Parametric Definition and 674 Threads

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...