Calculate , z² dS if S is the prism whose base is the triangle in the limited xy plane by the x axis and by the lines y=x and x= 1, the top of which is in the z= 2 - y plane. 2 z= 2 - y y =x

Q: 3. [For students with ID # ending in 4 or 5.] Through the point (4, 2, -5) and perpendicular to the…

A: Given, through the point (4, 2, -5) and perpendicular to the plane…

Q: 1. The plane containing the point (1,-5,8) and orthogonal to the line given b x=-3+15t, y=14-t,…

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Q: 9. Find the equation for the plane through Po(-2,3,9) perpendicular to the line x = -2 – t, y = -3 +…

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Q: Use the applet to translate quadrilateral ABCD 2 units left to create quadrilateral A'B'C'D', then…

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Q: 3. Find the point in which the line x=+3t , y=1- 2t , and z=1+3t meets the plane x+y-z=1.

A: Here, given equation of line is,   And the given equation of plane is, From (1) and (2),

Q: What angle does the line of interaction of the planes 2x+y-z = 0 and x+y+2z= 0 make with the…

A: The direction vector of the line of the interaction of the two planes is equal to the cross product…

Q: 2. The x- and y-axes divide the coordinate plane into four regions called

A: Given: The x and y axes divide the coordinate plane into four regions

Q: 3. Find an equation of the plane parallel to the plane 4x -z- 3y -4 = 0 and passes through the point…

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

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Q: Please

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Q: Suppose the solution set of x1 + x2+2x4 What are the equations of the plane at (1,2,3,4) which is…

A: First we find direction vectors of the plane of solutions.

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Q: Suppose C is the triangle with vertices (3, 0, 0), (0, 4, 0), and (0, 0, 1) oriented…

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Q: 02. A. Show that the plane 3x + y - z = 9 and the line {x = 2,y = -1+ 3t ,z = 1+ 3t} are parallel,…

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.