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3 years ago

A certain connected graph has 68 vertices and 72 edges. Does it have a circuit?

Mathematics

1 answer:

OLEGan [10]3 years ago

5 0

Answer:

Yes.

Step-by-step explanation:

If a graph G doesn't have a circuit, we must have that

$|E(G)|=|V(G)|-1$

where $|E(G)|$ is the number of edges of the graph and $|V(G)|$ the number of vertices. However, in this case it holds that

$|E(G)|=72>68=|V(G)|.$

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A particle is moving with the given acceleration function and initial conditions. Find the velocity function and the position fu

Lerok [7]

Answer:

The velocity function is the particle is $v(t)=-2\cos (t)-4\sin (t)-1$ .

Step-by-step explanation:

The acceleration function of a moving particle is

$a(t)=2\sin (t)-4\cos (t)$

The initial conditions are v(0) = −3, s(0) = 5.

Integrate the acceleration function with respect to time to find the velocity function.

$\int a(t)=\int (2\sin (t)-4\cos (t))dt$

$v(t)=-2\cos (t)-4\sin (t)+C_1$

Use the initial condition v(0) = −3 to find the value of C₁.

$-3=-2\cos (0)-4\sin (0)+C_1$

$-3=-2(1)-4(0)+C_1$

$-3=-2+C_1$

$-3+2=C_1$

$-1=C_1$

So the velocity function is the particle is

$v(t)=-2\cos (t)-4\sin (t)-1$

Integrate the acceleration function with respect to time to find the position function.

$\int v(t)=\int (-2\cos (t)-4\sin (t)-1)dt$

$s(t)=-2\sin (t)+4\cos (t)-t+C_2$

Use the initial condition s(0) = 5 to find the value of C₂.

$5=-2\sin (0)+4\cos (0)-(0)+C_2$

$5=-2(0)+4(1)+C_2$

$5=4+C_2$

$1=C_2$

So, the position function is the particle is $s(t)=-2\sin (t)+4\cos (t)-t+1$ .

5 0

3 years ago

If b^2 - 4ac < 0, then the roots of the equation ax^2 +bx +c =0 must be?

salantis [7]

Complex numbers.

$b^2-4ac$ no solutions in real numbers.

8 0

3 years ago

(1.357 X 10^9) + 590,000 =

borishaifa [10]

Answer:

1.35759 x 10 ⁹

Step-by-step explanation:

i hope this helped

7 0

3 years ago

Kelsey buys several pairs of uniform pants for $17.95 each, and a sweater for $24. Jeana shops at a different store and buys sev

Vitek1552 [10]

Answer:

Options A, C and F are correct

Step-by-step explanation:

The expression in the question has a slight error in it

<em>"17.75x + 24 = 18.95x + 18"</em> is mearnt to be 17.95x + 24 = 18.95x + 18

Options A, C and F is correct

Given the expression for the situation

17.95x + 24 = 18.95x + 18

collect like terms

17.95x-18.95x=18-24

-x=-6

divide both sides by -1 and solve for x we have

x=6

The girls will both pay the same if they buy six pairs of pants and one sweater.

5 0

3 years ago

Help me help hep plsssssssss

omeli [17]

The axis of symmetry is X=-2

The vertex is (-2,4)

The maximum is 4

There is no minimum as the maximum is also the vertex of the parabola.

The zeros are (-4,0) and (0,0) or just 0 and -4

The domain is all real numbers from negative infinity to positive infinity

The range contains all real numbers less than or equal to 4 :)

3 0

3 years ago