Last minute proofs etc (1 Viewer)
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Aerath
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Is that the one using that weird triangle thing?
kwabon
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numerous (two that i know of) to prove the reflection property, but yes the weird isosceles triangle is one of the method.
Bunzhou
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(ii) P is a point on the ellipse x^2/a^2+y^2/b^2=1 with centre O. A line drawn from O, parallel to the tangent to the ellipse at P, meets the ellipse at Q.Prrove that the area of the triangle OPQ is independent of the position of P.I've tried doing this proof for about half an hour now and I cant get it ><"... I got co-ordinates of Q(asintheta,-bcostheta) and I did (OPxOQ)/2 for area..and nothing cancels..zzz
DW
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Monsterman
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how come it equals zero at the end? its a bit odd..=a_{n}x^n+a_{n-1}x^{n-1}+...+a_{1}x+a_{0}\\\text{ Let }z\text { be a complex root of }P(x)\\\therefore P(z)=a_{n}z^n+a_{n-1}z^{n-1}+...+a_{1}z+a_{0}=0\\P(\overline{z})=a_{n}\overline{z}^n+a_{n-1}\overline{z}^{n-1}+...+a_{1}\overline{z}+a_{0}\\=a_{n}\overline{z^n}+a_{n-1}\overline{z^{n-1}}+...+a_{1}\overline{z}+a_{0}, \text{ using }\overline{z}^n=\overline{z^n}\\=\overline{a_{n}z^n}+\overline{a_{n-1}z^{n-1}}+...+\overline{a_{1}z}+\overline{a_{0}}, \text{ using } k\overline{z}=\overline{kz}\text{ and }k=\overline{k}, \ k\text{ real}\\=\overline{{a_{n}z^n+a_{n-1}z^{n-1}+...+a_{1}z+a_{0}}},\text{ using }\overline{z_{1}}+\overline{z_{2}}+...+\overline{z_{n}}=\overline{(z_{1}+z_{2}+...+z_{n})}\\=\overline{P(z)}\\=0\\\therefore \overline{z} \text{ is also a root of }P(z))
Bunzhou
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The assumption is z is a complex root and since P(Z) = 0, the conjugate of P(Z) is also zero..
jet
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He showed that
@untouchablecuz: Do you explain the intermediate steps, or do you normally write the working out without explanation. I'm just wondering whether the markers will realise that you understand what you are doing or not.
untouchablecuz
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well, if i feel the steps need explanation, i provide it; but in this proof, it doesn't seem like anything needs any explanation, except for the fact that the co-efficients must be integral (thanks for pointing it out)
youngminii
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I
Am
Fucked
Am
Fucked
Revelrous
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haha yes you are fucked loser
lol, I did without a calculator for my MX2 exam
untouchablecuz
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Revelrous
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theres a difference between doing an exam and not getting zero for an exam
i believe our friend here didnt do the latter - ha ha
i believe our friend here didnt do the latter - ha ha
Well for starters the whole exam was theoretical... There wasn't really any nasty calculations involved.
I rarely use a calculator anyway, I make too many mistakes.
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untouchablecuz
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wat about the latter part of the mechanics Q
did you do it in your head
did you do it in your head
It was just pi/4 < alpha < pi/2 IIRC... I don't think you need a calculator solve values for which tan alpha < 1 ???
You mean coefficients must be real, not integral? Or am I mistaken?
untouchablecuz
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untouchablecuz
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nah nah, the Q7 mechanics