Hi, I am having trouble reversing the formula x=R(\theta - \sin(\theta)) to get \theta in terms of x. Am I missing something obvious or is it just impossible?
To put it into context this is part of the parametric equation for a cycloid. The other part of the parametric equation is y = R (1-...
Homework Statement
Show that every point on the line v = (1,-1,2) + t(2,3,1) satisfies the equation
5x - 3y - z - 6 = 0
Homework Equations
The Attempt at a Solution
So what I did was solve the equation v by adding the x,z,and z components to get
x = 1 + 2t
y = -1 + 3t
z =...
Homework Statement
how can we eliminate the parameter of these functions:
x= t-2
y= t^2 +1
and sketch its curve
Homework Equations
The Attempt at a Solution
I can't find the relations between these 2 functions
Homework Statement
sketch the curve of parametric equations:
x= e^-t + t
y= e^t - t
Homework Equations
The Attempt at a Solution
I don;t know how to eliminate the parameter
Can anyone help me?
Homework Statement
At time t, a projectile launched with angle of elevation a and initial velocity Vo has position x(t)=(Vocosa)t and y(t)=(Vosina)t-0.5gt^2, where g is the accerleatio due to gravity.
The Attempt at a Solution
(a) A football player kicks a bal at an angle of...
Homework Statement
Each of the three circles A, B and C of the figure below can be parameterized by equations of the form
x = a + k cos t, y = b + k sin t, 0 ≤ t ≤ 2.
What can you say about the values of a, b and k for each of these circles?
(figure attached below)
The Attempt at a...
I have been working through the book:
"Almost All About Waves"
John R. Pierce
Dover
2006
This is a fascinating read & offers some deep insights into the inner workings of waves, from a practitioner's perspective.
Chapter 13 - Parametric Amplifiers - is extremely interesting & is...
My book really doesn't go into a lot of depth but I was wondering if this is correct
If we are asked to find the tangent line of a specific value of t for a given parametric equation then we can find the equation of the tangent line in either rectangular or parametric functions.
Rectangular...
Homework Statement
A particle moves in the xy-plane so that its position at any time t, 0 =< t =< pi, is given by:
x(t) = \frac{t^2}{2}-ln(1+t)
y(t) = 3sint
-- At that time is the particle on the y-axis on the interval? Find the speed and acceleration vector of the particle at this time...
f(t)=(t^3, |t|^3) is a parametric representation of y=f(x)=|x|.
Consider y=|x|,
the left hand derivative f '-(0)=-1 and the right hand derivative f '+(0)=1, so f(x) is clearly not differentiable at 0.
But
f '(t)=(3t^2, 3t^2) for t>=0
f '(t)=(3t^2, -3t^2) for t<=0
f '(0)=(0,0) and f(t)...
Just wanted to check and see if this is right. The k-component of the vector is what I'm unsure of...I've always sucked at converting to parametric form. :)
Homework Statement
Convert to parametric form:
x^{2} + y^{2} = 9, z = 4arctan(y/x)
The Attempt at a Solution
The i- and...
Hey I have a problem with question 4 of this problem set
http://www.physics.ubc.ca/~mattison/Courses/Phys170/p170-ps5.pdf Number 4.
I have found Vmin to be 0.84m/s which i know it is correct, but i cannot solve Vmax?
i thoguht you could maybe approach this question with 2 parametric...
Homework Statement
At what point does the curve x = (1-2cos^2(t), y=(tan(t))(1-2cos^2(t)) cross itself? Find equations of both tangents at that point.
Homework Equations
The Attempt at a Solution
To begin, I figured that x=y when it crosses itself, so I set x=y and got 1 = tan(t), so t=\pi/4...
Homework Statement
Find the area of the region enclosed by the parametric equation
x=t^3-5t
y=7t^2
Homework Equations
The Attempt at a Solution
I know how you set it up \int (7t^2)(3t^2-5)dt, but how do you find the bounds. I tried finding t and got t= (+/-)\sqrt{y/7} and you...
Homework Statement
Find parametric equations of the osculating circle to the helix r(t)=cos(t)i+sint(t)j+tk corresponding to t=pi. Recall that the osculating circle is the best possible circle approximating a curve C at a given point P. It lies in the osculating plane (i.e., the plane...
Q: A particle is following the path C: f(t)=(2cos(t), 2sin(t), t), t>=0, and flies off on the tangent line at time t=3pi/2. Find the position of the particle at time t=5pi/2.
Solution:
f'(t)=(-2sint,2cost,1)
f'(3pi/2)=(2,0,1)
f(3pi/2)=(0,-2,3pi/2)
Equation of the tangent line...
Homework Statement
Give a parametric representation of the plane x + y + z = 5.
Homework Equations
I am really not sure, I've been over the chapters we've covered for a little over an hour now, and the only mention i can find of a parametric representation of a plane is in passing...
[SOLVED] Converting from Cartesian to Parametric form
Homework Statement
Find a parametric vector equation of for the plane in R^3 having cartesian equation
4y + 5z = - 6
Homework Equations
None
The Attempt at a Solution
What I did was, first I turned the equation into 4x +...
so the question is:
eliminate the parameter in the pair of parametric equations
x = h + a secθ
y = k + b tanθ
to find the corresponding rectangular equation.
im taking an online course of calculus and i can't find an explanation of how to do this anywhere...ive been trying but it...
i have a couple questions that confuse me that would help me on doing my homework on parametric equations...
do the parametric equations x=t^2 and y=t^2 describe the line y=x?
and if y is a function of t and x is a function of t, then is y a funcion of x?
and last, does x=cos t, y=cos^2(t)...
I have an upcoming exam, and I'm having trouble grasping some concepts. The things that are currently perplexing me are parametric equations and rectangular equations and converting between the two. I have a problem like this
Given the parametric equations x = e^(-t) + 1 and y = e^(-2t) -...
I am confused myself, so I post the Q.
when we talk about "definite integral of area" in rectangular or polar coordinates, the "area" is quite clear, at least people do it in this way in general:
rectangular coordinate: area between locus y=f(x) and x axis.
polar coordinate: sector area...
I need samples of parametric equations:
x=Fx(t);
y=Fy(t);
the samples must be useful or famous in math, physics or engineer, not be created randomly meaningless.
one that I know is to describle ellipse:
x=A*cos(t);
y=B*sin(t);
I need 2 or more good samples for my report.
thanks...
Sketch and represent parametrically the following: (a) \mid z+a+\iota b\mid =r \ \mbox { clockwise}\\ , (b) ellipse 4(x-1)^2 + 9(y+2)^2 =36 \ .
Taking (a) first \mid z + a + \iota b \mid = r \mbox{- is the distance between the complex numbers }\ z=x+\iota y \ \mbox{ and } \ a + \iota b \...
I CAN'T SEEM TO GET THE ANSWER THAT IS CONSISTENT WITH MY UNDERSTANDING OF THE USE OF DOT AND CROSS PRODUCTS AND THE USE OF THE PARAMETRIC EQUATION OF THE LINE.
LOOK AT THIS PLEASE:
the parametric equation of the line is:
x = 2 + 3t
y = -4t
z = 5 + t
the plane is 4x + 5y - 2z = 18...
parametric and cartesian equations?? HELP!
1. x = 3t, y = 9t^2, negative infinity<t<positive infinity
2. a) What are the initial and terminal points, if any? Find a Cartesian equation for a curve that contains the parametrized curve. What portion of the grap of the Cartesian equation...
OK, I'm a wee bit sleep deprived and cannot recollect some facts about the Dirac quantization of gauge theories. With the quantization of the parametrized nonrelativistics particle, do we still change the Poisson bracket into commutators?
More specifically, for the non-relativistic particle...
Okay, I was doing 3D modelling. To save space I used vector functions to render terrain. Anyway, I came up with 3 parametric equations - each a function of an axis: e.g.: x=4t, y=5t+6, z=7t-9. How can you convert this into a Cartesian Equation?:confused:
Homework Statement
The equation X(t)=A+tL is the parametric equation of a line through the point P:(2,-3,1). The parameter t represents distance from point P, directed so that the I component of L is positive. We know that the line is orthogonal to the plane with the equation 4x-6y+5z=6...
Homework Statement
Consider a particle along a curve C and whose position is given by the vector:
s(t) = < sqrt(t2), t3 - 3t >
Last part of the question:
There is an unknown force that is keeping this particle on trajectory C. At what value of t must the force cease in order for the...
Homework Statement
Give parametric questions for the plane : 2x-3y+z-6=0
The Attempt at a Solution
i know that the normal is (2,-3,1)
how do i find the direction vector of the plane?
Suppose that you have a parametric curve given by
x = f(t), y = g(t), a ≤ t ≤ b
What will the Surface of revolution and Volume of revolution around the x-axis be?
I have two candidates:
Surface: S = 2*pi*int( |g(t)|*sqrt( (df(t)/dt)^2+(dg(t)/dt)^2 ) , t=a..b)
Volume: V = pi*int(...
What are you trying to do when you find parametric equations for a geodesic lines on a surface?
Take the metric ds^2 = dq^2 + (sinh(q)*dp)^2
Are you simply trying to get q as a function of s? and p as a function of s?
If so, why?
Thanks
Determine the vector and parametric equations of the plane that contains point C(1,-2,6) and the z-axis
I take this to mean that any point on the z-axis is valid so does that mean either (0, 0, 1) or (1, -2, 5) are also on the plane?
3-dimensional parametric equations [Updated]
Look lower for update...
Homework Statement
Well, my problem is that I need to give some examples on 3-dimensional parametric equations. So far I've found out what parametric equations are, and more specifically what 3-dimensional parametric...
Homework Statement
5. Find parametric equations for the tangent line to the curve of intersection of the surfaces
z^2 = x^2 + y^2 and x^2 + 2y^2 + z^2 = 66 at the point (3, 4, 5).
The Attempt at a Solution
f(x,y,z) = x^2 + y^2 - z^2
g(x,y,z) = x^2 + 2y^2 + z^2
Partial derivz...
Given:
\begin{array}{l}
x = 2\cos t \\
y = 2\sin t \\
\end{array}
find
\frac{{dy}}{{dx}}
I started by finding dy/dt and dx/dt
\begin{array}{l}
\frac{{dy}}{{dt}} = 2\cos t \\
\frac{{dx}}{{dt}} = - 2\sin t \\
\end{array}
Now, dy/dx = (dy/dt) / (dx/dt)...
I am trying to represent a helical pipe in x,y,z co-ordinants, would the x and y co-ordinants simply be multiplied by the equation of a circle if the growth of the helix is in the z direction?
Any help would be appreciated.
Thanks
Homework Statement
Notice the curve given by:
f(t) = x = 36-t^2
g(t) = y = (t^3)-25*t
The curve makes a loop which lies along the x-axis. What is the total area insde the loop.
Homework Equations
Integral from alpha to beta of g(t)*f'(t) dt
The Attempt at a Solution
Ok, so I...
Homework Statement
\frac{x^2}{a^2}+\frac{y^2}{a^2(1-e^2)} =1
The ellipse meets the major axis at a point whose abscissa is \lambda. Find lim \theta ->0.
Homework Equations
Parametric coordinates of an ellipse: (acosx,bsinx)
The Attempt at a Solution
The abscissa is the x...
Hi,
Can someone explain to me what a parametric equation is exactly? Why it is used (instead of a normal function)? In other words, what is the significance of it?
Second, to be more specific, in my book, there is an example where
r(t) 2 costi + 2sintj + tk t>0.
Then what they say is...
The semicircle \mbox{f(x) = }\sqrt{a^2-x^2} \mbox{ -a} <=\mbox{ x }<= \mbox{a }, ( see my last thread) has the parametric equations x= }a cos\theta\mbox{, y=} a sin\theta, 0 <= \theta <= \pi, show that the mean value with respect to \theta of the ordinates of the semicircle is 2a/\pi(.64a)...
Hi, I have two parametric curves defined in three dimensions, which are functions of a variable t, like so:
x1 = f1(t)
y1 = f2(t)
z1 = f3(t)
x2 = f4(t)
y2 = f5(t)
z2 = f6(t)
I am trying to find the intersection of these two curves, but I am having some difficulty with the...
Homework Statement
Find equations of the tangents to the curve x=3t^2+1, y=2t^3+1 that pass through the point (4,3).
The Attempt at a Solution
I was able to find the equation y=x-1 as a tangent line through the point (4,3) for the part of the curve above the x-axis since (4,3) is on...
I learned that vertifcal tangents occur at a parametric curve if the derivative of the curve is undefined. That is given dy/dx = dy/dt / dx/dt, a vertical tangent occurs when dx/dt = 0.
I don't understand why this is so. I know that vertical tangents occur when the slope is infinite, but...
Homework Statement
1) Consider the paramerric curve given by x = t^2 + 3t and y = 4 - t^2
a) Find an equation of the tangent lne to the curve at the point (x,y) = (0,-5)
b) Determine the equation of every vertical tangent line to this parametric curve.
2)For each of the following...
Which one would you say this is :confused: :
E(|x1-x2|)
x1, x2, xn - a sample of n values on the underlying random variable...
I was thinking this is a statistic :frown:
Does anyone have any ideas on how to even start this problem? I am supposed to find a general solution in rational numbers for (aside from the trivial ones):
x^3+y^3=u^3+v^3
Actually, I'm given the answer (which is really messy) and am supposed to show how to derive it. The book gives the...
Hello,
My textbook says that to determine concavity we calculate the second derivative of the curve. This is a problem from my book,
x = t^2 and y = t^3 - 3t
the second derivative of this is (3(t^2+1))/(4t^3)
I know all the steps to get to this point.. However, the book says that...