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Can anyone solve this? (1 Viewer)
- Thread starter yodela123
- Start date
For part a:
you basically need to know that
using the cosine rule we can deduce that
^2-2(r)(2r)\cos(\theta)\\\\PA=\sqrt{5r^2-4r^2\cos(\theta)}\\\\PA=r\sqrt{5-4\cos(\theta)})
Sub PA back into the equation
})
for part b) i):
we gotta differentiate the equation we got from part a, also not that r does not change so we can treat it like a constant
)^{\frac{1}{2}})\\\\= \left (\frac{1}{2} \right )r((5-4\cos(\theta))^{-\frac{1}{2}}(-4(-\sin(\theta))\\\\=\frac{4r\sin(\theta)}{2\sqrt{5-4\cos(\theta)}})
Now when M is travelling up it means that x is increasing, meaning that we have to find when
Also we should impose the restrictions
since we are only dealing with a circle in this question
}{2\sqrt{5-4\cos(\theta)}}>0\\\\\4r\sin(\theta)>0\\\\\sin(\theta)>0\\\\0\degree<\theta<180\degree)
it's best if you look at the sine graph for this, or you can look at the circle itself as it rotates.
part b) ii)
same thing as part b) i) but then now we have a less than symbol, answer should be
for part c:
We basically have to solve
as we are trying to find the stationary points of 
-5\cos(\theta)+2)}{(5-4\cos(\theta))^{\frac{3}{2}}}=0\\\\2\cos^2(\theta)-5\cos(\theta)+2=0\\\\(\cos(\theta)-2)(2\cos(\theta)-1)=0\\\\\cos(\theta)=\frac{1}{2}\\\\\theta=\frac{\pi}{3}, \theta=\frac{5\pi}{3})
Just sub the answer into, probably leave it in exact form. Both of the angles should give the same answer just one is negative and one is positive
part d)
not really sure on that, my brain is dead rn
you basically need to know that
using the cosine rule we can deduce that
Sub PA back into the equation
for part b) i):
we gotta differentiate the equation we got from part a, also not that r does not change so we can treat it like a constant
Now when M is travelling up it means that x is increasing, meaning that we have to find when
Also we should impose the restrictions
part b) ii)
same thing as part b) i) but then now we have a less than symbol, answer should be
for part c:
We basically have to solve
Just sub the answer into
part d)
not really sure on that, my brain is dead rn
Last edited:
thank uuFor part a:
you basically need to know that
using the cosine rule we can deduce that
Sub PA back into the equation
for part b) i):
we gotta differentiate the equation we got from part a, also not that r does not change so we can treat it like a constant
Now when M is travelling up it means that x is increasing, meaning that we have to find when
Also we should impose the restrictions
part b) ii)
same thing as part b) i) but then now we have a less than symbol, answer should be
for part c:
We basically have to solve
Just sub the answer into
part d)
not really sure on that, my brain is dead rn
thanks!The last part is that the stationary point corresponds tobeing a tangent to the circle.
