4
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{19552108-0808-4946-a937-9074d58519b2-2_506_758_1292_657}
\captionsetup{labelformat=empty}
\caption{Fig. 4}
\end{figure}
Fig. 4 shows sector OAB with sector angle 1.2 radians and arc length 4.2 cm . It also shows chord AB .
- Find the radius of this sector.
- Calculate the perpendicular distance of the chord AB from O .
\(5 \quad \mathrm {~A}\) and B are points on the curve \(y = 4 \sqrt { x }\). Point A has coordinates \(( 9,12 )\) and point B has \(x\)-coordinate 9.5. Find the gradient of the chord AB .
The gradient of AB is an approximation to the gradient of the curve at A . State the \(x\)-coordinate of a point C on the curve such that the gradient of AC is a closer approximation.