Notes

To determine the interval of convergence for the given series: `sum_(n=1)^oo(-1)^nx^n/n` , we may apply Root Test. In Root test , we determine the limit as: `lim_(n-gtoo) root(n)(|a_n|)=L` or  `lim_(n-gtoo) |a_n|^(1/n)=L` The series is   absolutely convergent if it satisfies the Root test condition: L` lt1.` For the  given series: `sum_(n=1)^oo(-1)^nx^n/n` , we have: `a_n= (-1)^nx^n/n`  Then, set-up the limit as: `lim_(n-gtoo) |(-1)^nx^n/n|^(1/n) =lim_(n-gtoo) |x^n/n|^(1/n)` Note: `|(-1)^n|=1` and `1*|x^n| =|x^n|` . Apply Law of exponents: `(x/y)^n =x^n/y^n` and `(x^n)^m= x^(n*m).` `lim_(n-gtoo) |x^n/n|^(1/n)=lim_(n-gtoo) |(x^n)^(1/n)/n^(1/n)|`                         `=lim_(n-gtoo) |x^(n*1/n)/n^(1/n)|`                         `=lim_(n-gtoo) |x^(n/n)/n^(1/n)|`                          `=lim_(n-gtoo) |x^1/n^(1/n)|`                          `=lim_(n-gtoo) |x/n^(1/n)|` Evaluate the limit. `lim_(n-gtoo) |x/n^(1/n)| =( lim_(n-gtoo) |x|)/( lim_(n-gtoo) |n^(1/n)|)`                      `= |x...

The theme of "The Way Up to Heaven" is essentially revenge. Mr. Foster has been secretly tormenting his wife for years with his procrastination and deliberate delays. She doesn't resent his behavior because she can't be sure whether he is doing it intentionally or it is just an annoying character trait. One morning, she find definite evidence that he is a sadist who enjoys torturing her because he knows how important it is to her to be on time for appointments. Since Mr. Foster uses passive aggression to torment his wife, it is poetic justice that she should get revenge through the same passive aggression. She doesn't actively do anything to kill her husband; she only refrains from doing something. When Mr. Foster delays their trip to the airport by pretending he left something behind in their house, Mrs. Foster, waiting in the car, hears a sound of the elevator getting stuck between the floors. Instead of helping him, she proceeds to the airport, thereby letting ...

Dramatic irony occurs when the reader knows or understands something about the events that are unfolding that the characters do not.  This can often be tragic, such as in Shakespeare's Romeo and Juliet when the audience knows that Juliet is only asleep, but Romeo takes his own life because he believes that she is dead.  However, it can also be used for comedy, as it is in this story.  The narrator, although he is writing as an older man reflecting on his past experiences, speaks with a child's understanding of life and family.  When his mother says that she cannot afford a baby, he takes her literally, imagining that different babies come at different costs.  He thinks that his mother must be holding out for an expensive baby, saying, "The Geneys up the road had a baby, and everyone knew they couldn't afford seventeen and six.  It was probably a cheap baby, and Mother wanted something really good, but I felt she was too exclusive.  The Geneys' baby would have done...

Isabel takes three things from Miss Finch's home.  She takes her blankets, her shoes, and some flower seeds that her mother had collected.   Isabel's mother had collected the flower seeds and put them in a jar, but Isabel doesn't know what they will grow into.   At this point in the story, Mr. Robert is taking Isabel and Ruth to be sold, but he allows the two girls to go back into the house to collect their blankets and shoes.  He's not doing it to be nice either.  Having shoes and blankets will increase the slave value of Isabel and Ruth, and Mr. Robert is greedy.  Mr. Robert will  not allow Isabel to take anything else, so she needs to grab something that is easily transported and easily hidden.  The seeds fill both of those requirements and have the added sentimental value of reminding Isabel of her mother.   I looked around our small room, searching for a tiny piece of home I could hide in my pocket.  What to take? Seeds. On the hearth stood the jar of flower seeds...

Fossils are remnants of plants and animals that once lived. When they died, some of them had their bodies buried in the soil or water. Over time, deposition caused the formation of rocks, and these dead plants and animals were fossilized and preserved in these rocks. When we dig through rock layers, we sometimes come across fossils and scientists can use them to determine the age of the rocks they were buried in. The age of a fossil is determined by radiometric dating. The method uses the knowledge of half lives of radioactive isotopes of elements and the presence of these isotopes in animal/plant bodies. One such isotope is carbon-14, which has a half life of 5,730 years. This obviously cannot be used with Jurassic fossils or rocks, since the Jurassic period existed between 150-200 million years ago. For such samples, we can use Uranium-235, which has a half-life of about 700 million years and it decays to lead-207. Thus, knowing the ratio of U-235 and Pb-207, we can determine the age...

`a_n=nsin(1/n)` Apply n'th term test for divergence, which states that,  If `lim_(n->oo) a_n!=0` , then `sum_(n=1)^ooa_n` diverges `lim_(n->oo)nsin(1/n)=lim_(n->oo)sin(1/n)/(1/n)`   Apply L'Hospital's rule, Test L'Hospital condition:`0/0` `=lim_(n->oo)(d/(dn)sin(1/n))/(d/(dn)1/n)`  `=lim_(n->oo)(cos(1/n)(-n^(-2)))/(-n^(-2))` `=lim_(n->oo)cos(1/n)` `lim_(n->oo)1/n=0` `lim_(u->0)cos(u)=1`  By the limit chain rule, `` `=1!=0`  So, by the divergence test criteria series diverges.   ` `

`int1/(x^2-4x+9)dx` Let's complete the square for the denominator of the integral as: `(x^2-4x+9)=(x-2)^2+5`   `(x-2)^2+(sqrt(5))^2` `int1/(x^2-4x+9)dx=int1/((x-2)^2+(sqrt(5))^2)dx` Let's apply the integral substitution, substitute `u=x-2` `du=1dx` `=int1/(u^2+(sqrt(5))^2)du` Now use the standard integral :`int1/(x^2+a^2)=1/aarctan(x/a)` `=1/sqrt(5)arctan(u/sqrt(5))` substitute back u=(x-2) and add a constant C to the solution, `=1/sqrt(5)arctan((x-2)/sqrt(5))+C`

England's Industrial Revolution began in 1760 due to a number of factors. First, England was experiencing an economic boom due to trade, and the money was invested in financial institutions that funded factories. Additionally, the 18th-century Agricultural Revolution in England resulted in an increase of food production and less need for agricultural workers due to technological improvements. These changes both decreased the number of agricultural jobs relative to factory jobs and lowered food costs, allowing families to spend more money on manufactured goods. England also possessed natural resources that facilitated the rise of industry; for example, the country contained a massive supply of coal to power their new factories. In the early 18th century, railroads were improved throughout England, which made exchange of raw materials and manufactured goods across the country much easier than it had been prior to the 18th century.

I would say the Articles of Confederation provided the United States with a government that was effective enough to keep the country functioning in the short term, but not one that was effective enough to last in the long term. In the time from 1781 to 1789, it was not clear that the United States would be able to stay together.  The country was made up of thirteen different states that did not necessarily feel as if they were connected to one another.  The Articles of Confederation created a government that the various states could accept.  This kept the country together, which was very important. In addition, the government was effective enough to take care of at least one important issue.  It was able to bring about a consensus on the issue of the Northwest Territory.  The various states were in conflict with one another as to who should control this area.  The government was effective enough to create the Northwest Ordinance, which settled the issue of the territory and allowed the...

In Chapter 8, Miss Maudie's house catches on fire. During the night, many people help put the fire out. Boo Radley had placed a blanket on Scout's shoulders while she watched the fire, but she didn't notice. This is an instance that shows Boo's bravery (helping out with the fire) but it also shows his shy nature. He puts the blanket on Scout but avoids being noticed.  We’d better keep this and the blanket to ourselves. Someday, maybe, Scout can thank him for covering her up.” “Thank who?” I asked. “Boo Radley. You were so busy looking at the fire you didn’t know it when he put the blanket around you.” At the end of the novel, Boo Radley saves Jem and Scout when Bob Ewell attacks them. This clearly shows his bravery. Shortly after this, he is with Atticus, Tate, and Scout as they watch over Jem. Scout notes his shyness:  Boo saw me run instinctively to the bed where Jem was sleeping, for the same shy smile crept across his face. Hot with embarrassment, I tried to cover u...

The correct answer is (b) Judge Taylor . Judge Taylor closes his eyes at times, but he is not asleep. Instead, he is listening carefully. In Chapter 16, Scout alludes to Judge John Taylor as "a sleepy old shark," meaning that he appears to be sleeping, but he is as swift as a shark to react if anyone disrupts his court. Alluding to one instance in which a lawyer thought that the judge was dozing, the attorney dropped books off the table, hoping to startle and embarrass the judge as he awakened. The angered judge simply opened one eye calmly and told the lawyer if he did this action again, there would be a large fine assessed. Further, Scout recounts that Judge Taylor conducts his court with a surprising informality as he often props up his feet and cleans his fingernails with a pocket knife. However, much like his apparent drowsiness, these rather rustic behaviors belie a sharp intellect and often deceive lawyers into thinking that they might be able to slip in some questions...

Ishmael Beah's novel  A Long Way Gone  opens when the protagonist is ten years old and completely innocent about the destructive nature of the civil war moving inexorably towards his village, Mogbwemo. Although Ishmael had previously encountered refugees fleeing the path of violence, he couldn't grasp the reality of war until rebels actually attacked Mogbwemo; Ishmael internalizes the chaos, confusion and bloodshed, which represents the loss of his innocence. Inevitably, he feels terrified, horrified, plagued by nightmares, and afraid of being caught and conscripted into the rebel army.  Dire necessity and extreme deprivation brought about by starvation slowly prompt Ishmael, his brother and their friends to abandon their pre-war ethics and morals in order to satisfy their basic needs. For example, while on the run from the rebels and overcome with hunger, Ishmael and his cohorts resort to stealing from strangers after they are unable to buy food; this is an injustice they woul...

These type of descriptions that you are asking about fall under two categories: Direct characterization and Indirect characterization. Faulkner uses both cleverly by juxtaposing the direct description of Emily, in contrast with her actions. He does this primarily to deflect the attention of the reader and, ultimately, cause the big shock at the end. Direct characterization happens when Faulkner gives us a step by step account of what Emily really looks like, for example:  [Emily is a] small, fat woman in black[...] Her skeleton was small and spare; [...]She looked bloated, like a body long submerged in motionless water, and of that pallid hue. Her eyes, lost in the fatty ridges of her face, looked like two small pieces of coal ... This direct characterization of Emily is meant to show that the woman whom so many in Jefferson County feared, and thought to be so enigmatic, is merely a short, plump lady of old age whose demeanor may seem unhappy, but is otherwise harmless.  It is almost a...

Bryon is amused and impressed with Mark's ability to get away with anything. Mark's humorous personality and likability allow him to get away with things that typical individuals would get punished for doing. Byron is so impressed with Mark's ability that he considers it a gift. Bryon realizes how rare it is to see a person get away with so much and is often shocked to find out what crimes Mark actually gets away with. When Terry tells him that Mark got away with "borrowing" the principal's car everyday, Bryon is dumbstruck. Mark's ability to get away with things can easily lead to more serious crimes. Without consequences, Mark will feel entitled to commit whatever crimes he chooses. This lack of accountability for committing crimes means that Mark is more likely to attempt serious offenses.

The ideal gas law provides a relationship between the pressure, temperature, volume, and number of particles of gases in a system in accordance to the kinetic theory of gases. This is founded on four assumptions: 1) The particles of gases are negligibly small compared to the distance between them, 2) The particles of gases are not interacting and are not affected by each other other than during collision (which are always elastic) which happens instantaneously, 3) Gases are in continuous random motion, 4) The average kinetic energy for all gases in the system is the same at a given temperature regardless of the type of gas. The ideal gas law states that: `PV = nRT` where P is the pressure, V is the volume, n is the moles of gases, R is the ideal gas constant, and T is the temperature. As can be seen here, keeping all things equal, as the number of moles increases, pressure increases . This is because an increase in the number of particles in the same volume will increase the number of ...

Scout learns several things throughout the novel from Calpurnia. In Chapter 2, Scout says  Calpurnia taught her how to write in cursive . In Chapter 3, Scout criticizes Walter Cunningham, Jr. for pouring molasses over his meat and vegetables during lunch. Calpurnia immediately takes Scout into the kitchen and teaches her a lesson on respecting guests. Later in the novel, Calpurnia takes the children to First Purchase African M.E. Church. During their visit, Scout gains valuable insight into the African American community. She learns being literate is rare in the black community and that Calpurnia lives a "modest double-life." Scout develops perspective and realizes that Calpurnia has a life of her own. Cal also teaches Scout that it is not becoming of a person to "tell all you know." Cal's lessons teach Scout how to treat others with respect and provide Scout with valuable insight which develops her perspective on life.

`sum_(n=1)^oo1/((2n+1)(2n+3))` Using partial fractions, we can write the n'th term of the sequence as, `a_n=1/(2(2n+1))-1/(2(2n+3))` Now the n'th partial sum is, `S_n=(1/(2(2+1))-1/(2(2+3)))+(1/(2(2*2+1))-1/(2(2*2+3)))+(1/(2(2*3+1))-1/(2(2*3+3)))+.............+(1/(2(2n+1))-1/(2(2n+3)))` `S_n=(1/6-1/10)+(1/10-1/14)+(1/14-1/18)+........+(1/(2(2n+1))-1/(2(2n+3)))` `S_n=(1/6-1/(2(2n+3)))` `sum_(n=1)^oo1/((2n+1)(2n+3))=lim_(n->oo)S_n` `=lim_(n->oo)(1/6-1/(2(2n+3)))` `=1/6`

We are given that a is parallel to b, b is parallel to c and c is perpendicular to d and we are asked to determine how line a is related to line d. There are two possibilities: (1) If all of the lines are in the same plane then a is perpendicular to d. It is always true that 2 lines parallel to a third line are parallel; thus since a and c are parallel to b then a is parallel to c. In a plane, parallel lines form congruent corresponding angles with a given transversal. Since c is perpendicular to d the angles formed are right angles so a forms right angles with d and is perpendicular to d. (2) If it is possible that the lines are not all coplanar then a and d could be skew . (Skew lines are noncoplanar lines that do not intersect.)  As asked, the answer is that the relationship cannot be determined.

When Odysseus and his crew find the cave of the Cyclops, along with all his animals and cheese, the crew begs him to take some food and return immediately to the ship.  The men seem to sense, intuitively, that they should not be found in the cave.  Even Odysseus had had a bit of a premonition, before he left the ship, that he would "meet a man arrayed in mighty power, a savage, ignorant of rights and laws."  He was right, because Polyphemus -- although he isn't ignorant of rights and laws -- chooses not to adhere to the codes that most ancient Greeks found acceptable.   Odysseus, hoping that the Cyclops would feel bound by the religious imperative to provide hospitality to travelers, since they were believed to be protected by Zeus himself, refuses his men, and he stays to meet the owner of the cave in the hope that "he might offer gifts."  Odysseus believes he might get a gift because, often, a host would offer such a guest-gift to a traveler as a kindness.  De...

Sam Spade does not have much concrete evidence that Brigid O'Shaughnessy killed Spade's partner Miles Archer. He puts her under extreme emotional and time pressure, while the police are on their way to his apartment, to break down and confess to him by explaining his reasons for suspecting her. He makes her believe that if she tells him the true facts he will continue to protect her from the authorities. She is extremely young and inexperienced. In her initial interview with Spade, she tells him she is five years older than her mythical seventeen-year-old missing sister. She relied on Floyd Thursby for protection before, and now she is relying on Sam Spade, another tough, worldly man. If she doesn't break down and confess to him, he will turn her over to the police when they arrive. They haven't made a thorough investigation of the crime scene at Burritt Street because they assumed Miles Archer was killed by Floyd Thursby, who was killed a short time later on Geary Stre...

In the story, Michael Obi has been appointed the principal of Ndume Central School. With his wife, Nancy, Michael hopes to modernize academic instruction at the school. As the headmaster, he is resolved that the teachers must be held to a high standard and that all old-fashioned and traditional ideas about education must be discarded. To the Obis, the only thing holding back progress is the presence of "old and superannuated people in the teaching field who would be better employed as traders in the Onitsha market." The husband and wife team also plan to modernize the school grounds by planting beautiful gardens. With this two-pronged approach, the Obis hope to bring progress to what they consider a primitive school system. Unfortunately for the Obis, neither bargained for the communal pride of the older villagers. Because of their disrespect for religious traditions in the school district, both the Obis failed in their quest to affect change at Ndume Central School.

To determine the convergence or divergence of the series `sum_(n=1)^oo (-1)^(n+1)/n^2` , we may apply Alternating Series Test. In  Alternating Series Test , the series `sum (-1)^(n+1)a_n` is convergent if: `1) a_n` is monotone and decreasing sequence. `2) lim_(n-gtoo) a_n =0` `3) a_ngt=0` For the series `sum_(n=1)^oo (-1)^(n+1)/n^2` , we have: `a_n = 1/(n^2)` which is a decreasing sequence. As "`n` " increases, the `1/n^2 ` decreases. Then, we set-up the limit as : `lim_(n-gtoo)1/n^2 = 1/oo =0` By alternating series test criteria, the series`sum_(n=1)^oo (-1)^(n+1)/n^2 ` converges . The series `sum_(n=1)^oo (-1)^(n+1)/n^2` has positive and negative elements. Thus, we must verify if the series converges absolutely or conditionally. Recall: a) Absolute Convergence :  `sum a_n`  is absolutely convergent if `sum|a_n|`   is convergent.   b) Conditional Convergence :  `sum a_n`  is conditionally convergent if `sum|a_n|`  is divergent and `sum a_n`  is convergent.   We evaluate th...

Earth has three layers: the uppermost crust, the middle mantle and the innermost core. The outer layer of Earth- the crust, can be classified as either continental crust or oceanic crust, depending upon whether it houses the continents or the oceans. The crust is divided into a number of fragments, each known as a tectonic plate. These plates are in constant motion. Oceanic and continental plates commonly meet at convergent margins or boundaries. Oceanic plates are generally denser as compared to continental plates and slide under the lighter continental plates. This process is known as subduction. Since continental plates are lighter as compared to the oceanic plates, they are more buoyant. Continental plates are also older as compared to the oceanic plates. Another difference is the thickness of these plates. Continental plates are generally thicker as compared to the oceanic plates. Hope this helps. 

Integrate `int(x+4)/(x^2+2x+5)dx` `int(x+4)/(x^2+2x+5)dx=int(x+1)/(x^2+2x+5)dx+int3/(x^2+2x+5)dx` Integrate the first integral on the left side of the equation using the u-substitution method. Let `u=x^2+2x+5` `(du)/(dx)=2x+2` `dx=(du)/(2(x+1))` `int(x+1)/(x^2+2x+5)dx` `=int(x+1)/u*(du)/(2(x+1))` `=1/2ln|u|+C` `1/2ln|x^2+2x+5|+C` The second integral on the left side will match the form  `intdx/(x^2+a^2)=1/atan^-1(x/a)+C` after you complete the square in the denominator. `int3/(x^2+2x+5)dx` `=3intdx/[(x^2+2x+1)+5-1]` `=3intdx/[(x+1)^2+2^2]` `=3(1/2)tan^-1((x+1)/2)+C` `=(3/2)tan^-1[(x+1)/2]+C`  The final answer is:   `1/2ln|x^2+2x+5|+(3/2)tan^-1[(x+1)/2]+C`

`(1/(2x-5)-7/(8x-20))/(x/(2x-5))` `=(1/(2x-5)-7/(4(2x-5)))/(x/(2x-5))` LCD of all the denominators in the complex fraction is `(2x-5)` Multiply both the numerator and denominator of the complex fraction by LCD, and use the distributive property, `=((2x-5)(1/(2x-5))-(2x-5)(7/(4(2x-5))))/((2x-5)(x/(2x-5)))` Simplify, `=(1-7/4)/x` `=((4-7)/4)/x` `=(-3/4)/x` `=-3/(4x)`

In one of the novel's opening scenes, Holden provokes his roommate, Stradlater, by trying to pry information out of him about his date with Jane Gallagher. Because Stradlater is not completely forthcoming about the date, Holden becomes upset and worried that Stradlater has somehow hurt or defiled Jane. Holden calls Stradlater a "moron" and hurls other insults at him and then tears up the composition he has written for him. Stradlater retaliates by pinning Holden down and hitting him. In chapter 17, Holden meets Sally Hayes for a date. At the ice-skating rink, Holden rants to Sally about all the "phonies" he has met at school and in New York. He proposes that they run away together to a cabin; when she ridicules his idea, he calls her a "royal pain in the ass." Their date ends with Sally in tears. When Holden visits Phoebe in chapter 21, he admits to her that he has been kicked out of Pencey Prep and tells her he is thinking of going to a ranch in Color...

Miss Temple has a lasting effect on the girls because she genuinely cares about them and shares their trials. Mr. Brocklehurst, on the other hand, is a hypocrite who lives well while lecturing the girls on their need for humility and austerity. He doesn't see them as fully human, is insensitive to their needs, and doesn't genuinely care about them. While Mr. Brocklehurst specializes in humiliation, such as making Jane stand on a stool while he tells the whole school she is a liar, Miss Temple is kind and merciful, putting her arm around Jane after the ordeal, kissing her and saying she believes Jane's side of the story. Helen Burns says of her:  Miss Temple is full of goodness; it pains her to be severe to any one, even the worst in the school: she sees my errors, and tells me of them gently; and, if I do anything worthy of praise, she gives me my meed liberally. When Jane breaks her slate, Miss Temple says she won't be punished because she knows it was an accident. Whi...

History is very interesting because it does help us today. So many events in history have relevance to current events. History repeats itself over and over again. The names and places may change, but the basic events are very similar. If you can see the similarities between past and present events, you should see how relevant history is. It is our job to learn from the past so we don’t keep repeating the same mistakes now and in the future. A fairly recent example of this can be seen with the Great Recession of 2008-2010. There are some parallels between the events of the Great Recession to the events of the Great Depression of the 1930s. One of the events leading to the Great Depression was risky investment practices. In the 1920s, banks made loans to many people who were already in debt or who didn’t have an income level that could support the loans they were receiving. People were also investing in companies without doing much research on these companies. In the Great Recession of 2...

In the first stanza of the poem, the imagery of the "grey sea and the long black land" is rather dark, and the idea of the "startled little waves that leap / In fiery ringlets from their sleep" is not a particularly positive one (lines 1, 3-4).  Gray and black do not have light-hearted or hopeful connotations; they are often seen as rather sad, even morbid.  Then, the waves are personified as being startled (usually not a good thing).  This stanza is characterized less by a tone of excitement and more by the speaker's sorrow over being at such a great distance from his love.  Things seem to be moving slowly. However, after the break, in the second stanza, the pace picks up and the speaker uses imagery that is much more pleasing with a much more positive connotation: the "warm sea-scented beach" and "two hearts beating each to each."  The narrator's sense of anticipation and excitement seems conveyed by the more precise distances he must t...

The main character in "The Yellow Wallpaper," Jane, is mentally ill. The story, written in first person epistolary style, is rife with dramatic irony because of its unreliable narrator. Readers have to ferret out the true psychological condition from what Jane says and from what she doesn't exactly say. At the beginning of the story, Jane suffers from what today's mental health professionals would term post-partum depression. The baby isn't mentioned often, but the couple has retained hired help to care for the baby because he makes Jane "so nervous." Jane's husband, a physician, tells her she has "temporary nervous depression" and "a slight hysterical tendency," but "he does not believe [she] is sick." Thus he prescribes various tonics, but the primary therapy is "the rest cure," which means she isn't allowed to do any work or to socialize much. Under the negative effects of the rest cure, Jane's condi...

Peter Pan has lost his shadow. After the Darling children are asleep, he calls to Tinker Bell, who is hiding in a jug, to ask where it is. She responds that it is in the big box in the drawer. In his eagerness to get it back, which shows the kind of impulsive, enthusiastic creature Peter Pan is, he scatters the contents of the drawer all over the floor looking for it. He is so delighted to have found his shadow that he closes Tinker Bell into the drawer without even realizing it and forgets all about her. Then, when he can't figure out how to reattach his shadow to his body, the mercurial boy sits down and sobs until he wakes up Wendy. Wendy sews it back on. 

2016 seems to be a watershed year, and the spotlight is definitely on the presidential election. Whatever the outcome may be, the focus is centered on the two major candidates for the presidency: Hillary Clinton and Donald Trump. The pros and cons for voting may boil down to the national mood. According to Forbes , the six top issues for voters in 2016 are the economy (84%), terrorism (80%), foreign policy (75%), health care (74%), gun policy (72%), and immigration (70%). One benefit of voting is that voters can decide the nation's course for the next four years. Voters will decide America's foreign policy and her attitude towards race relations, illegal immigration, gun rights, the Affordable Care Act, and terrorism. Half the country may not like who the new president will be. Supporters of Hillary Clinton will be irretrievably disappointed if Donald Trump becomes president, while supporters of Donald Trump will be similarly frustrated if Hillary Clinton becomes Commander-in-...

Given ` xdy = (x + y + 2)dx ` => `xdy/dx = (x + y + 2)` => `y'=1+y/x+2/x` => `y'-y/x = 1+2/x` => `y'-y/x =(x+2)/x` when the first order linear ordinary differential 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/x =(x+2)/x--------(1)` `y'+p(x)y=q(x)---------(2)` on comparing both we get, `p(x) = -1/x and q(x)=(x+2)/x` 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 (-1/x) dx) *((x+2)/x)) dx +c)/e^(int (-1/x) dx)` first we shall solve `e^(int (-1/x) dx)=e^(ln(1/x)) = (1/x)`      so proceeding further, we get y(x) =`((int e^(int (-1/x) dx) *((x+2)/x)) dx +c)/e^(int (-1/x) dx)` =`((int (1/x) *((x+2)/x)) dx +c)/(1/x)` =`(int (1/x) *((1+(2)/x)) dx +c)/(1/x)` =` x(ln(x)-2/x +c)` so now let us find the particular solution of differential equation at y(1)=10 `y(1) = 1(ln(1)-2/1 +c)` =...

When our plan of government was established under the Constitution, three branches of government were created. Each branch had a different job to do, and each branch could control the other branches. One weakness of the legislative branch is that it has had a hard time getting back some of the power that belongs to the legislative branch. There is a very good example of this weakness in recent U.S. History. In 1964, Congress passed the Gulf of Tonkin Resolution. The Gulf of Tonkin Resolution basically gave President Johnson the power to do whatever was necessary to be successful in the Vietnam War. This gave the President some powers regarding the use of our military that are normally reserved for Congress. Congress tried to regain some of this power by passing the War Powers Act of 1973. The law limits the ability of the President to commit our troops abroad without getting approval from Congress. However, several presidents have ignored this law because there is no penalty for breaki...

That's a little tough to answer since your subjective experience of the play will change the way how you think the audience would feel. However, I'll give you my opinion based on my own take on the play, and hopefully that will give you some inspiration to write your own answer. For my part, I would answer a "How Would the Audience Feel" question by saying that the audience would probably feel conflicted emotions in regards to the happy conclusion of Bassanio and Antonio's plot and the sad conclusion of Shylock's plot.  Antonio and Bassanio are undeniably supposed to be the main characters in the play, as most of the main action revolves around their storylines. As such, we naturally want to see their stories end happily. However, though Antonio and Bassanio get what they want by the end of the play, their happy ending comes at the expense of Shylock the Jewish moneylender. Now, Shylock is usually seen as the villain of the play, as he basically wants to murde...

According to the author, the John Birch Society spearheaded the anti-liberal revolt against New Deal politics. To recap, the John Birch Society was founded by Robert Welch in 1958 to combat communism in American society. Although the John Birch Society stressed its support for welfare reform and for free market capitalism, it doomed its political efforts because of its penchant for entertaining spurious conspiracy theories. Welch's promotion of the idea that the Illuminati was leading communist efforts to subjugate America was less than helpful. However, what the John Birch Society did do was to promote the argument that the entertainment media and education system were promoting a preference for "welfare" and "security" against responsibility and opportunity; making an ever larger...percentage of American industry, commerce, agriculture, education, and individuals accustomed to receiving, and dependent on government checks..." The Society maintained that N...

We are asked to graph the function `y=(2x)/(x^2-1) ` : Factoring the denominator we get: `y=(2x)/((x+1)(x-1)) ` The graph has vertical asymptotes at x=1 and x=-1. The horizontal asymptote is y=0. The y-intercept is 0 as is the only x-intercept. The first derivative is ` y'=(-2(x^2+1))/((x^2-1)^2) ` so the function is decreasing on its domain. The graph:

In Chapter 10, Bruno walks for almost an hour along the fence at Auschwitz and is just about to turn back and head home, when he sees a small dot appear in the distance. Initially, Bruno thinks that he may be looking at a mirage, but as he gradually walks closer, it is revealed that Bruno is actually staring at a young boy. Bruno had read enough books to realize that explorers could never be sure what they were going to find. He believes that there are essentially two categories of discovery. The first category belongs to things that explorers find interesting and are "waiting to be discovered," like the Americas. The second category belongs to things that explorers discover that are better left alone, like dead mice in the back of a cupboard. Bruno immediately puts the boy into the first category because the boy is simply sitting there, waiting to be discovered. Bruno politely introduces himself to the boy, and they have a pleasant conversation.

Paul Fleishman's novel  Seedfolks is a series of character vignettes centered around a young girl named Kim who plants seeds in a vacant lot in the neighborhood. This begins a community garden in which many members of the community contribute.  Kim is a Vietnamese immigrant living in the city of Cleveland, Ohio. Kim's father died eight months before she was born. She decides to plant the lima beans in the vacant lot in honor of him. This is what she says: "But in that vacant lot he would see me. He would watch my beans break ground and spread, and would notice with pleasure their pods growing plump. He would see my patience and my hard work. I would show him that I could raise plants, as he had. I would show him that I was his daughter." The vacant lot is filled with trash, old tires, a rusty refrigerator, and an old couch.   Ana is the subject of the next character vignette in the novel. She was born in 1915. She has seen a lot of changes in the neighborhood over th...

The term tone is defined as the author's attitude toward the subject or the audience. Tone is expressed through the writer's word choices, which helps capture the way in which the writer is addressing the central theme in the work ( "Tone," Literary Devices ). Tone contrasts with mood in that mood is the atmosphere of the work, the emotions the writer evokes within the reader. While the mood in Toni Cade Bambara's short story "Blues Ain't No Mockin' Bird" is fairly comical, the story deals with very serious subject matter, and Bambara deals with that subject matter through a very serious, indignant tone , the serious subject matter being racial discrimination and treatment of the poor and suffering . To feel indignant is to feel a strong sense of disapproval about "something considered unjust, offensive, insulting or base" ( Random House Dictionary ). Bambara particularly reveals her tone in Granny's speech about the treatment...

The author Somerset Maugham frequently wrote frankly autobiographical short stories. "The Luncheon" is one of them. He was conned into treating the woman to a luncheon at Foyot's in Paris because he was still quite young, was just getting started in his chosen career as a writer, and was concerned about good manners. He tells the reader why he couldn't refuse to take this pushy woman to Foyot's at her request.  Foyot’s is a restaurant at which the French senators eat and it was so far beyond my means that I had never even thought of going there. But I was flattered and was too young to have learned to say no to a woman . Maugham also believed her when she said: "I never eat anything for luncheon." One of the things that always seems to be present in Maugham's encounters with other people is his impeccable good manners. Throughout "The Luncheon," as the woman continues to pile up charges by ordering a la carte items, the author shows his inh...

By definition, electric current is the amount of electric charge that flows through the cross-section of a conductor in a given unit of time: `I = (Delta Q)/(Delta t)` In SI (International System of units) the charge ( Q ) is measured in Coulombs, and the time is measured in seconds. The unit for current then equals 1 Coulomb/second, and it is called 1 Ampere, or, sometimes, 1 amp. In this question, the amount of charge flowing through the heating element is `Delta Q = 2400 C` in `Delta t = 200 s` . This means the current flowing through the heating element is `I = 2400/200 A = 12 A` . Please check out the reference website for the further discussion of the definition and units of measurement of electric current. The current flowing through heating element is 12 A (Amps)

We can deduce the exact date of Tom Robinson's death based on context clues author Harper Lee leaves for us in chapters 24 and 25 of To Kill a Mockingbird . Chapter 24 opens with Scout having been invited to join Aunt Alexandra and her missionary circle for refreshments while Jem is off teaching Dill how to swim at Barker's Eddy. The first important clue we are told at the start of this chapter is that summer is almost over and "Dill would be leaving for Meridian tomorrow." It is on the exact same day Scout announces Dill's upcoming departure that Tom Robinson is killed. More importantly, we know the day takes place at the end of August since Scout also describes, "August was on the brink of September." On the same day in August that Scout joins the ladies for refreshments, Atticus rushes home and interrupts the meeting to inform Calpurnia and others of Robinson's death.    Later, in Chapter 25 , Dill has already left for the summer, and Scout...

Although we are told that the man traveling alone in the Yukon is not much of a thinker, he does recall the advice of the old man on Sulphur Creek six times during his journey.  It is significant that the old timer doesn’t come to mind, however, until nearly halfway into the man’s journey, when he is already having trouble.  He is simply too stubborn and prideful to follow the old expert’s advice. The traveler first thinks of the old man when he is unable to eat his sandwich, ironically because his mouth is literally frozen shut by the 75 degree below zero weather.  The man realizes that the old timer was right that it gets cold in the Yukon, and he recounts how he had laughed at the man, admitting to himself that “one must not be too sure of things.” Yet instead of turning back at this realization, our traveler stubbornly continues his fateful journey. After falling through the ice up to his knees, the man thinks in more detail about the advice the old timer had given him:  don’t fail...

What an interesting idea for an assignment (which I assume will eventually be an essay).  I find it interesting because the theme of confinement is not necessarily a common theme mentioned in Pale Horse, Pale Rider , but you can definitely make a case that the theme is both present in and important to the story. First, let me comment on your original ideas.  Your ideas are superb, but they just need to be honed a bit.  You do too much summarizing in the beginning of your thought process here.  However, your ideas behind the confinement theme are wonderful.  For example, you are correct in asserting that Miranda is confined by influenza during the epidemic. Secondly, you can definitely prove that Miranda is further confined to live in a world without Adam after Adam dies.  (Luckily, her friends will not accept Miranda giving up on life like this.)  Your ideas about confinement, though, are hidden within sentences full of summary.   If your goal is to discuss (and prove) the theme of con...

The point of view of "The Lottery" is the third person point of view.   A third person point of view places the narrator outside of the events happening in the story.  The narrator obviously knows characters and things that are happening, but a third person narrator means that the story's narrator is not a character within the story.  More specifically, the narrator of "The Lottery" is narrating from the third person objective point of view.  This allows the narrator to jump from person to person and group to group.  Readers are allowed to listen in on various conversations as if we are eavesdropping on everybody.   The fact that the narrator is only capable of eavesdropping on people is why this story's point of view is third person objective and not third person omniscient.  An omniscient narrator is privy to the internal thoughts of characters, and the narrator of "The Lottery" never indicates that knowledge. That's a good thing for this st...

Although both Advanced Placement (AP) and International Baccalaureate (IB) classes give students the opportunity to take college-level courses in high school, the structure of the programs and how colleges treat the work done in those courses differ. Students can take a single AP class in high school and take its accompanying test to see if, based on how well they do, they can qualify for college credit. Likewise, an individual IB class can be taken, but IB also exists as a two-year program. Although some schools offer pre-IB classes leading up to the final two years of high school, IB classes officially start in a student's junior year of high school. While all AP classes are a year long, only standard-level IB classes are. So-called "higher-level" classes last two years, and students seeking a full IB diploma must take at least three higher-level IB classes. Additionally, they must fulfill a community service requirement, write an extended essay, and take a class on the...

The Middle Colonies were primarily populated by small family farms and small towns.  Many farmers grew crops more to feed and clothe their families, rather than to sell or trade them.  This caused slow economic growth in the region. Early settlers in the Middle Colonies faced hardships.  The climate and landscape in the Middle Colonies was unfamiliar to them.  They were not accustomed to the humid summers and sometimes marshy landscape.  Some of the land was not good for farming. Those living in the Middle Colonies feared attacks by Native Americans.  Many Quakers lived in the Middle Colonies, especially in Pennsylvania.  Quakers were especially eager to live peaceably with their Native American neighbors.  Overall, Native Americans did live peaceably with people in the Middle Colonies.  There were isolated instances, however, of children and adults being attacked or even taken captive by Native Americans.  Many times children were adopted into a Native American family when they were c...

The idea of McDonaldization is the idea that society as a whole is becoming more like a fast-food restaurant. That is, it is becoming as efficient as possible and is giving up on the idea of subjective quality in favor of objective quantity.  It is trying to turn out as much of a given thing as efficiently as it can, regardless of ideas like quality or diversity in tastes. How might you see this in your life?  Let me suggest two ways in which you have probably encountered McDonaldization in your life.  First, you have surely encountered automated processes in various parts of your life. Have you ever been to a store where you checked out your purchases through an automated, self-check system? Have you ever tried to call for customer service only to get an automated voice telling you to press certain numbers on your phone depending on what you want?  If so, you were experiencing McDonaldization because one aspect of this trend is the trend toward control of the workforce through the use...

Limit comparison test is applicable when `suma_n` and `sumb_n` are series with positive terms. If `lim_(n->oo)a_n/b_n =L` where L is a finite number and `L>0` , then either both series converge or both diverge. Given series is `sum_(n=1)^oo(2n^2-1)/(3n^5+2n+1)` Let the comparison series be `sum_(n=1)^oon^2/n^5=sum_(n=1)^oo1/n^3` `a_n/b_n=((2n^2-1)/(3n^5+2n+1))/(1/n^3)` `a_n/b_n=(n^3(2n^2-1))/(3n^5+2n+1)` `a_n/b_n=(2n^5-n^3)/(3n^5+2n+1)` `lim_(n->oo)a_n/b_n=lim_(n->oo)(2n^5-n^3)/(3n^5+2n+1)` `=lim_(n->oo)(n^5(2-n^3/n^5))/(n^5(3+(2n)/n^5+1/n^5))` `=lim_(n->oo)(2-1/n^2)/(3+2/n^4+1/n^5)` `=2/3>0` The comparison series `sum_(n=1)^oo1/n^3` is a p-series with `p=3` As per p-series test `sum_(n=1)^oo1/n^p` is convergent if `p>1` and divergent if `0<p<=1`   Since the comparison series `sum_(n=1)^oo1/n^3` converges, so the series `sum_(n=1)^oo(2n^2-1)/(3n^5+2n+1)` as well ,converges by the limit comparison test.

The given two points of the exponential function are (2,24) and (3,144). To determine the exponential function `y=ab^x` plug-in the given x and y values. For the first point (2,24), the values of x and y are x=2, y=24. Plugging them, the exponential function becomes: `24=ab^2`     (Let this be EQ1.) For the second point (3,144), the values of x and y are x=3 and y=144. Plugging them, the function becomes: `144=ab^3`     (Let this be EQ2.) To solve for the values of a and b, apply substitution method of system of equations. To do so, isolate the a in EQ1. `24=ab^2` `24/b^2=a` Plug-in this to EQ2. `144=ab^3` `144 = 24/b^2 * b^3` And, solve for b. `144=24b` `144/24=b` `6=b` Now that the value of b is known, plug-in this to EQ1. `24=ab^2` `24=a*6^2` And, solve for a. `24=36a` `24/36=a` `2/3=a` Then, plug-in the values of a and b to `y=ab^x` So this becomes `y=2/3*6^x` Therefore, the exponential function that passes the given two points is `y=2/3*6^x` .

To solve for the average velocity, apply the formula: `v_(ave) = (Delta x)/ (Delta t)` where `v_(ave)` is the average velocity `Delta x` is the displacement  `Delta t` is the time elapsed In the problem, the body goes from A to B and then from B to A. Since the body returns to its original position, its displacement is zero. Plugging in `Delta x = 0` to the formula  yields, `v_(ave) = 0/ (Delta t) =0` Therefore, the average velocity of the body is 0 m/s.

Existentialism plays a significant role in each of these works, although its role is perhaps most obvious in The Stranger . The Metamorphosis The Metamorphosis uses a strange metaphorical transformation to illustrate the themes of existentialism and its role in the human condition. The main character, Gregor, discovers that he is undergoing a grotesque transformation into a giant insect. This transformation is used to illustrate Gregor's alienation from society and his family, which is a common theme in existentialist thought. The existentialist theme of consequence presents itself as well. Gregor chooses to do meaningless work he hates in order to care for his family and, by doing so, creates his own meaning in life. This story illustrates the painful aspect of alienation in the human condition. In doing what he believes is right, Gregor becomes isolated from his fellow man and loses his humanity. This story could also be considered an example of Absurdism (closely related to Exi...

At the start of the chapter Jack is on the hunt and most of the descriptions regarding his actions equate him to an animal on the prowl - a predator seeking its prey. In the first paragraph we read: Jack was bent double . He was down like a sprinter, his nose only a few inches from the humid earth ... ...Then dog-like , uncomfortably on all fours yet unheeding his discomfort, he stole forward five yards and stopped. The highlighted words indicate that he has assumed the position of an animal. In paragraph two it is suggested that even his body seemed like that of some creature: ...his bare back was a mass of dark freckles and peeling sunburn . He is described as naked (except for his shorts) and that his nostrils were  flared - a description usually used to describe an animal. To further emphasize Jack's animal-like behavior, we read in paragraph three that: ...he stole forward and cast this way and that over the ground . And, in paragraph four: Jack himself shrank at this cry w...

Monosaccharides contain the elements carbon, hydrogen and oxygen, with twice as many H to O atoms. An example of a monosaccharide is glucose. Monosaccharides are the building blocks of more complex carbohydrates. Two monosaccharides can join by a covalent bond called a glycosidic linkage to form a disaccharide. An example is sucrose, or table sugar which is formed when the monosaccharides glucose and fructose are chemically joined. When several monosaccharides join by glycosidic linkages, this forms large polymers called polysaccharides including starch and cellulose. A diagram depicting a monosaccharide can show its carbon skeleton in a linear arrangement. However, in an aqueous solution, the carbon skeleton of sugar can form a ring. The answer to your question is that the ring structure of glucose indicates that it is a monosaccharide or choice A. If it were a disaccharide, there would be two rings therefore it cannot be answer B. It cannot be choice C as a fatty acid is a long line...

Tension, or suspense, is built through a series of events that involve Scout and Jem walking home alone at night and Boo Radley saving them from Bob Ewell.  Many little hints are dropped throughout the chapter that foreshadow this event. It is very dark, and there is no moon. Boo Radley, and the fact that the children used to be afraid of him, is mentioned.  The children seem a little scared. “It is a scary place though, ain’t it?” I said. “Boo doesn’t mean anybody any harm, but I’m right glad you’re along.” “You know Atticus wouldn’t let you go to the schoolhouse by yourself,” Jem said. (Ch. 28) The children laugh at how they were afraid of things in their childhood. It is quiet, but they hear a mockingbird. Scout asks Jem how he knows where they are.  They say they should have brought a flashlight. Cecil Jacobs scares them. Scout misses her cue at the pageant. Scout decides not to take her costume off. The children decline a ride home. Scout realizes she forgot her shoes. Jem tells S...