Sketch the described surfaces. Give a parametrization of each. (Be sure to include bounds of para...
Sketch the described surfaces. Give a parametrization of each. (Be sure to include bounds of parameters as necessary):
(a) A cone with its point at (1, 3, 4) and its base a circle of radius 6 on the plane z = 7, centered at (1, 3, 7)
(b) A cylinder of radius 3/2 centered at the y-axis, with a base
on the plane y = 0 and height going on to y = +
(c) The plane 2x+3y+z=10 restricted to the first octant
(d) The sphere of radius 5 centered at (1,1,1)
Homework Answers
Add Answer to:
Sketch the described surfaces. Give a parametrization of each. (Be sure to include bounds of para...
Parameterize the following surfaces in R3. Describe if the surface is open or closed. If the surf...
Parameterize the following surfaces in R3. Describe
if the surface is open or closed. If the surface is open, give a
parameterization of its boundary,
6. Parametrize the following surfaces in R3. Describe if the surface is open or closed. If the surface is open, give a parametrization of its boundary (positively oriented). (a) The part of the plane z - 2y 3 inside the cylinder 2 y16 (b) The sphere of radiuscentered at the origin. (c) The part of...
Find a parametrization for each of the following surfaces. [Note: There are many correct answers!] Show...
Find a parametrization for each of the following surfaces. [Note: There are many correct answers!] Show how you arrived at your answer. Hint: It is often helpful to construct your parametrization using (a) cylindrical coordinates, (b) spherical coordi- nates, or (c) by using a parametrization such as (:2, y, 2) = (u, v, f(u, v)) for the surface 2= f(, y). (a) The portion of the sphere x² + y2 + z2 = 9 that is above the cone z...
Q1. Sketch and find a parameterization of the following surfaces (a) (Spherical cap) The portion of the sphere by *+y+-16 cut by the vertical plane y 3, containing the point (0,4,0) (b) (Circular cyl...
Q1. Sketch and find a parameterization of the following surfaces (a) (Spherical cap) The portion of the sphere by *+y+-16 cut by the vertical plane y 3, containing the point (0,4,0) (b) (Circular cylinder band) The portion of the cylinder y+z+5)2 25 between the planes x--2 and x-2.
Q1. Sketch and find a parameterization of the following surfaces (a) (Spherical cap) The portion of the sphere by *+y+-16 cut by the vertical plane y 3, containing the point (0,4,0) (b)...
#48 #46 and #48 In Exercises 39-48, find a parametrization of the curve. 39. The vertical...
#48
#46
and #48
In Exercises 39-48, find a parametrization of the curve. 39. The vertical line passing through the point (3,2,0) 40. The line passing through (1,0,4) and (4.1.2) 41. The line through the origin whose projection on the xy-plane is a line of slope 3 and whose projection on the yz-plane is a line of slope 5 (ie, Az/Ay = 5) 42. The circle of radius 1 with center (2, -1, 4) in a plane parallel to the...
(i) The sides of a given grain silo are represented by the equation of the cylinder x2 +y-3. The top of the silo...
(i) The sides of a given grain silo are represented by the equation of the cylinder x2 +y-3. The top of the silo is the portion of the sphere x2 + y2 + z2-7 lying within the cylinder and above the zy plane. Sketch and find the volume of the silo using an appropriate coordinate system Q2. [10] (ii) Given that C is the boundary of the plane 2x +2y+z = 6 that lies in the first octant and F...
Find the slope of the curve below at the given points. Sketch the curve along with...
Find the slope of the curve below at the given points. Sketch the curve along with its tangent lines at these points. r= - 4+4 cos 0; O= The slope at the point o = 5 is (Simplify your answer.) The slope at the point 0 = (Simplify your answer.) is Identify the curve r= - 4 + 4 cos 0. OA. OB. OC. Give a geometric description of the set of points in space whose coordinates satisfy the given...
All of 10 questions, please. 1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the...
All of 10 questions, please.
1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz...
(1 point) Let F(x, y, z) = 5yj and S be the closed vertical cylinder of...
(1 point) Let F(x, y, z) = 5yj and S be the closed vertical cylinder of height 4, with its base a circle of radius 3 on the xy-plane centered at the origin. S is oriented outward. (a) Compute the flux of F through S using the divergence theorem. Flux = Flux = || F . dà = (b) Compute the flux directly. Flux out of the top = Į! Įdollar Flux out of the bottom = Flux out of...
Revised by Prof. Kostadinov, Fall 2015, Fall 2014, Fall 2013, Fall 2012, Fall 2011, Fall 2010 Revised by Prof. Africk and Prof. Kostadinov Fall 2015, Spring 2016, #1 Identify the horizontal a...
Revised by Prof. Kostadinov, Fall 2015, Fall 2014, Fall 2013, Fall 2012, Fall 2011, Fall 2010 Revised by Prof. Africk and Prof. Kostadinov Fall 2015, Spring 2016, #1 Identify the horizontal and vertical asymptotes of the following functions using the limit definitions: 2x2 o) yA- #2 Find the derivatives of the following functions using the definition of derivative: a) f(x)-2x-5x #3 Find the derivative v dr of the following functions, using the derivative rules: b) f(x)--2x +3x-4 #4 Find the...
Q4 only: Question 3. Consider the region of R3 given by V is bounded by three surfaces. Si is a disc of radius 1 in the plane z -0. S3 is a disc of radius 2 in the plane z 3 and a) Make a clear sketc...
Q4 only:
Question 3. Consider the region of R3 given by V is bounded by three surfaces. Si is a disc of radius 1 in the plane z -0. S3 is a disc of radius 2 in the plane z 3 and a) Make a clear sketch of V. (Hint: You could consider the cross-section of S2 with y-0, and then use the circular symmetry. (b) Express V in cylindrical coordinates. (c) Calculate the volume of V, working in cylindrical...
Parameterize the following surfaces in R3. Describe
if the surface is open or closed. If the surface is open, give a
parameterization of its boundary,
6. Parametrize the following surfaces in R3. Describe if the surface is open or closed. If the surface is open, give a parametrization of its boundary (positively oriented). (a) The part of the plane z - 2y 3 inside the cylinder 2 y16 (b) The sphere of radiuscentered at the origin. (c) The part of...
Find a parametrization for each of the following surfaces. [Note: There are many correct answers!] Show how you arrived at your answer. Hint: It is often helpful to construct your parametrization using (a) cylindrical coordinates, (b) spherical coordi- nates, or (c) by using a parametrization such as (:2, y, 2) = (u, v, f(u, v)) for the surface 2= f(, y). (a) The portion of the sphere x² + y2 + z2 = 9 that is above the cone z...
Q1. Sketch and find a parameterization of the following surfaces (a) (Spherical cap) The portion of the sphere by *+y+-16 cut by the vertical plane y 3, containing the point (0,4,0) (b) (Circular cylinder band) The portion of the cylinder y+z+5)2 25 between the planes x--2 and x-2.
Q1. Sketch and find a parameterization of the following surfaces (a) (Spherical cap) The portion of the sphere by *+y+-16 cut by the vertical plane y 3, containing the point (0,4,0) (b)...
#48
#46
and #48
In Exercises 39-48, find a parametrization of the curve. 39. The vertical line passing through the point (3,2,0) 40. The line passing through (1,0,4) and (4.1.2) 41. The line through the origin whose projection on the xy-plane is a line of slope 3 and whose projection on the yz-plane is a line of slope 5 (ie, Az/Ay = 5) 42. The circle of radius 1 with center (2, -1, 4) in a plane parallel to the...
(i) The sides of a given grain silo are represented by the equation of the cylinder x2 +y-3. The top of the silo is the portion of the sphere x2 + y2 + z2-7 lying within the cylinder and above the zy plane. Sketch and find the volume of the silo using an appropriate coordinate system Q2. [10] (ii) Given that C is the boundary of the plane 2x +2y+z = 6 that lies in the first octant and F...
Find the slope of the curve below at the given points. Sketch the curve along with its tangent lines at these points. r= - 4+4 cos 0; O= The slope at the point o = 5 is (Simplify your answer.) The slope at the point 0 = (Simplify your answer.) is Identify the curve r= - 4 + 4 cos 0. OA. OB. OC. Give a geometric description of the set of points in space whose coordinates satisfy the given...
All of 10 questions, please.
1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz...
(1 point) Let F(x, y, z) = 5yj and S be the closed vertical cylinder of height 4, with its base a circle of radius 3 on the xy-plane centered at the origin. S is oriented outward. (a) Compute the flux of F through S using the divergence theorem. Flux = Flux = || F . dà = (b) Compute the flux directly. Flux out of the top = Į! Įdollar Flux out of the bottom = Flux out of...
Revised by Prof. Kostadinov, Fall 2015, Fall 2014, Fall 2013, Fall 2012, Fall 2011, Fall 2010 Revised by Prof. Africk and Prof. Kostadinov Fall 2015, Spring 2016, #1 Identify the horizontal and vertical asymptotes of the following functions using the limit definitions: 2x2 o) yA- #2 Find the derivatives of the following functions using the definition of derivative: a) f(x)-2x-5x #3 Find the derivative v dr of the following functions, using the derivative rules: b) f(x)--2x +3x-4 #4 Find the...
Q4 only:
Question 3. Consider the region of R3 given by V is bounded by three surfaces. Si is a disc of radius 1 in the plane z -0. S3 is a disc of radius 2 in the plane z 3 and a) Make a clear sketch of V. (Hint: You could consider the cross-section of S2 with y-0, and then use the circular symmetry. (b) Express V in cylindrical coordinates. (c) Calculate the volume of V, working in cylindrical...
Most questions answered within 3 hours.
-
Given the following table of high speed internet access vs.
annual home income:
Home Income
%...
asked 13 minutes ago -
A baseball batter hits a 0.145kg baseball straight up into the
air. The baseball leaves the...
asked 45 minutes ago -
An FM modulator is tested using
single-tone baseband signal with frequency of 50kHz and a sprectrum...
asked 1 hour ago -
Write the ionic equations for the first stage of salts
hydrolysis.
Anion, Cation?
Na2S
NiSO4
K2SO4...
asked 2 hours ago -
suppose there is a normally distributed population with a mean of
250 and a standard deviation...
asked 3 hours ago -
Question Three
Suppose you as project manager are using the Waterfall
development methodology on a large...
asked 4 hours ago -
Which statement is not true about welfare in Canada?
A.Benefits typically vary based on one's ability...
asked 4 hours ago -
Please help me with FLOWCHART and UML diagram for class,
thank you!
#include <iostream>
#include <fstream>...
asked 5 hours ago -
3. Describe the “logic circuit” of the Lac operon. Which
proteins are bound or not to...
asked 5 hours ago -
Ayesha’s adjusted gross income is $60,000 in 2019. She donated a
piece of artwork with a...
asked 5 hours ago -
For Dijkstra’s shortest path algorithm:
a. Give the Big-O time for Dijkstra’s shortest path algorithm
and...
asked 5 hours ago -
Phosphorus violates the 'octet rule' in biological molecules,
forming more covalent bonds than expected based on...
asked 6 hours ago