MHB Find Linear Equation: C=f(F) Temp Conversion

[Teh]

a. Find the linear C=f(F) that gives the reading the reading on the Celsius temperature scale corresponding to a reading on the Fahrenheit scale. Use the facts that C=0 when F=32 ​(freezing point) and C=100 when F=212 ​(boiling point).

b.At what temperature are the Celsius and Fahrenheit readings​ equal?*It is asking for a linear equation but so far i have slight idea that i have to use the idea of "f o g" and "g o f" or find the slope, after solving for the slope I used the point-slope to get the equation, but my answer is wrong...what I am doing wrong

my answer for part a is:

m = F2-F1\C2-C1 *slope intercept form*

m = 212-32/100-0 = 9/5

F-F1=m(C-C1) *point slope*

F-32 = 9/5(C-0)

F = 9/5C+32

MY ANSWER: 9/5C+32

*tried use the commands and symbols but didnt work for me*

 

[MarkFL]

Well, if you are supposed to use the calculus here, I would begin with:

$$9\,dC=5\,dF$$

Integrating (and using our known boundaries), we get:

$$9\int_0^C\,du=5\int_{32}^F\,dv$$

Applying the FTOC, there results:

$$9C=5(F-32)$$

Hence, solving for $C$, we obtain::

$$C(F)=\frac{5}{9}(F-32)$$

To answer part b), we need to solve:

$$C(F)=F$$

$$\frac{5}{9}(F-32)=F$$

What do you get for $F$ here?

 

[HallsofIvy]

a. Find the linear C=f(F) that gives the reading the reading on the Celsius temperature scale corresponding to a reading on the Fahrenheit scale. Use the facts that C=0 when F=32 ​(freezing point) and C=100 when F=212 ​(boiling point).

b.At what temperature are the Celsius and Fahrenheit readings​ equal?*It is asking for a linear equation but so far i have slight idea that i have to use the idea of "f o g" and "g o f"

No, this has nothing to do with the composition of functions, there is only one function involved.

or find the slope, after solving for the slope I used the point-slope to get the equation, but my answer is wrong...what I am doing wrong

my answer for part a is:

m = F2-F1\C2-C1 *slope intercept form*

You mean m= (F2- F1)/(C2- C1), right?

m = 212-32/100-0 = 9/5

F-F1=m(C-C1) *point slope*

F-32 = 9/5(C-0)

F = 9/5C+32

MY ANSWER: 9/5C+32

You mean F= (9/5)C+ 32.

*tried use the commands and symbols but didnt work for me*

Perhaps that was because you were asked to find C as a function of F not the other way around! F- 32= (9/5)C so C= (5/9)(F- 32).

For the second question, "Celsius and Fahrenheit readings​ equal" when C= F= (5/9)(F- 32). Solve that equation for F.