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Let C be the curve which is the intersection of the half-cone S1 = {(x,y,z)|z=sqrt(x^2 + y^2} and the paraboloid S2 = {(x,y,z)|2z=3-x^2-y^2}. Find C.

a)Make a 3-D sketch to show S1, S2, and C

b) Show that at each point on C the normals to these two surfaces are perpendicular to each other.

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