The base of an aquarium with given volume v is made of slate and the sides are made of glass. if the slate costs five times as much (per unit area) as glass, use lagrange multipliers to find the dimensions of the aquarium that minimize the cost of the materials. (enter the dimensions as a comma separated list.)

There is an entrance to the computer room at point e which lies on ab and is 5 feet from point a. plot point e on the coordinate plane. find the distance from the entrance at point e to the printer at point e

The radius of the earth is two times the radius of the moon. what fraction of the volume of the earth is the volume of the moon?

Given: lines a and b are parallel and line c is a transversal. prove: 2 is supplementary to 8 what is the missing reason in the proof? statement reason 1. a || b, is a transv 1. given 2. ∠6 ≅ ∠2 2. ? 3. m∠6 = m∠2 3. def. of congruent 4. ∠6 is supp. to ∠8 4. def. of linear pair 5. ∠2 is supp. to ∠8 5. congruent supplements theorem corresponding angles theorem alternate interior angles theorem vertical angles theorem alternate exterior angles theorem