If $[\sin x] +[\frac{x}{2 π}] + [\frac{2x}{5 π}]= \frac{9x}{10π}$, then the number of solutions in the interval (30, 40) is _____.
Answer & explanation
The given equation is valid, if
$\frac{9x}{10π}$ is an integer
$⇒x=10π,20π,30π, ...$
$⇒x=10π$ $[∵30<x<40]$
Hence, the given equation has only one solution.