Tagged Questions
0
votes
5answers
37 views
Parametric equations for given line
How would you find the parametric equations for:
1) a line through $(3,1)$ and $(-5,4)$.
2) a segment joining $(1,1)$ and $(2,3)$.
Can anyone show me the steps of doing it cause the way my textbook ...
5
votes
2answers
36 views
Parametrizing a given line and equations
1) Parametrizethe given line contraining the points (3,2) and (-5,6).
2) Find the parametric equations for the segment joining the given points (2,3) and (5,5) where $0\leq t \leq 1$.
...
3
votes
1answer
61 views
Find the second derivative ${{{d^2}y} \over {d{x^2}}}$ in terms of t when $x = 3 - 2{t^2}$ and $y = {1 \over t}$
This is my attempt:
$\eqalign{
& x = 3 - 2{t^2} \cr
& y = {1 \over t} \cr
& {{dx} \over {dt}} = - 4t \cr
& {{dy} \over {dt}} = - {t^{ - 2}} = {{ - 1} \over {{t^2}}} ...
1
vote
1answer
18 views
position question from velocity and given point.
A particle moves along the $x$-axis so that at any time $t\geq 0$, its velocity is given by $v\left(t\right)=\sin\left(2t\right)$. If the position of the particle at time $t = \frac{\pi}{2}$ is $x = ...
1
vote
0answers
28 views
Vector Tangent to Curve of Intersection
I am having problems solving this.
Find a vector tangent to the curve of intersection of $z = 4x^2 + y^2$ and $z=(27-x^2-y^2)^{1/2}$ at the point $(1,1,5)$.
I'm able to do this kind of thing using ...
1
vote
3answers
43 views
How to take parametric equations (x, y) to create a derivative formula?
I always thought that if I take the derivative of the y and x equation and divide y' by x', then that would be the derivative in formula form.
Is this correct?
1
vote
1answer
37 views
Parameterization of the surface a torus
For a calculus question I have I need to parameterize the surface of the torus generated by rotating the circle given by $(x-b)^2+z^2=a^2$ around the z-axis (with $0<a<b$).
I've had a go at ...
0
votes
0answers
35 views
parametric equation derivative question: can someone help me understand this question?
I am given $x$ and $y$ coordinates in parametric form with equations...
$x(t)$ and $y(t)$.
The questions asks to calculate $f'(x)$ for when $x = x(2\pi/5)$.
Now am I first to calculate the ...
0
votes
1answer
33 views
Parametric problem: do these 2 comets collide. Am I solving this correctly?
$\text{comet1} = x_1(t), y_1(t)$
$\text{comet2} = x_2(t), y_2(t)$
set $x_1(t) = x_2(t)$ and solve for $t$. Since $t$ had a square, I had 2 possible values for $t$ ($t_1$ and $t_2$).
substitute ...
3
votes
2answers
116 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 $b<a$.
...
4
votes
1answer
28 views
Parametric plots: Determine if 2 comets collide at a given time. Am I solving it correctly?
There are $2$ comets
comet 1 $(x(t), y(t))$,
comet 2 $(x_1(t), y_1(t))$
I need to determine if these two comets collide. From reading my steps below, is this the proper way to solve this?
$1.$ set ...
1
vote
1answer
40 views
Parametric motion question
What exactly happens when both $\frac{\mathrm{d}y}{\mathrm{d}t}$ and $\frac{\mathrm{d}x}{\mathrm{d}t}$ equal zero?
I know that if $\frac{\mathrm{d}y}{\mathrm{d}t} =0$ then its a vertical tangent with ...
1
vote
1answer
63 views
How to calculate a double integral over a triangle by transforming to polair coordinates & by using a transformation
Let T be the triangel with vetrices $( 0,0 ) , ( 1,0 )\mbox{ and } ( 0,1 ) $. Evaluate the integral :
$$
\iint_D e^{\frac{y-x}{y+x}}
$$
a) by transforming to polar coordinates
b) by using the ...
0
votes
0answers
27 views
0
votes
1answer
43 views
Line integrals of vector fields
Consider the vector field:$$\vec G = \left(\frac y{x^2+y^2}, \frac {-x}{x^2+y^2}\right)$$ compute $\int_\Gamma \vec G$ where $\Gamma$ is the proportion of a parabola $y=a(x-1)^2$ from (1,0) to (2,a). ...
1
vote
1answer
52 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 ...
0
votes
2answers
34 views
what's the algebra (if any) behind converting f(x) for a circle to a parametric equation
I'm sure there has to be some algebra behind it. My problem called to covert
$$(x - 2)^2 + (y - 9)^2 = 4$$
if $x = 2 + 2cos(t)$
then $y = ? $
I know the answer is $9 + 2\sin(t)$ but I simply got ...
4
votes
3answers
293 views
Writing Polar Equations In Parametric Form
For an example problem, in my textbook, the author wanted to demonstrate how to graph a polar function. Deeming it most convenient, my author took the polar function $r=2\cos 3\theta$, and re-wrote it ...
0
votes
1answer
118 views
Arc Length Of Parametric Curve
I attached the problem as a file:
Where did the trig functions go? I sifted through the different trig identities and formulas, but couldn't find anything that I could use. What should I do?
2
votes
2answers
605 views
Finding Where A Parametric Curve Intersects Itself
The problem I am working on is to find the where the curve intersects itself, using the parametric equations.
These are: $x=t^2-t$ and $y=t^3-3t-1$
For the graph to intersect itself, there must be ...
2
votes
1answer
680 views
Finding Where A Parametric Curve Crosses Itself
The parametric functions I am dealing with are: $x=2\sin2t$ and $y=3\sin t$
I know for a parametric graph to cross itself, there must be two distinct $t$, $t_1$ and $t_2$, that when placed into the ...
1
vote
1answer
209 views
Finding Parametric Equations For A Rectangular Equation
I am trying to find a general way of finding parametric equations for a rectangular equation.
The problem I am working on is $y=x^3$, and I have to find two examples of parametric equations. ...
1
vote
2answers
102 views
Parametric Equation Problem
The problem is, "to determine any differences between the curves of the parametric equations. Are the graphs the same? Are the orientations the same? Are the curves smooth? Explain."
(a) $x=t;\quad ...
1
vote
1answer
63 views
Restriction Of Parametric Functions Domain
The problem I am working on is, "Sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by
eliminating the ...
0
votes
0answers
63 views
complex circular motion
Assume the planet orbits its star in a circular orbit of 100 units with period 360 days. The moon in turn orbits its planet at a radius of 10 units and period 28 days. Finally the moon rotating, we ...
0
votes
1answer
57 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 ...
0
votes
1answer
223 views
Find the area bounded by the parametric curve…
Find the area bounded by the parametric curve $x = \cos(t)$, $y = e^t, 0 < t < \pi/2$, and the lines $y = 1$ and $x = 0$.
I do not even know where to start with this problem. I know that I need ...
0
votes
1answer
80 views
How do we find the length of the line (parametric curve)?
A curve in the $xy$-plane is given parametrically by
$$x(t) = e^{2t}, \quad y(t) = e^{2t} \sin(2t), \quad t \in [0, \pi/2].$$
What is the length of this curve?
Ok, actually I know what to do, ...
1
vote
2answers
102 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 ...
0
votes
1answer
119 views
variation problem of constrained area and minimized distance
$$c=\int_{x_1}^{x_2}f_{gr}(x)\;dx$$
The integral is a time-like curve between $x_1$ and $x_2$ and at imagine fgf(x1) is a lower left corner of the rectangle and fgf(x2) is the upper right corner and ...
1
vote
2answers
110 views
Stuck on space curves for vector valued functions
I'm working through the James Stewart Calculus text to prep for school. I'm stuck at this particular point.
How would you sketch the graph for the parametric equations:
$x = \cos t$, $y = \sin t$, ...
4
votes
4answers
830 views
Arc Length Problem
I am currently in the middle of the following problem.
Reparametrize the curve $\vec{\gamma } :\Bbb{R} \to \Bbb{R}^{2}$ defined by $\vec{\gamma}(t)=(t^{3}+1,t^{2}-1)$ with respect to arc length ...
2
votes
2answers
2k views
Polar to Parametric Equation?
I'm struggling with this problem, I'm still only on part (a). I tried X=rcos(theta) Y=rsin(theta) but I don't think I'm doing it right.
Curve C has polar equation ...
2
votes
1answer
445 views
Equation for control point distance for fixed-length cubic Bézier path (with specific constraints)
A particular Stack Overflow question asks how to construct a specific cubic Bézier path of constant length. I have experimentally determined the ideal distances of the control points from the nearest ...
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 ...
0
votes
2answers
660 views
How to find a smooth parametrization of a Curve
In order to solve a line integral, I need to establish a smooth parametrization of the curve over which it is supposed to be integrated.
The curve, $D$, is the intersection of the surfaces $x^2 + ...
0
votes
2answers
220 views
Parametrization of curve length in D dimensional space. How is it done?
Sorry, its been a while and my calculus was never good. This is really a very elementary question which I am unable to un -complicate from its shroud of notation. My difficulty is how does this ...
1
vote
3answers
137 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 $y$.
1
vote
1answer
366 views
Parameterization of an implicit function
I'm trying to find the area of an irregular domain that is bounded by $x = c$, $y = c$, and $c = -A\sin(x/2)\sin(y/2)+\cos(x/2)\cos(y/2)$, where A can vary in the range [-1,1], and x and y are only ...
7
votes
3answers
1k views
Parametrization of a line
This is a very basic question, and its funny that I'm able to solve more advanced problems like this, but I was presented with a basic one and got stumped. I have the equation
$$y=-\frac{3}{4}x+6.$$
...
2
votes
2answers
341 views
Reparametrizing a curve in terms of the arc length
We want to reparametrize the curve
$$\displaystyle \vec{r}(t)=<t^3+1, t^2-1, \frac{\sqrt{5}}{2}t^2>$$
in terms of the arc length measured from the point t=0 in the direction of increasing t.
...
