CALCULUS II HELPNOTE: Please explain why, or how which answer is right. Please High Light in red the correct answer as well.
Q1: Determine A so that the curvey = 3x + 5 can be written in parametric form as x(t) = t−2, y(t) = At−1.
1. A = 53. A = −4 4. A = 45. A = −5 6. A = 3
Q2: Find a Cartesian equation for the curve given in parametric form byy(t) = 1/2t^2, x(t) =1/8 t^3.
My Choices: 2. y = 2x^2/34. y = x^3/25. y = x^2/36. y = 2x^3/2
Q3: Describe the motion of a particle with position P(x, y) when x = 3sint, y = 4cost as t varies in the interval 0 ≤ t ≤ 2π.
My choices:
1. Moves once clockwise along the ellipse x^2/9 + y^2/16 = 1, starting and ending at (0, 4).
2. Moves once counterclockwise along the ellipse (3x)^2 + (4y)^2 = 1,starting and ending at (0, 4).
3. Moves along the line x/3 + y/4 = 1, starting at (0, 4) and ending at (3, 0).
4. Moves once clockwise along the ellipse(3x)^2 + (4y)^2 = 1, starting and ending at (0, 4).
5. Moves along the line x/3 + y/4 = 1, starting at (3, 0) and ending at (0, 4).
6. Moves once counterclockwise along the ellipse x^2/9 + y^2/16 = 1,starting and ending at (0, 4).
Q4: Find the path (x(t), y(t)) of a particle that moves once counter-clockwise around the curve x^2 + (y −3)^2 = 49, starting at (7, 3).My options.1. (−7cost, 3−7sint), 0 ≤ t ≤ π 2. (7cost, 3−7sint), 0 ≤ t ≤ π 3. (−7cost, 3−7sint), 0 ≤ t ≤ 24. (7cost, 3 + 7sint), 0 ≤ t ≤ 2π 5. (7cost, 3−7sint), 0 ≤ t ≤ 2π 6. (7cost, 3 + 7sint), 0 ≤ t ≤ π
Q5: A ladder 16 feet in length slides down a wall as its bottom is pulled away from the wall as shown in the image below.
Using the angle θ as parameter, find the parametric equations for the path followed by the point P located 2 feet from the top of the ladder.My Choices1. (14cosθ, 2sinθ)2. (2sinθ, 14cosθ)3. (14tanθ, 2secθ)4. (14secθ, 2tanθ)5. (2cosθ, 14sinθ)6. (14sinθ, 2cosθ)7. (2secθ, 14tanθ)8. (2tanθ, 14secθ)
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