Question 1

Find the speed of a particle in a circular orbit with radius 1021m around an object of mass 1018kg. (G = 6.67 *10-11m/kg·s2)

Accepted Answer

A)  1.50 * 1013m/s 
B)  6.67*10-14m/s 
C)  3.87 * 106m/s 
D)  2.58 * 10-7m/s 
E)  4.91 *10-7m/s 
A)  1.50 * 1013m/s 
B)  6.67*10-14m/s 
C)  3.87 * 106m/s 
D)  2.58 * 10-7m/s 
E)  4.91 *10-7m/s

Question 2

Is   a smooth function of the parameter of t?

Accepted Answer

The answer of Is   a smooth function of...

Question 3

A particle moves through 3-space in such a way that its velocity is   . Find the coordinates of the particle at t = 1 second if the particle was initially at   at t = 0 seconds.

Accepted Answer

The answer of A particle moves through 3-space in such...

Question 4

Find the domain of   and calculate   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    2i 
A)    
B)    
C)    
D)    
E)    2i

Question 5

If   find

Accepted Answer

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

Question 6

Find the curvature for x = 2e t , y = 11 + 2e-t at t = 0.

Accepted Answer

Question 7

Find the domain of

Accepted Answer

The answer of Find the domain of  ...

Question 8

Let   . Find the equation of the line tangent to the graph of   at the point   .Write your answer using parametric equations.

Accepted Answer

The answer of Let   . Find the equation...

Question 9

If   , find

Accepted Answer

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

Question 10

Find the curvature   for r(t) = (16 + sin t) i + (16 + cos t) j.

Accepted Answer

A)  1 
B)  -1 
C)  0 
D)  sin2t - cos2t 
E)  - sin2t + cos2t 
A)  1 
B)  -1 
C)  0 
D)  sin2t - cos2t 
E)  - sin2t + cos2t

Question 11

Write down parametric equations representing the intersection curve of the following surfaces. Use parameter x = t.   .

Accepted Answer

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

Question 12

If, for an elliptical orbit, rmin = 1025km and e = 0.55, find a, the semimajor axis.

Accepted Answer

A)  2.44*1025km 
B)  2.22 * 1025km 
C)  2.44 * 1024km 
D)  2.22 * 1024km 
E)  1.72 *1025km 
A)  2.44*1025km 
B)  2.22 * 1025km 
C)  2.44 * 1024km 
D)  2.22 * 1024km 
E)  1.72 *1025km

Question 13

Find the velocity, speed, and acceleration of a particle whose position is given by r(t) = e t i + e2t j at t = 0 seconds, then sketch the path of the particle together with the velocity and acceleration vectors at t = 0 seconds.

Accepted Answer

@#IMG-DLM& , @#IMG-DLM& , a(0)

Question 14

Express   as a parametric equation.

Accepted Answer

The answer of Express   as a parametric equation....

Question 15

If   find

Accepted Answer

The answer of If   find  ...

Question 16

An object in an elliptical orbit has   and   Find rmin.

Accepted Answer

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

Question 17

Find the arc length of the graph of

Accepted Answer

A)  3 
B)  1.959 
C)  1.781 
D)  1.603 
E)  1.581 
A)  3 
B)  1.959 
C)  1.781 
D)  1.603 
E)  1.581

Question 18

Find the curvature for x = -11 + t3, y = 2t2  at t = 1.

Accepted Answer

Question 19

If   find

Accepted Answer

The answer of If   find  ...

Question 20

Describe the graph of   .

Accepted Answer

A)  Twisted cubic 
B)  Straight line 
C)  Spiral 
D)  Parabola 
E)  Circle 
A)  Twisted cubic 
B)  Straight line 
C)  Spiral 
D)  Parabola 
E)  Circle

Find the speed of a particle in a circular orbit with radius 10²¹m around an object of mass 10¹⁸kg. (G = 6.67 *10^-11m/kg·s²)

Is a smooth function of the parameter of t?

A particle moves through 3-space in such a way that its velocity is . Find the coordinates of the particle at t = 1 second if the particle was initially at at t = 0 seconds.

Find the domain of and calculate .

If find

Find the curvature for x = 2e ^t , y = 11 + 2e^-t at t = 0.

Find the domain of

Let . Find the equation of the line tangent to the graph of at the point .Write your answer using parametric equations.

If , find

Find the curvature for r(t) = (16 + sin t) i + (16 + cos t) j.

Write down parametric equations representing the intersection curve of the following surfaces. Use parameter x = t. .

If, for an elliptical orbit, r_min = 10²⁵km and e = 0.55, find a, the semimajor axis.

Find the velocity, speed, and acceleration of a particle whose position is given by r(t) = e ^t i + e²^t j at t = 0 seconds, then sketch the path of the particle together with the velocity and acceleration vectors at t = 0 seconds.

Express as a parametric equation.

If find

An object in an elliptical orbit has and Find r_min.

Find the arc length of the graph of

Find the curvature for x = -11 + t³, y = 2t² at t = 1.

If find

Describe the graph of .

Limits and Continuity

The Derivative

Topics in Deifferentiation

The Derivative in Graphing and Applications

Integration

Applications of the Definite Integral in Geometry, Science and Engineering

Principle of Integral Evaluation

Mathematical Modeling With Differential Equations

Infinte Series

Parametric and Polar Curves; Conic Sections

Three-Dimensional Space; Vectors

Partial Derivatives

Multiple Integrals

Topics in Vector Calculus

Filters

Exam 12: Vector-Valued Functions

Find the speed of a particle in a circular orbit with radius 1021m around an object of mass 1018kg. (G = 6.67 *10-11m/kg·s2)

Is a smooth function of the parameter of t?

A particle moves through 3-space in such a way that its velocity is . Find the coordinates of the particle at t = 1 second if the particle was initially at at t = 0 seconds.

Find the domain of and calculate .

If find

Find the curvature for x = 2e t , y = 11 + 2e-t at t = 0.

Find the domain of

Let . Find the equation of the line tangent to the graph of at the point .Write your answer using parametric equations.

If , find

Find the curvature for r(t) = (16 + sin t) i + (16 + cos t) j.

Write down parametric equations representing the intersection curve of the following surfaces. Use parameter x = t. .

If, for an elliptical orbit, rmin = 1025km and e = 0.55, find a, the semimajor axis.

Find the velocity, speed, and acceleration of a particle whose position is given by r(t) = e t i + e2t j at t = 0 seconds, then sketch the path of the particle together with the velocity and acceleration vectors at t = 0 seconds.

Express as a parametric equation.

If find

An object in an elliptical orbit has and Find rmin.

Find the arc length of the graph of

Find the curvature for x = -11 + t3, y = 2t2 at t = 1.

If find

Describe the graph of .

Limits and Continuity

The Derivative

Topics in Deifferentiation

The Derivative in Graphing and Applications

Integration

Applications of the Definite Integral in Geometry, Science and Engineering

Principle of Integral Evaluation

Mathematical Modeling With Differential Equations

Infinte Series

Parametric and Polar Curves; Conic Sections

Three-Dimensional Space; Vectors

Partial Derivatives

Multiple Integrals

Topics in Vector Calculus

Filters

Find the speed of a particle in a circular orbit with radius 10²¹m around an object of mass 10¹⁸kg. (G = 6.67 *10^-11m/kg·s²)

Find the curvature for x = 2e ^t , y = 11 + 2e^-t at t = 0.

If, for an elliptical orbit, r_min = 10²⁵km and e = 0.55, find a, the semimajor axis.

Find the velocity, speed, and acceleration of a particle whose position is given by r(t) = e ^t i + e²^t j at t = 0 seconds, then sketch the path of the particle together with the velocity and acceleration vectors at t = 0 seconds.

An object in an elliptical orbit has and Find r_min.

Find the curvature for x = -11 + t³, y = 2t² at t = 1.