Final answer:
A recall is a mechanism for citizens to remove an elected official from office through a public vote. The mayor-council system separates executive power in the hands of the mayor and legislative power within the city council. Public approval ratings for a mayor can change over time, reflecting the satisfaction or dissatisfaction of the constituents with the official's performance.
Step-by-step explanation:
Recall elections are a form of direct democracy that allows citizens to remove elected officials from office. If a significant number of votes are cast in favor of the recall, the official is ousted. This method checks the power of officials and ensures they are accountable to the public. Recall elections are not as common as other political processes, but they are an important tool for voters dissatisfied with their elected representatives.
The mayor-council system divides responsibilities between an elected mayor, who performs the executive functions, and an elected city council, which is responsible for legislative tasks. The authority granted to the mayor can vary greatly under different systems. In a strong mayor system, the mayor often has more direct control over the city's operations.
Considering the popularity of a mayor, public opinion can change over time based on the mayor's actions and decisions. Public approval ratings can be measured through polls. For example, if early in the year, 60 percent of the population approves of the mayor's actions, but by late in the year, the approval drops to 42 percent, this could suggest waning support due to unpopular decisions or events.