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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 a 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-azis, what is the volume of the slide? You may find it helpful to use Se - $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 a.

Problem 3. (i) Chris wants to build an infinitely long slide, whose height (in feet) is h(x) = 10e-², where a 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-azis, what is the volume of the slide? You may find it helpful to use Se - $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 a.

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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