Questions[latex]

I am trying to forcefully accommodate text and images in the indicated order , however in the sheet changes if the image does not fit but more text does, Latex fills that space with the following text, that makes it not follow the order that I want to achieve. It would be very helpful if you could guide me, thanks!

I went through this documentation , however I couldn't achieve what I wanted

Here's an example of how I'm arranging things

\begin{tabbing} 
    Obtenemos:
    \= $ equation$ \\
    \> $ equation$ \\
\end{tabbing}

\begin{figure}[!h]
    \centering
    \includegraphics[height=0.5\textwidth]{img.png}
    \caption{Circuito equivalente de la figura~\ref{fig:circuit2-1}}
    \label{fig:circuit2-2}
\end{figure}
                
\begin{tabbing} 
    Partiendo de~\ref{fig:circuit2-2} tenemos:
    \= $ equation$ \\
    \> $ equation$ \\
\end{tabbing}

\begin{figure}[!h]
    \centering
    \includegraphics[height=0.5\textwidth]{img2.png}
    \caption{Circuito equivalente de la figura~\ref{fig:circuit2-2}}
    \label{fig:circuit2-3}
\end{figure}
                

I have tried to graph some trigonometric functions in LaTex and I succeeded but I couldn't with this sin(8πx) which could be approximated as sin(25x) but it seems that the bigger the number that multiplies x, the more LaTex starts to show the graph every time more deformed until it no longer shows it. Is there a way to graph that function?

This is my code:

\begin{center}
\begin{tikzpicture}
\draw [->] (-3.5,0) -- (3.5,0) node[below] {$x$};
\draw [->] (0,-1.5) -- (0,1.5) node[left] {$y$};
\draw (3.14,0) node[below] {$\pi$};
\draw (-3.14,0) node[below] {$-\pi$};
\draw [color=olive, thick,domain=-3.14:3.14] plot (\x,{sin(25*\x r)});
\end{tikzpicture}
\end{center}

In image 1 you see sin(20x). In image 2 it shows me sin(25x)

I am doing an article with two columns in Latex and in the Appendices instead of putting the title and then the image, 2 titles are put on one page and then the images on the others. It is not a problem of sizes because I have tried with everything and nothing, also specifying [h!] and [htb]. I attach photos of how it is now and how I would like it to be (marked in red in the image):

Title page only:

Image only page:

Code:

\subsection{Casos de Uso}
\label{casosuso}

\begin{figure*}[ht]
\begin{minipage}[b]{0.45\linewidth}
\centering
\includegraphics[width=\linewidth]{img/CasosUsoAdmin.png}
\caption{Diagrama de casos de uso - Administrador.}
\label{casoadmin}
\end{minipage}
\hspace{0.5cm}
\begin{minipage}[b]{0.45\linewidth}
\centering
\includegraphics[width=\linewidth]{img/casosUsoUser.png}
\caption{Diagrama de casos de uso - Usuario.}
\label{casouser}
\end{minipage}
\end{figure*}

\newpage 
\subsection{Diagrama E-R}
\label{diagramaer}
\begin{figure*}[ht]
\centering
    \includegraphics[width=1\textwidth]{img/DiagramaER.png}   
    \caption{Diagrama E-R de la Base de Datos.}
    \label{er}
\end{figure*}

\end{document}

Any ideas?

I have the following code in Overleaf:

\begin{align}
\frac{\partial\Lagr}{\partial x_{1}} &= x_{2} + 2x_{1}\lambda_{1} = 0 \\ \frac{\partial\Lagr}{\partial x_{2}} &= x_{1} + x_{3} + 2x_{2}\lambda_{1} + \lambda_{2} = 0\\
%
\frac{\partial\Lagr}{\partial x_{3}} &= x_{2} + \lambda_{2} = 0\\
%
\frac{\partial\Lagr}{\partial \lambda_{1}} &= x_{1}^2 + x_{2}^2 - 2 = 0 \\ \frac{\partial\Lagr}{\partial \lambda_{2}} &= x_{2} + x_{3} -2 = 0 
\end{align}

Which generates this:

Which is what I want, however, later I do another one \begin{align}in which I want the numbers of the equations to be reset, to start from 1 again, this has the following code:

\begin{align}
-2\cdot\alpha_{1} &= 0\\
2\cdot\alpha_{1} + \alpha_{2} &= 0\\
\alpha_{2} &= 0\\
\Rightarrow \alpha_{1} = \alpha_{2} &= 0
\end{align}

And this continues with the sequence of numbers:

Which is not what I want.

There I found commands like:

1. \newcounter{foo}[counter]
2. \setcounter{counter}{0}

And they don't work for me, or I don't know how to use them in these sections.

When writing documents in LaTeX (specifically, I use LyX for it), I'd like to use some custom color for the text; for example, instead of using \textcolor{red}{abc}(red RGB(255,0,0), which works perfectly) I'd like to use something like \textcolor{#990000}{abc}(dark red RGB(153,0,0)this throws an error).

So my specific question is:

• How can I define the color of the text in LaTeX?
• Is it possible to define a custom color to use within my document?
  For example, would it be possible to define a color rojo_oscurowith value #990000and use it in my document like \textcolor{rojo_oscuro}{def}?