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Math Help - Maths Problems

  1. #1
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    Maths Problems

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    Last edited by mathsB; August 19th 2007 at 10:51 PM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by mathsB View Post
    Hi, I'm relatively new to this forum but i hope you will be able to help me with my maths problems.

    Problem1.) An ant is at one corner of a cube side length one unit. the ant needs to get from his corner to the corner on the opposite side of the cube (at the top of the cube not the bottom) he must stay on the outside of the cube (on the side or edges) as he cannot fly and the inside of the cube is an open space. What is the least distance he needs to travel to get to the other corner??

    N.B. a student came up with a solution of 2.26 using Pythagoras' theorem by folding the side of the cube up and working it out in 2D . Your task is to prove this answer is correct using optimization of calculus.

    (Any sort of formula would b a great help)
    See attachment.

    Now the square of the path length is:

    <br />
l^2=(1+x^2) +((1-x)^2+1)<br />

    Now the minimum path length corresponds to a minimum of the square path length, so we differentiate l^2 with respect to x and set this to zero.

    <br />
\frac{d}{dx}l^2=2x-2(1-x)=4x-2 =0<br />

    so the required x=1/2 and the length is:

    <br />
l=\sqrt{5}<br />

    RonL
    Attached Thumbnails Attached Thumbnails Maths Problems-gash.jpg  
    Last edited by CaptainBlack; August 14th 2007 at 04:02 AM.
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    Last edited by mathsB; August 19th 2007 at 10:51 PM.
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    Post deleted by user.
    Last edited by mathsB; August 19th 2007 at 10:52 PM.
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by mathsB View Post
    Just one more question. How do u get the equation for L^2?? I know you have to work it in with side X but how do you get the different numbers in there?? And also what geometrical formula do you substitute in?? Any help appreciated
    Pythagoras' theorem applied to the two straight line segments on the two faces.

    RonL
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  6. #6
    Grand Panjandrum
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    Quote Originally Posted by mathsB View Post
    Post deleted by user.
    Don't delete your questions, others may benefit from the question and answer. Besides, as your question has been quoted you cannot delete
    errase what you have asked.

    RonL
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