SOLUTION: A rectangular piece of cardboard twice as long as wide is to be made into an open box by cutting 2" squares from each side and bending up the sides... Express the volume V of th

Algebra ->  Volume -> SOLUTION: A rectangular piece of cardboard twice as long as wide is to be made into an open box by cutting 2" squares from each side and bending up the sides... Express the volume V of th      Log On


   

Question 515619: A rectangular piece of cardboard twice as long as wide is to be made into an open box by cutting 2" squares from each side and bending up the sides...
Express the volume V of the box as a function of the width w of the piece of cardboard
Find the domain of the function
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A rectangular piece of cardboard twice as long as wide is to be made into an open box by cutting 2" squares from each side and bending up the sides...
Express the volume V of the box as a function of the width w of the piece of cardboard
:
(2w-4) = the length
(w-4) = the width
2 = the height
:
V = 2(2w-4)(w-4)
FOIL
V = 2(2w^2 - 8w - 4w + 16)
V = 2(2w^2 - 12w + 16)
V(w) = 4w^2 - 24w + 32
:
Find the domain of the function
Find w
4w^2 - 24w + 32 = 0
Simplify, divide by 4
w^2 - 6w + 8 = 0
Factor to
(w-4)(w-2)
w = 4
and
w = 2
:
Domain: w=<2 and w=>4