Algebra 2 (1st Edition)

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

Chapter 4 Quadratic Functions and Factoring - 4.5 Solve Quadratic Equations by Finding Square Roots - 4.5 Exercises - Problem Solving - Page 270: 39


See below.

Work Step by Step

Each rock hits the surface when $h=0$ and the $t$'s must be positive. Thus when we take the square root, we only need to consider the positive cases. Hence: Earth: $0=-\frac{32}{2}t^2+150\\16t^2=150\\t^2=\frac{150}{16}=\frac{75}{8}\\t=\sqrt{\frac{75}{8}}$ Mars: $0=-\frac{12}{2}t^2+150\\6t^2=150\\t^2=\frac{150}{6}=25\\t=\sqrt{25}=5$ Jupiter: $0=-\frac{76}{2}t^2+150\\38t^2=150\\t^2=\frac{150}{38}=\frac{75}{19}\\t=\sqrt{\frac{75}{19}}$ Saturn: $0=-\frac{30}{2}t^2+150\\15t^2=150\\t^2=\frac{150}{15}=10\\t=\sqrt{10}$ Pluto: $0=-\frac{2}{2}t^2+150\\t^2=150\\t=\sqrt{150}$
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