Acargo container (in the shape of a rectangular solid) must have a volume of 480 cubic feet. the bottom will cost $5 per square foot to construct, and the sides and the top will cost $3 per square foot to construct. use lagrange multipliers to find the dimensions of the container of this size that has minimum cost.

If two metal balls each have a charge of -10^-6 c and the repulsive force between them is 1 n, how far apart are they? (coulomb's constant is k = 9.0x 10^9 n-m^2/c^2? 9.5 m 9.0 mm 9.5 cm 0.9 m .

Aplane takes off from an airport and flies to town a, located d1 = 215 km from the airport in the direction 20.0° north of east. the plane then flies to town b, located d2 = 230 km at 30.0° west of north from town a. use graphical methods to determine the distance and direction from town b to the airport. (enter the distance in km and the direction in degrees south of west.)

From center station, a train departs every 30 minutes on the fast line and a train departs every 50 minutes on the state line. if two trains depart from center station at 8: 00 a.m., one on each of the two lines, what is the next time that two trains, one on each line, will depart at the same time?