Let z = z = 8 (cosine (StartFraction pi Over 3 EndFraction) + I sine (StartFraction pi Over 3 EndFraction) ) and w = 3 (cosine (StartFraction pi Over 6 EndFraction) + I sine (StartFraction pi Over 6 EndFraction) ). Which statement describes the geometric construction of the product zw on the complex plane?

Stretch z by a factor of 3 and rotate StartFraction pi Over 2 EndFraction radians counterclockwise.
Stretch z by a factor of 3 and rotate StartFraction pi Over 6 EndFraction radians counterclockwise.
Stretch z by a factor of 24 and rotate StartFraction pi Over 2 EndFraction radians counterclockwise.
Stretch z by a factor of 24 and rotate StartFraction pi Over 6 EndFraction radians counterclockwise.

△cde maps to △stu with the transformations (x, y) arrowright (x − 2, y − 2) arrowright (3x, 3y) arrowright (x, −y). if cd = a + 1, de = 2a − 1, st = 2b + 3 and tu = b + 6, find the values of a and b. the value of a is and the value of b is .

Acable company wants to provide cell phone service for residents on an island. the function for the cost of laying the cable from the island to the mainland is c(x)= 6.500 square root x2+4, where x represents the length of the cable in feet. what are the domain and range of the function? a) domain: all real numbers range: all real numbers greater than or equal to 17,000 b) domain: all real numbers greater than or equal to 0 range: all real numbers greater than or equal to 17,000 c) domain: all real numbers greater than or equal to 0 range: all real numbers greater than or equal to 13,000 d) domain: all real numbers greater than or equal to 13,000 range: all real numbers greater than or equal to 0

Select the correct answer from the drop-down menu. this graph represents the inequality x+2< 4,2x> 3,x+6< 12,2x> 12