HW02-solutions - le(chl528 HW02 Gilbert(57195 This...

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le (chl528) – HW02 – Gilbert – (57195) 1 This print-out should have 13 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) 677 439 299 134 15 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 = 14 2. slope = 16 . 5 3. slope = 28 . 4 correct 4. slope = 56 . 8 5. slope = 37 . 8 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 = 15 299 25 15 = 28 . 4 . 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 19 23 41 53 65 Find the average velocity for the time period beginning when t = 1 and lasting 2 seconds. 1. average vel. = 12 feet/sec 2. average vel. = 10 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 = 1 and t = 1 + h is given by dist. travelled time taken = s (1 + h ) s (1) h . When h = 2, therefore, s (1 + 2) s (1) 2 = s (3) s (1) 2 = 41 19 2 . Consequently, over the time interval from t = 1 to t = 3 the car has average velocity = 11 ft/sec . 003 10.0 points The position as a function of time t of a car initially heading due north on IH35 is shown in 2 4 6 2 4 time position
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