A trough is 16 feet long (see figure). Its cross sections are isosceles triangles with each of
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A trough is 16 feet long (see figure). Its cross sections are isosceles triangles with each of the two equal sides measuring 18 inches. The angle between the two equal sides is θ.
(a) Write the volume of the trough as a function of and determine the value of such that the volume is a maximum.
(b) The maximum error in the linear measurements is one-half inch and the maximum error in the angle measure is 2º. Approximate the change in the maximum volume.
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