Question

please solve this please i give brainliest​

Answer 1

Answer:

R = regions created on plane by these lines

D = difference in no. of regions created by n lines w.r.t (n-1) lines

One can derive the no of regions for by using the D and R columns :

No. of regions by n lines = no. of regions by (n-1) lines + n = 2+ [2+3+...+(n-1)] + n

= n*(n+1)/2 + 1

So, for n= 10, no. of regions = 10* 11/2 +1 = 56

hope it helps

Answer 2

If there are n number of non-parallel lines, then the maximum number of regions into which the plane is divided is given by,

$\boxed{\bold{n(\frac{n+1}{2})+1}}$

Here, n = 10

⇒ Number of regions = (10×11)/2 + 1

⇒ Number of regions by 10 lines = 55 + 1

$\boxed{\bold{\therefore{Number\:of \:regions \:by \:10 \:lines = 56}}}$

In the attached file,

• n = Number of regions.

• R = regions created on plane by these lines

• D = difference in no. of regions created by n lines w.r.t (n-1) lines