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)
Answer:
D. ![10*6^2](https://tex.z-dn.net/?f=10%2A6%5E2)
Step-by-step explanation:
This fits the problem as long as there were 10 rows. The 10 signifies the number of rows while the
is the number of bricks per row. This would be a total of 360 bricks.
Answer:
y = 110°
Step-by-step explanation:
The inscribed angle CHF is half the measure of its intercepted arc CDF
The 3 arcs in the circle = 360°, thus
arc CDF = 360° - 160° - 60° = 140°, so
∠ CHF = 0.5 × 140° = 70°
∠ CHF and ∠ y are adjacent angles and supplementary, thus
y = 180° - 70° = 110°
Answer:
y=200(1.13)^6= 416.39
Step-by-step explanation: