Posted in ask uncle colin.

Dear Uncle Colin, I want to stretch my Year 12 Further Maths class - what extra-curricular topics would you recommend? Something To Really Engage Their Creative Reasoning Hello, STRETCH, and thanks for your message! How excellent to be looking beyond the curriculum for ways to engage and develop your young

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Posted in ask uncle colin.

Dear Uncle Colin, I’ve figured out that $x^{x^{x^{\dots}}} = 2$ when $x = \sqrt{2}$, but I’m struggling to make sense of the function - it seems to have a vertical gradient when $x = e^{\frac{1}{e}}$, but it doesn’t seem to have what I think of as an asymptote there. What

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Posted in ask uncle colin.

Dear Uncle Colin, On a recent revision course, my tutor couldn’t integrate $\int_0^{\piby2} \frac{\sin(2\theta)}{1+\cos(\theta)} \d \theta$. Can you? - Reasonable Expectation For University’s Nameless Don? Hi, REFUND! Far be it from me to disparage a fellow professional’s integration skills, especially in the heat of the moment; I frequently mistake $2\times

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Posted in ask uncle colin.

Dear Uncle Colin I wonder: at what height is the volume of a cone above that height equal to the volume below? What about the surface area? Are there any cones where it’s the same height? Finally Researching Uniformly Splitting Things Up, Mate Hi, FRUSTUM, and thanks for your message!

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Posted in ask uncle colin.

Dear Uncle Colin, Can you explain why $\frac{a+b}{c + d}$ is between $\frac{a}{c}$ and $\frac{b}{d}$? - Grinding Out Solid Proof Explaining Rationals Hi, GOSPER, and thanks for your message! As per usual, there are several methods to show this. I’m going to assume (since it hasn’t been stated) that $\frac{a}{c}$

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Posted in ask uncle colin.

Dear Uncle Colin, I need to solve $5^{2x+2} +16\cdot 15^x - 9^{x+1} = 0$ but I’ve hit a dead end! Can you help? - Puzzling Out Wild Exponent Relations Hi, POWER, and thanks for your message! From the working you sent, it looks like you’ve picked a good strategy: you’ve

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Posted in ask uncle colin, vectors.

Dear Uncle Colin, I know a 3D circle passes through $A(4,-4,5)$, $B(0,4,1)$ and $C(0,0,5)$ and I need to find its centre and radius. I could do it in 2D, but I’m a bit stuck here! Can’t Interpret Radius/Centre, Looked Everywhere Hi, CIRCLE, and thanks for your message! There are, as

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Posted in ask uncle colin.

Dear Uncle Colin, I have the graphs of $y=\sin(x)$ and $y=\cos(x)$ for $0 < x < 2\pi$. They cross in two places, and I need to find the area enclosed. I’ve figured out that they cross at $\piby 4$ and $\frac{5}{4}\pi$, but after that I’m stuck! - Probably A Simple

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Posted in ask uncle colin.

Dear Uncle Colin, My textbook gives me an arithmetic sequence that starts $3 + 8 + 13 + \dots$, and asks me to find where the sum is 1575. I’ve got it down to $\frac{-1 \pm \sqrt{63,001}}{10}$, but I don’t know how to work out that square root without a

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Posted in ask uncle colin.

Dear Uncle Colin, How would you go about factorising $6x^2 - xy - y^2 + 7x - y + 2$? - Argh! Getting Nowhere. Expression Simplification Impossible. Hi, AGNESI, and thanks for your message! I have, historically, not been a fan of these. However, I’ve recently come across a method

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