Question 1

Find   given the following vector function: ​   ​

Accepted Answer

A)    
B) 0 
C)    
D)    
E)    
A)    
B) 0 
C)    
D)    
E)    D

Question 2

The position vector   describes the path of an object moving in space.Find the speed s(t)of the object. ​

Accepted Answer

A) 21 
B)    
C)    
D) 149 
E)    
A) 21 
B)    
C)    
D) 149 
E)    E

Question 3

Suppose a gun with a muzzle velocity of 1200 feet per second is fired at an angle of 4° above the horizontal.Find the horizontal component of the velocity.Round your answer to two decimal places. ​

Accepted Answer

A) 1,240.08 ft/sec 
B) 2,395.15 ft/sec 
C) 1,197.08 ft/sec 
D) 2,393.15 ft/sec 
E) 1,209.08 ft/sec 
A) 1,240.08 ft/sec 
B) 2,395.15 ft/sec 
C) 1,197.08 ft/sec 
D) 2,393.15 ft/sec 
E) 1,209.08 ft/sec C

Question 4

The vector v and its initial point is given.Find the terminal point. ​   ,initial point   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 5

The position vector   describes the path of an object moving in space.Find the velocity v(t)of the object. ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 6

The parametric equations for the path of a projectile launched at a height h feet above the ground,at an angle θ with the horizontal and having an initial velocity of v0 feet per second is given by   and   .The center field fence in a ballpark is 10 feet high and 400 feet from home plate.The ball is hit   feet above the ground.It leaves the bat at an angle of θ degrees with the horizontal at a speed of 100 miles per hour as shown in the figure.Find the minimum angle at which the ball must leave the bat in order for the hit to be a home run using the parametric equations   and   .Round your answer to one decimal place. ​   ​

Accepted Answer

A) 25.5° 
B) 19.5° 
C) 3.4° 
D) 4.5° 
E) 11.3° 
A) 25.5° 
B) 19.5° 
C) 3.4° 
D) 4.5° 
E) 11.3°

Question 7

​A particle moves in the xy-plane so that its velocity for time   is given by the parametric equations   and ​   .​ An expression for the distance traveled by the particle on the interval   is ​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
A) ​   
B) ​   
C) ​   
D) ​

Question 8

Find vectors u and v whose initial and terminal points are given.Determine whether u and v are equivalent. ​
U: (6,5), (9,11)v: (3,-5), (6,1)
​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 9

​A particle moves in the xy-plane for   so that   and   .At time   ,the particle is moving ​

Accepted Answer

A) ​to the right and up 
B) ​to the left and up 
C) ​to the left and down 
D) ​​to the right and down 
A) ​to the right and up 
B) ​to the left and up 
C) ​to the left and down 
D) ​​to the right and down

Question 10

Find a vector-valued function,using the given parameter,to represent the intersection of the surfaces given below. Surfaces
Parameter     ​

Accepted Answer

A)    ​ 
B)    ​ 
C)    ​ 
D)    ​ 
E)    ​ 
A)    ​ 
B)    ​ 
C)    ​ 
D)    ​ 
E)    ​

Question 11

Find the area of the surface generated by revolving the curve   ,   about the x-axis on the interval   . ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 12

Find the directrix of the parabola given by   . ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 13

Suppose a plane flies at a constant groundspeed of 600 miles per hour due east and encounters a 10 mile-per-hour wind from the northwest.Both the airspeed and the compass direction must change to for the plane to maintain its groundspeed and eastward direction.Find the airspeed to maintain its groundspeed and eastward direction.Round your answer to two decimal places. ​

Accepted Answer

A) 177.63° 
B) 131.32° 
C) 106.32° 
D) 89.32° 
E) 179.63° 
A) 177.63° 
B) 131.32° 
C) 106.32° 
D) 89.32° 
E) 179.63°

Question 14

Find a set of parametric equations for the rectangular equation   that satisfies the condition   at the point   . ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 15

Find all points of intersection of the graphs of the equations. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 16

Evaluate the definite integral below. ​
​   ​
​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 17

Find   and   if possible,and find the slope and concavity (if possible)at the point corresponding to   . ​   ​

Accepted Answer

A) ​   ,
  ;at
  : slope
  and concave down 
B)    ,   ;at
  : slope
  and concave down 
C) ​   ,
  ;at
  : slope
  and concave up 
D)    ,   ;at
  : slope
  and concave up 
E)    ,   ;at
  : slope of
  and concave down 
A) ​   ,
  ;at
  : slope
  and concave down 
B)    ,   ;at
  : slope
  and concave down 
C) ​   ,
  ;at
  : slope
  and concave up 
D)    ,   ;at
  : slope
  and concave up 
E)    ,   ;at
  : slope of
  and concave down

Question 18

To carry a 500-pound cylindrical weight,two workers lift on the ends of short ropes tied to an eyelet on the top center of the cylinder.One rope makes a 20° angle away from the vertical and the other makes a 30° angle as shown in the figure below.Find the vertical component of each worker's force.Round your answer to two decimal places. ​
​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 19

Find the area of the interior of   . ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 20

The quarterback of a football team releases a pass at a height of 8 feet above the playing field,and the football is caught by a receiver 38 yards directly downfield at a height of 4 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. ​

Accepted Answer

A) 33.169 feet per second 
B) 59.366 feet per second 
C) 19.462 feet per second 
D) 118.732 feet per second 
E) 190.165 feet per second 
A) 33.169 feet per second 
B) 59.366 feet per second 
C) 19.462 feet per second 
D) 118.732 feet per second 
E) 190.165 feet per second

Find given the following vector function:

The position vector describes the path of an object moving in space.Find the speed s(t)of the object.

Suppose a gun with a muzzle velocity of 1200 feet per second is fired at an angle of 4° above the horizontal.Find the horizontal component of the velocity.Round your answer to two decimal places.

The vector v and its initial point is given.Find the terminal point. ,initial point

The position vector describes the path of an object moving in space.Find the velocity v(t)of the object.

A particle moves in the xy-plane so that its velocity for time is given by the parametric equations and . An expression for the distance traveled by the particle on the interval is

Find vectors u and v whose initial and terminal points are given.Determine whether u and v are equivalent. U: (6,5), (9,11)v: (3,-5), (6,1)

A particle moves in the xy-plane for so that and .At time ,the particle is moving

Find a vector-valued function,using the given parameter,to represent the intersection of the surfaces given below. Surfaces Parameter

Find the area of the surface generated by revolving the curve , about the x-axis on the interval .

Find the directrix of the parabola given by .

Find a set of parametric equations for the rectangular equation that satisfies the condition at the point .

Find all points of intersection of the graphs of the equations.

Evaluate the definite integral below.

Find and if possible,and find the slope and concavity (if possible)at the point corresponding to .

Find the area of the interior of .

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques, L'Hôpital's Rule, and Improper Integrals

Infinite Series

Mechanical Ventilation and Sedation: Assessment, Medications, and Complications

Filters

Exam 10: Parametric Equations, Polar Coordinates, and Vectors

Find given the following vector function: ​ ​

The position vector describes the path of an object moving in space.Find the speed s(t)of the object. ​

Suppose a gun with a muzzle velocity of 1200 feet per second is fired at an angle of 4° above the horizontal.Find the horizontal component of the velocity.Round your answer to two decimal places. ​

The vector v and its initial point is given.Find the terminal point. ​ ,initial point ​

The position vector describes the path of an object moving in space.Find the velocity v(t)of the object. ​

​A particle moves in the xy-plane so that its velocity for time is given by the parametric equations and ​ .​ An expression for the distance traveled by the particle on the interval is ​

Find vectors u and v whose initial and terminal points are given.Determine whether u and v are equivalent. ​ U: (6,5), (9,11)v: (3,-5), (6,1) ​

​A particle moves in the xy-plane for so that and .At time ,the particle is moving ​

Find a vector-valued function,using the given parameter,to represent the intersection of the surfaces given below. Surfaces Parameter ​

Find the area of the surface generated by revolving the curve , about the x-axis on the interval . ​

Find the directrix of the parabola given by . ​

Find a set of parametric equations for the rectangular equation that satisfies the condition at the point . ​

Find all points of intersection of the graphs of the equations. ​ ​

Evaluate the definite integral below. ​ ​ ​ ​

Find and if possible,and find the slope and concavity (if possible)at the point corresponding to . ​ ​

Find the area of the interior of . ​

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques, L'Hôpital's Rule, and Improper Integrals

Infinite Series

Mechanical Ventilation and Sedation: Assessment, Medications, and Complications

Filters

Find given the following vector function:

The position vector describes the path of an object moving in space.Find the speed s(t)of the object.

Suppose a gun with a muzzle velocity of 1200 feet per second is fired at an angle of 4° above the horizontal.Find the horizontal component of the velocity.Round your answer to two decimal places.

The vector v and its initial point is given.Find the terminal point. ,initial point

The position vector describes the path of an object moving in space.Find the velocity v(t)of the object.

A particle moves in the xy-plane so that its velocity for time is given by the parametric equations and . An expression for the distance traveled by the particle on the interval is

Find vectors u and v whose initial and terminal points are given.Determine whether u and v are equivalent. U: (6,5), (9,11)v: (3,-5), (6,1)

A particle moves in the xy-plane for so that and .At time ,the particle is moving

Find a vector-valued function,using the given parameter,to represent the intersection of the surfaces given below. Surfaces Parameter

Find the area of the surface generated by revolving the curve , about the x-axis on the interval .

Find the directrix of the parabola given by .

Find a set of parametric equations for the rectangular equation that satisfies the condition at the point .

Find all points of intersection of the graphs of the equations.

Evaluate the definite integral below.

Find and if possible,and find the slope and concavity (if possible)at the point corresponding to .

Find the area of the interior of .