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# Find a differential equation for water escaping from a cuboid tank watch

1. Greetings,

I'm really stuck on the following question and I feel like I'm simply not understanding something basic about the topic, but I can't figure out what that might be. Any help would be greatly appreciated.

The way I've tried to solve it was by writing:

V=102h - kh^0.5 +2t

Then finding that dh/dV = 1/100 - (2h^0.5)/k
And dV/dt = 2

I've also tried starting with dV/dt = 2 - kh^0.5

After that I just plug this into dh/dt = dh/dV * dV/dt

Either way I get a wrong answer.

Of course this method works perfectly if you assume that V=100h and therefore dh/dV = 1/100
But surely that can't be right, as dV/dt clearly suggests that there's more terms involved in the value of V. Not just 100h.

The correct answer is supposed to be (2-kh^0.5)/100.

How do I even begin with a problem like this?

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Updated: February 22, 2018
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