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A V-shaped tube attached to the ground with its vertex. It's one leg makes an angle of \( 30 ^\circ\), and the other leg makes an angle of ...

\[\large \frac{1}{a}+\frac{1}{b}=\frac{1}{100000}\]

How many distinct ordered pairs of positive integers \((a,b)\) are there which satisfy the above equation?

The denominators of two irreducible fractions are 600 and 700. Find the minimum value of the denominator of their sum when it is written as an irreducible fraction.

In the competition of Tour de France, the cyclists have to go over a parabolic hill. The leading cyclist is riding at a constant speed ...

\[\begin{eqnarray} f(15) &=& 125 \\ f(16) &=& 150 \\ f(17) &=& 210 \\ f(18) &=& 275 \\ f(19) &=& 365 \\ \end{eqnarray} \]

Let ...

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