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Yep, not to mention its a lot quicker than induction...lolokay said:n3 - (n-1)3 + (n-1)3 - ... -13 + 13 - 03 = n3
is that fine?
Yep, not to mention its a lot quicker than induction...lolokay said:n3 - (n-1)3 + (n-1)3 - ... -13 + 13 - 03 = n3
is that fine?
I may be wrong on this, but I'm prtty sure there should only be one solution of alpha. The reason there is a constant (alpha) is to shift the sine or cosine curve along the t axis, ie because at t = 0, it is not at the origin or one of the endpoints.Pratham said:hey guys, this doesnt really have to do with any of the questions, but its a doubt i have so i was wondering if someone can clarify (sorry if im breaking the rules a bit).
Lets say that in a simple harmonic motion we are given a set of initial conditions and we can say something like; in general x= Acos/sin(nt[+/-]alpha) +B. Now lets say the questions says find apha, and we do so by plugging in the intial conditions. Now in most 3u cases we take alpha as the positive value and forget about the various quadrants and where what is positive/negative (A,S,T,C), but sometimes in 4u (and 3u) we have to determine whether alpha is positive or negative....now heres the question (finally!)...the way i do it is by using the intial input values/conditions e.g. at time t=o x(dot)>0 etc. but from what i understand there is a easier way using a unit circle. Firstly, how does this method work and secondly what are the principles behind it...is it kinda like evaluating shm to circular motion???? PLEASE HELP
clintmyster said:no solution?
Umm for "the total number of Ps together is basically =5!/2!2!" you don't need to divide by another 2! as you haven't arranged the Ps to begin with. So really it should be 5!/2!lyounamu said:Tommy, I don't think your answer for Q9 is correct. The total number of perm is 6!/2!2! = 180
And the total number of Ps together is basically = 5!/2!2! = 30
So the total number of Ps separaed is = 150.
yep, you are right. I misinterpreted my own working.independantz said:Umm for "the total number of Ps together is basically =5!/2!2!" you don't need to divide by another 2! as you haven't arranged the Ps to begin with. So really it should be 5!/2!
Correct me if i'm wrong.
1b). dv/dt = 500lolokay said:some calculus questions
1. a) differentiate xx
b) 'Air is being pumped into a spherical balloon at a rate of 500cm3/s. Find the rate of increase of surface area S when the radius is 20cm' [S = 4pi r2, V = 4/3 pi r3]
c) show by differentiating from first principals that the derivative of ln[x] is 1/x using the definition e=lim[n->infinite](1+1/n)n
2. by considering the graph of each function, evaluate:
a) ∫[0->a*] sqrt(9 - x2) *(0 =< a <=3)
b) ∫[0->a] arctan[x].dx
3. a) ∫1/(1+2e3x) .dx
b) ∫(1+x)2/(2+x)6 .dx
c) ∫1/(1+2tan2x) .dx
hopefully those are all written how I wanted
(x2)x-1lolokay said:some calculus questions
1. a) differentiate xx
no itskaz1 said:(x2)x-1
x2x-2
Is this right?
Thanks. Please excuse my noobishness in Maths.tacogym27101990 said:no its
x^x(lnx+1)
no worrieskaz1 said:Thanks.Please excuse my noobishness in Maths.
Damn, you post up answer too quickly~lolokay said:if you don't know implicit dif. you can just use
xx
= exlnx
the derivative of which is (1+lnx)exlnx
= (1+lnx)xx
(5! x 4 x 3 x 3!)/10 = 864independantz said:Q: In how many ways can 5 women and 5 men be arranged in a circle so that the men are separated and two particular women must not be next to a particular man?
The answer is:
Answer: 864
M@ster P said:Expand cos (2A + B) and hence prove that 1/4cos3(A) = cos^3(A) - 3/4cos(A).
Putting x = Kcos(A) and giving K a suitable value, use the preceding formula to find the three roots of the equation 27x^3 - 9x = 1.
Hence write down the value of the product cos20.cos60.cos100.cos140