What role did the Articles of Confederation play in the development of the American government? How did it impact the American government in the...

You have asked several questions in this post. I will answer the first question you asked.

The Articles of Confederation played a significant role in the development of the American government. The Articles of Confederation was our first plan of government. It created a weak federal government. This was deliberately done because we feared having a strong central government since we had just fought for our independence from Great Britain, which had a strong government. The federal government created by the Articles of Confederation wasn’t able to levy taxes, control trade, or require people to join the military. The weaknesses of this government quickly became clear. The federal government had financial problems, had trouble maintaining order, and had issues dealing with other countries. This led people to conclude that a new plan of government was needed.

Many people believed the new plan of government needed to have a federal government that had more power. There was a great deal of discussions about how much power the federal government should have. There was concern that individual liberties weren’t protected, so an agreement was made to add a Bill of Rights. The new federal government that was created did have more power. The federal government was able to levy taxes, make trade treaties, and control interstate trade. Many of these changes occurred because of the problems that existed when the Articles of Confederation was our plan of government. Our experiences during the time the Articles of Confederation was our plan of government impacted the creation of the plan of government we have today.

What are the similarities and differences between the novels Angela's Ashes (Frank McCourt) and Night (Elie Wiesel)?

Both books tell very powerful stories of suffering and survival from a young boy's perspective. While at first glance, they may seem quite different, they actually do have some similarities.

One of the key similarities between Angela's Ashes and Night is that both tales are about family tragedy. In Angela's Ashes, a young boy (the protagonist) suffers because of his family's poverty and his father's alcoholism. In Night, a young boy (the protagonist) suffers because of the family's persecution by the Nazis and his father's illness. Both stories are non-fiction memoirs and explore the obstacles the protagonists must overcome to survive. Another similarity is that there is a sense of community in both stories; other poor families in McCourt's story and other Jewish prisoners in Wiesel's story give support to the protagonists.

One of the key differences between Angela's Ashes and Night is the setting. McCourt's story takes place in Ireland, whereas Wiesel's take place primarily in Germany. Another difference is that McCourt's mother is a key character in his story, while Wiesel's mother and sister are separated from him early in the story, never to be seen again.  

`int(x-15)/((x^2+2x+5)(x^2+6x+10))dx` Please, help with this integral! I've been struggling for three days. It's partial fractions...

We are asked to find `int (x-15)/((x^2+2x+5)(x^2+6x+10))dx`

We will use partial fractions to rewrite the integrand:

`(x-15)/((x^2+2x+5)(x^2+6x+10))=(Ax+B)/(x^2+2x+5)+(Cx+D)/(x^2+6x+10)`

Now multiply both sides of the equation by the LCD to get:

`x-15=(Ax+B)(x^2+6x+10)+(Cx+D)(x^2+2x+5)`

Distributing and collecting like terms we get:

`x-15=(A+C)x^3+(6A+B+2C+D)x^2+(10A+6B+5C+2D)x+(10B+5D)`

Equating the coefficients we get A+C=0,6A+B+2C+D=0

10A+6B+5C+2D=1 and 10B+5D=-15

Solving the system yields A=B=1,C=-1,D=-5. Thus

`int (x+1)/(x^2+2x+5)dx-int (x+5)/(x^2+6x+10)dx`

The first integral can be done by letting `u=x^2+2x+5` and `du=2x+2 dx ` so

` int (x+1)/(x^2+2x+5)dx=1/2int (du)/u = 1/2 ln|x^2+2x+5| `

 Rewrite the second integral as:

`int (x+5)/(x^2+6x+10)dx = int (2x+6)/(x^2+6x+10)dx - 4int (dx)/(x^2+6x+10)`

Then we get:

`1/2 ln|x^2+6x+10|`

and 

`-4 int (dx)/((x+3)^2+1)=-4tan^(-1)(x+3)`

Thus:

`int (x-15)/((x^2+2x+5)(x^2+6x+10))dx='`

`1/2(ln|x^2+2x+5|-ln|x^2+6x+10|)-4tan^(-1)(x+3)+C 

Why does Atticus consider Mrs. Dubose a "great lady"? How does this fit in with his explanation of why he is defending Tom Robinson?

Atticus considers Mrs. Dubose a "great lady" for her courageous insistence on breaking herself free from her addiction to painkilling drugs, even though the end of her life was quickly approaching, and even though the process was painful. No one told Mrs. Dubose to do this: she took up the task on her own, enduring the excruciating and undignified fits that accompanied her body's withdrawal from the drugs.

Mrs. Dubose's willingness to fight for something worthwhile, something at the root of her own principles, is recognized and appreciated by Atticus. More than that, Atticus identifies with her struggle. He knows that he can't win Tom Robinson's case. Further, he knows it'll be difficult and dangerous. But he takes up the case anyway, and does his best, because it's the right thing to do. Tom is clearly innocent, and his only chance for survival is depending on a capable lawyer like Atticus. Yet the racist townspeople reject Atticus and even his children for his willingness to defend Tom, showing more and more hatred to them as the story unfolds. Like Mrs. Dubose, Atticus is willing to exert courage and effort in the face of nearly-certain failure in order to take a stand for what matters.

Recall from Chapter 9 that Atticus told his daughter: "Simply because we were licked a hundred years before we started is no reason for us not to try to win." He's explaining his belief that we must fight for what matters, even if we're certain to lose. Later, toward the end of Chapter 11, Atticus is trying to explain to Jem why Mrs. Dubose is a "great lady." It's because she's courageous and determined. Here, Atticus's words echo those he used earlier with Scout:

"It’s when you know you’re licked before you begin but you begin anyway and you see it through no matter what. You rarely win, but sometimes you do. Mrs. Dubose won, all ninety-eight pounds of her. According to her views, she died beholden to nothing and nobody. She was the bravest person I ever knew."

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In "The Signal-Man" by Charles Dickens, when the narrator encounters the signalman for the first time, he notices that the man appears to be under...

In "The Signal-Man," one of the narrator's earliest observations of the signalman relates to his strange behaviour and agitated manner. We see evidence of this early in the story, as the narrator makes his way to the signal box:

His attitude was one of such expectation and watchfulness that I stopped a moment, wondering at it.

Similarly, the narrator notices this a second time, as he observes the signalman carrying out his duties. He is unable to conjure an explanation for such behaviour, though he clearly finds it compelling:

He directed a most curious look towards the red light near the tunnel’s mouth, and looked all about it, as if something were missing from it, and then looked it me.

Finally, though the narrator does not yet know the reason for the signalman's strange behaviour, he begins to wonder if he is mentally ill:

I have speculated since, whether there may have been infection in his mind.

It is also worth noting that these quotes are effective at building suspense as the narrative develops. This is because they foreshadow the final appearance of the ghost in which the signalman tragically loses his life. 

In Gary Soto's Buried Onions, what five items might Eddie pack in a duffel bag when he leaves for the navy at the end of chapter nine?

Eddie is the main character in Gary Soto's novel Buried Onions. At the end of the book, after dropping out of college and failing in his attempt to hold down a productive job, Eddie joins the navy and is leaving his hometown of Fresno in the final chapter. If he were to take five meaningful items along with him in a duffel bag he might choose things that were symbolic of what he has left behind.

First, he might take a vocational text book on air conditioning, reflecting his failed attempt at pursuing higher education. For Eddie, however, the classes he was taking at Fresno City College seemed more an extension of high school and a waste of time. 

Second, Eddie could include a can of spray paint, symbolic of his failed attempt at work. He goes into the better neighborhoods of Fresno and paints street numbers on the curbs. When he does land a good job with Mr. Stiles, the crime and poverty of his neighborhood spoils his chance at legitimate employment.

Third, Eddie would take a crucifix, symbolic of his encounter with Angel, who wore a stolen crucifix around his neck. Angel, whose name is meant ironically, is the symbol of all that is negative in the neighborhood where Eddie grew up.

Fourth, Eddie would have a picture of his nina's (godmother) dog Queenie, symbolic of the death which pervades the novel. Eddie goes along with her to the SPCA when the dog is euthanized.

Finally, Eddie would have to pack an onion, symbolic of the sorrows which cling to the novel's characters. He believes there is a large onion buried under Fresno which causes the grief and tears in his lower class neighborhood. His friend Juan's sister even has a tattoo of a tear on her cheek.