Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 4 Quadratic Functions and Factoring - 4.7 Complete the Square - 4.7 Exercises - Quiz for Lessons 4.5-4.7 - Page 291: 19


$t\approx 1.68$

Work Step by Step

Write height function. $ h=-16t^{2}+h_{0}\qquad$ ...Substitute $0$ for $h$ and $45$ for $h_{0}$ $ 0=-16t^{2}+45\qquad$ ...add $16t^{2}$ to each side $ 16t^{2}=45\qquad$ ...divide both sides of the expression with $16$ $ t^{2}=\displaystyle \frac{45}{16}\qquad$ ...take square roots of each side. $ t=\pm\sqrt{\frac{45}{16}}\qquad$ ...simplify $\displaystyle \sqrt{\frac{45}{16}}=\frac{\sqrt{9\cdot 5}}{\sqrt{16}}=\frac{3\sqrt{5}}{4}$ $\qquad$ ...since we are calculating time, we can discard the negative solution $t=\displaystyle \frac{3\sqrt{5}}{4}$ $t\approx 1.68$
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