Onboard Note

If $\displaystyle f(x) = \frac{x^2 + 1}{x - 2}$, find $f'(a)$. Using the definition of the derivative $ \begin{equation} \begin{aligned} f'(a) &= \lim_{h \to 0} \frac{f(a + h) - f(a)}{h} && \\ \\ f'(a) &= \lim_{h \to 0} \frac{\displaystyle \frac{(a + h)^2 + 1}{a + h - 2} - \frac{a^2 + 1}{a - 2}}{h} && \text{Substitute $f(a + h)$ and $f(a)$}\\ \\ f'(a) &= \lim_{h \to 0} \frac{(a - 2)(a^2 + 2ah + h^2 + 1) - (a^2 + 1)(a + h - 2)}{(h)(a + h -2)(a - 2)} && \text{Get the LCD of the numerator and simplify}\\ \\ f'(a) &= \lim_{h \to 0} \frac{a^3 + 2a^2 h + ah^2 +a - 2a^2 - 4ah - 2h^2 - 2 - a^3 - a^2 h +2a^2 - a - h + 2}{(h)(a + h -2)(a - 2)} && \text{Expand the equation}\\ \\ f'(a) &= \lim_{h \to 0} \frac{\cancel{a^3} + 2a^2 h + ah^2 + \cancel{a} - \cancel{2a^2} - 4ah - 2h^2 - \cancel{2} - \cancel{a^3} - a^2 h + \cancel{2a^2} - \cancel{a} - h + \cancel{ 2}}{(h)(a + h -2)(a - 2)} && \text{Combine like t...

Vera asks Nuttel all the questions because she wishes to set him up for a scare. She knows he is down for a "nerve" cure and so thinks it would be fun to truly frighten the already nervous man. He comes across as a bore, so Vera probably also wants to get rid of him as a guest. When Vera learns he knows nothing of her aunt or her family or any of the people in the area, she is then free to tell him almost any story she wants and be believed. Because Mr. Nuttel doesn't realize that her aunt's husband and two brothers are alive, Vera makes up a story that they disappeared a year ago and are presumed dead, but she says that her aunt leaves the window (we would call it a French door) open in the hopes they will return. When Mr. Nuttel sees the very much alive threesome coming home, he thinks he is seeing ghosts and flees. At the beginning of the story, Framton Nuttel arrives at Mrs. Sappleton's home with a letter of introduction and is greeted by her mischievous niece...

Using evidence from the text, the reader can find indications that John Byro suspected the boys had his horse in “The Summer of the Beautiful White Horse” by William Saroyan. John Byro was not part of Aram and Mourad’s Armenian family. He was a lonely man who learned the Armenian language in order to communicate with and relate to the family. One day, after his horse was gone for a month, Byro walked ten miles to visit with Aram’s mother and uncle. He explained that his horse was missing, which rendered his surrey useless. The uncle becomes animated and tells John Byro to pay no mind to his missing horse. If a man walks ten miles just to have coffee and a smoke but brings up his missing horse in conversation, it is a good indication there was more to his visit than just a friendly discussion. Then another visitor arrived, a farmer named John Byro, an Assyrian who, out of loneliness, had learned to speak Armenian. My mother brought the lonely visitor coffee and tobacco and he rolled a c...

Suppose that a rock is thrown upward on the planet Mars with a velocity of $10$ m/s, its height in meters $t$ seconds later is given by $10t-1.86t^2$. a. Find the average velocity over the given time intervals: (i) [1,2] (ii) [1,1.5] (iii) [1,1.1] (iv) [1,1.01] (v) [1,1.001] Average velocity = $\frac{\delta distance}{\delta time} = \frac{y_2 - y_1}{t_2 - t_1}$ $ \begin{equation} \begin{aligned} \begin{array}{|c|c|c|c|c|c|} \hline\\ & t_1(s) & t_2(s) & y_1 (m) = 10t_1 - 1.86 t_1^2 & y_2(m) = 10t_2 - 1.86t_2^2 & V_{ave}(m/s) = \frac{y_2 - y_1}{t_2 - t_1} \\ \hline\\ (i) & 1 & 2 & 8.14 & 12.56 & 4.42 \\ \hline\\ (ii) & 1 & 1.5 & 8.14 & 10.815 & 5.35 \\ \hline\\ (iii) & 1 & 1.1 & 8.14 & 8.7494 & 6.094 \\ \hline\\ (iv) & 1 & 1.01 & 8.14 & 8.2026 & 6.26 \\ \hline\\ (v) & 1 & 1.001 & 8.14 & 8.1463 & 6.3\\ \hline \end{array} \end{aligned} \end{equation} $ b. Estimate ...

What makes "The Village Blacksmith" particularly inspiring is the way the man himself goes about his work every day no matter what life throws at him. Being a blacksmith is hard, physical work and requires a lot of strength. That in itself is inspiring. And we're left in no doubt by Longfellow that the blacksmith is a hard worker: His brow is wet with honest sweat, He earns whate'er he can, And looks the whole world in the face, For he owes not any man. Not only is he a hardworking man, he's also fiercely independent. He can stand tall and look his fellow men in the eye because he works for himself; he's not reliant on anyone else for his daily bread. In many respects, the village blacksmith is the epitome of the age-old American tradition of rugged individualism. At the same time, he's unmistakably a part of his community, going to church every Sunday and listening to his daughter sing in the choir. As a widowed father he cares deeply for his daughter and...

The three leads of the play are Mama Nadi, Josephine, and Sophie. The three women have very different specific objectives that all lead to essentially the same outcome: survival. Mama Nadi achieves her objective of surviving the conflict in the Congo by running a bar and brothel to the best of her business-like abilities. She maintains a sense of order in her establishment in order to ensure that her customers know what to expect, an objective that protects her financially. Sometimes, Mama Nadi sacrifices her own integrity to make sure that her business is running, but maintaining integrity is a less important objective than survival. Josephine achieves her objective of survival by using her body as a form of sexual insurance. She looks to please the men in her world as a way to make sure she has a means to a better life. Though attention and ego-boosts appear as if they are important objectives to Josephine, ultimately, they both contribute to her goal of surviving the war. Sophie is ...

Because the genre of literary magical realism began, at the earliest, in the twentieth century, literary scholars would not place "The Black Cat," published by Edgar Allan Poe in 1843, in that movement. Magical realism is a type of fiction characterized by a realistic setting that is somehow affected by elements that are magical or supernatural.  The narrator of "The Black Cat" kills Pluto, his first cat, and sometime later, a cat that looks very much like but not identical to Pluto enters his life.  The narrator's perversity turns him against this cat as well, and the narrator ends up accidentally killing his wife when he is aiming his ax at the cat.  He inadvertently walls the cat up with his wife's corpse, but, days later, it makes enough noise to attract the police's attention, and the narrator's crime is revealed. It is quite plausible that two black cats can look extremely similar except for a single marking, and it is also possible that a cat ...

There are a number of approaches to enumerating the fundamental principles of leadership. Some approaches enumerate eight or ten principles while others enumerate five principles. In general, though, there are two essential approaches, and there is a great deal of cross-over between all approaches. One essential approach focuses on ethical and respectful behavior, stressing that the person is never the problem; the situation external to the person is the problem; constructive relationships and leading by example are necessary. The other essential approach focuses on qualifications for leadership, stressing such things as communication skills, decision-making proficiency, taking responsibility, providing information, delegating tasks, flexibility, passing on the vision, and enabling employees.One five-step model for the fundamental principles of leadership developed by the Leadership Challenge relies heavily on the personal qualities of the leader. This five-step model advocates: Modeli...

There are three methods of heat transfer that come to mind. The first is conduction. Conduction is when the excited particles of one atom or molecule touch the excited particles in the atoms or molecules of another substance. This is how heat goes from one solid to another, or from single particles to other single particles, in typical usage. The second is convection. Through convection, energy is transferred in the same way as conduction, but instead of a solid absorbing the energy, a fluid, such as a liquid or gas, absorbs the energy. In addition, the absorption of energy causes the fluid to move about, generating convection currents. These convection currents are common in ovens, the ocean, and even the earth's mantle. Finally, radiation is a way that heat is transferred. This is when the atoms and molecules of the substance eject energized parts of themselves to increase entropy. Common radiation includes alpha, beta, and gamma decay, which you can learn more about here. This r...

1776 focuses primarily on military events because the author covered political events of the same year in a previous book: John Adams. The first important event described in the war actually took place in October 1775, in London. King George III gave an important speech to British Parliament in which he promised to crush the rebellion. After that speech, peaceful reconciliation was out of the question. The second key event happened in March 1776. The Americans put cannons in Dorchester Heights, forcing the British to evacuate Boston. Henry Knox, head of artillery, had dragged the cannons 300 miles from Ticonderoga to Boston. The third major event, which the author describes as the most important event in the book, was George Washington's escape from Brooklyn in August. Despite being defeated in battle, Washington managed to extricate his weakened army. Had the British managed to trap Washington, the war would have been over. A fourth significant event was at the end of 1776. The Br...

Odysseus reaches Ithaca thanks to the Phaeacians, who listen to his incredible story and decide to help him get back to Ithaca after twenty years of traveling. King Alcinous and Princess Nausicaa give Odysseus a ship and many gifts to take home, and Odysseus sails back to Ithaca safely. He disguises himself as a beggar before proceeding towards the town. He is not shipwrecked and does not sleep on the beach. The island where Odysseus is shipwrecked and is found in a deep sleep on the beach is not Ithaca but the island of the Phaeacians. Before reaching the island, Odysseus was supposed to be sailing home. Earlier in the story, in fact, Odysseus leaves Calypso with his men in order to return home. However, the god Poseidon sends out a storm which causes Odysseus's ship to sink. In fact, Poseidon is angry because Odysseus previously blinded his son Polyphemus (a cyclops who, in Odysseus's defense, was actually trying to eat him and all his men). Odysseus ends up as the only survi...

With the exception of the war in Iraq, no other war in American history has divided historians as much as the Vietnam War. You are right that some historians blame the United States for increased tensions during the Vietnam War, while others hold the USSR responsible. Let's begin with historians who blame the United States. The most widely read historians of this stripe were William J. Duiker, Arthur M. Schlesinger, Jr., Gabriel Kolko, John W. Lewis, David Halberstam, and George McTurnan Kahin. Kahin and Lewis co-wrote The United States in Vietnam, a book highly critical of American war policy in Southeast Asia. In particular, Kahin was a staunch supporter of the Khmer Rouge communist insurgency and strongly condemned South Vietnam's goal of separation from North Vietnam. Many of the above historians were strongly critical of South Vietnamese president Ngo Dinh Diem and the support he received from the American government and military apparatus. Here are two quotes from Kahin...

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)=x^2e^(-x) , we may apply the formula for Maclaurin series. To list f^n(x) up to n=4 , we may apply the following formula: Product rule for differentiation: d/(dx) (u*v) = u' *v +u*v' Derivative property: d/(dx) (f+-g+-h) = d/(dx) f +-d/(dx) g+-d/(dx) h Power rule for differentiation: d/(dx) x^n =n*x^(n-1) Derivative formula for exponential function: d/(dx) e^u = e^u * (du)/(dx) f(x)=x^2e^(-x) Let u =x^2 then u' = 2x       v = e^(-x)  then v' = e^x*(-1) =-e^(-x) d/(dx) (x^2e^(-x)) = 2x*e^(-x) + x^2*(-e^(-x))                         = 2xe^(-x) -x^2e^(-x) Let: u =x then u' =1         v = e^(-x)  then v' =-e^(-x) Note: c = consta...

The derivative of y with respect to is denoted as y' or (dy)/(dx) .  For the given equation: y = arctan(x/2) -1/(2(x^2+4)) , we may apply the basic property of derivative: d/(dx) (u-v) =d/(dx) (u) - d/(dx)(v)   Then the derivative of y will be: y' = d/(dx)(arctan(x/2) -1/(2(x^2+4))) y' =d/(dx)(arctan(x/2)) - d/(dx)( 1/(2(x^2+4))) To find the derivative of the first term: d/(dx)(arctan(x/2)) , recall the basic derivative formula for inverse tangent as: d/(dx) (arctan(u)) = ((du)/(dx))/(1+u^2) With u = x/2 and du=(1/2) dx or (du)/(dx) =1/2 , we will have: d/(dx)(arctan(x/2)) = (1/2) /(1+(x/2)^2)                            = (1/2) /(1+(x^2/4)) Express the bottom as one fraction: d/(dx)(arctan(x/2)) = (1/2) /((x^2+4)/4) Flip the bottom to proceed to multiplication: d/(dx)(arctan(x/2)) = 1/2*4/(x^2+4)                           = 4/(2(x^2+4))                           =2/(x^2+4)   For the derivative of the second term: d/(dx)(1/(2(x^2+4))) , we can rewrite it using the basic pro...

Here is another good quote from the book Farewell to Manzanar: Like so many of the women there, Mama never did get used to the latrines. It was a humiliation she just learned to endure: shigata ga nai, this cannot be helped. She would quickly subordinate her own desires to those of the family or the community, because she knew cooperation was the only way to survive (30). In this excerpt, Jeanne speaks about the ways her mother adapts to life at Manzanar, the relocation camp where the family is forced to live because they are Japanese-Americans during World War II. She writes that her mother adapts an attitude of quiet resilience and accommodation. Mama accepts that nothing can be done except to live in the crowded camp as best she can, and she is guided by her commitment to her family and her community. She suppresses her own needs and wants, even though she desperately wants privacy, in favor of living amiably with others and doing the best she can for her family. The author writes t...

Jhumpa Lahiri's The Namesake fits the description of a bildungsroman, which is a work of literature that tells the story of a protagonist's formative years. The protagonist of The Namesake is Gogol, who eventually changes his name to Nikhil as a way of displaying his own independence from his parents. The novel begins, as many bildungsromans do, with the story of Gogol's birth. The reader gets to know his parents and other people in Gogol's life while the events in the plotline unfold, focusing on the childhood, adolescence, and early adulthood experiences of Gogol. These descriptions of Gogol's parents and their families provide the reader with a thorough backdrop of cultural information; the reader understands through these details the life into which Gogol emerges on the day he is born. Because the reader has an intimate understanding of Gogol before Gogol himself even appears, the reader feels invested in the development of the hero of the novel. As protagonist,...

"Swing Low, Sweet Chariot" is an African-American spiritual, a song written in a distinctive style combining Christianity with the slave experience. Spirituals are influenced by African musical traditions. While spirituals were originally monodic (all singers sang a single melody in unison), they have evolved to include intricate choral harmonies.  "Swing Low, Sweet Chariot" may actually have been written by Wallis Willis, a member of the Choctaw tribe. It was popularized by the Jubilee Singers of Fisk University and became increasingly popular in the 1960s as part of a folk and protest song movement.  The song is narrated in the first person and takes the form of direct address, with the speaker asking the "chariot" to swing low and "carry me home." The home in question is Heaven. Specifically, the speaker states: I looked over Jordan, and what did I see... A band of angels coming after me, The angels are crossing the Jordan River to take the sp...

Carbon dioxide and other greenhouse gases including methane, nitrous oxide, tropospheric ozone and CFC's are all accumulating in the atmosphere due to human activities. They are the causes of global climate change.  In an actual greenhouse, its glass panels allow sunlight in, but trap heat energy, preventing it from escaping. This causes the temperature inside a greenhouse to be quite warm. Greenhouse gases absorb infrared radiation, the electromagnetic radiation that is radiated heat from the sun. As sunlight strikes Earth, some of it is converted to heat which should radiate back into space. However, the greenhouses gases in the atmosphere slow this process down and warm the temperature of the lower atmosphere. This leads to global warming. Infrared radiation has longer wavelengths than visible light, but shorter wavelengths than microwaves along the electromagnetic spectrum. The shortest wavelengths on the electromagnetic spectrum are gamma rays, followed by X-rays, ultraviolet,...

I think what you are asking is "where is the poet" in this poem. In order to answer that, we need to clarify the idea that the poet is not necessarily the actual narrator of the poem. We have no idea where the poet "is" in the poem. However, Whitman gives us a number of clear details to allow us to determine where the narrator of the poem is located. In line four, the narrator specifically states that they are "sitting" in a "lecture room" of some sort. There is also clear indication that the narrator is not alone in the lecture room, as there is also the "learn'd astronomer," one of the central focuses of the poem, but also "much applause" based on what the astronomer is saying. The first three lines also make it clear that the narrator is listening to some sort of specific lecture, as "proofs," "figures," and "charts and diagrams" are all "ranged out" and "shown" by the a...

Illustrate the linear inequality $x + y \leq -3$ in two variables. To graph $x + y \leq -3$ we must graph the boundary line $x + y = -3$ first. To do this, we need to find the intercepts of the line $x$-intercept (set $y = 0$): $ \begin{equation} \begin{aligned} x + 0 &= - 3\\ \\ x &= -3 \end{aligned} \end{equation} $ $y$-intercept (set $x = 0$): $ \begin{equation} \begin{aligned} 0 + y &= - 3\\ \\ y &= - 3 \end{aligned} \end{equation} $ Now, by using test point. Let's say point $(-4,-2)$ from the left of the boundary line. $ \begin{equation} \begin{aligned} x + y &\leq - 3\\ \\ -4 + (-2) &\leq -3 \\ \\ -4 - 2 &\leq -3\\ \\ -6 &\leq -3 \end{aligned} \end{equation} $ Since the inequality symbol is $\leq$, then the boundary line must be solid. Moreover, since the test point satisfy the i...

In the effort to reduce workplace stress for first responders, managers must act as counselors, mentors, communicators, administrators, and care supervisors/overseers. The role of communicator is probably the most important one for managers. Managers must make themselves available to listen to the concerns of first responders and to assure their employees that any negative feelings (fear, grief, anger, and shock) that surface in the line of duty are perfectly natural. In this way, managers act as mentors who provide emotional guidance during local and national disasters. A manager's level-headed response to trauma assures first responders that they too can maintain functionality despite high stress levels. Managers also play an important administrative role in mitigating stress at the scene of the tragedy or disaster. This administrative role overlaps with the care overseer role. Basically, managers must make available respite areas at the scene of the tragedy, where first responde...

While works we would now consider literature have existed for several thousand years, dating back before the invention of writing, literature being used as a category is relatively recent. The ancient Greeks had several terms referring to what we now would call literature. Poetry, divided into drama, epic, and lyric sub-genres, was understood as a genre. Prose fiction was not developed until late antiquity. In general, poetry was considered part of the educational discipline of grammar, and taught as part of instruction in reading. Prose, and the art of prose composition, fell under rhetoric. In Latin, similarly, poetry was part of secondary education in "letters." The study of style was equally applied to prose and poetry, and included examples from the poets, Plato, oratory, and history. Our modern notion of "literature" as something distinct from pedagogical environment and meter (or lack thereof) is essentially Romantic and tries to divide literature from nonlit...

Gretchen P. Lewis is Squeaky's main competitor at the upcoming May Day races and is also considered a talented runner. Like Squeaky, Gretchen is also confident in her racing abilities. At the beginning of the story, Squeaky mentions that Gretchen has been telling everyone that she will win the first-place medal in the May Day fifty-yard dash. However, Squeaky believes that she will beat Gretchen because she considers herself to be the "fastest thing on two feet." Squeaky mentions numerous times throughout the story that she is not interested in trading insults with other girls and would much rather fight someone than verbally spar with another person. Similarly, Gretchen is depicted as a rather reserved girl, who is more concerned about her actions than insults. In the scene where Gretchen and her friends approach Squeaky and Raymond on the street, Gretchen is the only person who does not speak. As her friends make rude comments toward Squeaky, Gretchen simply crosses her...

Ancient Nubia was located in southern Egypt and northern Sudan and was divided into two parts--Upper Nubia, or Kush, which was the southern portion, and Lower Nubia, the northern portion. The people of ancient Nubia depended on the flooding of the Nile to grow and irrigate their crops. While people in the desert areas of Nubia remained pastoral nomads, Lower Nubia developed one of the first states in the world, which was settled by the so-called A-Group culture (which developed from about 3800 BCE-3100 BCE; they were given this name because their ancient name is not known). Their remains show that they had similar symbols to those of Egyptian kings, and their civilization was strengthened through trading such items as ebony, ivory, gold, and carnelian with Egypt until their civilization was taken over by the Egyptians during the First Dynasty. Later, around 2000 BCE, the C-Group culture also developed along the Nile, as did the Kerma or Kush culture around 1500 BCE. As the Kush culture...

Determine the formula for a function that has vertical asymptotes $x = 1$ and $x = 3$ and horizontal asymptotes $y = 1$. The vertical asymptotes must make the denominator of the function 0. So we have, $ \begin{equation} \begin{aligned} (x - 1)(x - 3) =& 0 \\ \\ x^2 - 3x - x + 3 =& 0 \\ \\ x^2 - 4x + 3 =& 0 \end{aligned} \end{equation} $ Since we know that the degree of the denominator is 2, we must introduce a variable $x$ in the numerator with degree of 2 to make the horizontal asymptote equal to 1, because to find the horizontal asymptote we need to find the highest degree of $x$ in numerator and denominator. So we have, $y = x^2$ Hence, $\displaystyle y = \frac{x^2}{x^2} = 1$ Therefore, The equation of the function is $\displaystyle f(x) = \frac{x^2}{x^2 + 4x + 3}$ or $\displaystyle f(x) = \frac{x^2}{(x - 1)(x - 3)}$

In the final chapter of the book, Nahir Miguel warns Santiago Nasar that the Vicario brothers are planning to kill him. The text tells us that Santiago is more perplexed than frightened by the warning. Nahir Miguel gives Santiago two options: either to hide in the Miguel home or to face the Vicario brothers with a rifle. Despite the warning, Santiago makes no concrete plans to protect himself. Here, we can see that Santiago would have lived had he taken up Nahir Miguel's offer of protection. Instead, Santiago decides to leave the Miguel home. As he walks past the town square, he receives still more warnings from the townsfolk. Someone shouts at him to go by the old dock instead of heading home. Santiago chooses to ignore the advice. Then, Yamil Shaium yells at Santiago to seek refuge in his store while he looks for his hunting gun (and cartridges). At this time, there are many voices clamoring for Santiago's attention, but he decides to ignore them all. Because Santiago cannot ...

Dexter's memories of the summer are idealized and unrealistic. For example, when he is young and working as a golf caddy, he dreams during the winter of a fantastical summer in which he is a golf champion. In these dreams, he owns a Pierce-Arrow, a very high-end car, and is a well-respected member of the golf club--so well respected, in fact, that he is followed by an adoring crowd who also admire his diving ability with mouths open in wonder. Years later, he also succumbs to a kind of summer fantasy when he meets Judy Jones again and thinks that he can make her be faithful to him. During this time, he is wildly unrealistic about who Judy is and even asks her to marry him, which never happens. He loses his sense of reality and thinks of his relationship with her in the same idealized way he dreamed of becoming a rich golf champion when he was a boy.

Prejudice against vulnerable individuals is illustrated by the way Jack and his hunters treat Piggy, Simon, and the littluns. Both Piggy and Simon are vulnerable because they are viewed as outcasts among the group of boys and are easily intimidated by Jack and his hunters. Piggy is overweight, asthmatic, and easily frightened by Jack. Similar to the littluns, Piggy relies on Ralph's protection to survive. Simon is vulnerable because he is known to faint and is considered extremely weird by the group of boys. Simon also has difficulty expressing his feelings, which is one reason he is ridiculed and overlooked. The littluns are not only physically weak but are too young to challenge Jack and his hunters, and they cannot make rational decisions without the help of Ralph and Piggy. Jack and his hunters continually taunt Piggy, interrupt him during assemblies, and physically threaten him. They understand that Piggy is too weak and afraid to defend himself, which makes him an easy target...

I am going to assume that the question is asking about events that occur during chapter 9 of Ender's Game.  Near the start of the chapter, Peter approaches Valentine about the state of the world.  He sees a great world war coming.  He's afraid that mankind is on the verge of destroying itself, and he wants to stop it: "Do you understand? I want to save mankind from self-destruction." She had never seen him speak with such sincerity. With no hint of mockery, no trace of a lie in his voice. He was getting better at this. Or maybe he was actually touching on the truth. "So a twelve-year-old boy and his kid sister are going to save the world?"  Of course Valentine is very skeptical.  She believes that her brother is smart enough and power-hungry enough to make a power play of his own; therefore, she is not immediately willing to help her brother out.   After some more talking, Peter eventually convinces Valentine to help; however, she still doesn't think the...

Millay's poem is sonnet, a poem of fourteen lines, written in an elegiac style. An elegy is a lament, usually for the dead or to regret a loss. In the sonnet, Millay mourns her aloneness, and, implicitly, her aging. In the first octet (eight lines) she is remembering the many loves she once had, so many she can't remember them. She is regretting not remembering them, but more profoundly, that they are "ghosts" who will not come again. As she puts it, she feels a "pain": For unremembered lads that not again Will turn to me at midnight with a cry. In the sestet or last six lines of the poem, she compares herself to a tree in winter that is "lonely." Just as she has gradually lost her lovers, so the tree has one by one lost its songbirds, until it is all alone. Millay uses conventional metaphors or comparisons to make an emotional point about loneliness and age: winter, for example, is traditionally associated with getting old and dying. But despite ...

This series is the sum of an infinite geometrical progression with the common ratio of  3/p. It is well known that such a series converges if and only if its common ratio is less than 1 by the absolute value. In this problem we have the condition  |3/p| lt 1, or  |p| gt 3. Because we are asked about positive p's, we have  p gt 3. The answer: for positive p this series converges if and only if  p gt 3.  http://tutorial.math.lamar.edu/Classes/CalcII/Series_Special.aspx

A character sketch is a short written description of a person's qualities. Such a description will, therefore, include details of the person's personality as well as information about his or her physical attributes. We learn much about Portia in act one. When Bassanio describes her to Antonio in scene one, we learn that she is a wealthy heiress, "richly left," that she is beautiful ("she is fair, and, fairer than that word"), and that she possesses many other amazingly benevolent qualities (she is "Of wondrous virtues"). In Bassanio's contention, then, Portia would be an excellent bride. This fact is proven when he speaks about how men of stature, wealth, and prestige have come from far and wide to woo her, as he says, "the four winds blow in from every coast / Renowned suitors." It is also evident that Portia is blond and that her beauty has driven many on a quest to win her affections. Bassanio states that "her sunny locks / Ha...

There are certain aspects of Odysseus that compare to the legendary boxer Muhammad Ali. As a young man, Muhammad Ali was unafraid to brag about himself, calling himself "the greatest" and telling reporters that he could "float like a butterfly, sting like a bee." Similarly, Odysseus was a bit of a braggart, and this attitude got him in trouble more than once with Poseidon and Polyphemus.   Another quality that Muhammad Ali and Odysseus share was that neither was faithful to his wife. On his voyage home to Ithaca, Odysseus was involved with Calypso and Circe, and Muhammad Ali had an affair with the woman who would become his third wife while still married to his second wife.  Both Odysseus and Muhammad Ali were courageous and accomplished great feats: Odysseus defied the gods and made his way home after a decade of arduous travel, and Muhammad Ali became a world famous, highly successful professional athlete in a violent sport. Both had a defiant streak; Muhammad Ali...

The answer to this question is made a bit difficult due to the narrative perspective of this story. The story is told from the third-person perspective; however, readers only really get a good look into Krebs's mind. He thinks about girls for a number of paragraphs, so we have a good understanding of how he sees girls, but we don't get to listen in on how the girls see themselves. I think Krebs shows readers two things about women for sure. He likes to look at them, and he thinks they are complicated. What's unfortunate about Krebs's attitude is that he thinks the girls are complicated because they have their own thoughts, dreams, desires, and he can understand their language. Krebs will repeatedly tell readers that he likes to look at the girls. He also says over and over again that they are complicated. Then readers are hit with an important single line. Now he would have liked a girl if she had come to him and not wanted to talk. In my opinion, this tells readers tha...

In James Baldwin's short story about two brothers who finally come to understand one another through the medium of music, the brother who is the narrator is a round character. That is, he is a character who experiences an essential change in attitude. The brother who acts as narrator in "Sonny's Blues" has been alienated from Sonny for years because he has become a drug addict. When the narrator reads in the newspaper about Sonny's arrest for heroin, he becomes perturbed, reminded of his students in Harlem who also are growing up in "the killing fields" with limited prospects in life. After encountering a drug addict who is an old acquaintance of Sonny's, the narrator feels guilty about failing in his promise to his mother to watch out for his brother. So, he decides to find Sonny and bring him back home to Harlem. After the narrator locates his brother, Sonny agrees to come home with the narrator; nevertheless, the narrator is concerned that Sonny m...

While Iroquois women tended to the longhouses and were responsible for collecting and making food, the men were traditionally warriors, defending their people from attacks. As the source below explains, men prepared for warfare through activities such as lacrosse (now a popular sport in the United States and elsewhere). In addition, men carried on trade with other tribes. They became important as middlemen in the fur trade between the western tribes and European settlers, including the Dutch and English, until the supply of pelts dried up. In addition, the men hunted deer to feed their tribe. In the spring, they fished. Though women were responsible for collecting the beans, squash, and corn that the tribe grew, the men cleared and planted the crops (see the source below). Men served on the Iroquois Confederacy as sachems or representatives from the tribes, but women were responsible for selecting the people who served. http://web.pdx.edu/~caskeym/iroquois_web/html/iroquoisman.htm The...

“Lunch Money” proposes the idea that a young person can accomplish as much as an adult through hard work and determination. Greg embodies the young entrepreneur that has a knack for making money through various means. From doing chores to helping around his neighborhood, Greg is motivated to do whatever it takes to make money. He begins to expand his operation to selling candy, toys, and books in elementary school, occasionally facing opposition from the principal. But by the sixth grade, Greg has to deal with competition from Maura, who started making books around the same time Greg started selling his first comic book. As Greg’s childhood rival, Maura intimidates Greg through her similar entrepreneurial pursuits. Tension initially rises between the two when they confront each other about their products, but they eventually see the value in each other and decide to work together. By putting their heads together, Greg and Maura put aside their differences to accomplish things that they...

Life of Pi is about the persistence of faith against all odds. Pi survives a shipwreck in the company of a tiger named Richard Parker, though no one believes this story afterward. Instead, Pi is reduced to telling the story of his survival at sea in a more believable, albeit less magical and mystical, way. This story is not about the faith of any one religion, as Pi is a believer in multiple religions. It is instead about faith and the existence of miracles. Whether or not this book altered your beliefs in these concepts is up to you. There is no doubt that the author, Yann Martel, suggests that miracles surround us, though they seem to defy reason and rationality. You might have had experiences that have convinced you that miracles can really occur. In other words, this book might remind you of situations that seem miraculous in your own life. If so, this book might change your beliefs about whether miracles are real and whether we should have faith in a divine power. There is no sing...

F. Scott Fitzgerald's The Great Gatsby exemplifies Modernist writing with its limited and imperfect narrator, its lack of chronological order, its themes, its use of images as symbols, and its insight on moral corruption. The narrative of The Great Gatsby is a fragmented one, told by a flawed narrator. Evidence that Nick is a flawed narrator becomes apparent when he declares himself a man who reserves judgments, yet he, in reality, often does judge other characters. In the first chapter, for instance, Nick comments on Daisy's murmuring which "was only to make people lean toward her; an irrelevant criticism that made it no less charming." Further, he describes Daisy's voice as "the kind...that the ear follows up and down as if each speech is an arrangement of notes that will never be played again" (Ch.1). Later in the narrative, Nick no longer finds any charm in Daisy as he speaks of her and Tom after the death of Myrtle Wilson: ...they were careless peop...

Determine a equation in slope intercept form (where possible) for the line that goes through $\displaystyle \left( -2, \frac{3}{4} \right)$ and $\displaystyle \left( \frac{2}{3} , \frac{5}{2} \right)$ Let $\displaystyle (x_1 , y_1) = \left( -2, \frac{3}{4} \right)$ and $\displaystyle (x_2, y_2) = \left( \frac{2}{3} , \frac{5}{2} \right)$. Then, by using two point form $\displaystyle y - y_1 = \frac{y_2 - y_1}{x_2 - x_1} (x - x_1)$ $ \begin{equation} \begin{aligned} y - \frac{3}{4} &= \frac{\frac{5}{2} - \frac{3}{4}}{\frac{2}{3} - (-2) } ( x - (-2))\\ \\ y - \frac{3}{4} &= \frac{\frac{10-3}{4}}{\frac{2}{3}+ 2} (x + 2)\\ \\ y - \frac{3}{4} &= \frac{\frac{7}{4}}{\frac{8}{3}} ( x + 2)\\ \\ y - \frac{3}{4} &= \frac{21}{32} (x + 2)\\ \\ y - \frac{3}{4} &= \frac{21}{32}x + \frac{21}{16}\\ \\ y &= \frac{21}{32}x + \frac{33}{16} \end{aligned} \end{equation} $

George, like many other people in this dystopian world, is forced to wear a handicap to drag him down to the general level of mediocrity. As George is intelligent this means that his thoughts must be constantly disrupted. This is achieved by making him wear a radio that emits noise at regular intervals. Just for good measure, he needs to wear weights round his neck to compensate for his physical strength. Strange as it may seem, George is quite accepting of his handicaps. Although that may have something to do with the fact that the regular blasts of radio noise don't give him much time to think about them. Whatever the reason, George just tries to get on with life as best he can. He's certainly no rebel like his son, Harrison. The laws may very well be unjust and frankly absurd, but George believes that if people start to pick and choose which laws to obey, then society will descend into anarchy and chaos.

Thanks! Initially, Bud is excited to meet Herman Calloway and believes that Herman is his father. Bud looks up to Herman and idolizes him by examining his band's flyers on his trip to Grand Rapids. Upon meeting Herman, Bud realizes that he is actually a grumpy old man who doesn't care about him. However, Bud is befriended by the members of Herman Calloway's band who are kind to him. When Bud goes to dinner with the band, Herman refuses to sit by him and even calls him a "scamp." Bud quickly begins to understand that Herman is not a sympathetic, positive individual, and he is happy to see Herman leave the dinner table. When Bud gets invited to stay at Grand Calloway Station, he tries his best to avoid Herman. Later on in the novel, it is revealed that Herman is actually Bud's grandfather and the dynamic of their relationship changes. Upon learning that Bud is his grandson and that his daughter has passed away, Herman breaks down and cries. Herman is overcome wi...

int_(pi/6)^(pi/3)csc^3(x)dx Apply the integral substitution, Let u=tan(x/2) =>du=1/2sec^2(x/2)dx using pythagorean identity: 1+tan^2(theta)=sec^2(theta) du=1/2(1+tan^2(x/2))dx du=1/2(1+u^2)dx =>dx=(2/(1+u^2))du csc(x)=1/sin(x)=1/(2sin(x/2)cos(x/2)) =(1/(cos^2(x/2)))/((2sin(x/2)cos(x/2))/(cos^2(x/2))) =(sec^2(x/2))/(2tan(x/2)) =(1+tan^2(x/2))/(2tan(x/2)) =(1+u^2)/(2u) Now let's evaluate the indefinite integral, intcsc^3(x)dx=int((1+u^2)/(2u))^3(2/(1+u^2))du =int(1+u^2)^2/(4u^3)du =int(1+2u^2+u^4)/(4u^3)du =1/4int(1/u^3+2/u+u)du =1/4(int1/u^3du+2int1/udu+intudu) =1/4((u^(-3+1)/(-3+1))+2ln|u|+u^2/2) =1/4(-1/(2u^2)+2ln|u|+u^2/2) Substitute back u=tan(x/2) =1/4(-1/(2tan^2(x/2))+2ln|tan(x/2)|+1/2tan^2(x/2) =1/4(1/2tan^2(x/2)-1/2cot^2(x/2)+2ln|tan(x/2)|) Add a constant C to the solution, =1/4(1/2tan^2(x/2)-1/2cot^2(x/2)+2ln|tan(x/2)|)+C int_(pi/6)^(pi/3)csc^3(x)dx=[1/4(1/2tan^2(x/2)-1/2cot^2(x/2)+2ln|tan(x/2)|)]_(pi/6)^(pi/3) =[1/4(1/2tan^2(pi/6)-1/2cot^2(pi/6)+2ln|tan(pi/6)|]-[1/4(...

A "stereotypical" woman meddles in affairs she knows little or nothing about in an attempt to achieve social standing through manipulating her husband. Lady Macbeth does this. In Act 1, she takes charge of planning the "business" of murdering King Duncan after worrying that her husband is too kind to do so. This demonstrates a naive blindness to Macbeth's true nature. In Act 1 scene 2, we find out that he hacked a man in two in battle. She doesn't know what he is capable of until it is too late. Second, when Macbeth expresses doubts about the plan to murder Duncan, Lady Macbeth attacks his masculinity and tells him that she measures his love by his willingness to execute her plan. That is an interesting question, because Lady Macbeth would not usually be described as a "stereotypical woman" in any way. Her ambition, her savagery (including her willingness to sacrifice a baby, if she had one, to that ambition), and her complicity in a brutal murder ...

“Ravens” by Ted Hughes is an account of a father explaining to his child on a “blue and warm” spring day the facts of life and death, when the child “has eyes only” for a lamb that was born dead. At the beginning of the poem, before the mundane tragedy of the dead lamb is introduced, Hughes mentions the raven that “bundled itself into midair,” the phrase suggesting haste and secrecy; the raven is “low and guilty” in its flight, anticipating the later reveal of what it has done. The newborn lamb which “died being born” has been torn apart by the raven, its insides pulled out. The lamb is, to the sheep, inconsequential: the poet cannot tell which is its mother, and already it is being succeeded by a black lamb unfolding the “tripod” of its legs. However, to the child, the lamb and its possible suffering are of vital importance, as the child repeats, “Did it cry?” The poem conveys both the mundanity of death as a part of life, something animals easily move on from, and the huge significan...

If you are nostalgic, you look fondly back to an earlier point in time. Nostalgia is wishing for a return to the way life was in the "good old days." Nostalgic people tend to remember the past as better than it actually was, regretting the good aspects of old times that are lost and forgetting about the bad aspects that perhaps we are glad to have lost. To be wistful, on the other hand, is to wish or yearn for things to be different. It could include a longing for the past, but it could also include a desire for a better future. It's a more general longing than nostalgia. It could simply be longing—being wistful for—finding that perfect mate when you see a happy couple get married. Both terms carry with them a tinge of melancholy or sweet sadness.

African American physicians and nurses raised and sent financial aid to assist in war efforts being supported by the United States. For instance, African American physicians and nurses provided medical supplies and volunteered to treat the wounded after Italy’s invasion of Ethiopia. African Americans served directly on the battlefront and supported the Abraham Lincoln Brigade sent to assist the left-leaning Republic of Spain. Participation of African Americans in wars abroad against fascism motivated them to continue with their push for justice and equality back home. The idea of opening two fronts to fight oppression, dubbed the “Double V” campaign, led to public discussions about discrimination in the military program. A push by leaders of the different African American groups led to the passage of Executive Order 8802 by Roosevelt that denounced discrimination in the employment of workers. Steps in the right direction were being made in the civilian sector, but a lot more needed to ...

The region bounded by y=sin(x) , y =0 , x=0 ,and x=pi revolved about the x-axis is shown on the attached image. We may apply Disk Method wherein we use a rectangular strip representation such that it is perpendicular to the axis of rotation. The vertical orientation of the rectangular strip shows the thickness of strip =dx.  That will be the basis to use the formula of the Disc method in a form of: V = int_a^b A(x) dx where A(x) = pir^2 and r =y_(above)-y_(below) . The r is radius of the disc which is the same as the length of the rectangular strip. Then, r = sin(x)=0 = sin(x) with boundary values of x from x=0 to x=pi. The integral will be: V = int_0^pi (sin(x))^2 dx V = x/2-(sin(x)cos(x))/2|_0^pi  Using the definite integral formula: int_a^b f(x) dx = F(b) - F(a) , we get: V =[pi/2-(sin(pi)cos(pi))/2] -[0/2-(sin(0)cos(0))/2] V = [pi/2-(0*(-1))/2] -[0-(0*1)/2] V = [pi/2-0]-[0-0] V = pi/2

Cultural nationalism can be defined as nationalism that is based around the idea of a cultural community, not around the idea of creating a nation-state for the people of a given nation.  In other words, we could argue that ISIS is an example of political nationalism because it is ostensibly trying to make a state that will include all Muslims.  Meanwhile, we could say that the Muslim Brotherhood is more of an example of cultural nationalism since it is trying to revive what it sees as a true Muslim community within a state that already exists. I would say that one of the main roles of cultural nationalism in our world today is to resist globalization.  Cultural nationalism often works hand in hand with political nationalism to try to fight back against globalization.  We can see this in such phenomena as the recent Brexit vote and in the rise of nationalist thinking in the US and in various European countries.  When people engage in cultural nationalism, they often will at least suppo...

The starting point here is to explain that Bill Bryson is a popular journalist and travel writer trying to write a travelogue of ideas and science. He writes with a journalist's eye for anecdote, and many readers find his accounts of scientists, as opposed to their discoveries, the most riveting elements of the book.  A useful way to think about how power functions in the book is to analyze the "great man" version of the history of science. Consider the major discoveries in the history of science. For each discovery, you would investigate how we tie that discovery to an origin story centered on a "great man": Einstein and relativity, Newton and gravitation, Copernicus and the heliocentric solar system, Darwin and evolution, etc. Even though Bryson often debunks "great man" and "great moment" foundation stories, emphasizing the accidental nature of discovery and the human quirks and foibles of discoverers, his history of modern science is one ...

In the book, Anton is handsome, charming, courageous, kind, and humble. He treats Patty with great kindness and old-world courtesy. When Patty presents a shirt to her father as a Father's Day gift, her father is barely civil in his response. Hurt by his indifference, Patty gives the shirt to Anton. For his part, Anton responds with affection and appreciation; his grateful response overwhelms Patty with emotion. When Patty's father beats her for playing with Freddy Dowd, a poor white boy, Anton tries to save his friend. For her part, Patty screams at Anton to go away when she sees that he's about to reveal himself. Anton's courageous behavior is demonstrated in his willingness to assume a huge risk on Patty's behalf. Despite his courageous behavior, however, Anton doesn't gloat. He feels that he's been a coward for too long, and he's glad that he's finally acting with courage: "After almost two years of being as inconspicuous a coward as possible...

Personification is a literary device whereby non-human things and objects are endowed with human characteristics. There are a number of such examples in "Composed upon Westminster Bridge, September." Wordsworth uses personification to make the city of London come alive, to convey the sense of a city waking up to a bright, beautiful morning. Using personification allows us to get closer to that sense of wonder that Wordsworth must have felt when writing his poem. The city is no longer just an urban landscape; it has recognizably human characteristics that make us identify more closely with the poet and the remarkable scene unfolding before his eyes. This City now doth, like a garment, wear  The beauty of the morning; silent, bare . . . The city, waking up to another day, puts on the beauty of the morning in the way that someone would put on their clothes. The river glideth at his own sweet will:  Dear God! the very houses seem asleep;  And all that mighty heart is lying still!...

Roger does not flee because he is moved by the kindness and caring nature of Mrs. Luella Bates Washington Jones, and he does not want her to think poorly of him. When Mrs. Jones collars Roger and drags him up the street after putting him in a wrestling hold to stop him from stealing her purse, the boy is humiliated. She tells Roger he needs his face washed, and she drags him home with her. Once he and Mrs. Jones reach the boarding house, Roger hears voices in distant rooms. He realizes other people are living in this house. He does not try to run because if he does, he might experience even more embarrassment at the hands of the formidable Mrs. Jones. Then, as she prepares her supper, Mrs. Jones thinks aloud that Roger must be hungry to have snatched her purse from her. Roger tells her that he wanted some suede shoes. “Well, you didn’t have to snatch my pocketbook to get some suede shoes,” said Mrs. Luella Bates Washington Jones. “You could of asked me.” Roger is taken aback by this ge...