word problem?

Question

Each of the three dimensions of a cube with a volume of y^3 cubic centimeters is decreased by a whole number of centimeters. If the new volume is y^3 - 13y^2 + 54y - 72 cubic centimeters and the new width is y - 6 centimeters, then what are the new lenght and height?

Answer 1

You know that the product of the three sides of the cube is the volume.
We know the volume is
We know one side is
We divide this into the volume to get the product of the other two sides.
(y^3 - 13y^2 + 54y - 72) / (y-6) = y^2 - 7y + 12
Now we factor that to get its roots (y-4)(y-3)

Answer 2

Without getting too technical, if the new width is y-6, the volume/(y-6) is a quadratic whose factors indicate the decrease in the other two sides. Doing the division yields y^2-7y+12, which factors to (y-3)*(y-4). The other sides are reduced by 3 and 4 cm respectively.

Answer 3

if new cube = (y-6)(y-a)(y-b) with a and b being length and width

then y^3 - 6y^2 - ay^2 - by^2 - 6ay - 6by - aby - 6ab =
y^3 - 13y^2 + 54y - 72

therefore (6+a+b) y^2 = 13y^2
6 + a + b = 13
a + b = 7
b=7-a
if 6ab=72
then ab =12

a(7-a)=12
7a - a^2 - 12 = 0
a^2 -7a +12 = 0
(a-4)(a-3) = 0


so a = 4, b= 3
or a =3, b = 4

Answer 4

U NEED TO DO UR HOMEWORK