Monday
May 20, 2013

# Homework Help: calculus

Posted by Maria on Tuesday, November 1, 2011 at 10:45pm.

A rectangular beam is cut from a cylindrical log of radius 25 cm. The strength of a beam of width w and height h is proportional to wh2. (See Figure 4.70.) Find the width and height of the beam of maximum strength.

• calculus - Steve, Wednesday, November 2, 2011 at 11:22am

Draw a diagram. Given an inscribed rectangle of width w and height h, the diagonal of the rectangle is a diameter of the circle.

w^2 + h^2 = d^2
h^2 = 2500 - w^2

s = kwh^2 = kw(2500-w^2) = 2500kw - kw^3
s' = 2500k - 3kw^2

max strength is where s' = 0

3w^2 = 2500
w = 28.87

Now you can find h.

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