Calculus: Graphical, Numerical, Algebraic

3rd Edition

ISBN: 9780133688399

Author: Finney, Ross L.

Publisher: Pearson/Prentice Hall

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Question

Chapter 1.6, Problem 44E

(a)

To determine

To find: The highest and lowest temperature in Fairbanks, Alaska.

(a)

Expert Solution

Answer to Problem 44E

The highest temperature is 62°F and the lowest temperature is −12°F .

Explanation of Solution

Given information: The given model is,

Calculus: Graphical, Numerical, Algebraic, Chapter 1.6, Problem 44E , additional homework tip 1

The equation for the given model is f(x)=37sin[2π365(x−101)]+25 .

Calculation:

It is known that for sine function with real parameters, the maximum value will be 1 and the minimum value will be −1 .

To find the highest temperature, substitute 1 for sin[2π365(x−101)] in the equation f(x)=37sin[2π365(x−101)]+25 .

Thighest=37(1)+25=62°F

To find the highest temperature, substitute −1 for sin[2π365(x−101)] in the equation f(x)=37sin[2π365(x−101)]+25 .

Tlowest=37(−1)+25=−12°F

Therefore, the highest temperature is 62°F and the lowest temperature is −12°F .

(b)

To determine

To find: The average of the highest and lowest temperature.

(b)

Expert Solution

Answer to Problem 44E

The average of the highest and lowest temperature is 25°F .

Explanation of Solution

Given information: The given model is,

Calculus: Graphical, Numerical, Algebraic, Chapter 1.6, Problem 44E , additional homework tip 2

Calculation:

From part (a), the highest temperature is 62°F and the lowest temperature is −12°F .

The average of the two temperatures is:

Tavg=62+(−12)2=502=25°F

The average obtained is the same as the vertical shift because the average of the highest and lowest values 1 and −1 respectively of the function y=sinx is 0 .

Therefore, the average of the highest and lowest temperature is 25°F .

Chapter 1.6, Problem 43E

Chapter 1.6, Problem 45E

Chapter 1 Solutions

Calculus: Graphical, Numerical, Algebraic

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