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hw2 - Granillo Yvette Homework 2 Due Sep 8 2005 3:00 am...

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Granillo, Yvette – 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) 672 479 232 159 16 0 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 PQ when Q = (25 , V (25)). 1. slope = - 44 2. slope = - 21 . 6 correct 3. slope = - 7 . 3 4. slope = - 43 . 2 5. slope = - 24 . 7 Explanation: When P = (15 , V (15)) , Q = (25 , V (25)) the slope of the secant line PQ is given by rise run = V (25) - V (15) 25 - 15 . From the table of values, therefore, we see that slope = 16 - 232 25 - 15 = - 21 . 6 . 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) 0 1 2 3 4 5 s (feet) 0 10 18 32 36 54 Find the average velocity for the time period beginning when t = 2 and lasting 2 seconds. 1. average vel. = 9 feet/sec correct 2. average vel. = 10 feet/sec 3. average vel. = 6 feet/sec 4. average vel. = 8 feet/sec 5. average vel. = 7 feet/sec Explanation: Average velocity between times t = 2 and t = 2 + h is given by s (2 + h ) - s (2) h . When h = 2, therefore, s (2 + 2) - s (2) 2 = 36 - 18 2 . Consequently, over the time interval from t = 2 to t = 4 the car has average velocity = 9 ft/sec . keywords: Stewart5e, average velocity, table of values, 003 (part 1 of 1) 10 points A car is driven at increasing speed. Sketch a graph of the position of the car as a function of time.

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Granillo, Yvette – Homework 2 – Due: Sep 8 2005, 3:00 am – Inst: Edward Odell 2 1. time position correct 2. time position 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.
Granillo, Yvette – 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 [5 , 6] , m 2 = instantaneous velocity at t = 4 , m 3 = average velocity on [2 , 4] , m 4 = instantaneous velocity at t = 1 , in increasing order.

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