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    can someone help me with this question please?

    because the water is entering and leaving the cylinder simultaneously, I figured that dv/dt = 1600 - \sqrt{h}

    ????

    \sqrt{h} because its leaving at a rate proportional to the square root of the height?

    should I look for dv/dt in terms of dv/dt = (dh/dV)(dV/dt) ??
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    dh/dt= dh/dv times dv/dt. Find expressions for both and use the fact that V=4000h
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    (Original post by Maths&physics)
    can someone help me with this question please?

    because the water is entering and leaving the cylinder simultaneously, I figured that dv/dt = 1600 - \sqrt{h}

    ????

    \sqrt{h} because its leaving at a rate proportional to the square root of the height?
    Not quite.

    The total volume of the cylinder is V=\pi r^2 h. Using the fact that the cross section is 4000 \mathrm{cm^{2}}, you can find the radius of the cylinder r=R.

    Differentiating V=\pi R^2h w.r.t time yields \dfrac{dV}{dt} = \pi R^2 \dfrac{dh}{dt}.

    We know that \dfrac{dV}{dt} = 1600 - k\sqrt{h} so we can use this with the first eq. and obtain the answer.
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    (Original post by RDKGames)
    Not quite.

    The total volume of the cylinder is V=\pi r^2 h. Using the fact that the cross section is 4000 \mathrm{cm^{2}}, you can find the radius of the cylinder r=R.

    Differentiating V=\pi R^2h w.r.t time yields \dfrac{dV}{dt} = \pi R^2 \dfrac{dh}{dt}.

    We know that \dfrac{dV}{dt} = 1600 - k\sqrt{h} so we can use this with the first eq. and obtain the answer.
    isn't the volume of a cylinder: V=(1/3)\pi r^2 h

    dV/dh = A

    4000 = A
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    (Original post by Maths&physics)
    isn't the volume of a cylinder: V=(1/3)\pi r^2 h
    That formula is for the volume of a cone.
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    (Original post by RDKGames)
    That formula is for the volume of a cone.
    thank you!

    im not with it today
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    (Original post by RDKGames)
    That formula is for the volume of a cone.
    I would do
    dV/dh = \pi r^2

     A = \pi r^2

    ?
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    (Original post by Maths&physics)
    I would do
    dV/dh = \pi r^2

     A = \pi r^2

    ?
    Not sure why...

    I outlined the approach in my first reply. Follow it.
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    (Original post by RDKGames)
    Not sure why...

    I outlined the approach in my first reply. Follow it.
    thanks but I dont understand why youre differentiating volume with respect to time?
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    (Original post by Maths&physics)
    thanks but I dont understand why youre differentiating volume with respect to time?
    Because the information tells how much flows in and how much flows out every second therefore it is logical to try to obtain \dfrac{dV}{dt}.
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    For these types of questions, I like to start by writing out what it is you want to find.

    In this case, you are solving for dh/dt
    You also need to identify that dv/dt = 1600 - C\sqrt h

,
    where C is some constant of proportionality.
    Now we see that we have 3 different variables, h, t, and
    v, so it would be make sense to apply the chain rule in order to solve for dh/dt.
    So, dh/dt = dh/dv\times dv/dt
    Since v=\pi r^2 h, we can obtain dv/dh = \pi r^2 and so dh/dv is simply its reciprocal. We also know this to be dh/dv = 1/4000
    Now we just have to substitute our differentials into our chain rule equation, and acquire an expression for dh/dt
    Once you multiply this through, you'll find that your answer looks very similar to what the question is asking for. But remember that C is just some constant, and so we can define a new constant k in terms of the coefficients of \sqrt h

    Hope this helps!
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    (Original post by RDKGames)
    Because the information tells how much flows in and how much flows out every second therefore it is logical to try to obtain \dfrac{dV}{dt}.
    does \dfrac{dV}{dt} give us area? I thought \dfrac{dV}{dh} gave us area?
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    (Original post by Maths&physics)
    does \dfrac{dV}{dt} give us area? I thought \dfrac{dV}{dh} gave us area?
    TBH just use the solution that was posted above, I feel like my approach is only confusing you...
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    (Original post by RDKGames)
    TBH just use the solution that was posted above, I feel like my approach is only confusing you...
    yeah, im pretty confused
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    (Original post by RDKGames)
    Not sure why...

    I outlined the approach in my first reply. Follow it.
    That's not very helpful - you need to explain why.
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    (Original post by DisneylandChina)
    For these types of questions, I like to start by writing out what it is you want to find.

    In this case, you are solving for dh/dt
    You also need to identify that dv/dt = 1600 - C\sqrt h

,
    where C is some constant of proportionality.
    Now we see that we have 3 different variables, h, t, and
    v, so it would be make sense to apply the chain rule in order to solve for dh/dt.
    So, dh/dt = dh/dv\times dv/dt
    Since v=\pi r^2 h, we can obtain dv/dh = \pi r^2 and so dh/dv is simply its reciprocal. We also know this to be dh/dv = 1/4000
    Now we just have to substitute our differentials into our chain rule equation, and acquire an expression for dh/dt
    Once you multiply this through, you'll find that your answer looks very similar to what the question is asking for. But remember that C is just some constant, and so we can define a new constant k in terms of the coefficients of \sqrt h

    Hope this helps!
    dh/dv = 1/\pi r^2, dh/dv = 1/4000

    I get that.

    and you do: 1/\pi r^2 = 1/4000

    where do you go from here?
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    (Original post by Maths&physics)
    yeah, im pretty confused
    DO you want someone else to try and help you?
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    (Original post by Muttley79)
    That's not very helpful - you need to explain why.
    Half the stuff he writes doesn't make sense, or is hard to follow where it comes from, or is unclear as to what he's trying to do with it so I give up after a while. I don't really need to explain anything.
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    (Original post by Muttley79)
    DO you want someone else to try and help you?
    all help is welcome.

    I thought: dV/dh = A or dV/dr = A

    but I'm unfamiliar with his approach although its probably the best. however, I still get stuck in the next part.


    4000 = A

    so, 4000 =\pi r^2

    or in the case of RDK: 4000 = \pi r^2 (dh/dt)
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    (Original post by Maths&physics)
    all help is welcome.

    I thought: dv/dh = A or dv/dr = A

    but I'm unfamiliar with his approach although its probably the best. however, I still get stuck in the next part.


    4000 = A

    so, 4000 =\pi r^2

    or in the case of RDK: 4000 = \pi r^2 (dh/dt)
    \dfrac{dV}{dh} = 4000 since V=\pi R^2 h hence \dfrac{dV}{dh} = \pi R^2 = A, so that's fine.

    But I don't understand where you pull the last line from. The RHS of it is basically \dfrac{dV}{dt} = \pi R^2 \dfrac{dh}{dt} = \dfrac{dV}{dh} \dfrac{dh}{dt}. So the LHS needs to reflect that it is change in volume over time, and dV/dt is most certainly not 4000 as you have it.
 
 
 
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