Notes

From the opening lines of this poem, Frost establishes that walls must be actively maintained or else they will erode away. People willingly devote their labor to this, but why? The reader is presented with several possible answers, but they seem inadequate. The fact that people persist building walls suggests that it is in our nature, and because it's in our nature, we can expect to see this happening both between individuals and between large groups. In essence, Frost forces the reader to arrive at this conclusion by process of elimination. Here, he suggests, is a case where the material and economic reasons don't justify a wall, but the men continue to maintain it anyway. The narrator has an apple orchard; his neighbor's land is "all pines." There can be no mistaking where one property ends and the other begins. It's demarcated by these natural features, and, as the narrator notes, there is no threat of encroachment: My apple trees will never get across And...

The most striking symbols are the canary and the bird cage. The canary symbolizes the role of a woman in this kind of male-dominated society. The bird is kept in a cage and its only means of expression in this prison is to sing. Analogously, the traditional stereotype of the submissive woman was that she should stay in the home while the husband goes out into the world to work. So, the cage and the limits of the home are both like prisons. Mrs. Wright was faced with a similar dilemma. Her farm was a good distance away from other people, including her friends. So, she was even more isolated. When her husband killed the canary, he essentially stifled the canary's only means of expression: singing. This evidently affected Mrs. Wright so much, that she decided to take out her vengeance upon him. When he killed the bird, he symbolically killed Mrs. Wright's "song." Mrs. Hale says of Mrs. Wright, "She used to sing. He killed that too." Mr. Wright killed the canary...

The Renaissance can be considered a time very similar to our own in that the Renaissance looked back to an earlier period (ancient Greece and Rome) as kind of a "golden era" that it sought to emulate.  Today's politicians, while the stakes are not life and death (as they were with the Medici in Italy) look back to earlier days for guidance.  One branch of the Republican party looks back to Thomas Jefferson in its attempt to minimize the role of government--this can be the Tea Party.  Another branch looks to Reagan in terms of tax breaks and military power.  The Democrats in this election are moving towards the left with Clinton and Sanders's tax plans for the rich and promises to working class Americans. Just like in the days of the Renaissance, most politicians are quite wealthy and they have followers who can work for them.  While the politicians of the Renaissance used the arts to hopefully gain a positive place in history, today's politicians use news sources ...

Indefinite integral are written in the form of `int f(x) dx = F(x) +C`  where: `f(x)` as the integrand            `F(x)` as the anti-derivative function of `f(x)`            `C`  as the arbitrary constant known as constant of integration To evaluate the integral problem:` int sqrt(x)/(x-4)dx` , we may apply u-substitution by letting: `u=sqrt(x) ` then `u^2 =x` and `2u du = dx` Plug-in the values, we get: `int sqrt(x)/(x-4)dx=int u/(u^2-4)* 2udu`                   ` = int (2u^2)/(u^2-4)du`  To simplify, we may apply long division:`(2u^2)/(u^2-4) =2 +8/(u^2-4)` To expand `8/(u^2-4)` , we may apply partial fraction decomposition. The pattern on setting up partial fractions will depend on the factors  of the  denominator. The factored form for the difference of perfect squares: `(u^2-4)= (u-2)(u+2)` . For the linear factor `(u-2)` , we will have partial fraction: `A/(u-2)` . For the linear factor `(u+2)` , we will have partial fraction: `B/(u+2)` . The rational expression becomes: `8/(u^2-...

I will focus on the United States and three significant effects on Americans' family life. The first was the huge mobilization of troops needed to fight a war on two fronts in Europe and Asia. Most able-bodied men under age 38 were either drafted or chose to enlist in the armed forces. This left many young families with absentee fathers. Second, the loss of male workers combined with the need for factories to run nonstop to support the war effort threw masses of women into the workforce. Women earned their own money and had a taste of freedom, but children were often left in daycare or, if older, to fend for themselves. Finally, rationing, which conserved resources for the war effort, left most families with little to buy and, because of gas rationing, few opportunities to travel. Instead, families were encouraged to grow Victory Gardens so more food would be available and to collect tin cans and other resources that could be recycled for the war effort. Families, when they did hav...

To determine the power series centered at c, we may apply the formula for Taylor series : `f(x) = sum_(n=0)^oo (f^n(c))/(n!) (x-c)^n` or `f(x) =f(c)+f'(c)(x-c) +(f''(c))/(2!)(x-c)^2 +(f^3(c))/(3!)(x-c)^3 +(f'^4(c))/(4!)(x-c)^4 +...` To list the `f^n(x) ` for the given function ` f(x)=3/(2x-1)` centered at `c=2` , we may apply Law of Exponent: `1/x^n = x^-n`  and  Power rule for derivative: `d/(dx) x^n= n *x^(n-1)` . `f(x) =3/(2x-1)`           ` =3(2x-1)^(-1)` Let `u =2x-1` then `(du)/(dx) = 2` `d/(dx) c*(2x-1)^n = c *d/(dx) (2x-1)^n`                            `= c *(n* (2x-1)^(n-1)*2`                             ` = 2cn(2x-1)^(n-1)` `f'(x) =d/(dx) 3(2x-1)^(-1)`             `=2*3*(-1)(2x-1)^(-1-1)`             `=-6(2x-1)^(-2) or 2/(2x-1)^2` `f^2(x) =d/(dx) -6(2x-1)^(-2)`             `=2*(-6)(-2)(2x-1)^(-2-1)`             ` =24(2x-1)^(-3) or 24/(2x-1)^3` `f^3(x) =d/(dx) 24(2x-1)^(-3)`            `=2*(24)(-3)(2x-1)^(-3-1)`           ` =-144(2x-1)^(-4) or -144/(2x-1)^...

Atticus gives his children a lot of advice in Lee's  To Kill a Mockingbird . Without knowing what this question is asking specifically, here are a few of the main pieces of advice that Jem and Scout receive from their father. First, Atticus teaches his children about courage when Mrs. Dubose dies. He informs them that Mrs. Dubose overcame an addiction to morphine before she died, and then he gives the following lecture: "I wanted you to see what real courage is, instead of getting the idea that courage is a man with a gun in his hand. It's when you know you're licked before you begin but you begin anyway and you see it through no matter what. You rarely win, but sometimes you do. Mrs. Dubose won, all ninety-eight pounds of her. According to her views, she died beholden to nothing and nobody. She was the bravest person I ever knew" (112). The advice from the above passage teaches the kids that courage is not found behind the barrel of a gun; rather, it is found ins...

The information that can be determined by observing the spacing of contour lines on a topographic map is relative steepness.  It's relative steepness because without knowing the map's relief or the map's contour interval, all that a user can do is see that certain areas are steeper than others.  Contour lines that are closely spaced indicate a steeper section than contour lines that are widely spaced.  In order to know exactly how steep a particular slope is, the map user will need to know the contour interval.  The contour interval is the change in elevation from one contour line to the next contour line.  Once the elevation change is known, the user would need to know what the map's scale is. By knowing the contour interval and the map's scale, a person can then calculate the actual steepness of a slope. 

Rip falls asleep after drinking a flagon of the beer with the odd, old-fashioned Dutch people he runs into in the mountains. We learn that his senses are overpowered, his eyes swim, and his head gradually droops before he falls into a deep sleep, indicating that this beer is more powerful than what Rip is used to consuming. We don't learn anything about his sleep, such as whether he dreamed, but when he wakes up he is surprised that he might have slept all through the night. Although he has been snoozing deeply for 20 years, on awakening, he has no inkling of this. Instead, he worries about what excuse he can give Dame Van Winkle when he gets back home and wonders why his body feels so stiff in his joints, not yet associating this with aging.

John Hancock was the first person to sign the Declaration of Independence. Hancock was the President of the Second Continental Congress, a meeting of delegates from the Thirteen Colonies, which declared its independence from Great Britain in 1776. Hancock made the first signature on this famous document, a signature which is notable for its large and bold letters. It is rumoured that Hancock signed his name so large because he wanted the king, George III, to be able to read it without having to wear glasses. (You can view the signature using the reference link provided). After Hancock, the Declaration was signed by the secretary of the Congress, Charles Thompson, and then by the remaining delegates, bringing the total number of signatures to 56. (See the second reference link for more information about the men who signed this document).

Given , `y = 9-x^2 , y = 0` first let us find the total area of the bounded by the curves. so we shall proceed as follows as given , `y = 9-x^2 , y = 0` =>` 9-x^2=0` => `x^2 -9 =0` =>` (x-3)(x+3)=0` so `x=+-3` the the area of the region is = `int _-3 ^3 (9-x^2 -0) dx` =`[9x-x^3/3] _-3 ^3` =` [27-9]-[-27+9]` =`18-(-18) = 36` So now we have  to find the horizonal line that splits the region into two regions with area 18 as when the line y=b intersects the curve `y=9-x^2` then the ared bounded is 18,so let us solve this as follows first we shall find the intersecting points as , `9-x^2=b` `x^2= 9-b` `x=+-sqrt(9-b)` so the area bound by these curves `y=b` and `y=9-x^2 ` is as follows A= `int _-sqrt(9-b) ^sqrt(9-b) (9-x^2-b)dx = 18` => `int _-sqrt(9-b) ^sqrt(9-b)(9-x^2-b)dx=18` => `[-bx +9x-x^3/3]_-sqrt(9-b) ^sqrt(9-b)` =>`[x(9-b)-x^3/3]_-sqrt(9-b) ^sqrt(9-b)` =>`[((sqrt(9-b))*(9-b))-[(sqrt(9-b))^(3)]/3 ]-[((-sqrt(9-b))*(9-b))-[(-sqrt(9-b))^(3)]/3]` =>`[(9-b)^(3/2) -...

Some historians have actually called him Machiavellian, but Richard Nixon is a good example of following Machiavelli's teachings.  One of the most famous quotes attributed to Machiavelli is "The ends justify the means."  Nixon promised "peace with honor" in Vietnam and promised to extricate the American military from the country, yet he authorized the invasions of Laos and Cambodia by Special Forces in order to interdict the Ho Chi Minh Trail.  Nixon also undercut the popularity of those on the Left by authorizing Earth Day, establishing OSHA, and giving money to the humanities.  He also increased federal funding to cancer research.  By adopting these policies of the Left, Nixon had bipartisan appeal.  Nixon's downfall was that he was too Machiavellian--he was distrustful and he knew a great deal about the spying against the Democratic Party headquarters.  Still, Nixon enjoyed a long political career and was able to (mostly) steer between being loved and hat...

There are several occasions where the fire burns low or burns out in Lord of the Flies . The first fire the boys make in chapter 2 is a huge bonfire that reaches twenty feet high, but it "diminished quickly; then the pile fell inwards with a soft, cindery sound." This is on page 46 in my copy, but if you have a different version, it's just over halfway through chapter 2. Unfortunately, the fact that this fire has burned low is deceptive; it soon catches again when it spreads to the "great patch where they had found dead wood" and engulfs a huge section of the island, killing one of the little boys. In chapter 4 Jack takes Samneric away from tending the signal fire, and Ralph finds that it has died just as a ship passes the island. In my version, on page 77, it says, "The fire was dead." This is just over halfway through chapter 4. At the beginning of chapter 6, Samneric have been on night duty tending the fire, and it almost goes out while they sleep. ...

The volunteer hours are important because Elders observe children to determine their skills and interests. From the age of eight, children in Jonas’s community have to meet a requirement of a certain number of volunteer hours.  The volunteer hours are actually very important, because they are essentially a test.  The children are carefully observed to determine where their skills and interests lie.  The Elders observe where the children are volunteering and how well they work, and use that to determine what job they are assigned. Jonas’s father explains to him how the Elders knew to give him the assignment of Nurturer, or caretaker for the babies. “…But again and again, during free time, I found myself drawn to the newchildren. I spent almost all of my volunteer hours helping in the Nurturing Center. Of course the Elders knew that, from their observation." (Ch. 2)  The volunteer hours are so important to determining assignments that children will not be assigned a job until they h...

`sum_(n=0) (7/6)^n` To verify if the series is divergent, apply the Geometric Series Test. Take note that a geometric series has a form `sum ar^n` It converges if `|r|lt1` . And it diverges if `|r|gt=1 ` . In the series the value of a and r are: `a=1` `r=7/6` Taking the absolute value of r, it yields `|r|=|7/6|` `|r|=7/6` Since `|r|>1` ,  the series is divergent.

This is a really important aspect of writing papers about literary works at the university level. Perhaps the major difference is that a summary adds nothing to a work, but is just repeating what the work says in a more condensed form. There is nothing one learns from a summary beyond what one one would discover simply by reading the work in question.  An analysis, on the other hand, tries to add something to the reader's experience. It might supply information not readily apparent to readers or it might do very close examination of a work to understand some particular aspect of the work that would not be apparent to a more casual reader. Analyses are distinguished structurally from summaries by being organized conceptually rather than following the order of the original text. An historical analysis of a work might look, for example, at how a work was influenced by the political, religious, or cultural beliefs of its period. A source study might look at specific influences on a wor...

Dill Harris is an innocent child who shows his true sweetness of character by being overwhelmed to the point of tears by the way Mr. Gilmer treats Tom Robinson in court. Mr. Gilmer talks down to Tom in such an evil and mean way that Dill picks up on it internally. The tension increases for Dill as Mr. Gilmer continues to speak disrespectfully to Tom; yet, Tom continues to speak calmly and respectfully to Mr. Gilmer. This goes on for some time, at which point Dill's emotions pour out of his eyes. Jem tells Scout to take Dill outside for a break from the trial, at which point Scout tries to calm her friend by telling him that's just how court proceedings go. Dill's response is as follows: "I don't care one speck. It ain't right, somehow it ain't right to do 'em that way. Hasn't anybody got any business talkin' like that--it just makes me sick" (199). This comment shows that Dill is able to empathize with the way Tom might feel when being spok...

The mass of a body is the amount of matter contained in the body and hence stays the same unless we put on more matter. Many times, people use mass and weight interchangeably, which is not correct. Weight, unlike mass, is a force and is the force with which Earth (or any other celestial body one is on) attracts the body. According to Newton's second law, the force is calculated as: F = m x a where m is the mass of body and a is its acceleration. For determining weight, a = g, acceleration due to gravity. On the Moon, g = 1.568 m/s^2. Mass, however, remains the same on both Earth and the Moon. Thus, the boy's weight on the Moon = m x g = 40 kg x 1.568 m/s^2 = 62.72 N Thus, the weight of the boy would be 62.72 N on the Moon. Hope this helps.

In this poem by English poet Ivor Gurney, a soldier reflects on having shot an enemy soldier to death. The speaker struggles with guilt: he quotes someone saying "couldn't be helped"; he states no one can blame him for shooting the enemy because otherwise he himself would have died; he muses that his victim may have been an only son; and he mentions the lack of guidance from God on the issue. He imagines himself being shot to death in battle and in Heaven finding the man he shot in order to apologize. Finally, in the last stanza, he summarizes his tangled emotions and concludes that the war "is a bloody mess indeed." The poem uses enjambment and caesura to break up what otherwise would become a sing-songy iambic rhythm. Lines that carry over to the next line (enjambment) are 1, 3, 5, 6, 7, 11 and 13. Caesura (a hard stop in the middle of a line) occurs in lines 2, 7, and 17. Examples of alliteration include "For w orst is w orst, and w orry's done,...

During the trial, King's lawyer, Asa Briggs, cross-examines Detective Karyl and asks him if he dusted the area for any fingerprints. Karyl says that the crime-scene technicians didn't find any fingerprints that they could establish belonging to the perpetrator. Briggs then asks him if it is true that they hurried the investigation in order to seek informants willing to give information on the case. Karyl responds by saying that they treat each case carefully and that they don't just go through the motions. Briggs then asks Karyl if they found any fingerprints on the cash register or the counter. Karyl tells him that none of the prints were clear enough to use. Asa Briggs then comments that it isn't hard to find people in jail that are willing to swear that somebody else is a bad guy. After Karyl says that they check every story and give everybody the benefit of the doubt, Briggs says, " But you don't check for fingerprints? " (Myers 80). Briggs is attem...

After Juliet learns that the young man with whom she's fallen in love at first sight is the son of her father's great enemy, she says, "My only love sprung from my only hate!" (1.5.152).  This is a paradox (a statement or situation that appears to be contradictory but is nonetheless true).  What she means is that she has neither loved before she saw Romeo nor hated anyone other than a Montague, and now the two -- love and hate -- have converged in one person.  You could, perhaps, draw Romeo -- one half of him looking lovable and smiling, hand extended, the other half of him looking devilish, angry and frowning, hand curled into a fist. Juliet voices another paradox after she learns that it was Romeo who killed her cousin, Tybalt.  She asks, "Was ever book containing such vile matter / So fairly bound? O, that deceit should dwell / In such a gorgeous palace!" (3.2.89-91).  She marvels that Romeo could be a murderer and yet seem so good and sweet and be so han...

The question is to compare the importance of the function(s) performed by each level of management, using the concept of a pyramid to describe the hierarchy of management in a typical organization. By definition, each level is “important” to the extent it is deemed necessary by the organization; i.e. these are all jobs which “must” be done to operate the organization, otherwise they would be eliminated. Therefore, the concept of importance is really more one of what the key functions of each level are. Most people tend to think of management hierarchies in terms of organizational charts with various job titles arranged in reporting relationships. The permutations of this approach are legion, but they can be simply distilled into three basic levels, namely “front-line,” middle, and executive. Front-line managers are primarily responsible for coordinating the daily productive activities of the organization’s non-managerial personnel, issuing tasks, monitoring output, and training such pe...

Lennie is described as an animal. His arms hang at his sides "the way a bear drags his paws." When he gets to the pool, he drinks like a horse. Lennie is large and simple-minded. He is like an animal. It is fitting that the is so affectionate with smaller animals. Lennie is strikingly strong but he wants nothing more than to live on a farm and care for small, cute animals.  Lennie claims to have found the dead mouse and instead of throwing it out, he wants to keep it in his pocket so that he can keep petting it. George tells Lennie to give up the mouse because it isn't sanitary. Lennie recalls how his Aunt Clara used to give him mice. George reminds him that she stopped giving Lennie mice because he would accidentally kill them.  At the end of the chapter, they discuss the incident in Weed in which Lennie tried to pet a girl's dress. Lennie says, "Jus’ wanted to feel that girl’s dress—jus’ wanted to pet it like it was a mouse . . ." This tells us that Lennie...

Lois Lowry's novel, The Giver , takes place in a constructed world in which emotion, choice, and memory have been removed from the human community. Upon first introduction, this world seems perfect. Everything has an order to it, and nothing seems to ever go wrong. However, once more of Lowry's world is revealed, we see that there is actually a lot wrong with it. Humans do not love, nor do they feel pain. Jonas learns that individuals that do not fit perfectly into the community are "released" (killed). The humans in this community are living lives without passion or personal purpose. The Giver is a cautionary tale that warns against giving too much power to governing bodies in exchange for comfort. Individuals living in the world of The Giver want for nothing in terms of daily comfort. Their dwellings, partners, family units, and occupations are arranged for them. In exchange for this security, however, they have forfeited personal choice. The Giver shows that whi...

Goodwife Cruff is a woman who lives in Wethersfield, Connecticut. Kit first meets Goodwife Cruff, along with her husband and daughter, on the ship from Saybrook to Wethersfield. Goodwife Cruff is a cold, impatient, and opinionated woman. She is serious, and Kit describes her as having a "hard thin mouth" (Chapter 11). Kit describes Goodman Cruff as Goodwife Cruff's "cowed shadow of a husband," and Prudence as a "miserable little wraith of a child" (Chapter 2). Goodwife Cruff does not hide that she dislikes Kit. Kit later sees her gossiping in town with several other ladies. Goodwife Cruff refuses to let Prudence go to the dame school like other children. Goodman Cruff wants Prudence to go, but his wife says Prudence is stupid. Later, Goodwife Cruff is one of Kit's accusers. She also points out that Nat is in the town even though he has been banished.

Shirley Jackson's "The Lottery" is meant to demonstrate the negative impacts of blindly following "tradition" and avoiding societal change. In the story, the lottery is a traditional event that occurs every year on June 27th. The lottery has been an annual event since the first settlers arrived in the town long ago. Although a few things have changed slightly throughout the years, the townspeople refuse to completely change the lottery or to get rid of it entirely. The most likely reason for their hesitation to end the lottery is that they believe canceling the lottery will cause them to have poor crop growth during the coming season. Jackson does not make the reasoning explicit, but the likelihood of this reasoning can be inferred from statements she has placed throughout the story. As the townspeople discuss nearby towns who have cancelled the lottery entirely, Old Man Warner refers to their decision as foolish and states that there used to be a saying, "...

Alexie declares "a smart Indian is a dangerous person, widely feared and ridiculed by Indians and non-Indians alike" to explain why, in his opinion, the Indians he lived with on the Spokane Reservation did not value formal education in the reservation schools. Alexie recognizes that his peers had plenty of intelligence, citing the complexity of their stories, songs, and jokes, but that they did not want to display it.   Alexie's family was different: they provided a home rich in books, and as he grew up, he sought out anything with text: auto repair manuals, cereal boxes, and books from the library and secondhand shops. He realizes his attitude is different from other Indians he knew, writing "I refused to fail. I was smart. I was arrogant." Near the end of his essay, Alexie observes that in today's reservation schools, he sees two kinds of Indian students: voracious readers who write their own poems, stories, and novels and "sullen and already defeated...

To a certain extent, this is an opinion based question.  Feel free to state why you think Travis is annoyed with Eckels, and then defend it.   In my opinion, Travis is annoyed with Eckels because Eckels is annoying.  Stick with me.  I relate much better to Travis than I do with Eckels.  I find Eckels annoying, so I figure that Travis finds him annoying for all of the same reasons that I find Eckels annoying.  Eckels is annoying because he is cocky and pompous.  Eckels is annoying from the very moment that he walks into the Time Safari, Inc. office and waves around his check.  I don't mind people being generous with their money, but people that openly flaunt their wealth are annoying.  Eckels waves his check in the air as if trying to prove to everybody else that he is better than they are because he can write a big check.  That's annoying.  Next, Eckels is annoying because he's selfish.  Eckels is  part  of a safari expedition into the past.  There are  other paying custom...

To evaluate the integral problem: `int_1^2 x^4ln(x) dx` , we follow the formula from basic integration table. For the integrals with logarithm, the problem resembles the formula: `int x^n ln(x) dx = x^((n+1)) ( ln(x)/(n+1)- 1/(n+1)^2), n!= -1` . By comparison of `x^n ` with `x^4` ,  we let `n=4` which satisfy that condition n!=-1 to be able to use the aforementioned integral formula.  Then the integral problem is evaluated as: `int_1^2 x^4ln(x) dx= [x^((4+1)) ( ln(x)/(4+1)- 1/(4+1)^2)]|_1^2` ` = [x^(5) ( ln(x)/5- 1/5^2)]|_1^2` `= [x^(5) ( ln(x)/5- 1/25)]|_1^2` `= [(x^(5) ln(x))/5- x^5/25]|_1^2` Apply definite integral formula: `F(x)|_a^b = F(b) - F(a)` . `[(x^(5) ln(x))/5- x^5/25]|_1^2=[(2^(5) ln(2))/5- 2^5/25]-[(1^(5) ln(1))/5- 1^5/25]` `=[(32 ln(2))/5- 32/25]-[(1ln(1))/5- 1/25]` `=(32 ln(2))/5- 32/25 -(1ln(1))/5+ 1/25` `= (32 ln(2))/5 -0/5+ (1-32)/25` `=( 32ln(2))/5 -31/25` or `3.196` (approximated value).

In a rather subtle way, O. Henry shows that Jimmy Valentine is coming to the realization that he is getting to be too well-known in the area around Indiana where he usually commits his safecracking crimes. This is indicated by the fact that he usually got "sprung" from prison in a few months because of his many connections, but when the story opens he has already been serving ten months in prison for a job he pulled in Springfield, Indiana. The Warden seems to know all about Jimmy, including his modus operandi and his social and political connections. The following jocular dialogue by the Warden is revealing: “Oh, no,” laughed the warden. “Of course not. Let's see, now. How was it you happened to get sent up on that Springfield job? Was it because you wouldn't prove an alibi for fear of compromising somebody in extremely high-toned society? Or was it simply a case of a mean old jury that had it in for you? It's always one or the other with you innocent victims.” T...

When potential energy and kinetic energy are combined, they indicate total mechanical energy .  Mechanical energy is the energy that an object has due to its motion and/or due to its position.  Energy of motion is kinetic energy, and energy of position or shape is potential energy.  Think of mechanical energy like you would an addition problem.   Mechanical energy = kinetic energy + potential energy All three of those energies are measured in Joules, so there is no need to even worry about converting units.   When I teach my students about mechanical energy, I like to use a roller coaster as an example.  When the roller coaster is at the top of the highest hill, it has all gravitational potential energy (just pretend the roller coaster stops for a second before going down the hill).  Halfway down that hill, the roller coaster is moving quickly, so it has kinetic energy; however, it still has potential energy because it's only halfway down. At the bottom of the hill, all of the pote...

The periodic table of elements provides specific information about each element. The atomic number  is the number of protons found inside the nucleus of an atom. Protons have a positive charge. Once the number of protons is known, there is an equal number of negative electrons orbiting around the nucleus in specific energy levels.  The atomic mass of an atom is the sum of the protons and neutrons it contains. Neutrons are neutral particles found in the nucleus. The atomic mass is calculated using the protons and neutrons but not the electrons, as their mass is negligible. In an example, the element oxygen has an atomic number of 8 and an atomic mass of 16. Therefore, 8 protons are in the nucleus, and if we subtract the atomic number from the atomic mass, (16-8) we will find there are 8 neutrons also located in the nucleus. To place the 8 electrons in their orbitals, the first energy level holds two electrons. That leaves 6 electrons to be placed in the next energy level which can hold...

The Electoral College is the actual system by which the President of the United States is elected. The President is not actually elected directly by the voters; rather, there are 538 electors, chosen to represent each state based on the number of Representatives and Senators that state has in Congress. This system was defined by the Constitution, and created primarily because it offered a compromise between electing the President by the legislature as in a parliamentary system, and electing the President directly. Many of the Founding Fathers were uncomfortable with the idea of giving the people that much direct power, and wanted there to be some sort of filtering mechanism; but others felt that allowing the legislature to elect the President would give them too much power, so a compromise was struck. Each state can choose how their electors will cast votes for the President. Most states are "winner-takes-all", meaning that whoever wins the popular vote in that state will win...

After fleeing their comfortable home in Johannesburg, Maureen Smales and her family are taken in by the family of their servant, July. July and his family live in a rural village that lacks the amenities Maureen has grown used to in Johannesburg. In the bush, she has no access to electricity or modern plumbing. It is this stark change in surroundings that sparks a conscious awakening in Maureen. You can find an example of this idea in the line, "It pressed in upon her and filled her as someone's breath fills a balloon's shape." This line refers to Maureen's feeling of being taken over by or becoming one with the nature that suddenly surrounds her. Prominent Examples In Chapters 18 and 19, you can find multiple examples of Maureen's oneness with nature. This is not always a positive experience for Maureen, as seen when she travels into the woods in search of July. She begins to dissociate, feeling as if she is not present in the physical world and that the bush...

In a U.S. court of law, summation speeches are given first by the prosecuting attorney, which is Mr. Gilmer in Harper Lee's To Kill a Mockingbird, and second by the defense attorney, Atticus. One main goal of a summation speech is to summarize the facts and evidence of the case as they have been presented by the witnesses to the court. However, the main purpose of a summation speech is to persuade the jury to take the side of either the prosecution or the defense. To persuade the jury, both the prosecuting and defense attorneys will extensively use rhetorical devices in their summation speeches such as logos, ethos, and pathos . Logos is an appeal to reason. The presentation of all of the facts of the case serves as logos. So, one thing you will want to do in writing your summation speech for Mr. Gilmer is summarize all of the details of the case as they were presented by both Mayella Ewell, the alleged victim, and her father, the alleged witness of the crime. For example...

Hello! By definition, a parabola is the locus of points `(x,y)` whose distances to the directrix and to the focus are equal. These equal distances in our case are `|y-2|` and `sqrt(x^2+(y-4)^2).` Square the equation and obtain `(y-2)^2=x^2+(y-4)^2,` or `y^2-4y+4=x^2+y^2-8y+16,` or `4y=x^2+12,` or finally `y=(x^2)/4+3.` So the right answer is (4) .

Given to solve `y' = sqrt(tan x) *(sec^4 x)` => `y = int sqrt(tan x) *(sec^4 x) dx` so , we have to solve `int sqrt(tan x) *(sec^4 x) dx` = `int sqrt(tan x) *(sec^2 x) *(sec^2 x) dx` = `int (1+tan^2 (x))*(sec^2 x)*(sqrt(tan x)) dx` let , `u= tan x` so, `du = sec^2 (x) dx` so , `int (1+tan^2 (x))*(sec^2 x)*(sqrt(tan x)) dx` =` int (1+u^2)(u^(1/2)) du` = `int (u^(1/2)+u^(5/2)) du` =` (u^((1/2) +1))/((1/2)+1) +(u^((5/2) +1))/((5/2)+1) ` = `(u^((3/2) ))/((3/2)) +(u^((7/2) ))/((7/2))` = `2/3u^(3/2) +2/7u^(7/2)` = `2/3(tan x)^(3/2 ) +2/7(tan x)^(7/2)`

Both the Virginia Colony and the Massachusetts Bay Colony were not officially meritocracies.  There were, however, elements of a meritocracy in both colonies. In the early days of the Virginia Colony, times were difficult.  Very few people survived past the first year.  John Smith, who was a soldier, helped the desperate people by calling for order and training them to farm.  He also insisted that everyone work hard.  He had natural abilities as a strong leader, and he rose to prominence because of these abilities.  It was his merit that gave him power. In the Massachusetts Bay Colony, many men became prominent due to their abilities and achievements.  The New World was a fresh start, and many people achieved more than they would have back home.  John Cotton was an incredibly influential man.  He was a gifted speaker who greatly influenced both government and church affairs.  His merit and abilities helped him rise to prominence in Massachusetts.

Many people have been inspired by Helen Keller's autobiography, The Story of My Life .  This book has been inspiring others to persevere in difficult circumstances for over one hundred years.   Helen Keller was deaf and blind for a large portion of her childhood.  She not only learned how to communicate and read with the help of her teacher, Miss Sullivan, but she also became a successful writer.  She completed school and college.  She even learned how to speak.  Helen had to work extremely hard to accomplish all these things.   The Story of My Life was filled with Helen's inspirational words about her journey.  Helen wrote about her teacher and how the woman made learning a beautiful thing: It was because she seized the right moment to impart knowledge that made it so pleasant and acceptable to me.  She realized that a child's mind is like a shallow brook which ripples and dances merrily over the stony course of its education and reflects here a flower, there a bush, yond...

To determine the convergence or divergence of the series `sum_(n=1)^oo (-1)^n/sqrt(n)` , we may apply the 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`  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 given series `sum_(n=1)^oo (-1)^n/sqrt(n)` , we have `a_n =(-1)^n/sqrt(n).` Applying the Root test, we set-up the limit as:  `lim_(n-gtoo) |(-1)^n/sqrt(n)|^(1/n) =lim_(n-gtoo) (1/sqrt(n))^(1/n) Note: |(-1)^n| = 1` Apply radical property: `root(n)(x) =x^(1/n) ` and Law of exponent: `(x/y)^n = x^n/y^n` . `lim_(n-gtoo) (1/sqrt(n))^(1/n) =lim_(n-gtoo) (1/n^(1/2))^(1/n)`                          ` =lim_(n-gtoo) 1^(1/n) /n^(1/2*1/n)`                          ` =lim_(n-gtoo) 1^(1/n) /n^(1/(2n))`                    ...

`log_125 (625)` To evaluate, factor 625. `=log_125 (5^4)` Then, apply the formula of change base `log_b(a) = (log_c(a))/(log_c(b))` . `= (log_5 (5^4))/(log_5 (125))` `= (log_5 (5^4))/(log_5 (5^3))` Also, apply the rule `log_b (a^m) = m*log_b(a)` . `= (4* log_5(5))/(3*log_5 (5))` Take note that when the base and argument of logarithm are the same, it results to 1, `log_b(b) = 1` . `= (4*1)/(3*1)` `=4/3` Therefore, `log_125 (625)=4/3` .

`sum _(n=2)^oo ln n/n` To determine if the series converges or diverges, apply integral test. `int_2^oo lnn/n dn` `= lim_(t->oo) int_2^t ln n/n dn` To take the integral, apply u-substitution method. `u=ln u`           `du = 1/n dn` `int lnn/n = int ln n * 1/ndn = int u du = u^2 /2= (ln n)^2/2` Then, plug-in the upper and lower limit to evaluate the improper integral. = `lim_(t->oo) [ (ln n)^2/2]|_2^t` = `lim_(t->oo) [(lnt)^2/2- (ln2)^2/2]` And, take the limit of it as t approaches infinity. `= oo` Since `int_2^oo lnn/n dn` is divergent, therefore the series `sum_(n=2)^oo ln/n` is divergent .

Manifest destiny was the belief that God wanted the United States to spread out over the North American continent, taking control of as much territory as possible.  Americans of the time believed in it because their country was strong compared to its neighbors and because this was a time in history when essentially everyone believed that might made right. In the phrase “manifest destiny,” the word “manifest” means something like “obvious.”  The phrase, then, referred to America’s obvious destiny.  People believed that it was obvious that God wanted their country to succeed, grow, and spread.  This was part of what motivated the Mexican-American War and the westward expansion across the continent that snapped up Indian lands and pushed the natives onto reservations (or simply killed them). People believed this because the US was clearly the strongest country on the continent.  Mexico was weak and constantly wracked with internal disorder.  Canada was not a country yet, just a colonial o...

The men who were tried at Nuremberg (1945-1946) were not all held responsible and prosecuted for crimes relating to the Holocaust. To understand why, it is important to note a few key facts about these famous trials. Only 21 Nazis were actually tried. Martin Bormann, for example, was tried in absentia while Dr Robert Ley committed suicide in his cell before the proceedings began. Another of the defendants, Gustav Krupp von Bohlen und Halback, was declared too weak to face trial. Many of these men were not actually soldiers. Julius Streicher, for instance, published an anti-Semitic newspaper but did not have a role in the actual extermination of the Jews or other minorities. Some men were acquitted of any wrongdoing. Hans Fritzsche, for instance, worked in the news division of the Propaganda Ministry and was tried in place of Joseph Goebbels (who had committed suicide with his family). He was cleared of any crimes. For a full list of the defendants, their crimes and verdicts, please see...

A federal system is one in which power is shared between a national government and lower levels of governments, typically called state or provincial governments.  In such a system, a constitution sets out what powers each level of government has and neither level can simply take power from the other level.  The main merits of such a system are that it A) allows a diverse country to stay together, B) enables people in each state or province to feel that they rule themselves, and C) provides an opportunity for states and provinces to operate as “laboratories.” Political scientists generally say there are three types of government.  These are unitary, confederal, and federal.  In a unitary system, the national government has all the power and the states have no powers or rights except those (if any) that the national government allows them to have.  In a confederal system, the provincial governments have all the power.  The national government only has such powers as the provinces allow i...

Evil in Macbeth is best illustrated by the actions of the the three witches, Macbeth, Lady Macbeth, the assassins hired by Macbeth later to commit his evil, the king of Norway, and the traitors, Macdonwald and the thane of Cawdor. In contrast to this, good is best depicted by King Duncan, his older son, Malcolm - rightful heir to the throne, Banquo, Macduff, Lady Macduff and the king of England, Edward, as well as the forces who are gathered to overthrow the usurper and tyrant, Macbeth. It is ironic that Macbeth, who virtually becomes the epitome of evil, is initially depicted as good and honorable. An injured sergeant's report of him at the beginning of the play speaks of a courageous general who was prepared to sacrifice his life for king and country, as illustrated in the following extract: For brave Macbeth--well he deserves that name-- Disdaining fortune, with his brandish'd steel, Which smoked with bloody execution, Like valour's minion carved out his passage... It is...

Slaves and indentured servants both made up a significant portion of the workforce during the early days of the English Colonies. Both slaves and indentured servants worked without pay, but they had many differences. Slaves were brought from Africa to the New World against their will. Once they arrived, they were usually sold at a slave auction to the highest bidder. Once sold, a slave would have to spend the rest of his or her life working for a master. The slaveowner provided housing, food, and other basic necessities, but no wages. Indentured servants were typically from Europe. They willingly entered into a contract with an employer in which they would work without pay for a set term. These terms were usually not more than seven years. In exchange for their years of service, the employer would provide housing, food, and often passage by ship across the Atlantic Ocean.

I would probably argue that Alyce is exactly what Jane  needed in an apprentice; however, Alyce is exactly what Jane did not want in an apprentice.  Alyce is a motivated young lady.  She wants to learn Jane's trade.  She wants to help with bringing new life into the world, and she wants to help people get better.  She's intelligent, eager to learn, and isn't afraid of challenges.  Alyce is exactly the kind of student that a teacher wants to work with.  Unfortunately, Jane is not looking for a motivated student to teach.  Jane is looking for a helper with a weak will.  That way Jane can control her apprentice.  Jane wants an apprentice who does exactly what she is told to do and nothing more.  Jane doesn't want competition in her trade, which is why she intentionally keeps pertinent midwife training and knowledge away from Alyce.  In Jane's opinion, Alyce isn't what she needs, because Jane is too much of an independent apprentice.  

McCulloch v Maryland was an important court case. The question that needed to be decided was if a state could tax a federal institution such as the national bank. Maryland taxed the national bank. The bank’s cashier, James McCulloch, refused to pay the tax. Maryland then sued the national bank. The Supreme Court ruled that a state couldn’t tax a federal institution. Therefore, the national bank didn’t have to pay the tax that Maryland imposed on it. However, the ruling went much further. The Supreme Court ruled that a loose interpretation of the Constitution was legal. This would allow the federal government to do many things unless the Constitution specifically prevented the government from doing them. The ruling also reinforced the idea that federal laws take priority over state laws. This ruling significantly enhanced the power of the federal government. McCulloch v Maryland was an important case that had far reaching consequences.

Cell phones are undoubtedly necessary in a fast-paced world we live in today. Although they are extremely useful on so many levels, they also have their disadvantages. I will discuss both the advantages and disadvantages below. Advantages A cell phone enables us to connect with others anytime, anywhere. It has never been easier to connect with our friends and family. We can reach one another instantly, whenever we desire, and wherever we go as long as there is network coverage. For example, in case of an emergency, one can easily get help if one carries a cell phone.  In addition, a cell phone has become like a little computer, consisting of many programs and applications that enable us to do whatever we want. We can browse websites, send emails, watch movies, listen to music, play games, book flights, check for weather updates, and more. A cell phone is a powerful device that enables us to perform many tasks and get the results or solutions we need. Disadvantages  By relying so much o...

Your question can be answered from more than one perspective. For instance, for those whose ancestors were already in America between 1846 and 1873, especially in California during those dates, there is a great potential for a transformation of understanding identity, community, group, others and history. While for those whose ancestors came to America after those dates the potential for transformed sense of self and community is, it seems, both less and different, although the potential for a transformed sense of others and of history seems equally great. As one instance to consider for an example, both my maternal and paternal ancestors came to America in 1907 (pure coincidence), and while, as a first-generation American, I don't feel a shift in my identity, I do feel a new sense of shame, regret and sorrow over the events Madley reveals as having been foundational to the existence of my home state of California. My sense of community, though not transformed, is jolted since some...

The Mayflower Compact is an agreement signed by settlers who came to what is now the United States aboard the ship Mayflower .  In this document, the men (the document was signed only by male heads of households) agree to be governed by a government that they will set up.  This document is important in American history because it is the first written framework for a government produced anywhere in what is now the United States. When the Pilgrims and others left England on the Mayflower , they expected to go to Virginia.  They had made a deal with the government in Virginia to live there.  However, storms blew them off course and they landed far to the north.  They decided to stay there, but they did not have a legitimate government set up at that point.  They felt that they needed to set up a government that they all could agree to.  They especially needed the non-Pilgrims to agree to obey the government.  In the Mayflower Compact, they did this.  They agreed to have a government and t...

The narrator in Hemingway's short story "In Another Country" is recuperating in the Italian city of Milan after being wounded during World War I. The story may be somewhat autobiographical as Hemingway was wounded on the Italian front in 1918 while driving an ambulance for the Red Cross. Hemingway received his wounds while handing out chocolates to Italian soldiers at the front. While he considers the young Italian officers his friends, the narrator says, I was never really one of them after they had read the citations, because it had been different with them and they had done very different things to get their medals. The suggestion is that the Italians won their medals through bravery and combat while the narrator received his because he was an American. He readily admits that he may never have been able to do the things which the Italians did to get their medals: I knew that I would have never done such things, and I was very much afraid to die and wondering how I woul...

To determine the convergence or divergence of the series `sum_(n=1)^oo (-1)^n/(n!)` , we may apply the Ratio Test. In Ratio test , we determine the limit as: `lim_(n-gtoo)|a_(n+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 given series `sum_(n=1)^oo (-1)^n/(n!)` ,  we have `a_n =(-1)^n/(n!)` .  Then, `a_(n+1) =(-1)^(n+1)/((n+1)!)` . We set up the limit as: `lim_(n-gtoo) | [(-1)^(n+1)/((n+1)!)]/[(-1)^n/(n!)]|`  To simplify the function, we flip the bottom and proceed to multiplication: `| [(-1)^(n+1)/((n+1)!)]/[(-1)^n/(n!)]| =| (-1)^(n+1)/((n+1)!)*(n!)/(-1)^n|` Apply Law of Exponent: `x^(n+m) = x^n*x^m` . It becomes: `| ((-1)^n (-1)^1)/((n+1)!)*(n!)/(-1)^n|` Cancel out common factors `(-1)^n` and apply `(-1)^1 = -1` `| -(n!)/((n+1)!) |` Simplify: `| -(n!)/((n+...

The European Union (EU) was decades in the making, but it came into being in its modern form with the Maastricht Treaty in 1993. There are currently 28 members of the EU, 19 of which are in the so-called Eurozone, which uses the common currency called the Euro. The primary function of the EU is economic: to create a large, single European market that gives the member countries the competitive advantages that go with size. This also helps break down barriers to free trade that can impede individual economies. The EU also provides for free movement between member countries, so that citizens and workers can easily relocate to meet employment and labor needs. The EU also works on some of the pressing matters in modern life, such as climate change and providing aid to developing countries.

This question can be solved by using the equation that Work = Force x Distance.  The force provided is 1.2 Newtons and the distance moved is 4 meters.   Work = 1.2 x 4 Work = 4.8 Joules A Joule is the unit for work, and it is equivalent to one Newton of force causing a movement of one meter.  What's interesting about work is the fact that a distance of movement must occur in the direction of the force for work to have been done.  Mathematically, it looks simple.   Work = 50 N x 0 meters Work = 0 Joules Mathematically, that looks completely legitimate; however, there are some frustrating examples of forces doing zero work.  I like to demonstrate by having a student push against my classroom wall as hard as they can for 30 seconds or so.  Students are shocked to find out that despite being tired, they did zero work.  The wall didn't move.  

Release from the world's limitations would be something that Junior would want from another person. The removal of limitations is something that defines the arc of Junior's narrative. He finds himself as a "part-time" Indian because he wants more. Junior seeks to be released from this world of limitations and looks for this experience in other people. Junior sees this in Penelope. When she speaks of wanting to go to Stanford and creating something lasting that represents beauty, it triggers specific feelings inside Junior. He longs to escape the life of "the Rez" and seeks something more than what is around him. His whole desire to go to Reardon is rooted in wanting to expand his horizons. Junior sees Penelope as trying to be more than the world around her, something he identifies in himself. At the end of the novel, when Junior is playing basketball with Rowdy, they are not keeping score. Their friendship has transcended limitations. They have moved past th...

It's a little of both; the expansion of the power of the President of the United States has been going on for a long time, but it hasn't simply been a gradual progression toward ever-greater power. Instead it's more what biologists would call punctuated equilibrium ; most of the time it stays fairly constant, and then there are large, relatively sudden disruptions which shift it forward. The main cause of such expansions of Presidential power has been wars. Abraham Lincoln greatly expanded Presidential power in the Civil War. Woodrow Wilson greatly expanded it in WW1. Franklin Roosevelt expanded it again in WW2. Lyndon Johnson expanded it in the Vietnam War. Even when we weren't actually at war, expansion of Presidential power has usually been accompanied by some sort of crisis or panic, such as a recession or a major terrorist attack. People look to the President to save them from danger, and expand his power (particularly his military power) in order to do that. This ...

Friar Laurence is a priest (a Friar is another term for a Catholic holy man) and not labeled as a doctor in Shakespeare's Romeo and Juliet . It is likely, however, that, like other religious men of his day, he dabbled in chemistry and the creation of herbal mixtures like the one he gives Juliet. Science was often a natural pastime of religious men who were prohibited from marrying and raising a family. Some of the greatest scientists in history, including Albertus Magnus (described the qualities of arsenic), Gregor Mendel (genetics), and Roger Bacon (scientific method) were monks or priests. The fact that Friar Laurence is somewhat of a scientist is revealed in Act II, Scene 3 as he is in his garden gathering weeds and flowers. He describes how herbs can be used as both medicine and poison. In the following lines he tells how one such flower, if smelled, provides pleasure, but if tasted could cause death: Within the infant rind of this weak flower Poison hath residence and medicine...