Notes

There was unrest in the Thirteen Colonies for many years before the Revolutionary War.  New taxes, such as the Sugar Act and the Stamp Act, were considered unfair.  The Colonists were not represented in Parliament, and because of this they had no one to speak on their behalf.  The Townshend Revenue Act of 1967 taxed tea and other common commodities.  All of the taxes were eventually repealed except for the one on tea.  Protests in Boston led to British troops occupying the city.  The unrest continued, and led to the Boston Massacre. The Tea Act was made to benefit the East India Company, which was having financial difficulties.  They had an overstock of tea, which was to be sold cheaply in Boston.  Concern that this would have a negative impact on local merchants combined with the unrest led to the Boston Tea Party.  Tea from ships in the Boston Harbor were thrown into the water in protest.   Troops were quartered in private homes and buildings, which led to further dissatisfaction wit...

In the forest primeval, Young Goodman Brown suffers a fall from innocence that is not unlike that of Adam. When Brown ventures into the forest in order to test his faith, he loses this faith after witnessing the black mass and seeing his wife Faith there. As the pink ribbons of his once innocent wife "flutter lightly down through the air," Goodman cries, "My Faith is gone!" and he learns the terrible significance of this loss. Goodman Brown experiences such a dramatic change in his character because he is initially so confident in his faith. But, this faith is challenged as one by one the seemingly saintly members of his community demonstrate that they are in league with the devil. For instance, when Brown happens upon Goody Cloyse, who has taught him his catechism and who he recognizes as "a very pious and exemplary dame," he is surprised to see her in the forest. Then, he is shocked when this "pious old lady" notices the traveler "put fort...

`int1/(4+4x^2+x^4)dx` Let's rewrite the integrand as : `=int1/((x^2)^2+2(2)(x^2)+2^2)dx` `=int1/(x^2+2)^2dx` Apply integral substitution:`x=sqrt(2)tan(u),u=arctan(x/sqrt(2))` `dx=sqrt(2)sec^2(u)du` `=int(sqrt(2)sec^2(u))/((sqrt(2)tan(u))^2+2)^2du` `=int(sqrt(2)sec^2(u))/(2tan^2(u)+2)^2du` `=int(sqrt(2)sec^2(u))/(2^2(tan^2(u)+1)^2)du` Take the constant out, `=sqrt(2)/2^2int(sec^2(u))/(tan^2(u)+1)^2du` Use the identity:`1+tan^2(x)=sec^2(x)` `=sqrt(2)/4int(sec^2(u))/(sec^2(u))^2du` `=sqrt(2)/4int1/(sec^2(u))du` `=sqrt(2)/4intcos^2(u)du` Use the trigonometric identity:`cos^2(x)=(1+cos(2x))/2` `=sqrt(2)/4int1/2(1+cos(2u))du` Take the constant out, `=sqrt(2)/8int(1+cos(2u))du` Apply the sum rule, `=sqrt(2)/8{int1du+intcos(2u)du}` Apply the common integral:`intcos(x)dx=sin(x)` `=sqrt(2)/8{u+1/2sin(2u)}` Substitute back `u=arctan(x/sqrt(2))` `=sqrt(2)/8{arctan(x/sqrt(2))+1/2sin(2arctan(x/sqrt(2)))}` `=sqrt(2)/8{arctan(x/sqrt(2))+1/2(2sin(arctan(x/sqrt(2)))cos(arctan(x/sqrt(2))))}` `=sqrt(2...

Poe actually never has Montresor state the specific reasons behind his wanting revenge, though he hints at several possibilities. Although he does mention injuries and insults, he never reveals details. First, Montresor seems vindictive and almost paranoid. It could well be that the wrongs for which he is obtaining revenge never actually happened and are products of Montresor's imagination.  Another possibility is that Montresor comes from a wealthy family now on hard times. He may blame Fortunato for the change in his family's fortunes or may simply resent Fortunato for being a nouveau riche . Both men are wine connoisseurs and possibly merchants. There appears to be some rivalry concerning expertise in wines, or perhaps there was some sort of commercial rivalry in the past. Part of the point of of this vagueness is to convey the idea that the desire for vengeance has become so overwhelming that the original cause no longer matters; instead, the vengeance and its planning have...

The main problem confronting France in the late eighteenth century (at least as regards taxation) was that the first two estates--the clergy and the nobility, respectively--were not really taxed at all. The complex network of privileges that undergirded Bourbon society placed the tax burden most heavily on the Third Estate. This presented a major problem as the French Crown faced a severe fiscal crisis in the wake of its participation in the wars of the American Revolution. Louis XVI attempted, through his ministers, to secure at least moderate tax reforms, but the nobles, who had control of the French courts, blocked these measures. By the time Louis XVI called the Estates General to address the crisis, his kingdom was basically insolvent as a result of the unbalanced tax system. As to how this system affected the people of each of the orders, ordinary Frenchmen found the gabelle , a tax on salt, to be particularly odious. The bourgeoisie, a growing class of merchants and professional...

Human Papillomavirus, or HPV, is a common sexually transmitted disease. The infection caused by the virus is responsible for two illnesses: genital warts, and various types of cancer, including cervical cancer. There are over 120 strains of Human Papillomavirus. All of these strains are similar: they are all sexually transmitted and cause genital infection. Strains that cause genital warts but not cancer are considered low-risk, while strains that cause cervical cancer are considered high-risk. Certain strains are more likely to cause infections that lead to cervical cancer. The HPV strains linked to cervical cancer are HPV 16 and HPV 18. These two strains are responsible for 70% of cervical cancer caused by HPV infections. At this time, these two strains are the known HPV strains that cause cervical cancer, but medical research may reveal others in the future.

Despite using distances that are big, this question is using a basic equation.  Speed = Distance/Time.  That equation can be reordered to read Time = Distance/Speed.   The distance in this case is 34 astronomical units.  I'll leave it in that unit.  Converting to miles or kilometers will make these numbers huge.  The speed of light is 300,000,000 m/s.  It is going to work best to convert the speed of light into astronomical units per second.  That number is 0.00200399 AU/sec. We can now use the initial equation.   Time = Distance/Speed Time = 34 / 0.00200399 Time = 16966.1525257 seconds Let's round that to 16,966 seconds.  Divide by 60 to get minutes.   That's about 282.767 minutes.  Divide by 60 again to get hours.     That's roughly 4.713 hours. In hours, minutes, and seconds, that comes out to be 4 hours, 42 minutes, and 46 seconds.   

The center of mass is the unique point at the center of a distribution of mass in space. It has the property that the weighted position vectors relative to this point sum to zero.  It is given by; Center of mass  `= [sum_(i=1)^nm_ixxx_i]/(sum_(i=1)^nm_i)` We have 5 point masses here. Center of mass `=[sum_(i=1)^5m_ixxx_i]/[sum_(i=1)^5m_i]` `= (8xx(-2)+5xx6+5xx0+12xx3+2xx(-5))/(8+5+5+12+2)` `= (-16+30+0+36-10)/(32)` `= 40/32` `= 5/4` `= 1.25` So the center of mass of the point masses lying on the x-axis is 5/4 or 1.25  

Sal tells us this story at the end of the first chapter, called “A Face at the Window.” She says that when they lived in the old farmhouse, her parents were taking the time to restore it. This explains why her father was “chipping away” at the plaster wall in the living room, at first. When he got the news that his wife (Sal’s mother) was not coming back to Kentucky, “he pounded and pounded on that wall with a chisel and a hammer,” Sal says. This time, he was probably taking out his anger, frustration, and grief on the wall. He uncovered a brick fireplace hiding behind it, too. This quick vignette foreshadows the truth unspoken throughout most of the book—the mystery of what happened to Sal’s mother. Here, Sal also uses it as a metaphor in the telling of her own story: The reason that Phoebe’s story reminds me of that plaster wall and the hidden fireplace is that beneath Phoebe’s story was another one. Mine.

Before Mrs. Sappleton arrived to greet the visitor, Vera had prepared Framton Nuttle to believe that her aunt was insane. "Poor aunt always thinks that they will come back someday, they and the little brown spaniel that was lost with them, and walk in at that window just as they used to do....Do you know, sometimes on still, quiet evenings like this, I almost get a creepy feeling that they will all walk in through that window - " Naturally her aunt expects the three hunters to come back, since they have only been gone for their day's shooting. But Nuttle believes they have been gone for three full years and that Mrs. Sappleton lost her mind three years ago as a result of that tragic occurrence. He turns to give Vera a look of understanding and compassion because he is sure that her aunt must be having another hallucination when she appears to be seeing all three men returning for tea. Evidently she has been imagining them returning every evening for these three years and...

This problem is much more difficult. Let's try to solve it. First, assume temporarily that two "i" letters are different, call them i_1 and i_2. Also call three "a" as a_1, a_2 and a_3, and two h as h_1 and h_2. Then there are 11*10*9*8*7 = 55440 possible "words" (the first letter is any of 11, the second is any of 10 and so on). But because equal letters actually make the same "words", some "words" was counted twice or more times. We have to subtract the number of "parasitic" counts although it is relatively small. The words that counted more than once are divided into several disjoint sets: 1) with two i's but without repetitions of a and h; 2) with two h's but without repetitions of a and i; 3) with two a's but without repetitions of i and h; 4) with three a's but without repetitions of i and h; 5) with two i's and two a's; 6) with two i's and tree a's; 7) with two i's and two h's...

At the beginning of the novel, Bud recalls a conversation he had with his mother about his name. She would remind him that his name was Bud and that he should never let anyone call him Buddy. She told him that Buddy was a dog's name and that when people call him Buddy they are being "false-friendly." She then told him that a bud is a "flower-to-be" that is waiting for the right love and warmth to unfold. Throughout the novel, Bud refuses to allow people to call him Buddy and develops friendships with various caring individuals. Eventually, Bud travels to Grand Rapids, where he meets his grandfather, Herman Calloway. The Dusky Devastators of the Depression take Bud into their group, and he becomes a part of their family. Bud fulfills the meaning of his name by finding a home full of caring, sympathetic individuals. Bud is happy to be surrounded by people who support and love him. Myers implies that Bud will enjoy a life full of happiness where he will blossom i...

The complete ionic equation for a chemical reaction involving ions is to break each species into its component ions and show what each ion does.  The net ionic equation focuses only on the ions involved in the key chemical reaction and eliminates the unimportant spectator ions.  Sodium hydroxide (NaOH) is a compound made up of the sodium ion (Na+) and the hydroxide ion (OH)-.  Hydrochloric acid (HCl) is a chemical made up of a proton (H+) and a chloride ion (Cl-).  The molecular chemical equation is given below: `NaOH + HCl -> NaCl + H2O` This shows that sodium hydroxide and hydrochloric acid react to form sodium chloride (salt: NaCl) and water (H2O).  Since this reaction takes place in water, the component ions are what are actually present in solution to perform the reaction.  The complete ionic equation is shown below: `Na^(+) + OH^(-) + H^(+) + Cl^(-) -> Na^(+) + Cl^(-) + H2O` The sodium and chloride ions remain unchanged in solution so they are spectator ions.  The net ion...

Because the cotton gin was highly efficient and slavery made the cost of producing cotton (from the owner's perspective) artificially cheap, cotton was a highly profitable industry, more than it really should have been if workers had been free to choose other jobs. As a result, almost all of the investment in the South during this period (what we now call "antebellum," meaning "before the war") was in cotton production; while the North had a diversified economy with many agricultural products as well as industrial manufacturing, the South became almost entirely dependent upon cotton exports for its whole economy---and hence, on slavery. Without the need for skilled engineers and factory workers, there was little incentive to invest in education; so literacy rates were low. Cotton was profitable enough on its own, so aside from some minor improvements in the cotton gin there was little incentive to invest in technology. Inequality in the South was extraordinarily...

Integrate `int(x^2-2x-1)/[(x-1)^2(x^2+1)]dx` Rewrite the rational function using partial fractions. `(x^2-2x-1)/[(x-1)^2(x^2+1)]=A/(x-1)+B/(x-1)^2+(Cx+D)/(x^2+1)`  `x^2-2x-1=A(x-1)(x^2+1)+B(x^2+1)+(Cx+D)(x-1)^2` `x^2-2x-1=A(x^3-x^2+x-1)+Bx^2+B+(Cx+D)(x^2-2x+1)` `x^2-2x-1=Ax^3-Ax^2-Ax-A+Bx^2+B ` `+ Cx^3-2Cx^2+Cx+Dx^2-2Dx+D ` `x^2-2x-1=(A+C)x^3+(-A+B-2C+D)x^2 ` `+(A+C-2D)x+(-A+B+D)` Equate coefficients and solve for A, B, C, and D. `0=A+C` `A=-C`  `-2=A+C-2D` `-2=-C+C-2D` `-2=-2D` `D=1` `1=-A+B-2C+D` `1=C+B-2C+1` `0=-1C+B` `B=C ` `-1=-A+B+D` `-1=C+B+1` `-2=B+B` `-2=2B` `B=-1` `C=-1` `A=1` `int(x^2-2x-1)/[(x-1)^2(x^2+1)]dx` `=int[1/(x-1)]dx-int[1/(x-1)^2]dx+int[(-1x+1)/(x^2+1)]dx` `=int[1/(x-1)]dx-int[1/(x-1)^2]dx+int[-x/(x^2+1)]dx+int[1/(x^2+1)]dx` The first integral follows the pattern `int(du)/u=ln|u|+C` ` ` `int[1/(x-1)]dx=ln|x-1|+C` Integrate the second integral using u-substitution. Let `u=x-1` `(du)/(dx)=1` `du=dx` `-int1/(x-1)^2dx` =`-intu^-2du` `=1/u+C` `1/(x-1)+C` Integrate the ...

Recall that indefinite integral follows `int f(x) dx = F(x) +C` where: `f(x)` as the integrand function `F(x)` as the antiderivative of `f(x)` `C` as the constant of integration. The given  integral problem: `int arcsec(2x)dx` resembles one of the formulas from the integration table. We follow the integral formula for inverse secant function as: `int arcsec(u) du =u*arcsec(u) - ln|u+sqrt(u^2-1)|+C `                        or    `u*arcsec(u)-cosh^(-1)|x|+C` For easier comparison, we may apply u-substitution by letting: `u = 2x` then `du = 2 dx` or `(du)/2 =dx` . Plug-in the values, we get: `int arcsec(2x)dx=int arcsec(u) * (du)/2` Apply the basic integration property: `int c*f(x) dx = c int f(x) dx` . `int arcsec(u) * (du)/2= 1/2int arcsec(u) du` Apply aforementioned integral formula for inverse secant function: `1/2int arcsec(u) du =1/2*[u*arcsec(u) - ln|u+sqrt(u^2-1)|]+C`                                    `=(u*arcsec(u))/2 -( ln|u+sqrt(u^2-1)|)/2+C` Plug-in `u =2x` on `(u*arcsec(u))/...

Given the curve equations ,they are `y_1 = x^2 -4x + 3 ` -----(1) ` y_2 = -x^2 + 2x + 3` -----(2) to get the boundaries or the intersecting points of the curves we have to equate the curves . `y_1=y_2` => `x^2 -4x + 3 = -x^2 + 2x + 3` => `2x^2-6x =0` => `2x(x-3)=0` => `x=0 or x=3` Area = `int_0^3 ((-x^2 + 2x + 3)-(x^2 -4x + 3)) dx `     = `int _0 ^3 (6x -2x^2) dx `  = `[6x^2 /2 -2x^3 /3]_0 ^3` = `[6(3)^2 /2 -2(3)^3 /3]-[0]` =`3^3 -2*3^2 = 27-18 = 9` so the area of the region between the curves is `9`

This is a great question, because alcohol use, love, and identity are all major themes in Ernest Hemingway's  The Sun Also Rises . Below, you'll find an explanation for how each of these themes works in the novel: Alcohol Use: Alcohol is almost always present in Hemingway's novel, as most of the narrative focuses on the main characters' experiences at a raucous festival in Spain. During the course of the novel, Jake and his friends party their way across Europe, guzzling liquor in Parisian clubs and in Spanish cafes. The more drinking we see, the more apparent it is that alcohol is a coping mechanism. Most of the main characters in the book are harboring secret fears, disappointments, and doomed hopes, and alcohol is a tool that allows them to avoid thinking about or dealing with the many problems they're facing. Love: Most of the characters in the novel are looking for love in one way or another, but few of them find it. Much of the narrative focuses on the unrequi...

In Act 2, scene 4, Romeo is horsing around in the streets with his friends, but when Juliet's nurse approaches him in order to learn what arrangements he has made for his marriage to Juliet, he and she retire to speak privately of it.  Romeo purposely gets rid of Benvolio and Mercutio, telling them, "I will follow you," when Mercutio asks if he will go with them to his father's house (2.4.144).  Only after Romeo's friends depart does he tell the nurse of his plans.  He says, "Bid [Juliet] devise / Some means to come to shrift this afternoon, / And there she shall at Friar Lawrence' cell / Be shrived and married" (2.4.183-185).  His instruction, then, is that Juliet should make up a story, some reason that she needs to go to confession this afternoon; instead, however, when she gets there, she and Romeo will be wed.  Juliet would not have to lie about the reason for her going to church if the marriage were not a secret.  Further, at the end of Act 2, ...

Yes and no.  Hamlet does succeed in killing his uncle and stepfather, Claudius, the man who murdered his father and married his mother fewer than two months after the funeral.  In the final scene of the play, after Hamlet is mortally wounded by Laertes's poisoned rapier and Gertrude falls, poisoned by the wine Claudius prepared for Hamlet, Hamlet does mortally wound Claudius with the poisoned rapier and force him to drink the wine.  The king dies soon after.  So, in that sense, Hamlet does "set it right" in that he's exacted revenge on his father's brother and murderer, the king. However, Hamlet loses his own life in the process.  Further, many other people who are innocent of the murder of old King Hamlet lose their lives before Hamlet successfully exacts revenge on his uncle: Polonius, Ophelia, Rosencrantz and Guildenstern, Gertrude, and Laertes all die while Hamlet is still figuring out how to avenge his father's murder.  On one hand, Hamlet is eventually s...

Gatsby attempts to achieve the American Dream, the idea that anyone can prosper with enough hard work and perseverance, but he ends up resorting to illegal means in order to acquire his fortune.  He is a bootlegger -- someone who profits from the illegal production, sale, and distribution of alcohol during Prohibition.  One who has earned their fortune by illegal means can hardly be said to have actually achieved the American Dream.  Further, Gatsby's attempt to achieve the Dream by becoming rich and securing the affections of the woman he loves end up costing him his life. Myrtle is married to a man who also tries to achieve the American Dream, and her husband's absolute failure to do so is yet another clue that the dream is actually an impossible one. Her husband, George, works hard and tries to get ahead legally, but he finds it essentially impossible.  Myrtle attempts to achieve the dream in her own way -- by allowing her married lover, Tom Buchanan, to buy her expensive th...

This essay prompt wants you to address how events in the book influenced Ponyboy. Ponyboy’s life is greatly influenced by external forces.  This just means factors outside of himself that he cannot control.  In writing your essay, these are the points you will want to include. One of the biggest external factors is that he is a greaser, in a town where the greasers and Socs are always at odds.  This influences most of his life and all of the events in the book. Greasers can't walk alone too much or they'll get jumped, or someone will come by and scream "Greaser!" at them, which doesn't make you feel too hot, if you know what I mean. We get jumped by the Socs. (Ch. 1)  Pony is proud of the fact that he is a greaser, but it is a source of shame and worry too.  He worries that the Socs will jump him, but he is also aware that everyone is judging him.  He likes being a greaser because it gives him a sense of belonging, but he doesn’t like the fighting.  The biggest ex...

Evaluate `sum_(n=1)^(oo)(ln(n))/n^3 ` We are asked to use the ratio test to determine if the series converges. We take the limit as n tends to infinity of the (n+1)st term over the nth term: if the limit is less than 1 in absolute value the series converges, if greater than 1 the series diverges, and if equal to 1 there is no conclusion. `lim_(n->oo)(ln(n+1)/(n+1)^3)/(ln(n)/n^3) ` `=lim_(n->oo)(ln(n+1)/(n+1)^3)*n^3/(ln(n)) ` `= lim_(n->oo) (ln(n+1))/(ln(n))*lim_(n->oo)n^3/(n+1)^3 `  Using L'Hopitals rule on the first factor `=lim_(n->oo)(1/(n+1))/(1/n)*lim_(n->oo)1/(1+3/n+3/n^2+1/n^3) ` `=lim_(n->oo)n/(n+1)=1 ` Thus the ratio test is inconclusive. (The series does converge -- use a comparison test. Note that `(ln(n))/n^3<n/n^3=1/n^2 ` which converges.)

I do not feel that Gatsby is fair to Daisy throughout the novel. Gatsby naively believes that Daisy should leave her husband who she has a child with in order to be with him. He gives her an ultimatum and believes that she should choose him. They have not seen each other in five years, and Gatsby feels that Daisy should ruin her marriage to start a relationship with him. Gatsby had spent years amassing a fortune through illegal means to live up to Daisy's high standards. However, Gatsby allows money to corrupt him through his efforts to become rich. When Gatsby finally does become wealthy, he believes that he now has everything that Daisy could possibly want. Despite the fact that Gatsby is wealthy and physically attractive, Daisy does not feel comfortable living an insecure life. Being in a relationship with Gatsby is too risky for Daisy, and she cannot leave her secure life behind. Daisy expects Gatsby to be financially secure at all times, while Gatsby believes that Daisy's ...

In Chapter One of Blink , Gladwell discusses the work of University of Washington researcher John Gottman, who claims he can predict marital outcome with 95% accuracy after coding a one-hour videotape of a married couple talking (the rate is reduced to 90% if the tape is 15 minutes) (page 10). Gladwell writes of Gottman: "He’s gotten so good at thin-slicing marriages that he says he can be in a restaurant and eavesdrop on the couple one table over and get a pretty good sense of whether they need to start thinking about hiring lawyers and dividing up custody of the children" (page 15). Gladwell says that Gottman can take a very small sample of a marriage, what he refers to as "thin-slicing," and understand its totality, or signature. Gladwell believes that Gottman's predictions about the outcome of a marriage are accurate. However, according to an article in Slate by Laurie Abraham (March 8, 2010), Gottman's results were misleading. Gottman knew in advance w...

Dalton's atomic theory was composed of the following postulates: Matter is composed of individual particles called atoms. Atoms of the same element have the same mass and are different from atoms of different elements. Atoms can't be created or destroyed. Atoms can combine in different ratios to form compounds. Atoms are the smallest unit of matter involved in chemical reactions. In 1897, J. J. Thomson conducted a series of experiments using cathode rays. Thomson's experiments indicated that atoms were composed of smaller, negatively charged particles. These particles were later called electrons. Electrons were the first subatomic particles to be discovered. Other subatomic particles, including protons and neutrons, were later discovered.  The discovery of subatomic particles proved that the first of Dalton's postulates was incorrect. The discovery of subatomic particles proved that atoms were not indivisible. Dalton's actual model of the atom was uncharacterized o...

Throughout most of Act I of Shakespeare's Romeo and Juliet Romeo is depressed over his unrequited love for Rosaline. Though she never actually appears in the play she is an important factor in establishing Romeo as a passionate and emotional character. Apparently she has spurned his affection, sending him into the doldrums, so much so that his father describes how he comes home and draws the shades in his room to block out the light of day. In Scene 1 he explains to Benvolio he is "out of her favor where I am in love" and that no matter what he does she has "forsworn to love." At one point Romeo alludes to mythology when he explains Rosaline's coldness toward his affection: Well in that hit you miss. 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 ...

Harrison's parents are not emotionally affected much at all by the death of their son because they cannot be.   For Harrison's mother, Hazel, her "perfectly average" intelligence does not allow her to become emotionally invested in much of anything. Even when she speaks to her husband in a caring manner about his health, it is quite shallow. She calls George "honeybunch," but the word feels void of emotion. Hazel's intelligence only allows the most basic of human responses. Even when the story reveals that Hazel has cried after viewing the death of her son, Vonnegut makes it clear that she cannot sustain thought or emotion by including this exchange between George and Hazel: "You been crying?" he said to Hazel. "Yup," she said. "What about?" he said. "I forget," she said. "Something real sad on television."   Harrison's father, George, could be emotionally affected by the death of his son if he did n...

The "poison tree" you ask about is the central image in William Blake's poem "A Poison Tree." In that poem, the narrator gets angry with a friend. After he becomes angry, he does not let the anger pass. Instead, he feeds it with fear, crying, and deception. It blossoms into an apple that appears lovely, but in reality, is poisonous. That poisonous fruit kills his former friend. The poison tree is what becomes of your soul when you feed it with negativity. By implication, your soul could become a positive and nutritious element of your being if you fed it with love, confidence, and honesty. The poison tree is a soul that has been fed with all the violent, corrosive emotions people feel. A poison tree is an angry, deceptive, hurtful soul (that doesn't have to be that way).

In The Red-Headed League , Sherlock Holmes is initially drawn into the mystery presented by Jabez Wilson, a pawn shop owner bestowed with a head of fiery red hair.  Wilson has an opportunity to make a tidy sum performing menial work.  Holmes uncovers a more sinister plot, that of a bank robbery led by Vincent Spaulding, a young apprentice at the shop. Saxe-Coburg square is described as a dingy and shabby square in a less part of town.  Upon arrival Holmes' first act is to pause in front of Wilson's pawn shop and look it over.  Next he proceeds to walk up the street and "down again to the corner" looking at all the houses.  Finally he returns to the pawnbroker's door and thumbs his cane upon the walk. The first action, the overview of the pawnbroker's shop is to further his knowledge of the client, Mr. Wilson.  Judging the paint, the exterior door, dimensions and overall character of the establishment he can gather any information on the story provided.  He may...

The density of a material is defined as a mass per unit volume. So if an object has a mass m, and the volume V, its density can be found as `D = m/V` . As described in the question, a balance can be used to measure the mass of the mineral sample. The volume of the sample can be determined by placing the sample in the graduated cylinder filled with water or another liquid. The level of the liquid in the cylinder rises as the sample displaces some of the liquid. The change of the level, measured by the markings on the cylinder, indicates the volume of the displaced liquid and thus, the sample. The density of the sample with the given mass and volume then equals `D = m/V=(14.7 g)/(2.2 cm^3) = 6.68 g/(cm^3)` . Converted to the SI of the units of measurements, the density would be  `D = 6.68*10^3 (kg)/m^3` . The density of the given sample is 6.68 gram per cubic centimeter.

First of all, I would say that essentially every person who has ever lived has been some combination of good and evil.  Both seem to be innate parts of our human nature.  Columbus was certainly both.  He was a man who had good qualities, but whose ambition led him to do thing that we, today, would see as evil. If we can say that ambition and perseverance are good qualities in a person then Christopher Columbus was good in some ways.  Columbus had strong ambitions.  He wanted to be an important and respected person.  He was also willing to strive hard and to never give up in pursuit of his ambitions.  He tried time and again to get his voyage of exploration funded until finally he succeeded.  He pushed his men to continue the voyage when they were afraid that they were doomed.  We tend to honor people who are determined and driven.  Columbus definitely had these qualities. On the other hand, Columbus did things that we certainly do not approve of today. When he saw the “Indians,” his ma...

To understand why Kipling wrote this poem, we should look at its full title: "The White Man's Burden: The United States and the Philippine Islands." Using the second part of this title, it becomes clear that Kipling directed this poem to the United States who, in 1899 (the time of publication), were involved in a war with the Philippines. The reasons for this war originate in events from the previous year when the United States defeated the Spanish and purchased from them a number of islands, including the Philippines. But this small nation had no intention of becoming a U.S. colony and, in February 1899, declared war on the United States. (Please see the reference links provided for more information). Kipling thus intended that his poem would inspire and encourage the Americans to overcome the people of the Philippines. He wanted them to realise that empire-building was a challenging endeavour that involved hard work and sacrifice. This sentiment is echoed throughout the...

Juliet is somewhat concerned that things are moving too quickly.  She cautions Romeo against swearing his love to her.  She says, "At lovers' perjuries, / They say, Jove laughs.  O gentle Romeo, / If thou dost love, pronounce it faithfully" (2.2.97-99).  She employs an allusion to refer to Jove, the most powerful Roman god, who laughs, she says, when lovers lie to one another.  She's nervous about any deceitfulness on Romeo's part.  The theme of deceitfulness is shown as the lovers proceed to marry, bed, and correspond in secret and when Juliet ultimately fakes her own death. Then, as Romeo and Juliet are preparing to part, she says, "I would have thee gone, / And yet no farther than a wanton's bird, / That lets it hop a little from his hand, / Like a poor prisoner in his twisted gyves, / And with a silken thread plucks it back again, / So loving-jealous of his liberty" (2.2.190-195).  Thus, Juliet means that she wants to keep Romeo close and compare...

Recall binomial series  that is convergent when `|x|lt1` follows:  `(1+x)^k=sum_(n=0)^oo (k(k-1)(k-2)...(k-n+1))/(n!)x^n`    or         `(1+x)^k= 1 + kx + (k(k-1))/(2!) x^2 + (k(k-1)(k-2))/(3!)x^3 +(k(k-1)(k-2)(k-3))/(4!)x^4-` ...  For given function `f(x) =1/(1+x)^2` , we may  apply Law of Exponents: `1/x^n = x^(-n)` to rewrite it as: `f(x) = (1+x)^(-2)` This now resembles `(1+x)^k` for binomial series.   By comparing "`(1+x)^k` " with "`(1+x)^(-2)` ", we have the corresponding values: `x=x ` and `k = -2` .  Plug-in the values  on the formula for binomial series, we get: `(1+x)^(-2)=sum_(n=0)^oo (-2(-2-1)(-2-2)...(-2-n+1))/(n!)x^n`                `= 1 + (-2)x + (-2(-2-1))/(2!) x^2 + (-2(-2-1)(-2-2))/(3!)x^3 +(-2(-2-1)(-2-2)(-2-3))/(4!) x^4-` ...              `= 1 -2x + 6/(2!) x^2 -24/(3!)x^3 +120/(4!)x^4-` ...               `= 1- 2x +3x^2 -4x^3 +5x^4-` ...               or  `sum_(n=0)^oo (-1)^n (n+1)x^n` Therefore, the Maclaurin series  for  the function `f(x) =1/(...

There are multiple ways to solve this problem but I will just compute the arc length of sine and cosine over half a period, or one hump. The arc length formula for a function is: `L=int_a^b sqrt(1+f'(x)^2) dx` Let f(x)=cos(x) and g(x)=sin(x). Then we want to see if: `int_a^b sqrt(1+f'(x)^2) dx=int_c^d sqrt(1+g'(x)^2) dx` `int_(-pi/2)^(pi/2) sqrt(1+cos(x)'^2) dx=int_0^pi sqrt(1+sin(x)'^2) dx` `int_(-pi/2)^(pi/2) sqrt(1+sin(x)^2) dx=int_0^pi sqrt(1+cos(x)^2) dx` `int_(-pi/2)^(pi/2) sqrt(2-cos(x)^2) dx=int_0^pi sqrt(2-sin(x)^2) dx` `sqrt(2) int_(-pi/2)^(pi/2) sqrt(1-1/2 cos(x)^2) dx=sqrt(2) int_0^pi sqrt(1-1/2 sin(x)^2) dx` Use symmetry to change the bounds of integration. `2 sqrt(2) int_(0)^(pi/2) sqrt(1-1/2 cos(x)^2) dx=2 sqrt(2) int_0^(pi/2) sqrt(1-1/2 sin(x)^2) dx` We need to manipulate the left hand side (LHS) to get it into a similar form as the right hand side. Make a dummie variable u-substitution and then use a trigonometric identity: `x=pi/2-u, dx=-du` `LHS: ...

Egypt gained its independence by rebelling against the British, who were in control of the country. This revolution occurred throughout the country in 1919 and led to the declaration of Egyptian independence in 1922. There was a group of Egyptian nationalists who approached the British to request independence. They were led by Saad Zaghlul and included Ali Sha'rawi Pasha, Abd al-Aziz Fahmi Bay, Muhammad 'Ali Bay, 'Abd al-Latif al-Makabati Bay, Muhammad Mahmud Pasha, Sinut Hanna Bay, Hamd Pasha al-Basil, Gurg Khayyat Bay, Mahmud Abu al-Nasr Bay, Mustafa al-Nahhas Bay and Dr. Hafiz 'Afifi Bay. The British leaders in Egypt decided that they were a serious threat to the peace and arrested and exiled Zaghlul and two others. This was the spark that led to the uprising throughout the country.  The leaders of the delegation and many others were convinced that Egypt was capable of ruling itself, and they wanted to establish a secular democracy with popular representation in the ...

This problem is solved using Boyle’s law, a gas law. It gives the relation between volume and pressure of a given mass of a gas at a constant temperature. According to Boyle’s law, volume of a given mass of a gas is inversely proportional to the pressure of the gas, at a given temperature. Hence, if pressure of a gas is increased, the volume of the gas decreases or the gas gets compressed and if the pressure is reduced, the volume of the gas increases or the gas expands. Mathematically the law can be expressed as P α 1/V P = constant  x 1/V Or PV=constant. Thus if V1 is the volume of a given mass of a gas at pressure P1, and if the pressure is changed to P2, then according to Boyle’s law, the volume of the gas will change to V2 in such a way that P1V1 =P2V2 This equation can be used to solve the given problem. Given that the volume of the gas is 6.0 L (V1) under a pressure of 1 atm (P1), when the pressure is changed to 190 mmHg (P2), the new volume can be calculated by first converting...

This is, in some ways, a variant on the "trolley problem" in philosophy. One of the main issues here is that it forces a choice in a way that may not be entirely realistic. Thus my response would be to return to the flaw in the premise of the argument and use it to suggest how I would approach the problem. A key part of the premise is that the lifeboat is an absolute dictatorship in which all authority is ceded to one person. I think that in this sort of situation that authoritarianism is a morally problematic approach to the issue. I do not support dictatorship. In a situation in which everyone is affected by a decision, everyone needs to have a voice in the decision. The first step would be to ask for volunteers. In the crisis in the aftermath of the Fukushima nuclear power station disasters, many elderly people volunteered to expose themselves to radiation to help save others. As many people are willing to sacrifice themselves for the common good, this would be the ideal s...

An unstable government can be problematic. When a government is perceived as unstable, other countries are less likely to be able to predict what may happen to that country in the future. This could have serious economic ramifications. If a country is perceived as unstable, there may be less investment in that country. Those who do invest will want a higher rate of return. This will increase economic costs for the unstable country. An unstable country is very risky to support politically and militarily. If there is a good chance that the government will be overthrown, it might not be wise to provide weapons that could fall into the hands of a new, possible unfriendly, government. Supporting a government politically when that government might get overthrown may also cause diplomatic problems in the future. Unstable countries might resort to tactics that suppress individual freedoms. The government might restrict freedom of speech or freedom of the press in order to try to suppress disse...

O. Henry's "After Twenty Years" may be interpreted as a tale of friendship since the two old friends both return to their favorite restaurant after twenty years as they have promised each other they would. The story may, perhaps, be interpreted as a tale of betrayal because Jimmy Wells seems to lack the courage to confront 'Silky' Bob himself. In another sense, 'Silky' Bob betrays the honor of his and Jimmy's friendship because he has turned to a life of crime. As an undetected Policeman Wells talks with Bob, whom he has recognized as a wanted man in the light of a match, Bob declares, "But I know Jimmy will meet me here if he's alive, for he always was the truest staunchest old chap in the world. He'll never forget. I came a thousand miles to stand in this door to-night, and it's worth it if my old partner turns up." At this point, Wells could have arrested Bob, but "somehow" (he later writes) he cannot bring himself to...

Tom Godwin's story "The Cold Equations" is a science fiction story about a girl who stows away on a supply ship bound for a planet called Woden. Like any good science fiction, the story derives its drama from a realistic and believable situation that involves science. The story is set in the future when interplanetary travel has become frequent and mankind has begun to colonize other worlds.  The story takes place inside a space vehicle called an Emergency Dispatch Ship, or EDS. These ships carry a relatively small amount of rocket fuel that is carefully calculated to be just enough to get them to their destination and back. When the girl stows away in hopes of visiting her brother on Woden, she adds extra weight to the ship. This will cause the ship to burn more fuel than expected, which would lead to its destruction. The ship's pilot, Barton, discovers the stowaway and contacts his superior for instructions. In fact, Barton knows that he is supposed to jettison the ...

The idea to kidnap the young boy and demand ransom seemed brilliant to both Sam and Bill. However, the situation changed when they actually got the boy. They did not anticipate any hardships in getting the money from the boy’s father and pulling off their planned fraudulent scheme in Western Illinois. Sam left Bill and the boy at the hideout, but upon his return, Bill was hurt, and the boy was enjoying the wild. The situation was not going as expected and Bill was terrified of the boy. The boy was responsible for the bruises on Bill’s body after hitting him as they played. I jumped up to see what the matter was. Red Chief was sitting on Bill's chest, with one hand twined in Bill's hair. In the other he had the sharp case-knife we used for slicing bacon; and he was industriously and realistically trying to take Bill's scalp. The situation affected Bill’s resolve to get the ransom. He convinced Sam to ask for less in order to return the boy to his parents. The boy’s father of...

A company manufactures headphones for $35. They want to make a profit of 24%, so they want to know how much they should charge for the headphones. One way to approach this problem is to reason that if 24% of the price is profit, then 76% of the price covers the cost. Then if r is the retail price we have 76% of r is $35. .76r=35 ==> r=$46.05 Another approach is to use the equation cost = retail times the cost complement where cost is the cost to manufacture, retail is the selling price and the cost complement is the percentage of the selling price devoted to covering the cost. The cost complement is 1-(profit percent). So here we would have 35=r*.76 so r is 46.05 again. *********************************************************** In order to have a 24% profit, the company should sell the headphones for $46.05 ***********************************************************

This is a question that can be answered in many ways.  In Golding's Lord of the Flies , Jack is portrayed as having the most dramatic change.  He begins the novel as the leader of a choir, who can sing C sharp, becomes the formidable leader of the hunters and eventually the tyrannical leader of the entire island, and ends by being reduced to a sniveling red-headed boy.  Because he goes through so many changes, it is difficult to pinpoint when he betrays himself.   At the beginning of the novel, his freckles betray his feelings of mortification when he is not elected chief.   Later in the novel, he betrays his friend Ralph, but in so doing he betrays himself.  In Chapter 3, Golding writes that  they look at each other in love and hate. At first, Ralph and Jack, as the oldest boys on the island, are friends and allies.  Ralph is the chief and appoints Jack leader of the hunters.  But as priorities change, and Ralph becomes more interested in rescue and shelters while Jack becomes mor...

Tom's newfound philosophy is one based on racism. According to the text, Tom has been reading a book named "The Rise of the Colored Empires" by someone named Goddard. Tom's book, of course, is fictional, but it alludes to a book that actually discusses everything Tom's book does. That book would be The Rising Tide of Color by Lothrop Stoddard, a man who advocated the principles of white supremacy through the use of eugenics. Eugenics is the science of heredity and breeding: white supremacists like Stoddard believed that if white birth rates did not increase, the "colored" races would inundate and destroy western civilization completely. Like the fictional Goddard, Lothrop Stoddard advocated what Tom refers to as scientific racism (or the use of eugenics to ensure the dominance of the white races). This is why, when Tom tries to rationalize his racist beliefs, he keeps repeating that it's "all scientific stuff; it’s been proved." Basically,...

Stephen Hawking is widely accepted as one of the most brilliant theoretical physicists of all time. His early work gave us our best understanding of the make-up of black holes; by defining the heat loss from the edges of black holes—dubbed Hawking Radiation—and shows how black holes degrade over time.  One of the difficulties Hawking had to overcome was his own brilliance and the laxness that came with being an undergraduate who feels he or she already knows everything. As an undergraduate, Hawking did not have to study or work very hard to understand concepts, causing him to be bored much of the time. He was also younger than many of his classmates, as he began his undergraduate program at 17. He combated this by joining the school rowing team as their coxswain, which gave him an opportunity to be 'one of the boys'. The biggest challenge Hawking has dealt with is his degenerative nerve disorder ALS. ALS, also known as Lou Gehrig's Disease, is where the neurons that control...

This is a penetrating question.  Of course, the main emphasis is the non-movement, the inertia of inactivity in the plot (emphasized by the important last line: “They do not move.”)  But there are two other “movements” in any stage performance.  “Blocking” (the changes of position by the actors) and “gesture” (the language of stage gestures, both realistic and artificial, of the actors’ hands, head, posture, etc.)  In blocking, Beckett has prescribed much of it:  Pozzo and Lucky’s entrance, for example. But the director must choose the proxemics (the closeness and distance between characters at any time).  In stage “business,” for example in the burlesque business of changing hats, or the examining of boots, the director must select details of the movements for rhythm and realism. But what makes your question so intriguing is the overriding thematic idea that movement itself, for Gogo and Didi, is simply a means to “pass the time.”  The meaninglessness of all effort is emphasized by th...

The two sounds that stand out in Helen's memory of the night of her sister's death are described by her to Sherlock Holmes at their initial meeting in the early morning. As I opened my door I seemed to hear a low whistle , such as my sister described, and a few moments later a clanging sound , as if a mass of metal had fallen.  The reader will not understand the meaning of either of these sounds until late into the story. The low whistle was used by the evil Dr. Roylott to recall his poisonous snake, "the speckled band," from the room next to his. He had trained the reptile to return in response to his whistle. He would blow the whistle at around three o'clock in the morning in order to make sure the girl would still be sound asleep and not discover a snake in her bed. But evidently he did not realize that Julia had just been bitten at the time he blew the whistle--and perhaps Julia herself did not realize it until the poison started to take its effect. She woke u...

When a ball is dropped from a given height h, it has potential energy proportional to that height:  `E^(pot) = mgh` (considering that the potential energy on the ground, at h = 0, is zero.)  As the ball reaches the ground, all of its potential energy transfers to the kinetic energy, which is proportional to the square of the ball's speed just before it hits the ground:  `E^k = mv^2/2` . Since the energy is conserved during the ball's fall,  `E^k = E^(pot) = mv^2/2 = mgh` . If during the collision the ball loses 10% of its kinetic energy, it will bounce back up with the kinetic energy equal to 90% of the original energy, or `0.9mv^2/2 = 0.9 mgh` . As the ball flies up, its kinetic energy is again converted to potential energy. At the maximum height, the kinetic energy is zero and the potential energy equals the kinetic energy with which the ball left the ground, or 0.9 mgh . This means the maximum height to which the ball will rise is 0.9 of the original height, 0.9 m, or 90 cm....

Joyce Carol Oates wrote her short story "Where Are You Going, Where Have You Been?" after reading about the 1950s serial murders of Charles Schmid, a story that was profiled in Life magazine. For one thing, she was concerned with the increasing fixation on sexual themes in the youth culture of the 1960s. Then, the inspiration to write this story came to Oates with Bob Dylan's song "It's All Over Now, Baby Blue." Some critics perceive Oates's narrative as an allegory for an encounter with the devil in the person of Arnold Friend, and others perceive it as criticism of contemporary youth and its obsession with sexual themes in the music to which they listen (not unlike Dylan's song). Representative of this sex-obsessed youth, Connie is a pretty girl who knows that beauty "is everything." While her plain sister June saves money and helps to clean the house and cooks, Connie does nothing because she is occupied with her "trashy daydreams....

 Arc length of curve can be denoted as "`S` ". We can determine it by using integral formula on a closed interval [a,b] as: `S = int_a^b ds` where: `ds = sqrt(1+ ((dy)/(dx))^2 )dx`  ` if y=f(x)` or `ds = sqrt(1+((dx)/(dy))^2) dy if x=h(y)` `a` = lower boundary of the closed interval `b` =upper boundary of the closed interval From the given problem: `y =ln(x), [1,5]` , we determine that the boundary values are: `a= 1` and `b=5` Note that `y= ln(x)` follows `y=f(x)` then the formula we will follow can be expressed as `S =int_a^bsqrt(1+ ((dy)/(dx))^2 )dx` For the derivative of ` y` or `(dy)/(dx)` , we apply the derivative formula for logarithm: `d/(dx)y= d/(dx) ln(x)` `(dy)/(dx)= 1/x`  Then` ((dy)/(dx))^2= (1/x)^2`  or `1/x^2` . Plug-in the values  on integral formula for arc length of a curve, we get: `S =int_1^5sqrt(1+1/x^2 )dx` Let `1 = x^2/x^2` then we get: `S=int_1^5sqrt(x^2/x+1/x^2 )dx`     `=int_1^5sqrt((x^2+1)/x^2 )dx`     `=int_1^5sqrt(x^2+1)/sqrt(x^2 )dx`     `=int_1^5...

The formula for the Taylor polynomial of degree `n` centered at `x_0` , approximating a function `f(x)` possessing `n` derivatives at `x_0` , is given by `p_n(x)=f(x_0)+f'(x_0)(x-x_0)+f''(x_0)/(2!)(x-x_0)^2+f'''(x_0)/(3!)(x-x_0)^3+...` `p_n(x)=sum_(j=0)^n (f^((j))(x_0))/(j!) (x-x_0)^j` For `f(x)=e^x, f^((j))(2)=e^2` for all `j` . Therefore to fourth order in `x` about the point `x_0=2` `e^x~~p_4(x)=e^2+e^2(x-2)+e^2/2(x-2)^2+e^2/(3!)(x-2)^3+e^2/(4!)(x-2)^4` Notice the graph below. The function `p_4(x)~~e^x` (red) the most at `x=2` . It will become more and more approximate to `e^x` the higher order the approximation.