help me solve these math problems

0 Question 41 v 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 (12, 0) in the asy-plane, Springfield is at (0, 8), and Shelbyville is at (0, 8). The cable runs from Centerville to some point (ac, 0) on the x-axis where it splits into two branches going to Springfield and Shelbyville. Find the location (:6, 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 CB: f(w) =l i We find that f(ZU) has a critical number at :13 2' I To verify that f(m) has a minimum at this critical number we compute the second derivative f"(a:) and find that its value at the critical number is' I , a positive number. Thus the minimum length of cable needed is l I Submit Question 0 Question 42 v A cylinder is inscribed in a right circular cone of height 4 and radius (at the base) equal to 6. What are the dimensions of such a cylinder which has maximum volume? 0 Question 43 v Glorious Gadgets is a retailer of astronomy equipment. They purchase equipment from a supplier and then sell it to customers in their store. The function C(m) = 2:13 + 8250w'1 l 5500 models their total inventory costs (in dollars) as a function of cc the lot size for each of their orders from the supplier. The inventory costs include such things as purchasing, processing, shipping, and storing the equipment. What lot size should Glorious Gadgets order to minimize their total inventory costs? (NOTE: your answer must be the whole number that corresponds to the lowest cost.) l What is their minimum total inventory cost? $ l Question Help: El Video Submit Question X Question 44 V Score on last try: 0 of 1 pts. See Details for more. > Next question You can retry this question below The concentration of a drug t hours after being injected is given by C(t) : t2+47' Find the time when the concentration is at a maximum. Give your answer accurate to at least 2 decimal places. 0 Question 45 v A fence 12 feet tall runs parallel to a tall building at a distance of 3 ft from the building as shown in the diagram. LADDE 12f; 3ff We wish to find the length of the shortest ladder that will reach from the ground over the fence to the wall of the building. [A] First, find a formula for the length of the ladder in terms of 6. (Hint: split the ladder into 2 parts.) Type theta for 9. new: [B] Now, find the derivative, L'(0). Type theta for (9. L'=l l [C] Once you find the value of 6 that makes L'(6) : 0, substitute that into your original function to find the length of the shortest ladder. (Give your answer accurate to 5 decimal places.) L(0min) % feet _