Use Lagrange multipliers to find the maximum area S of a rectangle inscribed in the ellipse 1 16 49 (-х, у) (x, y) (-x, -y) (x.-y) (Give your answer as a whole or exact number.)

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Q: 3. The sides of the base of a rectangular cardboard shoe box are 3x and 2x cm respectively. The…

A: Let's find.

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Q: Use Lagrange multipliers to find the dimensions of the box with volume 216 cm3 that has minimal…

A: Given: The volume of the box is 216cm3 . Calculation: Let the dimensions be x, y and z. The volume…

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Q: Q2. Use the Method of Lagrange Multipliers to find the dimensions of the closed right circular…

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Q: 9. A copper sheet with 16 cm by 16 cm dimension has to be made as a square box with no top cover.…

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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: A rectangle is inscribed in a parabola y²=8x with one of its vertical side passes through the point…

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Q: Use the method of Lagrange multipliers to find the maximum value for the volume of a rectangular box…

A: Dimension of box is  length l=x Breadth b=y Height h=z Hence, Volume is given by V=xyz And given…

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Q: Use the method of Lagrange Multipliers to find the dimensions of the rectangle of maximum area with…

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Q: Cuboid warehouse will have volume V=216 m^3 For the builidng of walls they are using boards in the…

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Q: 3.4 Applied Optimization Activity 3.4.5. A trough is being constructed by bending a 4 x 24 (measured…

A: Here we solve the given problem.

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Q: Find the minimum distance from the point to the plane x - y + z = 5. (Hint: To simplify the…

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Q: 8. A rectangle is bounded by the x-axis and the semicircle y = v64 – x². What length and width…

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Q: Use Lagrange multipliers to find the maximum area S of a rectangle inscribed in the ellipse 36 1 49…

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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: A farmer has 8 km of fencing wire and wishes to fence a rectangular piece of land . One boundary of…

A: Given: A farmer has 8 km of fencing wire and wishes to fence a rectangular piece of land . One…

Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 10 –…

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Q: a) Find the maximal volume of the rectangular box whose three faces belong to the coordinate planes…

A: Given: x+y+z=3

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Q: Use Lagrange multipliers to find the dimensions of a box with volume 1000 cm3 that has minimal…

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Q: Use Lagrange multipliers to find the dimensions of the right circular cylinder with maximum volume…

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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…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 2. A right circular cylindrical container with volume 167 cm³ is to be made. Use the method of…

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Q: 1. A closed box, with a rectangular base, whose length is twice its width, is to have a surface of…

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Q: An open–top box with a square base is to be constructed from two materials, one for the bottom and…

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Q: Use Lagrange multipliers to find the dimensions of the right circular cylinder with maximum volume…

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Q: A playpen is to be set up in a family’s recreation room using a 48 foot long flexible fence. Find…

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