$\"\"$

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Electrical wires suspende between two towers form a caternary modeled by the equation

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$\"\"$ , $\"\"$ .

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Where $\"\"$ and $\"\"$ are measured in meters.

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The curve is $\"\"$ .

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Find the length of the suspended cable.

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Definition of the arc length:

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If the curve $\"\"$ , $\"\"$ , then the length of the curve is defined as,

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$\"\"$ .

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Find $\"\"$ .

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Consider $\"\"$ .

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$ .

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$\"\"$

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Length of the suspended cable is arc length of the graph in the indicated interval.

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Substitute $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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Arc length of the graph in the indicated interval is $\"\"$ units.

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Length of the suspended cable is $\"\"$ .

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$\"\"$

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Length of the suspended cable is $\"\"$ .