Use the gauss-seidel method with over-relaxation (λ = 1.2) to solve the following system of linear equations to a tolerance of εs = 5 %. carry-out pivoting to ensure convergence before the iterations.
− − = −38
− − + = −34
− + − = −20
(note: show at least one complete iteration in detail, preferably the first iteration.)

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?