Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 1 - Section 1.2 - Exponents and Radicals - 1.2 Exercises - Page 24: 102

Answer

Approximation: $D = 40mi$ Actual: $D = 40.78mi$

Work Step by Step

$D=\sqrt{2*3960mi*1135ft*{1135ft}^{2}}$ $D=\sqrt{2*3960mi*0.21mi*{0.21mi}^{2}}$ This is really time-consuming, but its solvable $D=\sqrt{1603.2mi}$ Now, let us get an approximation of the square root of 1603.2: $\sqrt{1603.2}$ $= \sqrt{16032 * \frac{1}{10}}$ $= \sqrt{1002 * 16 * \frac{1}{10}}$ $=4\sqrt{1002 * \frac{1}{10}}$ $=4\sqrt{10.02 * 100 * \frac{1}{10}}$ $=40\sqrt{10.02 * \frac{1}{10}}$ $=40\sqrt{10.02 * \frac{1}{10}}$ $=40\sqrt{1.002}$ Claim this answer if I am wrong, but since the square root of 1.002 is basically just 1 (and since we have to answer in the least number of sig. figures, we may leave it at 40) $D=40$
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