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Aregular hexagon rotates counterclockwise about its center. it turns through angles greater than 0° and less than or equal to 360°. at how many different angles will the hexagon map onto itself?

In the diagram, points d and e are marked by drawing arcs of equal size centered at b such that the arcs intersect ba and bc. then, intersecting arcs of equal size are drawn centered at points d and e. point p is located at the intersection of these arcs. based on this construction, m , and m

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 =