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Answer :
To solve the problem of determining how high you have to preheat your oven when a recipe from your cookbook calls for a temperature in degrees Celsius, we will follow these steps:
1. Convert Celsius to Fahrenheit:
The cookbook gives the temperature in degrees Celsius, but your oven uses degrees Fahrenheit. We use the formula to convert Celsius to Fahrenheit:
[tex]\[
F = \frac{9}{5} \times C + 32
\][/tex]
where [tex]\( C \)[/tex] is the temperature in Celsius, and [tex]\( F \)[/tex] is the temperature in Fahrenheit.
2. Adjust for Oven Running Hot:
Once we have the Fahrenheit temperature, we need to adjust it because the oven runs hot. We have to decrease the temperature by 15 degrees Fahrenheit:
[tex]\[
\text{Adjusted Temperature} = F - 15
\][/tex]
3. Compose the Functions:
By using these two steps, you can calculate how hot to preheat your oven when given a temperature in Celsius. First, convert the temperature from Celsius to Fahrenheit, then adjust it by subtracting 15 degrees Fahrenheit to account for your oven running hot.
For instance, if we use an example temperature of [tex]\( 100^\circ C \)[/tex]:
- Convert [tex]\( 100^\circ C \)[/tex] to Fahrenheit using the formula:
[tex]\[
F = \frac{9}{5} \times 100 + 32 = 180 + 32 = 212^\circ F
\][/tex]
- Adjust for the oven's temperature correction:
[tex]\[
\text{Adjusted Temperature} = 212 - 15 = 197^\circ F
\][/tex]
Therefore, you would need to preheat your oven to 197 degrees Fahrenheit when the cookbook specifies [tex]\( 100^\circ C \)[/tex].
1. Convert Celsius to Fahrenheit:
The cookbook gives the temperature in degrees Celsius, but your oven uses degrees Fahrenheit. We use the formula to convert Celsius to Fahrenheit:
[tex]\[
F = \frac{9}{5} \times C + 32
\][/tex]
where [tex]\( C \)[/tex] is the temperature in Celsius, and [tex]\( F \)[/tex] is the temperature in Fahrenheit.
2. Adjust for Oven Running Hot:
Once we have the Fahrenheit temperature, we need to adjust it because the oven runs hot. We have to decrease the temperature by 15 degrees Fahrenheit:
[tex]\[
\text{Adjusted Temperature} = F - 15
\][/tex]
3. Compose the Functions:
By using these two steps, you can calculate how hot to preheat your oven when given a temperature in Celsius. First, convert the temperature from Celsius to Fahrenheit, then adjust it by subtracting 15 degrees Fahrenheit to account for your oven running hot.
For instance, if we use an example temperature of [tex]\( 100^\circ C \)[/tex]:
- Convert [tex]\( 100^\circ C \)[/tex] to Fahrenheit using the formula:
[tex]\[
F = \frac{9}{5} \times 100 + 32 = 180 + 32 = 212^\circ F
\][/tex]
- Adjust for the oven's temperature correction:
[tex]\[
\text{Adjusted Temperature} = 212 - 15 = 197^\circ F
\][/tex]
Therefore, you would need to preheat your oven to 197 degrees Fahrenheit when the cookbook specifies [tex]\( 100^\circ C \)[/tex].
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