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Re: HSC 2015 2U Marathon 3^{2x}+2.3^{x}-15=0 \Rightarrow (3^{x})^2+2(3^{x})-15=0 \Rightarrow (3^{x}-3)(3^{x}+5)=0 \Rightarrow x=1 . Note that the 2.3^{x} term actually means 2 \times 3^{x} .

Re: HSC 2015 3U Marathon NEW QUESTION: Prove that if m and n are positive integers, then (mn)!\geq{m^{n}(n!)^{m}} .

Re: UNSW Chit Chat Thread 2015. MATH3411 a good course?

Re: UNSW Chit Chat Thread 2015. IPT

Re: UNSW Chit Chat Thread 2015. 5 day week for me as well (that's what happens when you do a Maths/Stats major), plan for now is ACTL3141, ACTL3151, MATH3901, MATH3911 (R.I.P) not sure if I will do the MATH courses next year though, might do them in 4th year and do some relatively easier...

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread For part (a) use, \sin{B}=\sqrt{1-\cos^{2}{B}} . Use a similar method for (b) as well.

Bring everything to the LHS and factorise to get (\sqrt{3}\cos\theta+\sin\theta)(\cos\theta-\sin\theta)=0 \Rightarrow \theta=\frac{\pi}{4}, \frac{5\pi}{4}, \frac{2\pi}{3}, \frac{5\pi}{3} where 0\leq{\theta}\leq{2\pi}.

Re: HSC 2015 3U Marathon Here's is one method: http://mathschallenge.net/library/number/sum_of_cubes

Re: HSC 2015 3U Marathon The answer is 1/4. The sum 1^3+2^3+...+n^3 can be simplified to \frac{n^2(n+1)^2}{4} , which you can substitute into the expression and simplify accordingly.

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Note that \log{1}=0 , so taking the logarithm of this will give us an undefined output. We need to take values of x such that \log{x}>0 which happens only when x>1 (since log is an increasing function). Sketch a graph of...

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread The domain would be \left\{x\in\mathbb{R}|x>1\right\} i.e. the set of all positive real numbers strictly greater than 1.

Re: UNSW Chit Chat Thread 2015. I'm actually glad they're changing the structure tbh, this time I feel you will actually have time to think about what's going on when answering questions, as opposed to In-Class Quiz 1, which was primarily testing speed (they should have given 40 mins) (as...

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Because the region you are rotating is bounded by the y-axis (not x-axis), so you are taking the the difference of volumes when rotating around the x-axis. In this case you are findig the volume of solid of revolution of the...

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Take the difference volumes and you should get V={\pi}\int_{0}^{1} 5^2-(5x)^2 \text{d}x=\frac{50\pi}{3}

Re: HSC 2015 4U Marathon That's assuming |a| > 1, what happens when |a|\leq{1} ?

Re: Does dropping a course before the census date 31 August have any academic penalty According to the UNSW Enrolment Dates - Semester 2 T2 ENROLMENT deadline 2 Aug 2015, 11:59pm Last day to change T2 enrolment and timetable via myUNSW This means you can change anything (swapping lectures...

Since (x+y)^n=(y+x)^n swapping the x with y doesn't change anything, as long as it is consistent it should work. Based on what the general term is, try to find which variable goes first and which one goes second manipulate your expression from there.

Put simply, Maths and Stats at uni is much more advanced than high school, it gets increasinly deeper as you progress through your degree (I'm a 2nd year Maths/Stats major). If you really find maths interesting enough, then I'd say go for it, it's much more interesting since it's all about the...

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread That's just for the upper triangle (draw a diagram), for the lower triangle bounded between the given curves, the area is \frac{1}{2}\times{5}\times{5}=12.5 , so the total area is 12.5+0.5=13 sq. units. (No need to use...