What is the quotient of (x^3+3x^2-4x-12) / (x^2+5x+6)?

The quotient is x -2

Step-by-step explanation:

1. Let's simplify and find out the quotient of the following division:

(x^3+3x^2-4x-12) / (x^2+5x+6)

(x³ + 3x² - 4x - 12)/ (x² + 5x + 6)

(x + 2) (x² + x - 6) / (x + 2) (x + 3) ⇒ Factorizing on the numerator and the denominator

(x² + x - 6) / (x + 3) ⇒ Eliminating (x + 2) on the numerator and the denominator

(x + 3) (x - 2) / (x + 3) ⇒ Factorizing on the numerator

x - 2 ⇒ Eliminating (x + 3) on the numerator and the denominator

The quotient is x -2

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80π/3 or about 83.775

step-by-step explanation:

since a cone is 1/3 of a cylinder, we need to find the base's area. since area = πr^2, we get 16π. then, multiplying this by 5, we get 80π. dividing by 3, since the cone's volume is 1/3 of that of a cylinder's, we get 80π/3.

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