Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 3 - Section 3.4 - Real Zeros of Polynomials - 3.4 Exercises - Page 286: 105

Answer

$88in$

Work Step by Step

We have $l+4b=108$ and the volume $b^2l=2200$ using $l=108-4b$ we have $b^2(108-4b)=2200$ or $4b^3-108b^2+2200=0$ or $b^3-27b^2+550=0$ Solving this equation numerically gives two positive values $b=5, 26.2$, hence the length of the box is $l=108-4b=88in$ or $3.2in$ We discard the value of 3.2in as it does not fit the definition of the length of the box.
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