Jan, mya, and sara ran a total of 64 miles last week. jan and mya ran the same number of miles. sara ran 8 less miles than jan and mya. how many miles did sara run?

Prove sin2a + cos2a - 1 / sin2a + cos2a + 1 = 1 - tana / 1 + cota

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?

1/2+1/6-3/4 simplify the given expression leaving the answer in improper fraction form.