HSC 2013-14 MX1 Marathon (archive) (3 Viewers)

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Sy123

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Re: HSC 2013 3U Marathon Thread







 

RealiseNothing

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Re: HSC 2013 3U Marathon Thread

I'm just going to do the last part and leave the first two if some one else wants to write up a solution.

If we expand the brackets and take individual summations we get:



We know the 2nd summation from previous parts and so it is:



Now lets look at the 1st summation:







If we break this up into individual series we get:







Adding all these up gives:





But the 3rd summation was:



So they somewhat cancel out when we add the 1st and 3rd summation, and after adding the 2nd summation we are left with:



 

Sy123

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Re: HSC 2013 3U Marathon Thread

I'm just going to do the last part and leave the first two if some one else wants to write up a solution.

If we expand the brackets and take individual summations we get:



We know the 2nd summation from previous parts and so it is:



Now lets look at the 1st summation:







If we break this up into individual series we get:







Adding all these up gives:





But the 3rd summation was:



So they somewhat cancel out when we add the 1st and 3rd summation, and after adding the 2nd summation we are left with:



Yep nice work.

====





 

hayabusaboston

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Re: HSC 2013 3U Marathon Thread

there are 20 men on a hockey team. There are 2 goalies, 6 defensemen, and 12 forwards. How many lineups can be created if there must be 1 goalie, two defensemen and three forwards, and if two players insist on being in the same line together (like, defense or forward) or they dont want to play at all, while three others refuse to be in the same line (defense line or forward line)?
 
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study1234

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Re: HSC 2013 3U Marathon Thread

(From Yr 12 Cambridge 3u)

A large vertical wall stand on horizontal ground. The nozzle of a water hose is positioned at a point C on the ground at a distance d from the wall and the water jet can be pointed in any direction from P. Also the water issues from the nozzle with speed V .
If V = 2√(gd) prove that the portion of the wall that can be reached by the jet is a parabolic segment of height (15d)/8 and area (5√15(d^2))/2.
 

hayabusaboston

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Re: HSC 2013 3U Marathon Thread

there are 20 men on a hockey team. There are 2 goalies, 6 defensemen, and 12 forwards. How many lineups can be created if there must be 1 goalie, two defensemen and three forwards, and if two players insist on being in the same line together (like, defense or forward) or they dont want to play at all, while three others refuse to be in the same line (defense line or forward line)?
Fuuuck my question must be tough if even realisenothing and sy123 havent answered it yet LOLOL
 

Sy123

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Re: HSC 2013 3U Marathon Thread

there are 20 men on a hockey team. There are 2 goalies, 6 defensemen, and 12 forwards. How many lineups can be created if there must be 1 goalie, two defensemen and three forwards, and if two players insist on being in the same line together (like, defense or forward) or they dont want to play at all (1), while three others refuse to be in the same line (defense line or forward line)? (2)
There is a fault in your question.

And I only just got to look at this question now.

edit: I wasn't thinking properly and made a mistake, I was confused with the conditions and I thought that the team couldn't play in some conditions but I see you resolved that in your question, so yes there is no mistake :)

Ok I'll try with this attempt, first name the conditions in the question, (1) and (2).

There then initiates four cases that we only observe for Defense (D) and Forwards (F)

It's possible to do this because your conditions don't make sense if they apply for people among different lines.









We will simply ignore all arrangements for goalies, I'll multiply my answer by arranging defence and forward by 2 at the end.

Case 1:



Case 2:



Case 3:



Case 4:




So my final answer is:

10808

Is it? It might be wrong because I'm quite weak with permutations and combinations.
 
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hayabusaboston

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Re: HSC 2013 3U Marathon Thread

There is a fault in your question.

And I only just got to look at this question now.
Well if there's a fault, naturally you would have mentioned what the fault was. Since u havent, we can all assume u are making shit up.
 
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