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14. Find the distance between and on the polar plane.

14. Convert the points to Cartesian coordinates.

becomes

(7 cos(217/180 π), 7 sin(217/180 π)) ≈ (-5.59, -4.21)

and is

(5 cos(-23/36 π), 5 sin(-23/36 π)) ≈ (-2.11, -4.53)

Then the distance between the two points is

16. Between the first two seconds, the ball rolls 2 ft. If the distance traveled by the ball between each second forms an arithmetic sequence, then the distances themselves are

1, 3, 5, 7, 9, ...

That is, the distances form a sequence where

We can solve for the n-th distance in terms of the first using the recursive rule above.

and so on, up to

x= -3

step-by-step explanation:

step 1: simplify brackets

4 - x - 1 = 6

step 2: simpilfy

3 - x = 6

step 3: subtract 3 from both sides

-x = 6 - 3

step 4: simpilfy 6 - 3

-x = 3

step 5: multiply both sides by -1

x = -3

answer: 25.4 units

step-by-step explanation: radius = 12.7 units

diameter = twice the radius

diameter = 12.7 x 2

= 25.4