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Math Help - Quadratic equations

  1. #1
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    Quadratic equations

    Could someone please help me with this problem?






    An object moves back anf forth along a straight line, with distance, s, in inches from its starting point, given by the equation.
    s=10^{2}-50t




    a) How far is it from its starting point after 4 seconds?
    Why do I get -40?



    b) How long will it take before it returns to its starting point?



    Thank you!
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  2. #2
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    Quote Originally Posted by Coach View Post
    An object moves back anf forth along a straight line, with distance, s, in inches from its starting point, given by the equation.
    s=10t^{2}-50t
    I presume I have corrected the equation correctly?

    Quote Originally Posted by Coach View Post
    a) How far is it from its starting point after 4 seconds?
    Why do I get -40?
    The distance is given by s, so
    s(4) = 10\cdot 4^2 - 50 \cdot 4 = 160 - 200 = -40
    so you were right. BUT you are looking for the distance from the starting point, so your answer is 40. (The negative sign means that, if you are plotting this on a number line, the object's position is on the left of the origin.


    Quote Originally Posted by Coach View Post
    b) How long will it take before it returns to its starting point?
    We want a t for s = 0. Thus
    0 = 10t^2 - 50t

    0 = (10t)(t - 5)

    So either
    10t = 0 \implies t = 0
    or
    t - 5 = 0 \implies t = 5

    The t = 0 solution is obviously true, since this is the starting point. So we are looking for the t = 5.

    -Dan
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