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resolute  
If you describe someone as resolute, you approve of them because they are very determined not to change their mind or not to give up a course of action. 
FORMAL  adj  (=determined) 
Voters perceive him as a decisive and resolute international leader...  
 resolutely    adv ADV with v, ADV adj 
He resolutely refused to speak English unless forced to..., The United States remains resolutely opposed to this.