Calculus 10th Edition

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

Chapter 10 - Conics, Parametric Equations, and Polar Coordinates - 10.4 Exercises - Page 722: 57

Answer

$d \approx 5.62$

Work Step by Step

$$\eqalign{ & {\text{Let the points: }}\underbrace {\left( {2,0.5} \right)}_{\left( {{r_1},{\theta _1}} \right)}{\text{ and }}\underbrace {\left( {7,1.2} \right)}_{\left( {{r_2},{\theta _2}} \right)} \cr & {\text{Apply }}d = \sqrt {r_1^2 + r_2^2 - 2{r_1}{r_2}\cos \left( {{\theta _1} - {\theta _2}} \right)} \cr & d = \sqrt {{{\left( 2 \right)}^2} + {{\left( 7 \right)}^2} - 2\left( 2 \right)\left( 7 \right)\cos \left( {0.5 - 1.2} \right)} \cr & {\text{Simplifying}} \cr & d = \sqrt {4 + 49 - 28\cos \left( { - 0.7} \right)} \cr & d \approx \sqrt {53 - 21.4156} \cr & d \approx \sqrt {31.584} \cr & d \approx 5.62 \cr} $$
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