147 1.5 Applications and Modeling with Quadratic Equations 6. Height of a Projectile If a projectile is launched vertically upward from the ground with an initial velocity of 60 ft per sec, then neglecting air resistance, its height s (in feet) above the ground t seconds after projection is given by s = -16t2 + 60t. Which equation should be used to determine the time at which the height of the projectile reaches 40 ft? A. s = -1614022 + 60 B. s = -1614022 + 601402 C. 40 = -16t2 + 60t D. 40 = -16t2 7. Height of a Projectile If a projectile is launched vertically upward from the ground with an initial velocity of 45 ft per sec, then neglecting air resistance, its height s (in feet) above the ground t seconds after projection is given by s = -16t2 + 45t. Which equation should be used to determine the height of the projectile after 2 sec? A. s = 21-16t2 + 45t2 B. s = -161222 + 45122 C. 2 = -16t2 + 45t D. 2 = -16t2 8. New Car Sales Suppose that the quadratic equation S = 0.0538x2 - 0.807x + 8.84 models sales of new cars, where S represents sales in millions, and x = 0 represents 2000, x = 1 represents 2001, and so on. Which equation should be used to determine sales in 2020? A. 20 = 0.0538x2 - 0.807x + 8.84 B. 2020 = 0.0538x2 - 0.807x + 8.84 C. S = 0.053812022 - 0.8071202 + 8.84 D. S = 0.05381202022 - 0.807120202 + 8.84 To prepare for the applications that come later, work the following basic problems that lead to quadratic equations. Unknown Numbers Use the following facts. If x represents an integer, then x + 1 represents the next consecutive integer. If x represents an even integer, then x + 2 represents the next consecutive even integer. If x represents an odd integer, then x + 2 represents the next consecutive odd integer. 9. Find two consecutive integers whose product is 56. 10. Find two consecutive integers whose product is 110. 11. Find two consecutive even integers whose product is 168. 12. Find two consecutive even integers whose product is 224. 13. Find two consecutive odd integers whose product is 63. 14. Find two consecutive odd integers whose product is 143. 15. The sum of the squares of two consecutive odd integers is 202. Find the integers. 16. The sum of the squares of two consecutive even integers is 52. Find the integers. 17. The difference of the squares of two positive consecutive even integers is 84. Find the integers. 18. The difference of the squares of two positive consecutive odd integers is 32. Find the integers.
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