Question

the gray banded king snake requires an enclosure in which the length is at least 20 inches greater than the width and the height is 5 inches more than twice the width.

Answer 1

If we denote the width of the enclosure as W (in inches), then according to the description:

- The length L is W + 20 inches.

- The height H is 2W + 5 inches.

The volume V of a rectangular enclosure is given by the formula V = LWH.

Substituting L and H into the volume formula, we have:

V = (W + 20)(W)(2W + 5).

Simplifying this expression, we get:

V = 2W^3 + 45W^2 + 100W.

So, the volume of the enclosure in cubic inches is given by the polynomial expression 2W^3 + 45W^2 + 100W. If we compare this with a generic cubic polynomial AW^3 + BW^2 + CW, then A = 2, B = 45, and C = 100. Note that we don't have a constant term, so D = 0.