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lol over 6 year old thread cos 54 cos x + sin 54 sin x = sin 2x cos(54 - x) = cos(90 - 2x) now cos(54 - x) = cos(54 - x + 360*n) = cos(x-54 +360*n) so 90 - 2x = 54 - x + 360n x = 36 + 360n or 90 - 2x = x-54 +360*n 3x = 144 + 360n x = 48 + 120n

what's the volume of the cone in terms of a, and say, the height of the cone?

well you don't want the x on top, so you need to think of a way to get rid of it you could do this by

\frac{x^2}{\sqrt{1-x^2}}\\ = \frac{-(1-x^2)}{\sqrt{1-x^2}} + \frac{1}{\sqrt{1-x^2}}\\ = -\sqrt{1-x^2} + \frac{1}{\sqrt{1-x^2}}\\ \\ integrate first part with trig substitution

well if you accelerate the inside accelerator, to near C, then to the observer it will appear to be going at near C. if you also had a particle that was going at near C in the inner accelerator, relative to the inner accelerator, then to the outside observer it would look like it was going...

what are you learning this stuff in?

second bit is just sine rule

you only get one sin-1x value for every x value its range is -pi/2 =< sin-1x =< pi/2

inverse sin is only in the 1st and 4th quadrants if it's negative it has to be in 4th

for the second, you just have to figure out a way that you could get those odd powers to somehow cancel out. (looking at the RHS may give you an idea of something to try)

for the first one, when you integrated did you remember the constant of integration?

1/5 sounds right to me

lol

:cool:

when we use GPE in calculations we would be dealing with changes in the GPE, so it doesn't matter whether your GPE is positive or negative. it's just set it to which is most convenient

tan[\pi /4 \times (2[n+1]+1)]\\ = -tan[(n+1) \pi - (2[n+1]+1)]\\ = - tan[n \pi +\pi - n \pi/2 - 3\pi/4]\\ = - tan[ n \pi/2 + \pi/4]\\ = -tan[\pi/4(2n+1)] + all the other induction stuff

y = -2(x+3)(x+3)(x-5) ? just from factorising it + adding the constant the will make y(0) = 90

Re: If I roll a marble down a ramp and of the edge of a bench or something why does . ...?

Re: If I roll a marble down a ramp and of the edge of a bench or something why does . in that case it would probably some kind of friction issue? maybe friction for a rolling body along this surface is such that it has less effect on the heavier marble. i dunno oh wait yeah =/ i was thinking...

Re: If I roll a marble down a ramp and of the edge of a bench or something why does . he's just rolling the marbles off the ramp and then they fall through the air, right? in which case, the distance is dependent on velocity, and a larger radius should mean a smaller velocity (but then...