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: 3. Find the surface area of the surface created when the cylinder y + 2- intersects the cylinder 1²…

A: surface area of the surface given by equation z=f(x,y) A=∫∫Dfx2+fy2+1dA D is the region on xy plane

Q: Which of the following is the total length of the curve of intersection of the surfaces x2 + y? + 22…

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Q: Compute the surface area of the ellipse that lies on the plane z=11-3x+2y and inside the cylinder…

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Q: The vertical cross section of a dome is semi-elliptical in shape. The cross section is 270 feet long…

A: The people should stand on opposite sides of the room each being located at one of the foci  The…

Q: farmer who owns a field adjacent to a straight river wishes to fence a rectangular area. No fence is…

A: Given query is to find the dimensions of the rectangle.

Q: Q3: Find the points on the surface x^2+z^2-6=0, closest to the origin.

A: The distance of the point on the surface is given by d=x2+y2+z2. To obtain the distance insert the…

Q: A suspension bridge with weight uniformly distributed along its length has twin towers that extend…

A: The general equation for a parabola is given as, y=kx2 Let the x-axis represents the road surface…

Q: An equilateral triangle is placed above a rectangle creating a window. There is 40 ft of materials…

A: Suppose that one side of rectangle “x” ft and other side is “y” ft.   Since “x” is also side of…

Q: a parabolic arch of maximum height 40 m is 30 m wide at ground level. A horizontal beam of length 12…

A: The objective of the question is to find the height of the beam above the ground when it is placed…

Q: Find the area of the cap cut from the paraboloid y^2+z^2=2x by the plane x=2

A: To Find: Area of the cap cut from the paraboloid y2+z2=2x by the plane x=2.

Q: Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y = x and y =…

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Q: Find the surface area of the portion of 4x + 3y + 5z = 8 that lies inside the cylinder x² + y² = 49.

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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 certain parabolic monument has a base that is a parabola ( y=−.5x2+8y=−.5x2+8 ) And a front…

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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: nd the point (a, p) on the ellipse 4x adrant, so that the area enclosed by the

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Q: 2 1.² + a² 6² 1² Find the area enclosed by the ellipse x² that the area common to ellipse a² b² 2…

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Q: 6. The figure shows the surface created when the cylinder y² +2²=1 intersects the cylinder ²+²=1.…

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