Question

The volume of a box is represented by the function V(x) = x^3 + 6x^2 + 11x + 6. The height of the box is x + 2. If the area of the base is 24cm^2, determine the height of the box.

Answer 1

the equation for V=lwh

so we know
lw=24
h=x+2
V= x^3 + 6x^2 + 11x + 6
our equation now looks like this;

x^3 + 6x^2 + 11x + 6=(x+2)(24) divide both sides by x+2

Answer 2

what do you get??

Answer 3

I got x^2 + 4x + 3 on the left side and R = 0/x+2

Answer 4

On the right side, (x + 2)(24)...

(x+2)(24) = 24x+48.

I have to divide 24x+48 by (x+2)??? I am back to original if I divide it though..

Answer 5

ok
x^2 + 4x + 3=24 -->(x+2) cancel on rt

Answer 6

Yes

Answer 7

now subtract 24 from both sides and factor the quadratic equation

Answer 8

ohhhhhhh! Alright

Answer 9

what did you get

Answer 10

I am still solving!

Answer 11

(x-3) and (x+7) ???

Answer 12

set both those to zero and solve ignore the neg. answer

Answer 13

Okay, give me a sec

Answer 14

x-3=0
x+7=0

Answer 15

Yes, I am doing that currently!

Answer 16

Does this seem right? (x-3) is height.

Answer 17

x-3=0
x=3
so 3+2=5 is height

Answer 18

plug 3 in and check your answer

Answer 19

Alright, Thank you!

Answer 20

good job!!

Answer 21

:D Thank you so much!

Answer 22

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