Chapter 1.3, Problem 10E

a.

To determine

To write: An equation that represents degrees Fahrenheit in terms of degrees Celsius.

Answer to Problem 10E

The equation is $F=\frac{9}{5}C+32$ .

Explanation of Solution

Given Information: $0^{o}C$ corresponds to ${32}^{o}F$ and ${100}^{o}C$ corresponds to ${212}^{o}F$ .

Calculation:

Points are $(0,32)$ and $(100,212)$ ,

Slope intercept form: $y=mx+b$

$m=\frac{y_2-y_1}{x_2-x_1}$

$\begin{array}{l}m=\frac{212-32}{100-0}\\ \\ m=\frac{180}{100}\\ \\ m=\frac{9}{5}\end{array}$

When $x=0$ , $y=32$ ,

$\Rightarrow y-\mathrm{int}ercept=32$

Substituting the values derived so far in slope intercept form,

$y=\frac{9}{5}x+32$

In this case,

$F=\frac{9}{5}C+32$ where $F$ represents degrees Fahrenheit and $C$ represents degrees Celsius.

Thus, the equation is $F=\frac{9}{5}C+32$ .

b.

To determine

To convert: Given degrees Celsius value to degrees Fahrenheit.

Answer to Problem 10E

Value in degrees Fahrenheit is ${71.6}^{o}F$ .

Explanation of Solution

Given Information: Value to be converted is ${22}^{o}C$ .

Calculation:

$\begin{array}{l}F=\frac{9}{5}(22)+32\\ \\ F=\frac{198}{5}+32\\ \\ F=39.6+32\\ \\ F=71.6\end{array}$

Thus, value in degrees Fahrenheit is ${71.6}^{o}F$ .

c.

To determine

To rearrange: The equation derived in part $a$ .

Answer to Problem 10E

Rearranged equation is $x=\frac{5}{9}y-\frac{160}{9}$ .

Explanation of Solution

Given Information: Equation is $y=\frac{9}{5}x+32$ .

Calculation:

$\begin{array}{l}y=\frac{9}{5}x+32\\ \\ \frac{9}{5}x=y-32\\ \\ x=\frac{5}{9}y-\frac{160}{9}\end{array}$

Thus, rearranged equation is $x=\frac{5}{9}y-\frac{160}{9}$ .

d.

To determine

To convert: Given degrees Fahrenheit value to degrees Celsius.

Answer to Problem 10E

Value in degrees Celsius is ${28.33}^{o}C$ .

Explanation of Solution

Given Information: Value is ${83}^{o}F$ .

Calculation:

$x=\frac{5}{9}y-\frac{160}{9}$

$\begin{array}{l}x=\frac{5}{9}(83)-\frac{160}{9}\\ \\ x=\frac{415-160}{9}\\ \\ x=\frac{255}{9}\\ \\ x=28.33\end{array}$

Thus, value in degrees Celsius is ${28.33}^{o}C$ .