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Unformatted text preview: dy dx = 1 1 + x 2 for the derivative of y = tan-1 ( x ) by differentiating both sides of the equivalent equation tan ( y ) = x. Math 1110 (Fall 2011) HW8 Presentation Problems 2 Question 2. (12 points) Water is slowly leaking out of a bowl at a rate of π in 3 /min , as shown in the ﬁgure below. The bowl is a perfect hemisphere with radius 10 inches. If the water level is y inches, the volume of water in a hemispherical bowl of radius R is V = π 3 y 2 ( 3R-y ) . Cross − section R − y R=10 r The bowl y (a) At what rate is the water level changing when the water is 8 inches deep? (b) What is the radius r of the water’s surface when the water is y inches deep? (c) When the water level is 4 inches deep, the water level is changing at a rate of 1 64 inches per minute. At what rate is the radius of the water changing at that time?...
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