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A mirror is inclined at an angle of \(\theta\) with the horizontal. If a ray of light is incident at an angle \(\theta\) as shown, then find the acute angle ...

\[1+\sin^2 ax =\cos x\]

If the above equation has infinitely many solutions, which of the following is the most general statment that is still true about \(a\)?

\[\large \displaystyle \dfrac{a}{\frac{b}{c}} = \dfrac{\frac{a}{b}}{c}\]

The above equation is a common mistake made when interpreting fractions.

How many ordered triplets of integers ...

A man crosses a river in a boat. If he crosses the river in minimum time, he takes 10 minutes with a drift \(120\text{ m}\). If he crosses the ...

\[ \large (\log_5 x)^2 + \log_{5x} \left( \frac{5}{x}\right) = 1 \]

Find the sum of all integral roots to the equation above.

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