Notes

Hamlet suffers both as a result of his own flaw and as a result of other people's sins. When the play begins, he is miserably unhappy because of the sudden death of his father as well as the hasty remarriage of his mother, Gertrude, to his father's brother and Hamlet's own uncle, Claudius. Then, he learns from his dead father's ghost that it was actually Claudius, the new king and Hamlet's new step-father, who murdered him. All of these circumstances relate to other people's sinful behavior, and they make him quite miserable. However, Hamlet's unhappiness is extended by the fact that he is so reticent to avenge his father's death, as he's been charged to do by the ghost; this isn't really a sin, but his inability to act is a flaw. He spends almost the entirety of the play wondering how he could be so cowardly, but then he continues to do very little to actually exact his revenge. Even once he becomes convinced that Claudius really did kill his fa...

The pigs are becoming more argumentative .  Snowball and Napoleon are in disagreement about almost everything.  Snowball wants to electrify the farm with a windmill.  He wants to do everything by committee, and Napoleon is more controlling and does not really care about the comfort of the farm animals. Since the pigs are more argumentative, the animals are more divided .  For example, Molly wants luxuries like she had before such as ribbons and sugar.  The pigs and Clover do not approve.  Snowball’s ideas are favored by many animals on the farm, despite Napoleon’s objections. The animals had never heard of anything of this kind before (for the farm was an old−fashioned one and had only the most primitive machinery), and they listened in astonishment while Snowball conjured up pictures of fantastic machines which would do their work for them while they grazed at their ease in the fields or improved their minds with reading and conversation. (Ch. 5)  The animals also begin to be troubled...

History is important for the study of law because studying history teaches one to look for cause and effect relationships.  In order to fully appreciate an action, one must look at the reasons why the action took place.  This ability to analyze is important for both historians and lawyers.  Historians are also excellent writers who carefully check facts and are comfortable citing outside sources.  Lawyers have to write well in order to have influence and they cite precedents to make their arguments even stronger.   Also, much of history, especially political and legal history is the study of laws.  The Constitution is the supreme law of the United States.  Lawyers base their defenses and prosecutions on whether or not someone's constitutional rights were violated.  The more one can study the Constitution, the more likely one is to know his/her rights and can better exercise them.  

Sociology is the study of society, the formation of people into groups of various types and sizes.  A city is a society, made up of many smaller societies; thus, sociology is of great use in urban planning. Sociology addresses questions such as what makes people want to or not want to congregate in a public space, what makes people want to send their children to neighborhood schools, what makes a downtown area safe and lively and what makes a downtown area crime-ridden and frightening. An urban planner who wants to know how to make a successful park would be well-advised to consider the sociology of the issue, contemplating what elements of a park will draw large numbers of people and what elements will not.  Whether areas should be mixed commercial/residential or not is a question that sociology is likely to have some thoughts about. Similarly, urban planning that tries to have mixed socioeconomic neighborhoods is drawing on sociological research that demonstrates how terrible economi...

"Through the Tunnel" is a coming of age story for young Jerry.  Readers are privileged to watch him gain mental and emotional maturity and independence.  Paragraphs 8 and 9 help establish Jerry's desire to gain some independence from his mother.  Jerry loves his mother, but he also desires to establish his own presence in the world.  Instead of being somebody's son, he wants to be his own person.  Paragraph 8 shows that desire.   He ran straight into the water and began swimming. He was a good swimmer. He went out fast . . .  Readers can see there isn't a hesitation in Jerry's movements away from his mother.  He's goes straight for the water and goes in fast and hard.  The paragraph shows that Jerry desires some freedom.  The paragraph also shows that Jerry is confident in his own abilities, and courageous enough to quickly move himself into a foreign and potentially dangerous area.   . . . a middle region where rocks lay like discolored monsters under the...

Salman Rushdie’s seminal Man Booker Prize-winning novel Midnight’s Children is written as a first-person memoir from the perspective of Saleem Sinai, a man born at the exact moment that India became independent of British imperial rule. Rushdie upsets the conventions of typical memoirs by presenting readers with a distinctly unreliable narrator and incorporating elements of magical realism throughout Midnight’s Children . Indeed, Saleem acknowledges his way of incorporating details into his narrative: “Most of what matters in our lives takes place in our absence: but I seem to have found from somewhere the trick of filling in the gaps in my knowledge, so that everything is in my head, down to the last detail... everything, and not just the few clues one stumbles across” (14-15). Rushdie uses Saleem’s inconsistent narrative style to disorient readers who are accustomed to trusting narrators. Saleem is unable to provide a wholly trustworthy account of his own life, let alone the historic...

`int x^2/(x^4-2x^2-8)dx` To solve using partial fraction method, the denominator of the integrand should be factored. `x^2/(x^4-2x^2-8)=x^2/((x-2)(x+2)(x^2+2))` If the factor in the denominator is linear, its partial fraction has a form `A/(ax+b)` . If the factor is quadratic, its partial fraction is in the form `(Ax+B)/(ax^2+bx+c)` . So, expressing the integrand as sum of fractions, it becomes: `x^2/((x-2)(x+2)(x^2+2)) = A/(x-2) + B/(x + 2) + (Cx + D)/(x^2+2)` To determine the values of A, B, C and D, multiply both sides by the LCD of the fractions present `(x-2)(x+2)(x^2+2)*x^2/((x-2)(x+2)(x^2+2)) = (A/(x-2) + B/(x + 2) + (Cx + D)/(x^2+2))*(x-2)(x+2)(x^2+2)` `x^2=A(x+2)(x^2+2) + B(x-2)(x^2+2) + (Cx+D)(x-2)(x+2)` Then, assign values to x in which either `x-2`,`x+2` or`x^2+2`will become zero. So plug-in `x=2` to get the value of A. `2^2=A(2+2)(2^2+2) + B(2-2)(2^2+2) + (C*2+D)(2-2)(2+2)` `4=A(24)+B(0)+(2C+D)(0)` `4=24A` `1/6=A` Plug-in`x=-2` to get the value of B. `(-2)^2=A(-2+2)((-2)^2...

Women play a complex role in the society portrayed by The Epic of Gilgamesh . On the one hand, they are treated as sex objects. At the beginning of the story, Gilgamesh rapes any woman he wants to, and the priestess/prostitute (depending on your translation) Shamhat is sent into the wilderness to have intercourse with Enkidu. However, women also represented wisdom. Shamhat, for example, may have been used as a sex object, but the act of intercourse began the process of Enkidu's civilization from beast to man. Shamhat also taught Enkidu about clothing and human food, for instance. Another example of a woman representing wisdom is Siduri, the tavern keeper whom Gilgamesh asks about eternal life. Siduri tells Gilgamesh to stop focusing on immortality--an attribute of the gods--and instead focus on what it means to be human. Let your stomach be full, always be happy, night and day, make every day a delight, night and day play and dance. Your clothes should be clean, your head should be...

Kate Chopin depicts upper class marriage at the turn of the 19th century as confining and largely loveless.  When Mrs. Mallard is told her husband dies, the impression given to the reader is that she is grief-stricken. “She wept at once, with sudden, wild abandonment." When she goes upstairs, however, she undergoes a change.  Suddenly, the reader realizes that on some level she is glad her husband has died. Mrs. Mallard feels free.  “There would be no powerful will bending hers in that blind persistence with which men and women believe they have a right to impose a private will upon a fellow-creature." This quotation shows that Mrs. Mallard feels oppressed in her marriage—as if a powerful will is bending hers.   Her realization that she will no longer have to live under her husband’s rule makes her feel free.  “But she saw beyond that bitter moment a long procession of years to come that would belong to her absolutely. And she opened and spread her arms out to them in welcome...

Waverly doesn’t really see chess as her ticket to a bright future as much as her mother.  Her mother is proud of her, in the appropriate Chinese way.  Waverly is enjoying the game for the game’s sake.  She gets tired of her mother holding her up as some kind of prodigy.  She feels like her mother is making too much of a big deal out of her success. Waverly went from knowing nothing about chess to being amazingly successful.  Magazines had her on their cover and local shopkeepers displayed her success in cakes in their windows.  However, the success came at a cost for Waverly.  She felt that her mother became more and more controlling.  At first, it was just that her mother didn’t really seem to have the same priorities.  She did not even really seem to understand how chess worked. "Ma, it's not how many pieces you lose," I said. "Sometimes you need to lose pieces to get ahead." "Better to lose less, see if you really need." At the next tournament, I wo...

The coordinates of the point P which divides the line segment joining the points A (`x_1,y_1,z_1` ) and B (`x_2,y_2,z_2` ) in the ratio m:n are given by: `((mx_2+nx_1)/(m+n),(my_2+my_1)/(m+n),(mz_2+mz_1)/(m+n))` Now let's assume that the YZ plane divides the line segment joining the points (-2,4,7) and (3,-5,8) in the ratio k:1. Hence the coordinates of the point of intersection are given by, `((k(3)+(1)(-2))/(k+1),(k(-5)+1(4))/(k+1),(k(8)+(1)7)/(k+1))` `=>((3k-2)/(k+1),(-5k+4)/(k+1),(8k+7)/(k+1))` On the YZ plane, the x coordinate of any point is 0, `:.(3k-2)/(k+1)=0` `3k-2=0` `3k=2` `k=2/3` Thus, the YZ plane divides the line segment formed by joining the given points in the ratio 2:3 .

Integrate `int(x^2-x+6)/(x^3+3x)` Rewrite the rational function using partial fractions. `(x^2-x+6)/(x^3+3x)=(A/x)+(Bx+C)/(x^2+3)` `x^2-x+6=A(x^2+3)+(Bx+C)x` `x^2-x+6=Ax^2+3A+Bx^2+Cx` `x^2-x+6=(A+B)x^2+Cx+3A` Equate coefficients and solve for A, B, and C. `3A=6` `A=2` `C=-1` `A+B=1` `2+B=1` `B=-1` `int(x^2-x+6)/(x^3+3x)dx=int(2/x)dx+int[(x-1)/(x^2+3)]dx` `=int(2/x)dx+int[x/(x^2+3)]dx-int[1/(x^2+3)]dx` The first integral matches the form `int (du)/u=ln|u|+C` `int(2/x)dx=2int(1/x)dx=2ln|x|+C` Integrate the second integral using u-substitution. Let `u=x^2+3` `(du)/(dx)=2x``  `dx=(du)/(2x)` ` ` `-intx/(x^2+3)dx` `=-int(x/u)*(du)/(2x)` `=-1/2ln|u|` `=-1/2ln|x^2+3|` The third integral matches the form  `int(dx)/(x^2+a^2)=(1/a)tan^-1(x/a)+C` `-int1/(x^2+3)dx` `=-1/sqrt3tan^-1(x/sqrt3)+C` The final answer is: `2ln|x|-1/2ln|x^2+3|-1/sqrt3tan^-1(x/sqrt3)+C`

The answer to your question lies in Chapter 9. Godfrey's attitude about his father's methods of raising children can hardly be called complimentary. Basically, Godfrey doesn't think his father has any genuine interest in his sons at all; he views his father as an oppressive and antagonistic paternal figure, whose only concern is his money and his social reputation. The exchange between Godfrey and Squire Cass in this chapter is laden with conflict. Godfrey finds himself in the difficult position of explaining that he has given Fowler's rent to Dunsey, his brother. Because of his ill-placed trust in Dunsey, Godfrey now finds himself in debt to his father. Meanwhile, Squire Cass is apoplectic when he hears that Godfrey had given the money to Dunsey. Godfrey admits that he tried to sell his horse, Wildfire, in order to come up with the rent money. However, with Wildfire's untimely death, he now has no means of securing the hundred pounds. For his part, Squire Cass proc...

I am glad that you put in the part about "three of her children."  The specificity is good, because the answer changes with that added information.   Ann Putnam has lost seven total children.  She has one surviving child.  That child is Ruth.  Rebecca Nurse was Ann Putnam's midwife for all of those births, so Ann Putnam is a bit suspicious of Rebecca Nurse.  Putnam is also slightly resentful of Nurse, because Rebecca Nurse has successfully given birth to many children and has many grandchildren.   However, Ann Putnam does openly lay the blame for three of her children's deaths on Goody Osburn.  Tituba is being interviewed (interrogated) about her involvement with the girls, and I believe that Tituba simply names some names to get the attention and blame off of herself.  She names Goody Osburn a witch, and Ann Putnam jumps on it as Gospel truth.  Putnam deeply desires to put blame on somebody for the deaths of her children, and Goody Osburn is as good as the next.  Goo...

In the first stanza of "We Are Seven," a stanza composed by Samuel Coleridge and added to William Wordsworth's poem, Wordsworth and Coleridge seek to draw a contrast between the little girl's siblings who have passed away and the little girl herself. The living child, the eight-year-old "cottage Girl," is able to run around actively, playing and interacting with others in physical form. The narrator in the poem feels the need to point this difference out to the child in stanza 9:  “You run about, my little Maid,  Your limbs they are alive;  If two are in the church-yard laid,  Then ye are only five.”  It befuddles the narrator that the girl speaks of her brother and sister who are buried in the churchyard as if they are still part of her family. He seeks to impart reality to the girl by telling her that she is different from her dead siblings in that she can use her arms and legs. In the first stanza, the poem also points out that such a child "lightly ...

In  Fahrenheit 451 , Clarisse is different than most of her peers because of her unique way of thinking. Clarisse differentiates herself from other people because of the distinctive way she looks at the world. She reveals this in her conversations with Montag. For example, Clarisse talks to Montag about things he has never considered. She talks about the taste of rain and how there is someone on the moon. In these instances, Clarisse defies social expectations. She is willing to think and act very differently than conventional behavior. Clarisse identifies herself as different because of her willingness to think and articulate her thoughts. She enables Montag to realize there might be something deeper in the world: "You're one of the few who put up with me. That's why I think it's so strange you're a fireman, it just doesn't seem right for you, somehow.' He felt his body divide itself into a hotness and a coldness, a softness and a hardness, a trembling and...

In order to reach the climax of the play -- the moment when Proctor decides whether or not to allow the magistrates to retain his false confession -- Proctor must be accused of witchcraft, and since Abigail herself would never do it, someone else must.  That someone else is Mary Warren.  She is someone who the court would believe because she works for the Proctors and people would think that she has intimate knowledge of their home and family.  Without Mary Warren's involvement in the trials as one of the accusers, her voice would be relatively unimportant in town; however, since she is both an accuser and an employee of the Proctors', she is in the unique position to accuse him and be believed.  Without her accusation, he would not be arrested; neither would he go to prison nor be tempted to confess to witchcraft.  Without Mary's accusation, the play's climax would never occur, and John would never have the opportunity to redeem himself in his own eyes and regain a sen...

It is usually easier to use ratio test on these types of series that contain factorials. However, we can also use root test if we rewrite factorial using exponentials. This can be accomplished using Stirling's approximation `n! approx sqrt(2pi n)(n/e)^n` The reason why we can use this approximation is because it becomes more precise for greater values of `n,` in fact the ratio of the left and right hand side of the approximation converges to 1 as `n` tends to infinity. `lim_(n to infty)root(n)(2^n/n!) =lim_(n to infty) root(n)(2^n/(sqrt(2pi n)(n/e)^n))=lim_(n to infty)2/(root(n)(sqrt(2pi n))n/e)=` In order to calculate `lim_(n to infty) root(n)(sqrt(2pi n))` we need to use the following two facts: `lim_(n to infty) root(n)(c)=1,` `c in RR` and `lim_(n to infty)root(n)(n^p)=1,` `p in RR.`                                                                                                                     Applying this to our limit yields `lim_(n to infty)2/(root(n)(sqrt(2pi n))n/e)=li...

Lincoln's greatest fear politically was that he would be the last president of the United States of America--that the Confederate states would win their war for secession and that the Republic would collapse into a collection of micro-states.  Lincoln was willing to bend the rules of the Constitution--he suspended the writ of  habeas corpus  several times during the war to persecute Rebel sympathizers.  He authorized his armies to wage war against civilians in order to bring the states in rebellion under control.  He ignored pleas from his own party to free the slaves outright--the amendment which freed the slaves was only ratified upon his death in 1865.  Lincoln knew that he was not politically popular and did little to grow his party base or to make himself more re-electable in 1864; rather, he acted according to his conscience and kept the nation together as he swore to do when he took the oath of office.  

There are many forms of energy. Several examples that are concretely observable by human senses include heat, light, and sound. According to laws of physics, energy cannot be created or destroyed. It merely changes forms as it interacts with or transfers to other matter. Sound, in particular, travels in waves but behaves differently depending on the medium it is passing through. Sound traveling through a medium in a liquid state that is influenced by movement, such as water in a swimming pool, it can be refracted. Have you ever listened to someone speak while you are under water? Molecules of matter in the liquid phase shift and move, influencing sound wave energy in inconsistent but predictable ways. When a person listens to someone speak through water, a portion of the vocal sound waves emitted are refracted in the form of dispersion. Not all of the sound waves reach your ear drum because they have been absorbed. Their voice will also sound distorted, similar to an echo. Part of the ...

Although Ralph is not the most successful leader, he possesses several important attributes that qualify him as a good leader. One important trait that Ralph possesses is the ability to prioritize paramount issues, such as rescue and survival. He continually encourages the boys to maintain the signal fire and works tirelessly building shelters and collecting water. Ralph also tells the boys that there is a chance for rescue and establishes rules that allow everyone an equal chance to be heard. His democratic tendencies prove that he cares about each individual on the island and his encouraging comments give the boys a sense of hope. Ralph does not waiver or compromise his stance in the face of adversity. He is a strong-willed individual who is not afraid to voice his displeasure with Jack. Ralph also possesses courage, which is another significant leadership quality. He bravely leads the way while the hunters are exploring unknown parts of the island, and challenges Jack's autho...

Hello! In general, if `y(x)=f(u)` and `u=g(x),` then `(dy)/(dx)=(df)/(du)*(dg)/(dx),` or `y'(x)=f'(g(x))*g'(x).` In the given case, for `y(x)=(2x+1)^5,` we can use `f(u)=u^5` and `g(x)=2x+1,` then as required `y(x)=f(g(x)).` It is simple to compute the required derivatives, they are both from the table of well-known ones: `f'(u)=5u^4,` `g'(x)=2.` Therefore `(dy)/(dx)=5u^4*2=5(2x+1)^4*2=10(2x+1)^4.` This is the answer.

We are asked to solve ` 24^x=9/(xsqrt(3)) ` : We can multiply both sides by x and simplify the right-hand side to get: `x*24^x=3sqrt(3) ` I do not know of a simple algebraic way to solve this. We can use a graphing utility to graph the left side and the right side on the same coordinate axis and find the intersection. This yields `x~~.65275103 ` The graphs:

After spending about a year with her, the goddess Circe tells Odysseus to seek out the blind prophet, Teiresias, in the Underworld in order to procure instructions for how to make it safely home to Ithaca.  Odysseus carefully follows her directions, sacrificing animals and allowing their blood to draw the spirits toward him, allowing none of them to approach the blood until he could speak with the prophet.  When he does, Teiresias tells him that, when Odysseus arrives at Thrinacia and finds the sacred herds of Helios, he must "leave these unharmed and heed [his] homeward way."  If they follow this advice, there is yet a chance that they will make it back to Ithaca, though the way will be very hard (because Poseidon is holding a grudge due to the fact that Odysseus and his men blinded Poseidon's son, Polyphemus, the Cyclops).  If, however, either Odysseus or his men fail to take this warning to heart and harm even one member of the herd, all of the crew will perish.  Circe...

The resolution of a story comes right after the climax. After the climax when the outcome of the conflict is revealed, the resolution usually shows how the characters move forward or react afterward. For Ray Bradbury's "All Summer in a Day," the conflict is person vs. society as one little girl is bullied by her classmates because she has seen the sun before and they haven't. At first, the conflict revolves around Margot and William. Margot believes the sun will shine that day as the scientists predict; however, William dispenses negativity and doubt in the classroom. All of the children want to see the sunshine because they have never experienced it—or at least they don't remember it. Margot probably wants to see it shine more because she misses it.  When the kids shove Margot into a closet before the sun shines, the reader wonders if she will escape in time to enjoy the rays of the sun. Maybe someone will remember Margot in the closet and free her in time to pla...

Three key scenes from The Catcher in the Rye  are the following: After Holden has been expelled from Pency and his fight with Stradlater  Holden's date with Sally At home with Phoebe  1. This first scene introduces Holden's disdain for phoniness, as well as exemplifying Holden's silent contempt for adults.  After Holden is expelled, he goes to the house of Mr. Spencer, a teacher who has failed him. Mr. Spencer asks Holden if he does not have any qualms about what he has done and concerns about his future. Further, Mr. Spencer asks Holden if he has a grudge against him for having failed him. Then he lectures Holden about life being but a game that a person must play according to the rules. Holden expresses his contempt for what he perceives as phoniness: Some game. If you get on the side where all the hot-shots are, then it's a game, all right—I'll admit that. But if you get on the other side, where there aren't any hot-shots, then what's a game about it? Not...

The first thing to understand is that Weber (and other sociologists) does not necessarily believe rational societies are better ; normally, we think of being "rational" as a good thing, but in sociology the term is assigned a more neutral connotation. An "irrational" society is not necessarily a bad one; rather, it is one that uses something other than formal logical arguments to make decisions. The key difference in terms of criminal justice involves the sort of decision procedures that would be employed to decide whether and how someone should face punishment. In an irrational society, there would be vague, informal customs, which might hold a lot of authority but were never very clearly defined (a "traditional society"); or there could be a strong, charismatic leader who would issue orders more or less as they pleased (a "charismatic society"). Whether the results were cruel or merciful would depend upon the personality and whims of the leader...

Generally, coughing can be caused by irritation to the airway or obstruction in the throat, lungs, or brachia. People often experience coughing as a symptom of allergies, sometimes as a result of irritation to the lungs themselves by the irritant, or as a secondary symptom caused by post-nasal drip. Coughing is also a major sign of an upper respiratory infection, where mucus builds up in the sinuses and lungs. Coughing is a common symptom of many bacterial and viral infections of the body, so it's important to be aware of any other symptoms or health conditions. People who have asthma may experience chronic, ongoing coughing exacerbated by activity or irritants like smoke and pollen. This can make it more challenging to tell the difference between a person's "normal" level of coughing and coughing as a symptom of an infection. If you or someone you know is coughing a lot, consider whether there are any other symptoms. Does the cough produce an unnatural sound like a b...

Single protons that are not partnered with any electrons or neutrons are most commonly called "naked protons." A naked proton is the result of a hydrogen atom shedding it's electron once it reaches a gaseous state. Since hydrogen does not typically contain any neutrons, the release of the proton/electron bond leaves the proton as a free naked hydrogen nucleus, which is also referred to as H+. H+ protons can leap frog from acid to acid in its gaseous state, but is unable to do so in its liquid state due to the strength of the liquid positive and negative charges in hydrogen's respective protons and electrons.  The reference link below explains the value of naked protons in regards to atomic research and H+'s quirky and interesting behavior once it is free from hydrogen's balanced atomic charge.

One of the ways that Shakespeare's The Tempest is different from his other major works is that it seems to deal most directly with the concept of colonialism. Many scholars, for instance, have seen Prospero as a kind of colonizer, while Caliban is seen as the oppressed or enslaved native. While it can be difficult to ascertain if Shakespeare developed this theme intentionally, it's important to recognize that the play certainly does seem to deal with issues at least similar to colonialism: Prospero, a European individual, arrives at the island and establishes himself as a kind of king and forces Caliban, the native, into service. Caliban, likewise, is portrayed as a savage, while Prospero is portrayed as wise and learned. While connection to colonialism is not the only major difference in The Tempest , it certainly is one of them, and it's important to recognize, as it fundamentally changes the way you read the text or view the play. However, for all that, Shakespeare stil...

Brian's mother gives him a hatchet because she thinks he might be able to use it while out in the woods with his father.   When the story begins, Brian is on his way to Canada, where his father now lives. His mother and father recently went through a divorce, and the courts set up a system that has Brian living with his mom during the school year and with his dad during the summer. Dad now lives in a remote, wooded area. Brian's mom buys Brian the hatchet as a going-away present. She tells Brian he might be able to use it while out with his dad in the woods. Brian took the sack and opened the top. Inside there was a hatchet, the kind with a steel handle and a rubber handgrip. The head was in a stout leather case that had a brass-riveted belt loop. "It goes on your belt." His mother spoke now without looking at him. There were some farm trucks on the road now and she had to weave through them and watch traffic. "The man at the store said you could use it. You know...

Black Boy is Richard Wright's memoir and narrates his experience of growing up poor and black in the American South.  Wright's father left when he was young, requiring his mother to struggle to earn enough money to keep her and Wright housed and fed. For most of Wright's young life, he was moved around across the South to stay with different family members when his mother didn't have enough money to provide for them. In each of his various experiences in the South, Wright had encounters with white people that slowly revealed to him that he was the subject of incredible repression in the form of racial discrimination. He also realized that, even though he believed it was wrong, this racial discrimination had damaging effects on his sense of self. This realization--that the black person in America is suffering internally from the degrading effects of discrimination--is the defining realization of his bildungsroman  and the main idea of his memoir.  The passage below is a...

Tennyson's "Ulysses" is a meditation on old age. We meet an aged Ulysses bitterly reflecting on the glory of his legendary youth and contrasting it with the apparently dull state of his advanced years. Rather than fighting epic battles and exploring distant realms, for instance, Ulysses finds himself wasting away on the shores of Ithaca, tending to the "boring" needs of his family and subjects. The poem is, above all else, an evocation of yearning for the glory days.  Ulysses' solution is to abandon his family and his kingdom and set out in search of further adventures. According to the aged king, "Some work of noble note, may yet be done,/ Not unbecoming men that strove with Gods" (52-3), and in making this claim, Ulysses suggests that he's heading off in search of a chance to once again illustrate his heroism. In leaving home in search of adventure, Ulysses assumes he'll solve the problems of old age and reclaim his dignity. Interestingly...

Before we answer this question regarding the protagonist of William Shakespeare's tragedy  Romeo and Juliet , it's important to define the term "ambivalent." Many people consider it interchangeable with "ambiguous", which means "open to multiple interpretations" or "difficult to define." However, "ambivalent" is not a neutral term. Instead, it means "unable to make a choice, caused by the conflicting desire to do, say, or believe two opposite things."  With that in mind, we can now turn to Romeo's ambivalence. One side of Romeo's internal conflict regarding love is extremely negative. This side is primarily influenced by his unrequited love for Rosaline, which dictates many of Romeo's actions and choices at the beginning of the play. This experience leads Romeo to feel strongly against love and its ability to make a man feel happy.  However, once he meets Juliet, a conflicting perspective on love is introdu...

I think that one of the most effective scenes to mirror the Holocaust was where Bruno, Shmuel, and other people were herded into the gas chamber.  The panic that the scene captured, in terms of the people being taken inside and then when the doors closed was quite realistic.   The gas chamber was one of the most "efficient" ways that the Nazis killed their prisoners.  One detail that the film captures was how there was a panic-filled set of minutes between the locking of the door and the distribution of the pellets that would set off the reaction to release the fatal gas.  The way the film captured that sad moment was very reflective of the Holocaust time period. Kotler abusing Pavel and Shmuel are two scenes that reflect the cruelty of the Nazis during the Holocaust.  Pavel is an old man and Shmuel is a child. However, Kotler does not miss the chance to physically and emotionally abuse them.  The barbarism he displays is effective in recreating the terror that was the Holoca...

A solution is a mixture of a solid component called the solute and a liquid component called the solvent. Crystallization is the process by which the solute is formed into solid crystals and separated from the solution. Evaporation is the process by which the solvent is converted into vapor, leaving the solute component behind. Evaporation is a heat absorbing process requiring energy to take place. Crystallization occurs by letting a heated solution cool and letting formed crystals drop off. The better method would depend on the solution. Generally, crystallization would be better when a solution is saturated but would be less effective if the solution is dilute. Also, solutions containing solvents such as acetone or ether, which evaporate at lower temperatures, would be better separated by evaporation than solutions containing water as solvent which evaporates at a higher temperature.

`5log_4(2) + 7log_4(x) + 4log_4(y)` To express this as one logarithm, first apply the rule `log_b a^m = m*log_b(a)` . `= log_4(2^5) + log_4(x^7) + log_4(y^4)` `= log_4(32) + log_4(x^7)+log_4(y^4)` And, apply the rule `log_b (m * n) =log_b (m)+log_b(n)` . `= log_4 (32x^7y^4)` Therefore,  `5log_4(2) + 7log_4(x) + 4log_4(y)=log_4(32x^7y^4)` .

What we're really asking is this: What is the angle subtended by 1 AU at a distance of 3 parsecs? Is it less or greater than 0.1 arcseconds and 0.5 arcseconds respectively? So, let's get everything in the same units: Meters is usually a good choice. A parsec is about 3.1*10^15 m, so 3 parsecs is about 9.3*10^15 m. An AU is about 1.5*10^11 m. For angles this small, we can use the approximation ` tan x approx x` where x is measured in radians. So we want to get 0.1 arcseconds and 0.5 arcseconds into radians. 1 arcsecond is pi/180/3600 radians, or about 4.8*10^-6 radians. So 0.5 arcseconds is about 2.4*10^-6 radians, and 0.1 arcseconds is about 4.8*10^-7 radians. Now all we need to do is find the ratio of the two distances, which is the tangent of x, which we've just said is very close to x itself. (1.5*10^11 m)/(9.3*10^15 m) = 1.6*10^-5 radians This is larger than both of our given angular resolutions, so we can resolve the two stars with either telescope.

The enemy sniper is able to get a clear shot at the sniper because the sniper exposes himself long enough to shoot the man in the armored car and the old woman.  The sniper is a fairly brave man because he takes his two kill shots knowing that he is exposed to the enemy sniper.  The enemy sniper knows the protagonist's location because the "good guy" sniper gave away his position by smoking his cigarette.  The enemy sniper has already taken two shots at the sniper by the time the armored car and the old woman arrive.  The main sniper knows that he is outnumbered, so he decides to risk shooting the two people on the street.  He successfully kills both targets, but he gets shot in the arm by the enemy sniper.   Suddenly from the opposite roof a shot rang out and the sniper dropped his rifle with a curse. The rifle clattered to the roof. The sniper thought the noise would wake the dead. He stooped to pick the rifle up. He couldn’t lift it. His forearm was dead. “I’m hit,” he...

Cassie learns from Big Ma how Mr. Paul Edward, her grandfather and former slave, acquired the 400 acres of land in Spokane County, Mississippi, that once belonged to the Grangers. One day the children see Mr. Harlan Granger's expensive car pulling away from their dusty driveway. "Big Ma, what was Mr. Granger doing here?" Stacey asks her. Big Ma replies that he has just been "worrying" her about this land again. She explains that during Reconstruction the Grangers had to sell some of their land to Yankees in order to pay the taxes on the rest. The man who bought the land, Mr. Hollenbeck, sold him 200 acres. Later on, Mr. Hollenbeck offered to sell another 200 acres back to the Grangers at a lesser price than his purchase. But, "old Filmore Granger," who was "tight with a penny" refused to buy it. Later, a Mr. Charles Jamison from Vicksburg purchased it. However, he was not good at farming, so after he graduated from law school in the North, he...

In Chapter 3, Walter Cunningham Jr. is eating with the Finches. Scout makes fun of the way Walter eats and Cal scolds her for doing so. Cal tells her:  Don’t matter who they are, anybody sets foot in this house’s yo‘ comp’ny, and don’t you let me catch you remarkin’ on their ways like you was so high and mighty! Yo‘ folks might be better’n the Cunninghams but it don’t count for nothin’ the way you’re disgracin‘ ’em—if you can’t act fit to eat at the table you can just set here and eat in the kitchen!  By 'better than' ("better'n"), Cal means that even though the Finches are more educated and have more money, that doesn't mean they (or anyone) has the right to mock those of a lower social class. Scout probably doesn't grasp the notions of class here, but she does learn a lesson to be respectful to others, regardless of who they are or where they come from.  In Chapter 12, Scout discovers that Cal lives two separate lives: her life with the Finches and Cal...

`sum_(n=1)^oo1/(n(n+2))` We can write down the n'th term of the series as, `a_n=1/(n(n+2))` Using partial fractions, `a_n=1/(2n)-1/(2(n+2))` The n'th partial sum of the series is: `S_n=(1/(2*1)-1/(2(1+2)))+(1/(2*2)-1/(2(2+2)))+(1/(2*3)-1/(2(3+2)))+.........+(1/(2(n-1))-1/(2(n-1+2)))+(1/(2n)-1/(2(n+2)))` `S_n=(1/2-1/6)+(1/4-1/8)+(1/6-1/10)+..........+(1/(2(n-1))-1/(2(n+1)))+(1/(2n)-1/(2(n+2)))` This is telescoping form of the series, `S_n=(1/2+1/4-1/(2(n+1))-1/(2(n+2)))` `sum_(n=1)^oo1/(n(n+2))=lim_(n->oo)S_n` `=lim_(n->oo)(1/2+1/4-1/(2(n+1))-1/(2(n+2)))` `=(1/2+1/4)` `=3/4` So the series converges.

Chuchundra, the muskrat, is described as a "brokenhearted little beast." All night long he tries to get up the courage to be able to run into the middle of the room, but he is too cowardly to do so. Instead he just hugs the wall, whimpering and cheeping all night. Not surprisingly, then, when Rikki approaches him, he begs him, almost weeping, not to kill him. Of course, Rikki has no intention of harming the muskrat and tells him so. Then Chuchundra finds another reason to fear Rikki: He imagines that the cobra, Nag, will mistake Chuchundra for Rikki and kill him some night. That thought is equally ludicrous because Rikki is lithe and quick, while Chuchundra is heavy and plodding. Beyond that, Rikki points out that Nag lives in the garden, a place that Chuchundra doesn't go. Chuchundra's fear of Rikki, just like his fear of the middle of the room, is groundless. 

Finny's whole world is sports. Without sports, Finny is just a swimmer without a pool, or a runner without a track. Phineas is average when it comes to academics, but that doesn't mean that he isn't intelligent. It's just that his passion and talents are all wrapped up in sports, competition, and expressing himself through athletics. In fact, he creates a game called Blitzball in Chapter Three, which is still played at Devon nearly two decades later. He also creates a Winter Carnival in Chapter Nine that includes winter sports in a competitive spirit. Everyone involved in the carnival enjoyed the distraction from homework, cabin fever, and the looming war ahead of them. Phineas is humble, too. In Chapter Three, when he breaks the school swimming record with only Gene as a witness, he makes his best friend swear not to tell anyone about it. Unfortunately, when he breaks his leg in Chapter Four, the doctor later says that he will never be able to play sports again. This a...

"The Guest" uses vague descriptions of Daru and his surrounding circumstances to emphasize that he is disconnected from the world around him. The characters are necessarily generic, as they serve as vague representations of the themes and forces Camus experienced in his own life. Daru is briefly described and serves as a representation of Camus himself as well as the average person. Like Daru, Camus was a French-Algerian who found himself torn between the demands of his country and his desire to mediate between French authorities and the indigenous population. Balducci and the prisoner are also described in the vaguest possible terms. The prisoner represents the average person who is faced with the illusory choice between freedom and captivity. Balducci is a vague generalization of the overbearing police authority in Camus's time. Even the original French title of the story is vague in the sense that it could mean "the guest" or "the host" interchangea...

As per Hooke's Law, the force needed to stretch/compress a spring x units from its natural length is `F = kx` where F is the force in Newtons (N), x is the displacement of the object from its equilibrium position (x=0) in meters and k is the spring constant. To determine the variable force using the Hooke's Law, the spring constant should be solved. To do so, plug-in F = 250N and x = 0.30m. `250 = k * 0.30` `250/0.30=k` `2500/3=k` Plugging this to the formula of Hooke's Law, the force needed to stretch the spring x units from its natural length is `F = 2500/3x` Now that the expression that represents the variable force is known, let's determine the amount of work done in stretching the spring from 20 cm to 50cm. Take note that if the force applied is constant in moving an object from x=a to x=b, the formula is `W =F * Delta x` However, if the force is not constant, the amount of work done in moving an object from x=a to x=b is `W = int_a^b Fdx` Applying this formula, th...

Scout was very young when the Tom Robinson situation started.  She had limited understanding of the way the world worked.  Like most children, Scout was a product of her environment.  Although she had a father who was fighting for legal equality in court, she did not really understand the way the world of Maycomb worked. Scout was surprised when people at school began to tease her because her father was defending a black man. “Do you defend niggers, Atticus?” I asked him that evening. “Of course I do. Don’t say nigger, Scout. That’s common.” “‘s what everybody at school says.” “From now on it’ll be everybody less one—” “Well if you don’t want me to grow up talkin‘ that way, why do you send me to school?” (Ch. 9) For Scout, racism was a mystery.  Scout had limited understanding of class too, asking Atticus if they were poor.  She complained when Walter Cunningham ate his food differently, but she also explained to the teacher that she couldn’t lend the students money they couldn’t pay b...

Erdrich makes a number of claims and statements in this story. There is the theme of brotherhood in general, but this story particularly shows how American/European influence puts strains on Native American culture, family life, and that same brotherhood. Lyman and Henry bond over the red convertible. The car is an American symbol. Their trip to Alaska brings them together and the experience is more particular to their Native American heritage. In Alaska, with constant daylight, they experience something more like a dream, away from mainstream modern American life. With the convertible and this trip, they get a sense of both American and Native life. But this appealing blending of cultures is short-lived. Henry is drafted (forced to fight) in the Vietnam War. Consider this from his perspective. He is made to fight a war that has nothing to do with his heritage. Needless to say, Vietnam was never a real threat to America itself. It was a political war based on ideological differences. S...

The title of this story is very clever because it has multiple possible interpretations. Only one person is really being slaughtered. That is Patrick Maloney. He goes to the slaughter as meekly as a lamb because he doesn't suspect what is going to happen to him. The leg of lamb is used for the slaughter but it is not slaughtered--although it was slaughtered a long time ago and then frozen. Mary Maloney is not slaughtered, but she does the slaughtering. She has been as meek and docile as a lamb up to the point where she succumbs to a fit of rage and uses the frozen leg of lamb to slaughter Patrick. The detectives who come to the Maloney house might be compared to lambs going to the slaughter of Patrick. These detectives are all led by Mary as easily as is they were innocent lambs. Patrick is the only one actually slaughtered. 

Interesting question, and a complex one. Morally, the global community should not "embrace" its colonial history. Colonialism allowed major Western powers to exploit many peoples in Africa, Asia, Oceania, and the Americas for several centuries. Europeans justified their actions by claiming that they were civilizing their colonial subjects, bringing them Christianity and imposing Western forms of government.  However, Westerners could "embrace" colonialism to the extent that it contributed to Western nations' economic wealth; and those who were colonized could "embrace" the system to the extent that, arguably, colonialism was a precursor to multiculturalism. Let's begin with the economic issue. In his recent study  Empire of Cotton , historian Sven Beckert argues that the emancipation of slaves in the United States, itself a former colony, was the impetus for European nations to colonize countries in warmer climes where they could grow cotton, sugar...

The Kennedy Doctrine was the set of American policies towards Latin America during Kennedy's presidency, between 1961 and 1963. Prior to Kennedy's presidency, the US government backed Cuba's authoritarian government, then led by President Fulgencio Batista; however, Eisenhower's administration turned down Batista's request for weapons to defend his regime from revolutionaries, and in 1959 his presidency was overthrown. Relations between the US and Cuba in the era after the revolution but prior to Kennedy's policies were maintained, but limited. President Eisenhower avoided meeting with Fidel Castro, a leader of the revolution, for the rest of his presidency, although he did allow Vice President Nixon to host Castro during his visit to Washington, DC. When Cuba began negotiating with the USSR to purchase weapons in 1960, the US government condemned their relationship with communist countries. Towards the end of Eisenhower's presidency, in January 1961, he off...

A dominant theme in Mary Shelley's Frankenstein is responsibility for one's actions , especially responsibility for what one creates. The creature sees that Frankenstein has behaved recklessly by bringing him to life and carelessly by rejecting and abandoning him, actions that have caused him to suffer immensely. Because of his suffering, the creature feels Frankenstein has a moral obligation to take responsibility for the creature's suffering and to ease his suffering, just a little, by creating him a mate. In chapter 11, the creature begins relaying to Frankenstein his story of suffering . He starts by explaining he had developed his own education by observing the De Laceys in their cottage. While living in the De Laceys' shed, he discovered a leather trunk full of clothes and books, and he began reading the books. One of the books he read was Milton's Paradise Lost . From the book, the creature learned about how God created Adam to be a "perfect creat...

"Huswifery" is a classic Taylor poem in that it sets up a conceit, or an extended metaphor.  Throughout this conceit, Taylor uses first the parts of a spinning wheel and then the cloth spun with the thread from that wheel to ask God to use Taylor as an instrument for God's will.   In the first stanza, Taylor asks God to use his "Holy Word" to charge Taylor's "Affections," "Soul," and "Conversation" with the will of God.  It is in this stanza that Taylor uses the metaphor of the spinning wheel to create the image of God spinning the wheel to create the yarn, or to create Taylor, which He will then use to create the garment in the second stanza. In the second stanza, God becomes the weaver, and by weaving the yarn he creates a beautiful garment that is "pinked with varnished flowers of Paradise" (12).  With this garment, Taylor will be clothed with all of God's influence, thus making him an instrument for the will of...

Ray Bradbury’s novel  Fahrenheit 451 is suffused with vivid and meaningful imagery. Much of it is strange animal and nature imagery used as a motif to support the theme that living disconnected from nature causes us to lose touch with our own human nature. For example, our first glimpse of Montag’s wife Mildred is more about the snake-like machine used to pump her stomach after her sleeping pill overdose than it is about her. Montag likens the machine to a “black cobra,” and he wonders, “Did it suck out all the poisons accumulated with the years?” The imagery of the cobra with its blindly seeing eye shows just how black and empty Mildred is inside from living this shell of a life. Next we meet the Mechanical Hound, made of brass, copper and steel. Montag nervously passes it in the firehouse and observes the killing machine at rest. “Lights flickered on bits of ruby glass and on sensitive capillary hairs in the nylon-brushed nostrils of the creature that quivered gently, gently, its ei...

In "The Story of an Hour," the setting reflects the Victorian Age in which the feme covert laws were in effect. These laws that greatly restricted women and their ownership of property profoundly affected women, and these affects are  exemplified in the character of Louise Mallard.  A restricted life The repression under which Mrs. Mallard dwells is evinced in several ways. The doctor perceives her as a woman "with a heart trouble," and she must be treated with delicacy. So, when she must be told that her husband is on the list of those thought dead from the railroad disaster, Mr. Mallard's friend Richard hurries to the Mallard home in order to carefully break the news of the tragedy to his wife. And, when she is told, Mrs. Mallard does not stand stunned, but, instead, cries with "wild abandonment,"as though there were more than loss involved in her life. Then, she insists upon going up the stairs alone.  Her own room and a sense of freedom When Mrs. ...

Hello! We want to prove the identity  `log_(1/p)(x) = -log_p(x)`  (for all `xgt0,` `pgt0` and `p != 1` ). To do this, let's recall what logarithms are. By the definition,  `log_b(a)` is such a number `c` that  `b^c = a.`  It is known that such a number always exists and is unique (of course for `agt0,` `bgt0` and `b != 1` ). Therefore to verify this identity we raise `1/p` to the power of each side: `(1/p)^(log_(1/p)(x)) = (1/p)^(-log_p(x))` (the function `(1/p)^x` is one-to one on its domain, therefore this operation gives an equivalent equality). The left part is equal to `x` by the definition of logarithm, what about the right part? We'll use some properties of powers, `1/p=p^(-1)` and `(p^a)^b=p^(a*b):` `(1/p)^(-log_p(x)) =(p^(-1))^(-log_p(x)) =p^((-1)*(-log_p(x))) =p^(log_p(x)).` And this is equal to `x,` too, by the definition of logarithm. This way we proved the desired identity.

When the warmer objects (pieces of iron and copper) are placed in contact with the colder object (water), there will be a transfer of heat so that the iron and copper will cool off and the water will heat up.  According to the law of the conservation of energy, `Q_(hot) + Q_(cold) = 0` . Here, `Q_(hot)` is the heat leaving the warmer objects (it will have a negative value), and `Q_(cold)` is the heat acquired by the colder object as the result. In this case, `Q_(hot) = c_im_i(T_e - T_(ii)) + c_cm_c(T_e-T_(ic))` and `Q_(cold) = c_wm_w(T_e-T_(iw))` Here, c's denote the specific heat of iron, copper and water, m's denote the masses and `T_i`  - initial temperature of the objects.  `T_e` is the equilibrium temperature. Plugging in the values for given quantities (masses are in kilograms), and the table values for specific heat (in J/(kg*C)), we get `448*m_i*(40-215) + 387*20*(40-140) + 4186*25*(40-10) = 0` From here, `-78400*m_i - 774000+3139500 = 0 ` Solving for the mass of iron r...

In the story, Monsieur Armand Aubigny fell in love with Desiree when he spotted her standing against the stone gateway of the Valmonde estate. Accordingly, Desiree was adopted by the Valmondes as their daughter after she wandered onto their property eighteen years before. At the time, no one had known where the toddler had come from. There was speculation as to her origins, but in the end, Madame Valmonde had concluded that Desiree had come to her as a gift from God, 'seeing that she was without child of the flesh.' When Monsieur Armand Aubigny asked for Desiree's hand in marriage, Monsieur Valmonde had been wary. He raised the issue of the 'girl's obscure origin' to Monsieur Aubigny. But, the author tells us that Monsieur Aubigny did not care: He was reminded that she was nameless. What did it matter about a name when he could give her one of the oldest and proudest in Louisiana? He ordered the corbeille from Paris, and contained himself with what patience he c...