Question: This is on the application of differential equations , specifically targeting: Catenary (Second Order DE Application). A cable hangs between two poles that are 80-ft

This is on the application of differential equations, specifically targeting: Catenary (Second Order DE Application).

A cable hangs between two poles that are 80-ft apart. The two poles are both 40 foot high. Sag is observed in the middle of the cable 5 ft from the ground. Find the length of the cable.

a.) What is the working equation for a catenary forming cable? b.) What is the computed constant a up to 4 decimal places? c.) What is the catenary equation for the given problem? d.) What is the general equation for length of the cable S? e.) What are the boundary conditions for finding the total length of the cable S? f.) What is the length of the cable S? g.) If the cable is weighing 2 lbs per foot, find the horizontal tension of the cable.

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