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A locus is the description of a moving point that satisfy certain conditions. One of the most commonly used conditions for questions regarding locus is the point being equidistant from 2 other points or lines. But this is not the only condition possible for locus, you can have a point that is...

The best internet guide is at About LaTeX in this forum, you must enclose the code in [tex] code [/ tex] for [/ tex] there is ment to be no space between the forward slash and 'tex' The reason why i wrote it like that is because it would become the code (if i did it properly) ;D

P(2ap,\,ap^2) T(2aq,\,2apq - ap^2) M(x,y) = \left( \frac{ x_{1} + x_{2} }{2},\, \frac{ y_{1} + y_{2} }{2} \right) = \left( \frac{2ap +2aq}{2},\, \frac{ ap^2 + 2apq - ap^2 }{2} \right) = \left( \frac{2(ap +aq) }{2},\, \frac{ 2(apq) }{2} \right) = \left(ap +aq,\,apq \right) $Therefore the...

$The equation of the line through Q parallel to the y axis is$\,\,x = 2aq $We know that the equation of the tangent is$\,\,y=px - ap^2 $If we solve simultaniously, we can find the co-ordinate of the intersection, ie point T$ x = 2aq\;\,.\,\,.\,\,.\,\,.\, (1) y = px -...

$Proof$ x^2 = 4ay \therefore y= \frac{x^2}{4a} \frac{dy}{dx} = \frac{2x}{4a} = \frac{x}{2a} $At$\,\,P(2ap,\,ap^2) \frac{dy}{dx} = \frac{2ap}{2a} = p $The equation formula is$ \,\, y - y_{1} = m(x - x_{1}) \therefore y - ap^2 = p(x - 2ap) y - ap^2 = px - 2ap^2 y = px - ap^2

y^2 = ( \frac{1}{x} )^2 = \frac{1^2}{x^2} = \frac{1}{x^2} $this can be written also as $ x^{-2}

The best internet guide is at About LaTeX in this forum, you must enclose the code in [tex] code [/ tex] for [/ tex] there is ment to be no space between the forward slash and 'tex' (The reason why i wrote it like that is because it would become the code ;D

\frac{9^x-4^x}{9^x+6^x} \frac{(3^x)^2-(2^x)^2}{ (3\times 3)^x + (2\times 3)^x } \frac{(3^x-2^x)(3^x+2^x)}{3^x(3^x+2^x) } \frac{3^x-2^x}{3^x} $This can be the final answer, though you can write it as:$ 1 - (\frac{2}{3})^x

You just need to remember the types of stationary (turning) points $-maximum: when$\,\,\frac{dy}{dx} = 0\,\,$and$\,\,\frac{d^2y}{dx^2}<0 $-minimum: when$\,\,\frac{dy}{dx} = 0\,\,$and$\,\,\frac{d^2y}{dx^2}>0 $-inflexion: when concavity changes ie$\,\,\frac{d^2y}{dx^2}=0 $Now a horizontal...

Re: Where do you see yourself in the future? Deal! :haha:

Re: Where do you see yourself in the future? i only said it in a sarcastic way. I am aware that there are alot of people who are smarter than me. It was just a joke :D

Re: Where do you see yourself in the future? also the fields medal and the Nobel prize before 40 would be nice :D :D :D

... at my school we have 'bout 950 'dickheads' (and we only have 1100 people!)

Re: Where do you see yourself in the future? I havent really though about it much, but... I am aiming for a UAI of 99.5 or thereabouts. I will probably do 3 bachelor degrees with 1st class honors (or what ever the hell it is called???) at USYD in mathematics, physics and computer science...

^^Its called LaTeX. The best internet guide is at About LaTeX

lol

I do believe the shape in question we are looking at is a rectangular prism. The diagonal of the base of the prism is 10, one side is x. Let the other side be y; then: x^2+y^2 = 10^2 \,\,\,\,$(from pythagoras)$ \therefore y = \sqrt{100-x^2} \,\,.\,.\,. (1) $Now,$ $Volume$\,\,= x\times...

BIG DIAGRAMS! This is one of the key ingredients to solving those nasty 4 unit circle geometry problems. Draw them big. Write all necessary stuff into the diagrams. Yet keep them clean, always use rulers and compasses. It pays off to have a cleanly drawn diagram, no matter how long it takes (to...

It seams that you are suggesting that you hide your real self and pretend to act different in the real world to suit the personality of others "...because I cannot see your facial expression to gauge the reaction to what I have said" In such a case, it would seam that you act more like yourself...

If you love mathematics so much, as you claim, and the extension courses are true mathematics, as you implied, then why are you not going to do them??? I do agree that real mathematics is not being taught properly in NSW schools, but it is not going to deter me from pursuing real mathematics...