Find the maximum volume of a box that is resting on the xy-plane with one vertex at the origin and the opposite vertex in the given plane. 3x + 4y + 2z = 12

Q: Find the maximum value of f(x,y,z)=15x+y+6z on the sphere x²+y²+z²=441

A:

Q: Find the point on the plane 3x + 2y + z = 6 closest to the origin. (Hint: Use Lagrange multipliers.)

A: Given plane is, 3x+2y+z=6, we need to find the point on this plane closest to the origin.

Q: Find the maximum value of f(x,y,z)=2x+5y+13z on the sphere x²+y²+z²=36

A:

Q: Determine the diameter of a hole that is drilled vertically through the center of the solid bounded…

A:

Q: Identify and sketch the surfaces 4x2 + 4y2 + z2 = 4

A:

Q: Find the maximum value that ƒ(x, y, z) = x2 + 2y - z2 can have on the line of intersection of the…

A: Given and planes are

Q: Find the maximum and the minimum values of f(x.y.z) = 9x- 9y +2z on the sphere x +y +z = 166.

A:

Q: Find the maximum value of f(x,y,z)=D24x+18y+21z on the sphere x²+y2+z²=D49 256.324

A: Given query is to find the max value for f.

Q: The section of a certain solid cut by any plane perpendicular to the x-axis is a square with the…

A:

Q: Find the area of the cap cut from the sphere x2 + y2 + z2 = 2 by the cone z = sqrt(x2 + y2).

A:

Q: Find the area of the portion of the plane 2x + 3y + 4z = 28 lyingabove the rectangle 1 ≤ x ≤ 3, 2 ≤…

A: GIVEN  2x + 3y + 4z = 28  We need to find the area of the plane  lyingabove the rectangle 1 ≤ x ≤ 3,…

Q: Find the area of the part of the sphere x2 + y2 + z2 = 4z that lies inside the paraboloid z = x2 +…

A: Given, x2+y2+z2=4z  and  z=x2+y2 Equation of the sphere and paraboloid in cylindrical coordinates is…

Q: Find the dimensions of the largest rectangular box in the first octant (x, y, z > 0) with one corner…

A:

Q: Use the method of Lagrange multipliers to find the maximum and minimum values of 2х + у on the…

A: To find : maximum and minimum values of 2x+y on the ellipsoid x2a2+y2b2+z2c2=1, where a, b and c are…

Q: alculate and generate the graph of the following general cylinders and surfaces in three dimensions.…

A: The following is the ellipsoid.

Q: SET UP the necessary equations to find the point on the intersection of the surfaces x2 + 4y2 + 4z2…

A: The solution are next step

Q: Find the volumes of the regions. The wedge cut from the cylinder x2 + y2 = 1 by the planes z = -y…

A: Given Data The equation of a cylinder is x2+y2=1. z=-yz=0   Determine the interval of x and y,…

Q: Find the area of the surface.The part of the surface 2y + 4z − x2 = 5 that lies above the triangle…

A:

Q: Find the area of the vertical wall whose base is the semicircle {(x, y) | x² + y² = 1 and y>0} and…

A:

Q: Find the maximum volume of a box that is resting on the xy-plane with one vertex at the origin and…

A: Given the plane is 3x+4y+2z=12

Q: Find the area of the surfaces The surface cut from the bottom of the paraboloid z = x2 + y2 bythe…

A: The formula for the surfaces area of the paraboloid above the region R is: A=∬Rzx2+zy2+1dxdy Where,…

Q: Find the points on the cone z2 = x2 + y2 that are closest to the point (2, 2, 0).

A:

Q: Use Lagrange multipliers to find the volume of the largest rectangular box in the first octant with…

A: To find the value when the volume is the greatest possible value under the given constraints

Q: Find the area of the part of the sphere x2 + y2 + z2 = 100z that lies inside the paraboloid z = x2 +…

A:

Q: Determine the diameter of a hole that is drilled vertically through the center of the solid bounded…

A:

Q: Find the maximum volume of a box that is resting on the xy-plane with one vertex at the origin and…

A: Given, equation of the plane is  7x + 6y + 2z = 18 => 2z = 18 - 6y - 7x Therefore, z = ( 1/2)(18…

Q: Find the area of the surface. The part of the surface 2y + 4z - x2 = 5 that lies above the triangle…

A:

Q: Find the distance between the planes M: 3x – 4y + z – 17 = 0 and N: 6x – 8y + 2z + 68 = 0.

A:

Q: Find the point on the plane 3x + 2y + z = 6 closest to the origin. Hint: Use Lagrange multipliers.

A: The given plane: 3x+2y+z=6 To find the point on the plane 3x+2y+z=6 closest to the origin. Solution:…

Q: Explain why C lies on the surface of the cylinder x² + y² = 1.

A:

Q: The section of a certain solid cut by any plane perpendicular to the x-axis is a square with the…

A: Given y^2=9y x^2=9y   a particular solid cut by a plane perpendicular to the x-axis is a square…

Q: Find the points on the sphere at which the minimum and maximum distances between the sphere…

A:

Q: Use Lagrange multipliers to find the volume of the largest rectangular box in the first octant with…

A:

Q: Find the area of the surface. The part of the surface  2y + 4z − x2 = 5  that lies above the…

A: According to the given information, it is required to find the area of the surface.

Q: Find the extreme values of z on the surface 2x² + 3y2 + z2 - 12xy + 4xz = 35.(DO NOT USE LAGRANGE…

A: For the solution follow the next steps.

Q: Find the maximum value of f(r, y) = 10ry(4 – 8z - 4y) over the triangle with vertices (0, 0), (,0)…

A:

Q: Find the area of the surface. The part of the paraboloid x = y² + z² that lies inside the cylinder…

A:

Q: A cube of cheese from Italy with edge measure of 1 was cut by Mickey using a plane in a manner that…

A: Let us assume the the cordinates OA= OB= OC= 1

Q: Find the maximum value of  f(x,y,z)=27x+7y+3z on the sphere x2+y2+z2=81

A: For this question we will use Lagrange multipliers where f(x,y,z)=given function and…

Q: Use Lagrange multipliers to find the volume of the largest rectangular box in the first octant with…

A: Given,  Plane x + 3y + 4z = 9

Q: Find the maximum value of f(x,y,z)=9x+15y+9z on the sphere x2+y2+z²=100

A:

Q: What is the center of X x² + y² – 30x + 221 = 0? Show all work for full credit.

A: Topic = Geometry

Q: D is the region enclosed by the parabolas z = y²-9 and 2 - y² +9.

A: Let, I=∫∫Dx+y+2dA x=y2-9 and x=-y2+9 Power rule for the integration: ∫xndx=xn+1n+1+C ∫cdx=c∫x0dx=cx

Q: Find the absolute maximum and minimum values of f(r, y) = r-3r-y+12y, closed region D, where D is…

A: Given problem:-  Find the absolute maximum and minimum values of f(x, y) = x²-3x-y³+12y, on the…

Q: Find the area of the finite part of the paraboloid  y = x2 + z2 cut off by the plane y = 4.

A: To find the area of the finite paraboloid y=x2+z2 cutt off by the plane

Q: Find the maximum value of f(x,y,z)=9x+14y+29z on the sphere x2+y2+z²=25

A:

Q: Find the maximum value of f(x, y) = 4xy(9 – 72x – 9y) over the triangle with vertices -- - (0,0), (5…

A: Given: fx,y=4xy9-72x-9y vertices 0,0 18,00,1

Q: Find the points on the cone z2 = x² + y2 that are closest to the point (8, 2, 0).

A: we have given the equation of cone z2=x2+y2 and the point (8,2,0)to…

Q: Find the area of the surface. The part of the surface  2y + 4z − x2 = 5  that lies above the…

A:

Q: Find the area of the surface of the part of the plane 3x + 2y + 4z = 2 that lies inside the cylinder…

A: Here, surface S has an equation of the form z=f(x,y), where (x,y)  D and f has continuous partial…