Explanation Given information: H ( t ) = A sin ( B t ) + C Where H is the height (in meters) of the tide ‘t’ is time (hours since midnight) Formula used: For cos θ = 0 , θ is an odd integer multiple of π 2 Or θ = cos ( ( 2 n + 1 ) π 2 ) Calculation: H ( t ) = A sin ( B t ) + C Differentiate with respect to ‘ t’. H ' ( t ) = A B cos ( B t ) + 0 H ' ( t ) = A B cos ( B t ) Now for the critical points put H ' ( t ) = 0 H ' ( t ) = A B cos ( B t ) = 0 A B cos ( B t ) = 0 cos ( B t ) = 0 cos ( B t ) = cos ( ( 2 n + 1 ) π 2 ) B t = ( 2 n + 1 ) π 2 , where n = 0 , 1 , 2 , 3 , .... When n = 0 B t = ( 2 ⋅ 0 + 1 ) π 2 B t = π 2 B = π 2 t When n = 1 B t = ( 2 ⋅ 1 + 1 ) π 2 B t = 3 π 2 B = 3 π 2 t When t = 6 B = π 2 t B = π 2 × 6 B = π 12

4th Edition

ISBN: 9781319379421

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 1, Problem 47CRE

To determine

Calculate the value of A, B and C if the high tide of 18m occurs at 6:00 AM and the subsequent low tide of 15m occur at 6:00 PM.

H(t)=Asin(Bt)+C

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Chapter 1, Problem 46CRE

Chapter 1, Problem 48CRE

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Chapter 1 Solutions

CALCULUS 4E (HC) W/ ACHIEVE ACCESS

Ch. 1.1 - Prob. 1PQ Ch. 1.1 - Prob. 2PQ Ch. 1.1 - Prob. 3PQ Ch. 1.1 - Prob. 4PQ Ch. 1.1 - Prob. 5PQ Ch. 1.1 - Prob. 6PQ Ch. 1.1 - Prob. 7PQ Ch. 1.1 - Prob. 8PQ Ch. 1.1 - Prob. 9PQ Ch. 1.1 - Prob. 10PQ

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Calculate the value of A, B and C if the high tide of 18m occurs at 6:00 AM and the subsequent low tide of 15m occur at 6:00 PM. H ( t ) = A sin ( B t ) + C

Solution Summary: The author calculates the value of A, B, and C if the high tide of 18m occurs at 6:00 AM and the subsequent low tide

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Calculate the value of A, B and C if the high tide of 18m occurs at 6:00 AM and the subsequent low tide of 15m occur at 6:00 PM.

H(t)=Asin(Bt)+C

Want to see the full answer?

Chapter 1 Solutions

Calculate the value of A, B and C if the high tide of 18m occurs at 6:00 AM and the subsequent low tide of 15m occur at 6:00 PM. H ( t ) = A sin ( B t ) + C

Solution Summary: The author calculates the value of A, B, and C if the high tide of 18m occurs at 6:00 AM and the subsequent low tide

Concept explainers

Videos

Calculate the value of A, B and C if the high tide of 18m occurs at 6:00 AM and the subsequent low tide of 15m occur at 6:00 PM. H(t)=Asin(Bt)+C

Want to see the full answer?

Chapter 1 Solutions

Calculate the value of A, B and C if the high tide of 18m occurs at 6:00 AM and the subsequent low tide of 15m occur at 6:00 PM.

H(t)=Asin(Bt)+C