13. [0/1 Points] | DETAILS I l PREVIOUS ANSWERS I SCALCET9 4.7.036. 1/100 Submissions Used MY NOTES ASK YOUR TEACHER A rectangle has its base on the xaxis and its upper two vertices on the parabola y = 25 x2. What is the largest possible area (in squared units) of the rectangle? 96.24 squared units 3' 15. [112 Points] DETAILS PREVIOUS ANSWERS SCALCET9 4.7.044. 1/100 Submissions Used MY NOTES ASK YOUR TEACHER A piece of wire 22 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? Sm 16. [213 Points] I DETAILS I I PREVIOUS ANSWERS I SCALCET9 4.7.053. 1/100 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 6 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 6 the surface area S of the cell is S = 65h gsz cot(0) + 352 \\/ csc(9) 2 \\H'open 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. (15 I It . (a) Cacuaeda (b) What angle 9 should the bees prefer?'r (Round your answer to two decimal places.) - (c) Determine the minimum surface area of the cell (in terms of s and h). _ 3 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. [0/1 Points] | DETAILS I l PREVIOUS ANSWERS I SCALCET9 4.7.056. 1/100 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? B 3:90 3