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The document provides step-by-step worked solutions to pre-calculus problems involving sketching graphs based on transformations of an original function. The first problem involves calculating the length of an arc, area of a sector, and angle of an arc given information about a crop circle. The second problem involves sketching the graphs of three transformations - a stretch, inverse, and reciprocal - of an original function given in a graph. Detailed explanations and mathematical working is shown for arriving at the solutions to each part of the two problems.