Chapter 11, Problem 31CCSR

(a)

To determine

Transform the equation to find the Fahrenheit temperature F in terms of the Celsius temperature C.

Answer to Problem 31CCSR

  $\text{F}=\frac{9}{5}\text{C}+32$

Explanation of Solution

Given:

The formula $\text{C}\text{=}\frac{\text{5}}{\text{9}}\text{(F}-32)$ can be used to find the Celsius temperature C if you know the Fahrenheit temperature F.

Transform the equation to find the Fahrenheit temperature F in terms of the Celsius temperature C.

Concept Used:

Make a subject F from the equation $\text{C}\text{=}\frac{\text{5}}{\text{9}}\text{(F}-32)$

Calculation:

  $\begin{array}{l}\text{C}\text{=}\frac{\text{5}}{\text{9}}\text{(F}-32)\\ \text{9}·\text{C}\text{=}\text{9}·\frac{\text{5}}{\text{9}}\text{(F}-32)\text{[}\text{Multiply by 9 to both sides ] }\\ \text{9}\text{C}\text{=}5\text{(F}-32)\\ \text{9}\text{C}\text{=}5\text{F}-160\\ \text{9}\text{C}+160\text{=}5\text{F}-160+160\text{[}\text{Subtract 160 from both sides ] }\\ 5\text{F}=\text{9}\text{C}+160\\ \frac{5\text{F}}{5}=\frac{\text{9}\text{C}+160}{5}[\text{Divide each side by 5 }\text{] }\\ \text{F}=\frac{9}{5}\text{C}+32\end{array}$

Thus, $\text{F}=\frac{9}{5}\text{C}+32$

(b)

To determine

Use the formula in Part (a) to find the Fahrenheit temperature equivalent to ${35}^0\text{C}$

Answer to Problem 31CCSR

  $\text{F}={95}^0\text{F}$

Explanation of Solution

Given:

The formula $\text{C}\text{=}\frac{\text{5}}{\text{9}}\text{(F}-32)$ can be used to find the Celsius temperature C if you know the Fahrenheit temperature F.

Use the formula in Part (a) to find the Fahrenheit temperature equivalent to ${35}^0\text{C}$

Concept Used:

From Part a, we get the relation $\text{F}=\frac{9}{5}\text{C}+32$ . Now substitute $\text{C}={35}^0\text{C}$

Calculation:

  $\begin{array}{l}\text{When}\text{C}=35{}^0\text{C;}\text{find}\text{F}\\ \text{F}=\frac{9}{5}\text{C}+32\\ \text{F}=\frac{9}{5}·\text{35}+32=63+32={95}^0\text{F}\end{array}$

Thus, $\text{F}={95}^0\text{F}$