Tagged Questions
0
votes
1answer
22 views
Parametric Equation along a line segment
I am having some trouble understanding how to determine the parametric equation of a line segment between A(1,1) and B(-1,1).
I did some research and came across the following relation:
...
3
votes
2answers
114 views
Finding surface area of a cone
I will describe the problem then show what I tried to solve it.
I need to find the area of the cone defined as follows:
$$z^2=a^2(x^2+y^2)$$
$$0\leq z\leq bx+c$$
where $a,b,c>0$ and $b<a$.
...
1
vote
2answers
75 views
Eliminating parameters to obtain surface equation
Given the following vector equation, how do I eliminate the parameters $u,v$ to get an equation of a surface in rectangular coordinates?
$$\vec{r}(u,v)=3u\cos(v)\hat{\imath} + 4u\sin(v)\hat{\jmath} ...
1
vote
1answer
49 views
Representing A Plane Curve By A Vector Valued Function
I am given the function $x^2+y^2=25$, and I am suppose to write this as a vector valued function.
I have always been awful at these sort of problems, even with parametric equations, which requires ...
2
votes
0answers
179 views
Parametrization of square to calculate Dot-product in line-integrals and area-integrals, electric field from $\frac{dB}{dt}$?
I am calculating 3A of Tfy-0.1064 in Aalto University. I realized here that I am misunderstanding something in vector calculus: the thing market in green particularly.
I know
$$\nabla\times E= ...
0
votes
2answers
31 views
Need help with this parametric equation
$s(t)=(\frac{2}{t^2+1},\frac{2t}{t^2+1})$
I need to calculate a line integral along this path. But I have trouble understanding what it is. I did some googling and it looks that it is a parabola, but ...
1
vote
1answer
253 views
Parametric equation of a cone
I usually use the following parametric equation to find the surface area of a regular cone $z=\sqrt{x^2+y^2}$:
$$x=r\cos\theta$$
$$y=r\sin\theta$$
$$z=r$$
And make $0\leq r \leq 2\pi$, $0 \leq \theta ...
0
votes
1answer
56 views
parametrizing quarter of a circle
I am given the circle whose equation is: $(x-\frac{1}{2})^{2}+(y+\frac{1}{2})^{2}=\frac{1}{2}$. So, the coordinates of the origin of the circle are: $(\frac{1}{2},-\frac{1}{2})$ and the radius of the ...
1
vote
2answers
101 views
Finding Tangent line from Parametric
I need to find an equation of the tangent line to the curve $x=5+t^2-t$, $y=t^2+5$ at the point $(5,6)$.
Setting $x=5$ and $y = 6$ and solving for $t$ gives me $t=0,1,-1$. I know I have to do ...
2
votes
1answer
1k views
find length of curve of intersection
I have come to a dead end on a problem and I need someone to tell me either if I did it correctly, or how to fix it if I did not. This is Stewart Calculus 7th edition, problem 13.3.12.
Here is the ...
1
vote
1answer
73 views
Parametrization of a solid
Find a parametrization $\sigma : I \subseteq \mathbb{R}^3 \rightarrow \mathbb{R}^3$, with $I$ a parallelepiped, of $\lbrace (x,y,z) \in \mathbb{R}^3 : |z| \leq 4x^2 + 9y^2 \leq 1 \rbrace $.
1
vote
1answer
83 views
Parametric representation of rectangular form in terms of parameters $\rho$ & $\theta$
I need to represent the cone $z=\sqrt{3x^2+3y^2}$ parametrically in terms of $\rho$ and $\theta$ where $(\rho,\theta,\phi)$ are spherical coordinates.
Attempt. I tried using: ...
0
votes
1answer
91 views
How to find the parametric equations for: $zx + zy - xy = 0$
I'm trying to find the parametric equation for $zx + zy - xy = 0$ or equivalent $z = \frac{xy}{x+y}$ but couldn't find any hint in the web neither in a couple of calculus books for this particular ...
1
vote
3answers
136 views
Would this not take a ridiculously long calculation? (Surface area of parametric surface)
One of the question in my homework asks to verify that the surface are of
$ \mathbf{r} = a(1+\cos\phi)\sin\phi \cos\theta \mathbf{i} + a(1+\cos\phi)\sin\phi \sin\theta \mathbf{j} + ...
0
votes
1answer
2k views
Finding an equation and parametric description given 3 points
Let m be the plane through (0,1,1), (0,1,0) and (-2,-1,-1).
This concept has always confused me: How would I find the equation and parametric description given just these points??
I think the ...
6
votes
3answers
221 views
Curvature of the image of a curve projected onto a surface
(Adding a bounty since I need more details than I have so far)
Given a point
$$
s_{0}=S(u_{0},v_{0}) \;\;\;\; (S:\mathbb{R}^{2}\to\mathbb{R}^{3})
$$
and a point
$$
c_{0}=C(t_{0}) \;\;\;\; ...
1
vote
3answers
135 views
Express $z$ in terms of $x$ and $y$, i.e., find $z= f(x,y)$
I've been banging my head against the wall for a while now:
$x = s^2 - t^2$
$y = s + t$
$z = s^2 + 3t$
Express $z$ in terms of $x$ and $y$.
