Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - 12.2 Arc Length and Speed - Exercises - Page 611: 16



Work Step by Step

Since speed is given by \begin{align*} \frac{d s}{d t}&=\sqrt{x^{\prime}(t)^{2}+y^{\prime}(t)^{2}}\\ &=\sqrt{(15)^2 \cos 5t+( 40)^2 \sin^2 5t } \end{align*} Then \begin{align*} \frac{d s}{d t}\bigg|_{t= 2} &=\sqrt{(15)^2 \cos 5\pi/4+( 40)^2 \sin^2 5\pi/4 } \\ &=\sqrt{-\frac{225\sqrt{2}}{2}+800}\approx 25.316 \end{align*}
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