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    5) figure 2 shows a sketch of curve c with parametric equation

    X=√3 sin2t
    Y=4cos^(2)t
    O=<t=<π

    A) show that dy/dx = k√3 tan2t, where k is a constant to be determined

    B) find an equation of the tangent to C at the point where t=π/3
    Give your answer in the form y= ax+b

    C) find a Cartesian equation of c



    8) a) express 1/P(5-P) in partial fractions

    A team of conservationists is studying the population of meerkats on a nature reserve. The population is modelled by the differential equation

    Dp/dt = 1/15 P(5-P), t>=0
    Where P, in thousands, is the population of meerkats and t is the time measured in years since the study began.

    Given that when t=0, P=1

    B) solve the differential equation, giving your answers in the form,
    P= a/b+ce^(-t/3)

    Where a, b and c are integers

    C) hence show that the population cannot exceed 5000


    Tried multiple times to do them and cant, answers with working would be great! Thanks
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    we cannot do that. please post your workings so far and we can take it from there.
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    (Original post by JamesDS97)
    5) figure 2 shows a sketch of curve c with parametric equation

    X=√3 sin2t
    Y=4cos^(2)t
    O=<t=<π

    A) show that dy/dx = k√3 tan2t, where k is a constant to be determined

    B) find an equation of the tangent to C at the point where t=π/3
    Give your answer in the form y= ax+b

    C) find a Cartesian equation of c



    8) a) express 1/P(5-P) in partial fractions

    A team of conservationists is studying the population of meerkats on a nature reserve. The population is modelled by the differential equation

    Dp/dt = 1/15 P(5-P), t>=0
    Where P, in thousands, is the population of meerkats and t is the time measured in years since the study began.

    Given that when t=0, P=1

    B) solve the differential equation, giving your answers in the form,
    P= a/b+ce^(-t/3)

    Where a, b and c are integers

    C) hence show that the population cannot exceed 5000


    Tried multiple times to do them and cant, answers with working would be great! Thanks
    I would love to do your homework but at the moment I am doing mine ...
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    (Original post by the bear)
    we cannot do that. please post your workings so far and we can take it from there.
    What can't you do?


    (Original post by TeeEm)
    I would love to do your homework but at the moment I am doing mine ...
    Thanks for that
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    the rules fam.

    if we do like you want we is carded innit
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    (Original post by the bear)
    the rules fam.

    if we do like you want we is carded innit
    Do you know how to do them?
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    If you really just wanted the answer surely you should just google the question.
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    (Original post by JamesDS97)
    Do you know how to do them?
    Enough. We know how to do them but you need to post some working before we can tell you where you have gone wrong or become stuck.
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    (Original post by JamesDS97)
    Do you know how to do them?
    fo shizzle
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    (Original post by Mr M)
    Enough. We know how to do them but you need to post some working before we can tell you where you have gone wrong or become stuck.
    For 5 literally have no idea for part a
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    (Original post by Mr M)
    Enough. We know how to do them but you need to post some working before we can tell you where you have gone wrong or become stuck.
    X=√3sin2t
    DX/DT = 2√3cos2t

    Y=4cos^2t
    Dy/DT = -8sintcost

    Dy/dt / DX/DT
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    (Original post by JamesDS97)
    X=√3sin2t
    DX/DT = 2√3cos2t

    Y=4cos^2t
    Dy/DT = -8sintcost

    Dy/dt / DX/DT
    All correct.

    Note that \sin 2t = 2 \sin t \cos t
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    (Original post by Mr M)
    All correct.

    Note that \sin 2t = 2 \sin t \cos t
    So the differentiation is wrong and I need to use the product rule on 2sintcost?
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    (Original post by JamesDS97)
    So the differentiation is wrong and I need to use the product rule on 2sintcost?
    I've already said it is correct.

    I was trying to help you improve your expression for dy/dt to enable you to finish that part.
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    Y=4cos^2t
    Dy/Dt = -8sintcost

    Are you sure that is correct Mr M?
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    (Original post by Muttley79)
    Y=4cos^2t
    Dy/Dt = -8sintcost

    Are you sure that is correct Mr M?
    Yes.
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    (Original post by JamesDS97)
    So the differentiation is wrong and I need to use the product rule on 2sintcost?
    Doesnt it differentiate like this so no sin2t at this point?

    X= √3sin2t

    DX/DT = 2√3cos2t
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    When you differentiate y = 4cos 2t wrt t isn't dy/dt = -8sin 2t which is not -8sintcost
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    (Original post by Muttley79)
    When you differentiate y = 4cos 2t wrt t isn't dy/dt = -8sin 2t which is not -8sintcost
    Its cos(squared)t
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    (Original post by Muttley79)
    When you differentiate y = 4cos 2t wrt t isn't dy/dt = -8sin 2t which is not -8sintcost
    It isn't always easy but making sure you have interpreted the question correctly is a must in this Forum.
 
 
 
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