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
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 @