Assume S is the surface x1000 + y8000 + z1000 = 1,000,000 and F = [9 + ee^(xyz), x8yz, 3x - 5y - 6cos(zx)]. Explain why ∫∫scurl(F).dS = 0.

Please give me answer very fast in 5 min

Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y =x and y= 2- x if 8 = 4x + 9y + 2.

Which surface below is an elliptic paraboloid? O x^2 + y^2/4 - z^2 = 1 O z = -sqrt(x^2 + y^2) z = -x^2/4 - y^2 O z = y^2 - x^2/9

What is the shortest distance from the surface xy+3x+z^2=12 to the origin?

1szs 9-x² - y² and x' +y <1 Sketch the surface H.

7. Graph the surface z = f (x, y) = x ^ 2 + 2 y ^ 2 - 2x + 4y + 2. Also write the reduced equation of the intersection curve of the surface with the z = 0 plane.

Graph the surface 1 = y2 + z2 -- by first sketching at least three cross sections in each of the xy and yz planes.

sketch the solid and a washer for the graph of these two functions f(x) =2 -(x-2)^2, g(x)=-x after rotating the enclosed region around the line y=1

Find an equation of the tangent plane to the surface g(x, y) = x² - y² at the point (7,2, 45). -y O 14(x-7)+2(v-2)(z-45) = 0 O 14(x-7)+4(y-2) + (z-45) = 0 14(x-7)-4(y-2)-(z-45) = 0 O 7(x-7)-2(y-2)-(2-45)=0 O 14(x-7)-4(v-2) + (z-45) = 0