Rex Wu S22M171 Assignment 4.7 due 04/22/2022 at 08:00pm MDT 1. (1 point) Similar to 4.7.1 in Rogawski/Adams. Find the dimensions x and y of the rectangle of maximum area that can be formed from a 180-in. piece of wire. (Use decimal notation. Give your answer to at least three decimal places.) r Find the constraint and solve for y. y = Find a formula for the area in terms of x alone. A(x) = What is the interval of optimization? Is it open or closed? [?/Open/Closed] Solve the optimization problem. Maximum area is _ in Answer(s) submitted: (Use symbolic notation and fractions where needed. Give your answer in the form of comma separated list of the dimen- sions of the two sides.) . . The rectangle of maximum area has dimensions help (fractions) (incorrect) Answer(s) submitted: 2. (1 point) Similar to 4.7.12 in Rogawski/Adams. A flexible tube of length 14 m is bent into an L-shape. Where should the bend be made to minimize the distance between the two ends? (incorrect) -m. Answer(s) submitted: (incorrect) 4. (1 point) Similar to 4.7.25 in Rogawski/Adams. 3. (1 point) Similar to 4.7.17 in Rogawski/Adams. Find the angle 0 (in radians) that maximizes the area of the isosceles triangle whose legs have length /. Find the dimensions of the rectangle of maximum area that (Use symbolic notation and fractions where needed.) can be inscribed in a circle of radius r = 5.Answer(s) submitted: (incorrect) 7. (1 point) Similar to 4.7.52 in Rogawski/Adams. The rectangular plot in Figure 23 has size 100 ft by 200 ft. Pipe is to be laid from A to a point P on side BC and from there to C. The cost of laying pipe along the side of the plot is $ 44/ft and the cost through the plot is $ 80/ft (since it is underground). (a) Let f(x) be the total cost, where x is the distance from P What is the function that you are optimizing in terms of / and to B. Determine f(x), but note that f is discontinuous at x = 0 e? (Note: Input theta as theta.) (when x = 0, the cost of the entire pipe is $ 44/ft). What is the Function = minimal cost? 0 = radians help (fractions) (b) If the cost along the sides is $ 62/ft, what is the minimal cost? Answer(s) submitted: (incorrect) If you don't get this in 4 tries, you can get a hint. 5. (1 point) Answer(s) submitted: Similar to 4.7.30 in Rogawski/Adams. According to postal regulations, a carton is classified as "oversized" if the sum of its height and girth (the perimeter of (incorrect) its base) exceeds 98 in. Find the dimensions of a carton with 8. (1 point) square base that is not oversized and has maximum volume. Similar to 4.7.26 in Rogawski/Adams. (Use symbolic notation and fractions where needed.) A right circular cone has volume V = antrah and surface area S = arvr2+h2 Side length is in. help (fractions) Height is In. r Answer(s) submitted: (incorrect) 6. (1 point) Similar to 4.7.53 in Rogawski/Adams. Brandon is on one side of a river that is 80 m wide and wants to reach a point 250 m downstream on the opposite side as quickly as possible by swimming diagonally across the river and then running the rest of the way. Find the minimum amount of time if Brandon can swim at 2 m/s and run at 5 m/s. (Use decimal notation. Give your answer to at least two dec- Find the dimensions of the cone with surface area I and maxi- imal places.) mal volume. The minimum amount of time is seconds help (frac- tions