P_1 +2P_2+...+ nP_n= k1*x +k2 *x^2+k3*x^3...+kn*x^n
but co . efficient of x^2,3,4,5...=0 (as shown in 2 case above)
---> P_1+2P_2+...+nP_n= kx
;)
Ps: U can make it shorter by just using a general x^k and do the same as the case x^2k+1 :D
I think we can talk about electron moving in 1 direction in a magnetic field will experience a force resist to its motion(use a diagram)...Any1 got the answer for this ???
Q50:Use GP as UndertheSun:
1st one:GP with n+1 term common ratio = (1+x) ,then equal co. of x^r
2nd one : GP with n+1 term commonratio=(1+x)/x,then equal co. of x^r
Q51:
Consider co. of even power of x (x^2k) eg:X^2,4,6,8...
P_1= - n!/(n-2k)!*(2k-1)!
2kP_2k= n!/(n-2k)!*(2k-1)! --->...
let @ be angle of..., T be tension
w = 36*2(pi)/60=1.2(pi) rad/s
Resolve horizontally:
Tsin@= mw2r
but r = lsin@
--> T sin@=mw2lsin@
--> T= 5*(1.2(pi))^2 * 1=71 N
Resovle vertically :
Tcos@=mg
---> cos@= mg/T= 5*9.8/71
--->@=46.36 degree
In ND solution:
z1^2 + z2^2 +...+zn^2 = [Sum(zi)]^2 - 2Sum(zi*zj)
eg: a2+b2+c2= (a+b+c)2 - 2(ab+bc+ac)
---> so U dont have to worry 'bout missing z1z3 or z1z4:D
Btw do we need to prove this or just assume;)
I got Arnold-Arnold and Coroneos textbook but both of them dont have Proability( U can check that:D )...so can U guys give me some??? just post Ur question in this forum (and answer plz:) )
Can we assume this or we need to prove it ( 2No. is ok but for n No...:( )
Btw,can we use stuff that they dont teach us here (since I've learned some good stuff in my country:D )
In general, when U have a circular motion ,U need a centripetal force and in this case there 's no others than vertically gravity,and reaction force so Friction must be centripetal :D
(Actually,when the object occupy circular motion it'll tend to fall out of the disc,'n the friction resist this...
I 've seen this1 in Year10Physics in my country:D
Angular velocity of the object: w= 2*2(pi)/1=4(pi)
Friction play the role of centripetal force in this case; and the greatest value for friction is Mmg (ortherwise it will slip out of the disc):
Fc=mw2r=Mmg
--> m*16*(pi)2*r=Mmg...
Oh,I forgot to count AC case in my solution:D ;anyway I redo it 'n got this:
In 1B case there r 6 way
In 3B case there r 12 way
In 2Bs case there r 3 case:
C is the 1st--->(CB) is 1st ,there're 3!/2!=3
C is the last---> (BC) is last, there're 3!/2!=3
C in the middle--> (BCB) is a...
---> I dont really understand what U meant(coz of mine bad English:D ). Anyway,if C is between As then they have touched<--???
Explain for 2B in mine solution: let AAC be in a group(for touching) the others r 2 B --> no.of way is 3!/2! 'n in AAC there 's 3!/2! no.of arrangement.--> No. of way A...
I dont really understand the question,anyway here is my answer: :D ( I guess the question want U have both A 'n C in the five,if not U just add all the case where there's 1 of A or C :p)
If A cant touch C ,B must be in the five:
+ if 1 B: obviously there're 4 ways ...