Catherine L.

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Geometry

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Question:

The measure of an angle is 14 degrees. What is the complementary angle? What is the supplementary angle?

Catherine L.

Answer:

Complementary angles sum to 90 degrees. So the complementary angle can be modeled by the equation x + 14 = 90 Therefore, by subtracting 14 we get x = 76 Supplementary angles sum to 180 degrees. So the complementary angle can be modeled by the equation x + 14 = 180 Therefore, by subtracting 14 we get x = 166

Calculus

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Question:

Find the critical points of the following function: f(x) = 8x^3 + 81x^2 - 42x - 8

Catherine L.

Answer:

1. Take the derivative using the power rule. (Power Rule: If f(x) = x^n, then f'(x) = n * x^(n-1) f'(x) = 24x^2 + 162x - 42 2. Factor f'(x) 6(4x^2 + 27x - 7) 6(x+7)(4x-1) 3. Set f'(x) equal to zero 6(x+7)(4x-1) = 0 x = -7 x = 1/4

Algebra

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Question:

The ratio of two numbers is 5 to 1. The sum is 18. What are the two numbers?

Catherine L.

Answer:

The key words in this problem are "ratio" and "sum". This let's us know how to set up the equations. "Ratio" means that we need to set up a division problem. Let the two unknown numbers be 'x' and 'y'. We can set up a division of x / y and set it equal to 5 / 1. So the overall equation is x/y = 5/1. We can rearrange this to solve for x. Multiply each side by y x = 5y "Sum" means that we need to set up an addition problem. So the equation we write it x + y = 18. Since we solved for x in the first equation, we can replace it in the addition equation so we get only one variable. 5y + y = 18 Next, combine like terms: 6y = 18 Divide by 6: y = 3 y = 3 is one answer. To solve for x you can plug y into either of the original equations. Let's choose the addition equation: x + y = 18 x + 3 = 18 Subtract x from each side: x = 15

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