Question

The volume of a box, V(x) , is represented by the function V(x)=x(15-2x)(20-2x) , where x represents the width of the box.. What is the domain of V(x) ？

A. all real numbers greater than 0
B. all real numbers greater than 0 and less than 10
C. all real numbers greater than 0 and less than 15
D. all real numbers greater than 0 and less than 20
E. all real numbers greater than 0 and less than 30

Answer 1

The domain of V(x) is all real numbers greater than 0 and less than 7.5.

Step-by-step explanation:

The volume of a box is represented by the function V(x)=x(15-2x)(20-2x), where x represents the width of the box. To determine the domain of V(x), we need to find the values of x that make the equation valid.

Since the width of a box cannot be negative, we know that x must be greater than 0. Additionally, the expression (15-2x)(20-2x) must be greater than or equal to 0 for the volume to exist. Solving this inequality, we find that x must be less than 15/2 or 7.5. Therefore, the domain of V(x) is all real numbers greater than 0 and less than 7.5.