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blem 3. (i) Chris wants to build an infinitely long slide, whose height (in feet) is h(x) = 10e-², where r is the number of feet from the base. If the cross-sections of the slide are composed of squares centered at and perpendicular to the z-axis, what is the volume of the slide? You may find it helpful to use [4=√ (#)

blem 3. (i) Chris wants to build an infinitely long slide, whose height (in feet) is h(x) = 10e-², where r is the number of feet from the base. If the cross-sections of the slide are composed of squares centered at and perpendicular to the z-axis, what is the volume of the slide? You may find it helpful to use [4=√ (#)

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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Problem 3. (i) Chris wants to build an infinitely long slide, whose height (in feet) is h(x) = 10e-², where x is the number of feet from the base. If the cross-sections of the slide are composed of squares centered at and perpendicular to the x-axis, what is the volume of the slide? You may find it helpful to use [²° e ²² dx = √²/² (ii) Suppose that the concrete used to make the slide has the density 1kg/ft³, so that the mass and volume of any part of the slide are equal. Find the center of mass of the slide in z. (#)
Transcribed Image Text:Problem 3. (i) Chris wants to build an infinitely long slide, whose height (in feet) is h(x) = 10e-², where x is the number of feet from the base. If the cross-sections of the slide are composed of squares centered at and perpendicular to the x-axis, what is the volume of the slide? You may find it helpful to use [²° e ²² dx = √²/² (ii) Suppose that the concrete used to make the slide has the density 1kg/ft³, so that the mass and volume of any part of the slide are equal. Find the center of mass of the slide in z. (#)
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