Find the volumes of the solids generated by revolving the triangle with vertices (2,2), (2,7), and (6,7) about (a) the x-axis, (b) the y-axis, (c) the line x = 8, and (d) the line y = 2.

Q: Find the distance between the plane P:8x+3y+9%= 0 and the point (1,-5,20)

A:

Q: Find the distance from the point (2, 2, 3) to the plane 2x + 3y + 5z = 0.

A: Formula of distance of a point from a plane:

Q: Find the volume of a parallelepiped spanned by 2i - 5j - 7k, i-k and 9i – 3k.

A:

Q: 2. Consider the triangle with vertices at A = (0,0), B = (-6, –9), and C = (-15,0). (a) Find the…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: If (a,B.y) is a point at which the surface x2+y2-z²-2x+12=0 has a horizontal tangent plane, then y|…

A: As per guidelines, we will solve first question only. Let α,β,γ be the point on the surface…

Q: Consider the points A(3,-3, 2), B(6, -5,0), C(-1, –4,0), and D(6,3,-4). (a) Find the volume of the…

A:

Q: 14) Determine the distance between the parallel planes: 6z = 4y – 2x; and 9z = 1 – 3x + 6y.

A: Given:-planesP1: 6z=4y-2x2x-4y+6z=0x-2y+3z=0P2: 9z=1-3x+6y3x-6y+9z=1x-2y+3z=13To find : distance…

Q: Points A = (−5, 12, 0) and B = (13, 0, 0) are on the sphere x2 + y2 + z2 = 132. Find the distance…

A:

Q: Find the point on the plane 8x - y + 8z = 80 nearest the origin. (x, y, z) =

A: