A right circular cone is inscribed inside a larger right circular cone with a volume of 150 cm3. The axes of the cones coincide, and the vertex of the inner cone touches the center of the base of the outer cone. Find the ratio of the heights of the cones that maximizes the volume of the inner cone. The ratio of the height of the inner cone to the height of the outer cone is Two triangular pens are built against a barn. Three hundred twenty meters of fencing are to be used for the three sides and the diagonal dividing fence (see gure). What dimensions maximize the area of the pen? Let A be the area of the pen. What is the objective function in terms of the length of the side of the pen perpendicular to the barn, x. A = (Type an expression.) Find positive numbers x and y satisfying the equation xy = 20 such that the sum 4x + y is as small as possible. (:> Let S be the given sum. What is the objective function in terms of one number, x? S=D (Type an expression.)