Ask Question
19 February, 00:36

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?

+4
Answers (1)
  1. 19 February, 00:38
    0
    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
Know the Answer?
Not Sure About the Answer?
Find an answer to your 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 ...” in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers