How long would it take you to swim across a lake that is 900 meters across if you

600 seconds or equivalently 10 minutes

Explanation:

Use the formula for velocity, and solve for the unknown time (t), as follows:

Notice that all units are in the appropriate SI units, and therefore the answer for time comes in seconds.

600 seconds = 10 minutes

r = 4.24x10⁴ km.  

Explanation:

To find the radius of such an orbit we need to use Kepler's third law:

where T₁: is the orbital period of the geosynchronous Earth satellite = 1 d, T₂: is the orbital period of the moon = 0.07481 y, r₁: is the radius of such an orbit and r₂: is the orbital radius of the moon = 3.84x10⁵ km.                                                        

From equation (1), r₁ is:

Therefore, the radius of such an orbit is 4.24x10⁴ km.

I hope it helps you!