7. Let & be the region enclosed by the graphs of the functions given by f() = 42) and g(a) = a. Calculate the center of gravity (2,9) of A. 8. Let & be the region enclosed by the unit circle cantered at the origin and the circle with radius d centered at the point (6,0). Draw a picture of R (including pertinent labels), and then find the center of gravity of A. Does the center of gravity lie inside the larger circle? (Hint: See problem 32 of Section 6.5, on p. 406.) Explain. 9. Write down parametric equations for the portion of the circle centered at the point (0, -2) with radius 4 that lies to the loft of the y axis and is traversed in the clockwise direction when & increases Draw a picture of the situation. 10. (a) Let r > 0. The equations a = reos't and y = rain't parametrice an astroid (see Figure 6.84 in the book). Find the length Z of the astroid. (Hint: Square roots are nonnegative!) (b) Show that the astroid is alternatively the graph of a20 + y13 2/ in rectangular coordinates. Write down the formula for the length Z of the astroid in rectangular coordinates. DW FA