Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 2 - Derivatives - 2.7 Rates of Change in the Natural and Social Sciences - 2.7 Exercises - Page 179: 20

Answer

(a) $\frac{dF}{dr}$ = $-2\frac{GmM}{r^{3}}$ the minus mean the distance increases, the force decreases (b) $16$ $N/km$

Work Step by Step

(a) $\frac{dF}{dr}$ = $-2\frac{GmM}{r^{3}}$ the minus mean the distance increases, the force decreases (b) $F'(r)$ = $-2\frac{GmM}{r^{3}}$ $F'(20,000)$ = $-2\frac{GmM}{(20000)^{3}}$ $2$ = $-2\frac{GmM}{(20000)^{3}}$ $GmM$ = $-(20000)^{3}$ $F'(10,000)$ = $-2\frac{-(20000)^{3}}{(10000)^{3}}$ $F'(10,000)$ = $16$ $N/km$
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