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I know that med schools have alternate rural and indigenous pathways but I've also heard from my tutors that some universities have a bias when choosing applicants for medical school - i.e. choosing fewer asians/indians (perhaps maintaining a quota of other backgrounds hispanic, anglo-australian...

prove\ that\ the\ max\ value\ of\ |e^{i\theta}-2|+|e^{i\theta}+2|\ is\ 2\sqrt{5} How would you solve this? Apparently there are methods using geometrical graphing or using trig algebra - feel free to solve outside these methods tho. Much thanks! :D

~Much Appreciated!

Is there a technique that means opening line for "Maman died today." (The Stranger CAMUS)? Other macro/medial/micro techniques appreciated for quote thanks1

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2. Show that \left(1+x^2+2x\right)^{2n}=\sum _{k=0}^n\binom{2n}{k}x^{2n-k}\left(x+2\right)^{2n-k}.\: 3. It is known that x^{2n-k}\left(x+2\right)^{2n-k}=\binom{2n-k}{0}2^{2n-k}x^{2n-k}+\binom{2n-k}{1}2^{2n-k-1}x^{2n-k+1}+...+\binom{2n-k}{2n-k}2^{0}x^{4n-2k}. Show that \binom{4n}{2n}=\sum...

b) i. Show that for all positive integers n, x\left[\left(1+x\right)^{n-1}+\left(1+x\right)^{n-2}+...+\left(1+x\right)^{2}+\left(1+x\right)+1\right]=\left(1+x\right)^{n}-1. ii. Hence show that for 1≤k≤n, \binom{n-1}{k-1}+\binom{n-2}{k-1}+\binom{n-3}{k-1}+...+\binom{k-1}{k-1}=\binom{n}{k}...

Question and answer that I wrote = is this the correct answer/working? Thanks!

How many arrangements of the letters in the word ALGEBRAIC are possible if the vowels must occupy the 2nd, 3rd, 5th and 8th positions? ALGEBRAIC is a 9-letter word Vowels are AAEI, consonants are LGBRC I would solve this using cases: AA in 2rd, 3rd - e and i in 5th, 8th, alongisde 5 consonants...

If\:U_1=\int cot^nxdx,\:show\:that\:U_n=\frac{-1}{n-1}cot^{n-1}x-U_{n-2} I'm going to take a while to do latex so here's a picture of my working so far instead: I don't know how to work the integral on the last step. Maybe some hints? (use spoilers) Thanks so much for the help!

on such graph, impact velocity is 10sqrt21 from formula v^2 = xdot^2+ydot^2. I was just wondering, how do you know if we take the positive (as in this case) or the negative velocity? Thanks so much for your help! [edit:] Wait... maybe the answers supposed to be negative 10sqrt21 from...

It is known that z^{3}+\frac{1}{z^{3}}=w^{3}-3w. from this and the quoted solution above (|w^{2}-3|\ge|w|^{2}-3), prove by contradiction that |z^{3}+\frac{1}{z^{3}}|\le2\ \to|z+\frac{1}{z}|\le2. Assuming that |w^{3}-3w|\le2\ \to|w|\le2 to be true, LHS: |w||w^{2}-3|\le2 =...

What is this course about that's different to specialising in a clinic after MD? Do you have to take it if you want to become a surgeon? When can you even register to take this course (After Undergrad Med Science? After MD?) [general confusion]

I'm a pretty skinny (decently low body fat BMI 18) guy and I'm getting stomach creases from poor posture - I sit down for most of my day and mainly do lots of work on a laptop or with physical notes. Any tips for better posture and fewer stomach creases?

Evaluate \int _0^{\frac{\pi }{4}}\:sec^4x I know if I(n) = \int \:cos^n\left(x\right)dx then I(n) = \frac{1}{n}sin\left(x\right)cos^{n-1}\left(x\right)+\frac{n-1}{n}I\left(n-2\right) but how would we adapt that to sec^4x? Thanks for the help in advance!

Let z be a complex number. Let w=z+\frac{1}{z}. Show that \left|w^2-3\right|>\left|w\right|^2-3. LHS = \left|z^2+2+\frac{1}{z^2}-3\right| = \left|2cos\left(2\theta \right)-1\right| = 4cos^2x-2-1 = \left(2cos\theta \right)^2-3 RHS = \left|z+\frac{1}{z}\right|^2-3 = \left(2cos\theta \right)^2-3...

Let a, b be complex numbers that satisfy \frac{a}{b}+\frac{b}{a}+1=0. i) Prove that \frac{a^{3n}}{b^{3n}}+\frac{b^{3n}}{a^{3n}}=2 for n≥1, by using Mathematical Induction. - I proved true for n=1 and assumed true for n=k, just need help with Proving true for n=k+1 ii) Show that...

1992 3U HSC Q6c)ii) Show that 1-\frac{1}{2}\binom{n}{1}+\frac{1}{3}\binom{n}{2}-...+\left(-1\right)^{n}\frac{1}{n+1}\binom{n}{n}=\frac{1}{n+1} from 1+\binom{n}{1}x+\binom{n}{2}x^{2}+...+\binom{n}{n}x^{n}=\left(1+x\right)^{n}, I integrated both sides to get...

I was just wondering how I would paste the code in [e.g. \frac{1}{2}+\sin \left(\frac{\frac{\left(2n+1\right)}{2}\theta }{\:2sin\left(\frac{\theta }{2}\right)}\right) ] BoS with the latex formatting to make it come out as maths form? [I'm just very confused with usage of latex in general goog...

q6c 1990 3u HSC hints to start ii)? Much thanks