Search results

$In the word MOBILITY, the letter I appears twice, and the other letters (M,O,B,L,T,Y) each appear exactly once. We have two cases.$ $\underline{Case 1: 2 I's are chosen}.$ $In this case, we can choose where to put the I's first, in $\binom{5}{2}$ ways. We now have to choose and order three...

If that were the case, they should've make the exams harder, not easier?

It's been getting easier for decades.

$Continue by exponentiating both sides, so $P = e^{kt +c} = e^c e^{kt}\Rightarrow P = Ae^{kt}$, where $A = e^c$ is a constant (it ($A$) is the value of $P$ at $t=0$).$

That is already accounted for by taking the set of values such that the radicand is non-negative, since these values don't include values of x where the radicand has 0 denominator.

For 7, the answer will be the set of values of x such that the radicand (expression inside the radical (the square root)) is non-negative.

The spectral radiance vs. frequency graph was not predicted by Classical Physics (specifically, the Rayleigh-Jeans Law) to be exponential in fact, but rather polynomial (see https://en.wikipedia.org/wiki/Rayleigh%E2%80%93Jeans_law ).

$If instead the withdrawal were said to occur at the \emph{start} of each period, the formula would be $A_{n+1}=(A_n - W)(1+r)$, since you first take away $W$, and then the interest is earned on the amount left over ($A_n - W$).$

$If they withdraw at the end of the month, the interest accumulates first, and \emph{then} the withdrawal happens. In other words, if $r$ is the per-period interest rate, $A_n$ is the amount in the account at the \textsl{end} of period $n$ ($n=0,1,2,\ldots$), and $W$ is the amount withdrawn per...

Yeah.

$This isn't true, e.g. take $x=1$, then $2x>x^2\Longleftrightarrow 2 > 1$.$

$A real logarithm $\ln (f(x))$ is defined for all values of $x\in \mathbb{R}$ such that $f(x)$ is strictly positive (because you can take the log of any positive number, but can't take logs of 0 or negative values). Since in this case, the quadratic inside the log is positive for all real $x$...

Nope

$Yes, just simplify your answer in exact form using $15^2 = 225$ and $\sin \frac{\pi}{3} =\frac{\sqrt{3}}{2}$. In fact, you should be leaving your answers in exact and simplified form, in general. Generally, you should only round the answer if they're asking for the area to a certain number of...

We can only do this if x + 5 > 0. For the case where x + 5 < 0, we must flip the inequality sign, since multiplying through by a negative number flips inequality signs.

$(The example looked like $\frac{1}{x}+5$, it'd look clearer if written with brackets, like this: )$ 1/(x+5) $And we would only be able to multiply both sides through by $x+5$ and preserve the inequality if we stated or knew that $x+5>0$.$

(Yes, in general we can't just multiply through by a variable since the variable could be negative, and that would flip the inequality.)

Possibly the p is known to be positive from the question (is it a probability or something)? If so, we can just multiply through by p.

(For those who want to see, here is the 2009 HSC 4U paper: http://www.boardofstudies.nsw.edu.au/hsc_exams/hsc2009exams/pdf_doc/2009-hsc-exam-mathematics-extension-2.pdf (the relevant question is on Page 7). Here are the Board of Studies solutions...

$It did not claim this anywhere. The net horizontal force needs to point inwards in order to have uniform circular motion.$ $This is because $T\sin \alpha$ is the horizontal component of the tension, and $N\cos \alpha$ is the horizontal component of the normal force, but this points in the...