Mathematics MA 96 Exam tasks RIU Tantalus
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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 edges AB and AC,
2. equation of edge AB,
3. equation of the face ABC,
4. the equation of the height dropped from the vertex D to the face 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 terms of the basis AB, AC, AD, if it is one.
Task 2.
The second-order curve is given by the equation 9x2 + 25y2 - 72x + 150y + 144 = 0.
1. Reduce the equation to canonical form,
2. find all the characteristics of this curve,
3. Plot the graph of this equation,
4. Point out the similarities and differences between an ellipse, a hyperbola and a 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 edges AB and AC,
2. equation of edge AB,
3. equation of the face ABC,
4. the equation of the height dropped from the vertex D to the face 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 terms of the basis AB, AC, AD, if it is one.
Task 2.
The second-order curve is given by the equation 9x2 + 25y2 - 72x + 150y + 144 = 0.
1. Reduce the equation to canonical form,
2. find all the characteristics of this curve,
3. Plot the graph of this equation,
4. Point out the similarities and differences between an ellipse, a hyperbola and a 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.