The pythagorean sea, in southern antarctica has a depth that varies quadratically with its width. the width of the sea is 1000 meters. two hundred meters from shore, the depth is 20 meters. find the particular quadratic equation for the sea. compute the depth of the deepest portion of the sea.

The depth varies quadratically with the width, so the quadratic equation has the form

d = kw^2

where d is the depth, w is the width, and k is a constant.

We can use the given information to find k.

At a width of 200 m, the depth is 20 m.

20 = k(200)^2

k = 0.0005

The equation of the depth is

d = 0.0005w^2

Now use a width of 1000 m to find the depth at the greatest width.

d = 0.0005w^2

d = 0.0005(1000)^2

d = 500

500 m

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