What is the percent error if students were expected to produce about 80.0g of MgO and the amount they measured after the reaction was 74.6g of MgO?

Error in experimental results is the difference between the theoretical or known value and the experimentally obtained valued. This difference is also called absolute error. Percent error is the ratio of absolute error to the theoretical or expected value. It gives more meaning to the observed error. For example, if you measure a length with an error of 15 cm, it makes a difference if the length measured was 150 cm or 1500 cm. In...

Error in experimental results is the difference between the theoretical or known value and the experimentally obtained valued. This difference is also called absolute error. Percent error is the ratio of absolute error to the theoretical or expected value. It gives more meaning to the observed error. For example, if you measure a length with an error of 15 cm, it makes a difference if the length measured was 150 cm or 1500 cm. In the first case the percent error is 10% and in the second case it's 1%. Percent error puts the amount of error into perspective.

Here's the equation for percent error:

% error = [(theoretical value - experimental value)/theoretical value] x 100%

Using your data:

% error = (80.0g-74.6g)/80.0g x 100% = 6.75%

Why does Juliet tell Romeo not to "swear by the moon" in Romeo and Juliet?

Juliet tells Romeo not to swear by the moon because it changes.  

After the ball, Romeo sneaks into the Capulet orchard to get a look at Juliet.  There, he watches her before she knows he is there.  She sees him, and they engage in some wordplay. She asks if he loves her, and he offers to swear by the moon.

ROMEO

Lady, by yonder blessed moon I swearThat tips with silver all these...

Juliet tells Romeo not to swear by the moon because it changes.  

After the ball, Romeo sneaks into the Capulet orchard to get a look at Juliet.  There, he watches her before she knows he is there.  She sees him, and they engage in some wordplay. She asks if he loves her, and he offers to swear by the moon.

ROMEO

Lady, by yonder blessed moon I swear
That tips with silver all these fruit-tree tops--

JULIET

O, swear not by the moon, the inconstant moon,
That monthly changes in her circled orb,
Lest that thy love prove likewise variable. (Act 2, Scene 2)

Juliet doesn't want him to swear by the moon.  Like the sun, the moon goes up and down.  It is also, as Juliet notes, in a different place based on the month and season.  Therefore, when Romeo swears by the moon, Juliet chides him and tells him not to swear by it. 

Confused, Romeo asks her what he should swear by if not the moon.  She tells him not to swear at all, and if he has to swear, he should swear by himself.  She would believe him then, because she idolizes him.  Thus, the love story begins.

What were the overall messages Chopin wanted readers to understand by the end of the narrative of "A Pair of Silk Stockings"? (for an essay)

Two overall messages suggested in Chopin's "A Pair of Silk Stockings" are

1. Poverty imposes limits upon a mother that deny her expression of autonomy and some self-indulgence.


2. There is in every individual a desire for freedom in opposition to societal norms. 

In the thesis of the essay, the student should include both of these messages. For a five or six paragraph essay (2 paragraphs of the body may be needed for one point), there can be a thesis with 3 main points [See boldfaced words] which can, then, become the topic sentences of the body paragraphs.

Here, then, are some reflections upon the three main points which may assist in the composition of the support for the thesis:

As a mother, Mrs. Sommers has lost her individuality; for, she must consider the needs of her children first. After she has the windfall of fifteen dollars, she responsibly places it into her porte-monnaie and lays out plans in her mind for necessities; she is "absorbed in speculation and calculation." But, since she feels a sense of importance, also, there is the hint that she experiences an awakening of independence. And, the fact that on the day that she goes to town she feels "a little faint and tired" hints at her weakening will to a temptation to indulge herself so that she can again feel independent.
So, after she purchases the gloves and the stockings and gloves, Mrs. Sommers seems transformed from a mother to an individual lady who is able to fulfill her own desires. 

• Self-Indulgence

At the counter where there are gloves, "she grew aware that her hand had encountered something very soothing, very pleasant to touch." Because she feels light-headed and is overwrought with responsibilities to others, there is the temptation for Mrs. Sommers to indulge herself and recall those yesterdays when she was able to enjoy luxurious things. So, once she buys the gloves, she is, then, tempted by the silk stockings which remind her of "better days" that she once enjoyed.

• A Desire for Freedom from Societal Norms

The restrictions that a lack of financial independence place upon Mrs. Sommers cause her to desire freedom from her role as the dutiful mother and wife; indeed, she longs to escape her life of "enforced frugality." When the play that she has attended ends and she rides home on the cable car, Mrs. Sommers experiences "a powerful longing that the cable car would never stop anywhere...." and her dreamy day continue rather than return her to all her social and private responsibilities. 

What is Thoreau hinting at in "Civil Disobedience" when he says that the “remedy is worse than the evil”? Why does he condemn the men who do...

This phrase appears in the 16th paragraph of the essay:

Unjust laws exist: shall we be content to obey them, or shall we endeavor to amend them, and obey them until we have succeeded, or shall we transgress them at once? Men generally, under such a government as this, think that they ought to wait until they have persuaded the majority to alter them. They think that, if they should resist, the remedy would be...

This phrase appears in the 16th paragraph of the essay:

Unjust laws exist: shall we be content to obey them, or shall we endeavor to amend them, and obey them until we have succeeded, or shall we transgress them at once? Men generally, under such a government as this, think that they ought to wait until they have persuaded the majority to alter them. They think that, if they should resist, the remedy would be worse than the evil. But it is the fault of the government itself that the remedy is worse than the evil. It makes it worse. Why is it not more apt to anticipate and provide for reform? Why does it not cherish its wise minority?

Take, for example, Thoreau’s personal experience of being put in jail for non-payment of the state poll tax. He wanted to protest not only the fugitive slave laws but also the beginnings of the war with Mexico. He never intended to vote in an election, so he felt he shouldn’t have to pay a tax in order to be allowed to go to the polls. He made a quiet one-person protest. He didn’t wait for a large group of people to join him so they could launch a large-scale rally and have relative safety in numbers. He didn’t think a group was necessary. He knew that non-payment of any tax could lead to arrest. “The remedy” would be the arrest and night spent in jail, following your principles. “The evil” would be to support with money those government activities that you don’t agree with. Is it better to just send in your money and be angry and frustrated about it, or to serve some time to prove your point? Thoreau is making the case that, in a so-called democracy, some other outlet should be provided for individuals to disagree and to protest without being subjected to jail time, merely for finding fault with the rules. He looks down on anyone who doesn’t stand up for himself in this fashion, especially if the person is afraid to protest on his own without other folks to back him up. He encourages individuals to act in line with their own beliefs.

Where do Iyengars and Naidus belong in the caste hierarchy?

Iyengar (or Ayyengar) people are a group in the Brahmin caste of Tamil origin. The Brahmin caste is the highest ranking caste in the system, so Iyengar people are very high in this system. The Brahmin cast originated as a sect of society whose primary function was as priests or people who worked in temples

The Naidu group is part of the Kapu caste. Kapu is described as a forward caste, which means that they...

Iyengar (or Ayyengar) people are a group in the Brahmin caste of Tamil origin. The Brahmin caste is the highest ranking caste in the system, so Iyengar people are very high in this system. The Brahmin cast originated as a sect of society whose primary function was as priests or people who worked in temples

The Naidu group is part of the Kapu caste. Kapu is described as a forward caste, which means that they are not discriminated against by the Indian government or excluded from education and work. 

The Kapu caste is part of Shudra, which originated as a caste that serves the other three original caste groups. Shudra is the lowest ranking caste that is not considered "untouchable." The original caste system was divided into four groups and the untouchables, who are outsiders in society. 

Today, the caste system is much more complex, and it is difficult to accurately describe the interactions that determine today's caste status. In general, we can say that Iyengars are from the top of society, and Shudra are from the bottom, but above the lowest, the untouchables.

Why didn't Holden want to have sex with Sunny?

The scene with Sunny is one of the best in the whole novel. It is both sad and funny. Holden is trying to act "suave," to use his term, but he doesn't feel it. He tells the reader:

If you want to know the truth, I'm a virgin. I really am.

Most readers will not be surprised. Holden doesn't want to have sex with this tough, street-smart, tarnished girl because he doesn't feel sexually aroused....

The scene with Sunny is one of the best in the whole novel. It is both sad and funny. Holden is trying to act "suave," to use his term, but he doesn't feel it. He tells the reader:

If you want to know the truth, I'm a virgin. I really am.

Most readers will not be surprised. Holden doesn't want to have sex with this tough, street-smart, tarnished girl because he doesn't feel sexually aroused. He knows he would be unable to perform. It would be a dismal experience, and it would be his first experience. He feels nervous, He is afraid. He has a mixture of chilly feelings--but none of his feelings have to do with being aroused. He keeps stalling Sunny, hoping that some slight tingle of sexual desire will make itself felt.

His biggest problem is that he equates sex with love, and he can't evoke any feeling of love for this wretched girl. What he feels is pity more than anything else. She is being exploited by Maurice and by every man who uses her body for five bucks a throw, or fifteen till noon. She has become totally desensitized to sex. Her life is ruined although she is still very young. She is like many girls who get caught up in the so-called "oldest profession," which goes on all over the world and destroys countless young lives.

Holden shows how he feels about Sunny when he says:

I took her dress over to the closet and hung it up for her. It was funny. It made me feel sort of sad when I hung it up. I thought of her going in a store and buying it, and nobody knowing she was a prostitute and all. The salesman probably just thought she was a regular girl when she bought it. It made me feel sad as hell--I don't know why exactly.

Holden doesn't know "why exactly" he has a lot of the thoughts and feelings he has. He is a gentleman, a nice guy, a sensitive young man in an insensitive world. He is ashamed of not being able to perform a filthy, vulgar action with a complete stranger in a cheap transient hotel room, when he should feel justified in having such self-respect as well concern for a fellow human being, degraded as she is.

When Sunny and Maurice come back to try to coerce another five dollars out of Holden, the little prostitute shows that she has not been entirely oblivious of his sympathy and consideration. 

"Leave him alone, hey," Sunny said. "C'mon, hey. We got the dough he owes us. Let's go. C'mon, hey."

Religion as relates to US Constitution: was it directly confirmed or ruled not within the scope of the laws and government?

It is hard to answer this question in an objective way as the Constitution does not explicitly do either of these things. There is a great deal of controversy about what, exactly, the Constitution (or, to be more precise, the First Amendment) says about religion.

On the one hand, we can clearly say that the Constitution does not ever “directly confirm” religion.  The Constitution says very little on the subject of religion.  In the Constitution...

It is hard to answer this question in an objective way as the Constitution does not explicitly do either of these things. There is a great deal of controversy about what, exactly, the Constitution (or, to be more precise, the First Amendment) says about religion.

On the one hand, we can clearly say that the Constitution does not ever “directly confirm” religion.  The Constitution says very little on the subject of religion.  In the Constitution proper, there is only one mention, which comes in Article VI.  This passage states that

no religious Test shall ever be required as a Qualification to any Office or public Trust under the United States.

In the amendments to the Constitution, religion is only mentioned twice, both times in the First Amendment.  There are two important clauses in this amendment that have to do with religion.  First, the establishment clause says that  

Congress shall make no law respecting an establishment of religion.

What this literally means is that the government cannot create an official state religion.  Many people think that this clause means that religion is “ruled not within the scope of the laws and government.”  They think that it means that the government cannot prefer one religion over another and that it cannot prefer religion over a lack of religion (atheism or secularism).  However, there are people who think this is wrong.  In this link, we can see that Supreme Court Justice Antonin Scalia recently said that the government should be free to promote religion so long as it does not favor one religion over another.

Second, the free exercise clause says that

Congress shall make no law … prohibiting the free exercise thereof (of religion).

This means that the government cannot make laws that infringe on people’s rights to practice religion.  You could say that this means that religion is “ruled not within the scope of the laws and government” because it says that the government cannot make laws reducing religious freedom.

Clearly, then, the Constitution does not “directly confirm” religion.  However, it is not possible to say objectively whether the Constitution rules that religions is “not within the scope of the laws and government.”

What are the differences between modern and postmodern music?

Modernism and Postmodernism are distinct periods within the history of western European music. In order to understand their differences, it is important to know how they fit within the context of music history. The major periods in western European music history are: Medieval, Renaissance, Baroque, Classical, Romantic, Modern, and Postmodern, in chronological order. Since modernism follows the Romantic era, it can be seen as a reaction to romanticism; postmodernism is, in part, a reaction to...

Modernism and Postmodernism are distinct periods within the history of western European music. In order to understand their differences, it is important to know how they fit within the context of music history. The major periods in western European music history are: Medieval, Renaissance, Baroque, Classical, Romantic, Modern, and Postmodern, in chronological order. Since modernism follows the Romantic era, it can be seen as a reaction to romanticism; postmodernism is, in part, a reaction to modernism in music. 

The tonal system we use in music was refined into its modern form in the Baroque era, under the influence of J.S. Bach. This system remained in ascendance until the end of the Romantic era when Wagner and others began to expand tonality. The Romantic era also featured music that depicted emotions. 

As a reaction to romanticism, modernist composers began to expand tonality radically (Stravinsky) and question the need for privileging one note over another the way the first note of a scale is privileged in tonal music (12-tone composers, such as Schoenberg). Some modernists reacted to the emotionalism of romanticism by creating austere music (Webern) and others took that emotionalism to the extreme (Stravinsky, particularly in Rite of Spring). 

Postmodernist composers reacted to modernism by creating music that contrasted with that of the high modernist composers. The postmodern ethos allowed artists of all kinds (architects, visual artists, composers) to draw from all historical periods to create a pastiche, instead of simply rejecting music of prior eras. As a result, composers such as John Adams create music that has a stronger tonal feel to it. 

These are generalizations about tendencies within each era; it is important to look at the details and listen to a lot of music from each era to get a feel for similarities and differences. 

What are some repeating words, phrases, or character actions in the "Tell-Tale Heart" by Edgar Allen Poe?

I'll pick words and phrases that are repeated throughout "The Tell-Tale Heart."  The narrator, very early on in the story, tries to establish his sanity.  In fact, the narrator reminds the reader throughout the story that he is not crazy.  The words "mad" and "madness" are used a total of seven times throughout the text.  For example, from the opening paragraph:

I heard all things in the heaven and in the earth. I heard many...

I'll pick words and phrases that are repeated throughout "The Tell-Tale Heart."  The narrator, very early on in the story, tries to establish his sanity.  In fact, the narrator reminds the reader throughout the story that he is not crazy.  The words "mad" and "madness" are used a total of seven times throughout the text.  For example, from the opening paragraph:

I heard all things in the heaven and in the earth. I heard many things in hell. How, then, am I mad?

How is he not crazy?  The man just admitted to being able to hear stuff from heaven and hell.  That sounds crazy to me.  He continues to attempt to prove his sanity by telling the reader that he couldn't be consumed with madness, because he was really careful about stalking and killing the other guy.  

Now this is the point. You fancy me mad. Madmen know nothing. But you should have seen me. You should have seen how wisely I proceeded—with what caution—with what foresight—with what dissimulation I went to work!

I have news for the narrator.  Just because a person is careful and exercises caution, doesn't mean he is, or is not, crazy.  I'm sure certified serial killers in real life also think they are not crazy.  

`A = 24.3^@, C = 54.6^@, c = 2.68` Use the law of sines to solve the triangle. (Find missing sides/angles) Round answers to 2 decimal places.

Given: `A=24.3^@, C=54.6^@, c=2.68`

The Law of Sines:  `a/sin(A)=b/sin(B)=c/sin(C)`

`B=180-24.3-54.6=101.1^@`

`a/sin(24.3)=b/sin(101.1)=2.68/sin(54.6)`

`a/sin(24.3)=2.68/sin(54.6)`

`a=[2.68sin(24.3)]/sin(54.6)`

`a=1.35`

`b/sin(101.1)=2.68/sin(54.6)`

` ` `b=[2.68sin(101.1)]/sin(54.6)`

`b=3.23 `

``

Given: `A=24.3^@, C=54.6^@, c=2.68`

The Law of Sines:  `a/sin(A)=b/sin(B)=c/sin(C)`

`B=180-24.3-54.6=101.1^@`

`a/sin(24.3)=b/sin(101.1)=2.68/sin(54.6)`

`a/sin(24.3)=2.68/sin(54.6)`

`a=[2.68sin(24.3)]/sin(54.6)`

`a=1.35`

`b/sin(101.1)=2.68/sin(54.6)`

` ` `b=[2.68sin(101.1)]/sin(54.6)`

`b=3.23 `

``

If `sin(x) + cos(x) = 1,` find `sin^3(x) + cos^3(x).`

Hello!

1. It is simple to solve the equation `sin(x)+cos(x)=1` and substitute the result into the expression `sin^3(x)+cos^3(x).` But we may solve the problem without solving the equation.

First,

`sin^3(x)+cos^3(x)=`

`=(sin(x)+cos(x))^3-3sin(x)cos^2(x)-3sin^2(x)cos(x)=`

`=(sin(x)+cos(x))^3-3sin(x)cos(x)(sin(x)+cos(x))=`

`=1-3sin(x)cos(x).`

Also,

`1=sin^2(x)+cos^2(x)=(sin(x)+cos(x))^2-2sin(x)cos(x)=`

`=1-2sin(x)cos(x),` therefore `sin(x)cos(x)=0.`

Finally, `sin^3(x)+cos^3(x)=1-3sin(x)cos(x)=1,` which is the answer.

2. If we want to solve the equation first, we divide and multiply by `sqrt(2)` and recall that `1/sqrt(2)=sin(pi/4)=cos(pi/4).` Therefore

`sin(x)+cos(x)=sqrt(2)*(cos(x)*cos(pi/4)+sin(x)*sin(pi/4))=`

`=sqrt(2)*cos(x-pi/4)=1.`

So `cos(x-pi/4)=cos(pi/4),`

`x-pi/4=+-pi/4+2k pi,` where `k`...

Hello!

1. It is simple to solve the equation `sin(x)+cos(x)=1` and substitute the result into the expression `sin^3(x)+cos^3(x).` But we may solve the problem without solving the equation.

First,

`sin^3(x)+cos^3(x)=`

`=(sin(x)+cos(x))^3-3sin(x)cos^2(x)-3sin^2(x)cos(x)=`

`=(sin(x)+cos(x))^3-3sin(x)cos(x)(sin(x)+cos(x))=`

`=1-3sin(x)cos(x).`

Also,

`1=sin^2(x)+cos^2(x)=(sin(x)+cos(x))^2-2sin(x)cos(x)=`

`=1-2sin(x)cos(x),` therefore `sin(x)cos(x)=0.`

Finally, `sin^3(x)+cos^3(x)=1-3sin(x)cos(x)=1,` which is the answer.

2. If we want to solve the equation first, we divide and multiply by `sqrt(2)` and recall that `1/sqrt(2)=sin(pi/4)=cos(pi/4).` Therefore

`sin(x)+cos(x)=sqrt(2)*(cos(x)*cos(pi/4)+sin(x)*sin(pi/4))=`

`=sqrt(2)*cos(x-pi/4)=1.`

So `cos(x-pi/4)=cos(pi/4),`

`x-pi/4=+-pi/4+2k pi,` where `k` is any integer.

Therefore `x=2k pi` or `x=pi/2+2k pi.` Then `sin(x)=0,` `cos(x)=1` or `sin(x)=1,` `cos(x)=0.` And the expression in question always = 1.

In "Once Upon a Time," what do the changes to the neighborhood, including Gordimer's description of the "prison architecture," suggest about...

The changes to the neighborhood are multitudinous, and grow larger throughout the course of the story. In the beginning, the family is described as follows:

They were inscribed in a medical benefit society, their pet dog was licensed, they were insured against fire, flood damage and theft, and subscribed to the local Neighborhood Watch, which supplied them with a plaque for their gates lettered YOU HAVE BEEN WARNED over the silhouette of a would-be intruder.

These precautions are not particularly overdone: like the fence around the swimming pool, they serve a practical purpose. Most people have insurance, most people license their pets, many people subscribe to a neighborhood watch program—but the plaque adds an element of concern and foreshadowing. Unnecessarily antagonistic, it speaks not to pragmatism but to fear.

As the story continues, the neighborhood’s changes are driven less by reasonable precautions and more by fear. Security is paramount—it is the reason behind the electronically controlled gates and burglar alarms—but it quickly becomes evident that the security measures are ineffective. The alarms in particular are too easily triggered, often by pets or mice, and so:

The alarms called to one another across the gardens in shrills and bleats and wails that everyone soon became accustomed to, so that the din roused the inhabitants of the suburb no more than the croak of frogs and musical grating of cicadas' legs. Under cover of the electronic harpies' discourse intruders sawed the iron bars and broke into homes, taking away hi-fi equipment, television sets, cassette players, cameras and radios, jewelry and clothing, and sometimes were hungry enough to devour everything in the refrigerator or paused audaciously to drink the whiskey in the cabinets or patio bars.

Alarms are so named for a reason: they should shock people into realizing that something is wrong, so for them to be no more alarming than a cicada’s song means they have failed in their purpose. Adding insult to injury, the thieves actually take advantage of the noise to steal more. If the inhabitants of the neighborhood were more practical, they would realize the alarms have done far more harm than good. Instead, they keep the alarms and search for additional security measures. The very devices that they rely upon to keep them safe have quite obviously made them more vulnerable; at this point, it becomes evident that fear has overtaken reason. This pattern continues to escalate until the family’s son is caught in barbed wire and dies.

The story speaks of fear, just as the narrator’s frame does. Gordimer notes that “I have no burglar bars, no gun under the pillow, but I have the same fears as people who do take these precautions,” and proceeds to spin a story about how physical protection is no deterrent to fear. This fear leads to a mindset in which security is the only worthy value: worth more than empathy, as can be seen when the wife stops feeding people on the street; worth more than practicality or reason or pleasure; and, ultimately, worth more than their son’s life.

How does Shakespeare use magic and supernatural elements in play The Tempest?

In Shakespeare's play, The Tempest, magic is performed by Prospero and by his fairy servant Ariel throughout the play. Sometimes it is unclear who actually performs the magic, but since the magic performed by Ariel is directed by Prospero, we know he is the source of the magic that takes place during the play. The tempest itself that causes the shipwreck was Prospero's doing, and the various people from the ship are separated into...

In Shakespeare's play, The Tempest, magic is performed by Prospero and by his fairy servant Ariel throughout the play. Sometimes it is unclear who actually performs the magic, but since the magic performed by Ariel is directed by Prospero, we know he is the source of the magic that takes place during the play. The tempest itself that causes the shipwreck was Prospero's doing, and the various people from the ship are separated into their groupings according to Prospero's magic. Prospero puts a spell on Miranda and Ferdinand to make them fall in love. Ariel causes the King to fall asleep and wakes him up just as Sebastian and Antonio are about to murder him. Ariel harasses Caliban, Trinculo, and Stephano with strange noises and lures them to various parts of the island. Prospero also spreads a magical banquet before King Alonso and his party, but Ariel, in the guise of a harpy, makes it disappear. To celebrate the engagement of Ferdinand and Miranda, Prospero and the spirits present a magical wedding masque (play) for them. Finally, at the climax of the play, Prospero creates a magic circle and draws his brother, Antonio; the King, Alonso; and the rest of their party inside it where they are confronted with their sins and given a chance to repent. At the end of the play, Ariel is set free after he promises to do one last act of magic: to make sure the entire party has smooth sailing back to Milan. Prospero decides to give up magic as he returns to his role as Duke of Milan.

Is lifting the top to a paint can a first, second, or third class lever?

Lifting the lid of a can of paint (with a screwdriver, or other similar solid rod) is an example of a first class lever. Levers are one of the simple machine types known since ancient times.

Levers are defined as first, second, or third class depending on where the fulcrum (the pivot point around which the lever operates) is in relation to the load (the thing we are trying to move) and the effort (where...

Lifting the lid of a can of paint (with a screwdriver, or other similar solid rod) is an example of a first class lever. Levers are one of the simple machine types known since ancient times.

Levers are defined as first, second, or third class depending on where the fulcrum (the pivot point around which the lever operates) is in relation to the load (the thing we are trying to move) and the effort (where we exert force on the lever). Lifting a paint can lid uses a first class lever because the lid being lifted (the load) is at one end of the lever, the fulcrum (in this case the edge of the paint can) is in the middle) and the force (a person pushing down on the screwdriver outside of the paint can) is at the other end. A seesaw is another example of a first class lever.

Second class levers have the fulcrum at one end, and the effort at the other, with the load in between. Wheelbarrows and staplers are examples.

Third class levers have the fulcrum at one end, the load at the other, and the effort in between. An example for this type is use of a fishing pole. 

See the link below for diagrams that will help you to understand the differences.

In To Kill a Mockingbird, what might Scout's knowledge imply about the behaviors of the townspeople?

Throughout the novel, To Kill a Mockingbird, we are able to see Scout grow and mature as a character through the lessons Atticus teaches her and the events she experiences.  Even though Scout is a young child at the beginning of the novel, Harper Lee takes the reader through the process of Scout growing up.  Scout learns about how to respect and empathize with people like Walter Cunningham because of the lessons Atticus teaches...

Throughout the novel, To Kill a Mockingbird, we are able to see Scout grow and mature as a character through the lessons Atticus teaches her and the events she experiences.  Even though Scout is a young child at the beginning of the novel, Harper Lee takes the reader through the process of Scout growing up.  Scout learns about how to respect and empathize with people like Walter Cunningham because of the lessons Atticus teaches her.  She learns to “walk in another person’s skin”, and she is mature enough to understand Mayella Ewell’s loneliness because of the hopelessness in which Mayella exists.  To Kill a Mockingbird is a rite of passage for both Jem and Scout as they grow due to the decisions they make, the obstacles and hardships they face, and the lessons they learn. 

A lot of the people of Maycomb, however, have been so mired in the values and beliefs generations old that they cannot grow beyond what they have always known and lived.  Oppressive racists attitudes have been a way of life for so long that people didn’t know how or even want to change.  They live in the ignorance of their positions of power that are so hard to give up.  Although we see some changes in the Maycomb community in characters like Mr. Underwood and Dolphus Raymond, most of the town didn't have an “Atticus” to lead them down the right path of justice and understanding. 

Racism is a learned behavior, and for Scout, Atticus has done a wonderful job of teaching her about the similarities of people.  Because the majority of the white citizens of Maycomb have always lived in a system of racism and discrimination, it is harder for them to want to change their views.  Scout is a symbol of a new way of living one’s life free of racism and oppression of others. 

From what you have read about Odysseus, do you think his reputation is deserved? Support your opinion.

I do think that Odysseus deserves to be seen as a hero due to both his own qualities and actions as well as how his society defined a hero.  He does get a great deal of help in The Odyssey, mostly from Athena, but this is not uncommon among ancient Greek heroes.  Odysseus is clearly brave and he possesses determination and perseverance in spades: he willingly travels to the Underworld, despite his terrible fear,...

I do think that Odysseus deserves to be seen as a hero due to both his own qualities and actions as well as how his society defined a hero.  He does get a great deal of help in The Odyssey, mostly from Athena, but this is not uncommon among ancient Greek heroes.  Odysseus is clearly brave and he possesses determination and perseverance in spades: he willingly travels to the Underworld, despite his terrible fear, in order to speak with Teiresias, the blind prophet who can tell him how to get home; he forms a plan to blind the Cyclops, Polyphemus, so that he and his men will have the best chance of escape and he plays a key and dangerous role in that plan; on his quest to reach home, he willingly encounters many monsters -- the Sirens, Scylla, and Charybdis -- knowing that he could be injured or even killed, and so forth.  Is he perfect?  Nope, not at all.  He's arrogant, proud, and sometimes even greedy.  However, most heroes aren't perfect because they're human.  Thus, Odysseus has his flaws, but he has a number of heroic qualities that, in my opinion, outweigh them.

In To Kill a Mockingbird, what contradiction did Scout experience when Miss Gates explained the difference between America and Germany?

Throughout Miss Gates' lesson, Scout discovers the hypocrisy attached to condemning Hitler's treatment of the Jews, while supporting racial prejudice in Maycomb County. During a "Current Events" activity in school, Cecil Jacobs explains to the class how "Old Hitler has been after the Jews." (Lee 327) Miss Gates explains that Germany is a dictatorship, which is the reason Hitler can get away with such atrocities. Scout is praised after she repeats the definition of democracy,...

Throughout Miss Gates' lesson, Scout discovers the hypocrisy attached to condemning Hitler's treatment of the Jews, while supporting racial prejudice in Maycomb County. During a "Current Events" activity in school, Cecil Jacobs explains to the class how "Old Hitler has been after the Jews." (Lee 327) Miss Gates explains that Germany is a dictatorship, which is the reason Hitler can get away with such atrocities. Scout is praised after she repeats the definition of democracy, which is "equal rights for all, special privileges for none," and Miss Gates elaborates on the differences between Germany and the United States. She boldly proclaims that people in America do not believe in persecuting anybody because there is no prejudice in the United States. Scout takes note of Miss Gates' statement and remembers the time when Miss Gates was leaving the courthouse. Scout heard her say, "it's time somebody taught 'em a lesson, they were gettin' way above themselves, an' next thing they think they can do is marry us." (Lee 331) The contradiction lies in the fact that people are not being treated equally in America despite its democratic foundation. Scout witnesses prejudice towards African Americans each day in Maycomb, Alabama. Scout asks Jem the important question, "How can you hate Hitler so bad an' then turn around and be ugly to folks right at home?" (Lee 331)

What is the length of a planetary day on each planet?

Though I cannot give you information about the length of a day on every known planet — many are too far away to be reliably observed in this respect — I can tell you the length of a day on each of the planets in our solar system. The length of a day is determined by the amount of time it takes for a planet to complete a full rotation on its axis.

Mercury, the planet closest to the Sun, takes quite a long time to complete a rotation. One day on Mercury is 1,408 hours long — 58.7 Earth days! If you were to mark your calendar for a date two months from now, Mercury would experience just one day in that amount of time.

Venus is even slower in its rotation, taking 5,832 hours to complete a day! That's 243 Earth days.

Here on Earth, we experience days in the 23.9 hour rotation of our planet. 

Mars has a very similar rotation speed to our own planet, taking just 25 hours to complete one day.

Jupiter is speedy, taking only 10 hours to complete a day. That's less than half of one Earth day!

Saturn, too, has a quick rotation. Days on Saturn are just 11 hours long, just under half of one Earth day.

Uranus takes 17 hours to complete a rotation, which is nearly three-quarters of an Earth day.

Neptune's days are 16 hours long, two-thirds of an Earth day!

Though Pluto is no longer considered a planet, many people still have a soft spot for the celestial body. A day on Pluto is about 153 hours long, or over 6 Earth days.

What are the effects of war on people?

War can affect people in many ways. War may split families or keep them apart. When a soldier goes to a war zone, the family is no longer together. There is the possibility of death or serious injury. These injuries could be life-long, debilitating injuries. In the Civil War, family members took different sides in the war. Some family members fought each other because they were on different sides.

War can lead to a limitation of our freedoms. The Sedition Act in World War I made critical comments about the government or the war effort illegal. The Espionage Act allowed for anti-war activities to be punished. In World War II people were limited in the amount of certain items they can get each month. This system, called rationing, limited how much beef, gasoline, and sugar people could buy each month.

During a war, the government will increase its role in the economy. The government may decide what will be produced, how many will be produced, and who will produce the items. In World War I, the War Industries Board determined what war materials would be made. In World War II, the War Labor Board mediated labor disputes.

People have to make sacrifices during a war. People who might otherwise not be working may have to go to work in the war industries to make sure the military has enough supplies. The people may be strongly encouraged to loan the government money by purchasing war bonds. They may not be able to buy items that they want to buy, but don’t necessarily need to buy.

If a war is unpopular, such as the Vietnam War, it can lead to mass protests and open defiance of government policies. In the Vietnam War, some people refused to serve in the army. There were many protests against the war across the country, especially on college campuses. Violent actions occurred such as the shootings at Kent State University.

When a country goes to war, the people of that country are affected by the conflict in many ways. Sometimes, it can take decades to undo the effects of a war.

What were the benefits of being colonized by England?

Being colonies of Great Britain had several benefits. Great Britain was an established world power. The British had a developed economic system. We were able to benefit to some degree from that economic system. We got products from Great Britain. These products could be made cheaper in Great Britain than they could be made in the colonies. Thus, we did benefit to a degree economically by being British colonies.

We also received protection from the...

Being colonies of Great Britain had several benefits. Great Britain was an established world power. The British had a developed economic system. We were able to benefit to some degree from that economic system. We got products from Great Britain. These products could be made cheaper in Great Britain than they could be made in the colonies. Thus, we did benefit to a degree economically by being British colonies.

We also received protection from the British. The British navy was very powerful and effective. The British army also protected us during conflicts. When the French and Indian War occurred, the British protected us from the Native American and French attacks. Great Britain gave us protection that we would have been hard pressed to provide by ourselves.

Great Britain also showed us how to develop a government system and a political system. We learned from the British how to govern ourselves. The British showed us how to develop an effective government. They also showed us what not to do as a government with some of the mistakes that Great Britain made that led to the Revolutionary War. We also learned how to establish a judicial system by being under British rule.

Part of the reason for having colonies is for those colonies to one day become independent. Great Britain showed us how to run a government, how to develop an economy, and how to create a judicial system. Learning these ideas from Great Britain helped us a great deal when we became independent.

`int_(-pi/3)^(pi/3) x^4 sin(x) dx` Evaluate the definite integral.

You need to solve the definite integral, using fundamental theorem of calculus, such that:

`int_a^b f(x) dx = F(b) - F(a)`

First, you need to solve the indefinite integral `int x^4*sin x dx` , using parts, such that:

`int vdu = v*u - int udv`

If `v = x^4 and du = sin x` yields:

`dv = 4x^3 and u = -cos x`

`int x^4*sin x dx = -x^4*cos x + 4int x^3*cos x dx`

...

You need to solve the definite integral, using fundamental theorem of calculus, such that:

`int_a^b f(x) dx = F(b) - F(a)`

First, you need to solve the indefinite integral `int x^4*sin x dx` , using parts, such that:

`int vdu = v*u - int udv`

If `v = x^4 and du = sin x` yields:

`dv = 4x^3 and u = -cos x`

`int x^4*sin x dx = -x^4*cos x + 4int x^3*cos x dx`

Using parts again for `int x^3*cos x dx` yields:

`v = x^3 and du = cosx=> dv = 3x^2 and u = sin x`

`int x^3*cos x dx = x^3*sin x - 3int x^2*sin x dx`

Using parts again for `int x^2*sin x dx` yields:

`v = x^2 and du = sin x=> dv = 2x and u = -cos x`

`int x^2*sin x dx = -x^2*cos x + 2int x*cos x dx`

Using parts for the last time for `int x*cos x dx` yields:

`v = x and du = cos x => dv = 1 and u = sin x`

`int x*cos x dx = x*sin x - int sin x dx`

`int x*cos x dx = x*sin x + cos x`

Take the result `x*sin x + cos x` and replace it for `int x*cos x dx` above:

`int x^2*sin x dx = -x^2*cos x + 2x*sin x + 2cos x`

Take the result `-x^2*cos x + 2x*sin x + 2cos x` and replace it for `int x^2*sin x dx` above:

`int x^3*cos x dx = x^3*sin x - 3(-x^2*cos x + 2x*sin x + 2cos x)`

`int x^3*cos x dx = x^3*sin x + 3x^2*cos x - 6x*sin x - 6cos x`

Take the result `x^3*sin x + 3x^2*cos x - 6x*sin x - 6cos x` and replace it for `int x^3*cos x dx` above:

`int x^4*sin x dx = -x^4*cos x + 4int x^3*cos x dx`

`int x^4*sin x dx = -x^4*cos x + 4(x^3*sin x + 3x^2*cos x - 6x*sin x - 6cos x)`

`int x^4*sin x dx = -x^4*cos x + 4x^3*sin x + 12x^2*cos x - 24x*sin x - 24cos x`

Calculating the integral yields:

`int_(-pi/3)^(pi/3) x^4*sin x dx = (-x^4*cos x + 4x^3*sin x + 12x^2*cos x - 24x*sin x - 24cos x)|_(-pi/3)^(pi/3)`

`int_(-pi/3)^(pi/3) x^4*sin x dx = (-(pi/3)^4*cos (pi/3) + 4(pi/3)^3*sin (pi/3) + 12(pi/3)^2*cos (pi/3) - 24(pi/3)*sin (pi/3) - 24cos (pi/3) +(pi/3)^4*cos (pi/3) - 4(pi/3)^3*sin (pi/3) - 12(pi/3)^2*cos (pi/3) + 24(pi/3)*sin (pi/3) + 24cos (pi/3))`

Reducing like terms yields:

`int_(-pi/3)^(pi/3) x^4*sin x dx = 0`

You also may solve the integral by noticing the the function `f(x) = x^4*sin x` is odd and you may use the propert` int_(-a)^a f(x) dx = 0` if f(x) is odd.

You may prove that ` f(x) = x^4*sin x` is odd such that:

`f(-x) = (-x)^4*sin (-x) = x^4*(-sin x) = -x^4*sin x = -f(x)`

Hence, evaluating the definite integral, using either the fundamental theorem of calculus, or the property of odd functions `int_(-a)^a f(x) dx = 0` , yields `int_(-pi/3)^(pi/3) x^4*sin x dx = 0.`

What do the British and Americans have in common?

The British and the Americans had several things in common. The Americans were ruled by England as colonies for many years prior to the Revolutionary War. Once we got our independence from Great Britain, we modeled several important ideas after the British. Our system of government, while not identical, has similarities. Both countries elect their lawmakers. We modeled many of the ideas in the Declaration of Independence and in the Constitution after British ideas. The...

The British and the Americans had several things in common. The Americans were ruled by England as colonies for many years prior to the Revolutionary War. Once we got our independence from Great Britain, we modeled several important ideas after the British. Our system of government, while not identical, has similarities. Both countries elect their lawmakers. We modeled many of the ideas in the Declaration of Independence and in the Constitution after British ideas. The concept of natural rights and the idea of a Bill of Rights come from the philosophy of John Locke and from the English Bill of Rights.

There are other similarities. Our judicial system has similarities. Both countries have courts and believe in the idea that a person is innocent until proven guilty. Our language is also similar. Both countries believe in free market economic principles. Both countries have fought against the spread of authoritarian governments. We have worked to also prevent the spread of communism. There are many similarities between the British and the Americans.

Why does Mrs. Hale feel so guilty about not visiting Mrs. Wright more often? Why does Mrs. Hale feel such tremendous guilt about Mrs. Wright’s...

After she looks around the stark house of the Wrights, becoming disturbed by the worn and shabby clothes of Mrs. Wright, Mrs. Hale experiences guilt for not having visited Minnie Foster. For, she realizes how terribly deprived of comfort and lonely the woman has been.

Once alone in the kitchen, Mrs. Peters and Mrs. Hale talk. Examining the skirt that they have brought into the room, Mrs. Hale remarks,

"Wright was close [reclusive and unsociable]....

After she looks around the stark house of the Wrights, becoming disturbed by the worn and shabby clothes of Mrs. Wright, Mrs. Hale experiences guilt for not having visited Minnie Foster. For, she realizes how terribly deprived of comfort and lonely the woman has been.

Once alone in the kitchen, Mrs. Peters and Mrs. Hale talk. Examining the skirt that they have brought into the room, Mrs. Hale remarks,

"Wright was close [reclusive and unsociable]. I think maybe that's why she kept so much to herself. She didn't even belong to the Ladies' Aid. I suppose she felt she couldn't do her part, and then you don't enjoy things when you feel shabby.

Mrs. Hale contrasts Mrs. Wright with the former Minnie Foster who used to wear pretty clothes and be lively and outgoing; in fact, she even sang in the church choir. 

As Mrs. Hale reflects upon the social deprivation that Minnie Foster must have experienced living on this lonely farm with no children to brighten her life, she becomes ashamed of herself for not having reached out to her neighbor by visiting more frequently. But, she stayed away because the house that is down in a hollow has always seemed such "a lonesome place." Then, too, Mr. Wright has always been what she describes to Mrs. Peters as "a hard man" who did not make a person feel welcome. Nevertheless, now she wishes she had ignored these conditions and visited Mrs. Wright, who must have been so terribly isolated from cordial and feminine companionship.

I need some facts on New Imperialism.

New Imperialism was a period of territorial expansion by the countries of Europe, the U.S. and Japan which began around 1870 and lasted until the mid-twentieth century. During this time, these imperial nations colonised vast swathes of Asia, the Middle East and Africa. 

There are a number of factors which explain this sudden expansion in the late nineteenth century. First of all, these imperial nations had all reaped the benefits of industrialisation: they were at...

New Imperialism was a period of territorial expansion by the countries of Europe, the U.S. and Japan which began around 1870 and lasted until the mid-twentieth century. During this time, these imperial nations colonised vast swathes of Asia, the Middle East and Africa. 

There are a number of factors which explain this sudden expansion in the late nineteenth century. First of all, these imperial nations had all reaped the benefits of industrialisation: they were at the height of their economic, political and military power and wanted to demonstrate their wealth and prestige to the rest of the world. These nations also believed themselves to be culturally superior to other cultures, an idea we call 'ethnocentrism', and so expansion also provided them with an opportunity to transmit their norms, values and religious beliefs on other 'uncivilised' races.

The rise of New Imperialism had some important repercussions on these colonies. For a start, it destroyed many native customs and political and social institutions. The plundering of their natural resources also made these countries poorer as imperial nations grew richer.

Expansion also created rivalries between imperial nations which would have far-reaching consequences: conflict between France and Germany over Morocco and between France and Britain over the Sudan created the tensions which erupted in World War One.   

According to the Wife of Bath, in what way does life in her day differ from life in King Arthur’s time?

In the time of King Arthur, the natural environment blended with magical elements and creatures. However, all the elements and creatures had since disappeared and paved the way for modern religion.

According to the poem, there were plenty of magical creatures who existed in the natural environment. For instance, there were fairies and elves who danced in the open fields. There were mythical creatures, such as, the incubus who lived in the forest and made...

In the time of King Arthur, the natural environment blended with magical elements and creatures. However, all the elements and creatures had since disappeared and paved the way for modern religion.

According to the poem, there were plenty of magical creatures who existed in the natural environment. For instance, there were fairies and elves who danced in the open fields. There were mythical creatures, such as, the incubus who lived in the forest and made it dangerous for women who went there alone, because the incubus would impregnate them as they slept. These magical and mythical creatures were however replaced, and in their position, holy friars and limiters existed. The friars were assigned a specific area where they performed their religious duties and begged from passersby for their livelihood.

I speak of many hundred years ago.

   But now such elves no one is seeing. No,

   For now the prayers and charitable desires                

   Of limiters and other holy friars

   Who wander all the land, by every stream,

   As thick as specks of dust in a sunbeam,

   To bless our halls, chambers...

In summary, the difference was that magic and magical elements were restricted during her time as compared to King Arthur’s time. During King Arthur’s time, creatures such as fairies existed freely in the natural environment. 

In "The Open Window," why does Vera enjoy tricking people?

Vera is an example of how a skillful fiction writer will create a character to fit the needs of his plot. Such examples are to be found throughout the world's literature. Characters are not real people but illusions. The three characters in "The Open Window" were all created to fit the parts they needed to play. Framton Nuttel is a neurotic man who is only visiting the Sappletons because he has come to this part of the country for a "nerve cure." He doesn't know a thing about the Sappleton family or about the region. Mrs. Sappleton is an empty-headed woman who has no internal or external resources. She is as confined as a caged bird or a house cat. She is devoted to the three men in her life and has learned to talk their language, which is all about tramping around in the mud and killing birds. Saki needed a character who would tell the neurotic visitor a wild ghost story and set him up to be terrified when the three hunters appeared. The author invented a girl who was just young enough to be mischievous and just old enough to be believable. She is the best character in the story--but she is just a character and not a real, live human being. We can only speculate about her reasons for being slightly sadistic.

Vera is a girl. She can't go hunting and is confined to the house just like her aunt, and she may see her future in her aunt. She will get married and have to play hostess to unattractive men like Framton Nuttel and idiotic women like her aunt. If she marries a wealthy man she will have servants to do all the work, and she will have little to do except to read books and listen to male talk. Vera must feel resentful. She is introduced as a stand-in hostess while her aunt makes a few last-minute touches to her hair and dress. No doubt Mrs. Sappleton has sent Vera on ahead in order to give the girl some practice for the role of hostess she is destined to assume in the not-too-distant future. Vera knows this and resents it. She doesn't want to be another Mrs. Sappleton. Who would? Since Vera has virtually nothing to do but read, she has augmented her own vivid imagination with ideas she has picked up from her books. She suffocates in an environment she would like to escape from, so she might like escapist literature.

So Vera is resentful, bored, imaginative, and addicted to escapist reading as well as escapist fantasies. She resents being kept a prisoner in this country manor where everybody predictably does and says the same things day after day until they are driving her insane. She takes out her resentment and frustration on poor Framton Nuttel because he doesn't know anything about anybody in the region. She may not have intended to send him flying out into the night. If he had stayed, he would have met the three men and quickly realized the girl was only playing a practical joke. He could not have caused her trouble by repeating her ghost story. He might have given her a dirty look, and she might have returned it with a winsome conspiratorial grin. But because the author had created a "patsy" who was already a nervous wreck, Framton reacts more vigorously than the girl probably expected, and she has to invent another story as a cover-up.

"I expect it was the spaniel," said the niece calmly; "he told me he had a horror of dogs. He was once hunted into a cemetery somewhere on the banks of the Ganges by a pack of pariah dogs, and had to spend the night in a newly dug grave with the creatures snarling and grinning and foaming just above him. Enough to make anyone lose their nerve."

In Beka Lamb, in what chapter does Toycie die and how?

Mindlessly wandering through the mangoes during the hurricane, Toycie is struck on the head by a mango tree that is uprooted by the storm and falls directly on Toycie, breaking her skull. The letter from Miss Eila telling of her death, addressed to Daddy Bill, Beka's father, arrives and is brought home to Beka in Chapter 24.

Beka, Granny Ivy, her mother and father, Lilla and Bill, along with twenty-five other people weather the storm...

Mindlessly wandering through the mangoes during the hurricane, Toycie is struck on the head by a mango tree that is uprooted by the storm and falls directly on Toycie, breaking her skull. The letter from Miss Eila telling of her death, addressed to Daddy Bill, Beka's father, arrives and is brought home to Beka in Chapter 24.

Beka, Granny Ivy, her mother and father, Lilla and Bill, along with twenty-five other people weather the storm in their house, with its safe (they hope) concrete foundation. Lilla awakens Beka, who fell asleep with her head in her mother's lap, to tell her the storm is over. Light-headed from the lamps' kerosene oil smell, she's stunned to see that so many people were safe from the storm and are now milling about in their home.

The work of clearing the debris of fallen trees and up-torn belongings begins. The work of trying to obtain clean drinking water and washing water from the hurricane muck carries on alongside the chores of cleaning the house up again, and the report comes in that Toycie's Sibun area was hit hard by the hurricane.

A muddy stench lingered in the air, and no matter how the Lambs cleaned and scrubbed and polished, it would not go away. All drinking water had to be boiled, and to get enough clean water to wash clothes was a problem. ... [The] storm was known to have devastated the Sibun area, and there was a sense of waiting in the house.

Days into the clean-up, the schools are still closed, and Daddy Bill comes home one day unexpectedly, hissing through his teeth the way he does when he has bad news to bear. The letter he has tells them all that Toycie is dead. Beka, her heart already "thudding in her chest" with a kind of foreknowledge, gives in to the "tidal wave" that crashed in "her brain" and screams and screams inconsolably. Miss Eila's short letter tells how a mango tree in the hurricane ended Toycie's life.

   'Dear Mr Bill, just these few lines to let you know that Toycie died the night of the heavy storm. She was buried this day instant. My Toy wandered away in the confusion of preparation and mango tree fall to break her skull. ... Ever your Miss Eila.'

Daddy Bill holds Beka tight to try to stay her hysteria. Granny comforts her and shocks her in turns to bring her back to her senses. But nothing changes Beka's screaming until Miss Boysie appears at the back door roundly scolding Beka for the mess that the bougainvillea stump has gotten into. This surprise, completely irrelevant scolding recalls Beka to herself.

How do you put f(x)=x (x-4)^2 (x-8)(x^2+4) in standard form? This is in factored form by the way.

A polynomial is in standard form if it is written as follows:

`P(x) = ax^n + bx^(n-1) + cx^(n-2) +...`

The term with the highest degree comes first and is followed by the other terms in the order of decreasing powers of the variable.

To express the function

`f(x) = x(x-4)^2(x-8)(x^2+4)`

in standard form, let's first expand repeated factor.

The expanded form of the repeated factor is:

`@` `(x-4)^2=(x-4)(x-4) = x^2-4x-4x+16=x^2-8x+16`

The function becomes:

`f(x)=x(x^2-8x+16)(x-8)(x^2+4)`

...

A polynomial is in standard form if it is written as follows:

`P(x) = ax^n + bx^(n-1) + cx^(n-2) +...`

The term with the highest degree comes first and is followed by the other terms in the order of decreasing powers of the variable.

To express the function

`f(x) = x(x-4)^2(x-8)(x^2+4)`

in standard form, let's first expand repeated factor.

The expanded form of the repeated factor is:

`@` `(x-4)^2=(x-4)(x-4) = x^2-4x-4x+16=x^2-8x+16`

The function becomes:

`f(x)=x(x^2-8x+16)(x-8)(x^2+4)`

Then, multiply the factors. Let's start with the factors at the left.

`@` `x(x^2-8x+16)=x^3-8x^2+16x`

The function transforms to three factors.

`f(x)= (x^3-8x^2+16x)(x-8)(x^2+4)`

Then, multiply (x^3-8x^2+16x) with (x-8).

`@`  `(x^3-8x^2+16x)(x-8)`

   `=x^4-8x^3 -8x^3+64x^2+16x^2-128x`

  `= x^4-16x^3+80x^2-128x`

f(x) is reduced to two factors.

`f(x) = (x^4-16x^3+80x^2-128x)(x^2+4)`

Multiply these two factors.

`@`  `(x^4-16x^3+80x^2-128x)(x^2+4)`
  `= x^6 +4x^4-16x^5-64x^3+80x^4+320x^2-128x^3-512x`
  `= x^6 -16x^5+84x^4-192x^3+320x^2-512x`

The function is now converted to standard form.

Therefore the standard form of

`f(x) = x(x-4)^2(x-8)(x^2+4) `

is

`f(x)= x^6 -16x^5+84x^4-192x^3+320x^2-512x` .

What happens to Fleance in the play Macbeth?

Fleance is, of course, the son of Macbeth's friend and comrade Banquo. Macbeth comes to regard Banquo as a threat because he also saw the witches' prophecy and because the witches foretold that Banquo's descendants would be kings. Macbeth assigns assassins to murder Banquo and Fleance while they are out riding. The assassins are successful in killing Banquo, but Fleance escapes. We do know Fleance's sons will emerge to rule Scotland. Indeed, some at the...

Fleance is, of course, the son of Macbeth's friend and comrade Banquo. Macbeth comes to regard Banquo as a threat because he also saw the witches' prophecy and because the witches foretold that Banquo's descendants would be kings. Macbeth assigns assassins to murder Banquo and Fleance while they are out riding. The assassins are successful in killing Banquo, but Fleance escapes. We do know Fleance's sons will emerge to rule Scotland. Indeed, some at the time (including the King himself) traced the lineage of James I, king of England, to Banquo. Fleance's escape thus had modern relevance to Shakespeare's audiences. We are not told where Fleance went after escaping the murderers, only that he survived the attack.

What is the external conflict in Beverly Cleary's Dear Mr. Henshaw?

There are a couple of different external conflicts in Beverly Cleary's Dear Mr. Henshaw. The greatest external conflict concerns Leigh's difficulties in coping with his parents' divorce. He feels extremely sad and lonely, especially because he feels completely cut off from his father. As the book progresses, Leigh feels sadder the more his father breaks his promises to him; Leigh feels heartbroken to the point of thinking that his father doesn't really love him. Since Leigh is struggling so much with his father, we can call this an external character vs. character conflict, which is a conflict between two characters.

Leigh's external character vs. character conflict begins reaching its greatest point of intensity in early February of his sixth-grade year. That Christmas, Leigh received a gift from his father but didn't hear from him until the 8th of January. Though his father promised to call again in a week, Leigh doesn't hear from him for the rest of the month. Leigh begins feeling so lonely and desperate to hear from his father that, on February 4th, Leigh phones his father's trailer, not expecting his father to be home. The phone call is extremely upsetting to Leigh because he realizes his father actually was at home, sitting around not calling him. He also learns that his father lost Leigh's dog, Bandit, on the highway in a snowstorm. Worse yet, Leigh hears a strange boy asking, "Hey, Bill, Mom wants to know when we're going out to get the pizza?," which makes Leigh realize he is just not a part of his father's life anymore, making him feel unloved ("Sunday, February 4").

On top of Leigh's external character vs. character conflict with his father, Leigh is experiencing a second external character vs. character conflict at school because someone is bullying him by stealing from his lunch. Leigh feels that if his father were around, he would be able to handle the lunch thief better. Both character vs. character conflicts reach their climax when Leigh feels so angered by both his father and the lunch thief that he nearly kicks any random kid's sack lunch down the school hallway as an act of revenge. However, luckily, Leigh is stopped by Mr. Fridley, who tells Leigh he needs to stop being so absorbed with his own problems, start noticing everyone has problems, and start thinking positively.

Leigh resolves both character vs. character conflicts through positive thinking because positive thinking allows him to make friends, no longer care about who the lunch thief is, and to accept the fact his father will let him down. But Leigh also comes to realize that just because his father disappoints him doesn't mean his father doesn't love him. Leigh grows so understanding of his father's difficult job and loneliness that Leigh suggests his father keep Bandit once Bandit has been found.

If there is an infinite amount numbers from 1 to 2, how do we measure inches, meters, seconds, time, etc.? Or perhaps, 1 inch is infinite and...

This is an excellent question. First we make a distinction between a mathematical model and a physical model.

There are indeed an infinite number of real numbers between 0 and 1 on the real number line. Each number represents a mathematical point on the number line. But these numbers have no physical manifestation -- each point has no size (no length, width, nor height.) Even with the most powerful tools we have available, any "point"...

This is an excellent question. First we make a distinction between a mathematical model and a physical model.

There are indeed an infinite number of real numbers between 0 and 1 on the real number line. Each number represents a mathematical point on the number line. But these numbers have no physical manifestation -- each point has no size (no length, width, nor height.) Even with the most powerful tools we have available, any "point" we make takes up some finite volume in our three dimensional world.

In fact, it might not even make sense to speak of anything with spatial dimensions smaller than the Planck scale, as space might not exist at that scale.

So what do we mean by a measurement of 1 inch? If we say that something is 1 inch long, we are actually saying that it is somewhere between 1/2 and 3/2 inches long or `1/2 <= l < 3/2 ` . If we say that something is 1.0 inches, then we indicate that its length is between .99 and 1.05 inches, and so on. We must take into account the precision of the measurement device. In practice, for extremely delicate measurements we must use statistics to give the length.

So while we have a very precise definition of a second (as a number of vibrations of a cesium atom, etc...), this really represents a tiny range of values.

What is Washington Irving warning people about in "The Devil and Tom Walker"?

Irving almost certainly drew a lot of inspiration from the "Faust" storyline, which parallels "The Devil and Tom Walker" in many ways, including the moral lesson. Irving appears to have intended to simply retell the Faust story with more American elements woven into it. We might also contextualize the story in its historical place - Irving was struggling for inspiration to write a follow-up to his previous, successful collection of stories, and the collection in...

Irving almost certainly drew a lot of inspiration from the "Faust" storyline, which parallels "The Devil and Tom Walker" in many ways, including the moral lesson. Irving appears to have intended to simply retell the Faust story with more American elements woven into it. We might also contextualize the story in its historical place - Irving was struggling for inspiration to write a follow-up to his previous, successful collection of stories, and the collection in which "The Devil and Tom Walker" appeared was criticized for being too derivative and not representative of Irving's full creative power.

Like the Faust story, in which a man sells his soul to the Devil in exchange for material power, Tom's story is a fairly straightforward and simple one. Any reader may discern that Tom will come to regret his bargain in time and attempt to cheat his way out of it, or simply perceive that bargaining one's soul is a poor trade, but that immediate gratification is a powerful lure. Either way, Tom's story has little of the complexity that later versions of Faust portrayed, such as Faust being forgiven for his transgressions because of the purity of his intent. Tom, on the other hand, is simply a horrible person, and the story acts more as a fable; do not allow material wealth and power to blind you, because these things are fleeting and rarely bring both happiness and wholesome living. Likewise, in keeping with some of the Gothic themes of the story, Irving suggests that one take things at face value; a dark, evil-seeming place or person is almost certainly so.

Another theme of Animal Farm is that power corrupts those who possess it. How does Orwell bring out this idea through the character of Napoleon?

The animals rebel and take over the farm. The original intent of this rebellion is to make the lives of the animals better. The goal is for the animals to control their modes and means of production. They will determine their own work schedules and they will reap all of the benefits of their work. This is basic communism and if practically and responsibly applied in this small community, the animals could/should be better off....

The animals rebel and take over the farm. The original intent of this rebellion is to make the lives of the animals better. The goal is for the animals to control their modes and means of production. They will determine their own work schedules and they will reap all of the benefits of their work. This is basic communism and if practically and responsibly applied in this small community, the animals could/should be better off. In the beginning, their lives are better. However, like other historical examples of communism put into practice, their live gradually worsen and the leaders of the acquire too much power. 

Napoleon is a representation of Joseph Stalin, a leader of the Russian Revolution and eventual leader of Russia. He, like Napoleon, increasingly gained more power and the people of Russia (like the animals of the farm) saw living conditions worsen. 

Napoleon becomes more and more like a human. He distances himself from the other animals. This is contrary to Animalism (Communism). The original narrative of the rebellion is to show solidarity and unity among all animals, Napoleon included. But in his increasing desire for power, he clearly demonstrates that he (and some other pigs) require better nourishment and living conditions than the other animals. He raises and instructs nine puppies which will become his secret police, further isolating himself from the other animals. He ousts Snowball from the farm so he can have more power. At the end of Chapter VII, Napoleon has animals executed under the suspicion that they disagree with his policies or have rebellious thoughts. Napoleon also has Squealer occasionally change the tenets of Animalism to suit his growing greed. Each change signifies his increasing power and shows how the Animal Rebellion has gone further and further from its original intentions. 

What is the definition of domain?

Word domain can have several meanings in mathematics. Probably the most often used meaning is the one referring to domain of function (or map in general). In that sense domain of function `f:X to Y` is set `X` of all values for which function `f` is defined.

Another important term regarding domain of a function is natural domain. Natural domain is maximal set of values for which the function can be defined under real numbers. E.g. for...

Word domain can have several meanings in mathematics. Probably the most often used meaning is the one referring to domain of function (or map in general). In that sense domain of function `f:X to Y` is set `X` of all values for which function `f` is defined.

Another important term regarding domain of a function is natural domain. Natural domain is maximal set of values for which the function can be defined under real numbers. E.g. for function `f(x)=x^2` natural domain is set of all real numbers `RR` (because we can square every real number and we will get a real number), while for function `g(x)=\sqrt(x)` natural domain is set of all non-negative real numbers (if we take square root of a negative number, we get an imaginary number).

Word domain is also used in topology to denote a connected open set.

In number theory integral domain is ring that is commutative under multiplication, has multiplicative identity and no divisors of zero. Example of integral domain are integers.

In control theory and statistics frequency domain refers to function analysis with respect to frequency. E.g. each sound signal can be broken down to several different simple signals of different frequencies. Frequency domain is set of those simple signals.

There are still other usages of the word domain in mathematics: fundamental domain in group theory, domain of discourse in logic... There even a whole branch of mathematics called domain theory that studies partially ordered sets which are sometimes called domains.

Analyze the importance of history in education studies.

I would argue that history ought to be an important aspect of any course of study. But some specific reasons can be given for the importance of history to a curriculum in education studies. 

First, the study of history promotes critical thinking, and requires students to exercise metacognition, or thinking about how they learn. Many of the most important aspects of the study of history, including reading primary sources, evaluating different points of view on...

I would argue that history ought to be an important aspect of any course of study. But some specific reasons can be given for the importance of history to a curriculum in education studies. 

First, the study of history promotes critical thinking, and requires students to exercise metacognition, or thinking about how they learn. Many of the most important aspects of the study of history, including reading primary sources, evaluating different points of view on historical events, and especially evaluating the arguments of modern historians require the exercise of skills that people ought to be fostering in their students. 

Second, the study of history can help provide perspective on students themselves. Having taught in rural school districts in the South for many years, I learned that the legacies of slavery and Jim Crow are literally everywhere, and that they affected my students in ways I could only have recognized through the study of history. In this way, history fosters empathy--one of the most important skills an educator can have.

Finally, I would suggest that educators themselves ought to be aware of the importance of education, and this can only be gained through a study of history. Universal education is a fairly new phenomenon in historical terms, and again, using my own career as an example, the study of history made me aware of the options our work creates for students. Less than a century ago, children in the places I've taught would have had one of two futures to look forward to--farm or textile mill. Education creates opportunity, and educators need to know this.

What methods does Harper Lee use to present loneliness as the result of bad parenting in the novel To Kill a Mockingbird?

Lee employs a repetitive story structure in three subplots to help illustrate the message that bad parenting can lead the children to be lonely. We see this message in the parent/child relationships of Dill and his parents, Boo and his father, and Mayella and Bob Ewell.

Dill's mother divorced his father, and he seems to see very little of his biological dad. His "new dad" and his mom leave him in Maycomb each summer with...

Lee employs a repetitive story structure in three subplots to help illustrate the message that bad parenting can lead the children to be lonely. We see this message in the parent/child relationships of Dill and his parents, Boo and his father, and Mayella and Bob Ewell.

Dill's mother divorced his father, and he seems to see very little of his biological dad. His "new dad" and his mom leave him in Maycomb each summer with relatives and when they do spend time with him the rest of the year, it usually involves buying him things and letting him spend time on his own. He seems like a little boy desperate to be close to his own family. He is lonely boy because his parents simply don't care to spend much time with him.

Boo is described by Miss Maudie as being a very sweet boy when he was young, but then he pulled a childish prank and his father basically locked him up in the house. His father was also very religious, according to Miss Maudie, and this might have played a part in his reasoning for keeping Boo isolated. The result is that Boo never makes friends in town and is completely cut off from anyone his own age...anyone at all. He is desperate to reach out to Scout, Jem, and Dill through the knothole in the tree, as we see when he begins to leave them presents.

Mayella Ewell is also isolated from others in town as a result of her father, Bob Ewell, causing her to be incredibly lonely. She is physically, verbally, and probably sexually abused by Bob Ewell and is the default mother in the Ewell home, taking care of all of her younger siblings. Scout says at one point that "Mayella Ewell must have been the loneliest person in the world."

I'm writing an essay on the tragedy of Romeo and Juliet and I need some ideas on how to prove that Juliet is merely experiencing her first...

I agree with the previous answer. A good first step is to differentiate between love and infatuation. I also think it would be helpful to consult some online material on the topic. While it may seem a little silly, eHarmony has a good article about the difference between the two. In the article, eHarmony notes:

1. Real love is a conscious choice that often employs the rational part of our brains.

2. Real love accepts that...

I agree with the previous answer. A good first step is to differentiate between love and infatuation. I also think it would be helpful to consult some online material on the topic. While it may seem a little silly, eHarmony has a good article about the difference between the two. In the article, eHarmony notes:

1. Real love is a conscious choice that often employs the rational part of our brains.

2. Real love accepts that your partner is a fallible, imperfect human, just as you are. 

3. Real love ebbs and flows in terms of interest, ease, and feelings.

4. Real love is based on shared values and a solid friendship.

Now, let's examine the relationship of Romeo and Juliet. Their relationship progresses at an alarmingly rapid rate. Research on "real love" often discusses how love takes a lot of time to develop and mature. To many adults, love is seen as a deep and lasting bond. This bond, however, takes months and years to mature and develop. In Western culture, we are often inundated with depictions of love (like in Romeo and Juliet) that happen immediately. The phrase "love at first sight" is often used. However, psychologists and relationship experts deny this idea. If you were to use current text on love, like the one above, you would see that Romeo and Juliet are experiencing extreme infatuation. They are not rational, nor do they really understand each others' interests. Instead, they exhibit all the classic signs of infatuation. Of course, their infatuation could develop into a love, but the play does not give them enough time to mature their feelings for one another. 

In The Last Lecture, what does Randy see as the value of a positive attitude?

The ultimate value of a positive attitude in The Last Lecture is seen in how it teaches people to face challenging situations in their lives.

Randy is facing one of the most difficult realities after being diagnosed with only a few months to live.  For Randy, the value of a positive attitude lies in understanding the purpose of both his last lecture and his remaining moments.  Randy suggests that he needed to adopt a...

The ultimate value of a positive attitude in The Last Lecture is seen in how it teaches people to face challenging situations in their lives.

Randy is facing one of the most difficult realities after being diagnosed with only a few months to live.  For Randy, the value of a positive attitude lies in understanding the purpose of both his last lecture and his remaining moments.  Randy suggests that he needed to adopt a positive attitude in order to effectively face his adversary of cancer: "While I could easily feel sorry for myself, that wouldn’t do them, or me, any good." Randy understands that a positive attitude is the only approach he can take not only for himself, but for his family.  He emphasizes the importance of the legacy he will leave for his children.  If he takes a negative attitude, his children will take this with them as their final lesson from their father.  For Randy, the value of a positive attitude lies in the message it transmits to his children.

At the same time, the value of a positive attitude can be seen in his final lecture.   Randy knows that his last lecture cannot be a meditation on death and dying.  Being the "showman" he is, Randy knows that such a focus is not going to leave the audience with a worthwhile message.  As a result, Randy understands the importance of emphasizing a positive attitude throughout the lecture: "Many people might expect the talk to be about dying. But it had to be about living."  Randy knows that the value of a positive attitude is in the lecture's ability to get people to visualize a path through adversity. Randy opens his lecture with an activity that underscores this valuable idea:

I let the slide linger, so the audience could follow the arrows and count my tumors. "All right...That is what it is. We can’t change it. We just have to decide how we’ll respond. We cannot change the cards we are dealt, just how we play the hand."

A positive attitude is what Randy resolved to take when facing down cancer. Its value can be seen in the legacy he left to his family and to us as we read his final lecture.

How many licks does it take to get to the center of a Tootsie Pop?

That is an interesting question.  Unfortunately there are too many variables involved to get a definitive answer.  

One variable is the size of the Tootsie Pop.  I'm sure the Tootsie Pop company has a set margin of error for what is and is not an acceptable sized sucker; however, there is always going to be some variation in exactly how much hard candy coating is covering the inner chocolate.  

Another variable is the...

That is an interesting question.  Unfortunately there are too many variables involved to get a definitive answer.  

One variable is the size of the Tootsie Pop.  I'm sure the Tootsie Pop company has a set margin of error for what is and is not an acceptable sized sucker; however, there is always going to be some variation in exactly how much hard candy coating is covering the inner chocolate.  

Another variable is the size of the Tootsie in the middle.  A slightly larger Tootsie would result in a slightly thinner candy coating in order to have the same standard sized pop.  A thinner coat would require fewer licks.  

The duration and intensity of a lick are also variables that would have to be accounted for.  If a person left it in their mouth the entire time, does that count as one lick?  If a lick is defined as what the tongue touches while outside of the mouth, then tongue length would need to be standardized or accounted for.  A longer length tongue has the potential to get to the center with fewer licks, because it spends more time in contact with the candy coating.  Tongue pressure on candy is another variable.  The friction between the candy and tongue is going to be inversely proportional to the number of licks.  More friction, fewer licks. 

You could account for all of these variables by setting up a variety of controls and using a large sample pool of people.  Personally, I would rather just eat the candy and continue to wonder how many licks it really takes.  

If that's not good enough for you, Purdue and the University of Michigan have both done studies to answer your question.  Both studies used licking machines in order to reduce the number of variables, but both studies arrived at different answers.  I've linked them below. 

What are some critical works on feminism?

Many early works of literature and literary criticism address the social roles of women, beginning as early as the Renaissance with Christine de Pizan's 1405 The Book of the City of Ladies or Le Livre de la Cité des Dames . The nineteenth century brought with it an increase in gender equality and public debate over the role of women, sometimes called the "woman question." 

A Vindication of the Rights of Womanby Mary Wollstonecraft 1792...

Many early works of literature and literary criticism address the social roles of women, beginning as early as the Renaissance with Christine de Pizan's 1405 The Book of the City of Ladies or Le Livre de la Cité des Dames . The nineteenth century brought with it an increase in gender equality and public debate over the role of women, sometimes called the "woman question." 

A Vindication of the Rights of Woman by Mary Wollstonecraft 1792 is sometimes considered to mark the beginning of modern feminism. As well as more political works, feminist criticism in the late nineteenth and early twentieth centuries focused on attaining equality for women writers and asking that they be read seriously not just as exemplars of their gender.   

Two landmarks of feminist critical writing in the first half of the twentieth century were Virginia Woolf's A Room of One’s Own (1928) and Simone de Beauvoir's The Second Sex (1949; English translation 1953).

More recent feminist criticism has evolved in two directions. The first, sometimes referred to as "liberal" feminism emphasizes archival work and recovery of neglected female authors. This has made for a far more inclusive literary canon, with writers such as Zora Neale Hurston and Mary Elizabeth Braddon now having a much greater prominence in textbooks and reading lists. A second type of feminist criticism focuses on feminist theories, arguing that patriarchal viewpoints have affected not just the materials taught in the literary classroom but also critical perspectives. 

The Madwoman in the Attic: The Woman Writer and the Nineteenth-Century Literary Imagination (1979) by Sandra M. Gilbert and Susan Gubar, was a landmark in feminist criticism of women's writing. French critics such as Irigaray and Kristeva combine postmodern psychoanalytic theory and feminism, while writers such as Judith Butler and Eve Kosofsky Sedgwick have synthesized gender and queer theory. Gayatri Chakravorty Spivak combines feminist and post-colonial criticism.

Why should Lyddie not sign the petition?

In chapter 12 Lyddie's two remaining roommates, Amelia and Betsy, argue about signing the petition that the Female Labor Reform Association is circulating. The petition would reduce the work days at the factories from thirteen to ten hours. Amelia and Lyddie are against signing the petition, for different reasons, while Betsy is considering signing.

Amelia, the most religious of the girls, uses practical and moral arguments against signing. First she warns Betsy that, if she...

In chapter 12 Lyddie's two remaining roommates, Amelia and Betsy, argue about signing the petition that the Female Labor Reform Association is circulating. The petition would reduce the work days at the factories from thirteen to ten hours. Amelia and Lyddie are against signing the petition, for different reasons, while Betsy is considering signing.

Amelia, the most religious of the girls, uses practical and moral arguments against signing. First she warns Betsy that, if she signs, she will be dismissed from her job. The management of the factories keeps an eye on the "radicals" who spread dissatisfaction among the workers, and they fire people who sign the petition. Whether this is true or just a fear is unclear. Diana Goss is known to be involved with the FLRA, yet she still works at the factory. That could be because she is such a good worker. If a mediocre worker signed, perhaps she would be dismissed. Once a worker is fired without an honorable discharge, no other factory in town will hire that person, so the worker needs to get a different kind of job in town or move away. Amelia also argues against signing because "it does no good to rebel against authority." She goes on to say rebelling is "unladylike" and "against the Scriptures," at which Betsy scoffs.

Lyddie's reason for not signing is because she does not want to work fewer hours. She says, "But we'd be paid less." She wants her savings to accrue as quickly as possible, no matter how hard she has to work, so she can pay off her family's debts and bring her family back together again on their farm.

Betsy's reasons for signing the petition are that the factories are being unjust and the workers cannot keep up the pace that is demanded of them. Betsy compares their lifestyle to being "black slaves" because they have very little free time and must comply with the whims of factory owners. Indeed, the factories can require increased speeds and can drop the workers' wages even as they are working harder.

This chapter presents reasons for signing the petition as well as for not signing.

How do you describe the process of dissolving?

Dissolving involves a solute and a solvent. The solvent is the item that does the dissolving and the solute is the item that is dissolved. Dissolving implies that the solute and solvent interact to create a solution. As the solute dissolves in the solvent, the particles of the solute begin to separate. The solvent begins to surround these dissociated solute particles. In order for this to occur, the solvent particles need to collide with the...

Dissolving involves a solute and a solvent. The solvent is the item that does the dissolving and the solute is the item that is dissolved. Dissolving implies that the solute and solvent interact to create a solution. As the solute dissolves in the solvent, the particles of the solute begin to separate. The solvent begins to surround these dissociated solute particles. In order for this to occur, the solvent particles need to collide with the solute with enough force and in the correct orientation. Additionally, there needs to be enough attraction between the solute and the solvent. This attraction will ensure that the solvent continues to surround the solute to keep the particles in solution.

The term “likes dissolves likes” alludes to the fact that polar substances will dissolve in other polar substances, while nonpolar substances dissolve in other nonpolar substances.

How did slavery affect Africa socially, economically and politically?

Between the fifteenth and nineteenth centuries, an estimated 12 million Africans were enslaved and transported across the Atlantic Ocean. Socially, this process had a dramatic impact on Africa's population because it removed a huge number of men and women. By 1850, for example, the population of Africa was 25 million people but historians believe that it would have been double this number, had slavery not taken place. 

For those left behind, slavery had important economic...

Between the fifteenth and nineteenth centuries, an estimated 12 million Africans were enslaved and transported across the Atlantic Ocean. Socially, this process had a dramatic impact on Africa's population because it removed a huge number of men and women. By 1850, for example, the population of Africa was 25 million people but historians believe that it would have been double this number, had slavery not taken place. 

For those left behind, slavery had important economic consequences too. Because so many able-bodied men and women were transported abroad, Africa did not have enough workers and entrepreneurs to bring about an agrarian revolution and, in the longer-term, to industrialise. A number of Africans turned instead to working in the lucrative slave-trade and this created important political consequences because traders found it harder to enslave people during peace time. Slave traders, therefore, created political rifts and conflicts to ensure a steady supply of prisoners of war who could be sold into slavery. In Ghana, for example, the rise of slavery coincided with the introduction of gunpowder and explosives to the country. 

What were the major social, economic, and political changes that shaped American history from the Fifteenth Century until the end of the Civil War....

This question could take books to adequately answer. The four centuries between 1400 and 1865 saw tremendous changes in all areas of life on what is now called North America. Here is a quick overview of each part of the question.

Social With the voyages of Christopher Columbus, new cultural groups settled in the Americas. These cultural groups were very different from the native population. Ethnic groups that settled in the New World were English,...

This question could take books to adequately answer. The four centuries between 1400 and 1865 saw tremendous changes in all areas of life on what is now called North America. Here is a quick overview of each part of the question.

Social 
With the voyages of Christopher Columbus, new cultural groups settled in the Americas. These cultural groups were very different from the native population. Ethnic groups that settled in the New World were English, West African, French, Spanish, and Dutch. The European groups brought new languages, class systems, religions, and customs. Africans were subjected to chattel slavery and had no rights. There was a vast exchange of agricultural goods and animals between the natives and Europeans.

Economic
The greatest change in terms of economics was the introduction of a cash system by the new settlers. Surplus agriculture replaced the hunting and gathering that was practiced by native populations. Mercantilism, a precursor to the American capitalist system, was established in the 1500's in the new colonies. By the late 1700's, the North had moved to an industrial economy that relied on manufacturing. The South operated a cash crop economy based on agriculture.

Political
The Europeans brought Enlightenment ideas with them to the Americas. Ideas like individual freedom and representative government were established in the colonial governments and became the cornerstones of American independence and constitutional government. A political party system had taken root in the United States soon after the establishment of a Constitution. The Native American populations were marginalized politically and culturally.

A brick is 32 cm long, 10 cm wide and 10 cm thick. It weighs 16 N and is lying on the ground. Find the pressure exerted by the brick on the ground....

Hello!

By definition, a pressure is the force acting perpendicular to the surface divided by the area on which this force is distributed.

In our case, the force is the weight of a brick and it is given (16 N). The area on which the weight is distributed is equal to the length (32 cm) multiplied by the width (10 cm), so it is equal to 320 `cm^2.` So the pressure is

16/320 = 0.05 (`N/(cm^2)`).

...

Hello!

By definition, a pressure is the force acting perpendicular to the surface divided by the area on which this force is distributed.

In our case, the force is the weight of a brick and it is given (16 N). The area on which the weight is distributed is equal to the length (32 cm) multiplied by the width (10 cm), so it is equal to 320 `cm^2.` So the pressure is

16/320 = 0.05 (`N/(cm^2)`).

Probably it is better to express the pressure in canonical units, Pa, which are Newton by square meter, `N/m^2.` To do this we have to express the area in square meters, and it is 0.32 m * 0.1 m = 0.032 `m^2.` So the pressure may be also expressed as

16/0.032 = 500 (Pa). This is the answer. Note that for a fixed weight it doesn't depend on a thickness of a brick.

In Lord of the Flies chapter 4, what's the physical setting?

The setting of chapter four is the area of the beach where the boys have basically established a home base. There are the crude shelters that they have pieced together amidst the palm trees, and Golding spends some time describing the beauty of the island. He describes the coral reef and the glittering ocean and the power of the sun to create mirages that would flicker and disappear.

There is also the emerging darkness inside...

The setting of chapter four is the area of the beach where the boys have basically established a home base. There are the crude shelters that they have pieced together amidst the palm trees, and Golding spends some time describing the beauty of the island. He describes the coral reef and the glittering ocean and the power of the sun to create mirages that would flicker and disappear.

There is also the emerging darkness inside of the boys as Golding describes the scene with Henry and Roger. Henry is playing in the tidal pool and Roger throws rocks at him, just missing as he isn't quite ready to forget all the bonds of civilization.

Chapter four also includes a moment where the boys are staring out to sea and see the smudge of smoke on the horizon from a passing ship. When they rush to the top of the mountain to figure out where there was no signal fire, they are joined by Jack and his hunters who triumphantly return with a pig they killed.