The paraboloid z = 7-x-x2-3y2 intersects the plane x = 3 in a parabola. Find parametric equations in terms of t for the tangent line to this parabola at the point (3.1, -8). Use a computer to The temperature at a point (x,y) on a flat metal plate is given by T(x, y) = where I is measured in C and x, y in meters. Find the rate of change of temperature (in {: with (2 + x2 + y2)' 75 respect to distance at the point (2,1) in the x-direction and the y- direction. (a) the x-direction 5 (b) the y direction 771 graph the paraboloid, the parabola, and the tangent line on the same screen. (Enter your answers as comma-separated lists of equations. Use t as your parameter.)