Holt Mcdougal Larson Algebra 2: Student Edition 2012

1st Edition

ISBN: 9780547647159

Author: HOLT MCDOUGAL

Publisher: HOLT MCDOUGAL

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Expert Solution & Answer

Chapter 3.4, Problem 48PS

Solution

(a)

Find the inverse of the given model. Describe what information you can obtain from the inverse.

C−1=9F5+32

Given information:

At the start of a dog sled race in Anchorage, Alaska, the temperature was 5oC . By the end of the race, the temperature was −10oC . The formula for converting temperatures from degrees Fahrenheit F to degrees Celsius C is C=59(F−32) .

Concept used:

In order to find the inverse of a function y=fx, follow below steps:

Step 1: interchange x and y in the given function

Step 2: solve for y and that will give the required inverse function

Calculation:

The inverse of C=59(F−32) is -

C=59(F−32)y=Cy=59(F−32)swap F with yF=59(y−32)solve for yF=59(y−32)9F=5(y−32)9F5=y−32y=9F5+32C−1=9F5+32

Thus the inverse of the given function C=59(F−32) is C−1=9F5+32 .

From the inverse we obtained that adding 32 with 9/5 times Fahrenheit (F) temperature gives the degree Celsius (C) temperature.

(b)

Find the Fahrenheit temperatures at the start and end of the race.

Fahrenheit temperatures at the start F=410

Fahrenheit temperatures at the end F=140

Given information:

At the start of a dog sled race in Anchorage, Alaska, the temperature was 5oC . By the end of the race, the temperature was −10oC . The formula for converting temperatures from degrees Fahrenheit F to degrees Celsius C is C=59(F−32) .

Concept used:

In order to find the inverse of a function y=fx, follow below steps:

Step 1: interchange x and y in the given function

Step 2: solve for y and that will give the required inverse function

Calculation:

C=59(F−32)

At the start the temperature was 5oC .

Fahrenheit temperatures at the start −

C=59(F−32)5=59(F−32)9=F−32F=9+32F=410

At the end the temperature was −10oC .

Fahrenheit temperatures at the start −

C=59(F−32)−10=59(F−32)−905=F−32−18=F−32F=32−18F=14o

(c)

Use a graphic calculator to graph the original function and its inverse. Find the temperature that is the same on both temperature scales.

At -40 both temperature scales are same, C=F=−40o

Given information:

At the start of a dog sled race in Anchorage, Alaska, the temperature was 5oC . By the end of the race, the temperature was −10oC . The formula for converting temperatures from degrees Fahrenheit F to degrees Celsius C is C=59(F−32) .

Concept used:

In order to find the inverse of a function y=fx, follow below steps:

Step 1: interchange x and y in the given function

Step 2: solve for y and that will give the required inverse function

Calculation:

The graph of C=59(F−32) and C−1=9F5+32 is-

At −40o the temperature is same on both temperature scales.

C=F=−40

C=59(F−32)−40=59(−40−32)−360=5(−72)−360=−360

Chapter 3.4, Problem 47PS

Chapter 3.4, Problem 49PS

Chapter 3 Solutions

Holt Mcdougal Larson Algebra 2: Student Edition 2012

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Ch. 3.1 - Prob. 11GP Ch. 3.1 - Prob. 12GP Ch. 3.1 - Prob. 13GP Ch. 3.1 - Prob. 14GP Ch. 3.1 - Prob. 15GP Ch. 3.1 - Prob. 16GP Ch. 3.1 - Prob. 17GP Ch. 3.1 - Prob. 18GP Ch. 3.1 - Prob. 19GP Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E Ch. 3.1 - Prob. 7E Ch. 3.1 - Prob. 8E Ch. 3.1 - Prob. 9E Ch. 3.1 - Prob. 10E Ch. 3.1 - Prob. 11E Ch. 3.1 - Prob. 12E Ch. 3.1 - Prob. 13E Ch. 3.1 - Prob. 14E Ch. 3.1 - Prob. 15E Ch. 3.1 - Prob. 16E Ch. 3.1 - Prob. 17E Ch. 3.1 - Prob. 18E Ch. 3.1 - Prob. 19E Ch. 3.1 - Prob. 20E Ch. 3.1 - Prob. 21E Ch. 3.1 - Prob. 22E Ch. 3.1 - Prob. 23E Ch. 3.1 - Prob. 24E Ch. 3.1 - Prob. 25E Ch. 3.1 - Prob. 26E Ch. 3.1 - Prob. 27E Ch. 3.1 - Prob. 28E Ch. 3.1 - Prob. 29E Ch. 3.1 - Prob. 30E Ch. 3.1 - Prob. 31E Ch. 3.1 - Prob. 32E Ch. 3.1 - Prob. 33E Ch. 3.1 - Prob. 34E Ch. 3.1 - Prob. 35E Ch. 3.1 - Prob. 36E Ch. 3.1 - Prob. 37E Ch. 3.1 - Prob. 38E Ch. 3.1 - Prob. 39E Ch. 3.1 - Prob. 40E Ch. 3.1 - Prob. 41E Ch. 3.1 - 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Solution Summary: The author explains how to find the inverse of the given model.

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Chapter 3 Solutions