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18 May, 03:10

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?

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  1. 18 May, 05:48
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    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
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