Question

when the celsius temperature is 30°, the corresponding fahrenheit temperature is 86°. when the celsius temperature is 90°, the corresponding fahrenheit temperature is 194°. let c represent the celsius temperature and f the fahrenheit temperature. a. express f as an exact linear function of c. b. solve the equation in part a for c, thus expressing c as a function of f. c. for what temperature is f = c? a. express f as an exact linear function of c. f = \\(\frac{9}{5}\\)c + 32 (simplify your answer. do not include the degree symbol in your answer.) b. express c as an exact linear function of f. c = \\(\square\\) (simplify your answer. do not include the degree symbol in your answer.)

Explanation:

Step1: Start with the formula from part a

We have the linear function \( F = \frac{9}{5}C + 32 \). We need to solve this equation for \( C \) in terms of \( F \).

Step2: Subtract 32 from both sides

Subtract 32 from each side of the equation: \( F - 32=\frac{9}{5}C \).

Step3: Multiply both sides by \( \frac{5}{9} \)

To isolate \( C \), we multiply both sides of the equation by \( \frac{5}{9} \). So, \( C=\frac{5}{9}(F - 32) \). We can also expand this to \( C=\frac{5}{9}F-\frac{160}{9} \), but the factored form is also correct and a common way to express the Celsius to Fahrenheit conversion formula (rearranged).

Answer:

\( \frac{5}{9}(F - 32) \) (or equivalently \( \frac{5}{9}F-\frac{160}{9} \))