SOLUTION: given a piece of rectangular cardboard that measures 15 cm wide and 29 cm long. What is the measure of a side (X) of a square to be cut from each corner in order to make the larges

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: given a piece of rectangular cardboard that measures 15 cm wide and 29 cm long. What is the measure of a side (X) of a square to be cut from each corner in order to make the larges      Log On


   

Question 156413: given a piece of rectangular cardboard that measures 15 cm wide and 29 cm long. What is the measure of a side (X) of a square to be cut from each corner in order to make the largest volume open top box.
Write the polynomial that represents volume.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
given a piece of rectangular cardboard that measures 15 cm wide and 29 cm long.
What is the measure of a side (X) of a square to be cut from each corner in
order to make the largest volume open top box.
:
Write the polynomial that represents volume.
:
The dimensions of the box will be;
(15-2x) by (29-2x) by x
:
FOIL the base:
(15-2x)* (29-2x) = 435 - 30x - 58x + 4x^2 which is: 4x^2 - 88x + 435
;
Multiply the base by the height (x)
(4x^2 - 88x + 435) * x = 4x^3 - 88x^2 + 435x
:
Vol = 4x^3 - 88x^2 + 435x
;
:
The easiest way to determine what value of x produces max vol, is to graph it:
+graph%28+300%2C+200%2C+-4%2C+8%2C+-200%2C+700%2C+4x%5E3-88x%5E2+%2B+435x%29+
You can see max occurs when x is a little over 3"
the trusty ti83 says 3.1467"