Answer :
To solve this problem, we need to understand the relationship between Celsius and Fahrenheit and find if there's a temperature that is the same in both scales.
### Step 1: Define the conversion function from Celsius to Fahrenheit
The formula to convert a temperature from Celsius ([tex]\( c \)[/tex]) to Fahrenheit ([tex]\( f \)[/tex]) is:
[tex]\[ f(c) = c \times 1.8 + 32 \][/tex]
This formula is based on the fact that for every 1 degree increase in Celsius, the temperature in Fahrenheit increases by 1.8 degrees, and 0 degrees Celsius corresponds to 32 degrees Fahrenheit.
### Step 2: Determine if a temperature can be the same in Celsius and Fahrenheit
We want to find a temperature where:
[tex]\[ x \, \text{degrees Celsius} = x \, \text{degrees Fahrenheit} \][/tex]
This means we set up the equation using our conversion formula:
[tex]\[ x = x \times 1.8 + 32 \][/tex]
### Step 3: Solve the equation
Rearrange the equation by moving all terms involving [tex]\( x \)[/tex] to one side:
[tex]\[ x - x \times 1.8 = 32 \][/tex]
Factor out the [tex]\( x \)[/tex] from the left side:
[tex]\[ x(1 - 1.8) = 32 \][/tex]
Simplify [tex]\( 1 - 1.8 \)[/tex] to get [tex]\(-0.8\)[/tex]:
[tex]\[ -0.8x = 32 \][/tex]
Now, solve for [tex]\( x \)[/tex] by dividing both sides by [tex]\(-0.8\)[/tex]:
[tex]\[ x = \frac{32}{-0.8} \][/tex]
The result of the division is:
[tex]\[ x = -40 \][/tex]
### Conclusion
The temperature at which the Celsius and Fahrenheit values are the same is [tex]\(-40\)[/tex] degrees. So, [tex]\(-40\)[/tex] degrees Celsius is equal to [tex]\(-40\)[/tex] degrees Fahrenheit.
### Step 1: Define the conversion function from Celsius to Fahrenheit
The formula to convert a temperature from Celsius ([tex]\( c \)[/tex]) to Fahrenheit ([tex]\( f \)[/tex]) is:
[tex]\[ f(c) = c \times 1.8 + 32 \][/tex]
This formula is based on the fact that for every 1 degree increase in Celsius, the temperature in Fahrenheit increases by 1.8 degrees, and 0 degrees Celsius corresponds to 32 degrees Fahrenheit.
### Step 2: Determine if a temperature can be the same in Celsius and Fahrenheit
We want to find a temperature where:
[tex]\[ x \, \text{degrees Celsius} = x \, \text{degrees Fahrenheit} \][/tex]
This means we set up the equation using our conversion formula:
[tex]\[ x = x \times 1.8 + 32 \][/tex]
### Step 3: Solve the equation
Rearrange the equation by moving all terms involving [tex]\( x \)[/tex] to one side:
[tex]\[ x - x \times 1.8 = 32 \][/tex]
Factor out the [tex]\( x \)[/tex] from the left side:
[tex]\[ x(1 - 1.8) = 32 \][/tex]
Simplify [tex]\( 1 - 1.8 \)[/tex] to get [tex]\(-0.8\)[/tex]:
[tex]\[ -0.8x = 32 \][/tex]
Now, solve for [tex]\( x \)[/tex] by dividing both sides by [tex]\(-0.8\)[/tex]:
[tex]\[ x = \frac{32}{-0.8} \][/tex]
The result of the division is:
[tex]\[ x = -40 \][/tex]
### Conclusion
The temperature at which the Celsius and Fahrenheit values are the same is [tex]\(-40\)[/tex] degrees. So, [tex]\(-40\)[/tex] degrees Celsius is equal to [tex]\(-40\)[/tex] degrees Fahrenheit.
