(c) Semicircles (d) Isosceles right triangles y 2)

Q: Find the volumes of the solids z=1-r z=-sqrt(1-r^2)

A:

Q: 10. The part of the paraboloid x = y² + z² that lies inside the cylinder y² + z² = 9

A:

Q: Find the average distance from the origin of a point between the two spheres x ^ 2 + y ^ 2 + z ^ 2 =…

A: We have to find average distance from origin of a point between the two given spheres.

Q: Graph  the elliptical cylinder in 3 dimensions

A:

Q: the sum of the distances from (x,y) to (-1,0) and from (x,y) to (1,0) is 4. show x and y is related…

A: Distance from (x,y) to (-1,0) is:  Distance from (x,y) to (1,0) is:

Q: Draw the tetrahedron* whose vertices are at (0, 0, 0), (0, 4, 0), (3, 3, 0), and (1, 2, 3).…

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Q: Find the volume V which lies inside the sphere x^2+y^2+(z−4)^2=16 and outside the sphere…

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Q: to find the surface area cut from the sphere x^2+y^2+z^2=16 by the cylinder x^2+y^2-4y=0

A: To find the surface area cut from the sphere x2+y2+z2=16 by the cylinder x2+y2-4y=0.

Q: Which is the equation of a sphere with a center at (1,0,-2) with a volume of 36(pi)(u^3)? a.…

A: We first defined the equation of sphere and centre,volume . Using this formula we have equation (a)…

Q: Find the volume of the parallelepiped with adjacent edges −→OA = , −−→OB = , −−→OC = .

A: Volume of parallelepipe is given by=  | a.(b*c) |

Q: (x^2/25)+(y^2/9)+(z^2/16)=1 a. what does the cross section in xy plane look? b. What do the…

A:

Q: Given a parabola with equation y = ax^2 where a is a constant, determine the value of a for which…

A:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.