13) Find an equation of the plane that is through the point (1,1,2) and makes minimum volume in the first octant.

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

A:

Q: 13) Find an equation of the plane that is through the point (1.1.2) and makes minimum volume in the…

A: The equation of plane is given as, z-z0=ax-x0+by-y0 The points (1,1,2) is given Now substituting for…

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

A:

Q: 5. Show that the rectangular box of maximum volume inscribed in a sphere of radius r is a cube.

A:

Q: Find the plane x/a + y/b + z/c = 1 that pass-es through the point (2, 1, 2) and cuts off the least…

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Q: State the equstion of the yz plane

A: We have to find equation of yz plane

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A:

Q: Find the dimensions of the rectangular box of maximum volume with faces parallel to the coordinate…

A:

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

A:

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…

A:

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

A:

Q: Find the minimum distance from the point (6, 0, 9) to the plane x – y + z = 5. (Hint: To simplify…

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Q: What is the shortest distance from the surface ry + 15x + z2 = 204 to the origin? distance =…

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Q: Of all boxes with square base and a volume of 512 cm, which one has the minimum surface area? (Give…

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Q: Consider the lamina that occupies the triangular region with vertices (0, 0), (2, 2) and (2, –2),…

A: Given, the lamina that occupies the triangular region with vertices (0, 0), (2, 2) and (2, -2), with…

Q: Chapter 6, Section 6.2, Question 033 Find the volume of the solid generated when the region enclosed…

A: To find the volume of the solid.

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

A:

Q: A region in the xy-plane is bounded by y = 2x + 2, X = y + 2, y = -2, 2 y = 2. and

A: Given curves are y=2x+2 and x=y22+2 The limits are y=-2 and y=2 We isolate x from the first curve,…

Q: A uniform cubical box of edge a is placed on the top of a fixed sphere, the centre of the face of…

A:

Q: 3. Show that a closed right circular cylinder of given surface has maximum volume if its height…

A: Let r, h be the radius and height of the cylinder respectively and V, S be the Volume and Surface…

Q: find the dimension of a cylinder that can be inscribed in a given sphere if it's convex surface area…

A:

Q: Evaluate the integral hipxp hx^ 7 and the hyperbola ry = 13. where R is the region bounded by the…

A:

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: Find the maximum volume of a cylindrical can such that the sum ofits height and its circumference is…

A: Let r denotes radius       h denotes height Then       volume of cylinder (V) = πr2h Restriction is…

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A:

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

A:

Q: Find the dimensions of a rectangular box of maximum volume such that the sum of the lengths of its…

A:

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

A:

Q: Two factories are located at the coordinates (-x, 0) and (x, 0), and their power supply is at (0,…

A:

Q: Find the dimensions of the closed rectangular box with maximum volume that can be inscribed in the…

A: Let 2x, 2y, 2z be the dimensions of rectangular box. Then Let

Q: Show that the rectangular box of maximum volume that can be inscribed in the sphere x^2 + y^2 + z^2…

A:

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: 7. Show that a closed rectangular box of maximum volume having a prescribed surface area S is a…

A: Let the volume function be V=lbh and the surface area is 2lb+bh+lh=S. Take the constraint to be gl,…

Q: What is the minimum amount of unique shapes that could tessellate a plane?

A: Only three unique shape form tessalate

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A:

Q: Two factories are located at the coordinates (−x, 0) and (x, 0), and their power supply is at (0,…

A: To Determine: Find y such that the total length of power line from the power supply to the factories…

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A: Given sphere is

Q: Assume we wish to to make a right cylindrical can with a bottom and no top, and with a capacity of…

A: Solve it

Q: Calculate the volume under the elliptic paraboloid z=3x2+7y2 and over the rectangle R=[−2,2]×[−4,4

A: Explanation: We know that,  Volume =∬zdydx By using the double integral concept, the volume of the…

Q: 3. Find the volume of the tetrahedron in the first octant bounded by the coordinate planes and the…

A: Given

Q: \ Use optimization to find the maximum volume of a box with one corner at the origin and the…

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A:

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: