Final answer:
The question involves piecewise functions, quadratic equations, and correlation coefficients in the context of high school mathematics.
Step-by-step explanation:
The question pertains to mathematics, specifically piecewise functions and quadratic equations. The student is presented with a piecewise function r(x) that applies different formulas for values of x within and outside the range 0≤x≤20. Additionally, the question includes an estimation where the value of x is considered small relative to another value, allowing for simplification.
A quadratic equation x² +0.0211x -0.0211 = 0 is mentioned, which highlights solving methods for quadratic forms ax² + bx + c = 0. Finally, a reference to correlation coefficient analysis r = 0.4526 for data points is given, requiring knowledge of statistics and correlation significance testing.