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Answer :
To solve this problem, we need to find the range of Celsius temperatures when the Fahrenheit temperatures range from [tex]\(-21^\circ F\)[/tex] to [tex]\(116^\circ F\)[/tex]. We'll use the formula that converts Fahrenheit to Celsius:
[tex]\[ C = \frac{5}{9} (F - 32) \][/tex]
Step 1: Convert the lower Fahrenheit temperature to Celsius
1. Start with the lower bound of the Fahrenheit range: [tex]\(-21^\circ F\)[/tex].
2. Substitute [tex]\(-21^\circ F\)[/tex] into the conversion formula:
[tex]\[
C = \frac{5}{9} (-21 - 32)
\][/tex]
3. Simplify the expression inside the parentheses: [tex]\(-21 - 32 = -53\)[/tex].
4. Multiply:
[tex]\[
C = \frac{5}{9} \times (-53) = \frac{-265}{9} \approx -29.44
\][/tex]
5. Round to two decimal places: [tex]\(-29.44^\circ C\)[/tex].
Step 2: Convert the upper Fahrenheit temperature to Celsius
1. Now, take the upper bound of the Fahrenheit range: [tex]\(116^\circ F\)[/tex].
2. Substitute [tex]\(116^\circ F\)[/tex] into the conversion formula:
[tex]\[
C = \frac{5}{9} (116 - 32)
\][/tex]
3. Simplify the expression inside the parentheses: [tex]\(116 - 32 = 84\)[/tex].
4. Multiply:
[tex]\[
C = \frac{5}{9} \times 84 = \frac{420}{9} \approx 46.67
\][/tex]
5. Round to two decimal places: [tex]\(46.67^\circ C\)[/tex].
Final Answer
The corresponding Celsius range for Fahrenheit temperatures between [tex]\(-21^\circ F\)[/tex] and [tex]\(116^\circ F\)[/tex] is approximately [tex]\(-29.44^\circ C\)[/tex] to [tex]\(46.67^\circ C\)[/tex].
[tex]\[ C = \frac{5}{9} (F - 32) \][/tex]
Step 1: Convert the lower Fahrenheit temperature to Celsius
1. Start with the lower bound of the Fahrenheit range: [tex]\(-21^\circ F\)[/tex].
2. Substitute [tex]\(-21^\circ F\)[/tex] into the conversion formula:
[tex]\[
C = \frac{5}{9} (-21 - 32)
\][/tex]
3. Simplify the expression inside the parentheses: [tex]\(-21 - 32 = -53\)[/tex].
4. Multiply:
[tex]\[
C = \frac{5}{9} \times (-53) = \frac{-265}{9} \approx -29.44
\][/tex]
5. Round to two decimal places: [tex]\(-29.44^\circ C\)[/tex].
Step 2: Convert the upper Fahrenheit temperature to Celsius
1. Now, take the upper bound of the Fahrenheit range: [tex]\(116^\circ F\)[/tex].
2. Substitute [tex]\(116^\circ F\)[/tex] into the conversion formula:
[tex]\[
C = \frac{5}{9} (116 - 32)
\][/tex]
3. Simplify the expression inside the parentheses: [tex]\(116 - 32 = 84\)[/tex].
4. Multiply:
[tex]\[
C = \frac{5}{9} \times 84 = \frac{420}{9} \approx 46.67
\][/tex]
5. Round to two decimal places: [tex]\(46.67^\circ C\)[/tex].
Final Answer
The corresponding Celsius range for Fahrenheit temperatures between [tex]\(-21^\circ F\)[/tex] and [tex]\(116^\circ F\)[/tex] is approximately [tex]\(-29.44^\circ C\)[/tex] to [tex]\(46.67^\circ C\)[/tex].
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