   Chapter 8.4, Problem 68E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Meteorology The number of hours of daylight D in New Orleans can be modeled by D =   12.12   +   1.87  cos π ( t + 5.83 ) 6 where t is the time (in months), with t = 1 corresponding to January. Approximate the month t in which New Orleans has the maximum number of daylight hours. What is this maximum number of daylight hours?(Source: U.S. Naval Observatory)

To determine

To calculate: The maximum number of daylight hours from the function of the number of hours of daylight D=12.12+1.87cosπ(t+5.83)6 in New Orleans, where t is the time in months and t=1 means January.

Explanation

Given Information:

The number of hours of daylight in New Orleans is given by,

D=12.12+1.87cosπ(t+5.83)6

Where t is the time in months.

Formula used:

Cosine differentiation rule:

ddx[cosu]=sinududx

General power rule of differentiation:

ddx[xn]=nxn1

Calculation:

Consider the provided function:

D=12.12+1.87cosπ(t+5.83)6

Differentiate the above function using Cosine and general power rules of differentiation.

D=ddt[12.12]+ddt[1.87cosπ(t+5.83)6]=0+((1.87sinπ(t+5.83)6)(π6))=1.87π6sinπ(t+5.83)6

Thus,

D=1.87π6sinπ(t+5.83)6

Now, substitute D=0 to find the value of t.

0=1.87π6sinπ(t+5

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