MATHEMATICS (MA 96) Examination job RIU TANTAL

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MATHEMATICS (MA 96) Examination job RIU TANTAL

Exam papers
on discipline "Mathematics" (MA 96) Option 1

Task 1.
The pyramid ABCD is given coordinates of its vertices: A (t, -1,0), B (2, 3, t), C (-1, t, 1), D (4, 3, 5). Search for:
1. The angle between the edges AB and AC,
2. The equation of the edge AB,
3. equation verge ABC
4. The equation of the height dropped from the top of the D, to the brink of the FAA,
5. Determine whether the vectors of the form AB, AC, AD linearly independent system,
6. The coordinates of the vector MN, if M - mid rib AD, N - mid rib Bc,
7. Lay the basis for the vector MN AB, AC, AD, if he so is.

Task 2.
The curve of the second order is given by the equation + 9h2 25u2 - 72x + 150u + 144 = 0.
1. Give the equation to a canonical form,
2. Find all the characteristics of this curve,
3. Construct a graph of the equation,
4. specify the similarities and differences between the ellipse, parabola and hyperbola.

Task 3.
Conduct a thorough research of the function y = x3 / 2 (x + t) 2 and draw its graph.

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Option 1 will never be sold, with a cover sheet and a list of literature, a positive assessment.


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