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On his first day of school, Kareem found the high temperature in degrees Fahrenheit to be [tex]$76.1^{\circ}$[/tex]. He plans to use the function [tex]$C(F) = \frac{5}{9}(F-32)$[/tex] to convert this temperature from degrees Fahrenheit to degrees Celsius. What does [tex]$C(76.1)$[/tex] represent?

A. The temperature of 76.1 degrees Fahrenheit converted to degrees Celsius.
B. The temperature of 76.1 degrees Celsius converted to degrees Fahrenheit.
C. The amount of time it takes for a temperature of 76.1 degrees Fahrenheit to be converted to 32 degrees Celsius.
D. The amount of time it takes for a temperature of 76.1 degrees Celsius to be converted to 32 degrees Fahrenheit.

Answer :

We are given the function

[tex]$$
C(F) = \frac{5}{9}(F - 32)
$$[/tex]

which converts a temperature from degrees Fahrenheit to degrees Celsius. In this problem, we have a temperature of [tex]$76.1^\circ \text{F}$[/tex] and we want to find the equivalent temperature in Celsius.

Step 1: Subtract 32 from the Fahrenheit temperature

We start by subtracting [tex]$32$[/tex] from [tex]$76.1$[/tex]:

[tex]$$
76.1 - 32 = 44.1
$$[/tex]

Step 2: Multiply by [tex]$\frac{5}{9}$[/tex]

Next, we multiply the result by [tex]$\frac{5}{9}$[/tex]:

[tex]$$
C(76.1) = \frac{5}{9} \times 44.1
$$[/tex]

Multiplying the numerator:

[tex]$$
5 \times 44.1 = 220.5
$$[/tex]

Then, dividing by [tex]$9$[/tex]:

[tex]$$
\frac{220.5}{9} \approx 24.5
$$[/tex]

Thus, [tex]$C(76.1)$[/tex] is approximately [tex]$24.5^\circ \text{C}$[/tex].

Interpretation:

[tex]$C(76.1)$[/tex] represents the temperature of [tex]$76.1^\circ \text{F}$[/tex] converted to degrees Celsius.

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