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You have found the parametric coordinates of N. ie N(ap,0). Since there is no parameter in the y-coordinate (since y = 0, a constant), this is the locus of N. This is because no value of p can alter the y value. So the locus of N is y = 0. (Note: usually when this situation occurs, you...

That's a really nice method damo but KFunk, there's nothing wrong with yours. In fact, judging by the first two parts to the question, it's probably the way they wanted you to approach it. It's not that messy either, considering it's a Q8.

Hmm, I got the same answer as robbo, except with a pi² in the denominator... Ah well robbo, that's 119/120 :)

I'll give it a shot....(no pun intended :) ) P(Pat winning) = P(win in 3 sets) + P(win in 4 sets) + P(win in 5 sets) ........................= (2/3)³ + (2/3)*³C₁*(2/3)²*(1/3) + (2/3)*⁴C₂*(2/3)²*(1/3)²...

Yes, and how did you get it please?

Yeah, most people do the dry cell, so that question didn't help me very much at all. Now that I think of it though, I probably could've deduced the correct answer had I spent more time on it.

Hmm, what about the dry cell question in the multiple choice? Not very handy if you've studied the lead-acid cell. I was certain the syllabus only requires you to know one of the two, and not one in particular. Ah well...

Let f(x) = x^3 - 12x^2 + 45x then find the stationary points of y = f(x). Then work out how far you can bring down the graph so that the stationary points are on opposite sides of the x-axis (ie 3 distinct roots). This will give you the values of m.

Thanks for that. I did that test a while ago and have been looking for the solutions to it. Just a query regarding Q4 iv) (the locus question). Shouldn't you specify the restrictions of the locus? Obviously it can only exist between the y-axis and the right branch of the hyperbola, so...

There are two forces acting on the particle: 1) weight downwards = mg 2) resistance upwards = 0.1mv² Therefore, F = ma = mg - 0.1mv² giving the equation of motion: a = g - 0.1v² Now, terminal velocity, U, is approached as a --> 0 So...

1)ii) RTP: (1+sinz+icosz)^5+i(1+sinz-icosz)^5=0 (1+sinz+icosz)^5= -i(1+sinz-icosz)^5 (1+sinz+icosz)^5/(1+sinz-icosz)^5 = -i [(1+sinz+icosz)/(1+sinz-icosz)]^5 = -i LHS = (sinz+icosz)^5 {from i} .......= sin(pi) + icos(pi) .......= -i .......= RHS 2b) The locus in a) is a...

It took me a while to get it but I'll quickly list the steps I took... 1) Use the fact that max height = 2h to find an expression for h in terms of V, @ and g. 2) Use the quadratic formula to find the 2 values of t when y = h. 3) Use x = Vtcos@ and sub the previous values of t to find...

The R. Kelly ones that I think of straight away.... - If I Could Turn Back The Hands Of Time - I Wish - Heaven I Need A Hug - I'm Your Angel (with Celine Dion) - What I Feel/Issues

1) Who was your favourite character? Why? George, I just love the unfortunate circumstances he gets himself into... 2) Who did you least like? Why? Lloyd Braun - I just hate that smile, haha. 3) What's your favourite quote? George to unknown attractive woman: "Hey, my name's George, I'm...

Hmm, what if |x/a| > 1? The inverse sine is not defined for this.

Hold on, If a >= b, how can you say that this implies a > b, considering the case when a = b?

Regarding log functions in definite integrals, you can actually prove that ln(-x) will produce the same result as ln(x). However, this requires knowledge of Euler's formula and that's why absolute values are more encouraged in 4u.

Your algebraic reasoning is still correct. Just square both sides and you get the result.

you could probably do it by inspection, noticing that the derivative of secx is secxtanx

Yeah, I've seen the solution to this question and it involves coming up with a lot of identities and manipulating them to get the answer. Agreed.