University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 6 - Section 6.6 - Moments and Centers of Mass - Exercises - Page 390: 22


$\overline{x}=\dfrac{a}{3}$ and $\overline{y}=\dfrac{a}{3}$

Work Step by Step

We notice that the triangle with vertices $(0,0), (a,0), (0,a)$ has the x-coordinate a third of the distance $(a,0)$ from the edge, which corresponds to the $y$-axis. Also, the y-coordinate is a third of the distance of $(0,a)$, which corresponds to the $x$-axis. This means that $\overline{x}=\dfrac{a}{3}$ and $\overline{y}=\dfrac{a}{3}$
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