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I was trying to solve this calculus exercise:

The Saint Louis arch can be approximated by using a function of the form $y=b-a\mathrm{cosh}(x/a)$. Putting the origin on the ground and in the center of the arch and the $y$-axis upward, find an approximate equation for the arch given these dimensions: height 615 and width 530. (in other words find $a$ and $b$).

Now from these data I got two equations:

$b-a=615$

$b-a\mathrm{cosh}(265/a)=0$

but I have no idea how to solve this system. Could you help me?

(that's not homework)

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    ah yeah you're right2012-10-02

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Solve for $b$, getting $b = 615 + a$. Substitute into the non-linear equation: $ 615 + a = a \cdot \cosh \frac{265}{a} $ The equation is non-linear and is unlikely to admit a closed-form solution, but can be solved graphically (see for example Wolfram|Alpha), or using Newton's method, getting $a = 191.192$.