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27 March, 03:06

On a given dive, a platform diver's body follows a path that can be modeled by the equation d = - 4t^2 + 2t + 6, where d represents the diver's distance above the water after t seconds. Use this information to determine how long it will take a diver to reach the water's surface.

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  1. 27 March, 04:51
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    t = 1.5 seconds

    Step-by-step explanation:

    Given that d = - 4t^2 + 2t + 6,

    where d = distance above the water and

    t = seconds.

    Let assume that it's a perfect parabola

    At the symmetry

    t = - b/2a

    Where a = - 4, b = 2

    t = - 2/2 (-4)

    t = 1/4

    To determine how long it will take a diver to reach the water's surface

    d = - 4t^2 + 2t + 6

    At water surface d = 0

    4t^2 - 2t - 6 = 0

    Factorizing the above equation leads to

    4t^2 + 4t - 6t - 6 = 0

    4t (t + 1) - 6 (t + 1) = 0

    4t - 6 = 0

    4t = 6

    t = 6/4 = 3/2 = 1.5 seconds

    Since t can't be negative so we ignore the second factor.
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