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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During a 12.8-hour period, the water level at Bay of Fundy, Nova Scotia, started at mean sea level (h=0), rose to 23.8 ft above sea level, dropped to 23.8 ft below mean sea level, and then returned to mean sea level. Which of the following model describes the height of the tide in ft as a function of time in hours, h(t) ? 23.8 sin (12.8 t) 23.8 sin(12.8 t) 47.6 sin(0.15625 t) 47.6 sin(12.8 t) 23.8 sin(0.15625 t) 47.6 sin (12.8t)

4т f tan tan 9.

Pls help ASAP

Chapter 1 Solutions

CALCULUS 4E (HC) W/ ACHIEVE ACCESS

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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