## Answers

falling at a rate of 2ft /min

#### Explanation:

If you consider the generalised position when the depth of the water in the trough is at x where #x = x(t). Due to the similar triangles, the "width" of the water channel will also be x, as indicated in the drawing

We can say that the volume in the tank at that time,

so

taking the derivative wrt time

so

we know that

so so

so it's falling at a rate of 2ft /min at that moment

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