Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 1 - Section 1.7 - Modeling with Equations - 1.7 Exercises - Page 80: 88

Answer

Height of the screens is $\approx 13.1in$

Work Step by Step

Using the Pythagoras theorem, we can calculate the diagonals of both screens and write them down in term $h$. Diagonal of first screen: $=\sqrt{h^2+(1.8h)^2}=\sqrt{h^2+3.24h^2}=\sqrt{4.24h^2}$ Second screen diagonal: $=\sqrt{h^2+(h+7)^2}=\sqrt{h^2+h^2+14h+49}=\sqrt{2h^2+14h+49}$ As we know, the wider screen has $3in$ wider diagonal, so we can write: $\sqrt{4.24h^2}=\sqrt{2h^2+14h+49}+3$ To avoid a lot of math/calculation, we can use graphing calculator to find $h$, that is: $h_1\approx -3.87446$; We can simply cross out this one, as height cannot be negative number. $h_2\approx 13.12596$ So, the height is $\approx 13.1in$
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