SOLUTION: A raingutter is made from sheets of aluminum that are 18 inches wide by turning up the edges to form right angles. Determine the depth of the gutter that will maximize its cross-se
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Question 243238: A raingutter is made from sheets of aluminum that are 18 inches wide by turning up the edges to form right angles. Determine the depth of the gutter that will maximize its cross-sectional area and allow the greatest amount of water to flow. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! A rain gutter is made from sheets of aluminum that are 18 inches wide by turning up the edges to form right angles.
Determine the depth of the gutter that will maximize its cross-sectional area and allow the greatest amount of water to flow.
:
Let x = depth of the gutter
then
18-2x = width of the gutter
:
Cross section area:
A = depth * width
A = x(18-2x)
A = 18x - 2x^2
:
Axis of symmetry will give x value for max area: x = -b/(2a)
x =
x =
x = +4.5 inches is the depth for max area
:
:
Max area: 4.5 * 9 = 40.5 sq/in
