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Math Help - Please - Need help tonight on a couple more calc problems

  1. #1
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    Please - Need help tonight on a couple more calc problems

    thanks
    Last edited by JohnSena; May 23rd 2006 at 10:54 PM.
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    Quote Originally Posted by JohnSena
    1. Write an equation for the graph obtained by shifting the graph of y=x^3 vertically upward by 3 units, followed by vertically sketching the graph by a factor of 5.
    I guess,
    5(x^3+3)=5x^3+15
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    thanks for the quick answer
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    Quote Originally Posted by JohnSena

    4. A standard cup of coffee contains about 100mg of caggeine, and caffeine leaves the body at a rate of about 17% per hour. Give a formula for the amount of caffeine in the body after t hours. How much caffeine is left in the body after 3 hours?
    This is an exponential problem since you remove 17% it is the same as saying 83% of the total amount thus,
    A(t)=100(.83)^t

    For the second part you need to find,
    100(.83)^3\approx 57.18
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  5. #5
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    Quote Originally Posted by JohnSena

    2. A ball is thrown into the air at time t=0, and its height above ground (in feet) t seconds after it is thrown is given by f(t)=-16t^2+96t+6
    a) How long is it in the air?
    b) How high does it go?
    c) When does it reach its maximum height?
    a) the ball hits the ground when:

    <br />
f(t)=-16t^2+96t+6=0<br />

    This will have two roots, one positive and the other negative, the
    negative root is unphysical but the positive one is what you want.

    The roots are:

    <br />
-0.06186, 6.06186<br />

    So the ball is in the air \approx 6.06seconds.

    b) The maximum height is achieved when f(x) is
    a maximum. As this is a quadratic we know this occurs midway
    between the roots, so it occurs at (-0.06186+6.06186)/2=3,
    so the maximum height is:

    <br />
f(3)=16\ 3^2+96\ 3+6=438 feet.

    c) Already answered at t=3seconds.

    RonL
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