Question 70252: A rectangular sheet of aluminum 300 inches long and 12 inches wide is to be made into a rain gutter by folding up the two longer parallel sides the same number of inches at right angles to the sheet. How many inches on each side should be folded up so that the gutter will contain the maximum volume of rainwater possible? Solve algebraically.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A rectangular sheet of aluminum 300 inches long and 12 inches wide is to be made into a rain gutter by folding up the two longer parallel sides the same number of inches at right angles to the sheet. How many inches on each side should be folded up so that the gutter will contain the maximum volume of rainwater possible? Solve algebraically.
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Draw a rough diagram of the end of the gutter, like a "U".
Label the sides (height) as x, the bottom (width) = (12-2x)
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Vol = x * (12-2x)* 300, right?
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F(x) = 300(12x - 2x^2)
F(x) = -600x^2 + 3600x, would be the equation
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The max F(x) or volume would be at the axis of symmetry,
it's formula x = -b/(2a), in our equation a = -600, b = +3600
x = -3600/(2*-600)
x = -3600/-1200
x = +3 inches
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The max vol would be 3 * 6 * 300 = 5400 cu in
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