I'm quite confused with the racetrack principle and need on this problem. . suppose that f(t) is continuous and twice-differentiable for t> = 0. further suppose f''(t) > = 3 for all t> = 0 and f(0) = f'(0) = 0.. using the racetrack principle, what linear function g(t) can we prove is less than f'(t) (for t> = 0)? . g(t) = . then, also using the racetrack principle, what quadratic function h(t) can we prove is less than than f(t) (for t> = 0)? . h(t) = .

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?