If c(x) = 19000 + 600x − 2.6x2 + 0.004x3 is the cost function and p(x) = 1800 − 8x is the demand function, find the production level that will maximize profit. (hint: if the profit is maximized, then the marginal revenue equals the marginal cost.)

Write two subtraction equations that are equivalent to 5 + 12 = 17.

There are 3232 forwards and 8080 guards in leo's basketball league. leo must include all players on a team and wants each team to have the same number of forwards and the same number of guards. if leo creates the greatest number of teams possible, how many guards will be on each team?

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?