If a partner withdraws a fixed amount at the end of each quarter, the average period for which interest is charged is calculated as: \[ \text{Average Period} = \frac{\text{Time from First Withdrawal + Time from Last Withdrawal}}{2}. \] Withdrawals occur at the end of: 1st quarter: Remaining time is 9 months. - 2nd quarter: Remaining time is 6 months. - 3rd quarter: Remaining time is 3 months. - 4th quarter: Remaining time is 0 months. For average period: \[ \text{Average Period} = \frac{9 + 0}{2} = 4.5 \text{ months}. \] Hence, the correct answer is (D).
A racing track is built around an elliptical ground whose equation is given by \[ 9x^2 + 16y^2 = 144 \] The width of the track is \(3\) m as shown. Based on the given information answer the following: 
(i) Express \(y\) as a function of \(x\) from the given equation of ellipse.
(ii) Integrate the function obtained in (i) with respect to \(x\).
(iii)(a) Find the area of the region enclosed within the elliptical ground excluding the track using integration.
OR
(iii)(b) Write the coordinates of the points \(P\) and \(Q\) where the outer edge of the track cuts \(x\)-axis and \(y\)-axis in first quadrant and find the area of triangle formed by points \(P,O,Q\).