Calculus 8th Edition

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

Chapter 1 - Functions and Limits - 1.3 New Functions from Old Functions - 1.3 Exercises - Page 44: 58

Answer

(a) $d = 350t$ (b) $s= \sqrt{1+d^2}$ (c) $s= \sqrt{1+122500t^2}$

Work Step by Step

(a) Since speed is distance over time, we know that: $350 = \frac{d}{t}$ Which can be rearranged to: $d = 350t$ (b) The 1 mile between the plane and the radar station at $t=0$ and distance $d$ are two sides that form a triangle, where $s$ is the hypotenuse. Thus, using the Pythagorean theorem: $s^2=1^2 + d^2$ $s = \sqrt{1 + d^2}$ (c) $s$ can be expressed as a function of $t$ by inputting the equation in (a) into the equation in (s), as follows: $s = \sqrt{1 + (350t)^2}$ $s= \sqrt{1+122500t^2}$
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