Extension One Revising Game (2 Viewers)

[nerdsforever]

Re: 2009 3U Maths Marathon

solve: sin3x + sin2x = sinx
0 << x << 360

 

[Drongoski]

Re: 2009 3U Maths Marathon



Edit

Am I supposed to post a question ? I don't have one. Someone plz take over.

 

[nerdsforever]

Re: 2009 3U Maths Marathon

lol, x = 0, 60, 180, 300, 360.

 

[lolokay]

Re: 2009 3U Maths Marathon

I'm gonna change the x into t

ummmm..

 

[youngminii]

Re: 2009 3U Maths Marathon

ummmm..

LOL whoops?
I deleted my post. Can't be bothered to think about the question..
Wait was I wrong in the first place? o.o

 

[lolokay]

Re: 2009 3U Maths Marathon

well i see no error in gurmies' working, and time =/= displacement

 

[nerdsforever]

Re: 2009 3U Maths Marathon

1) An arithmetic series is 6.5, 9, 11.5, 14, 16.5 + .........

Find the sum of the first 500 terms.

 

[Trebla]

Define the arithmetic mean of a set of numbers x₁, x₂, ...., x_n as:

Show that:

 

[AnandDNA]

Re: 2009 3U Maths Marathon

1) An arithmetic series is 6.5, 9, 11.5, 14, 16.5 + .........

Find the sum of the first 500 terms.

Sum=1/2*n*(2a+(n-1)d)

=1/2*500(2(6.5)+(599)(2.5))

=377625

Solve abs((x+1)/(x-2)) >2

 

[gurmies]

Re: 2009 3U Maths Marathon

Solve abs((x+1)/(x-2)) >2

1 ≤ x ≤ 5, x ≠ 2

Define the arithmetic mean of a set of numbers x₁, x₂, ...., x_n as:



Show that:

 

[shaon0]

Re: 2009 3U Maths Marathon

1 ≤ x ≤ 5, x ≠ 2

nice solution.

 

[Trebla]

Might've have been quicker to do:



Question (relatively straightforward):

Recall that an object exhibits simple harmonic motion if:


Show that if a displacement x is a function consisting of a sum of sines and cosines of equal periods then it is simple harmonic, i.e. prove the following expression describes simple harmonic motion:

 

[Dragonmaster262]

Re: 2009 3U Maths Marathon

 

[Air Jordan]

Re: 2009 3U Maths Marathon

is it 3.5?

 

[Drongoski]

Re: 2009 3U Maths Marathon

is it 3.5?

Looks right !

 

[azureus88]

In answer to Trebla's question:

[maths]x=\sum_{i=1}^{k}\sin(nt+\alpha _i)+\sum_{j=1}^{r}\cos(nt+\alpha_j)[/maths]

[maths]\frac{dx}{dt}=n\sum_{i=1}^{k}\cos(nt+\alpha _i)-n\sum_{j=1}^{r}\sin(nt+\alpha_j)[/maths]

[maths]\frac{d^2x}{dt^2}=-n^2(\sum_{i=1}^{k}\sin(nt+\alpha _i)+\sum_{j=1}^{r}\cos(nt+\alpha_j))[/maths]

[maths]=-n^2x[/maths]

 

[studentcheese]

Nice and simple:

cos(@ + a) = cos@cosa - sin@sina

Derive the result for sin(@-a) using the above result.

 

[duckcowhybrid]

Replace sin(@-a) with cos (90-(@-a)) and solve.

 

[gurmies]

Replace sin(@-a) with cos (90-(@-a)) and solve.

I think since it said use the result above, they want the addition. What I mean is:

90 - (@ - a) = 90 + (a-@)

 

[Dragonmaster262]