Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter P - P.2 - Linear Models and Rates of Change - Exercises - Page 16: 23


(a) $\frac{1}{3}$ (b) $10\sqrt{10}$

Work Step by Step

(a) The slope can be found by dividing the rise by the run. The rise is 1 and the run is 3, so the slope is $\frac{1}{3}$ (b) Before finding the length of the conveyor, find the horizontal and vertical distance. The vertical distance is 10 feet. The horizontal distance can be found using the equation: $slope=\frac{vertical}{horizontal}$ $\frac{1}{3}=\frac{10}{horizontal}$ $horizontal=30$ Now the length of the conveyor can be found using the Pythagorean Theorem: $horizontal^2+vertical^2=length^2$ $30^2+10^2=length^2$ $1000=length^2$ $length=\sqrt{1000}$ $length=10\sqrt{10}$
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