# CALCULUS

**RELIGION**

**Describe some of the sacred rituals that take place along the Ganges River.**

The Ganges occupies much in way of significance. It is said that a devout Hindu must make at least one pilgrimage to the Ganges river before they die. One of the most basic reasons for this is…

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**THE GRAPES OF WRATH**

**Use The Grapes of Wrath to explain how the American Dream is unattainable to immigrants.**

I think that I would have to offer up some level of resistance to the question on two levels. I am not entirely certain that Steinbeck is directly speaking of the immigrant experience in his work….

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**ALGEBRA1**

**z=?What is the absolute value of z if 3z -9i = 8i + z + 4.**

It is given that 3z -9i = 8i + z + 4 3z -9i = 8i + z + 4 => 3z – z = 4 + 8i + 9i => 2z = 4 + 17i => z = 2 + 17i/2 |z| = sqrt (2^2 + (17/2)^2) => sqrt (4 + 289/4) => sqrt (305/4)…

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**CALCULUS**

**functionsUse the first principle to determine f'(3) whether f(x)=-5x^2.**

First find the derivative of f(x)=-5x^2. From first principles this is equal to lim h–>0 [(f(x + h) – f(x))/h] f(x) = -5x^2 lim h–>0 [(-5(x + h)^2 + 5x^2)/h] => -5*lim h–>0 [((x +…

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**TO KILL A MOCKINGBIRD**

**In To Kill a Mockingbird, what do you believe to be the answer to this question?”How can you hate…**

Human beings have an amazing capacity to maintain a double standard. No one has a patent on virtue or vice, all fall somewhere in between. People hate Hitler because of what he does, but that…

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**A WORN PATH**

**What are the first three obstacles Phoenix Jackson encounters in “A Worn Path”?**

Phoenix Jackson is shown to have to battle through a variety of difficulties to get to her goal and receive the medicine that her grandson needs. Firstly, it is shown that nature itself becomes an…

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**ALGEBRA1**

**math problem.log72 (6) + log 72 (8) = a and log6 4=b-1 . Prove that a(b+3)-3b+1=0.**

It is given that log(72) 48 = a and log(6) 24 = b a = log(72) 48 = log(6) 48/ log(6) 72 => log(6) (6*8)/log(6) 6*12 => [1 + log(6) 8]/[1 + log(6) 12] => [1 + 3*log(6) 2]/[2 + log(6) 2] b…

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**REFERENCE**

**Why should we only produce organic food?Why should we only produce organic food?**

If you had to argue this, you should point to the fact that chemicals can do so much harm to the environment. You can talk about how agricultural chemicals (for example) have run off into the…

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**HARD TIMES**

**What does the chapter “The Starlight” imply to the character, Stephen Blackpool in Hard Times?**

It is this chapter, of course, that poor Stephen Blackpool tragically meets his end, having tumbled down a shaft. He is brought up and rescued, but only to die shortly after from his wounds….

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**LAW AND POLITICS**

**Is there a law that states how often a landlord is REQUIRED to put in new carpeting?I live in…**

There may be a specific law in Michigan that requires as much; but I seriously doubt it. As a general rule, the Landlord has no obligation to the tenant other than to ensure his quiet enjoyment of…

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**CALCULUS**

**Derivativesfind the derivative of y=(2x+4)^1/2 using the first principle**

The derivative of a function f(x) from first principles is the value: lim h–>0 [(f(x + h) – f(x))/h] Here y = f(x) = (2x+4)^1/2 dy/dx = lim h–>0 [((2(x + h)+4)^1/2 – (2x+4)^1/2)/h] =>…

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**GEOMETRY2**

**PointsDetermine the distance between the point ( 2x+3, 8) and the point (2x, 4).**

The distance between any two points (x1 , y1) and (x2 , y2) is given as sqrt ((x1 – x2)^2 + (y1 – y2)^2) Here the points are ( 2x+3, 8) and (2x, 4) The distance between the two is sqrt [(2x + 3 -…

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**APPLICATIONS**

**mathWhat is the common difference of the sum of n terms of an arithmetic series If s= 5n^2-11n?**

The sum of n terms of an arithmetic series is given as: Sn = 5n^2 – 11n Sn-1 = 5(n – 1)^2 – 11(n – 1) => 5(n^2 + 1 – 2n) – 11n + 11 => 5n^2 + 5 – 10n – 11n + 11 => 5n^2 – 21n + 16 The term…

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**POETRY**

**What are some elements of performative qualities in poetry?**

Although “performative qualities” is a term unfamiliar to me, I would assume since we are speaking of poetry or drama, it deals with elements inherent in both literary types. Drama and poetry are…

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**APPLICATIONS**

**Tangent line equation.Given x = 5cost, y =3sint, what is the equation of the tangent line if t=pi/4.**

It is given that x = 5*cos t and y = 3*sin t. We have to find the equation of the tangent if t = pi/4 When t = pi/4 , x = 5*(1/sqrt 2) and y = 3/sqrt 2 dx/dt = -5*sin t and dy/dt = 3*cos t dy/dx =…

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**ALGEBRA1**

**logarithmsIf log x^3- log 10x = log 10^5 find x**

It is given that log x^3- log 10x = log 10^5. To determine x , use the property : log a – log b = log a/b log x^3- log 10x = log 10^5 => log (x^3 / 10x) = 10^5 => x^2 / 10 = 10^5 => x^2 =…

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**MATH**

**Function.What are the extreme values of the function f(x) = 2x-3x^2 + 5.**

The give function f(x) = 2x – 3x^2 + 5. At the extreme point f'(x) = 0 f'(x) = 2 – 6x 2 – 6x = 0 => x = 1/3 f(1/3) = 2*(1/3) – 3*(1/3)^2 + 5 => 2/3 – 1/3 + 5 => 1/3 + 5 => 16/3 The…

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**APPLICATIONS**

**If log72 48 = a and log6 24 = b prove that a(b+3) – 3b + 1 = 0If log72 48 = a and log6 24 = b…**

It is given that log(72) 48 = a and log(6) 24 = b a = log(72) 48 = log(6) 48/ log(6) 72 => log(6) (6*8)/log(6) 6*12 => [1 + log(6) 8]/[1 + log(6) 12] => [1 + 3*log(6) 2]/[2 + log(6) 2] b =…

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**APPLICATIONS**

**mathUse implicit differentiation if y= x^2-5xy+3y^2=7**

To find the derivative dy/dx of y= x^2-5xy+3y^2 implicit differentiation can be used and differentiation carried out in the following way: y= x^2-5xy+3y^2 dy/dx = 2x – 5*x*(dy/dx) – 5y +…

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**THE DEVIL AND DANIEL WEBSTER**

**Why does Jabez Stone make a deal with the Devil in “The Devil and Daniel Webster” by Stephen…**

We are told in the introduction to this story the reason why Jabez Stone was driven to making a deal with the Devil. Jabez Stone was so exasperated by his repeated bad luck that one day, after a…

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**GRAMMAR**

**Does “We are yet to receive your $300 check for the conference fee in the mail” means they…**

“We are yet to receive our check” is a polite way to say “we have not yet received our check.” It is a somewhat old-fashioned form, but its meaning is that we have not yet received it. Quite…

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**TO KILL A MOCKINGBIRD**

**I have to write a letter from the point of view of Boo Radley to Dill and I have no idea what to…**

For an assignment such as yours, you always want to try to stay “in character” as much as possible. That is, when you write the letter from Boo Radley of Harper Lee’s To Kill a Mockingbird, you…

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**A MIDSUMMER NIGHT’S DREAM**

**According to Shakespeare, how are love and art similar in power to transform people’s…**

In A Midsummer Night’s Dream, Shakespeare points out that both love and art suspend reality, making illusion the current reality. Both can suspend reality because both are based on emotions, which…

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**A MIDSUMMER NIGHT’S DREAM**

**What is Shakespeare’s view or outlook of the world, as portrayed in A Midsummer Night’s Dream ?**

Shakespeare uses A Midsummer Night’s Dream to point out social injustices and also to portray the foolishness of mankind. However, Shakespeare also gives us a happy ending for the play, making it a…

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**WHERE ARE YOU GOING, WHERE HAVE YOU BEEN?**

**What are the similarities between Arnold Friend in “Where Are You Going, Where Have You Been? “…**

Schmid becomes the basis for Arnold Friend in Oates’ short story. Some of the descriptions of Arnold Friend are extremely close to how Schmid actually was. The cowboy boots and the lifts inside…

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**SOCIAL SCIENCES**

**Do you prefer online shopping? Why…I like online shopping because it saves my time and money….**

One of the main reasons why I prefer on-line shopping is because it saves time and money. I can access many web sites within a very short duration of time to compare costs, quality, service and…

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**THE DEATH OF IVAN ILYICH**

**In “The Death of Ivan Ilyich,” what is implied in Tolstoy’s calling the colleagues not friends,…**

There is a certain irony in this use of the phrase “nearest acquaintances,” as actually, the news of the death of their colleague does not produce grief, as we might expect it to, but rather much…

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**WORLD WAR I**

**How did World War I impact the soldiers who fought in it?How did World War I impact the soldiers…**

World War I was one of the most horrible wars in history. Because of this, it had a terrible impact on many of the soldiers. Of course, millions of soldiers were simply killed or wounded. The…

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**LITERATURE**

**Summer Reading for TeachersWhat are you looking forward to reading this summer?**

I went to a used bookstore last week and bought three Leon Uris novels, Trinity, Exodus, and Mila 18. Read them all decades ago and for some reason just thought of him again here this year. Plus,…

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**MATH**

**Solve the following only by SUBSTITUTION method: x=y-6 and 3x+2y=2**

The following system of equations has to be solved: x = y – 6 …(1) 3x + 2y = 2 …(2) From (1) x = y – 6 Substitute for x in (2) => 3x + 2y = 2 => 3(y – 6) + 2y = 2 => 3y – 18 + 2y = 2…

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**POLITICAL SCIENCE**

**What was ideology which influenced the creation of the utopian socialism?A. Marxism B….**

Utopian Socialism is by definition is misleading. It is more accurate to view this socialist concept as being “scientific.” By analyzing the choices provided one can use the process of…

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**MATH**

**Solve the following ONLY by ELIMINATION method y=2x-52y-x=2**

The following system of equations have to solved: y = 2x – 5 …(1) 2y – x = 2 …(2) 2*(1) – (2) => 2y – 2y + x = 4x – 10 – 2 => x = 4x – 12 => 3x = 12 => x = 4 (1) – 2*(2) => y -…

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**MATH**

**Solve the following ONLY by substitution method: y=x-3 and 3x+y=5**

The following system of equations: y = x – 3 …(1) 3x + y = 5 …(2) has to be solved by substitution method. From (1) y = x – 3 substitute this in (2) => 3x + y = 5 => 3x + x – 3 = 5 =>…

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**MATH**

**For what values of k is the line y=k tangent to the graph (x-4)^2 + y^2 = 16**

The line y = k is tangent to the circle (x-4)^2 + y^2 = 16 if the center of the circle lies at a distance from the line equal to the radius of the circle. (x-4)^2 + y^2 = 16 => (x – 4)^2 + (y -…

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**ESSAY LAB**

**How can I write this sentence in an ornate style: the boy walked through the woods**

The boy walked through the woods. Ornate style asks that you elevate the diction (vocabulary) and syntax(structure) of the sentence to a higher level. Think of a regular, undecorated wall, and…

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**MATH**

**What is the largest 3-digit number that has only 2 and 5 as prime factors?**

We need to find the largest 3 digit number with only 2 and 5 as prime factors. The number can be expressed as 2^n*5^m. 2^n*5^m should be less than 1000. 2^2*5^2 = 4*25 = 100 It is possible to…

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**MATH**

**3 students are selected from a class that has 10 boys and 5 girls. What is the probability that 1…**

The class has 10 boys and 5 girls. In all there are 15 students. The number of ways in which 3 students can be selected is 3C15 => 15! / 3!*12! => 455 The number of ways that those selected…

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**HISTORY**

**How did American isolationism and neutrality actually contribute to the spread of WWII?How did…**

There is no way to conclusively prove that US isolationism and neutrality actually contributed to the spread of the war. However, you can argue that the US could have prevented the spread of war…

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**SCIENCE**

**Are you familiar the procedure used by astronaut to “weigh” in space?Let us discuss it in a…**

T=2pisqrt(m/k) The chair and spring make a SIMPLE HARMONIC OSCILLATOR. The equation above describes such a system mathematically. T = period of oscillation in seconds (1.45 or 3.5 in this…

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**SOCIAL SCIENCES**

**Which of the following works would be most likely to agree with the statement below? Business…**

The only possible answer to this question is B. The system described is compatible only with the Nazis’ ideology. The system that is described above cannot be either communism or capitalism. In…

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**MATH**

**If cot x= -3/4 and 90° < x < 180° how to find sin x**

In the interval 90 < x < 180, sin x is positive and cos x is negative. It is given that cot x = -3/4 and the value of sin x is required. cot x = cos x / sin x = -3/4 (cos x)^2 = 1 – (sin…

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**LAW AND POLITICS**

**What powers that were reserved for Congress are now in the hands of the President?**

I would say that the major power that was meant to reside with Congress, but has been taken by the Presidency, is the power to declare war. Although the president is the commander-in-chief of the…

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**MATH**

The expression given is (1/2)log(25) + log(20) To simplify this, use the property: a*log b = log b^a and log a + log b = log a*b. Also, log is usually used for logarithm to the base 10….

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**MATH**

**Solve the equation: 6a^-2 + a^-1 = 2**

The equation to be solved is 6a^-2 + a^-1 = 2 6a^-2 + a^-1 = 2 Let a^-1 = y => 6y^2 + y = 2 => 6y^2 + y – 2 = 0 => 6y^2 + 4y – 3y – 2 = 0 => 2y(3y + 2) – 1(3y + 2) = 0 => (2y – 1)(3y…

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**SOCIAL SCIENCES**

**Which of the following ideologies’ ideas is best represented by this statement?” We the working…**

Assuming that the phrase “oppression of the bourgeoisie” refers to the idea that the bourgeoisie are the ones oppressing others (as opposed to the idea that the bourgeoisie is being oppressed), the…

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**JULIUS CAESAR**

**In Julius Caesar, when Brutus says “now be still/ I kill’d not thee with half so good a will,” is…**

As with so many of Shakespeare’s speeches and lines that he gives to characters, I think it depends a lot on how a director of this excellent play wants to show these lines using subtext: what…

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**MATH**

**Prove that if x^y = y^x, then ln(x)/x = ln(y)/y.**

It is given that x^y = y^x Take the logarithm to the base e, or ln, of both the sides => ln [ x^y] = ln [ y^x] Use the property of log that log a^b = b*log a => y*ln x = x*ln y divide both…

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**MATH**

**What is the indefinite integral of (14x)/(x^4+1)**

The given function is f(x) = (14x)/(x^4+1). The integral of f(x) is required to be found. Int [ f(x) dx] => Int [ (14x)/(x^4+1) dx] let x^2 = y dy = 2x dx => Int [ 7/(1 + y^2) dy] => 7*arc…

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**BUSINESS**

“T-Letters” are used in applying for a job. They are a substitute for the standard cover letter that you might include with your resume. The “T-Letter” has a brief introductory paragraph,…

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**BUSINESS**

**What is understood by ‘nonsexist language’?**

The term “nonsexist language” refers to words and ways of speaking that do not imply that men are better than women. Because society (and especially the business world) has typically been male…

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