If the legislative body of any city finds that any public park, beach, golf course, or recreation ground belonging to the city is being used by large numbers of residents of the county generally who are not residents of the city, and that the use by the nonresidents of the city necessitates the enlargement or improvement or increases the cost of maintenance of the public park, beach, golf course, or recreation ground, it may request financial assistance from the county in which the city is situated by a resolution adopted by a vote of four-fifths of all its elected members.