تكلم مع الذكاء الاصطناعي
Deck 12: Section 4: Vector-Valued Functions
ملء الشاشة (f)
سؤال
Find the unit tangent vector 
for the line tangent to the space curve 
at point 
.
A)
B)
C)
D)
E)
for the line tangent to the space curve at point .A)
B)
C)
D)
E)
سؤال
Find 
at time 
for the plane curve 
. Round your answer to three decimal places.
A) -40.625
B) -39.209
C) -111.667
D) -46.016
E) -43.988
at time for the plane curve . Round your answer to three decimal places.A) -40.625
B) -39.209
C) -111.667
D) -46.016
E) -43.988
سؤال
Find 
at time 
for the space curve 
. Round your answer to three decimal places.
A) 0.062
B) 0.071
C) 0.659
D) 0.000
E) 0.753
at time for the space curve . Round your answer to three decimal places.A) 0.062
B) 0.071
C) 0.659
D) 0.000
E) 0.753
سؤال
Find the principle unit normal vector to the curve given below at the specified point. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find 
at time 
for the plane curve 
. Round your answer to three decimal places.
A) 6.581
B) 4.818
C) 3.407
D) 2.154
E) 4.962
at time for the plane curve . Round your answer to three decimal places.A) 6.581
B) 4.818
C) 3.407
D) 2.154
E) 4.962
سؤال
Find the principle unit normal vector to the curve given below at the specified point. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Use the result, "the tangential and normal components of acceleration for a projectile fired at an angle 
with the horizontal at an initial speed of 
are 
and 
respectively.", to find the tangential component of acceleration for a projectile fired at an angle of 
with the horizontal at an initial speed of 152 feet per second. What is the component when the projectile is at its maximum height?
A) 76
B) 32
C) 16
D) 152
E) 0
with the horizontal at an initial speed of are and respectively.", to find the tangential component of acceleration for a projectile fired at an angle of with the horizontal at an initial speed of 152 feet per second. What is the component when the projectile is at its maximum height?A) 76
B) 32
C) 16
D) 152
E) 0
سؤال
Find 
at time 
for the space curve 
.
A) 16
B) 0
C) 5
D) 25
E) 4
at time for the space curve .A) 16
B) 0
C) 5
D) 25
E) 4
سؤال
Find the unit tangent vector to the curve given below at the specified point. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find 
at time 
for the plane curve 
. Round your answer to three decimal places.
A) 11.077
B) 7.310
C) 11.797
D) 5.898
E) 5.538
at time for the plane curve . Round your answer to three decimal places.A) 11.077
B) 7.310
C) 11.797
D) 5.898
E) 5.538
سؤال
Find the unit tangent vector T(t) and then use it to find a set of parametric equations for the line tangent to the space curve given below at the given point. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Use the result, "the tangential and normal components of acceleration for a projectile fired at an angle 
with the horizontal at an initial speed of 
are 
and 
respectively.", to find the normal component of acceleration for a projectile fired at an angle of 
with the horizontal at an initial speed of 148 feet per second. What is the component when the projectile is at its maximum height?
A) 0
B) 74
C) 148
D) 32
E) 16
with the horizontal at an initial speed of are and respectively.", to find the normal component of acceleration for a projectile fired at an angle of with the horizontal at an initial speed of 148 feet per second. What is the component when the projectile is at its maximum height?A) 0
B) 74
C) 148
D) 32
E) 16
سؤال
Verify that the space curves intersect at the given values of the parameter. Find the angle between the tangent vectors at the point of intersection. 
, 
, 
A)
B)
C)
D)
E)
, , A)
B)
C)
D)
E)
سؤال
Find the principle unit normal vector to the curve given below at the specified point. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find 
at time 
for the space curve 
. Round your answer to three decimal places.
A) 0.970
B) 0.465
C) 0.930
D) 1.814
E) 1.060
at time for the space curve . Round your answer to three decimal places.A) 0.970
B) 0.465
C) 0.930
D) 1.814
E) 1.060
سؤال
Find a set of parametric equations for the tangent line to the graph at 
and use the equations for the line to approximate 
. 
A)
B)
C)
D)
E)
and use the equations for the line to approximate . A)
B)
C)
D)
E)
سؤال
Because of a storm, ground controllers instruct the pilot of a plane flying at an altitude of 1.6 miles to make a 
turn and climb to an altitude of 1.8 miles. The model for the path of the plane during this maneuver is 
where t is the time in hours and 
is the distance in miles. Determine the speed of the plane. Round your answer to the nearest integer.
A) 50 mi/h
B) 16 mi/h
C) 54 mi/h
D) 34 mi/h
E) 79 mi/h
turn and climb to an altitude of 1.8 miles. The model for the path of the plane during this maneuver is where t is the time in hours and is the distance in miles. Determine the speed of the plane. Round your answer to the nearest integer.A) 50 mi/h
B) 16 mi/h
C) 54 mi/h
D) 34 mi/h
E) 79 mi/h
سؤال
Find the unit tangent vector to the curve given below at the specified point. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find 
at time 
for the space curve 
. Round your answer to three decimal places.
A) 0.781
B) 0.724
C) 0.343
D) 0.686
E) 0.649
at time for the space curve . Round your answer to three decimal places.A) 0.781
B) 0.724
C) 0.343
D) 0.686
E) 0.649
سؤال
Find 
at time 
for the plane curve 
. Round your answer to three decimal places.
A) 18.724
B) 23.792
C) 22.264
D) 15.179
E) 22.764
at time for the plane curve . Round your answer to three decimal places.A) 18.724
B) 23.792
C) 22.264
D) 15.179
E) 22.764
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ملء الشاشة (f)
Deck 12: Section 4: Vector-Valued Functions
1
Find the unit tangent vector for the line tangent to the space curve at point .
A)
B)
C)
D)
E)
for the line tangent to the space curve at point .A)
B)
C)
D)
E)
2
Find at time for the plane curve . Round your answer to three decimal places.
A) -40.625
B) -39.209
C) -111.667
D) -46.016
E) -43.988
at time for the plane curve . Round your answer to three decimal places.A) -40.625
B) -39.209
C) -111.667
D) -46.016
E) -43.988
-46.016
3
Find at time for the space curve . Round your answer to three decimal places.
A) 0.062
B) 0.071
C) 0.659
D) 0.000
E) 0.753
at time for the space curve . Round your answer to three decimal places.A) 0.062
B) 0.071
C) 0.659
D) 0.000
E) 0.753
0.000
4
Find the principle unit normal vector to the curve given below at the specified point.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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5
Find at time for the plane curve . Round your answer to three decimal places.
A) 6.581
B) 4.818
C) 3.407
D) 2.154
E) 4.962
at time for the plane curve . Round your answer to three decimal places.A) 6.581
B) 4.818
C) 3.407
D) 2.154
E) 4.962
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6
Find the principle unit normal vector to the curve given below at the specified point.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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7
Use the result, "the tangential and normal components of acceleration for a projectile fired at an angle with the horizontal at an initial speed of are and respectively.", to find the tangential component of acceleration for a projectile fired at an angle of with the horizontal at an initial speed of 152 feet per second. What is the component when the projectile is at its maximum height?
A) 76
B) 32
C) 16
D) 152
E) 0
with the horizontal at an initial speed of are and respectively.", to find the tangential component of acceleration for a projectile fired at an angle of with the horizontal at an initial speed of 152 feet per second. What is the component when the projectile is at its maximum height?A) 76
B) 32
C) 16
D) 152
E) 0
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8
Find at time for the space curve .
A) 16
B) 0
C) 5
D) 25
E) 4
at time for the space curve .A) 16
B) 0
C) 5
D) 25
E) 4
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9
Find the unit tangent vector to the curve given below at the specified point.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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10
Find at time for the plane curve . Round your answer to three decimal places.
A) 11.077
B) 7.310
C) 11.797
D) 5.898
E) 5.538
at time for the plane curve . Round your answer to three decimal places.A) 11.077
B) 7.310
C) 11.797
D) 5.898
E) 5.538
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11
Find the unit tangent vector T(t) and then use it to find a set of parametric equations for the line tangent to the space curve given below at the given point.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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12
Use the result, "the tangential and normal components of acceleration for a projectile fired at an angle with the horizontal at an initial speed of are and respectively.", to find the normal component of acceleration for a projectile fired at an angle of with the horizontal at an initial speed of 148 feet per second. What is the component when the projectile is at its maximum height?
A) 0
B) 74
C) 148
D) 32
E) 16
with the horizontal at an initial speed of are and respectively.", to find the normal component of acceleration for a projectile fired at an angle of with the horizontal at an initial speed of 148 feet per second. What is the component when the projectile is at its maximum height?A) 0
B) 74
C) 148
D) 32
E) 16
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13
Verify that the space curves intersect at the given values of the parameter. Find the angle between the tangent vectors at the point of intersection. , ,
A)
B)
C)
D)
E)
, , A)
B)
C)
D)
E)
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14
Find the principle unit normal vector to the curve given below at the specified point.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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15
Find at time for the space curve . Round your answer to three decimal places.
A) 0.970
B) 0.465
C) 0.930
D) 1.814
E) 1.060
at time for the space curve . Round your answer to three decimal places.A) 0.970
B) 0.465
C) 0.930
D) 1.814
E) 1.060
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16
Find a set of parametric equations for the tangent line to the graph at and use the equations for the line to approximate .
A)
B)
C)
D)
E)
and use the equations for the line to approximate . A)
B)
C)
D)
E)
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17
Because of a storm, ground controllers instruct the pilot of a plane flying at an altitude of 1.6 miles to make a turn and climb to an altitude of 1.8 miles. The model for the path of the plane during this maneuver is where t is the time in hours and is the distance in miles. Determine the speed of the plane. Round your answer to the nearest integer.
A) 50 mi/h
B) 16 mi/h
C) 54 mi/h
D) 34 mi/h
E) 79 mi/h
turn and climb to an altitude of 1.8 miles. The model for the path of the plane during this maneuver is where t is the time in hours and is the distance in miles. Determine the speed of the plane. Round your answer to the nearest integer.A) 50 mi/h
B) 16 mi/h
C) 54 mi/h
D) 34 mi/h
E) 79 mi/h
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18
Find the unit tangent vector to the curve given below at the specified point.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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19
Find at time for the space curve . Round your answer to three decimal places.
A) 0.781
B) 0.724
C) 0.343
D) 0.686
E) 0.649
at time for the space curve . Round your answer to three decimal places.A) 0.781
B) 0.724
C) 0.343
D) 0.686
E) 0.649
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20
Find at time for the plane curve . Round your answer to three decimal places.
A) 18.724
B) 23.792
C) 22.264
D) 15.179
E) 22.764
at time for the plane curve . Round your answer to three decimal places.A) 18.724
B) 23.792
C) 22.264
D) 15.179
E) 22.764
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