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Hey, I saw I was reading through the 3U marathon and saw the following question: How exactly do you do this? There was a solution a post or two later which split the parabola into two branches, but I don't understand that method. Can someone please explain? Also is it possible to find the...

What does Further Trigonometry 2 include? I looked at the syllabus and I couldn't find a topic with that exact name. Do you need to know these results?: \begin{align*}sin\alpha sin\beta&=\frac{1}{2}[\cos{(\alpha-\beta)}-cos{(\alpha + \beta)}] \textup{ and similar results.}\\\sin\alpha +...

Hey, could someone please help with 2? \begin{align*}1&.\textup{ Solve the equation }2\sin^2(x)=1+\cos(2x)\textup{ for }0\leq x \leq 2\pi \\2&. \textup{ Show that if }0<x<\frac{\pi}{4}\textup{, then }\cos(2x)>2\sin^2(x)-1\end{align*} From the first question, I can see that there are no...

Could someone please help? \textup{Use mathematical induction to prove that }20^n-5^n>15^n\textup{ for }n>1.

\text{The area bounded by the parabola } y=x^2 \\ \text{, the line } y=2-x \textup{ and the x-axis is rotated about the x-axis.}\\ \textup{Find the volume of solid formed.}

Hey could someone please explain (iii)?

What exactly do you do for part (iv)?

If you had a galvanic cell with the following: Anode: Zn(s) Analyte: Zn(NO3)2(aq) Cathode: Fe(s) Cathylate: Fe(NO3)3(aq) Which of the following reduction reactions occurs?: Fe3+ + e- -> Fe2+ only Fe3+ + e- -> Fe2+ followed by Fe2+ + 2e- -> Fe(s)

Hey, was not sure if you're meant to use the power rule for part (ii).

Hey could someone please help me show the following? \text{Show that if } 0<x<\frac{\pi}{4}\text{, then } \sin{(2x)}>2\sin^2{(x)}. Thanks!

Hey could someone please help with the following induction question? Thanks!

Hey could someone help me with finding the range and domain of: y=x\arcsin{(x^2)} Also how would I graph the function? Thanks!

Hey, I didn't manage to get the right answer for these questions: Could someone please help? Thanks!

School rank: ~25 English Advanced: 117/131 Biology: 31/76 Chemistry: 44/107 Physics: 27/75 2U Maths: 5/122 3U Maths: 51/125 What English rank should I be aiming for to achieve a 97+ ATAR? I am certain that I can improve in all my science subjects and 3U Maths with sufficient practice and revision.