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Math question

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  • #1
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I have a major exam coming up and we've been given few past exam papers to go through to practice.

I have absolutely no idea what to do here :frown:, if people could help me out, work it out etc. It would be greatly appriciated.

Link 1: http://img72.echo.cx/img72/3763/question0ex.jpg

Link 2: http://www.storage4all.com/uploads/5983d1c9d4.jpg [Broken]

Thanks



Edit: Added a 2nd link, Link 1 seems to be slow at the moment
 
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Answers and Replies

  • #2
Zurtex
Science Advisor
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The Link doesn't work.
 
  • #3
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Edit: Added a 2nd link
 
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  • #4
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i might help you somewhat although i haven't got the complete solution:

you know that the volume of a cylinder is given by: V= Ah (where A is the area of the base).

so when deriving with respect to time ull have:
dV/dt = A*dh/dt

and given (from Toricelli's law) that dV/dt = -a*squared root(2gh)

you can set the two equalities and obtain:

dh/dt = (-a/A)*squared root(2g)*squared root(h)

therefore the alpha constant should be equal to the rate of the samller area (the circular hole) to the bigger area (the one of the cylinder base) times the squared root of 2g's.
that's for the first part.

for the second part you will have to integrate the squared root of h knowing that -alpha is a constant.
I'm not sure about it, maybe an expert will help you.

As for the third it's a numeral application for the second part.

I hope this helped.
 
  • #5
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Thank you very much.

I have worked it all out :)

3 questions left that I don't understand will post them later :p
 

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