30 POINTS Math question algebra 2 Please, I would appreciate if you don't do unhelpful answers. I appreciate the help thanks youuu.

If tan2a=cot(a+60), find the value of a, where 2a is an acute angle

If mary had 320 toy cars and she gave her friend 50 cars and then she gave her brother 72 more cars how much toy cars would mary have left ● explain with proper details

Acaterer knows he will need 60, 50, 80, 40 and 50 dinner napkins on five successive evenings. he can purchase new napkins initially at 25 cents each, after which he can have dirty napkins laundered by a fast one-day laundry service (i. e., dirty napkins given at the end of the day will be ready for use the following day) at 15 cents each, or by a slow two-day service at 8 cents each or both. the caterer wants to know how many napkins he should purchase initially and how many dirty napkins should be laundered by fast and slow service on each of the days in order to minimize his total costs. formulate the caterer’s problem as a linear program as follows (you must state any assumptions you make): a. define all variables clearly. how many are there? b. write out the constraints that must be satisfied, briefly explaining each. (do not simplify.) write out the objective function to be minimized. (do not simplify.)