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Find the volume of the solid obtained by rotating the region enclosed by the curves y=1x and y=7^-x about the x-axis. (use symbolic notation and fractions where needed.) volume =

The coordinates of vortex a’ are (8,4) (-4,2) (4,-,4) the coordinates of vortex b’ are (6,6)(12,-,12)(12,12) the coordinates of vortex c’ are(-2,,12)(4,12)(12,-4)

The architect's side view drawing of a saltbox-style house shows a post that supports the roof ridge. the support post is 8 ft tall. the distance from the front of the house to the support post is less than the distance from the post to the back of the house. how far from the front of the house is the support post positioned?