Use the formula $\omega=\frac{\theta}{t}$ to find the value of the missing variable.
$\theta=\frac{2 \pi}{3}$ radians, $\omega=\frac{3 \pi}{7}$ radian per minute
$\mathrm{t}=\square \min$ (Simplify your answer. Type an integer or a fraction.)
Answer
Final Answer: \(\boxed{\frac{14}{9}}\) minutes.
Step 1 ：We are given the formula \(\omega=\frac{\theta}{t}\) and we need to find the value of t. We can rearrange the formula to solve for t as follows: \(t=\frac{\theta}{\omega}\).
Step 2 ：We can then substitute the given values of \(\theta\) and \(\omega\) into the formula to find the value of t.
Step 3 ：Substituting the given values, we get \(t=\frac{2 \pi/3}{3 \pi/7}\).
Step 4 ：Simplifying the above expression, we get \(t=\frac{14}{9}\).
Step 5 ：Final Answer: \(\boxed{\frac{14}{9}}\) minutes.
