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Question 1087091: Water freezes at a temperature of 0° on the Celsius scale and 32° on the Fahrenheit scale. Water boils at a temperature of 100° on the Celsius scale and 212° on the Fahrenheit scale.
Use this information to express the Celsius temperature C as a linear function of the Fahrenheit temperature F. Enter exact answers only, no approximations.
C(F)=
Determine when the temperature reading on the Celsius scale is twice the temperature reading on the Fahrenheit scale. Enter exact answers only, no approximations.
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Water freezes at a temperature of 0° on the Celsius scale and 32° on the Fahrenheit scale. Water boils at a temperature of 100° on the Celsius scale and 212° on the Fahrenheit scale.
Use this information to express the Celsius temperature C as a linear function of the Fahrenheit temperature F.
100 degs change in C = 180 degs change in F
--> F = 1.8*C + k where k is a constant.
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F = 1.8*C + k
32 = 1.8*0 + k
k = 32
--> F = 1.8C + 32
C = (F - 32)/1.8 or (F-32)*5/9
C(F)= 5(F-32)/9
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Determine when the temperature reading on the Celsius scale is twice the temperature reading on the Fahrenheit scale. Enter exact answers only, no approximations.
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C(F)= 5(F-32)/9
2F = 5(F-32)/9
18F = 5F - 160
13F = -160
F = -160/13
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C = 5*(-160/13 - 32)/9 = (-800/13 - 2080/13)/9
C = -320/13 degs
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