13. [-11 Points] I DETAILS I SCALCET94.7.036. 0/100 Submissions Used MY NOTES ASK YOUR TEACHER A rectangle has its base on the X-axis and its upper two vertices on the parabola y = 25 x2. What is the largest possible area (in squared units) of the rectangle? |:| squared units 15. [-I2 Points] I DETAILS I SCALCET9 4.7.044. 0/100 Submissions Used MY NOTES ASK YOUR TEACHER A piece of wire 24 m long is cut into two pieces. One piece is bent into a square and the other is bent into a circle. (a) How much wire (in m) should be used for the square in order to maximize the total area? S m (b) How much wire (in m) should be used for the square in order to minimize the total area? Em 16. [-13 Points] DETAILS SCALCET9 4.7.053. 0/100 Submissions Used MY NOTES ASK YOUR TEACHER In a beehive, each cell is a regular hexagonal prism, open at one end; the other end is capped by three congruent rhombi forming a trihedral angle at the apex, as in the figure. Let 9 be the angle at which each rhombus meets the altitude, s the side length of the hexagon, and h the length of the longer base of the trapezoids on the sides of the cell. It can be shown that if s and h are held xed, then the volume of the cell is constant (independent of 9), and for a given value of 9 the surface area S of the cell is S = 65h gs: cot(6) + 352 csc(0) 2 \\Jopen end It is believed that bees form their cells in such a way as to minimize surface area, thus using the least amount of wax in cell construction. d5 Cl It . (a) acuaeda (b) What angle 9 should the bees prefer?+ (Round your answer to two decimal places.) |:l (c) Determine the minimum surface area of the cell (in terms of s and h). Z Note: Actual measurements of the angle 6 in beehives have been made, and the measures of these angles seldom differ from the calculated value by more than 2. 17. [-I1 Points] DETAILS SCALCET9 4.7.056. 0/100 Submissions Used MY NOTES ASK YOUR TEACHER A woman at a point A on the shore of a circular lake with radius 2 miles wants to arrive at the point C diametrically opposite A on the other side of the lake in the shortest possible time (see the gure). She can walk at the rate of 4 mi/h and row a boat at 2 mi/h. For what value of the angle 6 shown in the figure will she minimize her travel time? '3 A C 19. [-/2 Points] DETAILS SCALCET9 4.7.067. 0/100 Submissions Used MY NOTES ASK YOUR TEACHER A baseball team plays in a stadium that holds 55,000 spectators. With ticket prices at $10, the average attendance had been 16,000. When ticket prices were lowered to $8, the average attendance rose to 24,000. (a) Find the demand function (price p as a function of attendance x), assuming it to be linear. p(x) = (b) How should ticket prices be set to maximize revenue? (Round your answer to the nearest cent.) $20. [12 Points] DETAILS SCALCET9 4.7.074. 0/100 Submissions Used The frame for a kite is to be made from six pieces of wood. The four exterior pieces have been cut with the lengths indicated in the figure. To maximize the area of the kite, how long should the diagonal pieces be? 21. [-11 Points] I DETAILS l SCALCET94.7.079. 0/100 Submissions Used MY NOTES ASK YOUR TEACHER The upper right-hand corner of a piece of paper, 11 inches by 8 inches, is folded over to the bottom edge as shown in the gure. How would you fold the paper so as to minimize the length of the fold? In other words, how would you choose x (in inches) to minimize y? 22. [-11 Points] LSDETAI SCALCET9 4.7.084. 0/100 Submissions Used MY NTES ASK YOUR TEACHER A painting in an art gallery has height h and is hung so that its lower edge is a distance 0' above the eye of an observer (as in the figure). How far from the wall should the observer stand to get the best view? (In other words, where should the observer stand so as to maximize the angle 9 subtended at his eye by the painting?)