Stupid maths problem

[meghatronic]

Sorry to do this, but getting frustrated. Trying to help a friend with a maths problem, for which she has the answer, below:

I don't understand (read: have forgotten all my maths) how to get to the bit marked from what's previous.

Any help, please

 

[meghatronic]

If you've got that, you just factorise anything common out of the expression, at least thats what I think you've got to do.

Woops, I clarified the op. I meant how to get to the green line bit.

 

[meghatronic]

Hmm.

I think to get the green line from the one above, you've got to factorise or simplify the above expression. Not sure if it involves stuff to do with logs.

Just so I don't feel so useless, what level is this? As A2?

I think she's doing further maths, but this is an example from a random OU text book I think.

 

[meghatronic]

You're just taking out a factor of 3^(n-1)*4^(n-1)

4^(n+1) = 4^2 * 4^(n-1)
so 3^(n-1) * 4^(n+1) = 3^(n-1) * 4^(n-1) * 4^2 goes to 1 * 4^2, once the factor is taken out
The second bit goes to 1 * 3^2
and the last goes to 2 * 3 * 4
which is what's on the highlighted line.

Oh my gosh, why don't I remember this... at all!??!

Thanks

I heart OcUK.

 

[meghatronic]

Okay, this may have back fired as now she thinks I'm actually good at maths. Which I'm clearly not. She doesn't have the answer for this exercise - it's from her tutor, this time.

A triangle has vertices at the points X(5,−2), Y(0,0) and Z(4,2).
Suppose that the triangle is rotated through rθ so that XY lies along the positive x-axis.

Find the exact values of tan θ,cos θ and sin θ, and hence write down a formal definition of rθ using two-line notation. (There is no need to work out the value of the angle θ.)
Thus, find the co-ordinates of the images X' and Z' under rotation rθ.

I don't even understand what this is saying as it says theta value isn't needed. It's pretty much a 100% wtf for me - and prevents me helping her further.

Any pointers on how to do this would again be greatly appreciated... Last one I'm 'helping' her with anyway.

 

[meghatronic]

Isn't it just a case of working out the bracketed bit ie 4squared +3squared = 16+9 =25 and take away 2x3x4 = 24, so 25 - 24 = 1 therefore you can ignore this bit as you're multiplying the first bit outside the bracket by 1. Then 3(n-1)4(n-1) is the same as 3x4(n-1) = 12(n-1)?

Yeah, but it was how to get the green line that confused me, and her. But Haircut explained it tome.

Although new problem now .

 

[meghatronic]

Then Rθ = [Cosθ - Sinθ]
...............[Sinθ. Cosθ]

Thanks!

Although, I don't really understand where this bit comes from.

 

[meghatronic]

Rotation matrix

http://en.wikipedia.org/wiki/Rotation_matrix


Edit: Just read it says you have to use the dimension 3 rotation matrix if it's 3 points. I'm not sure. The bit I gave was the dimension 2 matrix, maybe have a check up on that.

Thanks. I've sent her the wiki to read, hopefully will help! I'm far too tired/out of my depth to help her directly! I was thrown off by the find "exact values" and the fact theta isn't needed. Which feel mutually exclusive.

 

[meghatronic]

Right let's see if i can go through this..

OMFG.

Epic post. Will take a while to digest... but I may just send it her and go to bed.

Thanks a lot

I've got sinθ = 2/√29
cosθ = 5/√29
tanθ = 2/5

I'm thrilled I somehow managed to get these right, prior to any understanding of the problem, just by ******* about

 

[meghatronic]

Happy to help any way i can

I've gone through it, I notice from your very thorough explanation, the problem wasn't actually that difficult and my random tinkering was on the right track. A bit embarrassed now! Although less bothered as it wasn't my problem in the first place (< saving face ), I stopped doing maths at A/S.