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Re: HSC 2016 3U Marathon Prove that a+b< c*sqrt(2) if a,b are two sides of a right angled triangle and c is the hypotenuse.

Triangle inequality

Re: UNSW chit chat thread 2016 Oo I was in the Ainsworth Building when the alarm started ringing and yeah everyone just walked out slowly

$ Draw up a circle with radius one and centre at the origin$ $Draw a line from the origin to the circumference of the circle in the second quadrant.$ ($This will satisfy the condition$ \ \frac{\pi}{4} < \theta < \pi ) $Understand that$ \ \cos \theta \ $can be found by drawing a line down...

edit \frac{x^2 - 1}{x} - \frac{18x}{x^2 - 1} = 3 x \neq 0, \pm 1 $ multiplying by$ x(x^2 - 1) $throughout$ \Rightarrow (x^2 - 1)^2 - 18x^2 = 3x(x^2 - 1) (x^2 - 1)^2 - 18x^2 - 3x(x^2 - 1) = 0 x^4 - 2x^2 + 1 - 18x^2 - 3x^3 + 3x = 0 x^4 - 3x^3 - 20x^2 + 3x + 1 $Notice the...

\sqrt{ax+b} \geq 0 $for real values of a,b and all x in its domain$ \Rightarrow \frac{1}{\sqrt{ax+b}} > 0

Because for |x-2|, for any number x>2 then x-2 > 0 and since x-2 > 0 then |x-2| = +(x-2) If x<2 then x-2<0 so |x-2| = -(x-2) = 2-x

I think your inbox is full haha

$ let $ y = \ln (\ln \left(e^{x}\right)) $ then $ y = \ln (x \ln e ) = \ln x $so$ y' = \frac{1}{x}

play magnus, reddit is fun, tripview, youtube

i believe yr 11 and yr 12 lets u join even if you failed the one given in yr 7 to 9

Around an hour for me. Couple of friends are having 1.5hr travel times

Re: HSC 2016 MX2 Combinatorics Marathon Satisfy the condition first (group the R's) so that they look like RRREEAANG Treat the Rs as one group and so there are 7 'groups'. Arranging these groups, the amount of ways this is possible is 7!/(2!2!) (Dividing by 2! And 2! because there are two of...

I don't think I looked at your profile before this?

Re: MX2 2016 Integration Marathon Not a fan of IBP so I think there would be an alternate method $ let $ y^3 = x 3y^2 dy = dx $I$ = \int \cot ^{-1} y * 3y^2 dy $Using IBP, letting u $ = \cot ^{-1} y $and$ dv = 3y^2 dy $I$ = y^3 \cot ^{-1}y + \int \frac{y^3}{y^2 + 1} dy = y^3...

Re: HSC 2016 3U Marathon $Question 1$ $ When the area in square units of an expanding circle is increasing twice as fast as its radius in linear units, what is the radius?$ $ Question 2 $ \lim_{t \rightarrow \infty} \left(4t^{2}\left(\sin \left(\frac{2}{t}\right)\right)^2 \right)

b actuarial studies @ unsw

Who else didnt get theirs yet? Did everyone here achieve their goals?

Re: Survey- Impact of mathematical education on answering simple Mathematics questio done

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread It's not a logarithm law. It's a variant of the quotient rule used in differentiation. Quotient rule: \left(\frac{u}{v}\right)' = \frac{u' v - v' u }{v^2} $ In this case, u = 1 and so u' = 0 $ Which will give you the rule...