A school district is planning a banquet to honor its teachers of the year and raise money for its scholarship foundation. The budget to hold the banquet in a hotel ballroom is at most $3,375. The venue can hold no more
than 125 guests. The cost is $45 per adult but only $15 per student because the caterer offers a student discount.

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?