$\"\"$

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The cable for a suspension bridge has the shape of a parabola with equation $\"\"$ .

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Draw the related diagram for the situation:

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$\"\"$

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Find the length of the 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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$\"\"$

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

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$\"\"$

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$\"\"$ .

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The highest point on the cable is $\"\"$ .

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

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$\"\"$

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$\"\"$ .

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

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$\"\"$ .

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$\"\"$

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

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$\"\"$

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$\"\"$

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Apply formula: $\"\"$ .

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$\"\"$

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The length of the cable is $\"\"$ .

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$\"\"$ .

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$\"\"$

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$\"\"$ .