Notes

The integral `int sin^3(3*x) dx` has to be determined. `int sin^3(3*x) dx` Let `y=3x` `dy/dx = 3` The given integral can be written as: `1/3int sin^3 y dy` = `1/3int sin y * sin^2 y dy` = `1/3int sin y * (1 - cos^2 y) dy` Let `z = cos` y, `dz/dy = -sin y` => `-(1/3)*int (1 - z^2) dz ` => `(-1/3)*(z - z^3/3)` As `z = cosy` => `-1/3(cos y - (cos^3y)/3)` And `y = 3x` => `-1/3(cos 3x - (cos^3(3x))/3)` The integral `int sin^3(3*x) dx = -1/3(cos 3x - (cos^3(3x))/3) + C`

To determine the convergence or divergence of the series `sum_(n=0)^oo (-1)^n/((2n+1)!)` , we may apply ratio test. In Ratio test , we determine the limit as: `lim_(n-gtoo)|a_(n+1)/a_n| = L` or `lim_(n-gtoo)|a_(n+1)*1/a_n| = L`  Then ,we follow the conditions: a) `L lt1` then the series converges absolutely . b) `Lgt1` then the series diverges . c)` L=1` or does not exist  then the test is inconclusive .The series may be divergent, conditionally convergent, or absolutely convergent. For the series `sum_(n=0)^oo (-1)^n/((2n+1)!)` , we have: `a_n=(-1)^n/((2n+1)!)` Then, `1/a_n=((2n+1)!)/(-1)^n` `a_(n+1)=(-1)^(n+1)/((2(n+1)+1)!)`             `=(-1)^(n+1)/((2n+2+1)!)`             `=(-1)^(n+1)/((2n+3)!)`             `=((-1)^n*(-1))/((2n+3)(2n+2)((2n+1)!))` Applying the Ratio test on the power series, we set-up the limit as: `lim_(n-gtoo) |((-1)^n*(-1))/((2n+3)(2n+2)((2n+1)!)) *((2n+1)!)/(-1)^n|` Cancel out common factors: `(-1)^n` and `(2n+1)!` . `lim_(n-gtoo) |(-1)/((2n+3)(2n+2))|` Evaluat...

In The Picture of Dorian Gray , Wilde uses a number of literary techniques to develop his characters and to enhance some of the novel's key themes. Allusions, for example, are widely used in Chapter One to reveal more about Dorian's appearance and character. He is likened to Adonis, a man of great beauty from Greek mythology, to demonstrate his visual appeal to the reader. He is also likened to Narcissus, another figure from Greek mythology, who fell in love with his own image and died because he could not stop looking at himself in the reflection of a pond. By including this allusion, Wilde also foreshadows Dorian's future and suggests that his self-love will develop into an unhealthy obsession. Wilde also uses a number of symbols in the novel. The portrait, for example, becomes a living representation of Dorian's soul which degrades as his levels of vice and immorality increase.  It also represents the unavoidable process of ageing which Dorian is so keen to prevent. ...

Throughout The Plague of Doves , Billy and Corwin Peace evolve in opposite ways. While Billy becomes a cruel tyrant, Corwin eventually grows from a troubled youth to a talented musician. Billy Peace As the younger brother of Maggie Peace, Billy starts out as a shy yet principled young man. When Maggie becomes pregnant with John Wildstrand's child, Billy overcomes his shy demeanor to demand that John treats his sister fairly. He is drawn into John's kidnapping scheme, and enlists in the military to avoid being arrested. War alters Billy's character, and he develops a fanatical perspective on religion that leads him to form his own cult. Billy changes from a shy youth to a charismatic religious leader, and he exerts absolute control over his congregation as well as his wife and children. He soon becomes abusive towards his family and dies at the hands of his own wife. Corwin Peace Corwin is the illegitimate son of Maggie Peace and John Wildstrand. He is also Billy Peace's...

Romeo is smitten with both Rosaline and Juliet, but his love for Rosaline is unrequited. Thus, we find him at the beginning of the play pining for Rosaline, who has decided to remain chaste. His friends urge him to get over Rosaline, but he only does so when he encounters Juliet. The Friar, to whom he has spoken at length about his love for Rosaline, is skeptical about his newly-professed love for Juliet. He understandably thinks that Romeo has impulsively given his love to another, which suggests that neither love was really sincere. It is hard to know whether his love for Rosaline was legitimate—it certainly seems so at the beginning of the play—but his love for Juliet certainly is. He is willing to die for her. I would argue Romeo loves both women passionately, but his love for Juliet seems more substantial.

First, what do you mean when you say "when he is precisely halfway between the planets as measured in the planet frame" and "the explosions are simultaneous in the frame of the planets"? The only option I see is: before the spaceship neared the first planet, observers on both planets synchronized their clocks (the speed of these clocks is the same because the planets are in rest relative to each other), measured the speed of the spaceship, and estimated when it would approach the first planet. Then they computed how much time it would take for a spaceship to travel half of the distance and wrote down that time. And, finally, they explode bombs (actually, emit light) when their clocks show this computed time. From the planets' point of view, the half of the flight will take `1/(0.6)` hours. Now let's look on this from an astronaut's point of view. He travels between planets with the same speed `0.6 c.` The distance between the planets for him is less than...

What Cassius says and does throughout the play paints a very negative picture of him. There is not much good one can say about him since he comes across as sly, scheming, manipulative, greedy, ruthless, corrupt and cowardly. In the end, one can understand Caesar's suspicion of him when he tells Antony, during the Lupercalian Festival, in Act 1, scene 2: Let me have men about me that are fat; Sleek-headed men and such as sleep o' nights: Yond Cassius has a lean and hungry look; He thinks too much: such men are dangerous. Caesar is accurate in his assessment. Cassius' 'lean and hungry look' portrays him as both a scavenger and a predator. He is hungry with ambition. The fact that 'he thinks too much' suggests that he is constantly plotting, which is exactly what Cassius does.  His scheming and manipulative nature is pertinently displayed when he draws the honourable Brutus into his web. He flatters him and says exactly what he knows Brutus wants to hear. He pr...

Helen Stoner tells Sherlock Holmes that she is at present unable to pay him for his services. Yet he takes on her case for at least two reasons. One is that he feels sympathetic for a young woman who is so frightened and helpless. The other is that he finds one aspect of the mystery especially intriguing. Dr. Watson frequently mentions in his Sherlock Holmes tales that the great detective is mainly motivated by mental challenges, since he has been successful enough in his investigations to have no further cares about money. What intrigues Holmes is that the case presents what is commonly called a "Locked Room Murder Mystery." As Holmes explains to Dr. Watson: “Yet if the lady is correct in saying that the flooring and walls are sound, and that the door, window, and chimney are impassable, then her sister must have been undoubtedly alone when she met her mysterious end.” Holmes senses that if he could unravel the mystery of how Helen's sister Julia came to be killed while ...

Leiningen learns that the ants are approaching his plantation because he is told by a Brazilian official that the ants will probably reach his plantation in approximately two days. When Leiningen hears the words of the official, he tells the man, "even a herd of saurians couldn't drive me from this plantation of mine." And, despite the official's explanation that the ants are "elemental" and an "act of God," Leiningen refuses to leave his plantation. For the past three years, he has been a planter and dealt with flood, plague, and other "acts of God." Furthermore, he prides himself on how he has triumphed over every difficulty. Even when he sees the legions of ants that march toward his land, eating everything in their paths, Leiningen refuses to leave because he believes the human mind can surpass the limitations of insects. Indeed, he believes he can win the war against them. The human brain needs only to become fully aware of its power...

To her great surprise, Leslie finds Janice Avery , the well-known bully, crying in the bathroom. Janice's father beats her, and when Janice finally confided this sad truth in her friends Wilma and Bobby Sue, they revealed her secret to everyone--and now, even the teachers know about Janice's sad situation. This betrayal of trust and the subsequent possible destruction of Janice's tough reputation are what make her cry in the bathroom. All this happens in Chapter 7, an important turning point in Jess and Leslie's maturity. They'd previously been obsessed with getting revenge on Janice for bothering Jess's little sister. But their childish vengeful attitudes give way to a better understanding of Janice as a person, as someone who is suffering and whose infliction of suffering on others is now easier to understand and excuse. Reading this story today, we might be confused about why it was a bad thing for the truth to come out about Janice's father abusing her. ...

Matt lives in an area known as the Fen, which is a lower-class area equivalent to a slum in our culture. Kira lives in the village, and those who live in the Fen are closely associated with village people in that they are part of the same large community. The villagers live in cotts (small homes) in a central area near the marketplace and not far from the Edifice. The Fen is farther removed from that area. When Kira and Thomas venture to the Fen, they first come to an area on the outskirts of their village where the huts are closer together. They then cross a makeshift bridge over a "foul-smelling stream," presumably flowing with human waste and refuse. "Poisonous oleander bushes" border the stream on the Fen side. Kira and Thomas then see a cluster of small cotts. Although the cotts are not that different from the one Kira grew up in, the area in which they are situated is shaded because of the tall trees, and the entire setting is damp and dirty, a breeding ground...

Madame John's original motive for not telling Tite Poulette of her parentage is twofold: the child is the orphan of Spaniards and would be taken from her because she is a quadroon. By keeping the child as her own she has, perhaps, made Monsieur John feel better because he knows the girl will be well cared for since he has put her under his legal protection as his child.  At the time of the setting of this story, there was an Orphan's Asylum where the beautiful Tite Poulette would probably have been taken if Mme. John had not claimed the child as her own. Because of his guilt about having given the baby's father coffee and toast which actually caused the death of the man suffering with yellow fever, Monsieur John felt responsible for the baby girl. Since he was not married and obviously loved Zalli (Mme. John), he left her his house. As he is dying, he tells the woman he loves that he is going and he recognizes how faithful she has been to him. He also remarks that with his ...

Given` y'+y*secx=secx` when the first order linear ordinary Differentian equation has the form of `y'+p(x)y=q(x)` then the general solution is , `y(x)=((int e^(int p(x) dx) *q(x)) dx +c)/ e^(int p(x) dx) ` so, `y'+y*secx=secx--------(1)` `y'+p(x)y=q(x)---------(2)` on comparing both we get, `p(x) = secx and q(x)=secx` so on solving with the above general solution we get: y(x)=`((int e^(int p(x) dx) *q(x)) dx +c)/e^(int p(x) dx)` =`((int e^(int secx dx) *(secx)) dx +c)/e^(int secx dx)` first we shall solve `e^(int secx dx)=e^(ln(secx +tanx)) = secx+tanx`      so proceeding further, we get y(x) =`((int e^(int secx dx) *(secx)) dx +c)/e^(int secx dx)` =`(int ((secx+tanx)*(secx)) dx +c)/(secx+tanx)` =`(int ((sec^2x+tanx*(secx)) dx +c)/(secx+tanx)` =`(int (sec^2x) dx+int (tanx*(secx)) dx +c)/(secx+tanx)` =`(tanx+secx +c)/(secx+tanx)` so `y(x)=(tanx+secx +c)/(secx+tanx)=1 +c/(secx+tanx)` Now we have to find the particular solution at y(0) =4 so ` y(x) =1 +c/(secx+tanx)` =>...

In Farewell to Manzanar,  the greatest effect of the camps on Jeanne can be seen in how she perceives her father's change.    Jeanne is vocal in describing how her Papa was in love with the United States. He had rejected Japan, and fully committed himself to America.  When Japan bombed Pearl Harbor, Papa burns his Japanese flag and cuts himself off from his past. Even though he is a man without a country, he feels that his adopted country is America. The unconditional love that Papa had for America left an impression on his daughter.    One of the most profound effects of the camps was how Jeanne saw her father change.  Papa is arrested and detained because he was suspected of conspiring against America.  When he returns to the family, Jeanne is struck with how he had been changed as a result of his time in the camps. His optimism and hope in America had been taken away.  Papa could not overcome the experience of being falsely accused, the loss of his possessions, and the stripping...

In order to start to answer the question, let’s take a look at how a music critic typically organizes his or her analysis. Looking at Rolling Stone’s online music reviews, they all seem to follow a pretty simple formula: Thesis that follows a “Who” + “Did What” + “When” + “How Well” formula Context for thesis through tonal analysis  Context for thesis through thematic analysis Applying this formula to Lennon’s “Borrowed Time,” we can start to outline a critical analysis like so: Given the fact that John Lennon’s pop single “Borrowed Time” was released following the beloved musician’s tragic assassination in 1984, the song’s simple lyrics evolve into an effective emotional reminder about how to appreciate the brevity of life. The hopeful tone indicates an appreciation of life, acknowledging that “the future is brighter and now is the hour.” Lennon’s death underscores the truth in the chorus’s repetition that we’re all “living on borrowed time.” The main theme of living in the moment ga...

At the beginning of the story, Whitney and Rainsford are standing on the deck of a ship.  It is nighttime.  Whitney points out into the darkness and tells Rainsford that there is indeed an island in the darkness.  Whitney further explains that sailors have a "curious dread" of the island, and the island also happens to be named "Ship-Trap Island."   "The old charts call it `Ship-Trap Island,"' Whitney replied." A suggestive name, isn't it? Sailors have a curious dread of the place. I don't know why." After falling overboard, Rainsford is forced to swim toward the island.  On the island, Rainsford meets Zaroff, and Zaroff explains why the island has been appropriately named.   Zaroff's island has electricity on it.  Additionally, Zaroff has placed electrical channel markers out in the island's waters.  The reality is that the channel markers do not actually indicate a real channel.  Zaroff has placed the markers to guide ships ...

Rome was established as a tribal village that later grew into a kingdom, then into a republic, and finally into an empire before its fall. Roman expansion resulted in the growth of the roman population. This was first achieved by the predominantly male group taking wives from neighboring native groups. Rome was also successful in conquering several regions and integrating their people into the Roman society. In order to achieve the notable victories in battle during the Roman expansion, the leadership was forced to invest heavily in their military capability. The investments resulted in the growth of the Roman military in numbers and resources. This improved their ability to defend and attack other territories in line with their expansion requirements. The expansion also resulted in the growth of the Roman economy. The territories that fell to the Romans paid tribute and provided the necessary resources which facilitated the growth of the economy. The expansion also resulted in both ex...

In Outliers , Gladwell theorizes why some people have success way outside of statistical norms. These statistical outliers, achieve at levels much higher than normal successful individuals do. One could say that Gladwell actually refers to his argument in the subtitle of his book. According to his theory of success, it is the story surrounding an individual that determines success much more so than an individual's drive, intelligence or other personal traits over which he has control. According to Gladwell, one is not highly successful in a vacuum of elements that he controls. He theorizes that for every highly successful individual, there was a recipe of experiences, culture, family and generation that boosted his success beyond societal norms. According to Gladwell, without these elements, individual efforts will only take a person to a normally successful level. His main argument then is that it is the elements in one's life that help most to make one highly successful. Glad...

`int (dx)/(x(x^2+4)^2)` `= int 1/(x(x^2+4)^2)dx` To solve, apply partial fraction decomposition. So to express the integrand as sum of proper rational expressions, set-up the equation as follows: `1/(x(x^2+4)^2) = A/x + (Bx+C)/(x^2+4) + (Dx+E)/(x^2+4)^2` Multiply both sides by the LCD. `1=A(x^2+4)^2 + (Bx+C)(x)(x^2+4) + (Dx+E)(x)` `1=Ax^4+8Ax^2+16A + Bx^4+Cx^3+4Bx^2+4Cx+Dx^2+Ex` `1=(A+B)x^4 + Cx^3 + (8A+4B)x^2+(4C+E)x +16A` Express the left side as polynomial with degree 4. `0x^4 + 0x^3+0x^2+0x+1 =(A+B)x^4 + Cx^3 + (8A+4B+D)x^2+(4C+E)x +16A` For the two sides to be equal, the coefficients of the polynomial should be the same. So set the coefficients of the two polynomials equal to each other. x^4: `0 = A + B `     (Let this be EQ1.) x^3: `0=C `     (Let this be EQ2.) x^2: `0=8A+4B+D`     (Let this be EQ3.) x: `0=4C+E `     (Let this be EQ4.) Constant: `1 = 16A`     (Let this be EQ5.) Notice that the value of C is already known. So let's solve for the values of A, B, D and E. Plug-i...

I assume you are referring to Macduff's plan to leave Scotland at his earliest convenience and seek assistance for Macbeth's overthrow. The plan is effective in the sense that firstly, Macduff, in leaving in such a hurry, denies Macbeth the opportunity to assassinate him as he had done with Banquo. Macbeth has been aware of Macduff's sentiments and knows where his loyalties lie and wants him dead. In fact, the murderers who kill Macduff's entire family come looking for him for, on their arrival, the first murderer asks Lady Macduff, "Where is your husband?" The murder of Macduff's entire family and his servants indicates how ruthless and bloodthirsty the tyrant has become. With his rushed escape Macduff had, essentially, abandoned his family and left them vulnerable and open to Macbeth's malice. In this regard, the plan was not entirely effective. In his defense, though, one can argue that he had no choice but to leave. If he had tarried, he would have...

The scene in "Rikki-Tikki-Tavi" where the family is eating breakfast on the veranda is full of suspense. First, Kipling foreshadows the life-and-death stakes of the scene twice before the scene actually occurs. When Nagaina is talking to Darzee's wife, Nagaina predicts that "before night the boy in the house will lie very still." Darzee's wife lets Rikki know of the cobra's murderous intent by telling him, "She means killing!"  The way Kipling describes the scene is full of tension. Nagaina is set to strike at Teddy, and the humans are very fearful. We can picture them: They aren't eating, they aren't moving a muscle, and their faces have gone pale. The father whispers to the little boy to remain perfectly still. Nagaina is coiled near enough to Teddy's chair that she can reach him in one strike. Her head is swaying menacingly as she stares unblinkingly at the humans.  The dialogue further adds to the suspense. The father whispers a...

Shading is a technique used in visual arts, such as pencil drawing, to create a sense of depth or dimension and express the relationship between the subject matter and a light source. Shading is very easy to achieve in pencil drawing by layering pigment in such a way that it creates a gradient from the brightest to darkest points of a drawing. This may be more difficult to achieve in mediums such as paint or pastel, which typically require introducing an entirely new color to the work, rather than simply layering more pigment. Shading can also be used to create a sense of contrast in monochrome works of art where there is no color used for differentiation of subject matter. For example, shading can be used to create the sense that an apple is of a different color than the table it sits upon. Additionally, shading can create a sense of movement and emphasize a particular mood the artist may wish to convey through his or her work.

I'm glad to hear you are interested in helping to protect our environment! There are lots of ways to help preserve nature for future generations, most of which fall into the categories of prevention or reparation. Acts of prevention are those which help to avoid pollution or degradation of the environment. This includes acts like recycling and composting waste rather than sending it all to a landfill, using renewable energy sources, and choosing to walk or bike as opposed to riding in a car. Acts of reparation are those which are intended to help fix some of the damage that has already been done to our planet. This can include planting trees or bushes to help clean carbon dioxide from the air, picking up litter in your community, and donating to conservation efforts. There are plenty of things you can do in your life to help preserve our environment, it mostly depends on the amount of time and money you can spare. One way that people can help reduce the amount of deforestation of o...

Sound is a longitudinal wave and needs a medium to transmit from one location to another. In air, the sound travels by compression and rarefaction of air in the direction of wave motion. In other words, the air molecules move back and forth (which causes compression and decompression of air pockets) in the direction of the sound wave and this causes them to transmit from one location to another. That is, in the simplest terms, sound cannot travel in the absence of a medium. Thus, in free space (or a vacuum), the speed of sound is zero. This is because there is no medium to transmit the sound wave. In comparison, in the case of a perfectly rigid rod, there is no free atom or molecule and all the particles move as a single body. Thus, the sound would be transmitted instantly from the rigid body and hence the speed of sound through a rigid body is infinite . Another way to understand this scenario is by mathematical formulation of the speed of sound, which is: `c = sqrt(E/rho)` Here, c i...

The story reaches its climactic moment when one morning while riding “the beautiful white horse,” Mourad and Aram accidentally run into John Byro. Byro is none other than the owner of the horse. Byro instantly recognizes the horse to be his. The speciality of this scene is that each of the three persons - Byro, Mourad and Aram - present there knows that the horse belongs to Byro, yet no one admits so. It’s clear to Byro that these boys had brought his horse. Still, instead of claiming his horse outright and accusing the boys of stealing it, he handles the situation with appreciable subtlety. He knows that Mourad and Aram belong to the Garoghlanian tribe, which is famous for their unwavering adherence to the virtue of honesty. He is sure that the boys couldn’t have stolen his horse for monetary gain, and that they would return his horse. So, he leaves only saying, “Tooth for tooth, he said. I would swear it is my horse if I didn’t know your parents. The fame of your family for honesty i...

The narrator of "The Leap" states that she owes her continued existence to her mother three times. If her mother were not in great physical condition, the narrator would not be alive. The first time that the narrator owes her existence to her mother is, of course, her birth. If Anna Avalon had not saved herself from falling when lightning hit the main circus pole, the narrator would never have been born. Anna was in great physical condition, and as she was falling from the collapse of the circus tent, she twisted her body toward one of the wires that was sizzling from the lightning that had run down it. She grabbed this wire and saved her life.  The second time the narrator owes her existence to her mother began while her mother recuperated in the hospital from her burns and accidental breaking of her arm by one of the men who rescued her. While Anna was in this hospital, she fell in love with her attending physician, who was a specialist in complicated breaks. He fell in lov...

In Chapter 1, Scout describes her hometown of Maycomb, Alabama. She says that Maycomb was a small, old town where people moved slowly. Scout says that in the summer the weather could become extremely hot to the point that men's stiff collars would wilt by nine in the morning. The ladies of Maycomb were gentle Southern Belles who would bathe at noon and fan themselves on their porches after they took their naps. People were in no hurry because there was nothing to do in Maycomb. Scout also mentions that people had little to no money to spend because of the economic crisis. No much in Maycomb had changed since the Civil War and most of the businesses were situated around the town center. Maycomb is also a rather melancholy town which is a common element of Southern Gothic literature. Since nothing goes on in the small town, most of the attention is focused on the controversial trial of Tom Robinson. 

I believe that Goodman Brown does not attend a witches' Sabbath led by the Devil.  The entire thing is a dream , and it did not really happen.  The final paragraph of the story admits to readers that Goodman Brown did indeed dream the events that occurred in the forest.  A stern, a sad, a darkly meditative, a distrustful, if not a desperate man did he become from the night of that fearful dream. Nevertheless, the result of the dream is that Goodman Brown's faith in the people of his town is destroyed.  He can no longer sing hymns in church or listen attentively to the minister.  Goodman Brown even shrinks away from his wife.  He has lost his faith in Faith.  The dream is simply a very real dream to Goodman Brown.  That makes sense to me.  I've had dreams that caused me to question whether or not I dreamed the events or actually experienced the events.   Science can explain this phenomenon.  Brain scans have been conducted on people that have been asked to perform a specifi...

Unstable nucleii undergo decay reactions in which particles and/or radiation are emitted and new daughter product/s are obtained. Thus, radioactive decay works by emission of particles and/or radiation. There are 3 common types of radioactive decay that elements undergo: alpha decay, beta decay and gamma decay. Alpha decay results in the emission of an alpha particle, which is nothing but a helium atom. In this process, the parent atom loses 2 protons and 2 neutrons; thus its atomic number decreases by 2 and mass number by 4. Beta decay is the emission of an electron. Beta decay is accompanied by an increase in the charge of the nucleus. Gamma decay is a result of the emission of gamma rays, which are nothing but electromagnetic radiation. Gamma decay does not change the charge or mass of the parent atom. Radioactive decay is a natural process. Scientists and engineers also make use of it for various purposes, such as electricity and heat generation, making weapons, and medicinal ap...

In Chapter 11 of To Kill a Mockingbird , two literary techniques author Harper Lee uses to represent Atticus's masculinity are imagery and figurative language . Throughout the novel, Lee uses Atticus to show us that masculinity necessitates bravery. However, interestingly, one way in which she defines bravery is the ability to pay the utmost respect to your fellow human beings at all times, regardless of any circumstances, something that takes a great deal of courage to do. In Chapter 11, Lee uses the scene Scout narrates of Atticus paying his respect to Mrs. Dubose to characterize his bravery and to show bravery's close relationship with respect. Imagery is first used to depict Atticus's bravery. Imagery is found in Scout's description of Atticus "sweep[ing] off his hat" and "gallantly" greeting Mrs. Dubose anytime he passes her house. Since we can visibly see hats, as well as hats being swept off a man's head, we know Scout's descripti...

We are asked to test the claim of the mean salary being $91,350 (`mu = 91350 ` ) using a sample of 60 salaries with a mean of $90,350 (` bar(x)=90350 ` ) and a population standard deviation of $5000 (s=5000.) ** I will recalculate if this is a sample standard deviation at the end.** (a) The sample mean is not the sought after population mean, but we do not reject the claim outright. We would not expect the sample mean to be exactly 91350; there is some variability expected. If we were to do another sample of 60 salaries it is unlikely that the mean of this new sample would be 90350. However, we do expect the sample means to be "close" to the population mean. In fact an application of the central limit theorem tells us that as the sample size grows, the means of the samples will be forced closer to the true population mean. We use hypothesis testing to determine if the sample mean is outside of the expected range of sample means assuming that the population mean is actually 91...

Framton Nuttel does not seem like a particularly attractive or likeable character. He seems to have been created to serve as the ideal victim for young Vera. He is neurotic and self-centered. Mrs. Sappleton describes him to her husband after Nuttel has fled. "A most extraordinary man, a Mr. Nuttel," said Mrs. Sappleton; "could only talk about his illnesses, and dashed off without a word of goodbye or apology when you arrived. One would think he had seen a ghost." Even Mrs. Sappleton, who leads a boring life, finds Nuttel boring. People who are always talking about their illnesses are never likeable. We start wondering whether some of those illnesses might be contagious. They make us feel a little bit itchy. We are not doctors and don't know how to respond except to ask, "Have you seen a doctor?" Which brings up another whole megillah. Framton can, and does, talk about all the doctors he has seen and what they have told him. "The doctors agree in o...

Edgar Allan Poe's use of onomatopoeia is rather subtle in "The Tell-Tale Heart," but it is present in at least three places after the narrator has killed the old man whose eye had disturbed him so terribly. After killing the old man and dismembering him, the narrator skillfully hides the body parts under the planks of the wooden floor in the old man's room. There are no traces of blood or obvious disturbances on the floor, and when the police come to follow up on a scream heard by a neighbor hours before, the narrator lets them in with confidence. As the police begin their investigation, the narrator becomes increasingly nervous and swings a chair across the floor; he says, [he] " grated it upon the boards." The guttural sound of the g and the percussive t mimic the harsh sound. As he begins to imagine the old man's heart " beating ," the two syllables of the word with the emphasis on the first, with its dull sound of the b , sounds like a h...

John Keats, English Romantic poet, had a remarkably short career; his greatest odes were written not long before his death at age twenty-five. Keats had lived at Hampstead, a rural area just north of London, when he wrote "Ode to a Nightingale." Because Keats had been looking after his brother, Tom, who was sick with tuberculosis, he had been thinking about the transient nature of life.  That train of thought, coupled with the bucolic setting in which he'd lived and heard bird songs, combined to produce the conceit of the song of the nightingale, in which Keats observes a sort of immortality.  Though the bird would pass away, its beautiful song would endure in the natural world.   Odes are addressed to a particular subject, and Keats' poem is meant to celebrate the bird whose song will remain immortal, a contrast to the lives of men.

Integrate `int(ds)/[s^2(s-1)^2]` Integrate the given rational function using the method of partial fractions. `1/[s^2(s-1)^2]=[A/s]+[B/s^2]+[C/(s-1)]+[D/(s-1)^2]` ` ` `1=As(s-1)^2+B(s-1)^2+Cs^2(s-1)+Ds^2` `1=As(s^2-2s+1)+B(s^2-2s+1)+Cs^3-Cs^2+Ds^2`  `1=As^3-2As^2+As+Bs^2-2Bs+B+Cs^3-Cs^2+Ds^2` `1=(A+C)s^3+(-2A+B-C+D)s^2+(A-2B)s+B` Equate coefficients and solve for A, B, C, and D. `B=1` `A-2B=0` `A-2(1)=0` `A=2` `A+C=0` `2+C=0` `C=-2` `-2A+B-C+D=0` `-2(2)+1-(-2)+D=0` `-4+1+2+D=0` `D=1` `int[2/s]+[1/s^2]+[-2/(s-1)]+[1/(s-1)^2]` `=2ln|s|-(1/s)-2ln|s-1|-1/(s-1)+C` The final answer is: `=2ln|s|-(1/s)-2ln|s-1|-1/(s-1)+C `

Chapter 9 is titled "The Emerald City and Beyond: Getting Your Entire Organization Above the Line." This chapter takes place in the third and final section of the book, which focuses specifically on how accountability within groups can achieve results. The authors emphasize that accountability within groups can occur once any individual person (presumably you, the reader) has made a conscious decision to commit to accountability and is willing to share the idea with others within his or her organization, including superiors and subordinates, peers, and even stakeholders. As mentioned many times previously in this book, accountability hinges on our ability to let go of the idea that we are the victim in any given situation and to decide to take ownership of a situation and its outcomes. Much of the chapter then is dedicated to five key activities that will help build accountability within groups: At every level within an organization, every person should receive training in ...

According to this list of characters, I would rank Judge Taylor and his family as the community members with the highest ranking socioeconomic status. Judge Taylor is the highest ranking member of the Maycomb judicial system, and appoints Atticus to defend Tom Robinson. As a judge, Taylor presides over every case in Maycomb, which is a very prestigious and important occupation. Next on the list is Atticus Finch , who is a highly respected lawyer and politician. He is continually re-elected to represent Maycomb in the Alabama state legislature and runs unopposed. His sister, Alexandra, also occupies the upper-class of Maycomb. She is the quintessential Southern Belle, who participates in social events and runs the missionary circle. Miss Maudie may not occupy the upper-class, but certainly would be considered upper-middle-class. She is the Finches neighbor who also participates in Alexandra's missionary circle which indicates that she is accepted by the upper-class Maycomb citi...

In this complex stanza, points are being made in reference to a Biblical allusion to Psalm 8:5: "You have made [humans] a little lower than the Angels and crowned [humans] with glory and honor" (Psalm 8:5). To describe laborers—as seen by him in the oil painting " L'homme à la houe " (1863) by Jean-François Millet—Edwin Markham enlarges the Biblical concept of "a little lower," making it a great "gulf" of separation between the laborer and the angels (seraphim). He assigns "Time's tragedy" to the laborer's "aching stoop." Dramatizing his point for the learned (non-laborers) who are reading his poem, he suggests that such stooped, lowly, "profaned and disinherited" laborers have no strength to consider the problems Plato poses or the theories he presents; they have no opportunity to unbend and turn their eyes skyward to contemplate the meaning of the movement of the starry Pleiades.  What gulfs between him...

There are more differences than similarities between the characters of Brutus and Cassius. The two men are similar in being courageous warriors, distinguished Romans, and in both being opposed to the obviously dangerous monarchical ambitions of Julius Caesar. Since Brutus and Cassius are the most important characters in the play, Shakespeare evidently wanted to distinguish them by highlighting their differences. Cassius is selfish, envious, and greedy. He is worldly wise and cunning. He is more outgoing than Brutus. He understands people far better than Brutus because he judges others by himself--and there are always more people like Cassius than like Brutus. Brutus is a loner, a book-lover, a philosopher. He is moved by ideals rather than by personal interests. Like Cassius, he judges others by himself and consequently makes bad mistakes, most notably by sparing Antony's life and giving him permission to speak at Caesar's funeral. Brutus is kind, generous, and patriotic. He an...

Pip’s childhood is overshadowed by the darkness of the marshlands. The first event of the book is him sitting in a cemetery when a convict comes up to him. Dickens describes the importance of the dreary marshlands for establishing the mood.  My first most vivid and broad impression of the identity of things, seems to me to have been gained on a memorable raw afternoon towards evening. At such a time I found out for certain, that this bleak place overgrown with nettles was the churchyard. . . (Chapter 1)  Light and dark can be metaphorical. For example, Miss Havisham keeps herself surrounded by darkness. She never leaves her house. Her isolation is a result of the difficult life she has led. The reason she remains hidden in the shadows is that she has lost faith in human nature and no longer wants to interact with people. The darkness is both literal and metaphorical when Pip sees what is left of Miss Havisham's wedding cake. Certain wintry branches of candles on the high chimneypie...

There are many strategies a company can use to improve its customer service. Here are a few. Inc.   says that customer service begins with hiring quality employees--particularly managers--who are likely to remain with the company for an extended period of time.  Forbes adds that employees should be available to customers who need help or have a complaint. However, employees should also not "crowd" customers who want to be left alone. It is also very important for employees to take interest in the products or services they are selling; knowledgeable employees can help customers make informed purchases, but employees who are unfamiliar the company's products (e.g. those at many big-box stores) cannot help customers. Employees should also be attentive to their customers' experiences so that they can correct problems before customers begin to complain.  Inc. gives the example of a customer at a restaurant who has not eaten any of his or her food but has not yet compla...

`sum_(n=1)^oo n^2/(n^2+1)` To verify if the series diverges, apply the nth-Term Test for Divergence. It states that if the limit of `a_n` is not zero, or does not exist, then the sum diverges. `lim_(n->oo) a_n != 0`      or      `lim_(n->oo) = DNE` `:.` `sum` `a_n` diverges Applying this, the limit of the term of the series as n approaches infinity is: `lim_(n->oo) a_n` `=lim_(n->oo) n^2/(n^2+1)` `= lim_(n->oo) n^2/(n^2(1+1/n^2))` `=lim_(n->oo)1/(1+1/n^2)` `=1/1+0` `=1` The limit of the series is not zero. Therefore, by the nth-Term Test for Divergence, the series diverges.

Evaluate `sum_(n=1)^(oo)n^(10)/10^n ` We are asked to use the ratio test: For the ratio test, we take the limit of the ratio of the (n+1)st term to the nth term of the sequence of partial sums. If this limit is less than 1 in absolute value, the series converges, if greater than 1 it diverges, and there is no conclusion if the limit is 1. `lim_(n->oo)((n+1)^10/(10^(n+1)))/(n^10/10^n) ` `=lim_(n->oo)((n+1)^10)/10^(n+1)*10^n/n^(10) ` `=lim_(n->oo)(n+1)^10/n^(10)*lim_(n->oo)10^n/10^(n+1) ` `=1*1/10=1/10 ` Since this is less than 1, the series converges. (The sum is a little more than 376.)

Phillip and his family lived in Curacao for a little bit less than three years.  I wish that I could be more specific than that, but the text is a bit vague on when Phillip and his family came to Curacao.  On page 15 (of my text), Phillip tells his readers that his family arrived on the island in "late 1939."  Due to the war, Phillip's family thinks that they will be safer back in the United States.  Phillip's father secures them passage in early April.  Unfortunately, the book doesn't give a year for that trip until the following chapter.  At the beginning of chapter three, Phillip tells his readers that the ship was torpedoed on April 6, 1942.  April of 1939 to April of 1942 would be three years on Curacao, but Phillip specifically said they arrived in late 1939.  I think Phillip lived in Curacao for two and a half years (give or take a month). 

Keep in mind that heuristics are methods or techniques that McRaney calls "mental shortcuts you use to solve common problems."  Also keep in mind that the full title of the book is as follows:   You are Not So Smart:  Why You Have Too Many Friends on Facebook, Why Your Memory is Mostly Fiction, and 46 Other Ways You're Deluding Yourself .  Understanding these two things clarifies the question a bit.  Your question is really about the techniques involved in our self-delusion.   The three main subjects in this book are cognitive biases, heuristics, and logical fallacies.  These are components in your mind, like organs in your body, which under the best conditions serve you well.  Life, unfortunately, isn't always lived under the best conditions.   This quotation contains the answer to your question.  McRaney admits here that heuristics do "serve you well," but only "under the best conditions."  Therefore, the answer to your question is that heuristic...

If x is a variable, then an infinite series of the form `sum_(n=0)^ooa_n(x-c)^n=a_0+a_1(x-c)+a_2(x-c)^2+.......+a_n(x-c)^n+......` is a power series centered at x=c, where c is a constant. Given `f(x)=5/(5+x^2), c=0` Let's write f(x) in the form `a/(1-r)` `f(x)=5/(5(1+x^2/5))` `f(x)=1/(1+x^2/5)` `f(x)=1/(1-(-x^2/5))` which implies that a=1 and r=`-x^2/5` So power series for f(x)=`sum_(n=0)^ooar^n` `=sum_(n=0)^oo(-x^2/5)^n` `=sum_(n=0)^oo(-1)^n(x^2)^n/5^n` `=sum_(n=0)^oo(-1)^nx^(2n)/5^n` This power series converges when `|r|<1` `=>|-x^2/5|<1` `|x^2|<5` `|x|<sqrt5` Interval of convergence is `(-sqrt5,sqrt5)`

The thesis for your essay could be something along the lines of the following: The Persian Gulf War began after Iraq under Saddam Hussein invaded Kuwait in 1990 and the U.S. spearheaded a campaign called Operation Desert Storm that appeared to achieve success; however, the war left behind unresolved issues that in part led to a second war in the region in 2003.  Here is some additional background information: Accusing Kuwait of taking oil from Iraqi oilfields, Saddam Hussein invaded Kuwait in August of 1990. He fully expected that other Arab states would back his actions. However, most of the countries condemned Iraq for its actions and called on the U.S. and NATO for help. In November of 1990, the U.N. resolved to carry out action against Iraq if it did not remove its troops from Kuwait, and the first U.S. air raids began in January of 1991. Using laser-guided missiles and night-bombing technology, the U.S. air attacks quickly disposed of Iraqi opposition, and the American troops move...

Many of the people depicted in Genesis are farmers and sheepherders, from the very beginning. Adam and Eve lived in a garden, after all.  When Adam and Eve were evicted from the garden, they had two sons, Cain and Abel, who were involved in agriculture. We see this from the offerings they made to God. Cain offered grain and Abel offered up one of his animals.  Later on, Abram and Lot had to part ways because the land they were living on was not sufficient to support the herds each man had. Animal sacrifice was hugely important in the entire Old Testament, beginning with Abel. In order to be able to support a large family and to be able to offer appropriate sacrifices to God, people needed large herds.  There are more incidents with the size of herds, such as when Laban tricked Jacob into marrying his older daughter, Leah. Jacob had to wait another seven years for Rachel and he ended up taking a large part of Laban's flock because he tricked Laban.  The story of Joseph and the Coat ...

We wish to divide this man's garden into the minimum number of square plots possible. A square has all four sides with the same length.Our garden is a rectangle, so the answer is clearly not 1 square plot. If we choose the wrong length for our squares, we may end up with missing holes or we may not be able to fit our squares inside the garden. So we have 84 meters in one direction and 56 meters in the other direction. When we start dividing the garden in square plots, we are "filling" those lengths in their respective directions. At each direction, there must be an integer number of squares (otherwise, we get holes or we leave the garden), so that all the square plots fill up the garden nicely. Thus, our job here is to find the greatest common divisor of 84 and 56. For this, we prime factor both of them: `56 = 2*2*2*7` `84 = 2*2*3*7` We can see that the prime factors and multiplicities in common are `2*2*7 = 28` . This is the desired length of the square plots. If you wi...

Balance of power is a very common relationship dynamic that provides many opportunities for emotional tension and plot movement in dramatic literature. When one character is perceived to hold power over another, tension results, because characters try to attain their goals and desires, and these can be at odds because of power dynamics. Holding power is a desirable state of being that builds contentment and satisfaction for some people, as it can allow people to move freely and do what they want. In some cases having power over others feeds the ego of those who hold the greater amount of power. In this way, an imbalance of power can be used to show the relative integrity of characters in relation to one another. The balance of power is very much a cultural issue, and one that has changed through the course of history. For example, in the Middle Ages, the various hierarchical roles assumed by knights, the monarchy and the peasants all fulfilled different roles within society. In some cu...

When answering this question, you should consider the themes of isolation and rejection in Frankenstein and “The Rime of the Ancient Mariner.” In Frankenstein , Walton, Victor, and the creature are all isolated. Walton is isolated on ship because he has no friends. “I have no friend, Margaret (Letter 2),” he tells his sister. Victor isolates himself when he chooses to study reanimation. “And the same feelings which made me neglect the scenes around me caused me also to forget those friends who were so many miles absent, and whom I had not seen for so long a time” (Chapter 4). The creature is similarly isolated when he is forced to roam alone in the mountains. When telling Victor his story, he concludes: “I am alone and miserable, man will not associate with me” (Chapter 16). In “The Rime of the Ancient Mariner”, the Mariner tells a story of death and isolation to the Wedding Guest. After killing the albatross, the Mariner is left alone when all the other sailors die. “I looked upon th...

Most of the criticism against Franklin Delano Roosevelt was aimed against his New Deal policies. The New Deal was a series of socially liberal legislative programs aimed at ending The Great Depression and creating protections to ensure that another depression would not occur. Some New Deal programs, such as the Works Progress Administration, were temporary and aimed at rekindling industry and business by employing men in public works projects. Others were intended to be permanent, such as the Federal Deposit Insurance Corporation (FDIC), which insures customers' accounts (up to $250,000) against bank defaults. Father Charles Coughlin was one New Deal critic. Coughlin hosted a popular radio program. While, initially, he had been supportive of Roosevelt, his favor had faded by 1934. Coughlin thought that Roosevelt's initiatives were still too friendly to banks. He argued instead for the nationalization of certain institutions, such as the Federal Reserve. He was staunchly against...

Walter Mitty's wife does not play any role in any of his fantasies. This is suggestive. Apparently his fantasies are, among other things, a means of escape from his hectoring wife. He has a "secret life" because his fantasies are kept a secret mainly from her. It is also suggestive that there is no apparent misogyny in his fantasies. If he hated his wife and wanted to get rid of her, these feelings might be detectable in his fantasies. But he seems to be dependent on her because he is absent-minded, incompetent and introverted. She takes care of all the practical matters of both their lives. He might be lost without her. He fantasizes about being a man of action, but he must know he really isn't. There is only one fantasy in which he appears to be fantasizing about being romantically involved with a another woman. That is the one in which he is testifying in a murder trial. A woman’s scream rose above the bedlam and suddenly a lovely, dark-haired girl was in Walter Mi...

Ultimately, I do not think think the characters would function differently if they were all female. Beckett grapples with the great existential dilemma: the point of existence. Godot, whether he is God, a god, a principle, a philosophy, or strictly human, comes to mean everything to Vladimir and Estragon. The absurdity in their situation derives from the fact that they are unable to ever encounter Godot. They are left with the choice to either commit suicide or continue waiting—to accept that life is inherently meaningless or to create their own meaning. This is, at least according to the existentialists, the universal condition of all humanity. Therefore changing the gender of the characters would not alter that fact. Women grapple with this struggle just as much as men do. There may need to be some cosmetic changes (name alterations, costume swaps), but I do not think a gender change would affect the essence of Beckett's characters. 

The United Nations began operations on October 24, 1945. After two devastating world wars in the first half of the twentieth century, its original intention was to help increase security and avoid future wars where possible. There have been plenty of wars since then, so it is hard to determine how successful the U. N. has been in that regard, but there have been several other successes. UNICEF: This is the United Nations Children's Emergency Fund. The U. N. formed UNICEF in 1946. It has helped millions and won a Nobel Prize. The United Nations Environmental Program: The Montreal Protocol was created to fight ozone depletion. In effect since the 1990's, the Antarctic ozone hole has finally begun shrinking. World Health Organization: The United Nations' health organization known as WHO (World Health Organization) was able to eradicate the deadly smallpox disease in 1980. Peacekeeping: United Nations peacekeeping troops, composed of soldiers from member countries, have bee...

Friction is resisting force - a type of force that resists movement. The type of friction that resists movement between two objects in contact with each other is dry friction. There is dry friction between a book and a table, or the wheels of a car and the road. Dry friction can be divided into two. Objects in contact against each other can be moving with respect to one another or stationary. When the objects are stationary, the friction between them is called static friction. Static friction resists movement. Imagine a box full of books on a floor. Initially, when you try to push the box, you struggle. This is because of the static friction between the box and the floor that resists the force you apply. Overcoming this, it becomes easier. Once the box starts to move, there is sliding friction. Sliding friction is the type of friction between objects moving relative to one another, and always opposes the acting force. Thus, it resists the movement as well as you push the box.  Friction...