Polar Definition and 1000 Threads

Homework Statement Evaluate the surface integral. ∫∫S x^2*z^2 dS S is the part of the cone z^2 = x^2 + y^2 that lies between the planes z = 1 and z = 3. Homework Equations \int \int _{S}F dS = \int \int _D F(r(u,v))|r_u\times r_v|dA x=rcos(\theta) y=rsin(\theta) The Attempt...

Okay, so I have just broken into the polar coordinate system, and I like to derive things on my own to strengthen my intuition. I decided to try and derive the equation of an ellipse swiftly on my own, and had the high ambitions of eventually deriving the area of an ellipse with polar...

I was looking at the equation of a circle in polar coordinates on wikipedia, http://en.wikipedia.org/wiki/Polar_coordinate_system and I understand that a is the radius of the circle, and that (r0, phi) is the center of the circle. But I don't see what the r and theta refer to :(.

Homework Statement Given the two polar equations r=5-3cos(θ) and r=5-2sin(θ) find the area of the region common to both curves. Homework Equations A= 1/2∫ r^2 dθ The Attempt at a Solution i understand that i plug in the two equations into the equation, but i don't know how to find the...

i just need to know something about the integral with polar coordinates , to know the interval of the teta angle of any domain the proffesor said that we put the pen on the x-axis and move it , i for one moment was not focusing and the doctor had to go to another class can anyone explain ? thank you

I'm studying for my final and tutors/my professor isn't available over the weekend. Could someone please spend a little time to help me? My problem is stated as: Let R be the right half of the circle x2+(y-1)2=1. Use a double integral polar coordinates to find the area of the region R. I...

Homework Statement Let Q be the region bounded by r=sin(3θ) in the first quadrant. Find the area of Q. Find the average distance of points in Q from the origin. The Attempt at a Solution I thought I could calculate area like so: \int_0 ^{pi/3} \int_0 ^{sin(3θ)} sin(3θ) dr dθ This gives...

Transformation from Cartesian to spherical polar coordinates In dimensions: x=r sinθ cos \varphi and y= r sin θ sin \varphi z=r cos θ Show one example of: ∂z\alpha/ ∂xμ . ∂xμ/ ∂z\alpha = δ\alpha\beta Now here is my answer: δyx=(∂y/∂r . ∂r/∂x) + (∂y/∂θ . ∂θ/∂x) + (∂y/∂\varphi...

Homework Statement I'm trying to find the best solution for solving a problem in which I must form an operation with three vectors in polar form, ending with a sum in rectangular form. The operation is as follows: (5 \angle 0°) + (20 \angle -90°) - (6 \angle180°) = Homework Equations...

I wanted to know whether H2S is a polar compound and hence does it have a dp dp interaction. An answer sheet says the H2S only has id-id. If this is true can some one explain it to me? cause sulphur is definitively polar, and considering h2s's V shape, it should be a polar molecule, thus having...

Homework Statement Let F = <-y/(x2+y2, x/(x2+y2>. Recall that F was not conservative on R2 - (0,0). In this problem, we show that F is conservative on R2 minus the non-positive x-axis. Let D be all of R2 except points of the form (-x,0), where x≥0. a) If (x,y) is included on D, show that...

I'm having trouble figuring out how to find what "r" is. I know r is the radius, but how do I go about finding it? Like what do I look for in a particular problem?

Homework Statement "Consider the graph of r = e^{\theta} in polar coordinates. Then consider the graph of (\theta \cos{\theta}, \theta \sin{\theta}) where \theta \in \mathbb{R} on the Cartesian plane (x - y axis). How are the two graphs related? What relationship (if any) can we define between...

Homework Statement f(x,y) = (x^{2} + y^{2})^-2 x^{2} + y^{2} ≤ 2 x ≥ 1 Homework Equations The Attempt at a Solution -4\pi ≤ θ ≤ 4\pi secθ ≤ r ≤\sqrt{2} are these the correct domain?

Homework Statement Use polar coordinates to compute the volume of the region defined by 4 - x^{2} - y^{2} ≤ z ≤ 10 - 4x^{2} - 4y^{2} Homework Equations The Attempt at a Solution I got z = 2 so set up the equation V = f^{2pi}_{0}f^{5/2}_{2}f^{0}_{2}r*dzdrdθ is the domain...

Homework Statement f(x,y) = e^{x^2+y^2} x^{2} + y^{2} ≤ R Homework Equations The Attempt at a Solution I believe this is a circle. f^{2pi}_{0}^{sqrt(R)}_{-sqrt(R)}e^{x^2+y^2}*r*dr*dθ = f^{2pi}_{0}f^{sqrt(R)}_{-sqrt(R)}e^{r^2}*r*dr*dθ after u substitution... =...

Homework Statement f(x,y) = y(x^{2} + y^{2})^-1 y ≥ \frac{1}{2}, x^{2} + y^{2} ≤ 1Homework Equations The Attempt at a Solution Would you check my domain please? f^{pi}_{0}f^{sqrt(3)/2}_{-sqrt(3)/2} sinθ drdθ

Homework Statement f(x,y) = xy x ≥ 0, y ≥ 0, x^{2} + y^{2} ≤ 4 Homework Equations The Attempt at a Solution f^{pi/2}_{0}f^{2secθ}_{0} rcosθ * rsinθ * r drdθ I just wanted to check... is this right?? because I really don't think it is

Homework Statement My textbook sets up the integral, but does not solve, claiming that it's "trivial to solve manually or by using a CAS". I put the integral into my TI-89, and sure enough, there is a solution, and that solution happens to be "8". However... Homework Equations The actual...

A bee goes from its hive in a spiral path given in plane polar coordinates by r = b*ekt , θ = ct, where b, k, c are positive constants. Show that the angle between the velocity vector and the acceleration vector remains constant as the bee moves outward. (Hint: Find v · a/va.) attempts...

The problem and my work is shown in the image below. However, I feel like I did something horrible wrong but I'm not sure where! I'm sorry if my handwriting is illegible. If you're having difficulties please leave a comment and I will not hesitate to type it out as a response. Any...

∫∫cos(x^2 + y^2)dA, where R is the region that lies above the x-axis within the circle x^2 + y^2 = 9. Answer: .5pi*sin(9) My Work: ∫(0 ->pi) ∫(0 -> 9) cos(r^2) rdrdθ u = r^2 du = 2rdr dr = du/2r .5∫(0 ->pi) ∫(0 -> 9) cos(u) dudθ .5∫(0 ->pi) sin(u)(0 -> 9) dθ .5∫(0 ->pi)...

Homework Statement Alright, here's the question, A stream function for a plane, irrotational, polar-coordinate flow is ψ=9r^2sin^θ. Find out the velocity potential in Cartesian Co-ordinate! Homework Equations The Attempt at a Solution Well, I can easily find out the velocity...

Homework Statement I'm trying to assign the spots for a TLC plate that I did in lab. http://imageshack.us/f/27/tlcpolar.png/ What is the order of polarity of these three molecules? Homework Equations The more polar something is, the lower it will stay on a TLC plate. The less...

Hi! Here's a question I am working on: Double integral of arctan(y/x). where R: 1≤x2+y2≤4, 0≤y≤x. I have the bounds for r as 1 to 2, but for θ I don't know if I should use ∏/4 to ∏/2 or 0 to ∏/2. How do I know which one? The integration is easy, but I need help with the bounds...

Homework Statement (a) we define the improper integral (over the entire plane R2) I=\int\int_{R^2}e^{-(x^2+y^2)}dA=\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}e^{-(x^2+y^2)}dy dx=\lim_{a\rightarrow\infty}\int\int_{D_{a}} e^{-(x^2+y^2)} dA where Da is the disk with radius a and center the...

we know that for any (x, y) in Cartesian system, there is such (r, θ) in Polar system, so x = r * cosθ and y = r * sinθ how you can calculate what corresponds to (Δx, Δy) in polar system? how come Δx * Δy = r * Δr * Δθ? Maybe this is very stupid question and has obvious answer...

I have a question regarding problem solving tips. When given an iterated integral and asked to convert it to polar coordinates, how do you select the bounds of theta - do you have to understand how the graph of r operates and therefore know where the theta bounds are based on the rectangular...

Homework Statement The question is to find the area of the region that lies inside both curves. The part I'm specifically having trouble with is finding the points of intersection. Homework Equations sin (2∅) cos (2∅) The Attempt at a Solution sin 2∅ = cos 2∅ 2 sin ∅ cos ∅ =...

How do you find these on the unit circle: 5pi/2 ? howabout pi/8 ? Converting from polar to rectangular? It says convert (-1, pi/8 ) from polar to rectangular coordinate? But there is no pi/8 on the unit circle? If the'yre on the unit circle just use x=rcosθ and y=rcosθ another example is for...

Equations given: r=A\theta \theta=\frac{1}{2}\alphat^{2} A=\frac{1}{\pi} meters per radian \alpha is a given constant Asks to show that radial acceleration is zero when \theta=\frac{1}{\sqrt{2}} radians. I have tried rearranging, plugging in, and deriving to try to solve this...

I have an ellipse. Quite simple, ecc=0.60. And I'm doodling with calculus I learned 40 years ago. I can find the tangent to the ellipse, that is, the slope of the tangent, using cartestian coordinates. At the point where the tangent skims the top of the minor axis (b) the slope is 0 and and...

I'm a bit confused about how polar molecules can be insoluble in water. Polar means they have a permanent dipole so I would have assumed that they would solvate water. An example of a polar insoluble compound is pyrantel embonate. Its used to treat hookworm and pinworm infections in the GI...

1. Homework Statement A point has coordinates (−5, 3*square root of 7). What is the polar coordinates of this point? (in the form a,b) 2. Homework Equations x= rcos theta y=rsin theta 3. The Attempt at a Solution Using phythagoras thrown -5=x=rcos theta (eq 1)...

Homework Statement Show that the parity operation (reflection through the origin) on a point (\rho, \varphi, z) relative to fixed (x, y, z) axes consists of the transformation: \rho \to \rho \varphi \to \varphi \pm \pi z \to -z Also, show that the unit vectors of the cylindrical polar...

Homework Statement Hi, I have the coordinates of an "expression" for a point in a cartesian coordinate system. I'm trying to write it in a polar coordiante system (in function of r and theta) but I don't know how to find the answer a = y-component of the point b = x-component of the point...

Homework Statement Find the points at which the following polar curves have a horizontal and vertical tangent line. (a) r = 3 + 6 cos(theta) Homework Equations The Attempt at a Solution x = r cos(theta) = (3 + 6 cos(theta)))cos(theta) = 3cos(theta) + 6 cos(theta)^2 y =...

In rectangular corr. 3i+j mean leght in x-direction =3 in y-3direction =1 However, how about in polar coorindate? 3r+1\theta (r and \theta are the unit verctor in polar coor., I don't know how to type it out, I hope you understand.) Dose it mean a line with length 3 from origin and angle...

Hello, friends. I read that polar anisotropy of the CMB shows that the solar sistem is moving towards the Virgin constellation. This polar anisotropy is not something which is not going to cause some problems... First question: Isn't this a sort of ABSOLUTE MOTION? i.e. we have found out...

Hi! Is there somebody, who can help me with this exercise: "Use polar coordinates to find the limit. [If (r, θ ) are polar coordinates of the point (x,y) with r ≥ 0, note that r --> 0+ as (x,y) --> (0,0)]

Homework Statement "Find the area of the region that lies inside both curves (as an example), r=((sqrt(3)) cos(theta)) , r=sin(theta). This is Calculus 3. Areas and lengths in polar coordinates. Homework Equations Guys, I'm very confused because when the polar graphs are complicated we...

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Hi, Say I have an acceleration vector in polar coordinates: a = -30e_r where the unit vector e_r points in the same direction as the Cartesian unit vector j. How can I integrate that vector so that I have the velocity vector in polar coordinates? I know that if I have an acceleration vector...

Homework Statement You're tracking a plane from the ground. The plane is at a constant height h from the ground, at a distance r from you at the illustrated instant, and at an inclination theta. The plane's speed is constant at 1200km/hr. Find the rate at which your tracking dish must rotate...

Homework Statement Find dy/dx Problem in picture below Homework Equations The Attempt at a Solution [PLAIN]http://img28.imageshack.us/img28/7162/76013837.png The answer for this is dy/dx = -cos\theta sin\theta + (1-sin\theta)cos\theta/-cos^2\theta - (1-sin/theta)sin\theta I cannot figure...

Or, at least, this young male suddenly appeared on board the cartographer ship "Hydrograf" 2AM. As can be seen on the video, it was very interested in the blue garbage container, and on one of the photos, it has smelled the humans observing it through a ventilation hatch to the (locked) cabin...

Homework Statement If z=x + iy, what is d/dz in polar coordinates? The Attempt at a Solution I know that expanded, d/dz = 1/2 (d/dx) - i (d/dy) Where to go from there?

can someone point me to a howto on doing this?

I took the divergence of the function 1/r2\widehat{r} in spherical coordinate system and immediately got the answer as zero, but when I do it in cartesian coordiantes I get the answer as 5/r3. for \widehat{r} I used (xi+yj+zk)/(x2+y2+z2)1/2 what am i missing?

Hey, I've been stuck on this question for quite a while now: Homework Statement 1a. Write down an expression for the position vector r in spherical polar coordinates. 1b. Show that for any function g(r) of r only, where r = |r|, the result \nabla x [g(r)r] = 0 is true. Why does this...