Question

W (t) models the daily water level (in cm) at a pond in Arizona, t days after the hottest day of the year. Here, t is entered in radians:
w(t) = 15 cos ((2pi / 365)t) + 43
What is the first time after the hottest day of the year that the water levels is 30 cm?

Answer 1

Answer:

152 days

Step-by-step explanation:

Given:

w(t) = 15 cos ((2π / 365)t) + 43

To find first time after the hottest day of the year that the water levels is 30 cm, substitute with w(t) = 30 and solve for t

30 = 15 cos ((2π / 365)t) + 43

30 - 43 = 15 cos ((2π / 365)t)

15 cos ((2π / 365)t) = -13

cos ((2π / 365)t) = -13/15

(2π / 365)t = cos⁻¹ (-13/15) = 150.07° ≈ (5/6) π

t = (365/2) * (5/6) ≈ 152 days

So, the first time after the hottest day of the year that the water levels is 30 cm is after 152 days