HSC 2013-14 MX1 Marathon (archive) (4 Viewers)

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Capt Rifle

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Re: HSC 2013 3U Marathon Thread

Ima post a hard conics question on 4u marathon see who gets it lol
 
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Re: HSC 2013 3U Marathon Thread

If you wanted some 'evidence' you split the numerator and write out a few terms. Mass cancellation and you're left with 1. :p
 

RealiseNothing

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Re: HSC 2013 3U Marathon Thread

I believe you this time :3

======================





As P approaches Q, the length PO approaches the length OQ. Also the length PQ approaches 0. Hence Pythagoras' Theorem holds:



So either angle OPQ or OQP is 90. But since the angles of a triangle add to 180, the other angle must also be 90. Hence since angle OQP is a constant, it is always 90.
 

Sy123

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Re: HSC 2013 3U Marathon Thread

As P approaches Q, the length PO approaches the length OQ. Also the length PQ approaches 0. Hence Pythagoras' Theorem holds:



So either angle OPQ or OQP is 90. But since the angles of a triangle add to 180, the other angle must also be 90. Hence since angle OQP is a constant, it is always 90.
Hmm what makes you think Pythagoras Theorem will hold?
 

Sy123

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Re: HSC 2013 3U Marathon Thread








 

Sy123

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Re: HSC 2013 3U Marathon Thread

I believe you this time :3

======================





As Q approaches P it is clear that the length QO is decreasing, and that the minimum distance is when Q is at P.

So therefore the shortest distance from O to Q is when Q coincides with P.

Now within HSC geometry, the shortest distance is always perpendicular distance.

Since OP is shortest distance, OP is perpendicular to QP
 
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Re: HSC 2013 3U Marathon Thread

The direction of your implication is incorrect. It should go: It is true for n=k+1 since it is true for n=k (you ASSUMED this).
 

RealiseNothing

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Re: HSC 2013 3U Marathon Thread

The direction of your implication is incorrect. It should go: It is true for n=k+1 since it is true for n=k (you ASSUMED this).
That's still not correct. You have to say "It is true for n=k+1 if it is true for n=k".
 
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Re: HSC 2013 3U Marathon Thread

I know what you meant :p

I'm just nit-picking.
I'm all for nit-picking, don't get me wrong hehe.

Someone do my question from way back. The one about intersecting tangents.
 
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