# Determine value of x

• Aug 9th 2009, 10:50 AM
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.

• Aug 9th 2009, 10:55 AM
Random Variable
$\displaystyle \cosh^{-1} x = \ln (x+ \sqrt{x^{2}-1} ) \ \text{for} \ x \ge 1$
• Aug 9th 2009, 11:09 AM
I'm still none the wiser, I need to know how to get x on it's own.
I'm struggling with this one.
• Aug 9th 2009, 11:14 AM
Random Variable
$\displaystyle 48 = 35 \cosh \Big(\frac{x}{35}\Big)$

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

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

$\displaystyle x = 35 \cosh^{-1} \Big(\frac{48}{35}\Big)$
• Aug 9th 2009, 11:17 AM
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.
• Aug 9th 2009, 11:26 AM
Random Variable
Quote:

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