Ray W
2022-07-28

You can still ask an expert for help

asked 2021-06-11

Find the area of the parallelogram with vertices A(-3, 0), B(-1, 5), C(7, 4), and D(5, -1).

asked 2021-03-01

Parametric equations and a value for the parameter t are given $x=(60cos{30}^{\circ})t,y=5+(60sin{30}^{\circ})t-16t2,t=2$ . Find the coordinates of the point on the plane curve described by the parametric equations corresponding to the given value of t.

asked 2021-10-30

Find the lengths of the sides of the triangle PQR. Is it a right triangle? Is it an isosceles triangle? P(3, -2, -3), Q(7, 0, 1), R(1, 2, 1)

asked 2022-07-01

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 parameter."

$x=\mathrm{sec}\theta \text{and}y=\mathrm{cos}\theta $

In the answer key, $0\le \theta <\pi /2$ and $\pi /2<\theta \le \pi $. What about the angle on the unit circle that are in the third and fourth quadrant?

Also, in the answer key, $|x|\ge 1$ and $|y|\le 1$. Why are x and y restricted in such a way?

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 parameter."

$x=\mathrm{sec}\theta \text{and}y=\mathrm{cos}\theta $

In the answer key, $0\le \theta <\pi /2$ and $\pi /2<\theta \le \pi $. What about the angle on the unit circle that are in the third and fourth quadrant?

Also, in the answer key, $|x|\ge 1$ and $|y|\le 1$. Why are x and y restricted in such a way?

asked 2022-06-15

The cubic Bezier curve can be given in matrix form as

$P(u)=({u}^{3}\text{}{u}^{2}\text{}{u}^{u}\text{}1)\left(\begin{array}{cccc}-1& 3& -3& 1\\ 3& -6& 3& 0\\ -3& 3& 0& 0\\ 1& 0& 0& 0\end{array}\right)\left(\begin{array}{c}{P}_{0}\\ {P}_{1}\\ {P}_{3}\\ {P}_{4}\end{array}\right)$

If a cubic Bezier curve is rotated by an angle 30 around x-axis what is the parametric function of the new Bezier curve?

$P(u)=({u}^{3}\text{}{u}^{2}\text{}{u}^{u}\text{}1)\left(\begin{array}{cccc}-1& 3& -3& 1\\ 3& -6& 3& 0\\ -3& 3& 0& 0\\ 1& 0& 0& 0\end{array}\right)\left(\begin{array}{c}{P}_{0}\\ {P}_{1}\\ {P}_{3}\\ {P}_{4}\end{array}\right)$

If a cubic Bezier curve is rotated by an angle 30 around x-axis what is the parametric function of the new Bezier curve?

asked 2021-08-16

Let C be the curve described by the parametric equations x(t)= t, y(t) =$t}^{3$

a) sketch a graph of C

b) find the vector-valued function f(t) associated with this parameterization of the curve C.

a) sketch a graph of C

b) find the vector-valued function f(t) associated with this parameterization of the curve C.

asked 2020-11-23

Find the coordinates of the point on the helix for arc lengths $s=\text{}\sqrt{5}\text{}and\text{}s=4$ .
Consider the helix represented investigation by the vector-valued function
$r(t)=\text{}\text{}2\text{}\mathrm{cos}\text{}t,\text{}2\text{}\mathrm{sin}\text{}t,\text{}t\text{}$ .