Answer :
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)
[tex]W(t) = 15\cos\left(\dfrac{2\pi}{365}t\right) + 43[/tex]
We want to determine the first time,t at which the water level is 30cm.
When W(t)=30
[tex]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)[/tex]
[tex]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)}[/tex]