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well for one you've got 25 in the matrix where it should be -25.

\(\begin{pmatrix} 1&-1&-2&|&-6\\ 3&2&0&|&-25\\ -4&1&-1&|&12 \end{pmatrix}\\ \begin{pmatrix} 1&-1&-2&|&-6\\ 0&5&6&|&-7\\ -4&1&-1&|&12 \end{pmatrix}\\ \begin{pmatrix} 1&-1&-2&|&-6\\ 0&5&6&|&-7\\ 0&-3&-9&|&-12 \end{pmatrix}\\\)

Now exchange rows 2 and 3 and normalize row 2

\(\begin{pmatrix} 1 & -1 & -2 & -6 \\ 0 & 1 & 3 & 4 \\ 0 & 5 & 6 & -7 \end{pmatrix}\\ \begin{pmatrix} 1 & 0 & 1 & -2 \\ 0 & 1 & 3 & 4 \\ 0 & 5 & 6 & -7 \end{pmatrix}\\ \begin{pmatrix} 1 & 0 & 1 & -2 \\ 0 & 1 & 3 & 4 \\ 0 & 0 & -9 & -27 \end{pmatrix}\\ \)

Normalize row 3 and continue

\(\begin{pmatrix} 1 & 0 & 1 & -2 \\ 0 & 1 & 3 & 4 \\ 0 & 0 & 1 & 3 \\ \end{pmatrix}\\ \begin{pmatrix} 1 & 0 & 0 & -5 \\ 0 & 1 & 3 & 4 \\ 0 & 0 & 1 & 3 \\ \end{pmatrix}\\ \begin{pmatrix} 1 & 0 & 0 & -5 \\ 0 & 1 & 0 & -5 \\ 0 & 0 & 1 & 3 \\ \end{pmatrix}\\ \)

\(\begin{pmatrix}x\\y\\z\end{pmatrix} = \begin{pmatrix}-5\\-5\\3\end{pmatrix}\)

arcos and cos cancel each other out and you are left with 7 R

7 Radians is equal to   7 - 2pi = .7168 R     ( As this is reference angle   -.7168  would give the same result)

Picture:

https://www.desmos.com/calculator/vxtm4fbbaa

b.  slope = 9/4      

       using point   -12 20        20 = 9/4 (-12) + b    b = 47

y = 9/4 x + 47

a.   slope =   y1-y2   /   x1-x2  ==== (8-17)/(4-8) = 9/4

     using y = mx+b     m = 9/4    and one of the points

                8 = 9/4(4) + b       b = -1

         y = 9/4 x -1  

Let's take two arbitrary numbers: \(n,m\) therefore we have \(n+m = 6\) and \(nm = 3\).

So we have to find the sum of the reciprocals or: \(\frac{1}n+\frac{1}m \)

Adding them we get: \(\frac{m+n}{nm}\) using the sum and product of the two numbers we can say \(\frac{m+n}{nm} = \frac{6}3 = \boxed{2}\)

x+y=6      y = 6-x

x * y = 3

x * (6-x) = 3

-x^2+6x-3=0       x = 3 +-sqrt6        y = 3 -+sqrt6

1/(3+sqrt6)  + 1/(3-sqrt6)   =  2  

first 20 digits: 73897156067403508131

last 20: 33408341373887572343

please correct me if i'm wrong :)

(4a - 4a ) + 4a  =

(0)  + 4a  =

4a

20 divided by 1/4 \(= \frac{20}{\frac{1}{4}} = 20 *4 = 80\)

9/10 divide by (-4/5)  \(= \frac{\frac{9}{10}}{\frac{1}{4}} = \frac{9*4}{10*1} = \frac{36}{10} = \frac{18}{5}\) or 3.6

Thanks a lot!

\(\left(7-\dfrac 2 x\right) = \sqrt{\dfrac 7 x}\\ \left(7-\dfrac 2 x\right)^2 = \dfrac{7}{|x |} \\ 49-\dfrac{28}{x} + \dfrac{4}{x^2} = \dfrac{7}{|x|}\)

\(\text{let $x>0$}\\ 49-\dfrac{28}{x} + \dfrac{4}{x^2} = \dfrac{7}{x}\\ 49x^2 - 28x + 4 = 7x\\ 49x^2 - 35x+ 4 = 0\\ x = \dfrac{35\pm \sqrt{(35)^2 - (4)(49)(4)}}{98} = \left(\dfrac 4 7,~\dfrac 1 7\right)\\ \text{We do however notice that $x = \dfrac 1 7$ is not a solution of the original equation $\\$ so it is discarded leaving only $x = \dfrac 4 7$}\)

\(\text{let $x\leq0$}\\ 49-\dfrac{28}{x} + \dfrac{4}{x^2} = -\dfrac 7 x\\ 49x^2-21x+4 = 0\\~\\ \text{We note that this equation has no real solutions and thus would not satisfy the original equation}\)

\(\text{So the only solution is $x= \dfrac 4 7$}\)

Thanks Rom,

Yes I like

x=f(y)     for x depends on y

eh same but i been banned so many times on this site