Question

module 11 (linear equations) assignment
score: 19/20 answered: 19/20
question 20
entomologists studying tree crickets have found that they chirp at different rates depending on the temperature.
the number of chirps per minute, c, that the tree cricket makes is linearly dependent on the temperature, t, in fahrenheit.
the number of chirps, c, as a function of the temperature, t is: c = 3.5t - 154
round to the nearest whole number:
(a) how many chirps per minute will crickets make at 64 degrees?
select an answer
(b) what is the temperature at when crickets make 18 chirps per minute?
select an answer
submit question

Explanation:

Part (A)

Step1: Substitute \( T = 64 \) into the formula \( C = 3.5T - 154 \)

We know the formula for the number of chirps \( C \) as a function of temperature \( T \) is \( C = 3.5T - 154 \). We need to find \( C \) when \( T = 64 \). So we substitute \( T = 64 \) into the formula:
\( C = 3.5\times64 - 154 \)

Step2: Calculate the value

First, calculate \( 3.5\times64 \). \( 3.5\times64 = 224 \). Then subtract 154 from 224: \( 224 - 154 = 70 \).

Step1: Substitute \( C = 18 \) into the formula \( C = 3.5T - 154 \) and solve for \( T \)

We have the formula \( C = 3.5T - 154 \), and we know \( C = 18 \). So we substitute \( C = 18 \) into the formula:
\( 18 = 3.5T - 154 \)

Step2: Solve for \( T \)

First, add 154 to both sides of the equation to isolate the term with \( T \):
\( 18 + 154 = 3.5T \)
\( 172 = 3.5T \)
Then, divide both sides by 3.5 to solve for \( T \):
\( T=\frac{172}{3.5}\approx49.14 \), and when we round to the nearest whole number, \( T\approx49 \).

Answer:

70

Part (B)