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Unformatted text preview: vu (tv2894) – Homework 12 (Section 3.8) – miner – (55096) 1 This print-out should have 7 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A rock is thrown into a still pond and causes a circular ripple. If the radius of the ripple is increasing at a rate of 4 ft/sec, at what speed is the area of the ripple increasing when its radius is 6 feet? 1. speed = 48 π sq. ft/sec correct 2. speed = 49 sq. ft/sec 3. speed = 46 π sq. ft/sec 4. speed = 48 sq. ft/sec 5. speed = 47 π sq. ft/sec 6. speed = 47 sq. ft/sec 7. speed = 45 sq. ft/sec 8. speed = 45 π sq. ft/sec Explanation: The area, A , of a circle having radius r is given by A = πr 2 . Differentiating implicitly with respect to t we thus see that dA dt = 2 πr dr dt . When r = 6 , dr dt = 4 , therefore, the speed at which the area of the ripple is increasing is given by speed = 48 π sq. ft/sec . 002 10.0 points A point is moving on the graph of xy = 3. When the point is at (4 , 3 4 ), its x-coordinate is increasing at a rate of 1 units per second. What is the speed of the y-coordinate at that moment and in which direction is it mov- ing? 1. speed = 35 16 units/sec, increasing y 2. speed = 19 16 units/sec, increasing y 3. speed = − 35 16 units/sec, increasing y 4. speed = − 19 16 units/sec, decreasing y 5. speed = − 3 16 units/sec, decreasing y 6. speed = 3 16 units/sec, decreasing y correct Explanation: Provided x, y negationslash = 0, the equation xy = 3 can be written as...
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This note was uploaded on 11/07/2010 for the course M 408N taught by Professor Gualdini during the Fall '10 term at University of Texas.
- Fall '10