# Tutor profile: Lauren S.

## Questions

### Subject: Geometry

Angles A and B are complementary. The measure of angle A is twice the measure of angle B. Find the measures of angles A and B.

First off, if angles are complementary, they add up to 90 degrees. So that means: A + B = 90 We also know that A is two times the size of B. So we can write that as: A = 2B We can replace A from our first equation with the new value from our second equation because they are equal. Now our equation looks like: 2B + B = 90 We can combine like terms and solve for B: 3B = 90 B = 90/3 B = 30 Now, we can put the number we just found for B into our second equation to solve for A: A = 2B A = 2(30) A = 60 So our answers are A = 60 degrees and B = 30 degrees.

### Subject: Calculus

Find the derivative of the given function: f(x) = (4x^{2} - x) (x^{3} - 8x^{2} + 12)

This problem can be most easily solved by using the product rule. The product rule is (f *g)' = f' * g + f * g' In our case, f = 4x^{2} - x g = x^{3} - 8x^{2} + 12 1) The first step is to find f': f' = 8x - 1 2) Next we find g': g' = 3x^{2} - 16x 3) Now, we multiply f' * g : (8x - 1) (x^{3} - 8x^{2} + 12) = 8x^{4} - 64x^{3} + 96x - x^{3} + 8x^{2} - 12 = 8x^{4} - 65x^{3} + 8x^{2} + 96x - 12 4) Next, we multiply f* g': (4x^{2} - x) (3x^{2} - 16x) = 12x^{4} - 64x^{3} - 3x^{3} + 16x^{2} = 12x^{4} - 67x^{3} + 16x^{2} 5) Finally, we add together f' * g + f * g': 8x^{4} - 65x^{3} + 8x^{2} + 96x - 12 + 12x^{4} - 67x^{3} + 16x^{2} = 20x^{4} - 132x^{3} + 24x^{2} + 96x -12

### Subject: Algebra

Simplify the following equation: 3(a + 3) - 2b + 4(a + 2b - 1) + 2

1) The first step is to multiply the factors: 3a + 9 - 2b + 4a + 8b - 4 + 2 2) Next, we combine the like terms. This means that all of the numbers with an 'a' get added together, all of the numbers with a 'b' get added together, and then all of the numbers without a letter are added together. I like to reorder the numbers so it's easier to do: 3a + 4a - 2b + 8b + 9 - 4 + 2 = 7a - 6b + 11

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