Browsing category ask uncle colin

Ask Uncle Colin: Remainders

Dear Uncle Colin, I need to find four consecutive numbers such that the first is a multiple of 5, the second a multiple of 7, the third a multiple of 9 and the fourth a multiple of 11. Can you find such a number? - Summing Up Needs Zero Intelligence

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Ask Uncle Colin: An Arcsine Inversion

Dear Uncle Colin, I’m trying to invert $y = \arcsin\br{x^2 + 4x - 5}$, but I get stuck at $x^2 + 4x = \sin(y) + 5$. Any pointers? - All Routine Calculations Should Invert Naturally Hi, ARCSIN, and thanks for your message! Just before I dive into this, I have

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Ask Uncle Colin: A Horrible-looking Limit

Dear Uncle Colin, I need to work out $\lim_{x\to\infty} \left\{ \left[ \frac{ 2^{1/x} + 8^{1/x} }{2} \right]^x \right\}$. The textbook says it’s four, but my engineering friends all get different answers. How would you work it out? - Giving Engineers Real Maths Analysis Is Naive Hi, GERMAIN, and thanks for

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Emergency Ask Uncle Colin: What happens now?

Dear Uncle Colin, I’m meant to be sitting my A-levels this summer and there’s an awful disease going around. I don’t know if school will be open next week or even if the exams will go ahead. I don’t know what that means for university. I’m scared. What do I

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Ask Uncle Colin: Long Division in Base 5

Dear Uncle Colin, I’ve been asked to show how to do $23241 \div 31$ in base 5 by long division - I can barely do it in base 10! Help! - Lots Of Number Games Hi, LONG, and thanks for your message! There are several steps to working a long

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Ask Uncle Colin: A Pointy Thing

Dear Uncle Colin, What do you call the ‘point’ of the absolute value graph - for instance, $(0,0)$ on the graph of $y=|x|$? It can’t be a minimum because the gradient is undefined! Proof Or It’s Not True Hi, POINT, and thanks for your message! I hate to go ‘well,

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Ask Uncle Colin: A Trigonometric Identity

Dear Uncle Colin, I got stuck trying to prove that $(\sec(x) - \tan(x))^2 \equiv \frac{1-\sin(x)}{1+\sin(x)}$. Can you help? - Bringing Over Is No Good! Bringing Over Is No Good! Hi, BOINGBOING, and thank you for your message! Here’s how I’d tackle it, starting from the left hand side: $\sec(x) -

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Ask Uncle Colin: The Twelve Coin Puzzle

Dear Uncle Colin, I have twelve coins, one of which is counterfeit. I don’t know if it’s heavier or lighter than the others, but I’m allowed three goes on a balance scale to determine which coin it is and whether it’s light or heavy. Can you help? Some Coins Are

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Ask Uncle Colin: A Pair of Vectors

Dear Uncle Colin, The question says "Under what circumstances does $|\mathbf{a} + \mathbf{b} | = | \mathbf{a} | + | \mathbf{b} |$ and I don’t have a clue. Can you help? Sines? Cosines? Angle Leaves A Residue Hi, SCALAR, and thanks for your message! I have several ways to approach

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Ask Uncle Colin: A horrible CDF

Dear Uncle Colin I have the set-up below - how do I find the cumulative density function for $d^2$? - Circles Don’t Fit Hi, CDF, and thanks for your message! Before I start, I’m going to make two simplifying assumptions that don’t change anything1 - that the radius of the

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