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Lesson%2026%20HW%20handout - rectangular area(Solution...

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MA153 JIN NOTE for HW 26 1. An object is projected vertically upward from the top of a building with an initial velocity of 112 ft/sec. Its distance in feet above the ground after t seconds is given by the equation Find its maximum distance above the ground. (Solution) The standard form of the quadratic function is Hence the maximum is 285. 2. Two thousand feet of chain-link fence is to be used to construct six animal cages, as shown in the figure. Express the width as a function of the length . . Hence Express the total enclosed area A of the cages as a function of . Find the dimensions that maximize the enclosed area. Change the quadratic function to the standard form Hence the maximum area is 3. A farmer wishes to put a fence around a rectangular field and then divide the field into five rectangular plots by placing four fences parallel to one of the sides. If the farmer can afford only 1,500 yards of fencing, what dimensions will give the maximum
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Unformatted text preview: rectangular area? (Solution) Similar to the problem 2. Let be the length and width of the rectangular field, respectively. Then . Thus, Thus the area The standard form of the quadratic function is Notice that we are interested in the y value which makes A maximum. Hence we don’t have to know ?? part now. Hence (width) and hence (length) 4. Flights of leaping animals typically have parabolic paths. The figure illustrates a frog jump superimposed on a coordinate plane. The length of the leap is 15 feet, and the MA153 JIN maximum height off the ground is 5 feet. Find a standard equation for the path of the frog. (Solution) The -coordinate of the parabola is , and the -coordinate of the parabola is 5. Hence the quadratic function is Since the parabola passes through the origin (0,0), Hence . Thus, . 5. [In class]...
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