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Re: HSC 2014 4U Marathon - Advanced Level Someone try this :D

Please help me with this problem

Okay good. Had the same solution but wasn't sure whether it was valid.

Sketch y = 2^x, then use the fact that the chord AB (where A(a,2^a) and B(b,2^b))lies above the curve to show that the geometric mean of two distinct positive numbers is less than their arithmeitc mean

Re: HSC 2014 4U Marathon - Advanced Level The lengths of the sides of a triangle form an arithmetic progression and the largest angle of the triangle exceeds the smallest by 90 degrees. show that the lengths of the sides of the triangle are in the ratio 7^(1/2) -1 : 7^(1/2):7^(1/2)+1

A simpler method is by oserving that triangle CAB is right angled at A (since the tangent to a radius is perpendicular). Then by pytahogras' theorem, AB^2 + AC^2 = BC^2

Okay I was hoping someone would answer your questions so i just ignored this thread but no body answered so...... Question 1) Once you construct a tangant at the point A, you just need to alt segment theorem and the angle sum of a triangle to figure this out. If you still need help, PM me...

Same lol. The question that follows (24 b)~c))requires a little more thinking, but it's still not that hard. Oh yeah and sorry bringing a dead thread lol. Was just bored and doing some maths after dinner

Just sub in the values of k you found in part 2, then sub into the coordinates of K you found in part a. . this will give you the coordinates of U and V (since there are two values of k). After that, deducing that they divide the interval Pq internally and externally in the same ratio is easy.

Question's not hard tbh i can't really see how you would end up with a 'complex fraction with many p's'

What?A couple of my seniors told me that the state ranks are merely ranks for the external component

Hi all. i heard that in the external HSC common paper, there is no such thing as half marks. So your raw mark must be an integer right? Then please explain to me this. For instance, each person in the top ten list is differentiated from another by 1 mark right??? That equates to a difference...

Re: HSC 2014 4U Marathon - Advanced Level BTw sy you made a silly in your response to my previous question, part A. you wrote -h+2 but it should be -h-2. But it doesn't really matter

Re: HSC 2014 4U Marathon - Advanced Level given that a>0, and b>0, prove that Integral(a->0) ln(x+1)dx + Integral(b->0) (e^x-1)dx is greater or equal to ab

Re: HSC 2014 4U Marathon I don't think anyone answered this so i'll answer it. Angle BKP = Angle BCA (subtended by same arc) Angle BCA = Angle BHK (exterior angle of cyclic quad) BP is common, and Angle BPH and Angle BPK are both 90 So triangle BPK is congruent to triangle BHP...

Re: HSC 2014 4U Marathon - Advanced Level Don't know how to use Latex so.... Given that f'(1) = 2, f(1) = 1, evaluate the following the limits A) Limit x->1 ( (f(x)-x^2*f(1)) / sin(x-1) ) B) Lim x->0 ( (f(2-cosx)-f(1)) / x^2)

PRove that in general that if P,Q,R and S are four colliear points such that Q divides PR internally in the same ratio as S divides PR externally, then R divides QS internally in the same ratio as P dividies QS externally. I know what I'm supposed to do, but I don't arrive at the answer...

Re: HSC 2014 4U Marathon - Advanced Level [/B] I was able to prove that if the intersection lies on the secant, the products would be equal. But is the bolded part really enough to show the converse is true? I posted the question because i had difficulty with the converse.

Re: HSC 2014 4U Marathon - Advanced Level 'Prove that the tangents at oppositve vertices of a cyclic quadrilateral intersect on the secant through the other two vertcies IF AND ONLY IF the two products of opposite sides of the cyclic quadrilateral are equal