Question

A box has a width 9 inches less than its height and a length 7 inches more than its height.

a. If h is the height of the​ box, write a polynomial that represents the volume of the box.
b. Use this polynomial to calculate the volume for h​ = 17 inches.

Answer 1

So everything in this problem is in terms of height (h). We'll abbreviate width to w and length to l and volume to v

l=h+7
w=h-9

a.
volume is height x width x length

v=h*(h+7)*(h-9)

now we have to multiply these values

h*(h+7)=h^2+7h

(h^2+7h)*(h-9)=h^3-9h^2+7h^2-63h=h^3-2h^2-63h

b.
now we plug in h=17
v=17^3 -2(17)^2 -63(17) = which comes out to 2686

note: **i suggest going through these steps on your own mostly because it's late and i'm tired and that seems like an awfully large number so you may want to check it