Question

The volume of a rectangular room, in cubic yards, is give by V(x)=x(2x)(x-3)=2x^(3)-6x^(2) where x is in yards. Write a function for the volume in cub feet if x is still in yards.

Answer 1

To convert the volume of a room from cubic yards to cubic feet, multiply the function V(x) = 2x^3 - 6x^2 by 27, resulting in the new function V(x) = 54x^3 - 162x^2.

Step-by-step explanation:

The volume of a rectangular room in cubic feet can be found by converting the given function V(x) = 2x^3 - 6x^2, where x is in yards, to cubic feet. Since there are 3 feet in 1 yard, and 1 cubic yard is equal to 27 cubic feet (3 feet × 3 feet × 3 feet), we need to multiply the given volume by 27 to convert it to cubic feet.

So, the function for the volume in cubic feet when x is still in yards is V(x) = 2x^3 - 6x^2 × 27.

Simplifying, we get the volume function in cubic feet as V(x) = 54x^3 - 162x^2, where x is still in yards.