Find the maximum volume of a rectangular box with faces parallel to the coordinate planes if one corner is at the origin and the diagonally opposite corner is on the first octant part of the surface xy + 2yz + 3xz = 18.

Q: Thermal nuclear reactor is subject to the constraint P(a,b,c) = 2m B, a constant. Find the ratios of…

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Q: Use the method of Lagrange Multipliers to find the area of the largest rectangle with edges parallel…

A: The rectangle inscribed the ellipse x218+y232=1. Let sides of rectangle be 2x and  2y.  Draw the…

Q: The plane x + y + 2z = 2 intersects the paraboloid z = x² + y² in an ellipse. Use Lagrange…

A: Note that here we have to extremize x2+y2+z2 , whch is eqivalently ,to extrimize x2+y2+z2.

Q: Find the dimensions of the rectangle of maximum area that can be drawn within a semicircle of radius…

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Q: Find the area of the portion of the surface z = 8x+4y that lies above the triangular region with…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: The first car A moves in the northern direction at a speed u(mph), and the second car B moves to the…

A: The first car A moves in northern direction i.e. towards positive y-axis and the second car B moves…

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: The cylinder x² + y² = 25 intersects the plane x + z = 5 in an ellipse. Find the point on such an…

A: Given:The cylinder is: .The plane is .The cylinder intersects the plane in an ellipse.

Q: A rectangular package to be sent by a postal service can have a maximum combined length and girth…

A: To find the maximum of Volume we use dV/dx=0

Q: A surface is defined by the following equation: 9x2 + 16y2 + 9z2 = 25. Make a sketch of the surface…

A: Any point on the three dimensional coordinate system is represented using the ordered pair: x, y, z.…

Q: Use calculus to show that the maximum possible area of a triangle with one vertex at (0, 0) and the…

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Q: 4. Use Geogebra or your favorite software to graph the part of the surface x² + y² + z² = 4z that is…

A: Below is a diagram of the given surface with the given domain and viewpoint.To find the surface area…

Q: Find the maximum area of an isosceles triangle inscribed inside the ellipse x²y² 1, + = a² 62 with…

A: Given problem:- Find the maximum area of an isosceles triangle inscribed inside the ellipse x2/a2…

Q: 3. Draw the standard yz- and xz- traces of the quadratic surface x² + y² − 2x − z + 1 = 0

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