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Unformatted text preview: Math 115 — Final Exam December 11, 2008 Name: EXAM SOLUTIONS Instructor: Section: 1. Do not open this exam until you are told to do so. 2. This exam has 8 pages including this cover. There are 9 problems. Note that the problems are not of equal difficulty, and it may be to your advantage to skip over and come back to a problem on which you are stuck. 3. Do not separate the pages of this exam. If they do become separated, write your name on every page and point this out to your instructor when you hand in the exam. 4. Please read the instructions for each individual problem carefully. One of the skills being tested on this exam is your ability to interpret mathematical questions, so instructors will not answer questions about exam problems during the exam. 5. Show an appropriate amount of work (including appropriate explanation) for each prob- lem, so that graders can see not only your answer but how you obtained it. Include units in your answer where that is appropriate. 6. You may use any calculator except a TI-92 (or other calculator with a full alphanumeric keypad). However, you must show work for any calculation which we have learned how to do in this course. You are also allowed two sides of a 3 ′′ × 5 ′′ note card. 7. If you use graphs or tables to find an answer, be sure to include an explanation and sketch of the graph, and to write out the entries of the table that you use. 8. Turn off all cell phones and pagers , and remove all headphones. Problem Points Score 1 12 2 10 3 20 4 11 5 15 6 7 7 8 8 12 9 5 Total 100 Math 115 / Final (December 11, 2008) page 2 1 . [12 points] In the 17th century, a ship’s navigator would estimate the distance the ship has traveled using readings of the ship’s velocity, v ( t ) , in knots (nautical miles per hour). Suppose that between noon and 3:00 pm a certain galleon is traveling with the wind and against the ocean current, and that its velocity is given as the difference between the wind velocity w ( t ) and the velocity of the ocean current c ( t ) , so that v ( t ) = w ( t )- c ( t ) , where t is in hours since noon. Consider the wind and ocean velocities for various times between noon and 3:00 p.m., given by the graphs below: c ( t ) w ( t ) t 1 t 2 t 3 t 4 t 5 t 6 t 7 a . [1 point] Using integral notation write an expression giving the distance the ship traveled from noon to 3:00 pm. Give units. Solution: d = integraldisplay 3 v ( t ) dt , with the distance in nautical miles. b . [1 point] Using integral notation write an expression giving the average velocity of the ship between noon and 3:00 pm. Give units. Solution: v av = 1 3 integraldisplay 3 v ( t ) dt , with the distance in nautical miles/hour, or knots....
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- Fall '08