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18 February, 04:47

A rollercoaster ride reaches a height of 80 feet before it sharply drops. The height above the ground of the rollercoaster car during the drop is modeled by the function, h (t) = 10t2-40t+80, where t is measured in seconds since the car started its decline. The model is accurate for 0≤t≤4. On this portion of the ride, how long does the car take to reach a minimum height from the ground before rising again?

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  1. 18 February, 06:56
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    Therefore the car takes 2 s to reach a minimum height from the ground before rising again.

    Step-by-step explanation:

    Given that a roller coaster ride reach a height of 80 feet.

    The height above the ground of the roller coaster is modeled by the function

    h (t) = 10t²-40t+80

    where t is measured in second.

    h (t) = 10t²-40t+80

    Differentiating with respect to t

    h' (t) = 10 (2t) - 40

    ⇒h' (t) = 20t-40

    To find the minimum height we set h' (t) = 0

    ∴20t-40=0

    ⇒20t = 40

    ⇒t=2

    The height of the roller coaster minimum when t=2 s.

    The minimum height of of the roller coaster is

    h (2) = 10 (2) ²-40.2+80

    =40-80+80

    =40 feet.

    Therefore the car takes 2 s to reach a minimum height from the ground before rising again.
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