College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 2 - Section 2.5 - Variation - 2.5 Assess Your Understanding - Page 192: 21

Answer

$F=6.67\displaystyle \times 10^{-11}\cdot\frac{mM}{d^{2}}$

Work Step by Step

$y$ varies ${\bf directly}$ with $x,$ or $y$ is directly proportional to $x$, if there is a nonzero number $k$ such that$ \ \ y=kx.$ The number $k$ is called the constant of proportionality. $y$ varies ${\bf inversely}$ with $x,$ or $y$ is inversely proportional to $x,$ if there is a nonzero constant $k$ such that $\displaystyle \ \ y=\frac{k}{x}$ --- We have a combined variation: $F=k(mM)$ and $F=\displaystyle \frac{k}{d^{2}}$ The combined varion is written as $F=k\displaystyle \frac{mM}{d^{2}}$ Given that $k=G=6.67\times 10^{-11},$ it means that $F=G\displaystyle \frac{mM}{d^{2}}$ or $F=6.67\displaystyle \times 10^{-11}\cdot\frac{mM}{d^{2}}$
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