A ladder rests with one end against a vertical wall, and the other end upon a horizontal floor. If the ladder fall by sliding along the floor, find the locus of its middle point.

Q: Find an equation for the plane through A(3, 3, 3), B(5,5,5) and C(0,5, 9).

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Q: Find a plane through the points (-2,6,6), (4,4,5), (2,-4,1) Calculator

A: Given :The points (-2,6,6), (4,4,5),(2,-4,1)

Q: please help me with this exercise

A: Given, the vertices of the parallelogram  A(-3, 5), B(-1, 8), C(3, 6), and D(1, 3).

Q: Find the intersection of the planes r + 2y - 3z 1 and x -y+ z 1 two different

A: Given: equation of planes We need to find intersection of above two planes.

Q: Find the coordinates of the vertices of the polygon after the indicated translation to a new…

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Q: You start at (2, 1). You move up 3 units and left 1 unit. Where do you end?

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Q: Rectangle DEFG is shown in the Cartesian plane below. у (ст) E D y==x+25 F(25,6) x (ст) G The rule…

A: Given: In rectangle DEFG, the equation of DE is y=25x+25, and point F(25, 6)

Q: SOLVE BY HAND LEGIBLE Find the point on the sphere that is closest to the point (1,-1,1)

A: Step 1:Step 2:Step 3:Step 4:

Q: (a) Complete the chart on the intersection of the plane. Geometric Model Description Normals…

A: If two planes are parallel then their normals are also parallel.If two planes are perpendicular to…

Q: Using a suitable variable change find

A: Change the given Cartesian coordinates into the polar form as.

Q: 2. Consider the plane determined by the three points (3,−1, 2), (8, 2, 4) and (−1, −2, —3). (a) Find…

A: Given: Three Points P=(3,-1,2),Q=(8,2,4) and R=(-1,-2,-3) PQ = <5, 3, 2> PR = <-4, -1,…

Q: 6) Consider the three points in the plane given by their coordinates: A=(0,0) B=(2,2) C=(3,5). Find…

A: Given: Coordinates: A=0, 0, B=2, 2, C=3, 5To find: The area of the triangle using the Heron's…

Q: Tools - / Question 2 A triangle in the xy-coordinate plane is formed by the points (2, 7), (2,-4),…

A: Since the exact answer is 24.8 Unfortunately this is not available in the option.

Q: Show that planes 2x- y + z = 0 and x+2y-z = 1 intersect according to a straight r.

A: General Equation of a Plane: A plane can be represented by an equation of first degree in such as…

Q: Find an equation of the plane. The plane through the points (0, 7, 7), (7, 0, 7), and (7, 7, 0)

A: Given:Plane passing through points 0,7,7 7,0,7 and 7,7,0To find; equation plane passing through…

Q: Find a plane containing the point (1,3,-6) and the line of intersection of the planes 8x - 8y- 5z =…

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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.