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3 years ago

Let a graph have vertices {L, M, N, O, P, Q, R, S} and edge set {{L,R}, {M,P}, {M,Q}, {N,Q}, {P,R}, {Q,S}, {R,S}} .

Mathematics

1 answer:

Verdich [7]3 years ago

3 0

Answer:

a) The degree of vertex P is 2.

b) The degree of vertex O is 0.

c) The graph has 2 components.

Step-by-step explanation:

a) The edges that have P as a vertice are {M,P} and {P,R}.

b) There is no edge with extreme point O.

c) One of the components is the one with the only vertex as O and has no edges. The other component is the one with the rest of the vertices and all the edges described.

The file has a realization of the graph.

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Consider the vector space p2 of polynomials of degree at most 2. let t be the linear transformation given by t(p(x)) = p(x − 1)

Goryan [66]

Observe what happens to the basis components under the transformation $T$ :

$T(1)=1+1=2=2\cdot1+0\cdot x+0\cdot x^2$
$T(x)=(x-1)+(x+1)=2x=0\cdot1+2\cdot x+0\cdot x^2$
$T(x^2)=(x-1)^2+(x+1)^2=2x^2+2=2\cdot1+0\cdot x+2\cdot x^2$

So we can represent $T$ with the matrix

$\mathbf T=\begin{bmatrix}2&0&2\\0&2&0\\0&0&2\end{bmatrix}$

To check this answer: If we take an arbitrary polynomial $\mathbf p\in\mathbb P_2$ , i.e. the vector

$\mathbf p=\begin{bmatrix}c\\b\\a\end{bmatrix}$

corresponding to the polynomial $p(x)=c+bx+ax^2=c\cdot1+b\cdot x+a\cdot x^2$ , we get

$\mathbf{Tp}=\begin{bmatrix}2a+2c\\2b\\2a\end{bmatrix}=(2a+2c)\cdot1+2b\cdot x+2a\cdot x^2$

Substituting $\mathbf p$ into the rule above, we get

$p(x-1)+p(x+1)=a(x-1)^2+b(x-1)+c+a(x+1)^2+b(x+1)+c$
$p(x-1)+p(x+1)=(2a+2c)+2bx+2ax^2$

as expected.

6 0

3 years ago

Find the equation of the line that is perpendicular to y = 2x + 8 and passes though the point (8, –8).

irina1246 [14]

Answer:

y= -1\2x-4

Step-by-step explanation:

y=mx+c

perpinicular means you flip the slop and change the sign so the slope(m) become -1\2

y=-1\2x+c

since he gives you (8,-8) meaning x=8 and y= -8

we substitute

-8=(-1\2 x 8) +c

now we isolate c

-8+4=c

c=-4

the equation will be

y= -1\2x-4

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Inga [223]

It's the letter B. lol

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2 years ago

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Maru [420]

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2 years ago

The sum of 19 and a number X is equal to 22

madreJ [45]

x is 3. you would subtract 19 from 22 to get your answer

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3 years ago

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