7.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{877d03f2-d62c-4060-bdd2-f0d5dfbe6203-22_775_837_251_557}
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\caption{Figure 3}
\end{figure}
The line \(l _ { 1 }\) has equation \(4 y + 3 x = 48\)
The line \(l _ { 1 }\) cuts the \(y\)-axis at the point \(C\), as shown in Figure 3.
- State the \(y\) coordinate of \(C\).
The point \(D ( 8,6 )\) lies on \(l _ { 1 }\)
The line \(l _ { 2 }\) passes through \(D\) and is perpendicular to \(l _ { 1 }\)
The line \(l _ { 2 }\) cuts the \(y\)-axis at the point \(E\) as shown in Figure 3. - Show that the \(y\) coordinate of \(E\) is \(- \frac { 14 } { 3 }\)
A sector \(B C E\) of a circle with centre \(C\) is also shown in Figure 3.
Given that angle \(B C E\) is 1.8 radians,
- find the length of arc \(B E\).
The region \(C B E D\), shown shaded in Figure 3, consists of the sector \(B C E\) joined to the triangle \(C D E\).
- Calculate the exact area of the region \(C B E D\).