Recent content by Bread18

One way to do it would be to rewrite it as n^2 - n -1 > 0, and show that that is true for n > 1

What did you do to get to (\frac{-3a^2}{a^2-1} * \frac{(a+1)(a^2-a+1)}{a(a-1)(a^2+a+1)})?

a^4 - a = a(a^3 - 1)

Put the sqrt on the other side of the eqn and square both sides, should be able to do it from there.

I did it and got \frac{1}{a-1}. First I would get rid of the divide then remember that a^3 -1 = (a-1)(a^2 + a + 1) See how you go from there.

a_i is just some natural number. For n to be palindromic, a_i = a_{k-i} For example, with the number n = 12321, we have n = \sum^{k}_{i=0}a_ib^i. n has 5 digits, so k = 4, and it's a base 10 number, so b = 10. so we have n=\sum^{4}_{i=0}a_i10^i = a_0 10^0 +a_1 10^1 +a_2 10^2 + a_3 10^3 +...

Yeah that's right.

What do you mean by "throw away the first 23 dots"? Think of it as having 7 dots in each x_n and then place 5 'anti dots' into any of the x_n. This is the same as having x_1 + x_2 + x_3 + x_4 + x_5 = 5. (5 'anti dots' and 4 lines).

Each x_n can have a maximum of 7 dots. So we can rewrite it as y_n = 7 - x_n. Subbing this into the eqn you will get the answer to be C(9,4)

I'm not sure exactly what you have done, I don't do these questions this way. The easy way to do it is to let z=x + iy and then sub into \left|z-3-5i\right|= 2. Now you just find the modulus as if it were an complex number and you end up with an eqn for a circle.

This is where your error is. You should get, by multiplying everything by x(x^2+1)^2 a(x^2+1)^2 + (bx+c)(x^2+1)x + (dx+e)x = 1 From there expand, equate coefficients etc, and you'll get the right answer.

Ok, thanks for your help, I think I'm going to go to bed now (2am here). Hopefully When I wake up it'll all become obvious...

So I want y = 0?

Haha yeah, we've all been missing simple things..:rolleyes: I don't see how this ties in with it not hitting the semi circle though.

Haha well spotted :smile: So, now with that fix, I get 2v_i^2(y-R)=ax^2 \\ 2v_i^2(y-R)=a(R^2 - y^2) \\ 2v_i^2 = -a(R+y) \\ v_i^2 = \frac{g}{2}(R+y)