Question

When power cables are suspended between two towers they form a curve called the catenary
shown below. The equation of the curve is given by: y=acosh(x/a) where the distance between the two towers is 2b. Find the slope of the catenary where the cable meets the right hand tower.

Answer 1

that is the drawing that it gives me

Answer 2

I am not sure how to start it

Answer 3

d/dx sinh(x)=cosh(x)
d/dx cosh(x)=-sinh(x)
to derive these formulas use the equivalent cosh(x)=(e^x+e^-x)/2 and sinh(x)=(e^x-e^-x)/2

Answer 4

\[y=a(\frac{ e^(x/a)+e^(-x/a) }{ 2 })\]

Answer 5

the (x/a)'s are exponents

Answer 6

does x=b? since I am trying to find the slope of the right side

Answer 7

yeah prolly

Answer 8

but there's no need to use the expanded form.
just do d/dx cosh(x)=-sinh(x)