12 Fig. 12 shows a window. The base and sides are parts of a rectangle with dimensions \(2 x\) metres horizontally by \(y\) metres vertically. The top is a semicircle of radius \(x\) metres. The perimeter of the window is 10 metres.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{73d1c02b-1b7b-426d-a171-c762597cfed4-4_428_433_1638_766}
\captionsetup{labelformat=empty}
\caption{Fig. 12}
\end{figure}
- Express \(y\) as a function of \(x\).
- Find the total area, \(A \mathrm {~m} ^ { 2 }\), in terms of \(x\) and \(y\). Use your answer to part (i) to show that this simplifies to
$$A = 10 x - 2 x ^ { 2 } - \frac { 1 } { 2 } \pi x ^ { 2 }$$
- Prove that for the maximum value of \(A\), \(y = x\) exactly.
\section*{MEI STRUCTURED MATHEMATICS }
\section*{CONCEPTS FOR ADVANCED MATHEMATICS, C2}
\section*{Practice Paper C2-B
Insert sheet for question 11}
11 Speed-time graph with the first two points plotted.
\includegraphics[max width=\textwidth, alt={}, center]{73d1c02b-1b7b-426d-a171-c762597cfed4-5_768_1772_1389_205}