A shop sells matching hats and scarves. The scarves cost 1.5 times as much as the hats. Write two patterns that could represent the costs of 1,2,3,4, and 5 hats and scarves. List the first 5 terms of each pattern. Then explain how to find the cost of 6 hats and scarves using the patterns you wrote.

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?