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$\noindent If you started at $n=1$, the sum would be $a+ar$ (since it ends at $ar^n$, which is $ar$ when $n=1$). Were you just doing $a$?$

$\noindent Let the mass as a function of time be $M=M(t)$ (assume it is a smooth function). Then $\bold{F}_G = M\bold{a}_G$, where $\bold{a}_G$ is the acceleration due to gravity (which depends on position, and hence also time), and $\bold{F}_G$ is the force due to gravity on the object (again...

Re: MX2 2016 Integration Marathon $\noindent For the second one, let $I = \int _0 ^1 \frac{\mathrm{d}x}{\lfloor 1-\log_2 {(1-x)}\rfloor} =\int _0 ^1 \frac{\text{d}x}{\lfloor 1- \log_2 {x}\rfloor}$. Note $\log_2 x < 0$ for $0<x<1$, so $1- \log_2 x > 1$ for $0<x<1$. Note that for $i...

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Get everything to one side (rearrange), so that we have a quadratic expression on one side and 0 on the other.

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread $\noindent Consider separately the cases where $x <-3$, $-3\leq x \leq 2$, $x >2$. In each case, eliminate the absolute value bars appropriately. Then we just need to solve a quadratic equation for each case.$

For anyone curious, I believe this was the thread you were referring to: http://community.boredofstudies.org/238/extracurricular-topics/342550/announcement-bostes-significant-change-calculus-courses.html . (There was also another one, created by Carrotsticks, I think.)

This is a maths question?

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread $\noindent The tedious and expected way to do it is to first find the equations of the tangents at the $x$-intercepts, i.e. at the points where $x=\alpha$ and $x=\beta$ (finding these equations is done by finding the slopes at...

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread $\noindent One word: symmetry. :$\mathcal{P}$$

$\noindent We have$ $$\begin{align*} \int _{ -1 }^{ 0 }{ (3x+2)^{ 3 } } \text{ d}x &= \left[\frac{(3x+2)^{4}}{3\times 4} \right]_{ -1 }^{ 0 } \\ &= \frac{1}{12}\Big{[}(3x+2)^{4} \Big{]}_{ -1 }^{ 0 } \\ &= \frac{1}{12}\left(2^4 - (-1)^4\right) \\ &= \frac{15\color{cyan}\div 3 \color{black}}{12...

Re: HSC 2016 4U Marathon - Advanced Level $\noindent (Note that this is the case if and only if the real number $R$ is a \emph{positive} real.)

$\noindent This is not a polynomial question. This question is asking us to show that the given quantity is divisible by 3 for any integer $x$. We prove this below.$ $\noindent Call the given expression $\Psi$, and note that we can simplify it as $\Psi = 6x+2(-1)^x + (-1)^x = 6x+3(-1)^x$ (using...

Wait, so you actually need to measure conductivity? You'd need to measure the area and length then, which would be easy to screw up probably. If you have time, you should probably ask your teacher. Did your teacher say to use current divided by voltage? If so, they were telling you to calculate...

He said it's the ''second dot point on chemical earth''. Edit: said above

So yes, if you want to calculate the conductance for your piece of metal, it's just the current divided by the voltage (so the technically correct thing to do is write 'conductance' for the table heading). Here are some useful links with more info if you're curious: •...

$\noindent Conducitvity isn't the inverse of resistance, it's the inverse of \emph{resistivity}, which is an intrinsic property of the metal, whereas resistance depends on other factors like the length and cross-sectional area of the actual piece of metal. The formula connecting resistivity and...

Biology generally involves a lot of rote learning as there is usually a lot of content. (You can try using mnemonics etc. to help memorise things.)

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Base e.

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread That is correct.

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread What you have done is known as logarithmic differentiation. I don't think 2U students are expected to know this (but it is definitely handy).