(a) Explanation Given information: He has run out of books, to entertain himself he uses measurements of the water in his cooking pot to model the flow as w ( t ) = 15 ( 1 + cos ( 2 π ( t − 16 ) 24 ) ) Where t is the time in hours after midnight and w ( t ) is the rate at which snow is melting into his pot, in gallons per hour. Calculation: Now, consider w ( t ) = d V d t 15 ( 1 + cos ( 2 π ( t − 16 ) 24 ) ) = d V d t d V = 15 ( 1 + cos ( 2 π ( t − 16 ) 24 ) ) d t Integrating from t = t 1 to t = t 2 V = 15 ( ( t 2 − t 1 ) + 24 sin ( 2 π ( t 2 − 16 ) / 24 ) / 2 π − 24 sin ( 2 π ( t 2 − 16 ) / 24 ) 2 π ) So, given t 1 = 4 pm = 16 hrs V = 2 quart = 0 (b) To determine To find: the total amount of water that flows out of the snowfield in a single day. (c) To determine To write; an expression for the total amount of water that flows from the snowfield between any starting time t 0 and an ending time t . (d) To determine To find: the length must wait until he comes back to a full pot.

14th Edition

ISBN: 9781464151088

Author: Associate Professor Laura Taalman, Peter Kohn

Publisher: W.H. Freeman & Company

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Question

Chapter 4.7, Problem 62A

(a)

To determine

To find: the length does it take Ian to fill his 2 quart pot at 4 in the afternoon.

(b)

To determine

To find: the total amount of water that flows out of the snowfield in a single day.

(c)

To determine

To write; an expression for the total amount of water that flows from the snowfield between any starting time t0 and an ending time t .

(d)

To determine

To find: the length must wait until he comes back to a full pot.

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Chapter 4.7, Problem 61A

Chapter 4.7, Problem 63P

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Chapter 4 Solutions

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the length does it take Ian to fill his 2 quart pot at 4 in the afternoon.

Solution Summary: The author explains how Ian uses measurements of the water in his cooking pot to model the flow.

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To find: the length does it take Ian to fill his 2 quart pot at 4 in the afternoon.

To find: the total amount of water that flows out of the snowfield in a single day.

To write; an expression for the total amount of water that flows from the snowfield between any starting time t0 and an ending time t .

To find: the length must wait until he comes back to a full pot.

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