If a, b, and c are positive constants, then the transformation x = au, y = bv, z = cw can be rewritten as 18 No = w, and hence it maps the spherical region u + 12 + w? 1 into the ellipsoidal region x2 2 2 2 + 3 +9 251 b In this exercise, perform the integration by transforming the ellipsoidal region of integration into a spherical region of integration and then evaluating the transformed integral in spherical coordinates. , where G is the region enclosed by the ellipsoid 9x² + 16y2 + z2 = 16. Give the exact answer in the form of a fraction.

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?