Ce Use the formula \( \omega=\frac{\theta}{t} \) to find the value of the missing variable. \( \theta=\frac{2 \pi}{3} \) radians, \( \omega=\frac{10 \pi}{11} \) radian per minute \( t=\square \min \) (Simplify your answer. Type an integer or a fraction.)

To find the value of \( t \) using the formula \( \omega = \frac{\theta}{t} \), we can rearrange the formula to solve for \( t \): \[ t = \frac{\theta}{\omega} \] Now, we can substitute the given values of \( \theta \) and \( \omega \): \[ \theta = \frac{2\pi}{3} \text{ radians} \] \[ \omega = \frac{10\pi}{11} \text{ radians per minute} \] Substituting these values into the equation for \( t \): \[ t = \frac{\frac{2\pi}{3}}{\frac{10\pi}{11}} \] To simplify this expression, we can multiply by the reciprocal of the denominator: \[ t = \frac{2\pi}{3} \times \frac{11}{10\pi} \] The \( \pi \) in the numerator and denominator cancels out: \[ t = \frac{2 \times 11}{3 \times 10} = \frac{22}{30} \] Now, we can simplify \( \frac{22}{30} \): \[ t = \frac{11}{15} \] Thus, the value of the missing variable \( t \) is: \[ \boxed{\frac{11}{15}} \text{ min} \]