the Pythagorean Theorem, we also know that when y = 30 and x = 45, z = 54.08.
Step 4: Now we plug everything into the equation from Step 2 and solve for .
(45)(18) + (30)(12) = (54.08)
1,170 = (54.08)
21.63 =
- B This question is testing your knowledge of the rules of definite integrals.
Step 1: Generally speaking, f(x)dx + f(x)dx = f(x)dx.
So here, f(x) dx + f(x) dx = f(x) dx.
If we substitute f(x) dx = A and f(x) dx = B, we get f(x) dx + B = A.
- D This problem requires you to know how to find the derivative of an inverse function.
Step 1: The rule for finding the derivative of an inverse function is
If y = f(x) and if g(x) = f −1(x), then g′(x) =
Step 2: In order to use the formula, we need to find the derivative of f and the value of x that
corresponds to y = 10.
First, f′(x) = 6x − 1. Second, when y = 10 we get 10 = 3x^2 − x.
If we solve this for x, we get x = 2 and x = − , but we’ll use 2—it’s easier.
Step 3: Plugging into the formula, we get .
Note: There was another possible answer using x = − , but that doesn’t give us one of the
