# math test 5

Decide whether the given sequence is finite or infinite.

-4, -3, -2, -1

 Finite Infinite

2.1 points

### Question 2

1. Evaluate the expression.

(10
2)

 1,814,400 22 5 45

2.1 points

### Question 3

1. Evaluate the series, if it converges.

9 – + + . . .

 – 1 8 Does not converge

2.1 points

### Question 4

1. Evaluate the sum.

 218 173 124 162

2.1 points

### Question 5

1. Evaluate the sum. Round to the nearest hundredth, if necessary.

 42 20 44 54

2.1 points

### Question 6

1. Evaluate the terms of the sum using the given information.

x 1 = 4, x 2 = 1, x 3 = 0, and x 4 = -1

 12 – 3 + 4 + 5 -20 – 5 – 4 – 5 -12 + 5 – 4 + 5 -20 + 3 – 4 – 3

2.1 points

### Question 7

1. Find a general term an for the geometric sequence.

a 1 = 3, r = 3

 an = 6n an = 3n an= 3 + 6(n – 1) an = 3n-1 + 2

2.1 points

### Question 8

1. Find a rectangular equation for the plane curve defined by the parametric equations.

x = , y = 2t + 5, for t in (0, âˆž)

 y = 2 + 5, x in (0, âˆž) y = 2×2 + 5, x in (0, âˆž) y = 2 – 5, x in (0, âˆž) y = 2×2 – 5, x in (0, âˆž)

2.1 points

### Question 9

1. Find an equation for the conic. If the conic is a parabola, assume that the vertex is at the origin. If the conic is an ellipse or hyperbola, assume that it is centered at the origin.

Focus at (0, -6) and e = 1

 y = – x2 x = – y2 y = x2 y = – x2

2.1 points

### Question 10

1. Find an equation for the parabola with vertex at the origin.

Through (9, 8), opening to the right

 y = x2 x = – y2 x = y2 x = y2

2.1 points

### Question 11

1. Find an equation of a parabola that satisfies the given conditions.

Vertex (3, -10), focus (3, -8)

 8(y – 10) = (x + 3)2 (y + 10)2 = 8(x – 3) (x – 3)2 = 8(y + 10) y – 10 = 8(x + 3)2

2.1 points

### Question 12

1. Find an equation of the ellipse.

An ellipse with center at origin, length of major axis 6 and y-intercepts

 + = 1 + = 1 + = 1 + = 1

2.1 points

### Question 13

1. Find an equation of the hyperbola.

Vertices at (0, 3), (0, -3); foci at (0, 9), (0, -9)

 – = 1 – = 1 – = 1 – = 1

2.1 points

### Question 14

1. Find the center and radius of the circle.

x 2 + y 2 + 12x – 2y = -1

 (1, -6), r = 6 (6, -1), r = 36 (-1, 6), r = 36 (-6, 1), r = 6

2.1 points

### Question 15

1. Find the center-radius form for the circle having the given endpoints of a diameter.

( -3, -5) and (7, 7)

 (x + 2)2 + (y + 1)2 = -11 (x + 2)2 + (y + 1)2 = 61 (x – 2)2 + (y – 1)2 = -11 (x – 2)2 + (y – 1)2 = 61

2.1 points

### Question 16

1. Find the center-radius form of the equation of the circle satisfying the given conditions.

Center ( -10, 0), radius 1

 (x + 10)2 + y2 = 1 x2 + (y – 10)2 = 1 (x – 10)2 + y2 = 1 x2 + (y + 10)2 = 1

2.1 points

### Question 17

1. Find the common difference for the arithmetic sequence.

3, 5, 7, 9, …

 2 0.02 -2 6

2.1 points

### Question 18

1. Find the common ratio r for the given infinite geometric sequence.

4, -12, 36, -108, 324, …

 -3 3 -16 –

2.1 points

### Question 19

1. Find the coordinates of the vertex and the direction of opening of each parabola.

y = (x + 2) 2 + 7

 (-7, 2) opens upward (7, -4) opens downward (7, -2) opens downward (-2, 7) opens upward

2.1 points

### Question 20

1. Find the eccentricity of the ellipse or hyperbola.

x 2 – y 2 = 49

 1 0

2.1 points

### Question 21

1. Find the first six terms of the sequence.

a 1 = -9, a n = 5 âˆ™ a n-1

 -9, -45, -225, -1125, -5625, -28,125 -9, -45, -40, -35, -30, -25 -45, -225, -1125, -5625, -28,125, -140,625 0, 5, -45, -40, -35, -30

2.1 points

### Question 22

1. Find the sum of the arithmetic series using a formula.

1 + 3 + 5 + … + 515

 66,049 66,822 66,564 67,081

2.1 points

### Question 23

1. Find the sum of the first n terms of the following arithmetic sequence.

a 1 = -10, d = -2; n = 4.

 -40 -10 -52 -18

2.1 points

### Question 24

1. Find the sum of the geometric series.

 -156 -7710 -2460 244

2.1 points

### Question 25

1. Find anand a6 for the following arithmetic sequence.

-1, 1, 3, 5, 7

 an = 3n – 2; a6 = 16 an = n + 2; a6 = 8 an = 2n – 3; a6 = 9 an = -1(2)n-1; a6 = -32

2.1 points

### Question 26

1. For the given parabola, give the coordinates of the vertex, the axis, the domain, and the range.

x = (y – 8) 2 + 6

 vertex: (-6, 8);axis: y = 8;domain: [-6, âˆž)range: (-âˆž, âˆž); vertex: (8, 6);axis: y = 6;domain: [8, âˆž)range: (-âˆž, âˆž); vertex: (-6, -8);axis: y = -8;domain: [-6, âˆž)range: (-âˆž, âˆž); vertex: (6, 8);axis: y = 8;domain: [6, âˆž)range: (-âˆž, âˆž);

2.1 points

### Question 27

1. Give the focus, directrix, and axis for the parabola.

x 2 = y

 (0, -3), y = 3, y-axis (0, 3), y = -3, y-axis (-6, 0), x = 3, x-axis (0, -3), y = 3, x-axis

2.1 points

### Question 28

1. Graph the circle if possible.

(x – 1) 2 + (y – 3) 2 = 16