Question

6. If you draw 35 lines on a piece of paper so that no two lines are parallel to each

Answer 1

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

$n = 35$ --- the number of lines

$d = 3$ --- 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:

• 0 intersection for 1 line
• 1 intersection for 2 lines
• 3 intersections for 3 lines
• 6 intersections for 4 lines

Following the above sequence, the number of intersections for n lines is:

$n_k = \frac{n \times (n - 1)}{2}$

In this case, $n = 35.$

So, we have:

$n_k = \frac{35 \times (35 - 1)}{2}$

$n_k = \frac{35 \times 34}{2}$

$n_k = 35 \times 17$

$n_k = 595$

Hence, there will be 595 intersections for 35 lines, where no 3 lines are concurrent.

Read more about lines of intersections at:

brainly.com/question/22368617

Answer 2

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