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Answer :
To solve the question, we need to create a function that converts Celsius to Fahrenheit and determine if there is a temperature that is the same in both scales.
Step 1: Create the conversion function
We know that for every 1 degree Celsius increase, the Fahrenheit temperature increases by 1.8 degrees. Additionally, 0 degrees Celsius is equivalent to 32 degrees Fahrenheit. This gives us the formula for converting Celsius to Fahrenheit:
[tex]\[ f(c) = 1.8c + 32 \][/tex]
So, the function [tex]\( f(c) \)[/tex] is:
[tex]\[ f(c) = 1.8 \cdot c + 32 \][/tex]
Step 2: Determine if there is a temperature that is the same in both Celsius and Fahrenheit
We need to find if there's a temperature [tex]\( c \)[/tex] where [tex]\( f(c) = c \)[/tex]. This means Celsius and Fahrenheit readings are the same. Let's set up the equation:
[tex]\[ 1.8c + 32 = c \][/tex]
To find [tex]\( c \)[/tex], first subtract [tex]\( c \)[/tex] from both sides:
[tex]\[ 1.8c - c + 32 = 0 \][/tex]
This simplifies to:
[tex]\[ 0.8c + 32 = 0 \][/tex]
Now, subtract 32 from both sides:
[tex]\[ 0.8c = -32 \][/tex]
Finally, divide by 0.8 to solve for [tex]\( c \)[/tex]:
[tex]\[ c = \frac{-32}{0.8} \][/tex]
This calculation results in:
[tex]\[ c = -40 \][/tex]
Therefore, the functions and solutions are as follows:
- The conversion function is [tex]\( f(c) = 1.8c + 32 \)[/tex].
- The temperature that is the same in both Celsius and Fahrenheit is [tex]\(-40\)[/tex] degrees.
Step 1: Create the conversion function
We know that for every 1 degree Celsius increase, the Fahrenheit temperature increases by 1.8 degrees. Additionally, 0 degrees Celsius is equivalent to 32 degrees Fahrenheit. This gives us the formula for converting Celsius to Fahrenheit:
[tex]\[ f(c) = 1.8c + 32 \][/tex]
So, the function [tex]\( f(c) \)[/tex] is:
[tex]\[ f(c) = 1.8 \cdot c + 32 \][/tex]
Step 2: Determine if there is a temperature that is the same in both Celsius and Fahrenheit
We need to find if there's a temperature [tex]\( c \)[/tex] where [tex]\( f(c) = c \)[/tex]. This means Celsius and Fahrenheit readings are the same. Let's set up the equation:
[tex]\[ 1.8c + 32 = c \][/tex]
To find [tex]\( c \)[/tex], first subtract [tex]\( c \)[/tex] from both sides:
[tex]\[ 1.8c - c + 32 = 0 \][/tex]
This simplifies to:
[tex]\[ 0.8c + 32 = 0 \][/tex]
Now, subtract 32 from both sides:
[tex]\[ 0.8c = -32 \][/tex]
Finally, divide by 0.8 to solve for [tex]\( c \)[/tex]:
[tex]\[ c = \frac{-32}{0.8} \][/tex]
This calculation results in:
[tex]\[ c = -40 \][/tex]
Therefore, the functions and solutions are as follows:
- The conversion function is [tex]\( f(c) = 1.8c + 32 \)[/tex].
- The temperature that is the same in both Celsius and Fahrenheit is [tex]\(-40\)[/tex] degrees.
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