1 0/29I2O1 7Section 4.4-Oiive Carver 7, A 6it-taence uns parallel to a wall of a house at a distance of 30 ft. Find the length ofthe shortest ladde that extends from the ground, OVer the fence, to the house, Assume the verticai waIi of the house and the hoizontaI ground have inite extent. Let L be the length ofthe ladder, X be the distance from the base ofthe ladde to the fence, d be the distance fOm the fence to the house and h be the distance fom the ground to the point the laddertouches the house. What is the objective functionn tems of x? = (ype an expression.) The interval of interest of the oPjective function is (Simpiify you answer. Type your answer in intervaI notation,) The Iength of the shortest ladder is ft. (Round the final answer to the neaest tenth as needed. Round antermediate values to the nearest thousandth as needed.) 8. A rectang-e is constructed with its base on the x-aXis and two of its vertices on the paabo-a y =484 -X2. what ae the dimensions of the ectangIe with the maximum area? What is that aea? Let A be the area ofthe ectangie. What is the objective function that reIates A and x? A (Type an expression.) he interval of interest of the objective function is (SimpIify you answe. Type your answe in intervaI notation.) ln the ectangle with the maximum aea, the shorter dimensjon is about and the longe dimension is about (Round to two decimal places as needed.) The maximum aea ofthe ectangle is about (Round to two decimal piaces as needed.) 9. A cone is constructed by cutting a secto from a circuIar sheet of metal with radius 28. The cut sheet is then foIded up and welded (See figure), Find the radius and height ofthe cone with maximum voiume that can be formed in this Way Wite the oPjective function eIating V and h in a fom that does not include . V= (Type an expession. 1ype an exact answer. using 7t aS needed.) he intervai of interest of the oective function is (SimpIify your answer. Type your answer in intervaI notation.) The adius is =and the height is h= (Type exact answers, uSjng radicals as needed.) 3, a. A ectangua Pen is buiIt with one side against a bam, If 900 m offencing are used forthe othethree sides ofthe pen, What dimensions maximize the area of the pen? b, A ancher plans to make fou identical and adjacent rectangu!a PenS against a Barn barn, eaCh with an aea of 225 m2 (See figue). What ae the dimensions of each pen that minimize the amount of fence that must be used? a Let A be the area ofthe rectangular pen and let x be the length of the sides perpendicuIar to the ban. Write the ojective function in a fom that does not include the length ofthe side paalleI to the bam. A (Type an expression.) The intervaI of interest of the objective function is (SimpIify your answer Type you answer in intervaI notation" Do not use commas in the individua! endpoints.) lt) maXimize the area of the pen, the sides perpendicula to the bam should be m long and the side paa!lel to the barn shouId be m long. (Type exact answeS, uSing adicals as needed.) b. Let x be the Iength of the sides perpendicula to the bam and let L be the total length of fence needed. Write the objective function. = (Type an expression.) Theerval of interest of the objective function is (Simplify your answer. Type you answer in intervaI notation. Do not use commas in the individuai endpoints,) Tb minimize the amount offence that must be used, eaCh ofthe sides pePendicular to the ban shouId be m long and each ofthe sides paraIiel to the ban shouId be m Iong, (Type exact answers, uSing adicais as needed.) 4. A stoage shed is to be built in the shape of a box with a square base, lt is to have a vo!ume of 539 cubic feet, The concrete fo the base costs $2 per square foot, the materia! for the roof costs $9 per squae foot, and the material for the sides costs $3.50 per squae foot. Find the dimensions of the most economicai shed, Let x represent the Iength of one of the sides of the base and let C repesent the cost of the shed. What is the ojective function? C (lype an expession.) The intervai of interest of the oPjective function is (SimpIify your answer. 1ype your answe in interval notation. The Iength of one side ofthe shed's base is ft. he height ofthe shed is ft