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Re: HSC 2015 3U Marathon h depends on d?

re: HSC Physics Marathon Archive A 5 kg mass slides at a constant speed of 2.0 m/s down a plane inclined at 30 deg to the horizontal. Determine the reaction force of the plane on the mass.

re: HSC Physics Marathon Archive no, just another question

re: HSC Physics Marathon Archive Find the ratio of the forces of gravity on the moons.

Re: HSC 2014 4U Marathon - Advanced Level Sorry That I am doing it again. If x^2 + y^2 = 1 in your last example? Have you got a counterexample for zero degree cyclic rational functions? Thanks for your patience. To make clear, I wasn't trying to make any claim at the start, purely to do Sy's...

Re: HSC 2014 4U Marathon - Advanced Level Thank you. Something wrong with my last post. I totally agree with you.

Re: HSC 2014 4U Marathon - Advanced Level But this revised constraint is excluding x^2+y^2<1. I was thinking of all x and y > 0 including 0 if defined as pointed out in Sy's.

Re: HSC 2014 4U Marathon - Advanced Level Thanks again for another 'counterexample'. Is 0 the minimum of x+y when x=y=0?

Re: HSC 2014 4U Marathon - Advanced Level Thank you all for the thoughts. I certainly have put time in analysing the idea. The idea is not baseless. Well known geometric facts support that, such as the question I posted a+b+c>=abc in a unit circle; area of a rectangle; volume of a cuboid. What...

Re: HSC 2014 4U Marathon - Advanced Level Thanks. Please look for one defined when a=b=c=..

Re: HSC 2014 4U Marathon - Advanced Level Thanks for the example. I am beginning to see your point. Will the reasoning apply to cyclic rational functions of degree 0 with positive variables?

Re: HSC 2014 4U Marathon - Advanced Level I meant homogenous cyclic polynomials. Sy's example is just that if multiplied by (a+b)(b+c)(c+a) Forgotten to mention positive a, b and c, as stated in Sy's Can apply to both max and min. xy/(x^2+y^2) has a max of 1/2 for positive x, y

Re: HSC 2014 4U Marathon - Advanced Level Thanks to all your comments. I can see the difference between your examples and Sy's. Sy's is homogeneous but yours are not. If your last example is changed to homogeneous by changing (x-1) to X and (x+1) to P etc i.e...

Re: HSC 2014 4U Marathon - Advanced Level Can you think of a counterexample for n=3?

Re: HSC 2014 4U Marathon - Advanced Level Well done. My solution: a+b+c=abc when the triangle is equilateral, a=b=c=sqrt3 a+b+c is the perimeter of the triangle and abc is proportional to its area. Symmetry gives minimum perimeter and maximum area. When the triangle deviates from equilateral...

Re: HSC 2014 4U Marathon - Advanced Level I have made a mistake in my last post. Change x+1 to X and y+1 to Y, P(X,Y)=(X^2+(Y-2)^2)\cdot((X-2)^2+Y^2) Symmetry is preserved. Your counterexample is valid. Why does your "rule" apply for the question Sy asked, but not for the expression in this...

Re: HSC 2014 4U Marathon - Advanced Level Because of the constants. Change x+1 to X and y-1 to Y, P(X,Y)=(X^2+Y^2)\cdot((X-2)^2+(Y+2)^2)

Re: HSC 2014 4U Marathon - Advanced Level Look at some easier examples to picture. Area of a rectangle of fixed perimeter = xy, symmetry in x and y; volume of a cuboid of fixed surface area = xyz, symmetry in x, y and z.

Re: HSC 2014 4U Marathon - Advanced Level In this case the minimum 3/4 is given. The expression equals the min value when a=b=c, this is chosen due to symmetry, or should I say the cyclic nature of the expression. If a, b and c are different then the expression will be >= 3/4.

Re: HSC 2014 4U Marathon - Advanced Level A triangle with side lengths a, b, c is inscribed in a circle of radius 1. Prove that a+b+c>=abc.