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yeah, just use the hint ^

say the projectile starts at the origin and has moved to point (x,y) y = g/2v2cos[a]2 x2 + tan[a] x (from basic projectile motion equation. derive if necessary) y' = g/v2cos[a]2 x + tan[a] tan[@] = y/x 2y/x - tan[a] = g/v2cos[a]2 x + tan[a] so 2tan[@] - tan[a] = y' (the direction of motion) = y'

was standing pretty close to the front but got pushed back a bit I liked virgin black too. Rowan London's vocals are so damn good

1. x4 + 2x2 + 1 - x2 = (x2 + 1 - x)(x2 + 1 + x) 2. x6 + 2x4 + x2 + x2 + 1 = (x2 +1 )(x4 + x2) + (x2 + 1) = (x2 +1 )(x4 + x2 +1 ) = (x2 + 1 - x)(x2 + 1 + x)(x2 +1 )

mikael makes me lol

it's a series. You have 5000*(1.06)9 + 5000*(1.06)8 ... + 5000 [they don't put any money in until the end of year 1. This $5000 is compounded over 9 years, the second $5000 compounded over 8 years etc. and then $5000 at the end of the 10th year which is not compounded. I think the question is...

I don't really think there's anything wrong with expanding it. I would imagine that that's how it's meant to be done (considering you've found the expression for each part already)

it's the number of ways of choosing 2 from each set of parallel lines, isn't it? 6C2 * 9C2 = 540

not sure that I get what you're asking the induction above doesn't work for negative numbers, since it is specified that n>0 - and the equation only asks for n>= 1 if you mean why the inequality happens to work for all negative numbers, you could solve that by saying when that when n=0,1 then...

a) 2^4 ways for the ceilings, 3^4 for the walls total = 2^4*3^4 = 1296 b) i) 1/3 *1/2 = 1/6 ii) 6 different combiantions per room, so 1/6 iii) no off white, therefore all vivid white this can be done in 1 way, but the ceilings can be painted in 2^4 = 16 ways so 1/16 iv) all walls the same...

9. x = a tan@ dx/d@ = a sec2@ and sec@ = r/a so dx/d@ = r[/sup]2[/sup]/a d@/dx = a/r[/sup]2[/sup] we have dx/dt = u d@/dx * dx/dt = ua/r[/sup]2[/sup] = d@/dt

http://www.intmath.com/Differential-equations/DEs-intro.php - for an introduction http://ocw.mit.edu/OcwWeb/Mathematics/18-03Spring-2006/CourseHome/ - free MIT lecture videos + notes

yeah I think you just say 2n >= n+1 2*2n = 2n+1 >= 2n + 2 >= (n+1) +1 [since n>0] I think what you did is pretty much right

yeah the solvable ones seem pretty easy apparently there's only really a few ways to solve them, and the rest is putting them in the solvable forms I think a large part of it though is what to do when you come across ones that can't be solved (much more common I think) anywayz, you should learn...

for y′ + 3y = 10e2x: y'e3x + 3e3x y = 10e5x (multiplying through by integrating factor) ye3x = 2e5x + C (integrating each side) y = 2e2x + Ce-3x

wow, good question =/ "4U MATH: 94"

not enough episodes imo :( they should've done more with the old cast

using quotient rule: d/dx u/v = (v.du - u.dv)/v2 ln[x2] = 2lnx d/dx 1/(2x ln[x]) = -(2ln[x] + 2)/(2x ln[x])2 = -(ln[x] + 1)/4x2lnx d/dx (98+5x)/(3x2 + 1) = ( 5(3x2 + 1) - 6x(98+5x) )/((3x2 + 1)2 = ( -15x2 - 588x + 5 )/(3x2 + 1)2 there's a derivative solver here...

"(B) identify ONE reason for the difference in above values (C) relate the ionisation energies to the observed conductivity of lithium and hydrogen in the liquid state (D) relate the ionisation energies to the type of ions formed by each of the above elements" b) oxygen has a smaller radius...

can't you just separate variables + integrate through? for the question, you know that at t=0, dy/dt = 2%y = 0.02y and the rate falls at a rate of (2-1.5)%t/10 = 0.05%t = 0.00005t which gives you the given equation, and if you want to solve for population as a function of time just separate...