Tagged Questions
1
vote
2answers
23 views
Prove using an example that there is no plane on R3 that contains every group of 4 points
Well, this is a homewrok question (which I know I should not be asking, but I cannot find an answer to this anywhere):
The exercise is as follows:
i) Find the equation of the plane of R3 that ...
2
votes
2answers
34 views
Parameterized curve describing trajectory of thrown object
We describe the trajectory of a thrown object (neglecting friction and similiar effects) with the curve
$$k(t) = \left(v_0\cos(\beta)t,\,v_0\sin(\beta)t-\frac{g}{2}t^2\right)$$
with ...
0
votes
0answers
87 views
Show that the tractrix is orthogonal to certain half-circles
Show that the tractrix discussed in Example 1.17 is orthogonal to the lower half of each circle with radius $a$ and center on the positive $y$-axis.
Example 1.17:
...
1
vote
1answer
197 views
Find the area of the region determined by two curves
Find the area of the region $R$ given by two curves.
So the region $R$ describes the area that is common between the two curves:
$$\begin{align*}
\text{Function 1: } r&= 2\sin(\theta)\\
...
5
votes
2answers
669 views
Is $r=2\cos(\theta)$ a one-petal polar function?
I'm currently learning about polar functions and their graphs in precalculus, and one of the questions on my homework is to identify the shape of the function $r=2\cos(\theta)$. We were taught that ...
1
vote
0answers
103 views
Vector equation and curvature
Vector equation
$r(t)=2\cos(t)\mathbf i + 3\sin(t)\mathbf j\ \ (0 \le t \le 2\pi)$
represents ellipse.
I need to find curvature of this ellipse on endpoints of x and y axis that are given with ...
6
votes
2answers
239 views
Need help with Curves and parameterizations
I'm having some trouble solving a couple of problems:
I know this one must be pretty easy but can't find the way to solve it.
I need to find the arc length of a curve described by $ r=1- ...
