# Math- Calculus

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A company needs to produce a cylindrical can to hold water. It must have a volume of 500ml. The side of the can will cost 40\$/m^2 to produce and the top and bottom of the can will cost 50\$/m^2 to produce. Find the most economical dimensions.

• Math- Calculus -

Find the compound interest and the compound amount of the following #2ooo at 4/2 % compounded annually for 7yr

• Math- Calculus -

since pi r^2 h = 500, h = 500/(pi r^2)

the cost function is

c = 40 * 2pi r h + 2*50*pi r^2
= 80 pi r (500/(pi r^2)) + 100 pi r^2
= 40000/r + 100 pi r^2

dc/dr = 200 pi r - 40000/r^2
= 200 (pi r^3 - 200)/r^2

dc/dr = 0 when pi r^3 = 200

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