Chapter 1 - Equations and Inequalities - 1.5 Applications and Modeling with Quadratic Equations - 1.5 Exercises - Page 133: 48

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Given $s=-2.7t^2+30t+6.5$, let $s=100$, we have $100=-2.7t^2+30t+6.5$ or $2.7t^2-30t+93.5=0$ Let $a=2.7, b=-30, c=93.5$, we can get $b^2-4ac=-109.8\lt 0$ which mean that there is no real solution to the equation, that is the ball will not reach this height.