C4 Maths help needed!!!

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

we cannot do that. please post your workings so far and we can take it from there.

I would love to do your homework but at the moment I am doing mine ...

the rules fam.

if we do like you want we is carded innit

Do you know how to do them?

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.

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

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?

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

Are you sure that is correct Mr M?

So the differentiation is wrong and I need to use the product rule on 2sintcost?

When you differentiate y = 4cos 2t wrt t isn't dy/dt = -8sin 2t which is not -8sintcost

When you differentiate y = 4cos 2t wrt t isn't dy/dt = -8sin 2t which is not -8sintcost