According to coulomb's law, the electrostatic field e at the point (x, y,z) due to a charge q at the origin is given by the formula below. ( r = x i +y j +z k and q is a constant.) e (x, y,z) = q r r 3 (a) compute div e = 0 (b) let sa be the sphere of radius a centered at the origin and oriented outward. can we use the divergence theorem to find flux of e out of sa ? yes because e is not defined at the origin which is inside sa . yes because e satisfies the conditions of the theorem. yes because dive = 0 . no because dive = 0 . no because e is not defined at the origin which is inside sa .

Divide the following fractions 3/4 ÷ 2/3 1/2 8/9 9/8 2

Given: ∆mop p∆mop =12+4 3 m∠p = 90°, m∠m = 60° find: mp, mo

1. an economy consists of three workers: larry, moe, and curly. each works 10 hours a day and can produce two services: mowing lawns and washing cars. in an hour, larry can either mow one lawn or wash one car; moe can either mow one lawn or wash two cars; and curly can either mow two lawns or wash one car. a. calculate how much of each service is produced under the following circumstances: a. all three spend all their time mowing lawns. b. all three spend all their time washing cars. c. all three spend half their time on each activity d. larry spends half of his time on each activity, while moe only washes cars and curly only mows lawns b. using your answers to part a, draw a production possibilities frontier and label points a, b, c, and d on your graph. explain why the production possibilities frontier has the shape it does. c. are any of the allocations calculated in part a inefficient? explain.