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Math Help - need help with optimization problems!

  1. #1
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    need help with optimization problems!

    hi! I'm new in here, and I was wondering if I could get some help in a couple of math problems I have difficulties with:

    1. A funnel of specific volume has the shape of a right circular cone. Determine the reason from the height to the radius of the base so that the minimal quantity of material is used in it's construction.

    2. The transversal section of a drinking trough has the shape of a reversed isósceles triangle. If the length of a side is 15 inches, determine the size of the angle shaped by two sides that provides the drinking trough it’s maximum capacity. (here's the draw that came with the problem: http://i610.photobucket.com/albums/t...l777/draww.jpg)

    Thank you!!!
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  2. #2
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    1. You are given clues to help you evaluate the differential. The tell you that you have a specefic volume, which means you're volume will be fixed. So we can then say that:

    V=\frac{1}{3}\pi*r^2h;
    Area=\pi*r\sqrt{r^2+h^2}

    You can solve for H in the equation for volume, and then plug it into the area of a right cone. From there you simply differentiate to obtain the optimum radius that will help you minimize the construction of the cone.

    #2 is solved in the same way: determining what the question is asking, gathering necessary equations, and seeing what variables we can eliminate through substitution.
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  3. #3
    MHF Contributor Calculus26's Avatar
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    I'll help you with 1 -- I believe you want the ratio of the height to radius

    See attachment if you run into difficulty
    Attached Thumbnails Attached Thumbnails need help with optimization problems!-funnel.jpg  
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