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Answer :
To determine the range of Celsius temperatures given the Fahrenheit range from -35°F to 128°F, we use the formula for converting Fahrenheit to Celsius:
[tex]\[ C = \frac{5}{9} (F - 32) \][/tex]
We'll convert the lower and upper bounds of the Fahrenheit range to Celsius by following these steps for each boundary.
### Step-by-Step Solution:
1. Convert [tex]\( -35^{\circ}F \)[/tex] to Celsius:
[tex]\[
C = \frac{5}{9} ( -35 - 32 )
\][/tex]
[tex]\[
C = \frac{5}{9} ( -67 )
\][/tex]
[tex]\[
C \approx -37.22
\][/tex]
So, the Celsius temperature corresponding to [tex]\( -35^{\circ}F \)[/tex] is approximately [tex]\( -37.22^{\circ}C \)[/tex].
2. Convert [tex]\( 128^{\circ}F \)[/tex] to Celsius:
[tex]\[
C = \frac{5}{9} ( 128 - 32 )
\][/tex]
[tex]\[
C = \frac{5}{9} ( 96 )
\][/tex]
[tex]\[
C \approx 53.33
\][/tex]
So, the Celsius temperature corresponding to [tex]\( 128^{\circ}F \)[/tex] is approximately [tex]\( 53.33^{\circ}C \)[/tex].
### Final Answer:
- For the lower bound of [tex]\( -35^{\circ}F \)[/tex], the corresponding Celsius temperature is [tex]\( -37.22^{\circ}C \)[/tex].
- For the upper bound of [tex]\( 128^{\circ}F \)[/tex], the corresponding Celsius temperature is [tex]\( 53.33^{\circ}C \)[/tex].
Therefore, the range of Celsius temperatures corresponding to the given Fahrenheit range of -35°F to 128°F is from [tex]\( -37.22^{\circ}C \)[/tex] to [tex]\( 53.33^{\circ}C \)[/tex].
[tex]\[ \boxed{-37.22^{\circ}C \text{ to } 53.33^{\circ}C} \][/tex]
[tex]\[ C = \frac{5}{9} (F - 32) \][/tex]
We'll convert the lower and upper bounds of the Fahrenheit range to Celsius by following these steps for each boundary.
### Step-by-Step Solution:
1. Convert [tex]\( -35^{\circ}F \)[/tex] to Celsius:
[tex]\[
C = \frac{5}{9} ( -35 - 32 )
\][/tex]
[tex]\[
C = \frac{5}{9} ( -67 )
\][/tex]
[tex]\[
C \approx -37.22
\][/tex]
So, the Celsius temperature corresponding to [tex]\( -35^{\circ}F \)[/tex] is approximately [tex]\( -37.22^{\circ}C \)[/tex].
2. Convert [tex]\( 128^{\circ}F \)[/tex] to Celsius:
[tex]\[
C = \frac{5}{9} ( 128 - 32 )
\][/tex]
[tex]\[
C = \frac{5}{9} ( 96 )
\][/tex]
[tex]\[
C \approx 53.33
\][/tex]
So, the Celsius temperature corresponding to [tex]\( 128^{\circ}F \)[/tex] is approximately [tex]\( 53.33^{\circ}C \)[/tex].
### Final Answer:
- For the lower bound of [tex]\( -35^{\circ}F \)[/tex], the corresponding Celsius temperature is [tex]\( -37.22^{\circ}C \)[/tex].
- For the upper bound of [tex]\( 128^{\circ}F \)[/tex], the corresponding Celsius temperature is [tex]\( 53.33^{\circ}C \)[/tex].
Therefore, the range of Celsius temperatures corresponding to the given Fahrenheit range of -35°F to 128°F is from [tex]\( -37.22^{\circ}C \)[/tex] to [tex]\( 53.33^{\circ}C \)[/tex].
[tex]\[ \boxed{-37.22^{\circ}C \text{ to } 53.33^{\circ}C} \][/tex]
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