Answer:
Step-by-step explanation:
Robert Boyle was one of the most prolific figures in the scientific revolution and the leading scientist of his day. He discovered the Boyle's law, which shows that the volume and pressure of a gas are proportionally related.
Answer:
99,900
Step-by-step explanation:
What?
And you spelled answer wrong
Answer:
t=152 days (in radians)
Step-by-step explanation:
W(t)models the daily water level at a pond in Arizona, t days after the hottest day of the year. (t is entered in radian)
![W(t) = 15\cos\left(\dfrac{2\pi}{365}t\right) + 43](https://tex.z-dn.net/?f=W%28t%29%20%3D%2015%5Ccos%5Cleft%28%5Cdfrac%7B2%5Cpi%7D%7B365%7Dt%5Cright%29%20%2B%2043)
We want to determine the first time,t at which the water level is 30cm.
When W(t)=30
![30 = 15\cos\left(\dfrac{2\pi}{365}t\right) + 43\\30-43=15\cos\left(\dfrac{2\pi}{365}t\right)\\-13=15\cos\left(\dfrac{2\pi}{365}t\right)\\-\dfrac{13}{15} =\cos\left(\dfrac{2\pi}{365}t\right)\\cos^{-1}(-\dfrac{13}{15})=\dfrac{2\pi}{365}t\right)\\cos^{-1}(\dfrac{13}{15})=\dfrac{2\pi}{365}t\right)](https://tex.z-dn.net/?f=30%20%3D%2015%5Ccos%5Cleft%28%5Cdfrac%7B2%5Cpi%7D%7B365%7Dt%5Cright%29%20%2B%2043%5C%5C30-43%3D15%5Ccos%5Cleft%28%5Cdfrac%7B2%5Cpi%7D%7B365%7Dt%5Cright%29%5C%5C-13%3D15%5Ccos%5Cleft%28%5Cdfrac%7B2%5Cpi%7D%7B365%7Dt%5Cright%29%5C%5C-%5Cdfrac%7B13%7D%7B15%7D%20%3D%5Ccos%5Cleft%28%5Cdfrac%7B2%5Cpi%7D%7B365%7Dt%5Cright%29%5C%5Ccos%5E%7B-1%7D%28-%5Cdfrac%7B13%7D%7B15%7D%29%3D%5Cdfrac%7B2%5Cpi%7D%7B365%7Dt%5Cright%29%5C%5Ccos%5E%7B-1%7D%28%5Cdfrac%7B13%7D%7B15%7D%29%3D%5Cdfrac%7B2%5Cpi%7D%7B365%7Dt%5Cright%29)
![cos^{-1}(\dfrac{13}{15})=\dfrac{2\pi}{365}t\right)\\t=\dfrac{365}{2\pi}\cdot cos^{-1}(\dfrac{13}{15})\\t=152.16\\\approx 152 days \text{ (to the nearest whole day)}](https://tex.z-dn.net/?f=cos%5E%7B-1%7D%28%5Cdfrac%7B13%7D%7B15%7D%29%3D%5Cdfrac%7B2%5Cpi%7D%7B365%7Dt%5Cright%29%5C%5Ct%3D%5Cdfrac%7B365%7D%7B2%5Cpi%7D%5Ccdot%20cos%5E%7B-1%7D%28%5Cdfrac%7B13%7D%7B15%7D%29%5C%5Ct%3D152.16%5C%5C%5Capprox%20152%20days%20%5Ctext%7B%20%20%20%28to%20the%20nearest%20whole%20day%29%7D)
Solution:
<u>In this case, we are given:</u>
- Equation: y = -2x
- Slope = -2
- y-intercept = 0
Looking at Option A, we can tell that its <u>slope is -2 and y-intercept is 0.</u>
Since this is matching with the info we are given, Option A is correct.