Parametric Definition and 650 Threads

Find the parametric representation for the surface: The part of the sphere x^2 + y^2 + z^2 = 16 that lies between the planes z = -2 and z = 2. okay, i know that i have to use spherical coordinates which is x = 4sin(phi)cos(theta) y = 4sin(phi)sin(phi) z = 4cos(phi) i know how to find...

How does one conclude that \frac{d^{2} y}{dx^{2}} = \frac{dy\'/dt}{dx/dt} ? Thanks

If someone could check my work and make sure I'm doing these problems right, I would really appreciate it. 1.Eliminate the parameter and obtain the standard form of the rectangular equation. Circle: x= h + r cos \theta , y= k + r sin \theta (x-h/r)^2 + (y-k/r)^2 = 1 2.Find the arc length...

Find an equation of the tangent line to the curve with parametric equations x=tsint, y=tcost at the point (0,-π). went dy/dt / dx/dt --> cost - tsint/sint + tcost t not given so figured it could be: x=t(sin(1)) --> t= x/sin(1) or y=t(cos(1)) --> t= y/cos(1) wondering if...

F(x,y,z)=(-\frac{y^2+2z^2}{x^2},\frac{2y}{x},\frac{4z}{x}) "Find parametric representations of the field lines." How do I parametrize all possible field lines?

Hello everyone, I'm having troubles seeing how this works. The directions are: Find parametric equations for the tagent line to the curve with the given parametric equations at the specified point. Here is my work and problem...

Can someone please help me with this question? x = 1-sint, y = 2+cost, rotate about y = 2 Find the surface area of the parametric curve. I don't know how to do it with y=2, I only know how if the question askes for rotating about the x-axis. The answer to the question is 2(pi)^2.

need parametric equations to the tangent line at the point (cos 0pi/6, sin 0pi/6, 0pi/6) on the curve x = cost, y = sint, z = t x(t) = ? y(t)=? z(t)=? now from my understanding, i have to find the derivatives of x, y, and z right? and i did this... now alll i should do is plug in the...

Hello everyone I did the following problem: Click http://img220.imageshack.us/img220/8486/untitled1copy4oq.jpg to view the problem and my answer. The row reduced form is: 1 5 0 0 -7 6 -7 0 0 1 0 -1 1 -1 0 0 0 1 - 2 -4 8 Any help would be great

I was wondering what the surface area would be when the curve: x=e^tsint, and y=e^tcost where (t) is greater than or equal to (0) and (t) is less or equal to pi divided by (2). when it is revolved about a) the x-axis b) the y-axis (approximation...

(1)If you are given the parametric equations x = sin(2\pi\t) y = cos(2\pi\t) and 0\leq t\leq 1 how would you find the cartesian equation for a curve that contains the parametrized curve? Using the identity \sin^{2}\theta + cos^{2}\theta = 1 would it be x^{2} + y^{2} = 1 ? Thanks

Find parametric equations for the tangent line at the point (cos(-4pi/6),sin(-4pi/6),-4pi/6) on the curve x=cost, y=sint,z=t x(t) = _________ y(t) = _________ z(t) = _________ r'(t) = <-sin(t), cos(t), 1> r'(0) = <0,1,1> my answer: x = cos(-4pi/6) + 0t y = sin(-4pi/6) +1t z =...

I need to find a set of parametric equations for a hyperbolic paraboloid. The hint is that I should review some trigonometric identities that involve differences of squares that equal 1. The equation is: \frac{y^2}{2}- \frac{x^2}{4} - \frac{z^2}{9} = 1 And what I have is...

The problem says; Suppose that a bicycle wheel of radius a rolls along a flat surface without slipping. If a reflector is attached to a spoke of the wheel at a distance b from the center of the resulting curve traced out by the reflector is called a curtate cycloid. I need to find...

Stewart uses the chain rule to show how to find the tangent to parametric curves. Given: x=f(t) and y=g(t), and that y can be written in terms of t, in other words, y=h(x) then the chain rule gives us, dy/dx = (dy/dt)/(dx/dt). Thats fine. The same argument holds for polar coordinates...

calc 2 problem (area bound by parametric eq.) I'm having a problem with this question: Find the area bounded by the curve x=cos{t}\ y= e^t, 0\geq t\leq\pi/2\ , and the lines y=1\ x=0 ... I came up with \int e^t(-sin{t})dt from 0\to\pi/2 But apparently I'm missing steps...

x(t)= \left( u\cos A \right) t and y(t)= \left( u\sin A \right) t - \frac{gt^2}{2} + h represent the horizontal and vertical coordinates of a batted or thrown baseball. A is the initial angle of elevation and u is the initial speed of the ball. I need to plot x(t) and y(t)...

I have x(t)=t(1-t) and y(t)=t(1-t^2). As t goes from 0 to 1 in forms a loop and I need to know the point where the tangent line is vertical. I know this must be easy but I'm clueless right now. Any help?

Hi, I've been trying to do this one question: Let R be the region enclosed by the graph x=t^2-2 y=t^3-2t. Set up the integral for the area of R. I know that if y is continuous function of x on an interval a ≤ x ≤ b where x=f(t) and y=g(t) then \int_{a}^{b} y dx =\int_{t1}^{t2} g(t)f'(t)dt...

Hi, I'm doing a project which involves parametric curves that I have to present to a class. Basically, I'm completely exercises and I know that most computer-aided design works with parametric curves, specifically Bezier curves. For the project, I'd like to draw something in CAD or whatever and...

I've recently attempted the following problem, http://domino.research.ibm.com/Comm/wwwr_ponder.nsf/challenges/June2001.html with the following solution http://domino.research.ibm.com/Comm/wwwr_ponder.nsf/solutions/June2001.html I've managed to form the meaningful derivatives (as...

If f(\theta) is given by:f(\theta) = 6cos^3(\theta) and g(\theta) is given by:g(\theta) = 6sin^3(\theta) Find the total length of the astroid described by f(\theta) and g(\theta). (The astroid is the curve swept out by (f(\theta),g(\theta)) as \theta ranges from 0 to 2pi ) f/d(\theta) =...

Consider the parametric curve given by the equations x(t) = t^2+30t-11 y(t)=t^2+30t+38 How many units of distance are covered by the point P(t) = (x(t),y(t)) between t=0, and t=9 ? well since the bounds are already given (0->9), i just need help on setting up the integral. here's what i...

Find the area of the region enclosed by the parametric equation x=t^3-2t y=9t^2 dx/dt = 3t^2-2 9t^2 - 1 = 0 t=\pm \sqrt {1/9} \int_{-1/3}^{1/3} (9t^2)*(3t^2-2) dt = -2/5 anyone know where i went wrong?

The following parametric equations trace out a loop x = 8 - 3/2t^2 y = -3/6t^3+3t+1 1.) Find the t values at which the curve intersects itself. wouldn't i just have to solve for t for one of the equaltion to find t? also, can you find the intersects using a TI-83 plus to check your...

Okay, is it possible to transform an "x-y" equation into a parametric "equation"? If so, how would I go about it? For example, if I am given the equation (x^2)/1-(y^2)/25=1, what process would I have to use to find the Parametric equations? Thank You.

find \frac{d^2y}{dx^2} as a function of t, for the given the parametric equations: x = 2-4*cos(t) y= 4+cos(t)^2 \frac{d^2y}{dx^2} = _______ dy/dt = -2*cos(t)*sin(t) second derv. 2*sin(t)^2-2*cos(t)^2 dx/dt = 4*sin(t) second derv. 4*cos(t) \frac{d^2y}{dx^2} =...

x = cos(t)^7 y= 8sin(t)^2 Find \frac{d^2y}{dx^2} expressed as a function of t \frac{d^2y}{dx^2} = _________ well second derivative for y is \frac{d^2y}{dt} = (16*cos(2t)) dx/dt = (-7*cos(t)^6*sin(t)) so dx^2 = ((-7*cos(t)^6*sin(t)))^2 right? so...\frac{d^2y}{dx^2} =...

The circle (x-3)^2 + (y-4)^2 = 9 can be drawn with parametric equations. Assume the circle is traced clockwise as the parameter increases. if x = 3+3cos(t) then y= _______? wouldnt y just be 3+4sin(t)?

The ellipse \frac{x^2}{3^2} + \frac{y^2}{4^2} = 1 can be drawn with parametric equations. Assume the curve is traced clockwise as the parameter increases. If x=3cos(t) then y = ___________________________ wouldnt i just sub x into the ellipse equation and solve for y? well i did...

Describe the motion of the particle with position (x,y) as t varies over the given interval. x=2+cost y=3+sint where t is greater than or equal to 0 and less than or equal to 2 pi i've tried to eliminate t and came up with y=3+sin(arccos(x-2)) i don't know if...

given the parametric eqns for a spiral x=kt cos t y=kt sin t where k is a constant give a function of 't' that calculates the length of the spiral.

Our lecture today covered Equations of Lines and Planes in 3D. Is this the only approach to learning line and plane equations in 3-d? Honestly do we need r = ro + t*v? To me this seems like a very hard way to learn equations of lines and planes. Maybe I should learn it to be a...

URGENT help needed please... I have been having problems with this problem...it says... A graph of the Lissajous figure is given by the paraetric equations: x=sin2t and y=cost Show that the curve has two tangents at the point (0,0) and find their equations Can someone please help me...

well, I am lost...im not sure if this goes in college or k-12, but I am in grade 12 in Canada...and I am learning here, so i guess I am at the right place, any wyas...i need help, with parametric and vector eqns of lines, since I am failing this course horribly...my teacher sucks and marks hard...

Original question: a) Say r'(t) = 3t^2 i - cost j + 2t k, and r(0) = i + k. Find r(t). b) Find T(t). c) Find parametric equations for the tangent line to the curve at t=1. I have done parts a and b and got the following results: a) r(t) = t^3 + 1 i - sint j + t^2 + 1 k b)T(t) =...

How does one find the equation of a line from parametric equations? In spefiic I'm looking at this: x(t) = 1+2t , y(t) = -1 + 3t , z(t) = 4+t... I think i got to use something liek x-1/a = y-1/b=z-1/c or something like that. If what i just said is true, then I'm lost on what to do next...

Hi...i was just wondering if anyone gets the same answer to what i get for the following question...thanks... find \frac{dy^2}{dx^2} in terms of t for... x = 2cost - cos2t, y = 2sint + sin2t... i got my answer to be \frac{1 + cost}{2sin^3t(1 -2cost)} the answer is given as...

I am asked to find the equation of the tanget line to the curve at the givien points. (y -y1 = m(x1-x)) The point is: (-2/sqrt(3), 3/2) Parametric Equations are: where t = theta x = 2*cot(t) y = 2*sin^2(t) How would i find what theta is in this set, inorder to solve dy/dx...

Hello, First I will post the question. Now I see that my instructor is trying to progressively guide us through the steps to find the area of the surface S. I have done part a. And I think I know how to do part c and d. But I am confusing myself with part b. Which is frustrating since...

[SOLVED] Parametric Surfaces and Their Areas Hello, I am having problems visualizing a concept. First I will post my question as it is given in Jame's Stewart's Fourth Edition Multivariable Calculus text, Chapter 17, section 6, question 17. Find a parametric representation for the given...

Another question... If I were given these equations: x = e^t y = e^-t Then I have to find the cartesian product for this parametric curve and then I have to sketch the graph of the curve. So here's the cartesian product I came up with: Solve for t in y, so: y = e^-t ln y = ln...

I've searched the web for information on Parametric Equations, and most of them only give me information on how to find y = f(x) when given y = y(t) and x = x(t). Is there any sort of method for doing the reverse? I'm told that there are theoretically an infinite number of parametric...

Hi! I am supposed to write the hyperboloid x^2 + y^2 - z^2=1 as a parametric funktion and find an expression for the tangent plane in an arbitary point in terms of the parameters. I think I have figured out that the parametric funktion is \left\lbrace\begin{array}{ccl} x &=&...

I know that the equation for the surface area of any solid of revolution around, say, the x-axis is SA = 2\pi\int_{a}^{b} y\sqrt{1 + (\frac{\,dy}{\,dx})^2} \,dx What I need is the same formula except in parametric terms, like if the problem was given in terms of x(t) and y(t). Any takers?

i have a geometry/algebra test tommorow and i have been sick for the whole unit, and my darn teacher is making me do it tommrow, even though i have no idea wuts going on...its on lines with parametric equations...if anyone has anything (tutorials, sites,etc.) anything that will help me...

suppose u have an ellipse and u put a rope around it and at distance h from the original ellipse. Any point from the ellipse to the rope wrap around the ellipse is = to distance h. what is the rope's parametric equation? What shape is this rope in?

Hi, Im trying to find more information about the following projectile equation: y = (vi/k)(1-e^-kt))(sin a) + (g/k^2)(1-kt-e^-kt)) I apologize for posting this, but I have been looking high and low for this!

Hi, I'm looking for the derivative of the projectile parametric y-component? The y component is: y = (vi/k)(1-e^-kt)(sin a) + (g/k^2)(1 - kt - e^-kt) I seem to be doing something wrong and my derivative isn't working out, I just want to check it against the final answer to see where...

Parametric "amplification" of energy on capacitors Hello. My last post was about how geometry affected potential and electric energy transfers. Some people send me interesting information about that, and I've been thinking about parametric power conversion. We usually relate E to a...