**Polar Coordinates and Graph Matching** The task is to match each polar graph with its corresponding equation. Each graph is a limaçon, which is a special type of polar graph. **Equations:** a. \( r = 1 + 4 \cos(\theta) \) b. \( r = 4 \cos(\theta) \) c. \( r = 4 + 4 \cos(\theta) \) d. \( r = 5 + 4 \cos(\theta) \) e. \( r = 9 + 4 \cos(\theta) \) **Graph Descriptions:** - **Graph 1:** A limaçon with an inner loop, centered around the origin. This shape typically corresponds to equations with a smaller constant compared to the coefficient of \( \cos(\theta) \). - **Graph 2:** A cardioid, a specific type of limaçon where the graph resembles a heart shape. This occurs when the constant and the coefficient of \( \cos(\theta) \) are equal. - **Graph 3:** A dimpled limaçon that does not have an inner loop, indicating the constant is slightly larger than the coefficient of \( \cos(\theta) \). - **Graph 4:** A convex limaçon with no inner loop, larger than the previous graphs, suggesting a significantly larger constant in the equation. - **Graph 5:** Having the largest size and convex shape, this graph matches with an equation where the constant is much greater than the coefficient of \( \cos(\theta) \). **Objective:** Match each graph type described above with its corresponding equation from the list. The image shows a series of concentric circles arranged vertically along a dashed line. Each set of circles is accompanied by a dropdown menu, indicating that it might be part of an interactive educational activity, possibly involving configurable options or questions. The circles vary in size, with smaller circles appearing at the top and larger ones toward the bottom. There is a "Submit Question" button below the circles, suggesting an interactive component where students may select an option from each dropdown and submit their answers for evaluation. The application appears to be a part of an educational platform, as seen from the visible headers indicating tabs such as “WileyPLUS,” “Microsoft Office H,” and “Chem101.”