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Showing posts from August, 2010

What does Atticus explain about the jury system?

The answer to this question can be found in Chapter 23 of To Kill a Mockingbird . Everyone is still very upset about Tom's conviction, and Jem makes the comment that the system would be more fair without juries. Atticus does not go this far, but he says that "people have a way of carrying their resentments right into a jury box." In other words, juries are reflections of the societies from which they draw their members. Even though a courtroom is supposed to be a place where justice is blind, the reality is that they are prejudiced and sometimes unfair. The conversation turns to a broader discussion about race, and Atticus gets highly animated discussing the racial prejudice that is rampant in Maycomb. The broader point, however, is that a black man cannot get a fair trial in Alabama or anywhere else in the Deep South, and this is the point that Atticus raises: Until people's mentalities change, true change is unattainable. He does suggest, in light of this reality, t...

What are three reasons why many Maycomb citizens do not want to serve on the jury?

In Chapter 23, Jem voices his frustration regarding the Tom Robinson trial. During the conversation, he wonders aloud why Maycomb residents don't sit on juries. Atticus responds that there are three reasons for this. First, he states that most people in Maycomb aren't interested in serving on juries. Second, he states that some Maycomb residents are afraid of the consequences of serving on one. Atticus provides an example to explain the second reason. He states that businessmen like Link Deas would find it difficult to decide on cases that could potentially involve regular Maycomb customers he will have to face on a daily basis. If Link serves on a jury, he may find himself offending a customer, and his business may suffer. Fear is a very powerful deterrent against serving on a jury in a town like Maycomb. Third, Atticus states that "Serving on a jury forces a man to make up his mind and declare himself about something. Men don’t like to do that. Sometimes it’s unpleasant....

What is register in linguistics?

Register is a part of sociolinguistics, which is the study of the way in which we use language in a social context. MAK Halliday (whose linguistic theory is discussed in the link below) developed and expanded this concept during the 1960s and 70s. To best understand the concept of registers, here is an example: You probably use multiple registers without realizing it. For example, if you are writing a formal academic paper, the language you use is different from what you might post on Twitter or some other social media. This is because you have audiences with two different expectations about your language and you know how to adjust for these audiences.  Formal language might sound strange on social media, not to mention being too wordy for the Twitter platform, and informal language will get you a bad grade in academia.  Language is not just a set of things (words in sentences) that make the same meaning all the time; the people involved in this meaning-making also influence how someth...

What does chapter 1 of The Hunger Games suggest about life in the future?

Protagonist Katniss introduces the reader to a dystopia in the first chapter of The Hunger Games . The issues at hand are starvation and general lack of resources, mistreatment of the working class, and an oppressive government. The chapter opens with Katniss describing her hatred toward her sister Prim’s mangy cat. The cat presents only another mouth to feed to Katniss, introducing us to the topic of limited resources in Katniss’s District 12. ”District Twelve. Where you can starve to death in safety,” Katniss says. Katniss then remarks that electricity is only provided to residents for two or three hours an evening, further demonstrating the lack of resources in District 12. Lastly, she explains the concept of “tesserae,” wherein children can enter their names more times into the drawing for the Hunger Games in exchange for food and resources. The working class in District 12 is described as having slouched-over shoulders and being so dirty from their coal mining that they no longer ...

In Shakespeare's Romeo and Juliet, when is Romeo passionate?

Romeo displays a passionate spirit throughout Shakespeare's Romeo and Juliet,  for good and for bad. He is particularly passionate about love, but, in Act III and Act V, he also demonstrates passion in his loyalty to his friend Mercutio and then to his love, Juliet. This passion reveals itself in four particular scenes. In Act I, Scene 1, Romeo is intensely passionate over his love for Rosaline, who has spurned his affection. He does not understand the girl's ability to seemingly live without love and he laments the fact that she has refused his advances. He tells Benvolio, She’ll not be hit With Cupid’s arrow. She hath Dian’s wit, And, in strong proof of chastity well armed, From love’s weak childish bow she lives uncharmed. She will not stay the siege of loving terms, Nor bide th’ encounter of assailing eyes, Nor ope her lap to saint-seducing gold. O, she is rich in beauty, only poor That, when she dies, with beauty dies her store. Benvolio attempts to convince Romeo to forge...

Why does Duong Thu Huong open her book Novel Without a Name with an eerie description of the Gorge of Lost Souls in which nature is perceived as...

In Novel Without a Name , author Duong Thu Huong tells the story of the Vietnam War from the perspective of Communist soldiers fighting on the North Vietnamese side of the war. Though the war is called "The American War" in Vietnam and looked at as a great source of pride due the North's conquests, Duong's novel surprisingly shares themes found in Western novels on the topic of the Vietnam War such as novels written by Tim O'brien. As the characters progress through the war, especially Quan, just like their Western counterparts, they begin feeling disillusioned with the war they were once so proud to join. The atrocities they witness allow them to see the war as an act of senseless killing. Since the Vietnamese worship their ancestors , being surrounded by masses of unburied dead would have a significant impact on their emotional and psychological states. It is this impact we witness in Duong's book. As worshipers of their ancestors, the Vietnamese believe t...

Why does the narrator in "The Cask of Amontlllado" "re-echo" and even "surpass" Fortunato's yelling?

Montresor re-echos and surpasses his victim's desperate cries for help in order to show Fortunato that his cries are useless. By doubling the volume of the noise being made, Montresor demonstrates that the catacombs, deep underground and surrounded by granite, are virtually soundproof. Montresor also gets sadistic pleasure out of adding to Fortunato's torment in this way. He is showing his poor victim that he already thought of everything. The trap is perfect. Fortunato's last hope is futile. Nobody can hear him now, and nobody will be able to hear him after Montresor leaves him to die alone in agony. This incident also demonstrates to the reader the same thing that is demonstrated to Fortunato. As Montresor explains: Unsheathing my rapier, I began to grope with it about the recess; but the thought of an instant reassured me. I placed my hand upon the solid fabric of the catacombs , and felt satisfied. I reapproached the wall; I replied to the yells of him who clamoured. I ...

Which quotes from “Raymond's Run” by Toni Cade Bambara show that Squeaky isn’t afraid to stand up for herself?

Squeaky stands up for herself.  She is a tough little girl, and she has to be because her brother has developmental delays and kids often make fun of him.  Squeaky always stands up for him, and for herself, when people tease them. Squeaky says that if anyone wants to mess with Raymond, they have to come through her. And I don’t play the dozens or believe in standing around with somebody in my face doing a lot of talking. I much rather just knock you down and take my chances even if I am a little girl with skinny arms and a squeaky voice, which is how I got the name Squeaky. She says that if things get to be too much for her, she runs.  Squeaky is a very good runner.  She loves to race, and she practices all of the time.  Even though her mother thinks it looks silly, Squeaky trains.  She is the fastest runner in the neighborhood. Squeaky doesn’t just stick up for her brother; she also sticks up for herself.  When Gretchen and her friends suggest that Squeaky is not going to win the May ...

Is there a protagonist, and if so, is he static or dynamic in "Soldier's Home"?

Krebs is the protagonist and he is a dynamic character who has undergone change from his war experiences; he also shifts in his actions at the end of the story.  For the most part, the change in Krebs has taken place before most of the narrative as it is in the exposition that the reader learns how the war and Kreb's return home has affected him: At first Krebs...did not want to talk about the war at all. Later he felt the need to talk but no one wanted to hear about it....Krebs found that to be listened to at all he had to lie, and after he had done this twice he, too, had a reaction against the war and against talking about it. A distaste for everything that had happened to him in the war set in because of the lies he had told.  Now, having returned to his home, Krebs cannot relate to his family or to the town in which nothing has changed. While the young girls have grown up, Krebs does not "feel the energy or the courage" to break into their circles....They were too co...

If a Constitutional Amendment were to be proposed and passed, what do you think it would be?

Many people believe that the 28th Amendment should be the so-called Schwarzenegger Amendment (a reference to Arnold Schwarzenegger, who was born in Austria and who many people thought or still think should run as a Republican candidate for President), which would allow foreign-born people to become President (if they have become American citizens and fulfill the other requirements to be President). As of now, the Constitution states that a candidate for the presidency has to be a "natural born citizen," which means someone born with American citizenship. The idea to change this requirement has been proposed in the Congress many times over the years, even going back to the 1800s, but it has not passed. The Founders of the country and Constitution permitted foreign-born people to run for the presidency if they had been become naturalized American citizens by 1787, the year the Constitution was ratified. 

How did Ray Bradbury use action in the story "All Summer in a Day"?

All Summer in a Day has contrasting moods and tones that help the reader to experience the dark, gloomy day to day conditions on the planet Venus. It is on Venus that some children are living in constant rainy conditions where the sun shines only once every seven years. Bradbury uses action to help convey the mood and tone as well as to build suspense in the story. In the beginning of the story, not much is going on beyond conversation. The conditions on Venus are described as well as why the children live there. The children begin to talk with each other and at first, as the rain and gloom is described outside, there is little action. It soon becomes clear from the narration and the conversation that the children resent Margot a great deal. As the children confront Margot, the only child who has seen the sun and can remember it, and the conflict between them builds, the action in the story increases. A boy shoves Margot, more of them push her and soon, she is pushed down a hallway, i...

Why does Don John tell Claudio that Hero was being disloyal?

Don John is the prince Don Pedro’s illegitimate brother. The two have only recently become reconciled, but Don John still deeply resents Don Pedro. He feels trapped: “I had rather be a canker in a hedge than a rose in his grace … I am trusted with a muzzle and enfranchised with a clog.” Don John is so eager to spite his brother and his friends, he latches onto Borachio’s news of an impending marriage between Hero and Claudio. He expresses jealousy of Claudio’s esteemed position with the prince. Don John and Borachio trick Claudio into thinking that Don Pedro wants Hero for himself. Don John seems to genuinely believe that his brother is that selfish and duplicitous: “Sure my brother is amorous on Hero and hath withdrawn her father to break with him about it.” Claudio briefly falls for this plot, but the deception is soon cleared up. However, Don John and Borachio do not give up. Don John says, “Only to despite them, I will endeavour any thing.” He pays Borachio to help him. Borachio pl...

What is the metaphor of Jane "kept all her kings in the back row" in the book Catcher in the rye?

It's interesting to view Jane's checker-playing as a metaphor for her approach to life. Kings in the back row might stand for self-discipline, reserve, or a hidden ally. One thing Holden remembers from playing checkers with Jane is that, when she got a king, she would keep it in the back row. She would line up her kings because "she just liked the way they looked when they were all in the back row." This is unusual because a king in checkers is a powerful piece. Most people are eager, as soon as they get a king, to use it to help them win the game.  We can tell from this that winning was not Jane's primary concern in checkers.  She wanted things to look a certain way. This might tell us that she was a precise person who liked things arranged just so. Holden tells us that she was a ballet dancer, and "used to practice about two hours every day, right in the middle of the hottest weather and all." This shows us that Jane has a lot of self-discipline.   Jan...

A curve has equation y= x^2 + 5x + 7 (i) Find the coordinates of the vertex of the curve (ii) State the equation of the line of symmetry of the...

Given ` x^2+5x+7 ` : (i) Find the vertex: (a) Rewrite in vertex form: `x^2+5x+7 `  Add and subtract the square of 1/2 the linear term, `(5/2)^2`, to get ` =x^2+5x+25/4-25/4+7 ` `=(x+5/2)^2+3/4 ` is now in vertex form with vertex `(-5/2,3/4) ` (b) Or find the axis of symmetry ` x=(-b)/(2a) ` so `x=(-5)/(2) ` ; The value of the expression at this point is 3/4 so the vertex is at `(-5/2,3/4) ` (ii) The line of symmetry is given by `x=(-b)/(2a) ` where the expression is given as `ax^2+bx+c ` ; here a=1, b=5, and c=7. So the axis (line) of symmetry is ` x=-5/2` . (iii) The graph is a parabola, opening up, normal width, with vertex `(-5/2,3/4) ` The y-intercept can be found by setting x=0 to get 7. Some points (found by choosing convenient x-values near the vertex and symmetry) include (0,7),(-1,3),(-2,1),(-3,1), (-4,3),(-5,7) The graph: ** The vertex form is `y=(x+5/2)^2+3/4 ` . The 5/2 shifts the graph of `y=x^2` left 2.5 units; the `3/4` term shifts the graph of `y=x^2` up`3/4` of a unit....

What events are included in the rising action of "Harrison Bergeron" by Kurt Vonnegut?

The rising action of a story or novel is made up of all of the events that build up towards the climax, which is the highest point of excitement.  Rising action is also how the conflict of the story builds.  Once the author has set the scene and established the characters, the rising action begins, and events start to happen that move the story and the conflict forward and build up tension.  Often, as in Harrison Bergeron, the rising action begins when an event disrupts or changes the main character's daily life.   In Harrison Bergeron, the author sets the scene by describing George and Hazel Bergeron and an average day of their lives in 2081.  The rising action begins when the couple's television program is interrupted by a "news bulletin" stating, "Harrison Bergeron, age fourteen...has just escaped from jail, where he was held on suspicion of plotting to overthrow the government. He is a genius and an athlete, is under-handicapped, and should be regarded as ext...

Based on Chapters 5-9 of Ian Haney López's Dog Whistle Politics: How Coded Racial Appeals Have Reinvented Racism and Wrecked the Middle Class:...

Haney Lopez writes that during Bill Clinton's 1992 election campaign, "Clinton did not depend on an economic message alone; rather, he decided to engage in his own racial pandering" (page 108). Clinton ran his 1992 campaign as a "New Democrat" who was tough on crime and anti-welfare. Clinton also tried to show, the author writes, that he "was not beholden to African American interests" (page 108). He tried to protect himself against charges that he was soft on African-American criminals. Clinton's strategies were in part a reaction to the tactics of George H.W. Bush, who had used the story of Willie Horton (an African-American furloughed prisoner) to tag Michael Dukakis, who was Governor of Massachusetts when Horton was released on furlough, as weak on crime during the 1988 Presidential campaign. To combat this idea, Clinton returned home to Arkansas during the 1992 campaign for the execution of a mentally impaired African-American man named Ricky ...

How do Banquo's children become king after Macbeth dies?

Banquo is Macbeth's closest friend and fellow thane.  He, in a way, represents wisdom, morality and rational thought.  Unfortunately, he doesn't live long, but we will get to that later. After Macbeth and Banquo leave the scene of battle and head towards their king's encampment, they meet the three witches in the woods.  They declare a prophecy for Macbeth that he will be given a new title and soon be king. Indeed, these both come true. Banquo's prophecies are less clear.  The final one is as follows: Thou shalt get kings, though thou be none.(70) So all hail, Macbeth and Banquo! The implication is that Banquo will be the father of a line of kings, but not be a king himself.  As a result, Macbeth's reign will be short, without any of his future children ruling at all.  Macbeth decides to kill Banquo, and his son, in the hopes of changing the prophecy.  While he succeeds in killing Banquo, he does not succeed in killing Banquo's son, Fleance.   We can assume that...

What are the differences and similarities between human body tissues and plant tissues?

All living organisms are made up of cells. A group of cells that work together performing a function are called tissues. For both plants and animals, tissues are a group of cells working together. These tissues vary in their structure, function, and origin. Animals have four tissue types: epithelial, connective, muscle, and nervous. Epithelial tissue covers the surface of all internal and external organs. Muscle tissue forms the three types of muscles: skeletal, cardiac, and smooth. They help in movement by contracting and relaxing. Connective tissue connects the different tissues, organs, and parts of the body. Examples include fat, blood, bone, and cartilage. Nervous tissue is made up of nerve cells. They conduct and transmit electrical impulses. Plant tissue is divided into two groups: meristematic tissue and permanent tissue. Meristematic tissue includes cells with the capability to divide. This allows the cells to enlarge and then increase the length and width of the stem, roots, ...

Why does Tom play hooky after his argument with Becky?

Interesting question! In the book The Adventures of Tom Sawyer by Mark Twain, Tom plays hooky after his fight with Becky. After his fight with Becky, Tom feels unloved and unappreciated. Tom believes that if he could be dead for a short time, people would appreciate him more. As the text reveals: “She [Becky] would be sorry some day — maybe when it was too late. Ah, if he could only die TEMPORARILY!” “Tom’s mind was made up now. He was gloomy and desperate. He was a forsaken, friendless boy, he said; nobody loved him . . .” Thus, Tom decides to run away. He believes that if he runs away, people might appreciate him more due to his absence. However, Tom also begins to enjoy his time playing hooky. Instead of attending school, he plays pirate and spends time with his friends. Eventually, Tom returns to his home. Although Tom enjoys his time playing hooky, he desires to return home and receive the extra attention from being gone and even presumed dead.

What did The Lives of the Saints mean to Ren before and after he left St Anthony's?

Before Ren left Saint Anthony's, The Lives of the Saints meant escape from the pain of punishment and the freedom to explore the fantastic--or miraculous--world of the saints. After he left, rather after he was forced to leave Saint Anthony's, the volume meant comfort. Later, it meant money. After that it meant a memory and a reference point to judge other events by. As events progressed, not to his liking, it meant a marker of a different kind of life. Ren took the volume after Father John punished him on the "whipping stool." He later told Brother Joseph that he stole it because he wanted to "hear the rest of Saint Anthony's story." He wanted to read about more saints. He wanted to read the stories in the night more than he wanted to eat or to sleep. Before Ren left Saint Anthony's, The Lives of the Saints meant the hope of real miracles. [H]e'd read about Saint Veronica curing Tiberius with her veil; Saint Benedict flowing water from a rock;...

Why did the Senate want to kill Julius Caesar?

Julius Caesar was a very popular reformer and military general in Rome. He brazenly led his troops across the Rubicon River in 49 BC in an effort to secure complete control of Rome from his rival, Pompey. He was successful in his quest to utilize his loyal military forces to control the entire peninsula. Pompey did not have success against Caesar and fled to Greece and then Egypt. Caesar's forces pursued Pompey to both places and had him eliminated in Egypt. This left the Senate with a vexing question: What is to be done with Caesar? It seemed that his political influence and power could not be contained. Caesar even declared himself dictator for life, which was unprecedented. The Senate was very concerned about the power that he acquired in such short order and they decided that he should be assassinated for the good of the Republic.

In The Story of My Life, what evidence suggests that the author's main purpose was probably to inform others about what life is like for people...

It is true that The Story of my Life is both engaging and entertaining, but it also deeply moving and educational in helping readers to identify with those with sensory disabilities; therefore it does seem that the author's main purpose was probably to spread awareness and openness about an issue that was often pushed under the carpet back in the times when this piece was written. The author does seem to have wanted to inform others about what life is like for people with visual and/or hearing impairments, probably due to a suspicion that attitudes of intolerance and shame around sensory impairments and learning disabilities were often born of ignorance and prejudice. Helen Keller’s story of conquering her deaf/blind issues seems colored by her justified angry response to this prejudice against those with disabilities, and if her motive was to inform and educate, then she certainly succeeded in raising public awareness as new audiences became aware and rallied to her call. The hum...

What quotes from Salinger's The Catcher In The Rye describe the way Holden feels about Jane Gallagher? How do those quotes connect to the theme...

Throughout  The Catcher in the Rye , Holden mentions his desire to give Jane Gallagher a call. In fact, his fight with Stradlater occurs because he's afraid that his roommate gave Jane "the time" in the back of Ed Banky's car without really caring about the girl. Jane's one feature that Holden obsesses over is her habit of keeping all of her "kings in the back row" when playing checkers. He says that she doesn't do this for strategy or anything, but because she "liked the way they looked." Because Stradlater is incapable of recognizing this girl's unique habit, Holden loses his mind and attacks his roommate, repeatedly calling him a "stupid moron" who "didn't even care if a girl kept all her kings in the back row or not." Then Holden tells Stradlater that he can't see a girl for who she is and that he doesn't "even know if her first name is Jane or Jean, ya goddam moron!" But there is a lot more...

`int sqrt(16-4x^2)dx` Find the indefinite integral

 Given , `int sqrt(16-4x^2)dx` This Integral can be solved by using the Trigonometric substitutions  (Trig substitutions) For `sqrt(a-bx^2)` we have to take `x=` `sqrt(a/b) sin(u)` so here , For `int sqrt(16-4x^2)dx -----(1)`  `x` can be given as `x= sqrt(16/4) sin(u)= sqrt(4) sin(u) = 2sin(u)` so,` x= 2sin(u)` => `dx = 2 cos(u) du` Now substituting `x` in (1) we get, `int sqrt(16-4x^2)dx ` =`int sqrt(16-4(2sin(u))^2) (2 cos(u) du)` = `int sqrt(16-4*4(sin(u))^2) (2 cos(u) du)` = `int sqrt(16-16(sin(u))^2) (2 cos(u) du)` = `int sqrt(16(1-(sin(u))^2)) (2 cos(u) du)` = `int sqrt(16(cos(u))^2) (2 cos(u) du)` = `int (4cos(u)) (2 cos(u) du)` =` int 8cos^2(u) du` = `8 int cos^2(u) du` = `8 int (1+cos(2u))/2 du` = `(8/2) int (1+cos(2u)) du` = `4 int (1+cos(2u)) du` = `4 [int 1 du +int cos(2u) du]` = `4 [u+(1/2)(sin(2u))] +c`   but `x= 2sin(u)` => `(x/2)= sin(u)` => `u= sin^(-1) (x/2)` so, `4 [u+(1/2)(sin(2u))] +c` =`4 [sin^(-1) (x/2)+1/2sin(2(sin^(-1) (x/2)))] +c`   so, `int sqrt(16-4...

What discoveries led scientists to conclude that atoms were made up of smaller particles?

The ancient Greeks hypothesized that all physical structures were made up of smaller particles too small to detect with the human eye. In the early 19th century, scientist John Dalton refined the Greek model and defined atoms as the fundamental building blocks of nature. Nearly a century later, J.J. Thomson discovered that atoms contained electrons. He theorized that negatively charged electrons and other positively charged particles floated around inside an atom’s hard shell, like raisins in “plum pudding.” In 1911, Ernest Rutherford argued that an atom’s positive charge must be a result of an atomic nucleus and that electrons orbit the nucleus like planets around the sun. Just a few years later, Niels Bohr expanded Rutherford’s model introduced the idea that electrons orbit the atomic nucleus at varying energy levels. Bohr’s ideas inform the work of today’s scientists as they study the mysteries of quantum mechanics and how to harness nuclear energy.

A substance changes from a solid to a liquid during the process of melting. What happens to the temperature and arrangement of the particles in the...

First of all you need to understand that molecules have motion.  All molecules higher than the temperature of absolute zero (0 degrees Kelvin) move in proportion to their temperature.  In other words, hot molecules will have a higher degree of motion than cold molecules.  When a solid is heated up, its molecules will absorb that energy and increase their molecular motion.  So as the material goes from a solid to a liquid, the molecular motion increases as does the space between the molecules.  This increased space and motion is what allows a liquid to be less dense than a solid (in general) and allows it to move spontaneously to fill the space of its container.  Continued heating will allow the liquid to absorb even more energy and boil to become a gas, which is even less dense with more space between molecules and a higher degree of molecular motion than either a liquid or a solid.

In Treasure Island, why does Captain Smollett raise the British colors in the stockade even though the mutineers use it to aim their attacks?

Chapter 18 opens with both the crew and the mutineers racing toward the stockade. After a skirmish that leaves one dead on either side of the conflict, Captain Smollett and the crew occupy the log-house (the main building in the stockade). The captain proceeds to empty his pockets of several things he grabbed from aboard the ship, including the British colours, or, flag. The captain then sets a tree against the corner of the log-house and climbs onto the roof in order to raise the colours. Doctor Livesey, who narrates the chapter, comments "This seemed mightily to relieve him." Shortly after, the captain uses a second flag to cover the corpse of Tom, the sailor who was killed by the mutineers. These two actions serve to illustrate how much the flag means to Captain Smollett. Thus, when the squire suggests lowering the flag to make it more difficult for the mutineers to shoot at the log-house, Captain Smollett responds: "Strike my colours! No, sir, not I!" The doctor...

In Part One of Ray Bradbury's Fahrenheit 451, what question does Montag ask Mildred and how does she respond?

The day after Mildred's overdose, Montag asks her if she is okay. She has trouble recalling anything and refuses to believe that she would have taken too many pills.  Later in Part One, after witnessing a woman burn with her books, Montag goes home and asks Mildred how they met. She can not remember and concludes that "It doesn't matter." Mildred's life has been dominated by parlour (television) shows and sleeping pills. She lives vicariously through these shows. She's lost interest in any meaningful relationship with Montag. This is why she is indifferent when she can't recall how they met.  Montag also asks her if it would be alright for him to quit his job for a while. She is not happy about it because she fears any kind of change.  "You want to give up everything? After all these years of working, because, one night, some woman and her books--" Mildred doesn't want anything to disrupt or change her daily routine. So, when Montag's sug...

`f(x) = (4x)/(x^2+2x-3) ,c=0` Find a power series for the function, centered at c and determine the interval of convergence.

` f(x)=(4x)/(x^2+2x-3), c=0` Let's first factorize the denominator of the function, `x^2+2x-3=x^2+3x-x-3` `=x(x+3)-1(x+3)` `=(x+3)(x-1)` Now let, `(4x)/(x^2+2x-3)=A/(x+3)+B/(x-1)` `4x=A(x-1)+B(x+3)` `4x=Ax-A+Bx+3B` `4x=(A+B)x-A+3B` equating the coefficients of the like terms, `A+B=4`    ----------------(1) `-A+3B=0`   ------------(2) From equation 2, `A=3B` Substitute A in equation 1, `3B+B=4` `4B=4` `B=1` Plug in the value of B in equation 2, `-A+3(1)=0` `A=3` The partial fraction decomposition is thus, `(4x)/(x^2+2x-3)=3/(x+3)+1/(x-1)` `=3/(3(1+x/3))+1/(-1(1-x))` `=1/(1-(-x/3))+(-1)/(1-x)` Since both fractions are in the form of `a/(1-r)` Power series is a geometric series, `=sum_(n=0)^oo(-x/3)^n+sum_(n=0)^oo(-1)x^n` `=sum_(n=0)^oox^n/(-3)^n+sum_(n=0)^oo(-1)x^n` `=sum_(n=0)^oo(1/(-3)^n-1)x^n` Interval of convergence `|-x/3|<1,|x|<1` `|x/3|<1`  and `|x|<1` `-3<x<3` and `-1<x<1` Interval of convergence is the smaller of the intervals of convergence of the tw...

Describe the relationship between Steve Harmon and Kathy O'Brien.

Steve Harmon's lawyer, Kathy O'Brien, successfully wins the case by presenting Steve in a positive light. She not only encourages Steve but also gives him advice on how to act in the courtroom that will sway the jury's opinion of him. She also goes over the questions he will answer while he is on the witness stand which helps Steve win the case. Although Kathy supports Steve and wants him to be found not guilty, their relationship is strictly professional. Steve wants to know Kathy on a personal level, but she is reluctant to disclose aspects of her personal life. At the end of the novel, Steve is found not guilty and turns to hug Kathy. However, Kathy backs away from him and looks at Steve like he is a "monster." Her reaction suggests that she believes that Steve is guilty of participating in the crime and is not interested in becoming friends. Steve is hurt by her reaction and continues to struggle with his identity.

In the beginning of the story, how did the beliefs and hopes of Jing-Mei's mother contribute to her desire to see her daughter succeed?

Jing-Mei begins the story by telling the reader that her mother completely buys into an ideal interpretation of the American Dream. Her mother thinks that with hard work, anyone can accomplish anything in America. Her mother even tells Jing Mei, "you can be a prodigy, too." This shows her mother's rather unrealistic idealism. With hard work, Jing-Mei could certainly become a good, or even great, pianist, but a person is a prodigy based upon some innate ability. Jing-Mei is not a prodigy, but her mother insists she can work to achieve the same ability that a prodigy would have. This is not impossible. It's just very difficult. As Jing-Mei is trying to assert herself and develop her own individual personality, her mother's insistence on molding her daughter into a prodigy becomes a burden to her (Jing-Mei). Considering what her mother has gone through, the promises of the American Dream must have been extremely appealing and uplifting: America was where all my mothe...

What organs eventually develop from the ectoderm layer?

The term  ectoderm  comes from the Greek for "outside skin." The ectoderm is the outermost germ layer in embryonic development. Several organs develop from this layer, including our own outermost organ--the skin! Differentiation of the ectoderm layer also gives rise to the nervous system (including the brain, spinal cord, and nerves), the enamel of teeth, hair, nails, and the lining of our bodily passages. The sinuses and nasal cavity, the mouth, the sweat glands, and the anal cavity are all lined with epithelial tissue that develops from the ectoderm layer.  The other two germ layers of embryonic development are the  mesoderm  (meaning "middle skin") and the  endoderm (meaning "inside skin"). These layers on to form other tissues, organs, and systems of the body, including the respiratory organs, blood vessels, digestive tract, and muscles. 

Who presents Macbeth with a new title and why does King Duncan visit Macbeth's castle?

Immediately following Macbeth's first meeting with the Weird Sisters in Act I, Ross and Angus meet with Macbeth and Banquo. Angus conveys Duncan's thanks for Macbeth's bravery and success in battle, and Ross tells Macbeth that Duncan has awarded him the title of Thane of Cawdor. After announcing that his son Malcolm will be named Prince of Cumberland in Act I, Scene 4, Duncan tells Macbeth that he and others will be rewarded with titles for their loyalty. Duncan invites himself to Macbeth's castle at Inverness and tells Banquo that he believes Macbeth has no equal among the Scottish thanes. The visit from Duncan is meant to honor Macbeth, but ironically, the visit prompts the murder plot Macbeth and Lady Macbeth have only begun to consider.

In Where the Red Fern Grows, what did Billy do with the money he earned from selling the hides of the raccoons he and his dogs hunted?

Billy turned over the money he earned to his father. In Chapter 10, the text tells us that Billy enjoyed hunting raccoons for their skins. Accordingly, a good-sized hide could fetch anywhere from four to ten dollars, depending "on the grade and quality" of the hide. Although Billy made good money from selling the hides, he didn't care much about the money itself. He turned over all his profits to his father and asked no questions about what his father did with the money. To Billy, the most important things in life were his dogs, Old Dan and Little Ann. With Old Dan and Little Ann by his side, Billy hunted coons with relish. The text tells us that Billy only stayed home from coon-hunting when the weather turned bad, and even then, his mother "all but had to hog-tie" him at home. Billy sold his coon hides at his grandfather's store.

What was the economic impact of the Columbian Exchange on European mercantilism?

Mercantilism is the belief that national power is derived from wealth and that wealth is accumulated through a favorable trade balance.  In other words,  a nation that sells more goods to foreign markets than it buys will acquire wealth.  The voyages of Christopher Columbus were motivated by the need to establish new trade routes in the pursuit of profit.  The Columbian Exchange played a significant role in the primacy of mercantilism as economic policy.  The exchange introduced new agricultural goods like potatoes, maize, and tomatoes to Europe.  This new abundance of food caused greater nutritional variety to the diet and enabled the populations to grow.  The larger populations would spark the introduction of factory systems to western Europe.  A larger population also created pressures on the economies of Europe.  This pressure was relieved to some degree through the establishment of colonies in the New World.  It was through the colonies that mercantilism really took off.  The colo...

When Rainsford calls himself a beast at the end of the story, what does the description foreshadow in "The Most Dangerous Game" by Richard Connell?

When Rainsford calls himself a beast, it foreshadows him killing Zaroff.   Foreshadowing is when the author hints at something that will happen later in the story.  When Rainsford first met General Zaroff, he considered his game of hunting human beings murder.  He could not believe Zaroff was for real at first, and then told him that there was no way he would participate as a hunter.  He had no idea he was going to be the game.  Zaroff tells Rainsford that his idea about hunting people being murder is old-fashioned.  “…I'll wager you'll forget your notions when you go hunting with me. You've a genuine new thrill in store for you, Mr. Rainsford." "Thank you, I'm a hunter, not a murderer." "Dear me," said the general, quite unruffled, "again that unpleasant word. But I think I can show you that your scruples are quite ill founded." Rainsford has a difficult time accepting his role as prey.  He gets somewhat intimidated and discouraged wh...

How did the Romans tell their story about the twins Romulus and Remus and why did they tell it?

The story of Romulus and Remus was part of the mythical foundation history of Rome. It was therefore recounted in history books as part of chronologically ordered accounts of Rome's early histories. It was normally narrated in the third person in a context that emphasized the growth in power of the city and its conflicts with neighboring tribes. As with most foundation myths, the story emphasizes supernatural occurrences as a way of highlighting the city's strong connection to the gods and the way in which the greatness of Rome was ordained and aided by the gods. The reason why the story was told was to emphasize the greatness of Rome. The lineage that traces the parentage of Romulus and Remus to Aeneas (a Trojan prince) also provides a legendary explanation of and justification for conquests of Carthage and Greece, as well as a pedigree that allows Rome to appropriate Homer and claim a unique cultural heritage, different from that of the Etruscans and Greeks but equally venera...

Can you analyze the poem "Absolution" by Siegfried Sassoon?

Sure! Siegfried Sassoon fought in World War I and was wounded in battle; he spent much of his life speaking out against war, and these pacifist feelings are easy to see in his poems. This one, "Absolution," was published in 1917, the same year that Sassoon was hospitalized for what we know today as post-traumatic stress disorder. "Absolution" is a short poem that contains three stanzas of four lines each. The word "absolution" means "forgiveness," and the verb form is "absolve," meaning "forgive." So, this is a poem about war; it's saying that war is essentially a terrible sin that brings destruction to humanity and to the earth, but when it's over--when we forgive ourselves for the sin of war-- we're left with more wisdom, freedom, and happiness than we had before, and we find a deeper understanding about how valuable time is and how fast it goes by. Whether you believe the speaker is expressing these sentiments g...

What is the lesson in Ray Bradbury's "All Summer In A Day"?

There can be more than one lesson to learn from any story in literature. More often than not, people apply the messages from stories to their own lives in different ways and based on personal experiences. (This is where themes come from, too.) Bradbury's "All Summer in a Day" is a story that addresses human nature and group mentality. For example, it is human nature to doubt one person's experiences when everyone else in a group has not had that same experience. Margot remembers seeing the sun when she lived on Earth, but children on Venus doubt that she ever saw the sun because they do not have the same experience. Not only do Margot's classmates doubt that she remembers the sun, but William in particular vocally challenges her about it. Either William is jealous that Margot remembers the sun while he doesn't, or he simply doesn't believe that the sun will ever shine. If the second is true, then William's behavior towards Margot might be hostile becau...

Was Michelangelo di Lodovico Buonarroti Simoni an atheist?

No, Michelangelo was not an atheist.  Like many people in Renaissance society, Michelangelo was Catholic. Prior to the Renaissance, nearly everyone associated themselves with the Catholic faith. Humanist ideas began to enter society during the Renaissance. Some people did turn away from Catholicism in favor of a humanist worldview, but most adopted humanist ideas and remained Catholic. It was socially unacceptable to deny God completely, so many chose to espouse both Catholic and humanist beliefs. This was the case with Michelangelo, though he was particularly devout in his Catholic faith. Michelangelo was heavily influenced by the Bible and Christianity in his artwork. Among those art pieces inspired by the Bible were  Pietà , David, and the ceiling of the Sistine Chapel. Michelangelo sometimes combined Biblical references with mythology and other non-Biblical references. An example of this are the female mythological figures painted on the ceiling of the Sistine Chapel. During the R...

How was England different from France according to Charles Dickens in A Tale of Two Cities?

The dichotomy of London and Paris is a central element of the setting of the novel. From the first paragraph, Dickens shows that the two are completely different in their rulers, people, and culture. This is symbolized in numerous instances. London could be represented by Tellson’s Bank and Mr. Lorry’s attitude and personality of order, rules, and trustworthiness. In contrast, Paris is disordered and violent. When the emigrants from Paris arrive in London, they bring that chaos into the bank, causing trouble for Mr. Lorry. The class system can also be seen in the vast gap between rich and poor in France. In London, however, the classes mix to a certain extent, such as Jerry Cruncher being part of the “family” of the Manettes. While there is obviously a class structure in England, the people in those classes interact more than those in France, where they are in conflict to the point of destruction. The families represented in the story also symbolize the differences in the two cities. C...

Compare and contrast the common theme in Everyman to Chaucer's "The Pardoner's Tale."

The medieval morality play Everyman and Chaucer's "The Pardoner's Tale" have some similarities with regard to theme, but also have distinctions. Both plays focus on the inevitability of death and the futility of riches to help one in the afterlife. In the opening of Everyman , Everyman is enjoying his life and his riches, taking no thought of God or eternity. He learns he must give an account to his Maker and begins a quest to find someone to go with him to help him plead his case. He repents and embraces the teachings of the church, and he finds joy in Heaven. In "The Pardoner's Tale," the three rioters are drinking in a tavern and go on a quest to find and kill Death. On their way, they find treasure and end up killing each other because of greed.  Both stories emphasize the truth that death faces all men . In the first lines of Everyman delivered by the Messenger, the Messenger states that the play will show life is not man's to keep and that ma...

What are the uses of land on a typical sugar plantation?

Many sugar plantations in the Caribbean were originally producers of cotton and tobacco. In the mid 17th century, many growers switched due to the higher profitability of sugar and the fact that the land tended to lend itself to sugar production. In order to increase production, many plantations also developed various methods of irrigating the land as sugar is a crop that demands a great deal of water. The land that was typically used was often close to the coast of the various islands in the Caribbean as well as valley floors and plains in other tropical regions. The land could also be used to grow rice in addition to the other crops mentioned above.  In many places where land close to island coast lines was used for sugar plantations, farmers found it more valuable to sell the land to be developed for residential or tourist-use than to continue cultivating sugar.

When Tom and Huck decide never to tell about the murder they saw, what do they seal their agreement with?

Interesting question! In the book The Adventures of Tom Sawyer by Mark Twain, Tom Sawyer and Huckleberry Finn witness a murder. Because the boys are afraid of the murderer, they make an oath with one another to never tell. In the book, Tom and Huck witness a murder; however, they decide to make an oath to never tell. Tom and Huck are afraid that the murderer, Injun Joe, might also murder them if they tell. As Huck reveals: “What are you talking about? S’pose something happened and Injun Joe DIDN’T hang? Why, he’d kill us some time or other, just as dead sure as we’re a laying here.” And: “Tom, we GOT to keep mum. You know that. That Injun devil wouldn’t make any more of drownding us than a couple of cats, if we was to squeak ‘bout this and they didn’t hang him.” Thus, the boys make an oath to not tell anyone about the murder. Instead of making a simple verbal oath, the boys determine to finalize their promise by writing the oath down and signing it in their own blood. As the text revea...

What are the main conflicts of each act in A Midsummer Night's Dream?

In Act I, Duke Theseus directs Hermia to marry Demetrius. He has her father Egeus’s permission, but Hermia and Lysander are in love. The duke says she must marry the man of her father’s choosing, die, or “live a barren sister all [her] life.” Adding further conflict to this lovers’ conundrum is Helena, who adores Demetrius. Meanwhile, Peter Quince casts his play Pyramus and Thisby . There are a few small conflicts about who will play whom, but the main tension in this act is between the lovers and the law. Act II introduces the fairies and the clash between Queen Titania and her husband Oberon, who quarrel over the possession of “a little changeling boy.” Titania says that their argument is disrupting nature’s cycles: “this same progeny of evils comes / From our debate, from our dissension.” Oberon puts a love potion in his wife’s eyes as she sleeps, and, mistaking him for Demetrius, Puck enchants Lysander. Helena pursues Demetrius, to his chagrin, before stumbling across Lysander. Whe...

Explain why Squeaky makes Raymond walk on the inside when they walk down Broadway.

In Toni Cade Bambara’s story “Raymond’s Run” Squeaky takes care of her older brother Raymond, who lives with developmental delays. This is her family contribution which allows her mother to care for their home.  While caring for Raymond, she often takes him for walks in the city. Squeaky practices her breathing and high stepping with Raymond tagging along. Unfortunately, there are times when he pretends the curbing along the road is a tight rope, or he plays in the puddles. If he goes home with wet pants legs, Squeaky is disciplined for Raymond’s actions. There are times he runs into traffic and out onto the island in Broadway causing the pigeons to scatter. These actions upset the people who are eating lunch or just relaxing in the sun, and Squeaky must make amends. Therefore, Squeaky devised a system to have Raymond walk on the inside between her and the buildings. This system keeps Raymond safe and Squeaky in her parent’s good graces. So I keep Raymond on the inside of me, and he pl...

How does a chain fountain work?

A chain fountain is the name given to the phenomenon where a chain flows upward against gravity and pours out of its container. This might appear illogical and almost magical, but it is governed by the same physics as everything else. Let's define a chain first since its unique properties make this phenomenon possible. A chain is a flexible series of links and is usually made of metal. These interconnected links can give a chain the appearance of a string, but it is functionally distinct because the metal links that make up the chain are actually rigid rods and not flexible on their own. This is very important to the function of the chain fountain because it is the qualities of an inflexible rod that create the fountain effect as the chain flows out of its container. When the chain fountain experiment begins, someone lifts the end of the chain out of its container and pulls it. Before someone pulls the chain out of the container the system is at rest, so it is important to note tha...

`sum_(n=2)^oo 1/(nsqrt(ln(n)))` Confirm that the Integral Test can be applied to the series. Then use the Integral Test to determine the...

The Integral test is applicable if `f` is positive and decreasing function on infinite interval `[k, oo)` where `kgt= 1` and `a_n=f(x)` . Then the series `sum_(n=k)^oo a_n` converges if and only if the improper integral` int_k^oo f(x) dx ` converges. If the integral diverges then the series also diverges. For the given series `sum_(n=2)^oo 1/(nsqrt(ln(n)))` , the `a_n =1/(nsqrt(ln(n)))` then applying` a_n=f(x)` , we consider: `f(x) =1/(xsqrt(ln(x)))` .   The graph of f(x) is: As shown on the graph above, the function `f(x)` is positive and decreasing on the interval `[2,oo)` . This implies we may apply the Integral test to confirm the convergence or divergence of the given series. We may determine the convergence or divergence of the improper integral as: `int_2^oo 1/(xsqrt(ln(x)))= lim_(t-gtoo)int_2^t 1/(xsqrt(ln(x)))dx` To determine the indefinite integral of `int_2^t1/(xsqrt(ln(x)))dx` , we may apply u-substitution by letting: `u = ln(x)` and `du = 1/x dx` .  The integral becomes...

What was the lasting impact of President Reagan on the United States?

Reagan was one of America's most popular presidents.  The former actor had a real gift for explaining his vision for America so that all could understand.  President Reagan was a leader in ending the Cold War and building positive Russian-American relations. Reagan was also a leader in the War on Drugs and his wife Nancy's campaign of "Just Say No" was quite popular.    Politically, Reagan did have some problems, however.  Reagan was president during the Iran-Contra scandal and somehow managed to avoid punishment.  Reagan's policies of financial deregulation helped to bring about the Savings and Loan crisis of the late 1980s which hurt the presidency of his successor, George H.W. Bush.  Reagan's increased military spending led to massive deficits that America continues to pay on today.  Today Reagan is considered a hero of the Republican party, but his massive military spending and deficits would make him a liability for fiscal conservatives.  

"We paused before a House that seemed A Swelling of the Ground –" What image does the language in these lines create?

The image created by these lines is of a grave that has been recently dug, with the coffin placed inside and the dirt heaped back over on top of it. The result is like a mound rather than a smooth, flat replacement of the soil, since the coffin took up some of the space inside the hole. It's like the ground has swollen up to create a little bump. If you were reading these lines literally, out of context, you may have imagined instead an actual house that's just a bit squat and earthy-looking, like it grew up out of the ground. (Perhaps a Hobbit house came to mind!) But consider the lines in the context of the poem. Up until this point, Death has been riding in the carriage with the speaker; they drove around town until the sun went down and it got chilly. Now they're pulling up to a "House," where centuries will fly by. It's pretty clear that this "House" is where the speaker will remain; it's where Death is bringing her. So it's a grave. You...

What is the best answer for the radius of a spherical atom?

By definition, density is mass divided by volume, `D = m/V` , so if we are given the mass and density, we can solve for the volume by `V = m/D` . The density is `1.0*10^14 g/cm^3` and the mass is `2.0*10^-23 g` . `V = m/D = (2.0*10^-23 g)/(1.0*10^14 g/cm^3) = 2.0*10^-37 cm^3` We're told to assume the atom is spherical, so we can get the radius by using the volume formula for a sphere, `V = 4/3 pi r^3`, which we solve for r to get `r = (V/(4/3pi))^(1/3)`. `r = ((2.0*10^-37 cm^3)/(4/3 pi))^(1/3) = (4.775*10^37 cm^3)^(1/3) = 3.628*10^-13 cm.` The result is `3.6*10^-13 cm`, which is choice A.

How does A Theory of Justice by John Rawls relate to urban planning?

Rawls does not specifically discuss urban planning in the book, which is more theoretical and philosophical than most books about such a pragmatic topic as urban planning. Essentially, Rawls argues in the book that if we were able to choose the kind of society we lived in, we should do it from behind a veil of ignorance, meaning that we don't know what our own abilities, or position in society will be. Without knowing where we would fall in society, we would probably choose a society with the kind of social safety nets that protect everyone's basic welfare. Because urban planning is fraught with social issues, we could suggest the same thing about it. All sorts of issues related to urban planning have social implications. Gentrification, equal access to utilities, schools, public parks, and de facto segregation are all issues that involve the kind of fundamental justice that Rawls advocates for society as a whole. If we could choose the ideal city, all things being equal, we wo...

"If Aunt Alexandra could be a lady at a time like this, so could I." What do you think Scout meant by this?

This quote comes at the end of chapter 24. In this chapter, Aunt Alexandra is hosting the missionary circle, and many women are at the Finch home for the meeting. Atticus comes home and calls Aunt Alexandra into the kitchen, where he informs Calpurnia and Alexandra of Tom Robinson's death. Scout sees that her aunt is highly distressed by this turn of events. She is upset that the people in the town have left it to Atticus to try to achieve justice for the black residents of the county when all of them should have been advocates for Tom, who was obviously falsely accused. Aunt Alexandra's voice is shaking and she sits down with her head in her hands. Scout thinks she might be crying. She's not, but she is angry and upset. Nevertheless, she composes herself and goes out to serve the ladies, allowing Calpurnia to go with Atticus to comfort Tom's wife. Even though Aunt Alexandra has anger toward some of the women who are her guests, she serves them graciously and doesn'...

What should I include in a character profile for Romeo from Act 2 Scene 4?

In Act 2, scene 4, we see Romeo with his friends: here, he behaves like sort of a stereotypical young man of his age.  He is playful and fun-loving, he engages in a bit of sexually suggestive banter, he endures some good-natured ribbing and he gives back as good as he gets.  However, then Juliet's nurse arrives to speak with Romeo, and his demeanor changes.  He sort of blows off his friends, saying that he'll follow them to his father's house, but he really has no such intention.  To the nurse, he speaks sincerely and with emotion about the plans he has made for a marriage with Juliet.  Further, he is courteous and even offers her money for delivering their messages.  Thus, in this scene, Romeo seems a bit immature at first, but he quickly sobers when faced with responsibility and something that is important to him.

What does Mr. Martin buy at the cigar store in "The Catbird Seat"? Why is this unusual?

James Thurber's story "The Catbird Seat" opens with the following sentence: Mr. Martin bought the pack of Camels on Monday night in the most crowded cigar store on Broadway. This purchase was extremely unusual for Mr. Martin, the protagonist and viewpoint character, because he was known to be a nonsmoker. He plans to use one of the cigarettes to plant a false clue in Ulgine Barrows' apartment after he murders her. She smoked Lucky Strike cigarettes. Camels and Luckies were the two leading brands at the time the story was published in 1942. Both brands were heavily advertised on the radio, in magazines, on billboards, and on posters all over "point-of-purchase" settings. Television had not been introduced to American consumers at that time because World War II was still in progress and monopolized manufacturing production. It was his idea to puff a few puffs on a Camel (after the rubbing-out), stub it out in the ashtray holding her lipstick-stained Luckies, a...

Who is the father of physics?

Although the title "Father of Physics" has not been given to a single individual, Galileo Galilei, Sir Isaac Newton, and Albert Einstein have all been called fathers of physics in western cultures. Galileo Galiliei (1564-1642), known colloquially as Galileo, is best known for his contributions to observational astronomy. His accomplishments include the telescopic confirmation of the phases of Venus (similar to moon phases), the discovery of Jupiter's four largest moons (Io, Europa, Ganymede, and Callisto), and his observation of sunspots. Additionally, Galileo is recognized for his political contributions in spreading scientific knowledge during the Scientific Revolution. Newton (1643-1727), a key character in the scientific revolution, is best known for his three laws of motion, which laid the foundation for classical mechanics. In summary, these laws state that 1) objects in motion stay in motion unless acted upon by a force, 2) force is equal to the product of mass and...

What is the chemical test for alkanes and alkenes?

Alkanes and alkenes are both hydrocarbons. Alkanes, however, contain only single bonds between the carbons while alkenes contain at least one double bond between carbons. Tests can be conducted to differentiate these two groups of molecules based on whether or not the double bonds can be broken by a halogen. If one takes two test tubes with bromine water and adds an alkene to tube A and an alkane to tube B and then shakes the two tubes, a color change will occur in tube A (the color of the solution will change from brown to colorless) while no color change will occur in tube B. This is because in tube A, the double bond is broken and the carbons become halogenated while no reaction occurs in tube B. The reaction that occurs in tube A is as follows: Bromine is a diatomic element. It regularly occurs as Br2. In a molecule of Br2 one bromine has a partial positive charge and the other has a partial negative charge. It only becomes polarized as it approaches the electron-dense double bond ...

`sum_(n=1)^oo (n!)/2^n` Verify that the infinite series diverges

`sum_(n=1)^oo (n!)/2^n` To verify if the series diverges, apply the ratio test. The formula for the ratio test is: `L = lim_(n->oo) |a_(n+1)/a_n|` If L<1, the series converges. If L>1, the series diverges. And if L=1, the test is inconclusive. Applying the formula above, the value of L will be: `L = lim_(n->oo) |(((n+1)!)/2^(n+1))/ ((n!)/2^n)|` `L= lim_(n->oo) |((n+1)!)/2^(n+1) * 2^n/(n!)|` `L=lim_(n->oo) | ((n+1)*n!)/(2*2^n) * 2^n/(n!)|` `L = lim_(n->oo) | (n+1)/2|` `L = 1/2 lim_(n->oo) |n+ 1|` `L=1/2 * oo` `L=oo` Therefore, the series diverges.

What does Romeo say will happen to his eyes if he sees a woman more beautiful than Rosaline at Capulet's party?

In Act I, Scene 2 Romeo and Benvolio meet Capulet's servant in the street. The servant has been tasked with giving out invitations for Capulet's party to be held that same night. Unfortunately, the servant has been given a written list but cannot read, so he asks Romeo for help. Romeo reads the list out loud and discovers that Rosaline, the girl he is in love with, has been invited. After the servant leaves, Benvolio suggests that they go to the party and he will show Romeo more beautiful women than Rosaline: Go thither, and with unattainted eye Compare her face with some that I shall show, And I will make thee think thy swan a crow. Romeo replies that there is no chance that a more beautiful woman exists and that his eyes will be lying to him if there is. He tells Benvolio that he would rather have his tears turn to flames and burn his eyes if they lie to him that way. He claims that even the sun has never before seen any woman as beautiful as Rosaline: When the devout religio...