According to zimmels (1983), the sizes of particles used in sedimentation experiments often have a uniform distribution. in sedimentation involving mixtures of particles of various sizes, the larger particles hinder the movements of the smaller ones. thus, it is important to study both the mean and the variance of particle sizes. suppose that spherical particles have diameters that are uniformly distributed between .01 and .05 centimeters. find the mean and variance of the volumes of these particles. (recall that the volume of a sphere is (4/3)πr 3 .)

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?