Data tables in Pivot Tables allow dynamic analysis of data by varying input values and observing their impact on outputs. The two main types of data tables are:
1. Single-variable data tables: - Used to evaluate how changes in a single input affect the outcome of a formula. - For example, testing the impact of varying interest rates on loan repayments while keeping other variables constant.
2. Two-variable data tables: - Analyze the combined effect of two different variables on a formula. - For instance, examining the impact of varying both interest rates and loan amounts on monthly installments.
Key Features of Data Tables: - Automatically update results when input values or the linked formula changes. - Provide a structured format to visualize multiple scenarios. - Simplify sensitivity analysis for decision-making processes.
Advantages of Data Tables: - Useful in "What-If" analysis to model different scenarios efficiently. - Help users make informed decisions by comparing outcomes under varying assumptions. - Time-saving for repetitive calculations, as they eliminate the need to create multiple individual formulas.
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 \(P,O,Q\).