Real-World Applicationshard
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A hollow torus (donut-shaped tank) with major radius meters and minor radius meter is oriented vertically. Water leaks out of a small hole of area m at the bottom of the torus under the influence of gravity ( m/s). By Torricelli's Law, the rate of change of water volume is , where is the current height of the water level from the bottom hole. When the water level is exactly at the center of the torus ( meter), what is the rate of change of the water height in meters per minute?
A hollow torus (donut-shaped tank) with major radius meters and minor radius meter is oriented vertically. Water leaks out of a small hole of area m at the bottom of the torus under the influence of gravity ( m/s). By Torricelli's Law, the rate of change of water volume is , where is the current height of the water level from the bottom hole. When the water level is exactly at the center of the torus ( meter), what is the rate of change of the water height in meters per minute?