Question

Can someone help me with this math problem :)!? I added some pictures.

Answer 1

Answer:

V = 4x^3-39x^2+93.5x

Domain: 0 < x < 4.25

Using the graph the maximum volume is about V = 66 inches ^3  at about x = 1.6  

Step-by-step explanation:

V = l*w*h

The length is 11 -2x

The width is 8.5 -2x

The height is x

V = ( 11 -2x) ( 8.5 -2x) x

FOIL ( first outer inner last)

V = (93.5 -22x - 17x +4x^2) x

Combine like terms

V =( 4x^2-39x+93.5)x

Distribute the x

V = 4x^3-39x^2+93.5x

The domain is the values that x can take

Looking at the picture

2x can be no largest than 8.5 or there will be no width

2x < 8.5

x < 4.25

If x ≤ 0 there is no height so x > 0

0 < x < 4.25

Using the graph the maximum volume is about V = 66 inches ^3  at about x = 1.6