The height in feet above the water of a diver can be modeled by the function f(x) = -3x 2+ 6x + 24, where x is the time in seconds after the diver begins the dive. How long does it take the diver to reach the water? What is the maximum height achieved by the diver? When does it occur? How high is the diver after 2.4 seconds? When is the diver 15 feet above the water? What is a reasonable domain for this situation? What is a reasonable range?

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?