7. parallelepiped that can be inscribed in the ellipsoid defined by x +4y² +9z =9. Use Lagrange multipliers to find the volume of the largest rectangular

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

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Q: 4. Determine the dimensions of the cone of maximum volume that can be inscribed in a sphere of…

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

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

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Q: 3. Use Lagrange Multipliers to find the dimensions of the closed right cylindrical can of smallest…

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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: 1.)A truck hauling cylindrical steel tank has to pass under an overhead parabolic arch bridge which…

A: Given:

Q: 5. Assume an American football has an ellipsoid shape and has a length of 27 cm and a height of 16…

A: Length in x-direction = 27cm    The point endsheight in  y-direction = 8cmheight in  z-direction =…

Q: A manufacturer is making cylindrical cans that hold 200 cm3. The dimensions of the can are not…

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Q: Consider an axis-aligned cuboid (i.e. with one vertex at the origin and with the 3 edges connected…

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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: 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: B A A cone-shaped cup is made from a circular piece of paper of radius 7 by cutting out a sector and…

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Q: Find the dimensions of a cylindrical can with a bottom but no top of volume 4 m3 that uses the least…

A: To Find: Dimension of a cylindrical can with a bottom but no top of volume 4 m3that uses the least…

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

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Q: Consider a rectangular box B that has a bottom and sides but no top and has minimal surface area…

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Q: Suppose a cylindrical package has height h and a base with a radius r. Find the values r and h that…

A: Solve the following

Q: A thin plate of constant density k, bounded by the parabola y=3x² and the line y=3 has a mass 4k.…

A: If mass of a region R bounded between y=f(x) and y=g(x) from x=a  to x=b  Then there two moments,…

Q: 1. A long metal sheet with a width of L meters is formed into a gutter by bending up two of its…

A: A roof gutter is to be made from a long strip of sheet metal L units wide, by bending up equal…

Q: As a hardworking student, plagued by too much homework, you spend all night doing math homework. By…

A: Region bounded by the curves

Q: Find the dimensions (radius r and height h) of the cone of maximum volume which can be inscribed in…

A: According to our company policy, I am supposed to answer only one question at a time so for the rest…

Q: 2. Use the Lagrange multipliers method to determine the minimum length of the diagona of a…

A: We have to find the minimum diagonal.

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

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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: 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

Q: Find the surface area of the portion of the half ball with radius a which cuts off by the cylinder…

A: The equation of a ball with radius a is x2+y2+z2=a2. The surface area of the function z=fx,y over…

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…

Q: West Coast Customs is constructing a closed-top, square-based, rect- angular subwoofer box that will…

A: Here we use application of derivatives to find the minimum surface area and find it's dimensions.

Q: A cylindrical can has a volume of 1024r cm. What dimensions yield the minimum surface area?

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Q: 4. Find the radius of the right circular cone with least volume that can be circumscribed about the…

A: Formula Used: Volume of Cone = 13πR2h where R,h denote the radius and height of right circular…

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

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Q: A rectangular box has three of its faces on the coordinate planes and one vertex in the first octant…

A: Given,The box's volume is  V = xyz  but we know that   z = 4 − x2 − y2V = xyz    = xy ( 4 − x2 − y2…

Q: 8 A rectangulaer garden with an area of 30m is Surrounded by a grass border Im wide on two Sides 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: A rectangular box is to be inscribed inside the ellipsoid 2x< + y2 + 4z2 = 12 Find the largest…

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Q: 10. A silo consists of a right circular cylinder surmounted by a right circular cone cover. What is…

A: Volume is also known as the capacity of a figure that is the filled part of the container.  Maximum…

Q: Consider a rectangle of sides x and y with fixed perimeter of 40 units. Find the maximum and minimum…

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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: 6. Find the dimensions of the rectangle enclosed in the semicircle y = v144 – x² with largest…

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Q: 5. Find the dimensions x, y, and z (in inches) of the rectangular box with the largest volume that…

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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: The area in the first quadrant bounded by a parabola 12y = x2, the y=axis, and the line y = 3,…

A: Given:       Parabola x2=12y                      y=x212              line y=3 The parabola and line…

Q: 7. A solid dome is to be constructed with the ellipse x² + 3y² = 6 as a base. Using infinitely many…

A: Volume is evaluated. Integration is done in x variable.

Q: A cylindrical diet coke can is being made out of 54π in2 of material. What dimensions maximize the…

A: Given Material used in cylindrical diet coke= 54π in2 Want to maximize the volume of A cylindrical…

Q: 4. West Coast Customs is constructing and open-top, square-based, rect- angular subwoofer box that…

A: West Coast Customs is constructing and open-top, square-based.rectangular subwoofer box that will…

Q: suppose  we are planing to make a taco from a round tortilla with diameter 8 inches by bending the…

A: