College

On his first day of school, Kareem found the high temperature to be [tex]$76.1^{\circ}F$[/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 conversion function

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

which converts a temperature in degrees Fahrenheit to degrees Celsius. Here, the variable [tex]$F$[/tex] represents the temperature in Fahrenheit.

Step 1: Substitute the given Fahrenheit temperature

The problem provides a temperature of [tex]$76.1^\circ$[/tex] F. Substitute this value into the function:

[tex]$$
C(76.1) = \frac{5}{9}(76.1 - 32)
$$[/tex]

Step 2: Compute the difference from 32 (the freezing point in Fahrenheit)

Subtract [tex]$32$[/tex] from [tex]$76.1$[/tex]:

[tex]$$
76.1 - 32 \approx 44.1
$$[/tex]

Step 3: Multiply by the conversion factor

Multiply the result by [tex]$\frac{5}{9}$[/tex]:

[tex]$$
C(76.1) \approx \frac{5}{9} \times 44.1 \approx 24.5
$$[/tex]

This value, approximately [tex]$24.5$[/tex], represents the temperature in degrees Celsius.

Conclusion

Thus, [tex]$C(76.1)$[/tex] represents the temperature of [tex]$76.1^\circ$[/tex] Fahrenheit converted to degrees Celsius.