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Rates of change question Watch

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Size:  308.7 KBQuestion is confusing as I don't know what formula I should use for a cylindrical tank and it says find rate of fluid in proportion to square root of V, though I am meant to show it satisfies an equation with the square root of h?
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    (Original post by TSRforum)
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Size:  308.7 KBQuestion is confusing as I don't know what formula I should use for a cylindrical tank and it says find rate of fluid in proportion to square root of V, though I am meant to show it satisfies an equation with the square root of h?
    dV/dt = dV/dh dh/dt
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    (Original post by TeeEm)
    dV/dt = dV/dh dh/dt
    Do I use V= 1/3(pi)(r)^2(h)?
    If so then dV/dt = 2/3(pi)(r)(h) x dh/dt
    Then what?
    Edit: h= 3v/(pi)(r^2) do I sub that into -k(h)^1/2 and put it into the equation?
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    (Original post by TSRforum)
    Do I use V= 1/3(pi)(r)^2(h)?
    If so then dV/dt = 2/3(pi)(r)(h) x dh/dt
    Then what?
    you do but note r is constant, h is varying
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    (Original post by TeeEm)
    you do but note r is constant, h is varying
    How does knowing that help me?
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    (Original post by TSRforum)
    How does knowing that help me?
    I do not understand what is the problem.
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    (Original post by TeeEm)
    I do not understand what is the problem.
    I'm still confused, how exactly am I satisfying dh/dt by using dv/dt?
    Do I need to re-arrange v into h=3V/(pi)(r)^2 and sub that into -k(V)^1/2 which I then put into dv/dt?
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    (Original post by TSRforum)
    I'm still confused, how exactly am I satisfying dh/dt by using dv/dt?
    Do I need to re-arrange v into h=3V/(pi)(r)^2 and sub that into -k(V)^1/2 which I then put into dv/dt?
    Are you happy with post 2?
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    (Original post by TeeEm)
    Are you happy with post 2?
    no, I'm still confused. I'd rather you tell me the answer as I don't have it in the book I am using
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    (Original post by TSRforum)
    no, I'm still confused. I'd rather you tell me the answer as I don't have it in the book I am using
    I would of course tell you the answer but some people here do not like this.
    I will look into my resources to find the most similar worked example to yours if you give me 5 minutes
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    (Original post by TSRforum)
    no, I'm still confused. I'd rather you tell me the answer as I don't have it in the book I am using
    (Original post by TeeEm)
    I would of course tell you the answer but some people here do not like this.
    I will look into my resources to find the most similar worked example to yours if you give me 5 minutes
    this is the closest match I can find
    Hopefully this will help you with yours
    All the best
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  1. File Type: pdf ODE EXAMPLE.pdf (165.0 KB, 45 views)
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    (Original post by TeeEm)
    this is the closest match I can find
    Hopefully this will help you with yours
    All the best
    Thanks! I'm assuming you can only do v = Ah instead of 1/3(pi)(r)^2h in "show that" type questions or can you use it in other rate of change questions?
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    (Original post by TSRforum)
    Thanks! I'm assuming you can only do v = Ah instead of 1/3(pi)(r)^2h in "show that" type questions or can you use it in other rate of change questions?
    in your question you have V = 1/3(pi)r2h
    but your dV/dh = 1/3(pi)r2 = constant which you can absorb into k
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    (Original post by TeeEm)
    in your question you have V = 1/3(pi)r2h
    but your dV/dh = 1/3(pi)r2 = constant which you can absorb into k
    Oh ok, also what about this question?Name:  image.jpg
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Size:  312.6 KB There's way too little info for me to reach an answer. Is my working out wrong?
 
 
 
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