Question

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.

Answer 1

y = ax^2 y = depth x = width

x = 200 y = 20 replace 20 = a (200)^2
20 / 40000 = a
a = 1/ 2000

then the equation is y = (1/ 2000) x^ 2

Depth of the deepest portion of the sea. x = 1000
then
y = (1/ 2000) (1000)^2
y = (1/ 2000) 1000000
y = 500 meters

Answer 2

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