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Unformatted text preview: silva (jrs4378) Review 2 gualdani (56455) 1 This print-out should have 18 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points Find the rate of change of q with respect to p when p = 20 q 2 + 5 . 1. dq dp = 5 q 2 p 2. None of these 3. dq dp = 10 qp 2 correct 4. dq dp = 5 qp 2 5. dq dp = 10 qp Explanation: Differentiating implicitly with respect to p we see that 1 = 2 q parenleftBig 20 ( q 2 + 5) 2 parenrightBig dq dp , and so dq dp = ( q 2 + 5) 2 40 q . But q 2 + 5 = 20 p . Consequently, dq dp = 10 qp 2 . 002 10.0 points A car is given a push down the roller-coaster at Six Flags. If it travels a distance s = 5 t + 4 t 2 in t seconds, find its velocity after 4 seconds. 1. velocity = 40 ft/sec 2. velocity = 39 ft/sec 3. velocity = 37 ft/sec correct 4. velocity = 38 ft/sec 5. velocity = 41 ft/sec Explanation: The velocity of the car after t seconds is given by v ( t ) = ds dt = 5 + 8 t . Consequently, after 4 seconds its velocity = 37 ft/sec . 003 10.0 points If a tank holds 2000 gallons of water, and the water can drain from the tank in 40 min- utes, then Torricellis Law gives the volume V of water remaining in the tank after t minutes as V = 2000 parenleftbigg 1 t 40 parenrightbigg 2 . Find the rate at which water is draining from the tank after 10 minutes. 1. rate = 70 gal/min 2. rate = 78 gal/min 3. rate = 75 gal/min correct 4. rate = 77 gal/min 5. rate = 79 gal/min Explanation: silva (jrs4378) Review 2 gualdani (56455) 2 By the Chain Rule, V ( t ) = 2000 20 parenleftBig 1 1 40 t parenrightBig = 100 parenleftBig 1 1 40 t parenrightBig , the negative sign indicating that the volume is decreasing. Consequently, after 10 minutes the water is draining from the tank at a rate = 100 parenleftbigg 1 10 40 parenrightbigg = 75 gal / min . 004 10.0 points A point is moving on the graph of xy = 2. When the point is at (2 , 1), its x-coordinate is increasing at a rate of 6 units per second. What is the speed of the y-coordinate at that moment and in which direction is it mov- ing? 1. speed = 5 units/sec, increasing y 2. speed = 5 units/sec, decreasing y 3. speed = 3 units/sec, decreasing y correct 4. speed = 3 units/sec, decreasing y 5. speed = 4 units/sec, increasing y 6. speed = 4 units/sec, increasing y Explanation: Provided x, y negationslash = 0, the equation xy = 2 can be written as y = 2 /x . Differentiating implicitly with respect to t we thus see that dy dt = 2 x 2 dx dt . whenever x negationslash = 0. When x = 2 , dx dt = 6 , therefore, the corresponding rate of change of the y-coordinate is given by dy dt vextendsingle vextendsingle vextendsingle x =2 = 6 parenleftBig 2 x 2 parenrightBigvextendsingle vextendsingle vextendsingle x =2 = 3 ....
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This note was uploaded on 08/29/2010 for the course M 46455 taught by Professor Gualdani during the Spring '10 term at University of Texas at Austin.

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review 2 - silva (jrs4378) Review 2 gualdani (56455) 1 This...

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