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From the figure above, find the area of the coloured regions \(x + y\) to two decimal places. Use \(\pi \approx \frac{22}{7}\).

Let \(\theta \) be an acute angle which satisfies the equation \[\sum_{n = 0}^{\infty} \sin^{2n + 1} \theta = 1.\] The value of \( 2 \, \tan^8 \theta \) can be expressed in ...

A construction worker is building a straight walking path that is 5m long from a client's front door to the sidewalk. The path is to be built out of ...

Let \(x, y, z\) be the real roots of the cubic equation

\[2u^3-799u^2-400u-1=0\]

and let \(\omega = \tan^{-1} x+\tan^{-1} y+\tan^{-1} z\). If ...

What is the remainder when

\[ \sum_{i=1}^{101} i! i \]

is divided by \(101\)?

This problem is posed by Budi U.

Details and assumptions

You may use the fact ...

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