Question

Some of the highest tides in the world occur in the Bay of Fundy on the Atlantic Coast of Canada. At Hopewell Cape, the water depth at low tide is about 2.0 m and at high tide, it is about 12.0 m. The natural period of oscillation is a little more than 12 hours, and on June 30, 2009, high tide occurred at 6:45 AM. This helps explain the following model for the water depth D (in meters) as a function of the time t (in hours after midnight) on that day: D(t) = 7 + 5 cos[0.503(t - 6.75)]. How fast was the tide rising (or falling) at the following times? (Round your answers to two decimal places.) (a) 5:00 AM m/h (b) 6:00 AM m/h (c) 8:00 AM m/h (d) 11:00 AM

          Some of the highest tides in the world occur in the Bay of Fundy on the Atlantic Coast of Canada. At Hopewell Cape, the water depth at low tide is about 2.0 m and at high tide, it is about 12.0 m. The natural period of oscillation is a little more than 12 hours, and on June 30, 2009, high tide occurred at 6:45 AM. This helps explain the following model for the water depth D (in meters) as a function of the time t (in hours after midnight) on that day: D(t) = 7 + 5 cos[0.503(t - 6.75)]. How fast was the tide rising (or falling) at the following times? (Round your answers to two decimal places.)
(a) 5:00 AM m/h 
(b) 6:00 AM m/h 
(c) 8:00 AM m/h 
(d) 11:00 AM

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Added by Katherine D.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert William Semus

10/27/2022

Step 1

503(t - 6.75)]** The derivative of a constant is 0, and the derivative of cos(x) is -sin(x). Using the chain rule, the derivative of cos[0.503(t - 6.75)] is -0.503 * sin[0.503(t - 6.75)]. Therefore, the derivative of D(t) is: D'(t) = -0.503 * 5 * sin[0.503(t - Show more…

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Some of the highest tides in the world occur in the Bay of Fundy on the Atlantic Coast of Canada. At Hopewell Cape, the water depth at low tide is about 2.0 m and at high tide, it is about 12.0 m. The natural period of oscillation is a little more than 12 hours, and on June 30, 2009, high tide occurred at 6:45 AM. This helps explain the following model for the water depth D (in meters) as a function of the time t (in hours after midnight) on that day: D(t) = 7 + 5 cos[0.503(t - 6.75)]. How fast was the tide rising (or falling) at the following times? (Round your answers to two decimal places.) (a) 5:00 AM m/h (b) 6:00 AM m/h (c) 8:00 AM m/h (d) 11:00 AM

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00:01 So in this question, they say some of the highest tides in the world occur in the bay of fundy on the atlantic coast of canada.

00:09 At hopewell cape, the water depth at low tide is about 2 meters, and at high tide it is about 12 meters.

00:15 The natural period of oscillation is a little more than 12 hours, and on june 30, 2009, high tide occurred at 6 .45 a .m.

00:25 This helps explain the following model for the water depth d in meters as a function of time t, in hours after midnight on that day.

00:35 What we have in this question is d of t, and my d of t is equal to 7 plus 5 times the cosine of the quantity of 0 .503 times the quantity of t minus 6 .75.

00:55 I want to know how fast was the tide rising or falling at the following times.

00:59 I'm going to round my answer to two decimal places.

01:03 5 a .m.

01:04 6 .m.

01:04 6.

01:04 7.

01:04 6 a .m., 8 a .m.

01:06 And 11 a .m.

01:08 So if i want the rate of change of the tide's height, i need my derivative.

01:15 I need my d prime of t.

01:18 So what's my derivative? the derivative of 7 is 0.

01:22 The derivative of that constant is 0.

01:25 The derivative of this second term, i'm going to use the chain...

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