Electrical wires suspended between two towers form a catenary modeled by the equation where x and y are measured in meters. The towers are 50 meters apart. Find the length of the suspended cable. Round your answer to three decimal places.
A) 94.421m
B) 50.000 m
C) 64.077 m
D) 40.048 m
E) 47.211 m

Question

Electrical wires suspended between two towers form a catenary modeled by the equation  where x and y are measured in meters. The towers are 50 meters apart. Find the length of the suspended cable. Round your answer to three decimal places. 
A) 94.421m 
B) 50.000 m 
C) 64.077 m 
D) 40.048 m 
E) 47.211 m

Quizplus · Accepted Answer

The length of the suspended cable is given by the formula L = ∫ [1 + (dy/dx)^2]^(1/2) dx, where the limits of integration are x = 0 to x = 50 (the distance between the towers).

Differentiating the given equation for the catenary, we get: 
dy/dx = 11cosh^-1(x/11)

Substituting this into the formula for L and simplifying, we get: 
L = 11sinh(50/11) + 11(50/11)

Using a calculator, we find L ≈ 64.077 meters, which is closest to option C.

Electrical Wires Suspended Between Two Towers Form a Catenary Modeled