The formula [tex]F=\frac{9}{5} C+32[/tex] may be used to convert Celsius temperatures to Fahrenheit temperatures. What is the range of Celsius temperatures if the Fahrenheit range is [tex]-15^{\circ}[/tex] to [tex]35^{\circ}[/tex]? The corresponding Celsius range would be [$\square$] [tex]^{\circ}[/tex]C to [$\square$] [tex]^{\circ}[/tex]C. Round Celsius temperature answers to 2 decimal places.

Substitute F = − 15 into the formula F = 5 9 ​ C + 32 and solve for C , which gives C ≈ − 26.1 1 ∘ C .
Substitute F = 35 into the formula F = 5 9 ​ C + 32 and solve for C , which gives C ≈ 1.6 7 ∘ C .
The Celsius range is from − 26.1 1 ∘ C to 1.6 7 ∘ C .
The corresponding Celsius range is − 26.11 ​ ∘ C to 1.67 ​ ∘ C .

Explanation

Understanding the Problem We are given the formula to convert Celsius to Fahrenheit: F = 5 9 ​ C + 32 . We need to find the range of Celsius temperatures that correspond to the Fahrenheit range of − 1 5 ∘ F to 3 5 ∘ F .

Calculating the Lower Bound First, let's find the Celsius temperature corresponding to − 1 5 ∘ F . We substitute F = − 15 into the formula and solve for C :
− 15 = 5 9 ​ C + 32 Subtract 32 from both sides: − 15 − 32 = 5 9 ​ C − 47 = 5 9 ​ C Multiply both sides by 9 5 ​ :
C = − 47 × 9 5 ​ C = 9 − 235 ​ C ≈ − 26.1 1 ∘ C

Calculating the Upper Bound Next, let's find the Celsius temperature corresponding to 3 5 ∘ F . We substitute F = 35 into the formula and solve for C :
35 = 5 9 ​ C + 32 Subtract 32 from both sides: 35 − 32 = 5 9 ​ C 3 = 5 9 ​ C Multiply both sides by 9 5 ​ :
C = 3 × 9 5 ​ C = 9 15 ​ C = 3 5 ​ C ≈ 1.6 7 ∘ C

Finding the Celsius Range Therefore, the corresponding Celsius range is approximately − 26.1 1 ∘ C to 1.6 7 ∘ C .


Examples
Temperature conversion is essential in many real-world applications. For instance, scientists often need to convert between Celsius and Fahrenheit when sharing data. In cooking, recipes might provide temperatures in one scale, requiring conversion to another for accurate baking or food preparation. Understanding temperature scales and conversions is also crucial in weather forecasting and climate studies, ensuring consistent and comparable data across different regions and sources.

Answered by GinnyAnswer | 2025-07-04

The Celsius temperature range corresponding to the Fahrenheit range of -15°F to 35°F is approximately -26.11°C to 1.67°C. This is derived using the formula for converting Fahrenheit to Celsius. The calculations involve substituting the Fahrenheit values into the formula and solving for Celsius.
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Answered by Anonymous | 2025-08-23