SOLUTION: A trough at the end of a gutter is meant to direct water away from a house. The homeowner makes the trough from a rectangular piece of aluminium that is 20 in long and 12 in wide.

Question 1109658: A trough at the end of a gutter is meant to direct water away from a house. The homeowner makes the trough from a rectangular piece of aluminium that is 20 in long and 12 in wide. he makes a fold along the two sides a distance of x inches from the edge:
write a function to represent the volume in terms of x? what is max volume?

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A trough at the end of a gutter is meant to direct water away from a house.
The homeowner makes the trough from a rectangular piece of aluminium that is 20 in long and 12 in wide.
he makes a fold along the two sides a distance of x inches from the edge:
write a function to represent the volume in terms of x? what is max volume?
:
End of the trough looks like this. x= the height; w = the width
x|_w_|x
:
From the information given we know
2x + w = 12
or
w = (12-2x)
the volume
V = 20 * x * w
replace w with (12-2x)
V = 20x(12-2x)
V(x) = -40x^2 + 240x is the function
:
Max area occurs at the axis of symmetry: x=-b/(2a); where a=-40, b= 240
x =
x = +3 in for max volume
Find the vol when x = 3
V(3) = -40(3^2) + 240(3)
V(3) = -360 + 720
V(3) = 360 cu\in is max vol

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