For questions about parametric equations, their application, equivalence to other equation types and definition.

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1answer
79 views

System of parametric inequalities

I'm still struggling with the parametric inequalities.I'm doing some systems of parametric inequalities, but I can not understand how to proceed.This is the system: $x-2a<1+a$ $\frac x2 ...
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53 views

Equation of a polygon

I need a parametric equation for a filled polygon defined by 3 or more points. The closest I've got is by using 3 points in this equation - $polygon = p1 + u(p2-p1) + v(p3-p1)$. But by using points ...
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2answers
97 views

Find Vector and Parametric Equation

I'm having some trouble finding answers to these problems. When i try to find help online, all i find are (x,y,z) problems and I'm simply looking for a PreCalculus (x,y) problem solving technique: ...
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1answer
35 views

Parametric inequality problem

I would ask for help regarding a problem with the parametric inequalities. $\dfrac{(x+a)}{(a-1)}+\dfrac{(x-a)}{(a+1)}-\dfrac{x}{(a+1)}-\dfrac{2(x-1)}{(a-1)}\ge 0\ \text{for}\ a<-1$ Since ...
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2answers
79 views

Supremum Definition in context of a Rectifiable/Differentiable Curve

I am trying to prove that if I have 2 paramterizations of the same curve $\gamma$ and $\sigma$ (i.e. there is continuous bijective map $\phi$ such that $\sigma = \gamma \circ \phi$) then if the curve ...
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0answers
49 views

Inverse ease-in-out parametric function

I'm trying to create an inverse ease-in-out function that given values from 0 to 1, produces values from 0 to 1. Opposite of a typical ease-in-out function, though, I want it to start accelerated, ...
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3answers
80 views

Surface integral

Problem statement $$ \mbox{Calculate the surface integral}\quad \int_{Y}\ y\,\sqrt{z\,}\,\sqrt{4x^{2} + 4y^{2} + 1\,}\,\,{\rm d}S $$ where $Y$ is the surface $\left\{\left(x,y,z\right)\ \ni\ ...
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93 views

Paramtrizing a counterclockwise circle vs. a clockwise one

Does it make a different when you parametrize a counterclockwise full circle and a clockwise circle in the complex plane? For example, I am looking at computing an integral $\int_\gamma ...
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351 views

Wolfram and solids of revolution

I'm looking for the easiest method of having WolframAlpha calculate the volume of a solid of revolution. I've been working on a particular Project Euler problem for a long time. So far, I think I ...
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1answer
36 views

ratio of tangent to the ellipse

The tangent at point $P = ( a \cos \phi, b \sin \phi)$ on the ellipse $\frac{x^2} {a^2} + \frac{y^2}{b^2}=1$ meets the $x$ and $y$ axes at the points $X$ and $Y$, respectively. Find in terms of ...
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48 views

Parabolic flight. h(t) vs 2 parametric equations.

Often you have something like: $$h(t)=-16t^2+V_0t+C$$ I have little experience with parametric equations, but I have also seen parabolic functions represented this way: $$x=x_0 + V_{0_x}*t$$ ...
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123 views

How to construct a parametric cubic B spline?

If I am given n+1 control point Pi(xi,yi), Po .... Pn , how do I construct a parametric relationship to draw a curve ? From what I understand , a parametric relationship is that you can express x and ...
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1answer
81 views

Express parametric curve as graph of a function

I have a parametric curve in $\mathbb{R}^2$ given by $$ t\mapsto f(t)\left(\begin{array}{c}1\\1\end{array}\right)+\sqrt{-f'(t)}\left(\begin{array}{c}1\\-1\end{array}\right),\quad ...
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63 views

How are massive parametric functions that make a picture (example inside) created?

[Here's] (http://www.wolframalpha.com/input/?i=sergey+brin+curve) an example of what I'm talking about. The equation might take a second to load. How are these generated, computer algorithms? I ...
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1answer
179 views

Asymptote of a parametric equation (with Arctan)

I need to find the asymptotes of a parametric equation. My book says you have a vertical asymptote when $y\to \infty$. But the parametric equation is the following: $$x= \frac 13t^3-\pi,y= \frac ...
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1answer
31 views

Does this limit of arc length exist?

We have a parametrized curve $\gamma: \mathbb{R} \rightarrow \mathbb{R^2}$ given by $\gamma (t) = \langle e^t\cos (t), e^t\sin(t)\rangle$. I want to compute the arc-length of this curve on $[a,b]$ in ...
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55 views

Eliminate the parameter from the parametric equations

$$x=\frac{3t}{1+t^3} , y=\frac{3t^2}{1+t^3} , t \neq -1,$$ and hence find an ordinary equation in x and y for this curve, The parameter t can be interpreted as the slope of the line joining the ...
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3answers
65 views

Find rectangular equation from parametric equation???

Find rectangular equation from parametric $ x = t^{2} + t $ $ y = t^{2} - t $ I tried finding the equation but I am stuck here: $ x - t^{2} = t $ $ y = t^{2} - t $ $ y = t^{2} - ({x - t^{2}}) ...
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43 views

How to parametrise this surface integral

This is the question: $ S $ is the boundary of the region $ \{(x,y,z):0≤z≤h, a^2 ≤x^2+y^2 ≤b^2 \}$ where $ h,a,b$ are positive and $a<b$. ${\bf F(r) } = \exp(x^2+y^2){\bf r}$ where $ {\bf ...
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31 views

Parametric Derivatives

I recently wanted to derive a parametric equation which is as follows: $x(t) = t \cos(\frac{p\pi}{2t})\\ y(t) = t \sin(\frac{p\pi}{2t})$ I derive both equations in terms of $t$ but when I go to ...
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1answer
1k views

Finding a vector parametric equation given P and Q equations?

Find a vector parametric equation $r⃗(t)$ for the line through the points $P=(3,5,4)$ and $Q=(1,4,7)$ for each of the given conditions on the parameter $t$. If $r⃗ (0)=(3,5,4)$ and $r⃗ (7)=(1,4,7)$, ...
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2answers
102 views

parametrization of plane in $\mathbb R^3$

Parametrize the plane in $\mathbb R^3$ with direction vectors $\hat u$ and $\hat v$ and through the point $p$ as in representation as the range of a $C^1$ function $f:\mathbb R^2\to\mathbb R^3$. ...
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1answer
29 views

Can you give a general expression for the rate of rising water poured in an object?

Given an 3-d object defined by a set of parametric equations (x, y, z), can you write a formula expressing the rate that a liquid rises as it's poured into this object at a constant flow rate? Assume ...
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44 views

Removing parameter $t$ from $z$-axis

How do I remove the parameter $t$ from the $z$-function in the following: $$\begin{align}x&=a\cos{t}-a\\ y&=a\sin{t}\\ z&=nt\end{align}$$ (where $n,a$ are arbitrary coefficients) So far I ...
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166 views

Arc length paramatrizations satisfy original system of differential equations?

Say we have a system of differential equations $$ \begin{cases} x'''(t)+f(t)x'(t)=0\\ y'''(t)+f(t)y'(t)=0 \end{cases} $$ on an interval $[a,b]$, along with the restriction that $$ x'(t)^2+y'(t)^2=1 $$ ...
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1answer
80 views

How can I increase the resolution of a 3d plot in Sage to see all the details of the noodle? [closed]

I want to plot my noodle with a high resolution to see all the details. How can I achieve this with Sage? Here is my parametric, piecewise function: ...
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3answers
96 views

Parametrization of $y^2 - x^2=1$

I have found parametrizations for the level curve $y^2-x^2=1$, however, I have a question regarding one of them. From the Pythagorean trigonometric identity $\cos^2 x + \sin^2 x =1$ we obtain ...
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2answers
55 views

Find a parametrization of the intersection curve between surfaces

Find a parametrization of the intersection curve between the surfaces $−3x^2+2z=10$ and $4x^2+10y^2=5$. You should parametrize such that $y=k\sin(t)$ for some constant k. The answer should be in ...
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1answer
136 views

Gradient of a rational Bezier curve

I'd appreciate help working out the gradient of a rational Bezier curve $C = (\,x(t) \,, \,C_y(t) \,)$. I know that the gradient $g$ of a the parametric curve is $$ g(t) = \left( \frac{dy(t)}{dt} ...
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1answer
81 views

Find the shaded areas A1, A2, A3

I think i know how to find the angles KAG and KAH that's what i did: (this is the picture from my assignment sheet) then i have to find the shades areas A1,A2 and A3 but i don't know how to ...
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18 views

Derivative of a parametrized vector on a nonfixed basis

Suppose a curve defined by a vector parametrized through the variable $u$, and expressed on a non-fixed base, like the polar coordinates base. You derive it with respect to that parameter. What ...
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1answer
335 views

Coordinate of intersection between line and square

TL;DR given a square and a point $p$, I need the intersection between the perimeter of the square and a ray cast from the center of the square through point $p$. This is my approach so far, but I will ...
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1answer
85 views

sketch the line segment whose parametric equations

Sketch the line segment whose parametric equations are $x=2+t, v=t^2-1, t∈[0,3]$ That's what i did $t=x-2$ $v=(x-2)^2-1$ $v=x^2-4x+3 $ $v=(x-3)(x-1)$ $x=3,1$ and that's my sketch I am not ...
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378 views

Find a vector equation and parametric equations or the line in R^3 that passes through the point (1,2,-3) and is parallel to the vector u=(4,-5,1).

Find a vector equation and parametric equations or the line in $\mathbb{R}^3$ that passes through the point $(1,2,-3)$ and is parallel to the vector $u=(4,-5,1)$. Find two points on the line that are ...
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1answer
52 views

Quick Parameterization Help

I've been trying to paramaterize $$x^2+y^2+z^2=9,\ x^2-y^2=3$$ but haven't had any luck. I was thinking to let $x=\sqrt{3}\ \sec(t), y=\sqrt{3}\ \tan(t)$ to complete the identity on the right ...
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1answer
334 views

Find a vector equation and parametric equations of the line in $\mathbb{R}^2$ passing through the origin and is parallel to the vector $\vec{u}=(2,3)$

anyone can help me? :< Are there any equations that I could use in this question? I am so confused. I only know how to do the question if it changes "parallel" to "perpendicular" because I only ...
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2answers
258 views

Parametric equations and specifications of a triskelion (triple spiral)

I haven't been able to find the parametric equations and specifications to form a triskelion, a triple spiral (this is made of three interlocked couples of spirals). Using the parametric equation of ...
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1answer
19 views

Parametrizing curve with not only one peak

I obtained experimental data (thermal analysis) and need to parametrize the resulted curves for modeling. An example of two curves obtained: I tried to use a Weibull distribution, but since I ...
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1answer
131 views

Circle On Sphere

Sorry if this sounds too silly but my math skills are very poor and I just need this problem fixed. I made this graphic with geogebra 3D and it was quite easy there but I don't know how to write ...
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2answers
72 views

When does this parametric curve cross itself?

Find the points where the curve given parametrically by$$\mathbf{r}(t)=\left(2+\cos\frac{3}{2}t\right)\left(\begin{matrix}\cos t\\\sin t\end{matrix}\right)$$crosses itself. So, I understand that ...
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1answer
59 views

There exists a constant arc length parametrization

I heard that for any curve in the plane that can be given parametrically by $\vec{r}(t)=\langle x(t),y(t)\rangle$ for $a\leq t\leq b$ that there exists a constant arc length parametrization, i.e. ...
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705 views

Understanding the Equation of a Möbius Strip

I am in HL Math and trying to finish my IA. My topic is the Möbius band. The only problem is, I do not understand the formula that defines it and everywhere I have looked has just given me a ...
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1answer
113 views

Tangent Line of a Parametric Curve

Deduce the equation of the tangent line to the curve defined by the equations x=cosh(t), y=sinh(t), and z=ct I have somewhat of a good grip on the definition of a ...
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1answer
64 views

Find slope of a curve without calculus

Is it possible to find the slope of a curve at a point without using calculus?
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163 views

What is the parametric and cartesian equation of a hyperbolic paraboloid formed by the intersection of two cylinders of radius “A” & “B”?

What is the parametric and cartesian equation of a hyperbolic paraboloid formed by the intersection of two cylinders of radius "A" & "B", which intersect at a distance of "H" from its Axis at an ...
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0answers
41 views

Line integral, Parametrization

I have this line $A=\{(x,y) \in R^2 : y^2+4x^4-4x^2=0\}$ , $(x>0)$ I parametrized it like that : $b(t) = (t, \sqrt{4t^2- 4t^4})$. And my $F$ is $F(x,y) = (x+y,-x)$. But when I calculate my ...
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60 views

Searching for a probability distribution appropriate for my task

I'm making a game (not important), but I'd like to have real probability distribution function (instead of classical dice notation). I like the normal distribution, but I would like to also shift the ...
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2answers
103 views

Cartesian equation of $ \vec{r}(t)=\left(e^{\omega t}(\cos(\omega t)+\sin(\omega t)),2\omega e^{\omega t} \cos(\omega t)\right) $

I have this parametric equation: $$ \vec{r}(t)=\left(e^{\omega t}(\cos(\omega t)+\sin(\omega t)),2\omega e^{\omega t} \cos(\omega t)\right) $$ and I have to obtain the Cartesian equation. Any ...
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1answer
37 views

can the derivative of a closed complex contour at any point be zero?

If C is a closed contour in the complex plane parametrized by z(t)=u(t)+i*v(t), can there be any point where z'(t)=0?
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55 views

Parametrize $|x|+|y|+|z|=1$

How can we parametrize the surface $|x|+|y|+|z|=1$? Here I mean differentiable parametrize. I think we may need to divide it into 8 pieces and consider them respectively.