What advice does the Nurse give to Juliet in Act III when Juliet says she doesn't want to marry Paris?

At the end of Act III, Scene 5, after being chastised by her father over refusing to agree to the arranged marriage with Count Paris, Juliet seeks comfort and advice from her mother and then the Nurse. When Lord Capulet storms from the room Juliet pleads with her mother to delay the marriage and ambiguously threatens suicide, which could be interpreted as foreshadowing:

O sweet my mother, cast me not away.Delay this marriage for...

At the end of Act III, Scene 5, after being chastised by her father over refusing to agree to the arranged marriage with Count Paris, Juliet seeks comfort and advice from her mother and then the Nurse. When Lord Capulet storms from the room Juliet pleads with her mother to delay the marriage and ambiguously threatens suicide, which could be interpreted as foreshadowing:

O sweet my mother, cast me not away.
Delay this marriage for a month, a week,
Or, if you do not, make the bridal bed
In that dim monument where Tybalt lies.

Her mother will not help her, saying, 

Talk not to me, for I’ll not speak a word.
Do as thou wilt, for I have done with thee.

With no sympathy from her parents, who are totally unaware of Juliet's relationship with Romeo, Juliet turns to the Nurse, who does know about Romeo, asking for "some comfort." The Nurse surprises Juliet by telling the girl to forget Romeo and go through with the marriage to Paris. She now claims, in contradiction to her earlier statements, that Paris is a better match for Juliet and that Romeo is nothing compared to the Count. She argues that since Romeo is banished Juliet should forget him. Moreover, Romeo will never be able to return to Verona to claim Juliet. She should simply consider Romeo dead. The Nurse says,

Romeo is banished, and all the world to nothing
That he dares ne’er come back to challenge you,
Or, if he do, it needs must be by stealth.
Then, since the case so stands as now it doth,
I think it best you married with the County.
O, he’s a lovely gentleman!
Romeo’s a dishclout to him. An eagle, madam,
Hath not so green, so quick, so fair an eye
As Paris hath. Beshrew my very heart,
I think you are happy in this second match,
For it excels your first, or, if it did not,
Your first is dead, or ’twere as good he were
As living here and you no use of him.

After this statement, a shocked Juliet vows never to listen to the Nurse again. Even though the Nurse had been an extremely close confidant and friend, Juliet basically ends the relationship with her in an aside at the close of the scene:

Ancient damnation, O most wicked fiend!
Is it more sin to wish me thus forsworn
Or to dispraise my lord with that same tongue
Which she hath praised him with above compare
So many thousand times? Go, counselor.
Thou and my bosom henceforth shall be twain.

Which area of the world is the most prone to volcanoes?

A volcano is an opening in the surface of planet Earth (or any other planet). Through this opening, molten rocks and gases emerge from deep interiors of the planet. The volcanic eruption can be gradual or violent, depending on the pressure built up underneath it. 

Volcanoes are typically found at the edge of the tectonic plates. That is, at the plate boundaries.Earth's core is composed of a number of fragments, each called a tectonic...

A volcano is an opening in the surface of planet Earth (or any other planet). Through this opening, molten rocks and gases emerge from deep interiors of the planet. The volcanic eruption can be gradual or violent, depending on the pressure built up underneath it. 

Volcanoes are typically found at the edge of the tectonic plates. That is, at the plate boundaries. Earth's core is composed of a number of fragments, each called a tectonic plate, all of which float over a liquid layer underneath them. Volcanoes are generally found at the diverging and converging boundaries of these tectonic plates. 

Volcanoes can also be found in the middle of the tectonic plates due to volcanic hotspots. These are fixed regions of hot material discharge from the core-mantle boundaries. As the tectonic plates move over them, we get new volcanoes while old ones become dormant. The Hawaiian islands are an example of these volcanoes.

Thus, regions where plate boundaries or hotspots exist are more likely to have volcanoes. An example of this is The Ring of Fire, an area with an especially high amount of volcanoes. The Ring of Fire mostly follows the perimeter of the Pacific Plate.

Hope this helps.

Anne writes strong opinions about Mrs. Frank and Peter van Daan. How well does she get along with each Peter and Mrs. Frank?

Mrs. Frank and Anne's relationship is as full of misunderstandings, hurt feelings, and strife as any young teenager's relationship with her mother. Anne often feels that her parents prefer the mature, quiet Margot over her. She is especially hurt by instances where she feels her mother is mocking her or leaving her out. She recalls with fury and despair slights like not being invited out with Margot and her mother before the war. Even though it seems that Mrs. Frank suffers from the struggles with her daughter, Anne often sees that emotion as manipulative:

"Yesterday Mother and I had another run-in and she really kicked up a fuss. She told Daddy all of my sins and started to cry, which made me cry too, and I already had such an awful headache. I finally told Daddy that I love "him" more than I do Mother, to which he replied that it was just a passing phase, but I don’t think so. I simply can’t stand Mother, and I have to force myself not to snap at her all the time, and to stay calm, when I’d rather slap her across the face." (10/3/1942.2)

Despite their strife, it does seem that Anne and her mother have a lot in common. They are both strong women who speak their mind and rarely hold back. This is likely a source of their conflict, but also a strong point of connection for them. 

When it comes to Peter, Anne goes through a big change in the novel. At first, she thinks he is too quiet and boring to make an interesting companion. As the months go on, though, Anne's lack of other friend options, loneliness, and maybe a bit of teenage hormones help to drive her and Peter together, first as friends and later as romantic lover interests. Anne writes about Peter in passionate terms often. However, she also notes that:

"I now know well that he was my conquest, and not the other way around. I created an image of him in my mind, pictured him as a quiet, sweet, sensitive boy badly in need of friendship and love! I needed to pour my heart out to a living person. I wanted a friend who could help me find my way again" (7/15/1944.9)

Anne seems to know that her and Peter's relationship stems mostly from necessity and not from compatibility and shared interests. 

What is the theme of insanity in general? What does it teach us?

Insanity in The Pearl is linked to ideas of stability and continuity. Despite Kino’s poverty at the story’s outset, we can see that as long as his life remains undisturbed he has a chance at being happy (and sane). Only when his circumstances change drastically does Kino begin to suffer in lasting ways, both from his poverty and from a loss of stability.

Steinbeck scholar Peter Lisca summarizes Kino’s plight succinctly, suggesting that Kino's newfound ambition to send his son to school is accompanied by disaster.

"[Lisca] sees that Kino finds himself possessed of the means to buy into that world but he also finds his house burned down, his wife physically beaten, his only son killed, and the lives of three men on his soul." (qtd. in )

If sanity is derived from a sense of continuity and stability, we can see quite graphically in the story of Kino what happens when these essential factors are disturbed.

As much as we can agree with Kino’s motivations to raise his family from a poverty that denies them access to schools and basic health care and doctor’s visits, we can see too a commentary on unmooring, uprooting, and divorcing from the past.

There are costs to great change. This may be one of the messages we see in The Pearl, and it is a rather disturbing one given the fact that Kino’s hoped-for change seems so natural and humble.

Sanity then becomes associated with one of the novel’s central conflicts, which is a desire for positive change and the costs that are associated with such change. Does Kino lose himself in his (understandable) desire to raise his family out of poverty? Does he fall into a sort of insanity wherein he is blinded to certain realities, preferring to recognize only the potential for achieving his desires and nothing more? If the answer to these questions is yes, should we then judge Kino or commiserate with him instead?

If this novel plays into Steinbeck's non-teleological bent of his Sea of Cortez period (where the parable of the pearl is first mentioned), we have reason to wonder if the author is suggesting that the attempted leap from one system of thought to another can be seen as a kind of hubris that fails to recognize the natural course of human development.

While this reading presumes a borderline condescension from Steinbeck, it is in keeping with his comments in Sea of Cortez. In that book, Steinbeck rejects teleological thinking (a mode of thought that presumes order and purposeful, conscious directionality) in favor of a view that accepts the natural world as being driven by unconscious systems. In doing so, he suggests at times that the populations he encounters around the Sea of Cortez belong to a world that is different than the one he (Steinbeck) comes from. No "mind" can bridge the gap, it would seem, and so an attempt to straddle these different worlds might lead to insanity.

There is no easy way to square the ethics of a view that suggests people should be accepted as they are (and so also accept for themselves their place in the world) with Steinbeck's view of the desire for change.

If "a dissatisfaction with the status quo of which Steinbeck approves" is "'one of the greatest talents the species has and one that has made it superior to animals that are satisfied with what they have,'” how can we properly resolve the story of Kino's tragedy with this championed view of ambition?

Is Kino insane to try to leave his past behind? Is he denying something essential about his very nature (according to the non-teleological view)? These questions are troubling echoes of the themes in the text.

Whats' the difference between the Trapezoidal Rule and Simpon's Rule for approximating integrals? What're the advantages/disadvantages of each...

Trapezoidal Rule and Simpson's rule are both numerical method in approximating values of a definite integrals. They both use a tabulated data of the function values for each subinterval. The primary difference is the formula for each rule.

Trapezoidal rule follows the formula for average of the left-hand Riemann Sum  and the right-hand Riemann sum .  It uses trapezoids or similar to a rectangle that has straight line segments with slanted top to approximate the area under the graph of the function.  The integral will be evaluated as:

`int_a^b f(x)dx = Deltax/2 [f(x_0)+f(x_1)]+Deltax/2 [f(x_1)+f(x_2)]+...

`+Deltax/2 [f(x_(n-1))+f(x_n)].`

Factoring out the `Deltax/2` and adding duplicated functions, we may simplify it as:

`int_a^b f(x)dx = Deltax/2 * [f(x_0)+2f(x_1)+2f(x_2)+2f(x_3)+...

`+2f(x_(n-1))+f(x_n)]` 

Note that all the function values has a coefficient of 2 except` f(x_0)` and `f(x_n)` .

While Simpson's rule differs since it has "parabola" across a pair of subintervals. The integral will be evaluated as:

`int_a^b f(x)dx = Deltax/3* [f(x_0)+4f(x_1)+2f(x_2)+4f(x_3)+...

`+2f(x_(n-2))+4f(x_(n-1))+f(x_n)]` 

Note that all the function values  at `x_(odd)` has a coefficient of 4. Function values at `x_(even)` , except with` f(x_0)` and `f(x_n)` , has coefficient of 2.

For the advantages of Trapezoidal rule, it is more accurate integral approximation than a single Riemann sum. It can be used regardless if we have even or odd number of subintervals. Its concept and derivation of formula is easier than the Simpson's rule using average for two consecutive function values . As for its disadvantage, it is less accurate than the Simpson's rule. This method is preferred when you have odd numbers of subintervals

For the advantages of Simpson's rule, it is more accurate due to the use of "parabolic top". It also achieves higher level of accuracy faster using less number of subintervals. For its disadvantage, it is restricted to even subintervals since it has to consider a "pair" of subintervals for each parabolic top. Thus, we prefer this method when we have quadratic polynomial or even number of subintervals.

In To Kill a Mockingbird, what does Dill see on the Radley porch?

Dill, Scout, and Jem decide to spy on Boo Radley. They wait until it is dark outside and they quietly sneak onto the Radley property. They open the creaking gate and step inside the fenced area, which every other kid in Maycomb is terrified to do. Dill, Scout, and Jem walk around to the rear of the house and see the Radleys' back porch. The porch makes the house look abandoned:

The back of the...

Dill, Scout, and Jem decide to spy on Boo Radley. They wait until it is dark outside and they quietly sneak onto the Radley property. They open the creaking gate and step inside the fenced area, which every other kid in Maycomb is terrified to do. Dill, Scout, and Jem walk around to the rear of the house and see the Radleys' back porch. The porch makes the house look abandoned:

The back of the Radley house was less inviting than the front: a ramshackle porch ran the width of the house; there were two doors and two dark windows between the doors.  Instead of a column, a rough two-by-four supported one end of the roof.  An old Franklin stove sat in a corner of the porch; above it a hat-rack mirror caught the moon and shone eerily (To Kill a Mockingbird, Chapter 6).

The children run into some chickens as they prowl around the back yard. Dill peers into a window on the side of the house, but he cannot see anything except for curtains. Dill suggests looking through the back window, but Scout protests. He goes around to the back anyway with Scout and Jem following. Jem quietly climbs onto the run-down porch and looks through the window. Then Scout notices something:

Then I saw the shadow. It was the shadow of a man with a hat on. At first I thought it was a tree, but there was no wind blowing, and tree-trunks never walked. The back porch was bathed in moonlight, and the shadow, crisp as toast, moved across the porch toward Jem.

After this, Dill sees the shadow,too. Afraid, he covers his face with his hands. Jem is the last one to see the shadow. Terrified, the children run as fast as they can to escape.

Can you give me a summary of Matilda by Roald Dahl?

Matildaby Roald Dahl is the story of a gifted, extraordinarily talented girl born to boring, unimaginative parents. From the time she is born, Matilda is different than other children. She is a genius who finds an outlet from her parents when she teaches herself to read, and finds refuge in the local library. Her parents find her to be a trying child who they wish would vegetate in front of the television. Instead, Matilda...

Matilda by Roald Dahl is the story of a gifted, extraordinarily talented girl born to boring, unimaginative parents. From the time she is born, Matilda is different than other children. She is a genius who finds an outlet from her parents when she teaches herself to read, and finds refuge in the local library. Her parents find her to be a trying child who they wish would vegetate in front of the television. Instead, Matilda would rather read or do mathematical computations far above her years. Matilda applies her brilliance to trick her parents and she discovers that she has telekinetic abilities that allow her to move things with her mind.

Once Matilda goes to kindergarten, her teacher, Miss Honey, realizes that she is a genius but even Matilda is unaware of her hidden talent. Miss Honey takes Matilda under her wing and nurtures her. While they share time in Miss Honey’s modest cottage, Matilda finds out that Miss Trunchbull, the abusive headmistress of the school, is Miss Honey’s unscrupulous aunt. Matilda uses her telekinetic skills to scare off Miss Trunchbull. When the chalk independently writes a message on the classroom chalkboard, Miss Trunchbull leaves, never to return.

Matilda’s parents move away leaving her with Miss Honey, who challenges the child’s intellect.