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Sagot :
To solve the given problem, we need to determine what the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] represents. This function is used to convert temperatures from one unit to another.
Step-by-step solution:
1. Identify the Function and Variables:
- The function given is [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex].
- Here, [tex]\( C(F) \)[/tex] is a function of [tex]\( F \)[/tex].
2. Interpret the Function:
- The function [tex]\( C(F) \)[/tex] takes an input [tex]\( F \)[/tex] and performs specific operations to convert [tex]\( F \)[/tex] to another value.
- Looking closely at the formula [tex]\( \frac{5}{9}(F - 32) \)[/tex], it follows the standard formula used to convert a temperature from degrees Fahrenheit to degrees Celsius.
3. Understand the Conversion Process:
- The term [tex]\( F - 32 \)[/tex] adjusts the temperature value to match the Celsius zero point corresponding to 32 degrees Fahrenheit.
- Multiplying by [tex]\( \frac{5}{9} \)[/tex] scales the temperature from Fahrenheit units to Celsius units.
4. Relating [tex]\( C(F) \)[/tex] and [tex]\( F \)[/tex]:
- [tex]\( F \)[/tex] represents the temperature in degrees Fahrenheit.
- [tex]\( C(F) \)[/tex] represents the converted temperature in degrees Celsius.
5. Determine the Correct Interpretation:
- We need to choose the option that accurately describes the conversion function [tex]\( C(F) \)[/tex].
Options Analysis:
- Option 1: The temperature of [tex]\( F \)[/tex] degrees Fahrenheit converted to degrees Celsius.
- This correctly states that the function [tex]\( C(F) \)[/tex] converts a temperature [tex]\( F \)[/tex] in Fahrenheit to a corresponding temperature in Celsius.
- Option 2: The temperature of [tex]\( F \)[/tex] degrees Celsius converted to degrees Fahrenheit.
- This is incorrect because [tex]\( F \)[/tex] is in degrees Fahrenheit, not Celsius.
- Option 3: The temperature of [tex]\( C \)[/tex] degrees Fahrenheit converted to degrees Celsius.
- This is incorrect as [tex]\( C \)[/tex] is the result in Celsius, not Fahrenheit.
- Option 4: The temperature of [tex]\( C \)[/tex] degrees Celsius converted to degrees Fahrenheit.
- This is also incorrect; [tex]\( C \)[/tex] is already in Celsius, and the function [tex]\( C(F) \)[/tex] is converting from Fahrenheit to Celsius, not the other way around.
Based on the above analysis, the correct interpretation of the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] is:
The temperature of [tex]\( F \)[/tex] degrees Fahrenheit converted to degrees Celsius.
Thus, the correct choice is:
1. The temperature of [tex]\( F \)[/tex] degrees Fahrenheit converted to degrees Celsius.
Step-by-step solution:
1. Identify the Function and Variables:
- The function given is [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex].
- Here, [tex]\( C(F) \)[/tex] is a function of [tex]\( F \)[/tex].
2. Interpret the Function:
- The function [tex]\( C(F) \)[/tex] takes an input [tex]\( F \)[/tex] and performs specific operations to convert [tex]\( F \)[/tex] to another value.
- Looking closely at the formula [tex]\( \frac{5}{9}(F - 32) \)[/tex], it follows the standard formula used to convert a temperature from degrees Fahrenheit to degrees Celsius.
3. Understand the Conversion Process:
- The term [tex]\( F - 32 \)[/tex] adjusts the temperature value to match the Celsius zero point corresponding to 32 degrees Fahrenheit.
- Multiplying by [tex]\( \frac{5}{9} \)[/tex] scales the temperature from Fahrenheit units to Celsius units.
4. Relating [tex]\( C(F) \)[/tex] and [tex]\( F \)[/tex]:
- [tex]\( F \)[/tex] represents the temperature in degrees Fahrenheit.
- [tex]\( C(F) \)[/tex] represents the converted temperature in degrees Celsius.
5. Determine the Correct Interpretation:
- We need to choose the option that accurately describes the conversion function [tex]\( C(F) \)[/tex].
Options Analysis:
- Option 1: The temperature of [tex]\( F \)[/tex] degrees Fahrenheit converted to degrees Celsius.
- This correctly states that the function [tex]\( C(F) \)[/tex] converts a temperature [tex]\( F \)[/tex] in Fahrenheit to a corresponding temperature in Celsius.
- Option 2: The temperature of [tex]\( F \)[/tex] degrees Celsius converted to degrees Fahrenheit.
- This is incorrect because [tex]\( F \)[/tex] is in degrees Fahrenheit, not Celsius.
- Option 3: The temperature of [tex]\( C \)[/tex] degrees Fahrenheit converted to degrees Celsius.
- This is incorrect as [tex]\( C \)[/tex] is the result in Celsius, not Fahrenheit.
- Option 4: The temperature of [tex]\( C \)[/tex] degrees Celsius converted to degrees Fahrenheit.
- This is also incorrect; [tex]\( C \)[/tex] is already in Celsius, and the function [tex]\( C(F) \)[/tex] is converting from Fahrenheit to Celsius, not the other way around.
Based on the above analysis, the correct interpretation of the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] is:
The temperature of [tex]\( F \)[/tex] degrees Fahrenheit converted to degrees Celsius.
Thus, the correct choice is:
1. The temperature of [tex]\( F \)[/tex] degrees Fahrenheit converted to degrees Celsius.
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