Cables are used to suspend bridge decks and other structures. If a heavy uniform cable hangs suspended from its two endpoints, it takes the shape of a catenary curve whose equation is
where a is the height of the lowest point on the chain above some horizontal reference line, x is the horizontal coordinate measured to the right from
the lowest point, and y is the vertical coordinate measured up from the reference line.
Let a = 10 m. Plot the catenary curve for -20 ≤ x ≤ 30 m. How high is each endpoint?
