Rail cars travellind down to a mine have to pass through the tunnel entrance show. The tunnel entrance is in the form of a semi-elliptical arch 6 metres wide and 4 metres tall. Each rail car is 4 metres wide and passes through the middle of the tunnel. The rail cars have a rectangular cross-section and come in three types with three differnt heights as show in the table.

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Rail cars travellind down to a mine have to pass through the tunnel entrance show. The tunnel entrance is in the form of a semi-elliptical arch 6 metres wide and 4 metres tall. Each rail car is 4 metres wide and passes through the middle of the tunnel. The rail cars have a rectangular cross-section and come in three types with three differnt heights as show in the table.

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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rail car height The alpha 2m The beta 2.5m the gamma 3.2m
Which of these types of rail car will pass safely through the tunnel entrance?
Write down the semi-ellipse as a formula and then determine how high it is at the points 2m from the middle.

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