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Well here's my diagram to get things started :p

i'm not sure why you used 1/(26!)2 :confused: im guessing you said that we should sort the lower case letters and then the upper case letters, right? I said 52! because i considered each letter as an individual in one whole set rather than labelling them upper or lower case and then sorted them...

i always thought that if you had one of those bic 4 coloured pens that you could write out some notes, roll them up and then seal them in the pen. when required open the pen and check ur notes... but i haven't tried it and i wouldn't dare :p

For the second one: (a-b)2>=0 (a-b)2 + 4ab>=4ab (a+b)2>=4ab a+b>=(4ab)/(a+b) .: 1/b + 1/a>=4/(a+b) New Question: A particle of weight 4 newton, intiially at rest, falls vertically in a resisting medium with a retarding force of kv newton, where k is a constant and v m/s is the velocity of...

For the first one: Arranging lower case letters in alphabetical order= 1 way Arranging upper case letters in alphabetical order= 1 way Arranging these two sets amongst themselves = 2 ways .: Total = 2 ways Arranging of letters without restriction = 52! .:P(upper and lower in order)= 2/52!

Usually the module A stuff is an essay and the other two can be a dialogue, essay or speech

i have both and love them both :)

i'm so scared of english :(

Ok, i read somewhere that we can't choose the road not taken or the journey to the interior from the stimulus booklet because they're poems. Is this true?

i like you :)

yup! i didn't think about cos being even :p

sorry i meant the part where you actually find the exact values of cos(2pi/5) and cos(4pi/5). :p

Ok and how about this... Show that cos 5@=16cos5@-20cos3@+5cos@. Hence solve the equation 16x5-20x3+5x-1=0 and deduce the exct values of cos(2pi/5) and cos(4pi/5). I'm stuck on the second part.

then how else would you prove that q=1+s :confused:

nah there aren't any... thats it... i got square roots n stuff so i jst gave up n assumed i was wrong because it just looked to "retarded" :p

the problem i had was actually finding the value of one of the roots.. in ur working out that would be 'b'. From (1) would you expand and then use the quadratic?

ok how do you do this one P(x)=x4+px3+qx2+rx}s=0 has two roots which are reciprocals and two other roots which are opposites. Show that q=1+s and r=ps. I know that you have to use the relationship between the coefficients and roots but i think im mucking up with the algebra. Can someone have a...

For the first part of the second image: (x-y)2=>0 .: x2+y2-2xy=>0 .: x2+y2=>2xy Let x=x2 and y=y2 .: x4+y4=>2x2y2 I can't read the second part... it comes up blurred

thx guys

Hiya, how would you go about answering this: Sketch the graphs of x2-y2=0 and xy=2 on the same axes. By observing the number of points of intersection of the graphs, deduce that the equation of z2=4i has at least one root (in fact two roots). Now what i did is i drew the curves and they...