In the methane molecule, CH4, each hydrogen atom is at a corner of a regular tetrahedron with the carbon atom at the center. In coordinates where one of the C-H bonds is in the direction of i^+j^+k^, an adjacent C-H bond is in the i^-j^-k^ direction. Calculate the angle between these two bonds.

Q: Find distance from point (-6, 3, 5) to the plane – 2y – 4z = 8| -

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Q: Describe the product of two glide reflections whose axes are parallel.

A: The magnitude of the cross product of two parallel vectors was asked in this question. A glide…

Q: find a parametrization of the curve. The line passing through (1, 0, 4) and (4, 1, 2)

A: Given: A line is passing through the points 1, 0, 4 and 4, 1, 2.

Q: 2. CENTER AT (-3, 4); V(-10, 4) length of minor axis = 9

A: Here is the solution

Q: Find a parametrization for the line segment beginning at P,(4, - 7,- 7) and ending at P2(0, - 7,2).

A: The line segment beginning at P1<4, -7, -7> and ending at P2<0, -7, 2>

Q: If the point (2,5) is shifted 3 units to the right and 2 units down,what are its new coordinates?

A: To find the new coordinates of point if the point (2,5) is shifted 3 units to the right and 2 units…

Q: Suppose point A(9,10) was rotated 270 degrees counterclockwise around the origin.  What is the y…

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Q: What 3 dimensional shape will be created by spinning this rectangle on the indicated axis (the…

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Q: What type of three-dimensional object will form from rotating this two-dimensional object around its…

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Q: Verify that ду дх %3D дх ду

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Q: Verify the points (1,5) ,(2,3) and (-2,-1) are collinear or not

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Q: Which point is closest to the yz-plane? ? What is the distance from the yz-plane to this point?

A: The distance of a point from the yz-plane is given by the x coordinate of the point. Because, the x…

Q: A million years ago, an alien species built a vertical tower on a horizontal plane. When they…

A: Consider the given points.P = (0, 0, 0)Q = (2, 2, 0)R = (0, 1, 2)

Q: If the coordinates of the mid-points of the sides of a triangle are (1,1) ,(2,-3) and (3,4) .Find…

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Q: are the new coordinates of A(-5,4) B(-1,3) and C(-4,1) when rotated 75 degrees counterclockwis

A: To find the new coordinates of A(-5,4), B(-1,3) and C(-4,1) when rotated 75° counter clockwise.

Q: What is the 180 degree counter clock wise rule which transformed the pre-image ordered pairs (3,6)…

A: We see that 3 has been transformed to -3 and 6 to -6. Hence

Q: 4/2 cis(-30°) 2/2 cis(-60°)

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Q: Show that the point (5,4,2), (6,2,-1) and (8,-2,-7) are collinear

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Q: Find the centroid of the triangle whose vertices are at points (3,4). (6.-9) and (6,-2). asap pls

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Q: Point Q of quadrilateral QRST Is (-9,2). What Is the image of Q after QRST has been reflected across…

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Q: What is the image of the point (3,-6) after a rotation of 90° counterclockwise about the origin?

A: Consider the given point 3,-6

Q: If the point (6, -1) is reflected over line y = 2 then dilated by 2, what would the new points be?

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Q: Describe the bifurcation that occurs when A = -1.

A: The bifurcation that occurs when λ=-1 is described as shown below

Q: Find a parametric representation of a straight line passing through (1,2,1) in the direction of…

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Q: What is the 270 degree counter clockwise rule which transformed the pre-image ordered pairs (3,6) to…

A: To find The 270 degree counter clockwise rule which transformed the pre image ordered pairs (3,6) to…

Q: What is the image of the point (-6,4) after a rotation of 180° counterclockwise about the origin?

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Q: Compute the original coordinates with respect to x and y axes if the translated coordinates of this…

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Q: Find a parametrization for the line segment beginning at P, (-5, - 2,3) and ending at P2 0, 5/4

A: We have to use parameterization of the line.

Q: What is the image of (-6,0) after a reflection over the line y = -x? %3D

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Q: Graph the image of UVW after a rotation 90 degrees counterclockwise around the origin. Give me the…

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Q: Explain how to find the distance between two parallel planes.

A: Explain how to find the distance between two parallel planes.

Q: Find the distance from the point (1, -4, 4) to the plane −2x−4y+3z=5

A: Given:The point (1, –4,4) and the equation of the plane –2x–4y+3z=5.The distance from the point…

Q: Find a parametrization for the line SEGMENT between (- 5, 7, 6) and (2, – 6, – 9). |

A: Parameterizing a line segment, which joins the points (x1,y1,z1) and (x2,y2,z2), helps in obtaining…

Q: What is the image of the point (-7, -8) after a rotation of 180 counterclockwise about the origin?

A: Under rotation 180° about origin,a point (x,y)→(-x,-y)Hence (-7,-8)→(7,8)

Q: what solid is formed when a right triangle is rotated around a line containing one of its legs

A: When a right triangle is rotated around a line containing one of its legs, a cone is formed .

Q: Which of the following is the equation with center (-9, 8) Major axis = 10? %3D 20 and minor axis…

A: To find the equation of the vertical ellipse with center (-9,8) . Major axis = 20 and minor axis =…

Q: Draw the left and front vlews of the solid below. Left Front

A: Solid shapes are nothing but solids that consist of 3 dimensions, namely length, breadth, and…

Q: 0,change from poler to Cartesian Co-ovdinate VE-2- COSE9

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: What is the image of the point (6,-3) after a rotation of 180° counterclockwise about the origin?

A: Our Aim is to tell the image of the point (-6,-3) after a rotation of 180°counterclockwise about the…

Q: What is the image of the point (-7,5) after a rotation of 180° counterclockwise about the origin?

A: Rule for rotating 180⁰ counterclockwise about the origin If we are rotating any point (x,y) about…

Q: The accompanying diagram shows a right triangle. If the triangle is rotated 90° counterclockwise…

A: Given that  A right angle triangle is rotated in 90° in counter clockwise about the origin.

Q: When a figure is dilated and the segments pass through the center of dilation, the pre-image will be…

A: Here, we have given that a figure is dilated and the segments pass through the center of dilation.

Q: What 3 dimensional shape is created when this shape is rotated around the axis

A: To find the correct option

Q: What is the 270 degree clockwise rule which transformed the pre-image ordered pairs (5,-8) to it's…

A: Solution  Given image is transformed 270⁰ clockwise Pre image coordinates (x,y)=(5 ,-8) Image…

Q: A long suspension bridge 180 meters from end,has towers 60 meters tall,where suspension cables are…

A: Given : from the data given above  the graph of the parabola is:

Q: What is the image of the point (-7,9) after a rotation of 270 counterclockwise about the origin

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Q: What is the image of the point (0,-2) after a rotation of 90° counterclockwise about the origin?…

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Q: What coordinate system is suggested if the integrand of a tripleintegral involves x2 + y2?

A: Given: The integrand of a triple integral involves x2 + y2

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.