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

Answer :

To convert the average cat's body temperature from Celsius to Fahrenheit, we'll use the conversion formula:

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

We want to find the temperature in Fahrenheit, [tex]\( F \)[/tex], so we'll rearrange this formula to solve for [tex]\( F \)[/tex]:

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

Here’s how you can calculate it step-by-step:

1. Start with the cat's temperature in Celsius:
[tex]\[ C = 38.6^\circ \text{C} \][/tex]

2. Multiply by [tex]\(\frac{9}{5}\)[/tex]:
[tex]\[ 38.6 \times \frac{9}{5} = 69.48 \][/tex]

3. Add 32 to the result from step 2:
[tex]\[ F = 69.48 + 32 = 101.48 \][/tex]

Therefore, the average cat’s temperature in Fahrenheit is approximately [tex]\( 101.48^\circ \)[/tex] Fahrenheit.

The correct answer is:
B) [tex]\( 101.48^\circ \)[/tex] Fahrenheit