13. Find an equation of the sphere with center (-3, 2, 5) and radius 4. What is the intersection of this sphere with the yz-plane?
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- 1. Determine the equation of the line through the given point (a) parallel and (b) perpendicular to the given line Given: Point: ( -1,-4) Line: 4x-2y=3(Conversion) An object’s polar moment of inertia, J, represents its resistance to twisting. For a cylinder, this moment of inertia is given by this formula: J=mr2/2+m( l 2 +3r 2 )/12misthecylindersmass( kg).listhecylinderslength(m).risthecylindersradius(m). Using this formula, determine the units for the cylinder’s polar moment of inertia.Find the equation of the parabola with focus (−4, 0) and directive x = 2
- Find a transformation of a triangle A(1, 0) B(0, 1) C(1, 1) by one unit in x and y translating directions and then rotating 45' about the origin.Determine the Miller indices of the plane that passes through three points having the following coordinates: (a) (0, 0, 1); (1, 0, 0); and (1/2, 1/2, 0) (b) (1/2, 0, 1); (1/2, 0, 0); and (0, 1, 0) (c) (1, 0, 0); (0, 1, 1/2); and (1, 1/2, 1/4) (d) (1, 0, 0); (0, 0, 1/4); and (1/2, 1, 0)4. Find the reflection of the triangle (2, 1), (6,1), (4,6) based on а. Хахis b. Y axis c. Origin d. Line x = y
- Q1: Consider a surface of revolution generated by a Bezier curve defined by the four control points P(0,0,0), (2,1,2), P₂ (3,3,0) P, (2,2,3) respectively, rotating about the X-axis. Calculate the point on the surface at u = 0.25, 0= π/2.Find the volume of the given solid Bounded by the coordinate planes and the plane 3x +2y + z = 6The quarter ring shown has a mass m and was cut from a thin, uniform plate. Knowing that ri = r2, determine the mass moment of inertia of the quarter ring with respect to (a) the axis AA', (b) the centroidal axis CC' that is perpendicular to the plane of the quarter ring. A' 12 B' C' A
- Find the equation of the plane through the point (2, 4, 5) perpendicular to the line: X-5+t, y=1+3t, z= 0+4tPoint k at end of the rod as in Fig. slides along the fixed path (x-y/30), where x and y in (mm). y coordinate of k varies according to the relation y- 4i+5t (mm). take y=20 mm, determine (a) the velocity of k; and (b) the acceleration of k. 50 mmWhat is the implicit equation of the plane through 3D points (1,0,0), (0, 1, 0), and (0, 0, 1)? What is the parametric equation? What is the normal vector to this plane?