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Math Help - Determine value of x

  1. #1
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    Determine value of x

    Can anyone please tell me where to go with this problem.
    A chain hangs in a shape called a catenary, the equatio of which is;

    f(x) = a*cosh(x/a)

    Determine value ox when f(x)=48 and a=35.

    Thanks in advance.
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  2. #2
    Super Member Random Variable's Avatar
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     \cosh^{-1} x = \ln (x+ \sqrt{x^{2}-1} ) \ \text{for} \ x \ge 1
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  3. #3
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    I'm still none the wiser, I need to know how to get x on it's own.
    I'm struggling with this one.
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  4. #4
    Super Member Random Variable's Avatar
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     48 = 35 \cosh \Big(\frac{x}{35}\Big)

     \frac{48}{35} = \cosh \Big(\frac{x}{35}\Big)

     \cosh^{-1} \Big(\frac{48}{35}\Big) = \frac{x}{35}

     x = 35 \cosh^{-1} \Big(\frac{48}{35}\Big)
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  5. #5
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    Hi, I have tried that but when I place the value of x back into original formula it doesn't come back to f(x)=48.
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  6. #6
    Super Member Random Variable's Avatar
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    Quote Originally Posted by ady72 View Post
    Hi, I have tried that but when I place the value of x back into original formula it doesn't come back to f(x)=48.
     35 \cosh \Big(35 \frac{\cosh^{-1} \Big(\frac{48}{35}\Big)}{35} \Big)  = 35 \cosh \Big(\cosh^{-1} \frac{48}{35}\Big) = 35 \Big(\frac{48}{35}\Big) = 48
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  7. #7
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    Sorry, I,ve got it now.
    I wasn't putting it to calculator correctly.
    Thanks for your advice!!
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