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mezya [45]
3 years ago
5

Multiply 3xyz ^ 2 / 6y ^ 4 by 2y / x z ^ 4

Mathematics
2 answers:
Marat540 [252]3 years ago
8 0

\dfrac{3xyz^2}{6y^4}=\dfrac{3}{6}\cdot\dfrac{xyz^2}{y^4}=\dfrac{1}{2}\cdot\dfrac{xz}{y^3}=\dfrac{xz}{2y^3}\\\\\\\dfrac{3xyz^2}{6y^4}\cdot\dfrac{2y}{xz^4}=\dfrac{xz^2}{2y^3}\cdot\dfrac{2y}{xz^4}=\dfrac{2}{2}\cdot\dfrac{xyz^2}{xy^3z^4}=1\cdot\dfrac{1}{y^2z^2}=\dfrac{1}{y^2z^2}

ohaa [14]3 years ago
8 0
<h2>Answer:</h2>

The product  of the expression is:

                      \dfrac{1}{y^2z^2}

<h2>Step-by-step explanation:</h2>

We are asked to multiply the expression:

\dfrac{3xyz^2}{6y^4}\times \dfrac{2y}{xz^4}

i.e.

The numerator terms get multiplied to each other and the denominator terms get multiplied to each other

i.e. we may write the expression as follows:

=\dfrac{(3xyz^2)\cdot (2y)}{(6y^4)\cdot (xz^4)}\\\\\\=\dfrac{6xy^2z^2}{6xy^4z^4}\\\\=\dfrac{6}{6}\times \dfrac{x}{x}\times \dfrac{y^2}{y^4}\times \dfrac{z^2}{z^4}\\\\=y^{2-4}\times z^{2-4}\\\\=y^{-2}\times z^{-2}\\\\i.e.\\\\=\dfrac{1}{y^2}\times \dfrac{1}{z^2}\\\\=\dfrac{1}{y^2z^2}

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Answer:

The solution of the system of linear equations is x=3, y=4, z=1

Step-by-step explanation:

We have the system of linear equations:

2x+3y-6z=12\\x-2y+3z=-2\\3x+y=13

Gauss-Jordan elimination method is the process of performing row operations to transform any matrix into reduced row-echelon form.

The first step is to transform the system of linear equations into the matrix form. A system of linear equations can be represented in matrix form (Ax=b) using a coefficient matrix (A), a variable matrix (x), and a constant matrix(b).

From the system of linear equations that we have, the coefficient matrix is

\left[\begin{array}{ccc}2&3&-6\\1&-2&3\\3&1&0\end{array}\right]

the variable matrix is

\left[\begin{array}{c}x&y&z\end{array}\right]

and the constant matrix is

\left[\begin{array}{c}12&-2&13\end{array}\right]

We also need the augmented matrix, this matrix is the result of joining the columns of the coefficient matrix and the constant matrix divided by a vertical bar, so

\left[\begin{array}{ccc|c}2&3&-6&12\\1&-2&3&-2\\3&1&0&13\end{array}\right]

To transform the augmented matrix to reduced row-echelon form we need to follow these row operations:

  • multiply the 1st row by 1/2

\left[\begin{array}{ccc|c}1&3/2&-3&6\\1&-2&3&-2\\3&1&0&13\end{array}\right]

  • add -1 times the 1st row to the 2nd row

\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&-7/2&6&-8\\3&1&0&13\end{array}\right]

  • add -3 times the 1st row to the 3rd row

\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&-7/2&6&-8\\0&-7/2&9&-5\end{array}\right]

  • multiply the 2nd row by -2/7

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  • add 7/2 times the 2nd row to the 3rd row

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  • multiply the 3rd row by 1/3

\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&1&-12/7&16/7\\0&0&1&1\end{array}\right]

  • add 12/7 times the 3rd row to the 2nd row

\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&1&0&4\\0&0&1&1\end{array}\right]

  • add 3 times the 3rd row to the 1st row

\left[\begin{array}{ccc|c}1&3/2&0&9\\0&1&0&4\\0&0&1&1\end{array}\right]

  • add -3/2 times the 2nd row to the 1st row

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From the reduced row echelon form we have that

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Since every column in the coefficient part of the matrix has a leading entry that means our system has a unique solution.

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