Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 1 - Section 1.5 - Equations - 1.5 Exercises - Page 57: 131

Answer

(a) $S = 0.00055$ $12.018 \space m$ (b) $234.375 \space kg/m^3$

Work Step by Step

(a) 1. Find $S$, if $w = 250$: $$S = \frac{0.032(250) - 2.5}{10000} = \frac{8 - 2.5}{10000} = \frac{5.5}{10000} = 0.00055$$ 2. Calculate the length that disappears due to shrinkage: $$L_{d} = 12.025 \space m \times 0.00055 \approx 0.006614 \space m$$ 3. Find the actual length. $$L = 12.025 \space m- 0.006614 \space m = 12.018 \space m$$ (b) 1. Find $w$, if $S = 0.00050$ $$0.00050 = \frac{0.032w - 2.5}{ 10000}$$ $$(10000)(0.00050) = 0.032w - 2.5$$ $$5 = 0.032w - 2.5$$ $$5 + 2.5 = 0.032w$$ $$7.5 = 0.032 w$$ $$\frac{7.5}{0.032} = w$$ $$w = 234.375$$
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