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

User Bigreddot
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2 Answers

2 votes

Answer:

The answer is 9/5c + 32

User Mgcm
by
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3 votes

Answer:


f(x)=(9)/(5)x+32 converts Celsius to Fahrenheit.


g(x)=(5(x-32))/(9) converts Fahrenheit to Celsius.

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=(9)/(5)

Substitute it into the first equation:


68=20\cdot (9)/(5)+b\Rightarrow b=68-36=32

So,


f(x)=(9)/(5)x+32

This is the function which converts Celsius to Fahrenheit.

And function


g(x)=(5(x-32))/(9) converts Fahrenheit to Celsius.

User Nche
by
8.5k points
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