AnswersPrecalculusApplying Vectors in the Plane

Applying Vectors in the Plane — Cumulative exam Answers

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The center of an earthquake was detected along the Pacific Rim. Geologists determined that the distance the seismic waves traveled is represented by r = 15sin(θ), where r is in miles. Which graph represents the distance the waves traveled?

A
On a polar coordinate plane, a circle goes through (15, 0) and (15, StartFraction pi Over 2 EndFraction)
Option A
B
On a polar coordinate plane, a circle goes through (30, 0) and (30, StartFraction pi Over 2 EndFraction).
Option B
C
On a polar coordinate plane, a circle goes through (0, 0) and (3, StartFraction pi Over 2 EndFraction).
Option C
D
On a polar coordinate plane, a circle goes through (0, 0) and (25, StartFraction pi Over 2 EndFraction).
Option D
2
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An ellipse has a center at the origin, a vertex along the major axis at (0, 17), and a focus at (0, −8).Which equation represents this ellipse?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
3

A surveyor is studying a map of the community and is using vectors to determine the distance between two schools. On the map, the surveyor determined that school A is at (7, 12), and school B is at (–21, –13). The scale of the map is 1 unit = 100 meters.Which vector represents the path from school A to school B, and what is the actual distance between them?

A
components: , actual distance: about 37.54 meters
Option A
B
components: , actual distance: about 3,754 meters
Option B
C
components:, actual distance: about 37.54 meters
Option C
D
components:, actual distance: about 3,754 meters
Option D
4

Which of the following is the correct expanded form for the series below?

Question illustration
A
mc005-2.jpg
Option A
B
mc005-3.jpg
Option B
C
mc005-4.jpg
Option C
D
mc005-5.jpg
Option D
5

Question text not available

Question illustration
A
(−8, −1) and (−2, −1)
B
(−6, −1) and (−5, −1)
C
(−5, −4) and (−5, 2)
D
(−5, −2) and (−5, 0)
6

Question text not available

Question illustration
A
y = 3x + 10
B
y = –3x + 8
C
y = x + 2
Option C
D
y = x
Option D
7

Review the graph of z2.

Question illustration
A
A
B
B
C
C
D
D
8

What is the difference between and ?

Question illustration
A
0
B
2
C
5
D
6
9

A ship travels 60 miles in the direction S 45° E, then travels 150 miles in the direction S 20° W. What is the distance, x, from the starting location?

A
135.99 mi
B
149.32 mi
C
172.93 mi
D
183.60 mi
10

Sheila is building a triangular sandbox in her backyard. She has obtained the measurements in the diagram below. The angle is measured in degrees. [Not drawn to scale]What is the unknown side length (x)? Round the answer to the nearest tenth.

Question illustration
A
5.6 ft
B
6.4 ft
C
31.5 ft
D
40.5 ft
11

What is the value of S4 for ?

Question illustration
A
48
B
84
C
90
D
96
12

Let v =. What is the approximate direction angle of v?

Question illustration
A
7°
B
83°
C
173°
D
353°
13

Review the graph.

Question illustration
A
The magnitude is 11.2, and the direction angle is E 49.09° N.
B
The magnitude is 11.2, and the direction angle is E 40.91° N.
C
The magnitude is 7.94, and the direction angle is N 40.91° E.
D
The magnitude is 7.94, and the direction angle is N 49.09° E.
14

Maddie converts z = 8(cos(300°) + isin(300°)) into rectangular form z = a + bi and determines that a = 4 and b = .Which statement identifies whether her values for a and b are correct?

Question illustration
A
Both values a and b are correct.
B
Both values a and b are incorrect.
C
The value of a is correct, but the value of b is incorrect.
D
The value of a is incorrect, but the value of b is correct.
15

Classify the conic represented by the following equation.x2 – 10x + 7y2 + y + 8 = 0

A
circle
B
ellipse
C
parabola
D
hyperbola
16

The path of a seat on a new Ferris wheel is modeled by x = –25sin and y = –25cos + 30, where distances are measured in feet. What is the maximum height a rider will experience?

Question illustration
A
50 feet
B
55 feet
C
60 feet
D
80 feet
17

Question text not available

Question illustration
A
(1,−15)
B
(1,−2)
C
(1,3)
D
(1,11)
18

Which graph represents the polar curve r = 1 + sin(θ)?

A
On a polar coordinate plane, a circle crosses the y-axis at (0, 0) and (0, negative 2). It has a cardioid at (0, 0).
Option A
B
On a polar coordinate plane, a circle crosses the y-axis at (0, 0) and (0, 2). It has a cardioid at (0, 0).
Option B
C
On a polar coordinate plane, a circle crosses the x-axis at (0, 0) and (negative 2, 0). It has a cardioid at (0, 0).
Option C
D
On a polar coordinate plane, a circle crosses the x-axis at (0, 0) and (2, 0). It has a cardioid at (0, 0).
Option D
19

Which equation represents a hyperbola with a center at (0, 0), a vertex at (0, 60), and a focus at (0, −65)?

A
= 1
Option A
B
= 1
Option B
C
= 1
Option C
D
= 1
Option D
20

A series contains 18 numbers and has a sum of 4,185. The last number of the series is 275. What is the first number?

A
42.5
B
190.0
C
465.0
D
740.0

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