Explanation Given information: In Wolf Point, Montana: Length of day varies from a shortest day of approximately 8.1 hours to a longest day of approximately 15.9 hours. In Mexico City: Length of day varies from a shortest day of approximately 10.7 hours to a longest day of approximately 13.3 hours. The function L ( t ) = 12 + A sin ( 2 π 365 t ) approximates the length of day, in hours, where t represents the day in the year assuming t = 0 is the spring equinox on March 21 . Calculation: As per the given information, The function L ( t ) = 12 + A sin ( 2 π 365 t ) approximates the length of day, in hours, where t represents the day in the year assuming t = 0 is the spring equinox on March 21 . In Wolf Point, Montana: Length of day varies from a shortest day of approximately 8.1 hours to a longest day of approximately 15.9 hours. This means length of day oscillates between lowest 8.1 hours to highest 15.9 hours throughout the year. Since midpoint of ( 12 − A ) = 8.1 and (12 + A ) = 15.9 is 12. Therefore, value of amplitude A = 3.9 . Thus, L ( t ) = 12 + 3.9 sin ( 2 π 365 t ) model the length of day in Wolf Point Montana. Similarly, in Mexico City: Length of day varies from a shortest day of approximately 10.7 hours to a longest day of approximately 13.3 hours. This means length of day oscillates between lowest 10.7 hours to highest 13.3 hours throughout the year. Since midpoint of ( 12 − A ) = 10.7 and (12 + A ) = 13.3 is 12. Therefore, value of amplitude A = 1.3 . Thus, L ( t ) = 12 + 1.3 sin ( 2 π 365 t ) model the length of day in Mexico city. Now on April 1, t = 12 , Length of the day in Wolf Point Montana, L ( 12 ) = 12 + 3.9 sin ( 2 π 365 × 12 ) = 12.018 hours

4th Edition

ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 1.4, Problem 41E

To determine

The function that approximates the length of a day, in hours, for each location.

The comparison between day's length in each location on April 1, June 15, and November 1.

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Chapter 1.4, Problem 40E

Chapter 1.4, Problem 42E

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Chapter 1 Solutions

CALCULUS W/SAPLING ACCESS >IC<

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The function that approximates the length of a day, in hours, for each location. The comparison between day's length in each location on April 1, June 15, and November 1.

Solution Summary: The author explains the function that approximates the length of a day, in hours, for each location.