Determine the coordinates of the center and the value of the ra sphere x2- y2-2- 10x - 6y - 12z --54 C(5, 3, 6), a -4 C(5, 3, 6), a- 16 O (-5, 3, -6), a- 16 C(-5, -3, -6), a-4

Which set of coordinates follows these two rules? • X-coordinate: Start with 4 and add 4 to each term. • y-coordinate: Start with 4 and multiply each term by 2. @ (4, 4), (8, 8), (12, 16) ® (4, 4), (8, 8), (16, 16) ©(4, 4), (6, 16), (8, 64) O (4, 4), (8, 6), (12, 8)

3. Complete the square for y = 4x^2 + 24x - 3 to determine the coordinates of the vertex. a. (3, 39) b. (4, 24) c. (-3, -39) d. (3, 4) I need a thorough explanation & step-by-step answer.

A tunnel is being constructed through a mountain range where the tunnel is being constructed from both ends at the same time. One end of tunnel starts at the point A (80, -287, 106) and is constructed in a straight line in the direction 2î - 8j+ 3 k whilst the other end of tunnel starts at the point B (-395,263, -89) and is constructed in a straight line in the direction 9i - 6j +2k. The starting points and the direction vectors of both ends of the tunnel are measured in metres. Verify that the tunnels being constructed from both ends meets by first finding the equations of both tunnels and then finding their intersection point P.

How would i determine whether the three points are collinear?   (0,-7), (-3,-21), (2,3)

The image of the point (8, 6)(8,6) under a translation is (13, 1)(13,1). Find the coordinates of the image of the point (-7, -5)(−7,−5) under the same translation.

Show how to find the equation otthe containing the points (2,1,-2), (-3,-8, 4) & 12,3,1).