By laying on the short edge the frame of it is 6
Use Pascal's Triangle
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1
1 8 28 56 70 56 28 8 1
1 9 36 84 126 126 84 36 9 1 (this is the row you use)
So, the seventh term of (3x + 2y)^9 will be 84xy
You're looking for c, so you want to isolate it or get it by itself. To get rid of the /3 you multiply since the opposite of division is multiplication and to get rid of it, you do the opposite (like -9 you would add 9 to get it to 0). Now you are left with -19+c = 24 (the 24 is 8*3 because what you do to one side you do to the other. Now you get c by itself so you add 19 to both sides which leaves you with C= 43. Sorry if this was confusing!
A few ways. you can enter it into a calculator for one, but the easiest way would be to reference a unit circle and look for an ordered pair where sin (the y value), is equal to -1/2
on a unit circle, the sin value is -1/2 at 7pi/6 and 11pi/6
because sin is the y value, it will additionally be in the quadrants III or IV based on the fact that (-1/2) as a sin value IS a negative and would have to be found in a quadrant in which sin is negative (the lower half of a coordinate plane, in this case)
