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.

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.

anonymous · Answer

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anonymous · Answer

that is the drawing that it gives me

anonymous · Answer

I am not sure how to start it

inkyvoyd · Answer

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

anonymous · Answer

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

anonymous · Answer

the (x/a)'s are exponents

anonymous · Answer

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

inkyvoyd · Answer

yeah prolly

inkyvoyd · Answer

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