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worty [1.4K]
3 years ago
15

John is going on a trip and the country he is traveling to uses the Celsius scale. He is curious about converting Celsius temper

atures to Fahrenheit. John determines 68°F is equivalent to 20°C and 86°F is equivalent to 30°C.
Which function models the relationship between Fahrenheit and Celsius?
Mathematics
2 answers:
Feliz [49]3 years ago
8 0

Answer:

The answer is 9/5c + 32

Setler79 [48]3 years ago
4 0

Answer:

f(x)=\dfrac{9}{5}x+32 converts Celsius to Fahrenheit.

g(x)=\dfrac{5(x-32)}{9} converts Fahrenheit to Celsius.

Step-by-step explanation:

Write given data in the table

\begin{array}{cc}x&f(x)\\^{\circ}\text{C}&^{\circ}\text{F}\\20&68\\30&86\end{array}

Let the expression for the function be

f(x)=ax+b

Note, that this equation is linear equation and it is well-known fact that the Celsius to Fahrenheit dependence is linear.

Substitute corresponding values into this expression:

68=20a+b\\ \\86=30a+b

Subtract these two equations:

86-68=30a-20a\\ \\10a=18\\ \\a=\dfrac{9}{5}

Substitute it into the first equation:

68=20\cdot \dfrac{9}{5}+b\Rightarrow b=68-36=32

So,

f(x)=\dfrac{9}{5}x+32

This is the function which converts Celsius to Fahrenheit.

And function

g(x)=\dfrac{5(x-32)}{9} converts Fahrenheit to Celsius.

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