<ol class="i-list" start="7"><li><div class="list-item-paragraph"> [The area of a sector is \(\frac{1}{2} r^2 \theta\), where&nbsp;\(\theta\) is the angle, in radians, subtended by the arc at the centre of the circle of radius \(r\).]</div><div class="content-block list-item-image" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1776340596839-folnwqh2q84.png" alt="List item image" class="aligncenter custom-width" style="max-width: min(220px, 100%); height: auto;" /></div><div class="list-item-paragraph">In the diagram, \(O\) is the centre of the circle with diameter \(BC\) and radius \(10\) cm.<br>\(A\) is the shaded area enclosed by the chord \(CD\), the diameter \(BC\) and the minor arc \(BD\). <br>Angle \(BCD = x\) radians.</div><ol class="abc-list"><li><div class="list-item-paragraph">Show that&nbsp;\(A = 100x + 50 \sin 2x\).<span class="inline-marks">[3]</span></div></li><li><div class="list-item-paragraph">If&nbsp;\(x\) is increasing at a rate of \(0.2\) radian/second, find the rate of change of \(A\) when&nbsp;\(x = \frac{\pi}{6}\).<span class="inline-marks">[3]</span></div></li><li><div class="list-item-paragraph">Find the value of \(x\) when the rate of change of \(A\) is \(50\) times the rate of increase of \(x\).<span class="inline-marks">[3]</span></div></li></ol></li></ol>

 [The area of a sector is \(\frac{1}{2} r^2 \theta\), where \(\theta\) is the angle, in radians, subtended by the arc at the centre of the circle of radius \(r\).]

In the diagram, \(O\) is the centre of the circle with diameter \(BC\) and radius \(10\) cm.
\(A\) is the shaded area enclosed by the chord \(CD\), the diameter \(BC\) and the minor arc \(BD\). 
Angle \(BCD = x\) radians.

TKSS 4AM 2022 Prelims P2 Q7

TKSS 4AM 2022 Prelims P2 Q7