Evaluate ∫ cot 2x dx. a. 1⁄2 ln csc 2x + c b. 1⁄2 ln cos 2x + c c. 1⁄2 ln sin 2x + c d. 1⁄2 ln sec 2x + c

Beatrice decides she wants to babysit a few children at the same time to earn the money faster. she tells parents that if they allow her to babysit their children at her house, she will eliminate her automatic $5 tip and will give them an additional $5 discount. (a) write an equation showing the total cost for each client. identify all variables. (b) four parents bring their children to beatrice’s house at the same time for babysitting. beatrice wants to find out how many hours she must babysit the 4 children to earn exactly the $100 she needs in order to buy the present for her mother. write and solve an equation to find the number of hours. justify each step in the solution. (c) one parent decides not to drop off her child. the remaining 3 parents drop their children off at 9 a.m. two of the parents say they will be back at 1 p.m. the third parent says she will pick up her child at 2 p.m. at noon, beatrice realizes she needs feeding the 3 ch

Identify an equation in point slope form for the line perpendicular to y=3x+5 that passes through (4,-1)

Which shows the correct solution of the equation 1/2a+2/3b=50, when b=30?