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hat instead of having a box with square ends, you have a box with square sides so that its dimensions are h by h by w and the girth is 2h +2w. What dimensions will give the box its largest volume now? Graph the volume as a fu

hat instead of having a box with square ends, you have a box with square sides so that its dimensions are h by h by w and the girth is 2h +2w. What dimensions will give the box its largest volume now? Graph the volume as a fu

Advanced Engineering Mathematics
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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Please help me solve parts A and B of questions 21. 

Suppose that instead of having a box with square ends, you
have a box with square sides so that its dimensions are h by h
by w and the girth is 2h +2w. What dimensions will give the
box its largest volume now?
Graph the volume as a function of h and compare what you
see with your answer in part (a).

b. Graph the volume of a 108-in. box (length plus girth equals 108 in.) as a function of its length and compare what you see with your answer in part (a). (Continuation of Exercise 20.) a. Suppose that instead of having a box with square ends, you have a box with square sides so that its dimensions are h by h by w and the girth is 2h + 2w. What dimensions will give the box its largest volume now? Girth h T b. Graph the volume as a function of h and compare what you see with your answer in part (a). 22. A window is in the form of a rectangle surmounted by a semicircle. The rectangle is of clear glass, whereas the semicircle is of tinted glass that transmits only half as much light per unit area as clear glass does. The total perimeter is fixed. Find the proportions of the window that will admit the most light, Neglect the thickness of the frame.
Transcribed Image Text:b. Graph the volume of a 108-in. box (length plus girth equals 108 in.) as a function of its length and compare what you see with your answer in part (a). (Continuation of Exercise 20.) a. Suppose that instead of having a box with square ends, you have a box with square sides so that its dimensions are h by h by w and the girth is 2h + 2w. What dimensions will give the box its largest volume now? Girth h T b. Graph the volume as a function of h and compare what you see with your answer in part (a). 22. A window is in the form of a rectangle surmounted by a semicircle. The rectangle is of clear glass, whereas the semicircle is of tinted glass that transmits only half as much light per unit area as clear glass does. The total perimeter is fixed. Find the proportions of the window that will admit the most light, Neglect the thickness of the frame.
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