A rectangular reservoir has a horizontal base of area 1000 m^2. At time t = 0, it is empty and water begins to flow into it at a constant rate of 30 m^3 /s. At the same time, water begins to flow out at a rate proportional to sqrt of h, where h m is the depth of the water at time t s. When h = 1, dh/dt=0.02.

show that h satisfies the differential equation ....

Question

A rectangular reservoir has a horizontal base of area 1000 m^2. At time t = 0, it is empty and water begins to flow into it at a constant rate of 30 m^3 /s. At the same time, water begins to flow out at a rate proportional to sqrt of h, where h m is the depth of the water at time t s. When h = 1, dh/dt=0.02.

show that h satisfies the differential equation ....

anonymous · Answer

this differential equation 
$$\frac{ dh }{ dt } = 0.01 (3-\sqrt{h} )$$

kainui · Answer

So any ideas? Best place to start is to draw out a picture and label everything with units.

anonymous · Answer

Well ,  I was trying to find out a starting point but I failed tbh lol . I mean why did they give me the area and the constant rate ? 
I dont think there should be a diagram because when a picture is needed they usually attach it with the question, but in this question theres no pic .

kainui · Answer

Well I don't see why you shouldn't create something that may be useful to you to solve the problem just because "that's how they usually do it". It might help you out to see what's going on! I mean, unless you have a better idea. You have to move forward somehow right? So give it a try =P

anonymous · Answer

lol thanks for the whole paragraph above to convince me drawing it. lol anyways gimme some seconds then @Kainui

anonymous · Answer

okai idrew the thing but didn't help me in  any way :|

anonymous · Answer

is it 
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