Jordan is designing the battery box for his high school solar car team. He needs the height of the box to be 10 inches in order to accommodate the batteries. The length of the box will be 14 inches more than the width. Write an equation that can be used to find the width of the battery box, w, if the final design has a volume of 3,510 cubic inches.

3,510 = 10w^2 + 140w

Step-by-step explanation:

The volume of a rectangular prism can be found using the equation V = l · w · h where l is the length, w is the width, and h is the height, and V is the volume.

It is given that the height is 10 inches, the volume is 3,510 cubic inches. The length is 14 inches longer than the width. Thus, the length can be represented by the equation l = w + 14.

Substitute V = 3,510, h = 10, and l = w + 14 into the equation for the volume of a rectangular prism and distribute to find the standard form equation.

Therefore, the equation that can be used to find the width of the battery box is 3,510 = 10w2 + 140w.

(Literally copied and pasted from plato)

w^2 + 14w - 351 = 0.

Step-by-step explanation:

If the width is w then the length is w + 14 inches.

The volume = width * length * height, so we have the equation:

3510 = w (w + 14) * 10

10w (w + 14) = 3510

10w^2 + 140w - 3510 = 0

This can be simplified to:

w^2 + 14w - 351 = 0 (answer).