52. Suppose you need to know an equation of the tangent plane to a surface S at the point P(2, 1, 3). You don't have an equation for S but you know that the curves \"(22) = (2 313,1 t2, 3 4t + t2) r2(u) = (1u2,2'u3 1,211+ 1) both lie on S. Find an equation of the tangent plane at P. 42. The radius of a right circular cone is increasing at a rate of 1.8 in/s while its height is decreasing at a rate of 2.5 in/s. At what rate is the volume of the cone changing when the radius is 120 inches and the height is 140 inches? 46. A manufacturer has modeled its yearly production function P (the value of its entire production, in millions of dollars) as a Cobb-Douglas function P(L, K) = 1.47L0~"5K0-35 where L is the number of labor hours (in thousands) and K is the invested capital (in millions of dollars). Suppose that when L = 30 and K = 8, the labor force is decreasing at a rate of 2000 labor hours per year and capital is increasing at a rate of $500,000 per year. Find the rate of change of production