Final answer:
Although the provided texts do not detail Carnegie's specific actions after bridge construction to ensure public trust, his reputation for utilizing modern technologies and promoting safety likely played a role in establishing the credibility of his infrastructure projects.
Step-by-step explanation:
After the bridge was built, Andrew Carnegie, being an innovative industrialist and a shrewd businessman, used various methods to convince the public that his bridges were safe. While the given texts do not provide a specific instance regarding Carnegie and his methods for convincing the public of safety post-construction, based on his business practices, we can infer that he likely used his marketing acumen and trust in his enterprise's reputation for using up-to-date machinery and equipment to promote the safety of his bridges. For instance, if we consider other historical scenarios related to public works, such as the construction of the Golden Gate Bridge, public confidence is often won by showcasing the strength and reliability of these structures through demonstrations or by highlighting the rigorous engineering methodologies that ensure maximum safety.