Sarah M.

Columbia Engineering student and former STEM instructor with a lot of teaching experience

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SAT

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Question:

If 3x - y = 12, then what is the value of (8^x)/(2^y)

Sarah M.

Answer:

We can rewrite (8^x)/(2^y) as (2^3)^x*2^-y. Combining the exponents, we get 2^(3x-y) the initial condition gives us: 3x-y=12, therefore our solution is: 2^12

Calculus

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Question:

The function f is defined by: f(x) = (x^3)-5x Write an equation for the line tangent to the graph at x=2

Sarah M.

Answer:

First, we need to differentiate x, using power rule. f'(x)= (3x^2)-5 at x = 2, f'(x) = 7. This is the slope of the tangent line. Our tangent line is then of the form: y = 7x+b. In order to find b, we must find the point of intersection, or the point where both f(x) and y share the same values for x and y. f(2)=8-10 = -2 we know that (2, -2) is the point at which the two curves intersect. -2= 7(2)+b solving for b, we get b=-16 Thus, the equation for the line is: y=7x-16

ACT

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Question:

For all real numbers "b" and "c" such that the product of c and 4 is b, which of the following expressions represents the sum of c and 4 in terms of b?

Sarah M.

Answer:

The first step here is to notice that the question has given us the following piece of information: 4c = b, or b/4=c. The question asks for the sum of c+4 in terms of b. We substitute in b/4 for c, giving us the final answer: b/4 + 4

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