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Hey guys, I'm wondering which of those subjects to do for my second semester. I'm a first year doing Civil Engineering/Commerce. I was considering doing CHEM1011 since I've heard it's easier than MATS1101, but MATS1101 is the recommended elective so I'm not sure if I should. Also, instead of...

http://www.dailytelegraph.com.au/newslocal/macarthur/hurlstone-agriculture-high-school-to-relocated-to-hawkesbury-in-2020/story-fngr8h70-1227613681204?nk=397c885e7bd4ed622c08b1f4bb127d82-1447815725...

Not sure if they've been uploaded yet: http://imgur.com/a/ByfFx

http://imgur.com/a/tA61F Question 11: http://imgur.com/ntz14kz

Hey can someone do this question for me: $Find the general solution(s) of $\sin{x}+\cos{x}=\cos{2x}$.

$The polynomial $x^3-3x+2=0$ has roots $\alpha, \beta, \gamma$. Find $\alpha^4+\beta^4+\gamma^4$. What's the easiest way to do this? Also, how do you do those questions where you are asked to find a polynomial with roots $\alpha^2, \beta^2, \gamma^2, given that another polynomial (e.g...

$Prove for $n\in \mathbb{N}$, that $\sqrt{n} \leq \sum_{r=1}^{n}\frac{1}{\sqrt{r}} \leq 2\sqrt{n}-1$. Not sure how to do this. Tried splitting the inequality up into \sqrt{n} \leq \sum_{r=1}^{n}\frac{1}{\sqrt{r}} and \sum_{r=1}^{n}\frac{1}{\sqrt{r}} \leq 2\sqrt{n}-1 and then prove these...

Can someone explain how you do this? Here is an example question:

School rank: 24 English Advanced: 92/131 Biology: 27/75 Chemistry: 36/106 Physics: 28/74 2U Maths: 3/104 3U Maths: 46/120

$5(i) In the expansion of $(2x+5)^{20}$ in ascending powers of $x$ show that there are two successive terms with the same coefficient, which is the greatest of any of the coefficients. Express this coefficient in index form.$ \\ \\$I've found the coefficient to be $\binom{20}{15}2^55^{15}$. and...

braintic's posts in the 3U and 4U sections reminded me that I had these: https://drive.google.com/open?id=0B_8TuhB8fbqDaUFGcXNCSDVnaDg

$Sand is pouring from a chute at the rate of 12 m^3$/$min. The falling sand forms a conical pile on the ground, whose altitude is always equal to the diameter of the base. Show that when the altitude is $h$ m, the volume $V$ m$^3$ of sand in the pile is given by $V=\frac{\pi h^3}{12}$. I...

$A moving particle has an acceleration $a$ metres per second per second at time $t$ seconds $(t\geq0)$. The acceleration of the particle is given by $a=2\pi^2\cos{(\pi t)}$. At time $t=0$, the object is at the point $x=0$ and has a velocity $v=\pi$ metres per second. \\(c) Show that the...

$If $2^x=5^y=10^z$, using logarithms to base 10, or otherwise, show that $\frac{1}{z}=\frac{1}{x}+\frac{1}{y}$.

Was looking through the 3U marathon and saw this question. Can someone help?

If you had a group of 20 unique objects, and were asked to choose 5 of those objects (where order does not matter), would the number of ways of doing this be 20C5=15504 or 20x19x18x17x16=1860480? I've been told it is the first option, but I don't see why the second option is wrong. Choosing 1...

Saw this question in an exam paper but unfortunately there were no answers. Could someone please assist? In the Michaelson and Morley experiment the pair was attempting to prove the existence of the luminiferous aether by setting up the equipment as show below. Mistakenly, they used a...

I was looking at the in2Physics@HSC textbook and saw this example question. Can someone please explain how they get the formula for number of photons per second for b.?

Hey how would you do this question without using substitution? \int \frac{1}{\sqrt{a^2-(x-b)^2}} \,dx

Hey could someone please help with the following? \textup{For the domain }-1\leq x\leq1\textup{, show that }\cos(\sin^{-1}(x))=\sqrt{1-x^2}, and also: For 14i., what exactly is the question asking me to do?