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HSC 2015 MX2 Marathon (archive) (1 Viewer)

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Ekman

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Re: HSC 2015 4U Marathon

a little change would make a good question:

I did something a little different. I made a geometric sum of this:



Then made the whole geometric series sum and got all imaginary bits:





But if I was to sub in 4030 instead of 3030, it would get the same answer...
 

FrankXie

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Re: HSC 2015 4U Marathon

There are seven different coloured jars. Each jar contains ten identical marbles, each being the
same colour as the jar it is in. A total of ten marbles is selected from these seven jars.
(a) How many different selections are possible if at least one marble is selected from each jar?
(b) How many different selections are possible if no restrictions?
 

FrankXie

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Re: HSC 2015 4U Marathon

I did something a little different. I made a geometric sum of this:



Then made the whole geometric series sum and got all imaginary bits:





But if I was to sub in 4030 instead of 3030, it would get the same answer...
sorry 3030 was a typo, i actually corrected into 4030
 

braintic

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Re: HSC 2015 4U Marathon

There are seven different coloured jars. Each jar contains ten identical marbles, each being the
same colour as the jar it is in. A total of ten marbles is selected from these seven jars.
(a) How many different selections are possible if at least one marble is selected from each jar?
(b) How many different selections are possible if no restrictions?
(a) Not sure ... is it 343 ?

(EDIT : no, I'm double counting, aren't I)
 

seanieg89

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Re: HSC 2015 4U Marathon

I did something a little different. I made a geometric sum of this:



Then made the whole geometric series sum and got all imaginary bits:





But if I was to sub in 4030 instead of 3030, it would get the same answer...
The common ration has modulus 1, so this is not a convergent series. Using the infinite geometric series formula here is meaningless.
 

Drsoccerball

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Re: HSC 2015 4U Marathon

Using cartesian coordinates, show that the sum of the distance from any point P on the ellipse

Ekman dont post your solution let someone else do it i want to see their method
 

VBN2470

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Re: HSC 2015 4U Marathon

Using cartesian coordinates, show that the sum of the distance from any point P on the ellipse

Ekman dont post your solution let someone else do it i want to see their method
 
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VBN2470

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Re: HSC 2015 4U Marathon

It is the standard definition of the ellipse you learn when you start Conics i.e. the ellipse is defined as the set of points such that the distance from any point in that set to a given point in the plane (a focus) is a constant positive fraction less than 1 (the eccentricity) of the perpendicular distance of the point in the set to a given line (called the directrix) or mathematically,
 
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Drsoccerball

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Re: HSC 2015 4U Marathon

It is the standard definition of the ellipse you learn when you start Conics i.e. the ellipse is defined as the set of points such that the distance from any point in that set to a given point in the plane (a focus) is a constant positive fraction less than 1 (the eccentricity) of the perpendicular distance of the point in the set to a given line (called the directrix) or mathematically,
Weve started conics we did the ellipse but how does that make PS=ePM
 

Drsoccerball

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Re: HSC 2015 4U Marathon

I think we should start posting conics and harder extension 1 questions :)
 

VBN2470

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Re: HSC 2015 4U Marathon

NEW QUESTION (HARDER):

 
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