Notes

`x/(x+1)=3/(x+1)` cross multiply, `x(x+1)=3(x+1)` `x*x+x*1=3*x+3*1` `x^2+x=3x+3` `x^2+x-3x-3=0` Factorize, `x(x+1)-3(x+1)=0` `(x+1)(x-3)=0` use zero product property, `x+1=0`   or  `x-3=0` `x=-1`  or  `x=3` Now let's check the solutions by plugging them in the original equation, For x=-1 `(-1)/(-1+1)=3/(-1+1)` `(-1)/0=3/0` It's an extraneous solution, as it leads to division by zero. For x=3, `3/(3+1)=3/(3+1)` `3/4=3/4` It's true. So, the solution of the equation is x=3 

At the end of chapter 73, Pi first divulges the fact that he had started a diary after about a week alone at sea. Pi claims that he wrote about "practical stuff" (208) such as what he caught for food, foreseeable problems and solutions, Richard Parker, and reflections about specific events that occurred. In a sense, Pi is the captain of his ship; therefore, he must take responsibility for himself and his crew. He can do this by writing down events, problems and solutions, and reflections to look back on when confronted with repeated problems. It can help him to consider pros and cons when faced with new and unforeseen dilemmas as well. In addition, keeping a diary provides Pi with a medium through which he can keep himself focused on reality. He doesn't waste his paper on whining about his circumstances, for example. He uses the limited supply of paper to write down the reality of his situation and to keep a realistic dialog going with himself in order to analyze issues a...

The arena could represent quite a few different things depending on who you are.  For somebody from the Capitol or even Districts 1 and 2, the arena is representative of entertainment.  The people from the Capitol love The Hunger Games.  They throw parties before it, during it, and after it.  They get together to watch it in big groups.  I remember when my friends in college did this with the show  Survivor.  For Districts 1 and 2, the arena might additionally represent fame and glory.  Those two districts raise and train career tributes, and they win more often than not.  The dynasty they've built is big bragging rights.   However, for all of the other districts (and most readers), the arena is representative of death, violence, and oppression.  The Hunger Games feature children fighting to the death and encourage creative and brutal killing styles.  The Hunger Games themselves exist to remind the other districts of how they are at the Capitol's mercy.  For most districts, wa...

To find the arc length of a curve , we follow the formula: `S = int_a^b sqrt(1+((dy)/(dx))^2)`  if `y=f(x)` , `alt=xlt=b` or ` [a,b]` . For the given problem: `y =x^2/2` on interval `[0,4]` , we have boundary values: `a= 0` and `b=4` .   Apply Power Rule for differentiation:` d/(dx) x^n = n * x^(n-1) * dx` . `(dy)/(dx) = d/(dx) (x^2/2)`      ` = 1/2d/(dx) (x^2)`      ` = 1/2 * [ 2 *x^(2-1) * 1 ]`      ` =1/2 * [ 2x]`     ` = (2x)/2 `       ` = x` Plug-n `a=0` , `b = 4` , and `(dy)/(dx)= x` on the formula `S = int_a^b sqrt(1+((dy)/(dx))^2)` , we get: `S = int_0^4 sqrt(1+x^2) dx` From indefinite integral table, the problem resembles the formula for integral with roots: `int sqrt(u^2+-a^2) dx=1/2usqrt(a^2+-u^2)+-1/2a^2ln|u+sqrt(u^2+-a^2)|` . Take note we have "`+` " sign inside the radical part then we follow formula as: `int sqrt(u^2+a^2)dx=1/2*usqrt(a^2+u^2)+1/2*a^2ln|u+sqrt(u^2+a^2)|` . Applying the formula, we get `S = int_0^4 sqrt(1+(x)^2)` ` =[1/2*xsqrt(1^2+x^2)+1/2*1^2ln|...

One song that could represent Ponyboy is "Buddy's Song" by Fleetwood Mac, as part of the lyrics are "Think it over before you leavev/ I got the love, that kind you need." This is similar to what Darry, Ponyboy's older brother, tells him--that Ponyboy should not leave home. When Darry tells Ponyboy, "Sure, little buddy," Ponyboy knows from this name that Darry loves him and wants him to stay at home. Another song that could represent Ponyboy is "Land of Confusion" by Genesis, which is about constant fighting. Part of the lyrics are "There's too many men / Too many people / Making too many problems / And not much love to go round." Ponyboy wants an end to the fighting between the Socs and Greasers and an end to the misunderstanding between them. He isn't really a fighter, and he understands that the Socs are similar to him in some ways.  Finally, "Little Brother" by Hootie and the Blowfish is representative of Po...

When we think about the climax of a story, we can think of it in two different ways. First, we can think of it as the turning point where the main character makes a decision and/ or takes an action that sets up the resolution of the conflict, for good or for ill. Second, we can think of it as the high point of the story's action where the reader experiences the most tension, after which the tension subsides as the story's action falls. In "Once Upon a Time," the climax according to the first approach occurs in the penultimate paragraph when the family installs the "razor-bladed coils" atop the walls around their house. This is the decision that finally resolves their fears so they can stop worrying about invaders. Until this point, the statement "You're right" often precedes the family's next effort to improve their security. Now, the statement "You're wrong" appears, signalling a change. This coil will never rust; even the ca...

The capacitance per unit length is `C/L=Q/(VL)` . So lets find the voltage of this configuration. In order to do that use Gausses' law to find `E` from the charge distribution. Make a Gaussian cylinder. `int int_A E*dr=Q_(enc)/epsilon_0` We know that we will enclose part of the charge distribution when `0ltrlta` so make a Gaussian cylinder. Make a surface `r` between `0` and `a` . ` ` `E 2pi rL=(rho*pi r^2 L)/epsilon_0` `E(r)=(rho r )/(2 epsilon_0)` `0ltrlta.` in the +r direction Now we must find the field between `altrltb` . Make a cylindrical surface a distance `r` between `a` and `b` . `int int_A E*dr=Q_(enc)/epsilon_0` `E (2pi r L)=(rho pi a^2 L)/epsilon_0` `E(r)=(rho a^2)/(2epsilon_0 r)`  in the +r direction for `altrltb` Now since surface `b` is a grounded conductor it will take up an equal and opposite total charge. Therefore Gausses' law says that the E-field is zero for `rgtb` . Since we now know `E` for all of space we can integrate for the potential of t...

Jing-Mei Woo (who has the nickname of "June") prepares for the talent show by taking piano lessons from the deaf Mrs. Chong (who is a retired piano teacher).  Therefore, although June does prepare for the talent show, she certainly does not prepare well. Instead, June puts her hope in the idea that she is truly a "prodigy" and does not need too much practice.  It is June's mother who is most looking forward to the performance so that her daughter can show her great talent to the Joy Luck Club.  June has been told so often that she is a prodigy she "almost" believes it as the talent show begins.  Unfortunately, she gives a poor performance of Schumann's piece called "Pleading Child."  Only Mrs. Chong applauds for June.  Of course, June is not really a prodigy; therefore, her talent was not enough to impress June's mother and her friends.

The narrator describes the entire setting and his own mood in the first five paragraphs of the story and then mentions, almost as an incidental observation, a flaw in the front of the big building. Perhaps the eye of a scrutinising observer might have discovered a barely perceptible fissure, which, extending from the roof of the building in front, made its way down the wall in a zigzag direction, until it became lost in the sullen waters of the tarn. This one long sentence serves at least two purposes. It is a very subtle foreshadowing of the "fall" of the House of Usher which will be described at the very end of the story. It also explains what will cause that catastrophic fall. There has to be a physical reason as well as a symbolic or poetic reason for the great building to collapse into the tarn the way the narrator describes it at the end of this bizarre tale. The radiance was that of the full, setting, and blood-red moon which now shone vividly through that once barely-...

Is the "gamification" of education a passing fad or the tip of the iceberg?   I'm going to say both, but I need to explain why.  Ultimately, it will be a passing fad, but the fad may last for many decades.  I've been teaching long enough to have seen and been through styles of teaching that have been around for many, many years, and I have seen long standing, traditional styles of education begin to fade out.  I believe that given enough time, any current style of teaching and learning has the ability to go away.  Games to learn math through isn't any different.  I believe the better question is how long will it stick around?   I believe that it will stick around for a long time.  I do indeed believe that it is the tip of the iceberg.  For example, the school that I teach at is in the second year of one to one education.  That means every student has a laptop.  My school is  not the only school in San Diego to do this.  It has to be stated that the way teachers i...

It is apparent from the very beginning of Steinbeck's Of Mice and Men that Lennie is mentally challenged. Steinbeck first suggests this when Lennie is quite pleased with himself after producing splash rings in the river where he and George stop in Chapter One. Lennie is also carrying a dead mouse in his pocket, symbolic of his childlike obsession with petting soft things. Lennie is also obsessed, like a child waiting for Christmas, with the prospects of "tending rabbits" on the farm which he and George hope to one day own. George is obviously Lennie's caretaker, making sure that Lennie eats regularly and has a job. Lennie had originally been cared for by his Aunt Clara, but when she died, he went on the road with George. George makes important decisions for Lennie and in Chapter One, he is holding Lennie's work card, which will be used to work on the ranch where they are headed near the small central California town of Soledad. Lennie is, however, quite a handful...

In this soliloquy, Macbeth expresses the despair he feels upon Lady Macbeth's death.  This despair is darkened further by the sense of meaninglessness and doom as Macbeth contemplates his empty future which was once so full of promise and ambition.  The juxtapositions in the passage serve to intensify this portrayal of despair.   For example, there is the juxtaposition of light versus dark.  The past is marked by "lighted fools" while the future ends in the darkness of death.  "Out, out, brief candle!" describes the individual's death.  The interim, life, is "but a walking shadow."  Darkness can signify the corruption of Macbeth's soul in the course of the play's events as well as the growing influence of the "weird sisters" (demonic forces).   Another juxtaposition is sound and silence.  There are parallels in the descriptions of life as a poor player strutting upon the stage only to be "heard no more" and life as a tal...

The Kiowa story of creation explains why the Kiowas are such a small tribe. According to this story, every Kiowa came into the world through a hollow log. The Kiowas essentially originated from a "sunless" world into a world brightened by the light of the sun. Because of this, the Kiowas forever worshiped the sun deity through their yearly Sun Dance rituals. It was said that, despite the Kiowa desire to emerge into the world, not all of the tribe were so fortunate to make their way through. Many had become stuck in a dark world because a pregnant woman had gotten lodged in the log.  After her, no one else could get through, and this is said to be the reason Kiowas are such a small tribe of people. Upon coming out into the world, the Kiowas had originally called themselves Kwuda, which means "coming out." Later, they called themselves Tepda and Gaigwu. Kiowa is thought to have been derived from the Comanche form of Gaigwu.

The North and the South had different economies. Because the climate of the North was cooler than the South’s climate, there was less farming in the North. The North also had soil that was less suited for farming, unlike the South that had very fertile soil. As a result, the North developed many industries while the South was mainly an agricultural region. Because the economic activities were different in each region, the regions supported different policies. For example, the North supported protective tariffs and internal improvement projects. Protective tariffs helped northern industries grow. The tariffs made European products more expensive. This encouraged people to buy from American industries. However, this hurt southerners because it cost them more money to buy products. The North wanted more roads, railroads, and canals to be built. The South depended mainly on river travel. The internal improvement projects had more of a benefit for the North than for the South. However, thes...

When Gulliver frees his left arm, the Lilliputians ran out of his reach and then launched a volley of arrows into him. Of course, he is so big that the arrows do not cause him serious harm, but they hurt very badly, and Gulliver is in considerable discomfort as a result. He thus decides to stop struggling to break free of the cables he is ensnared in, and to simply wait until the Lilliputians retire for the night, at which point he plans to set himself free. His captors have other plans. They build a platform on which a dignitary stands, delivering a speech to Gulliver while he is still tied to the ground. Gulliver does not understand the little man's speech, and gestures that he is hungry, at which point the Lilliputians supply him with mountains of food and entire hogsheads full of wine. Gulliver then considers himself "bound by the laws of hospitality" not to resist the Lilliputians violently.

Most workers in the 1880s did not live outside city limits.  This was because of the lack of good transportation for workers which would have allowed them to live outside the cities in which they worked. In the 1800s, it was not easy to travel long distances to work.  There were streetcars and trolleys, but those forms of mass transit did not generally reach very far and were not widespread.  The average worker needed to live close enough to his or her place of work to be able to walk to and from work every day.  Because they needed to commute by foot, they had to live relatively close to their jobs.  This meant that they could not generally live outside city limits. Because of a lack of good transportation options, most workers in the 1880s still lived inside city limits.

If you click on the reference link below you will get the whole text of the Sherlock Holmes story "The Adventure of the Speckled Band." The story opens with the early-morning visit of Helen Stoner. She tells Holmes and Watson a very long backstory involving herself, her sister Julia, her stepfather Dr. Grimesby Roylott, and her deceased mother. Helen is afraid her life is in danger. She thinks someone may be trying to kill her in the same way that an unknown person killed her sister Julia two years ago when Julia was sleeping in a room with the door locked and the window securely covered with a bolted shutter. Now Helen is occupying that same room. She keeps the door locked and the window shuttered, but still she is afraid that someone is trying to get at her. Holmes promises to come down to Stoke Moran to examine the premises. Holmes' inspection of the bedrooms at Stoke Moran is the only important part of his examination of the premises. There are three bedrooms all in a...

The Red Death is a terrible, deadly disease that has devastated the country ruled by Prince Prospero. In fact, the narrator tells us, no disease has ever been as deadly or awful as this one. It is called the Red Death because the victims of this disease begin to bleed from all their pores, in addition to the dizziness and sharp pains they experience. The diseased can easily be identified by the red stains all over their bodies, especially on their faces. These individuals, once spotted, immediately become shut out from the aid and sympathy of all their fellows and even their friends because the disease is so contagious. Further, the disease is so deadly and moves so quickly that the whole progression from contraction to the victim's death takes only thirty minutes.

For the first time, the narrator sees the sight that the signal-man had described to him earlier: Close at the mouth of the tunnel, I saw the appearance of a man, with his left sleeve across his eyes, passionately waving his right arm. This seizes the narrator with a "nameless horror" because he believes he is seeing the ghost whose appearances have tormented the signal-man. This quickly passes when he realizes he is seeing one of a group of men investigating an accident scene: The signal-man has been killed by a train. Dickens has laid the groundwork for this terror by his eerie, sympathetic, and lonely portrayal of the signal-man. Reviewing this background helps us understand why the narrator felt fear. The signal-man works in a bleak and desolate place, and believes he has been visited by a ghostly apparition on repeated occasions. The signal-man believes the ghost is attempting to announce impending disaster or death. Twice, the ghost's appearance was followed by deat...

To solve the indefinite integral, we follow `int f(x) dx = F(x) +C` where: `f(x)` as the integrand function `F(x)` as the antiderivative of `f(x)` `C` as the constant of integration. For the given integral problem: `int sqrt(25x^2+4)/x^4dx` , we may apply integration by parts: `int u *dv = uv - int v *du` . Let: `u =sqrt(25x^2+4)` Apply Law of Exponent: `sqrt(x) = x^(1/2)` , we get:  `u =(25x^2+4)^(1/2)` To find the derivative of `u` , we may apply Power rule for derivative: `d/(dx) u^n= n* u^(n-1) * d/(dx)(u)` `u' = 1/2 *(25x^2+4)^(1/2-1) * d/(dx) (25x^2+4)` `u' = 1/2*(25x^2+4)^(-1/2)* (50xdx)` `u' = 25x(25x^2+4)^(-1/2)dx` Apply Law of exponent: `1/x^n =x^(-n)` . `u' = (25x)/(25x^2+4)^(1/2)dx or(25x)/sqrt(25x^2+4)dx`  Let: `v' = 1/x^4 dx` To find the integral of `v'` , we apply  Law of exponent: `1/x^n =x^(-n)` and Power rule for integration:`int x^n dx = x^(n+1)/(n+1) +C` . `v = int v'`   `= int 1/x^4 dx`   `= int x^(-4) dx`   `= x^(-4+1)/(-4+1)`   `= x^(-...

Coleridge's poem expresses a very dreamy, imaginative vision that is characteristic of the Romantic emphasis on individualism and the importance of one person's unique perceptions. Coleridge prefaces the poem with the description, "Or, a vision in a dream. A Fragment," conveying to the reader that the vision conveyed in the poem came to him in a dream and has all the confusing and imaginative symbolism of a dream. The vastness and eeriness of the landscape and the solitary people in the poem enhance the idea of the lone individual. The poem begins by describing Xanadu and its surroundings, including the river Alph and "caverns measureless to man," conveying a sense that humans are lost and alone in the vastness of nature and highlighting the idea that the individual is alone in this dreamy and vast landscape. The palace is "With walls and towers...girdled round," suggesting that the people in the tower are isolated individuals, cut off from the res...

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'(c))/(2!) (x-c)^2+ (f'(c))/(3!) (x-c)^3+ (f'(c))/(4!) (x-c)^4+...` To determine the Taylor series for the function `f(x)=ln(x^2+1) ` centered at `c=0` , we may list the `f^n(x)` as: `f(x)=ln(x^2+1)` Applying derivative formula for logarithmic function: d`/(dx) ln(u) = 1/u *(du)/(dx)` . Let `u = x^2+1` then `(du)/(dx)=2x` `f'(x) = d/(dx)ln(x^2+1)`        `= 1/(x^2+1) *2x`        `=(2x)/(x^2+1)` Applying Quotient rule for differentiation: `d/(dx) (u/v) = (u' *v - u*v')/v^2` . Let `u = 2x` then `u'= 2`       `v = x^2+1` then `v'=2x`  and` v^2 = (x^2+1)^2` `f^2(x) = d/(dx)((2x)/(x^2+1))`        `= ( 2*(x^2+1)-(2x)(2x))/(x^2+1)^2`        `=( 2x^2+2-4x^2)/(x^2+1)^2 ` ...

There are many different ways to classify people into "groups." You can, for instance, separate people by gender, by religion, by race, or by a number of other different subsets or preferences, such as "does the person like vegetables?" Once people are separated into different groups, they often tend to stay within that group for reasons such as lack of conflict and having things in common. If you love a TV show, and you have a group of friends who also love that TV show, what reason do you have to try to separate? Similarly, many people choose to remain in cohorts of their biology. Many people choose to befriend people of similar races, genders, hair colors, ages, etc. This is associative, because people assume that people who look the same will, in some facet, also behave the same. By remaining with people who are like you, you will limit potential conflicts of interest. The issue there is that you will never grow. Meeting and learning about other groups of people...

The conflict between Cory and his father Troy is understood by each man differently. The idea expressed in the struggle between the father and son is connected to this difference in perspective, to some degree, and also hinges on the twin ideas of accepting others and accepting the past in order to live a life in the present (and so not remain trapped in the past). To offer a brief synopsis of the meaning of the conflict between these characters, we might start at the end of the story and look at how the conflict is resolved. Cory finally agrees to attend Troy's funeral, singing Troy's song about Old Blue with Raynell, his half-sister (from Troy's adulterous affair). In this moment, Cory comes to hold a balanced view of his father, which is to say that he develops the capacity to see the good along with the bad. In finding a way out of the reductionist tendency that had previously shaped his view as a black-or-white, judgement-laden perspective, Cory is able to rise above t...

Alban's main point in the article "Antony and Cleopatra; Gorgon or Mars, Whore or Goddess" is that Shakespeare presents an oxymoronic interpretation of the characters in this tragedy. Antony and Cleopatra present a variety of qualities that were both human and divine. The author uses various illustrations within the text to show this contrast. Antony and Cleopatra Alban examines the analysis of Shakespeare's Antony and Cleopatra in Ted Hughes' "Shakespeare and the Goddess of Complete Being." Antony and Cleopatra, much like Romeo and Juliet, commit suicide because of a tragic misunderstanding. Cleopatra's identity exists on two levels, both as the "whore" and the goddess. She is both Isis, a goddess of motherhood, and Venus, the goddess of love and female empowerment. Antony's identity is also twofold as both a libertine or a Gorgon and a demi-Atlas, or the pillar of the world. His identities are echoed in the deities Dionysus, Adonis, ...

I'll focus on the two most popular movie adaptations of Shakespeare's play, the 1968 Zeffirelli version and the 1996 Baz Luhrmann version with Leonardo DiCaprio as Romeo. The Zeffirelli film is probably the most faithful. It was filmed in Italy in a setting that has the look of Verona during the Renaissance. The actors look much as you might expect. Olivia Hussey looks almost young enough to play Juliet (she was sixteen during the filming), Leonard Whiting portrays an emotional and impetuous Romeo, and John McEnery is brilliant as Mercutio. The first Act is almost word for word up until the scene at Capulet's party, where Zeffirelli adds a "troubadour" who would have been a common attraction at such a gathering. He sings a song called "What Is a Youth," which is a delightful Renaissance-type ballad and employs lyrics which are very much in line with the plot and theme of the play. Likewise, Acts II and III are virtually word for word. The fight scene in ...

LCD is an acronym for least common denominator . It is the product of distinct factors on the denominator side. Basically, find LCD is the same as finding the LCM (least common multiple) of the denominators. For the given equation `18/(x^2-3x)-6/(x-3)=5/x` , the denominators are `(x^2-3x)` , `(x-3)` , and `x` . Note: The factored form of the denominator `x^2-3x` is ` x(x-3)` . Based on the list of factors, The distinct factors are `x` and `(x-3).` Thus,` LCD= x*(x-3) `  or `(x^2-3x)` . To simplify the equation, we multiply each term by the LCD. `18/(x^2-3x)*(x^2-3x)-6/(x-3)*x*(x-3) =5/x*x*(x-3) ` Cancel out common factors to get rid of the denominators. `18 -6*x =5*(x-3)` Apply distribution property. `18-6x=5x-15` Subtract 18 from both sides. `18-6x-18=5x-15-18` `-6x= 5x -33` Subtract `5x ` from both sides of the equation. `-6x-5x= 5x -33-5x` `-11x=-33` Divide both sides by `-11` . `(-11x)/(-11)= (-33)/(-11)` `x=3` To check for extraneous solution, plug-in `x=3` on `18/(x^2-3x)-6/(x-3...

`log(12x-11)=log(3x+13)` Using the property of logarithmic equality, `12x-11=3x+13` `=>12x-3x=13+11` `=>9x=24` `=>x=24/9` `=>x=8/3` Let's plug back the solution in the equation to check the solution: `log(12(8/3)-11)=log(3(8/3)+13)` `log(4*8-11)=log(8+13)` `log(32-11)=log(21)` `log(21)=log(21)` So, it's true. Solution is `x=8/3`

Scout and Aunt Alexandra hear of Tom Robinson's death from Atticus Finch in the Finch family's kitchen. Scout hears the news and watches the reactions of her father, Miss Maudie, Calpurnia, and her aunt, commenting that "...I found myself shaking and couldn't stop." Scout's aunt Alexandra, Atticus' sister, initially "put her hands to her mouth" in shock, and later sat down at the kitchen table. Alexandra summarily engaged Maudie in an appeal that revealed that Alexandra was disapproving of her brother's efforts to defend Tom, saying to Atticus, after he revealed Tom's death, "This is the last straw." Maudie, however, rebukes Alexandra's failure to recognize the moral courage Atticus showed in ably defending Tom, telling her: "Have you ever thought of it this way, Alexandra? Whether Maycomb knows it or not, we're paying the highest tribute we can pay a man. We trust him to do right. It's that simple." Scout ...

Hello! If we divide a polynomial `f(x)` by a monomial `(x-d)` with a reminder, `f(x)` becomes expressed as `f(x)=(x-d)p(x)+c,` where `c` is a reminder (a constant). Therefore `f(d)=c.` So we know from the conditions that `f(1)=0` and `f(2)=-18.` From this we obtain `4+a+b+4=0` and `32+4a+2b+4=-18.` This is the same as `a+b=-8` and `2a+b=-27.` It is a linear system for a and b, and subtracting these equations we obtain `a=-19.` Thus `b=-8-a=11,` and this is the (unique) answer for the problem. So the complete expression is `f(x) = 4x^3 - 19x^2 + 11x + 4`

King Hamlet, the father of Prince Hamlet, only appears briefly in Shakespeare's play, in the form of a ghost urging his son to take revenge on Claudius for his murder. The reason that there are not many examples of the differences between the two brothers is that King Hamlet has been murdered before the play starts and therefore is not a central character. We don't receive much characterization to attribute to Kind Hamlet. Prince Hamlet, in certain ways, idealized his father and Shakespeare may have intended to suggest that King Hamlet was an ideal ruler and Claudius a bad one. First, Claudius poisoned his brother, which is a morally wrong act. The marriage to Gertrude, despite Hamlet's protestations, may actually have been a moral act, a way of taking care of his brother's widow. Although it may have been intended to suggest adultery before King Hamlet's death. Hamlet points out the difference between her current and former husband to Gertrude in the following line...

This detail tells us several crucial things about government in this story. First, it tells us the government in this story is still technically the government of the United States. This is not some alien world or another country with a different legal tradition. This also suggests the oppressive actions the government in this story take come from principles and ideals that already exist in the United States. Third, the number 213 is extremely high. Right now, there have only been 27 amendments to the Constitution, and when Vonnegut wrote the story, there were even fewer (22). This means there has been a tremendous amount of change in the intervening years. The government in this society has introduced change after change, modification after modification. It suggests democracy is out of hand, and the people are making changes to get what they want that ignore the core principles upon which America was founded. Finally, this means this is a government that keeps the appearance of legiti...

 In using  Root test  on a series `sum a_n` , we determine the limit as: `lim_(n-gtoo) root(n)(|a_n|)= L` or `lim_(n-gtoo) |a_n|^(1/n)= L` Then, we follow the conditions: a) `Llt1` then the series is  absolutely convergent . b) `Lgt1` then the series is  divergent . c) `L=1` or  does not exist   then the  test is inconclusive . The series may be divergent, conditionally convergent, or absolutely convergent. We may apply the  Root Test  to determine the convergence or divergence of the  series  `sum_(n=1)^oo ((2n)/(n+1))^n` . For the given series `sum_(n=1)^oo ((2n)/(n+1))^n` , we have `a_n =((2n)/(n+1))^n.` Applying the Root test, we set-up the limit as:  `lim_(n-gtoo) |((2n)/(n+1))^n|^(1/n) =lim_(n-gtoo) (((2n)/(n+1))^n)^(1/n)`  Apply the Law of Exponents:`(x^n)^m= x^(n*m)` . `lim_(n-gtoo) (((2n)/(n+1))^n)^(1/n) =lim_(n-gtoo) ((2n)/(n+1))^(n*(1/n) )`                                  `=lim_(n-gtoo) ((2n)/(n+1))^(n/n )`                                  `=lim_(n-gtoo) ((2n)/(n+1))^1`    ...

In Toni Cade Bambara's story "Raymond's Run," Squeaky's family responsibility is to care for her disabled brother, Raymond. Due to Raymond's developmental disabilities he needs constant care to keep him safe and out of trouble. Squeaky takes this responsibility very seriously so that her mother can concentrate on caring for the family home. Raymond tags along with Squeaky wherever she goes in their Harlem neighborhood. While she practices her breathing and high-stepping, Raymond can be seen prancing along pretending he is driving a carriage. When Raymond runs through the pigeons or into the puddles along the street, Squeaky is quick to correct his actions so that she does not get in trouble at home. If the other children mock Raymond for his large head or mental deficits, Squeaky quickly comes to his defense by fighting the perpetrator. She is a loyal, caring sister who looks out for her brother's well-being.

There are three forces acting on the lead cube: gravitational force with the magnitude `Mg` downwards, buoyant (Archimedes') force `mg` upwards, lifting force of unknown magnitude `F` upwards. Here `g` is the gravity acceleration, M is the mass of the cube and m is the mass of water in the volume of the cube. Note that  `M = rho_l V,`  `m = rho_w V,`  `V = a^3,` where `a` is the side length, `V` is the volume of the cube, `rho_l` is the density of lead and `rho_w approx1 g/(cm)^3` is the density of water. If we find `F_0` such that these forces will be balanced, then any lifting force magnitude greater than `F_0` value will be suitable. Considering the directions, the equation becomes `F_0 +rho_w a^3 g =rho_l a^3 g,`  or `F_0 =rho_l a^3 g -rho_w a^3 g = (rho_l -rho_w) a^3 g.` We need to divide this by `1000` to obtain kilograms from grams. The numerical result is about  `(11 - 1)*10^3*10/1000 = 100 (N).` Thus the answer is: at least 100 N force is needed to lift the cube.

Ray Bradbury’s 1951 short story “The Pedestrian” takes place on a November evening in the year 2053. The protagonist, Leonard Mead, is engaging in his favorite pastime—taking a solitary walk around his suburban neighborhood. Bradbury introduces Leonard’s feelings of loneliness and isolation in the first paragraph when he says, “he was alone in this world of A.D. 2053, or as good as alone.” The empty streets Leonard walks down are described as being like a “graveyard,” where “gray phantoms” appear at the windows of “tomb-like” buildings lit up only by the glow of the “viewing screens” everyone but Leonard seems to own and watch nightly. The autumn setting, with its dead, “skeletal” leaves and misty air, also contributes to the lonely, melancholy mood, and the cold temperature echoes the emotional coldness of this future world. Leonard seems to enjoy the exhilarating feeling of the “good crystal frost,” but it is a lonely enjoyment: he has nowhere in particular to go, so he is wandering ...

To summarize any article, we start by identifying the thesis statement . The thesis statement expresses the writer's claim or opinion, what the writer aims to prove throughout the whole article. The thesis can always be identified first in the abstract, if there is an abstract, then in the introduction. Depending on the length of the article, an introduction may be multiple paragraphs long, but the thesis is always easy to spot because it clearly expresses the writer's debatable, defendable opinion . Luckily, Margaret Raymond's introduction is only one short paragraph long, and her thesis can easily be recognized at the end of the introduction: I agree with Professor Fyfe's first two points, but have some significant concerns about the third. The points she is referring to that she agrees and disagrees with can be found in the earlier sentences. She agrees that the decision of Terry v. Ohio grants police an effective tool for investigations. The decision of Terry v. ...

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=a` . The general formula for Taylor series is: `f(x) = sum_(n=0)^oo (f^n(a))/(n!) (x-a)^n` or `f(x) =f(a)+f'(a)(x-a) +(f''(a))/(2!)(x-a)^2 +(f^3(a))/(3!)(x-a)^3 +(f'^4(a))/(4!)(x-a)^4 +...` To apply the definition of Taylor series for the given function `f(x) = e^(2x)` , we list` f^n(x)` using the derivative formula for exponential function: `d/(dx) e^u = e^u * (du)/(dx)` . Let `u =2x ` then `(du)/(dx)= 2` Applying the values on the derivative formula for exponential function, we get: `d/(dx) e^(2x) = e^(2x) *2`               ` = 2e^(2x)` Applying `d/(dx) e^(2x)= 2e^(2x)`   for each` f^n(x)` , we get: `f'(x) = d/(dx) e^(2x)`            `= 2e^(2x)` `f^2(x) = 2 *d/(dx) e^(2x)`            `= 2*2e^(2x)`            `=4e^(2x)` `f^3(x) = 4*d/(dx) e^(2x)`             `= 4*2e^(2x)` `f^4(x) = 8*d/(dx) e^(2x)`   ...

Milton wrote his sonnet "On His Blindness" after he went completely blind in middle age. The sonnet is autobiographical and written in the first person. Since Milton was a deeply religious writer, he tried to understand his blindness within the context of his faith. The octave of the sonnet laments Milton's loss of sight. As a writer, Milton strove to serve God by writing on various religious topics. His greatest work, Paradise Lost , tried to "justify the ways of God to men." In light of this, Milton feels his blindness prevents him from serving God, and wonders why God would deprive him of the means by which he expresses his faith. In the sestet, Milton realizes the thoughts he had in the octave spring from his own egotism and false understanding of God. He realizes, God doth not need Either man's work or his own gifts. Instead, what God desires of humans is faith and obedience, and Milton discovers that one can best serve God by subordinating one's ow...

I suggest tackling the last three, because they are relatively easy to tie together. You can frame your discussion as a comparison of non-experimental versus experimental methods. To see how the topics connect, read on. 1. What is the difference between systematic observation and naturalistic observation? Naturalistic observation involves collecting information that is offered spontaneously by the environment. Unlike an experimenter, the observer doesn't attempt to manipulate conditions. This can be a strength if you want to know how people behave in the real world. You don't have to worry so much that people are reacting in ways that are specific to the laboratory setting. Simple observation doesn't allow you to pin down causation, though, and it can lead to biases. For example, how do you, the observer, decide if a person is sad? Your perceptions might be colored by your interests, preconceptions, cultural training, and so forth. To reduce observer bias, researchers often...

Givne to solve , `lim_(x->oo)ln(x^4)/x^3` = `lim_(x->oo) 4 ln(x)/x^3` = `4lim_(x->oo) ln(x)/x^3` as `x->oo` then the `ln(x)/x^3 =oo/oo` 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 `4lim_(x->oo) ln(x)/x^3` =`4lim_(x->oo) (ln(x)')/((x^3)')` = `4lim_(x->oo) (1/x)/(3x^2)` = `4lim_(x->oo) (1/(3x^3))` so on plugging the value x= oo we get = `4(1/(3(oo)^3))` = `0`

The sculptor's mother has a violent face when she cries over her son's casket, when she interacts with her husband, and when she scolds her maid. When Steavens, who has ridden with the hearse, arrives at the Merrick house, a "naked weatherbeaten frame house," the same group of men that have been at the station are at the gate, which hangs on only one hinge. Carrying the casket across warped planks through the dilapidated gate is difficult for these men. As they struggle with it, they hear the front door yanked open and a large, bulky woman breaks through violently, calling out loudly to her dead son in a maudlin way as she falls over upon his coffin. Steavens cannot believe this woman is his mentor's mother; she is coarse and loud and brutish. She has power, yet she possesses a kind of "brutal handsomeness, that is scarred and furrowed by violence." This violence is evinced when she acts, as well. When, for instance, her frail husband tries to console he...

Yes, the animals are more or less behaving like humans. This is because Orwell wrote the story to illustrate in very simple terms, term that the average person could grasp, how political movements originally based on ideals of justice and fairness can be hijacked by those hungry for power. The specific reference point is the Russian Revolution and its aftermath, with Napoleon representing Stalin and Snowball Trotsky, but the implications are broader. Orwell hopes his audiences will see how they can be like the innocent animals in the story, duped when the "pigs" (in the broadest sense representations of power-hungry people) manipulate language and violence to serve their own agendas. Language was important to Orwell and he wanted to show us, as humans, how important it is to carefully examine what is being said to us to make sure it makes sense and that, under the guise of protecting our rights, words aren't twisted to steal our rights. By using animals, which provided so...

Helen Keller had an interest in nature even as a toddler.  She loved to be out in nature.  It brought her both comfort and joy.  When learning, the study of nature was a topic of special interest to her.  She was especially drawn to science and geography for this reason.  Before she lost her sight and hearing, she enjoyed observing nature.  Helen recalled a memory from when she was one year old.  One day, she was "attracted by the flickering shadows of leaves that danced in the sunlight on the smooth floor" ( The Story of My Life , Chapter I).  After Helen became deaf and blind, she found solace in nature.  Her senses of smell and touch let her enjoy the beauty of nature.  When Helen was frustrated, she ran to the garden.  She especially loved the flowers there. After Miss Sullivan came and taught Helen how to communicate, she began teaching her young pupil about nature.  Miss Sullivan took Helen to the river, where she finger spelled lessons into her palm.  The teacher taugh...

In Chapter 23, Atticus discusses the trial with Jem and Scout and explains to his children that there was a member of the jury who was a relative of the Cunninghams that argued for an outright acquittal. Jem is shocked and comments, " Golly Moses...One minute they're tryin' to kill him and the next they're tryin' to turn him loose...I'll never understand those folks as long as I live " (Lee 136). Atticus then tells his children that they just had to know them . He goes on to explain that the Cunninghams hadn't taken anything from or off of anybody since they immigrated to America. The other thing about the Cunninghams was that once you earned their respect, "they were for you tooth and nail." Atticus tells Jem and Scout that after their encounter with the Old Sarum bunch that night outside of the jailhouse, they earned the Cunningham's respect. Atticus is essentially teaching his children not to judge individuals until they get to know th...

Let's use the method of disc for evaluating the volume of the solid generated. As per the method of discs `V=intAdx`  or `V=intAdy`  , where A stands for Area of a typical disc , `A=pir^2`  and`r=f(x)`  or `r=f(y)` depending on the axis of revolution. Given `xy=3 , y=1 , y=4 , x=5` and the region is rotated about the line x=5 Consider a disc perpendicular to the line of revolution, Then the radius of the disc will be `(5-x)` Since  `xy=3, x=3/y` Radius of the disc = `(5-3/y)` `V=int_1^4pi(5-3/y)^2dy` `V=piint_1^4(25-2(5)(3/y)+(3/y)^2)dy` `V=piint_1^4(25-30/y+9/y^2)dy` `V=pi[25y-30ln(y)+9(y^(-2+1)/(-2+1))]_1^4` `V=pi[25y-30ln(y)-9/y]_1^4` `V=pi{[25(4)-30ln(4)-9/4]-[25(1)-30ln(1)-9/1]}` `V=pi(100-9/4-30ln(4)-25+9)` `V=pi(84-9/4-30ln(4))` `V=pi(327/4-30ln(4))` `V~~126.17`

A simile is a comparison that uses the words "like" or "as." There are many comparisons within The Boy in the Striped Pajamas , and most of them are found in the narration of the book (as opposed to the dialogue) because a young boy like Bruno would be less likely to use such a literary concept. One example of a simile can be found on page 211: There was some sort of disturbance towards the back, where some people seemed unwilling to march, but Bruno was too small to see what happened and all he heard was loud noises, like the sound of gunshots, but he couldn't make out what they were. The comparison here is that of "loud noises" compared to "gunshots." The word connecting the comparison is the word "like," which makes this a simile. This is a perfect example of Bruno's misunderstanding of what is really going on as the Jewish prisoners at Auschwitz are marched into the gas chamber. The sound "like gunshots" was likely...

The setting of the short story "Raymond's Run" is Manhattan in New York. Manhattan contains a lot of people, but the area itself isn't that large; however, that's still a fairly broad location. In the sixth paragraph of the story, Squeaky narrows down the setting location. She tells readers that she lives in Harlem. Harlem is located just north of Central Park and just southwest of Yankee Stadium. I believe that the story takes place on the western edge of Harlem because Squeaky mentions two specific streets. She mentions Amsterdam Avenue and Broadway. As for the time setting, nothing specific is given to readers. The original publication date of the story is 1971, and the story is likely taking place around that date. Readers do know that the story is taking place during the months of April and May because Squeaky is running in the annual May Day races (May Day is May 1st).

`int(sec^2(x))/(tan^2(x)+5tan(x)+6)dx` Let's apply integral substitution:`u=tan(x)` `=>du=sec^2(x)dx` `=int1/(u^2+5u+6)du` Now we have to write down integrand as sum of partial fraction function, but first we will have to factor the denominator, `1/(u^2+5u+6)=1/(u^2+2u+3u+6)` `=1/(u(u+2)+3(u+2))` `=1/((u+2)(u+3))` Now let's create partial fraction template, `1/((u+2)(u+3))=A/(u+2)+B/(u+3)`   Multiply the above equation by the denominator, `=>1=A(u+3)+B(u+2)` `1=Au+3A+Bu+2B` `1=(A+B)u+3A+2B` Equating the coefficients of the like terms, `A+B=0`      -----------------(1) `3A+2B=1`  -----------------(2) From equation 1:`A=-B` Substitute A in equation 2, `3(-B)+2B=1` `-3B+2B=1` `=>B=-1` Plug in the values in the partial fraction template, `1/((u+2)(u+3))=1/(u+2)-1/(u+3)` `int1/(u^2+5u+6)du=int(1/(u+2)-1/(u+3))du` Apply the sum rule, `=int1/(u+2)du-int1/(u+3)du` Use the common integral:`int1/xdx=ln|x|` `=ln|u+2|-ln|u+3|` Substitute back `u=tan(x)` and add a constant C to the...

There are several scenes throughout the novel that depict the citizens of Maycomb taking pride in conformity and distrusting those who are different. One of the most notable examples of people taking pride in conformity takes place in Chapter 24 during Aunt Alexandra's missionary circle. Miss Merriweather discusses her prejudiced views and boastfully says, " At least we don’t have that sin on our shoulders down here. People up there set ’em free, but you don’t see ’em settin’ at the table with ’em. At least we don’t have the deceit to say to ’em yes you’re as good as we are but stay away from us. Down here we just say you live your way and we’ll live ours. I think that woman, that Mrs. Roosevelt’s lost her mind—just plain lost her mind coming down to Birmingham and tryin’ to sit with ’em. If I was the Mayor of Birmingham I’d— " (Lee 142). She is proud to live in the South where citizens are unapologetic about segregating their society based on race. Miss Merriweather als...

"To S.M., A Young African Painter, on Seeing His Works," is a poem by Phyllis Wheatley. Wheatley, an eighteenth-century poet, was the first female African American poet published. She became a slave at the age of seven and was emancipated upon the death of her master John Wheatley. Although she was a slave, the Wheatley family took a great interest in her education, and her first volume of poems was published while she was still a slave. This particular poem addresses Scipio Moorhead, who was a poet, an artist, and a slave. He drew the portrait of Wheatley which appeared on her volume of poems, so there was a personal connection. Wheatley begs Moorhead to hold tight to any fame he has, but to fix his eye on his legacy. Their shared bond as artist and slave was a unique one and the position they found themselves in as African American artists in a time in the South when African Americans were considered possessions meant it was even more important for them to create a legacy t...

A great example of the difference between the letter of the law and the spirit of the law can be seen in chapter 30 after Boo Radley saves the Finch children from Bob Ewell's attack on their lives. Atticus is a proponent of upholding the law even if it means that his son has to take responsibility for killing Bob Ewell in self-defense. Heck Tate tells him that it wasn't Jem who killed Ewell, but Boo Radley. As sheriff, Tate represents law enforcement, so what he determines in the case can be analyzed by the state. If anyone is to be held responsible for Ewell's death, which would be based on self-defense, it would all be determined from Tate's report. Tate tells Atticus the following about his decision: "To my way of thinkin', Mr. Finch, taking the one man who's done you and this town a great service an' draggin' him with his shy ways into the limelight--to me, that's a sin. It's a sin and I'm not about to have it on my head. If it was a...

The two main characters are Zaroff and Rainsford. Zaroff has no internal conflicts. He is single-minded. He believes that he is a hunter and that role dictates his life. He has no ethical problem with hunting humans or any other animal. For Zaroff, there is nothing morally conflicting. While on the yacht, Rainsford has no real conflicts either. He tells Whitney that there are two kinds of people: "the hunters and the huntees."  At this point, he is not as radical as Zaroff, but he expresses the same ideology that Zaroff follows. If Rainsford is hunting a jaguar, he doesn't care how the jaguar feels. He is the hunter and the jaguar is the prey. However, when Rainsford learns that Zaroff hunts humans, he is appalled and, hopefully, so is the reader. Rainsford would never hunt humans himself, so he has an ethical disagreement with Zaroff. Then, Rainsford becomes Zaroff's prey and he (Rainsford) has an entirely new appreciation for the fear and anguish of being preyed upo...