The measure of an angle is 14 degrees. What is the complementary angle? What is the supplementary angle?
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
Find the critical points of the following function: f(x) = 8x^3 + 81x^2 - 42x - 8
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
The ratio of two numbers is 5 to 1. The sum is 18. What are the two numbers?
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