The number of chirps per minute, C, that the tree cricket makes is linearly dependent on the temperature, T, in Fahrenheit. The crickets do not chirp at all at 45 degrees and at 75 degrees they chirp about 126 times per minute. A) Express the number of chirps, C, in terms of the temperature, T. C= B) How many chirps per minute will crickets make at 90 degrees? chirps per min.

Answer:

The answer is below

Step-by-step explanation:

A linear equation is represented by the equation y = mx + b, where m is the rate of change, b is the value of y at x = 0, y is a dependent variable and x is an independent variable.

a) Given that number of chirps per minute, C is dependent on the temperature, T, when T = 45 degrees, C = 0, this can be represented as (45, 0).

Also at 75 degrees, C = 126 it can be represented as (75, 126).

Using (45, 0) and (75, 126), we can determine the equation of the line from:

[tex]C-C_1=\frac{C_2-C_1}{T_2-T_1}(T-T_1)\\ \\C-0=\frac{126-0}{75-45}(T-45)\\ \\C=4.2(T-45)\\\\C=4.2T-189\\\\[/tex]

b) At t = 90°:

C = 4.2(90) - 189

C = 189 chirps per min

a. The expression of the number of chirps should be C =  4.2T - 189

b. The number of chirps per minute should be 189 chirps per min.

Since The crickets do not chirp at all at 45 degrees and at 75 degrees they chirp about 126 times per minute.

So, here we used (45, 0) and (75, 126), we can measure the equation of the line from

[tex]C- C_1 = \frac{C_2-C_1}{T_2-T_1} (T_2 - T_1)\\\\C- 0 = \frac{126-0}{75-45} (T - 45)\\\\[/tex]

C = 4.2(T - 45)

C = 4.2T - 189

b. When T = 90 degrees

So,

C = 4.2(90) - 189

= 189 chirps

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