The base of an aquarium with given volume V is made of slate and the sides are made of glass. If the slate costs three 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.)

For problems 29 - 31 the graph of a quadratic function y=ax^2 + bx + c is shown. tell whether the discriminant of ax^2 + bx + c = 0 is positive, negative, or zero.

Bradley and kelly are out flying kites at a park one afternoon. a model of bradley and kelly's kites are shown below on the coordinate plane as kites brad and kely, respectively: kites adbr and kely are shown on a coordinate plane. the vertices of adbr are a is at 9, 1; d is at 1, 5; b is at 9, 9; and r i which statement is correct about the two kites? (1 point) they are similar because segment br to segment db is 1: 2 and segment ke to segment yk 1: 2. they are not similar because segment br to segment db is 1: 5 and segment ke to segment yk is 1: 2. correct! they are not similar because segment br to segment db is 1: 2 and segment ke to segment yk is 1: 5. they are similar because segment br to segment db is 1: 5 and segment ke to segment yk is 1: 5.

∠a and ∠ b are complementary. if m∠ b = 80°, what is the measure of ∠ a? 10° 80° 90° 100°