# Tutor profile: Elizabeth S.

## Questions

### Subject: Writing

Write a short persuasive essay about something important to you. Use correct grammar.

Green energy is a very important fuel source in today's world. Not only can it cut down on greenhouses gases that warm the atmosphere (which is changing the way all earth's creatures live), but it is renewable. Unlike coal or natural gas, sunlight is available every day. And, in certain parts of the sky, the wind is always blowing. Our society should use more solar and wind energy to give people a higher quality of life with less pollution, more consistent temperatures that are not rapidly climbing, and a more efficient way to power their houses, cars, and various electronics. *The main way this paragraph became persuasive is with the words: "our society SHOULD". The author is encouraging the audience to follow a certain path or to think a certain way. The author also used facts or supporting information, to back up his/her claims to make his/her argumentative more persuasive. The author ended the persuasive paragraph by giving the audience strict guidelines to follow while still making his/her argument sound more appealing, which makes it more compelling to the reader.

### Subject: Calculus

What is the derivative of y = 4(x + 3)^2 + 5?

To find the derivative of the above equation, we must employ the chain rule. Or, treat the information inside the parenthesis like a variable Z. That way, chain rule is as follows: y' (derivative of y) = 2* [ derivative of (4*Z^2) ] * derivative(Z) Also, since there is a 'plus sign' between the two main terms, we can take the derivative of the equation in parts. The first part to look at is 4*Z^2. The derivative of this can be found with the power rule OR: leave the constant 4 alone, multiple Z by the power, then subtract 1 from the power. Thus we get: 4*2 * Z^(2-1) = 8*Z^(1) = 8*Z Now, we must look at the actual derivative of Z, which remember, represents x + 3. Let's employ power rule again. 1*1 * x^(1-1) = x^0 = 1 *it is important to note that anything with the exponent of 0 always equals 1. The derivative of a constant (3, in this case) is always 0. Thus, we end up with 1 + 0 = 1. Last, let's take the derivative of 5, which is again 0. The derivative of any constant is 0. Now, we are left with y'= 8*Z * derivative(Z) + 0 where Z = x+3 y'= 8*(x+3) * 1 + 0 y'= 8*(x+3) now, distribute the 8 into the parenthesis y'= 8x + 24

### Subject: Algebra

One car A is moving at 25 miles per hour. Another car B is moving at 30 miles but is 10 miles behind car A. How long will it take car B to reach car A?

To solve the problem, we can set up 2 equations relating distance, x, to time, t. Car A: x = 25 * t + 10 OR distance = 25miles * time (in hours) + 10miles (that it started at when car B started moving) Car B: x= 30 * t OR distance = 30miles * time (in hours) + 0 Thus, to find the exact distance where the two cares meet is as simple as setting the two equations equal to each other. 25*t + 10 = 30*t Now, the goal is to solve for t (time in hours). Thus, to solve for 't' we must isolate it on one side of the equal sign. This can be done by subtracting 25*t from both sides. 10 = 30*t - 25*t 10 = 5*t One last step: divide both sides by 5. 2 = t In exactly 2 hours, car B will reach the same distance as car A.

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