5. find the derivative matrices of the following composition of functions (a) f. g where f(x, y)= 2x -3y, g(u, v) = (usinu, usinu) (b)fg where f(x. y. 2) = (x2 + y + ,x-y+ 22), g()= (21, ,2r*) (c) f. g where f(x, y, z) = (xyz, xyxz - yz) where gu, u, w) = (uc, uu, vu)

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?