The mass of a cube in grams is M=x^3+0.1x^4, where x is the length of one side in centimeters. If the length is increasing at a rate of 0.03 cm/hr, at what rate is the mass of the cube increasing when its length is 6 cm?

Uranium has two naturally occurring isotopes. 238u has a natural abundance of 99.3% and 235u has an abundance of 0.7%. it is the rarer 235u that is needed for nuclear reactors. the isotopes are separated by forming uranium hexafluoride uf6, which is a gas, then allowing it to diffuse through a series of porous membranes. 235uf6 has a slightly larger rms speed than 238uf6 and diffuses slightly faster. many repetitions of this procedure gradually separate the two isotopes. what is the ratio of the rms speed of 235uf6 to that of 238uf6? express your answer to five significant figures.

Atruck with 34-in.-diameter wheels is traveling at 55 mi/h. find the angular speed of the wheels in rad/min, *hint convert miles to inches & hours to minutes:

In a game of pool, ball a is moving with a velocity v0 of magnitude v0 = 15 ft/s when it strikes balls b and c, which are at rest and aligned as shown. knowing that after the collision the three balls move in the directions indicated and assuming frictionless surfaces and perfectly elastic impact (that is, conservation of energy), determine the magnitudes of the velocities va, vb, and vc.