List the coefficients in the row of Pascal's triangle corresponding to n = 7.

9514 1404 393

  1 7 21 35 35 21 7 1

Step-by-step explanation:

Numbering from k=0 to k=7, the k-th coefficient in the row is ...

  C(7, k) = 7!/(k!(7-k)!)

You know the first two in row 7 are 1 and 7. There are 8 in the row, and the row is the same forward and backward. This means you only need to find C(7, 2) and C(7, 3). These are ...

  C(7, 2) = 7!/(2!(5!)) = 7·6/(2·1) = 21

  C(7, 3) = 7!/(3!(4!)) = 7·6·5/(3·2·1) = 35

So, row 7 is ...

  1, 7, 21, 35, 35, 21, 7, 1

answer: the distance

step-by-step explanation:

to calculate the distance d of a line segment with endpoints (x1, y1) and (x2, y2) use the formula d (x2 x1)2 (y2 y1)2. to calculate the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) use the formula