### Home > CALC > Chapter 7 > Lesson 7.2.2 > Problem 7-74

7-74.

The city planning board 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 8-mile wide city is shown below. The equations below represent the river banks where *x* is the number of miles east of City Hall and *y* is the number of miles north of City Hall. Find the location for the shortest bridge that will span the Newton River. Homework Help ✎

**North Bank: ***y* = cos

**South Bank: ***y* = ln(9 − *x*)

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

Optimize.