I need help finding the answers to this optimization problem and an explanation on how to find them. Find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius r.widthheightunitsunits

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Answered: Find the dimensions of the rectangle of…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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In this question, you will work step-by-step through an optimization problem. Many airlines restrict the size of carry on item in terms of their combined length, width and height (L+W+H). I am due to fly on an airline that states "The sum of the length, the width and height of your item must be at most 50 inches". Suppose I want to take a box (cuboid) on my trip that will allow me to carry on as much as possible, and that I also want this box to have a square base. The questions we will answer using optimization are: What dimensions should the box have, and what would be the resulting maximum volume? If the base of the box is a square whose sides have length x, and the height of the box is h (both measured in inches), enter expressions for the volume of the box, V, and the sum of the length, width and height of the box in terms of x and h. V : Sum L+W+H : Since the sum of the length, width and height must be less than or equal to 50 inches, and it is clearly best to choose this…

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Find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius r. width height units units