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)94.421 m
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)94.421 m 
B)50.000 m 
C)64.077 m 
D)40.048 m 
E)47.211 m

Quizplus · Accepted Answer

We know that the formula for a catenary is given by:
y = a cosh((x-b)/a), where a is the scaling factor and b is the offset parameter.
Comparing this to the given equation, we can see that a = 5 and b = 25. 
Now, we need to find the length of the cable between the two towers. This can be done using the formula:
L = a sinh(d/a)
where d is the distance between the two towers. Substituting the values, we get:
L = 5 sinh(50/5)
L = 64.077
Therefore, the length of the suspended cable is 64.077 meters, which is closest to option C (64.077 m).

Electrical Wires Suspended Between Two Towers Form a Catenary Modeled