Question

A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 12 in. by 20 in. by cutting out equal squares of side x at each corner and then folding up the sides

a) Find the values of x for which the volume is greater than 230 in³. (Round your answers to three decimal places. Enter your answer using interval notation.)

Answer 1

To find the values of x for which the volume is greater than 230 in³, we need to solve a cubic inequality. The values of x lie within the interval (4.526, 6.242).

Step-by-step explanation:

To find the values of x for which the volume is greater than 230 in³, we need to set up an equation for the volume and solve for x.

The volume of the box is given by V = x(12-2x)(20-2x). We can simplify this equation to V = 4x³ - 64x² + 240x. Setting V greater than 230, we have 4x³ - 64x² + 240x > 230.

Solving this cubic inequality, we find that x lies within the interval (4.526, 6.242).