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Calculus/Closing off the First Quadrant

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Expert: - 11/5/2008


Question
You are planning to close off a corner of the first quadrant with a line segment 20 units long running from (a, 0) to (0, b).  Show that the area of the triangle enclosed by the segment is largest when a = b.

Answer
Take some point x on the x-axis.  This would make the point on the y-axis 20-x.  The triangle area is then the base times the height over 2, or x(20-x)/2, which can rewritten as 10x - x²/2.

Take the derivative, set it equatl to 0, solve for x, and show that x = 20 - x (in other words, show that x is 10).

Calculus

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Any kind of calculus question you want. I also have answered some questions in Physics (mass, momentum, falling bodies), Chemistry (charge, reactions, symbols, molecules), and Biology.

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