Parametric Definition and 674 Threads

is there any good reviews on parametric down conversion? i want to know something about squeezed state and this effect is often used to do the work. thanks a lot!

Hello, I am an amateur developing the math to describe the motion of a robot of sorts. At this stage I'd like to use http://en.wikipedia.org/wiki/Bézier_curve" as user input to describe the motion path/s that it will make over time... (imagine it sitting flat on the cartesian 'floor')...

Homework Statement The parametric function : x = cos(5t) y= cos(3t) t belongs to R Question : find the coordinates (x, y) of the double points Homework Equations The Attempt at a Solution OK so first of all,i find an interval of t where to study - periodic of 2Pi - M(t) = M(-t) - M(t+Pi) is...

Homework Statement Find the area of the region enclosed by the asteroid: x=a*cos^{3}\theta y=a*sin^{3}\theta Homework Equations A = \int\sqrt{\frac{dy}{d\theta}^{2}}+\frac{dx}{d\theta}^{2}The Attempt at a Solution \frac{dy}{d\theta} = 3asin^{2}\theta(cos\theta) \frac{dx}{d\theta} =...

1. I found the parametric equation of a plane; \left(\begin{array}{ccc}x\\y\\z\end{ar ray}\right) = \left(\begin{array}{ccc}1\\2\\3\end{ar ray}\right) +s\left(\begin{array}{ccc}1\\1\\0\end{ar ray}\right) +t \left(\begin{array}{ccc}2\\1\\-1\end{ar ray}\right) s,t ∈ R. I was asked to...

Homework Statement Question is "The Cartesian equation of the plane containing the line x=3t , y =1+t , z=2-t and passing through the point (-1,2,1) is?" Homework Equations \begin{array}{l} n \bullet (r - r_0 ) = 0 \\ < n_1 ,n_2 ,n_3 > \bullet < x - x_0 ,y - y_0 ,z - z_0 >...

Homework Statement Find the line tangent to the point 2pi/3 when x=cost y=sqrt3 cost. Also find the value of d2y/dx2 at the point given. Homework Equations I found dy/dx to be -sqrt3 sint/ -sint. I found that to be just sqrt3. This matched what my calculator told me the slope was...

Do the two photons (signal and idler) created by PDC always have equal energy? (Of course, it depends on the Lorentz frame, but I mean in the frame in which the nonlinear crystal is at rest.)

Homework Statement x = e^{t} , y = (t-1)^{2} , (1,1) Find an equation of the tangent to the curve at a given point by two methods. Without eliminating the parameter and by first eliminating the parameter. The answer in the book says y = -2x + 3 and I cannot see how you get it. So...

Find a vector parametric equation of the line in R^{2} with equation 2x-3y = 4 Attempt at a solution I haven't seen this type of question before so I don't know where to start. I suppose that the equation 2x-3y = 4 is a vector equation of that line and is in the form x = x0 + tv. I...

Homework Statement The points P(2ap, ap^{2}) and Q(2aq, aq^{2}) lie on the parabola x^{2} = 4ay. The equation of the normal to the parabola at P is x + py = 2ap + ap^{3} and the equation of the normal at Q is x + qy = 2aq + aq^{3}. These normals intersect at R. Find the locus of R if PQ is a...

I'm having trouble seeing how an example comes out because the "worked example" skips about 5 steps and I can't get from point a to b. It starts as: \frac{\frac{d}{dt}(\frac{3t^{2}-3}{3t^{2}-6t})}{3t^2-6t} and is meant to end up as: \frac{-2(t^{2}-t+1)}{3t^{3}(t-2)^{3}} I end up with a...

Homework Statement Consider the parameterization of the unit circle given by x=cos(3t^{2}-t), y=sin(3t^{2}-t) for t in (-\infty,\infty). In which intervals of t is the parameterization tracing the circle out in a clockwise direction? In which intervals of t is the parameterization tracing...

Homework Statement If a string wound around a fixed circle is unwound while held taut in the plane of the circle, its end P traces an involute of the circle. In the accompanying figure, the circle in question is the circle (x^2)+(y^2)=1 and the tracing point starts at (1,0). The unwound...

Homework Statement Determine if any of the lines are parallel or identical L1 (x-8)/4 = (y+5)/-2 = (z+9)/3 L2 (x+7)/2 = (y-4)/1 = (z+6)/5 L3 (x+4)/-8 = (y-1)/4 = (z+18)/-6 L4 (x-2)/-2 = (y+3)/1 = (z-4)/1.5 Homework Equations L1 pt(8,-5,-9) V<4,-2,3> L2 pt(-7,4,-6) V<2,1,5> L3 pt(-4,1,-18)...

Homework Statement Let R be the region in the 1st quadrant in the region enclosed by x=2cos(\theta) and y=sin(2\theta) Suppose R is rotated around the x-axis. Find the volume of the resulting solid. Homework Equations The formula for the solid of revolution is: V= \pi\int...

Consider the line L(t)=<4t-1,2+2t>. Then L intersects: 1. the x-axis at point ____ when t=____ 2. the y-axis at point ____ when t=____ 3. the parabola y=x^2 at the points _____ and _____ when t=_____ and t=______ I am confused on how to approach this problem. Do I just make x=4t-1 and y=2+2t?

Consider the two lines L1: x=-2t y=1+2t z=3t and L2: x=-9+5s y=36+2s z=1+5s Find the point of intersection of the two lines. My teacher said that I should use system of equations to solve for the point, but I am sort of confused on what to do because there are 2...

Homework Statement Find a vector equation and parametric equations in t for the line through the point and parallel to the given line. (0, 12, -11) x = -5 + 3t, y = 4 - 2t, z = 1 + 8t Homework Equations x = x0 + at y = y0 + bt z = z0 + ct The Attempt at...

Hi, I've got these 2 questions left on an advanced Mathematics assignment (due Monday morning :( ) that I've been trying to crack but I'm not sure if what I have done is correct. Any help at all is greatly appreciated. Question: (1) (a) According to the Flat Mars Society, Mars is also a plane...

Write parametric and symmetric equations for the z-axis. I'm not sure i am on the right track; here is my attempt to an answer. [0, 0, z] where z can equal any number. a = [0, 0, 1] b = [0, 0, z] Parametric equations x = 0 y = 0 z = 1 + tz Symmetric equations...

Homework Statement Consider the parametric surface r(u,v)=<vsinu, vcosu, v^2> a) Identify the shape of the surface b) The point (1,1,2) is on the surface. Find: i) A grid curve wit hv constant that contains this point ii) A grid curve with u constant that contains this point c)...

Here is my question: When given three distict points A, B, C, find the parametric equations for the plane throught these three points. I was able to get the plane through these three points, first of all by getting the normal vector n = ABxAC, then by multiplying this vector by...

Homework Statement I've uploaded a scan of the questions. Questions 4, 5, and 6 are given in the 3 files uploaded. They all come from the given information from the first scan of the problem. Homework Equations The Attempt at a Solution I've worked everything I could on paper...

Homework Statement Find the area of the region enclosed by the parametric equation x=t^3-8t y=2t^2 The Attempt at a Solution I am not even sure how to start this problem. I read somewhere that to start with you solve for t in one of the equations. when i solve for t I end up...

Homework Statement i. x = 3cost, ii. y = 9sin2t, iii. 0\leq t < 2\pi iv.\int_0^\frac{\pi}{2} Asin2tsint \ dt 2. The attempt at a solution So this is what I am given and I am supposed to be able to show that this is the integral for the shadded area between the curve and the...

Homework Statement a curve has parametric equations: x = t - 2sin t y = 1 - 2cos t R is enclosed by the curve and the x axis. Show that the area of R is given by the integral: \int^{\frac{5\pi}{3}}_{\frac{\pi}{3}} (1-2\cos t)^{2} Homework Equations The Attempt at a...

x = 2cot t y = (sin t)^2 t is greater than 0 but less than or equal to pi/2 The cartesian can be found using trig identities to be: y = 8/ (4+ x^2) What would be the range of the cartesian equation? I think it would be x is greater than or equal to 0, since when t = pi/2, x =...

Homework Statement Describe motion of a particle w/ position xy Homework Equations x=cospi(t) y=sinpi(t) The Attempt at a Solution solving for t t=x/cospi so y=sinpi(x)/cospi y=tanpi(x) interval=at least one at most 2 since tan(x)=0 at pi and 2pi and this is where the...

Homework Statement A curve has parametric equaions: x = 2cot t, y = 2sin²t, 0 < t <= pi/2 Find an expression for dy/dx in terms of the parameter t The Attempt at a Solution Not sure where to go. Do i need to make a Cartesian equation first? Thanks :)

Homework Statement A particle is located at r=(2i+4j)m at t=0s. At t=3s it is at r=(8i-2j)m and has velocity v=(5i-5j)m/s a)what is the particles acceleration vector a? Homework Equations r1=r0+v0(t1-t0)+1/2a(t1-t0)^2 v1=v0+at The Attempt at a Solution v1=v0+at...

Homework Statement Find parametric equations for the line in which the planes 3x − 6y − 2z = 15 and 2x + y − 2z = 5 intersect. Homework Equations The Attempt at a Solution <2, 1, -2> - <3, -6, -2> = <-1, 7, 0> x = 2 - t, y = 1 + 7t, z = -2 Did I do this correctly??

I just have a question, when I am rotating something let's say around y=2 and the two equations are x=t^3 + 1 and y = 4t+1 how would i set it up?

A parametric equation, say r(t), is smoothly parametrized if: 1. its derivative is continuous, and 2. its derivative does not equal zero for all t in the domain of r. Now that sounds simple enough. Now let's say we have the tractrix: r(t) = (t-tanht)i + sechtj, ... then r'(t) = [...

I've just had a brain block... how do I work out the distance between a point (-5,10,13) and a parametric equation: x(t) = 57- 4t y(t) = 75 + 5t z(t) = -t

Calculate the distance between the 2 lines and use this distance to prove that the are not going to intersect. x(t) = 2 + t y(t) = -1 –t z(t) = t x(t) = 3 – s y(t) = 1 z(t) = 1 + s I have no idea where to start with this question! please help!

Homework Statement x(t)=2t-1 y(t)=t^2 algebraically eliminate the parameter to create a rectangular equation Homework Equations There was an example in our book that showed how to do this if the two equations contained sine and cosine, however nothing was said if they didn't. I...

Homework Statement Identify and sketch the curve represented by the parametric equations: x=1+cost y=1+sin^2t Homework Equations The Attempt at a Solution I have to isolate t in one of these equations and sub whatever t equals into the other equation right? So how do I get rid of the...

Homework Statement At which point is the tanget line to the following curve horizontal? y= a sin^{3}\theta x = acos^{3}\theta Homework Equations The Attempt at a Solution \frac{dy}{dx}=\frac{\frac{dy}{d\theta}}{\frac{dx}{d\theta}} When \frac{dy}{dx} = 0 , this means that that the tanget...

Homework Statement Find the place where the parametric curve intersect itself x = 1-2cos^{2}t y = tant(1-2cos^{2}t) Homework Equations The Attempt at a Solution So I started with the x values.. 1-2cos^{2}t_{1} = 1-2cos^{2}t_{2} By canceling the same stuff on...

Homework Statement Find and verify parametric equations for an ellipse. Homework Equations x=acost y=bsint The Attempt at a Solution lets say the equation is x=3cost, y=3sint, domain: 0 to 2pi x2 y2 -- + -- = 1 a2 b2 point does verify when t=0 x=3, y=0 which =1...

So this seems to be a pretty straightforward question but I keep getting the arc length to be 0 and I redid this question many times.. Find the length of the parametrized curve given by x(t) =t^{2}-8t + 24 y(t) =t^{2}-8t -7 How many units of distance are covered by the point P(t)...

Question: If f is a vector-valued function defined by f(t)=(e^(-t), cos(t)), find f''(t). I'm not even quite sure how to start. Any help would be loved! Thank you!

Homework Statement Let: a matrix be: -5 -0.5 -0 -8 Find an invertible P and a diagonal D such that PDP(inverse) Homework Equations DET( (I)Lamda-A))= 0 for Eigenvalues The Attempt at a Solution when y=0 at the end matrix for finding the...

I was wondering if someone could give me an overview of what they are and how to get them. Thanks

Homework Statement i want to make t the subject of any of the following equations inorder to find the cartesion equation. any ideas?: x=t^2+t y=t^2-t Homework Equations The Attempt at a Solution

Homework Statement Reduce these parametric functions to a single cartesian equation: $\displaylines{ x = at^2 \cr y = 2at \cr} $ $\displaylines{ x = 3{\mathop{\rm Sec}\nolimits} \left( \alpha \right) \cr y = 5{\mathop{\rm Tan}\nolimits} \left( \alpha \right) \cr} $...

[SOLVED] Parametric equation of the intersection between surfaces Homework Statement Given the following surfaces: S: z = x^2 + y^2 T: z = 1 - y^2 Find a parametric equation of the curve representing the intersection of S and T. Homework Equations N/A The Attempt at a Solution The...

Homework Statement Consider the curve of intersection of the cylinders [x^2+y^2=4] and [z+x^2=4]. Find parametric equations for this curve and use them to write a position vector. Homework Equations Thats what I am looking for. What to set t equal to. The Attempt at a Solution I set...

Find the parametric and symmetric equations of the line of intersection of the planes x+y+z=1 and x+z=0. I got the normal vectors, <1,1,1> and <1,0,1> and their cross product <1,0,-1> or i-k. I set z to 0 and got x=0, y=1, z=0. How do I form parametric equation out of this?? I know...