Math homework Definition and 54 Threads

I need help please with all these questions. 1. How many different paths on the diagram below will spell PASCAL? * This diagram is a little wrong because i don't know how to do it on the forums, but anyways the letters should be spaced out so that they are in between each of the spaces...

does this seem right? lim (sin3x)/(x+3x^2) x->0 =(sin3x)/[3x^2(1/3x+1)] =1/[(1/3(0)+1)(sin3(0))] =undefined

If sin(x) = 8/17, what would sin(x/2) = ? I knew how to get 8/17, but i have no idea where to go from here Would you just times the denominator by 2?

I'm lost with this problem. If anyone can help at all I'd really appreciate it. What are the dimensions of the base of the rectangular box of greatest volume that can be constucted from 100 suqare inches of cardboard if the base is to be twice as long as it is wide? Assume that the box has...