Answer :
To find the temperature increase in degrees Fahrenheit that corresponds to a 10 degrees Celsius increase, we need to understand how the conversion between Celsius and Fahrenheit works. The relationship is given by the formula:
[tex]\[ f(c) = 32 + 1.8 \times c \][/tex]
where [tex]\( f \)[/tex] is the temperature in degrees Fahrenheit and [tex]\( c \)[/tex] is the temperature in degrees Celsius.
Here’s how we find the equivalent increase:
1. Identify the given temperature increase in Celsius:
We are given that the temperature increases by 10 degrees Celsius.
2. Understand the conversion rate:
From the formula, we see that for every 1 degree Celsius increase, the temperature in Fahrenheit increases by 1.8 degrees (this is the conversion factor).
3. Calculate the Fahrenheit increase:
To find out the increase in degrees Fahrenheit, we multiply the Celsius increase by the conversion factor:
[tex]\[
\text{Temperature increase in Fahrenheit} = 10 \times 1.8 = 18 \text{ degrees Fahrenheit}
\][/tex]
Therefore, a temperature increase of 10 degrees Celsius is equivalent to an increase of 18 degrees Fahrenheit.
[tex]\[ f(c) = 32 + 1.8 \times c \][/tex]
where [tex]\( f \)[/tex] is the temperature in degrees Fahrenheit and [tex]\( c \)[/tex] is the temperature in degrees Celsius.
Here’s how we find the equivalent increase:
1. Identify the given temperature increase in Celsius:
We are given that the temperature increases by 10 degrees Celsius.
2. Understand the conversion rate:
From the formula, we see that for every 1 degree Celsius increase, the temperature in Fahrenheit increases by 1.8 degrees (this is the conversion factor).
3. Calculate the Fahrenheit increase:
To find out the increase in degrees Fahrenheit, we multiply the Celsius increase by the conversion factor:
[tex]\[
\text{Temperature increase in Fahrenheit} = 10 \times 1.8 = 18 \text{ degrees Fahrenheit}
\][/tex]
Therefore, a temperature increase of 10 degrees Celsius is equivalent to an increase of 18 degrees Fahrenheit.
