The minimum value of f(x,y,z) = x^2 -2y + 2z^2 on the sphere x^2 + y^2 + z^2 =1 is ....?

Q: find the center of mass of a thin plate of constant density d covering the given region. The region…

A: Given: y=2x2-4x and y=2x-x2 Graph:

Q: The solid bounded by the surfaces S1: 2x + 3z = 6, S2: y = 2, S3: (y-2)² = 2x -2, S4: x = 0, S5: y =…

A: To find- The Solid bounded by the surfaces S1 : 2x + 3z = 6, S2 : y = 2, S3 : y - 22 = 2x - 2, S4 :…

Q: Obtain the DE based on given conditions solve for item 1 only.

A:

Q: Bounded by the cylinder x 2 + y 2 = 1 and the planes y= z x =0 z= 0 in the first octant

A:

Q: Find the centroid of the region bounded by y = 9 – x² and the x-axis.

A: Given, y=9-x2or let fx=9-x2and x-axis y=0or let gx=0

Q: Find the centroid of the region bounded by the given curves y=8sin 5x, y=0, x=0,x=  π/5

A:

Q: Find  the Volumeof the largest rectangular box lying above the xy-plane, with y less that or equal…

A: considerlength of rectangular box =x width of rectangular box  =yheight of rectangular box =z

Q: Classify all critical points for the surface flaiy)= 2x-y-2xy.

A: We have to classify all the critical points for the surface…

Q: A solid formed by revolving about the y-axis, the area bounded by the curve y=x4, the y-axis, and…

A: Given that  area bounded by the curve y=x4, the y-axis, and the line y=16.  To find the centroid of…

Q: Find the surface area cut from the cone 2x2 + 2y2 = 5z2, z > 0, by the cylinder x2 + y2 = 2y

A: To find the surface area cut from the cone 2x2 + 2y2 = 5z2, z > 0, by the cylinder x2 + y2 = 2y

Q: 4. Find the volume of the wedge cut from the first octant by the cylinder z = 12 - 3y2, and the…

A: We have to find volume.

Q: 1. Find the minimum distance from the point (0, 0, 0) to the plane x- y+z = 3.

A: perpendicular distance

Q: A container with a height of 3/2 is made by rotating the curve y = 3/2x^2, Osx<1, about the axis x =…

A:

Q: The surface area of the surface generated by revolving y=x^3 , 0<=x<=1 about the x-axis is

A: We have to find the surface area of the region generated by y=x^3, 0&lt;=x&lt;=1 about the x-axis. I…

Q: The tangent plane and the normal line of the surface y = x² + z – 6 at the point (2, -1, 1) have the…

A:

Q: Determine the maximum highest point (x, y,=) the surface on z = 1+ 4x + 4y- x* - y*

A:

Q: A solid is formed by revolving about the y-axis, the area bounded by the curve x^3=y, the y-axis,…

A: Solution :-

Q: . The solid bounded by z = 1 – x², z = 5 – 2x², y = 0, and y – z = 6. |

A:

Q: 3 Find the abscissa of the centroid of the region between the parabola y = 9 − x2 and the line y…

A: Given :The parabola y=9-x2 and the line y=2-2x from x=0 to x=2.To find :The abscissa of the centroid…

Q: A _____ is the set of points (x, y) in a plane such that the difference in distances between (x, y)…

A: The standard form of the equation of the hyperbola is,

Q: Find the points on the hyperbolic cylinder x2 - z2 -1 = 0 that are closest to the origin. please…

A:

Q: Find the centroid of the triangular region cut from the first quadrant by the line x + y = 3.

A: We will find the x and y-intercept of the triangle.  To find x-intercept we plug y=0 and find x…

Q: A region in the xy-plane is bounded by y = 2x + 2, X = y + 2, y = -2, 2 y = 2. and

A: Given curves are y=2x+2 and x=y22+2 The limits are y=-2 and y=2 We isolate x from the first curve,…

Q: The diagram shows a small block B, of mass 0.2kg, and a particle P, of mass 0.5kg, which are…

A:

Q: Find the volume of the solid that is bounded by the cylinder z = 4x2, on the sides by the cylinder…

A: Let's find volume of solid.

Q: A region R consists of a square bounded by the lines x = -1, x = 1, y = 0, and y = -2 and a half…

A: The given region is as follows: The area of region is  A=∬RdA  =Area of semi-circle of radius…

Q: The path C is a line segment of length 5 in the plane starting at (4, 1). For f(x, y) = 4x + 3y,…

A:

Q: volume of solid of as revolution y^2=4x and x^2=4y about the x axis

A:

Q: The path C is a line segment of length 13 in the plane starting at (2, 2). For f(x, y) = 5x + 12y,…

A:

Q: Find the volume of the solid bounded from up by surface f (x,y) = 2x + y2 and from below by the…

A: According to question, surface :f(x, y) = 2x+ y2,Traingle vertices : 0, 2, 0, 0 and 3, 2

Q: 1_2 Can you please help me with this example in a step by step guide. Thank you very much!!

A: To calculate the coordinates (x,y,z) and also define the absolute extremum for the provided surface…

Q: Find the maximum and minimum values of x^2 + y^2 − 2x − 2y on the disk of radius √ 8 centered at the…

A: Given function is  fx,y=x2+y2-2x-2y where bounded region is  x2+y2≤8.

Q: The region is bounded by the curves y = x² and y = 4x - x² and is rotated about the line X = 4. %3D…

A:

Q: find the areas of the surfaces generated by revolvingthe curves about the given axes. x = √4y - y2,…

A:

Q: Find the points on the hyperbolic cylinder x2 - z2 -1 =0 that are closest to the origin. please…

A: The parametric equation of hyperbolic cylinderx2-z2-1=0 is , x=cos hθ                          y=y…

Q: Find the area of the surface given by z = f(x, y) that lies above the region R. 3 + 6x3/2 f(x, y) R:…

A: In this question, we need to find the area of the surface.

Q: 4. Parameterize the curve of intersection of the surfaces z = x² + y² and y² + (z – 1)² = 1.

A: parameterisation

Q: find the areas of the surfaces generated by revolving the curves about the given axes. 27. x = 24y -…

A: To determine the surface area of solid of revolution about the y-axis.

Q: A solid is obtained by rotating the shaded region about the specified line. about the line y = 5 y x…

A: NOTE: Refresh your page if you can't see any equations. . given functions are

Q: How would I go about solving ∭xzdV, where E is bounded by the planes z = 0, z=y, and the cylinder x2…

A: We will find out the limits first.

Q: Find the volume of the wedge cut from the first octant by the cylinder z = 12 - 3y2 and the plane x…

A: Given Data The equation of the cylinder is z=12-3y². The equation of the plane is x+y=2.   Let, The…

Q: find the points of the surface x^2-y^2+z^2=1 which corresponds to the extreme value of…

A:

Q: Calculate the volume under the elliptic paraboloid z=3x2+7y2 and over the rectangle R=[−2,2]×[−4,4

A: Explanation: We know that,  Volume =∬zdydx By using the double integral concept, the volume of the…

Q: Calculate the point on the surface z =1 - x2 - y2 that has a maximum value for the sum of its…

A:

Q: 6) Find the volume of the solid in the first octant bounded by the plane 3x +4z=12, y=2 and the 3…

A:

Q: Find the centroid of the region bounded by the graphs of the equations using any method y = √(1 −…

A: Consider the given equations y=fx=1-x2y=gx=0 First, find the point of intersection of the given…

Q: Find the abscissa of the centroid of the region between the parabola y = 9 − x^2 and the line y = 1…

A:

Q: find the areas of the surfaces generated by revolvingthe curves about the given axes. y = x3/3, 0 ≤…

A:

Q: 2. Determine the centroid of the area bounded by the curves y = 4x + 16, x = -2, x = 5 and x-axis.

A:

Q: Find the minimum distance from the point (0, 0, 4) to the surface  z = (1-2x-2y)^1/2   (Round your…

A: Solution:

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.