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Do you actually need to flip that curve? Or would any concave function suffice? Or do you need certain properties? Even if we wanted to flip that curve, there's more than one way to do it. To flip it how you want, you'd want to reflect it about a line of the form y = -x + b for some b > 0...

What was the reason he did such frequent reprinting? Was it to get mainly just to get rich??

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Yes, there is also a combinatorial proof that can be given. (Note that cj is just n choose j, from the Binomial Theorem.) $\noindent Imagine a group of $n$ males and $n$ females (total $2n$ people) from which we wish to select...

It's based on the properties of variance. If a is a constant and X is a random variable, remember that Var(aX) = a2 Var(X) and Var(X + a) = Var(X). Hence if b is also a constant, we in general have Var(a + bX) = Var(bX) = b2 Var(X).

Re: HSC 2016 2U Marathon Intuitively if two events A and B are independent, it means that knowledge about whether A happened doesn't affect the probability of B happening. For example, say someone tosses a coin and rolls a die. Let A be the even the coin landed Heads and B be the event that...

Re: HSC 2016 2U Marathon $\noindent The definition of two events $\mathcal{A}$ and $\mathcal{B}$ being independent is that $\Pr \left(\mathcal{A} \text{ and }\mathcal{B}\right) =\Pr \left(\mathcal{A} \right)\Pr \left(\mathcal{B}\right)$. If this is not the case, then the events $\mathcal{A}$...

I believe this Q. was asked here before, and answered by Sy123: http://community.boredofstudies.org/238/extracurricular-topics/321437/intermediate-value-theorem-question.html .

Re: MATH1131 help thread $\noindent It's just a standard power rule. If $y=\sqrt{x-1}$, then $y=\left(x-1\right)^{\frac{1}{2}}$. So $y^{\prime} = \frac{1}{2}\left(x-1\right)^{\frac{1}{2}-1}=...

Re: MATH1131 help thread We should get the same answer. I can't see the specific Q., but if it's that function over an interval (assuming it's well-defined there, i.e. x > 1 there), then the derivative should be what I posted.

Re: MATH1131 help thread $\noindent What is the full question? If the answers use the definition, maybe the question has something in it requiring us to do so. Incidentally, if $y=\sqrt{x-1}$, then $y^{\prime} = \frac{1}{2\sqrt{x-1}}$.$

Re: HSC Chemistry Marathon 2016 Oops careless me. I meant *, not / at the end. Thanks!

I was testing to see if the emojis stay in the quote when I reply to them.

Testing again.

Testing to see if the emojis stay.

Re: HSC Chemistry Marathon 2016 The solution's concentration of sodium carbonate is 0.2296 mol/L, and there is 0.365 L of it, so the quantity of sodium carbonate used is 0.2296 mol/L * 0.365 L = 0.083804 mol. Now that we know the quantity of sodium carbonate used to prepare Solution A, since...

Re: HSC 2016 MX2 Combinatorics Marathon $\noindent An urn contains $r$ red marbles and $g$ green marbles, where $r,g$ are fixed positive integers. Alice randomly draws $n$ marbles from the urn without replacement (where $n$ is a fixed positive integer, at most $r+g$). For $j\in \left...

Since we are only interested in 180° < θ < 270°, clearly 90° < θ/2 < 135°, so tan(θ/2) (i.e. t) has to be negative (since θ/2 is in the second quadrant). (And of course, that equation very easy to solve without t-method.)

$\noindent Hint: Recall the identities $2\cos^2 \frac{\theta}{2}=1+\cos \theta$ and $\sin \theta = 2\sin \frac{\theta}{2} \cos \frac{\theta}{2}$.$

Re: HSC 2016 2U Marathon $\noindent Your final answer is correct, but the reasoning is a bit faulty. The function $\ln |x|$ is defined when $x$ is negative. Its graph is here:$...

To see whether your calculator is in degree or radians, it should display at the top of the screen a letter "D" if it's in degrees mode, or "R" if it's in radians mode (for the usual Casio calculators).