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 z-axis, what is the volume of the slide? You may find it helpful to use [*° e ²² dx = √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. (#)
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 z-axis, what is the volume of the slide? You may find it helpful to use [*° e ²² dx = √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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Do part ii urgently
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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