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coldgirl [10]
3 years ago
14

A student drops their notes and their papers scatter. The fact that the papers scatter and do not remain neatly stacked is an il

lustration of :
Mathematics
1 answer:
Serggg [28]3 years ago
8 0

Answer:

-- increase in entropy

-- second law of thermodynamics

Step-by-step explanation:

The 1st law of thermodynamic states that there is conservation of energy, i.e. we cannot create energy and we cannot destroy energy also in an isolated system.

The given example is not a representative of the 1st law.

The \text{2nd law of thermodynamics} states that there is a natural tendency of an isolated system to \text{degenerate} into a more \text{disordered state.} Before dropping the notes and papers were in an isolated ordered system.

After dropping the papers scattered and did not remain in a stack position. It moves into a more disordered state.

Begore dropping down the notes and papers, they were in a stable position, i.e. no kinetic energy is there. No randomness when the notes and the papers were dropped. There is an increase in kinetic energy. There is randomness among the molecules by bombardment. So there is an increase in entropy.

Thus, above illustrations represents :

  • an increase in entropy
  • the second law of thermodynamics
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Step-by-step explanation:

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3 years ago
The given matrix is the augmented matrix for a linear system. Use technology to perform the row operations needed to transform t
shtirl [24]

Answer:

x_{1} = \frac{176}{127} + \frac{71}{127}x_{4}\\\\ x_{2} = \frac{284}{127} + \frac{131}{254}x_{4}\\\\x_{3} = \frac{845}{127} + \frac{663}{254}x_{4}\\

Step-by-step explanation:

As the given Augmented matrix is

\left[\begin{array}{ccccc}9&-2&0&-4&:8\\0&7&-1&-1&:9\\8&12&-6&5&:-2\end{array}\right]

Step 1 :

r_{1}↔r_{1} - r_{2}

\left[\begin{array}{ccccc}1&-14&6&-9&:10\\0&7&-1&-1&:9\\8&12&-6&5&:-2\end{array}\right]

Step 2 :

r_{3}↔r_{3} - 8r_{1}

\left[\begin{array}{ccccc}1&-14&6&-9&:10\\0&7&-1&-1&:9\\0&124&-54&77&:-82\end{array}\right]

Step 3 :

r_{2}↔\frac{r_{2}}{7}

\left[\begin{array}{ccccc}1&-14&6&-9&:10\\0&1&-\frac{1}{7} &-\frac{1}{7} &:\frac{9}{7} \\0&124&-54&77&:-82\end{array}\right]

Step 4 :

r_{1}↔r_{1} + 14r_{2} , r_{3}↔r_{3} - 124r_{2}

\left[\begin{array}{ccccc}1&0&4&-11&:-8\\0&1&-\frac{1}{7} &-\frac{1}{7} &:\frac{9}{7} \\0&0&- \frac{254}{7} &\frac{663}{7} &:-\frac{1690}{7} \end{array}\right]

Step 5 :

r_{3}↔\frac{r_{3}. 7}{254}

\left[\begin{array}{ccccc}1&0&4&-11&:-8\\0&1&-\frac{1}{7} &-\frac{1}{7} &:\frac{9}{7} \\0&0&1&-\frac{663}{254} &:-\frac{1690}{254} \end{array}\right]

Step 6 :

r_{1}↔r_{1} - 4r_{3} , r_{2}↔r_{2} + \frac{1}{7} r_{3}

\left[\begin{array}{ccccc}1&0&0&-\frac{71}{127} &:\frac{176}{127} \\0&1&0&-\frac{131}{254} &:\frac{284}{127} \\0&0&1&-\frac{663}{254} &:\frac{845}{127} \end{array}\right]

∴ we get

x_{1} = \frac{176}{127} + \frac{71}{127}x_{4}\\\\ x_{2} = \frac{284}{127} + \frac{131}{254}x_{4}\\\\x_{3} = \frac{845}{127} + \frac{663}{254}x_{4}\\

6 0
3 years ago
Using the following equation, find the center and radius of the circle. You must show all work and calculations to receive credi
adoni [48]

Answer:

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(2, -4)

Step-by-step explanation:

We have the following equation

x^2 - 4x + y^2 + 8y = -4

The general equation of a circle has the following form

(x-h)^2 + (y-k)^2 = r^2

Where r is the radius and the point (h, k) is the center of the circle

To transform the given equation in the general equation of a circumference we must use the method of square completions

Step 1

(x^2 - 4x) + (y^2 + 8y) = -4

<u>Step 2</u>

<u> </u>Add and subtract (\frac{b}{2})^2 For an equation of the form

ax^2 +bx +c

(x^2 - 4x +4)-4 + (y^2 + 8y +16) -16= -4

<u>Step 3  </u> Factor the expressions within the parentheses

(x-2)^2-4 + (y+4)^2 -16= -4

<u>Step 4 Simplify</u>

(x-2)^2 + (y+4)^2= -4+16+4

(x-2)^2 + (y+4)^2= 4^2

Finally

r = 4

The center is:

(2, -4)

7 0
3 years ago
A bag contains 1 red, 1 yellow, 1 blue, and 1 green marble. What is the probability of choosing a green marble, not replacing it
Karolina [17]

Answer:

\frac{1}{12}

Step-by-step explanation:

P(G) =\frac{1}{4} *P(R)=(\frac{1}{3} )\\(\frac{1}{4} )(\frac{1}{3} ) = \frac{1}{12}

4 0
3 years ago
Read 2 more answers
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