The rotational speed of a driven gear is inversely proportional to the number of teeth on the gear. You are replacing a 200 tooth gear which runs at 500 RPM with a gear that runs at 2,000 RPM. How many teeth does the new gear have?

Two conductors, a and b, are each in the shape of a tetrahedron. but of different sizes. they are charged in the following manner: 1. tetrahedron a is charged from an electrostatic generator to charge q. 2. tetrahedron a is briefly touched to tetrahedron b. 3. steps 1 and 2 are repeated until the charge on tetrahedron b reaches a maximum value. if the charge on tetrahedron b was q/4 after the first time it touched tetrahedron a. what is the final charge qbmax on tetrahedron b?