Iた The planet Uranus has a radius of 16000 miles and rotates one revolution every 16 hours, What is the linear speed of a point on its equator, in miles per hour? The linear speed is approximately \( \square \) miles per hour. (Round to the nearest integer as needed.)

To calculate the linear speed of a point on the equator of Uranus, follow these steps: 1. **Calculate the Circumference:** The circumference \( C \) of a planet is given by: \[ C = 2\pi r \] where \( r \) is the radius. For Uranus: \[ C = 2 \times \pi \times 16,000 \text{ miles} \approx 100,530.96 \text{ miles} \] 2. **Determine the Linear Speed:** The linear speed \( v \) is the circumference divided by the rotation period \( T \): \[ v = \frac{C}{T} \] Given that Uranus completes one revolution every 16 hours: \[ v = \frac{100,530.96 \text{ miles}}{16 \text{ hours}} \approx 6,283.19 \text{ miles per hour} \] 3. **Round to the Nearest Integer:** Rounding \( 6,283.19 \) to the nearest integer gives: \[ v \approx 6,283 \text{ miles per hour} \] **The linear speed is approximately \( 6,\!283 \) miles per hour.**