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Math Help - Find k

  1. #1
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    Find k

    An archer shoots an arrow into the air such that its height at any time, t, is given by the function h(t) = -16t^2 + kt + 3. If the maximum height of the arrow occurs at time t = 4, what is the value of k?

    (1) 128 (3) 8
    (2) 64 (4) 4
    Last edited by symmetry; January 18th 2007 at 06:33 PM. Reason: Forgot to square
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by symmetry View Post
    An archer shoots an arrow into the air such that its height at any time, t, is given by the function h(t) = -16t^2 + kt + 3. If the maximum height of the arrow occurs at time t = 4, what is the value of k?

    (1) 128 (3) 8
    (2) 64 (4) 4
    Max height is when the derivative of the height function goes to 0. So:
    h'(t) = -32t + k = 0

    Thus k = 32t = 32 \cdot 4 = 128

    -Dan
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  3. #3
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    ok

    Derivative is a calculus word.

    I am not asking calculus questions at this point in the study book.

    Thanks anyway!
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  4. #4
    Forum Admin topsquark's Avatar
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    All right. In that case we need to look at the height function a bit more carefully. It is an inverted parabola. The maximum height will be at the vertex of the parabola, which is on the axis of symmetry.

    Given a parabola y = ax^2 + bx + c the axis of symmetry will be the line x = -\frac{b}{2a}.

    We have the parabola h = -16t^2 + kt + 3. We know that the location of the max height is the line t = 4, which is our axis of symmetry. So:
    t = - \frac{k}{2 \cdot -16} = 4

    So
    k = 128.

    -Dan
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  5. #5
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    ok

    Dan,

    Thanks for breaking the question some other way.

    I am not ready for calculus questions at this point in the course of my review for the June state test.

    Thanks!
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  6. #6
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    Quote Originally Posted by symmetry View Post
    Dan,

    Thanks for breaking the question some other way.

    I am not ready for calculus questions at this point in the course of my review for the June state test.

    Thanks!
    I think we would all be interested to know what test you are preparing for.
    Its always nice to have some context when subjected to an avalache of
    questions

    RonL
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