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dimulka [17.4K]
3 years ago
11

A) Find the value of N if, Kn has 105 edges.

Mathematics
1 answer:
blagie [28]3 years ago
7 0

The number of edges can be calculated from the number of vertices.

  • <em>There are 14 vertices for 105 edges</em>
  • <em>There are 200 vertices for 19900 edges</em>

The variable N is used to always represent the number of vertices.

So, we represent the edges as:

E \to Edges

<u />

<u>(a) The value of N for 105 edges</u>

The relationship between N and E is:

E = \frac{N \times (N - 1)}{2}

Substitute 105 for E

105 = \frac{N \times (N - 1)}{2}

Multiply through by 2

210 = N \times (N  - 1)

210 = N^2  - N

Rewrite as:

N^2 - N - 210 = 0

Expand

N^2 +14N - 15N - 210 = 0

Factorize

N(N +14) - 15(N + 14) = 0

Factor out N + 14

(N - 15) (N + 14) = 0

Solve for N

N = 15 or N = -14

The number of vertices (N) cannot be negative. So:

N = 15

<u>(b) The value of N for 19900 edges</u>

We have:

E = \frac{N \times (N - 1)}{2}

Substitute 19900 for E

19900 = \frac{N \times (N - 1)}{2}

Multiply through by 2

39800 = N \times (N  - 1)

39800= N^2  - N

Rewrite as:

N^2 - N - 39800= 0

Expand

N^2 +199N - 200N - 39800= 0

Factorize

N(N +199) - 200(N + 199) = 0

Factor out N + 199

(N + 199) (N - 200) = 0

Solve for N

N = 200 or N = -199

The number of vertices (N) cannot be negative. So:

N = 200

<em>Hence, there are 200 vertices for 19900 edges</em>

Read more about vertices and edges at:

brainly.com/question/22118318

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