2 years ago

Find the greatest common factor of the following monomials 50n2 45n3

Mathematics

1 answer:

Sloan [31]2 years ago

3 0

5n^2 is the greatest common factor

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2 years ago

Find the cross product of <img src="https://tex.z-dn.net/?f=-%20%5Cfrac%7B3%7D%7B4%7Dv" id="TexFormula1" title="- \frac{3}{4}v"

dsp73

For any scalars $c_1,c_2$ , we have

$c_1\mathbf v\times c_2\mathbf w=c_1c_2\mathbf v\times\mathbf w$

So

$\left(-\dfrac34\mathbf v\right)\times\left(-\dfrac12\mathbf w\right)=\dfrac38\mathbf v\times\mathbf w$

We have

$\mathbf v\times\mathbf w=\begin{vmatrix}\mathbf i&\mathbf j&\mathbf k\\-2&12&-3\\-7&4&-6\end{vmatrix}$
$=\begin{vmatrix}12&-3\\4&-6\end{vmatrix}\mathbf i-\begin{vmatrix}-2&-3\\-7&-6\end{vmatrix}\mathbf j+\begin{vmatrix}-2&12\\-7&4\end{vmatrix}\mathbf k$
$=-60\,\mathbf i-(-9)\,\mathbf j+76\,\mathbf k$
$=\begin{bmatrix}-60\\9\\76\end{bmatrix}$

which makes

$\left(-\dfrac34\mathbf v\right)\times\left(-\dfrac12\mathbf w\right)=\dfrac38\begin{bmatrix}-60\\9\\76\end{bmatrix}=\begin{bmatrix}-\frac{45}2\\\\\frac{27}8\\\\\frac{57}2\end{bmatrix}$

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3 years ago