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Chris L.
College Student, Tutor for 3 Years
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Algebra
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Question:

If 2(x-3) = 14, what is x^2 - 6x + 9?

Chris L.

The first step is to figure out (1) what information you have and (2) what information you need. First, we can quickly figure out what x-3 is from the first equation. Second, realize that x^2 - 6x + 9 is equivalent to the expression (x-3)^2. Putting (1) and (2) together, we find that x-3 = 7, so x^2 - 6x + 9 = 7^2 = 49.

Calculus
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Question:

Differentiate y = (3x+1)^2.

Chris L.

There are two ways to do this: chain rule or simplifying the expression. In the interest of furthering our understanding of the chain rule, we'll try the first option. The expression $$(3x+1)^2$$ looks like $$x^2$$, except x is replaced by $$3x+1$$. Using the chain rule, the derivative of $$(3x+1)^2$$ will be $$[2*(3x+1)]$$ * [the derivative of $$3x+1$$]. Trivially, we find that this is equal to $$2*(3x+1)*3 = 18x+6$$. We can verify by simplifying the expression to $$(3x+1)^2 = 9x^2+6x+1$$, whereupon it becomes clear that $$18x+6$$ is indeed the correct answer.

Chemistry
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Question:

How many calories of energy are needed to heat 50g of water from 15.0 to 45.0 degrees Celsius?

Chris L.

First, we must recognize that this is a standard heat problem, which requires the heat formula Q = mc($$\Delta$$T), where m = 50g, c = 1 $$\frac{calorie}{gram\ C}$$, and change in temperature $$\Delta$$T = 30 degrees Celsius. Therefore, the amount of calories, Q = 50 * 1 * 30 = 1500 calories.

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