13. Consider the solid Q drawn in the first octant, as shown below, consisting of the surfaces x = (y -3) +1, 3x + 4z =15, x=1, y=1, z=0 2 If the point density of the solid is determined by the function p(x, y, z) = 2x kg/m^3 and if the scale of the axes is in meters, then the mass of the solid is approximately: A) 52.8134 kg B) 31.8857 kg C) 21.2571 kg D) 20.5710 kg 14. Consider z as a function of the variables x, and which is defined by Z = In(x5y8) + " and let P (-1, 1) be a point. Also consider the vectors u = (a, B), w = (a, -B), such that lull = V41 . If 48V41 32V41 Duz(P) = 41 y Du=(P) = 41 determine: The value of a: The value of B:15. Let f be a function that admits continuous second partial derivatives, for which it is known that: Vf(x,y) = (4x3 - 9ry?, 36y3 - 9x y + 72y? + 36y) fix = 1202 - 972 fyy = 108y? - 9x2 + 144y + 36 y fry = -18ry Consider the critical point (a, b) with positive x-coordinate, such that said critical point generates a local minimum. Determine the value of a: Determine the value of b: 16. If f(x,y) = 23 - y' + xy - 4x + 79 then in the process of obtaining Its critical points the equation is obtained: ay" + by' + cy+d=0 Determine the value of a is: Determine the value of d is: 17. Consider the equation of the surface S given by 2xyz -x"2' + 3y = 6, where a is an odd number and B is an even number. An equation for the normal line to S at the point (-1, -1, 1) is given by: (x, y, z) = (-1, -1, 1) +t(-5, -20,7), tER The value of a is given by: The value of B is given by