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1) Find the angle between the surfaces defined by r^2=9 and x+y+z^2=1 at the point (2,-2,1).

2) The height of a hill is given by z = 2xy - 3x^2 - 4y^2 - 18x +28y +12. x is the distance east and y is the distance north of the origin. i) Where is the top of the hill and how high is it? ii) What is the angle between a vector perpendicular to the hill and the z axis? I really have no idea where to start with this one!!!