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Math Help - hyperbolic functions #1

  1. #1
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    hyperbolic functions #1

    I need help with these two problems in a hurry. Thanks very much!!
    1. The Gateway Arch in St. Louis was designed by Eero Saarinen and was constructed using the equation: y=211.49 -20.96 cosh .03291765x for the central curve of the arch, where x and y are measured in meters and lxl < or equal to 91.20.
    so the question is how do I graph the central curve.
    2. Verify that the function y=f(x)= T/pg cosh (pgx/T) is the solution of the differential equation d^2y/dx^2 = pg/T squareroot 1 + (dy/dx)^2
    Last edited by mr fantastic; October 5th 2009 at 03:31 AM. Reason: Re-titled post
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  2. #2
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    Quote Originally Posted by jsu03 View Post
    2. Verify that the function y=f(x)= T/pg cosh (pgx/T) is the solution of the differential equation d^2y/dx^2 = pg/T squareroot 1 + (dy/dx)^2
    y = \frac{T}{pg} \cosh \frac{pgx}{T}

    y' = \frac{T}{pg} \cdot \frac{pg}{T} \sinh \frac{pgx}{T} = \sinh \frac{pgx}{T}

    y'' = \frac{pg}{T}\cosh \frac{pgx}{T}

    Now, \frac{pg}{T}\cosh \frac{pgx}{T} = \frac{pg}{T} \sqrt{1+\sinh^2 \frac{pgx}{T} } it follows that y'' = \frac{pg}{T}\sqrt{1+(y')^2}.
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