Quadratics and inequalities

77 more missing numbers find two real numbers that

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77. More missing numbers. Find two real numbers that have a sum of 6 and a product of 4. 78. More missing numbers. Find two real numbers that have a sum of 8 and a product of 2. 79. Bulletin board. The length of a bulletin board is one foot more than the width. The diagonal has a length of 3 feet (ft). Find the length and width of the bulletin board. 80. Diagonal brace. The width of a rectangular gate is 2 meters (m) larger than its height. The diagonal brace measures 6 m. Find the width and height. 81. Area of a rectangle. The length of a rectangle is 4 ft longer than the width, and its area is 10 square feet (ft 2 ). Find the length and width. 82. Diagonal of a square. The diagonal of a square is 2 m longer than a side. Find the length of a side. If an object is given an initial velocity of v 0 feet per second from a height of s 0 feet, then its height S after t seconds is given by the formula S 16 t 2 v 0 t s 0 . 83. Projected pine cone. If a pine cone is projected upward at a velocity of 16 ft/sec from the top of a 96-foot pine tree, then how long does it take to reach the earth? 84. Falling pine cone. If a pine cone falls from the top of a 96-foot pine tree, then how long does it take to reach the earth? 85. Tossing a ball. A ball is tossed into the air at 10 ft/sec from a height of 5 feet. How long does it take to reach the earth? 86. Time in the air. A ball is tossed into the air from a height of 12 feet at 16 ft/sec. How long does it take to reach the earth? 87. Penny tossing. If a penny is thrown downward at 30 ft/sec from the bridge at Royal Gorge, Colorado, how long does it take to reach the Arkansas River 1000 ft below? 88. Foul ball. Suppose Charlie O’Brian hits a baseball straight upward at 150 ft/sec from a height of 5 ft. a) Use the formula to determine how long it takes the ball to return to the earth. b) Use the graph on the next page to estimate the maximum height reached by the ball. Figure for Exercise 80 6 m x 2 x dug22241_ch10a.qxd 11/10/2004 18:30 Page 637
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638 Chapter 10 Quadratic Equations and Inequalities 10-22 Solve each problem. 89. Kitchen countertop. A 30 in. by 40 in. countertop for a work island is to be covered with green ceramic tiles, except for a border of uniform width as shown in the figure. If the area covered by the green tiles is 704 square inches (in. 2 ), then how wide is the border? 90. Recovering an investment. The manager at Cream of the Crop bought a load of watermelons for $200. She priced the melons so that she would make $1.50 profit on each melon. When all but 30 had been sold, the manager had recovered her initial investment. How many did she buy originally? 91. Baby shower. A group of office workers plans to share equally the $100 cost of giving a baby shower for a coworker. If they can get six more people to share the cost then the cost per person will decrease by $15. How many people are in the original group?
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