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Uploaded: 13.08.2011
Content: 10813134924717.doc (333 kB)

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1. Given the coordinates of the vertices of the triangle ABC. Search:
1.dlinu side AB;
2.uravneniya sides AB and BC and their angular coefficients;
3.ugol in radians up to two digits;
CD 4.uravnenie height and its length;
5.uravnenie medians AE and coordinates of the point to the intersection of the median with a height of CD;
6.uravnenie line passing through the point to the parallel side AB;
7.koordinaty point M, point A is arranged symmetrically with respect to the line CD.
2. Given the coordinates of points A () B () and circle radius R, whose center is at the origin. Required:
1. create a canonical equation of the ellipse passing through these points A and B;
2. Find the axis, tricks and eccentricity of the ellipse;
3. Find all points of intersection of the ellipse with a given circle;
4. Construct an ellipse and a circle.
3. Solve the system of three equations with three unknowns using determinants.
4. Given the coordinates of the vertices of the pyramid ABCD. Required:
1.zapisat vectors in the ORT and find modules of these vectors;
2.Find angle between the vectors;
3.nayti projection of a vector;
4.nayti area of \u200b\u200bthe face ABC;
5.nayti volume of the pyramid ABCD.
5. Given the coordinates of points A, B, C and M. Search:
1.uravnenie plane Q, through the points A, B and C;
2.kanonicheskoe equation of the line passing through M perpendicular to the plane Q;
3.tochki crossing the line obtained with the plane Q and the xy coordinate planes, hOz, yOz.
4.rasstoyanie from the point M to the plane Q.
5. This system of equations written in matrix form and then solve using the inverse matrix.
6. Investigate the system of equations on the consistency and solve it, if it is compatible.

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