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Answer :
To convert a range of Fahrenheit temperatures to Celsius, you can use the formula [tex]\( C = \frac{5}{9} (F - 32) \)[/tex]. Here's a step-by-step solution to find the corresponding Celsius range for the given Fahrenheit range of [tex]\(-33^\circ F\)[/tex] to [tex]\(20^\circ F\)[/tex].
1. Identify the given Fahrenheit range:
- Minimum Fahrenheit temperature, [tex]\( F_{min} = -33^\circ F \)[/tex]
- Maximum Fahrenheit temperature, [tex]\( F_{max} = 20^\circ F \)[/tex]
2. Convert the minimum Fahrenheit temperature to Celsius:
Using the formula [tex]\( C = \frac{5}{9} (F - 32) \)[/tex]:
[tex]\[
C_{min} = \frac{5}{9} (F_{min} - 32) = \frac{5}{9} (-33 - 32)
\][/tex]
[tex]\[
C_{min} = \frac{5}{9} (-65)
\][/tex]
[tex]\[
C_{min} = -36.11 \,\text{(rounded to 2 decimal places)}
\][/tex]
3. Convert the maximum Fahrenheit temperature to Celsius:
Using the same formula:
[tex]\[
C_{max} = \frac{5}{9} (F_{max} - 32) = \frac{5}{9} (20 - 32)
\][/tex]
[tex]\[
C_{max} = \frac{5}{9} (-12)
\][/tex]
[tex]\[
C_{max} = -6.67 \,\text{(rounded to 2 decimal places)}
\][/tex]
4. State the corresponding Celsius range:
- The minimum Celsius temperature is [tex]\(-36.11^\circ C\)[/tex].
- The maximum Celsius temperature is [tex]\(-6.67^\circ C\)[/tex].
Therefore, the Celsius range corresponding to the Fahrenheit range of [tex]\(-33^\circ F\)[/tex] to [tex]\(20^\circ F\)[/tex] is [tex]\(-36.11^\circ C\)[/tex] to [tex]\(-6.67^\circ C\)[/tex].
1. Identify the given Fahrenheit range:
- Minimum Fahrenheit temperature, [tex]\( F_{min} = -33^\circ F \)[/tex]
- Maximum Fahrenheit temperature, [tex]\( F_{max} = 20^\circ F \)[/tex]
2. Convert the minimum Fahrenheit temperature to Celsius:
Using the formula [tex]\( C = \frac{5}{9} (F - 32) \)[/tex]:
[tex]\[
C_{min} = \frac{5}{9} (F_{min} - 32) = \frac{5}{9} (-33 - 32)
\][/tex]
[tex]\[
C_{min} = \frac{5}{9} (-65)
\][/tex]
[tex]\[
C_{min} = -36.11 \,\text{(rounded to 2 decimal places)}
\][/tex]
3. Convert the maximum Fahrenheit temperature to Celsius:
Using the same formula:
[tex]\[
C_{max} = \frac{5}{9} (F_{max} - 32) = \frac{5}{9} (20 - 32)
\][/tex]
[tex]\[
C_{max} = \frac{5}{9} (-12)
\][/tex]
[tex]\[
C_{max} = -6.67 \,\text{(rounded to 2 decimal places)}
\][/tex]
4. State the corresponding Celsius range:
- The minimum Celsius temperature is [tex]\(-36.11^\circ C\)[/tex].
- The maximum Celsius temperature is [tex]\(-6.67^\circ C\)[/tex].
Therefore, the Celsius range corresponding to the Fahrenheit range of [tex]\(-33^\circ F\)[/tex] to [tex]\(20^\circ F\)[/tex] is [tex]\(-36.11^\circ C\)[/tex] to [tex]\(-6.67^\circ C\)[/tex].
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