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Answer :
To find the corresponding range of Celsius temperatures when given a range in Fahrenheit from [tex]\(-23^\circ F\)[/tex] to [tex]\(80^\circ F\)[/tex], we will use the formula to convert Fahrenheit to Celsius. The formula is:
[tex]\[ C = \frac{5}{9}(F - 32) \][/tex]
Let's apply this formula step by step to convert the given Fahrenheit temperatures into Celsius.
1. Convert [tex]\(-23^\circ F\)[/tex] to Celsius:
- Start with the formula: [tex]\(C = \frac{5}{9}(F - 32)\)[/tex].
- Substitute [tex]\(-23\)[/tex] for [tex]\(F\)[/tex]:
[tex]\[
C = \frac{5}{9}(-23 - 32)
\][/tex]
- Simplify inside the parentheses:
[tex]\[
-23 - 32 = -55
\][/tex]
- Now, plug in and calculate:
[tex]\[
C = \frac{5}{9} \times -55
\][/tex]
[tex]\[
C = \frac{-275}{9} \approx -30.56
\][/tex]
So, [tex]\(-23^\circ F\)[/tex] is approximately [tex]\(-30.56^\circ C\)[/tex].
2. Convert [tex]\(80^\circ F\)[/tex] to Celsius:
- Use the same formula: [tex]\(C = \frac{5}{9}(F - 32)\)[/tex].
- Substitute [tex]\(80\)[/tex] for [tex]\(F\)[/tex]:
[tex]\[
C = \frac{5}{9}(80 - 32)
\][/tex]
- Simplify inside the parentheses:
[tex]\[
80 - 32 = 48
\][/tex]
- Now, plug in and calculate:
[tex]\[
C = \frac{5}{9} \times 48
\][/tex]
[tex]\[
C = \frac{240}{9} \approx 26.67
\][/tex]
Therefore, [tex]\(80^\circ F\)[/tex] is approximately [tex]\(26.67^\circ C\)[/tex].
Conclusion:
The corresponding Celsius range is approximately [tex]\(-30.56^\circ C\)[/tex] to [tex]\(26.67^\circ C\)[/tex].
[tex]\[ C = \frac{5}{9}(F - 32) \][/tex]
Let's apply this formula step by step to convert the given Fahrenheit temperatures into Celsius.
1. Convert [tex]\(-23^\circ F\)[/tex] to Celsius:
- Start with the formula: [tex]\(C = \frac{5}{9}(F - 32)\)[/tex].
- Substitute [tex]\(-23\)[/tex] for [tex]\(F\)[/tex]:
[tex]\[
C = \frac{5}{9}(-23 - 32)
\][/tex]
- Simplify inside the parentheses:
[tex]\[
-23 - 32 = -55
\][/tex]
- Now, plug in and calculate:
[tex]\[
C = \frac{5}{9} \times -55
\][/tex]
[tex]\[
C = \frac{-275}{9} \approx -30.56
\][/tex]
So, [tex]\(-23^\circ F\)[/tex] is approximately [tex]\(-30.56^\circ C\)[/tex].
2. Convert [tex]\(80^\circ F\)[/tex] to Celsius:
- Use the same formula: [tex]\(C = \frac{5}{9}(F - 32)\)[/tex].
- Substitute [tex]\(80\)[/tex] for [tex]\(F\)[/tex]:
[tex]\[
C = \frac{5}{9}(80 - 32)
\][/tex]
- Simplify inside the parentheses:
[tex]\[
80 - 32 = 48
\][/tex]
- Now, plug in and calculate:
[tex]\[
C = \frac{5}{9} \times 48
\][/tex]
[tex]\[
C = \frac{240}{9} \approx 26.67
\][/tex]
Therefore, [tex]\(80^\circ F\)[/tex] is approximately [tex]\(26.67^\circ C\)[/tex].
Conclusion:
The corresponding Celsius range is approximately [tex]\(-30.56^\circ C\)[/tex] to [tex]\(26.67^\circ C\)[/tex].
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