- A rain gutter is to be constructed from a metal sheet of width 30 cm
by bending one-third of the sheet on each side through an angle θ: How
should θ be chosen so that the gutter will carry a maximum amount of
water? Express the answer in terms of π:
- (a) Find the derivative of the function
(b) Find the limit
- (a) where the numbers a, b are to
(b) A wedge is cut out of a circular cylinder of radius 3 by two planes.
One plane is perpendicular to the axis of the cylinder. The other
plane intersects the first plane at an angle of 60° along the diameter of
the cylinder. Find the exact volume of the wedge.
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