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anonymous

  • 5 years ago

An archer shoots an arrow into the air such tht its height at any time, t, is given by the function h(t) = -16t² + kt + 3. If the maximum height of the arrow occurs at time t = 4, what is the value of k?

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  1. anonymous
    • 5 years ago
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    h'(t) = 0 gives you maximum height, so assuming k is a constant, h'(t)=-32t+k 0=-32t+k if t=4 then k= 32*4 k=128 Double check, h(t)=-16t^2+ 128t+ 3 h'(t)=-32t+128 h'(t)=0=-32t+128 128/32 = t 4=t. There you go.

  2. anonymous
    • 5 years ago
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    you can also just find the x coordinate of the vertex which is -k/(-2*16) =4 k/32=4 4X32 Since it is a parabola the maximum height will occur at the vertex

  3. anonymous
    • 5 years ago
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    thanks you

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