What is the distance between the sun and the earth in kilometers?

Find all real solutions to the equation (x² − 6x +3)(2x² − 4x − 7) = 0.

Jet001 [13]

Answer:

x = 3 + √6 ; x = 3 - √6 ; $x = \frac{2+3\sqrt{2}}{2}$ ; $x = \frac{2-(3)\sqrt{2}}{2}$

Step-by-step explanation:

Relation given in the question:

(x² − 6x +3)(2x² − 4x − 7) = 0

Now,

for the above relation to be true the following condition must be followed:

Either (x² − 6x +3) = 0 ............(1)

or

(2x² − 4x − 7) = 0 ..........(2)

now considering the equation (1)

(x² − 6x +3) = 0

the roots can be found out as:

$x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}$

for the equation ax² + bx + c = 0

thus,

the roots are

$x = \frac{-(-6)\pm\sqrt{(-6)^2-4\times1\times(3)}}{2\times(1)}$

or

$x = \frac{6\pm\sqrt{36-12}}{2}$

or

$x = \frac{6+\sqrt{24}}{2}$ and, x = $x = \frac{6-\sqrt{24}}{2}$

or

$x = \frac{6+2\sqrt{6}}{2}$ and, x = $x = \frac{6-2\sqrt{6}}{2}$

or

x = 3 + √6 and x = 3 - √6

similarly for (2x² − 4x − 7) = 0.

we have

the roots are

$x = \frac{-(-4)\pm\sqrt{(-4)^2-4\times2\times(-7)}}{2\times(2)}$

or

$x = \frac{4\pm\sqrt{16+56}}{4}$

or

$x = \frac{4+\sqrt{72}}{4}$ and, x = $x = \frac{4-\sqrt{72}}{4}$

or

$x = \frac{4+\sqrt{2^2\times3^2\times2}}{2}$ and, x = $x = \frac{4-\sqrt{2^2\times3^2\times2}}{4}$

or

$x = \frac{4+(2\times3)\sqrt{2}}{2}$ and, x = $x = \frac{4-(2\times3)\sqrt{2}}{4}$

or

$x = \frac{2+3\sqrt{2}}{2}$ and, $x = \frac{2-(3)\sqrt{2}}{2}$

Hence, the possible roots are

x = 3 + √6 ; x = 3 - √6 ; $x = \frac{2+3\sqrt{2}}{2}$ ; $x = \frac{2-(3)\sqrt{2}}{2}$

7 0

3 years ago

g show that the hamiltonian-path problem from exercise 34.2-6 can be solved in polynomial time on directed acyclic graphs. give

NISA [10]

The efficient algorithm can be given in polynomial time.

For this particular problem ,we could find a polynomial time solution for it and then it is proven it could be solved in polynomial time.

1. You must have a source node with an in-degree of zero for a directed acyclic graph, so look for a path in the original graph G that has that value. Since each node must be visited, there is no solution if there are multiple nodes. However, the zero degree should be visited first, and if there are multiple points, there must be some nodes that cannot be visited initially.

2. Assuming that the left graph is G', remove the source node with in-degree zero and its surrounding edges to find the next node to start at.

3. As I mentioned in 1), there is no way to visit those nodes since their in-degree is zero and there should only be one to visit after its predecessor. If the left graph G' has more than two nodes or vertices with the in-degree of zero, then we could conclude that it is unsolvable.

4. Continue performing step 3 until we reach the endpoint, where there are no more nodes to visit. If there are some nodes that are not visited but we can't find an edge to get to them, then the problem cannot be solved; otherwise, we ought to have the answer.

We have discovered the answer to the Hamiltonian-path from the aforementioned steps.

its complexity is O(|E|+|V|) where E is number of edges and V is number of vertexes in directed acyclic graph because from $v_{1}$ to $v_{n}$ , we must trace the vertices and their surrounding edges. It is completed in polynomial time, as we are aware.

To know more about Hamiltonian- path here:

brainly.com/question/27586562

#SPJ4

4 0

1 year ago

Complete the net worth statement. What is the net worth of the individual?

Shtirlitz [24]

Considering it's concept, it is found that the net worth of the individual is given by:

D) $26,595.

<h3>What is the net worth of an individual?</h3>

It is given by the <u>sum of the individual assets subtracted by the sum of it's liabilities</u>.

Researching the problem on the internet, we have that:

The sum of the assets, in dollars, is of 545 + 165000 + 6100 = 171645.

The sum of the liabilities, in dollars, is of 144000 + 1050 = 145050.

Hence, his net worth is given by:

N = 171645 - 145050 = $26,595.

More can be learned about net worth at brainly.com/question/12371230

8 0

2 years ago

0.25e − 14 = 26 <br> please anwser i need a tutor for math

Scorpion4ik [409]

0.25e − 14 = 26 Then you add 14 from both sides

0.25e=40 Then you divide both sides by 0.25

e=160

Then to check you work you do this:

0.25(160)-14=26

40-14=26

26=26 Correct!!!!

4 0

4 years ago

Read 2 more answers

On average, Scott drinks ½ of a 6-ounce glass of water in ⅔ hour. How much water does he drink in an hour?

PolarNik [594]

1/2 a 6 ounce glass is 3 ounces. He drinks 3 ounces in 2/3 of an hour.

3/2 = 1.5. He drinks 1.5 ounces in one third of an hour. 1.5 * 3 = 4.5

C. 4.5 ounces in one hour

7 0

3 years ago