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arrg i had a writter for that thest and he was so slow i only got the first 80 marks out, i no i could of got the last 4 if he was faster

well i spend hours finding paturns, appliny formular to them and i got out a really long equasion, and i simplified it and simplified it and proved that x3[/ = x3

i spent abput 2-3 hours on this question and a massive 10+ page proof that i am not typing up proves that x3 = x3 if any one can prove that 3n2 + 3n + 1 cannont be a perfect cube that can you tell me. it would help with this proof

i dont thin that this is true 12 + 22 + 32 +42 + 52 + 62 + 72 = 140 7*8*9/6 = 84

could you please explain what you did

thanks for tring but that doesn't work it is not a geometric or a aritmatic progrretion unfortunalty

what would this simplify too the sum of 3(t-1)(t-2) fron t = 1 to t = n-1 n is just a constant, any help greatly appreaciated

when usinmg indution k =2 is easy cause you can use and pythogorain triad to prove there is at least 1 sol eg x=3,y=4 z=5 to prove for k = n+1 il try lhs = xn+1 + yn+1 = x(xn + yn) + yn+1 -xyn =xzn +y(yn + xn) -xyn - yxn = xzn + yzn - xy(yn-1 + xn-1) =...

no im not thats why im timsing it by (1 - 7/28) that gets rid of all the solution where AA and A are together i assumed all the A's were identical, if they werent then the solution should be timsed by 6, but i think they are

read the paper throulg in reading time and deside what is the eaisest for you then if this means doing question 1-3 them going to 7 and working bacwards do it my advise is do question 1-3 first, no matter what order you do the last 4 in

threat two of the a's as 1 letter so there are 8 letters and 2 thant can be together = 8! * (1 - 7/28) = 30,240 8! is the amount of ways they can be aranged 7 is the amount of pairs that are together in any 1 combo 28 is the amount of pairs of letters

Question 29 i am x meteres away from a diving board, the angle (as i see it) between then 1 m and the 4m board is @, they are vertically alinged show that @ = tan-1(4/x_ - tan-1(1/x) show @ is a min when x=2 deduce that the min @ = tan-1 (3/4)

this would me much eaiser proved without induction, but any way Q 27 a projectile is launced of a 50m cliff and hits the ground 200 from the foot of the cliff. it was fired with a velocity 40m/s and angle @ find the 2 posible values of @

q 23 proove by indution 1 + 2 + 4 + ... +2n - 1 = 2n-1

you left of values by not concidering cos2x=- √3/2 eg 5π/12

was that question in the 4 unit exam? i rember it but i dont know from where

Question 20 show that xn(1 + x)n(1 + 1/x)n = (1+x)2n hence prove that 1 + nC12+ nC22+ ... + nCn2 = + 2nCn

it could be like gragh this bitch y = 3xsinx -ex -7loge(tan-13x)2

is that exacly as it was as in is that it word for word was there any previous work that might help it did it step it out at all thats dam hard, only way i can think of is with a massive tree

ingenious thakyou all very much