In a lecture hall at a collage, the number of seats per row increased at a constand rate. the professor counts 21 seats in row 3 and 33 seats in row 7. how many sets are there in row 18?

  66 seats

Step-by-step explanation:

The rate of increase is ...

  (change in seats)/(change in rows) = (33 -21)/(7 -3) = 12/4 = 3 . . . seats/row

Then row 18 will have (18-3)·3 = 45 more seats than row 3, hence ...

  21 + 45 = 66 . . . . seats in row 18

An explicit formula for the number of seats can be written as ...

  s = 21 +3(n-3) = 12 +3n

For n=18, this is ...

 s = 12 + 3(18) = 12 +54 = 66 . . . seats in row 18

56.6

step-by-step explanation:

the ratio of the perimeters is equal to the scale.

the ratio of the areas is equal to the square of the scale.

34 / 20 = k

a / 19.6 = k²

substituting:

a / 19.6 = (34 / 20)²

a = 19.6 (34 / 20)²

a ≈ 56.6