Posted in podcasts

In the 71st episode of Wrong, But Useful, we’re joined by @nookiedv, who is Anouk de Vos in real life. We discuss: Number of the podcast: 1729, a fairly uninteresting number. Sums of cubes updates: 33 42 3 is also interesting as there are two solutions but it’s unknown if

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Posted in ask uncle colin

Dear Uncle Colin, I just solved $2\cos^2(4x)=1$ between 0 and $2\pi$ and found four solutions: $\frac{1}{16}\pi$, $\frac{3}{16}\pi$, $\frac{5}{16}\pi$ and $\frac{7}{16}\pi$. The answer scheme says there are sixteen solutions! Where have I gone wrong? Have You Perhaps A Trig Identity Answer? Hi, HYPATIA, and thanks for your message! Looking at your

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Posted in Uncategorized

A puzzle via @CmonMattTHINK (Matt Enlow): There is a line that is tangent to the curve y = x^4 - x^3 at two distinct points. What is its equation? (Can you find it without calculus?) #iteachmath #math #maths #mathchat #mathschat — Matt Enlow (@CmonMattTHINK) December 21, 2018 (I think we

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Posted in ask uncle colin

Dear Uncle Colin, I have a little problem. You see, there’s this bird, A, in its nest at time $t=0$ - the nest is at $(20, -17)$ - and it travels with a velocity of $-6\bi + 7\bj$ (in the appropriate units). But there’s another bird, B, whose nest is

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Posted in number theory

My cunning plan, back last August, was sadly foiled: @christianp refused to rise to the bait. I'd written a post about finding the smallest number such that moving its final digit to the front of the number doubles its value. It turned out, to my surprise, to be 17 digits

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Posted in ask uncle colin

Dear Uncle Colin, I’m told that the graphs of the functions $f(x) = x^3 + (a+b)x^2 + 3x -4$ and $g(x) = (x-3)^3 + 1$ touch - and I need to express $a$ in terms of $b$. Can you help? - Can’t Understand Basic Introductory Calculus Hi, CUBIC, and thanks

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Posted in dome

I… I… I… *Looks up Ito’s Lemma* *Reaches for bargepole, then doesn’t touch it.* I… I… I… Oh! It says here, there’s a thing called Ivory’s Theorem1! What is Ivory’s Theorem? Despite the main paper I could find about it calling it “the famous Ivory’s Theorem”, it was fairly tricky

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Posted in ask uncle colin

Dear Uncle Colin, I need to find the area between the curves $y=16x$, $y= \frac{4}{x}$ and $y=\frac{1}{4}x$, as shown. How would you go about that? Awkward Regions, Exhibit A Hi, AREA, and thanks for your message! As usual, there are several possible approaches here, but I’m going to write up

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Posted in ninja maths

The Mathematical Ninja peered at the problem sheet: Given that $(1+ax)^n = 1 - 12x + 63x^2 + \dots$, find the values of a and n Barked: “$n=-8$ and $a=\frac{3}{2}$.” The student sighed. “I get no marks if I just write down the answer.” Snarled: “You get no

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Posted in ask uncle colin, big in finland

Dear Uncle Colin, A seven-digit integer has 870,720 as its last six digits. It is the product of six consecutive even integers. What is the missing first digit? Please Reveal Our Digit! Underlying Calculation Too Hi, PRODUCT, and thanks for your message! There are several approaches to this (as usual)

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