Notes

Gonzales describes the uneven development of Latin America and the United States as an issue of exploitation and dominance.  Latin America has been viewed by the United States as a region that could be exploited for financial gain.  The United States has always viewed itself as superior to the Latino populations.  The Monroe Doctrine established a mindset that the countries to America's south were unfit to govern themselves and therefore needed the protection of the United States.  The exploitation of the resources and labor of Latin America has been a consistent theme since the period of independence. The United States has used its military in the region to subjugate Latino populations since the 1700's.  Examples of this interventionist lean are seen in the Mexican-American War, Spanish-American War, and a variety of Central Intelligence Agency operations to undermine the sovereignty of Latin American nations.  This paternal relationship that the United States has fostered in ...

Multicellular organisms are made up of a large number of cells, while unicellular organisms are made up of one cell each. Unicellular organisms depend on the processes of diffusion and osmosis for exchanging the materials with their immediate environment. However, multicellular organisms are much larger in size and are much more complex, as compared to unicellular organisms. In the case of multicellular organisms, most of the cells are further away from the environment and cannot rely on osmosis and diffusion for direct material exchange with the environment. This means that an elaborate transport system is needed to take the nutrients to the appropriate body part or cell and to take the waste material to the external environment. Thus, we have a heart, blood, veins, arteries, etc. for carrying out the material transport. The presence of an elaborate and specialized transport system is the reason multicellular organisms can grow to large sizes and have complex organ systems. Hope this ...

Tom Canty displayed a thirst for knowledge by reading widely and consulting those in the position to help him in his quest. In leadership, some level of knowledge and wisdom is required in order to effectively lead the people, and Tom yearned for knowledge. Tom was ambitious and yearned for a better life. He hoped to improve his condition despite the negativity and ridicule he encountered from his family and friends. When the opportunity presented itself, Tom organized a royal court and established an elaborate mimic kingdom. Through his character and mannerisms, Tom became influential among his friends and the community at large. Tom earned the respect of the older people from his community because he offered them solutions when they  consulted him concerning the issues they faced. When he found himself in the real royal court, Tom learned fast and tried to adjust to his new condition. Despite the different mishaps that led the people in the court to believe that he was mad, Tom succe...

Since this question was listed under "Literature," I am going to assume that we are considering a thesis statement for a literary analysis, although I can see a basis for arguing that support for this contention can be generalized to other forms of essays.  In short, a thesis statement reflects the opinion of an individual and in the United States, it is an easy leap to say this represents American individualism.  A thesis statement for a literary analysis is the writer's opinion on a literary text, along with the writer's support for that opinion.  Thus, a literary analysis of a particular text is one shake of the kaleidoscope, with an almost infinite number of combinations of opinion and support that other writers might write.  Each person's reading experience is truly ineffable, since each of us, while reading the very same words, brings to the reading a different mind, an individual take on a text.    However, while I am by no means an expert on thesis stateme...

At the end of Shakespeare's Romeo and Juliet the Prince has entered Capulet's tomb, learning of Romeo and Juliet's fate. Friar Lawrence details the couple's plans and his role in their actions. His story is corroborated by Romeo's suicide letter. The Prince ultimately becomes quite angry and addresses Lord Capulet and Lord Montague, blaming them for not only the deaths of their daughter and son but also for the deaths of Mercutio and Paris: See what a scourge is laid upon your hate, That heaven finds means to kill your joys with love, And I, for winking at your discords too, Have lost a brace of kinsmen. All are punished. A "scourge" is something which causes great suffering. It definitely applies to the feud between the Montagues and Capulets as it has caused the deaths of six people in only a few days during the course of the play. Two of the dead, Mercutio and Paris, were the Prince's relatives. Finally, in the last words of the play the Prince adv...

Macbeth and Lady Macbeth are punished by their guilt.  Both of them succumb to guilt in different ways.  Macbeth slowly loses his mind, and eventually his nerve, as a result of his actions.  Lady Macbeth also goes mad, and kills herself.  Malcolm is rewarded for being brave and loyal to his kingdom, because his army defeats Macbeth’s and he becomes king.  Macbeth’s madness started right when he killed Duncan. He said he thought he heard one of the guards say “Glamis hath murder'd sleep.”  This is the beginning of his paranoia.  He has Banquo murdered, and then sees his ghost at the banquet.  Macbeth shouts at the ghost.  MACBETH Thou canst not say I did it: never shake Thy gory locks at me. (Act 3, Scene 4)  Macbeth does not stop there though.  He has Macduff’s wife and children murdered.  When he hears the second set of prophecies from the witches, they tell him to beware Macduff.  He is so concerned about this that Macduff is able to easily confuse and upset him when the two face...

Thomas Paine was an Englishman who emigrated to North America during the Revolutionary War period. He developed strong opinions about the role of England's form of government, parliamentary monarchy, and its role in colonized America. He published his opinions in pamphlets. In 1776, Thomas Paine authored an influential pamphlet called "Common Sense" a mere six months before the United States declared themselves a nation through The Declaration of Independence.   In it, he advocated for the colonies to develop their own government. Paine suggestion that replacing England's government of the colonies with a local republican form of government would result in a greater success. The new nation would be more successful because they, rather than England, would own the wealth of their considerable natural resources.

`int_0^1 (x^3+2x)/(x^4+4x^2+3)dx` To solve, apply u-substitution method. Let `u = x^4+4x^2+3` Then, differentiate u. `du=(4x^3 + 8x)dx` `du=4(x^3+2x)dx` `(du)/4=(x^3+2x)dx` And, determine the values of u when x=0 and x=1. `x=0` `u=0^4+4(0)^2+3=3` `x=1` `u=1^4+4(1)^2+3=8` So expressing the integral in terms of u it becomes: `int_0^1(x^3+2x)/(x^4+4x^2+3)dx ` `= int_3^8 1/u * (du)/4 ` `= 1/4int_3^8 1/u du` `= 1/4 ln u |_3^8` `= 1/4 (ln 8 - ln 3)` `=0.2452` Therefore,  `int_0^1 (x^3+2x)/(x^4+4x^2+3)dx = 0.2452` .

The first census to identify Native Americans occurred in 1860, and counted 339,421 Native Americans in the modern U.S. excluding Alaska. In 1900, the Native American population was approximately 237,000. This is a decrease of about 102,421, or 30.2% of the population in 1860, over the course of 40 years. This decrease in population can be explained by a number of factors, including violent conflict between Native Americans and European colonizers and displacement of Native American populations. For example, in the mid-19th century, many Native American populations were pushed westward. Displacement from land and traditional ways of life resulted in higher death rates and increased infant mortality. The disruption in daily life caused by displacement and movement to reservations also decreased birth rates because of societal changes. Additionally, Native Americans often married European-descended Americans, and their children may not have been identified as Native American on census fo...

Atticus was a good lawyer because although he was appointed to defend Tom Robinson and the case was unpopular, he still tried his best.  He wanted to defend Tom Robinson even if it seemed impossible for them to win. When Scout asks him why he is doing something so unpopular, he tells her that he could not hold his head up or tell his children what to do if he didn’t take the case. Scout, simply by the nature of the work, every lawyer gets at least one case in his lifetime that affects him personally. This one’s mine, I guess. You might hear some ugly talk about it at school, but do one thing for me if you will: you just hold your head high and keep those fists down. (Ch. 9)  Atticus is willing to risk his reputation in town and the effect it will have on his family, because it is his job and because he believes that taking the case and defending Tom Robinson is what is right.  He explains to his brother, Jack, that he hopes his children can get through the case without becoming racists...

High and low (air) pressures are caused by the motion of air. When air gets warm, its density decreases and it rises up. This causes a region of low air pressure near the surface of the earth. In contrast, when air get colder, its density increases and it starts settling towards the surface. This results in a region of high pressure near the surface. In areas of low pressure, caused by ascending warm air, wind rushes in from the vicinity. This causes a counterclockwise (or anticlockwise) motion of wind in the Northern hemisphere. The rising warm winds generally result in precipitation and hence low pressure systems are associated with unsettled weather. In comparison, winds rushes out of high pressure regions and we observe clockwise wind flow in such regions in the Northern hemisphere. High pressure regions generally have calmer weather. Hope this helps. 

To determine the convergence or divergence of the series `sum_(n=1)^oo (-1)^n/2^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/2^n` , we have `a_n =(-1)^n/2^n` .  Then, `a_(n+1) =(-1)^(n+1)/2^(n+1)` . We set up the limit as: `lim_(n-gtoo) | [(-1)^(n+1)/2^(n+1)]/[(-1)^n/2^n]|`  To simplify the function, we flip the bottom and proceed to multiplication: `| [(-1)^(n+1)/2^(n+1)]/[(-1)^n/2^n]| =| (-1)^(n+1)/2^(n+1)*2^n/(-1)^n|` Apply Law of Exponent: `x^(n+m) = x^n*x^m` . It becomes: `| ((-1)^n (-1)^1)/(2^n *2^1)*2^n/(-1)^n|` Cancel out common factors `(-1)^n` and `(2^n)` . `| (-1)^1/ 2^1 |` Simplify: `| (-1)^1/ 2^1 | =| (-1)/ 2 |...

In Laurie Halse Anderson's young adult novel,  Speak,  Melinda Sordino must face both her freshman year of highschool and the trauma of sexual assault in great isolation. At a party over the summer, a schoolmate assaulted Melinda. All of her old friends and classmates are angry with her because she called the police, who came to break up the party. She has lost her friends and becomes increasingly anxious about speaking to anyone at all, despite desperately wanting to open up about what happened to her. What's worse, the boy who assaulted Melinda begins to taunt her in school. On Job Day, Melinda and her classmates take a career aptitude test which gauges their skills and pleasures in life and suggests a career for them. Melinda doesn't care about taking this test and it stresses her out to think too far into the future. She simply wants to make it through her freshman year without succumbing to her anxiety! The aftermath of trauma, a loss of friends, and feeling neglected ...

Bananas are naturally radioactive, and the reason is that bananas are rich in potassium (K), a vital ingredient required by all animals, including humans, for maintaining proper body functions. The average banana contains about half a gram of potassium and only a very small fraction of that potassium is radioactive (K-40). It is estimated that only about 0.012% of the total potassium is radioactive. The non-radioactive varieties of potassium (K-39 and K-41) make up the rest. While it is true that bananas are rich in potassium and a very small fraction of that potassium is radioactive, eating bananas would not increase exposure to radiation because the body has its own mechanism for maintaining a relatively tight control over potassium levels. This mechanism ensures that the level of the radioactive potassium (K-40) is always kept in check.

For the given equation `0.5^x-0.25=4` , we may simplify by combining like terms. Add `0.25` on both sides of the equation. `0.5^x-0.25+0. 25=4+0.25` `0.5^x=4.25` Take the "`ln` " on both sides to be able to bring down the exponent value. Apply the natural logarithm property: `ln(x^n)= n*ln(x)` . `ln(0.5^x)=ln(4.25)` `xln(0.5)=ln(4.25)` To isolate the x, divide both sides by `ln(0.5)` . `(xln(0.5))/(ln(0.5))=(ln(4.25))/(ln(0.5))` `x=(ln(4.25))/(ln(0.5))` `x=(ln(17/4))/(ln(1/2))` `x=(ln(17) -ln(4))/(ln(2^(-1)))` `x=(ln(17) -ln(2^2))/(ln(2^(-1)))` `x=(ln(17) -2ln(2))/(-ln(2))` `x=(ln(17))/(-ln(2)) -(2ln(2))/(-ln(2))` `x= -(ln(17))/(ln(2)) +2 or -2.087` (approximated value) Checking: Plug-in `x=-2.087` on `0.5^x-0.25=4` . `0.5^(-2.087)-0.25=?4` `(1/2)^(-2.087)-0.25=?4` `(2^(-1))^(-2.087)-0.25=?4` `2^((-1)*(-2.087))-0.25=?4` `2^(2.087)-0.25=?4` `4.25-0.25=?4` `4=4 `   TRUE Note: `2^(2.087)=4.248636746 ~~4.25` Therefore,there is no extraneous solution. The `x=-(ln(17))/(ln(2)) +2` ...

Maclaurin series  is a special case of Taylor series which is centered at a=0 . We follow the formula: `f(x) =sum_(n=0)^oo (f^n(0))/(n!)x^n` or `f(x) = f(0) + (f'(0))/(1!)x+(f''(0))/(2!)x^2+(f'''(0))/(3!)x^3 +(f^4(0))/(4!)x^4 +(f^5(0))/(5!)x^5 +...` To list of `f^n(x)` up to `n=10` , we may apply the Product rule for differentiation: `d/(dx) (u*v) = u'*v +u*v` '. `f(x) = xsin(x)` `f'(x) = xcos(x)+sin(x)` `f''(x) = 2cos(x)-xsin(x)` `f'''(x) =- xcos(x)-3sin(x)` `f^4(x) = xsin(x)-4cos(x)` `f^5(x) = xcos(x)+5sin(x)` `f^6(x) = 6cos(x)-xsin(x)` `f^7(x) = -xcos(x)-7sin(x)` `f^8(x) = xsin(x)-8cos(x)` `f^9(x) = xcos(x)+9sin(x)` `f^(10)(x)= 10*cos(x)-x*sin(x)` Note: `d/(dx)x=1` ,  `d/(dx) cos(x) =-sin(x)` , and `d/(dx) sin(x)=cos(x)` . Plug-in x =0, we get: `f(0) = 0*sin(0)`          `=0*0`          `=0` `f'(0) = 0*cos(0)+sin(0)`          `=0*1+0`          `=0` `f''(0) = 2cos(0)-0*sin(0)`            `=2*1-0*0`            `=2` `...

For this question we need Martian radius, which is about 3390 km (see the link attached). Actually, enough accuracy is reached if we assume the layer is flat with the given thickness and with the surface area as of Mars. The formula for the surface of a sphere is `4 pi R^3.` Numerically we obtain `0.003*4*pi*3390^2 approx433242 km^3.` The mass of one cubical kilometer of water is `10^9` kg, so the total mass is about `4.3*10^14 kg.` This is about `10^6` times less than the given mass of Venus's atmosphere.

In a general sense, Napoleon's tactics lead to greater productivity on the farm. His insistence that the animals follow instructions and remain loyal guarantees that the animals remain committed and unquestioning. In such a system, more focused and productive labor ensures greater returns and bigger profits. Furthermore, the tactic guarantees a servile attitude and minimizes the risk of recalcitrance and rebellion. Napoleon ensures that the animals remain obedient not only through propaganda, misinformation, and deceit, but also brutally enforces control by slaughtering those who dare rebel against him. The best example of this occurs in chapter seven, when the three hens who resisted his instruction to sacrifice their eggs are executed by his dogs. Animals who supposedly plotted against him also suffer the same fate. In this manner, Napoleon establishes a merciless tyranny. He becomes supreme leader and his authority cannot not be questioned. The success of this strategy is proven...

It is important to know that Reconstruction was a project that was never completed. The purpose of Reconstruction, which was started in 1865 and was discontinued after Rutherford B. Hayes signed the Compromise of 1877, was not only to rebuild, or reconstruct, the South, but also to provide black people with political agency and property. The promise of "forty acres and a mule" was made during Reconstruction, but was never fulfilled. Southern whites' resentment of the federal government and of the North may have intensified during this period. Firstly, there was the matter of black people becoming members of Congress. Secondly, federal troops continued to occupy the South. Thirdly, opportunistic northerners, frequently called "carpetbaggers," went south to profit off of the South's diminished status. Given the historical record, in my view Southern blacks were hurt most -- not by Reconstruction, but by its unfulfilled promise. Hayes's compromise with Sout...

In a plant cell there are many chloroplasts where photosynthesis occurs. Photosynthesis is broken up into two main steps: the light-dependent reactions and the light-independent reactions (sometimes called the dark reactions). The light reactions occur within the thylakoid membranes of the chloroplasts and produce oxygen that is released as a byproduct of splitting water and also the ATP and NADPH that are required for the light-independent reactions. The light-independent reactions of photosynthesis occur in the stroma of the chloroplasts. The NADPH and ATP made during the light reactions along with carbon dioxide from the atmosphere enter a cycle known as the Calvin cycle. The first step of the Calvin cycle combines RuBP (an organic intermediate within the cycle) with the carbon dioxide to create 3-PGA. The enzyme that catalyzes this reaction is RuBisCO and it is the most abundant enzyme on this planet! The conversion of the 6 3-PGA molecules to 6 GA3P molecules utilizes 6 ATP and 6...

This story uses the first person point of view. Brother, a character in the story, is the narrator. Using first person narration, Brother is able to tell the story from his own perspective and personal experience. So, the reader gets the events from Brother's own memory. Although this is not a series of diary entries, Brother does recall these events in a similar way. This story is Brother's confession about how he treated and mistreated his younger brother, Doodle.  So, it is similar to a story like Edgar Allen Poe's "The Cask of Amontillado." The clear difference is that Poe's narrator (Montresor) confesses with hardly any remorse whereas Brother's confession in "The Scarlet Ibis" is filled with remorse and regret.  Brother recounts the events in hindsight. This is why he uses the past tense from the very beginning. In retelling the story, Brother is older and wiser and therefore better able to reflect upon his mistakes with Doodle. When Brothe...

Organisms can be categorized as either prokaryotes or eukaryotes. A prokaryote is a simple organism and is unicellular in nature. Bacteria are prokaryotes or prokaryotic organisms. In comparison, a eukaryote is a complex organism and is multicellular in nature. Animals (including human beings), plants, etc., all are eukaryotes or eukaryotic organisms. Eukaryotes are much more complex in comparison to prokaryotes and have dedicated systems for carrying out life functions. Life originated in the form of the simplest organisms and later on more complexity was developed. Hence, prokaryotes developed first and eukaryotes evolved out of prokaryotes. From the fossil records, it has been established that prokaryotes were present on Earth as far as 3.5 billion years ago, about 1 billion years after Earth was formed. In comparison, eukaryotes appeared around 1.7 billion years ago.  Hope this helps. 

Antoine de Saint-Exupery's The Little Prince contains two central themes: the importance of finding one's child self and the importance of love. Furthermore, Saint-Exupery shows that real love can only be experienced when one is in tune with one's child self. While the title character grows to understand what love really is and its importance, it's really the narrator , the main protagonist, who comes to reconnect with his child self , and it is the prince who helps him find this reconnection, making the narrator's reconnection with his child self the central story. The reconnection with one's child self is really a personal story . An outsider would not be able to fully understand the story without an internal look at the protagonist's thoughts and feelings. Therefore, since the central story is about the narrator reconnecting with his child self, a story that cannot be seen without a look inside the narrator's heart and mind, it is necessary for ...

In Zora Neale Hurston's  Their Eyes Were Watching God , some people of Eatonville, usually men, like to gather on the porch at Joe Starks' store to tell stories and to socialize. One favorite story told and retold is about a yellow mule, which Janie loves to listen to because it provides some distracting entertainment from tending the store. She wishes that she could share stories that she makes up about the mule, too. In chapter 6, though, Joe forbids his wife to participate in the stories on the porch because of the following reason: "He didn't want her talking after such trashy people. 'You'se Mrs. Mayor Starks, Janie. I god, Ah can't see what uh woman uh yo' stability would want tuh be treasurin' all dat gum-grease from folks dat don't even own de house dey sleep in . . . They's jus' some puny humans playin' round de toes uh Time'" (54). From what Joe says above, he doesn't want his wife fraternizing with locals who ...

We are asked to write a function whose domain is all real numbers except -8 and whose range is all real numbers except 3. An example of a function with similar restrictions on the domain and range is the hyperbola y=1/x. We would need to apply transformations to this function including a translation left of 8 units and a translation up of three units. We could then apply a vertical dilation of almost any sort. An example would be `y=1/(x+8)+3 ` or the equivalent version `y=(3x+25)/(x+8) ` The graph:

The "Gilded Age" is the period of time during the late 1800s and early 1900s during which a high level of corruption, shoddiness, fakery, and little substance was rampant. The name comes from Mark Twain's novel of the same name. Perhaps the spoils system is one of the main reasons why this time period became known as the "Gilded Age." In the spoils system, an elected official would unabashedly dole out jobs and favors to friends, family, and others. These favors manifested themselves in different ways, but it was common to see jobs given in exchange for political favors, and nepotism was obvious in multiple levels of government. One egregious example of the spoils system was evident when U.S. President Ulysses S. Grant oversaw the insertion of several of his wife's family members into federal government positions. During the tenure of Chester A. Arthur as president, he oversaw the implementation of the Civil Service Commission. This was the beginning of the ...

The main character of  The Graveyard Book,  by Neil Gaiman, is Nobody Owens. Nobody, called Bod, is an orphan who escaped the murder of his family. His parents and siblings were killed by "the man Jack," and Bod survived by wandering away and into a graveyard. When he arrived there, a lady ghost protected him and decided that he should live in the graveyard but have the freedom to walk among both living and dead. This lady ghost and her equally spectral husband raise Bod in the graveyard, and he learns many supernatural powers from his ghost companions. Though Bod's childhood is unusual, he makes friends with both the living and the dead, and is well provided for by Silas, who can move among the living with ease. Throughout the course of the book, Bod must confront the man who killed his family as well as the fact that he cannot stay among the dead forever.

As we command and consume the resources of the earth, all that we reap is what our children will not be able to reap.  Every redwood that is cut down is borrowed from our progeny.  Every barrel of oil we take from the ground is a barrel of oil our children will be unable to use.  Every acre of woods that we built a McMansion on is an acre of land that the next generation cannot enjoy. The destruction of the rain forest is a borrowing from our offspring, not only its destruction, but also potential cures not yet found.  As we continue in this manner, it may very well be that we are not simply borrowing this earth, but that we are making it impossible for the next generation to use it at all.  If we were to begin to behave as caretakers of the earth for our children, we would have something to hand down.  What we borrow now can never be paid back - or forward.

I think most readers would agree that the dramatic climax of Jane Eyre occurs just before the most frequently quoted line from this novel; that is to say, "Reader, I married him." The scene just prior to this finds Jane going back to Thornfield to see Rochester, and discovering that he has been injured and blinded in a fire that was set by his wife Bertha. Since his wife has died, Rochester is now free to marry Jane, without worrying about social stigma. But it is here that Jane makes a crucial choice. She could decide not to marry Rochester, who is much older than she, and now also physically disabled. After fleeing Thornfield, becoming lost on the moors, and being taken in by strangers, Jane regains her focus and confidence and realizes that, regardless of whether it is right or wrong, she loves Rochester and must see him again. When she hears about the fire, her sympathy is aroused. It is tempting to think that Jane's decision to marry Rochester is one born of pity. B...

D. A. Carson's How Long, O Lord? is a text which examines Biblical passages as they pertain to the suffering of mankind; it is written through the lens of Evangelical Christianity. Chapter five, entitled "The Suffering People of God," deals with the particular sufferings of Christians who are confronted with growing "anti-Christian pressures" in the West and official persecution in other parts of the world. Carson says the most dominant type of suffering which Christians find "peculiar" is the suffering which is dealt out by God himself—a "fatherly" kind of punishment which is the hallmark of being a child of God and is done for our good so "we may share in his holiness" and steer clear of sin.  One of the most interesting arguments made here is that many of God's punishments—including war, illness, financial troubles, death, and personal losses—are inherently considered evil and can easily be conflated as the work of Satan. Ca...

Solitude helped Thoreau to appreciate society better because, as he writes in the chapter entitled "Solitude," "Society is commonly too cheap."  In other words, we spend so much time with other people: at every meal, at the post office, at the fireside at night, and so on.  We are constantly running into one another, and so we don't really have an opportunity to miss other people.  Have you ever heard of the expression Absence makes the heart grow fonder ?  Thoreau's sentiment is quite similar to this idea.  He says that our constant company renders it like a "musty cheese" that we foist on each other over and over.  He believes that, when we are always with other people, "we [...] lose some respect for one another."  More solitude gives us the opportunity to be truly glad when we do have company and it prevents this company from becoming a "musty cheese" that we must endure and instead becomes enjoyable.

Brown v. Board of Education  was a landmark case in United States history as it arguably launched the civil rights movement. The Little Rock Nine were the first black students to enact this ruling of the Supreme Court. Brown v. Board of Education was a consolidation of cases from five jurisdictions that concerned the same problem of segregated schools: At the time of this case, most of the segregated schools were not "separate but equal." Often the buildings of the black schools were in ill repair, books were the ones used for years by the white schools and were dirty and torn, and indoor toilet facilities did not exist. Nonetheless, the purpose of the consolidation of these cases was not the physical conditions, but the fact that segregation itself was "inherently unequal and a violation of the equal protection clause of the 14th amendment of the Constitution." The unanimous decision of the Supreme Court in Brown v. the Board of Education was that an education o...

Maclaurin series is a special case of Taylor series that is centered at `c=0` . The expansion of the function about `0` follows the formula: `f(x)=sum_(n=0)^oo (f^n(0))/(n!) x^n`  or `f(x)= f(0)+(f'(0))/(1!)x+(f^2(0))/(2!)x^2+(f^3(0))/(3!)x^3+(f^4(0))/(4!)x^4 +...` To determine the Maclaurin polynomial of degree `n=4` for the given function `f(x)=xe^x` , we may apply the formula for Maclaurin series. To list `f^n(x)` up to `n=4` , we may apply the Product rule for differentiation: `d/(dx) (u*v) = u' *v +u*v'` and derivative property: `d/(dx) (f+g) = d/(dx) f +d/(dx) g` . `f(x)=xe^x` Let: `u =x` then `u' = 1`       `v = e^x`  then `v' = e^x` `d/(dx) (xe^x) =(1*e^x) + (x*e^x)`                   `=e^x +xe^x` `f'(x)=d/(dx) (xe^x)`             `= e^x +xe^x` `f^2(x) = d/(dx) (e^x +xe^x)`            `=d/(dx) e^x + d/(dx) xe^x`            `= e^x + (e^x+xe^x)`            `= 2e^x+xe^x` `f^3(x) = d/(dx) ( 2e^x +xe^x)`             `=d/(dx) 2e^x + d/(dx) xe^x`             `...

There are no chores Tuck gives Winnie in Natalie Babbitt's Tuck Everlasting , but he does charge her with a task to fulfill . The task he gives her is keeping the secret of the spring in the wood her family owns. When Winnie meets Jesse, Miles, and Mae Tuck, she learns that 87 years ago the Tucks passed through the wood and stopped for a drink at the spring. The spring gave them eternal life and froze them in their current ages so that the Tucks never grew older, got sick, or changed in any other way. The Tucks then carry her to their home to speak with Mr. Tuck so that Mr. Tuck can convince her to keep the spring a secret. While out in the rowboat with Winnie after dinner, Tuck explains to Winnie about the circle of life, how everything is constantly moving and changing and that death is a part of this endless circle, keeping the circle going. Tuck further explains that, since his family members drank from the spring, he and his family members are no longer part of this circle. ...

`sum_(n=0)^oo x^(5n)/(n!)` To determine the interval of convergence, use Ratio Test.  The formula in Ratio Test is: `L= lim_(n->oo) |a_(n+1)/a_n|` If L <1, the series is absolutely convergent.  If L>1, the series is divergent. And if L = 1, the test is inconclusive. The series may converge or diverge. Applying the formula, the value of L will be: `L= lim_(n->oo) |(x^(5(n+1))/((n+1)!))/(x^(5n)/(n!))|` `L= lim_(n->oo)|x^(5(n+1))/((n+1)!) * (n!)/x^(5n)|` `L= lim_(n->oo) | x^(5n+5)/((n+1)n!) * (n!)/x^(5n)| ` `L= lim_(n->oo) |x^5/(n+1)|` `L = x^5* lim_(n->oo) |1/(n+1)|` `L = x^5 * 0` `L=0` Since the value of L is less than 1, the given series converges for all values of x. Therefore, the interval of convergence is `(-oo, oo)` .

Given` 3(y-4x^2)dx + xdy = 0` =>` 3y - 12x^2 +xdy/dx=0` =>` ( 3y - 12x^2)/x +dy/dx=0` =>` 3y/x - 12x +dy/dx=0` => `y'+(3/x)y=12x` 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'+(3/x)y=12x--------(1)` `y'+p(x)y=q(x)---------(2)` on comparing both we get, `p(x) = (3/x) and q(x)=12x` 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 (3/x) dx) *((12x)) dx +c)/e^(int (3/x) dx)` first we shall solve `e^(int (3/x) dx)=e^(ln(x^3))=x^3`      so proceeding further, we get y(x) =`(int e^(int (3/x) dx) *((12x)) dx +c)/e^(int (3/x) dx)` =`(int x^3 *((12x)) dx +c)/x^3` =`(int 12x^4 dx +c)/x^3`  `=(12x^5/5 +c ) /x^3` so `y=(12x^5/5 +c )/x^3`

The three friends—narrator J., George, and Harris—thought they needed a change of scenery. They were all feeling listless. Each one of them even experienced occasional “fits of giddiness.” As J. tells it in Chapter I, they discussed their maladies with each other one day and decided that they were all overworked. They needed a vacation, away from the city. George suggested that they make a boat trip along the River Thames. Travel would be important for their collective well-being. The others agreed, figuring they would get “fresh air, exercise, and quiet.” The only member of the group who wasn’t enamored with the river idea was Montmorency, the fox terrier. He was bored by boats and water. He would rather chase cats. Still, the vote was three to one, so the boat trip passed. We read of their travels here. And although the four later cut their two-week outing down to ten days, they all agreed they had a pleasant time.

In this deleted scene, Abigail tells John that her "spirit's changed entirely. [She] ought to be given Godly looks when [she] suffer[s]" for the people as she does. Abigail shows John the marks she claims to have received from the specters of various accused witches, and the stage direction says that John " see[s] [her] madness now ." Abigail seems sincere when she accuses John of being hypocritical and speaking for his wife Elizabeth because Abigail believes John secretly wants her dead.  I think such a scene casts Abigail's state of mind into doubt: has her mind really turned?  If so, if she has gone mad as a result of the hysteria, then this might cause the audience to feel sympathy for her, and Miller doesn't want us to sympathize with Abigail. He wouldn't want to lessen the amount that we can blame her for what has happened because Abigail, in many ways, represents Senator Joseph McCarthy, the congressman who led the witch hunt for Communists in...

As the remainder of this quote indicates, the meaning here is that the valentine is a small thing that hints at potentially enormous change, or  "contemptibly little suggesting possibilities of the infinitely great."  To understand that comparison, you need to know about what Columbus and his men experienced on their voyage of discovery in 1492 -- information that Hardy assumes his audience shares. About a week after the sailors finally lost sight of the land they had departed from, Columbus (writing in his log) wrote that they began to encounter "large patches of weeds very green, and which appeared to have been recently washed away from the land." This caused excitement and hope, because the men "concluded that it must come from some nearby land. But at the same time, it caused some of them great apprehension because in some places it was so thick that it actually held back the ships." Weeks later, they were still at sea -- longer than anyone had anticip...

The two, in both the novel and the play, thematically represent the destructive forces within man. In Macbeth, the three witches are the personification of evil and in Lord of the Flies, the beast is an imaginary evil creature existing within the boys' consciousness.  In Macbeth, evil is represented in its physical form by the three witches and their leader, Hecate. The witches' strange appearance and disappearance on the heath when they encounter Macbeth and Banquo, epitomize their supernatural design. They are abnormal creatures and come to represent, to Macbeth, his destiny. He becomes dependent on their predictions and is a willing victim of their manipulation. The witches tap into Macbeth's innate evil and exploit it to fulfill their pernicious purpose which is to overturn the natural order of things and encourage evil. It is they, as the agents of the lord of all malice, Satan, who motivate the gullible Macbeth and drive him to commit the most pernicious acts: the bet...

Nitrogen and oxygen both are constituents of our atmosphere and make up about 78% and 21% of our air. Nitrogen gas has a molecular formula of N2 and a molecular weight of 28 g/mol. Thus, 1 mole of nitrogen gas weighs 28 g. Similarly, oxygen gas has a molecular formula of O2 and a molecular weight of 32 g/mol. Thus, 1 mole of oxygen gas weighs 32 g. At STP, 1 mole of each gas occupies 22.4 l. Thus, in case of nitrogen, there would be 28 g in 22.4 l of nitrogen gas. Similarly, there would be 32 g oxygen in 22.4 l gas. This means that there is more oxygen than nitrogen in the same volume of gas. Thus, oxygen is heavier than nitrogen gas and not the other way around. Hope this helps.

It is significant that the grandmother brings up the Misfit at the beginning of the story because it foreshadows the events that occur later in the story when the family has an accident and the Misfit and his cohorts stop and kill them.  She says, "'I wouldn't take my children in any direction with a criminal like that aloose in it.  I couldn't answer to my conscience if I did.'"  Ironically, this is just about the only time in the story that the grandmother is actually right about anything; it really would have been best for the family to avoid Florida.  We also get to see what the grandmother's response to a person like the Misfit is when she's not actually faced with the person.  In the end, we see the grandmother kind of buttering up the Misfit, insisting that he's a "good man," but this is such a contrast with her earlier description of him that we can see that she's only being nice to him to save her own skin.  Her first referen...

This saying means that if, as we go through life, our eyes are firmly fixed only on where we are going, we are going to miss our entire lives! Essentially, life consists of all the moments on the way to our various destinations, and when our focus is on the destination, we are not living in these moments. There are many small and large examples of this, literally and figuratively. As I leave my house, I have a destination, the school where I teach. If that is all that I think about on the way, I am missing out on a great deal. I will miss the cherry tree that just blossomed, the eagle that was perched on a rail on the road, some small children playing while waiting for their school bus to pick them up, and so much more. When I get to school, if I am not in the moment, but focused on my next stops, the bank and the library, I will not be in the here and now for my students. When you start college, if all you are focused on is your destination, which is to get a degree, you will be missi...

New conservatism or neoconservatism was a movement centered around a group of liberal intellectuals in New York City in the late 1960's.  They were increasingly disillusioned with many of the social and political movements of the 1960's. Intellectuals like Nathan Glazer , James Q. Wilson and Daniel Patrick Moynihan  were alarmed by the dramatic and swift move to the left demonstrated in American politics at the time.  They opposed the presidential aspirations and campaign of Democrat George McGovern in 1968.  Examples of movements that concerned the neocons were the black power movement, college activism, environmentalism, and radical feminism. Neocons opposed the Great Society program of Lyndon B. Johnson and did not support social engineering initiatives like affirmative action and wealth redistribution.  Neocons would play important roles in the Republican administrations of Ronald Reagan, George H.W. Bush and George W. Bush.   

The speaker admires the river. Note that he calls the Nile "Chief" of the pyramids and the crocodiles. That is to say, the Nile is the leader or guiding force of culture (pyramids) and nature (crocodiles). The Nile has been the "nurse" of many African nations. Here, the speaker notes how the river has helped civilization develop along its banks. Without this great river, these civilizations would not have developed so well or they would have developed elsewhere. Being along a large river or a body of water helps a society in terms of having a water supply, transportation, ports, fish, and so on. The Nile has clearly been useful for a number of societies, namely ancient Egypt.  The speaker says the Nile is fruitful, but then asks if this is actually true. Is the Nile fruitful or does it just "beguile" (charm) those who live on its banks to stay there and develop their societies? The speaker supposes that the Nile would have to be fruitful and charming to ke...

Records of the earliest Hindu beliefs can be found in the Vedas and the later Brahamanas, Aranyakas, and  Upanishads  (philosophical commentaries on the  Vedas ), which record beliefs that date from between 1500–500 BCE (although these was not written down until much later; they were part of an oral tradition). There is also no definite starting point for Hinduism and we know very little about the religious traditions of the Indus Valley Civilization, which existed before 2000 BCE. The Indus Valley Civilization did place emphasis on ritual bathing, sacrifice, and goddess worship; these connect it to Vedic and later Hinduism. However, the Indus Valley religion shares almost as much with other contemporaneous ancient religions.  While the language of the Indus Valley Civilization is still unknown (the script is made up of symbols that have been partially deciphered), the Hindus of the Vedic period ( 1500-500 BCE ) spoke Sanskrit. We consequently know more about the religion of this per...

Goodman Brown is surprised by the people he sees in the forest because he would never have expected so many folks who seem to upright and honest to be in attendance at a Witches' Sabbath or to be in league with the Devil.  Brown might have expected to see "men of dissolute lives and women of spotted fame," or other people who are suspected of terrible crimes and those who are well-known for their vices.  However, to see these kinds of people mixing with those church members who are "famous for their especial sanctity" as well as many others who all have excellent, pious reputations, is quite shocking to him.  The narrator says, "It was strange to see, that the good shrank not from the wicked, nor were the sinners abashed by the saints."  In other words, Brown is very surprised to note that there seems to be no difference at all in the behavior of those people he once believed to be good and those people he knows to be sinful.  Further, there is no sign...

In Elie Wiesel’s memoir, Night , chapter one goes into detail about what Elie’s life was like in the two years leading up to the German invasion of Hungary. From these pages the reader learns that Sighet’s Jewish community is not worried about the rumors of what Hitler is doing to the Jewish people. Even the horrific story told by Moshe the Beadle seems to have no effect on them. Even when the Nazi’s invade in the spring of 1944, no one Elie knows attempts to flee. There are many reasons why the Jews of Sighet are optimistic until the very end. First of all, the radio reports suggest that the advancing Soviet army will drive the Nazis out of Europe for good. Because of this, many Jews in Sighet believe that the war will not last long enough for Hitler to interfere with their lives. The second reason is that the rumors they do hear seem too outrageous to believe. Moshe the Beadle tells the truth when he describes the Nazis using Jewish babies for target practice. Yet it does not make se...