Onboard Note

The differential of a polynomial term like Ax^n is nAx^(n-1) If f(x)=x^4-2x^3+x^2 then f'(x)=(4)(1)x^(4-1)-(3)(2)x^(3-1)+(2)(1)x^(2-1) Completing the basic math we get f'(x)=4x^3-6x^2+2x Looking at the graphs of the original function (black) and it's derivative (blue), we see: For X values less than 0, the slope of the original function (black) is negative (as x values increase towards 0 from the left, the function decreases in value), therefore it's derivative (blue) is negative. From x=0 to x=0.5, the slope of the original function becomes positive (the value of the function rises as x increases), therefore the derivative (blue) is positive for this duration. From x=0.5 to x=1, the slope of the original function (black) is again negative as shown by the derivative (blue) again being below the x axis. For x values above 1, the original function again has a positive slope, resulting in a positive derivative.

Dogs do not lay eggs. In fact, dogs, like humans, are members of the mammal animal classification. In order for an animal to be classified as a mammal, they must* possess the following traits: Have hair or fur Give birth to live young Drink milk from their mother Are warm blooded Are vertebrates Because dogs are mammals, they do not lay eggs. They, (like us humans!) have all the characteristics of a mammal including giving birth to live young. *It is important to note that the duck billed platypus, as well as a couple species of ant eaters, lay eggs even though they are mammals. Dogs do not lay eggs. Instead, they are classified as mammals and give birth to live young. When females become sexually mature, they can become pregnant. They have an estrous cycle, whereby reproductive hormones cause changes that can lead to pregnancy. Their reproductive cycle lasts from two to four weeks. Female dogs reach puberty between eight and eighteen months, depending on the breed. The hormon...

I believe the lottery in this story is taking place in a small town in the northeast United States. Some of this is based on explicit statements, like the way Jackson calls the place a "village." This refers to small settlements. Some of this is based on the names of the characters in the story. The names are either English (Summers, Graves) or French (Delacroix) in origin. This fits the New England area. Some, like Hutchinson, were actual names from Puritan history. New England is one of the few places in the United States where historical traditions are well enough established to support a ritual like the lottery, which is old enough to have sayings and superstitions about it. Based on the outcome of this story, I believe Jackson is saying people can follow social pressure and established traditions too far--that they are willing to kill or die to follow them.  

Mean Value Theorem states a function f(x) that the satisfies the following hypotheses: 1. a function f(x) that is continuous on the closed interval [a,b] 2. differentiable on the open interval (a,b) Then there is a number “c” such that a ltcltb and f'(c) =(f(b)-f(a))/(b-a) or f(b) – f(a) = f’(c) (b-a). Mean Value Theorem indicates that at least one number “c” will exists within the said function. To be able to solve the value of “c”, we consider the special case of Mean Value theorem where we assumed f(a)= f(b) (Rolle’s Theorem). A. For the given function f(x) = e ^(-x) with closed interval [0,2], we solve first for the endpoints. Plug-in x= 0 in f(x)=e^(-x) : f(0) = e^(-0) =e^(0) =1 First endpoint: (a, f(a)) = (0,1) Plug-in x= 2 in f(x)=e^(-x): f(0) = e^(-2) = (1)/(e^ (2)) or 0.135335 then (b, f(b)) = (2,(1)/(e^(2)) ) Second endpoint: (b, f(b)) = (2,(1)/(e^(2)) ) Law of Exponent: x^(-n) = (1)/(x^(n)) B. Solve for the slope of the secant li...

Baldeo is the main character in this great and terribly sad short story. He is a married man and a father of two children. He has a daughter and a 12-year-old son named Tembu. Baldeo and his family are not wealthy, and they live near a forest in India. Baldeo provides for his family in two ways. He works their small rice field but is forced to supplement the remainder of the family's income by working for the railroad. He is one of the line's watchmen, and his job is to make sure that the railway track through a nearby tunnel stays clear. There is also a signal lamp that he tends to. Baldeo is a hard working man, as evidenced by the long hours he puts in to ensure that his family has enough to eat. We also know that he cares deeply for the safety of his son. That is why Baldeo doesn't have Tembu accompany him to check the tunnel and the lamp. Baldeo knows that the jungle can be a dangerous place, and he has been hearing stories of a man-eating tiger. I believe that it also ...

Find the derivative of $\displaystyle f(x) = mx + b$ using the definition and the domain of its derivative. $ \begin{equation} \begin{aligned} \qquad f'(x) &= \lim_{h \to 0} \frac{f(x + h) - f(x)}{h} && \\ \\ \qquad f'(x) &= \lim_{h \to 0} \frac{m (x + h) + b - (mx + b)}{h} && \text{Substitute $f(x + h)$ and $f(x)$} \\ \\ \qquad f'(x) &= \lim_{h \to 0} \frac{\cancel{mx} + mh + \cancel{b} - \cancel{mx} - \cancel{b}}{h} && \text{Combine like terms} \\ \\ \qquad f'(x) &= \lim_{h \to 0} \frac{m \cancel{h}}{\cancel{h}} && \text{Cancel out like terms} \end{aligned} \end{equation} $ $\qquad \fbox{$f'(x) = m$}$ Both $f(x)$ and $f'(x)$ are linear functions that extend on every number. Therefore, their domain is $(-\infty, \infty)$

Jean Liedloff's definition of continuum states that human beings require some form of natural experience to attain the most favorable physical, mental, and emotional progress. Natural experience is based on activities that have been dictated by the evolution process. Based on Liedloff's interpretation, sexual orientation is a continuum, in that it's defined by the experiences and the environment that an individual is exposed to. A person can be straight because he or she grew up in a heterosexual family and was constantly showered with love from both the mum and dad. Alternatively, a person may be attracted to another from the same sex because it gives him or her the highest form of satisfaction. In other words, sexual orientation is a continuum because it contributes toa person's existence. http://www.continuum-concept.org/cc_defined.html Sexual orientation can be viewed as a continuum because people's preferences can lie on a continuous spectrum between exclusive...

The Awakening is told from a third-person omniscient point of view. It is tempting to say that it is limited omniscient because the narrator spends so much time detailing Edna's thoughts and feelings, but the narrator does offer the thoughts and feelings of other characters at times. The settings, New Orleans and Grand Isle, are of import, in part, because Edna is an outsider here. She is not used to the Creole way of life, which is something made painfully transparent to her when a salacious novel makes its way through Grand Isle society. The Creole men and women read it openly while Edna feels she must hide it when it is her turn. Edna's outsider status gives her even more to contemplate. It further distances her outward life, and the way in which she must conform in order to retain social acceptance, from her inner life, the way in which she would like to behave and the choices she would prefer to make: the two are often at odds. The individual is almost always at odds with ...

Chapter 28 of To Kill a Mockingbird is quite an exciting chapter. It is in this chapter that Scout and Jem are attacked in the darkness by Bob Ewell on their way home from the schoolhouse. A man intervenes on their behalf and carries Jem home. Soon after, Dr. Reynolds and Heck Tate arrive at the Finch home. Suggesting that everybody take a seat, Atticus proceeds to get another chair from the living room. All of the adults in the room are seated with the exception of one. Scout believes that Atticus knows "the ways of country people," so it does not strike her as particularly odd that a man is left standing. She assumes that the man prefers to stay where he is. Eventually, Scout tells her story of what happened. As she identifies the man standing as the one that must have intervened in the scuffle, she looks up at his face and says, "Hey, Boo." The man without a chair is Boo Radley, their reclusive neighbor. Atticus knows that Boo would prefer to go unnoticed, so he ...

Diffusion and osmosis are both examples of passive transport. Passive transport does not require any energy to happen. It is a natural process that moves materials from an area of higher concentration to an area of lower concentration. The differences in concentration of materials is called a concentration gradient, and substances naturally move down (higher to lower) the gradient.  For example, when you put a drop of food coloring in a glass of water, the food coloring will begin moving from where there is a high concentration of food coloring to where there is a lower concentration of food coloring.  This will occur until equilibrium is reached and the food coloring is evenly spread out.  Osmosis and diffusion both work passively based on a concentration gradient.  A difference between osmosis and diffusion is that diffusion can occur in any mixture (with or without a semipermeable membrane), but osmosis always occurs across a semipermeable membrane. Another key difference is that os...

Determine the horizontal and vertical asymptotes of the curve $\displaystyle F(x) = \frac{x - 9}{\sqrt{4x^2 + 3x + 2}}$ Solving for the vertical asymptotes We set the denominator equal to zero $4x^2 + 3x + 2 = 0$ Using the discriminant of $ax^2 + bx + c$ which is $\Delta = b^2 - 4ac$. (If $\Delta $ \begin{equation} \begin{aligned} \Delta =& (3)^2 - 4 (4)(2) \\ \\ \Delta =& 9 - 32 \\ \\ \Delta =& -23 \end{aligned} \end{equation} $ But $-23 So $4x^2 + 3x + 2 = 0$ has no real solution. Therefore, $F(x)$ has no vertical asymptotes Solving for the horizontal asymptotes In the function $\displaystyle F(x) = \frac{x - 9}{\sqrt{4x^2 + 3x + 2}}$ we remove everything except the biggest exponents of $x$ found in the numerator an denominator. So we have $ \begin{equation} \begin{aligned} F(x) =& \frac{x}{\pm \sqrt{4x^2}} \qquad \text{where $F(x) = y$} \\ \\ y =& \frac{\cancel{x}}{\pm 2 \cancel{x}} \\ \\ y =& \pm \frac{1}{2} \end{aligned} \end{equation} $ Thus, the horizonta...

There is a menacing tone to "The Most Dangerous Game." Connell's use of dark foreshadowing with the exotic setting, the strange occurrences, and bizarre characters introduced in the exposition quickly puts readers "on edge," as they fear what will happen next. This element of danger is immediately introduced as Rainsford and Whitney travel to hunt jaguar; then, when Rainsford falls overboard and must swim for a long time before finding any shoreline, there is clearly a forbidding tone. Later, Rainsford's frightening encounter with the massive Ivan, whose tongue has been cut out is, indeed, disconcerting. The greatest menace is presented in the form of the owner of the chateau, "a lofty structure with pointed towers plunging upward into the gloom." This man is the Russian General Zaroff, whose "dead black eyes" do not change as he calmly speaks of his bizarre penchant for hunting "the most dangerous game." After Rainsford becomes...

Arguably, every aspect of "The Story of An Hour" is minimal and short-lived. First, there is no overuse of language or stylistic devices. As the title suggests, the story itself is quite short. Also, a quick look at all the other short-lived and minimally described elements of this story lets us know that Chopin is writing for something other than mere literary entertainment. She wants to make a point. Short-lived elements (regarding Louise Mallard): her happiness : she only gets to experience it while she thought her husband died. her dreams: they surfaced as soon as she felt that she was finally free. her hopes: same as her dreams. her life: she is relatively young. Minimally-described things: her emotions: we only see the phrase, "yet, she loved him," but when did she? the home: like your question states, minimal description is provided. the husband: we only know that his name is Brent and that he is a relatively decent man. her family: we know very little of her...

Suppose that $f(x)$ is your height at age $x$. Determine whether it is one to one. We know that a person's height remains constant after a certain age, so there are more than two years at which a person has the same height. Thus, $f(x)$ is not a one to one

To find the relative extrema of a function, we may apply the First derivative test on a open interval before and after x=c. It states: a) f'(x) gt0 from the left and f'(x)lt0 from right of x=c then there is local maximum at x=c b)f'(x) lt0 from the left and f'(x)gt0 from right of x=c then there is local minimum at x=c . * A sign change of f'(x) from left and right of x=c will indicate a possible relative extrema (local minima/local maxima). If f'(x) has the same sign on both sides of x=c then there is inflection point at x=c . For the given function:f(x) = arcsec(x)-x , we have the first derivative: f'(x) =1/(sqrt(x^2)sqrt(x^2-1) )-1 . Equate f'(x) =0 to solve for x=c : 1/(sqrt(x^2)sqrt(x^2-1) )-1 = 0 Multiply both sides by sqrt(x^2)sqrt(x^2-1) to get 1 -sqrt(x^2)sqrt(x^2-1) = 0 Move sqrt(x^2)sqrt(x^2-1) to the other side to get 1 = sqrt(x^2)sqrt(x^2-1) Square both sides: 1 =x^2 *(x^2-1) Expand: 1=x^4-x^2 or x^4-x^2-1=0 Apply Quadratic formula...

According to the author, the Tea Party was not motivated by outright racism but by the coded racial hatreds contained in dog whistle politics. While members of the Tea Party denied being motivated by racism, they were, the author points out, "united in their hostility towards Obama" (page 150) because they did not feel that Obama could possibly represent them. This rejection of the idea that Obama could be President motivated their continuing the falsehood that Obama was not born in the U.S.--the so-called "birther" movement. The Tea Party was motived, the author suggests, by the following "four hatreds (page 152):" Welfare: The Tea Partiers see welfare as taking money away from hardworking white people and giving it to the undeserving poor (who are, in their minds, nonwhite). Immigration by undocumented people: The Tea Party sees immigrants, particularly brown immigrants, as taking money away from white taxpayers and causing crime. Arab Muslims: Tea Parti...

In Chapter 15, a large storm washes over the island. The wind blows over the hut in which Phillip and Timothy live, and Timothy protects Phillip by covering Phillip's body with his own. They spend two hours that way, as the storm blows over them with lashing rains and strong winds. The storm is so harsh that they can barely breathe. As the sea begins to come up the beach, Timothy brings Phillip to the palm trees on the rise for shelter. Timothy ties Phillip and himself to the tree. Water laps against their ankles and feet, and Timothy continues to protect Phillip with his body against the driving wind. They remain that way for about an hour, until the wind dies down and they can untie themselves from the tree. When the eye of the storm passes over and the winds pick up again, worse than ever, Timothy again ties Phillip to the tree and protects the boy with his body. Several large waves pass over them, and, in the end, the storm kills Timothy while Phillip survives. Timothy gives hi...

A function f(x, y) is called homogenous (homogeneous) of degree n, if for any x, y we have f(tx, ty) = t^n f(x, y). The given function is homogenous of degree 0, because f(tx, ty) = 2ln((tx)/(ty)) = 2ln(x/y) = f(x, y) = t^0 f(x,y). The difficulty is that this function is not defined for all x and y. The above equality is true for all x and y for which it has sense. Given f(x,y)=2ln(x/y) if the function has to be homogenous then it has to be of the form f(tx,ty)=t^n f(x,y) so, f(tx,ty)=2ln((tx)/(ty))= 2ln(x/y) as , on cancelling t . so the function is of the form f(tx,ty)=t^n f(x,y) and the degree is n=0

In the book's final scene, the men gather around a fire for warmth and cooking, as human beings have done for thousands of years.  Though it is a significant departure from how fire is used earlier in the novel, fire is used here as a means of organizing the men and ensuring their survival.  The image of the men silently watching the ritual of the bacon cooking is a reflection of social conformity: people gathering to share a meal. As Granger, Montag and the other men break camp and begin their hike north, the men fall back to allow Montag to take the lead.  The fact that they have tacitly chosen Montag to lead them is another symbol and an image of social conformity. The men are free to think and act independently, yet they choose to stay together and allow a single man to lead them.  As they walk on, Montag rehearses in his mind what words he will later say to these men who look to him for guidance.

In On Liberty, John Stuart Mill wrote that an individual was allowed to do harm to himself or herself but not to others. He believed that government and authority over others should exist only to prevent individuals from doing harm to others.  While an individual can, he believed, choose to harm himself or herself, a person does not exist in isolation. Therefore, harm done to oneself (in this case, Alex's lie that he completed all the necessary safety tests) can in fact hurt others. Therefore, while the product seems to be safe, it may have defects down the line that have not yet been discovered. Therefore, Alex's decision to lie about having carried out the safety tests may eventually hurt other people. His lie has the capacity to harm others and not just himself. Accordingly, he violates John Stuart Mill's "harm principle." In addition, Mill considered acts of harm possible from omission, not just commission. In other words, an individual can do harm by not doin...

"Salvation" by Langston Hughes is a short essay and a chapter of his memoir, entitled The Big Sea. By definition, memoir and essay are both nonfiction forms. A memoir is similar to an autobiography in that it has the writer remembering moments from his life and relaying those to the audience. Hughes is most famous for his poetry, but "Salvation," as a personal essay is definitely a nonfiction text. The essay is told in first person, as Hughes begins by saying, "I was saved by sin when I was going on thirteen. But not really saved. It happened like this." We can tell from the start that he is going to tell an autobiographical story about his salvation, or his lack thereof. From there, Hughes tells about an experience he had at church as a child. His aunt told him that he would see Jesus and be saved. When he saw Jesus, he would go to the altar and be welcomed by the church community as one of their own. In brief, Hughes never sees Jesus, but he thinks the o...

Romeo and Juliet both make impulsive, bad decisions that end with each of them committing suicide. First, Romeo shows his impulsive nature when he says, O, she doth teach the torches to burn bright! It seems she hangs upon the cheek of night Like a rich jewel in an Ethiope’s ear; Beauty too rich for use, for earth too dear! So shows a snowy dove trooping with crows, As yonder lady o’er her fellows shows. The measure done, I’ll watch her place of stand, And, touching hers, make blessed my rude hand. Did my heart love till now? forswear it, sight! For I ne’er saw true beauty till this night. (act 1, scene 5) Here he is proclaiming his love for Juliet, whom he just met—right after wallowing in his sadness over his unrequited love for Rosaline. He changes his mind quickly and doesn't think things through. Later, Juliet shows her impulsive nature when she talks about marrying Romeo. Even though she knows they are moving too fast, she is caught up in her love, or infatuation, for him. Th...

John Rawls's seminal work, A Theory Justice (1971), returned political philosophy to many of its founding questions about the nature of freedom, justice, and fairness found in Plato and Aristotle. Rawls here attempts to answer the question: what makes for a just society? This is a question that ultimately comes down to the distribution of both political rights and economic goods. A well-ordered society for Rawls is one in which all citizens are treated equally under the law and which promotes individual liberty to the extent that it does not infringe on the well-being of others. Rawls carefully navigates a debate still prevalent in political discourse today, that between equality of opportunity and equality of outcomes. Rawls doesn't fall on one side of this debate, he attempts to seek a compromise. Rawls thinks that a well-ordered society should guarantee equality of opportunity but also thinks it should be governed according to what he calls "The Difference Principle....

I would argue that the relationship between Dante and Virgil doesn't change that much over the course of The Inferno. When Virgil first appears in canto 1, he offers to help Dante, who has been stalled by the she-wolf blocking his path to the hill (Heaven). Virgil tells him that he knows another way; it involves traveling through all of the circles of Hell, but Virgil promises to be Dante's guide and companion. As Virgil leads Dante through the vestibule of Hell in canto 3 and all of the nine circles that follow, he repeatedly prepares Dante for what he is about to see and protects him from those who question his presence (since he is not dead nor damned yet). Virgil tells Charon, for example, that it is not his place to question what God has deemed necessary. Dante faints repeatedly, overcome by his fear and disgust, and Virgil supports him and helps him move on to the next level. Finally, in the last ring of the ninth circle, the poets see Satan and the three worst traitors o...

You need to notice that the given function is continuous on [-1,1] and differentiable on (-1,1), since it is a polynomial function. You need to verify if f(-1)=f(1), hence, you need to evaluate the values of function at x = 0 and x = 1. f(-1) = sqrt(2 - root(3)((-1)^2))^3 = 1 f(1) = sqrt(2 - root(3)((1)^2))^3 = 1 Since f(-1)=f(1) = 1 and the function is continuous and differentiable on the given interval, the Rolle's theorem may be applied, hence, there is a point c in (-1,1) , such that: f'(c)(1+1) = 0 You need to find the derivative of the function, using chain rule: f'(c) = (sqrt(2 - root(3)(c^2))^3) f'(c) = (3/2)(2 - c^(2/3))^(3/2-1)*(2 - c^(2/3))' f'(c) = (3/2)(-2/3)*c^(2/3-1)*(2 - c^(2/3))^(1/2) f'(c) = -c^(-1/3)*(2 - c^(2/3))^(1/2) f'(c) = -(sqrt(2 - c^(2/3)))/(root(3) c) Replacing the found values in equation 2f'(c) = 0 yields: -2(sqrt(2 - c^(2/3)))/(root(3) c)) = 0 => sqrt(2 - c^(2/3)))/(root(3) c) = 0 Raise to 2rd power both sides: (2 ...

George Washington's (1732 - 1799) early experiences as commanding general of the Continental Army directly exposed him to the brittle unity and inefficiency created by competing state governments, each jealous of the other and focused on their own benefit and survival over that of the nation as a whole. Based on these early experiences, Washington realized that the United States would be a frail nation in the absence of national unity and that the inter-state jealousies he'd previously witnessed might again manifest themselves if there was not a collective sense among the citizenry that was not split by regional and partisan considerations. This focus on national togetherness was a recurrent theme in Washington's public life. His proclamation designating November 26, 1789 as the first Thanksgiving was intended to promote that national unity he sought to inspire. In his farewell address of 1796, Washington offered a final reminder of his appeal for a sense of union transcend...

Kino decides to take his pearl to the capital himself so that he can’t be cheated.  Kino thinks that he has solved all of his problems when he finds the Pearl of the World.  He has never had more than a few little tiny pearls before, and now he thinks he will be rich.  The problem is that the pearl itself is not money.  He has to sell it in order to get rich.  The pearl buyers are incredibly selfish.  They have long-ago come up with a way to collude and cheat the helpless pearl sellers who are at their mercy.  The pearl buyers also try to cheat Kino, wanting to convince him that his pearl is not worth as much as he thought it was.  "You have heard of fool's gold," the dealer said. "This pearl is like fool's gold. It is too large. Who would buy it? There is no market for such things. It is a curiosity only. I am sorry. You thought it was a thing of value, and it is only a curiosity." (Ch. 4)  The townspeople, who have been curious about the pearl all along, a...

The production or manufacturing sector has seen a lot of automation across many countries. This can be partly attributed to the application of the principles of specialization and division of labor in production processes, especially when it comes to mass production of commodities. New inventions have introduced specialized machines and robots that are able to perform more complex tasks than before. According to the Brookings Institute, the total number of industrial robots in use is increasing with time. In the year 2013, there were about 1.2 million robots in use in various industrial plants worldwide. This number increased to about 1.5 million in the year 2014. This has resulted in huge savings in labor costs, as machines perform tasks that were previously done by humans. In fact, labor cost savings in industrialized countries average 16%. Increased automation of tasks has also led to increased production of goods and services. However, a big downside is the effect this has had on e...

a_3=19 a_15=-1.7 Let a_1 be the first term and d be the common difference of the sequence. a_15=a_1+14d a_1+14d=-1.7 ---------- (1) a_3=a_1+2d a_1+2d=19 ----------- (2) Now let's solve the equations 1 and 2 to get the a_1 and d, Subtract equation 2 from equation 1, 14d-2d=-1.7-19 12d=-20.7 d=-20.7/12 d=-1.725 Plug the value of d in equation 2, a_1+2(-1.725)=19 a_1-3.45=19 a_1=19+3.45 a_1=22.45 a_2=a_1+d a_2=22.45+(-1.725) a_2=20.725 a_3=a_2+d a_3=20.725+(-1.725) a_3=19 a_4=a_3+d a_4=19+(-1.725) a_4=17.275 a_5=a_4+d a_5=17.275+(-1.725) a_5=15.55 So the first five terms of the sequence are 22.45,20.725,19,17.275 and 15.55

One of the vertex form of the parabola is, (y-k)^2=4p(x-h)   where (h,k) is the vertex and  p is the distance between vertex and focus and also the same distance between the vertex and the directrix, Given equation is x=4y^2 Graph of the equation is attached. Rewrite the equation in the standard form, y^2=1/4x 4p=1/4 =>p=1/16 (y-0)^2=4(1/16)(x-0) Vertex is at (h,k) i.e (0,0) Focus is at (h+p,k) i.e (1/16,0) Axis of symmetry is the horizontal line passing through the vertex, i.e y=0 Directrix being perpendicular to the axis of symmetry is the vertical line, Directrix is x=h-p Directrix is x=0-1/16=-1/16  

For the function $f(x) = 5x^2$ (a) Determine the simplified form of the difference quotient (b) Complete the table. a.) For $f(x) = 5x^2$ $f(x + h) = 5(x + h)^2 = 5x^2 + 10xh + 5h^2$ Then, $f(x + h) - f(x) = 5x^2 + 10xh + 5h^2 - 5x^2 = 10xh + 5h^2$ Thus, $\displaystyle \frac{f(x+h)-f(x)}{h} = \frac{10xh+5h^2}{h} = \frac{h(10x+5h)}{h} = 10x + 5h$ b.) $ \begin{array}{|c|c|c|} \hline x & h & \displaystyle \frac{f(x+h)-f(x)}{h} \\ \hline 5 & 2 & 60 \\ \hline 5 & 1 & 55 \\ \hline 5 & 0.1 & 50.5 \\ \hline 5 & 0.01 & 50.05 \\ \hline \end{array} $

Find the equation of the circle shown in the figure. *Refer to the figure in the book* By observation, the center of the circle is at $(-1, 1)$ and it passes through point $(2, 0)$. Recall that the general equation for the circle with circle $(h,k)$ and radius $r$ is.. $ \begin{equation} \begin{aligned} (x - h)^2 + (y - k)^2 =& r^2 && \text{Model} \\ \\ (x - (-1))^2 + (y - 1)^2 =& r^2 && \text{Substitute the value of the center} \\ \\ (x + 1)^2 + (y - 1)^2 =& r^2 && \text{Simplify} \end{aligned} \end{equation} $ Since the circle passes through the point $(2,0)$, we can say that the point is a solution for the equation. $ \begin{equation} \begin{aligned} (2 + 1)^2 + (0 - 1)^2 =& r^2 \\ \\ (3)^2 + (-1)^2 =& r^2 \\ \\ 9 + 1 =& r^2 \\ \\ 10 =& r^2 \end{aligned} \end{equation} $ Thus, the equation of the circle is.. $(x + 1)^2 + (y - 1)^2 = 10$

The most obvious source of sympathy for Shylock is that he is part of a despised minority, treated with contempt and loathing on the basis of his religion. As a Jew in an overwhelmingly Christian city, Shylock is subjected to all kinds of humiliating restrictions, both legal and social. Money-lending, or usury, to give it its old-fashioned name, was one of the few occupations open to Jews at that time, as it was regarded as sinful for Christians to lend money at interest. Despite having little choice in the matter, Jews were loathed by Christians for engaging in the very occupation which they themselves had forced the Jews to pursue. Shylock's treatment by his daughter Jessica is also appalling. She runs off with her Christian lover, Lorenzo, but not before stealing some of her father's hard-earned money. Although Shakespeare's portrayal of Jessica is largely sympathetic, her behavior does come across as willful, selfish, and ungrateful. And even if we do find Shylock a tad...

Elie Wiesel's motives are to survive the horrific Holocaust and to stay by his father's side at all times. During Elie's time spent in the Nazi concentration camps, his main goals are to stay healthy, find food, avoid the violent Nazi officers, and to not lose his father. Throughout his experience in the Holocaust, Elie relies on the advice of his fellow inmates and illustrates his will to survive by braving the elements and horrific conditions inside the concentration camps. Elie's father motivates him to stay alive, and Elie relies on his father for support during the Holocaust. Elie makes sure to never abandon his father like Rabbi Eliahu's son and selflessly provides for his father during his last moments before he passes away. Following the death of his father, Elie mentions that his only motive was to feed himself and says that he no longer cared about anything else in life. Overall, Elie's main motives were to stay alive and remain by his father's sid...

A psychoanalytical reading of "The Yellow Wallpaper" could focus on the narrator's incipient mental illness.  She could be viewed as suffering from postpartum depression after the birth of her child, or perhaps psychosis, as she sees a woman trapped in the wallpaper and works to free her.  Alternatively, a psychoanalytic reading could focus on Charlotte Perkins Gilman, the author, the unhappiness she felt in her own marriage, and her feelings about feminism and paternalism in the lives of women.  Formalist readings do not take into account anything external to the text.  A formalist reading of the story would focus on its structure:  how the narrative is organized, its tone, imagery, and style.  A formalist reading of "The Yellow Wallpaper" would focus on the first-person narration, the reliability of the narrator, how the word choices create the story's tone, symbolism, and the development of the plot.

There are advantages to each of these programs, as well as disadvantages. First, we'll take a look at the advantages of AP and IB programs. Then, we'll explore the advantages of community college courses. Finally, we'll look at some disadvantages to each of these programs.  AP stands for Advanced Placement and is administered by The College Board. These courses are designed to give students a rigorous, college-level curriculum. In some schools, AP courses are weighted higher than regular courses, giving students the possibility of raising their grade point average. Some students have been able to graduate with greater than a 4.0 this way. At the end of the course, students have the option of taking an examination. There is a cost associated with taking this exam. Students receive a rating of 1-5 upon completion of the exam. Many colleges accept certain scores on AP exams as credit for general education coursework. Taking the exam is usually less expensive than a college cou...

There are several lines in the poem "The Listeners" that give readers a general idea of what time of day it is. However, if you are looking for an exact hour, the poem does not give that accurate of a time frame. The most specific time that I can give is that the poem takes place sometime during the night. In line two of the poem, the narrator tells his audience that the Traveler is knocking on the moonlit door. An argument can be made that the moon is sometimes visible during the day; however, sunlight overpowers the moonlight during the day. The poem specifically mentions several times that it is the moon lighting up parts of the house. Knocking on the moonlit door; Then a bit later the following lines appear. Stood listening in the quiet of the moonlight       To that voice from the world of men:  Stood thronging the faint moonbeams on the dark stair,    These lines further detail the fact that the poem takes place at night. It mentions more moonlight and dark stairs.

The answer to this question can be found in the final paragraphs of the story. The first thing that happens is he rejoins his father, and then John prays and is purified. John's father is quite proud with his son, and John's father announces that John has now come back a man and a priest. He touched my lips and my breast, he said, "You went away a boy. You come back a man and a priest." Next, John announces to his father what he discovered. John tells his father that the "gods" that lived in the Place of the Gods were just regular men and women. John then tells his father about the entire trip. John wants to tell the rest of his people about his discovery, but his father warns him against it. His father tells him that knowing the truth might be dangerous for a people so used to believing something else entirely. John decides that his father is correct. "Truth is a hard deer to hunt. If you eat too much truth at once, you may die of the truth. It was not...

The author of Evicted, Matthew Desmond, offers some practical solutions to the housing crisis. His main proposal is for the introduction of vouchers as a means of institutionalizing affordable housing. The principle on which this proposal is based is the same as that of food stamps. Just as food stamps allow poor families to buy groceries virtually anywhere, housing vouchers would enable families below a certain income level to obtain housing in many locations. Effectively, this would be a federal subsidy designed to ensure that the poor would have somewhere to live, while at the same time allowing landlords to continue to make money from their property investments. Desmond's voucher proposal represents a radical departure for those advocating government involvement in housing. Instead of federal funds being used to build housing projects, they're to be put directly into the pockets of prospective tenants to give them some degree of choice as to how and where they'll spend ...

In William Bradford's telling, the Pilgrims indeed experienced expectation, suffering, success, and disappointment in the long journey that took them to the Netherlands, back to England, and then to New England. In History of Plymouth Plantation, Bradford explains each of these experiences as united by a central theme. Each is, according to Bradford, part of God's plan for the Pilgrims. Bradford describes the sense of expectation the Pilgrims felt when they landed in New England: Being thus arrived in a good harbor, and brought safe to land, they fell upon their knees and blessed the God of Heaven who had brought them over the vast and furious ocean, and delivered them from all the perils and miseries thereof, again to set their feet on the firm and stable earth, their proper element. They believed that they had arrived in a land where they could live independently of the Church of England as a free community of believers. Once they arrived, however, they experienced considerab...

The speaker of this poem is trying to answer the question: "What happens to a dream deferred?" (line 1).  Deferred means delayed or withheld.  Typically, if one defers something, one puts it off until later.  Therefore, the question is really asking what happens to a dream if it is delayed or put off.  The speaker then offers a number of possibilities or outcomes of this dream; they are all similes until the very last one, which is a metaphor.  First, he wonders if it dries up "like a raisin in the sun" (3).  Next, he considers the possibility that it will fester and run (with pus), like an untreated sore.  Next, he wonders if it will be comparable to food gone bad: will it "stink like rotten meat" or become inedible and crusted with sugar like a "syrupy sweet" (6, 8).  In the final simile, the speaker considers that the dream might simply weigh a person down, sagging "like a heavy load" (10).  Finally, in the only metaphor of the poem,...

The word "release" in this book is a euphemism. It takes the place of a word that sounds harsh. That's an advantage in a community that is trying to stabilize all emotions. If this question is asking about advantages to actually euthanizing people, then I believe that readers could find certain advantages to that practice. One advantage is that it functions as a population control measure. Jonas's society schedules births, so it makes sense that they also schedule deaths. This has the benefit of making sure the population is stable. Generally, the elderly are released. That helps to make sure that the people who are no longer capable of contributing work efforts to the operation of society are not resource drains for too many years. Another advantage is that releasing a person could be seen as humane. A person that has a terminal illness could choose to be released in order to secure a pain-free death. This scenario could also apply to a community member that sustains...

On any contentious issue, the actions of two opposing sides often lead to an escalation of tensions. It was no different in the case of the Berlin Wall. According to the State Department's Office of the Historian, the Berlin crisis was precipitated in part by the USSR's actions. In a 1958 speech, Khrushchev demanded that the Americans pull out of Western Germany. His words were taken as an ultimatum and a demonstration of Soviet resolve; for his part, President Eisenhower wasn't about to give in to Soviet demands. The two held talks at Camp David in 1959, but no consensus was reached at that point. In 1960, the Soviets shot down an American U-2 spy plane, which they claimed had trespassed onto Soviet territory. This hostile action killed any future peaceful negotiations regarding the Berlin Wall. For more, please refer to the link I have provided. After the Berlin Wall was taken down, many historians credited the United States and Allied powers for the victory. However, the...

Determine the determinant of the matrix $\displaystyle A = \left[ \begin{array}{ccc} 2 & 4 & 0 \\ -1 & 1 & 2 \\ 0 & 3 & 2 \end{array} \right]$ and if possible, the inverse of the matrix. Using the formula $\displaystyle |D| = \left[ \begin{array}{ccc} 2 & 4 & 0 \\ -1 & 1 & 2 \\ 0 & 3 & 2 \end{array} \right] = 2 \left| \begin{array}{cc} 1 & 2 \\ 3 & 2 \end{array} \right| -4 \left| \begin{array}{cc} -1 & 2 \\ 0 & 2 \end{array} \right| + 0 \left| \begin{array}{cc} -1 & 1 \\ 0 & 3 \end{array} \right| = 2 (1 \cdot 2 - 2 \cdot 3) - 4 (-1 \cdot 2 - 2 \cdot 0) = 0$ Since the determinant of $A$ is zero, $A$ cannot have an inverse, by the invertibility criterion.

Prepare a report on the Kelvin scale. Include in your report an explanation of how to convert between the Kelvin scale and the Celsius scale. KELVIN SCALE Kelvin is a temperature scale designed so that zero degrees K is defined as absolute zero (at absolute zero, a hypothetical temperature, all molecular movement stops - all actual temperatures are above absolute zero) and the size of one unit is the same as the size of one degree Celsius. Water freezes at 273.16K; water boils at 373.16K. $\displaystyle \left[ K = C + 273.16^{\circ}, F = \left( \frac{9}{5} \right) C + 32^{\circ} \right]$. This temperature scale was designed by Lord Kelvin (William Thomson, 1824-1907). Kelvin was a British inventor and scientist (he was born in Belfast, Northern Ireland in 1824). In addition to his work on temperature, Kelvin invented over 50 devices (including the mirror galvanometer, which detects and measures weak electric fields), discovered the second law of thermodynamics (the amount of usable ene...

In Chapter 23 of the novel, readers may infer that the Cunninghams did not agree with the verdict of the trial. In a conversation with Jem, Atticus notes that not all of the jurors wanted to convict Tom Robinson, and there was at least one jury member who wanted an acquittal. Atticus confirms that the jury member was the double first cousin of Walter Cunningham. In Chapter 15, Atticus had left the house in the evening to sit outside of the jail house to prevent Tom Robinson from being harmed. Curious about where Atticus was going so late at night, Jem, Scout, and Dill follow him, only to find him reading a newspaper. At this point, the Old Sarum mob show up to injure, if not lynch, Tom Robinson. As the mob members close in on Atticus, Scout recognizes one of the men as Mr. Cunningham. She interrupts the men and goes on to ask Mr. Cunningham about how his entailment is going as well as tell him to say "hi" to Walter. This conversation between Scout and Mr. Cunningham relieves ...

According to historians John Hope Franklin and Alfred A. Moss, Jr., more than three million black men registered for the Selective Service. However, they were refused at a rate of 18.2 percent, compared to just 8.5 percent for whites.  Discrimination was rampant in the armed forces, though black soldiers had more opportunities than in the First World War. They were included in the infantry, the coast and field artillery, the engineer corps, the medical corps, and many other branches. When the Women's Army Corps was organized (WAC), black women were included. By the end of the war, more than 4,000 women had enlisted in the organization. The next step was to get black soldiers recommended for advanced training at officer training schools. Blacks were not admitted to officer training schools in high numbers until the Secretary of War issued an order stating that blacks were to be admitted. The integration of the military began in 1945, first on the war front in Germany. In 1948, sever...

Lincoln decided to issue the Emancipation Proclamation only after a lot of consideration.  Lincoln did not want to alienate the border states, particularly Missouri, Kentucky, and Maryland, who still owned slaves.  If these states went to the Southern camp, it would provide a large morale boost to the Confederacy and present a border that was harder to defend for the North.  It would also surround Washington D.C. with hostile territory.  Lincoln only freed the slaves in the Confederate states.  Lincoln wanted to curry international favor by issuing the Emancipation; Britain had already ended slavery in its colonies and was quite active in ending the global slave trade.  Lincoln also wanted to placate abolitionists back home, though right after the Proclamation went into effect there was some discontent in the Union army when some soldiers said that they did not sign up to free slaves.  Lincoln also wanted to give slaves in the South incentive to escape; the prospect of slaves escaping ...

A discussion of all the deaths would be a very long answer, as quite a few people die in this book. A partial list would start with Oliver’s mother, Agnes, who dies in the very first chapter. There are several named paupers who die; these include Sally, the woman who attended Oliver’s birth, and Dick, the child who was Oliver’s friend at the parochial farm. There are several deaths mentioned while Oliver is apprenticed to Mr. Sowerberry; I believe most of these are used to advance the story, as they are related to the undertaker’s trade. And then there are the deaths of the criminals, including Nancy, Bill Sikes, and Fagin. It sounds like you need to give your opinion about the deaths that occur in the novel, and that should of course be based on what you believe. It is my belief that an author considers killing off their characters in a story very carefully and does not do so just for the sake of having a death in the story. It’s important, then, to consider what the author is trying ...

Methodology is an analysis of the methods used to make inquiries or to do research in a particular field of study. In the field of history, for instance, historiography is the study of methods used to analyze and interpret historical events. Historiography applies the method of analyzing multiple sources—written documents, but also music, art, and objects of everyday use. There are some methods of historiography that have chosen to examine history through the experiences of a particular group. For example, there are some historians and scholars in American Studies who examine history through the experiences of Black Americans or women. In the field of British history, E.P. Thompson wrote a well-known book, The Making of the English Working Class, in which he considered them as agents of history, with more influence on British culture than many people had previously realized, especially given that most methodologies had focused on the middle-class.

Suppose the matrices $A, B, C, D, E, F, G$ and $H$ are defined as $ \begin{equation} \begin{aligned} A =& \left[ \begin{array}{cc} 2 & -5 \\ 0 & 7 \end{array} \right] && B = \left[ \begin{array}{ccc} 3 & \displaystyle \frac{1}{2} & 5 \\ 1 & -1 & 3 \end{array} \right] &&& C = \left[ \begin{array}{ccc} 2 & \displaystyle \frac{-5}{2} & 0 \\ 0 & 2 & -3 \end{array} \right] &&&& D = \left[ \begin{array}{cc} 7 & 3 \end{array} \right] \\ \\ \\ \\ E =& \left[ \begin{array}{c} 1 \\ 2 \\ 0 \end{array} \right] && F = \left[ \begin{array}{ccc} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right] &&& G = \left[ \begin{array}{ccc} 5 & -3 & 10 \\ 6 & 1 & 0 \\ -5 & 2 & 2 \end{array} \right] &&&& H = \left[ \begin{array}{cc} 3 & 1 \\ 2 & -1 \end{array} \right] \end{aligned} \end{equation} $ Carry out the ind...

Find the function $f \circ g \circ h$. $f(x) = x+1 , \qquad \quad g(x) = 2x ,\qquad \quad h(x) = x - 1$ $ \begin{equation} \begin{aligned} f \circ g \circ h &= f(g(h(x)))\\ \text{Solving for $g \circ h$}\\ g(h(x)) =& 2x && \text{Substitute the given function $h(x)$ to the value of $x$ of the function $g(x)$}\\ g(x -1) =& 2x \\ g(x -1) =& 2(x - 1) &&\text{ Simplify the equation}\\ g \circ h =& 2x -2 \\ \text{Solving for $f \circ g \circ h$}\\ g \circ h =& 2x -2\\ f \circ g \circ h =& f(g(h(x)))\\ f(2x - 2) =& x+1 && \text{ Substitute the value of $x$}\\ f(2x - 2) =& 2x - 2 +1 && \text{ Combine like terms}\\ \end{aligned} \end{equation} $ $\qquad \qquad \boxed{f \circ g \circ h = 2x - 1}$

The family has always liked Rikki-tikki. When the family first meets Rikki-tikki, he is half-drowned. Teddy even thinks Rikki-tikki is dead; however, the mother and father decide to nurse Rikki-tikki back to health. Even by the first night, Rikki-tikki goes to bed with Teddy. The mother is a little worried about the situation, but the father states that Teddy is safer with the mongoose than without.   "I don't like that," said Teddy's mother. "He may bite the child." "He'll do no such thing," said the father. "Teddy's safer with that little beast than if he had a bloodhound to watch him. If a snake came into the nursery now—" Rikki-tikki proves his value as a protector and snake killer by killing Karait. The family then treats Rikki-tikki even better than before. They let him wander around the dinner table while they are eating. He gets to sit on Teddy's shoulder at the dinner table, and Teddy's mother has taken to petting...

The reader knows the result of Tom Robinson's trial in Chapter 21 of To Kill a Mockingbird. In Chapter 22, Maudie shares with the children that there are more people on their father's side than they might think. For example, she says that Judge Taylor knew what he was doing by naming Atticus to defend Tom. She also believes that Heck Tate did what he could to help Tom. However, we do not become aware of the opinions of many neighbors until Aunt Alexandra's missionary circle meeting in Chapter 24. Mrs. Merriweather offers her opinion that the black citizens of Maycomb County just need to know that they are forgiven. Once they are, "then this whole thing'll blow over." Referring to the decision in Tom's trial, she believes that "the cooks and field hands are just dissatisfied, but they're settling down now." Mrs. Merriweather believes that by showing disappointment, one is simply not being a good Christian. Next, Mrs. Farrow shares her feelings...

In answering this question, it's important to understand the importance of the Declaration of Independence's overall rhetorical strategy. It was written primarily to persuade Americans who might otherwise be skeptical at the very idea of independence—that this was the only way forward. It was also written with the intent of persuading the rest of the world that the American colonists had been unfairly treated at the hands of their colonial overlords and that this why they had decided to bite the bullet and declare independence from Great Britain. In general terms, the Declaration expresses the colonists' conviction that they'd been pushed into a corner by the arrogance and intransigence of the British and therefore had no alternative but to declare independence: Such has been the patient sufferance of these Colonies; and such is now the necessity which constrains them to alter their former Systems of Government. The history of the present King of Great Britain is a hist...

The only music Henrik Ibsen wrote into his play A Doll's House is the music to the tarantella, which Nora practices dancing to in preparation for the costume party she and Torvald attend on Christmas Eve. However, when the play is performed, different directors may add other music to further develop the play and their interpretation of the play as they choose. The tarantella is an Italian folk dance that symbolizes a person being bitten by the poisonous wolf spider of the region. The poisonous bite causes hysteria in its victims. The dance became a means of trying to exorcise the poison and its symptoms. The dance also evolved into a courtship dance, danced by couples; however, since Nora is dancing a solo, she is most likely dancing the original dance representing hysteria.The scene, found in Act 2, is an extremely emotional one. In order to distract Torvald from discovering the letter Krogstad has put in his letter box, Nora asks Torvald to direct her while she rehearses her danc...