2solution - hernandez(aah955 HW02 milburn(54885 This...

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hernandez (aah955) – HW02 – milburn – (54885) 1 This print-out should have 11 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 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) 615 500 255 184 22 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 = 36 2. slope = 46 . 6 3. slope = 24 . 5 4. slope = 23 . 3 correct 5. slope = 7 . 1 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 = 22 255 25 15 = 23 . 3 . 002 10.0 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 17 23 35 49 55 Find the average velocity for the time period beginning when t = 2 and lasting 2 seconds. 1. average vel. = 15 feet/sec 2. average vel. = 13 feet/sec correct 3. average vel. = 17 feet/sec 4. average vel. = 14 feet/sec 5. average vel. = 16 feet/sec Explanation: Average velocity between times t = 2 and t = 2 + h is given by dist. travelled time taken = s (2 + h ) s (2) h . When h = 2, therefore, s (2 + 2) s (2) 2 = s (4) s (2) 2 = 49 23 2 . Consequently, over the time interval from t = 2 to t = 4 the car has average velocity = 13 ft/sec . 003 10.0 points A car is driven at a constant speed. Sketch a graph of the position of the car as a function of time. 1. time position correct
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hernandez (aah955) – HW02 – milburn – (54885) 2 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.
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