Volume 2011 JRAHS Trial (1 Viewer)

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Untitled picture.jpg

Done part i...I'm unsure about part ii and iii). Just started volumes...

Can anyone help?

Thanks
 

lolcakes52

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Okay, it does take a while to get your head around it but its easy enough once you do some doodling. I found the y value of the elipse for any value of x, ((4-x^2)^(1/2))/2 and the value of x for the corresponding point on the parabola mentioned in part i. Simply put, I found the corresponding focal lengths for each parabola and let them be equal so I could find the value of x in terms of a.
This yielded 2a=((4-x^2)^(1/2))/2
which became a=((4-x^2)^(1/2))/4.
I then subbed this into the equation in part i and gained the correct expression for A(x).
Part ii is quite easy after this.

∂V=∂x*A(x)
V is the integral of A(x)dx from 2 to -2
 
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AbsoluteValue

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It says the focal chord is perpendicular to the axis, therefore you are looking at the area between y=0 and y=a. So just integrate x=(4ay)^0.5 in that limit, I think you should get the area.
 
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THANKS!! I knew I had to use the latus rectum length somewhere (4a)...Thanks

From the same paper...can't get my head around this one!

asasd.png
 
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Well I did it via the rectangle from -2a to 2a minus the the integral

 
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You have to type [ tex ] [ /tex ] around what you want latexed.

And yes, I have that expression, but how do I get it to ?
 

AbsoluteValue

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[ tex ] 2\pi \int_{0}^{\frac{\pi }{2}} x(1-sinx)dx [ /tex ]
Doesn't work :(
 
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rolpsy

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Siddy123

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iv seen that question before in a really old sydney tech paper.
i think 80's
 
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Absolute, without the spaces! (in the tex tags)
 
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well you know that



so you can say



use the slicing method and you should get it :)

edit:

you have to put
[noparse][/noparse] (no spaces)

HO. LY. WHAT THE HELL MIND BLOWN O__________________________________O. Did not know you could do that. It's so simple. Yet amazing. Whoa. Thankyou. I will put that in the books.
 

AbsoluteValue

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HO. LY. WHAT THE HELL MIND BLOWN O__________________________________O. Did not know you could do that. It's so simple. Yet amazing. Whoa. Thankyou. I will put that in the books.
whaaat, they never teach this technique to us :(
 
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Yeah IKR...Wuttt

So slices, just normal discs, holy...
 

rolpsy

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HO. LY. WHAT THE HELL MIND BLOWN O__________________________________O. Did not know you could do that. It's so simple. Yet amazing. Whoa. Thankyou. I will put that in the books.
Oh lol

Terry Lee's book makes quite a fuss about it

anyway the solutions are here
 

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