Ling makes bracelets and necklaces and sells them at different craft fairs. The table shows how much string is used to make each item. PieceString Needed (in.)
bracelet 712
small necklace 15
large necklace 1914

Ling plans to make at least 20 bracelets. Write and solve an inequality to determine the minimum length of string that she needs to buy.

Ling will need at least
inches of string.

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?