10. [-/5 Points] DETAILS SCALCET9 7.1.074. MY NOTES A rocket accelerates by burning its onboard fuel, so its mass decreases with time. Suppose the initial mass of the rocket at liftoff (including its fuel) is m, the fuel is consumed at rate r, and the exhaust gases are ejected with constant velocity v, (relative to the rocket). A model for the velocity of the rocket at time t is given by the equation v(t) = gt v, In(m - rt) m where g is the acceleration due to gravity and t is not too large. If g = 9.8 m/sz, m = 28,000 kg, r = 160 kg/s, and Vo = 2,900 m/s, find the following. (a) the height of the rocket (in meters) one minute after liftoff (Round your answer to the nearest meter.) [ m (b) the height of the rocket (in meters) after it has consumed 1,000 kg of fuel (Round your answer to the nearest meter.) [ m 11. [0/5 Points] DETAILS PREVIOUS ANSWERS SCALCET9 7.1.077. MY NOTES 4 Suppose that f(1) = 2, f(4) = 6, f'(1) = 3, f'(4) = 2, and f" is continuous. Find the value of / xf"(x) dx. x