Notes

mattbrady's answer is correct. The Sun is a yellow main-sequence star near the middle of its life, so it is currently in the process of converting hydrogen into helium by fusion. In several billion years it will run out of hydrogen; when that happens, it will expand dramatically into a  red giant (most likely engulfing all the inner planets, including Earth), and begin to fuse helium into carbon. Well before that, however, the Sun will partially deplete its hydrogen reserves. If astronomers took precise enough spectral measurements over a long enough period of time (unlikely, but impossible---if we can measure gravity waves, we might just be able to do this), they would observe very subtle changes in which the quantity of hydrogen detected slightly decreased and the quantity of helium detected slightly increased. Within a human lifetime or even the lifetime of a civilization, this effect would be very small---about one one-millionth of the Sun's total hydrogen has been used up...

People in the penumbra of the Moon's path during an eclipse see only a very slight, partial eclipse. There are three types of lunar eclipses, and depending on where you are in the world during an eclipse event, you may see one of these variations. The first type of eclipse is a total eclipse. This is where the shadow, or umbra,  of the Earth entirely passes over the moon. A partial eclipse occurs when only some of Earth's umbra passes over the moon. A  penumbral  eclipse occurs when just a little bit of Earth's umbra passes near or over the Moon. A penumbral eclipse may be barely noticeable.  Strictly speaking, people are not  in  the penumbra or umbra of Earth but may observe these variations of shadows from Earth. 

Historically, European interaction with the non-western world has often been colored by ethnocentrism, exploitation, and violence. During the Crusades, the Latin Church sanctioned a series of religious wars from the 11th to the 16th centuries, seeking to recapture Christian territory, defend Christians in non-Christian lands, gain political and territorial advantage, and combat paganism. The capture of Jerusalem from Islamic rule can be seen as the first experiment in European colonialism. Other lands and properties were also seized from pagans on religious grounds. These events resulted in lasting mistrust between the Latin Church and the Islamic and Orthodox religions. However, another consequence of the Crusades was increased trade and contact between Western Europe and the Islamic world, leading, some argue, to improved perceptions of Islamic culture among Europeans. Western Europe’s interactions with non-western Empires during the early modern period (late 15th century to the late...

The Economic Order Quantity (EOQ) is the optimal solution for how much product to order, assuming that you are buying from a vendor and all orders will be filled completely and immediately. For producing a product, the optimal solution would actually be the Economic Production Quantity (EPQ), but in this case we couldn't determine that because we didn't know the production rate. For an order/setup cost of K, a demand rate of D, a holding cost of F, and a production rate of P, these are the equations for each quantity: EOQ = sqrt(2DK/F) EPQ = sqrt(2DK/(F(1-D/P)) Thus, the two quantities differ only by a ratio of 1/sqrt(1-D/P). We are given that the demand rate is 80% of the production rate, so D/P = 0.8, and 1/sqrt(1-D/P) = 2.24. Therefore, we are not holding enough of the product, by a factor of 2.24. In other words, we are only holding 44.7% of the quantity we should be. This is because the production rate is only slightly faster than the demand rate, so we can barely keep up ...

`3^(x+4) = 6^(2x-5)` To solve, take the natural logarithm of both sides. `ln (3^(x+4)) = ln (6^(2x-5))` To simplify each side, apply the logarithm rule `ln (a^m) =m*ln(a)` . `(x+4)ln(3) = (2x-5) ln (6)` `xln(3)+4ln(3) = 2xln(6) - 5ln(6)` Then, bring together the terms with x on one side of the equation. Also, bring together the terms without x on the other side of the equation. `xln(3) - 2xln(6) = -4ln(3) -5ln(6)` At the left side, factor out the GCF. `x(ln(3) - 2ln(6)) =-4ln(3) -5ln(6)` And, isolate the x. `x = (-4ln(3) - 5ln(6))/(ln(3)-2ln(6))` `x~~5.374` Therefore, the solution is `x~~5.374` .

World War I changed Europe in several ways. One change was that it brought an end to several empires. After World War I ended, the Empire of Austria-Hungary and the Ottoman Empire disappeared. Much of the Empire of Austria-Hungary was divided into several new nations based on the concept of self-determination. Another change that occurred was that in some countries people wanted less to do with world affairs. In Great Britain and France, many people wanted to avoid another costly war. World War I devastated so much land and killed so many people that some countries in Europe tried to prevent another war from occurring. In part because of the Great Depression and in part because of the damage, death, and destruction caused by World War I, some European leaders ignored aggressive actions by Germany, Japan, and Italy in the 1930s. The leaders of Great Britain and France hoped appeasing Adolf Hitler would prevent another war from occurring. However, that didn’t work. Many European people a...

Early in Gary D. Schmidt's story Trouble, while Franklin is still in the hospital prior to his death, Henry learns that his Whittier Academy crew team will be competing in the Cape Ann Coastal Invitational against the very first crew team from Merton. Merton happens to be the town Chay Chouan is from, the boy who was convicted of accidentally hitting Franklin in his truck. When Henry begins preparing for the race that day on the Charles River , he sees that one of the crew team members from Merton he is racing against is Chay's younger brother . When Henry walks up to the dock after his Whittier team returns from warm-ups, Sanborn points out to Henry that the first rower on the Merton crew team is Chay's younger brother. Henry then notices the rest of the Chouan family, including Chay, in the the crowd, ready to cheer on the young Chouan. This troubling news disturbs Henry so much he makes a mistake that nearly costs the Whittier team the race.   At one point during the ...

he upper control limit is 3 standard deviations above the expected number of defects, while the lower control limit is 3 standard deviations below. When we know the proportion that will not have defects is 0.975, the proportion that will have defects is just 1 minus that: p = 0.025. For an np chart, we calculate these figures in terms of actual numbers of items; but the process is basically the same as for a p chart where we only calculate them in terms of proportions of items (the only difference is you multiply by n ). So the expected number of defects per sample is: `np = (450)(0.025) = 11.25` The standard deviation is given by: `sigma = sqrt{n p (1-p)} = sqrt{450(0.025)(0.975)} = 3.312` Then, we can get the upper and lower control limits: `UCL = np + 3sigma = 11.25 + (3)(3.312) = 21.19` `LCL = np - 3sigma = 11.25 - (3)(3.312) = 1.31`` ` If the process is under control, the number of defects should be between these two values in each sample. The total amount produced turns out not ...

Better than it had been before, but still not all that great. When they established the Raj, the British introduced a lot of Western ideas and institutions into India, some good, some bad. One of the good ones was women's rights, and the British quickly moved to end a number of cultural practices in various regions of India that were particularly oppressive to women. A famous example was the burning of widows; this was never all that common, but it was something certain Hindu sects did. The British banned it. They also instituted age minimums for marriage; previously, girls who hadn't even entered puberty could be pressed into marriage with adult men. In 1891, the British raised the minimum age to 12, so that girls would at least be pubescent before they could be married. The British instituted some reforms in the property and inheritance system, so that women could own and inherit property in some circumstances---but there was still a substantial bias toward men. The Raj also ...

Willy Loman lives in New York City. According to the brief paragraph preceding Act One: The action takes place in Willy Loman's house and yard and in various places he visits in the New York and Boston of today.  In the opening of Act One, Willy has returned home. He tells his wife that he wasn't able to make it past Yonkers. I suddenly couldn't drive any more. The car kept going of onto the shoulder, y'know? Yonkers is a suburb of New York. It is only about two miles north of the northernmost past of Manhattan. Willy was just starting on a business trip to cover his New England territory. The fact that he was still in New York City shows that this is where he lives. He is obviously getting too old to continue covering such and extensive territory as Maine, Vermont, New Hampshire, Massachusetts, Connecticut and Rhode Island, which make up New England; but when he asks to be transferred to a territory closer to home, it leads to an argument with his boss that results in ...

Deoxyribonucleic acid (DNA) is found in the membrane-bound nucleus within a eukaryotic cell. It contains the genetic blueprint of the organism and contains the instructions to produce all the necessary proteins for life to continue. The central dogma is DNA-RNA-Protein. This describes the flow of information from the DNA in the nucleus, to RNA which copies the genetic code and can travel out to the cytoplasm, where the genetic code can be translated into proteins at the ribosomes. DNA is a double-stranded molecule in the shape of a double helix and contains a sugar-phosphate backbone with complementary base-pairs of nucleotides in the center, held together by hydrogen bonds. The bases are adenine, thymine, cytosine and guanine--with adenine and thymine forming pairs and cytosine and guanine forming pairs. The mitochondria is an additional location for DNA to be found in the eukaryotic cell. At fertilization, an egg cell contains mitochondrial DNA while the sperm will not contribute an...

I assume that you are talking about Arthur Costa's levels of questioning, as discussed in works like Developing Minds: A Resource Book for Teaching Thinking (see third link below). According to Costa's ideas, a level one question asks students to retrieve facts or details from a text. The student doesn't have to interpret anything. The student is merely asked to find the desired information. Here are examples of a level one question: "What does Mrs. Ttt say the name of her planet is?" "Who kills the captain?" Level two questions ask students to make sense of the information that they gather from the text. These questions often include words like why or how. They might ask the reader to analyze, compare, contrast, infer, or explain.  They differ from level three questions in that they don't ask students to make generalizations, judgments, or evaluations that force them to go beyond the text. They don't ask the reader to speculate, hypothesi...

`` The initial displacement of the car on the x-axis is  2.21 km (East). The car then turns left bearing at an angle of 65.5 degrees from East, to now travel NE. It then travels 1.78 km in that new direction. To find the negative displacement on the x-axis following this change of course, we can use the trigonometric relation cos (theta) = A/H where x is the angle between the adjacent side A of the triangle and the hypotenuse H of the triangle. We already have theta = 65.5 degrees and H = 1.78 km Solving for the length A, we obtain the positive displacement on the x-axis. A = cos (65.5) x H = 0.41469 x 1.78 = 0.7382 km Adding this from the initial displacement of the car on the x-axis we find that the final resulting net displacement on the x-axis is. 2.21 km + 0.7382 km = 2.9482 km The net displacement of the car on the x-axis is 2.9482 km.

After the switch is closed, the charge on the capacitor decreases as `Q(t)=Q_0e^(-t/(RC))` The initial energy of the capacitor is  `U=Q_0^2/(2C)` So we want to solve for a time such that `Q(t)^2/(2C)=1/2 Q_0/(2C)` `2= e^((-2t)/(RC))` `t=(RC ln(2))/2`

There are four main types of tissues present in the human body. They include: epithelial, muscular, nervous, and connective. Epithelial tissue covers the body surface and is the lining for most internal cavities. This includes your skin and linings of your mouth and nose, for example. The function of epithelial tissue is protection, secretion, absorption, and filtration. Some diseases that affect epithelial tissue include eczema, psoriasis, and asthma. Eczema affects the epithelial cells of the skin by causing inflammation represented by rashes. Connective tissue is the most abundant of the tissue types. The function of connective tissue is support and protection. Some examples of connective tissues are fat tissue, cartilage, bone, and blood. A disease that affects connective tissue is arthritis. Rheumatoid arthritis, for example, is when immune cells attack and inflame the membrane around joints. Muscle tissue is, as its name suggests, muscles. There are three types of muscle tissue. ...

In both the middle colonies and the southern colonies, farming was an important economic activity. However, there were some differences between these regions. In the southern colonies, farming was the main economic activity. There was very little industry in the southern colonies. The soil was fertile, and the climate was suited for farming. In the southern colonies, farmers grew tobacco, indigo, and rice. Many slaves were used on the large farms in the South. In the middle colonies, there were a variety of economic activities. There was more manufacturing in the middle colonies than in the southern colonies. Farming was important, but it wasn’t the only economic activity. Farmers in the middle colonies were known for the grains they grew. Wheat was one crop that was grown and sold. The middle colonies are often called “the breadbasket colonies” because of the grain that was grown in this region. Slavery did exist in the middle colonies. However, since the farms in the middle colonies ...

 The encounter between the two ghosts takes place in Chapter Three of "The Canterville Ghost." In this scene, it is late at night and all members of the Otis family are asleep in bed. The ghost is planning to frighten Washington Otis but, as he makes his way towards the boy's room, he is confronted by a terrible sight: Right in front of him was standing a horrible spectre, motionless as a carven image, and monstrous as a madman's dream! After using heavy description to portray this other ghost, Wilde quickly switches his tactic by employing humour to describe the Canterville ghost's reaction: Never having seen a ghost before, he naturally was terribly frightened, and, after a second hasty glance at the awful phantom, he fled back to his room. This use of humour is effective in lightening the mood of the story. That the Canterville ghost has never seen a ghost before is also an example of irony, used here for comic effect. Wilde further adds to the humour when the ...

Andrew Clements's  Frindle tells the story of fifth grader Nick Allen and his attempt to create a new word. Nick is inspired to invent a word when he asks his strict English teacher, Miss Granger, where the words in the dictionary come from. When she assigns her students an essay based on the question, Nick uses the opportunity to invent the word "frindle," meaning pen. The word grows in popularity, first with Nick's friends, then throughout his entire school, and soon enough the word is in use throughout his town. His teachers and principal consistently try to stop the spread of the word, but soon realize it is beyond his control. The climax of the story occurs when Nick's new word becomes so famous that national media outlets begin asking to interview him. This realization inspires Nick's father to sell the rights to the word and invest the earnings in Nick's college fund. Nick's world returns to normal after this; his teachers and school administrat...

Appeal to fear is a technique propagandists use to make people forget about the truth and instead get so scared that they believe what the person is saying. Squealer is Napoleon’s propagandist. That means he is charge of getting the animals so confused that they do not know what to believe, so they believe him. He gives speeches to the animals to explain what Napoleon is doing and try to convince the animals to go along with Napoleon's plans. Appeal to fear is one of Squealer’s favorite techniques. He tells the animals that Jones will come back if they do not go along with Napoleon. He distracts the animals from what is really happening. A good example of this is when the other animals discover the pigs are consuming the milk and apples. By way of explanation, Squealer says, "It is for your sake that we drink that milk and eat those apples. Do you know what would happen if we pigs failed in our duty? Jones would come back! Yes, Jones would come back! Surely, comrades," cr...

`5^(x-4)=25^(x-6)` To solve, factor the 25. `5^(x-4)=(5^2)^(x-6)` To simplify the right side, apply the exponent rule `(a^m)^n = a^(m*n)` . `5^(x-4)=5^(2*(x-6))` `5^(x-4)=5^(2x-12)` Since both sides have the same base, to solve for the value of x, set the exponent at the left equal to the exponent at the right. `x-4=2x-12` `x-2x=4-12` `-x=-8` `x=8` Therefore, the solution is `x=8` .

Taylor series is an example of infinite series derived from the expansion of `f(x)` about a single point. It is represented by infinite sum of `f^n(x)` centered at `x=c` . The general formula for Taylor series is: `f(x) = sum_(n=0)^oo (f^n(c))/(n!) (x-c)^n` or `f(x) =f(c)+f'(c)(x-c) +(f^2(c))/(2!)(x-c)^2 +(f^3(c))/(3!)(x-c)^3 +(f^4(c))/(4!)(x-c)^4 +...` To apply the definition of Taylor series for the given function `f(x) = e^(-4x)` centered at `x=0` , we list `f^n(x)` using the derivative formula for exponential function: `d/(dx) e^u = e^u * (du)/(dx)` . Let `u =-4x` then `(du)/(dx)= -4` . Applying the values on the derivative formula for exponential function, we get: `d/(dx) e^(-4x) = e^(-4x) *(-4)`                  `= -4e^(-4x)` Applying `d/(dx) e^(-4x)= -4e^(-4x)` and `d/(dx) c*f(x) = c d/(dx) f(x)`   for each` f^n(x)` , we get: `f'(x) = d/(dx) e^(-4x)`            `= -4e^(-4x)` `f^2(x) = -4 *d/(dx) e^(-4x)`             `= -4*(-4e^(-4x))`             `=16e^(-4x)` `f^3(x) =...

In the first few words of John Updike's story "A Sandstone Farmhouse," details of Joey's physical health and his emotional nature are included as he is described as "asthmatic" and "sensitive." Joey is physically and emotionally frail. The family moves from the town of Olinger to the farmhouse where his mother was born, but the old house is cold and drafty, a condition that causes thirteen-year-old Joey to be ill frequently, another negative condition added to his alienation from the former life he had enjoyed with friends. Joey makes several trips with his mother on the bus to the farmhouse before they move in, as she wants to plant things. However, Joey feels humiliated as they drag shovels onto the bus and the driver stores them in the luggage area. Yet, after they trudge down the dirt road, Joey feels somehow "heroic in the periodic trudge," as he is determined to win back his mother's love from the place that she apparently loves...

Romeo impulsively moves from being the courtly lover to becoming the impetuous, impulsive lover and fighter, and then the depressed lover. Act I Early in the play Romeo reacts emotionally to the news that his beloved Rosaline is going to a convent as he speaks dramatically in oxymorons: "O heavy lightness! serious vanity!" (1.1.168). But in a few scenes, he is excited again, and becomes instantly in love at his first sight of Juliet: Oh, she doth teach the torches to burn bright! It seems she hangs upon the cheek of night Like  a rich jewel in an Ehiop's ear-- Beauty too rich for use, for earth too dear! (1.5.43-45) After seeing Juliet at the Capulet masque, Romeo rushes toward her when he finds a chance to speak with her, recklessly disregarding the fact that she is of the opposing family:  If I profane with my unworthiest hand This holy shrine,... (1.5.87-88)  and he even boldly asks to kiss her: Then move not while my prayer's effect I take. Thus from my lips by th...

The first section of the Declaration of Independence essentially stated the purpose of government. Borrowing heavily from John Locke's Second Treatise on Civil Government (1689), the document laid out what is often called the "social contract" theory of government. Men are created equal, the Declaration says, and are endowed with "certain unalienable rights." These rights include "life, liberty, and the pursuit of happiness," and the purpose of government is to protect and preserve these rights. When governments fail to do so, or become "destructive" of these rights, then it is the right of the people to "alter or abolish it." The Declaration went on to give a host of examples of the ways in which King George III had, in fact, acted in violation of these rights, a "long train of abuses," that, according to the revolutionaries, justified revolution and colonial independence from Great Britain. In short, the British governm...

The name "Diana Moon Glampers" is full of allusion and allows a great deal of interpretation that can enrich the meaning of Vonnegut's "Harrison Bergeron."  First, the name as a whole sounds funny and presents a stark contrast within itself. Diana is a lovely, flowing name that means heavenly, divine, or perfect. But Glampers is a clumsy, ordinary, even ugly name. The contrast corresponds to the society the Handicapper General works for; it is ostensibly perfect because all people are finally equal. In reality, it is a very ugly society that removes everything beautiful its citizens are capable of. The wry humor of the name is menacing in the way that the final joke of the story is more sickening than cheering. The name Diana is an allusion to the ancient Roman goddess of the moon and the hunt. Diana Moon Glampers is a goddess in the sense that she has supreme power over the subjects of the United States in 2081. She also proves to be an excellent hunter when sh...

Orwell’s viewpoint is that revolutions are often controlled by individuals who manipulate the masses into following an ideology when all they really want is power.  Although the story is an allegory of the Russian Revolution, it can represent any revolution.  Many revolutions follow this pattern. In the story, Old Major is the visionary. He tells the animals about a perfect world where they are in control of their own destiny.  He says that the humans are exploiting them.  They do not need people. "Man is the only creature that consumes without producing. … Yet he is lord of all the animals. He sets them to work, he gives back to them the bare minimum that will prevent them from starving, and the rest he keeps for himself.” (Ch. 1)  Then Old Major dies.  That might have been the end of it, except that the animals are not fed and they decide to take matters into their own hands and get their own food.  The humans try to stop them, and the animals fight back.  A revolution is born. ...

In Chapter 11, Jem and Scout are subjected to the racial slurs and derogatory remarks from the community's most prolific racist, Mrs. Dubose. Mrs. Dubose tells the children, "Your father's no better than the niggers and trash he works for!" (Lee 135). Mrs. Dubose is obviously prejudiced against black people and disagrees with Atticus' decision to defend Tom Robinson. Another quote that reflects a prejudiced mindset is found in Chapter 23 when Alexandra tells Scout that she is not allowed to play with Walter Cunningham Jr. When Scout asks her aunt why, Alexandra says, "Because---he---is---trash, that's why you can't play with him. I'll not have you around him, picking up his habits and learning Lord-knows-what. You're enough of a problem to your father as it is" (Lee 301). Alexandra's comments reflect her prejudiced mindset towards individuals of a lower social class. In Chapter 25, Scout mentions that the community of Maycomb lost int...

The three main branches of modern Christianity are Catholic, Protestant, and Eastern Orthodox. The Catholic Church is the oldest; Catholicism dates its founding to the original church founded by Jesus, but reliable historical records only go back as far as the Council of Nicea in 325 AD. Catholicism is at least as old as that, and probably older. Catholicism is the world's largest religious sect, and is particularly prevalent in Latin America. The Catholic Church is headed by a single Pope, who lives in the autonomous region of Vatican City, legally defined as its own country separate from Italy, which completely surrounds it. The Eastern Orthodox Church emerged in the 4th century and is centered in Eastern Europe, especially Greece and Russia. The Orthodox Church does not have one single leader, but it does have a number of high-level authorities known as Holy Synods. Theologically there are not many differences between the Catholic and Orthodox Church; it's more of a differen...

The United States did not suffer any immediate aftermath for rejecting the Versailles Treaty and the League of Nations.  The United States signed a separate peace treaty with German in 1921, thus formally ending the war.  The United States was unable to alter the level of blame leveled at Germany since the chief negotiator, Woodrow Wilson, contracted Spanish Influenza while in Versailles--this gave the British and French more power at the treaty table as they could always point to their losses and say that they deserved reparations more.  As news leaked from the treaty conference that the victorious Allied powers were using the war as an excuse to add to their already-impressive empires, the American people also lost patience with the treaty negotiations, thus giving Senate Republicans more power to go against Wilson and his internationalism.  The United States started to suffer for its isolationism during the 1930's.  Since the U.S. did not join the League of Nations, there was no...

Antony was clearly the more effective speaker. It was his speech that drove the gathered crowd into a frenzy. At the end of his oration, the crowd had become enraged at what, he made them believe, had been a great injustice against their murdered leader. They immediately sought retribution and were intent on ripping the conspirators apart, as the following extract clearly indicates:  Second Citizen We will be revenged. All Revenge! About! Seek! Burn! Fire! Kill! Slay! Let not a traitor live! Brutus adopted a rational approach in which he explained the purpose behind Caesar's assassination. He convinced the crowd that Caesar's death was necessary for the survival of Rome and the good of all its citizens. The crowd was satisfied with his clinical, matter-of-fact and commonsense explanation and believed what he said. Antony, conversely, appealed to the crowds' emotions. He was passionate and drew them in by making them believe that they had suffered a deep and personal loss wh...

For the given integral problem: `int (x^3+3x-4)/(x^3-4x^2+4x)dx` , we may simplify  by applying long division since the highest degree of x is the same from numerator and denominator side. `(x^3+3x-4)/(x^3-4x^2+4x) = 1+(4x^2-x-4)/(x^3-4x^2+4x)` . Apply partial fraction decomposition on the expression `(4x^2-x-4)/(x^3-4x^2+4x)` . The pattern on setting up partial fractions will depend on the factors of the denominator. For the given problem, the factored form of the denominator will be: `(x^3-4x^2+4x) =(x)(x^2-4x+4)`                             `=(x) (x-2)(x-2)`  or `x(x-2)^2` For the linear factor `(x)` , we  will have partial fraction: `A/x` For the repeated linear factor `(x-2)^2` , we will have partial fractions: `B/(x-2) + C/(x-2)^2` . The rational expression becomes: `(4x^2-x-4)/(x^3-4x^2+4x) =A/x +B/(x-2) + C/(x-2)^2` Multiply both side by the `LCD =x(x-2)^2` : `((4x^2-x-4)/(x^3-4x^2+4x)) (x(x-2)^2)=(A/x +B/(x-2) + C/(x-2)^2)(x(x-2)^2)` `4x^2-x-4=A*(x-2)^2+B*(x(x-2)) + C*x` We ap...

As the poem begins, the setting of the desolate, frigid, former site of the persona's childhood home sets, in the first two stanzas, the tone for a poem expressive of the feelings of shame, guilt and regret. Maria feels that Henry duped her into a relationship that seduced her away from her familial obligations. She left "with him to roam" and believed her "days in joy would roll." Ultimately, Henry rejected her; she believes it is because her father "was poor/No golden store/ Had he, no earthly treasure."  She recognizes that the only valuable thing her father had was his love for her, his daughter. Maria is guilt-stricken when she observes "I see his tears/ I hear his groans of sadness" and reflects on how after his death, her guilt over abandoning him haunts her. As the poem closes, Maria is alone, having been abandoned by her false lover for "a wealthier bride" and her father's death.  She is "An outcast hurl’d/From all...

One lesson the authors learned about prejudice and homelessness also happens to be a main theme of this non-fiction book, and it has to do with social class differences. There is a common misconception that poverty and wealth are a natural dividing line between people, and that across this line, common ground does not nor cannot exist. Ron Hall and his wife Deborah are on the rich side of the line. Denver Moore is on the poor side.  When their lives collide and an unlikely friendship forms, Ron learns (with Deborah's help and prompting) that many people harbor prejudices against the poor, himself included. Before working at the soup kitchen, Ron Hall, an art dealer, would never have assumed that a man like Denver Moore would have anything valuable to offer him. He would have assumed that Denver, who is homeless, lacked a proper education and common experiences. To Ron, this meant he also lacked the kind of life-wisdom Ron had grown accustomed to in dealing with mostly rich people. ...

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

We are asked to graph the function `y=log_3x+4 ` : The graph is a translation of the graph `y=log_3x ` up 4 units. Some points on the graph: (1/27,1),(1/9,2),(1/3,3),(1,4),(3,5),(9,6) The domain is x>0 and the range is all real numbers. There is a vertical asymptote at x=0, and the function is increasing and concave down on its domain.  The graph:

Hello! I agree with your answer to the part a ), the only possible series is  `U_n = 4*3^(n-1).` The question b ) becomes simple if we recall the formula of the sum of `N` terms of a geometric progression `U_n` with the common ratio `r:` `sum_(n = m)^(m+N) U_n = ((U_((m+N))) - (U_m))/(r-1).` I give the more general form of the common formula because sometimes there is a confusion related with the starting index of the sum (0 or 1). In this from, the sum is ((the last summed up term of the series) - (the first summed up term of the series)) above (the common ratio - 1). We know already that  `U_n = 4*3^(n-1),`  `m = 1` and `N = 20.` Therefore  `U_(m+N) = U_21 = 4*3^(21 - 1) = 4*3^20`  and the sum is equal to `(4*3^20 - 4*3^0)/(3 - 1) = 4/2 * (3^20 - 1) = 2*(3^20 - 1).` Hence the statement we need to prove is true and   K = 2 . This is the answer.

Sarah Orne Jewett uses Sylvia's interest in birds to advance the plot when we learn that the visiting hunter's priority is locating the nest belonging to the white heron he's seen in the woods.  On the night he arrives, Sylvia's grandmother tells him that "'the wild creatur's counts her one o' themselves.  Squer'ls she'll tame to come an' feed right out o' her hands, and all sorts o' birds.'"  The hunter didn't even attend to the personal information Mrs. Tilley shared because of "his eager interest in something else.  'So Sylvy knows all about birds, does she?' he exclaimed."  Thus, Sylvia's knowledge of the birds makes her useful to the hunter, and so he prolongs his visit with her and her grandmother in an attempt to put her knowledge to use for him.  Were it not for her interest in and knowledge of the birds, he would likely not have stayed with them as long as he does.  He proceeds to charm her...

The verbal exchange between the prince of Morocco and Portia occurs at the beginning of Act ll, Scene 1. The prince has obviously arrived to chance his luck to win Portia's hand by participating in the lottery her deceased father concocted. The prince blathers on about his greatness and asks Portia not to discriminate against him because of his darker complexion. He comes across as quite boastful and conceited. Portia's retort encourages him. She informs the prince that her choice for a husband is not limited only to what she might see as attractive but that the lottery bars her from making any choice whatsoever. In this sense, then, the prince has as much a chance as any of her suitors. In response, the prince thanks Portia for her kind remark and begins bragging again about his prowess as a soldier and the quality of his courage—all skills he would use to win Portia's heart. He alludes to characters in Greek mythology when making the point that just as Hercules might lose...

Since we make them for $0.10 and sell them for $2.00, each bottle we sell will make us a profit of $1.90. But since we can only resell them later for $0.05, each bottle we make but do not sell will force us to take a loss of $0.05. We don't know how many we will sell, but we know that it is normally distributed with a mean of 10,000 and a standard deviation of 1,000. The goal is to find the amount of production that will maximize our expected profit. To do this, we want to find the point where the marginal expected profit from making another bottle is zero, which is the point where the probability of selling that bottle and making $1.90 is exactly balanced by the probability of not selling that bottle and losing $0.05. Thus, we know that the following holds, at the desired number of bottles n , with p(n) being the probability of selling the n th bottle: `p(n) (1.90) - (1-p(n)) (0.05) = 0` `1.90 p(n) + 0.05 p(n) - 0.05 = 0` `1.95 p(n) = 0.05` `p(n) = 0.05/1.95 = 0.0256` This is esse...

It sounds like the phrase in your question is related to the aphorism, "Guns don't shoot people; people do." Both this phrase and the simpler, "Guns never shoot," may be used in discussions about laws regulating the ownership, handling, and use of guns. The argument that "guns don't shoot people" is championed by organizations like the National Rifle Association in the United States as a means of emphasizing responsible gun ownership. You see, a gun on its own is an inanimate object. A gun cannot shoot anyone or anything without intentional manipulation by a person. Of course, there are accidents where people do not mean to fire, or even drop their weapon and cause a misfire, which may result in injury or death. The act of shooting, most often, comes from a person who is handling the firearm. Phrases like those mentioned above are intended to draw a distinction between the gun itself, which is not an inherently bad thing, and the actions of people ...

It's a little bit difficult to give a concrete answer to your question, because anatomy can vary from person to person, and not all of the muscle tissues of the human body can be neatly differentiated from one another. Even physicians and muscle specialists disagree as to the precise count of muscles in the body. That being said, here are some estimates: The scientific community is generally in agreement that there are about six-hundred and forty  skeletal muscles in the human body. These are the muscles which connect to and lie alongside bone and help us perform activities like walking, lifting, and balancing. There is also  cardiac  muscle-- the heart-- and  smooth  muscle, like the muscles of our digestive tract. Combining these three types of muscle, an estimated total of muscles in the human body could be as high as nine-hundred. Unfortunately, this estimate doesn't account for lots of the teeny-tiny muscles that are so difficult to count but play an important part in our...

An author uses direct characterization to tell his/her readers what a certain character is like. For example, an author can state that the hero in his novel is fearless, stubborn, or even meticulous. In direct characterization, the author directly reveals to us the personality of the character by using adjectives and other descriptive words and phrases. For example, we are told that the king in the story is "semi-barbaric" or "barbaric" in nature. He is also said to be a man of "exuberant fancy," with "an authority so irresistible that, at his will, he turned his varied fancies into facts." He is introspective, a man "greatly given to self-communing." Similarly, his daughter is directly characterized as having the same barbaric nature; she is also "intense and fervid" (passionate) in temperament. In indirect characterization, an author reveals what a character is like through an account of his/her thoughts, actions, speech, fa...

In Volume II, Chapter 3, when Miss Manette testifies about the prisoner's line of work, this is what she says: "He told me that he was travelling on business of a delicate and difficult nature, which might get people into trouble, and that he was therefore travelling under an assumed name." She goes on to explain that the prisoner's business requires him to travel often between France and England. So, although she doesn't say it directly, Miss Manette's testimony hints that the prisoner was a spy . By saying that he traveled under a fake name, that his work was secret and delicate and difficult, and that his work might get people into trouble, Miss Manette is making it pretty clear that the prisoner is working as a secret agent. The fact that she feels kindness and pity for the prisoner makes it hard for her to say anything that might damage his reputation, which probably explains why she didn't just come right out and say what she thought the prisoner...

From the table of power series, we have: `e^x = sum_(n=0)^oo x^n/n! `      `= 1+x+x^2/(2!)+x^3/(3!)+x^4/(4!)+x^5/(5!)+` ...  To apply this on the given integral `int_0^1 e^(-x^2)dx` , we replace the "`x` " with "`-x^2` ". `e^(-x^2)= sum_(n=0)^oo (-x^2)^n/(n!) `             ` =sum_(n=0)^oo ((-1)^n*x^(2n))/(n!) `           `= 1/(0!) -x^2/(1!)+x^4/(2!) - x^6/(3!) +x^8/4!-x^(10)/(5!)+x^(12)/(6!)` -...           `= 1 -x^2 +x^4/2-x^6/6 +x^8/24-x^(10)/120+x^(12)/(6!)-` ... The integral becomes: `int_0^1 e^(-x^2)dx =int_0^1 [1 -x^2 +x^4/2-x^6/6 +x^8/24-x^(10)/120+x^(12)/720-...]dx` To determine the indefinite integral, we integrate each term using Power Rule for integration: `int x^ndx =x^(n+1)/(n+1)` . `int_0^1 [1 -x^2 +x^4/2-x^6/6 +x^8/24-x^(10)/120+x^(12)/720-...]dx` `=[x-x^3/3 +x^5/(2*5)-x^7/(6*7) +x^9/(24*9)-x^(11)/(120*11)+x^(13)/(720*13)-...]|_0^1` ` =[x-x^3/3 +x^5/10-x^7/42+x^9/216-x^(11)/1320+x^(13)/9360-...]|_0^1` Apply definite integral formula: `F(x)|_a^b = F(b)...

As a young teenager, Michelangelo was became the apprentice to Domenico Ghirlandaio.  Ghirlandaio was a famous painter in the Italian city of Florence.  As an apprentice, Michelangelo trained under Ghirlandaio and learned some of his skills.  Some of the skills that Michelangelo learned specifically in the field of sculpture were learned from Bertoldo di Giovanni.  He was a friend of the Medici family, who Michelangelo had grown close to.   Michelangelo painted the ceiling of the Sistine Chapel in Vatican City over a period of approximately four years.  His work began in 1508 and ended in 1512.  Painting the ceiling was both dangerous and exhausting.  Michelangelo created his own scaffolding to paint the ceiling.  It was makeshift scaffolding, and was not very sturdy.  Michelangelo had to turn his head up toward the ceiling as he stood on the scaffolding to do his work.  This was exhausting as he tried to control his balance.  A fall from the scaffolding could have resulted in serious ...

Researchers in many fields -- including animal behavior, anthropology, psychology, and sociology -- study social behavior. The term "social behavior" may be defined slightly differently depending on the field, but this definition (from biologist Terrence McGlynn) captures the main idea: "Social behavior consists of a set of interactions among individuals of the same species." This definition (from Biology Reference) is also helpful: "Social behavior is defined as interactions among individuals, normally within the same species, that are usually beneficial to one or more of the individuals." But it's important not to conflate "social behavior," which is neutral with respect to the nature of the social interactions, with terms like "prosocial behavior," which specify behavior that is intended to help others. Social behavior can be friendly and mutualistic, as when two monkeys groom each other. Both parties receive immediate benefits. ...

Laurie’s parents would probably talk about how much trouble Laurie has been in at school, and why he created Charles to tell them about his antics.   A dialogue is a conversation between two people.  In this case, Laurie’s parents have thought he was a normal boy, despite the trouble he got into at home.  Both are busy with the new baby and their lives, and they did not really notice. Laurie has told his parents that there was a little boy at school who was causing a lot of trouble.  “What did he do?” I asked. “Who was it?” Laurie thought. “It was Charles,” he said. “He was fresh. The teacher spanked him and made him stand in a corner. He was awfully fresh.”  I imagine the dialogue would go something like this. “You will never believe what I found out at the PTA Meeting!” Laurie’s mom exclaimed as soon as she came in the door. “What? Did you meet Charles’s mother?” Her husband asked absentmindedly. “You could say that.”  She paused.  “ I am Charles’s mother.” This got his attention.  ...

Given to solve, `lim_(x->0) x/arctan(2x)` as `x->0` then the `x/arctan(2x) =0/0` form so upon applying the L 'Hopital rule we get the solution as follows, as for the general equation it is as follows `lim_(x->a) f(x)/g(x) is = 0/0` or `(+-oo)/(+-oo)` then by using the L'Hopital Rule we get  the solution with the  below form. `lim_(x->a) (f'(x))/(g'(x))` so , now evaluating `lim_(x->0) x/arctan(2x)` =`lim_(x->0) (x')/((arctan(2x))')` = `lim_(x->0) 1/((arctan(2x))')` First let us compute the `(arctan(2x))' ` let `u= 2x` => so, `(arctan(2x))'= d/dx (arctan(2x)) ` =`d/(du) (arctan(u)) d/dx (u)`             [as `d/dx f(u) = d/(du) f(u) * d/dx (u)]` = `(1/(u^2+1) d/dx (2x)` =`(1/(u^2+1) )(2)` =`(2/(u^2+1))` but u= `2x` ,so =`2/((2x)^2+1)` = `(2/(4(x)^2+1)) ` now coming back to the limits , we have `lim_(x->0) 1/(arctan(2x))'` = `lim_(x->0) 1/(2/(4x^2+1))` as x->0 , we get =`1/((2/(4(0)^2+1)) )` =` 1/2` so , we can state...

O. Henry's "The Last Leaf" is a story of hope, friendship, and sacrifice because Sue and Mr. Behrman do not give up on restoring Johnsy's will to live. Instead, they offer their loving efforts to help Johnsy regain her health, and Mr. Behrman even sacrifices his life for Johnsy. Johnsy, who becomes ill with pneumonia, speaks despairingly of the leaves outside that drop from the vine because of the icy weather. In her despair she tells her roommate and friend Sue that she "must go, too." Sue rejects this despair, saying, "Oh, I never heard of such nonsense... What have ivy leaves to do with your getting well?" Sue further offers hope by lying to Johnsy and telling her the doctor says her chances of getting well are "ten to one!" and that is as good a chance as they have when they ride on the street cars. To change the subject and be more encouraging, Sue then urges her to sleep. Friendship When Johnsy suggests that Sue sketch in the other ...

Our relationship with Great Britain was deteriorating after the Boston Tea Party. The Intolerable Acts were passed to punish the colonists, mainly those in Massachusetts, for the Boston Tea Party. The colonists refused to obey the Intolerable Acts, and they began to form their own militias. Relations deteriorated further after the battles at Lexington and at Concord. Both sides suffered casualties in these battles. Many colonists believed that war was inevitable. The relationship continued to deteriorate as more fighting occurred. During the battle at Bunker Hill, which really was fought at Breed’s Hill, the colonists were able to hold their own against the British military. It took the British three attempts to capture the hill. They succeeded only after the colonists ran out of ammunition. While the colonists didn’t want to lose the battle, they were pleased that they were able to hold their own against the British. This gave them confidence that they might be able to do well if a wa...

It is virtually impossible to know exactly what audiences of Shakespeare's day thought of the Bard's skill as an actor. Surprisingly, not much is really known of Shakespeare's life as an actor in London. One surviving document of the day, written by Robert Greene, was quite critical of Shakespeare, calling him an "upstart crow" who "supposes he is well able to bombast out blank verse as the best of you." Later critics, however, thought differently. In his early biography of Shakespeare, John Aubrey concluded that Shakespeare "did act exceedingly well," although this opinion is dubious considering Aubrey never saw Shakespeare on the stage. In the article, "Was Shakespeare a Good Actor" ( The Atlantic , April, 2014), John Paul Rollert argues that Shakespeare, while quite accomplished, was never the main "box-office draw." Actors such as Will Kemp, Richard Burbage and Edward Alleyn often overshadowed Shakespeare in the theater ...

The mechanical work done on this system is going to be equal to the change in energy of the system. The energy stored in the electric field of the capacitor is: `E=1/2 CV^2` A dielectric also increase the capacitance by a the factor `kappa` . Therefore the new capacitance `C_f` in relation to the original capacitance C would be: `C_f=kappa*C` `W=Delta E=E_f-E_i=1/2V^2(C_f-C)=1/2V^2(kappa*C-C)` `W=1/2V^2(kappa-1)C` `W=1/2V^2(2-1)C` `W=1/2V^2C`

Bernoulli equation has form `y'+P(x)y=Q(x)y^alpha.` We can convert any such equation into linear equation differential equation by using substitution `z=y^(1-alpha).` To learn more about this method of solving Bernoulli equation check out the links below. We will show a somewhat different method which can also be used for solving linear equations. `y'+y/x=x sqrt(y)` Make substitution `y=uv` `=>` `y'=u'v+uv'` `u'v+uv'+(uv)/x=x sqrt(uv)`  `v(u'+u/x)+uv'=x sqrt(uv)`                                                                (1) Let us now assume that the expression in brackets equals zero (we can choose almost anything instead of zero, but this makes the calculation easier) in order to calculate `u.` `u'+u/x=0` `u'=-u/x` `(du)/u=-dx/x` Integrating both sides yields `ln u=-ln x` `ln u=ln x^-1` `u=x^-1` Plugging that into (1) gives `x^-1 v'=x sqrt(x^-1 v)` Now we multiply by `x` to get only `v'` on the left hand side.  `v'=x^2x^...

The concept of shifting standards is defined as the idea that our judgements are based on something we hold to be standard, and these standards may shift depending on multiple factors. For example, we all have the ability to judge that another person is tall, yet how do we define tall? Our perception of tallness changes, or shifts, based on if we are judging a man or a woman. Scholars Monica Biernat and Melvin Manis (1994) give us the example that a woman measuring 5'9" might be considered "very tall," but the same height would not be considered tall for a man ( "Shifting Standards and Stereotype-Based Judgements, " Journal of Personality and Social Psychology , vol. 6, no. 1). Stereotypes often produce shifts in standards . To prove the existence of shifting standards, researchers have designed studies in which they compare participants' subjective judgements with objective judgements. In their article, Biernat and Manis refer to an earlier study do...

I would absolutely go with Friedrich Nietzsche, not so much on the basis of "God is dead," as the last 40 years have been characterized by a revival of religious faith and religious conflict, especially in the Middle East, but because of his impact on how we understand language. While Enlightenment philosophers saw language as a clear window pane revealing truth: they thought that to get the precise words down meant to have captured truth itself, Nietzsche turned that concept on his head. Language he said is not a clear window pane but a prison. We are caught, he famously wrote, in a " prisonhouse of language ." What he meant by this is that while we need language to think, the language we learn is already tainted by the misconceptions and prejudices of past generations. As young children learning the language, we internalize all its limitations and errors before we are able to evaluate them. We are imprisoned by language that itself limits and distorts our ability ...

Marxist criticism examines literary works as "'products' of the economic and ideological determinants specific to that era" (Abrams 149). In other words, literature reflects class struggle along with materialism and oppression. Marxists view literature as reflective of the social class of the author or as an analysis of class relations. Class relations and conflict Certainly, Charlotte Bronte's  Jane Eyre  contains elements of class struggle, since early in the narrative after Jane is orphaned and left penniless, she is forced to live with her uncle's family. There, she is abused and berated by her cousins, and told by her male cousin that she has no right to read their books, and he adds that she should not even be living with "gentlemen's children like them." When her uncle dies, Jane is sent to Lowood, a school for orphans, where she suffers humiliation and deprivation. After her friend Helen dies, Jane must remain at the school, but she is nu...