How deep is searchlight shaped like paraboloid of revolution, Mathematics

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How deep is searchlight shaped like paraboloid of revolution

1. The searchlight is shaped like the paraboloid of revolution. If light source is situated 5 feet from base along axis of symmetry and opening is 8 feet across, how deep should searchlight be?

2. The child on the swing sweeps out the distance of 20 ft on first pass. If she is permitted to continue swinging until she stops, and if on each pass she sweeps out the distance 3/4 of previous pass, how far does child travel?

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Mathematics: How deep is searchlight shaped like paraboloid of revolution

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