CALCULUS: EARLY TRANS 4TH ED W/ ACCESS
4th Edition
ISBN: 9781319309671
Author: Rogawski
Publisher: MAC HIGHER
expand_more
expand_more
format_list_bulleted
Question
Chapter 15.4, Problem 34E
To determine
Express the triple integral in cylindrical coordinates
Expert Solution & Answer
![Check Mark](/static/check-mark.png)
Want to see the full answer?
Check out a sample textbook solution![Blurred answer](/static/blurred-answer.jpg)
Students have asked these similar questions
Brazilian soccer star Marta has a penalty kick in the quarter-final match. She kicks the soccer ball from ground level with
the (x, y)-coordinates (76, 21) on the soccer field shown in the figure and with initial velocity vo = 8i - 4j+23k ft/s.
Assume an acceleration of 32 ft/s² due to gravity and that the goal net has a height of 8 ft and a total width of 24 ft.
105 ft
105 ft
ri =
rj =
165 ft
rk =
e
165 ft
Determine the position function that gives the position of the ball t seconds after it is hit.
(Use symbolic notation and fractions where needed.)
r(t) = r(t)i + r(t)j +rk(t)k
12
12
X
Brazilian soccer star Marta has a penalty kick in the quarter-final match. She kicks the soccer ball from ground level with
the (x, y)-coordinates (76, 21) on the soccer field shown in the figure and with initial velocity vo = 8i - 4j+23k ft/s.
Assume an acceleration of 32 ft/s² due to gravity and that the goal net has a height of 8 ft and a total width of 24 ft.
105 ft
1
105 ft
r₁ =
rj =
rk =
165 ft
Determine the position function that gives the position of the ball t seconds after it is hit.
(Use symbolic notation and fractions where needed.)
r(t) = ri(t)i + rj(t)j + rk(t)k
Incorrect
81+76
-41+21
↓
23r+1672²
165 ft
12
12
Parametrize y = -x2 + 4 in terms of u and v
%3D
Chapter 15 Solutions
CALCULUS: EARLY TRANS 4TH ED W/ ACCESS
Ch. 15.1 - Prob. 1PQCh. 15.1 - Prob. 2PQCh. 15.1 - Prob. 3PQCh. 15.1 - Prob. 4PQCh. 15.1 - Prob. 5PQCh. 15.1 - Prob. 6PQCh. 15.1 - Prob. 1ECh. 15.1 - Prob. 2ECh. 15.1 - Prob. 3ECh. 15.1 - Prob. 4E
Ch. 15.1 - Prob. 5ECh. 15.1 - Prob. 6ECh. 15.1 - Prob. 7ECh. 15.1 - Prob. 8ECh. 15.1 - Prob. 9ECh. 15.1 - Prob. 10ECh. 15.1 - Prob. 11ECh. 15.1 - Prob. 12ECh. 15.1 - Prob. 13ECh. 15.1 - Prob. 14ECh. 15.1 - Prob. 15ECh. 15.1 - Prob. 16ECh. 15.1 - Prob. 17ECh. 15.1 - Prob. 18ECh. 15.1 - Prob. 19ECh. 15.1 - Prob. 20ECh. 15.1 - Prob. 21ECh. 15.1 - Prob. 22ECh. 15.1 - Prob. 23ECh. 15.1 - Prob. 24ECh. 15.1 - Prob. 25ECh. 15.1 - Prob. 26ECh. 15.1 - Prob. 27ECh. 15.1 - Prob. 28ECh. 15.1 - Prob. 29ECh. 15.1 - Prob. 30ECh. 15.1 - Prob. 31ECh. 15.1 - Prob. 32ECh. 15.1 - Prob. 33ECh. 15.1 - Prob. 34ECh. 15.1 - Prob. 35ECh. 15.1 - Prob. 36ECh. 15.1 - Prob. 37ECh. 15.1 - Prob. 38ECh. 15.1 - Prob. 39ECh. 15.1 - Prob. 40ECh. 15.1 - Prob. 41ECh. 15.1 - Prob. 42ECh. 15.1 - Prob. 43ECh. 15.1 - Prob. 44ECh. 15.1 - Prob. 45ECh. 15.1 - Prob. 46ECh. 15.1 - Prob. 47ECh. 15.1 - Prob. 48ECh. 15.1 - Prob. 49ECh. 15.1 - Prob. 50ECh. 15.1 - Prob. 51ECh. 15.1 - Prob. 52ECh. 15.1 - Prob. 53ECh. 15.1 - Prob. 54ECh. 15.1 - Prob. 55ECh. 15.2 - Prob. 1PQCh. 15.2 - Prob. 2PQCh. 15.2 - Prob. 3PQCh. 15.2 - Prob. 4PQCh. 15.2 - Prob. 1ECh. 15.2 - Prob. 2ECh. 15.2 - Prob. 3ECh. 15.2 - Prob. 4ECh. 15.2 - Prob. 5ECh. 15.2 - Prob. 6ECh. 15.2 - Prob. 7ECh. 15.2 - Prob. 8ECh. 15.2 - Prob. 9ECh. 15.2 - Prob. 10ECh. 15.2 - Prob. 11ECh. 15.2 - Prob. 12ECh. 15.2 - Prob. 13ECh. 15.2 - Prob. 14ECh. 15.2 - Prob. 15ECh. 15.2 - Prob. 16ECh. 15.2 - Prob. 17ECh. 15.2 - Prob. 18ECh. 15.2 - Prob. 19ECh. 15.2 - Prob. 20ECh. 15.2 - Prob. 21ECh. 15.2 - Prob. 22ECh. 15.2 - Prob. 23ECh. 15.2 - Prob. 24ECh. 15.2 - Prob. 25ECh. 15.2 - Prob. 26ECh. 15.2 - Prob. 27ECh. 15.2 - Prob. 28ECh. 15.2 - Prob. 29ECh. 15.2 - Prob. 30ECh. 15.2 - Prob. 31ECh. 15.2 - Prob. 32ECh. 15.2 - Prob. 33ECh. 15.2 - Prob. 34ECh. 15.2 - Prob. 35ECh. 15.2 - Prob. 36ECh. 15.2 - Prob. 37ECh. 15.2 - Prob. 38ECh. 15.2 - Prob. 39ECh. 15.2 - Prob. 40ECh. 15.2 - Prob. 41ECh. 15.2 - Prob. 42ECh. 15.2 - Prob. 43ECh. 15.2 - Prob. 44ECh. 15.2 - Prob. 45ECh. 15.2 - Prob. 46ECh. 15.2 - Prob. 47ECh. 15.2 - Prob. 48ECh. 15.2 - Prob. 49ECh. 15.2 - Prob. 50ECh. 15.2 - Prob. 51ECh. 15.2 - Prob. 52ECh. 15.2 - Prob. 53ECh. 15.2 - Prob. 54ECh. 15.2 - Prob. 55ECh. 15.2 - Prob. 56ECh. 15.2 - Prob. 57ECh. 15.2 - Prob. 58ECh. 15.2 - Prob. 59ECh. 15.2 - Prob. 60ECh. 15.2 - Prob. 61ECh. 15.2 - Prob. 62ECh. 15.2 - Prob. 63ECh. 15.2 - Prob. 64ECh. 15.2 - Prob. 65ECh. 15.2 - Prob. 66ECh. 15.2 - Prob. 67ECh. 15.2 - Prob. 68ECh. 15.2 - Prob. 69ECh. 15.2 - Prob. 70ECh. 15.3 - Prob. 1PQCh. 15.3 - Prob. 2PQCh. 15.3 - Prob. 3PQCh. 15.3 - Prob. 1ECh. 15.3 - Prob. 2ECh. 15.3 - Prob. 3ECh. 15.3 - Prob. 4ECh. 15.3 - Prob. 5ECh. 15.3 - Prob. 6ECh. 15.3 - Prob. 7ECh. 15.3 - Prob. 8ECh. 15.3 - Prob. 9ECh. 15.3 - Prob. 10ECh. 15.3 - Prob. 11ECh. 15.3 - Prob. 12ECh. 15.3 - Prob. 13ECh. 15.3 - Prob. 14ECh. 15.3 - Prob. 15ECh. 15.3 - Prob. 16ECh. 15.3 - Prob. 17ECh. 15.3 - Prob. 18ECh. 15.3 - Prob. 19ECh. 15.3 - Prob. 20ECh. 15.3 - Prob. 21ECh. 15.3 - Prob. 22ECh. 15.3 - Prob. 23ECh. 15.3 - Prob. 24ECh. 15.3 - Prob. 25ECh. 15.3 - Prob. 26ECh. 15.3 - Prob. 27ECh. 15.3 - Prob. 28ECh. 15.3 - Prob. 29ECh. 15.3 - Prob. 30ECh. 15.3 - Prob. 31ECh. 15.3 - Prob. 32ECh. 15.3 - Prob. 33ECh. 15.3 - Prob. 34ECh. 15.3 - Prob. 35ECh. 15.3 - Prob. 36ECh. 15.3 - Prob. 37ECh. 15.3 - Prob. 38ECh. 15.3 - Prob. 39ECh. 15.3 - Prob. 40ECh. 15.3 - Prob. 41ECh. 15.3 - Prob. 42ECh. 15.3 - Prob. 43ECh. 15.3 - Prob. 44ECh. 15.3 - Prob. 45ECh. 15.3 - Prob. 46ECh. 15.4 - Prob. 1PQCh. 15.4 - Prob. 2PQCh. 15.4 - Prob. 3PQCh. 15.4 - Prob. 4PQCh. 15.4 - Prob. 5PQCh. 15.4 - Prob. 1ECh. 15.4 - Prob. 2ECh. 15.4 - Prob. 3ECh. 15.4 - Prob. 4ECh. 15.4 - Prob. 5ECh. 15.4 - Prob. 6ECh. 15.4 - Prob. 7ECh. 15.4 - Prob. 8ECh. 15.4 - Prob. 9ECh. 15.4 - Prob. 10ECh. 15.4 - Prob. 11ECh. 15.4 - Prob. 12ECh. 15.4 - Prob. 13ECh. 15.4 - Prob. 14ECh. 15.4 - Prob. 15ECh. 15.4 - Prob. 16ECh. 15.4 - Prob. 17ECh. 15.4 - Prob. 18ECh. 15.4 - Prob. 19ECh. 15.4 - Prob. 20ECh. 15.4 - Prob. 21ECh. 15.4 - Prob. 22ECh. 15.4 - Prob. 23ECh. 15.4 - Prob. 24ECh. 15.4 - Prob. 25ECh. 15.4 - Prob. 26ECh. 15.4 - Prob. 27ECh. 15.4 - Prob. 28ECh. 15.4 - Prob. 29ECh. 15.4 - Prob. 30ECh. 15.4 - Prob. 31ECh. 15.4 - Prob. 32ECh. 15.4 - Prob. 33ECh. 15.4 - Prob. 34ECh. 15.4 - Prob. 35ECh. 15.4 - Prob. 36ECh. 15.4 - Prob. 37ECh. 15.4 - Prob. 38ECh. 15.4 - Prob. 39ECh. 15.4 - Prob. 40ECh. 15.4 - Prob. 41ECh. 15.4 - Prob. 42ECh. 15.4 - Prob. 43ECh. 15.4 - Prob. 44ECh. 15.4 - Prob. 45ECh. 15.4 - Prob. 46ECh. 15.4 - Prob. 47ECh. 15.4 - Prob. 48ECh. 15.4 - Prob. 49ECh. 15.4 - Prob. 50ECh. 15.4 - Prob. 51ECh. 15.4 - Prob. 52ECh. 15.4 - Prob. 53ECh. 15.4 - Prob. 54ECh. 15.4 - Prob. 55ECh. 15.4 - Prob. 56ECh. 15.4 - Prob. 57ECh. 15.4 - Prob. 58ECh. 15.4 - Prob. 59ECh. 15.4 - Prob. 60ECh. 15.5 - Prob. 1PQCh. 15.5 - Prob. 2PQCh. 15.5 - Prob. 3PQCh. 15.5 - Prob. 1ECh. 15.5 - Prob. 2ECh. 15.5 - Prob. 3ECh. 15.5 - Prob. 4ECh. 15.5 - Prob. 5ECh. 15.5 - Prob. 6ECh. 15.5 - Prob. 7ECh. 15.5 - Prob. 8ECh. 15.5 - Prob. 9ECh. 15.5 - Prob. 10ECh. 15.5 - Prob. 11ECh. 15.5 - Prob. 12ECh. 15.5 - Prob. 13ECh. 15.5 - Prob. 14ECh. 15.5 - Prob. 15ECh. 15.5 - Prob. 16ECh. 15.5 - Prob. 17ECh. 15.5 - Prob. 18ECh. 15.5 - Prob. 19ECh. 15.5 - Prob. 20ECh. 15.5 - Prob. 21ECh. 15.5 - Prob. 22ECh. 15.5 - Prob. 23ECh. 15.5 - Prob. 24ECh. 15.5 - Prob. 25ECh. 15.5 - Prob. 26ECh. 15.5 - Prob. 27ECh. 15.5 - Prob. 28ECh. 15.5 - Prob. 29ECh. 15.5 - Prob. 30ECh. 15.5 - Prob. 31ECh. 15.5 - Prob. 32ECh. 15.5 - Prob. 33ECh. 15.5 - Prob. 34ECh. 15.5 - Prob. 35ECh. 15.5 - Prob. 36ECh. 15.5 - Prob. 37ECh. 15.5 - Prob. 38ECh. 15.5 - Prob. 39ECh. 15.5 - Prob. 40ECh. 15.5 - Prob. 41ECh. 15.5 - Prob. 42ECh. 15.5 - Prob. 43ECh. 15.5 - Prob. 44ECh. 15.5 - Prob. 45ECh. 15.5 - Prob. 46ECh. 15.5 - Prob. 47ECh. 15.5 - Prob. 48ECh. 15.5 - Prob. 49ECh. 15.5 - Prob. 50ECh. 15.5 - Prob. 51ECh. 15.5 - Prob. 52ECh. 15.5 - Prob. 53ECh. 15.5 - Prob. 54ECh. 15.5 - Prob. 55ECh. 15.5 - Prob. 56ECh. 15.5 - Prob. 57ECh. 15.5 - Prob. 58ECh. 15.5 - Prob. 59ECh. 15.5 - Prob. 60ECh. 15.5 - Prob. 61ECh. 15.5 - Prob. 62ECh. 15.5 - Prob. 63ECh. 15.5 - Prob. 64ECh. 15.5 - Prob. 65ECh. 15.5 - Prob. 66ECh. 15.6 - Prob. 1PQCh. 15.6 - Prob. 2PQCh. 15.6 - Prob. 3PQCh. 15.6 - Prob. 4PQCh. 15.6 - Prob. 1ECh. 15.6 - Prob. 2ECh. 15.6 - Prob. 3ECh. 15.6 - Prob. 4ECh. 15.6 - Prob. 5ECh. 15.6 - Prob. 6ECh. 15.6 - Prob. 7ECh. 15.6 - Prob. 8ECh. 15.6 - Prob. 9ECh. 15.6 - Prob. 10ECh. 15.6 - Prob. 11ECh. 15.6 - Prob. 12ECh. 15.6 - Prob. 13ECh. 15.6 - Prob. 14ECh. 15.6 - Prob. 15ECh. 15.6 - Prob. 16ECh. 15.6 - Prob. 17ECh. 15.6 - Prob. 18ECh. 15.6 - Prob. 19ECh. 15.6 - Prob. 20ECh. 15.6 - Prob. 21ECh. 15.6 - Prob. 22ECh. 15.6 - Prob. 23ECh. 15.6 - Prob. 24ECh. 15.6 - Prob. 25ECh. 15.6 - Prob. 26ECh. 15.6 - Prob. 27ECh. 15.6 - Prob. 28ECh. 15.6 - Prob. 29ECh. 15.6 - Prob. 30ECh. 15.6 - Prob. 31ECh. 15.6 - Prob. 32ECh. 15.6 - Prob. 33ECh. 15.6 - Prob. 34ECh. 15.6 - Prob. 35ECh. 15.6 - Prob. 36ECh. 15.6 - Prob. 37ECh. 15.6 - Prob. 38ECh. 15.6 - Prob. 39ECh. 15.6 - Prob. 40ECh. 15.6 - Prob. 41ECh. 15.6 - Prob. 42ECh. 15.6 - Prob. 43ECh. 15.6 - Prob. 44ECh. 15.6 - Prob. 45ECh. 15.6 - Prob. 46ECh. 15.6 - Prob. 47ECh. 15.6 - Prob. 48ECh. 15.6 - Prob. 49ECh. 15.6 - Prob. 50ECh. 15.6 - Prob. 51ECh. 15.6 - Prob. 52ECh. 15 - Prob. 1CRECh. 15 - Prob. 2CRECh. 15 - Prob. 3CRECh. 15 - Prob. 4CRECh. 15 - Prob. 5CRECh. 15 - Prob. 6CRECh. 15 - Prob. 7CRECh. 15 - Prob. 8CRECh. 15 - Prob. 9CRECh. 15 - Prob. 10CRECh. 15 - Prob. 11CRECh. 15 - Prob. 12CRECh. 15 - Prob. 13CRECh. 15 - Prob. 14CRECh. 15 - Prob. 15CRECh. 15 - Prob. 16CRECh. 15 - Prob. 17CRECh. 15 - Prob. 18CRECh. 15 - Prob. 19CRECh. 15 - Prob. 20CRECh. 15 - Prob. 21CRECh. 15 - Prob. 22CRECh. 15 - Prob. 23CRECh. 15 - Prob. 24CRECh. 15 - Prob. 25CRECh. 15 - Prob. 26CRECh. 15 - Prob. 27CRECh. 15 - Prob. 28CRECh. 15 - Prob. 29CRECh. 15 - Prob. 30CRECh. 15 - Prob. 31CRECh. 15 - Prob. 32CRECh. 15 - Prob. 33CRECh. 15 - Prob. 34CRECh. 15 - Prob. 35CRECh. 15 - Prob. 36CRECh. 15 - Prob. 37CRECh. 15 - Prob. 38CRECh. 15 - Prob. 39CRECh. 15 - Prob. 40CRECh. 15 - Prob. 41CRECh. 15 - Prob. 42CRECh. 15 - Prob. 43CRECh. 15 - Prob. 44CRECh. 15 - Prob. 45CRECh. 15 - Prob. 46CRECh. 15 - Prob. 47CRECh. 15 - Prob. 48CRECh. 15 - Prob. 49CRECh. 15 - Prob. 50CRECh. 15 - Prob. 51CRECh. 15 - Prob. 52CRECh. 15 - Prob. 53CRECh. 15 - Prob. 54CRECh. 15 - Prob. 55CRECh. 15 - Prob. 56CRECh. 15 - Prob. 57CRECh. 15 - Prob. 58CRECh. 15 - Prob. 59CRECh. 15 - Prob. 60CRECh. 15 - Prob. 61CRE
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Similar questions
- Sketch the curve whose vector equation is Solution r(t) = 6 cos(t) i + 6 sin(t) j + 3tk. The parametric equations for this curve are X = I y = 6 sin(t), z = Since x² + y² = + 36. sin²(t) = The point (x, y, z) lies directly above the point (x, y, 0), which moves counterclockwise around the circle x² + y2 = in the xy-plane. (The projection of the curve onto the xy-plane has vector equation r(t) = (6 cos(t), 6 sin(t), 0). See this example.) Since z = 3t, the curve spirals upward around the cylinder as t increases. The curve, shown in the figure below, is called a helix. ZA (6, 0, 0) (0, 6, 37) I the curve must lie on the circular cylinder x² + y² =arrow_forwardLet C be the curve defined by the following system of equations: √x+6y²-2²=0 3y = zarrow_forwardWhere does the parametric line ( 2 + 2 t , t , t ) intersect the plane x+y-3z=4?arrow_forward
- Describe the given set of rectangular coordinates in cylindrical coordinat x2 + y? yarrow_forwardAn airplane took off from point (3, 0, 0) at an initial velocity, v(0)= 3j with an acceleration vector of a(t) = (-3 cos t)i + (-3 sin t)j + 2k. Determine the vector function, r(t), to represent the path of the airplane as a function of t.arrow_forwardWrite x²-y²-(z-1)²=9 in cylindrical system and what surface does it representarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning
![Text book image](https://www.bartleby.com/isbn_cover_images/9781285741550/9781285741550_smallCoverImage.gif)
Calculus: Early Transcendentals
Calculus
ISBN:9781285741550
Author:James Stewart
Publisher:Cengage Learning
![Text book image](https://www.bartleby.com/isbn_cover_images/9780134438986/9780134438986_smallCoverImage.gif)
Thomas' Calculus (14th Edition)
Calculus
ISBN:9780134438986
Author:Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:PEARSON
![Text book image](https://www.bartleby.com/isbn_cover_images/9780134763644/9780134763644_smallCoverImage.gif)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:9780134763644
Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:PEARSON
![Text book image](https://www.bartleby.com/isbn_cover_images/9781319050740/9781319050740_smallCoverImage.gif)
Calculus: Early Transcendentals
Calculus
ISBN:9781319050740
Author:Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:W. H. Freeman
![Text book image](https://www.bartleby.com/isbn_cover_images/9780135189405/9780135189405_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781337552516/9781337552516_smallCoverImage.gif)
Calculus: Early Transcendental Functions
Calculus
ISBN:9781337552516
Author:Ron Larson, Bruce H. Edwards
Publisher:Cengage Learning
Introduction to Triple Integrals; Author: Mathispower4u;https://www.youtube.com/watch?v=CPR0ZD0IYVE;License: Standard YouTube License, CC-BY