M408K Hm. 2 Solutions

M408K Hm. 2 Solutions - Mahon, Kevin Homework 2 Due: Sep 8...

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Unformatted text preview: Mahon, Kevin Homework 2 Due: Sep 8 2005, 3:00 am Inst: Edward Odell 1 This print-out should have 18 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points A tank holds 1000 gallons of water, which drains from the bottom of the tank in half an hour. The values in the table t (min) 5 10 15 20 25 30 V (gal) 654 430 243 103 22 show the volume, V ( t ), of water remaining in the tank (in gallons) after t minutes. If P is the point (15 , V (15)) on the graph of V as a function of time t , find the slope of the secant line P Q when Q = (25 , V (25)). 1. slope =- 22 . 1 correct 2. slope =- 41 . 1 3. slope =- 18 . 7 4. slope =- 14 5. slope =- 44 . 2 Explanation: When P = (15 , V (15)) , Q = (25 , V (25)) the slope of the secant line P Q is given by rise run = V (25)- V (15) 25- 15 . From the table of values, therefore, we see that slope = 22- 243 25- 15 =- 22 . 1 . keywords: Stewart5e, slope, table of values, 002 (part 1 of 1) 10 points The position of a car as a function of time is given by the values in table t (seconds) 1 2 3 4 5 s (feet) 16 22 34 50 56 Find the average velocity for the time period beginning when t = 3 and lasting 2 seconds. 1. average vel. = 10 feet/sec 2. average vel. = 12 feet/sec 3. average vel. = 9 feet/sec 4. average vel. = 8 feet/sec 5. average vel. = 11 feet/sec correct Explanation: Average velocity between times t = 3 and t = 3 + h is given by s (3 + h )- s (3) h . When h = 2, therefore, s (3 + 2)- s (3) 2 = 56- 34 2 . Consequently, over the time interval from t = 3 to t = 5 the car has average velocity = 11 ft/sec . keywords: Stewart5e, average velocity, table of values, 003 (part 1 of 1) 10 points A car first speeds up, but then slows down. Sketch a graph of the position of the car as a function of time. Mahon, Kevin Homework 2 Due: Sep 8 2005, 3:00 am Inst: Edward Odell 2 1. time position 2. time position correct 3. time position 4. time position 5. time position 6. time position Explanation: When the position of the car is plotted against time, the slope of the graph indicates the speed of the car, the greater the slope, the greater the speed, and the car is stationary when the slope is zero. Thus of the graphs, only time position has the given properties. Mahon, Kevin Homework 2 Due: Sep 8 2005, 3:00 am Inst: Edward Odell 3 Keywords: Harvard2e, graphical interpreta- tion speed, position v. time graph 004 (part 1 of 1) 10 points The position of a car initially heading due north on IH35 as a function of time t is shown in 2 4 6 2 4 time position List the values of m 1 = average velocity on [4 , 5] , m 2 = instantaneous velocity at t = 3 , m 3 = instantaneous velocity at t = 6 , m 4 = average velocity on [1 , 3] , in increasing order.in increasing order....
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This note was uploaded on 04/15/2008 for the course M 408k taught by Professor Schultz during the Fall '08 term at University of Texas at Austin.

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M408K Hm. 2 Solutions - Mahon, Kevin Homework 2 Due: Sep 8...

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