Answer:
![\left[\begin{array}{ccc}x1\\x2\\x3\\x4\end{array}\right] =\left[\begin{array}{ccc}4\\2\\2\\3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx1%5C%5Cx2%5C%5Cx3%5C%5Cx4%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%5C%5C2%5C%5C2%5C%5C3%5Cend%7Barray%7D%5Cright%5D)
4KO2 + 2CO2 → 2K2CO3 + 3O2
Step-by-step explanation:
First we write the reaction in the asked form :
x1 KO2 + x2 CO2 → x3 K2CO3 + x4 O2
In a chemical equation, tha amount of substance that react is the same amount that is formed :
On each side of the equation we must have the same amount of K,C and O.
Let's write this in equations :
K balance : ![x1 =2x3](https://tex.z-dn.net/?f=x1%20%3D2x3)
C balance : ![x2=x3](https://tex.z-dn.net/?f=x2%3Dx3)
O balance : ![2x1+2x2=3x3+2x4](https://tex.z-dn.net/?f=2x1%2B2x2%3D3x3%2B2x4)
The linear equations system is :
![x1=2x3\\2x1+2x2=3x3+2x4\\x2=x3](https://tex.z-dn.net/?f=x1%3D2x3%5C%5C2x1%2B2x2%3D3x3%2B2x4%5C%5Cx2%3Dx3)
Let's equal to 0 to obtain a homogeneous equations system (for convenience) :
![x1-2x3=0\\2x1+2x2-3x3-2x4=0\\x2-x3=0](https://tex.z-dn.net/?f=x1-2x3%3D0%5C%5C2x1%2B2x2-3x3-2x4%3D0%5C%5Cx2-x3%3D0)
Let's work with the extended system matrix :
![\left[\begin{array}{ccccc}1&0&-2&0&0\\2&2&-3&-2&0\\0&1&-1&0&0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccc%7D1%260%26-2%260%260%5C%5C2%262%26-3%26-2%260%5C%5C0%261%26-1%260%260%5Cend%7Barray%7D%5Cright%5D)
Working with the matrix :![\left[\begin{array}{ccccc}1&0&-2&0&0\\0&2&1&-2&0\\0&1&-1&0&0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccc%7D1%260%26-2%260%260%5C%5C0%262%261%26-2%260%5C%5C0%261%26-1%260%260%5Cend%7Barray%7D%5Cright%5D)
→
![\left[\begin{array}{ccccc}1&0&-2&0&0\\0&1&1/2&-1&0\\0&1&-1&0&0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccc%7D1%260%26-2%260%260%5C%5C0%261%261%2F2%26-1%260%5C%5C0%261%26-1%260%260%5Cend%7Barray%7D%5Cright%5D)
→![\left[\begin{array}{ccccc}1&0&-2&0&0\\0&1&-1&0&0\\0&1&1/2&-1&0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccc%7D1%260%26-2%260%260%5C%5C0%261%26-1%260%260%5C%5C0%261%261%2F2%26-1%260%5Cend%7Barray%7D%5Cright%5D)
→![\left[\begin{array}{ccccc}1&0&-2&0&0\\0&1&-1&0&0\\0&0&3/2&-1&0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccc%7D1%260%26-2%260%260%5C%5C0%261%26-1%260%260%5C%5C0%260%263%2F2%26-1%260%5Cend%7Barray%7D%5Cright%5D)
→![\left[\begin{array}{ccccc}1&0&-2&0&0\\0&1&-1&0&0\\0&0&1&-2/3&0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccc%7D1%260%26-2%260%260%5C%5C0%261%26-1%260%260%5C%5C0%260%261%26-2%2F3%260%5Cend%7Barray%7D%5Cright%5D)
→![\left[\begin{array}{ccccc}1&0&0&-4/3&0\\0&1&0&-2/3&0\\0&0&1&-2/3&0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccc%7D1%260%260%26-4%2F3%260%5C%5C0%261%260%26-2%2F3%260%5C%5C0%260%261%26-2%2F3%260%5Cend%7Barray%7D%5Cright%5D)
The matrix is extended to the following linear system :
![x1-\frac{4}{3} x4=0\\x2-\frac{2}{3} x4=0\\x3-\frac{2}{3} x4=0](https://tex.z-dn.net/?f=x1-%5Cfrac%7B4%7D%7B3%7D%20x4%3D0%5C%5Cx2-%5Cfrac%7B2%7D%7B3%7D%20x4%3D0%5C%5Cx3-%5Cfrac%7B2%7D%7B3%7D%20x4%3D0)
![x1=\frac{4}{3}x4\\ x2=\frac{2}{3} x4\\x3=\frac{2}{3}x4](https://tex.z-dn.net/?f=x1%3D%5Cfrac%7B4%7D%7B3%7Dx4%5C%5C%20x2%3D%5Cfrac%7B2%7D%7B3%7D%20x4%5C%5Cx3%3D%5Cfrac%7B2%7D%7B3%7Dx4)
![\left[\begin{array}{c}x1&x2&x3&x4\end{array}\right] =\left[\begin{array}{c}\frac{4}{3} x4&\frac{2}{3}x4 &\frac{2}{3}x4 &x4\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx1%26x2%26x3%26x4%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D%5Cfrac%7B4%7D%7B3%7D%20x4%26%5Cfrac%7B2%7D%7B3%7Dx4%20%26%5Cfrac%7B2%7D%7B3%7Dx4%20%26x4%5Cend%7Barray%7D%5Cright%5D)
![\left[\begin{array}{c}\frac{4}{3}&\frac{2}{3}&\frac{2}{3}&1 \end{array}\right] x4=\left[\begin{array}{c}\frac{4}{3}&\frac{2}{3}&\frac{2}{3}&1 \end{array}\right]t](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D%5Cfrac%7B4%7D%7B3%7D%26%5Cfrac%7B2%7D%7B3%7D%26%5Cfrac%7B2%7D%7B3%7D%261%20%20%20%5Cend%7Barray%7D%5Cright%5D%20x4%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D%5Cfrac%7B4%7D%7B3%7D%26%5Cfrac%7B2%7D%7B3%7D%26%5Cfrac%7B2%7D%7B3%7D%261%20%20%20%5Cend%7Barray%7D%5Cright%5Dt)
t∈ IR
Let's choose t=3 to eliminate the fractional numbers →
![\left[\begin{array}{c}x1&x2&x3&x4\end{array}\right] = \left[\begin{array}{c}4&2&2&3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx1%26x2%26x3%26x4%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D4%262%262%263%5Cend%7Barray%7D%5Cright%5D)
Hint #2 is a or b so ya, and 3 is c
Answer:
Variability
Step-by-step explanation:
Variability in simple terms may be described as differences in measurement or reading of a certain construct or phenomenon. Variability measures include range, standard deviation or variance. In most cases, variation or degree of Variability is measured about a central value called the mean. This is because same measurement about a certain phenomenon or study would usually not yield the same result value. Hence, the mean is used to record the average of these measurement and the differences in each measurement from the mean is also recorded, this is called the standard deviation which is a Variability measure.
Thus VARIABILITY means successive observation of a phenomenon do not yield exactly the same result.
Answer:
I only know the first one.
The surface area of the prism is <u>900</u> cm2
Step-by-step explanation:
To solve the surface area, we need to find the area of the SURFACE not the inside of the cube. Lets do the rectangles first.
28 x 13 = 364
28 x 5 = 140
28 x 12 = 336
1 1
336
+ 140
364
-------------
8 4 0
Now lets do the triangles.
Remember! To find the area of a triangle, you have to do Base x Height x 1/2 because it's half a rectangle.
(The triangles have the same area)
12 x 5 x 1/2 = 30
12 x 5 x 1/2 = 30
30
+ 30
--------
60
The last step is to add the areas of the triangles and the rectangles.
1
840
+ 60
------------
900 cm2
<em>The answer is 900cm2</em>
<em />
This <u>Is not</u> copy pasted, I actually put in all this effort.
Hope this helps :) And have a wonderful day! :D