Questions about example sentences with, and the definition and usage of "Resolutely"

A: resolutely is an adjective that means “in a determined manner”

for example, you resolutely sat down to do your homework, meaning you sat down determined to do it and get it done.

A:

* During the conference call, the prime minister stuck resolutely to the line that the suspension was simply aimed at paving the way for his new government to press on with its domestic agenda.

*
What the season resolutely lacked was the sort of cautious complacency that smothers so much of the classical world.

* I resolutely refused to look at them or speak to them .

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A: They're the same thing except well maybe that firmly can also describe the physical state of something (This pillow is very firm OR He firmly gripped his pencil) You wouldn't say he resolutely gripped his pencil.

Resolutely almost always refers to your stance/position on a topic if I'm not mistaken. (When he pitched his proposal to the boss, he very resolutely said no.)