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Math Help - inequality word problem

  1. #1
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    inequality word problem

    The height of a particular ball is given by the formula h=12t-5t^2 where h is the height above the ground in metres and t is the time in seconds.

    Form and solve an inequality to find when the height of the ball above the ground is less than 4 metres.


    i'm not quite sure how to go about this....
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  2. #2
    Junior Member
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    We want h < 4
    but h = 12t-5t^2

    so 12t-5t^2 < 4

    subtract 4 from both sides gives

    12t- 5t^2 - 4 <0

    Rearrange as -5t^2 +12t -4 <0

    Now consider the graph of -5t^2 +12t -4 (where t is on the X axis)
    because this is a quadratic equation with a negative coefficient to the squared term we can say it has an "n" shape

    At the axis the graph has a value of zero
    -5t^2 +12t -4 =0
    Factorise
    (-5t +2)(t-2)=0

    so t=2/5 or t = 2

    This tells us the graph cuts the axis at t=2/5 and t=2

    And the graph is negative (-5t^2 +12t -4 <0) below the axis ,which because of the "n" shape is to the left of t=2/5 and to the right of t=2
    so 2/5 > t > 2
    Also t cannot be negative so 0=< t < 2/5 and t>2
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