O Question 2 v Textbook i' Q Videos if [+] Centerville is the headquarters of Greedy Cablevision Inc. The cable company is about to expand service to two nearby towns, Springfield and Shelbyville. There needs to be cable connecting Centerville to both towns. The idea is to save on the cost of cable by arranging the cable in a Y-shaped configuation. Centerville is located at (9,0) in the my-plane, Springfield is at (O, 7), and Shelbyville is at (0, 7). The cable runs from Centerville to some point (512,0) on the sis-axis where it splits into two branches going to Springfield and Shelbyville. Find the location (2:, 0) that will minimize the amount of cable between the 3 towns and compute the amount of cable needed. Justify your answer. To solve this problem we need to minimize the following function of m: M) =: We find that f(w )has a critical number at w To verify that f(;:) has a minimum at this critical number we compute the second derivative f\"(w) and find that its value at the critical number is [: , a positive number. Thus the minimum length of cable needed is :] A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 250 cubic centimeters of soup. The sides and bottom of the container will be made of Styrofoam costing 0.04 cents per square centimeter. The top will be made of glued paper, costing 0.06 cents per square centimeter. Find the dimensions for the package that will minimize production cost. Helpful information: h : height of cylinder, r : radius of cylinder Volume of a cylinder: V : 7r'r2h Area of the sides: A : 27r'rh Area of the top/bottom: A : 717-2 To minimize the cost of the package: Height: [ ] cm X Question 4 v Textbook __' @ Videos __' [+1 Score on last try: 0 of 1 pts. See Details for more. ('3 Get a similar question You can retry this question below Major is a lifeguard and spots a drowning child 30 meters along the shore and 70 meters from the shore to the child. Major runs along the shore for a while and then jumps into the water and swims from there directly to the child. Major can run at a rate of 3 meters per second and swim at a rate of 0.9 meters per second. How far along the shore should Major run before jumping into the water in order to save the child? Round your answer to three decimal places. m... 0 Question 1 v Textbook C @ Videos C [+] For the given cost function C(39) = 25600 + 700:1: + :32 find: a) The cost at the production level 1900 :] b) The average cost at the production level 1900 I: c) The marginal cost at the production level 1900 I: d) The production level that will minimize the average cost :] e) The minimal average cost [: _ . ... au.... 0 Question 2 v Textbook @ Videos [+1 Score on last try: 0 of 1 pts. See Details for more. > Next question 8 Get a similar question You can retry this question below /f(w) = es'\" 5 (7,0) X A rectangle is constructed under the graph of f(w) :6?\" with one corner at (7,0) and one corner on the graph of an) = 68m where 0 S m S 7. Find the exact value of :1: that will maximize the area of the rectangle. X Question 1 Score on last try: 0 of 1 pts. See Details for more. > Next question Get a similar question You can retry this question below Determine the following limits. Enter DNE if a limit fails to exist, except in case of an infinite limit. If an infinite limit exists, enter co or -co, as appropriate. 4 - a . lim x->0 9 - 3x 4 - x lim x->-0 9 - 3x Determine the equation of the horizontal asymptote that corresponds to the limit as n + co. O Equation of horizontal asymptote: O No horizontal asymptote corresponds to the limit as n + co. Determine the equation of the horizontal asymptote that corresponds to the limit as n - -co. OFanation of horizontal acumntate. IX Question 2 Score on last try: 0 of 1 pts. See Details for more. > Next question Get a similar question You can retry this question below Determine the following limits. Enter DNE if a limit fails to exist, except in case of an infinite limit. If an infinite limit exists, enter co or -oo, as appropriate. -2x2 - 24 + 14x lim -3x2 + 23 + 15 - 13x -2x - 24 + 14x lim 20- -00 -3x2 + 23 + 15 - 13x Determine the equation of the horizontal asymptote that corresponds to the limit as n -> co. OEquation of horizontal asymptote: No horizontal asymptote corresponds to the limit as n - co. X Determine the equation of the horizontal asymptote that corresponds to the limit as n -> -co. O Equation of horizontal asymptote: O No horizontal asymptote corresponds to the limit as n - -co. X. Question 16 Score on last try: 0.2 of 1 pts. See Details for more. > Next question Get a similar question You can retry this question Evaluate each of the following limits. If needed, enter oo for oo and -oo for -co (a) lim (2x5) = - 00 ac - - 00 (b) lim (2x-5) OO (c) lim 7Vx = - 00 X (d) lim 74x = c->OO (e) lim 4. (0.38") = - 00 X ac - - 00 (f) lim 4 . (0.383) = (g) lim 3 In* = -00 X (h) lim 3 In x =X Question 17 v Score on last try: 0 of 1 pts. See Details for more. 8 Get a similar question You can retry this question below Determine the following limit. Enter DNE if a limit fails to exist, except in case of an infinite limit. If an infinite limit exists, enter 00 or oo, as appropriate. lim _ Sin 6512 _C] $400 9.1