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The city planning commission has set aside funds to build a bridge going north and south across the Newton River. To save money, they have agreed to build the shortest bridge possible. A map for the -mile wide city is shown at right. The equations below represent the riverbanks where x is the number of miles east of City Hall and y is the number of miles north of City Hall. Determine the location for the shortest bridge that will span the Newton River.

North Bank: South Bank:

At any give value of , the distance between the North and South Banks is:


First quadrant, x axis labeled east, y axis labeled north, origin labeled city hall, decreasing concave down curve starting about 1 fourth up on y axis, ending at x axis, horizontal distance to end point, labeled 8 miles, region below curve shaded, horizontal line at top, vertical distance from x axis labeled, 10 miles, periodic curve starting 3 fourths up on y axis, with 3 visible turning points, region between horizontal line & periodic curve shaded, both curves labeled, riverbanks.