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The elements in a row of the Pascal's triangle are given by C(n, r) where n in the row number and r is the element in the row. Let 1, 10 , 45 be the first three elements of row n. C(n, 0) = 1...

I see freedom being slavery in life when we make a choice with our freewill that over time becomes something we are bound to. Orwell's entire point in writing 1984 had to do with warning even the...

As an aesthete, Walter Pater would contend that literature, like Art, should be for the sake of literature, itself. Hence, Pater welcomes literature as a conduit of beauty, much like Art. The...

Even before Macbeth suspects anyone is plotting against him, he feels guilty, paranoid, and always anxious that his crimes will be discovered and/or he will be overthrown. In Act 3, Scene 1,...

In many ways, Oscar Wilde's The Importance of Being Earnest, as its title suggests, represents a quest for authenticity. Although the mode of presentation is satiric, as all satire, it has a point....

We have to verify the identity: `cos x/(1 + sin x) = csc x - cot x` `cos x/(1 + sin x)` => `cos x*(1 - sin x)/((1 + sin x)(1 - sin x))` => `(cos x - cos x*sin x)/(1 - sin^2x)` => `(cos x -...

A mountain range can sometimes produce separate types of climates on either of its sides, depending on other meteorological conditions and factors. A mountain range can sometimes trap moisture on...

I think that there are some ironies in the book outside of the most evident one of a Jewish girl in love with a Nazi. The fact that Patty's parents, especially her father, displays nothing but...

There are a number of key differences in the nature of the combatants and the background to the struggles themselves that have necessitated a different approach in the case of the Taliban in...

`2Li+2H_2O rarr 2LiOH+H_2` Molar masses Li = 7 g/mol H = 1 g/mol O = 16 g/mol When the reaction takes place `H_2` gas will be removed from the system. Amount of Li added = 28/7 = 4 mol Amount of...

In Western forms of Protestant and Catholic practice of Christianity, fasting is an optional-only practice that is infrequently used and for which there are no longer any governing rules. This...

Jim, of course, is drawn to other children. His neighbor's children provide him with diversion and a sense of family. He plays with the family, and with Antonia when she comes to work in the...

One of the most lasting acts that was created out of the New Deal was the FDIC Legislation. This act helped to ensure that banks would not go insolvent as the federal government would protect...

This phrase is found in Act 2 of The Importance of Being Earnest after Algernon shows up in Jack's estate in the country pretending to be Jack's fictitious wicked brother Ernest. After arguing back...

Karma literally means action or 'to do.' It is active and dynamic. Many people mistake karma to mean 'predestination' as the Calvinists believe. Yet, this is not quite accurate. For example, you...

Chapter 5 brings one of the strongest denunciations from Eliezer regarding the presence of God. The arrival of Rosh Hashanah prompts Eliezer to launch into a pointed and brutal tirade about where...

The primary reason why Lennie has a mouse in his pocket is that he likes to stroke it and play with it. The reason he *constantly* puts mice in his pockets is that he has an unfortunate habit of...

Caligula AD 37-41 was probably the most cruel of the Roman Emperors. Caligula was greedy and bloodthirsty. He frequently insisted on being worshipped as a god. He was murdered on the capitol...

Use acceleration due to gravity: g = -32ft/sec^2, initial velocity of 0, and initial height of 200 in the equation: `h(t) = -1/2 g t^2+v_0t+h_0` So we have `h(t)=-16t^2+200` Solve for t when h(t) =...

Scout in Chapter 6 is very much like Scout in the rest of the novel. She's good-hearted, precocious, stubborn as a mule, etc. The main difference there is that in that chapter she mentions that she...

Guy de Maupassant wrote often of the petty bourgeosis of whom Maitre Hauchecorne is one. And, for this class, Maupassant had a certain disdain. The tone of this disdain prevails in his short...

Jonas and his father were worried about Gabe's fretfulness at night because it was an indication that he was not developing at the rate that was expected and could result in release. Jonas lives in...

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In 1945, Japan surrendered to the USA, and forfeited all territory it had captured in World War II, including the Korean Peninsula. The Soviet Union had also been at War with Japan, and an...

(I) How much should you deposit at the end of each month into an account that pays 9% compounded monthly to have $2 million when you retire in 35 years? To solve, apply the formula: `P =...

The given functions are: f(x)= (6x^2 + 7x - 3)/(2x + 3) and g(x) = 3x(3x+1) - (1 + 9x^2) f(x)=6x^2+7x-3/2x+3 => f(x) = (6x^2 + 9x - 2x - 3)/(2x + 3) => f(x) = (3x (2x + 3) - 1(2x + 3))/(2x +...

It is given that the figure when rotated in a counter clockwise manner by 90 degrees rests in the second quadrant. The same can be achieved by rotating the figure in the clockwise manner. The...

It is given that 300kd(kd/2)=8*1500(500-kd). This equation has to be solved to determine kd. 300kd(kd/2)=8*1500(500-kd) => kd^2 = 80(500 - kd) => kd^2 = 40000 - 80 kd => kd^2 + 80kd -...

I have changed your topic to "Falconer," since eNotes provides much valuable information about the book, including Themes, which you can access by clicking on the link below. It seems to me that...

The time it usually takes the to fill the tank using the pipe is 2 hours. In one hour 1/2 of the tank is filled. With the leak, it take 30 minutes more or 2.5 hours. In one hour, 1/2.5 of the tank...

The relation between the harmonic mean H of two numbers x and y and the numbers is 2/H = 1/x + 1/y or H = 2xy/(x + y). Here x = 8 and y = 12 The harmonic mean of the two numbers is 2*8*12/20 =>...

I would say that racism in sports has diminished. Like a couple of other posters have mentioned the playing field seems to have leveled, however the management positions are more likely to be held...

We have to evaluate `3*ln e^(1/4)` Use the property of logarithms: `log b^a = a*log b^a` `3*ln e^(1/4)` => `3*(1/4)*ln e` => `(3/4)*ln e` ln is used for logarithm that has the base e =>...

You would like to know the value of 2X + 14Y + 5. X and Y are variables and can take on any value. It is not possible to determine what the value of 2X + 14Y + 5 is unless further information is...

We have to find the derivative of the function f(x) = [(2x -1)/ (x +7)] ^3. Start by using the Power rule. This gives f’(x) = 3*[(2x -1)/ (x +7)] ^2 * d/dx [(2x -1)/ (x +7)]. Now use the quotient...

Atticus Finch shows various forms of bravery throughout the Harper Lee novel, To Kill a Mockingbird. As a young man, he leaves the family homestead at Finch's Landing to pursue a law degree....

We have 2z - 3 + i = (3-i)/(2+4i). We have to find z and |z|. 2z - 3 + i = (3-i)/(2+4i) => 2z - 3 + i = (3-i)(2 - 4i)/(2+4i)(2 - 4i) => 2z - 3 + i = (3-i)(2 - 4i)/(4+16) => 2z - 3 + i =...

In order to answer this, one needs to reference many news accounts written at the time of the event. In general though, after the first whispers of the anthropophagy that was necessary for survival...

You want 405x to the 4th power and y to the 13 power and 6 times 32 expressed as radicals. 405x to the 4th power can be written as 405*x^4 y to the 13 power can be written as y^13 6 times 32 can be...

John Milton is regarded as one of the greatest writers of all time. I will be happy to provide you with some details regarding his life. More information is available at the at the reference links...

Janine stands 30 m away from the base of a communication tower. Her eyes are 1.8 m above the ground. She is looking at the top of the tower and the angle of elevation is 70 degrees. Consider a...

The band U2 has a song called "Do you feel loved?" on their Pop album. The song is a somewhat cutting commentary on what people will do when they don't feel loved. One could argue that Macbeth,...

We have to solve log(4)(x+4)-2(log(4)(x+1))=1/2 Use the property log a - log b = log(a/b) and a*log b = log a^b log(4)(x+4)- 2(log(4)(x+1))=1/2 => log(4)(x+4) - log(4)(x+1)^2 = 1/2 =>...

Because DNA is a double helix with two chains that are complementary, either side may act as a template for its replication. DNA is the only molecule that can copy itself. Its subunits are called...

The original question had to be edited. Lanchester's argument is a fairly interesting one related to economic expansion and fairness convergent with the end of the Cold War. Essentially, the...

Rosetta Stone recently added a fully online component to their language training programs that give you both the work at home CD and allow you to work and practice with others on the web as well....

We are given that the points (1,2) and (0, 3) are on the graph of f(x)=ax^2+x+c. We can write the following equations: 3 = a*0 + 0 + c = c and 2 = a +1 +c = a + c + 1 Now from the first equation...

We have to find the equation of a circle with center (0,0). The circle touches the line 5x - 12y = 52. So the line is a tangent. The radius of the circle is the distance from (0,0) to the line 5x -...

We have to find the sum 1/[1+x/(y+z)]+1/[1+y/(z+x)]+1/[1+z/(x+y)] 1/[1+x/(y+z)]+1/[1+y/(z+x)]+1/[1+z/(x+y)] => (y + z)/(x + y + z) + (z + x)/(x + y + x) + (x + y)/(x + y + z) => (y + z + z +...

It is given that 18 added to x gives y => 18 + x = y Also, 18 multiplied by 4x gives y^2 => 18*4x = y^2 Now substituting y = 18 + x in 18*4x = y^2 => 18*4x = (18 + x)^2 => 72x = 18^2 +...