Chat with AI
Deck 12: Vector-Valued Functions
Full screen (f)
Question
A particle moves in the yz-plane along the curve represented by the vector-valued function 
. Find the maximum value of 
.
A) 8
B) 6
C) 9
D) 7
E) 3
. Find the maximum value of .A) 8
B) 6
C) 9
D) 7
E) 3
Question
Find the indefinite integral below. 
Do not include an arbitrary constant vector.
A)
B)
C)
D)
E)
Do not include an arbitrary constant vector.A)
B)
C)
D)
E)
Question
Find 
at time 
for the plane curve 
. Round your answer to three decimal places.
A) -30.406
B) -29.533
C) -81.262
D) -35.346
E) -33.994
at time for the plane curve . Round your answer to three decimal places.A) -30.406
B) -29.533
C) -81.262
D) -35.346
E) -33.994
Question
The graph below is most likely the graph of which of the following equations? 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the curvature of the plane curve 
at 
. Round your answer to three decimal places.
A) 0.986
B) 0.658
C) 0.114
D) 0.036
E) 0.027
at . Round your answer to three decimal places.A) 0.986
B) 0.658
C) 0.114
D) 0.036
E) 0.027
Question
Find the curvature K of the curve 
at the point 
. Round your answer to three decimal places.
A) 1.400
B) 1.599
C) 0.192
D) 0.435
E) 0.053
at the point . Round your answer to three decimal places.A) 1.400
B) 1.599
C) 0.192
D) 0.435
E) 0.053
Question
Find the curvature 
of the curve given below. 
A)
B)
C)
D)
E)
of the curve given below. A)
B)
C)
D)
E)
Question
The position vector 
describes the path of an object moving in space. Find the velocity 
of the object.
A)
B)
C)
D)
E)
describes the path of an object moving in space. Find the velocity of the object.A)
B)
C)
D)
E)
Question
Evaluate the limit given below. 
A)
B)
C)
D)
E) The limit does not exist.
A)
B)
C)
D)
E) The limit does not exist.
Question
Find the open interval on which the curve given by the vector-valued function 
is smooth.
A)
B)
C)
D)
E)
is smooth.A)
B)
C)
D)
E)
Question
A baseball is hit 5 feet above the ground at 160 feet per second and at an angle of 
with respect to the ground. Find the maximum height. Round your answer to the nearest integer.
A) 247 feet
B) 235 feet
C) 205 feet
D) 218 feet
E) 220 feet
with respect to the ground. Find the maximum height. Round your answer to the nearest integer.A) 247 feet
B) 235 feet
C) 205 feet
D) 218 feet
E) 220 feet
Question
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)
Question
The position vector 
describes the path of an object moving in space. Find the speed 
of the object.
A) 17
B)
C)
D) 115
E)
describes the path of an object moving in space. Find the speed of the object.A) 17
B)
C)
D) 115
E)
Question
Find the point on the curve 
at which the curvature K is a maximum.
A)
B)
C)
D)
E)
at which the curvature K is a maximum.A)
B)
C)
D)
E)
Question
Sketch the curve represented by the vector-valued function 
and give the orientation of the curve.
A)
B)
C)
D)
E)
and give the orientation of the curve.A)
B)
C)
D)
E)
Question
Match the equation with the graph shown in red below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find 
at time 
for the plane curve 
. Round your answer to three decimal places.
A) 5.315
B) 3.010
C) 7.491
D) 3.745
E) 2.657
at time for the plane curve . Round your answer to three decimal places.A) 5.315
B) 3.010
C) 7.491
D) 3.745
E) 2.657
Question
The position vector 
describes the path of an object moving in the xy-plane. Sketch a graph of the path and sketch the velocity and acceleration vectors at the point 
.
A)
B)
C)
D)
E)
describes the path of an object moving in the xy-plane. Sketch a graph of the path and sketch the velocity and acceleration vectors at the point .A)
B)
C)
D)
E)
Question
Determine the maximum height of a projectile fired at a height of 5 feet above the ground with an initial velocity of 600 feet per second and at an angle of 
above the horizontal. Use the model for projectile motion, assuming there is no air resistance. Round your answer to three decimal places.
A) 8,440.000 feet
B) 8,442.500 feet
C) 4,221.250 feet
D) 4,223.750 feet
E) 8,447.500 feet
above the horizontal. Use the model for projectile motion, assuming there is no air resistance. Round your answer to three decimal places.A) 8,440.000 feet
B) 8,442.500 feet
C) 4,221.250 feet
D) 4,223.750 feet
E) 8,447.500 feet
Question
Find the length of the plane curve given below. 
A) 14
B) 8
C) 11
D) 13
E) 12
A) 14
B) 8
C) 11
D) 13
E) 12
Question
Find a vector-valued function, using the given parameter, to represent the intersection of the surfaces given below. Surfaces
Parameter
A)
B)
C)
D)
E)
Parameter
A)
B)
C)
D)
E)
Question
Suppose the two particles travel along the space curves 
and 
. A collision will occur at the point of intersection P if both particles are at P at the same time. Find the point of collision.
A)
B)
C)
D)
E)
and . A collision will occur at the point of intersection P if both particles are at P at the same time. Find the point of collision.A)
B)
C)
D)
E)
Question
Use the properties of the derivative to find 
given the following vector-valued functions. 
A) 1
B)
C)
D) 6
E) 0
given the following vector-valued functions. A) 1
B)
C)
D) 6
E) 0
Question
Find the point on the curve given below at which the curvature K is zero. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Represent the following curve by a vector-valued function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
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)
Question
A baseball is hit 5 feet above the ground at 80 feet per second and at an angle of 
with respect to the ground. Find the arc length of the trajectory. Round your answer to one decimal place.
A) 194.2 feet
B) 212.3 feet
C) 210.1 feet
D) 171.4 feet
E) 236.5 feet
with respect to the ground. Find the arc length of the trajectory. Round your answer to one decimal place. A) 194.2 feet
B) 212.3 feet
C) 210.1 feet
D) 171.4 feet
E) 236.5 feet
Question
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)
Question
The quarterback of a football team releases a pass at a height of 6 feet above the playing field, and the football is caught by a receiver 78 yards directly downfield at a height of 4 feet. The pass is released at an angle of 
with the horizontal. Find the time in seconds the receiver has to reach the proper position after the quarterback releases the football. Round your answer to one decimal place.
A) 2.2 seconds
B) 12.8 seconds
C) 22.2 seconds
D) 3.7 seconds
E) 7.4 seconds
with the horizontal. Find the time in seconds the receiver has to reach the proper position after the quarterback releases the football. Round your answer to one decimal place.A) 2.2 seconds
B) 12.8 seconds
C) 22.2 seconds
D) 3.7 seconds
E) 7.4 seconds
Question
Find the domain of the vector-valued function given below. 
where 
A)
B)
C)
D)
E)
where A)
B)
C)
D)
E)
Question
Find the vectors 
and 
for the following vector function. 
A)
B)
C)
D)
E)
and for the following vector function. A)
B)
C)
D)
E)
Question
Find the indefinite integral below. 
Do not include an arbitrary constant vector.
A)
B)
C)
D)
E)
Do not include an arbitrary constant vector.A)
B)
C)
D)
E)
Question
Find the length of the space curve given below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use the properties of the derivative to find 
given the following vector-valued functions. 
A)
B)
C)
D)
E)
given the following vector-valued functions. A)
B)
C)
D)
E)
Question
Use the properties of the derivative to find 
given the following vector-valued functions. 
A)
B)
C)
D)
E)
given the following vector-valued functions. A)
B)
C)
D)
E)
Question
Determine the range of a projectile fired at a height of 3 feet above the ground with an initial velocity of 500 feet per second and at an angle of 
above the horizontal. Use the model for projectile motion, assuming there is no air resistance. Round your answer to three decimal places.
A) 2,669.517 feet
B) 1,764.116 feet
C) 5,337.349 feet
D) 6,767.555 feet
E) 3,525.690 feet
above the horizontal. Use the model for projectile motion, assuming there is no air resistance. Round your answer to three decimal places.A) 2,669.517 feet
B) 1,764.116 feet
C) 5,337.349 feet
D) 6,767.555 feet
E) 3,525.690 feet
Question
Suppose the outer edge of a playground slide is in the shape of a helix of radius 8 meters. The slide has a height of 2 meters and makes one complete revolution from top to bottom. Find a vector-valued function for the helix.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Question
Sketch the curve represented by the vector-valued function 
and give the orientation of the curve.
A)
B)
C)
D)
E)
and give the orientation of the curve.A)
B)
C)
D)
E)
Question
Find the unit tangent vector to the curve given below at the specified point. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the domain of the vector-valued function given below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
A particle moves in the yz-plane along the curve represented by the vector-valued function 
. Find the minimum value of 
.
A) 3
B) 2
C) 5
D) 6
E) 8
. Find the minimum value of .A) 3
B) 2
C) 5
D) 6
E) 8
Question
Find a vector-valued function, using the given parameter, to represent the intersection of the surfaces given below. Surfaces
Parameter
A)
B)
C)
D)
E)
Parameter
A)
B)
C)
D)
E)
Question
Find 
given the following vector function. 
A) 1
B) -18
C) 18
D) 0
E) 3
given the following vector function. A) 1
B) -18
C) 18
D) 0
E) 3
Question
Find 
at time 
for the space curve 
. Round your answer to three decimal places.
A) 0.816
B) 0.389
C) 0.777
D) 1.864
E) 0.889
at time for the space curve . Round your answer to three decimal places.A) 0.816
B) 0.389
C) 0.777
D) 1.864
E) 0.889
Question
Find 
given the following vector function: 
A)
B) 0
C)
D)
E)
given the following vector function: A)
B) 0
C)
D)
E)
Question
Find 
at time 
for the space curve 
. Round your answer to three decimal places.
A) 1.069
B) 0.963
C) 0.468
D) 0.936
E) 0.848
at time for the space curve . Round your answer to three decimal places.A) 1.069
B) 0.963
C) 0.468
D) 0.936
E) 0.848
Question
Given the vector-valued function below, evaluate 
. 
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
Question
The position vector 
describes the path of an object moving in space. Find the velocity 
of the object.
A)
B)
C)
D)
E)
describes the path of an object moving in space. Find the velocity of the object.A)
B)
C)
D)
E)
Question
Evaluate the limit given below. 
A)
B)
C)
D)
E) The limit does not exist.
A)
B)
C)
D)
E) The limit does not exist.
Question
Find 
at time 
for the plane curve 
. Round your answer to three decimal places.
A) 28.451
B) 28.636
C) 28.400
D) 28.111
E) 20.897
at time for the plane curve . Round your answer to three decimal places.A) 28.451
B) 28.636
C) 28.400
D) 28.111
E) 20.897
Question
The smaller the curvature in a bend of a road, the faster a car can travel. Assume that the maximum speed around a turn is inversely proportional to the square root of the curvature. A car moving on the path 
(x and y are measured in miles) can safely go 30 miles per hour at 
. How fast can it go at 
? Round your answer to two decimal places.
A)
mi/h
B)
mi/h
C)
mi/h
D)
mi/h
E)
mi/h
(x and y are measured in miles) can safely go 30 miles per hour at . How fast can it go at ? Round your answer to two decimal places.A)
mi/hB)
mi/hC)
mi/hD)
mi/hE)
mi/h Question
Find 
at time 
for the space curve 
.
A) 9
B) 0
C) 8
D) 64
E) 3
at time for the space curve .A) 9
B) 0
C) 8
D) 64
E) 3
Question
Use the properties of the derivative to find 
given the following vector-valued functions. 
A)
B)
C)
D)
E)
given the following vector-valued functions. A)
B)
C)
D)
E)
Question
The quarterback of a football team releases a pass at a height of 6 feet above the playing field, and the football is caught by a receiver 30 yards directly downfield at a height of 5 feet. The pass is released at an angle of 
with the horizontal. Find the speed of the football when it is released. Round your answer to three decimal places.
A) 32.979 feet per second
B) 57.483 feet per second
C) 18.863 feet per second
D) 114.967 feet per second
E) 189.144 feet per second
with the horizontal. Find the speed of the football when it is released. Round your answer to three decimal places.A) 32.979 feet per second
B) 57.483 feet per second
C) 18.863 feet per second
D) 114.967 feet per second
E) 189.144 feet per second
Question
Use the properties of the derivative to find 
given the following vector-valued functions. 
A)
B)
C)
D)
E)
given the following vector-valued functions. A)
B)
C)
D)
E)
Question
Find 
at time 
for the plane curve 
. Round your answer to three decimal places.
A) 4.575
B) 3.841
C) 2.716
D) 1.718
E) 4.685
at time for the plane curve . Round your answer to three decimal places.A) 4.575
B) 3.841
C) 2.716
D) 1.718
E) 4.685
Question
A baseball is hit 5 feet above the ground at 160 feet per second and at an angle of 
with respect to the ground. Find the vector-valued function for the path of the baseball.
A)
B)
C)
D)
E)
with respect to the ground. Find the vector-valued function for the path of the baseball.A)
B)
C)
D)
E)
Question
Find 
at time 
for the space curve 
. Round your answer to three decimal places.
A) 0.041
B) 0.093
C) 0.406
D) 0.000
E) 0.914
at time for the space curve . Round your answer to three decimal places.A) 0.041
B) 0.093
C) 0.406
D) 0.000
E) 0.914
Question
Determine the interval on which the vector-valued function 
is continuous.
A)
B)
C)
D)
E)
is continuous.A)
B)
C)
D)
E)
Question
Use the given acceleration function and initial conditions to find the position at time t = 1. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
A baseball, hit 7 feet above the ground, leaves the bat at an angle of 
and its caught by an outfielder 7 feet above the ground and 400 feet from home plate. How high does the ball rise? Round your answer to the nearest integer.
A) 180 feet
B) 18 feet
C) 397 feet
D) 278 feet
E) 50 feet
and its caught by an outfielder 7 feet above the ground and 400 feet from home plate. How high does the ball rise? Round your answer to the nearest integer. A) 180 feet
B) 18 feet
C) 397 feet
D) 278 feet
E) 50 feet
Question
Use the given acceleration function and initial conditions to find the position at time t = 4. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the curvature K of the curve 
at the point 
. Round your answer to three decimal places.
A) 0.728
B) 0.970
C) 0.158
D) 0.057
E) 0.126
at the point . Round your answer to three decimal places.A) 0.728
B) 0.970
C) 0.158
D) 0.057
E) 0.126
Question
The quarterback of a football team releases a pass at a height of 6 feet above the playing field, and the football is caught by a receiver 62 yards directly downfield at a height of 3 feet. The pass is released at an angle of 
with the horizontal. Find the maximum height of the football. Round your answer to one decimal place.
A) 337.1 feet
B) 16.3 feet
C) 245.4 feet
D) 85.8 feet
E) 17.5 feet
with the horizontal. Find the maximum height of the football. Round your answer to one decimal place. A) 337.1 feet
B) 16.3 feet
C) 245.4 feet
D) 85.8 feet
E) 17.5 feet
Question
Find 
given the following vector function. 
A)
B)
C)
D)
E)
given the following vector function. A)
B)
C)
D)
E)
Question
Find a vector-valued function, using the given parameter, to represent the intersection of the surfaces given below. Surfaces
Parameter
A)
B)
C)
D)
E)
Parameter
A)
B)
C)
D)
E)
Question
Find 
given the following vector function. 
A)
B)
C)
D)
E)
given the following vector function. A)
B)
C)
D)
E)
Question
Because of a storm, ground controllers instruct the pilot of a plane flying at an altitude of 3.2 miles to make a 
turn and climb to an altitude of 3.4 miles. The model for the path of the plane during this maneuver is 
where t is the time in hours and r is the distance in miles. Determine the speed of the plane. Round your answer to the nearest integer.
A) 201 mi/h
B) 64 mi/h
C) 173 mi/h
D) 137 mi/h
E) 255 mi/h
turn and climb to an altitude of 3.4 miles. The model for the path of the plane during this maneuver is where t is the time in hours and r is the distance in miles. Determine the speed of the plane. Round your answer to the nearest integer.A) 201 mi/h
B) 64 mi/h
C) 173 mi/h
D) 137 mi/h
E) 255 mi/h
Question
Find the unit tangent vector to the curve given below at the specified point. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the arc length for 
over the interval 
. Round your answer to two decimal places.
A) 110.36
B) 140.93
C) 129.56
D) 57.80
E) 102.75
over the interval . Round your answer to two decimal places. A) 110.36
B) 140.93
C) 129.56
D) 57.80
E) 102.75
Question
The position vector 
describes the path of an object moving in space. Find the acceleration 
of the object.
A)
B)
C)
D)
E)
describes the path of an object moving in space. Find the acceleration of the object.A)
B)
C)
D)
E)
Question
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)
Question
Find a vector-valued function, using the given parameter, to represent the intersection of the surfaces given below. Surfaces
Parameter
A)
B)
C)
D)
E)
Parameter
A)
B)
C)
D)
E)
Question
A baseball is hit 3 feet above the ground at 95 feet per second and at an angle of 
with respect to the ground. Find the range. Round your answer to one decimal place.
A) 285 feet
B) 352.2 feet
C) 370.7 feet
D) 501.9 feet
E) 300 feet
with respect to the ground. Find the range. Round your answer to one decimal place.A) 285 feet
B) 352.2 feet
C) 370.7 feet
D) 501.9 feet
E) 300 feet
Question
Find the radius of curvature of the plane curve 
at 
. Round your answer to three decimal places.
A) 1021.045
B) 2340.571
C) 1374.626
D) 1565.001
E) 1571.001
at . Round your answer to three decimal places.A) 1021.045
B) 2340.571
C) 1374.626
D) 1565.001
E) 1571.001
Question
The position vector 
describes the path of an object moving in space. Find the speed 
of the object.
A)
B)
122
C)
D)
E)
18
describes the path of an object moving in space. Find the speed of the object. A)
B)
122C)
D)
E)
18 Question
A baseball player at second base throws a ball 95 feet to the player at first base. The ball is thrown 8 feet above the ground with an initial velocity of 46 miles per hour and at an angle of 
above the horizontal. At which height does the player at first base catch the ball? Round your answer to three decimal places.
A) 2.908 feet
B) 2.008 feet
C) 0.808 feet
D) 1.408 feet
E) 0.908 feet
above the horizontal. At which height does the player at first base catch the ball? Round your answer to three decimal places.A) 2.908 feet
B) 2.008 feet
C) 0.808 feet
D) 1.408 feet
E) 0.908 feet
Question
Evaluate the definite integral below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find 
given the following vector function. 
A)
B)
C)
D)
E)
given the following vector function. A)
B)
C)
D)
E)
Unlock Deck
Sign up to unlock the cards in this deck!
Unlock Deck
Unlock Deck
1/85
Play
Full screen (f)
Deck 12: Vector-Valued Functions
1
A particle moves in the yz-plane along the curve represented by the vector-valued function . Find the maximum value of .
A) 8
B) 6
C) 9
D) 7
E) 3
. Find the maximum value of .A) 8
B) 6
C) 9
D) 7
E) 3
C
2
Find the indefinite integral below. Do not include an arbitrary constant vector.
A)
B)
C)
D)
E)
Do not include an arbitrary constant vector.A)
B)
C)
D)
E)
D
3
Find at time for the plane curve . Round your answer to three decimal places.
A) -30.406
B) -29.533
C) -81.262
D) -35.346
E) -33.994
at time for the plane curve . Round your answer to three decimal places.A) -30.406
B) -29.533
C) -81.262
D) -35.346
E) -33.994
D
4
The graph below is most likely the graph of which of the following equations?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
5
Find the curvature of the plane curve at . Round your answer to three decimal places.
A) 0.986
B) 0.658
C) 0.114
D) 0.036
E) 0.027
at . Round your answer to three decimal places.A) 0.986
B) 0.658
C) 0.114
D) 0.036
E) 0.027
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
6
Find the curvature K of the curve at the point . Round your answer to three decimal places.
A) 1.400
B) 1.599
C) 0.192
D) 0.435
E) 0.053
at the point . Round your answer to three decimal places.A) 1.400
B) 1.599
C) 0.192
D) 0.435
E) 0.053
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
7
Find the curvature of the curve given below.
A)
B)
C)
D)
E)
of the curve given below. A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
8
The position vector describes the path of an object moving in space. Find the velocity of the object.
A)
B)
C)
D)
E)
describes the path of an object moving in space. Find the velocity of the object.A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
9
Evaluate the limit given below.
A)
B)
C)
D)
E) The limit does not exist.
A)
B)
C)
D)
E) The limit does not exist.
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
10
Find the open interval on which the curve given by the vector-valued function is smooth.
A)
B)
C)
D)
E)
is smooth.A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
11
A baseball is hit 5 feet above the ground at 160 feet per second and at an angle of with respect to the ground. Find the maximum height. Round your answer to the nearest integer.
A) 247 feet
B) 235 feet
C) 205 feet
D) 218 feet
E) 220 feet
with respect to the ground. Find the maximum height. Round your answer to the nearest integer.A) 247 feet
B) 235 feet
C) 205 feet
D) 218 feet
E) 220 feet
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
12
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)
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
13
The position vector describes the path of an object moving in space. Find the speed of the object.
A) 17
B)
C)
D) 115
E)
describes the path of an object moving in space. Find the speed of the object.A) 17
B)
C)
D) 115
E)
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
14
Find the point on the curve at which the curvature K is a maximum.
A)
B)
C)
D)
E)
at which the curvature K is a maximum.A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
15
Sketch the curve represented by the vector-valued function and give the orientation of the curve.
A)
B)
C)
D)
E)
and give the orientation of the curve.A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
16
Match the equation with the graph shown in red below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
17
Find at time for the plane curve . Round your answer to three decimal places.
A) 5.315
B) 3.010
C) 7.491
D) 3.745
E) 2.657
at time for the plane curve . Round your answer to three decimal places.A) 5.315
B) 3.010
C) 7.491
D) 3.745
E) 2.657
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
18
The position vector describes the path of an object moving in the xy-plane. Sketch a graph of the path and sketch the velocity and acceleration vectors at the point .
A)
B)
C)
D)
E)
describes the path of an object moving in the xy-plane. Sketch a graph of the path and sketch the velocity and acceleration vectors at the point .A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
19
Determine the maximum height of a projectile fired at a height of 5 feet above the ground with an initial velocity of 600 feet per second and at an angle of above the horizontal. Use the model for projectile motion, assuming there is no air resistance. Round your answer to three decimal places.
A) 8,440.000 feet
B) 8,442.500 feet
C) 4,221.250 feet
D) 4,223.750 feet
E) 8,447.500 feet
above the horizontal. Use the model for projectile motion, assuming there is no air resistance. Round your answer to three decimal places.A) 8,440.000 feet
B) 8,442.500 feet
C) 4,221.250 feet
D) 4,223.750 feet
E) 8,447.500 feet
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
20
Find the length of the plane curve given below.
A) 14
B) 8
C) 11
D) 13
E) 12
A) 14
B) 8
C) 11
D) 13
E) 12
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
21
Find a vector-valued function, using the given parameter, to represent the intersection of the surfaces given below. Surfaces
Parameter
A)
B)
C)
D)
E)
Parameter
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
22
Suppose the two particles travel along the space curves and . A collision will occur at the point of intersection P if both particles are at P at the same time. Find the point of collision.
A)
B)
C)
D)
E)
and . A collision will occur at the point of intersection P if both particles are at P at the same time. Find the point of collision.A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
23
Use the properties of the derivative to find given the following vector-valued functions.
A) 1
B)
C)
D) 6
E) 0
given the following vector-valued functions. A) 1
B)
C)
D) 6
E) 0
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
24
Find the point on the curve given below at which the curvature K is zero.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
25
Represent the following curve by a vector-valued function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
26
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)
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
27
A baseball is hit 5 feet above the ground at 80 feet per second and at an angle of with respect to the ground. Find the arc length of the trajectory. Round your answer to one decimal place.
A) 194.2 feet
B) 212.3 feet
C) 210.1 feet
D) 171.4 feet
E) 236.5 feet
with respect to the ground. Find the arc length of the trajectory. Round your answer to one decimal place. A) 194.2 feet
B) 212.3 feet
C) 210.1 feet
D) 171.4 feet
E) 236.5 feet
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
28
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)
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
29
The quarterback of a football team releases a pass at a height of 6 feet above the playing field, and the football is caught by a receiver 78 yards directly downfield at a height of 4 feet. The pass is released at an angle of with the horizontal. Find the time in seconds the receiver has to reach the proper position after the quarterback releases the football. Round your answer to one decimal place.
A) 2.2 seconds
B) 12.8 seconds
C) 22.2 seconds
D) 3.7 seconds
E) 7.4 seconds
with the horizontal. Find the time in seconds the receiver has to reach the proper position after the quarterback releases the football. Round your answer to one decimal place.A) 2.2 seconds
B) 12.8 seconds
C) 22.2 seconds
D) 3.7 seconds
E) 7.4 seconds
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
30
Find the domain of the vector-valued function given below. where
A)
B)
C)
D)
E)
where A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
31
Find the vectors and for the following vector function.
A)
B)
C)
D)
E)
and for the following vector function. A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
32
Find the indefinite integral below. Do not include an arbitrary constant vector.
A)
B)
C)
D)
E)
Do not include an arbitrary constant vector.A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
33
Find the length of the space curve given below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
34
Use the properties of the derivative to find given the following vector-valued functions.
A)
B)
C)
D)
E)
given the following vector-valued functions. A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
35
Use the properties of the derivative to find given the following vector-valued functions.
A)
B)
C)
D)
E)
given the following vector-valued functions. A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
36
Determine the range of a projectile fired at a height of 3 feet above the ground with an initial velocity of 500 feet per second and at an angle of above the horizontal. Use the model for projectile motion, assuming there is no air resistance. Round your answer to three decimal places.
A) 2,669.517 feet
B) 1,764.116 feet
C) 5,337.349 feet
D) 6,767.555 feet
E) 3,525.690 feet
above the horizontal. Use the model for projectile motion, assuming there is no air resistance. Round your answer to three decimal places.A) 2,669.517 feet
B) 1,764.116 feet
C) 5,337.349 feet
D) 6,767.555 feet
E) 3,525.690 feet
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
37
Suppose the outer edge of a playground slide is in the shape of a helix of radius 8 meters. The slide has a height of 2 meters and makes one complete revolution from top to bottom. Find a vector-valued function for the helix.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
38
A 5800-pound vehicle is driven at a speed of 25 miles per hour on a circular interchange of radius 90 feet. To keep the vehicle from skidding off course, what frictional force must the road surface exert on the tires? Round your answer to one decimal place.
A) 2,716.9 lb
B) 3,396.4 lb
C) 3,046.0 lb
D) 2,707.6 lb
E) 3,565.1 lb
A) 2,716.9 lb
B) 3,396.4 lb
C) 3,046.0 lb
D) 2,707.6 lb
E) 3,565.1 lb
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
39
Sketch the curve represented by the vector-valued function and give the orientation of the curve.
A)
B)
C)
D)
E)
and give the orientation of the curve.A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
40
Find the unit tangent vector to the curve given below at the specified point.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
41
Find the domain of the vector-valued function given below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
42
A particle moves in the yz-plane along the curve represented by the vector-valued function . Find the minimum value of .
A) 3
B) 2
C) 5
D) 6
E) 8
. Find the minimum value of .A) 3
B) 2
C) 5
D) 6
E) 8
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
43
Find a vector-valued function, using the given parameter, to represent the intersection of the surfaces given below. Surfaces
Parameter
A)
B)
C)
D)
E)
Parameter
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
44
Find given the following vector function.
A) 1
B) -18
C) 18
D) 0
E) 3
given the following vector function. A) 1
B) -18
C) 18
D) 0
E) 3
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
45
Find at time for the space curve . Round your answer to three decimal places.
A) 0.816
B) 0.389
C) 0.777
D) 1.864
E) 0.889
at time for the space curve . Round your answer to three decimal places.A) 0.816
B) 0.389
C) 0.777
D) 1.864
E) 0.889
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
46
Find given the following vector function:
A)
B) 0
C)
D)
E)
given the following vector function: A)
B) 0
C)
D)
E)
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
47
Find at time for the space curve . Round your answer to three decimal places.
A) 1.069
B) 0.963
C) 0.468
D) 0.936
E) 0.848
at time for the space curve . Round your answer to three decimal places.A) 1.069
B) 0.963
C) 0.468
D) 0.936
E) 0.848
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
48
Given the vector-valued function below, evaluate .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
49
The position vector describes the path of an object moving in space. Find the velocity of the object.
A)
B)
C)
D)
E)
describes the path of an object moving in space. Find the velocity of the object.A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
50
Evaluate the limit given below.
A)
B)
C)
D)
E) The limit does not exist.
A)
B)
C)
D)
E) The limit does not exist.
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
51
Find at time for the plane curve . Round your answer to three decimal places.
A) 28.451
B) 28.636
C) 28.400
D) 28.111
E) 20.897
at time for the plane curve . Round your answer to three decimal places.A) 28.451
B) 28.636
C) 28.400
D) 28.111
E) 20.897
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
52
The smaller the curvature in a bend of a road, the faster a car can travel. Assume that the maximum speed around a turn is inversely proportional to the square root of the curvature. A car moving on the path (x and y are measured in miles) can safely go 30 miles per hour at . How fast can it go at ? Round your answer to two decimal places.
A) mi/h
B) mi/h
C) mi/h
D) mi/h
E) mi/h
(x and y are measured in miles) can safely go 30 miles per hour at . How fast can it go at ? Round your answer to two decimal places.A)
mi/hB)
mi/hC)
mi/hD)
mi/hE)
mi/h Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
53
Find at time for the space curve .
A) 9
B) 0
C) 8
D) 64
E) 3
at time for the space curve .A) 9
B) 0
C) 8
D) 64
E) 3
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
54
Use the properties of the derivative to find given the following vector-valued functions.
A)
B)
C)
D)
E)
given the following vector-valued functions. A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
55
The quarterback of a football team releases a pass at a height of 6 feet above the playing field, and the football is caught by a receiver 30 yards directly downfield at a height of 5 feet. The pass is released at an angle of with the horizontal. Find the speed of the football when it is released. Round your answer to three decimal places.
A) 32.979 feet per second
B) 57.483 feet per second
C) 18.863 feet per second
D) 114.967 feet per second
E) 189.144 feet per second
with the horizontal. Find the speed of the football when it is released. Round your answer to three decimal places.A) 32.979 feet per second
B) 57.483 feet per second
C) 18.863 feet per second
D) 114.967 feet per second
E) 189.144 feet per second
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
56
Use the properties of the derivative to find given the following vector-valued functions.
A)
B)
C)
D)
E)
given the following vector-valued functions. A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
57
Find at time for the plane curve . Round your answer to three decimal places.
A) 4.575
B) 3.841
C) 2.716
D) 1.718
E) 4.685
at time for the plane curve . Round your answer to three decimal places.A) 4.575
B) 3.841
C) 2.716
D) 1.718
E) 4.685
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
58
A baseball is hit 5 feet above the ground at 160 feet per second and at an angle of with respect to the ground. Find the vector-valued function for the path of the baseball.
A)
B)
C)
D)
E)
with respect to the ground. Find the vector-valued function for the path of the baseball.A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
59
Find at time for the space curve . Round your answer to three decimal places.
A) 0.041
B) 0.093
C) 0.406
D) 0.000
E) 0.914
at time for the space curve . Round your answer to three decimal places.A) 0.041
B) 0.093
C) 0.406
D) 0.000
E) 0.914
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
60
Determine the interval on which the vector-valued function is continuous.
A)
B)
C)
D)
E)
is continuous.A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
61
Use the given acceleration function and initial conditions to find the position at time t = 1.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
62
A baseball, hit 7 feet above the ground, leaves the bat at an angle of and its caught by an outfielder 7 feet above the ground and 400 feet from home plate. How high does the ball rise? Round your answer to the nearest integer.
A) 180 feet
B) 18 feet
C) 397 feet
D) 278 feet
E) 50 feet
and its caught by an outfielder 7 feet above the ground and 400 feet from home plate. How high does the ball rise? Round your answer to the nearest integer. A) 180 feet
B) 18 feet
C) 397 feet
D) 278 feet
E) 50 feet
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
63
Use the given acceleration function and initial conditions to find the position at time t = 4.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
64
Find the curvature K of the curve at the point . Round your answer to three decimal places.
A) 0.728
B) 0.970
C) 0.158
D) 0.057
E) 0.126
at the point . Round your answer to three decimal places.A) 0.728
B) 0.970
C) 0.158
D) 0.057
E) 0.126
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
65
The quarterback of a football team releases a pass at a height of 6 feet above the playing field, and the football is caught by a receiver 62 yards directly downfield at a height of 3 feet. The pass is released at an angle of with the horizontal. Find the maximum height of the football. Round your answer to one decimal place.
A) 337.1 feet
B) 16.3 feet
C) 245.4 feet
D) 85.8 feet
E) 17.5 feet
with the horizontal. Find the maximum height of the football. Round your answer to one decimal place. A) 337.1 feet
B) 16.3 feet
C) 245.4 feet
D) 85.8 feet
E) 17.5 feet
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
66
Find given the following vector function.
A)
B)
C)
D)
E)
given the following vector function. A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
67
Find a vector-valued function, using the given parameter, to represent the intersection of the surfaces given below. Surfaces
Parameter
A)
B)
C)
D)
E)
Parameter
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
68
Find given the following vector function.
A)
B)
C)
D)
E)
given the following vector function. A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
69
Because of a storm, ground controllers instruct the pilot of a plane flying at an altitude of 3.2 miles to make a turn and climb to an altitude of 3.4 miles. The model for the path of the plane during this maneuver is where t is the time in hours and r is the distance in miles. Determine the speed of the plane. Round your answer to the nearest integer.
A) 201 mi/h
B) 64 mi/h
C) 173 mi/h
D) 137 mi/h
E) 255 mi/h
turn and climb to an altitude of 3.4 miles. The model for the path of the plane during this maneuver is where t is the time in hours and r is the distance in miles. Determine the speed of the plane. Round your answer to the nearest integer.A) 201 mi/h
B) 64 mi/h
C) 173 mi/h
D) 137 mi/h
E) 255 mi/h
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
70
Find the unit tangent vector to the curve given below at the specified point.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
71
Find the arc length for over the interval . Round your answer to two decimal places.
A) 110.36
B) 140.93
C) 129.56
D) 57.80
E) 102.75
over the interval . Round your answer to two decimal places. A) 110.36
B) 140.93
C) 129.56
D) 57.80
E) 102.75
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
72
The position vector describes the path of an object moving in space. Find the acceleration of the object.
A)
B)
C)
D)
E)
describes the path of an object moving in space. Find the acceleration of the object.A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
73
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)
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
74
Find a vector-valued function, using the given parameter, to represent the intersection of the surfaces given below. Surfaces
Parameter
A)
B)
C)
D)
E)
Parameter
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
75
A baseball is hit 3 feet above the ground at 95 feet per second and at an angle of with respect to the ground. Find the range. Round your answer to one decimal place.
A) 285 feet
B) 352.2 feet
C) 370.7 feet
D) 501.9 feet
E) 300 feet
with respect to the ground. Find the range. Round your answer to one decimal place.A) 285 feet
B) 352.2 feet
C) 370.7 feet
D) 501.9 feet
E) 300 feet
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
76
Find the radius of curvature of the plane curve at . Round your answer to three decimal places.
A) 1021.045
B) 2340.571
C) 1374.626
D) 1565.001
E) 1571.001
at . Round your answer to three decimal places.A) 1021.045
B) 2340.571
C) 1374.626
D) 1565.001
E) 1571.001
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
77
The position vector describes the path of an object moving in space. Find the speed of the object.
A)
B) 122
C)
D)
E) 18
describes the path of an object moving in space. Find the speed of the object. A)
B)
122C)
D)
E)
18 Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
78
A baseball player at second base throws a ball 95 feet to the player at first base. The ball is thrown 8 feet above the ground with an initial velocity of 46 miles per hour and at an angle of above the horizontal. At which height does the player at first base catch the ball? Round your answer to three decimal places.
A) 2.908 feet
B) 2.008 feet
C) 0.808 feet
D) 1.408 feet
E) 0.908 feet
above the horizontal. At which height does the player at first base catch the ball? Round your answer to three decimal places.A) 2.908 feet
B) 2.008 feet
C) 0.808 feet
D) 1.408 feet
E) 0.908 feet
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
79
Evaluate the definite integral below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
80
Find given the following vector function.
A)
B)
C)
D)
E)
given the following vector function. A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
Unlock Deck
k this deck
Unlock Deck
Unlock for access to all 85 flashcards in this deck.
