Question

convert the following temperatures from fahrenheit to celsius or vice versa. c = \frac{f - 32}{1.8}, f = 1.8c + 32 a. 25°f b. 45°c c. - 20°c a. 25°f = □°c (type an integer or decimal rounded to one decimal place as needed.)

Explanation:

Step1: Convert 25°F to Celsius

Use the formula $C=\frac{F - 32}{1.8}$. Substitute $F = 25$ into the formula: $C=\frac{25-32}{1.8}$.

Step2: Calculate the numerator

$25 - 32=-7$, so the expression becomes $C=\frac{-7}{1.8}$.

Step3: Calculate the value of C

$C=\frac{-7}{1.8}\approx - 3.9$.

Step4: Convert 45°C to Fahrenheit

Use the formula $F = 1.8C+32$. Substitute $C = 45$ into the formula: $F=1.8\times45 + 32$.

Step5: Calculate 1.8×45

$1.8\times45 = 81$, so $F=81 + 32$.

Step6: Calculate the value of F

$F=81+32=113$.

Step7: Convert - 20°C to Fahrenheit

Use the formula $F = 1.8C+32$. Substitute $C=-20$ into the formula: $F=1.8\times(-20)+32$.

Step8: Calculate 1.8×(-20)

$1.8\times(-20)=-36$, so $F=-36 + 32$.

Step9: Calculate the value of F

$F=-36+32=-4$.

Answer:

a. $-3.9$
b. $113^{\circ}F$
c. $-4^{\circ}F$