Question

An electric cable is hung between two towers that are 200 feet apart. The cable takes the shape of a catenary whose equation is y = 75(eˣ/150 + e⁻ˣ/¹⁵⁰) = 150cosh(x/150). Find the arc length of the cable between the two towers.

Answer 1

To find the arc length of the catenary shape cable between the two towers, we need to integrate the arc length formula over the given interval. The formula for arc length of a curve is sqrt(1 + (f'(x))^2) dx, where f(x) is the equation of the curve.

Step-by-step explanation:

The equation for the catenary shape of the electric cable is given by y = 75(eˣ/150 + e⁻ˣ/¹⁵⁰) = 150cosh(x/150). To find the arc length of the cable between the two towers, we need to integrate the arc length formula over the given interval. The arc length formula for a curve y = f(x) is given by the integral of sqrt(1 + (f'(x))^2) dx. In this case, f(x) = 75(eˣ/150 + e⁻ˣ/¹⁵⁰), so we need to find f'(x) and then evaluate the integral.