# intersection

1. ### Intersecting reciprocal trig functions

Hi, I hope someone can help. I'm trying to understand intuitively why y=cscx intersects y=secx at (pi/4, 1.414) and (pi/4, -1.414)? Can someone please explain why? I noticed that the parent functions of both reciprocals intersect at (pi/4, 0.707) and (pi/4, -0.707). I also noticed that 1.414...
2. ### More Friendly "Optional" Proof Questions - Part 1

Let A, B, C⊆ U. Assume (A∩C) ⊆B. Show that (A - B)⊆ (A - C). So here is what I have so far: "Let L= A-B and R=A-C. For A-B⊆ A-C, then L⊆R. Show L⊆R. Assume XeL, and let XeA. Either XeA or X∉B." My question (among looking for a clear cut proof) is should I actually start by stating that because...
3. ### Rectangle Intersection

Hello All, I'm doing a coding challenge in which I have to write a formula that returns the intersection of two rectangles. But before I do that, I want to attempt this mathematically. Can anyone provide resources to familiarize myself with on how to calculate the intersection of two...
4. ### Help with union and intersection problem

Hi all, I'm struggling with a problem like this: Let E, F and G be three events in S with P(E) = 0.4, P(F) = 0.56, P(G) = 0.45, P(E ∩ F) = 0.22, P(E ∩ G) = 0.17, P(F ∩ G) = 0.21, and P(E ∩ F ∩ G) = 0.12. Find P(EC ∪ FC ∪ GC). P(EC ∪ FC ∪ GC) = ? For whatever reason, I can't figure this out. I...
5. ### the intersection number between a trivial loop and a meridian in the torus

Let A and B be two closed curves intersect on the torus transversally at a point, the intersection index of the crossing point is defined to be positive if the tangent vectors to A and B form an oriented basis for the tangent plane of the torus and negative otherwise. Then the intersection...
6. ### Intersection between 2 Planes

I need to find the vector equation that describes the intersection between the plane 121x+115y+12 674 660z=-890383 and the plane z=0. I understand how to find intersections of 2 planes using matrix row reduction, but the z=0 part threw me off. Any help would be greatly appreciated. Thanks I
7. ### Intersection between Bezier curve and Line segment

Hi, I'm trying to find the intersection between a Bezier curve and line. I have the parametric equation for a quadratic Bezier curve: X(t) = (1-t)^2X_0 + 2t(1-t)X_1 + t^2X_2\\ Y(t) = (1-t)^2Y_0 + 2t(1-t)Y_1 + t^2Y_2 I know the control points for the curve. I have the equation for a line...
8. ### Intersection points between circle and parabola

Hello, I'm trying to find how many points a certain circle and parabola intersect (see attachment). Equation for circle is x^(2) + y^(2) =9 and for the parabola y=(x+3)^(2) -2. The answer is 2. Without a graphing calculator, what is a simple way to solve this? I set the equations equal to one...
9. ### Intersection proof

"Consider the set S of those rational points of the open interval (0,1) obtained by dividing the interval into two equal parts, then dividing each of these two intervals into two equal parts and so on. More precisely, let S = U(n=1 to infinity) Sn where Sn = {k/2^n | k = 1, 2, ... , 2n-1}. T =...
10. ### Determining cone to spherical triangle intersection

I have a sphere (x+x0)^2 + (y+y0)^2 + (z+z0)^2 = 1 formed of spherical triangles. The initial position of the sphere is not defined. Each triangle is determined by 3 normalized vectors (literally spherical triangle is part of a sphere bounded by three planes coming out of the sphere center)...
11. ### Intersection of infinite collection of sets

$A_n=\{n,n+1,n+2,...\}$ Can't see how it follows from the last sentence. Can someone explain?
12. ### line of intersection between two parallel planes

How can I find the line of intersection between the planes 2x-y+2x+1=0 and -4x+2y-4x-2=0 I realize these are parallel as they are multiples of each other, but I'm not sure how to solve for the point. I also have to convert this line into parametric, cartesian and vector form. Sorry for the...
13. ### How to find intersection of moving circle and line

Say I have a point, with position (x1,y1) at time t=0, with velocity dx1 and dy1 in the x and y directions respectively, which may or may not collide with a circular entity with radius r, centered at (x2,y2) when t=0, with speed dx2 and dy2. How do I find the time, and point of collision? I've...
14. ### Finding the intersection points on the graph y=sinx, y=cosx and y=tanx

Hi guys, I'm new to this site and it seems like it will be a great resource when I'm stuck on a problem. I'll firstly set out the question and then add in my working so far. Question: I was firstly asked to graph the trigonometric functions y=sinx, y=cosx and y=tanx in the interval where x is...
15. ### Contingency and the intersection of two events.

Hi everybody, Here is my problem: I am being asked to solve P(R|C). C=number of patients who have completed treatment, and R=number of return patients. However, my understanding is that I need to know the intersection of P(C) and P(R) in order to solve P(R|C). But, to solve for the...
16. ### Ti-89 Titanium: Saving an intersection point. Then using exact(ANS)

I was having an issue with transferring a data value from the [Graph] app of intersecting curves to the [Home] app on the TI-89 Titanium. Previously on my TI-83 Plus would accomplish this task seamlessly. Example: Y1= 1+sec(x) Y2= 3 [2nd] [Calc] [5] [First Curve] [Second Curve] [Guess]...
17. ### The intersection of 2 Generalized Eigenspaces

Suppose and with . Prove that . So far I've attempted the proof by contradiction, letting thus and . I'm stuck after this point, please don't solve the problem for me just hints would be fine.
18. ### interpretation of curve of intersection

I would like to understand the idea of a 'curve of intersection' in $\mathbb{R}^{3}$. Say we are given a surface $z = x^{\frac{1}{3}}y^{\frac{1}{3}}$ and a plane $y = x$. Then the curve of intersection is obtained by substituting $y=x$ into $z = x^{\frac{1}{3}}y^{\frac{1}{3}}$, thus we get \$z =...
19. ### Curve of intersection

Hi I have this equation \theta(x)=\bar{\theta}+\theta_0\cos\left(\omega t + \phi -Kx\right)\exp\left(-Kx\right) Where I need to find the value of x where \theta never falls below zero. I have the actual values for the constants. How would I find the curve of intersection of the z=0 plane...
20. ### Intersection of a closed convex set

Let X be a real Banach Space, C be a closed convex subset of X. Define Lc = {f: f - a ∈ X* for some real number a and f(x) ≥ 0 for all x ∈ C} (X* is the dual space of X) Using a version of the Hahn - Banach Theorem to show that C = ∩ {x ∈ X: f(x) ≥ 0} with the index f ∈ Lc under the...