Question

PLEASE ANSWER EACH QUESTION FOR UPVOTE! THANK U!
1.) Which of the following parametric equations are equivalent to the polar equation r(theta) = cos(theta) cot(theta)?
A) x = sin^2(theta) and y = sin^2(theta) cot(theta)
B) x = cos^2(theta) and y = cos^2(theta) cot(theta)
C) x = cos^2(theta) cot(theta) and y = cos^2(theta)
D) x = cos(theta) cot(theta) and y = cos(theta)
2.)Which describes the parametric equations x = 2t and y = 4sin t?
A) y = x^2 + 2
The orientation is down to the right, then up to the right.
B) y = x^2 + 2
The orientation is up to the right, then down to the right.
C) y = -x^2 + 2
The orientation is down to the right, then up to the right.
D) y = -x^2 + 2
The orientation is up to the right, then down to the right.
3.) Which describes the conic section with parametric equations x = 2cos t and y = 4sin t?
A) x^2 + y^2 = 4; a circle with radius 2
B) 1 = x^2 / 4 + y^2 / 16; an ellipse with vertical major axis
C) y = -x + 4; an inverted parabola with vertex (0,4)
D) y = -4x^2; an inverted parabola with vertex (0,0)
4.)

4 2

Which equations or set of equations could represent the graph shown? Select all that apply (3).
A) x = 3cos t and y = 3sin t
B) x = 9cos t and y = 9sin t
C) x^2 + y^2 = 9
D) x^2 + y^2 = 3
E) r = 3
F) r = 9
5.) A baseball is thrown with a velocity of 60 ft./s. The ball is thrown from a height of 5 ft. at an angle of 60 degrees. Which set of parametric equations represents the path of the ball? The acceleration due to gravity is 32 ft/s^2.
A) x = 30√3t + 5 and y = -16t^2 + 30t
B) x = 30√3t and y = -16t^2 + 30t + 5
C) x = 30t + 5 and y = -16t^2 + 30√3t
D) x = 30t and y = -16t^2 + 30√3t + 5

Answer 1

1)

r(t)cos(t) cot(t) ^ r(t)-r(t) cos(t) cos2(t) sin(t) y(t) r(t) sin(t)-cos2(t) COS

Correct option is C)

2) There is some issue with this question.
4 sin(t) 2t. y r
defines the equation
y-4 sin (r/2
where none of the given options fit

3) $x=2\cos(t),y=4\sin(t)\Rightarrow \left(\frac{x}{2} \right )^2+\left(\frac{y}{4} \right )^2=1$ which is an ellipse with vertical major axis (Correct option is B)

4) are the options which define a circle of radius 3

r 3 cos(t), y 3sin(t) and r2 +y-9 and r3 COS

Correct options are A, C, E

5)

rt) 60 cos(60)t 30t 322

Correct option is D)