Parametric Definition and 650 Threads

Find an equation of the tangent to the curve at the given point by both eliminating the parameter and without eliminating the parameter. x = tan(θ) y = sec(θ) (1 , √2) y = ? attempt ; y - y1 = m(x-x1) y = √2 x = 1 y1 = sec(θ) x1 = tan(θ) substituting and solving it...

Homework Statement Estimate the length of the curve with parametric equations x = t^3, y = t^3, z = t^4, 0<=t<=3. Round to the 3 decimals place. Homework Equations The Attempt at a Solution virst i found the magnitide.. ||v|| = (4t^2 + 9t^4 + 16t^6)^1/2 i tool the integral...

Homework Statement Hi all. I am given the following parametric function in the complex plane C: \gamma = \left\{ {\begin{array}{*{20}c} {t^2 + it\,\,\,\,\,\,\,\,{\rm{for }}\,\,t \in [0,1]} \\ {t + i\,\,\,\,\,\,\,\,\,\,\,\,{\rm{for }}\,\,t \in ]1,2]} \\ \end{array}} \right. In...

Homework Statement Find the length of the curve y=x^2-4|x|-x from x=-4 to x=4. The Attempt at a Solution I realized there is a corner at x=0 so i tried to get around this by pluggin in x for x>=0 and -x for x<0. However, my integrals don't match the answer...

I've been looking everywhere for a tutorial or lesson on Parametric equations and can't find one that shows how to derive the actual equations. Either they show how to eliminate the parameter or sketch the graph. Let's say you had a function like y = x^2 + x - 3 What would you do to find the...

Hey guys so I had trouble with this problem, I hope it's not too long and you can help me out. Homework Statement A point moves following (starting at λ = 0 and increasing): x = 4·cn(λ) y = 3·sn(λ) z= am(λ) Find the distance the point has traveled when the speed vector is parallel to (-4, 3...

What parametric equation would one use to describe a sphere in General Relativity in order to calculate curvature? My main problem is what to do with the time dimension... And no, this is not a homework question.

Homework Statement http://mathbin.net/equations/8457_0.png My result does not seem like a "valid" equation. Is there any other approach I can take or anything that I can do to make it look prettier? Thanks.

In both exercise, eliminate the parameter. Problem 1 : http://mathbin.net/equations/8157_0.png When I graph this, it is a circle. THAT does not appear like a circular equation.Problem 2 : http://mathbin.net/equations/8159_0.png I am afraid of the absolute value signs. How do I deal with this...

I'm currently making a two dimensional game on my computer and I'm having a problem that pertains to parametric curves. Currently I'm trying to figure out an equation for a graph on any angle (say a sin curve). The reason for this is to make the "flight paths" of the ships in the game more...

The center field fence in a ballpark is 10 feet high and 400 feet from home plate. A baseball is hit at a point 3 feet above the ground. It leaves the bat at an angle of (theta) degrees with a horizantal at a speed of 100 miles per hour. x = (v0 cos(theta))t and y = h + (v0 sin(theta))t -...

Homework Statement http://img21.imageshack.us/img21/7910/68588225.th.jpg Homework Equations The Attempt at a Solution I know that the velocity is the derivative of the position vector.. but I am kind of confused how to do this

Homework Statement (a) The parametric curve x = (3t + 4)2, y = (3t + 4)2 - 9 for 0 t 3 is a line segment. (b) A parameterization of the graph of y = lnx for x > 0 is given by x = et, y = t for - < t < . (c) The line parameterized by x = 8, y = 5t, z = 6 + t is parallel to the x-axis...

Hello! I'm having a pretty big problem intersecting parametric lines. I'm using the equations: x = x1 + t(x2 - x1) y = y1 + t(y2 - y1) Given the 2 lines: x = x1 + t(x2 - x1) y = y1 + t(y2 - y1) x = x3 + t(x4 - x3) y = y3 + t(y4 - y3) I calculate the intersection, using this: t...

Homework Statement Two equations for two planes in 3-D 2x+y-2z=1 x-2y+z=-3 Find the parametric equation for the line of intersection of the two planes by solving these two equations togeather. The Attempt at a Solution Gauss Jordan gives: 1 0 -3/5 -1/5 0 1 -4/5 7/5...

Hi everyone, I'm an 18-year-old from Germany and I'm making use of MIT's OpenCourseWare programme. Currently, I'm watching the Calculus II course, and am having some trouble understanding how to find the equation: z=z0 + a(x-x0) + b(y-y0) by using parametric equations/vectors. a and b being...

Homework Statement For the field \bold{F} = (y+z) \bold{i} - (x+z) \bold{j} + (x+y) \bold{k} find the work done in moving a particle around the following closed curve: from the origin to (0,0,2π) on the curve x=1-cos t, y=sin t, z=t; and back to the origin along the z-axis. The answer is 2π...

Homework Statement Can someone please tell me how to get the average speed of a particle moving along a path represented by parametric equations? Is it \frac{1}{b-a}\int_{a}^{b}\sqrt{\frac{dx }{d t}^2 + \frac{d y}{d t}^2} Isn't this the arc length formula?

Homework Statement Given a continuous parametric function f : R2 -> R3 specifying a 2D surface in 3D space, define a continuous implicit function g : R3 -> R corresponding to the same surface. Homework Equations You’ll likely want to use the infimum function. You can ignore the...

Homework Statement Find the equation of the following planes in cartesian and (vector) parametric form: a) the plane through the point (1,4,5) and perpendicular to the vector (7,1,4) b) the plane through the origin and the points (1,1,1) and (1,2,3) The Attempt at a Solution For part...

Homework Statement L1 L2 x= 1+t x= 1+2s y= 1+6t y= 5+15s z= 2t z= -2+6s My professor said to find a normal vector and project the lines, but I'm new to this calculus and all these words are just a fuzzy cloud over my head. Homework Equations Projection of c...

Homework Statement In the xy-plane, the curve with parametric equations x=cost and y=sint, 0<=t=<pi, has what length? The Attempt at a Solution I drew the graphs x=cost and y=sint and shaded the area where the graphs intersect between 0 and pi. I don't know where to go from here.

Homework Statement a particle is on a trajectory defined by the parametric equations x(t)= 2t^2,y(t)= t^2-4t, z(t)= 3t-5, where t is the time.Find the components of its velocity and acceleration at time =1, in the direcion i-3j+2k. Homework Equations what i thought is r(t)=x(t) i...

I haven't taken calculus yet, but I'd like to determine the closest parameter value for when a parametric curve crosses a line (for a program I'm writing). The curve is such that I need to use calculus in some way or another - it is unsolvable algebraically. Newton iteration will find a point...

How is the parametric form of the graph of an equation different from its standard graph and what the dots in the parametric form of a graph represent.

Homework Statement find the slope and concavity of the funtion at the given point. x=t^2 Y=t^2+t+1 (0,0) Homework Equations t=x^(1/2) The Attempt at a Solution t=0 when x=0 x'=2t y'=2t+1 M=2t/(2t+1)=0 for the second deritive would you take the deritive of 2t/(2t+1) devided by...

Homework Statement Find parametric equations of the tangent line at the point (-2,2,4) to the curve of intersection of the surface z=2x2-y2 and the plane z=4 Homework Equations Not sure The Attempt at a Solution Not sure quite how to approach this. take the gradient of...

I know this is very simple, but the end integral just kills me Homework Statement Given equation in Parametric form x=\sqrt{2t+1}), y=6t Find arc length Homework Equations The Attempt at a Solution take x' & y' then Take integral of \int\sqrt{1/(2t+1) + 36} This is where I got stuck ...is...

Greetings, I'm trying to find the surface area of the part of the sphere x^{2}+y^{2} + z^{2}=1 above the cone z=\sqrt{x^{2}+y^{2}}. I know, that a surface area of a surface r(u,v) = x(u,v) + y(u,v) + z(u,v) can be given by, A(S) = \int\int | r_{u} \times r_{v} | dA A function, z=f(x,y) can...

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...

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)...