# 31 pre calc questions

1. Solve the triangle.

A = 48Â°, a = 32, b = 27 (1 point)

 Cannot be solved B = 38.8Â°, C = 113.2Â°, c â‰ˆ 34.4 B = 38.8Â°, C = 93.2Â°, c â‰ˆ 43 B = 38.8Â°, C = 93.2Â°, c â‰ˆ 25.8
2. State whether the given measurements determine zero, one, or two triangles.

A = 80Â°, a = 24, b = 50 (1 point)

 Zero Two One Three
3. Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles.

A = 55Â°, a = 12, b = 14 (1 point)

 B = 72.9Â°, C = 52.1Â°, c = 12.5; B = 107.1Â°, C = 17.9Â°, c = 12.5 B = 72.9Â°, C = 52.1Â°, c = 11.6; B = 107.1Â°, C = 17.9Â°, c = 4.5 B = 17.1Â°, C = 107.9Â°, c = 10.3; B = 162.9Â°, C = 72.1Â°, c = 10.3 B = 17.1Â°, C = 107.9Â°, c = 13.9; B = 162.9Â°, C = 72.1Â°, c = 13.9
4. Solve the triangle.

A = 51Â°, b = 11, c = 7 (1 point)

 a â‰ˆ 12.8, C â‰ˆ 39.1, B â‰ˆ 89.9 a â‰ˆ 8.5, C â‰ˆ 39.1, B â‰ˆ 89.9 No triangles possible a â‰ˆ 12.8, C â‰ˆ 43.1, B â‰ˆ 85.9
5. Find the area of the triangle with the given measurements. Round the solution to the nearest hundredth if necessary.

B = 104Â°, a = 11 cm, c = 18 cm (1 point)

 192.12 cm2 96.06 cm2 23.95 cm2 99 cm2
6. Given that P = (-5, 11) and Q = (-6, 4), find the component form and magnitude of . (1 point)
 <-11, 7>, <-1, -7>, <1, 7>, 50 <1, 7>,
7. Let u = <5, 6>, v = <-2, -6>. Find -2u + 5v. (1 point)
 <-20, -42> <-20, 0> <0, 18> <-6, 0>
8. Find the dot product, a â€¢ b.

a = 6i + 5j, b = -5i + 4j (1 point)

 50 <1, 9> -10 <-30, 20>
9. Determine whether the vectors u and v are parallel, orthogonal, or neither.

u = <7, 2>, v = <21, 6> (1 point)

 Neither Orthogonal Parallel None of these
10. Find the first six terms of the sequence.

a1 = -3, an = 2 â€¢ an-1 (1 point)

 -6, -12, -24, -48, -96, -192 -3, -6, -12, -24, -48, -96 0, 2, -6, -4, -2, 0 -3, -6, -4, -2, 0, 2
11. Determine whether the sequence converges or diverges. If it converges, give the limit.

11, 22, 44, 88, … (1 point)

 Converges; 341 Converges; 165 Converges; 77 Diverges
12. Find an explicit rule for the nth term of the sequence.

2, -8, 32, -128, … (1 point)

 an = 2 â€¢ 4n+1 an = 2 â€¢ (-4)n an = 2 â€¢ 4n-1 an = 2 â€¢ (-4)n-1
13. Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are 36 and 2304, respectively. (1 point)
 an = 9 â€¢ 4n+1 an = 9 â€¢ 4n+3 an = 9 â€¢ 4n-1 an = 9 â€¢ 4n-2
14. Write the sum using summation notation, assuming the suggested pattern continues.

5 – 15 + 45 – 135 + … (1 point)

15. Find the standard form of the equation of the parabola with a focus at (0, 6) and a directrix at y = -6. (1 point)
 y2 = 6x y2 = 24x
16. A radio telescope has a parabolic surface, as shown below.

If the telescope is 9 m deep and 12 m wide, how far is the focus from the vertex? (1 point)

 4 m 3 m 1 m 9 m
17. Find the center, vertices, and foci of the ellipse with equation. (1 point)

 Center: (0, 0); Vertices: (-15, 0), (15, 0); Foci: (0, -9), (0, 9) Center: (0, 0); Vertices: (0, -15), (0, 15); Foci: (-9, 0), (9, 0) Center: (0, 0); Vertices: (0, -15), (0, 15); Foci: (0, -12), (0, 12) Center: (0, 0); Vertices: (-15, 0), (15, 0); Foci: (-12, 0), (12, 0)
18. Find the center, vertices, and foci of the ellipse with equation 2x2 + 7y2 = 14. (1 point)
 Center: (0, 0); Vertices: (-7, 0), (7, 0); Foci: Center: (0, 0); Vertices: ; Foci: Center: (0, 0); Vertices: ; Foci: Center: (0, 0); Vertices: (0, -7), (0, 7); Foci:
19. A satellite is to be put into an elliptical orbit around a moon.

The moon is a sphere with radius of 959 km. Determine an equation for the ellipse if the distance of the satellite from the surface of the moon varies from 357 km to 710 km. (1 point)

20. Find the vertices and foci of the hyperbola with equation. (1 point)

 Vertices: (-5, 15), (-5, -9); Foci: (-5, -9), (-5, 15) Vertices: (12, -5), (-6, -5); Foci: (-12, -5), (18, -5) Vertices: (-5, 12), (-5, -6); Foci: (-5, -12), (-5, 18) Vertices: (15, -5), (-9, -5); Foci: (-9, -5), (15, -5)
21. Find an equation in standard form for the hyperbola with vertices at (0, Â±6) and asymptotes at y = Â± x. (1 point)
22. Find all polar coordinates of point P where P = . (1 point)
 (3, + 2nÏ€) or (-3, + (2n + 1)Ï€) (3, + 2nÏ€) or (-3, + 2nÏ€) (3, + 2nÏ€) or (3, + (2n + 1)Ï€) (3, + (2n + 1)Ï€) or (-3, + 2nÏ€)
23. Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.

r = 3 – 4 sin Î¸ (1 point)

 y-axis only No symmetry Origin only x-axis only
24. Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.

r = 3 cos 5Î¸ (1 point)

 x-axis, y-axis x-axis, y-axis, origin y-axis only x-axis only
25. Find the derivative of f(x) = at x = -12. (1 point)
26. Find the limit of the function by using direct substitution. (1 point)

 Does not exist 4 0 -4
27. Find the limit of the function algebraically. (1 point)

 1 -8 Does not exist -4
28. Use the given graph to determine the limit, if it exists.

Find and . (1 point)

29. Use graphs and tables to find the limit and identify any vertical asymptotes of the function. (1 point)

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