The equation of the rotating light is an illustration of a secant function
The equation that represents the distance between the center of the circle and the light source is ![d(t) = 40\sec(\frac{\pi}{3}t)](https://tex.z-dn.net/?f=d%28t%29%20%3D%2040%5Csec%28%5Cfrac%7B%5Cpi%7D%7B3%7Dt%29)
<h3>How to determine the equation</h3>
The equation is a secant function represented by
![y =A\sec(Bt)](https://tex.z-dn.net/?f=y%20%3DA%5Csec%28Bt%29)
Where:
A represents the amplitude
So, we have:
--- the distance of the light from each square wall
B represents the period, and it is calculated as:
![B = \frac{2\pi}{T}](https://tex.z-dn.net/?f=B%20%3D%20%5Cfrac%7B2%5Cpi%7D%7BT%7D)
The light completes its full rotation every 6 seconds.
This means that,
T = 6
So, we have:
![B = \frac{2\pi}{6}](https://tex.z-dn.net/?f=B%20%3D%20%5Cfrac%7B2%5Cpi%7D%7B6%7D)
Simplify
![B = \frac{\pi}{3}](https://tex.z-dn.net/?f=B%20%3D%20%5Cfrac%7B%5Cpi%7D%7B3%7D)
Substitute values for A and B in ![y =A\sec(Bt)](https://tex.z-dn.net/?f=y%20%3DA%5Csec%28Bt%29)
![y = 40\sec(\frac{\pi}{3}t)](https://tex.z-dn.net/?f=y%20%3D%2040%5Csec%28%5Cfrac%7B%5Cpi%7D%7B3%7Dt%29)
Rewrite as a function
![d(t) = 40\sec(\frac{\pi}{3}t)](https://tex.z-dn.net/?f=d%28t%29%20%3D%2040%5Csec%28%5Cfrac%7B%5Cpi%7D%7B3%7Dt%29)
Hence, the equation that represents the distance between the center of the circle and the light source is ![d(t) = 40\sec(\frac{\pi}{3}t)](https://tex.z-dn.net/?f=d%28t%29%20%3D%2040%5Csec%28%5Cfrac%7B%5Cpi%7D%7B3%7Dt%29)
Read more about trigonometry functions at:
brainly.com/question/1143565
Answer:
come back
Step-by-step explanation:
Answer:
The probability that carbon emissions from the factory are within the permissible level and the test predicts the opposite to be true is 19.338% (Rounding to the next thousandth place)
Step-by-step explanation:
1. Let's review the information provided to us to answer the question correctly:
Probability that carbon emissions from the company’s factory exceed the permissible level = 35% = 0.35
Accuracy of the test of emissions level = 85% = 0.85
2. The probability that carbon emissions from the factory are within the permissible level and the test predicts the opposite to be true is?
These two events, carbon emissions from the company’s factory and the accuracy of the test are independent events, therefore:
Probability that carbon emissions from the factory are within the permissible level = 1 - 0.35 = 0.65
Probability that the test predicts the opposite to be true = 0..35 * 0.85 = 0.2975 (The opposite is that the carbon emissions from the company exceed the permissible level)
Probability that carbon emissions from the factory are within the permissible level and the test predicts the opposite to be true is:
0.65 * 0.2975 = 0.193375
The probability that carbon emissions from the factory are within the permissible level and the test predicts the opposite to be true is 19.338% (Rounding to the next thousandth place
MARK BRAINLIEST PLS