Calculus&Mathematica: Example 3

Example Solution

Producer: Bruce Carpenter

Publisher: Math Everywhere, Inc. Distributor: Wolfram Research, Inc.

EXAMPLE
SOLUTION

G.3) Line fundamentals*

G.3.c)

Water freezes at 32 degrees Fahrenheit and at 0 degrees Celsius. Water boils at 212 degrees Fahrenheit and at 100 degrees Celsius. Find the line function that takes Fahrenheit degrees as input and spits out he corresponding Celsius reading.

Give a plot depicting Fahrenheit readings versus Celsius readings for the range -25 Fahrenheit reading 120.

Answer

The idea here is to supply a Fahrenheit temperature and get back a Celsius temperature.

That looks like: Celsius[FahrTemp] = something involving Fahrenheit temperature.

What do I know?

I know that 32F <-> 0C and 212F <-> 100C

I also know this function should be a line function, because the problem says to find a line function. The general look of a line function is f(x) = a x + b. With my names that looks like

     Celsius[FahrTemp_] = a FahrTemp + b
     b + a FahrTemp

When FarhTemp = 32, Celsius is suppose to be 0.

     Celsius[32]
     32 a + b

When FarhTemp = 212, Celsius is suppose to be 100.

     Celsius[212]
     212 a + b
     Solve[{32 a + b == 0, 212 a + b == 100}, {a,b}]
     
     a = 5/9
     b = -160/9
     5/9
     -160/90
     Celsius[Fahrtemp]
     -160/9 + 5 Fahrtemp/9

Now, for a plot of my function...

     Plot[Celsius[x], {x,-25,120}];

It is crossing the horizontal axis (F) at 32 which is correct, because that is when Celsius (vertical axis) is zero.

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