Show that (u, v) = (8u + 3, u – v, 15u + v) parametrizes the plane 2x – y – z = 6. Then: (a) Calculate Tu , Tv, and n(u, v). (b) Find the area of S = +(D), where D = (u, v) : 0

Q: Find the distance between the planes 5x − 3y + z = 2 and 5x − 3y + z = −3

A:

Q: Find the points on the surface 1x? + 3y2 + 5z2 = 1 at which the tangent plane is parallel to the…

A:

Q: 1. Find all points Po on the ellipsoid 2x2 + 3y? + 2z2 plane x – 3y + 2z = 5. = 22 at which the…

A: To find points P0 on the ellipsoid 2x2+3y2+2z2=22   The tangent plane is parallel to the plane…

Q: Find the area of the surface 2x^(3/2) + 2y^(3/2) - 3z = 0 above the square R: 0<= x<= 1,…

A: find z.

Q: find a parametrization of the surface Parabolic cylinder between planes The surface cut from…

A: To find a parametrization of the surface: Given that, Between the planes z=0 & z=3 Thus, 0≤z≤3…

Q: The area of the plane z = 2x + 1 above the disk of radius 1 centered at the origin is (а) 4л. (b)…

A: As we know, z=fx,y defines a surface in xyz-space.  Formula for the surface area of the surface…

Q: Find the ar ea of sur face x - 2y - 2z = 0 that lies above the triangle bounded by the lines x = 2,…

A: Given :          The surface x2 - 2y - 2z = 0 that lies above the triangle bounded by the lines x…

Q: Find the average height of the hemispherical surface z = sqrt(a2 - x2 - y2 )above the disk x2 + y2…

A:

Q: Integrate ƒ(x, y) = sqrt(4 - x2) over the smaller sector cut from the disk x2 + y2 <=4 by the…

A:

Q: Solve Sff, 3x² + 3y²dV by using cylindrical coordinates, where G is a solid in the first octant that…

A:

Q: Find the points on the surface 2a2 + ly² + 522 = 1 at which the tangent plane is parallel to the…

A: We will use the following method for finding the two required point.

Q: Find an equation for the plane that is tangent to the surface z= Vy - I at the point (2, 3, 1).

A: We have to find partial derivatives first.

Q: Find all points on the ellipsoid 2x² + 3y² + 4z² = 9at which the plane tangent to the ellipsoid is…

A: Explanation: Given that,  Ellipsoid:2x2+3y2+4z2=9Plane:x-2y+3z=5⇒15x-25y+35z=1   Suppose point of…

Q: 2. Bounded by the paraboloid = 10 – 322 – 3y? and the plane z = 4 (using polar coordinates)

A: The paraboloid is bounded by z=10-3x2-3y2 . Now, converting in polar coordinates, z=10-3r2.

Q: Find a vector function that represents the curve of the intersection of the two surfaces. The…

A:

Q: /Sketch the Surface Z=V9-X+y- and verify that fxg = Exx %31

A: Second order Partial Differentiation

Q: Find an equation for the plane that is tangent to the surface z= In (x²+y^) at the point P(0,1,0).…

A:

Q: Find a vector parametrization for the intersection of the plane x + y+z = 3 and the cylinder x² + z2…

A: solution given below..

Q: The tangent plane to the elliptic paraboloid z = 2x2 + y² at the point (1, 1, 3) is %3D 1) 8x + 6y +…

A:

Q: Find the distance between the point (0, 0, 0) and the plane 2x + 3y + z = 12.

A:

Q: Find the distance from a point P(x1, y1, Z1) to the plane Ax + By + Cz = D.

A:

Q: Find the surface area of the part of the plane 7+ 2x + 5y that lies above the rectangle [1, 4] x [0,…

A: Given that  Z=7+2x+5y To find the area of the surface of the plane that lies above the rectangle

Q: Find for the point P(x,y,z) on the plane 3x + y – z – 15 = 0 that is closest to the origin.

A: The distance of the point P(x,y,z) from the origin is: d2=x2+y2+z2 Now we have to minimize d if the…

Q: Find the extreme values of ƒ(x, y, z) = x2yz + 1 on the intersection of the plane z = 1 with the…

A:

Q: Find the distance from the point S(0,0,0) to the plane 20x+10y+5z=70 (approxmate to two decimal…

A:

Q: Find all planes which (i) are tangent to the elliptic paraboloid z = x² + y², and (ii) pass through…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: Find the equation of the tangent plane to the sphere x² + y2 + z² = 1 at the point (1/ V3, 1/V3, 1/…

A:

Q: Calculate the positive value of m so that the x+y+2z=m plane is tangent to the spherical surface…

A:

Q: Find the area of the surface cut from the paraboloid x2 + y2 - z = 0 by the plane z = 2.

A:

Q: Find the points on the surface 2a2+ ly? + 522 = 1 at which the tangent plane is parallel to the…

A:

Q: Find the distance from the point (1, 1, 1) to the plane 2x + 2y + z = 0.

A:

Q: Find the orthogonal trajectories of the conicoid (x + y)z = 1 of the conics in which it is cut by…

A: Given:The equation of conicoid is (x+y)z=1The system of the plane is x-y+z=K, where k is…

Q: Find the distance between the point and the plane. (0, 0, 0) 2x + 6y + z = 12

A:

Q: ) Find the points on the ellipsoid 6x² + y² + 3z² = 4 where the tangent plane is parallel to the…

A:

Q: Find the area of the surface. The part of the plane  z = 4 + 3x + 2y  that lies above the rectangle…

A: Consider the part of the plane that lies above the rectangle .

Q: Find the average height of the hemispherical surface z = √(a2 - x2 - y2) above the disk x2 + y2 ≤ a2…

A:

Q: Find the points on the surface 1x^2+2y^2+5z^2=1 at which the tangent plane is parallel to the plane…

A:

Q: Find the distance between two planes a and a1 that are tangent to the ellipsoid 2 +2y? + z² = 5/8…

A: We have to find the distance between the two tangent planes parallel to x+y+z=0  that are tangent to…

Q: Find an equation for the plane that is tangent to the surface z = In (x² + y) at the point P(0,1,0).…

A:

Q: Find the area of the surface. The part of the plane z = 4 + 3x + 2y that lies above the rectangle…

A:

Q: Find the surface area of the part of the plane 3x + 3y+ z = 9 that lies above the triangle formed by…

A: In the question we have to find the surface area of the plane.

Q: Find a vector function that represents the curve of intersection of the surface 4x+2y-8z^2=16 and…

A: To find a vector function that represents the curve of intersection of the surface 4x+2y-8z2=16 and…

Q: Find the plane tangent to the surface z=x+ y at the point (3,4,25). a. 6x+8y-z=25 b. 6x-8y-z=25 c.…

A: We have to find the plane tangent for the given surface

Q: Find the area of the surface. The part of the plane z = 8 + 5x + 2y that lies above the rectangle…

A: Area of the surface z=f(x,y) A(s)=∬1+fx2+fy2f(x,y)=8+5x+2yfx=5fy=2

Q: Find the surface area of the part of the plane z = 4 + 6x + 2y that lies above the rectangle [1, 4]…

A:

Q: Find the point lying on the intersection of the plane x + + z = 0 and the sphere x2 + y2 + z2 = 25…

A: According to the given information, it is required to find a point lying on the intersection of the…

Q: Find the point lying on the intersection of the plane  x + (.5)y + (.25)z = 0  and the sphere  x2…

A:

Q: ~F = z(x2+ y2) ~k through the disk of radius 4 in the plane z = 2, centered on the z-axis, oriented…

A:

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.