Homework18 - vu (tv2894) – Homework 18 (Section 4.7) –...

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Unformatted text preview: vu (tv2894) – Homework 18 (Section 4.7) – miner – (55096) 1 This print-out should have 5 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A Pine Car Derby car rolls along a track with velocity v ( t ) = 3 + 2 t- t 2 feet per second. If it starts at time t = 0, after how many seconds will its position be maximized? 1. t = 9 seconds 2. none of these 3. t = 1 second 4. t = 0 seconds 5. t = 2 seconds 6. t = 3 seconds correct Explanation: Since we are maximizing the position, x ( t ), of the car, this will occur when x ′ ( t ) = 0, i.e. , when x ′ ( t ) = v ( t ) = 3 + 2 t- t 2 = 0 . But 3 + 2 t- t 2 = (3- t )(1 + t ) = 0 when t = 3 and when t =- 1. But t =- 1 is not allowed because the car starts at time t = 0. Now x ′′ ( t ) = v ′ ( t ) = 2- 2 t , so x ′′ (3) = 0. Hence the position of the car will be maximized after t = 3 seconds. 002 10.0 points A rectangular dog pound with three kennels as shown in the figure consists of a rectangular fenced area divided by two partitions. Determine the maximum possible area of this pound if 40 yards of chain link fencing is available for its construction....
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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.

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Homework18 - vu (tv2894) – Homework 18 (Section 4.7) –...

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