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# Honors Precalculus Question? ?

Question: The strength of a rectangular wooden beam is proportional to the product of the width and the square of its depth. If the beam is to be cut from a log in the shape of a cylinder of radius 3 feet, express the strength of S of the beam as a function of the width W.

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- Ian HLv 73 weeks ago
The strength of a rectangular wooden beam is proportional to the product of the width and the square of its depth.

S = kwd^2 ...............(1) ....for some unknown constant k

Assuming that we are next going to be asked for the width that gives max strength

Cylinder shaped log has diameter of 6 feet and this is hypotenuse

d^2 = 36 – w^2 ........(2)

S = k[36w – w^3)

dS/dw = k[36 – 3w^2] = 0 for max

w^2 = 12, so w = 2√(3) ~ 3.464 ft

d^2 = 24, so d = 2√(6) ~ 4.899 ft

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