College essay for UC Santa Barbara has to be 500 words long but the actual essay can vary by as much as 20 words. Write an absolute value inequality that could find the range of possible number of words for the essay. |x - 20| ≤ 500
|x + 20| ≥ 500
|x + 500| ≥ 20
|x - 500| ≤ 20

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?