Mathematics
Mathematics, 31.01.2020 23:45, dondre54

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15. find all polar coordinates of point p where p = ordered pair 1 comma pi divided by 3 .

a) (1, pi divided by 3 + 2nπ) or (-1, pi divided by 3 + (2n + 1)π)
b) (1, pi divided by 3 + (2n + 1)π) or (-1, pi divided by 3 + 2nπ)
c) (1, pi divided by 3 + nπ) or (-1, pi divided by 3 + nπ)
d) (1, pi divided by 3 + 2nπ) or (-1, pi divided by 3 + 2nπ)

16. determine two pairs of polar coordinates for the point (3, -3) with 0°≤ θ < 360°.

a) (3 square root of 2 , 315°), (-3 square root of 2 , 135°)
b) (3 square root of 2 , 225°), (-3 square root of 2 , 45°)
c) (3 square root of 2 , 45°), (-3 square root of 2 , 225°)
d) (3 square root of 2 , 135°), (-3 square root of 2 , 315°)

17. the graph of a limacon curve is given. without using your graphing calculator, determine which equation is correct for the graph.
a circular graph with an indentation on the left toward the origin, but not touching the origin

[-5, 5] by [-5, 5]

a) r = 2 + 3 cos θ
b) r = 3 + 2 cos θ
c) r = 2 + 2 cos θ
d) r = 4 + cos θ

18. determine if the graph is symmetric about the x-axis, the y-axis, or the origin.
r = 4 - 4 cos θ

a) no symmetry
b) x-axis only
c) y-axis only
d) origin only

19. a railroad tunnel is shaped like a semiellipse, as shown below.
a semiellipse is shown on the coordinate plane with vertices on the x axis and one point of intersection with the positive y axis.

the height of the tunnel at the center is 58 ft, and the vertical clearance must be 29 ft at a point 21 ft from the center. find an equation for the ellipse.

20. determine if the graph is symmetric about the x-axis, the y-axis, or the origin.
r = 4 cos 5θ

answer
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