Sin(a/2) = ± √(1 - cosa)/2 for all values of a. True or False? Help!!

Aschool typically sells 500 yearbooks each year for 50 dollars each. the economic calls does a project and discovers that they can sell 100 more yearbooks for every $5 decrease in price. the revenue for yearbook sales is equal to the number of yearbooks sold times the price of the yearbook. let x represent the number of $5 decrease in price. if the expression that represents the revenue is written in the form r(x)=(500+ax)(50-bx). to maximize profit, what price should the school charge for the yearbooks? what is the possible maximum revenue? if the school attains the maximum revenue, how many yearbooks will they sell?

Need this asap if anyone can i would be very grateful. if you could show workings that would really

Tickets to a science exposition cost $5.75 each for studentd and $7.00 for adults.how many students and adults went if the ticket charge was $42.75