The sides of a nuclear power plant cooling tower form a hyperbola. The diameter of the bottom of the tow is 286 feet. The smallest diameter of the tower is 168 which is 435 feet above the ground. The tower is 590 feet tall. 168 ft 590 ft 435 ft 286 ft Photo remixed from work by Jiří Sedláček r, cC-BY-SA Find the width of the tower at a height of 128 feet, to 1 decimal place.

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Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.