Find the dimensions of the rectangular box of maximum volume with faces parallel to the coordinate planes that can be inscribed in the ellipsoid 16x 2 + 4y 2 + 9z 2 = 144

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: Find the dimensions of the box of maximum volume with its sides parallel to the coordinate planes…

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Q: An open top box is to be made from 48 m of wood with dimensions x, y and z as shown in figure. Using…

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Q: Find the dimensions of the rectangular box of maximum volume that has three of its faces in the…

A: Let say that(a,b,c) is point in plane 4x+3y+z=12 and it is one vertex of requested rectanglar box.…

Q: Find the volume of the largest rectangular box in the first octant with three faces in the…

A: The given equation of plane is : x+2y+3z=6 x=6-2y-3z                   …(1) Volume of a rectangular…

Q: Find the dimensions of the rectangular box of maximum volume that has three of its faces in the…

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Q: Compute the area of surface generated by revolving the four-cusped of hypocycloid x⅔+ y⅔ =a⅔ about…

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Q: Find the centroid of the region with the indicated boundaries: The parabola y² = 4x, the Y-axis,…

A: We use the formula  x=MyM=∫abxfx-gxdx∫abfx-gxdxy=MxM=∫ab12fx2-gx2dx∫abfx-gxdx Now, fx=4, gx=4x, a=0,…

Q: Find the dimensions of the rectangle of largest perimeter that can be inscribed inthe ellipse x2/a2…

A: To find the dimensions of the rectangle of largest perimeter that can be inscribed in the…

Q: Find the volume of the largest rectangular box in the first octant with three faces in the…

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Q: A tank was modeled in a pyramid shape of heght 4 using four different planes -4/3x-4y+z=-4 ,…

A: Consider the equations of given four different planes, -43x-4y+z=-42x-4y+z=-42x+y+z=-4-43x+y+z=-4…

Q: parabola

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Q: Find the volume of the largest rectangular box in the first octant with three faces in the…

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Q: Find the volume of the shaped body bounded by the z = 3x2 + 3y2 and          z = 4 - x2 - y2…

A: We have to Find the volume of the shaped body bounded by the z = 3x2 + 3y2 and        z = 4 - x2 -…

Q: What is the volume of the largest rectangular parallelepiped which can be inscribed in the ellipsoid…

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

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Q: 13) Find an equation of the plane that is through the point (1,1,2) and makes minimum volume in the…

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Q: 3. What are the dimensions of the closed cylindrical can that has surface area 280 square…

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

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Q: Find the centroid of the region in the first quadrant bounded by the x-axis, the parabola y2 = 2x,…

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Q: Find the volume of the largest rectangular box in the first octant with three faces in the…

A: We have to find the volume of the largest rectangular box in the first octant with three faces in…

Q: Find the centroid of the region between the semicircle y = v1 – x2 and the top half of the ellipse y…

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Q: 7. parallelepiped that can be inscribed in the ellipsoid defined by x +4y² +9z =9. Use Lagrange…

A: the volume of rectangular parallelepiped V=8xyz=f(x,y,z) let g: x2+4y2+9z2=9

Q: Show that it is not possible to design a cylindrical can (with top and bottom) of volume 900 cubic…

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

A: Given :                 y = 2x2 - 4x  and y = 2x - x2    Graph :…

Q: Determine the centroid of the first-quadrant region bounded by the parabola y = 4 – x²

A: Given; parabola y=4-x^2

Q: An architect was commissioned to design a nuclear explosion resistant building in the shape of a…

A: The given dimenssions of ellipsoid area=25 mb=20mc=40 mthickness t = 1 m

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Q: find the center of mass of a thin triangular plate bounded by y-axis and the line y = x and y = 2-x…

A: The triangular plate is bounded by y-axis, y=x,y=2-x if ∂x,y=6x+3y+3. Thus, the region is…

Q: Find the dimensions of the box of maximum volume with its sides parallel to the coordinate planes…

A: Given :                    The ellipsoid is :                           xa2 + yb2 + zc2 = 1…

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A: Let fa,b,c=a2b2c2 subject to a2+b2+c2 =r2  The gradient equation is…

Q: To calculate: The dimension of the rectangular solid with a square base that yields the minimum…

A: The rectangular solid has a square base. Let the dimensions of the rectangular solid be x, x and y.…

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Q: (1 point) Calculate the volume under the elliptic paraboloid z = 2x2 +3y2 and over the rectangle R =…

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Q: For the pink region bounded by a parabola with vertex at (-1, 11 ) and the green line, solve for: a.…

A: The given equation of the parabola is y=-a(x-h)2+k, with vertex -1,11. ⇒y=-a(x+1)2+11 Given two…

Q: Calculate the volume under the elliptic paraboloid z = 4x² + 6y2 and over the rectangle R = [-2, 2]…

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Q: A closed rectangular box with faces parallel to the coordinate planes has one bottom corner at the…

A: Let x , y, z donate  the length, width and the height of the rectangular box.  Volume of the box is…

Q: Compute for the volume of the solid formed bounded by the equations (y- 4)2 = x - 3, x-10, y-4, and…

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Q: Calculate the volume under the elliptic paraboloid z = 4x2 + 6y2 and over the rectangle R = [-2, 2]…

A: The solution for the above question is shown below.

Q: The altitude of a cylinder of maximum volume that can be inscribed in a right circular cone of…

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Q: A rectangular box is to be inscribed inside the ellipsoid 2x< + y2 + 4z2 = 12 Find the largest…

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Q: Find the dimensions of the rectangular box of maximum volume that can be inscribed inside the sphere…

A: Given sphere is

Q: Find the center of mass of a thin plate of constant density & covering the given Region enclosed by…

A: Curve 1: y=x-x2 Curve 2: y=-x We have to find the center of mass.

Q: Find the volume of the reqion bauoded the parabolalde2=4-x2-42 3 below the parabolaid aboue by

A: We need to find the volume of the region bounded above by the paraboloid above z = 4 - x2 - y2 and…

Q: 2. Solve for the centroid of the shaded region. -zolx-1)

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Q: Consider the region in the first quadrant bounded by y=x^2, the y-axis, and y=4. -the y-axis using…

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Q: A right circular cylindrical container with volume 167 cm³ is to be made. Use the method of Lagrange…

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Q: Find the centroid when revolved in y-axis: y³ = x² ; y = 4.

A: As per the question we are given a solid of revolution obtained by rotating the area between y3 = x2…

Q: Find the volume of the largest rectangular box in the first octant with three faces in the…

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