help!!!

. Find the exact surface area of the surface obtained by rotating the curve y =1- .r2 where 0 S x S 1 about the y-axis. Suppose a two dimensional plate with uniform density occupies the region R = {(r, y)| y s sin(x) and y 2 0 and 0 S .r S It} . Find the exact coordinates of the center of mass (centroid) of the plate. Consider the curve given by the parametric equations: 2: = 42"?) y = 4: . (a) Carefully sketch (by hand) a graph of this curve. (b) Eliminate the parameter: to nd a Cartesian equation that determines the curve that you graphed in (a) (Note: you do not need to solve the equation you nd for y). Suppose the curve C is given by the parametric equations x =1+JE y =ar where r > 0. Find an equation of the tangent line to C at the point (2,2). For which values of r is the curve given by x =r3 +1 y = t2 t concave downward