تكلم مع الذكاء الاصطناعي
Deck 8: Additional Topics in Trigonometry
ملء الشاشة (f)
سؤال
Find the component form of v if 
and the angle it makes with the x-axis is .
A)
B)
C)
D)
E)
and the angle it makes with the x-axis is .A)
B)
C)
D)
E)
سؤال
A park ranger at point A observes a fire in the direction 
. Another ranger at point B, 5 miles due east of A, sites the same fire at 
. Determine the distance from point B to the fire. Round answer to two decimal places.
A) 2.18 miles
B) 4.55 miles
C) 2.51 miles
D) 4.84 miles
E) 4.20 miles
. Another ranger at point B, 5 miles due east of A, sites the same fire at . Determine the distance from point B to the fire. Round answer to two decimal places.A) 2.18 miles
B) 4.55 miles
C) 2.51 miles
D) 4.84 miles
E) 4.20 miles
سؤال
Determine the area of a triangle having the following measurements. Round your answer to two decimal places. 
A) 30.90 sq. units
B) 37.08 sq. units
C) 33.99 sq. units
D) 27.81 sq. units
E) 24.72 sq. units
A) 30.90 sq. units
B) 37.08 sq. units
C) 33.99 sq. units
D) 27.81 sq. units
E) 24.72 sq. units
سؤال
Find the component form of vector v. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
A vertical pole 29 feet tall stands on a hillside that makes an angle of 
with the horizontal. Determine the approximate length of cable that would be needed to reach from the top of the pole to a point 78 feet downhill from the base of the pole. Round answer to two decimal places.
A) 82.88 feet
B) 75.35 feet
C) 99.45 feet
D) 88.40 feet
E)
feet
with the horizontal. Determine the approximate length of cable that would be needed to reach from the top of the pole to a point 78 feet downhill from the base of the pole. Round answer to two decimal places.A) 82.88 feet
B) 75.35 feet
C) 99.45 feet
D) 88.40 feet
E)
feet سؤال
After a severe storm, three sisters, April, May, and June, stood on their front porch and noticed that the tree in their front yard was leaning 
from vertical toward the house. From the porch, which is 98 feet away from the base of the tree, they noticed that the angle of elevation to the top of the tree was 
. Approximate the height of the tree. Round answer to two decimal places.
A) 47.99 feet
B) 56.03 feet
C) 41.91 feet
D) 45.31 feet
E) 46.03 feet
from vertical toward the house. From the porch, which is 98 feet away from the base of the tree, they noticed that the angle of elevation to the top of the tree was . Approximate the height of the tree. Round answer to two decimal places.A) 47.99 feet
B) 56.03 feet
C) 41.91 feet
D) 45.31 feet
E) 46.03 feet
سؤال
final If 
and 
, and the vectors make angles of 0° and 60° and with the x-axis respectively, find the component form of the sum of u and v. Round answers to two decimal places.
A)
B)
C)
D)
E)
and , and the vectors make angles of 0° and 60° and with the x-axis respectively, find the component form of the sum of u and v. Round answers to two decimal places. A)
B)
C)
D)
E)
سؤال
Two ocean liners leave from the same port in Puerto Rico at 10:00 a.m. One travels at a bearing of 
at 15 miles per hour, and the other travels at a bearing of 
at 17 miles per hour. Approximate the distance between them at noon the same day. Round answer to two decimal places.
A) 44.71 miles
B) 23.86 miles
C) 30.37 miles
D) 27.02 miles
E) 39.96 miles
at 15 miles per hour, and the other travels at a bearing of at 17 miles per hour. Approximate the distance between them at noon the same day. Round answer to two decimal places.A) 44.71 miles
B) 23.86 miles
C) 30.37 miles
D) 27.02 miles
E) 39.96 miles
سؤال
Given 
, 
, and 
, use the Law of Sines to solve the triangle for the value of a. Round answer to two decimal places.
A) a= 8.37
B) a= 10.02
C) a= 5.92
D) a= 21.05
E) a= 7.14
, , and , use the Law of Sines to solve the triangle for the value of a. Round answer to two decimal places.A) a= 8.37
B) a= 10.02
C) a= 5.92
D) a= 21.05
E) a= 7.14
سؤال
Find the magnitude and direction angle of 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
سؤال
Find the component form of v if 
and the angle it makes with the x-axis is 150°.
A)
B)
C)
D)
E)
and the angle it makes with the x-axis is 150°.A)
B)
C)
D)
E)
سؤال
Determine the area of a triangle having the following measurements. Round your answer to two decimal places. 
A) 28.61 sq. units
B) 23.84 sq. units
C) 21.46 sq. units
D) 26.22 sq. units
E) 19.07 sq. units
A) 28.61 sq. units
B) 23.84 sq. units
C) 21.46 sq. units
D) 26.22 sq. units
E) 19.07 sq. units
سؤال
Given 
, 
, and 
, use the Law of Cosines to solve the triangle for the value of c. Round answer to two decimal places.
A) 16.29
B) 11.26
C) 15.57
D) 17.00
E) 14.13
, , and , use the Law of Cosines to solve the triangle for the value of c. Round answer to two decimal places.A) 16.29
B) 11.26
C) 15.57
D) 17.00
E) 14.13
سؤال
Determine the area of a triangle having the following measurements. Round your answer to two decimal places. 
A) 59.30 sq. units
B) 88.95 sq. units
C) 66.71 sq. units
D) 81.54 sq. units
E) 74.13 sq. units
A) 59.30 sq. units
B) 88.95 sq. units
C) 66.71 sq. units
D) 81.54 sq. units
E) 74.13 sq. units
سؤال
Find the component form of v if 
and the angle it makes with the x-axis is .
A)
B)
C)
D)
E)
and the angle it makes with the x-axis is .A)
B)
C)
D)
E)
سؤال
Find the component form of vector v with initial point 
and terminal point 
.
A)
B)
C)
D)
E)
and terminal point .A)
B)
C)
D)
E)
سؤال
Find the component form of v if 
and the angle it makes with the x-axis is .
A)
B)
C)
D)
E)
and the angle it makes with the x-axis is .A)
B)
C)
D)
E)
سؤال
Given 
, 
, and 
, use Heron's Area Formula to find the area of 
. Round answer to two decimal places.
A) 17.36 sq. units
B) 18.44 sq. units
C) 20.21 sq. units
D) 16.76 sq. units
E) 14.02 sq. units
, , and , use Heron's Area Formula to find the area of . Round answer to two decimal places.A) 17.36 sq. units
B) 18.44 sq. units
C) 20.21 sq. units
D) 16.76 sq. units
E) 14.02 sq. units
سؤال
Given 
, 
, and 
, use the Law of Sines to solve the triangle for the value of b. Round answer to two decimal places.
A) a= 14.57
B) a= 13.14
C) a= 11.24
D) a= 13.69
E) a= 12.46
, , and , use the Law of Sines to solve the triangle for the value of b. Round answer to two decimal places.A) a= 14.57
B) a= 13.14
C) a= 11.24
D) a= 13.69
E) a= 12.46
سؤال
A straight road makes an angle, A, of 
with the horizontal. When the angle of elevation, B, of the sun is 
, a vertical pole beside the road casts a shadow 8 feet long parallel to the road. Approximate the length of the pole. Round answer to two decimal places.
A) 4.78 feet
B) 9.04 feet
C) 7.08 feet
D) 12.32 feet
E) 5.87 feet
with the horizontal. When the angle of elevation, B, of the sun is , a vertical pole beside the road casts a shadow 8 feet long parallel to the road. Approximate the length of the pole. Round answer to two decimal places.A) 4.78 feet
B) 9.04 feet
C) 7.08 feet
D) 12.32 feet
E) 5.87 feet
سؤال
سؤال
Use DeMoivre's Theorem to find the indicated power of the following complex number. 
A)390,625
B)78,125
C)1,000,000
D)1,953,125
E) 3,125
A)390,625
B)78,125
C)1,000,000
D)1,953,125
E) 3,125
سؤال
Determine whether u are v and orthogonal, parallel, or neither. 
A) neither
B) parallel
C) orthogonal
A) neither
B) parallel
C) orthogonal
سؤال
Divide the complex numbers below and leave the result in trigonometric form.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in standard form. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Perform the indicated operation using trigonometric form. Leave answer in trigonometric form. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find the trigonometric form of 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
سؤال
سؤال
Perform the operation shown below and leave the result in trigonometric form.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Multiply the complex numbers below and leave the result in trigonometric form. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Multiply the complex numbers below and leave the result in trigonometric form. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find the standard form of the complex number shown below. Round answers to two decimal places. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find the product 
using trigonometric forms. Leave the result in trigonometric form.
A)
B)
C)
D)
E)
using trigonometric forms. Leave the result in trigonometric form.A)
B)
C)
D)
E)
سؤال
Find the standard form of the complex number 
. Round values to the nearest hundredth.
A)
B)
C)
D)
E)
. Round values to the nearest hundredth.A)
B)
C)
D)
E)
سؤال
The vector 
gives the number of units of two models of laptops produced by a company. The vector 
gives the prices (in dollars) of the two models of laptops, respectively. Use dot products to determine the revenue for these two laptops if the price of each is increased by 5.5%.
A) $10,701,150
B) $10,852,400
C) $11,003,650
D) $10,732,500
E) $10,812,433
gives the number of units of two models of laptops produced by a company. The vector gives the prices (in dollars) of the two models of laptops, respectively. Use dot products to determine the revenue for these two laptops if the price of each is increased by 5.5%.A) $10,701,150
B) $10,852,400
C) $11,003,650
D) $10,732,500
E) $10,812,433
سؤال
Determine whether u are v and orthogonal, parallel, or neither. 
A) neither
B) orthogonal
C) parallel
A) neither
B) orthogonal
C) parallel
سؤال
Find the standard form of the complex number shown below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find the projection of u onto v if 
, 
.
A)
B)
C)
D)
E)
, .A)
B)
C)
D)
E)
سؤال
Use DeMoivre's Theorem to find the indicated power of the following complex number. 
A) 3,125
B) 62,500
C) 15,625
D) 2,500
E) -2,500
A) 3,125
B) 62,500
C) 15,625
D) 2,500
E) -2,500
سؤال
Find the trigonometric form of 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
سؤال
Use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in standard form. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Use DeMoivre's Theorem to find the indicated power of the following complex number. 
A) 2048
B)
C) -4,096
D)
E) 4,096
A) 2048
B)
C) -4,096
D)
E) 4,096
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ملء الشاشة (f)
Deck 8: Additional Topics in Trigonometry
1
Find the component form of v if and the angle it makes with the x-axis is .
A)
B)
C)
D)
E)
and the angle it makes with the x-axis is .A)
B)
C)
D)
E)
2
A park ranger at point A observes a fire in the direction . Another ranger at point B, 5 miles due east of A, sites the same fire at . Determine the distance from point B to the fire. Round answer to two decimal places.
A) 2.18 miles
B) 4.55 miles
C) 2.51 miles
D) 4.84 miles
E) 4.20 miles
. Another ranger at point B, 5 miles due east of A, sites the same fire at . Determine the distance from point B to the fire. Round answer to two decimal places.A) 2.18 miles
B) 4.55 miles
C) 2.51 miles
D) 4.84 miles
E) 4.20 miles
4.55 miles
3
Determine the area of a triangle having the following measurements. Round your answer to two decimal places.
A) 30.90 sq. units
B) 37.08 sq. units
C) 33.99 sq. units
D) 27.81 sq. units
E) 24.72 sq. units
A) 30.90 sq. units
B) 37.08 sq. units
C) 33.99 sq. units
D) 27.81 sq. units
E) 24.72 sq. units
30.90 sq. units
4
Find the component form of vector v.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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5
A vertical pole 29 feet tall stands on a hillside that makes an angle of with the horizontal. Determine the approximate length of cable that would be needed to reach from the top of the pole to a point 78 feet downhill from the base of the pole. Round answer to two decimal places.
A) 82.88 feet
B) 75.35 feet
C) 99.45 feet
D) 88.40 feet
E) feet
with the horizontal. Determine the approximate length of cable that would be needed to reach from the top of the pole to a point 78 feet downhill from the base of the pole. Round answer to two decimal places.A) 82.88 feet
B) 75.35 feet
C) 99.45 feet
D) 88.40 feet
E)
feet فتح الحزمة
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6
After a severe storm, three sisters, April, May, and June, stood on their front porch and noticed that the tree in their front yard was leaning from vertical toward the house. From the porch, which is 98 feet away from the base of the tree, they noticed that the angle of elevation to the top of the tree was . Approximate the height of the tree. Round answer to two decimal places.
A) 47.99 feet
B) 56.03 feet
C) 41.91 feet
D) 45.31 feet
E) 46.03 feet
from vertical toward the house. From the porch, which is 98 feet away from the base of the tree, they noticed that the angle of elevation to the top of the tree was . Approximate the height of the tree. Round answer to two decimal places.A) 47.99 feet
B) 56.03 feet
C) 41.91 feet
D) 45.31 feet
E) 46.03 feet
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7
final If and , and the vectors make angles of 0° and 60° and with the x-axis respectively, find the component form of the sum of u and v. Round answers to two decimal places.
A)
B)
C)
D)
E)
and , and the vectors make angles of 0° and 60° and with the x-axis respectively, find the component form of the sum of u and v. Round answers to two decimal places. A)
B)
C)
D)
E)
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8
Two ocean liners leave from the same port in Puerto Rico at 10:00 a.m. One travels at a bearing of at 15 miles per hour, and the other travels at a bearing of at 17 miles per hour. Approximate the distance between them at noon the same day. Round answer to two decimal places.
A) 44.71 miles
B) 23.86 miles
C) 30.37 miles
D) 27.02 miles
E) 39.96 miles
at 15 miles per hour, and the other travels at a bearing of at 17 miles per hour. Approximate the distance between them at noon the same day. Round answer to two decimal places.A) 44.71 miles
B) 23.86 miles
C) 30.37 miles
D) 27.02 miles
E) 39.96 miles
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9
Given , , and , use the Law of Sines to solve the triangle for the value of a. Round answer to two decimal places.
A) a= 8.37
B) a= 10.02
C) a= 5.92
D) a= 21.05
E) a= 7.14
, , and , use the Law of Sines to solve the triangle for the value of a. Round answer to two decimal places.A) a= 8.37
B) a= 10.02
C) a= 5.92
D) a= 21.05
E) a= 7.14
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10
Find the magnitude and direction angle of .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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11
Find the component form of v if and the angle it makes with the x-axis is 150°.
A)
B)
C)
D)
E)
and the angle it makes with the x-axis is 150°.A)
B)
C)
D)
E)
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12
Determine the area of a triangle having the following measurements. Round your answer to two decimal places.
A) 28.61 sq. units
B) 23.84 sq. units
C) 21.46 sq. units
D) 26.22 sq. units
E) 19.07 sq. units
A) 28.61 sq. units
B) 23.84 sq. units
C) 21.46 sq. units
D) 26.22 sq. units
E) 19.07 sq. units
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13
Given , , and , use the Law of Cosines to solve the triangle for the value of c. Round answer to two decimal places.
A) 16.29
B) 11.26
C) 15.57
D) 17.00
E) 14.13
, , and , use the Law of Cosines to solve the triangle for the value of c. Round answer to two decimal places.A) 16.29
B) 11.26
C) 15.57
D) 17.00
E) 14.13
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14
Determine the area of a triangle having the following measurements. Round your answer to two decimal places.
A) 59.30 sq. units
B) 88.95 sq. units
C) 66.71 sq. units
D) 81.54 sq. units
E) 74.13 sq. units
A) 59.30 sq. units
B) 88.95 sq. units
C) 66.71 sq. units
D) 81.54 sq. units
E) 74.13 sq. units
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15
Find the component form of v if and the angle it makes with the x-axis is .
A)
B)
C)
D)
E)
and the angle it makes with the x-axis is .A)
B)
C)
D)
E)
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16
Find the component form of vector v with initial point and terminal point .
A)
B)
C)
D)
E)
and terminal point .A)
B)
C)
D)
E)
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17
Find the component form of v if and the angle it makes with the x-axis is .
A)
B)
C)
D)
E)
and the angle it makes with the x-axis is .A)
B)
C)
D)
E)
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18
Given , , and , use Heron's Area Formula to find the area of . Round answer to two decimal places.
A) 17.36 sq. units
B) 18.44 sq. units
C) 20.21 sq. units
D) 16.76 sq. units
E) 14.02 sq. units
, , and , use Heron's Area Formula to find the area of . Round answer to two decimal places.A) 17.36 sq. units
B) 18.44 sq. units
C) 20.21 sq. units
D) 16.76 sq. units
E) 14.02 sq. units
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19
Given , , and , use the Law of Sines to solve the triangle for the value of b. Round answer to two decimal places.
A) a= 14.57
B) a= 13.14
C) a= 11.24
D) a= 13.69
E) a= 12.46
, , and , use the Law of Sines to solve the triangle for the value of b. Round answer to two decimal places.A) a= 14.57
B) a= 13.14
C) a= 11.24
D) a= 13.69
E) a= 12.46
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20
A straight road makes an angle, A, of with the horizontal. When the angle of elevation, B, of the sun is , a vertical pole beside the road casts a shadow 8 feet long parallel to the road. Approximate the length of the pole. Round answer to two decimal places.
A) 4.78 feet
B) 9.04 feet
C) 7.08 feet
D) 12.32 feet
E) 5.87 feet
with the horizontal. When the angle of elevation, B, of the sun is , a vertical pole beside the road casts a shadow 8 feet long parallel to the road. Approximate the length of the pole. Round answer to two decimal places.A) 4.78 feet
B) 9.04 feet
C) 7.08 feet
D) 12.32 feet
E) 5.87 feet
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21
A 725-pound trailer is sitting on an exit ramp inclined at 36° on Highway 35. How much force is required to keep the trailer from rolling back down the exit ramp? Round answer to two decimal places.
A) 566.49 pounds
B) 546.44 pounds
C) 586.54 pounds
D) 506.34 pounds
E) 426.14 pounds
A) 566.49 pounds
B) 546.44 pounds
C) 586.54 pounds
D) 506.34 pounds
E) 426.14 pounds
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22
Use DeMoivre's Theorem to find the indicated power of the following complex number.
A)390,625
B)78,125
C)1,000,000
D)1,953,125
E) 3,125
A)390,625
B)78,125
C)1,000,000
D)1,953,125
E) 3,125
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23
Determine whether u are v and orthogonal, parallel, or neither.
A) neither
B) parallel
C) orthogonal
A) neither
B) parallel
C) orthogonal
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24
Divide the complex numbers below and leave the result in trigonometric form.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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25
Use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in standard form.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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26
Perform the indicated operation using trigonometric form. Leave answer in trigonometric form.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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27
Find the trigonometric form of .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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28
A force of 45 pounds is exerted along a rope attached to a crate at an angle of 30° above the horizontal. The crate is moved 23 feet. How much work has been accomplished? Round answer to one decimal place.
A) 965.7 foot-pounds
B) 1,035.0 foot-pounds
C) 1,195.1 foot-pounds
D) 896.3 foot-pounds
E) 1,080.4 foot-pounds
A) 965.7 foot-pounds
B) 1,035.0 foot-pounds
C) 1,195.1 foot-pounds
D) 896.3 foot-pounds
E) 1,080.4 foot-pounds
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29
Perform the operation shown below and leave the result in trigonometric form.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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30
Multiply the complex numbers below and leave the result in trigonometric form.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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31
Multiply the complex numbers below and leave the result in trigonometric form.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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32
Find the standard form of the complex number shown below. Round answers to two decimal places.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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33
Find the product using trigonometric forms. Leave the result in trigonometric form.
A)
B)
C)
D)
E)
using trigonometric forms. Leave the result in trigonometric form.A)
B)
C)
D)
E)
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34
Find the standard form of the complex number . Round values to the nearest hundredth.
A)
B)
C)
D)
E)
. Round values to the nearest hundredth.A)
B)
C)
D)
E)
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35
The vector gives the number of units of two models of laptops produced by a company. The vector gives the prices (in dollars) of the two models of laptops, respectively. Use dot products to determine the revenue for these two laptops if the price of each is increased by 5.5%.
A) $10,701,150
B) $10,852,400
C) $11,003,650
D) $10,732,500
E) $10,812,433
gives the number of units of two models of laptops produced by a company. The vector gives the prices (in dollars) of the two models of laptops, respectively. Use dot products to determine the revenue for these two laptops if the price of each is increased by 5.5%.A) $10,701,150
B) $10,852,400
C) $11,003,650
D) $10,732,500
E) $10,812,433
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36
Determine whether u are v and orthogonal, parallel, or neither.
A) neither
B) orthogonal
C) parallel
A) neither
B) orthogonal
C) parallel
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37
Find the standard form of the complex number shown below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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38
Find the projection of u onto v if , .
A)
B)
C)
D)
E)
, .A)
B)
C)
D)
E)
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39
Use DeMoivre's Theorem to find the indicated power of the following complex number.
A) 3,125
B) 62,500
C) 15,625
D) 2,500
E) -2,500
A) 3,125
B) 62,500
C) 15,625
D) 2,500
E) -2,500
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40
Find the trigonometric form of .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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41
Use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in standard form.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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42
Use DeMoivre's Theorem to find the indicated power of the following complex number.
A) 2048
B)
C) -4,096
D)
E) 4,096
A) 2048
B)
C) -4,096
D)
E) 4,096
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