Explanation Given: SorenSovndal is at point A on the north bank of a long, straight river 6 mi wide. Directly across from him on the south bank in a point B, and he wished to reach a cabin point C located s mi down the river from B. Soren can row at 6 mi/h (including the effect of the current) and run at 10 mi/h. In right-triangle A B P A P 2 = A B 2 + B P 2 [ By pythagoros theorem ] A P = 6 2 + x 2 Speed during cover AP is 6 mi/h Time taken for AP = A P 6 = 36 + x 2 6 From point P to C, Speed = 10 mi/h Distance = ( s − x ) Time for PC = s − x 10 Total time to cover A to C, T ( x ) = 36 + x 2 6 + s − x 10 For minimize the time differentiate w.r.t x T ' ( x ) = x 6 36 + x 2 − 1 10 For maximum/minimum to find critical point, T ' ( x ) = 0 x 6 36 + x 2 − 1 10 To determine To find: The minimum distance to travel from A to C for s = 6

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 4.6, Problem 37PS

To determine

To find:The minimum distance to travel from A to C for s=4

To determine

To find: The minimum distance to travel from A to C for s=6

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Chapter 4.6, Problem 36PS

Chapter 4.6, Problem 38PS

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Calculus

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The minimum distance to travel from A to C for s = 4

Solution Summary: The author explains that SorenSovndal is at point A on the north bank of a long, straight river 6 mi wide. He wished to reach the cabin point C located s mi down the river.