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.)

Someone answer this asap for the first five terms of a sequence are shown. 5, 11, 23, 47, 95, . . which recursive function defines the nth term in the sequence for n > 1? a. f(n) = f(n - 1) + 6 b) f(n) = f(n - 1) + 48 c) f(n) = 3 • f(n - 1) + 1 d) f(n) = 3 • f(n - 1) - 4

Astudent draws two parabolas on graph paper. both parabolas cross the x-axis at (–4, 0) and (6, 0). the y-intercept of the first parabola is (0, –12). the y-intercept of the second parabola is (0, –24). what is the positive difference between the a values for the two functions that describe the parabolas? write your answer as a decimal rounded to the nearest tenth

Estimate the time en route from majors airport (area 1) to winnsboro airport (area 2). the wind is from 340° at 12 knots and the true airspeed is 136 knots. magnetic variation is 5° east.