Answered: c=F - 32). C =

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

The formula for converting Fahrenheit temperature, F, to Celsius temperature, C, isIf Celsius temperature ranges from 15° to 35°, inclusive, what is the range for the Fahrenheit temperature? Use interval notation to express this range.

Expert Solution

Step 1

Given

$C = \frac{5}{9} (F - 32)$

C, is Celsius temperature ranges from 15° to 35°

Step 2

We can write

$15 \leq \frac{5}{9} (F - 32) \leq 35$

We have to find values of F for which $15 \leq C \leq 35$

We multiply by 9

$15 \times 9 \leq 5 (F - 32) \leq 35 \times 9 \Rightarrow 135 \leq 5 (F - 32) \leq 315 D i v i d e b y 5 \Rightarrow \frac{135}{5} \leq (F - 32) \leq \frac{315}{5} \Rightarrow 27 \leq F - 32 \leq 63 A d d i n g 32 \Rightarrow 27 + 32 \leq F - 32 + 32 \leq 63 + 32 \Rightarrow 59 \leq F \leq 95$

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