Onboard Note

A linear inequality describes an area of the coordinate plane that has a boundary line. Every point in that region is a solution of the inequality. In simpler speak, a linear inequality is just everything on ONE side of a line on a graph. There are a couple ways to determine whether the point (0,0) lies in the region described by the inequality, y You could graph the inequality on a coordinate plane. However, the easiest way is by using substitution. To do this take the x and y values from the ordered pair and substitute them into the inequality. Remember an ordered pair is always written (x,y). In this case x = 0 and y = 0. STEPS: 0 0 Since 0

The visions you’re referring to are those that are given to Macbeth by the three witches in Act IV. Following the prophecy the witches gave him at the beginning of the play, Macbeth is anxious to know what the conclusion will be, given that his wife has been having second thoughts. He seeks them out to “answer me / To what I ask you.” They respond by providing three speakers from their cauldron, and Macbeth sees their messages as a boon to his cause. He is told to beware the Thane of Fife (Macduff), that none of woman born shall harm him, and that he will not be defeated until Birnam Wood marches to high Dusninane Hill. Assuming these are all good tidings, and interpreting his victory as sure, Macbeth is in high spirits until the end of his meeting with the three hags: a line of kings, with the ghost of Banquo following. Macbeth is clearly appalled at the vision, for it serves to bolster the witches’ original prophecy for Banquo from Act I: “Thou shalt get kings, though thou be none.” ...

First, different types of tourists are influenced by different factors. A well-educated elderly couple spending a summer traveling around Europe may have very different motivations than a college student on spring break in Florida. People with young children will obviously prioritize locations that have activities and facilities geared towards family travel, while the elderly or disabled may be concerned about accessibility. The single most important factor influencing destination choice is recommendations from friends or family. This effect is amplified by social media, on which people often share vacation photographs and anecdotes. Price is an important factor, too, with sales or special offers sometimes motivating people considering a specific destination to decide to visit it; someone who is reluctant to visit a given hotel at $250/night might decide a $150/night special makes that hotel affordable.  Often, people enjoy visiting places they have seen or read about, with Jane Austen...

Evaluate $\displaystyle \frac{3}{8}(16 - 8c) - 9 \geq \frac{3}{5}(10c - 15) + 7$ $ \begin{equation} \begin{aligned} \frac{3}{8} (16) - \frac{3}{8} (8c) - 9 &\geq \frac{3}{5}(10c) - \frac{3}{5} (15) + 7 && \text{Use the Distributive Property to remove the parenthesis}\\ \\ 6 - 3c - 9 &\geq 6c - 9 + 7 && \text{Simplify}\\ \\ -3c - 6c &\geq - 9 + 7 - 6 + 9 && \text{Group terms}\\ \\ -9c &\geq 1 && \text{Combine like terms}\\ \\ \frac{-9c}{-9} &\geq \frac{1}{-9} && \text{Divide each side by -9}\\ \\ c &\leq -\frac{1}{9} && \text{Remember that if you divide or multiply numbers ,the inequality symbol reverses} \end{aligned} \end{equation} $

In the United States, there are three branches of government. Each branch of government has certain strengths. The strength of Congress is that it makes laws. Many of these laws also deal with spending money. This gives Congress a great deal of power and influence. One of the strengths of the executive branch is that the president has many opportunities to get his message to the American people. The president can have news conferences to explain his thinking or his actions. The president’s press secretary holds daily meetings with the press to answer questions about decisions the president has made or actions the president has taken. The president gives a yearly State of the Union speech where he can lay out his plans for the country. This speech is televised nationally and is held with all members of Congress present. The president can also go on national television during times of crisis or emergencies to talk to the American people. No other government official has the number of opt...

Miss Emily Grierson is responsible for the death of Homer Barron in William Faulkner's classic short story "A Rose for Emily." Miss Emily is depicted as a tortured soul, who grew up under her father's authoritative guardianship. After her father passes away, she initially refuses to acknowledge his death and rarely leaves her home. Once Homer Barron arrives in Jefferson, he begins courting Miss Emily and the entire town disapproves of their relationship, because they feel Miss Emily is dating below her social class. The community members also mention that Homer likes men and overhear him saying that he was not a marrying man. Miss Emily then purchases arsenic from a local pharmacy and refuses to give the pharmacist a reason for her purchase. After Miss Emily purchases the arsenic, Homer Barron is never seen or heard from again. Miss Emily's arsenic purchase coupled with Homer Barron's disappearance implies that she murdered him. There is ample evidence to sugg...

Initially, Scrooge believes that the appearance of Marley's ghost is a result of indigestion. However, once the ghost has gotten Scrooge to take the first steps toward understanding that the ghost is indeed "real," Scrooge begins to think of other reasons as to why it has appeared. As he continues to talk with Marley's ghost, it says, “I am here to-night to warn you, that you have yet a chance and hope of escaping my fate. A chance and hope of my procuring, Ebenezer.” To which Scrooge replies "You were always a good friend to me . . . Thank’ee!” Here Scrooge discerns another reason for the presence: his old friendship with Marley. In this moment, Marley's desire to help out his old friend has caused the ghost to appear. However, when the ghost tells him about the three spirits yet to come, "Scrooge’s countenance fell almost as low as the Ghost’s had done." Scrooge's understanding begins to shift again. This is no kind act of friendship; this is ...

a.) Suppose that $\displaystyle F(x) = \frac{5x}{ 1 + x^2}$, find $F'(2)$ and use it to find an equation of the tangent line to the curve $\displaystyle y = \frac{5x}{1 + x^2}$ at the point $(2,2)$ Using the definition of the derivative of a function $F$ at a number $a$, denoted by $F'(a)$, is $\qquad \displaystyle \qquad F'(a) = \lim_{h \to 0} \frac{F(a + h) - F(a)}{h}$ We have, $ \begin{equation} \begin{aligned} \qquad F'(a) =& \lim \limits_{h \to 0} \frac{\displaystyle \frac{5(a + h)}{1 + (a + h)^2} - \frac{5a}{1+ a^2}}{h} && \text{Substitute $F'(a + h)$ and $F(a)$}\\ \\ \qquad F'(a) =& \lim \limits_{h \to 0} \frac{(5a + 5h)(1 + a^2)- 5 a[1 + (a + h)^2]}{(h)(1 + a^2)[1 + (a + h)^2]} && \text{Get the LCD of the numerator}\\ \\ \qquad F'(a) =& \lim \limits_{h \to 0} \frac{5a + 5a^3 + 5h + 5a^2 h - 5a (a^2 + 2ah + h^2 + 1)}{(h)(1 + a^2)[1 + (a + h)^2]} && \text{Expand the equation} \\ \qquad F'(a) =& \lim \limits_...

A grief-stricken Hamlet is moping around Elsinore, still mourning the death of his father. In keeping with tradition, he is wearing black. Claudius isn't too happy that Hamlet hasn't been able to get over his loss and move on. For one thing, Hamlet's sad demeanor acts as a constant reminder of Claudius's villainous act. Hamlet doesn't know it yet, but his father was murdered by Claudius, and so it's not surprising that Claudius doesn't want to be reminded of this inconvenient fact. He then proceeds to give Hamlet a patronizing lecture, telling him that, although it's awfully sweet of him to show such grief over his father's death, he needs to move on, man up, and start acting like a prince: Tis sweet and commendable in your nature, Hamlet, / To give these mourning duties to your father: / But, you must know, your father lost a father; / That father lost, lost his, and the survivor bound / In filial obligation for some term To do obsequious sorrow. Bu...

You need to use the formula of dot product to find the angle between two vectors, u = u_x*i + u_y*j, v = v_x*i + v_y*j , such that: u*v = |u|*|v|*cos(theta) The angle between the vectors u and v is theta. cos theta = (u*v)/(|u|*|v|) First, you need to evaluate the product of the vectors u and v, such that: u*v = u_x*v_x + u_y*v_y u*v = cos(pi/4)*cos(pi/2) + sin(pi/4)*sin(pi/2) u*v = cos(pi/2-pi/4) = sin pi/4 = sqrt2/2 You need to evaluate the magnitudes |u| and |v|, such that: |u|= sqrt(cos^2(pi/4) + sin^2(pi/4)) => |u|= sqrt(1) =>|u|= 1 |v|= sqrt(cos^2(pi/2) + sin^2(pi/2)) => |v|= sqrt(1) =>|v|= 1 cos theta = (sqrt2/2)/(1*1) => cos theta = sqrt2/2 => theta = pi/4 Hence, the cosine of the angle between the vectors u and v is cos theta = sqrt2/2 , so, theta = pi/4.

You need to use mathematical induction to prove the formula for every positive integer n, hence, you need to perform the two steps of the method, such that: Step 1: Basis: Show that the statement P(n) hold for n = 1, such that: 1 = 1(1+1)/2 => 1 = 1*2/2 => 1=1 Step 2: Inductive step: Show that if P(k) holds, then also P(k + 1) holds: P(k): 1 + 2 + .. + k = (k(k+1))/2 holds P(k+1): 1 + 2 + ... + k + (k+1) = ((k+1)(k+2))/2 You need to use induction hypothesis that P(k) holds, hence, you need to re-write the left side, such that: (k(k+1))/2 + k + 1 = ((k+1)(k+2))/2 k(k+1) + 2k + 2 = k^2 + 2k + k + 2 k^2 + k + 2k + 2 = k^2 + 2k + k + 2 Notice that P(k+1) holds. Hence, since both the basis and the inductive step have been verified, by mathematical induction, the statement P(n): 1 + 2 + 3 + ... + n = (n(n+1))/2 holds for all positive integers n.

Decius advises Brutus that he is quite sure he can "o'ersway" Caesar, even if he has "resolved" not to come to the Capitol. He says that flattery is generally effective in persuading Caesar: But when I tell him he hates flatterers,He says he does, being then most flattered. Later, when Caesar asks Decius to tell the senators that he "will not come today," Decius calls him "Most mighty Caesar," beginning to wear him down with flattering epithets. Later, Decius offers a reinterpretation of Calpurnia's dream which paints Caesar as a font of goodness: "from you great Rome shall suck / Reviving blood." Caesar is, indeed, swayed by this argument; he allows Decius to convince him that the vision of a statue spouting blood could actually be a positive sign. Finally, Decius appeals to Caesar's desire for general approval and praise by telling him that the senate has decided "to give this day a crown to mighty Caesar." If Ca...

This is open to interpretation, and Mary's geraniums are actually mentioned only twice in the story. However, if we think about what Mary represents in a wider context, we can infer from that what her geraniums may symbolize. When the Doctor first sees Mary's geraniums, he is surprised that they are still blooming despite the fact that geraniums do not typically stay in flower in the winter. He asks her what she has done to keep the flowers alive, and remarks that every time he passes the house, it is always full of flowers. Mary doesn't answer his question, but she does immediately pluck one of the best geraniums and offer it to the doctor. The geraniums, then, represent the outcome of Mary's nurturing nature and her tenacity. Because Mary is an endless reserve of comfort and sustenance to her family, she is able to represent this physically by filling the house with the flowers which represent this sustenance and keep the house beautiful. Mary's dedication does no...

President Lincoln’s second inaugural address showed that his views had changed from when he gave his first inaugural address. When President Lincoln first took office, our country was splitting apart. Several states had left the Union already, and there was concern additional states could leave. As a result, President Lincoln had to make it very clear that he had no intention of ending slavery where it already existed. If he came out and said he was against slavery and wanted to end it, more states might have left the Union. He might also have lost the support of some people in the North who were not against slavery but were in favor of saving the Union. In his second inaugural address, President Lincoln made it very clear that he opposed slavery. He made it clear that the Civil War was about the issue of slavery, which he considered to be an evil institution. He believed it was our duty to solve the slavery issue. By this time, it was clear the North would win the war. This allowed Pr...

The Prophet Muhammad was the founder of Islam. Muhammad was a merchant who was born in and lived in Mecca, a commercial hub on the Arabian peninsula. He worked along the many trade routes that traversed the region and became wealthy in the process. As he entered middle age, the Archangel Gabriel appeared to him and commanded him to recite a series of revelations that he made to him. These became the foundation of the Qur'an, and the basic truth that was revealed was that there was no God other than Allah, a departure from the polytheism practiced throughout much of the region. Muhammad was forced to leave Mecca due to the unpopularity of his message with many of the wealthy merchants in that city, and went to Medinah in 622, a journey known as the hijrah. He returned triumphantly a few years later as his preaching had popularized his message to the point where even Mecca's elites had embraced it. After his death, Islam spread along trade routes and through Arab military expansi...

There are many aspects to Orwell's vision of the future in his famous novel. The basic outlines can be summarized as follows, with the proviso that in a relatively brief answer such as this, any description of the 1984 world must be simplified to an extent. We are told early on that the story is taking place in a world where a nuclear war has occurred, for there is a reference to the time early in Winston's memory "when the atomic bomb fell on Colchester." The actual details beyond that are not given, but the world has been reorganized into three "superstates": Oceania, which we are led to believe includes the British Isles, the United States, and the rest of the Americas, and possibly the other English-speaking parts of the world such as Australia; Eurasia, which includes the continent of Europe including the former Soviet Union and possibly the Middle East; and Eastasia, which would be China, Japan, Southeast Asia, and most of the Pacific islands, presumab...

There isn't any mention in the novel of Marmee saying anything in particular before Beth dies, although the novel does state that, in her final days and hours, Beth "clung to the hand that had led her all her life." Both Marmee and Beth's father accompany her as she dies, and Alcott makes a particular point of stating that dying utterances or last words to a dying person are rarely as momentous as they are in books. For Beth, "the tide went out easily" and without fanfare, and she dies cradled on her mother's bosom. The last words actually addressed to Beth in the book are from Jo, who has watched over Beth closely throughout her final illness. Jo promises she will try very hard to keep going after Beth's death, and not be too sad, knowing she is going to a better place.

Though this play, which includes people in a bar telling supernatural stories, does not involve a traditional protagonist or antagonist, the first three men in the bar—Jack, Brendan, and Jim—might be considered the protagonists. They anticipate the arrival of Valerie, a woman arriving in Sligo from Dublin, and they criticize their friend, Finbar, for escorting Valerie (as Finbar is married). When Valerie arrives in the pub, they vie for her attention and establish themselves as local experts, telling Valerie about the "faery" road that goes under the house that she has bought from Finbar. Jack, Brendan, and Jim establish Valerie as the antagonist, as she is new to town. However, after they tell traditional Irish tales of ghosts and the supernatural, Valerie contributes her own tale about the death of her daughter from drowning. Her sad tale turns the men's attitudes toward her from distrust and sexual tension to sympathy and connection. In this sense, Valerie is the antag...

This question almost certainly refers to the boundaries between lithospheric plates, also called tectonic plates. The outermost, solid part of the Earth is called the lithosphere. Large regions of the lithosphere are now known to move relative to one another, sliding on top of the asthenosphere, the layer beneath the lithosphere. The asthenosphere is the upper part of the Earth’s mantle and is described as “plastic,” meaning that even though it is solid, it deforms easily, allowing the plates of the lithosphere to slide on top of it. Lithospheric plates are large, often millions of square miles. Most of North America is on one plate, for example. Based on the movement of these plates, the continents of the Earth previously all came together and moved apart again. Lithospheric plates do not move fast—only one or a few centimeters in a year—but they do not all move in the same direction, so interesting things occur at the boundaries, the edges where two plates are in contact. Consider th...

A soliloquy occurs when a character speaks his thoughts aloud when the other characters are absent. Only the audience gets to hear what he is thinking. Macbeth's seven soliloquies help us to understand his thought processes and his inner conflicts. The soliloquies are key to adding dimension to his character. If we only saw him from the outside, we might think of him as nothing more that a sociopathic killer from the start. Knowing his thoughts helps us to understand that he begins with a conscience. Through his soliloquies we track how he becomes dehumanized over time as his path of bloodshed continues. We learn, for instance, in Macbeth's first soliloquy in act 1, scene 7, that he realizes and dreads the risks of killing Duncan. He wishes it could all end cleanly, with just this one death. However, he understands that once he starts down this road, it is likely to get bloodier and bloodier: he knows in his heart that Duncan's death won't be the end. He knows the blood...

Cross-multiplication is applicable when have two fractions or rational expressions equated to each other.  It is method wherein we multiply the denominator towards the numerator on the other side. This will helps to simplifying the equation by getting rid of the fraction form on each side. For a given equation:  a/b=c/d where b and are nonzero, we may cross-multiply to simplify it as:  a*d = c*b . Applying cross-multiplication on the given equation 9/(x^2-6x+9)=(3x)/(x^2-3x) , we get: 9*(x^2-3x)=(3x)*(x^2-6x+9) Apply distribution property. 9x^2-27x=3x^3-18x^2+27x Subtract 9x^2 from both sides of the equation. 9x^2-27x-9x^2=3x^3-18x^2+27x-9x^2 -27x=3x^3-27x^2+27x Add 27x  on both sides of the equation. -27x+27x=3x^3-27x^2+27x+27x 0=3x^3-27x^2+54x or 3x^3-27x^2+54x=0 Factor out the greatest common factor (GCF) 3x . (3x)(x^2-9x+18)=0 Apply x^2-9x+18= (x-3)(x-6) , we get: 3x(x-3)(x-6)=0 Apply zero-factor property to solve for x by equating each factor to 0 . 3x=0 (3x)/3 =0 x=0   x-3=0 x-3+...

As a respectable, God-fearing woman, Aunt Polly wants Tom to attend Sunday school and church. But for Tom, it's all a bit of a bore. He doesn't like being told what to do, especially if it involves sitting still for long periods of time when he could be out having fun. However, after Tom racks up an impressive collection of bible tickets in return for trading all the spoils he earned from his whitewashing scam, Sunday school suddenly becomes more interesting. Because now Tom is about to be awarded the prize of a Bible. This is his reward for supposedly memorizing lots of the good book's verses. But Tom being Tom, he didn't put in the necessary hard work; he obtained all this Bible tickets purely by fraud. So when Judge Thatcher calls on Tom to display his extensive knowledge of Scripture in front of the whole congregation, the mischievous young scamp makes a complete fool of himself. Tom Sawyer has a particular hatred for Sunday school and everything about it. He has a ...

Edgar Allan Poe's mystery stories broke new ground because of his imaginative plot lines.  Three of his stories are widely regarded to be the first American detective fictions: "The Murders in the Rue Morgue," "The Mystery of Marie Roget," and "The Purloined Letter," and feature a gifted amateur detective, C. Auguste Dupin. "The Murders in the Rue Morgue" was sensational because of its murderer: a razor-wielding orangutan.  Dupin is able to solve this, and the other two crimes, through his formidable intelligence, empathy, and his use of what Poe called "ratiocination," a technique of reasoning. Other Poe mysteries, "The Gold Bug," "Thou Art the Man," and "The Man of the Crowd" introduced staples of modern detective fiction including the use of surveillance, code-breaking, and forcing a suspect's confession. Sir Arthur Conan Doyle, British author of the Sherlock Holmes mysteries, called Poe's wo...

For the given problem: yln(x)-xy'=0 , we can evaluate this by applying variable separable differential equation in which we express it in a form of f(y) dy = f(x)dx . to able to apply direct integration: int f(y) dy = int f(x)dx . Rearranging the problem: yln(x)-xy'=0 yln(x)=xy' or xy' = y ln(x) (xy')/(yx) = (y ln(x))/(yx) (y') /y = ln(x)/x Applying direct integration, we denote y' = (dy)/(dx) : int (y') /y = int ln(x)/x int 1 /y (dy)/(dx) = int ln(x)/x int 1 /y (dy)= int ln(x)/x dx For the left side, we apply the basic integration formula for logarithm: int (du)/u = ln|u|+C int 1 /y (dy) = ln|y| For the right side, we apply u-substitution by letting u= ln(x) then du = 1/x dx . int ln(x)/x dx=int udu Applying the Power Rule for integration : int x^n= x^(n+1)/(n+1)+C . int udu=u^(1+1)/(1+1)+C =u^2/2+C Plug-in u = ln(x) in u^2/2+C , we get: int ln(x)/x dx =(ln(x))^2/2+C Combining the results, we get the general solution for differential equat...

Remembering that kennings offer a visual or sensory description of a word's meaning, I can offer some suggestions for thinking about the words you list, but very much want to emphasize that these are simply to offer guidance: you need to use these as a starting point for developing your own kennings. So let's think about what the command "compose" means: one meaning is to write something: what image comes into your mind when you think about composing or writing an essay or a poem? Do you think about paper and a pen? Do you think about words flowing in black ink across a white page? A kenning would involve this type of imagery. To compose could be to "page-ink." I am sure you can come up with other images. Could you think up an image that would picture composing on a computer? Likewise, what does "seek" conjure in your mind: to search for something? To head out on an adventure? Is it searching for a treasure? Could you call it "treasure hunt?...

What Wittgenstein is challenging is the dominant notion in contemporary philosophy that meaning can be reduced to propositions, that there is some underlying logic to our language which it is somehow the business of the philosopher to discover. To a large extent, this was Wittgenstein's position in his earlier work, most notably in the Tractatus. However, he subsequently abandoned that position to argue for meaning as being intimately bound up with how we use ordinary language in our daily lives. Let us take a brief example from Wittgenstein to illustrate the point. Although we can define a tree, for instance, for the purposes of scientific classification or compiling a dictionary, that definition is itself dependent on how we have already been using the word "tree" in our everyday language. In other words, we do not know what a tree is only because we read about it in a science book or a dictionary, we know about it because we have direct experience of trees and have bee...

Rhetorical devices are persuasive devices. To understand the rhetorical devices Swift is using, it is therefore helpful to understand what Swift is trying to persuade his readers to do. As a high ranking clergyman in Ireland, Swift was concerned with the plight of the poor and increasingly frustrated that year after year reasonable, mild, and doable solutions to the problem of acute poverty were brushed aside by the people with the power to make changes. Swift wanted to see starving mothers and children fed, tax burdens on the poor decreased, rents lowered, and decent job opportunities created. However, perceiving that sensible, rationale arguments were going nowhere, Swift determined to try a new approach. Central to this approach is hyperbole or exaggeration. Swift hoped that by creating a morally clueless narrator with a completely outrageous solution for the problem of poverty in Ireland, he would shock people and gain their attention. Ultimately, he hoped that the essay would enco...

According to Emerson, individuals should define their place in society by their own internal values. To Emerson, no one should have to rely on external verification from religious, social, philosophical, and political institutions to define their worth and purpose in life. During his time, Emerson was accused of atheistic (and, therefore, blasphemous) tendencies. He advocated the rejection of supernatural rationalism, which is the belief that religious truths can only be verified by historical factuality. Instead, Emerson promoted what many of his contemporaries maintain was a sacrilegious reliance on experiential intuition. In his essay on self-reliance, Emerson argues that intuition constitutes "primary wisdom" in man. He maintains that God himself designed us as vessels of truth. In other words, we can't help but absorb "immense intelligence": after all, we were made to do so. By extension, Emerson argues that whenever "a mind is simple, and receives a d...

Relevance: Henry's speech is relevant for many reasons, not least of all as a model of highly effective rhetorical techniques in action. His use of concession, refutation, appeals to logic and emotion, parallel structure, repetition, metaphors, allusions, and rhetorical questions make his speech a gold mine for analysis of rhetoric. "Speech in the Virginia Convention" is also relevant in that it speaks to the condition of oppressed and subjugated people in general. Though exhorting his audience to actual war, Henry's essential message is that when negotiation has been tried for decades, it is useless to continue using the same method to try to reach resolution; rather, new strategies must be applied. While war or other violent types of military intervention should be considered a last resort, they are in some cases justified. Mood/Tone/Effectiveness in Relation to Speech's Purpose: Since Henry was the only speaker that day in the House of Burgesses to advocate for...

The sum of two numbers is seven. Twice one number is four less than the other number. Which of the following equations does not represent this situation? a.) $2n = 7-n-4$ b.) $2(7-x) = x - 4$ c.) $2x + 4 = 7 -x$ d.) $2n -4 = 7-n$ In this case, we have $n+x = 7$ $n = 7-x \qquad$ Equation 1 And we have, $2n = x-4 \qquad$ Equation 2 If we substitute equation 2 to 1, we get the expression written in b $2(7-x) = x-4$ More over, if the equation 1 is to be $x=7-n$, then we obtain the expression written in a. $2n = (7-n)-4$ $2n = 7-n-4$ Therefore, the expressions written in c and d do not represent the given situation.

Discussions of World War II frequently involve a lot of “what ifs.” In other words, scholars and others enjoy speculating about the outcome of World War II in the event that specific decisions had not been made and specific actions had not been taken. These discussions often center around hypotheticals such as “what if Japan had not attacked American military installations in Hawaii and invaded the Philippine Islands” or “what if Germany had not delayed its invasion of Russia?” Another question involves the absence of American aircraft carriers from Pearl Harbor at the time of the Japanese surprise attack, which crippled the fleet of battleships but left the mobile airbases available to fight in the ensuing war against Japan. Just as hypothetical scenarios involving World War II often revolve around questions about timing and poor (in retrospect) decisions by Axis and Allied leaders alike, many question the importance of the economic strength of the Allies relative to that of the Axis ...

In Fritz Lang's expressionist masterpiece Metropolis, allusions to the Christian Bible can frequently be found. Where the underground workers are stuck in a hellish nightmare of darkness, fire, and endless labor, the citizens of upper Metropolis, particularly those who have access to the Eternal Gardens, are heavenly. These two worlds are split entirely into the workers (proletariats) and city folk (bourgeoisie), all while Joh Frederson (played by the German actor Alfred Abel) acts as a godlike figure that watches over all. In practicing a Judeo-Christian-like faith, these workers are rejecting the inherent godliness of Joh Frederson. By worshipping a higher power, all authority is consequently trumped. Joh Frederson acts godlike in his power, but when the workers replace his power with an actual deity, his power is limited. As most Judeo-Christian religions believe, all men are equal, and all men must answer to God. In this sense, these workers are finding comfort in the idea that...

Make a table of values and sketch the graph of the equation $y = |4 - x|$. Find the $x$ and $y$ intercepts. By using the Property of Absolute Value, $y = |4 - x| \to y = \left\{ \begin{array}{cc} 4 - x & \text{for } x > 0 \\ -(4 - x) & \text{for } x \end{array} \right.$ $ \begin{array}{|c|c|c|c|c|c|c|c|c|c|c|} \hline \text{Let} x & -2 & -1 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8\\ \hline\\ f(x) & -6 & -5 & 3 & 2 & 1 & 0 & 1 & 2 & 3 & 4\\ \hline \end{array} $ To solve for $x$ intercept, we set $y = 0$ $ \begin{equation} \begin{aligned} 0=& 4 - x \\ \\ x =& 4 \end{aligned} \end{equation} $ The $x$ intercept is at $(4,0)$ To solve for the $y$ intercept, we set $x = 0$ $ \begin{equation} \begin{aligned} y =& 4 - 0 \\ \\ y =& 4 \end{aligned} \end{equation} $ The $y$ intercept is at $(0, 4)$

Part 1 of Don Juan Tenorio consists of Acts 1–4. In this section of the play, the plot centers on the bet between Don Juan and Don Luis. Both men are profligate womanizers and excel in the craft of dueling. However, Don Juan's new bet highlights how honor is perceived and defined in a patriarchal system. Our protagonist crows that he can bed both an engaged woman and a novitiate. In a patriarchal system, the honor of a family greatly rests on the purity of its women. As such, Dona Ines exemplifies the epitome of feminine perfection: she is an obedient daughter, and when her father consigns her to a convent, she makes no objections. Her sexual (and, therefore, secular) desires are subsumed under the auspices of patriarchal honor. In the play, female purity not only bequeaths honor to a family, it also crowns a woman's reputation. Thus, any hint of deviancy or indiscretion renders her unsuitable for marriage. However, female desire is approached in very simplistic terms in the pl...

This question is asking about an event that happens in Chapter 13 of The Giver. The chapter begins by telling readers that Jonas is frustrated with his newly developing ability to see color. He is able to see the real color of objects, but he is only able to see it for short periods of time. Then the color returns to its "flat and hueless shade." The Giver tells Jonas that it will be a long time before the color stays constant. Jonas is very upset at the news and frustrated by the unfairness of it. The Giver questions what isn't fair about seeing or not seeing color. Jonas finally admits that the color isn't what's important. He wants the choice. For example, he wants to be able to choose what color to wear. Jonas and the Giver continue to discuss the power of choice, and Jonas eventually weakly admits that having choice wouldn't be safe. People could make wrong choices. This is what Jonas has learned about choice. Not having choices is a safer option than hav...

The decision by the United States to not ratify the Treaty of Versailles led to problems in the world that eventually created tensions. The United States didn’t ratify the Versailles Treaty because some United States Senators were concerned that we might have to get involved in conflicts that weren’t in our best interests. This was required by the charter of the League of Nations which was part of the Versailles Treaty. They asked President Wilson to accept amendments to the charter of the League of Nations which would exempt us from having to get involved in any actions recommended by the League of Nations if we felt these actions weren't in our best interests.  When President Wilson refused to do this, the Senate didn’t ratify the Versailles Treaty. Since we didn’t ratify the Versailles Treaty, we also didn’t join the League of Nations. The League of Nations was created to help prevent conflicts from arising. There were many issues with the League of Nations. One issue was that i...

When the trade deficit decreases due to government policy, domestic investment in the country does not decrease as well. This is because there is an indirect, or inverse, relationship between trade deficit and domestic investment. Conversely, there is a direct relationship between trade deficit and domestic savings. When the deficit decreases, savings decrease but investment does not decrease. The current account is equal to the sum of the trade balance [deficit or surplus] and national income plus debts, and it reflects the indirect relationship between domestic savings and domestic investment. It also reflects the indirect relationship between trade deficit and domestic investment. The current account balance is equal to "the difference between national saving and national investment" (Federal Reserve). Current account balance (deficit or surplus) is used interchangeably with trade balance, indicating either trade deficit or surplus. Consequently, the relationship between t...

The central theme can be expressed in a few different ways. One can be the resilience of the human spirit. In her book, Brooks particularly focuses on female courage. This central theme is mainly conveyed through the character of Anna Frith. You may wish to discuss the events that describe how she manages to save her own child and Mrs. Bradford's illegitimate child. The setting of the story definitely highlights Anna's courage in the face of adversity. Year of Wonders is set in the village of Eyam in Derbyshire, England, in the year 1666. History tells us that the Black Plague assaulted London society in the summer of 1665. More than 15% of the population died during that terrible summer. For more on the plague, please refer to the link below. The dark, sinister setting of the story serves as the backdrop for many of Anna's courageous exploits. An example of this type of setting can be found in Part Two, Chapters Four and Five, which describe Anys' murder and the afterm...

Because Silent Spring is an important scientific study and a passionate call for public policy changes, and deploys skillful writing in service of both those aspects, your evaluation of the author’s relative success or lack of it could apply to any of those dimensions. The question is calling for your personal critique, so, initially, you need to make some decisions about the importance of her goals and identify the ways in which she tries to support them. Silent Spring has gained countless supporters over the years, as most readers are convinced by the wealth of scientific evidence she uses to substantiate her claims that DDT and other chemical pesticides had numerous harmful effects. If you conclude that she did support her claims adequately, you would point out specific cases in which she uses particular kinds of evidence, such as her discussion of the molecular structure of pesticides. Carson also deploys numerous instances of practices and policies that she deems short-sighted, to...

Solve $-4 [x - 2 (2x - 3)] + 1 = 2x-3$ and check. $ \begin{equation} \begin{aligned} -4 [x - 2 (2x - 3)] + 1 =& 2x-3 && \text{Given equation} \\ \\ -4(x-4x + 6) + 1 =& 2x - 3 && \text{Apply Distributive Property} \\ \\ -4x + 16x - 24 + 1 =& 2x-3 && \text{Apply Distributive Property} \\ \\ -4x + 16x - 2x =& -3 + 24 -1 && \text{Subtract $2x$ and subtract } (-24+1) \\ \\ 10x =& 20 && \text{Simplify} \\ \\ \frac{\cancel{10}x}{\cancel{10}} =& \frac{20}{10} && \text{Divide by } 10 \\ \\ x =& 2 && \end{aligned} \end{equation} $ Checking: $ \begin{equation} \begin{aligned} -4 [2-2(2(2) - 3)] + 1 =& 2(2) - 3 && \text{Substitute } x = 2 \\ -4(2-2) + 1 =& 4-3 && \text{Simplify} \\ 1 =& 1 && \end{aligned} \end{equation} $

int (sin (omega))/(cos^3 (omega))d omega To solve, apply u-substitution method. So, let u be: u = cos (omega) The, differentiate u. du = -sin (omega) d omega Since the sine function present in the integrand is positive, divide both sides by -1. (du)/(-1) = (-sin (omega) d omega)/(-1) -du= sin (omega) d omega Plugging them, the integral becomes: = int (-du) / u^3 = int -u^(-3) du To take the integral of this, apply the formula int u^(n+1)/(n+1)+C . = -u^(-2)/(-2) + C = u^(-2)/2+C = 1/(2u^2)+C And, substitute back u = cos (omega) . = 1/(2cos^2(omega)) + C Therefore, int (sin (omega))/(cos ^3(omega)) d omega = 1/(2cos^2(omega)) + C .

Adaptation can be thought of as a set of special characteristics that may allow a living organism to successfully live in a particular environment. Adaptation allows an organism to adjust to the particular set of conditions it is exposed to and survive successfully. An animal may adapt to a different food, something other than the food which is consumed by all the other animals of the region. This adaptation will allow it to consume something that is not eaten by its competitors, thus allowing it to be the most significant consumer of that particular food. An animal may also adapt to consume the same food more efficiently. For example, a bird may adapt by developing a longer beak thus allowing it to consume nectar, ensuring it a dedicated food supply. All the other birds with smaller beaks will be unable to consume the nectar and will be outcompeted. Another adaptation could be a heightened sense of smell that may allow an adapted animal to find food faster than its competitors. Simila...

Both of these events marked political watersheds for the Democratic Party. The Kansas-Nebraska Act was the result of a collision between several political forces, all of which were embodied to one degree or another in Illinois senator Stephen Douglas, a Democrat. On one hand, Douglas promoted western expansion, a major political force, by attempting to open the territories of Kansas and Nebraska to settlement. He hoped that a railroad could be constructed that linked Chicago to the West Coast and that it would pass through Kansas and Nebraska. But Southern politicians hoped that such a railroad would originate in the South, and Douglas tried to win their support (or at least not alienate them) by potentially opening the region to slavery by allowing settlers to determine the legality of the institution there. This practice had been established in New Mexico and Utah, which were part of the Mexican Cession, but since Kansas and Nebraska were part of the Louisiana Purchase, Douglas's...

The diction and speed in the sentence are used to create a sense of anxiety, urgency, and movement. Lyman's description of Henry's state—moving and yet unmoving—is replicated in the reader as they complete the sentence. The tone is also urgent and somewhat helpless. Louise Erdrich achieves this by using short words and a long sentence length. These two things combined create the feeling of movement as a reader moves from one word to the next. The longest word in the sentence only has two syllables. The entire forty-one–word sentence only has seven words that are two syllables. It's a sentence meant to be read quickly so that the reader feels what Henry is feeling and what Lyman is observing—a sense of motion, anxiety, and urgency. Lyman is distressed over the change in Henry, but he can't do anything about it. Henry is experiencing these things in his own head, which is a place that Lyman can't reach him. Even when he tries, the attempt ultimately fails, and Henry d...

h(x) = 1/4sinh(2x) - x/2 To take the derivative of this function, refer to the following formulas: d/dx(u +-v) = (du)/dx+-(dv)/dx d/(dx)[sinh(u)]=cosh(u)*(du)/dx d/dx(cu)=c*(du)/dx d/dx(cx)=c  Applying them, h'(x) will be h'(x)=d/dx[1/4sinh(2x) - x/2 ] h'(x)=d/dx [ 1/4sinh(2x)]- d/dx(x/2) h'(x)=1/4d/dx[sinh(2x)] - d/dx(x/2) h'(x)=1/4* cosh(2x)*d/dx(2x) - 1/2 h'(x)=1/4*cosh(2x)*2 - 1/2 h'(x)=1/2cosh(2x)-1/2  Therefore, the derivative of the function is h'(x) =1/2cosh(2x)-1/2 .

In the book, Jody finds a new, red pony waiting for him in the barn one morning. However, even before he manages to get used to the idea of a pony in his life, his no-nonsense father, Carl, gives him an ultimatum. Carl orders Jody to carefully care for the pony, or he will sell it. Later, Jody finds out how the pony was acquired. According to Billy, Carl had bought the pony at a sheriff's auction. A traveling circus had amassed too many debts and had gone out of business in Salinas, so the sheriff had taken it upon himself to sell what remained of the circus' properties at the auction. Obviously pleased with the horse, Jody then asked if there was a saddle. Billy then takes Jody to the saddle-room; this is where he takes down a saddle of red leather for Jody. So, along with the pony, Jody receives a shining, red leather saddle to use when he rides.

An outline should be a detailed synopsis of the plot, following it in the sequence it unfolds and making sense of how the story is structured. I would go from the opening, which introduces the idea that something is going to happen, move to the fact that it has rained for seven years nonstop on Venus, and then move to the idea that the rain is about to stop and the sun to come out for an hour. Second, I would introduce the facts about Margot, the protagonist, especially that she is the only child in the class of expectant children who has ever seen the sun, that she is depressed by living on a rainy planet, and that she doesn't fit in with the other children, who are jealous of her for her knowledge of the sun. Finally, I would move to the high point of the story, in which the children lock Margot in the windowless closet, enjoy the thrill of an hour of sunshine, and return ashamed to release Margot from her prison. I would advise putting the opening about the rain and sun under th...

Hamlet, the prince of Denmark, is one of Shakespeare's most famous tragic figures, is one of the many that gives lengthy, poetic, and often insightful monologues. In the beginning of Act III, scene i, Hamlet gives what is perhaps the most famous monologue in all of Shakespeare's work, in which he ponders suicide: "To be, or not to be––that is the question." As the monologue continues, Hamlet reflects on the many things that make his life, and life in general, unpleasant. For who would bear the whips and scorns of time, The opressor's wrong, the proud man's contumely The pangs of déspised love, the law's delay, The insolence of office and the spurns That patient merit of the unworthy takes When he might his quietus make With a bare bodkin? (Act III, sc. i, 69-76) Here, Hamlet gives a list of the many cruelties and injustices of life. First, Hamlet describes the way men age and the way their bodies and minds deteriorate over time. All humans are destined to ...