at is the name of the three-dimensional shape formed if points M and N remain fixed, while line segment LM is rotated around lin

Q: Let / be the line given in parametric form by the equations x = -2 + 1A y = -1+6) z = -1+7A What is…

A: given line is                                               x=-2+λy=-1+6λz=-1+7λ any point on the…

Q: If a point, P1=[10,10,10], will be rotated by 60 degree about the Z-axis, find the final position…

A: Solution ) suppose P1 [ x1 y1 , z1] is rotated about z axis so new point P2 [ x2 , y2 , z2 ] is…

Q: Use Geogebra and the Klein - Beltrami model to show that in hyperbolic geometry you can draw a…

A: As per the question we have to use GeoGebra code and the Klein-Beltrami model to illustrate the…

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

A: Solution

Q: Determine the vertical traces of elliptic and parabolic cylinders in standard form.

A: Firstly the trace of a surface which is actually a cross section or the curves of intersection of a…

Q: A square is rotated about its center. Select all of the angles of rotation that will map the square…

A: A square has four equal sides and its adjacent sides are perpendicular to each other. That is, pairs…

Q: 5/1f the three points A ( are collinear then

A:

Q: 3. Determine the lengths of the radius vectors of the point P (2, 1) of the ellipse 27x² + 3y²-54x -…

A: The center of a ellipse (x-a)2/c2+(y-b)2/d2=1 is at (a,b).

Q: equation of the circle in standard form that satisfies the given conditions : circle has center (0,…

A:

Q: onsider the points A = (-2, 3, -1) and B = (4, -2, 1). (a) Draw a 3D coordinate system that follows…

A:

Q: II. Cylindrical to Spherical 6. (12, 45°, 12)

A: Conversion of cylindrical coordinates to spherical coordinates. Let,  ρ,θ,φ be the coordinates of a…

Q: (9, - 플이 2

A: Given, the  point (r, θ, z)=(9, -π2, 8).

Q: Segment AB has point A located at (6, 5). If the distance from A to B is 5 units, which of the…

A: The answer is given below:

Q: Q4\ find a polar equation for the circle x² + (y - 3)² = 9

A:

Q: Triangle ABC has vertices at A (2,1), B(4,2), and C(1,4). What would be the coordinates of the image…

A: we will be applying row transformation

Q: 1)calculate dedy ry where D is a parallelogram with vertices (0,0).(5,-1).(3,1) and (8,0) tip:Use…

A: Here we will use change of variable to find integral If we want to integrate f(x,y) over the region…

Q: A glass sphere given by the equation (x-1)²+(y-2)²+(-3)² = 36 is floating above the plane 2x + y -…

A: The given problem is to find the point on given sphere is farthest from the given plane. Given…

Q: Draw an example of two lines that illustrates the Spherical Geometry Parallel Postulate.

A: To draw an example of two lines that illustrates the Spherical Geometry Parallel Postulate.

Q: △ABC△ABC has vertices A(0,4), B(6,-1), and C(3,7). What are the coordinates of C' when the triangle…

A:

Q: Is a triange with the verticies A(7,1) B(0,4) and C(-4,-8) a right triangle yes or no?

A:

Q: Which quadric surfaces have both hyperbolas and parabolas as traces?

A: Consider the given: The intersection of a three-dimensional surface and a plane is called a trace.…

Q: 5) x2 (y - 6 ) 2 64 121 + - = 1

A: we will find the required.

Q: If the intersection points of the hyperbola 3x² – y² = 11 and the line 2x + y = 10 are P and Q,…

A:

Q: Write the equation of a sphere of radius 3 in all three coordinates--cartesian, cylindrical, and…

A: It is given that the radius of sphere is 3 .We have to find the equation of sphere in all three…

Q: Write the postulate contrary to that of parallels that serves as the basis for hyperbolic geometry

A: We will solve this question using basic familiarity with hyperbolic geometry and Euclid's fifth…

Q: Find the coordinates of the midpoint of the segment that joins the points a) (a, 0) and (0, b). b)…

A: Givena a, 0 and 0, bb 2a, 0 and 0, 2bMidpoint =x1 +x22 , y1+y22

Q: Suppose a triangle has the following vertices: v1 = (-2, 3, 6) v2 = (4, 5, -1) v3 = (3, 3, 0)…

A: As per the question we are given the following 3d coordinates of a triangle as : v1 = (-2, 3, 6) v2…

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.