Plot the point (3, 2pi/3), given in polar coordinates, and find other polar coordinates (r, θ )of the point for which the following are true.

(a) r> 0, -2 pi < 0
(b) r < 0, 0 < 2 pi
(c) r > 0, 2 pi < 4 pi

(a)

(b)

(c)

Step-by-step explanation:

All polar coordinates of point (r, θ ) are

and

where, θ is in radian and n is an integer.

The given point is . So, all polar coordinates of point are

and

(a)

Substitute n=-1 in , to find the point for which .

Therefore, the required point is .

(b)

Substitute n=0 in , to find the point for which .

Therefore, the required point is .

(c)

Substitute n=1 in , to find the point for which .

Therefore, the required point is .

10.416 meters per second

step-by-step explanation:

distance=1 00 meters

time= 9.6 seconds in decimal form or 9 3/5 as a mixed number

average speed= 100/9.6

=10.416 meters per second or 10 52/125 as a mixed number.