Notes

The word "plotting" refers to an act in which the perpetrator(s) secretly plan to commit an evil deed. In this sense, then, plotting, by its very nature, seeks a malicious outcome, meaning those who indulge in the act do not wish to do any good and are, consequentially, evil. Plotting in Act III, Scene 1 is important because it reveals the extent of Macbeth's perfidy. The scene illustrates that he has reached such a state of ruthless and cold-blooded malice, that he has lost all rectitude. There are no boundaries to his pervasive perversion, so much so that he plots the murder of his confidante and friend Banquo and Banquo's son, Fleance. It is clear from the beginning of the scene that Macbeth has already started plotting Banquo's assassination. Macbeth, who earlier somewhat reluctantly acquiesced to his wife's insistence on killing king Duncan, has now become a master in the art of murder. His conversation with Banquo most pertinently illustrates his sly and...

Dolly Winthrop coaches Silas Marner on how to care for Eppie, and she strongly urges him to be sure the baby is baptized and receives religious instruction. Gently, she makes suggestions and allows Silas to care for the child on his own. In this way, Eppie will be his "little un" and no one else's. Nevertheless, Dolly is adamant Silas have Eppie baptized, urging him to talk to Mr. Macey as soon as possible. She explains, For if the child ever went anyways wrong, and you hadn't done your part by it, Master Marner—'noculation, and everything to save it from harm—it 'ud be a thorn i' your bed for ever o' this side the grave (Chapter XIII). Silas Marner takes Dolly's advice to heart, and the baby is christened. To love another human being and share in her life provides Silas with a richness he never experienced with his gold. Further, as Eppie's mind grows, Silas's memory also grows. One day, Dolly warns Silas not to spoil Eppie, but Silas cann...

The successful use of the scientific method depends on constructing clearly-stated, testable, falsifiable hypotheses. Assuming your hypothesis is correct, what should we expect to see? And what sorts of things should not happen if the hypothesis is correct? Being testable is about being able to answer these questions. It has nothing to do with the truth value of the hypothesis. If a hypothesis is not testable, that doesn't imply that it's false.  Testability means that there is a way to settle a question based on evidence; there is a way to obtain evidence against an idea. If I claim that the moon is made of green cheese, that's testable. It's an idea that gives rise to predictions that we can operationalize (define in terms of concrete procedures and measurements) and test. Astronauts can collect samples; the samples can be analyzed for the presence of cheese. But if I claim that the moon is inhabited by a supernatural, ethereal being -- one that can't be detecte...

While “responsibility” for Mrs. Mallard’s death is a stretch of the events of Kate Chopin’s "The Story of an Hour," it is definite that her death resulted from a complication of her heart condition. She died of a “joy that kills.” The irony of that statement, a “joy that kills,” is that just before Mr. Mallard walked in the front door, unscathed, Mrs. Mallard was the most joyful that she had ever been. However, when she witnessed him, she released a piercing scream that relates to the reader that Mrs. Mallard was horrified that her newfound freedom had been so easily ripped right from under her feet. Chopin writes "The Story of an Hour" via the unique perspective of the late 1800’s in America, wherein it was expected that women would be married before they reached a certain age. Our deceased Mrs. Mallard was described as “young,” meaning that although her marriage was a relatively new one, it was still one that had taken a very large toll on her health. An important...

I don't think we can say with any assurance that Chris McCandless was relieved to have left behind Ronald Franz. McCandless seemed to really enjoy his time with Franz, and McCandless wrote lengthy letters to him and made sure to call him on his birthday. I believe that McCandless missed Franz, and looked forward to spending more time with him. I believe that because McCandless came back to spend more time with Franz. McCandless did that on his way back to Carthage after his stay in San Diego didn't go so well. Upon his release he had hitchhiked to Coachella, just southeast of Palm Springs, and called Franz. As soon as he hung up the phone, Franz rushed off to pick McCandless up. “We went to a Sizzler, where I filled him up with steak and lobster,” Franz recalls, “and then we drove back to Salton City.” I do understand your question, though. I found it odd that McCandless would enjoy being around Franz, and it makes sense to think that McCandless might have wanted some space fro...

As with most novels, there are a lot of literary techniques at work in this story. I'll start you off by discussing just a few of the author's main strategies. First, the author, Amy Tan, employs symbolism to get her point across. In The Joy Luck Club, the book  The Twenty-Six Malignant Gates  discusses all the dangerous things that can happen to children. One could say this book symbolizes a mother's love and her desire to protect her children. It could also symbolize the ways in which mothers constantly worry about their children. Another symbol is the Joy Luck Club itself, which is a weekly meeting between women that symbolizes the importance of community and mutual support. Second, Tan draws heavily on allegory, which is similar to symbolism in that it uses one thing to represent another thing. Allegories are stories that are meant to be interpreted to reveal their hidden meanings. Tan provides several allegories throughout this novel to explain larger concepts. For ex...

Cellular respiration is generally broken down into 3 main stages: glycolysis, the citric acid cycle (Krebs cycle), and oxidative phosphorylation. Because of this, I will assume that by "stage two" you are referring to the Krebs cycle. The main purpose of the Krebs cycle is to create electron-carrying molecules, specifically NADH and FADH2. Each cycle produces 1 FADH2 and 3 NADH molecules. These molecules will leave the Krebs cycle and carry their electrons to the electron transport chain in oxidative phosphorylation which ultimately results in the production of ATP. The Krebs cycle starts with a molecule of acetyl-CoA and proceeds through 10 steps before ending up with acetyl-CoA again, making the process a cycle. Carbon dioxide is produced as a waste product and ends up being transferred to the blood stream and then exhaled through the lungs. The benefit from the Krebs cycle comes from the production of NADH and FADH2 because they provide the energy for producing ATP. 

Given, `y= 2/(1+4x^2)` and the point is `(x_0,y_0)= (1/2,1)` First we have to find equation of the tangent line  by using the following formula:   `y=f'(x_0)(x-x_0)+y_0` In our case `f'(x)=y'=(2/(1+4x^2))' = -16x/(1+4x^2)^2` `f'(1/2)=-16(1/2)/(1+4(1/2)^2)^2=-(16(1/2))/(1+1)^2=-2` By plugging that into the formula for equation of the tangent line we get `y=(-2)(x-1/2)+1` `y=-2x+1+1=2-2x` `y=2-2x` Now we can draw both graphs of the function and its tangent line Now we need to calculate the area of the region, but before that we need to find point of intersection of the two graphs. We can do that by solving the following equations: `y=2-2x` `y=2/(1+4x^2)` => `2-2x=2/(1+4x^2)` `1-x=1/(1+4x^2)` => `(1+4x^2)(1-x)=1` => `1+4x^2-x-4x^3=1` => `4x^2-x-4x^3=0` =>-`x(-4x+1+4x^2)=0` =>`-x(2x-1)^2=0` =>` x=0 or 2x-1=0` => `x=0 x=1/2` so the area is given as Area= `int_0^(1/2) ((2/(1+4x^2))-(2-2x))dx` =`int_0^(1/2) (2/(1+4x^2))dx-int_0^(1/2) (2-2x)dx` `=[ta...

A work of literature is considered "a classic" if it has lasted through the proverbial test of time; that is, if it has an appeal that is enduring and it speaks in a universal manner to the human condition. Enduring appeal Despite the time period in which it is written, a classic work of literature remains appealing because it delights and interests readers on several levels. For example, Mark Twain's  The Adventures of Huckleberry Finn— certainly a classic—holds the interest of young readers who delight in the various escapades in which Huck is involved, such as the defeat of his cruel Pa and others who attempt to harm him and Jim, as well as Huck's maturation. Similarly, adult readers delight in Huck and Jim's escapades for their humor, but they are also able to enjoy the satire of society in Twain's writing. Universality Classics speak to the human condition; that is, there are themes and characterization in classic literature that address the basic aspects...

The basic theory of market economics states that free competition between companies providing consumer goods will lead to better products at lower prices.  On a personal level, when I go to the store, I look at the items on sale, and I can either select the cheapest, or I can select a more expensive item, in which case I generally have some reason for that preference.  In other words, if I choose to buy a more expensive item, it will be because I think it's better. If there are only two or three companies producing a particular item, and they collude, agreeing to all charge a higher price than the minimum that would allow them to stay in business, then I will be forced to pay more for my purchase than if they were really competing.  And since I will see the illusion of competition, it will not occur to me to start my own company competing with them.  If there would only be one monopoly producer, and I have an idea that I could make money selling their product cheaper than they do, ...

To apply  Root test  on a series `sum a_n` , we determine the limit as: `lim_(n-gtoo) root(n)(|a_n|)= L` or  `lim_(n-gtoo) |a_n|^(1/n)= L ` Then, we follow the conditions: a) `Llt1` 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. In order to apply  Root Test  in determining the convergence or divergence of the  series  `sum_(n=1)^oo ((-3n)/(2n+1))^(3n)` , we let: `a_n =((-3n)/(2n+1))^(3n)` We set-up the limit as:  `lim_(n-gtoo) |((-3n)/(2n+1))^(3n)|^(1/n) =lim_(n-gtoo) (((3n)/(2n+1))^(3n))^(1/n)` . Note: `| - f(n)| = f(n)` . Apply the Law of Exponents: `(x^n)^m= x^(n*m)`. `lim_(n-gtoo) (((3n)/(2n+1))^(3n))^(1/n)=lim_(n-gtoo) ((3n)/(2n+1))^(3n*(1/n))`                                     `=lim_(n-gtoo) ((3n)/(2n+1))^((3n)/n)`                                     `=lim_(n-gtoo) ((3n)/(2n+1))^3` Apply the limit ...

Sulfur dioxide emissions cause environmental problems such as acid rain and the technology used to remove sulfur dioxide from the exhaust gas of fossil-fuel power plants is called desulfurization. There are several methods of removing sulphur dioxide from exhaust gases. The method which utilizes calcium hydroxide slurry to remove sulphur dioxide is called wet scrubbing and the main product of that reaction is calcium sulphite. Ca(OH)2 (solid) + SO2 (gas) → CaSO3 (solid) + H2O (liquid) Sulfur dioxide is an acid gas, so other alkaline sorbent slurries or materials such as calcium carbonate and magnesium hydroxide may also be used for wet scrubbing. A natural alkaline that may be used to absorb the sulphur dioxide is sea water. Apart from web scrubbing using an alkaline sorbent, sulphur dioxide can be removed by spray-dry scrubbing, wet sulphuric acid, or dry sorbent injection systems, among others.

In this context, reviewing the field means becoming familiar with the existing scholarship on a problem and summarizing or analyzing it before putting forth one's own ideas. The first reason for doing this has to do with beginning to think about your potential audience. Although as a student you write for professors who are paid to read your work whether they find it interesting or not, once you graduate, you are writing for people who have no obligation to read what you have to say. You will need to convince an audience that your work is worth reading.  Given that many sociologists have written about your general topic, there is no reason for someone to read your writing unless you can show that you are adding something original to the existing body of scholarship. If you have not read the existing scholarship, an idea that might strike you as interesting and original may already have been thoroughly discussed and either proven or disproven.  By reviewing existing scholarship, you...

In Act I, Scene V of William Shakespeare’s Romeo and Juliet , Romeo, his cousin Benvolio and his close friend Mercutio sneak into the Capulets' masquerade ball so that Romeo can observe the target of his unrequited affections, Rosaline, a member of the Capulet clan—the family with whom the Montagues maintain a protracted and deadly rivalry. Romeo is deeply in love with Rosaline, despite the fact that she pays him no attention and has vowed to remain chaste. So depressed is Romeo about his failed efforts at wooing Rosaline that he and the other two conspire to crash the Capulets’ ball despite the risks inherent in such an action. As audiences and readers of Shakespeare’s play know from the outset, the rivalry between the two clans is serious, and any encounter between partisans of the two families will invariably turn violent. Earlier, in Act I, Scene II, so lovesick is Romeo that his cousin Benvolio suggests that they sneak into the Capulets' ball so that Romeo can, by compari...

`int(x^2-5x+16)/((2x+1)(x-2)^2)dx2` Let's first express the integrand as sum of proper rational expressions by applying partial fraction decomposition, `(x^2-5x+16)/((2x+1)(x-2)^2)=A/(2x+1)+B/(x-2)+C/(x-2)^2` `=(A(x-2)^2+B(2x+1)(x-2)+C(2x+1))/((2x+1)(x-2)^2)` `=(A(x^2-4x+4)+B(2x^2-4x+x-2)+C(2x+1))/((2x+1)(x-2)^2)` `=(A(x^2-4x+4)+B(2x^2-3x-2)+C(2x+1))/((2x+1)(x-2)^2)` `=(x^2(A+2B)+x(-4A-3B+2C)+4A-2B+C)/((2x+1)(x-2)^2)` Now equate the coefficients of the polynomial in the numerator on the both sides, `A+2B=1` --------------------------------(1) `-4A-3B+2C=-5`  -----------------(2) `4A-2B+C=16`  ----------------------(3) Now let's solve the above three equations by the method of substitution, From equation 1 :`A=1-2B` Substitute the above value of A in equation 2 , `-4(1-2B)-3B+2C=-5` `-4+8B-3B+2C=-5` `5B+2C=-5+4` `5B+2C=-1`     ------------------------ (4) Now substitute the value of A in equation 3, `4(1-2B)-2B+C=16` `4-8B-2B+C=16` `4-10B+C=16` `-10B+C=16-4` `-10B+C=12`    -----...

Martin Luther became dissatisfied with aspects of the Catholic Church after becoming a monk.  He saw corruption and immoral lifestyle choices among leaders in the Catholic Church.  He disapproved of this.  Martin Luther began studying the Bible more closely.  Through his studies, his beliefs experienced a shift.  Martin Luther came to believe that salvation came through faith alone, rather than by following the teachings of the Catholic Church. In 1517, Martin Luther wrote his 95 Theses in protest of the Pope's approval of the sale of indulgences.  His 95 Theses mainly centered on indulgences.  The Pope needed to raise money, so indulgences were exchanged for alms.  Indulgences were purchased for forgiveness of sins.  It was unusual at this time for people to protest the Catholic Church, which was strong and dominant.  It was especially unusual for someone who had been a monk to protest.  Martin Luther's actions led to the beginning of the Protestant Reformation.

As of 2012, the Bill and Melinda Gates Foundation has been developing policies and intervention strategies to help the poorest women and men of developing nations gain needed access to contraceptives. Currently, "less than 20 percent of women in sub-Saharan Africa and 34 percent of women in South Asia" have access to contraceptives ( "Family Planning" ). Pregnancy complications and childbirth complications are primary causes of death in the poorest nations. Unwanted births can lead to such complications as well as to unhealthy abortions, making lack of access to contraceptives one of the most critical health disparities. In addition to being able to prevent maternal and infant deaths, many methods of contraceptive are also able to prevent the transmittance of HIV, another primary cause of death in the poorest nations. Currently, the price of quality contraceptives is too high, and there is a lack of funding and donors. Due to these problems, one of the intervention...

One example of personification in "The Lady, or the Tiger?" by Frank R. Stockton is the following: This vast amphitheater. . . was an agent of poetic justice, in which crime was punished, or virtue rewarded, by the decrees of an impartial and incorruptible chance. The amphitheater itself is described as a person who can exercise judgment and bring about justice, so an inanimate object is personified (that is, made into a living being). In this example, the amphitheater becomes the agent of justice, rather than the king, which suggests the king does not really accept responsibility for the terrible system of justice he established. Instead, the building itself, with its constantly changing doors containing a maiden on one side and a tiger on the other, becomes the instrument of justice. The personification in this story is a deliberate choice the author makes to emphasize the way in which the king absolves himself of blame for the barbaric system he has established.

"In the Contents of the Dead Man's Pockets" Tom Benecke has a revelation about the direction of his life and his misguided use of time. Early in the story, Tom is focused on advancing his career at the expense of his relationship with his wife and his enjoyment of leisure activities. He spent most of his non-working hours doing research on an idea for making the grocery industry more efficient. Instead of balancing his work life with his home life, he put his relationship with his wife on hold, promising her things would be better when his idea came to fruition. His life was out of balance. After his ordeal on the ledge, which represented a near death experience, Tom realized his transgression. As he hung on the ledge, he realized how insignificant his life was, and how important his wife was to him. Once off the ledge, he rushed off to be with his wife as she enjoyed a movie. This is symbolic of his new appreciation for life and relationships.

Sufism developed as an aesthetic movement in the 8th and 9th centuries in Iran, Iraq, Syria, and Egypt. Its adherents were committed to a life of poverty and to meditation. During the Seljuk Turk Dynasty, Sufis became organized into fraternities and built lodges, called khānaqāh , in Persian, that functioned as hospice centers for Sufi travelers and centers of meditation and retreat. These lodges were often located next to schools, called  madrasas , or mosques. The sultans who ruled during this era had taken over without religious legitimacy, and their connection to Sufism provided them with religious authority. Sufis, long connected with the community, were able to help the sultans gain legitimacy with the populations over which they ruled. Sufism, guided by the philosophy of Ibn al-Arabi (1165–1240), focused on the ethical dimensions of being what Ibn al-Arabi called a "perfect man." Sufis were tolerant of a range of religious practices, including wandering dervishes, and ...

Greek history, philosophy and mythology show that the Greek community appreciated certain values among their folks. These values can be traced back to the Platonic virtues by the notable Greek philosopher Plato. He observed that there were four predominant virtues that were essential for human and communal well-being and these include: Courage Wisdom Temperament Justice These four values were of primary focus to the General Greek society. Leaders and the society, in general, were expected to exercise some level of wisdom in decision making. Greek literature, such as the Iliad demonstrated the importance of discussions before decisions were made. Rash decisions were often questioned and could only be justified if evidence was produced that showed there was some level of reason and caution observed. Courage was necessary among the Greek community as seen through the depiction of Greek heroes such as Achilles, Perseus, and Odysseus, who showed no fear in the face of danger. The importance...

There are a number of clues that a chemical reaction has taken place. If any of them are observed, we can surmise that a chemical reaction has taken place. Some of these clues are: Production of gas: a number of chemical reactions result in the generation of gas (or gases). Thus, a visual observation of gas generation is a clue to a chemical reaction. Heat change: A number of chemical reactions either need energy for completion or generate energy upon completion. Thus, if the reaction container gets hot or cold, this change in temperature of the container is a clue that a reaction has taken place. Change in color: A number of chemical reactions are accompanied by a color change, which is another clue. Smell or odor: A number of chemical reactions result in compounds that produce a smell, which can be used as another clue. Precipitate formation: A number of chemical reactions produce precipitates. Thus, if we observe some precipitate formation and settling, we can be sure that a chemica...

Woman in Red The first ways the woman in red was involved in Eva's death was to act as her controller or "minder." She physically led Eva from the stage at the end of each act and, along with Michael, interposed herself, especially at the park, to keep Rich/Howell properly away from Eva so he couldn't change the scripted lines and thus the outcome of the play. The three most critical ways the lady in red was involved in Eva's death occur in the third and fourth acts. At the close of Act III, the lady in red (let's call her Red) delivers the line that seeds the ultimate conclusion of the play, seen in Act IV. During Act IV, after the other Howell actor has torn and burned the letter from Michael, after Eva quietly weeps in relief, after Red enters and suggests Michael's departure from England is a ruse, and after Howell takes a phone call, making a movement that startles Eva so that she spills her tea as she is about to sip it, Red makes a "scandalized...

One of the main themes in this story is gratitude. The narrator is indebted to her mother for her life. She is grateful that her mother (Anna) has even made her life possible. This is why the narrator says "I owe her my existence three times." First, Anna saved her own life during a trapeze accident. Although Anna lost her first baby in childbirth following this accident, saving her own life allowed her to live on and eventually give birth to the narrator. The narrator is thankful a second time because Anna met her second husband during her hospital stay.  The "leap," first of all, refers to the actual leap the narrator's mother makes in saving her life during the house fire. This is the third time the narrator owes Anna her existence. To repay her mother for giving her life and/or saving her life, the narrator returns to take care of Anna. Anna's husband (narrator's father) has died and Anna has become blind. Anna loved to read. The narrator pledges to ...

Act II provides a clear delineation of the three characters. It is in this act that we learn what sets the three apart. The act also provides insight into how exactly Othello and Cassio, specifically, become targets for Iago's manipulation. We discover in scene one that Cassio, Othello's newly-appointed lieutenant, has recently set foot on Cyprus and is now, with some trepidation, awaiting the arrival of his master and his beautiful, newly-wed bride, Desdemona. Cassio expresses concern since he had lost contact with the general's ship during an inordinately rough period at sea. He is generous in his praise for Othello and seems genuinely concerned. He has only high praise for Desdemona and is full of complimentary rhetoric when asked about her. It is clear from his conversation that he has an open and generous nature, one who seems to see only the good in others. We soon discover this naivete is what Iago sees as a weakness which he can exploit. Next to arrive on the scene ...

Helen Keller's life was a remarkable one. Her life illustrates the quote, "I came, I saw, I conquered." She came into the world as a healthy child. When she was still a baby, she contracted an illness that left her blind, deaf, and mute. She nearly died from the illness, but slowly recovered, except for the loss of the senses mentioned above. Her family tried everything available to them in order to find a way to help Helen learn. Eventually, her mother pleaded with her father to give permission for them to hire a private teacher from a school in the north, who, hopefully, could help Helen to learn. Annie Sullivan, who was visually impaired herself, was hired to come and live with the Kellers and teach Helen. Annie worked with Helen and eventually devised a learning plan, in which, through the method of touch, Helen was able to learn to communicate. That's when the "saw" part of the quote began to happen.  As Helen continued to progress and learn more and mo...

The main word and concept you need to know is “daffodils.” You should know what these vivid, yellow flowers of spring look like, and how overwhelming it would be to see a field of 10,000 of them. You should know what they look like when a light wind blows over them, causing them to flutter, dance, and toss their heads, as Wordsworth aptly describes. I’ve placed a few links below that include some daffodil photographs. Five additional important words may be unfamiliar to contemporary readers, at least in the manner the poet used them. From the first verse: “vales” are valleys. From the third verse: “gay” is used to mean “happy,” “lively,” “merry,” or “joyous.”  “Jocund” means “pleasant” or “agreeable.” The viewer of the daffodils can’t be anything but happy and joyous at the sight of the field full of flowers. From the fourth verse: “vacant” here means “empty of thought,” or “listless.” Alternatively, “pensive” means “deep in thought.” From now on, no matter which mood the narrator is i...

In the traditional meaning of democracy, all members of a group contribute to the decision making process, typically through voting. In fact, the term "democracy" comes from the Greek  demokratia,  meaning "people's rule." In reality, there have been very few true democracies due to the difficulties of implementing this form of government on such a large scale. In Ancient Greece, where democracy originated, the only real acting members of a democracy were adult males of wealth. Children, for obvious reasons, were not allowed to vote, but neither were women or slaves. In more modern times, democracies exist based on the agreement that all persons, regardless of gender, class, bodily ability, or ethnicity, are given the right to vote. In the United States, this is the understanding, but it's much more complicated in implementation! Imagine if a group of one hundred people broke up into groups of ten and each elected an individual to vote in a committee of the ...

In Brave New World and in 1984 , as well, there are senseless rituals performed in which people participate mindlessly, just as they do in "The Lottery." Such rituals are used by these dystopian societies to exert mental control over the population and to emotionally engineer the people by directing them in venting innate sadistic tendencies as well as releasing primal unthinking urges. By means of these rituals, hostility is released in a controlled situation, and other urges such as individual expression are subdued. The Solidarity Service  In  Brave New World, the artificial atmosphere of the Solidarity Service is controlled through ritualistic activities that are something like an emotional religious revival. Everyone participates in the orgy-porgy,  a mockery of the communion service as they take the hallucinogenic soma and then engage in communal sexual acts. Afterwards, the participants feel "fused into the Greater Being." Most of the participants feel that ...

Ozone is a molecule made of three oxygen atoms. It is present in the upper atmosphere of Earth and protects us from the harmful ultraviolet radiations of the Sun. It was observed a few decades ago that the thickness of this friendly ozone layer is decreasing, especially over Antarctica. There are a couple of causes of this depletion of the ozone layer. Natural causes, such as stratospheric winds, can cause this depletion. However, this is a very minor cause.  The most significant reason for depletion of the ozone layer are certain chemicals that humans use, which are termed as ozone-depleting substances. Prominent among these is a class of chemicals known as CFCs or chloro-fluoro carbons. These chemicals were commonly used as refrigerants in air conditioners and refrigerators, in dry-cleaning agents, etc. These chemicals have since been banned. Some of the other man-made chemicals that are responsible for ozone depletion include carbon tetrachloride, halons, methyl chloroform, etc.  Ho...

Darkness is a recurring motif as well as a symbol found in Chapter 12 of Gary D. Schmidt's novel Trouble . Darkness fills the chapter from the start, as hitchhikers Henry, Sanborn, and Black Dog are finally picked up in the deepening twilight by a truck driven by Chay. As Chay drives on, the narrator notes that there are "[n]o stars in the sky yet. No moon" (p. 156). When they reach Portland, Maine, the narrator also notes that the water of Casco Bay "shone black obsidian" (p. 159). All of this darkness serves to symbolize trouble and grief both Henry and Chay are suffering from. The meaning of the symbol becomes clear as Henry and Chay enter into a heated conversation in the truck. At one point Henry tells Chay he "can't imagine" what Henry's mother sounds like as she grieves over Franklin's loss each night since his death (p. 156). However, Chay surprises Henry by giving the following response: She sounds like all she wants is to ...

First of all, we have to recognize that there are many people who would say that we do not need an equal rights amendment to the Constitution.  Some of these are conservatives who believe that women already have enough rights or that we should be careful about giving women equal rights because it would lead to women being drafted into the military or men being allowed in women’s bathrooms.  Others are not necessarily conservative but they believe that the problems that women face today are not really because of legal discrimination and would not be solved by an equal rights amendment.  For example, women tend to make less money than men today, but that is largely not because of any conscious discrimination.  Instead, women tend to cluster in poorly-paid jobs and women in good jobs often do not climb as high because they have to take time off to raise children.  An equal rights amendment would not solve either of these problems.  For these reasons, there are many people who would disagr...

Emily Dickinson's poem, "Because I could not stop for Death," describes how death comes for us whether we are ready or not. In this poem, the speaker discusses how unprepared she was for death and how she wasn't even thinking about it, when it came upon her. The last stanza when the speaker says that "tis Centuries--and yet Feels shorter than the day I First surmised the Horses' Heads Were toward Eternity," addresses how quickly time goes by without people realizing it. For this speaker, who is picked up in a carriage by a personified Death, she recognizes that while it may seem like centuries since Death came for her, it felt shorter than a single day. By mentioning time in the final stanza, the author emphasizes the importance of realizing that life is short and before one knows it, he or she could be headed toward eternity (or death). Sometimes people may not even realize it, like the speaker in this poem.

Separation of powers is not a concept that is discussed in the Preamble to the Declaration, (or elsewhere in the document.) Generally, the Declaration is an assertion of principles and a list of grievances against King George. Their focus is on the alleged abuses they have suffered as British subjects, not how government might be structured in such a way as to avoid these abuses. Their complaints were related to the imperial relationship between the colonies and the Crown and Parliament. They argued that the King (after spending years arguing against the usurpations of Parliament) had violated their rights as Englishmen. The idea of separation of powers was well-established in the Anglo-American world--the famous French philosopher Montesquieu had based his defense of the concept on the English constitution--but Jefferson and the authors of the Declaration did not assert it as a principle in the Preamble or elsewhere. To see what late eighteenth-century Americans thought about the impo...

One characteristic of Romanticism is that, since Romantic thinkers placed great value on the individual self, they also exalted the deeds performed by the social outcasts , those who were misjudged by society. In To Kill a Mockingbird , we particularly see Harper Lee employ this Romantic characteristic when she promotes the actions of Arthur (Boo) Radley .   The Radleys are considered social outcasts of Maycomb because they keep to themselves, never attend church, and keep their doors and windows shut on Sundays. Arthur is especially treated as an outcast because he never leaves his house. Since he never leaves his house, the townspeople have developed all kinds of rumors and myths about him that lead children to feel afraid of him. As the story progresses, however, Arthur is revealed to be a  caring and benevolent person and one of the novel's major heroes. Arthur demonstrates his caring and benevolent nature by leaving the children gifts, sewing Jem's torn trousers, an...

First, let me list down the given information: Si-28, 27.9769 amu, 92.20% Si-29, 28.9765 amu, 4.67%  Si has an atomic weight of 28.0855 amu (while this is not given, the information should be readily available in the periodic table. this is a crucial bit of information as you will see in the solution below.) The problem mentions that there are three isotopes. Hence, Si-28, Si-29, and Si-30 are all the isotopes of silicon and should make up 100% of the silicon in the world. This allows us to calculate the abundance of Si-30 - the sum of abundance of all isotopes should be 100%: Abundance of Si-30 = 100 - 92.2 - 4.67 = 3.13 Hence, 3.13% of all silicon reserves is silicon-30. The atomic weight of an element (listed in a reference such as the periodic table) is they weighted average of the masses of its isotopes. Hence, 28.0855 amu, the atomic weight of silicon, is a weighted average of the individual masses of its isotopes - that is, the mass multiplied by its abundance. Hence (let m be a...

Given to solve, `int sec^6 (4x)tan(4x) dx` let `u = 4x , du = 4dx` so, `int sec^6 (4x)tan(4x) dx` =` int sec^6 (u)tan(u) (du)/4` =` (1/4) int sec^6 (u)tan(u) du` let `secu = v` so, `dv = (sec u)(tan u) du` so , `(1/4) int sec^6 (u)tan(u) du` = `(1/4) int sec^5 (u) tan(u) *sec(u) du` =`(1/4) int (v)^5 dv` = `(1/4) v^6/6` =` (v^6)/24` = `((sec (u) )^6)/24` =`((sec (4x) )^6)/24 +c`

Progressivism in the United States was a movement based on the philosophy that progress in science, technology, economics, social organization, and politics is necessary for improving the human condition. The Progressive Era in America reached its height from the 1890s to World War 1 and continued until the onset of the Great Depression. The impulses driving the Progressive movement can be seen as emerging from the desire for a Utopian society, which resulted in various Utopian communities being established in the United States throughout the 19th century. Progressivism reshaped American life, especially in the areas of social class and business. Michael E. McGerr in A Fierce Discontent argues that the wide range of progressive impulses all revolved around the issue of class. He sees Progressivism as the American middle class’ response to extreme income inequality and the excesses of the industrial upper class. Increased regulation of business and the presidencies of Theodore Roosevel...

This is an interesting limit. Lets define a variable y as: `y=lim_(x->oo) (1+1/x)^(x+1/x)` Lets take the logarithm of both sides. `ln(y)=lim_(x->oo) ln[(1+1/x)^(x+1/x)]` `ln(y)=lim_(x->oo) (x+1/x) ln(1+1/x)` Now I am going to make a quick substitution in the logarithm on the right hand side. `u=1/x` `ln(y)=lim_(x->oo) (x+1/x) ln(1+u)` Now I will use a common taylor expansion, `ln(1+u)=sum_(n=0)^oo (-1)^(n-1)*(u^n)/n=u-1/2u^2+1/3u^3-...` `ln(y)=lim_(x->oo) (x+1/x) ln(1+u)` `ln(y)=lim_(x->oo) (x+1/x) (u-1/2u^2+1/3u^3-...)` Back substitute in to get in terms of x. `ln(y)=lim_(x->oo) (x+1/x) (1/x-1/(2x^2)+1/(3x^3)-...)` `ln(y)=lim_(x->oo) [x (1/x-1/(2x^2)+1/(3x^3)-...)+1/x(1/x-1/(2x^2)+1/(3x^3)-...)]` `ln(y)=lim_(x->oo) [(1-1/(2x)+1/(3x^2)-...)+(1/x^2-1/(2x^3)+1/(3x^4)-...)]` Now take the limit, every term that has an x in the denominator will go to zero leaving just one term. `ln(y)=1` Give both sides a new base e `e^ln(y)=e^1` `y=e` Remember our original defini...

Given to solve, `int sin^3 (2 theta) sqrt(cos(2 theta)) d(theta)` let `x= theta` (just for convinence) so, `int sin^3 (2 theta) sqrt(cos(2 theta)) d(theta)` =`int sin^3 (2x) sqrt(cos(2x)) dx` let `2x= u` so , `du = 2dx` then , `int sin^3 (2x) sqrt(cos(2x)) dx` =`int sin^3 (u) sqrt(cos(u)) (du)/2` =`(1/2)int sin^2 (u) sin u sqrt(cos(u)) du` = `(1/2)int (1-cos^2 (u)) sin u sqrt(cos(u)) du` let `cos u =t, so , dt = -sin(u) du` then, `(1/2)int (1-cos^2 (u)) sin u sqrt(cos(u)) du` = `(1/2)int (1-t^2) sqrt(t) sin u du` =`(1/2)int (1-t^2) sqrt(t) (-dt)` = `(-1/2)int (1-t^2) sqrt(t) (dt)` = `(-1/2) int (t^(1/2) - t^(5/2))dt` = `(-1/2) [(t^(3/2))/(3/2) - t^((5/2)+1)/((5/2)+1)]` = `(-1/2) [(t^(3/2))/(3/2) - (t^(7/2))/(7/2)]` but `t= cos u = cos(2x)` so, = `(-1/2) [((cos(2x))^(3/2))/(3/2) - ((cos(2x))^(7/2))/(7/2)]` = `(1/2)[((cos(2x))^(7/2))/(7/2) -((cos(2x))^(3/2))/(3/2)]` but `x= theta,` so = `(1/2)[((cos(2(theta)))^(7/2))/(7/2) -((cos(2(theta)))^(3/2))/(3/2)]` so, `int sin^3 (2 theta) sqrt(co...

One theme of Act IV is deception, the idea that appearances can be deceiving. In scene 1, the Weird Sisters seem to offer Macbeth some assurance that he will be safe indefinitely because they tell him that "none of woman born / Shall harm [him]" and, further, that "Macbeth shall never vanquished be until / Great Birnam Wood to high Dunsinane Hill / Shall come against him."  However, rather than assurances of safety, these are really just confusingly and mysteriously-worded statements of fact. The Sisters intend to deceive Macbeth in order to make him feel "secure," as Hecate previously said, and thus he will become overconfident and careless.  In scene 3, Malcolm purposely portrays himself as the most excessive, morally perverted contender for the throne in order to test Macduff's honesty.  He fears that Macbeth has sent Macduff to lure him home so that Macbeth can kill him.  As long as Macduff continues to protest and assure Malcolm that he is still a...

In Chapter 19, Daniel and a group of boys attempt to free Joel from a passing Roman caravan. Unfortunately, the boys are no match for the experienced Roman soldiers. At the beginning of the raid, Samson follows the group and rolls a massive boulder down into the valley, successfully breaking up the Roman forces. Daniel then attacks and overpowers a Roman soldier in order to reach Joel. While Daniel is freeing Joel, he is lifted from the ground and thrown against a rock. Daniel gets knocked out and wakes up to learn Samson saved his life. Daniel learns Samson threw him onto the rock and then freed Joel with his bare hands. Unfortunately, Samson is critically wounded by a spear and taken prisoner by the Romans. Kemuel then tells Daniel that Samson will not live to see the galleys.

Diversity Case Study One:  Culture Shock Warren Oats was a highly successful executive for American Auto Suppliers, a Chicago-based company that makes original-equipment specialty parts for Ford, GM, and Chrysler. Rather than retreat before the onslaught of Japanese automakers, AAS decided to counterattack and use its reputation for quality and dependability to win over customers in Japan. Oats had started in the company as an engineer and worked his way up to become one of a handful of senior managers who had a shot at the next open vice-presidential position. He knew he needed to distinguish himself somehow, so when he was given a chance to lead the AAS attack on the Japanese market, he jumped at it.  Oats knew he did not have time to learn Japanese, but he had heard that many Japanese executives speak English, and the company would hire a translator anyway. The toughest part about leaving the United States was persuading his wife, Carol, to take an eighteen-month leave from her...

The epicenter receives the highest intensity of the earthquake because it lies directly above the point of focus or the hypocenter of the earthquake. However, this might not always be the case when the magnitude of the earthquake is very high. The magnitude and other geological factors will force the impact to spread around and greatly affect areas further away from the epicenter. The areas further away might be affected more than the epicenter. Thus, an explosion at the hypocenter will generate vibrating waves that may travel directly to the epicenter and cause much damage in that area or travel in all directions and reach different parts of the earth. The epicenter can be termed as the most dangerous area during an earthquake. However, the situation may change depending on the magnitude and other geological conditions.

`sum_(n=0)^oo (-1)^n(x^n)/(n+1)` To find the radius of convergence of a series `sum` `a_n` , apply the Ratio Test. `L = lim_(n->oo) |a_(n+1)/a_n|` `L=lim_(n->oo) |((-1)^(n+1) x^(n+1)/((n+1)+1))/((-1)^n(x^n)/(n+1))|` `L=lim_(n->oo) | (-1) * (x^(n+1)/(n+2))/(x^n/(n+1))|` `L=lim_(n->oo) | (x^(n+1)/(n+2))/(x^n/(n+1))|` `L= lim_(n->oo) |x^(n+1)/(n+2) * (n+1)/x^n|` `L=lim_(n->oo) |(x(n+1))/(n+2)|` `L = |x| lim_(n->oo) |(n+1)/(n+2)|` `L=|x| * 1` `L=|x|` Take note that in Ratio Test, the series converges when L <1. `Llt1` `|x|lt1` By Ratio Test, the series converges when |x|<1. Therefore, the radius of convergence of the given series is `R=1` .

We learn that Margot, the protagonist, has not adjusted well to living on Venus, a planet where it almost never stops raining. Unlike the other children, who have been on Venus all their lives and don't recall the last time the sun came out (they would have been only two), she vividly remembers sunshine. She misses it and has begun to deteriorate so badly that her parents are considering returning to Earth. For example, one day Margot refuses to take a shower at the school, screaming that the water mustn't touch her head. She also stays aloof from the other children, not joining in their games.  When the hour of sunshine comes after seven years of rain, the other children lock Margot in a windowless closet and forget about her while they play outside. When they remember her, the rain has begun again. They return to the closet. She had been screaming and banging on the door earlier, but now they hear only silence. They let her out, and while we as readers don't know how she ...

Within the time period of the setting, the reader is given to understand that Mrs. Mallard, who does love her husband, has been repressed under the feme covert laws of the time, and is relieved to be "free" from her subservient social position after learning of Mr. Mallard's purported death. When Mrs. Mallard, who is "afflicted with a heart trouble," is told gently of her husband's death, she weeps with "wild abandonment," an indication that she does love the man . Then, she ascends to her room alone where she collapses into a comfortable armchair that faces a window. As Mrs. Mallard gazes out this window, which has apparently been her habit, she notices "the delicious breath of rain" and the "new spring life," both suggestive of a rebirth and hope. A young woman, whose face has lines that "bespoke repression," she begins to realize that a change is coming. At last she "abandoned herself" to this realizatio...

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 ln(n)/n^3` ,  `a_n =ln(n)/n^3` . Then applying `a_n=f(x)` , we consider: `f(x) =ln(x)/x^3` The graph of f(x) is: As shown on the graph, f is positive on the infinite interval `[1,oo)` . To verify of the function will eventually decreases on the given interval, we may consider the derivative of the function. Apply Quotient rule for the derivative:` d/dx(u/v) = (u'* v- v'*u)/v^2` . Let `u = ln(x)` then `u' = 1/x`       `v = x^3` then `v' = 3x^2` Applying the formula,we get: `f'(x) = (1/x*x^3- 3x^2*ln(x))/(x^3)^2`            `= (x^2-3x^2ln(x))/x^6`            `=(1-3ln(x))/x^4` Note that `1-3ln(x) lt0` for larger values of x whic...

Most of the characters in Murder on the Orient Express affect the conflict because they keep secrets about their true identity and play important parts in Ratchett’s murder. There are two notable exceptions: Monsieur Bouc, director of Compagnie Wagon Lits, is a former colleague of Hercule Poirot’s and brings him into the case immediately. The other is Dr. Constantine, the coroner who helps in the investigation. The rest all tell a series of lies in order to cover their guilt. Slowly Poirot catches them by realizing the smallest inconsistencies in their stories. Everything centers around the kidnapping and murder of young Daisy Armstrong. The major conflict involves the question of who killed Ratchett, the man who was responsible for her death and got away with it. Each character confuses the issue in order to fool Poirot. For example, Mrs. Hubbard is really Daisy’s grandmother; she makes up a story about a man in her cabin. Mary Debenham had been Daisy’s governess. Princess Dragomirof...

The Ptolemic Model of the planets relied on the notion that the planets' movements were determined by two different spheres: the deferent and the epicycle .  The deferent is just the sphere whose center point, called the eccentric , is an imaginary point offset a little from earth. The planets each have their own deferent, and revolve about it.  Of course, this alone would not be enough to fully explain the seeming motion of the planets. So the epicycle was posited, which was a second sphere that the planet moved around. Or, more accurately, the epicycle revolved around the deferent, and the planet itself revolved around the epicycle.  If that's confusing, then it is probably most easily understood by linking each term with its analogous counterpart in the modern model: The eccentric is the sun, and is the point about which all else revolves. The deferent  is earth's orbit around the sun. It is not an object in itself, just a path the planet follows. The epicycle is th...

To find examples of Miss Strangeworth being evil, look towards the end of the story when she is composing her next round of poison pen letters. Miss Strangeworth shows her darker side, for instance, by writing a letter to Mrs Crane which refers to their "idiot baby." Similarly, she also composes a letter to Mrs Harper in which she hints that Mr Harper is having an affair:  "Is the wife really always the last one to know?" These two examples are particularly evil because earlier in the story, Miss Strangeworth meets Mrs Crane and Mrs Harper in town and acts friendly and sympathetic towards them. Finally, Miss Strangeworth composes another letter, this time to Mrs Foster who is due to have an operation. In the letter, Strangeworth suggests that doctors routinely make mistakes and that her nephew might encourage the doctor to do so:  "Would Dr. Burns get his fee and a little extra from that nephew of yours?" 

In February of Gary Schmidt's The Wednesday Wars , Holling takes Meryl Lee Kowalski out on a date for Valentine's Day. Meryl Lee's father is the owner of Kowalski and Associates, the architecture firm Mr. Hoodhood is competing against for the contract to build the new junior high school. During the date, while sipping Cokes at Woolworth's, waiting for Meryl Lee's father to pick them up, Holling and Meryl Lee enter a candid conversation about their fathers' work on designs for the new school. Holling feels so comfortable with Meryl Lee that he actually draws out his father's design for her on his place mat. When her father arrives, Meryl Lee takes the "placemat as a souvenir." Soon after Meryl Lee takes the place mat, Holling has reason to suspect her of foul play. It's during this same month that Mrs. Baker assigns Holling to read Romeo and Juliet on Wednesdays. Because of his experience with Meryl Lee, Holling at first sees the play as a l...

Indefinite integral are written in the form of `int f(x) dx = F(x) +C`  where: `f(x)` as the integrand            `F(x)` as the anti-derivative function             `C`  as the arbitrary constant known as constant of integration To evaluate the given integral problem: `int 1/(t(1+(ln(t))^2)) dt` , we may apply u-substitution by letting: `u =ln(t)` then `du = 1/t dt` . Plug-in `u =ln(t)` and `du= 1/tdt` on `int 1/(t(1+(ln(t))^2)) dt` , the integral becomes: `int 1/(t(1+(ln(t))^2)) dt =int1/(1+(ln(t))^2) *1/t dt`                                    `=int1/(1+u^2) du` From the integration table, we have indefinite integration formula for rational function as: `int 1/(1+x^2) dx=arctan(x) +C` . The `int 1/(1+x^2)dx ` resembles the format of `int 1/(1+u^2) du ` where  " u" corresponds to "x" .  This is our clue that we may apply the aforementioned formula for rational function. We get: `int1/(1+u^2) du= arctan(u) +C` .  Plug-in `u =ln(t)` on `arctan(u) +C` , we get the ind...

Two old men named Mat and Chimley are out fishing when they are told about Mathu and what Candy wants them to do. After they consider the situation, they decide to help. Mat and Chimley, two men in their seventies, are fishing on a favorite bank when a young boy rushes up to them and tells them that Clatoo says that Miss Merle has told him to tell the two older men that Miss Candy Marshall wants them "on the place" right away. She wants them to bring twelve-gauge shotguns and to have some empty number five shells and get to the quarter right away. When the two old men ask what all this is about, the boy replies that it has something to do with Mathu, as well as something to do with Beau Boutan, who is dead in Mathu's yard.  After the boy departs, the two old friends sit where they are, and they ponder the situation, wondering what would happen to them if they were in the position of Mathu. The two men do not look at each other, for they are deep in their own thoughts of w...