SOLUTION: I am not sure if I am asking the right person (or section), but I posted my question on an image hosting site: http://i39.tinypic.com/2n7154w.jpg . It has something to do with "ca

Algebra ->  Finite-and-infinite-sets -> SOLUTION: I am not sure if I am asking the right person (or section), but I posted my question on an image hosting site: http://i39.tinypic.com/2n7154w.jpg . It has something to do with "ca      Log On


   

Question 303205: I am not sure if I am asking the right person (or section), but I posted my question on an image hosting site: http://i39.tinypic.com/2n7154w.jpg . It has something to do with "catenary" stuff. Can you help, please?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Wow, you're in the wrong location.
You need to find the arc length.
f%28x%29=a%2Acosh%28x%2Fa%29%2BC
You need to find the derivative of f(x).
df%2Fdx=a%2Asinh%28x%2Fa%29%2A%281%2Fa%29=sinh%28x%2Fa%29
The formula for arc length is



int%28sqrt%281%2B%28df%2Fdx%29%5E2%29%2C+dx+%2C+0+%2C+a+%29=a%2Asinh%28x%2Fa%29%2BC
int%28sqrt%281%2B%28df%2Fdx%29%5E2%29%2C+dx+%2C+0+%2C+a+%29=a%2Asinh%28x%2Fa%29%2BC

int%28sqrt%281%2B%28df%2Fdx%29%5E2%29%2C+dx+%2C+0+%2C+a+%29=a%2Asinh%281%29-a%2Asinh%280%29

.
.
.
sinh%28x%29=%281%2F2%29%28e%5Ex-e%5E%28-x%29%29
sinh%281%29=%281%2F2%29%28e-1%2Fe%29
sinh%280%29=%281%2F2%29%281-1%29=0
sinh%281%29-sinh%280%29=%281%2F2%29%28e-1%2Fe%29
.
.
.


int%28sqrt%281%2B%28df%2Fdx%29%5E2%29%2C+dx+%2C+0+%2C+a+%29=%28a%2F2%29%28e-1%2Fe%29
.
.
.
Now you have the arc length based on "a".
Use the values given in the problem to find "a" and "C" and you'll have the arc length.