Question

Find the linear function Cequals​f(F) that gives the reading on the Celsius temperature scale corresponding to a reading on the Fahrenheit scale. Use the facts that Cequals0 when Fequals32 ​(freezing point) and Cequals100 when Fequals212 ​(boiling point). b. At what temperature are the Celsius and Fahrenheit readings​ equal?

Answer 1

Answer:

C = (5/9) F - (160/9)

They both read equal at Z = - 40

Explanation:

We are looking for a linear function so we can write the following condition

Y = aX + b

Applying it to the exercise we got C = a F + b

Let's use the facts that C = 0 when F = 32 and C = 100 when F = 212

0 = 32 a + b            (1)

100 = 212 a + b       (2)

From (1) b = - 32 a , when we replace this in (2) we obtain a = (5/9)

and b = - (5/9)32 = - 160/9

Finally the linear function is C = (5/9) F - (160/9)

Both readings are equal at a Z number so

Z = (5/9) Z - 160/9

(4/9) Z = -160/9 and Z = - 40