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How many lines does a cone have?
Infinitely many. There are infinitely many lines from the apex to the base. Every point on each of these lines is on the surface of the cone.
How many lines are determined by 12 points no 3 of which are collinear?
There are 66 lines. As no 3 points are co-linear, every line passes through exactly two of the points. Thus every point is joined by one of the lines to every other point. So it looks like there are 12 × 11 = 132 lines. However, the line joining point A to point B is the same as the line joining point B to point A; in other words, every line has been counted twice, once for one of the points it passes through and again by the other point it passes through. Therefore there are half the number of lines discovered above, name 132 ÷ 2 = 66 lines. This is the same as the "handshake problem" where everyone at a party shakes hands with everyone else at the party and the question is how many handshakes are there; the points are the people and the lines are the handshakes.
Lines that meet at one point?
There is no specific name for lines that meet at one point, but lines that meet at a point, the point is called the intersection point.
How is the solution in a system of inequalities determine?
An inequality determines a region of space in which the solutions for that particular inequality. For a system of inequalities, these regions may overlap. The solution set is any point in the overlap. If the regions do not overlap then there is no solution to the system.
Two lines that meet at a point?
Two lines that meet at one point is called an intersection. More than two seperae lines can be intersected at one point.
