0
votes
1answer
31 views

Radial velocity

I need to calculate the radial velocity ($v_r$) of an object to another. For this I have the cartesian coordinates ($X_n$,$Y_n$,$Z_n$) and cartesian velocities, ($\dot{X_n}$,$\dot{Y_n}$,$\dot{Z_n}$) ...
1
vote
2answers
94 views

Help with the proof of the Witch of Agnesi curve

$a=1$ (The radius is 1). How do I prove that if we talking about $P=(x,y)$, then: $$y=\frac{8}{x^2+4}$$ I'd like to get any help! Thank you!
0
votes
1answer
55 views

Proof: The coordinates of the witch of Agnesi curve

I need to prove that the coordinates ofthe witch of Agnesi curve is: $$x=2a\cot \theta$$ and $$y=2a\sin ^2 \theta$$ Any idea how to prove it? And I don't understand how we got $a$... (because the ...
2
votes
3answers
106 views

Find radius of a circle which is tangent to three known lines

I need to find the equation for a circle which is tangent to the following three lines: y=0 x=0 y=-x+0.338334 For the last tangent line equation, I know that it is tangent at the point (0.169167, ...
2
votes
0answers
64 views

Quadratic equation and trig

If the quadratic equation $ax^2+bx+c=0$ has equal roots where $a, b$ and $c$ denote the lengths of the sides opposite to vertices A, B and C of a triangle ABC respectively, then find the sum of ...
1
vote
1answer
34 views

How to properly sort a set of axis-aligned boxes so they are drawn correctly under this projection?

Given a set S of axis-aligned, non-overlapping boxes {x,y,z,w,h,l}, where x,y,z are their center-positions and w,h,l their width, height and lengths, and given the following orthographic projection: ...
0
votes
0answers
71 views

Torus equation in terms of tangent

So if I have an equation for a torus in $F(a,b) = (X, Y, Z)$ where $X = (R + r\cos a)\cos b$ and $0 < r < R$, how would I go about rewriting this equation for $X$ in terms of $\tan(a/2)$ and ...
0
votes
1answer
412 views

Get Angle to Tangent that Intersects Point

I have a circle around a given point, call this point $(x_1, y_1)$. I know the radius of the circle around this point. I also have a second point $(x_2, y_2)$, that is a distance away, outside the ...
2
votes
2answers
122 views

Did I write the right “expressions”?

$9$. Consider the parametric curve $K\subset R^3$ given by $$x = (2 + \cos(2s)) \cos(3s)$$ $$y = (2 + \cos(2s)) \sin(3s)$$ $$z = \sin(2s)$$ a) Express the equations of K as polynomial ...
0
votes
2answers
212 views

Move an object along a straight path on an angle

I have an object at $x,y$ and I want it to move along a straight line on an angle of roughly $65^\circ$ and I know what the different of $X$ is but I do not know what the $Y$ should be. So for ...
50
votes
1answer
3k views

Trigonometric sums related to the Verlinde formula

Original question (see also the revised, possibly simpler, version below): Let $g > 1, r > 1$ be integers. Playing around with the Verlinde formula (see below), I came across the expression ...