Question

use the formula $c = \frac{5}{9}(f - 32)$ for conversion between fahrenheit and celsius to convert each temperature.
a. $54^\circ$f to celsius
b. $-10^\circ$f to celsius
c. $30^\circ$c to fahrenheit

a. $54^\circ$f = 12.2 $^\circ$c
(type an integer or decimal rounded to the nearest tenth as needed.)
b. $-10^\circ$f = -23.3 $^\circ$c
(type an integer or decimal rounded to the nearest tenth as needed.)
c. $30^\circ$c = $\square$$^\circ$f
(type an integer or decimal rounded to the nearest tenth as needed.)

Explanation:

Step1: Rearrange formula for F

First, solve $C = \frac{5}{9}(F - 32)$ for $F$:
Multiply both sides by $\frac{9}{5}$: $\frac{9}{5}C = F - 32$
Add 32 to both sides: $F = \frac{9}{5}C + 32$

Step2: Substitute C=30 into formula

Substitute $C=30$ into the rearranged formula:
$F = \frac{9}{5} \times 30 + 32$

Step3: Calculate the result

First compute $\frac{9}{5} \times 30 = 54$, then add 32:
$F = 54 + 32 = 86$

Answer:

a. $54^\circ\text{F} = 12.2^\circ\text{C}$
b. $-10^\circ\text{F} = -23.3^\circ\text{C}$
c. $30^\circ\text{C} = 86^\circ\text{F}$