\( 1< \) A tire is rotating 840 times per min. Through how many degrees does a point on the edge of the tire move in \( \frac{1}{7} \sec \) ?

To determine how many degrees a point on the edge of the tire moves in \(\frac{1}{7}\) seconds, we start by calculating how many rotations the tire makes in that time. 1. **Rotations per second:** Since the tire rotates 840 times per minute, we convert this to rotations per second: \[ \text{Rotations per second} = \frac{840 \text{ rotations}}{60 \text{ seconds}} = 14 \text{ rotations per second} \] 2. **Rotations in \(\frac{1}{7}\) seconds:** Now, we find out how many rotations occur in \(\frac{1}{7}\) seconds: \[ \text{Rotations in } \frac{1}{7} \text{ seconds} = 14 \text{ rotations/second} \times \frac{1}{7} \text{ seconds} = 2 \text{ rotations} \] 3. **Degrees moved in 2 rotations:** Since there are 360 degrees in one full rotation, we calculate the degrees moved in 2 rotations: \[ \text{Degrees moved} = 2 \text{ rotations} \times 360 \text{ degrees/rotation} = 720 \text{ degrees} \] Thus, a point on the edge of the tire moves through **720 degrees** in \(\frac{1}{7}\) seconds.