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Sunday Afternoon Maths XXIX

 Posted on 2014-09-21 

Double derivative

What is
$$\frac{d}{dy}\left(\frac{dy}{dx}\right)$$
when:
(i) \(y=x\)
(ii) \(y=x^2\)
(iii) \(y=x^3\)
(iv) \(y=x^n\)
(v) \(y=e^x\)
(vi) \(y=\sin(x)\)?

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Equal opportunity

Can two (six-sided) dice be weighted so that the probability of each of the numbers 2, 3, ..., 12 is the same?

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Three squares

Source: Numberphile
The diagram shows three squares with diagonals drawn on and three angles labelled.
What is the value of \(\alpha+\beta+\gamma\)?

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