10.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f953fd1c-447f-4e97-a42a-5264c053fda0-20_424_1241_246_299}
\captionsetup{labelformat=empty}
\caption{Figure 5}
\end{figure}
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f953fd1c-447f-4e97-a42a-5264c053fda0-20_385_1205_792_379}
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\caption{Figure 6}
\end{figure}
A suspension bridge cable \(P Q R\) hangs between the tops of two vertical towers, \(A P\) and \(B R\), as shown in Figure 5.
A walkway \(A O B\) runs between the bases of the towers, directly under the cable.
The towers are 100 m apart and each tower is 24 m high.
At the point \(O\), midway between the towers, the cable is 4 m above the walkway.
The points \(P , Q , R , A , O\) and \(B\) are assumed to lie in the same vertical plane and \(A O B\) is assumed to be horizontal.
Figure 6 shows a symmetric quadratic curve \(P Q R\) used to model this cable.
Given that \(O\) is the origin,
- find an equation for the curve \(P Q R\).
Lee can safely inspect the cable up to a height of 12 m above the walkway.
A defect is reported on the cable at a location 19 m horizontally from one of the towers. - Determine whether, according to the model, Lee can safely inspect this defect.