Notes

In Chapter 1, one of the first things we learn about Jess is this: he has gotten up early every morning in the summer to practice running, so that he can be the fastest kid in his grade when school starts again. He had gotten up early every day all summer to run. He figured if he worked at it - and Lord, had he worked-he could be the fastest runner in the fifth grade when school opened up. He had to be the fastest-not one of the fastest or next to the fastest, but the fastest. The very best. Jess first waits until he hears his dad's truck start up, so he knows that his dad will be out of the way, and while his mom and sisters are still in bed, Jess dresses quickly and sneaks outside. Then he runs for all he's worth, pushing himself hard to get faster and stronger. Running is a big deal among the other kids at school; it's a way that the kids compete against each other and determine among themselves who's the strongest and who's the best. Because Jess has never been ...

In the book "Number The Stars," Annemarie Johansen is a ten year old girl living in Denmark during World War II. At such a young age, she has already been called upon to make sacrifices, both for herself and for her Jewish friends. She learns tough lessons, such as how to ration food and go without, and that sometimes people lie to you in order to help you find your courage. In the book, her uncle admits that the family lied to Annemarie in order to help her be brave, and she learns to forgive them after she realizes that bravery isn't something that you already have inside of you, it occurs when you do something that's hard even though you're afraid. Before she learns that lesson, she tries desperately to hold onto her youth by telling herself that she is an ordinary person who doesn't have to be brave; she believes that Peter and Uncle Henrik have inherent courage, that they must not be afraid as she is, and that that is what allows them to act courageously....

Binding energy is the amount of energy generated when the protons and neutrons form a nucleus. It can also be thought of as the energy needed to break the nucleus into these individual sub-atomic particles. This is calculated by using Einstein's mass-energy equivalency relationship, E = mc^2 where, m is the mass defect and c is the velocity of light. Mass defect, m = actual mass of nucleons - actual mass of nucleus = number of protons x mass of protons + number of neutrons x mass of neutrons - mass of nucleus = 31 x 1.00783 + 38 x 1.00867 - 68.9257 = 0.6465 g/mol And thus, the binding energy = 0.6465 g/mol x (3 x 10^8 m/s)^2 = 5.8184 x 10^12 kg m^2/s^2/mol = 58.184 x 10^9 kJ/mol In terms of per nucleon, we can simply divide the binding energy by the number of nucleons (which is 69). Thus, binding energy = 58.184 x 10^9 kJ/mol / 69 = 8.43 x 10^8 kJ/mol/nucleon . Hope this helps.

Similar figures have the same "shape", but not necessarily the same size. For polygons in particular, the corresponding angles are congruent and corresponding side lengths are proportional. The constant of proportionality is called the scale factor. (This is also the dilation factor as similar figures can be considered as dilations of a preimage to an image.) If the scale factor is a:b then all  corresponding lengths are in the ratio of a:b. (e.g. lengths of corresponding sides, lengths of corresponding diagonals, radii, apothems, chords, etc...) If the scale factor is a:b then the ratio of corresponding areas is a^2:b^2. (e.g. area, lateral area, etc...) ** For polyhedra, if the scale factor is a:b corresponding volumes are in the ratio a^3:b^3. ** We are given similar rectangles whose lengths are x^2 and xy. Since the rectangles are similar, all corresponding lengths are proportional and the scale factor is x:y. (Write the proportion x^2:xy in simplest form; this is the sca...

Use conservation of linear momentum. `P_i=P_f` `mv_(m,i)=m v_(m,f)+M v_(M,f)` (1) `m(v_(m,i)-v_(m,f))=M v_(M,f)` Use conservation of kinetic energy since this collision is fully elastic. `KE_i=KE_f` `1/2 m v_(m,i)^2=1/2 m v_(m,f)^2+1/2 M v_(M,f)^2` Solve for `v_(m,i)` `m (v_(m,i)^2- v_(m,f)^2)=M v_(M,f)^2` `m (v_(m,i)- v_(m,f))(v_(m,i)+ v_(m,f))=M v_(M,f)^2` Plug in equation `(1)` . `M v_(M,f)(v_(m,i)+ v_(m,f))=M v_(M,f)^2` `v_(m,i)+ v_(m,f)=v_(M,f)` (2)    `v_(m,i)=v_(M,f)- v_(m,f)` Now we know the kinetic energy of the incoming particle will be minimized if `v_(m,f)^2` is at a minimum. So now lets again use the momentum conservation equation. `mv_(m,i)=m v_(m,f)+M v_(M,f)` `mv_(m,i)-M v_(M,f)=m v_(m,f)` Plug in `(2)` to eliminate `v_(m,i)` . `m(v_(M,f)- v_(m,f))-M v_(M,f)=m v_(m,f)` `mv_(M,f)-M v_(M,f)=2m v_(m,f)` `(m-M)v_(M,f)=2m v_(m,f)` `1/2 (1-M/m)v_(M,f)=v_(m,f)` Square both sides to make it proportional to `KE_i` . `1/4 (1-M/m)^2 v_(M,f)^2=v_(m,f)^2` Here you can see the m...

The poet admires the nightingale's song because the bird sings with "full-throated ease." The poet recognizes a freedom of creativity and art in the song. In the third stanza, the poet notes that the nightingale does not have the concerns that he, a human being, has: Fade far away, dissolve, and quite forget What thou among the leaves hast never known, The weariness, the fever, and the fret Here, where men sit and hear each other groan; The nightingale's song is beautiful and the poet recognizes the creativity of that song as something comparable to his art of poetry. So, he sees a common connection there. But the poet is particularly fascinated because the song comes from a creature who is not burdened by the realities of aging, sorrow, and death. To the poet, the nightingale sings without those concerns. He, on the other hand, writes poetry with those concerns always in mind. Keats was always too aware of his own mortality. And as an artist trying to create poetry t...

In my view, Churchill is not being inconsistent in his “Iron Curtain” speech. There are two reasons for this.  First, there is the fact that the Soviet Union was dominating many countries other than Germany whereas Churchill only argued that it should be secure from German aggression.  Second, I would argue that Churchill does present some arguments that can be seen as “concrete justifications” for his concerns about Soviet aggression. In his speech, Churchill does not say that the Soviets have an absolute right to secure their borders against any possible threat.  Instead, he says that he understands the Russian need to be secure on her western frontiers by the removal of all possibility of German aggression. Even if the Soviets have the right to be secure from German aggression, this does not mean that they have the right to dominate all the other countries of the region.  The parts of Germany that the West controlled were separated from the Soviet Union by the Soviet Zone of Germany...

The astrologer does not have any of his own lighting. When it gets dark he is dependent on the light of the groundnut vendor, whose place of business is nearby and who has a big flare for illumination. On this night the astrologer prepares to leave when the groundnut vendor puts out his flare. Without the flare the astrologer is in darkness except for a little shaft of green light which is insufficient for him to be noticed. He suddenly realizes that he has one customer who must have stopped in front of him just before the flare went out. He picked up his cowrie shells and paraphernalia and was putting them back into his bag when the green shaft of light was blotted out; he looked up and saw a man standing before him. He sensed a possible client and said: "You look so careworn. It will do you good to sit down for a while and chat with me." He is able to recognize the customer as Guru Nayak, but his former enemy does not recognize him because of the very bad lighting as well a...

The case Miranda v. Arizona (1966) stated that police officers must notify suspects being taken into police custody of their rights before questioning them. This means that officers must tell people what they are saying can be used against them in a court of law. Some people argue that this ties officers' hands because they cannot find out information without taking someone into custody and advising them of their rights. However, the court imposed these guidelines to protect defendants and make them aware of their rights before being taken into police custody. The court also wanted defendants to know they can have a lawyer present before being questioned so that the lawyer can advise the defendant about how to present his or her case in a way that protects his or her constitutional rights.  A recent case before the Supreme Court that weakened Miranda v. Arizona is Salinas v. Texas (2013). In this case, Houston police officers questioned a man named Genovevo Salinas about a doubl...

One of the characteristics of good science fiction writing is the ability to talk about our world in a world that doesn't look much like it. For example, most dystopian movies today, while science fiction, take pieces from 2016 America and extrapolate possibilities. Ray Bradbury's "There Will Come Soft Rains" (and the entire Martian Chronicles,  in fact) does a great job at exploring our world in a fictional future.  "There Will Come Soft Rains" explores the idea of what would happen to all of our "things" if a catastrophic event, like a nuclear strike, were to occur. The automated house, which is at the center of "There Will Come Soft Rains," acts as the main character in a human-less story. This house, despite the fact that the shadows of its owners are silhouetted on the side of the wall because of the blast ("The five spots of paint—the man, the woman, the children, the ball—remained. The rest was a thin charcoaled layer.") ...

There are many symbols and motifs throughout Dickens' famous work, a few of which can be found in Chapters 31-45. For example, Dickens uses the motif of "doubles" or "mirrors" throughout the entire novel. This means that there are many relationships depicted in the book which seem to mirror each other, as well as pairs of things, whether they be objects, concepts, or people that seem to show up time and time again. One small example of this motif would be on pages 311 and 312 when he makes mention of being paired up "two and two" and filing out of the room "two and two." Another allusion to this appears in the relationship between Pip and Magwitch, two characters who become "secret" benefactors. On pg. 368, Pip makes the startling revelation: "I have been informed by a person named Abel Magwitch that he is the benefactor so long unknown to me." From there, Pip goes on to become a secret benefactor of his own, inspired by t...

In Ken Kesey's  One Flew Over the Cuckoo's Nest , reality is a nebulous concept. This is due to the nature of the narrator that Kesey selected for his novel, a man known as Chief who suffers from paranoid delusions, auditory and visual hallucinations, and an obsession with McMurphy.  That said, when considering reality as it is presented by Chief, using a reader's critical lens to analyse his statements and not necessarily accept them as true, it is inarguable that the culture of fear and mistrust in the ward deeply impacts Chief's reality there. The symbol of machinery, which underlies the majority of Chief's delusions, is tied to the forces at work in the hospital. These forces, including Nurse Ratched, her aides, and the other nurses and doctors, seek to fix and transform the men of the ward to rejoin society. In the context of the novel, conformity had overwhelmed society as status quo, and as such, Chief aligns the ward with a kind of factory that resolves issu...

The historical setting of The Crucible  is 1692 in Salem, Massachusetts. As a Puritan community, God and religion were the center of people's lives, as well as the center of the government in Salem. The Puritans had a strict sense of what it meant to be a Christian and to behave in a godly way, setting up an automatic man vs. society conflict , as not every member of the community necessarily agreed with the prescribed behavioral expectations (consider John Proctor's stubborn personality, and even Elizabeth Proctor's choice to lie to protect her husband).  Additionally, the Puritans had a sense that the Devil and evil were very present and active in everyday life, which is why they are so ready to get carried away looking for witchcraft. This allows the man vs. society conflict to escalate and grow. Abigail and her friends rebel against society by dancing in the woods, then turn and position other members of the community against society by claiming they are witches, deflec...

There were several causes of World War I. One cause was the system of alliances that existed before the war began. There were two alliance systems before the start of World War I. The Triple Alliance included Germany, Austria-Hungary, and Italy. The Triple Entente included France, Great Britain, and Russia. In an alliance, countries agree to help each other if they are attacked. The danger of the alliance system is that if a member of one alliance declares war on a member of the other alliance, the conflict could quickly escalate if other members of each alliance join the war. A two-country conflict can quickly involve many nations as a result of the alliances that had been formed. This is what happened in World War I. In World War I, Austria-Hungary declared war on Serbia. Serbia and Russia were allies. Russia came to Serbia’s defense and declared war on Austria-Hungary. Thus, a member of each alliance had declared war on each other. After Russia declared war on Austria-Hungary, Germa...

`27^(4x-1)=9^(3x+8)` To solve, factor the 9 and 27. `(3^3)^(4x-1)=(3^2)^(3x+8)` To simplify each side, apply the exponent rule `(a^m)^n=a^(m*n)` . `3^(3*(4x-1))=3^(2*(3x+8))` `3^(12x-3)=3^(6x+16)` Since both sides have the same base, to solve for the value of x, set the exponent at the left equal to the exponent at the right. `12x-3=6x+16` `12x-6x=3+16` `6x=19` `x=19/6` Therefore, the solution is  `x = 19/6` .

A first thought would be via telegram, but although a telegraph line was established in the United States as early 1844, no telegraph to California was available in 1850: that would come a few years later. However, a person could use the U.S. postal service to mail a letter, since the post office started service to California in November, 1848. By late December, 1848, steamships were carrying letters to California from New York. The steamships would travel from New York to Panama, then, as the Panama Canal was not yet dug, canoes or pack animals carried the mail to the Pacific Ocean (about 50 miles away), where the letters would be loaded on to a waiting ship and carried up to California. As you might imagine, this process was not speedy, especially if you first had to get your letter to New York: there was no overnight communication across America in the year 1850. 

John Gedy, The Abbot of Aberbrothock and some monks made it to the location of the Inchcape Rock and installed a bell that sent an audible warning to seafarers. Historical sources observe that the warning bell was installed by the Abbot in the 14th century. Thus, it can be deduced that the Abbot lived between 1301 and 1399. Seafarers knew of the Inchcape rock, situated off Scotland’s east coast. The rock presented a formidable challenge to the seafarers because it was only visible for a short period of time when the waters were calm and low. During high tide and rough seas, the rock was completely covered, forcing the seafarers to avoid the coast even in the face of great storms. The bell installed by the Abbot of Aberbrothock saved many lives until Sir Ralph the Rover, a Dutch pirate, removed it. The pirate and his ship later perished at the same spot after losing their way during a storm.

In Chapter Two, Steinbeck introduces the main characters who work and live on the ranch. Not only are characters introduced but also three of the important conflicts which threaten both George's and Lennie's friendship and George's dream of owning his own farm. The first event which portends later complications is when George and Lennie see the boss. Rather than remembering to keep quiet, Lennie repeats George's words about being "strong as a bull" and causes the boss to become suspicious of George: "Now he's got his eyes on us. Now we go to be careful and not make no slips. You keep your big flapper shut after this." He fell morosely silent. George's morose silence is a sign of his growing discontent with Lennie, who always seems to act inappropriately at the wrong time. Second, Curley's appearance in the bunkhouse foreshadows the events in Chapter Three. He immediately seems to take a disliking to Lennie, sizing him up and insisting tha...

Integrate `int(x^3+4)/(x^2+4)dx` Rewrite the given function using long division.    `int[x+(-4x+4)/(x^2+4)]dx`          `=intxdx-int(4x)/(x^2+4)dx+int4/(x^2+4)dx` Integrate the first integral using the pattern `intx^n=x^(n+1)/n+C` `intx=x^2/2+C` Integrate the second integral using u-substitution. let `u=x^2+4` `(du)/dx=2x` `dx=(du)/(2x)` `-int(4x)/(x^2+4)dx` `=-4intx/u*(du)/(2x)` ` ` `=-2ln|x^2+4|+C` `=-2ln(x^2+4)+C` Integrate the third integral using the pattern  `int(dx)/(x^2+a^2)=(1/a)tan^-1(x/a)+C` `int4/(x^2+4)dx=(4)(1/2)tan^-1(x/2)+C=2tan^-1(x/2)+C`  The final answer is:  `1/2x^2-2ln(x^2+4)+2tan^-1(x/2)+C`

This question points to a significant difference between how we read fiction and nonfiction. Much of the interest in this narrative is due to its being an "authentic" account of the life a member of an African tribe sold into slavery and then eventually freed. The initial reception of the work and its contribution to the abolitionist movement are based on the premise of a reliable narrator. The problem here is that if the narrator proves unreliable in one factual detail, we begin to doubt his credibility on other details.  While Equiano's work would still be worth reading as a semi-fictional portrait of slavery even if the details of the narrator's life are fictional, just as Black Beauty is a fictional but moving portrait of cruelty to animals, as readers we tend to distrust writers who claim to be telling a true story but alter crucial details. If the story of Equiano's birth is a deliberate fiction to engage the reader's sympathy, we begin to suspect him o...

`intx/sqrt(x^2-6x+5)dx` Let's complete the square of the denominator of the integrand, `=intx/sqrt((x-3)^2-4)dx` Now apply integral substitution:`u=x-3` `=>du=1dx` `=int(u+3)/sqrt(u^2-2^2)du` Now apply the sum rule, `=intu/sqrt(u^2-2^2)du+int3/sqrt(u^2-2^2)du` Now let's evaluate the first integral , `intu/sqrt(u^2-4)du` Apply integral substitution:`v=u^2-4` `=>dv=2udu` `=int1/sqrt(v)(dv)/2` Take the constant out and apply the power rule, `=1/2(v^(-1/2+1)/(-1/2+1))` `=1/2(2/1)v^(1/2)` `=sqrt(v)` Substitute back `v=u^2-4` `=sqrt(u^2-4)` Now let's evaluate the second integral, `int3/sqrt(u^2-2^2)du` Take the constant out, `=3int1/sqrt(u^2-2^2)du` Use the standard integral:`int1/sqrt(x^2-a^2)dx=ln|x+sqrt(x^2-a^2)|` `=3ln|u+sqrt(u^2-2^2)|` , So add the result of the two integrals, `sqrt(u^2-4)+3ln|u+sqrt(u^2-4)|` Substitute back `u=x-3` and add a constant C to the solution, `=sqrt((x-3)^2-4)+3ln|x-3+sqrt((x-3)^2-4)|+C` `=sqrt(x^2-6x+9-4)+3ln|x-3+sqrt(x^2-6x+9-4)|+C` `=sqrt...

This depends on what you mean by color. Some objects, such as stars or metals, will change color as they increase in temperature, indicating that they're radiating different energies. However, if you mean the "real" color of something, such as a plant or a shirt, then yes, there is a direct effect on temperature based on the color of the object. The most clear connection between temperature and color will be based on interaction with light, as opposed to other methods of heat conduction such as convection. When light shines on an object, there are two possible effects; the object can either absorb the light, or reflect it. The color of the object corresponds to the wavelengths of light which that object reflects; oddly, when we say that something "is" this or that color, it's actually kind of the opposite.  Many objects absorb or reflect multiple different wavelengths, so it's not easy to say that red objects, which represent lower-energy reflections, ar...

“The Relic” by John Donne uses religious, archaic, and cultural allusions in order to portray the relationship between the poet and his pious “Mary Magdalen” (line 17). The poem is broken into three stanzas, the first of which discusses the rather macabre moment when the poet will be rediscovered by a gravedigger. The second and final stanzas discuss the honorable and even mystical nature of their relationship, concluding with a catalog of their miracles. In lines 1 through 4, when the poet states that his “grave [will be] broke up again/ [for] Some second guest to entertain,” he is referring to the practice of gravediggers reusing plots for multiple corpses. This practice can also be seen in Hamlet when Ophelia is buried in the grave of the jester Yorick. The poet declares this convention a “woman-head,” the archaic form of “womanhood,” in that it is a female trait to take in more than one man in a bed (line 3). The poet states that the gravedigger will then find a “bracelet of bright...

Most of the words that come out of Tessie Hutchinson's mouth are basically complaints about the fairness of the process of the lottery. That, in itself, shows the asinine nature of the practice, and the equally ignorant nature of the followers of such practice. It is clear the villagers cannot be bright and independent thinkers, otherwise this ridiculous tradition would have never become a reality in the first place. Also, if the villagers were rational beings, the lottery would have been abolished by the common sense of the people. Instead, we see the opposite. The villagers are entirely bound to the macabre tradition of the lottery. Their day depends on it. There are roles to be followed in the process, and there are no questions raised prior to the moment when it is the turn of the "winner" to die. Still, it is admitted in the story that the villagers do not quite know why they are really doing the lottery. Although the villagers had forgotten the ritual and lost the o...

Many people would argue that Thomas Jefferson himself was an Enlightenment philosopher, but if we are looking for someone besides Jefferson, the answer would be John Locke. While Locke was active as a writer before the eighteenth century Enlightenment, his works were very influential among the thinkers and writers generally associated with the Enlightenment. Jefferson famously asserted that Locke was, along with Francis Bacon and Isaac Newton, one of the three greatest men who ever lived. Locke's influence can be found in the first section of the Declaration. Here Jefferson and the members of the Continental Congress assert that "all men are created equal" and that they are "endowed by their Creator with certain unalienable rights," including "life, liberty, and the pursuit of happiness." In his Second Treatise on Civil Government Locke had asserted the following: Man being born, as has been proved, with a title to perfect freedom, and an uncontrolled...

As explanation for men's attraction to her, Maya Angelou's speaker describes the movements of her individual features and the poetry of her motions. These, she declares, are the reasons for her being a "phenomenal woman." In the first stanza, the speaker notes that pretty women are curious about her secret and ask her how she is able to be so attractive to men. However, when she explains that it is not just her features, "They think I'm telling lies." Nevertheless, she says that her "certain something" that is indefinable is found in the style of her movements and the grace of these movements: It's in the reach of my arms, The span of my hips, The stride of my step, The curl of my lips... The swing in my waist Then, too, she employs imagery to describe the unique features of her body: It's the fire in my eye, And the flash of my teeth The speaker then further explains that she has an inner mystery reflected by her body and move...

In Chapter 3, Jem stops Scout from beating up Walter Cunningham and invites him over for lunch. While Walter is eating, he carries on a conversation with Atticus about farming problems, and Atticus summons Calpurnia to bring the syrup pitcher over. Walter proceeds to pour syrup all over his vegetables and meat. Scout is appalled and asks what the "sam hill" he is doing. Walter gets embarrassed and quickly puts down the syrup pitcher. Atticus shakes his head at Scout, and she says, "But he's gone and drowned his dinner in syrup" (Lee 32). Calpurnia then requests Scout's presence in the kitchen and gives her a lecture on manners. Cal tells Scout that Walter is their company and Scout responds by saying, "He ain't company, Cal, he's just a Cunningham --- " (Lee 33). Cal then explains to Scout that it doesn't matter if the Finches are "better" than the Cunninghams, Scout needs to stop disgracing Walter and "act fit" to s...

The answer to this question depends on how one defines the word "freedom." African-Americans in the South were free in the sense that they were no longer enslaved. Slavery was formally abolished by the Thirteenth Amendment at the end of the Civil War. One might also argue that African-American men, at least, enjoyed a measure of political freedom during part of Reconstruction as they gained the right to vote in most states. In many areas, African-American sheriffs, legislators, and other political officials were put in office. But the end of Reconstruction brought an end to large-scale political participation, as Southern states enacted poll taxes, literacy tests, and other measures intended to disfranchise African-Americans. They also experienced the rise of Jim Crow laws that rigidly segregated Southern society. But throughout Reconstruction, most African-American people never experienced freedom in the sense that many of them understood it. For many black men in particular...

After Abraham Lincoln won the election of 1860, eleven southern states seceded from the Union. While they had various reasons for doing this, there were also good reasons why some southerners might have been opposed to secession. One reason why southerners might have opposed secession was that the odds of the South winning the Civil War were very low. The North had many advantages over the South. The North had more people, more minerals, more miles of railroad tracks, more factories, and more weapons. The North also had an established government with a brilliant leader. These advantages would make it very hard for the South to defeat the North. The South also didn’t have support from the European countries. The Europeans weren’t willing to risk angering the Union by the supporting the South. Since the odds were against the South winning the war, the European countries withheld their support from the Confederacy. The Europeans wanted to see if the South could win a significant battle in...

In "The Canterville Ghost," Wilde reverses many situations into their opposites. One example of this can be found in Chapter Four when the Canterville Ghost plans to scare the Duke of Cheshire by dressing up as "The Vampire Monk." Suddenly, however, the ghost has a change of heart: At the last moment, however, his terror of the twins prevented his leaving his room, and the little Duke slept in peace. Similarly, in Chapter Five, Wilde reveals that the ghost has used Virginia's paints to create the blood-stain in the library. Virginia is very annoyed at the ghost for stealing from her but, as the ghost says, he had his reasons for doing it: "It is a very difficult thing to get real blood nowadays." By taking a traditional idea and turning it on its head - the idea that a ghost might be afraid of children or that he uses paint instead of real blood - Wilde infuses his story with comedy. This contrasts sharply with the moments of horror and makes his story...

The poem "Legal Alien," by Pat Mora, describes the experiences of bilingual and bicultural Mexican-American individuals. It illustrates the transitions between two distinct languages and cultural contexts within daily life, and the feelings of isolation and alienation from being on the fringe of both cultures. The use of both Spanish and English within the poem illustrates these transitions, particularly in the line "able to slip from 'How's life?'/to ' Me'stan volviendo loca.' " The shift from Spanish to English is compared from the transition between typing in English in an American office building to ordering in Spanish from a Mexican restaurant. The use of the two languages in the poems conveys how fluidly bicultural individuals alternate between and navigate distinct cultures and tongues in their daily lives.

`int ( sin (theta))/(3-2cos(theta)) d theta` To solve, apply u-substitution method. `u = 3-2cos (theta)` `du = -2*(-sin (theta)) d theta` `du = 2sin (theta) d theta` `1/2du= sin (theta) d theta` Expressing the integral in terms of u, it becomes `= int 1/(3-2cos (theta)) * sin (theta) d theta` `=int 1/u * 1/2 du` `=1/2 int 1/u du` Then, apply the integral formula `int 1/x dx = ln|x| + C` . `= 1/2 ln|u| + C` And substitute back `u = 3-2cos(theta)` . `=1/2ln|3-2cos(theta)| + C` Therefore, `int ( sin (theta))/(3-2cos(theta)) d theta = 1/2 ln|3-2cos(theta)| + C` .

Although Antonio is the titular character, the drama of The Merchant of Venice  centers around Portia with the wonderful story of the caskets, her keen insight, her cleverness and devotion. The play does open with Antonio, who is beloved and admired for his good deeds. However, he suffers from a certain melancholy that portends events to come. Soon, Bassanio comes to him and tells him of his desire to have the lovely Portia for his wife. But, he needs money in order to compete with rivals who are princes and other wealthy men. Antonio, who loves his friend, tells Bassanio that presently he has invested all his money in his mercantile venture, but he will borrow some for him and "Try what my credit in Venice can do" (1.1.180). So, Antonio goes to Shylock, whom he knows is avaricious and will loan him the money because he can make interest on this loan.  When Antonio talks with Shylock, the usurer is quick to point out Antonio's past insults and prejudices; nevertheless, he...

It is really impossible to say if the man is an angel or a human being. The title of the story implies that he is indeed a man with wings; but the story and the symbolism behind the man resist interpretation. He is described as everything from an angel to a sailor. He is depicted as a buzzard and a hen "among the fascinated chickens." To some, he should be "the mayor of the world," and to others a "five-star general." The old man with wings is interpreted in many ways by the villagers and there is no final verdict. At the end of the story, he flies away and is seen as nothing more than "an imaginary dot on the horizon." There is no explanation for what the old man is or how he came to be. He does not respond to the villagers questions and cannot speak. In contrast, the spider woman who comes to town is able to explain her predicament clearly, and her story has a moral. Her story is "full of so much human truth." Unlike the spider woman ...

`f(x) = 4x^3-8` To determine its inverse, replace the f(x) with y. `y=4x^3 -8` Swap the x and y. `x=4y^3-8` Then, isolate the y.  `x+8=4y^3` `(x+8)/4=y^3` `root(3)((x+8)/4)=y` And replace the y with `f^(-1)(x)` . `root (3)((x+8)/4)=f^(-1)(x)` Therefore, the inverse function of `f(x) =4x^3-8`  is  `f^(-1)(x) = root(3)((x+8)/4)` .

This is the sort of question that is better answered through experiment than theory, since it's fairly simple to test and would provide an actual answer instead of a hypothesis. I've linked a clip from a television program in which this experiment was conducted, and confirmed the prediction that we would derive from math: both bullets hit the ground at the same time. This probably seems counter-intuitive because we think that, by traveling so much faster, the fired bullet must have some kind of different property relating to its vertical speed. In fact, the horizontal speed of the fired bullet is a completely different property, unrelated to gravity, that only determines how far the bullet is able to travel in a given amount of time. This is why muzzle velocity and elevation are so important in determining the strategic uses of various firearms. Mathematically, we could use the equation X = Vi - .5at^2 to solve this; The initial speed of both bullets is 0 (they are at rest rela...

Maclaurin series is a special case of Taylor series that is centered at a=0 . The expansion of the function about 0 follows the formula: `f(x)=sum_(n=0)^oo (f^n(0))/(n!) x^n`  or `f(x)= f(0)+(f'(0)x)/(1!)+(f^2(0))/(2!)x^2+(f^3(0))/(3!)x^3+(f^4(0))/(4!)x^4 +...` To determine the `4th` Maclaurin polynomial from the given function `f(x)=e^(4x)` , we may apply derivative formula for exponential function:` d/(dx) e^u = e^u * (du)/(dx)` Let `u =4x` then `(du)/(dx)= 4 ` Applying the values on the derivative formula for exponential function, we get:  `d/(dx) e^(4x) = e^(4x) *4` Applying `d/(dx) e^(4x)= 4e^(4x)`  for each `f^n(x)` , we get: `f'(x) = d/(dx) e^(4x)`           `=e^(4x) * 4`          `= 4e^(4x)` `f^2(x) = 4 *d/(dx) e^(4x)`            `= 4*4e^(4x)`            `=16e^(4x)` `f^3(x) = 16*d/(dx) e^(4x)`           `= 16*4e^(4x)`           `=64e^(4x)` `f^4(x) = 64*d/(dx) e^(4x)`       `= 64*4e^(4x)`       `=256e^(4x)` Plug-in `x=0` , we get: `f(0) =e^(4*0) =1` `f'(0) =4e^(4*0...

In his book Racism on Trial: The Chicano Fight for Justice, Haney Lopez defines common sense racism as "action arising out of racial common sense that furthers social hierarchy" (page 128). Common sense racism does not necessarily have the intention of doing harm, as overt racism does, but it still results in helping keep whites on top of the social hierarchy. In his book Dog Whistle Politics , Haney Lopez writes that whites have some seemingly rational reasons to engage in common sense racism, but their belief is largely guided by "the delusion that that racial superiority will restore a mythical middle-class wonderland" (page 173). In other words, white working-class voters believe that their common sense racism will help restore their lost incomes and lost economic status. However, the reasons that whites support common sense racism runs deeper than that. As Lopez Haney writes, white working-class voters engage in commonsense racism, even if it overtly goes agai...

In The Guest , Daru and the Arab prisoner make closely linked choices that determine their futures. The effect of each man's choice is multidirectional as the prisoner's decision to turn himself in will likely cost Daru's life in the end. There are examples of these types of existential moments all throughout literature. The works of Fyodor Dostoyevsky feature many existentialist themes and defining moments. Jean-Paul Sartre is an existentialist author whose work prominently features the theme of defining moments as well. Crime and Punishment In Crime and Punishment , which is perhaps Dostoyevsky's defining work, the main character, Raskolnikov, experiences a defining moment when he plots the murder of an elderly pawnbroker in his community. This defining moment is an interesting contrast to Daru's defining moment in "The Guest." While Daru's existential moment comes as a result of his decision to remain impartial in the middle of political turmoil, Ra...

Gulliver goes to Blefuscu to escape the Lilliputian emperor's growing displeasure, later to find out that he has been named a traitor to Lilliput for several reasons and that Lilliputian leadership agreed to starve him as punishment.  While in Blefuscu, Gulliver is treated well by its monarch.  When the emperor of Lilliput demands that the emperor of Blefuscu send Gulliver home, the Blefuscudin emperor secretly offers Gulliver his protection and refuses to send him back to Lilliput as prisoner.  When Gulliver finds a boat, the emperor of Blefuscu provides him with five hundred workmen to help him make sails while he repairs it, and he is given the tallow of three hundred cows for greasing the boat as well as the assistance of the king's ship carpenters.  When Gulliver is finally ready to leave, the king presents him with a number of gifts.  Gulliver doesn't do much in Blefuscu other than get ready to go home.

Waknuk was founded by David's grandfather, who was driven by "the ungodly ways of the East" to make a better society.  He developed the first district in Waknuk, and relied heavily on the Bible and "Nicholson's Repentances" to form his new society.  He was a farmer, and settled down.  Others followed, and a small farming settlement gathered around him there.   The place may have been called Waknuk then; anyway, Waknuk it had become; an orderly, law-abiding, God-respecting community of some hundred scattered holdings, large and small. (Ch. 2) Waknuk relies on ensuring order through a strict religious doctrine.  This is enforced through inspectors, who know what the True Image looks like and provide certificates to certify it.  Everything needs to conform to the True Image, from livestock and crops to infant humans.  When a baby is born, it has to be inspected and given a Normalcy Certificate. Waknuk is divided into districts.  All of them follow this same pri...

To evaluate the given integral problem `int sin(sqrt(x))dx` using u-substitution, we may let:`u = sqrt(x)` .  Square both sides of  `u = sqrt(x)` , we get: `u^2 =x` Take the derivative of `u^2 =x` , we get: `2udu =dx` . Plug-in the values: `u =sqrt(x)` and `dx = 2u du` , we get:  `int sin(sqrt(x))dx =int sin(u)* 2u du` Apply the basic integration property: `int c*f(x) dx = c int f(x) dx` . `int sin(u)* 2u du =2int sin(u)* u du` Apply formula for integration by parts: `int f*g'=f*g - int g*f'` . Let: `f =u`  then `f' =du`        `g' =sin(u) du` then  `g= -cos(u)` Note: From the table of integrals, we have `int sin(theta) d theta= -cos(theta) +C` . Following the  formula for integration by parts, we set it up as: `2int sin(u)* u du= 2 * [ u *(-cos(u)) - int (-cos(u)) du]`                                  `= 2 * [ -u cos(u)) + int (cos(u)) du]`                                  `= 2 * [ -u cos(u)) + sin(u)]+C`                                  `= -2ucos(u) +2sin(u) +C` Plug-...

This is a great question, as it wrestles with a fundamental problem in the text. In the fourth part of  Sir Gawain and the Green Knight , the Green Knight spares Gawain's life, although he chooses to cut Gawain's neck lightly with his sword to punish him for taking a magical belt/ girdle that, supposedly, would protect Gawain from harm. Originally, it was the Green Knight's wife, also known as Lady Bertilak, who convinced Gawain to take the magical belt (after also trying to seduce him to sleep with her on multiple occasions), so much of the blame for Gawain's failing falls onto her. In fact, when Gawain muses on Lady Bertilak's seductions, he basically blames the downfall of great men on women in general, thus supporting the sexist idea that women should be blamed for men's failings. As an example of this idea, take a look at this excerpt: But if a dullard should dote, deem it no wonder, And through the wiles of a woman be wooed into sorrow, For so was Adam by ...

Given to solve, `int (ln(x))/x^3 dx` let `u = ln(x) => u' = (1/x)` and `v' = (x^(-3)) => ` `v = x^(-3+1)/(-3+1)` `= x^(-2)/(-2)` `=(-1)/(2x^2)` by applyinght integration by parts we get, `int uv' dx = uv - int u'v dx` so , `int (ln(x))/x^3 dx ` =`(ln(x))((-1)/(2x^2)) - int (1/x)((-1)/(2x^2)) dx` = `-ln(x)/(2x^2) + int (1/x)((1)/(2x^2)) dx` = `-ln(x)/(2x^2) + int ((1)/(2x^3)) dx` =`-ln(x)/(2x^2) + (1/2) int ((1)/(x^3)) dx` =` -ln(x)/(2x^2) + (1/2) [x^(-3+1)/(-3+1)]` = `-ln(x)/(2x^2) + (1/2) [x^(-2)/(-2)]` =`-ln(x)/(2x^2) - 1/4 x^(-2) +c` = `1/(2x^2) (-lnx-1/2) + c`

At the end of "A Scandal in Bohemia," the king offers Sherlock Holmes an "emerald snake ring" as payment for his services. Sherlock rejects this generous offer, however, and asks instead for the photograph of Irene Adler, something which he finds far more valuable. In the final paragraph of the story, Watson gives us a clue as to why Sherlock chose the photograph over the ring: "And when he speaks of Irene Adler, or when he refers to her photograph, it is always under the honorable title of the woman." For Sherlock, then, Irene Adler is a woman who surpasses all other women. She is the only person who has (thus far) outwitted Sherlock, a feat she achieved using the medium of disguise, one of Sherlock's most famous methods. Before meeting Irene, Sherlock used to joke about women's lack of ability ("make merry over the cleverness of women") but Irene has forced him to dramatically re-evaluate his opinion. It is for this reason that he value...

In "Equality," the poet Maya Angelou describes her experiences as a Black woman and expresses a desire for equality and freedom to an intentionally indifferent audience. Angelou addresses the poem to someone who recognizes her suffering but claims to be unaware of the problems facing Black women. "Equality" is a poem that could change the perspective of one who feels indifferent to the experiences of Black women, because Angelou combines her repeated call for equality with an order to "take the blinders from your vision/take the padding from your ears" regarding the treatment of Black women. Angelou's cultural analysis, combined with her use of the second person to address readers who are willingly ignorant of her experiences, has potential to educate audiences and inspire them to gain awareness of the challenges facing African Americans and women.

A round character is one who is fully delineated. That means that the character's personality, circumstances, motives, and background are explained in detail. Other definitions also include that round characters face moral dilemmas from which they must make difficult choices. Elena's character falls under both definitions because not only do readers find out about her background as a Puerto Rican American, but also about her dreams, goals, and feelings. Then, Elena faces a moral dilemma: Should she stay home on the day of President Kennedy's assassination to attend church with her mother, or go next door for a study date with the boy she likes? Elena's mother pleads with her as follows: "You are forgetting who you are, Nina. I have seen you staring down at that boy's house. You are heading for humiliation and pain." Elena chooses to go to "that boy's" house instead of attending church that night. Things don't turn out the way Elena hopes,...

The arrival of European explorers was largely detrimental to indigenous populations. European exploration led to colonization, exploitation, enslavement, numerous wars, the spread of diseases including smallpox, and attempts to assimilate native populations to Christian European culture. During the exploration and colonization period, European presence resulted in the  death of millions. However, despite all of these shortcomings, there were some positives created by the initial arrival of Europeans, along with European trade and technology, to the Americas. In exchange for local crops such as tobacco, potatoes, and corn, the European explorers provided Native Americans with a variety of kitchen and hunting tools including knives, fish hooks, and utensils for cooking. In the earliest days of European colonization, the Iroquois began fur trapping in order to trade and provide their communities with more efficient European technologies. Early European exploration gave Native American com...

Television, music, and video games are significant forms of popular culture, but the internet might even be more significant because of social media and the ways people can interact on the internet.  Popular culture is what ordinary people care about and is influenced, if not created, by mass media. Social media is definitely a part of mass media, since social media is based on an intersection between corporate media producers (e.g., Facebook corporation and Google corporation) and ordinary people. In fact, the internet media is so powerful that we have a name for ideas that enter popular culture through this means: "viral memes." Look at the "ice bucket challenge" and see how this meme ran through social media for awhile; people influenced others' behavior by challenging their friends to dump ice water on their heads.  It is likely that social media is more powerful than television and music because social media websites invite active participation from users. ...

A parabola opens toward to the location of focus with respect to the vertex. When the vertex and focus has same y-values, it implies that the parabola opens sideways (left or right).  When the vertex and focus has same x-values, it implies that the parabola may opens upward or downward.  The given focus of the parabola `(5/2,0)` is located at the right side of the vertex (0,0). Both points has the same value of `y=0` . Thus, the parabola opens sideways towards to the right side of the vertex. In this case, we follow the standard formula: `(y-k)^2=4p(x-h).` We consider the following properties: vertex as `(h,k) ` focus as `(h+p, k) ` directrix as `x=h-p` Note: `p` is the distance of between focus and vertex or distance between directrix and vertex. From the given vertex point `(0,0)` , we determine `h =0 ` and `k=0` . From the given focus `(5/2,0)` , we determine `h+p =5/2 ` and `k=0` . Applying `h=0` on `h+p=5/2` , we get: `0+p=5/2` `p=5/2`  Plug-in the values: `h=0` ,`k=0` , and `p=5/...

Given to solve `int 1/(cos(theta) - 1) d theta` For convenience, let  `theta = x` => `int 1/(cosx - 1) dx` let `u = tan(x/2) => dx = (2/(1+u^2)) du` so , `cos(x) = (1-u^2)/(1+u^2)` (See my reply below for an explanation) so, `int 1/(cos(x) - 1) dx` = `int 1/((1-u^2)/(1+u^2) - 1) (2/(1+u^2)) du` = `int 1/(((1-u^2)-(1+u^2))/(1+u^2) ) (2/(1+u^2)) du` =`int (1+u^2)/(((1-u^2)-(1+u^2)) ) (2/(1+u^2)) du` =`int (2)/(((1-u^2)-(1+u^2)) ) du` =`int (2)/(((1-u^2)-1-u^2)) ) du` = `int (2)/(-2u^2) du` =` -int(1/u^2) du` = `-[u^(-2+1)/(-2+1)]` = `u^-1` = `1/u` = `1/tan(x/2) ` = `cot(x/2)+c` But `x= theta` so, `int 1/(cos(theta) - 1) d theta = cot(theta/2)+c`

On page 17 of The Omnivore's Dilemma , Pollan says that a consumer has "to be a fairly determined ecological detective" to figure out where processed food comes from, while it is easier to determine the origin of less or non-processed food. When he traced the long food chains of processed food (meaning determining where they came from), he found that many of them go back to the American Corn Belt and a single species called the Zea mays , or corn. For example, most cows, chickens, pigs, and even fish such as salmon feed on corn. In addition, processed food such as chicken nuggets are made up of chicken that has been fed on corn combined with corn (see page 18). The chicken nugget is fried in corn oil and mixed with corn flour. The additives, preservatives, and colorings also come from corn. Since the 1980s, most sodas and fruit drinks have been sweetened with high-fructose corn syrup (HFCS). As Pollan says on page 95, processing food can add months or even years to its sh...

In  Of Mice and Men,  the image of silence plays a vital role in communicating the difficulty with emotional commitment during the time period. The characters in  Of Mice and Men  struggle with poverty. The financial conditions that characters like George, Lennie, or Candy experience are trying. However, Steinbeck shows that poverty can also be emotional.  This emotional poverty prevents characters from supporting one another. Steinbeck shows emotional poverty is just as crippling as financial challenges. Steinbeck illuminates this when he discusses "the silence" in chapter three. When Carlson proposes shooting Candy's dog, Steinbeck writes that Candy "searched the faces" of the men in the bunkhouse for support and was unable to find any. The emotional poverty of the men in the bunkhouse is reflected in how no one speaks out against the killing of Candy's companion.  Even Candy is afflicted with a type of emotional poverty in how he does not bid the dog fare...

Macduff suspects Macbeth of murdering Duncan and the guards. Macbeth very reluctantly accompanied Macduff and Lennox when they came to wake the King early in the morning. Macbeth was behaving in a weird manner because of his guilt, remorse, and dread of the uproar that was about to occur when Macduff discovered the body. Macduff did not understand Macbeth's cold, stiff manner and curt replies at the time. He thought Macbeth was angry at being dragged out of bed by his persistent knocking. But later when he reflected on it, Macduff realized the truth. That was why he refused to attend Macbeth's coronation banquet. Banquo also suspects that Macbeth murdered Duncan and the guards. Banquo is the only person outside of Macbeth and his wife who knows that the Three Witches had promised Macbeth he would become king of Scotland. When Act III, Scene 1 opens, Banquo is reflecting on the matter in a soliloquy beginning as follows: Thou hast it now: King, Cawdor, Glamis, all, As the weird ...

To evaluate the given integral problem `int x^5e^((x^2))dx` using u-substituion, we may let: `u = x^2` then `du = 2x dx`  or `(du)/2 = x dx` Note that `x^5 = x^2*x^2*x`  or  ` (x^2)^2 *x` then `x^5dx = (x^2)^2 * x dx` Then, the integral becomes: `int x^5e^((x^2))dx =int (x^2)^2 * e^((x^2)) * xdx`  Plug-in  `u = x^2` then `du = 2x dx` , we get:  `int (x^2)^2 * e^((x^2)) * xdx =int (u)^2 * e^(u) * (du)/2` Apply the basic integration property: `int c*f(x) dx = c int f(x) dx` . `int (u)^2 * e^(u) * (du)/2= 1/2int (u)^2 * e^(u) du` Apply formula for integration by parts: `int f*g'=f*g - int g*f'` . Let: `f =u^2` then `f' =2udu`        `g' =e^u du` then  `g=e^u` Applying the formula for integration by parts, we get: `1/2int (u)^2 * e^(u) du =1/2*[ u^2 *e^u - int e^u * 2u du]`                              `=1/2*[ u^2 e^u - 2 int e^u *u du]`                              ` = ( u^2 e^u )/2- 2/2 int e^u *u du`                              ` = ( u^2 e^u )/2- int e^u *u du` Apply an...

The Citadel, written by A.J. Cronin, a physician and author, was published by Ryerson Press in September 1937. Ryerson, a Canadian publishing company, is based in Toronto.  It was operated by the United Church Publishing House from 1919-1970, and specialized in historical, educational, and literary titles.  In 1970, when UCPH sold its trade publishing arm to McGraw-Hill, the Canadian division was renamed McGraw-Hill Ryerson. The Citadel enjoyed more than a dozen reprintings before the year of 1937 was out. The book was the basis for a relatively faithful adaptation into a feature film of the same name in 1938. Though A.J. Cronin suffered ostracism by his profession because of his liberal views, curiously enough in the following decade, The Citadel is said to have paved the road for public acceptance of Britain’s National Health Service.

Recall the Ratio test determines the limit as: `lim_(n-gtoo)|a_(n+1)/a_n| = L`  Then ,we follow the conditions: a) `L lt1` then the series is absolutely convergent b) `Lgt1` then the series is divergent . c) `L=1` or does not exist  then the test is inconclusive . The series may be divergent, conditionally convergent, or absolutely convergent. We may apply the Ratio Test to determine the convergence or divergence of the series `sum_(n=1)^oo (-1)^n/e^n` . For the given series `sum_(n=1)^oo (-1)^n/e^n` , we have `a_n =(-1)^n/e^n` .  Then,` a_(n+1) =(-1)^(n+1)/e^(n+1)` . We set up the limit as: `lim_(n-gtoo) | [(-1)^(n+1)/e^(n+1)]/[(-1)^n/e^n]|`  To simplify the function, we flip the bottom and proceed to multiplication: `| [(-1)^(n+1)/e^(n+1)]/[(-1)^n/e^n]| =| (-1)^(n+1)/e^(n+1)*e^n/(-1)^n|` Apply Law of Exponent: `x^(n+m) = x^n*x^m` . It becomes: `| ((-1)^n (-1)^1)/(e^n *e^1)*e^n/(-1)^n|` Cancel out common factors `(-1)^n and`` e^n` . `| (-1)^1/ e^1 |` Simplify: `| (-1)^1/ e^1 | =| (...

Pope says here that "true wit," by which he means a wise, intelligent and incisive statement or turn of phrase, reflects a truth that already exists in nature but dresses it up or highlights it for people. True wit is not saying anything new or inventing anything new, but unearthing what already exists and making it clearer to people. It brings to clearer consciousness "what oft was Thought," in other words what was already hovering in a cloudy way in people's minds. However, before a person put the right words around a preexisting truth, that truth was somewhat inchoate (chaotic) or half-formed in people's minds. So people thought it but couldn't express it well: it was "ne'er [never] so well Exprest [expressed]." But once the right words describe the truth in question, we instantly know it to be true: that is the meaning of "Whose truth convinced at Sight we find." (We are convinced of the truth at the sight of the words that de...

The last thing the house says in Ray Bradbury's short story is the following line: Today is August 5, 2026, today is August 5, 2026, today is. . .  The line wraps up the entire story in a nice way because it reminds readers of how the story began. By the third paragraph of the story, the house is already talking. It is announcing to the inhabitants of the house what day it is. "Today is August 4, 2026," said a second voice from the kitchen ceiling, "in the city of Allendale, California." The house must start every day like this. My guess is that announcement functions like the alarm clock for the family who lives there. From the date announcement, the house continues to update inhabitants about important things that need to happen that day. It's basically a step up from somebody's Google calendar sending reminders via email. The story ends with the house making the same announcement with which it started. It's just the next day. While the house seems...

The living conditions for slaves were about as inhumane as one could imagine. Because the Africans were regarded as cargo, they were packed in the bottoms of ships as such. No considerations were made for pregnant women who gave birth on the ships, or, quite simply, for people who would need to use the bathroom. As a result, for weeks, human beings were forced to lie in their own blood, feces, urine, and vomit, as some of those transported became ill due to illness or from being overwhelmed by the smells. Slaves were packed very tightly into the bottoms of ships. The goal of the traders was to fit as many bodies in as possible. Mere inches of space separated one captured individual from another. More space was allowed only in instances in which a slave committed suicide by jumping off of a ship, or when those who had become too ill to be sold were forced overboard. Every few days, slaves would be brought out onto the deck of the ship. Here, they would get exposure to sunlight and were ...