A track-and-field coach wants two laps around the field to be 1000m. The physical education department needs a rectangular field that is as large as possible. Determine the dimensions of the track that will maximize the entire enclosed area. Do these dimensions meet the needs of the track coach and the physical education department? Explain. (There is also a diagram of a rectangle with two semicircles at each end. This represents the field.)

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A track-and-field coach wants two laps around the field to be 1000m. The physical education department needs a rectangular field that is as large as possible. Determine the dimensions of the track that will maximize the entire enclosed area. Do these dimensions meet the needs of the track coach and the physical education department? Explain. (There is also a diagram of a rectangle with two semicircles at each end. This represents the field.)

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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