If you are resolute, you have already made up your mind, and you will not be talked out of it. The firmness comes from something that matters to you — a belief, an aim, a promise — so the word feels stronger and a little more serious than just stubborn. A resolute person can be quiet; they do not have to shout. You meet it more in news and careful writing (remain resolute, a resolute stand) than in chat, where people often say determined or they won't give up. Though actually, English also uses it for a face or a mood — a resolute look — meaning the person already shows I am not backing down. It describes people and the way they hold a position, not things.