the recovery and return of such items. Thieves often have established networks through which they traffic stolen goods. Chop shops, for example, are regularly used in the trafficking of stolen automobiles and those vehicles can be on a freighter to another country in a matter of days.
One possible way of improving the way in which crime victims are treated is through better training of officers in public relations. Again, however, the pace of activity for the NYPD does not always allow for the practical implementation of such measures. Increasing the size of the department would certainly help but at a financial cost that is too high for the city to absorb.
Ultimately, an improvement in the treatment of crime victims can only occur when crime rates fall to the level that allows a more personable treatment of individual victims. The discussion, therefore, comes full-circle. A reduction in crime that passes the sniff test of those who monitor the NYPD's performance to guard against manipulation of data remains the most important challenge.

What is one impression of the mother in the poem "The Last Dollar" by Hillary Tham?

In "The Last Dollar," one impression of the mother is that she is completely dedicated to maintaining the well-being of her children. This is shown clearly in the first stanza of the poem when the narrator says that the mother "managed" to feed them vegetables with rice at the end of the month when all of the other children in the neighborhood ate "gruel."
In other words, the mother is so concerned with ensuring that her children do not go hungry that she carefully balances the household finances to guarantee that she has enough money left to buy vegetables and rice. This also shows a sound ability to manage the family finances, made even more impressive by the fact that the family is extremely poor and forced to scrimp every penny just to survive.
The mother, therefore, prioritizes the well-being of her children above all other things, making her both a committed and dedicated parent.

y=(2x)/(x^2-1) Graph the function.

We are asked to graph the function y=(2x)/(x^2-1) :
Factoring the denominator we get:
y=(2x)/((x+1)(x-1))
The graph has vertical asymptotes at x=1 and x=-1. The horizontal asymptote is y=0.
The y-intercept is 0 as is the only x-intercept.
The first derivative is y'=(-2(x^2+1))/((x^2-1)^2) so the function is decreasing on its domain.
The graph:

What role does technology play in archaeology and history?

When we think of archaeology we may think of adventure, Indiana Jones, and hired help painstakingly brushing away dust and dirt from the precious relics of times past.  This is not the case for the modern archaeologist, though adventure is still part of the thrill.  Modern technology has allowed archaeologists to use advanced excavation techniques, enabling greater recovery of fragile artifacts.  Using technology that ranges from lidar to x-ray guns, archaeologists can view sites without disturbing the soil and the objects beneath.  This allows for greater care and planning so that archaeologists can evaluate the layout of the excavation site to allow for maximum preservation of the artifacts, skeletons, and structures.  It also allows for preventing unnecessary excavation, preserving the surrounding landscape of the site.  Using advanced techniques, we have been able to peer deeper into the past than ever before.  A perfect example of this would be the study of the condition of the teeth and bones of ancient people through the eyes of modern dentistry and medicine.  Using their remains, we gain an insight into the health, diet, lifestyle, and cause of death of the subject.  As medical science advances, every bone that is recovered tells a piece of their story.

What is an ecological system?

I believe that this question is asking about Urie Bronfenbrenner's ecological systems theory. In his model, the ecological system is the environment that a child grows up in. That environment, which is made up of smaller environments, or systems, interacting with each other, affects and shapes that child's development.
The overall environmental system is divided into four subsystems or levels. The first system is the microsystem. This is the system that a child has the most direct contact and interaction with. It would include teachers, peers, siblings, parents, and so on. An example of how this system affects the child's development is that when a parent reads a bedtime story to the child, the child's language development is improved. Self-esteem can be improved by surrounding the child with encouraging friends.
The next system is the mesosystem. This one could look a lot like a food web because it involves all of the interactions that exist between components of the microsystem. Parent-teacher conferences or emails between teachers and parents are good examples of this. Both systems are involved with the care and development of the child, but they are involved in different ways; however, their combined efforts can greatly impact a child's development socially, mentally, and emotionally.
The third system is the exosystem. This system involves the connections that exist between a child and a setting that affects the child; however, the child has no (or almost no) contact with this system. A parent's place of work would be a part of this system. The school district and curriculum review boards would also count. Changes that are made to an entire school curriculum obviously will affect student learning and child development. A parent's stressful job or sudden loss of a job could affect the child as well. For example, if a family's income is suddenly cut in half, that child might not have as many social interactions as before, or physical development could even be affected if less food is being provided.
The final system is the macrosystem. This system involves cultural factors or even national factors. For example, poverty-stricken countries are likely to have fewer educational opportunities for children, and physical development may be hampered because of malnutrition.
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.471.7361&rep=rep1&type=pdf

Which ideas most influenced the founding fathers of the USA?

The Founding Fathers were the intelligent men who were able to draft the constitution that has endured for the last few centuries. The ideas that influenced them have equally endured.
First and foremost, they were religious men and saw religious freedom as a fundamental basis for a functioning society. Though they didn't believe in a God-given right to rule (as was the case with the English monarchy of the time), they believed all men were created equal before God and accordingly, rights were given. As it is stated in the Virginia Bill of Rights, Article 16 dated June 12, 1776,

[R]eligion, or the duty which we owe our creator, and the manner of discharging it, can be directed only by reason and conviction, not by force or violence; and therefore all men are equally entitled to the free exercise of religion, according to the dictates of conscience; and this is the mutual duty of all to practice Christian forbearance, love, and charity towards each other.

Note that the last part of the quote mentioning that all should practice Christian values means exactly that. It does not call for all to be Christians. Rather, the Founding Fathers called for a moral that could be found under the Christian heading.
The works that greatly influenced the Founding Fathers in their enterprise include John Locke's philosophical writings. His social contract in particular was of great use – ideas on property, where money came from and its moral use, and where possessing firearms to defend and possibly overthrow an unrighteous government is acceptable and necessary. (The relevant works include “Two treatise of Government” - arguably the most influential -, “An Essay Concerning Human Understanding”, “Reasonableness of Christianity”, and “Letter Concerning Toleration” among others.)
Another key document which influenced the Founding Fathers is the Magna Carta (its rightful name being Magna Carta Libertatum). The Magna Carta was a charter which was agreed to in 1215 by King John of England and a band of rebel barons. It guaranteed protection of church rights, illegal imprisonment of said barons, access to rapid justice, and allowed for a reduced and limited feudal payment to the Crown. The Magna Carta eventually served as the basis for English common law and became a symbol of freedom from oppression to Englishmen – including the Founding Fathers who found inspiration in it.
There are other authors and works that influenced the Founding Fathers such as the Bible, Montesquieu, Sir William Blackstone, and David Hume.
The first link gives good historical background and references at the end other documents that were influential.
This second link emphasizes the religious background and education of the Founding Fathers.
https://www.britannica.com/topic/The-Founding-Fathers-Deism-and-Christianity-1272214

https://www.ushistory.org/gov/2.asp

College Algebra, Chapter 3, 3.1, Section 3.1, Problem 20

Evaluate the function $f(x) = x^2 + 2x$ at $f(0), \quad f(3), \quad f(-3), \quad f(a), \quad f(-x), \quad f\left( \frac{1}{a} \right)$
For $f(0)$,

$
\begin{equation}
\begin{aligned}
f(0) &= (0)^2 + 2(0) && \text{Replace } x \text{ by } 0\\
\\
&= 0
\end{aligned}
\end{equation}
$


For $f(3)$,

$
\begin{equation}
\begin{aligned}
f(3) &= (3)^2 + 2(3) && \text{Replace } x \text{ by } 3\\
\\
&= 9 + 6 && \text{Simplify}\\
\\
&= 15
\end{aligned}
\end{equation}
$

For $f(-3)$,

$
\begin{equation}
\begin{aligned}
f(3) &= (-3)^2 + 2(-3) && \text{Replace } x \text{ by } -3\\
\\
&= 9 - 6 && \text{Simplify}\\
\\
&= 3
\end{aligned}
\end{equation}
$

For $f(a)$,

$
\begin{equation}
\begin{aligned}
f(a) &= (a)^2+ 2(a) && \text{Replace } x \text{ by } a\\
\\
&= a^2 + 2a
\end{aligned}
\end{equation}
$

For $f(-x)$,

$
\begin{equation}
\begin{aligned}
f(-x) &= (-x)^2 + 2(-x) && \text{Replace } x \text{ by } -x\\
\\
&= x^2 - 2x
\end{aligned}
\end{equation}
$



For $f\left( \frac{1}{a} \right)$,

$
\begin{equation}
\begin{aligned}
f\left( \frac{1}{a} \right) &= \left( \frac{1}{a} \right)^2 + 2\left( \frac{1}{a} \right) && \text{Replace } x \text{ by } \frac{1}{a}\\
\\
&= \frac{1}{a^2} + \frac{2}{a}
\end{aligned}
\end{equation}
$

Intermediate Algebra, Chapter 2, 2.1, Section 2.1, Problem 38

Solve the equation $- [6x - (4x + 8)] = 9 + (6x + 3)$, and check your solution. If applicable, tell whether the equation is an identity or contradiction.


$
\begin{equation}
\begin{aligned}

- [6x - (4x + 8)] =& 9 + (6x + 3)
&& \text{Given equation}
\\
- [6x - 4x - 8] =& 9 + (6x+3)
&& \text{Distributive property}
\\
- [2x - 8] =& 6x + 12
&& \text{Combine like terms}
\\
-2x + 8 =& 6x + 12
&& \text{Distributive property}
\\
-2x - 6x =& 12-8
&& \text{Subtract $(6x + 8)$ from each side}
\\
-8x =& 4
&& \text{Combine like terms}
\\
\frac{-8x}{-8} =& \frac{4}{-8}
&& \text{Divide both sides by $-3$}
\\
x =& - \frac{1}{2}
&& \text{Reduce to lowest term}

\end{aligned}
\end{equation}
$


Checking:


$
\begin{equation}
\begin{aligned}

- \left[ 6 \left( - \frac{1}{2} \right) - \left( 4 \left( - \frac{1}{2} \right) + 8 \right) \right] =& 9 + \left( 6 \left( - \frac{1}{2} \right) + 3 \right)
&& \text{Substitute } x = - \frac{1}{2}
\\
\\
- [-3-(-2 + 8)] =& 9 + (-3 + 3)
&& \text{Work inside parentheses first}
\\
\\
-(-3 - 6) =& 9 + 0
&& \text{Simplify}
\\
\\
-(-9) =& 9
&& \text{Simplify}
\\
\\
9 =& 9
&& \text{True}

\end{aligned}
\end{equation}
$

Which lines demonstrate the generation gap in the short story "The Lumber Room" by Saki?

There are a number of lines in the short story “The Lumber Room” by Saki that demonstrate the gap between the generations. The story illustrates the difference in reasoning skills between the generations, and it is not always the older person who is wiser and more intellectual. In fact, the child, Nicholas, is able to outsmart the adults, especially the aunt, who is the primary disciplinarian in the story.
When Nicholas attempts to tell the adults there is a frog in his breakfast, they admonish him. They tell him not to be silly.

Older and wiser and better people had told him that there could not possibly be a frog in his bread-and-milk and that he was not to talk nonsense; he continued, nevertheless, to talk what seemed the veriest nonsense, and described with much detail the coloration and markings of the alleged frog.

Of course, by Nicholas' own doing there is a frog in his bowl, and again the generation gap is expressed.

The sin of taking a frog from the garden and putting it into a bowl of wholesome bread-and-milk was enlarged on at great length, but the fact that stood out clearest in the whole affair, as it presented itself to the mind of Nicholas, was that the older, wiser, and better people had been proved to be profoundly in error in matters about which they had expressed the utmost assurance.

After a long afternoon of mentally sparring with the aunt, she ends up trapped in the water tank in the forbidden gooseberry garden. Again, Nicholas manages to outsmart her with his words. She finds herself stuck in the tank while Nicholas walks away knowing he reached his limits.

There was an unusual sense of luxury in being able to talk to an aunt as though one was talking to the Evil One, but Nicholas knew, with childish discernment that such luxuries were not to be over-indulged in.

How does the poet describe nature in "The Solitary Reaper?"

The poet describes nature here in a characteristically Romantic way. The vale in which the reaper sings and works is "profound" as it overflows with the melancholy sound of her voice. He describes the welcome felt by travelers when they hear the nightingale and know, then, that it is almost time to rest, as well as the thrill of hearing the cuckoo sing when one is at sea and its song lets one know that land is nearby. The poet compares the voice of the maiden to these birds' voices to show how much he is affected by her voice, likening her, then, to these natural singers. Nature, then, has the ability to affect us powerfully and profoundly, and the speaker shows how much he is affected by the song of the solitary reaper by suggesting that her voice is as, if not more, welcoming and thrilling than the birds' voices. The voice of the young woman and this natural setting combine to create an even greater impression of beauty on the poet than either would alone.

Unusually for Wordsworth, nature takes a back seat in "The Solitary Reaper." His main focus is on the Scottish lassie as she sings her beautiful song rather than the natural landscape in which she lives and works. It's notable in this regard that the speaker doesn't tell us much about the vale, except that it is "profound"—i.e., deep—and that its depths are overflowing with the sound of the reaper's song.
Later on, the speaker will compare the reaper's sweet, melodious song with certain features of the natural world, much to the latter's detriment. We are assured, for instance, that "A voice so thrilling ne'er was heard / In spring-time from the Cuckoo-bird". And the song of the nightingale, that bird so beloved by successive generations of poets, never gave

More welcome notes to weary bands
Of travellers in some shady haunt,
Among Arabian sands.

Nature may be a source of incredible beauty, but it cannot compare with the beguiling song of the solitary reaper.
https://www.poetryfoundation.org/poems/45554/the-solitary-reaper

In "The Solitary Reaper," Wordsworth describes nature in terms that are meant to trigger imagination and wonderment.
Wordsworth finds a vast amount of mystery in the natural world as the speaker in "The Solitary Reaper."  One example of this would be in the girl's song. Wordsworth considers her to be a part of the natural setting. The song of the "Highland Lass" has captured his imagination. Wordsworth is not clear as to what she is singing:  "Will no one tell me what she sings?"  In asking the meaning of her song and reflecting on what it might represent, Wordsworth expands his imagination to embrace what might be as opposed to what is.  In this way, the natural setting that includes the solitary reaper's song initiates wonderment.  Her song is a part of the beautiful mystery that is the natural world.
Once the speaker of the poem hears the song, his imagination begins to take over his sensibilities.  It does not matter that he lacks a clear understanding of the song's meaning.  The song inspires his mind to drift to alluring settings such as "Arabian sands," "the silence of the seas," and "the farthest Hebrides."  He does not think of the dreariness of the urban landscape or the blight of a slum.  The song moves Wordsworth's imagination to consider places in nature far removed from daily life. These natural settings initiate wide open thought.  When standing on the "Arabian sands" or in the midst of "the silence of the seas," one is able to engage in expansive thought.  This pondering might very well include the world and a person's place in it.  Wordsworth believes that broad level of thought is only possible when standing in the midst of nature.   In this way, the natural world is linked with wonderment and awe.  
Wordsworth believes that nature holds the key to unlocking our moral imagination.  Simply interacting with it in a meaningful way, as he does in "The Solitary Reaper," can unlock doors of thought and perception which embrace transformative possibilities.

What are examples of metonymy in Anthem by Ayn Rand?

Metonymy is the substitution of one word for another with which it is closely associated. For example, one could say that the orders came directly from the White House in order to indicate that the president gave orders; the phrase White House is substituted for the word president. In chapter 2, Equality 7-2521 describes seeing Liberty 5-3000. He says,

The women who have been assigned to work the soil live in the Homes of the Peasants beyond the City.

In this case, the word soil is used to describe not only the land but also the plants that grow from it. Liberty 5-3000 plows the earth, sowing seeds that will grow into crops that help to feed the community.
Equality 7-2521 says that his group of street sweepers is to clean the road that goes past the fields and the Home of the Peasants, and he loves this time because he hopes that he will see Liberty 5-3000. He says that, on each day after the first,

we knew the illness of waiting for our hour on the northern road.

This does not mean that the street sweepers are to spend exactly one hour cleaning this road, but Equality 7-2521 uses the word hour to mean his time on this road. We often measure time by hours, and so these words are closely related.

Metonymy involves using a word or concept associated with something instead of the thing itself. An example is "suit" for "business executive." An example in Anthem is the following from Chapter 1: "It is as if we were speaking alone to no ears but our own." In this case, "ears" comes to stand for the entire human being who the narrator, Equality 7-2521, is speaking to. Another example from Chapter 1 is the following: "We think there are mysteries in the sky and under the water and in the plants that grow." In this example, "the sky" stands for more than just the sky but represents the entire heavens, and the water represents the seas; the plants represent the entire natural world of flora and fauna. A final example from Chapter 1 is "no eyes can see us as we crawl under our seat and under the cloth of the tent." In this example, "eyes" stand for the ability of other people to see the narrator. 

Is mass conserved in both physical and chemical changes?

The Law of Conservation of Mass states that mass is neither created nor destroyed in a chemical reaction or a physical transformation. Hence, a short answer to the question is - yes, mass is conserved whether matter undergoes a chemical change or a physical change.
Physical changes are changes that involve a simply change in phase. Condensing of a gas is an example. Any change that does not involve a change in chemical composition is physical change. Tearing up paper does not change the chemical composition of the paper, but merely changes the size of the paper. In both examples, there is no change in identity of the atoms involved, or even the general chemical composition of the paper. If it were possible to look at and track the individual molecules in the paper before and after the change, then it will be possible to see that the number of molecules did not change. 
It is less intuitive for chemical changes. Chemical changes involve a reaction a change in chemical composition. For instance, hydrogen gas can react with oxygen gas to form water. While the individual atoms are still there, the chemical composition is different. This involved a rearrangement of chemical bonds. However, it can easily be justified where the atoms went - nothing disappeared, and nothing just appeared out of nowhere - mass is neither created nor destroyed. The chemical reaction simply resulted to the rearrangement of chemical bonds. 
Hence, in both cases - physical or chemical change - the mass is conserved.

Scout calls Dill a “pocket Merlin.” This is an allusion to what legend?

Calling Dill a pocket Merlin alludes to the legend of King Arthur, and particularly to Merlin, Arthur's magical wizard advisor who appears to be aging backwards. Merlin often has words of good advice for King Arthur.
To Scout, the small or pocket-sized Dill is like Merlin. He is magical in terms of his imagination and his many plans and ideas. His imagination can make him seem wiser than Scout or Jem, as if he is aging backward. Although only seven, he has snowy white hair, also reinforcing the idea of a wise child aging backwards. He seems to Scout to have appeared in Maycomb magically, out of nowhere, although he will eventually explain his background (however, Scout doubts his stories). Dill has even seen the movie Dracula, which impresses Jem.
Dill becomes a highly valued summer playmate to the Finch children.

The legend in question is that of King Arthur and the Knights of the Round Table. One of the most memorable characters in that epic tale is Merlin the wizard.
It is summertime in Maycomb and that means playtime for the kids, with lots of opportunities for getting into all kinds of scrapes and crazy adventures. Scout and Jem are pretty imaginative when it comes to thinking up new ways to occupy themselves during those long, hot summer months, but Dill is in a different class all of his own:

Thus we came to know Dill as a pocket Merlin, whose head teemed with eccentric plans, strange longings and quaint fancies.

So says Scout. The boy clearly has a rich, imaginative fantasy world, the kind of thing that most children would find themselves being drawn to immediately. Scout's reference to "pocket Merlin" also highlights Dill's somewhat diminutive stature. He is one year older than Scout, yet she still towers over him. But what little Dill lacks in height, he more than makes up for in personality and imagination.

How is Macbeth presented?

The character Macbeth is first presented as a good man who has won renown in battle and is loyal to his king. However, after he meets the three witches, who seemingly present a prophecy that Macbeth will become king of Scotland, this begins to change. 
As Macbeth considers the possibility that he should take action in becoming king, namely by killing King Duncan, his good nature is thrown into conflict with his newfound ambition. With the encouragement of his wife, Lady Macbeth, Macbeth gives in to his ambition and kills the king. The good man in Macbeth is horrified by what he has done, even as he ascends to the throne.  
The tension between who he was and who he is to become plays out over the rest of the play. After having his friend Banquo killed in order to solidify the crown for his possible heirs, Macbeth begins to be haunted by visions of his dead friend. At this point, Macbeth the king becomes more authoritarian, as well as more detached from his subjects, including his wife. 
By the last act of the play, the good man that Macbeth was before has been fully consumed by Macbeth the tyrant. His primary focus is to preserve his reign at any cost. Even learning of the death of Lady Macbeth does nothing to dissuade him from his objective. In the end, Macbeth becomes ruthless and cruel, a man driven mad by ambition and the horror of what he did to fulfill that ambition. It is only his death that releases Macbeth from the fallen man he became. 

Throughout The Plague of Doves, how do Billy and Corwin Peace evolve as characters?

Throughout The Plague of Doves, Billy and Corwin Peace evolve in opposite ways. While Billy becomes a cruel tyrant, Corwin eventually grows from a troubled youth to a talented musician.
Billy Peace
As the younger brother of Maggie Peace, Billy starts out as a shy yet principled young man. When Maggie becomes pregnant with John Wildstrand's child, Billy overcomes his shy demeanor to demand that John treats his sister fairly. He is drawn into John's kidnapping scheme, and enlists in the military to avoid being arrested. War alters Billy's character, and he develops a fanatical perspective on religion that leads him to form his own cult. Billy changes from a shy youth to a charismatic religious leader, and he exerts absolute control over his congregation as well as his wife and children. He soon becomes abusive towards his family and dies at the hands of his own wife.
Corwin Peace
Corwin is the illegitimate son of Maggie Peace and John Wildstrand. He is also Billy Peace's nephew. As Corwin grows up, he develops a mean streak. He mercilessly bullies Sister Mary Anita Buckendorf, his school teacher. Sister Mary Anita has a severe overbite, and Corwin leads the other children in referring to her as Godzilla. His bullying tactics reach their peak when he sets a wind-up Godzilla toy loose in class to mock her.
Despite his cruelty, Corwin wins the affections of Evelina Harp, his cousin and a kind young woman who works at the diner. Evelina is one of many reassuring figures in Corwin's life who invest in him emotionally and try to pull him away from the dangerous path he is headed down. Nonetheless, Corwin begins using and dealing drugs as a teenager. Corwin's delinquent behavior culminates in the theft of Shamengwa's violin. He is charged and arrested. Ultimately Shamengwa rehabilitates Corwin and teaches him to play the violin. Music is a crucial part of Corwin's transformation, and he eventually becomes a talented player.
While similar in their troubled origins, Billy and Corwin undergo vastly different transformations throughout The Plague of Doves. Billy begins as a good-hearted young man and turns into an abusive shell of his former self. On the other hand, Corwin evolves from a delinquent youth into a thoughtful and talented musician. It is worth noting that Shamengwa's compassion and interest in Corwin's life played a large role in keeping him from going down the same path as his uncle.

I need to write essay on "We are Seven" (poem) by William Wordsworth. The essay must be written in the following ways: 1. creative title 2. introduction 3. Biography of poet(context) 4. Structure/style/scansion 5. poetic techniques 6. meaning of poem 7. Symbol 8. conclusion. It must have 8 outside resources, 4-5 in-text quotations, and 5-6 block quotation. The essay must be 6-7 pages.

The title is your choice. However, it is important to choose a title that summarizes what you wrote about in the essay. For this reason, it is often best to choose a title after writing the essay.
In the introduction, I would recommend telling the reader what the poem is about and giving some historical context. This is a poem about a little girl who insists to the narrator that she is one of seven children, despite the deaths of two of her siblings. The poem was first published in 1798 when infant deaths were very common. You might want to find additional information about that and maybe find some historical information about how families who experienced this coped with such devastating loss.
The paragraph after this could be biographical information about Wordsworth. In the context of writing about this poem, which is about a difficult social issue, you might want to note that Wordsworth wrote numerous poems about social concerns, as did some other poets from the Romantic era, including William Blake.
In terms of style, the poem is easier to analyze than many others due to its relatively simple structure. It is written in four-line stanzas—with the exception of the final stanza, which is five lines. It has an abab rhyme scheme, which has the rhythm of a playful song or a nursery rhyme. You should think about why Wordsworth chose such a rhyme scheme to write about something so tragic. Additionally, why is the final stanza, which is written in an abccb rhyme scheme, different from all the others?
Next, think about some of the language that Wordsworth uses to describe the little girl and her appearance, such as "wildly clad." You should also consider the juxtaposition of mourning and joy in the thirteenth and fourteenth stanzas.
In terms of symbolism, why do you think Wordsworth made "a little cottage Girl" the source of his inspiration, as opposed to a child in London? Both would have known something about infant death, but what is different about the life of a child in the city compared to one in the country?
Your conclusion should summarize everything you discussed and should not introduce any new analyses or ideas about the poem. However, you could say something about the importance of poets talking about such topics in poetry and the importance of continuing to read these poems.
https://www.poetryfoundation.org/poems/52298/we-are-seven

What is the main job of the Judicial Branch?

If we think of the "judiciary branch" as referring to all the local, state, and federal courts in the United States, then its job is manifold. It is responsible for, among other things, deciding if there has been a violation of criminal law or civil code and deciding the necessary punishment for any violation.
If we think of the "judiciary branch" as mostly referring to the Supreme Court of the United States, then its function is to interpret the constitutionality of the laws and to serve as a check on the power of the other two branches of government.
However, that particular function of the judiciary branch was a point of contention between Federalists and Anti-Federalists. The sides strongly disagreed about whether or not the Supreme Court should have any right to decide whether or not laws were constitutional.
The Anti-Federalist Brutus argued that doctrine of judicial review would upset the balance of powers:

The power of this court is in many cases superior to that of the legislature. I have showed, in a former paper, that this court will be authorised to decide upon the meaning of the constitution; and that, not only according to the natural and obvious meaning of the words, but also according to the spirit and intention of it. In the exercise of this power they will not be subordinate to, but above the legislature.

The Federalist position--which is the position that eventually won out--was that the Supreme Court needed to have this power. In Federalist 78, Alexander Hamilton argued that the judiciary was the weakest branch because it had no ability to enforce its desires. Thus, it would not be inviting tyranny to grant the Court the power of judicial review:

It is far more rational to suppose, that the courts were designed to be an intermediate body between the people and the legislature, in order, among other things, to keep the latter within the limits assigned to their authority. The interpretation of the laws is the proper and peculiar province of the courts. A constitution is, in fact, and must be regarded by the judges, as a fundamental law. It therefore belongs to them to ascertain its meaning, as well as the meaning of any particular act proceeding from the legislative body.

It is important to note that, despite Hamilton's arguments, Article III of the U.S. Constitution did not specifically grant the Supreme Court the power of judicial review.
However, judicial review was institutionalized very early in the nation's history. Chief Justice John Marshall's famous opinion in Marbury v. Madison (1803) established judicial review in the United States and confirmed that the judicial branch's role is to interpret the law and protect the people from unconstitutional acts by the executive or legislative branches.
https://teachingamericanhistory.org/library/document/the-problem-of-judicial-review/

https://www.law.cornell.edu/constitution/articleiii

What were the Watergate burglars looking for?

The burglars, late known collectively as CREEP (Committee to Reelect the President), broke into the Democrat offices at Watergate to wiretap the offices and look for top secret documents. It doesn't appear that they were looking for anything in particular. They just wanted something that could give them an advantage over their opponents during the forthcoming election campaign. It is worth remembering in that particular election, the country had been deeply divided by the war in Vietnam and Nixon was in means guaranteed of a second term.
Nixon was eventually reelected in a landslide victory, but his campaign was marred by accusations of foul play. A month after the burglars had entered Watergate they had broken in again to redo the wiretaps and were caught. Though Nixon denied any wrongdoing, it soon became apparent he had paid the burglars hush money. Nixon's involvement was proved beyond all doubt, two years after his reelection, when he was forced to hand over the tapes that had him talking about and organizing the burglaries.
While Nixon was pardoned by Gerald Ford, many of Nixon's aides went to federal prison for their involvement.
https://www.history.com/topics/1970s/watergate

The Watergate building in Washington D.C. was where the Democratic National Committee had its headquarters. The Watergate burglars broke into the office to see if they could find any kind of compromising material that could be used against the Democratic Party. Some have suggested that the burglars were looking for evidence that the Democrats had been receiving secret donations from Castro's Cuba.
Whatever the initial motivation, the Watergate break-in was simply one of many illegal actions authorized by President Nixon and his staff against political opponents. Nixon was a deeply paranoid, insecure man, and he felt that everyone was out to get him. He wanted to get as much information on his perceived enemies in politics and the media as possible, and he was prepared to resort to all kinds of dirty, underhand methods to do so. The Watergate break-in may only have been a second-rate burglary, but it came to symbolize a systemic abuse of power at the very highest levels of government.

What charity was Andrew Carnegie involved in?

Andrew Carnegie, the richest person in the world during 1901, was known for his philanthropy as he supported many charities through financial contributions. Andrew Carnegie believed that wealthy people ought to give their money back to society.  This is known as the "Gospel of Wealth."
Although Carnegie was known to have given various sums of money to charitable causes prior to 1901, after his retirement in 1901 at the age of 66 his charitable contributions became much more numerous.  Perhaps his most notable charitable cause was his founding of the Carnegie Institution in 1902. During this time, Carnegie made a ten million dollar donation to fund research that forwarded science as well as created a pension for teachers.  
Throughout his life, Carnegie was an avid reader, and therefore it makes sense that Carnegie made numerous charitable contributions to reading and education.  Carnegie is known to have donated to the worthy cause of building over 2,000 public libraries.  He also founded the Carnegie Corporation to aid colleges and other educational institutions.  
Another belief of Carnegie's was his commitment to advancing world peace initiatives.  Carnegie created the Carnegie Endowment for International Peace. By 1911, showing his true belief in the "Gospel of Wealth", Carnegie had parted with 90 percent of his fortune as he donated all of this wealth to charity.   
http://www.americaslibrary.gov/aa/carnegie/aa_carnegie_phil_1.html

In the book The Giver, how does Jonas' character change?

Jonas begins in the story as an eleven year old boy, about to turn twelve. He believes, like all children he knows, that the community he lives in is a Utopian one, regulated perfectly so that everyone is happy and efficient in their lives. He is thoughtful, social, mature, and ready to live life the way he is "supposed" to.
When he is assigned the role of the new Receiver of Memory, all that changes. As he takes on more of the world's memories, Jonas, a twelve year old boy, becomes wiser and more emotionally aware than any adult in his community, except for the Giver. He begins to see through the lies of his community, and is overwhelmed by all the terrible things he knows are going on behind the scenes of everyday life. By the end of the book, Jonas is isolated and disillusioned, and knows that he can no longer stay in this dystopian nightmare. He does, however, retain his compassion.

List 5 strong adjectives that describe the the main character.

The fact that the sniper lights his cigarette and endangers himself depicts him as an audacious individual. Immediately after the sniper lights his cigarette, a bullet flies past his head. He compromises his location and safety by choosing to light the cigarette, which is a bold move.
The sniper is also a skilled marksman, who successfully shoots and kills an enemy soldier and an older woman acting as an informant. The fact that the Republican sniper is able to shoot and kill the enemy sniper stationed on the opposite rooftop also contributes to his status as a skilled marksman.
Once the sniper is shot in the forearm, he demonstrates valor and courage by overcoming the pain and cleaning his wound.
After the Republican sniper is shot in the forearm, he creates a successful ruse by placing his cap on the top of his rifle and raising it above the parapet. Once the enemy sniper shoots the cap off the rifle, the Republican sniper purposely drops his weapon to make it seem like he has been shot dead. The ruse is successful and depicts the Republican sniper as a resourceful individual.
The Republican sniper can be described as a conflicted individual. After shooting and killing the enemy sniper, the Republican sniper throws his pistol to the ground and curses the war, himself, and everybody. The Republican sniper is sick of the violence and desires to leave the war zone but cannot abandon his cause.

To avoid completing this homework assignment for you, I will list several important details in which Liam O’Flaherty characterizes the titular sniper in his short story.
In the second paragraph, the narrator describes the Sniper’s physical appearance, focusing particularly on his face. The text says it is “thin and ascetic,” with eyes “of a man who is used to looking at death.” This implies that the sniper is experienced.
In the third paragraph, the narrator reveals the sniper’s thoughts about whether he should smoke after eating. The sniper knows that the gleam from the match will reveal his position, but he decides “to take the risk” anyway. This could mean that the sniper believes he won’t get caught, or that he is prone to taking risks in everyday life, too.
When he is shot in the ensuing conflict with another sniper, the titular sniper treats his own bullet wound, despite the “paroxysm of pain” he experiences. This might be considered brave, because the sniper calmly treats himself without flinching.
In order to escape the roof, the sniper devises a plan to trick his opponent by placing his cap on top of the rifle and lifting it over the edge. After doing this, “a bullet [pierces] the center of the cap,” and the sniper pretends to be dead by slumping his good arm over the edge of the roof. This plan indicates that the sniper is good at thinking quickly under stressful circumstances.
After killing the enemy, the sniper’s teeth “chatter” as he curses “the war . . . himself . . . and . . . everybody.” He also takes a long drink from his flask of whiskey. This shows that while the sniper kills the enemy using his skills, he isn’t actually happy about killing anyone.
Overall, O’Flaherty creates a complex character in the sniper. To produce your list of adjectives, I suggest examining these details and others that paint a picture of the sniper’s character.

Imagine you are in the Great Depression. Explain how bad it is.

This question depends on what one's station is in life and where one is located. The Great Depression was especially bad for farmers who faced falling crop prices for most of the 1920s. Farmers in the Dust Bowl had the worst time of it since they could not grow anything due to extreme drought. Many would lose their farms and be forced to go into the cities or to go West in search of day labor. Workers in the cities experienced job losses as factories closed due to falling demand. Even workers who did not lose their jobs often faced reduced wages or reduced hours. At the bottom of the Great Depression in 1933, the unemployment rate was at 25 percent, but these numbers do not fully explain the effects of underemployment on the population. While relatively few people starved to death, many were forced to live on the streets in Hoovervilles and/or into public relief bread lines in order to survive. Many of these people had their savings wiped out as well when banks shuttered partially due to stock market speculation. Whether you decide to write about the life of a rural or urban American, you should focus on poverty and its widespread nature during the Depression.
https://www.history.com/topics/great-depression

Beginning Algebra With Applications, Chapter 8, 8.2, Section 8.2, Problem 58

Factor $c^2 - 3c - 180$

The factors must be of opposite signs


$
\begin{array}{c|c}
\text{Factors of -180} & \text{Sum} \\
\hline \\
-1,180 & 179 \\
1,-180 & -179 \\
-2,90 & 88 \\
2,-90 & -88 \\
-3,60 & 57 \\
3,-60 & -57 \\
-4,45 & 41 \\
4,-45 & -41 \\
-5,36 & 31 \\
5,-36 & -31 \\
-6,30 & 24 \\
6,-30 & -24 \\
-9,20 & 11 \\
9,-20 & -11 \\
-10,18 & 8 \\
10,-18 & -8 \\
-12,15 & 3 \\
12,-15 & -3
\end{array}

$


$c^2 - 3c - 180 = (c+12)(c-15) \qquad$ Write the factors of the trinomial

How does the short story "Everyday Use" by Alice Walker relate to the 1970s through feminist criticism?

"Everyday Use" is, perhaps, best understood through Walker's idea of Womanism. Walker developed the idea of "womanism" out of the Southern colloquialism of a black woman acting "womanish"—willful and outrageous. A womanist is a woman who loves other women—sexually or not sexually—and who is unabashed in her love for herself and her expression of her identity. In Walker's work, the character Shug Avery in The Color Purple could be characterized as a womanist.
In "Everyday Use," Dee, the narrator's daughter, renames herself "Wangero." She embraces the Afrocentric consciousness of the sixties and seventies, which inspires her renaming, as well as her clothing choices: "A dress down to the ground. . . . A dress so loud it hurts my eyes. There are yellows and oranges. . . . Earrings gold too. . . .  Bracelets dangling and making noises when she moves" 
Dee contrasts with her sister, Maggie, who is "homely" (or thinks she is) and "ashamed of the burn scars down her arms and legs." She thinks her sister has held always life in the palm of one hand; 'no' is a word the world never learned to say to her." Maggie seems defined by her perceived limitations: her awkwardness and thinner body, as well as the notion that her sister has "nicer hair and a fuller figure" and is "lighter than Maggie."
Dee (Wangero) has seemingly rejected the things that give her value in society. Her ability to find beauty and heritage in her mother's quilts is significant, but her appreciation of heritage does not create any desire in her to be more generous to her sister, who has been more forcefully impacted by racism and sexism than Dee. 
Dee, who is still discovering herself and her place in the world, has the external appearance of a womanist, but she lacks the consciousness exhibited by a character like Shug Avery, who is an exemplar of womanism due to her ability to acknowledge and express love to Celie, a woman Southern society has deemed insignificant. Maggie parallels Celie, not only in the ways in which she has been belittled, but, more importantly, in her ability to withstand abuses, including those inflicted by her sister.

What are some character traits that describe Gretel in The Boy in the Striped Pajamas?

Gretel is Bruno's big sister. Though older, she's not necessarily wiser. She is as ignorant of the outside world as her younger brother, having also been brought up in a closed society where independent thinking is considered an act of treachery. When her family arrives at Auschwitz, Gretel is as puzzled as Bruno as to what the concentration camp actually is. It looks like a big farm, she thinks, except that there don't appear to be any farm animals about the place.
Nevertheless, Gretel does develop much greater curiosity in relation to her surroundings and to the war in general. She knows, for example, that the fence separating her family from the inmates is to stop the Jews from getting out. Thanks to her indoctrination she's become a full-blown anti-Semite. As far as she's concerned, the Jews are the Germans' enemies and that's all there is to it.
Ironically, Gretel's curiosity simply leads to even deeper ignorance rather than enlightenment. Closely monitoring the troop movements of the Wehrmacht may be a completely different activity from playing with dolls, but it's still just a fantasy world to her all the same. Gretel symbolizes the inability of millions of Germans to face up to the grim realities of life in the Third Reich. Moreover, she's abdicated her responsibilities as an older sister. Instead of acting as a guide and mentor, she's separated herself from Bruno, becoming more of a Nazi fanatic as the war progresses. In the figure of Gretel we see an illustration of how authority figures in Nazi Germany abused their positions to keep millions of people in ignorant subjection while they set about the systematic extermination of Europe's Jewish population.

What is the climax of the story ''Raymond's Run'' by Toni Cade Bambara?

The climax of Toni Bambara's "Raymond's Run" occurs with the action described in the title. As Hazel Elizabeth Deborah Parker races during the May Day race, she glances to the other side of the fence and sees her brother Raymond speeding along with his arms at his side and the palms of his hands tucked up behind him, and she is stunned.

[i]t’s the first time I ever saw that and I almost stop to watch my brother Raymond on his first run.

Squeaky's remark on Raymond's running indicates how thrilled she is with her brother's ability. His style is unique, and his speed incredible. Fortunately, Squeaky catches herself in time and rushes past the white ribbon to win first place. Although she jumps up and down, Squeaky is more excited about Raymond's run. She notes that the crowd must think that she is thrilled about her win rather than about her brother's amazing accomplishment. As Raymond climbs over the fence, Squeaky grows even more excited,

By the time he comes over I’m jumping up and down so glad to see him—my brother Raymond, a great runner in the family tradition.

After realizing Raymond can also run swiftly, Squeaky considers the idea of being his coach. No longer focused on her own running, Squeaky looks at Gretchen, who smiles and recognizes Squeaky as the winner. Squeaky returns the respect, realizing Gretchen can help her coach Raymond.

We stand there with this big smile of respect between us. It’s about as real a smile as girls can do for each other.

Squeaky's consideration for her brother Raymond's talent at the climax of the story leads to her resolution to ask Gretchen to help her train Raymond. Truly, Hazel Elizabeth Deborah Parker matures from her experiences on May Day.

Glencoe Algebra 2, Chapter 2, 2.6, Section 2.6, Problem 30

f(x) = |2x| , the the domain and range is given as follows
(i)Domain definition:
The domain of a function is the set of the input or argument values for which the function is real and defined.
In this function, the function has no undefined points, so the domain is
-oo (ii)Range definition
It is the set of values of the dependent variable for which a function is defined.
For this function the interval has a minimum point at x = 0 with value f(x) = 0
so the range of |2x| is f(x) >= 0
It can also be observed from the graph below:

Single Variable Calculus, Chapter 3, 3.5, Section 3.5, Problem 87

Show that $\displaystyle \frac{d}{d \theta} (\sin \theta) = \frac{\pi}{180} \cos \theta$ by using Chain Rule such that $\theta$ is measured in degrees.


$
\begin{equation}
\begin{aligned}

\frac{d}{d \theta} =& \frac{d}{d \theta} \left( \sin \frac{\pi}{180} \theta \right) \text{ with $\theta$ in radians. So,}
\\
\\
\frac{d}{d \theta} \left( \sin \frac{\pi}{180} \theta \right) =& \frac{d}{d\left( \frac{\pi \theta}{180} \right) } \left( \sin \frac{\pi}{180} \theta \right)
\\
\\
\frac{d}{d \theta} \left( \sin \frac{\pi}{180} \theta \right) =& \cos \frac{\pi \theta}{180} \cdot \frac{d}{d \theta} \left( \frac{\pi \theta}{180} \right)
\\
\\
\frac{d}{d \theta} \left( \sin \frac{\pi}{180} \theta \right) =& \cos \frac{\pi \theta}{180} \cdot \frac{\pi}{180} = \frac{\pi}{180} \cdot \cos \left( \frac{\pi \theta}{180} \right)
\\
\\

\end{aligned}
\end{equation}
$




But we have in degrees,

$\displaystyle \frac{d}{d \theta} \left( \sin \frac{\pi}{180} \theta \right) = \frac{\pi}{180} \cdot \cos \theta$

The Lifeboat: You are the captain, and your ship struck an iceberg and sank. There are thirty survivors, but they are crowded into a lifeboat designed to hold just seven. With the weather stormy and getting worse, it is obvious that many of the passengers will have to be thrown out of the lifeboat, or it will sink and everyone will drown. Will you have people thrown over the side? If so, on what basis will you decide who will go? Age? Health? Strength? Gender? Size? After thinking carefully about the situation, describe the decision that you would make in this situation and explain why. Identify the moral value(s) or principle(s) on which you based your decision. Based on this analysis, describe your general conclusions about your own moral compass.

This is, in some ways, a variant on the "trolley problem" in philosophy. One of the main issues here is that it forces a choice in a way that may not be entirely realistic. Thus my response would be to return to the flaw in the premise of the argument and use it to suggest how I would approach the problem.
A key part of the premise is that the lifeboat is an absolute dictatorship in which all authority is ceded to one person. I think that in this sort of situation that authoritarianism is a morally problematic approach to the issue. I do not support dictatorship. In a situation in which everyone is affected by a decision, everyone needs to have a voice in the decision.
The first step would be to ask for volunteers. In the crisis in the aftermath of the Fukushima nuclear power station disasters, many elderly people volunteered to expose themselves to radiation to help save others. As many people are willing to sacrifice themselves for the common good, this would be the ideal solution.
If volunteers were not sufficient, one good way to choose would be by lot. Because this is random, it would be ultimately fair. I would still want to vote on whether people accepted this method, though. Even if I thought it fair, I would not consider that I had a right to impose my will on all the other people in the lifeboat.
https://www.bbc.com/news/world-asia-pacific-13598607

Calculus: Early Transcendentals, Chapter 4, 4.6, Section 4.6, Problem 32

For c>0 f(x) is defined and infinitely differentiable everywhere. For c=0 f is undefined at x=0, and for c<0 f is undefined for x<=sqrt(-c) and x>+-sqrt(-c).
Find f' an f'':
f'_c(x) = (2x)/(x^2+c),
f''_c(x) = 2*(c-x^2)/(x^2+c)^2.
1. For c<0:f' is negative for xlt-sqrt(-c), f decreases. f' is positive for xgtsqrt(-c), f increases.f'' is always negative, f is concave downward on (-oo,-sqrt(-c)) and on (sqrt(-c),+oo).
2. For c=0: (f(x)=2ln|x| )f'(x)=2/x is negative for x<0, f decreases, and positive for x>0, f increases.f''(x) = -2/x^2 is always negative, f is concave downward on (-oo,0) and on (0,+oo).
3. For c>0:f' is negative for c<0, f decreases, f' is positive for x>0, f increases. At x=0 f'(x)=0 and this is a minimum.f'' has roots at x=+-sqrt(c). F'' is negative for xlt-sqrt(c) and f is concave downward,F'' is positive for x on (-sqrt(c),+sqrt(c)) and f is concave upward,F'' is negative for xgtsqrt(c) and f is concave downward.So x=+-sqrt(c) are inflection points.

The only transitional value of c is zero.Please look at the graph here: https://www.desmos.com/calculator/89vayoctfv(the green graphs are for c>0, red for c<0 and blue for c=0)

How does The Hammurabi Code document represent its own culture?

This document can tell historians a great deal about the culture of ancient Mesopotamia. Laws represent the priorities of a society, which are, essentially, cultural. We can see, for example, that the security of one's property was important, as many of Hammurabi's laws are aimed at protecting it, including this one:

If any one is committing a robbery and is caught, then he shall be put to death.

But we can also see that Hammurabi's society viewed private property within a different cultural framework than our own, because if the robber mentioned in the above law was not caught, the public would be responsible for compensating the victim for his loss. We can also see, by looking at the laws, that family was important, and that in Babylonian culture, the home was highly patriarchal:

If a man's wife be surprised [having an affair] with another man, both shall be tied and thrown into the water, but the husband may pardon his wife and the king his slaves.
If a son strike his father, his hands shall be hewn off.

We can also see the nature of justice in Babylonian culture in the famous "eye for an eye" and "tooth for a tooth" laws that define justice in retributory terms. The code also tells us much about the various class relations within Babylonian society as well as the nature of slavery and gender relations. There are dozens of laws governing each of these aspects in the code.
https://avalon.law.yale.edu/ancient/hamframe.asp

What is the original source of “I am no bird; and no net ensnares me: I am a free human being with an independent will” from Charlotte Bronte's Jane Eyre?

This quote truly characterizes Jane Eyre; she demonstrates throughout the narrative of Charlotte Bronte's novel that she is a "free human being with an independent will."
Having been orphaned in her childhood, Jane must live with her uncle's wife, Mrs. Sarah Reed, who is very cruel to her and allows her spoiled children to taunt her. When her cousin John abuses her one day as she reads History of British Birds, Jane falls and hurts her head. Because she is hurt, Jane cries out and she fights back against John; as punishment the cruel aunt sends her to the "Red Room," the room in which her uncle has died. Little Jane is horrified in this room as she believes that she sees a ghost, but no one will let her out. Jane never forgets this experience and strengthens herself from it.
The headmaster of Lowood School comes to Gateshead Hall to meet with Jane; he questions her in a cruel manner. Nevertheless, the intrepid child replies bravely. When Mr. Brocklehurst inquires if she likes the Psalms, the candid and truthful girl bravely replies, “No sir.”
At Lowood School, Jane makes friends with a lovely girl named Helen Burns. Soon after they become friends, Helen is beaten by one of the teachers. When Jane talks to the long-suffering girl, Helen tells her, 

“Love your enemies; bless them that curse you; do good to them that hate you and spitefully use you.”

         Helen does not agree, saying that she could not possibly bless Mrs. Reed.
Having completed her studies at Lowood and taught there for a while, Jane Eyre is hired at Thornfield Hall, where she will work as the governess for Mr. Rochester's ward. There she develops a warm relationship with her employer. However, when it appears that he will marry, Jane feels that she must resign, telling him that she is "no bird" that can be ensnared. "I am a free human being with an independent will which I now exert...."
But Jane does not leave in Chapter 23 after she says these words, because Mr. Rochester proposes to her. Later, however, Jane discovers that Rochester is already married--to an insane woman. She departs then even though she has nowhere to go.
It is a starving and destitute Jane Eyre who unknowingly collapses at the home of her cousins. She does not expect charity and is glad when she is offered a position. 
When Jane receives her inheritance from her uncle, she divides her inheritance of £20,000 among her newfound relatives.  But because she will not be "ensnared" in marriage with St. John Rivers, whom she does not love, he becomes upset with her.
Jane tells Diana and Mary Rivers that she is going on a journey “to see or hear news of a friend about whom I had for some time been uneasy.” After she reaches Thornfield, she sees a "blackened ruin," so she stops at the Rochester Arms Inn and learns of the fire. She is told that Mr. Rochester now lives at his manor home, Ferndean. She flies freely to her one love, Edward Rochester.

This quote comes from Chapter 23 of Jane Eyre, a novel by Charlotte Brontë. Jane says this in response to Rochester, who tells her to stop struggling "like a frantic bird." Jane responds that rather than being a bird, she has no net. She is free and can exercise her free will to leave Rochester, which she then chooses to do. The metaphor of a bird runs throughout this passage, as Rochester likens her to a bird, and Jane refuses to characterize herself as a creature who is locked in a cage. Rochester thinks of a bird as wild, while Jane sees a bird as caged. In this instance, Jane can exercise her free will, which makes her very different than Bertha, Rochester's wife who is locked away in the third floor of Thornfield, Rochester's house.  

Calculus of a Single Variable, Chapter 6, 6.4, Section 6.4, Problem 23

Given xdy = (x + y + 2)dx
=> xdy/dx = (x + y + 2)
=> y'=1+y/x+2/x
=> y'-y/x = 1+2/x
=> y'-y/x =(x+2)/x
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'-y/x =(x+2)/x--------(1)
y'+p(x)y=q(x)---------(2)
on comparing both we get,
p(x) = -1/x and q(x)=(x+2)/x
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 (-1/x) dx) *((x+2)/x)) dx +c)/e^(int (-1/x) dx)
first we shall solve
e^(int (-1/x) dx)=e^(ln(1/x)) = (1/x)
so
proceeding further, we get
y(x) =((int e^(int (-1/x) dx) *((x+2)/x)) dx +c)/e^(int (-1/x) dx)
=((int (1/x) *((x+2)/x)) dx +c)/(1/x)
=(int (1/x) *((1+(2)/x)) dx +c)/(1/x)
= x(ln(x)-2/x +c)
so now let us find the particular solution of differential equation at y(1)=10
y(1) = 1(ln(1)-2/1 +c)
=> 10 = 0-2+c
c=12
y(x) =x(ln(x)-2/x +12) is the solution

Explain title of the novel White Teeth. Where does Smith explicitly reference the title in the novel and what does the scene demonstrate?

The title of White Teeth is instructive because it encapsulates one of the book's main themes—how society reinforces the harmful notion that our shared humanity is challenged and undermined by differences of race and culture. However, all of us, whatever our skin color, nationality, or racial heritage, have the same white teeth. It is the color of our teeth that identifies us all as being part of the same human family.
Paradoxically, white teeth can also symbolize racial differences. The children discover this in chapter 7 when they bring food from their school's Harvest Festival to an old man by the name of Mr. Hamilton. The old war veteran is an unabashed racist, and tells the children about the time he served with the British Army in the Congo. At that time, white teeth served to accentuate racial distinctions:

Clean white teeth are not always wise, now are they? Par exemplum: when I was in the Congo, the only way I could identify the n****r was by the whiteness of his teeth, if you see what I mean. Horrid business. Dark as buggery, it was. And they died because of it, you see? Poor bastards (p.113).

Ironically, Mr. Hamilton only has false teeth. This can be interpreted as further evidence of his general lack of humanity.

Calculus of a Single Variable, Chapter 6, 6.4, Section 6.4, Problem 62

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.

How does she explain where she is going to the hunter? How do we know how much old Phoenix loves her grandson?

In the story, Phoenix Jackson meets a young white hunter on her way to town. When the hunter asks Phoenix where she is going, she tells him that she is going to town. Upon hearing her answer, the hunter exclaims that the way to town is too far for an old woman like her. He then advises her to head for home.
For her part, Phoenix doesn't reveal exactly why she is going to town. She merely satisfies his curiosity with a general answer: "The time come around." From her answer, the hunter speculates that she is going to town to see Santa Claus. He assumes that she must be like other "old colored people" who make the journey to town for this purpose. Essentially, Phoenix Jackson provides no concrete details about her reason for going to town. She merely explains that she goes to town because she must.
We know how much Phoenix Jackson loves her grandson by her willingness to endure a long, arduous journey for his sake. Additionally, old Phoenix makes the journey regularly. During each trip, she must brave varied dangers. Her exchange with the white hunter reveals the low status of African Americans in her society.
When the hunter points his gun at Phoenix and asks her whether she is afraid of it, she remains calm; her reply is a simple "No, sir, I seen plenty go off closer by, in my day, and for less than what I done." Phoenix knows that her safety is not promised in such a society; yet, she makes the journey because she loves her grandson.

How is Rikki-tikki-tavi courageous?

The defining character traits of a mongoose are their inherent curiosity and bravery. Rikki-tikki-tavi’s character does not deviate from the norm, and he displays his bravery numerous times in the short story. After surviving a turbulent flood, he ends up in a lovely bungalow, which is inhabited by a pleasant British family. Rikki-tikki initially demonstrates his bravery by standing face-to-face with Nag in the garden and killing a deadly sand snake named Karait. Rikki-tikki once again displays his bravery by fighting and killing Nag in the family’s bathroom to prevent him from harming Teddy’s father. Despite being much smaller, Rikki-tikki defeats the large, intimidating male cobra. In Rikki-tikki’s most impressive display of bravery, he saves Teddy’s life and defeats Nagaina in her underground nest. Entering the cobra’s nest is an extremely courageous action and Rikki-tikki risks his life during his deadly fight with Nagaina. Overall, Rikki-tikki demonstrates his bravery by defeating the deadly snakes living on the compound and protecting the British family from the threatening cobras.

Bravery is one of Rikki-tikki-tavi's defining characteristics, and he displays great courage at many points throughout the story. He takes very seriously his role as protector and defender of Teddy and his family, and Rikki-tikki doesn't hold back on confronting any threatening snakes, no matter how poisonous they are. Nag and Nagaina are two fearsome cobras; they regard the family's garden as belonging to them as they were there before the bungalow was built. Not surprisingly, they aren't too happy to see human beings and a mongoose occupying their territory. But Rikki-tikki doesn't back down and confronts the dangerous cobras, killing Nagainia after Teddy's father shoots Nag.
In an even greater act of bravery, he also challenges Karait, a small, venomous sand snake even more deadly than a cobra. In fact, he even kills the snake, saving Teddy from certain death in the process.

How does Clarisse feel about technology in Fahrenheit 451?

In Fahrenheit 451, Clarisse McClellan is utterly disinterested in technology. She explains this to Montag when they first meet:

"I rarely watch the parlour walls or go to races or Fun Parks."

For Clarisse, life is about smelling the rain and collecting butterflies, not about spending time driving too fast or watching the family. Even at school, she finds that activities like "TV class" and "transcription history" are utterly pointless since they do not encourage students to think or ask questions:

"They run us so ragged by the end of the day we can't do anything but go to bed or head for a Fun Park to bully people around."

Because she is so disinterested in the technology which is available to her, she has been cast out by her society: she is under surveillance, for example, and is forced to see a psychiatrist. Labelled as "anti-social," Clarisse provides the impetus for Montag's rebellion but tragically loses her life, probably as a result of a hit-and-run accident.

What does Marta represent?

In "The Falling Girl," Marta is a young nineteen-year-old girl that represents a progression through life, and her fall represents expectations of society. As she falls, she rises in society until she reaches the lower levels. Marta begins the story as a young girl and ends as an older lady. This part of the story seems conventional. However, consider the time of day in which the story begins and ends. Dawn would normally be associated with a beginning and dusk with an end. This is not the case in "The Falling Girl." The author flips some of our expectations as readers. For example, Marta is nineteen when she begins her fall, and she sees "the city below shining in the dusk." Marta ages as she falls, and as she nears the street level, it is early in the morning.
The author shares that "flights of that kind" are not a rare occurrence in the skyscraper. People pay more to live in the upper floors so that they can see the beautiful girls fall. Near the bottom, the tenants are denied the privilege of the youthful falling girls, but they do get to "hear the thud when they touch the ground." This is a reflection on society. As Marta falls, she notices that girls dressed more beautifully are falling faster. The author refers to a "contest." Marta feels that they will reach the target before she does. This represents the race for the top in society. However, in Marta's case, it is a race for the bottom as she falls.