Rate of Change in Water Height in Tank with Two Inlets
Prompt
Visualize a metal tank being filled with water through two inlets, each of a different size, one being 1 inch in diameter and the other 3 inches. They are both one-dimensional, long, tube-like structures. The inlets are positioned at the top, allowing water to flow into the tank at different velocities, 3 ft/sec and 2 ft/sec respectively. The top of the tank has trapped air creating a buffer. A ruler indicates the height of the water in the tank, marked with the variable 'h'. Alongside the tank, there's a chalkboard explaining the mathematical problem of finding the rate of change of the water height (dh/dt), with the area of the tank (At) being 2 sq. ft.
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