(2.) (a.) Convert the integral (x² + y²)dzdydx to cylindrical coordinates. (b.) Evaluate it.

Determine the moments of inertia of the Z-section about its centroidal xo- and yo-axes. 25 mm Answers: Ixo Yo 165 mm = = i -110 mm i 25 mm 110 mm 25 mm (106) mm 4 (106) mm4

Determine the moments of inertia of the Z-section about its centroidal xo- and yo-axes. -130 mm 21 mm yo 155 mm 21 mm 21 mm -130 mm Answers: (106) mm4 i (106) mm4 i lyo II

Q3// B Verify that dv=p°sin Ddpd0dDwhen using spherical coordinate

c) Use spherical coordinate to evaluate V1-x2 1 Vx2 + y2 + 2 dz dy dx.

Determine the coordinates of the centroid of the shaded area in millimeters. y 2 mm у 3 (0.3 х* - 2.4 х) mm X = mm mm I| ||

Use sine and cosine to parametrize the intersection of the cylinders x² + y = 81 and x? + z? = 81. Find a vector parametrization r(t) = (x(1), y(t), z(1)). (Use symbolic notation and fractions where needed. Use cosine for parametrization x variable.) x(t) = y(t) = + z(t) =

r4–x²-y² x²y dz dx dy /2-y² Jx²+y² x² + y² by converting to cylindrical coordinates.

Find the vector equation that represents the curve of intersection of the cylinder x2 + y? = 9 and the surface z = x* + y. %3D Write the equation so the (t) term contains a cos(t) term. 2(t) = 3 cos (t) y(t) = 3 sin(t) %3D z(t) = 9 cos(t) + sin (t)

I need a 3d sketch of the equation  Z=x+xsiny+xy