Recent content by evansmiley

Homework Statement The sum of two consecutive squares can be a square: for instance, 32 + 42 = 52 (a) Prove that the sum of m consecutive squares cannot be a square for the cases m = 3; 4; 5; 6. (b) Find an example of eleven consecutive squares whose sum is a square. The Attempt at a...

Ah ok cool, I had tried factoring and leaving a seven outside too before going back and corssing out my work, but I think be both came to the same conclusion. Many thanks for your help dibyendu!

sorry, yes, you're completely right, i must have made a mistake. Ok so is this logic ok? 2S2 ≥ 3 + S1(4-S1) Well we already know that S1≥3 and S2 ≥ 3 So 2S2 ≥ 6 On the other hand, if we wish to maximise the right hand side of the equation, we want S1 to be its minimum, 3, hence the maximum...

I tried doing that, however i got 2S_1 rather than 4S_1, did you make an error calculating or was that me?

Oh yes i can see, it comes from the fact that (x-1)^2 ≥ 0 So logically it seems to me to try prove 4x + 4y + 4z + xy + yz +xz ≥ 15 Applying AM-GM we get : (4x + 4y + 4z) ≥ 12 So now we have xy + yz + zx ≥ 3 which is equivalent to 1/x + 1/y + 1/z ≥ 3 Now I am stuck :P

ok i can see how you rearranged the first inequality but i still don't know where to go from there ? ? ? And may i ask where the inspiration came from to arrange the inequality in that way? Sorry, i don't have much experience solving this kind of problem, so any tips would help immensely! Thanks

5. Suppose that x, y and z are positive real numbers such that xyz = 1. (a) Prove that 27 \leq(1 + x + y)^{2} + (1 + y + z)^{2} + (1 + z + x)^{2} with equality if and only if x = y = z = 1. (b) Prove that (1 + x + y)^{2} + (1 + y + z)^{2} + (1 + z + x)^{2} \leq 3(x + y + z)^{2} with...

ah ok nevermind i think i get it thanks

Thanks for the replies, the bit i don't understand is the use of the centripetal force equation though. In the derivation of the centripetal force f = mv^2/r, it was taken that the mass is moving at a uniform speed and it's acceleration vector was towards the centre of the circle, however if the...

ah ok. gravity and reaction?

ok i kind of see what you mean, but would it would be right to say that this is not uniform circular motion because the angular velocity is not constant?

but it starts off at rest so to have any velocity it must have accelerated ie the magnitude of it's velocity increases?

Homework Statement A particle of mass m kg lies on the top of a smooth sphere of radius 2 m. The sphere is fixed on a horizontal table at P. The particle is slightly displaced and slides down the sphere. The particle leaves the sphere at B and strikes the table at Q. Find (i) the speed...

Hi i found a question in number theory, involving two equations, it goes as follows: Let p1, p2, p3 and p4 be 4 different prime numbers satisfying the equations 2p1 + 3p2 + 5p3 + 7p4 = 162 11p1 + 7p2 + 5p3 + 4p4 = 162 Find all possible values of p1p2p3p4. Not knowing what to do, i used the...

Homework Statement A smooth wedge of mass 2m and slope 45 degrees is placed on a smooth horizontal surface. A particle of mass m is placed on the inclined face of the wedge. The system is released from rest. (i) Show on separate diagrams the forces acting...