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Maximum Height of Fountain in Semicircular Park

Hard Functions And Modeling Modeling With Geometry

A park is designed in the shape of a semicircle with a diameter of 80 meters. The park has a walking path along its edge, and there is a fountain at the center of the semicircle. The height of the fountain is given by the function:

$$ h(x) = 10 - rac{x^2}{160} $$

where $x$ is the horizontal distance from the center of the semicircle to the edge of the park in meters. Calculate the maximum height of the fountain above the ground when measured from the ground level.

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