ap03_calc_apcd_relate_29337

ap03_calc_apcd_relate_29337 - APCD CALCULUS: RELATED RATES...

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Related Rates Page 1 of 4 Copyright 2003 © by College Entrance Examination Board. All rights reserved. Available at apcentral.collegeboard.com APCD CALCULUS: RELATED RATES Worksheet to Accompany Exploration, Part 1 Directions: After completing the Exploration, answer the following additional questions. The Exploration is needed to answer some of these questions. 1. “Fill” the tanks to a “Maximum Depth” of 9. Then answer the following questions. a) What is the ratio of the volumes of tanks A and B ? b) What is the ratio of the times it takes to fill the two tanks in part (a)? c) What is the ratio of the volumes of tanks B and C ? d) What is the ratio of the times it takes to fill the two tanks in part (c)? e) What is the ratio of the volumes of tanks C and D ? f) What is the ratio of the times it takes to fill the two tanks in part (e)? 2. Now “Fill” the tanks to a “Maximum Depth” of 6. Then repeat parts (a) – (f) in problem 1. 3. Explain why the corresponding ratios in problem 2 differ from those in problem 1.
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Related Rates Page 2 of 4 Copyright 2003 © by College Entrance Examination Board. All rights reserved. Available at apcentral.collegeboard.com 4. Consider a tank that is a circular cylinder with a diameter of 8 feet. a) What is the volume if the tank is filled to a depth of 9 feet? b) How does the time required to fill this cylinder compare with the four tanks in the Exploration? c) How long would it take to fill it to a depth of 9 feet if 3 20 ft /min dV dt = ? d) What is dh dt for this tank? e) Why is dh dt for the cylinder the same as dh dt for all the tanks when h =9feet?
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ap03_calc_apcd_relate_29337 - APCD CALCULUS: RELATED RATES...

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