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Algebra/quadratic equation

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Question
diagram
diagram  
I have a piece of metal 10m long and 0.3m wide. I need to bend it into an open U shaped channel (gutter) by bending the 0.3m width twice. I need to use a quadratic equation to to determine where to make the bends to get the maximum volume.
Thankyou for your help. Peter

Answer
If the bottom has width x, the height is (0.3-x)/2.
This makes the cross sectional area into x(0.3-x)/2 = 0.15x - 0.5x^2.
Let this be f(x).

Maximize by finding f'(x), setting it to 0, and solving for x.
Note that here f'(x) = 0.15 - x, so the solution is x = 0.15.
This makes the height into (0.3-0.15)/2 = 0.075.

The cross sectional area is then 0.15 x 0.075 = 0.01125.

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Scott A Wilson

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Any algebraic question you've got. That includes question that are linear, quadratic, exponential, etc.

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I have solved story problems, linear equations, parabolic equations. I have also solved some 3rd order equations and equations with multiple variables.

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Documents at Boeing in assistance on the manufacturiing floor.

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MS at math OSU in mathematics at OSU, 1986. BS at OSU in mathematical sciences (math, statistics, computer science), 1984.

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Both my BS and MS degrees were given with honors.

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Students in a wide variety of areas since the 80's; over 1,000 of them have been in algebra.

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