Polar Definition and 1000 Threads

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...

This unique 6-minute video shows a she-bear and her two cubs devouring a seal, while mummy bear is growling for miles around to be heard, to warn off others from getting too close. http://www.dagbladet.no/2011/09/07/nyheter/innenriks/isbjorn/dyrenes_nyheter/17989869/

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...

Homework Statement The diagram (omitted) shows the curve C with polar equation r=e^(\theta), where 0\le\theta\le(pi/2). Find the maximum distance of a point of C from the line \theta=(pi/2), giving the answer in exact form. The Attempt at a Solution I'm not really sure how to attack...

After doing lots of research, (about 5 mins) i propose that we relocate polar bears to the antarctic. Plenty of food and plenty of ice. Job done.

http://www.guardian.co.uk/world/2011/aug/05/polar-bear-mauls-british-death Close to Longyear Town on Svalbard, a group of tourists was attacked by an irate polar bear Personally, I would never walk there on my own, but only accompanied by knowledgeable local guides who know the body language of...

Homework Statement Consider two non-identical, non-interacting particles of mass M that are constrained to move on a circle of radius R. Write down the Schrodinger equation for this problem and find the eigenfunctions and energy levels of this system. Homework Equations (see below)...

Homework Statement I need the steps to follow when finding the polar decomposition of a hermitian matrix If someone could direct me to a website that would help, or put up an example here please. thanks :) Homework Equations The Attempt at a Solution

If the polar ice caps were to melt... wouldn't the sea levels decrease? Water ice is less dense than liquid water, so the volume (and displacement of liquid water) is greater when its frozen. But when you melt that, the volume decreases, and some of the water that was initially displaced by...

I need to find the equation of the tangent line to the curve x=t4+1, y=t3+t; t=-1 I have already found that the slope of the line is -1 by finding (dy/dt)/(dx/dt) I just need to figure out how to solve for y1 and x1 Thanks in advance

Homework Statement Evaluate \int\intD(x+2y)dA, where D is the region bounded by the parabolas y=2x2 and y=1+x2Homework Equations dA = r*drd\vartheta r2=x2+y2 The Attempt at a Solution Well, I know I need to put D into polar coordinates, but I'm lost on this...

If you were add axis labels to a polar plot what would you use for labels in place for a y-axis label and a x-axis label?

Link: http://imageshack.us/photo/my-images/39/18463212.jpg/ This is a very long problem so I drew it to make things simpler. Part a) tells me to set up a double integral in polar coordinates giving the total population of the city. I have the following: 2π...4 ∫...∫ δ(r, θ) r dr...

Homework Statement I need to convert this to polar form; anyone have any ideas where to start? Homework EquationsThe Attempt at a SolutionI know this is incorrect but I am a bit overwelmed on this one. any help would be wonderful! thanks! Homework Statement Homework Equations The Attempt at...

Homework Statement Prove this equation Homework Equations The Attempt at a Solution I almost get the answer. But I don't know why all of the sin and cos are in reciprocal form.

Homework Statement The problem and answers are given in full through the following image: http://ekdhl.net/files/mechanics.JPGHomework Equations Equations 2/13 and 2/14 are these: \textbf{v} = r'e_{r} + r\theta 'e_{\theta} \textbf{a} = (r''-r\theta '^{2})e_{r} + (\theta ''r + 2r'\theta...