Question

The volume of a particular rectangular box is given by the equation v=6x^3 + 30x^2. The height is 2x and the length is x+5. Find the width of the box in terms of x.

A. 3x
B. 5x
C. 2x
D. x+2

Answer 1

The width of the box in terms of x is 3x^2 / (x+5).

Step-by-step explanation:

The volume of a rectangular box is given by the equation v=6x^3 + 30x^2, where the height is 2x and the length is x+5. To find the width of the box in terms of x, we can use the formula for volume of a rectangular box: V = L x W x H. Rearranging the equation, we have:

6x^3 + 30x^2 = (x+5) x W x 2x

Simplifying the equation, we get: 6x^3 + 30x^2 = 2x(x+5)W

Dividing both sides by 2x(x+5), we get: W = (6x^3 + 30x^2) / (2x(x+5))

Simplifying further, we get: W = 3x^2 / (x+5)

Therefore, the width of the box in terms of x is 3x^2 / (x+5).