150 CHAPTER 1 Equations and Inequalities 26 in. 37. Radius Covered by a Circular Lawn Sprinkler A square lawn has area 800 ft2. A sprinkler placed at the center of the lawn sprays water in a circular pattern as shown in the figure. What is the radius of the circle? 38. Dimensions of a Solar Panel Frame Yolanda has a solar panel with a width of 26 in. To get the proper inclination for her climate, she needs a right triangular support frame that has one leg twice as long as the other. To the nearest tenth of an inch, what dimensions should the frame have? 39. Length of a Ladder A building is 2 ft from a 9-ft fence that surrounds the property. A worker wants to wash a window in the building 13 ft from the ground. He plans to place a ladder over the fence so it rests against the building. (See the figure.) He decides he should place the ladder 8 ft from the fence for stability. To the nearest tenth of a foot, how long a ladder will he need? 4 ft 2 ft 8 ft 9 ft 40. Range of Receivers Tanner and Sheldon have purchased communications receivers. If they leave from the same point at the same time, Tanner walking north at 2.5 mph and Sheldon walking east at 3 mph, how long will they be able to talk to each other if the range of the communications receivers is 4 mi? Round the answer to the nearest minute. 41. Length of a Walkway A nature conservancy group decides to construct a raised wooden walkway through a wetland area. To enclose the most interesting part of the wetlands, the walkway will have the shape of a right triangle with one leg 700 yd longer than the other and the hypotenuse 100 yd longer than the longer leg. Find the total length of the walkway. 42. Broken Bamboo Problems involving the Pythagorean theorem have appeared in mathematics for thousands of years. This one is taken from the ancient Chinese work Arithmetic in Nine Sections: There is a bamboo 10 ft high, the upper end of which, being broken, reaches the ground 3 ft from the stem. Find the height of the break. (Modeling) Solve each problem. See Example 3. Height of a Projectile A projectile is launched from ground level with an initial velocity of v0 feet per second. Neglecting air resistance, its height in feet t seconds after launch is given by s = -16t2 + v 0t. In each exercise, find the time(s) that the projectile will (a) reach a height of 80 ft and (b) return to the ground for the given value of v0. Round answers to the nearest hundredth if necessary. 43. v0 = 96 44. v0 = 128 45. v0 = 32 46. v0 = 16 Sprinkler r
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