It is convenient to do part b first, then use that result to do part a.
b. For some pair of points (x1, y1) and (x2, y2), you want to find a point (a, b) such that (a, b) - (x1, y1) = (x2, y2) - (a, b). That is, the differences of coordinates from one end to the center are the same as the differences from the center to the other end. Adding (a, b) to the above equation gives 2(a, b) - (x1, y1) = (x2, y2) Adding (x1, y1) then gives 2(a, b) = (x1, y1) + (x2, y2) Finally, dividing by 2 gives a formula for (a, b):
(a, b) = ((x1, y1) + (x2, y2))/2 The midpoint is the average of the end points.
a. Using the result from part b, the midpoint is midpoint = ((2, 3) + (6, 7))/2 = (8, 10)/2 midpoint = (4, 5)
Step-by-step explanation: We know each page, or 1 page takes 1 hour to finish. We want to know how many hours it would take to take finish 8 pages of homework. To find this, simply multiply 1 by 8. (1 hour per page, or 1 hour for each of the 8 pages.)
1 x 8 = 8.
So it will take Meredith 8 hours to finish her homework.
To evaluate the combination we proceed as follows: 21C3 Given nCk we shall have: n!/[(n-k)!k!] thus plugging the values in the expression we get: 21!/[(21-3)!3!] =21!/(18!×3!) =1330 Answer: 1330
