Explanation Given: Function D ( t ) = 4 cos ( 2 π 365 ( t − 172 ) ) + 12 Formula Used: Formula of derivatives are as follows: d d x ( cos x ) = − sin x d d x ( x n ) = n x n − 1 d d x c . f ( x ) = c . d d x f ( x ) Calculation: Function is given as D ( t ) = 4 cos ( 2 π 365 ( t − 172 ) ) + 12 Derivative of the function is calculated as: d d t ( D ( t ) ) = d d t ( 4 cos ( 2 π 365 ( t − 172 ) ) + 12 ) D ′ ( t ) = d d t ( 4 cos ( 2 π 365 ( t − 172 ) ) ) + d d t ( 12 ) D ′ ( t ) = 4 d d t ( cos ( 2 π 365 ( t − 172 ) ) ) + 0 D ′ ( t ) = 4 ( − sin ( 2 π 365 ( t − 172 ) ) ) × 2 π 365 ( 1 − 0 ) D ′ ( t ) = − 8 π To determine (b) To find D ( 172 ) , D ′ ( 172 ) where D ( t ) is the approximation of number of hours of daylight in Paris with t being the number of days. D ( t ) = 4 cos ( 2 π 365 ( t − 172 ) ) + 12

6th Edition

ISBN: 9781119399322

Author: Hughes-Hallett

Publisher: WILEY

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Chapter 3.5, Problem 36P

To determine

(a)

To find D(40), D′(40) where D(t) is the approximation of number of hours of daylight in Paris with t being the number of days.

D(t)=4cos(2π365(t−172))+12

To determine

(b)

To find D(172), D′(172) where D(t) is the approximation of number of hours of daylight in Paris with t being the number of days.

D(t)=4cos(2π365(t−172))+12

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Chapter 3.5, Problem 35P

Chapter 3.5, Problem 37P

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(a) To find D ( 40 ) , D ′ ( 40 ) where D ( t ) is the approximation of number of hours of daylight in Paris with t being the number of days. D ( t ) = 4 cos ( 2 π 365 ( t − 172 ) ) + 12

Solution Summary: The author explains that the function is given as D(t)=4mathrmcos left, with t being the number of days.

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(a)

To find D(40), D′(40) where D(t) is the approximation of number of hours of daylight in Paris with t being the number of days.

D(t)=4cos(2π365(t−172))+12

(b)

To find D(172), D′(172) where D(t) is the approximation of number of hours of daylight in Paris with t being the number of days.

D(t)=4cos(2π365(t−172))+12

Want to see the full answer?

Chapter 3 Solutions

(a) To find D ( 40 ) , D ′ ( 40 ) where D ( t ) is the approximation of number of hours of daylight in Paris with t being the number of days. D ( t ) = 4 cos ( 2 π 365 ( t − 172 ) ) + 12

Solution Summary: The author explains that the function is given as D(t)=4mathrmcos left, with t being the number of days.

Concept explainers

Videos

(a) To find D(40), D′(40) where D(t) is the approximation of number of hours of daylight in Paris with t being the number of days. D(t)=4cos(2π365(t−172))+12

(b) To find D(172), D′(172) where D(t) is the approximation of number of hours of daylight in Paris with t being the number of days. D(t)=4cos(2π365(t−172))+12

Want to see the full answer?

Chapter 3 Solutions

(a)

To find D(40), D′(40) where D(t) is the approximation of number of hours of daylight in Paris with t being the number of days.

D(t)=4cos(2π365(t−172))+12

(b)

To find D(172), D′(172) where D(t) is the approximation of number of hours of daylight in Paris with t being the number of days.

D(t)=4cos(2π365(t−172))+12