HSC Mathematics Marathon (6 Viewers)

[Bored Of Fail 3]

if i = sqrt -1, find i^2.

thats just sad :|

 

[jyu]

If z = cos ?? + i sin ??, then show that (without using induction)

1-z=(1/2)sin(@/2)cis(@/2)
1-z^n=(1/2)sin(n@/2)cis(n@/2)

(1-z^n)/(1-z)=result

 

[jyu]

If 0 isn't a solution he has 4

You passed your subtraction test.

 

[Drongoski]

1-z=-2i sin(@/2)cis(@/2)
1-z^n= -2i sin(n@/2)cis(n@/2)

(1-z^n)/(1-z)=result

Shouldn't your 1st 2 lines be as modified above ??

You'll still get the same end result.

Whatever the answer to my query, still an elegant solution.

 

[cutemouse]

x=0 is not a solution (sub into original equation to see)

Or you can see it because the equation would be undefined (involves 1/x).

 

[deterministic]

New question:

How many ways are there to arrange 10 boys and 5 girls in a circle such that none of the girls are seated next to each other?

EDIT: it means that between any 2 girls, there must be at least 1 boy

 

[cutemouse]

New question:

How many ways are there to arrange 10 boys and 5 girls in a circle such that none of the girls are seated next to each other?

Consider the girls seated next to each other. This is done in 5! ways. This leaves 15-5+1=11 people units.

So No of ways girls sitting next to each other = 1*10!*5!

So No of ways girls not sitting next to each other = 1*14!-1*10!*5!=8.67*10^10 (3 sf).

 

[cutemouse]

New question:

[maths]x^2-(p+iq)x+3i=0[/maths] (p, q are real) has roots [maths]\alpha[/maths] and [maths]\beta[/maths]. The sum of the square of the roots is 8.

(i) Write down expressions for the sum of roots and product of roots.

(ii) Hence find the possible values of p and q.

 

[jyu]

Shouldn't your 1st 2 lines be as modified above ??

You'll still get the same end result.

Whatever the answer to my query, still an elegant solution.

Thanks
I checked my working, should be just 2i.

 

[Pyrobooby]

New question:

[maths]x^2-(p+iq)x+3i=0[/maths] (p, q are real) has roots [maths]\alpha[/maths] and [maths]\beta[/maths]. The sum of the square of the roots is 8.

(i) Write down expressions for the sum of roots and product of roots.

(ii) Hence find the possible values of p and q.

(i) [maths]\alpha[/maths] + [maths]\beta[/maths] = p+iq,
[maths]\alpha[/maths][maths]\beta[/maths]=3i

(ii) p=3, q=1 or p=-3, q=-1.

Am I supposed to put the working out too?

Am I even correct :\

 

[deterministic]

Consider the girls seated next to each other. This is done in 5! ways. This leaves 15-5+1=11 people units.

So No of ways girls sitting next to each other = 1*10!*5!

So No of ways girls not sitting next to each other = 1*14!-1*10!*5!=8.67*10^10 (3 sf).

Incorrect, perhaps I should clarify. No girls seated next to each other means a formation (assume a circle) BGGBGBGBBGBBBBB is invalid as 2 girls are next to each other. ie. between any 2 girls, there must be at least 1 boy.

 

[cutemouse]

Incorrect, perhaps I should clarify. No girls seated next to each other means a formation (assume a circle) BGGBGBGBBGBBBBB is invalid as 2 girls are next to each other. ie. between any 2 girls, there must be at least 1 boy.

In that case, it would be 1*6!*2!*7! = 7257600 I think...

 

[deterministic]

In that case, it would be 1*6!*2!*7! = 7257600 I think...

Its not correct but I'm curious about how you got this answer.

 

[cutemouse]

I had another answer up there but I thought it was wrong (in the order of 10^10).

EDIT: Yeah I think my other answer was correct: 1*14! - (10!*5!+11!*4!+12!*3!+13!*2!) = 7.05*10^10 (3 sf) ... maybe not though.

 

[deterministic]

Could you explain how you got these answers? Your answer is still not right.

 

[cutemouse]

Could you explain how you got these answers? Your answer is still not right.

If all 5 girls are together then no of ways that could happen is 1*10!*5!
4 girls ... 1*11!*4!
3 girls ... 1*12*3!
2 girls ... 1*13!*2!

total number of ways = 1*14!

So that's how I got that... But then again I only do General maths so what would I know...

EDIT: The above may be wrong since the 3, 4, 5 girls case contains the 2 girls case...

 

[Bored Of Fail 3]

. But then again I only do General maths so what would I know...
...

stfu, you are pathetic, you are that desperate for attention that you need to copy ohexploitable, you are such a fail

 

[cutemouse]

stfu, you are pathetic, you are that desperate for attention that you need to copy ohexploitable, you are such a fail

Have you got any tutees yet?

 

[jyu]

New question:

How many ways are there to arrange 10 boys and 5 girls in a circle such that none of the girls are seated next to each other?

EDIT: it means that between any 2 girls, there must be at least 1 boy

14!

 

[cutemouse]

14!

I don't think it's 14. I know at least 2 specific cases [BGBBGBBGBBGBBGB and BBGBGBGBGBGBGBG] with 48 and 6!*7! number of ways each...

EDIT: Oh 14! ... that's the total number of ways without restrictions.