Question
We can measure temperature in two different common units: degrees Celsius and degrees Fahrenheit.
The variable
\[F\] represents the temperature in degrees Fahrenheit that is equivalent to
\[C\], the temperature in degrees Celsius.
\[F=32+1.8C\]
What is the temperature increase in degrees Fahrenheit that is equivalent to a temperature increase of
\[10\] degrees Celsius?
degrees Fahrenheit
The variable
\[F\] represents the temperature in degrees Fahrenheit that is equivalent to
\[C\], the temperature in degrees Celsius.
\[F=32+1.8C\]
What is the temperature increase in degrees Fahrenheit that is equivalent to a temperature increase of
\[10\] degrees Celsius?
degrees Fahrenheit
Answers
GPT-4o mini
To find the temperature increase in degrees Fahrenheit that corresponds to a temperature increase of \(10\) degrees Celsius, we can start by looking at the linear relationship provided by the equation:
\[
F = 32 + 1.8C
\]
When the temperature increases by \(10\) degrees Celsius, we can express the new temperature in Celsius as \(C + 10\). We can calculate the new temperature in Fahrenheit using the same equation:
1. Original temperature in Fahrenheit:
\[
F_{original} = 32 + 1.8C
\]
2. New temperature in Fahrenheit after the increase:
\[
F_{new} = 32 + 1.8(C + 10)
\]
Now, let's simplify \(F_{new}\):
\[
F_{new} = 32 + 1.8C + 1.8 \times 10
\]
Calculating \(1.8 \times 10\):
\[
1.8 \times 10 = 18
\]
So, we have:
\[
F_{new} = 32 + 1.8C + 18
\]
\[
F_{new} = (32 + 18) + 1.8C
\]
\[
F_{new} = 50 + 1.8C
\]
Now we can find the change in temperature in Fahrenheit, \( \Delta F \), which is given by:
\[
\Delta F = F_{new} - F_{original}
\]
Substituting the expressions we found:
\[
\Delta F = (50 + 1.8C) - (32 + 1.8C)
\]
Notice that the \(1.8C\) terms cancel out:
\[
\Delta F = 50 - 32
\]
\[
\Delta F = 18
\]
Thus, the temperature increase in degrees Fahrenheit that is equivalent to a temperature increase of \(10\) degrees Celsius is \(\boxed{18}\) degrees Fahrenheit.
\[
F = 32 + 1.8C
\]
When the temperature increases by \(10\) degrees Celsius, we can express the new temperature in Celsius as \(C + 10\). We can calculate the new temperature in Fahrenheit using the same equation:
1. Original temperature in Fahrenheit:
\[
F_{original} = 32 + 1.8C
\]
2. New temperature in Fahrenheit after the increase:
\[
F_{new} = 32 + 1.8(C + 10)
\]
Now, let's simplify \(F_{new}\):
\[
F_{new} = 32 + 1.8C + 1.8 \times 10
\]
Calculating \(1.8 \times 10\):
\[
1.8 \times 10 = 18
\]
So, we have:
\[
F_{new} = 32 + 1.8C + 18
\]
\[
F_{new} = (32 + 18) + 1.8C
\]
\[
F_{new} = 50 + 1.8C
\]
Now we can find the change in temperature in Fahrenheit, \( \Delta F \), which is given by:
\[
\Delta F = F_{new} - F_{original}
\]
Substituting the expressions we found:
\[
\Delta F = (50 + 1.8C) - (32 + 1.8C)
\]
Notice that the \(1.8C\) terms cancel out:
\[
\Delta F = 50 - 32
\]
\[
\Delta F = 18
\]
Thus, the temperature increase in degrees Fahrenheit that is equivalent to a temperature increase of \(10\) degrees Celsius is \(\boxed{18}\) degrees Fahrenheit.