High School

The average cat has a normal body temperature of [tex]$38.6^{\circ}$[/tex] Celsius. The formula [tex]$C=\frac{5}{9}(F-32)$[/tex] can be used to convert Fahrenheit [tex]$F$[/tex] to Celsius [tex]$C$[/tex]. What is an average cat's temperature in Fahrenheit?

A) [tex]$101.05^{\circ}$[/tex] Fahrenheit
B) [tex]$102.59^{\circ}$[/tex] Fahrenheit
C) [tex]$101.48^{\circ}$[/tex] Fahrenheit
D) [tex]$100.35^{\circ}$[/tex] Fahrenheit

Answer :

To convert the average cat's temperature from Celsius to Fahrenheit, we start with the Celsius-to-Fahrenheit conversion formula:

[tex]$$
F = \frac{9}{5}C + 32
$$[/tex]

where [tex]$C$[/tex] represents the temperature in Celsius and [tex]$F$[/tex] represents the temperature in Fahrenheit.

1. Since the average cat's temperature is [tex]$38.6^\circ$[/tex] Celsius, we substitute [tex]$C = 38.6$[/tex] into the formula.

2. First, we calculate the term [tex]$\frac{9}{5}C$[/tex]:

[tex]$$
\frac{9}{5} \times 38.6 = 69.48
$$[/tex]

3. Next, we add [tex]$32$[/tex] to this result to convert to Fahrenheit:

[tex]$$
69.48 + 32 = 101.48
$$[/tex]

Thus, the average cat's temperature in Fahrenheit is [tex]$101.48^\circ$[/tex].

The correct answer is therefore:

C) [tex]$101.48^\circ$[/tex] Fahrenheit.