PLEASE HELP!!! FIRST PERSON TO ASNWER IN 5 MINUTES YOU WILL GET 100 POINTS!
Question 2(Multiple Choice Worth 5 points)
(08.01 MC)

Given point Q equals negative 6 radical 3 comma negative 6 in rectangular coordinates, what are the corresponding polar coordinates?

6 comma 5 times pi over 6
12 comma 5 times pi over 6
6 comma 7 times pi over 6
12 comma 7 times pi over 6

Question 3(Multiple Choice Worth 5 points)
(08.05 MC)
The parametric equations x = t + 2 and y = t 2 + 3t represent a plane curve. Which of the following rectangular equations represents the plane curve?

y = x2 − 4x + 7
y = x2 − x − 2
y = x2 + 3x
y = x2 + 7x + 10

Question 4(Multiple Choice Worth 5 points)
(08.05 MC)
A tennis player hits the ball with an initial speed of 62 feet per second at an angle of 15°, from a height of 2.2 feet. How far away does the ball land in feet?

47.293 feet
56.372 feet
60.646 feet
67.381 feet

Question 5(Multiple Choice Worth 5 points)
(08.03 MC)
Given z1 = 18(cos 225° + isin 225°) and z2 = 3(cos 240° + isin 240°), what is the product of z1 and z2?

54(cos 105° + isin 105°)
6(cos 105° + isin 105°)
54(cos 15° + isin 15°)
6(cos 15° + isin 15°)

Question 6(Multiple Choice Worth 5 points)
(08.02 MC)
Which of the following images represents the polar graph of r = 4cos 4θ?

a polar graph with 4 petals with a point at r comma theta equals 4 comma 0
a polar graph with 4 petals with a point at r comma theta equals 4 comma pi over 4
a polar graph with 8 petals with a point at r comma theta equals 4 comma pi over 4
a polar graph with 8 petals with a point at r comma theta equals 4 comma pi over 8
Question 7(Multiple Choice Worth 5 points)

(08.04 MC)
A collection of points is shown on the complex plane.

points on the complex plane, point z sub 1 at negative 5 comma 4, point z sub 2 at 3 comma 2, point P at 8 comma 6, point Q at negative 2 comma 6, point R at negative 5 comma negative 4, point S at 8 comma negative 2

Which point represents z1 + z2?

P
Q
R
S

Question 8 (Essay Worth 10 points)
(08.01, 08.02 HC)
A curve, described by x2 + y2 + 6y = 0, has a point A at (−3, −3) on the curve.

Part A: What are the polar coordinates of A? Give an exact answer.

Part B: What is the polar form of the equation? What type of polar curve is this?

Part C: What is the directed distance when theta equals 4 pi over 3 question mark Give an exact answer.





Question 9 (Essay Worth 10 points)
(08.02 HC)

A polar curve is represented by the equation r1 = 3 + 3sin θ.

Part A: What type of limaçon is this curve? Justify your answer using the constants in the equation.

Part B: Is the curve symmetrical to the polar axis or the line theta equals pi over 2 question mark Justify your answer algebraically.

Part C: What are the two main differences between the graphs of r1 = 3 + 3sin θ and r2 = 8 + 3cos θ?





Question 10 (Essay Worth 10 points)
(08.03, 08.04 HC)

Points z1 and z2 are shown on the graph.

complex plane, point z sub 1 at 3 to the right of the origin and 5 units up, point z sub 2 at 6 units to the right of the origin and 3 units down

Part A: Identify the points in standard form and find the distance between them.

Part B: Give the complex conjugate of z2 and explain how to find it geometrically.

Part C: Find z2 − z1 geometrically and explain your steps.





Question 11 (Essay Worth 10 points)
(08.05 HC)

A baseball is hit, following a path represented by x = 140t and y = 3.1 + 40t − 16t 2 for 0 ≤ t ≤ 3.

Part A: Find the ordered pairs, (x, y), when t = 0.2, 1.2, and 2.4.

Part B: The fence, which is 10 feet tall, lies 320 feet away from home plate. Does the baseball travel over the fence? Justify your answer mathematically.

Part C: Write a rectangular equation to represent the plane curve.