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n200080 [17]
2 years ago
6

If G has n vertices and is regular of degree r, how many edges has G?

Mathematics
1 answer:
sladkih [1.3K]2 years ago
4 0

Answer:

We know that the sum of the degrees of the vertices of the graph is twice the number of edges of the graph.

Let G be a graph with vertices v_1,v_2,\cdots,v_n

Then \sum_{i=1}^ndeg(v_i)=2e\\ where e is the number of edges of the graph. Since the graph is regular of degree r then all vertices have degree r. Thus,

\sum_{i=1}^n r=2e\\nr=2e\\e=\frac{nr}{2}

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Step-by-step explanation:

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First, let's look at the identities:

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The question asks to find sin(A - B); therefore, we need to use the difference identity.

Based on the given information (value and quadrant), we can draw reference triangles to find the simplified values of A and B.

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Plug these values into the difference identity formula.

sin(A - B) = sinAcosB - cosAsinB

sin(A - B) = (\frac{24}{25})(\frac{3}{5}) - (-\frac{4}{5})(\frac{7}{25})

Multiply.

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Add.

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This is your answer.

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