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David Williams @bewilda.bsky.social · 21/01/2026

127 is the first Friedman prime. My grandson and I were watching Australian Open tennis singles matches today and he asked how many players are in the main draw. My response was 128 and there has to be 127 matches to decide the winner (127 players have to lose). Tennis is so boring.

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David Williams @bewilda.bsky.social · 16/06/2025

Find the positive integer A such that exactly two of the following statements are true: (a) A + 82 is the square of an integer; (b) the last digit of A is 5; (c) A − 7 is the square of an integer.

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David Williams @bewilda.bsky.social · 24/04/2025

Consider the triangle ABC with AB = n^2, BC = 2n + 1 and AC = n(n+ 1) for all n > 1. Use the cosine rule and the sine rule to find angles B and C for at least 3 integer values of n. What do you notice? Can you prove your conjecture? What ”sublime” triangle is formed when AC = BC?

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David Williams @bewilda.bsky.social · 30/03/2025

Is this a valid approach? ∫ln(x - 4)dx = (x - 4)ln(x - 4) - ∫(x - 4)/(x - 4)dx = (x - 4)ln(x - 4) - ∫dx = (x - 4)ln(x - 4) - x + c

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David Williams @bewilda.bsky.social · 12/02/2025

It's the 43rd day of the year and it's a stifling 43⁰ C today in the city where I live. Fun fact: -40⁰ C = -40⁰ F.

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David Williams @bewilda.bsky.social · 11/02/2025

Fun fact: Today is the 42nd day of the year (Feb. 11th). 10! seconds is exactly 42 days.

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David Williams @bewilda.bsky.social · 18/01/2025

Along the lines of my previous post. Find the values of k such that the curves y = e^(-2x) and y = e^(-x) + k intersect at two points.

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David Williams @bewilda.bsky.social · 17/01/2025

From an NZQA exam. Find the value(s) of p for which the equation x -2√(x + p) = -5 has one real solution.

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David Williams @bewilda.bsky.social · 10/01/2025

Show that the area under the graph of y = x²/(x² + 4) between x = -2 and x = 2 is equal to the shade area between the square and the circle. www.desmos.com/calculator/l...

desmos.com

arctan

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David Williams @bewilda.bsky.social · 11/12/2024

The sides of a triangle are in an arithmetic progression with a common difference of 6. The largest angle is 120°. Find the exact area of the triangle (measurements in cm).

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David Williams @bewilda.bsky.social · 04/12/2024

Investigating students' "algebraic sense" - a sixth sense perhaps. Consider the function f(x)=(x^2+x+k)/(x^2-1) For what values of k will f(x) have no stationary points?

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David Williams @bewilda.bsky.social · 13/11/2024

From a final year of secondary school mathematics exam in Victoria today: For what values of b (a real constant) does the graph of the function g(x) = (x⁴ + b)/(1 - x²) have one, three or five stationary points?

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David Williams @bewilda.bsky.social · 07/11/2024

What is the measure of the largest angle of the triangle with sides, 3319, 1469 and 2331 units?

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David Williams @bewilda.bsky.social · 15/10/2024

What do you notice? The function, f(x) = √(7 - 3x) and its inverse.

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