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 58: 136

Answer

The "dead spot" is about 215 thousand miles from the center of the earth

Work Step by Step

1. Calculate $x$, if $F = 0$. $$0 = \frac{-K}{x^2} + \frac{0.012K}{(239-x)^2}$$ $$\frac K {x^2} = \frac{0.012 K}{(239-x)^2}$$ - Multiply both dividend and divisor of the left side fraction by 0.012, we get: $$\frac {0.012K} {0.012x^2} = \frac{0.012 K}{(239-x)^2}$$ Therefore: $$0.012x^2 = (239 - x)^2$$ - Since $x$ measures distance, it can't be negative: $$\sqrt{0.012x^2} = \sqrt{(239 - x)^2}$$ $$0.1095x = 239 - x$$ $$0.1095x + x = 239$$ $$1.1095x = 239$$ $$x = \frac{239}{1.1095} = 215$$
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