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C4 Differential equations question

Hello, pls can you help me with this question (question no 9 on here):
http://www.mei.org.uk/files/papers/2012_Jan_c4.pdf

I need you to pls check if my working is right. I am not very good at following mark schemes (If you scroll down a bit , you can find the mark scheme):

So for part i)

I did:
dv/ dx = 20x * pi - x^2 * pi
Then dx / dt = dx/dv * dv / dt

So dx/dt = 1/ (20x * pi - x^2 * pi ) * k (20-x)

then dx/dt = 1/ (pi*x) * k

therefore (x * pi) dx.dt = k

Is my working right?
Reply 1
Avatar for laurawoods
laurawoods
OP
8
Original post by laurawoods
Hello, pls can you help me with this question (question no 9 on here):
http://www.mei.org.uk/files/papers/2012_Jan_c4.pdf

I need you to pls check if my working is right. I am not very good at following mark schemes (If you scroll down a bit , you can find the mark scheme):

So for part i)

I did:
dv/ dx = 20x * pi - x^2 * pi
Then dx / dt = dx/dv * dv / dt

So dx/dt = 1/ (20x * pi - x^2 * pi ) * k (20-x)

then dx/dt = 1/ (pi*x) * k

therefore (x * pi) dx.dt = k

Is my working right?


Then for part iii) I did,
dx/dt = dx/dv * dv/dt
dx/dt = {1/ (20xpi - x^2*pi)} * - kx
dx/dt = -kx / (20xpi -x^2 pi )
x cancels out
so 20 pi - x pi dx /dt = -k

The mark scheme for those both are obvoiusly looking a bit diff
Reply 2
Avatar for TenOfThem
TenOfThem
18
Original post by laurawoods
Then for part iii) I did,
dx/dt = dx/dv * dv/dt
dx/dt = {1/ (20xpi - x^2*pi)} * - kx
dx/dt = -kx / (20xpi -x^2 pi )
x cancels out
so 20 pi - x pi dx /dt = -k

The mark scheme for those both are obvoiusly looking a bit diff


They are both fine

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