(a) Plot the point with cylindrical coordinates (2, 27/3, 1) and find its rectangular coordinates. (h) Find oulindriool oordinetes of the noint with reotengu nordinotog (3 7)
(a) Plot the point with cylindrical coordinates (2, 27/3, 1) and find its rectangular coordinates. (h) Find oulindriool oordinetes of the noint with reotengu nordinotog (3 7)
Trigonometry (MindTap Course List)
8th Edition
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
Publisher:Charles P. McKeague, Mark D. Turner
Chapter8: Complex Numbers And Polarcoordinates
Section: Chapter Questions
Problem 8CLT
Related questions
Question
100%
Answer number 1 only
![1. (a) Plot the point with cylindrical coordinates (2, 27/3, 1) and find its rectangular
coordinates.
(b) Find cylindrical coordinates of the point with rectangular coordinates (3, – 3, –7).
2. The point (0, 2 /3, –2) is given in rectangular coordinates. Find spheri cal coordinates for this point.
3. The point (2, T/4, 7/3) is given in spherical coordinates. Plot the point and find its rectangular coordinates.
V4-x²
4. Evaluate ", L(r² + y®) dz dy dx.
-2
4-x2
Hint:
This iterated integral is a triple integral over the solid region
z=Vx²+y?
E =
{(x, y, z) | –2 < x< 2, -/4 – x² < y< /4 – x², Vx² + y² < z < 2}
and the projection of E onto the xy-plane is the disk x² + y² < 4. The lower surface of
E is the cone z =
2
Vx² + y² and its upper surface is the plane z = 2. (See Figure 9.)
This region has a much simpler description in cylindrical coordinates:
FIGURE 9](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff23ce2a2-dc70-4088-a7c9-ea60f00346e6%2F218adae0-4fb3-4991-a12d-1c79b3181d31%2Fw3rx1l7_processed.png&w=3840&q=75)
Transcribed Image Text:1. (a) Plot the point with cylindrical coordinates (2, 27/3, 1) and find its rectangular
coordinates.
(b) Find cylindrical coordinates of the point with rectangular coordinates (3, – 3, –7).
2. The point (0, 2 /3, –2) is given in rectangular coordinates. Find spheri cal coordinates for this point.
3. The point (2, T/4, 7/3) is given in spherical coordinates. Plot the point and find its rectangular coordinates.
V4-x²
4. Evaluate ", L(r² + y®) dz dy dx.
-2
4-x2
Hint:
This iterated integral is a triple integral over the solid region
z=Vx²+y?
E =
{(x, y, z) | –2 < x< 2, -/4 – x² < y< /4 – x², Vx² + y² < z < 2}
and the projection of E onto the xy-plane is the disk x² + y² < 4. The lower surface of
E is the cone z =
2
Vx² + y² and its upper surface is the plane z = 2. (See Figure 9.)
This region has a much simpler description in cylindrical coordinates:
FIGURE 9
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 3 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Trigonometry (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781305652224/9781305652224_smallCoverImage.gif)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
![Trigonometry (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781337278461/9781337278461_smallCoverImage.gif)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning
![Trigonometry (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781305652224/9781305652224_smallCoverImage.gif)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
![Trigonometry (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781337278461/9781337278461_smallCoverImage.gif)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning
![Algebra and Trigonometry (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781305071742/9781305071742_smallCoverImage.gif)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,