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Math Help - parabolic

  1. #1
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    parabolic

    A parabolic solar dish for heating water measures 6 feet wide and 1 foot deep.





    1. Where should the water be placed in order to heat it most efficiently ( be specific )





    2. Find the equation of a model in standard form.




    3 Graph a parabolic model and label the vertex, focus and directrix.
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  2. #2
    MHF Contributor ebaines's Avatar
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    Use the standard form for a parabola:

    <br />
4p(y-y_1)=(x-x_1)^2<br />

    where (x_1, y_1) are the x,y coordinates of the vertex of the parabola, and p is the distance from the vertex to the focus of the parabola. The best place to put the wtaer is at the focus. Given the information that you have, you know that the parabola passes through the coordinates (-3,1), (0,0), and (3,1), so you should be able to determine the value for p.
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  3. #3
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    Just a little design consderation...

    You do NOT want to put any part of your container at the focus. It is unlikely that you can find a material that will withstand this kind of treatment and allow heat transfer. The focus probably should be inside your container, at the centroid of the water it contains. This should create the best heating environment.

    My views. I welcome others'.

    Note: If you've a small enough container, you should be able to flash boil the water. That might be a fun experiment. Please be careful. 9\pi ft^{2} of sunlight (less whatever shadow is cast by your container) is no joking matter. It's not as ridiculous as Liminy Snicket's death lens, but it will kill people.
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