SOLUTION: The width of a box is 200 cm less than the length. THe height is 100 cm less than the length. The volume of the box is 20 m^3. Write a polynomial function to describe the volume

Algebra ->  College  -> Linear Algebra -> SOLUTION: The width of a box is 200 cm less than the length. THe height is 100 cm less than the length. The volume of the box is 20 m^3. Write a polynomial function to describe the volume      Log On


   

Question 821135: The width of a box is 200 cm less than the length. THe height is 100 cm less than the length. The volume of the box is 20 m^3. Write a polynomial function to describe the volume. Find the dimensions of the box.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The width of a box is 200 cm less than the length.
Change 200 cm to 2 meter
W = L-2
:
THe height is 100 cm less than the length.
Change 100 cm to 1 meter
H = L-1
:
The volume of the box is 20 m^3.
L * W * H = 20
:
Write a polynomial function to describe the volume.
Replace W and H
f(L) = L * (L-2) * (L-1)
f(L) = L(L^2 - 3L + 2)
f(L) = L^3 - 3L^2 + 2L
:
Find the dimensions of the box.
L^3 - 3L^2 + 2L = 20
L^3 - 3L^2 + 2L - 20 = 0
Graphically
+graph%28+300%2C+200%2C+-6%2C+10%2C+-50%2C+50%2C+x%5E3-3x%5E2%2B2x-20%29+
L = 3.84 m (384cm), you can find W and H