The equation above shows how temperature F,measured in degrees Fahrenheit,Relates to temperature C,measured in degrees Celsius.Based on the equation,Which of the follow must be true?
Accepted Solution
A:
Check the complete question attached.
We have the equation [tex]C= \frac{5}{9} (F-31)[/tex] equation (1); solving for F we get: [tex] \frac{9}{5} C=F-31[/tex] [tex]F= \frac{9}{5} C+31[/tex] [tex]F= \frac{9}{5} (C+31)[/tex] equation (2)
I. To check this we are going to use equation (1) to see what hapen when temperature rises from 32 Fahrenheit to 33 Fahrenheit: For 32 Fahrenheit: [tex]C= \frac{5}{9} (32-31)[/tex] [tex]C= \frac{5}{9} (1)[/tex] [tex]C= \frac{5}{9} [/tex]
For 33 Fahrenheit: [tex]C= \frac{5}{9} (33-31)[/tex] [tex]C= \frac{5}{9} (2)[/tex] [tex]C= \frac{10}{9} [/tex] Now we are going to subtract the two temperatures in degrees Celsius: [tex] \frac{10}{9} - \frac{5}{9} = \frac{5}{9} [/tex] As you can see, the temperature increased [tex] \frac{5}{9} [/tex] degree Celsius.
We can conclude that a temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of [tex] \frac{5}{9} [/tex] degree Celsius.
II. To check this one we are going to use equation (2) to see what happens when temperature raises from 1 degree Celsius to 2 degrees Celsius: For 1 degree Celsius: [tex]F= \frac{9}{5} (C+31)[/tex] [tex]F= \frac{9}{5} (1+31)[/tex] [tex]F= \frac{9}{5} (32)[/tex] [tex]F=57.6[/tex]
For 2 degrees Celsius: [tex]F= \frac{9}{5} (C+31)[/tex] [tex]F= \frac{9}{5} (2+31)[/tex] [tex]F= \frac{9}{5} (33)[/tex] [tex]F=59.4[/tex] Now we are going to subtract the two temperatures in Fahrenheit: [tex]59.4-57.6=1.8[/tex] As you can see, the temperature increased 1.8 Fahrenheit.
We can conclude that a temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 Fahrenheit.
III. Since a temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of [tex] \frac{5}{9} [/tex] degree Celsius, we can conclude that this one is false.