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FoolForMath

  • 3 years ago

Another super easy problem, If an ant wants to crawl over the rectangular block of dimensions \( 6\times5\times4 \) from one vertex to a diagonally opposite vertex, what is the shortest distance it would need to travel?

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  1. binary3i
    • 3 years ago
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    \[\sqrt{125}\]

  2. FoolForMath
    • 3 years ago
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    No.

  3. rebeccaskell94
    • 3 years ago
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    Is it a flying ant?

  4. FoolForMath
    • 3 years ago
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    No, no :)

  5. apoorvk
    • 3 years ago
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    4 + sqrt(61)

  6. ninhi5
    • 3 years ago
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    sqr 74

  7. FoolForMath
    • 3 years ago
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    No No, http://www.nooooooooooooooo.com/

  8. Callisto
    • 3 years ago
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    No......

  9. FoolForMath
    • 3 years ago
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    Read the question carefully Parth.

  10. ninhi5
    • 3 years ago
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    sqr 117

  11. FoolForMath
    • 3 years ago
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    Bingo ninhi5! \(\sqrt{117} \) is the right answer.

  12. ninhi5
    • 3 years ago
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    hooray

  13. Arnab09
    • 3 years ago
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    15

  14. apoorvk
    • 3 years ago
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    The ant needs to travel one side, and one diagonal. We have three cases: side '4' + diagonal of (6 and 5) = 4 + sqrt61= 11.something side '6' + diagonal of (4 and 5) = 6 + sqrt41= 12.something side '5' + diagonal of (4 and 6) = 5 + sqrt52 =12.something hence shortest = 4 + sqrt61

  15. apoorvk
    • 3 years ago
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    Now where am I wrong?

  16. SmoothMath
    • 3 years ago
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    |dw:1338100316725:dw|\[\sqrt{x^2 + 5^2} + \sqrt{(6-x)^2 + 4^2}\] By the pythagorean theorem, the sum of those two diagonals is: To minimize this distance, derive and set equal to 0.

  17. ninhi5
    • 3 years ago
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    dont make it over complicated :)

  18. apoorvk
    • 3 years ago
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    Oh damn! I completely forgot that !! :/ Damn my soul

  19. FoolForMath
    • 3 years ago
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    There are only 3 possible roots, consistent to Smooth's diagram.

  20. binary3i
    • 3 years ago
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    |dw:1338145571548:dw|

  21. Ishaan94
    • 3 years ago
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    11.7? lol

  22. Ishaan94
    • 3 years ago
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    Oh No :(

  23. FoolForMath
    • 3 years ago
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    @ninhi5: Can you post the explanation?

  24. SmoothMath
    • 3 years ago
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    I let Alpha do the derivation and optimization for me. http://www.wolframalpha.com/input/?i=solve+%28x%2F%28sqrt%28x%5E2%2B25%29%29+-+%286-x%29%2F%28sqrt%28%286-x%29%5E2%2B16%29%29%29+%3D0%2Cx

  25. binary3i
    • 3 years ago
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    \[\sqrt{117}\]

  26. ninhi5
    • 3 years ago
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    i just use pythogorean theorem

  27. SmoothMath
    • 3 years ago
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    So x = 10/3, giving this distance: http://www.wolframalpha.com/input/?i=sqrt%28%2810%2F3%29%5E2%2B5%5E2%29%2Bsqrt%28%286-%2810%2F3%29%29%5E2%2B4%5E2%29

  28. ninhi5
    • 3 years ago
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    My new question guys

  29. rebeccaskell94
    • 3 years ago
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    can antonia travel around the outside of the box?

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