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Thanks a lot! Could you also help with this one? $Prove that if $n$ is an even positive integer the coefficient of the $k$th term in the expansion of $(x+1)^n$ in descending powers of $x$ is the greatest when $k=\frac{n}{2}+1$. \\ $So far I have: $T_{k+1}=\binom{n}{k}x^{n-k}$...

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Not sure what you have done here. If you draw a graph of y=cos(x) you'll see that the only solution in that domain is x=pi.

I think you start at r=0. Not sure about the absolute value signs though. The textbook only says what I've posted.

Could someone also help with this? $If the $r$th term in the expansion of $(1+x)^n$ where $n$ is a positive integer is the greatest in absolute magnitude, show that $r$ is the first integer greater than $\frac{x(n+1)}{x+1}$.

What do you mean by other value? Thanks!

$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...

After comparing Metropolis and Nineteen Eighty-Four, what conclusions have you drawn about their intertextual perspectives relating to authority and revolution?

Evaluate the way in which representations of political events and actions alter the way in which people perceive politics and political figures.

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

1. It is addition, not additional. You should state the double bonds are broken and monomers are added across the bond. I think it can happen with triple bonds too, but I am not certain. 2. Pretty much. Not sure if you have to mention that it happens through a chemical reaction though. 3. You...

No HSC equation that I know of for that. You are looking at concentration here, so think of the equations happening in the soft drink bottle. I think it reaches equilibrium so it would flatten out near the end, rather than reach zero.

8. The tricky part of this question is the way in which the monomer is presented. It is easier to do if you condense the methyl group on the right into CH3. In the polymerisation process, the double bond opens up and monomers join up, forming a polymer. Hopefully this picture helps:

$3. The reaction happening is: Mg + 2HCl $\to$ MgCl$_2$ + H$_2$. Using $n=\frac{m}{M}$, there is roughly 0.24681 moles of Mg present. Using $c=\frac{n}{V}\to n=cV$, there is 0.2 moles of HCl present. Since Mg and HCl react in a 1:2 ratio, 0.2 moles of HCl will react with 0.1 moles of Mg. Since...

Re: HSC 2015 3U Marathon $There is an induction proof which shows that $1^3+2^3+3^3+4^3+...+n^3=\frac{n^2(n+1)^2}{4}$. If you use this, you can write the limit as: \begin{align*}\lim_{n\to\infty} \frac{1^3+2^3+3^3+4^3+...+n^3}{n^4} &= \lim_{n\to\infty} \frac{\left (\frac{n^2(n+1)^2}{4} \right...

$The profit from selling one CD is equivalent to 50\% of the cost of the CD. Thus the profit from an $\$8$ dollar CD is $\$4$, from a $\$12$ dollar CD is $\$6$ and from a $\$16$ dollar CD is $\$8$. Let the amount of $\$12$ CDs sold be $x$. The profit made from selling $x$ of these CDs is equal...

$The first thing you have to do is change the two parametric equations (in terms of $t$) you are given into a single cartesian equations. This can be achieved by eliminating $t$ from both equations and combining them. If $x=2t$, then $t=\frac{x}{2}$. Using this, we can replace the $t$ in $y$...

If you enjoy it and understand the concepts, then you should keep 2U. However, you do have to do your homework and work hard, otherwise your marks probably won't improve. That being said, if you do put in a lot of effort but your marks don't improve at all, then you should consider whether 2U is...

Is it 84?

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread $If the diameter is 10cm, then the area is $25\pi$ cm$^2$, since $A=\pi r^2$. Subbing this into the formula, we have $25\pi=\frac{1}{2}e^{kt}$, where $k\approx0.23104$. To solve for $t$: \begin{align*}25\pi&=\frac{1}{2}e^{kt}...

By "these types of questions" do you mean calculations involving equilibrium constants? If so, have a read through this: http://chemwiki.ucdavis.edu/Physical_Chemistry/Equilibria/Chemical_Equilibria/The_Equilibrium_Constant. You don't need to know about the equilibrium constant of pressure.