Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.7 - Modeling with Equations - 1.7 Exercises: 79

Answer

1) V=180feet$^{3}$ 2) 2 feet by 6 feet by 15 feet

Work Step by Step

1) Volume = (length)*(width)*(height) Therefore the volume is 180 feet$^{3}$ 2) x(x-4)(x+9)=180 $x^{3}+5x^{2}-36x=180$ $x^{3}+5x^{2}-36x-180=0$ $x^{2}(x+5)-36(x+5)=0$ $(x^{2}-36)(x+5)=0$ $(x+5)(x+6)(x-6)=0$ x+5=0; x=-5 x+6=0; x=-6 x-6=0; x=6 x=6 is the only positive answer Therefore, the box would be 2 feet by 6 feet by 15 feet.
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