Mathematics MA 96 Exam tasks RIU Tantalus
Replenishment date: 26.02.2011
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Description
Exam assignments
in the discipline "MATHEMATICS" (MA 96) for the 1st option
Task 1.
The pyramid ABCD is given by the coordinates of its vertices: A (t, -1,0), B (2, 3, t), C (-1, t, 1), D (4, -3, 5). Find:
1.the angle between the ribs AB and AC,
2.equation of the edge AB,
3.equation of the ABC face,
4.equation of the height dropped from the vertex D to the edge ABC,
5.Find out whether the vectors AB, AC, AD form a linearly independent system,
6.coordinates of the vector MN, if M is the midpoint of the edge AD, N is the midpoint of the edge BC,
7. Expand the vector MN in the basis of AB, AC, AD, if it is.
Task 2.
The second-order curve is given by the equation 9x2 + 25y2 - 72x + 150y + 144 = 0.
1.Reduce the equation to the canonical form,
2. find all the characteristics of a given curve,
3.plot the given equation,
4. Indicate the similarities and differences between ellipse, hyperbola and parabola.
Task 3.
Do a complete study of the function and graph it.
in the discipline "MATHEMATICS" (MA 96) for the 1st option
Task 1.
The pyramid ABCD is given by the coordinates of its vertices: A (t, -1,0), B (2, 3, t), C (-1, t, 1), D (4, -3, 5). Find:
1.the angle between the ribs AB and AC,
2.equation of the edge AB,
3.equation of the ABC face,
4.equation of the height dropped from the vertex D to the edge ABC,
5.Find out whether the vectors AB, AC, AD form a linearly independent system,
6.coordinates of the vector MN, if M is the midpoint of the edge AD, N is the midpoint of the edge BC,
7. Expand the vector MN in the basis of AB, AC, AD, if it is.
Task 2.
The second-order curve is given by the equation 9x2 + 25y2 - 72x + 150y + 144 = 0.
1.Reduce the equation to the canonical form,
2. find all the characteristics of a given curve,
3.plot the given equation,
4. Indicate the similarities and differences between ellipse, hyperbola and parabola.
Task 3.
Do a complete study of the function and graph it.
Additional Information
Option 1. The work was handed over to the teachers of RIU Tantalum with a positive assessment.