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tankabanditka [31]
3 years ago
13

The outside temperature can be estimated based on how fast crickets chirp. At 104 chirps per minute, the temperature is 63 degre

eree F At 176 chirps per minute, the temperature is 81 degreeree F. Using this information you can make a formula that relates chirp rate to temperature. Assume the relationship is linear, that is, the points form a straight line when plotted on a graph. What is the temperature if you hear 124 chirps per minute? What is the temperature if you hear 68 chirps per minute?
Mathematics
1 answer:
Rasek [7]3 years ago
6 0

Answer:

For 124 chirps per minute the temperature is 68 ºF.

For 68 chirps per minute the temperature is 54 ºF.

Step-by-step explanation:

Linear functions are those whose graph is a straight line. A linear function has the following form

f(x)=b+mx

b is the constant term or the y intercept. It is the value of the dependent variable when x = 0.

m is the coefficient of the independent variable. It is also known as the slope and gives the rate of change of the dependent variable.

We know that

  • At 104 chirps per minute, the temperature is 63 ºF.
  • At 176 chirps per minute, the temperature is 81 ºF.

This information can be converted to Cartesian coordinates (x, y). Where x = the number of chirps per minute and  y = the temperature in ºF.

To find a linear function that let us find the outside temperature from how fast crickets chirp we must:

  • Find the slope:

m=\frac{y_2-y_1}{x_2-x_1}=\frac{81-63}{176-104}=\frac{1}{4}

  • Find the equation:

81=\frac{1}{4}\cdot 104+b

Solving for b

b=81-\frac{1}{4} (176)=37

Therefore, the linear function is

y=\frac{1}{4} \cdot x+37

Now, using this linear function we can know the temperature when we know the chirps per minute:

For 124 chirps per minute the temperature is:

y=\frac{1}{4} \cdot (124)+37=68

For 68 chirps per minute the temperature is:

y=\frac{1}{4} \cdot (68)+37=54

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