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.
$c = \frac{5}{9}(f - 32)$
(simplify your answer. do not include the degree symbol in your answer.)
c. for what temperature is f = c?
$c = \square$°
(simplify your answer.)

Explanation:

Step1: Set F = C in the linear function

We know from part a that \( F=\frac{9}{5}C + 32 \). Since we want to find when \( F = C \), we substitute \( F \) with \( C \) in the equation: \( C=\frac{9}{5}C + 32 \).

Step2: Solve for C

Subtract \( \frac{9}{5}C \) from both sides: \( C-\frac{9}{5}C=\frac{9}{5}C + 32-\frac{9}{5}C \).
Simplify the left side: \( \frac{5}{5}C-\frac{9}{5}C=-\frac{4}{5}C \), and the right side is 32. So we have \( -\frac{4}{5}C = 32 \).
Multiply both sides by \( -\frac{5}{4} \): \( C=32\times(-\frac{5}{4}) \).
Calculate \( 32\times(-\frac{5}{4})=-40 \).

Answer:

\( -40 \)