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  • 4 years ago

Optimization. A rectangle is to have an area of 32 square cms. Find its dimensions so that the distance from one corner to the mid point of a non-adjacent edge is a minimum

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  1. anonymous
    • 4 years ago
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    |dw:1328207321371:dw| xy = 32 makes y = 32/x \[z^2 = (32/x)^2 + (x/2)^2\] Isolate z \[z = 32/x + x/2\] Find dz/dx \[f \prime(z) = (x^2-64)/(2x^2)\] Set z' = 0, algebraically solving for x having \[x = \pm8\] Since you cannot have a dimension of -8, the only answer for x is 8. Go back to the original area equation; 32 = xy and plug in x making 32 = 8y y = 4

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