Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 2 - Review - Modeling with Functions - Problems - Page 244: 32

Answer

(a ) See prove below. (b)maximum $A=60$ when $x\approx4.6$

Work Step by Step

(a )The crosspieces divide the kite into two isosceles triangles with a common base length of $2x$ and their heights are given by the Pythagorean formula $h1=\sqrt {5^2-x^2}, h2=\sqrt {12^2-x^2}$. Thus, the total area is given by $A(x)=\frac{2x}{2}h1+\frac{2x}{2}h2=x(h1+h2)=x(\sqrt {25-x^2}+\sqrt {144-x^2})$ (b) Graph the function above as shown in the figure. A maximum can be found as $A=60$ when $x=4.615\approx4.6$
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