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Answer :
To convert the range of Fahrenheit temperatures to Celsius, we'll use the conversion formula [tex]\( F = \frac{9}{5} C + 32 \)[/tex]. Our goal is to find the corresponding Celsius temperatures for Fahrenheit temperatures ranging from [tex]\(-41^\circ \text{F}\)[/tex] to [tex]\(54^\circ \text{F}\)[/tex].
Step-by-step Solution:
1. Start with the conversion formula:
The formula to convert Celsius to Fahrenheit is:
[tex]\[
F = \frac{9}{5} C + 32
\][/tex]
We need to rearrange this formula to solve for [tex]\( C \)[/tex] (Celsius):
[tex]\[
C = \frac{5}{9} (F - 32)
\][/tex]
2. Convert the minimum Fahrenheit temperature to Celsius:
Substitute [tex]\(-41^\circ \text{F}\)[/tex] into the formula:
[tex]\[
C = \frac{5}{9} (-41 - 32)
\][/tex]
Calculate the value:
[tex]\[
C = \frac{5}{9} \times (-73) = -40.56
\][/tex]
So, the minimum Celsius temperature is approximately [tex]\(-40.56^\circ \text{C}\)[/tex].
3. Convert the maximum Fahrenheit temperature to Celsius:
Substitute [tex]\(54^\circ \text{F}\)[/tex] into the formula:
[tex]\[
C = \frac{5}{9} (54 - 32)
\][/tex]
Calculate the value:
[tex]\[
C = \frac{5}{9} \times 22 = 12.22
\][/tex]
So, the maximum Celsius temperature is approximately [tex]\(12.22^\circ \text{C}\)[/tex].
Therefore, the range of Celsius temperatures corresponding to [tex]\(-41^\circ \text{F}\)[/tex] to [tex]\(54^\circ \text{F}\)[/tex] is approximately [tex]\(-40.56^\circ \text{C}\)[/tex] to [tex]\(12.22^\circ \text{C}\)[/tex].
Step-by-step Solution:
1. Start with the conversion formula:
The formula to convert Celsius to Fahrenheit is:
[tex]\[
F = \frac{9}{5} C + 32
\][/tex]
We need to rearrange this formula to solve for [tex]\( C \)[/tex] (Celsius):
[tex]\[
C = \frac{5}{9} (F - 32)
\][/tex]
2. Convert the minimum Fahrenheit temperature to Celsius:
Substitute [tex]\(-41^\circ \text{F}\)[/tex] into the formula:
[tex]\[
C = \frac{5}{9} (-41 - 32)
\][/tex]
Calculate the value:
[tex]\[
C = \frac{5}{9} \times (-73) = -40.56
\][/tex]
So, the minimum Celsius temperature is approximately [tex]\(-40.56^\circ \text{C}\)[/tex].
3. Convert the maximum Fahrenheit temperature to Celsius:
Substitute [tex]\(54^\circ \text{F}\)[/tex] into the formula:
[tex]\[
C = \frac{5}{9} (54 - 32)
\][/tex]
Calculate the value:
[tex]\[
C = \frac{5}{9} \times 22 = 12.22
\][/tex]
So, the maximum Celsius temperature is approximately [tex]\(12.22^\circ \text{C}\)[/tex].
Therefore, the range of Celsius temperatures corresponding to [tex]\(-41^\circ \text{F}\)[/tex] to [tex]\(54^\circ \text{F}\)[/tex] is approximately [tex]\(-40.56^\circ \text{C}\)[/tex] to [tex]\(12.22^\circ \text{C}\)[/tex].
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