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HW04-solutions - kim(tk5895 HW04 Henry(54974 This print-out...

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kim (tk5895) – HW04 – Henry – (54974) 1 This print-out should have 20 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 (part 1 of 4) 10.0 points A Calculus student begins walking in a straight line from the RLM building towards the PCL Library. After t minutes his velocity v = v ( t ) is given (in multiples of 10 yards per minute) by the function whose graph is -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 2 4 6 8 10 2 2 4 6 2 t v How far is the student from the RLM build- ing at time t = 4? 1. dist = 75 yards correct 2. dist = 115 yards 3. dist = 95 yards 4. dist = 85 yards 5. dist = 65 yards Explanation: The student is walking towards the PCL Library whenever v ( t ) > 0 and towards RLM whenever v ( t ) < 0. The distance he has walked is given by 10 times the area between the graph of v and the t axis since 1 unit is equivalent to 10 yards. Now at t = 4 this area is 7 . 5 units, so the student has walked a distance of 75 yards. 002 (part 2 of 4) 10.0 points How far is the student from the RLM build- ing at time t = 7? 1. dist = 185 yards 2. dist = 215 yards 3. dist = 195 yards correct 4. dist = 205 yards 5. dist = 235 yards Explanation: The distance the student has walked is given by the area between the graph of v and the t axis. Now at t = 7 this area is 19 . 5 units, so the student has walked a distance of 195 yards. 003 (part 3 of 4) 10.0 points What is the total distance walked by the student from time t = 0 to t = 10? 1. dist = 235 yards 2. dist = 245 yards 3. dist = 285 yards 4. dist = 265 yards 5. dist = 255 yards correct Explanation: The distance the student has walked is given by the area between the graph of v and the t axis. Now at t = 10 this area is 25 . 5 units (area is always positive remember), so the student has walked a distance of 255 yards. 004 (part 4 of 4) 10.0 points How far is the student from the RLM build- ing when he turns back? 1. dist = 215 yards 2. dist = 285 yards
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kim (tk5895) – HW04 – Henry – (54974) 2 3. dist = 235 yards 4. dist = 245 yards correct 5. dist = 265 yards Explanation: The student will turn back when his veloc- ity changes from postive to negative, i.e. , at t = 9. At this time he is 245 yards from the RLM building. keywords: distance, time, graph, velocity, area 005 10.0 points Determine the indefinite integral I = integraldisplay 3 2 x x dx . 1. I = 3 x 1 / 2 + 2 3 x 3 / 2 + C 2. I = 6 x 1 / 2 + 4 3 x 3 / 2 + C 3. I = 3 x 1 / 2 4 3 x 3 / 2 + C 4. I = 3 x 1 / 2 + 4 3 x 3 / 2 + C 5. I = 6 x 1 / 2 4 3 x 3 / 2 + C correct 6. I = 6 x 1 / 2 2 3 x 3 / 2 + C Explanation: After division we see that 3 2 x x = 3 x 2 x = 3 x 1 / 2 2 x 1 / 2 .
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