# Pre-Calculus - [MCQ + Written Responses  Polar and Parametic QUESTIONS]

These are the possible topics for the answer:

08.01 Polar Coordinates
08.02 Polar Equations
08.03 Complex Numbers
08.04 Applications of Complex Numbers
08.05 Parametric Equations

Feel Free to ask any Questions!!!

I have also uploaded the rubric for the question, so make sure to have all the needed information.

QUESTION 1 (four options of graph):

QUESTION 2:

QUESTION 3:

QUESTION 4:

QUESTION 5:

QUESTION 6:

QUESTION 7:

QUESTION 8:

QUESTION 9:

QUESTION 10:

QUESTION 11:

Rubric:

• In the rubric questions 1 2 3 4, denotes for question 8,9,10,11. Thanks

• Kav10
+1

Hey Nicolas. I am gonna get started now. Would you be able to extend the deadline?

• I can, but would you finish ASAP, there technically no limit, but I just wanna check my answer.

• Yes. I have already started. I will let you know.

• I don't need steps for MCQ, just for the written ones

• How's it going?

• Just finishing up. One question is remaining. So many parts!

• Kav10
+1

I am gonna submit what I have so far, so you can start checking. Then, will work on the remaining and update. Sounds good?

• For the last one I got this, (I used my phone to transfer so it's kinda weird) Part A: Problem: Find the ordered pairs (x, y) for the baseball's path when t = 0.2, 1.2, and 2.2. Solution: For t = 0.2, using x = 135t and y = 3.3 + 38t - 16t^2: x(0.2) = 135 * 0.2 = 27 y(0.2) = 3.3 + 38 * 0.2 - 16 * (0.2)^2 = 3.3 + 7.6 - 0.64 = 10.26 For t = 1.2: x(1.2) = 135 * 1.2 = 162 y(1.2) = 3.3 + 38 * 1.2 - 16 * (1.2)^2 = 3.3 + 45.6 - 23.04 = 25.86 For t = 2.2: x(2.2) = 135 * 2.2 = 297

• y(2.2) = 3.3 + 38 * 2.2 - 16 * (2.2)^2 = 3.3 + 83.6 - 77.44 = 9.46 Final Answer for Part A: The ordered pairs are (27, 10.26) at t = 0.2, (162, 25.86) at t = 1.2, and (297, 9.46) at t = 2.2. Part B: Problem: Determine if the baseball goes over the fence that is 10 feet tall and 320 feet away from home plate. Solution: Find the time t when x = 320 by using x = 135t: 320 = 135t t = 320 / 135 t ≈ 2.37 Now, use this t value to find the height y: y(2.37) = 3.3 + 38 * 2.37 - 16 * (2.37)^2 y(2.37

• y(2.37) = 3.3 + 38 * 2.37 - 16 * (2.37)^2 y(2.37) = 3.3 + 89.86 - 89.58 y(2.37) ≈ 3.58 Final Answer for Part B: When the baseball is 320 feet away from home plate, its height is approximately 3.58 feet, which is below the fence height of 10 feet. Therefore, the baseball does not go over the fence. Part C: Problem: Convert the parametric equations to a single rectangular equation for the curve.

• Solution: We have the parametric equations x = 135t and y = 3.3 + 38t - 16t^2. To eliminate the parameter t and write the equation in rectangular form, we express t in terms of x: t = x / 135. Now, substitute t with x / 135 in the equation for y: y = 3.3 + 38(x / 135) - 16(x / 135)^2 To simplify, multiply each term by the corresponding power of 135 to eliminate the fraction: y = 3.3 + (38/135)x - (16/135^2)x^2

• y = 3.3 + (38/135)x - (16/135^2)x^2 Simplify the equation for y to get the rectangular form. Final Answer: The rectangular equation for the curve is y = 3.3 + 38x/135 - 16x²/18225, after simplification.

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• It took me full 2 hours to get all these ready. Please consider doubling the bounty or tip $50, if you agree. That will be roughly$4 per question. Thanks.
• Thanks for accepting. With your current bounty, it is roughly $2 per q! Please let me know if you disagree :-) The answer is accepted. Join Matchmaticians Affiliate Marketing Program to earn up to a 50% commission on every question that your affiliated users ask or answer. • answered • 289 views •$50.00