The point of intersection is the point where lines intersect.
There will be 595 intersections for 35 lines, where no 3 lines are concurrent.
Given
[tex]n = 35[/tex] --- the number of lines
[tex]d = 3[/tex] --- no three lines are concurrent
When no three line are concurrent, it means that no three lines meet at the same point.
So, the sequence of intersection is:
Following the above sequence, the number of intersections for n lines is:
[tex]n_k = \frac{n \times (n - 1)}{2}[/tex]
In this case, [tex]n = 35.[/tex]
So, we have:
[tex]n_k = \frac{35 \times (35 - 1)}{2}[/tex]
[tex]n_k = \frac{35 \times 34}{2}[/tex]
[tex]n_k = 35 \times 17[/tex]
[tex]n_k = 595[/tex]
Hence, there will be 595 intersections for 35 lines, where no 3 lines are concurrent.
Read more about lines of intersections at:
https://brainly.com/question/22368617
Number of intersections = 595 intersections
We are drawing 35 lines which must not be parallel to each other.
Also, which must not be concurrent that means they must not intersect at a single point.
Now, I have attached an image of 1 line, 2 lines, 3 lines, 4 lines to show where they are intersecting as regards the conditions given to us in the question.
Looking at the attached image, we see that;
For 1 line; 0 intersections
For 2 lines; 1 intersection
For 3 lines; 3 intersections
For 4 lines; 6 intersections
From this, we see that If we have n lines, the number of intersections increases by n for n + 1 lines.
Thus, the number of intersections can be expressed as; n(n-1)/2.
Where n is number of lines.
Since we have 35 lines, then;
Number of intersections = (35(35 - 1))/2
Number of intersections = 595 intersections
Read more at; brainly.com/question/13080629
