Triangle L N M is shown. Angle L N M is a right angle. An altitude is drawn from point N to point O on side L M, forming a right angle. Side L N is labeled m, side N M is labeled l, and line segment O M is labeled k. The length of N O is 4 and the length of L O is 8. What is the value of k?

Aspacecraft can attain a stable orbit 300 kilometers above earth if it reaches a velocity of 7.7 kilometers per second. the formula for a rocket's maximum velocity v in kilometers per second is vequalsminus0.0098tplusc ln upper r, where t is the firing time in seconds, c is the velocity of the exhaust in kilometers per second, and r is the ratio of the mass of the rocket filled with fuel to the mass of the rocket without fuel. find the velocity of a spacecraft whose booster rocket has a mass ratio of 20, an exhaust velocity of 2.1 km/s, and a firing time of 15 s. can the spacecraft achieve a stable orbit 300 km above earth?