# Solving Math Equations: Module 4

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MAT101, SLP4 Revised March 2012 (Dr. Rensvold) A company's costs, in millions of dollars, are given by the equation, C = x2 3x 27, where x is the number of items sold, in thousands. What are the costs when 1,000 items are sold? 1,500 items? (Hint: If the number of items sold is 1000, then x=1. C = 12 3(1) 27 C = 1.52 - 3(1.5) - 27 = 1 -3 27 = 2.25 4.5 - 27 C = -29 C = -29.25 \$29 million \$29,250,000 A company's costs, in millions of dollars, are given by the equation, C = x2 3x 27, where x is the number of items sold, in thousands. How many items must be sold for the costs to be zero? 0 = x2 -3x 27 3 Â± (-3)2 -4(1 x -27) / 2(1) 3 Â± 9+108 / 2 3 Â± 117 / 2 6.9 Approximately 6,900 items An object's height, in meters, when thrown vertically from the ground at a velocity of 80 m/s is given by the equation H = -4.9t2 + 80t. Ignoring wind resistance, what is the height of the ball after 2 seconds? 3 seconds? 10 seconds? H = -4.9(2)2 + 80(2) H = -4.9(3)2 + 80(3) H = -4.9(10)2 + 80(10) -4.9(4) + 160 -4.9(9) + 240 -4.9(100) + 800 -19.6 + 160 -44.1 + 240 -490 + 800 140.4 meters 195.9 meters 310 meters An object's height, in meters, when thrown vertically from the ground at a velocity of 80 m/s is given by the equation H = -4.9t2 + 80t. Ignoring wind resistance, how many seconds will it take the object to return to the ground? In other words, when is H = 0? 0 = -4.9t2 + 80t 0 = -4.9t + 80 -80 = -4.9t t = 16.326 seconds The distance d traveled by an object