Intersection Definition and 712 Threads

Does anyone know how to determine whether two ellipses intersect? I don't need the precise points but rather only the answer whether there are points. All my attempts led to 4th order polynomials, which are heavy to solve, but considering that I don't need the actual points I assume there must...

Homework Statement A solid has a circular base of radius r=4. Find in each case the volume of the solid if all intersection between the solid and a plane perpendicular to a set diameter is: a) A square b) A triangle rectangle isosceles which one of its sides is on the circular base. The...

I'm having a little trouble distinguishing the line between what the f.i.p implies and what it does not. **EDIT2** Hopefully this will make things more clear What I'm really interested in is a formal definition of the f.i.p regardless of the set in question or the field. Given the sequence...

Homework Statement P1 = 3x+4y=1 P2 = x +y -z=3 Find the intersection. Homework Equations x = x0 +at y = y0 + bt z = z0 + ct The Attempt at a Solution I used a quicker method. I first did P1 x P2 and got its cross product <-4,3,-1> Then I followed what our teacher had shown us in class -...

I'm working on tracing the beam path of a HeNe laser through two prisms, and I'm stuck on trying to find the incident plane in which to use Snell's law. Basically I have the equation of the angled surface of the prism, and I have the point where the beam intersects that plane. Now I need the...

I know that intersection tests can typically (for hit detection in games) be computed in log n time with reasonable accuracy, but there is a problem that I see with using hierarchical bounding volumes in ray tracing. For example, a ray may intersect a bounding volume however due to the shape...

I have been asked if the following is true or false the intersection of two connected sets is connected ? I would have thought that if their intersection was empty they wouldn't be connected. If they were disjoint or course it would be empty. any ideas?

Homework Statement find the area inside both of the curves r = 4 cos@ r = 2+2cos@ @ = theta Homework Equations ------- The Attempt at a Solution i will say 4cos@ = 2+2cos@ to find the intersection points 4cos@ = 2+2cos@ 2cos@ = 2 cos@ = 1 @ = 0 ! I need the other points!

Let G_{n} = (-1/n,1/n) for all n in N let G= \bigcap^{\inft}_{n=1}

Hello all, I am neither a physicist nor a mathematician, I am an archaeologist trying to develop a mathematical model for archaeological site detection. The problem is set up like this (and hopefully this will make some sense): The detector moves in parallel transects that can be of any...

Homework Statement Prove that r1 and r2 intersect at (1,1,3). Let r1 and r2 be defined as: r1(t)=t^2i+tj+3t^3k r2(t)=(t−1)i+(1/4)t^2j+(5−t)k Homework Equations Intersection is derived from r1=r2. The Attempt at a Solution I only formally get to this point and then start...

Homework Statement Find the equation of the plane that passes through the line of intersection of the planes 4x - 3y - z - 1 = 0 and 2x + 4y + z - 5 = 0 and passes through A(1, -3, 2). Homework Equations N/A The Attempt at a Solution I have no clue on how to start this question...

Can you please give me formulas which give intersection of two gaussian function f(x, mu, sigma) = 1/sqrt(2*pi*sigma^2) * exp(-(x-mu)^2 / (2*sigma^2)) for the case variances are different. (Note: I think it is time I learn how to use "tex" tags, do you know a good tutorial?)

Homework Statement Find the slope of the tangent line to the curve of intersection of the vertical plane x - y + 1 =0 and the surface z = x2+y2 at the point (1, 2, 5) Homework Equations Gradients, Cross products The Attempt at a Solution I'm pretty lost here. I think I have to...

Homework Statement Does the surface z = x^2 + y^2 - 4 * intersects the yz -plane? If so, find the equation of the curve and write down the points of intersection. The Attempt at a Solution yz-plane, so x=0 1) * becomes z = y^2 - 4 and this is the equation of the curve that intersects...

Homework Statement Let S be the solid region bounded by the paraboloid z = x^2 + y^2 - 4 for z \le 0 , 0 \le x \le \sqrt{4 - y^2} and 0 \le y \le 2 . Find the Cartesian equations of the curves if the surface S intersects the xy,xz , and yz planes. The Attempt at a Solution...

Hi, everyone: How do we show that 2 planar surfaces in R^4 intersect at points (possibly empty sets of points, but not in lines, etc.). I am curious to see how we justify the Poincare dual of the intersection form in cohomology being modular, i.e., integer-valued...

Homework Statement Use a dounble integral to find the area of the region inside r = 1+ cos (theta) and outside r = 2sin (theta). sketch region and indecate the points of intersection. I'm confused how to find the points of intersection of these two equations Homework Equations I've...

Homework Statement Suppose that a group G has a subgroup of order n. Prove that the intersection of all subgroups of G of order n is a normal subgroup of G. Homework Equations The Attempt at a Solution I know that I need to do the following: Let S be the set of all subgroups of...

Homework Statement Show that the following pairs of lines intersect. Determine the coordinates of the point of intersection. L1: r= (-3,-1) + t(3,4) L2: r= (6,2) + s(3,-2) Homework Equations ? The Attempt at a Solution I know that eventually the two lines will reach the...

Homework Statement Find the parametric equations of the line tangent to the curve of intersection of the paraboloid z = x² + y² and the ellipsoid 4x² + y² + z² = 9 at the point ( -1, 1, 2 ). Homework Equations Probable use of the gradient vector (as this is the chapter we are in)...

Homework Statement I have to find all of the points of intersection of the curves... r2 = sin(2θ) r2 = cos(2θ) The Attempt at a Solution sin(2θ) = cos(2θ) 2sinθcosθ = cos2θ - sin2θ 2sinθcosθ - cos2θ = -sin2θ cosθ(2sinθ - cosθ) = -sin2θ This is where I'm having a problem, I'm...

Homework Statement Given a common intersection point (3,4,5), find 3 different planes. Homework Equations None The Attempt at a Solution What I did is let a1x+a2y+a3z=a b1x+b2y+b3z=b c1x+c2y+c3z=c 3=Dx/D 4=Dy/D 5=Dz/D I set D=2, therefore Dx=6 Dy=8 Dz=10...

Homework Statement I have to find the area of the region that lies inside the curves: r = sin(θ) r = sin(2θ) The Attempt at a Solution I'm assuming the first step would be to find the points of intersection so I know WHERE to integrate from/to, so I set the equations equal to each...

Homework Statement Find the centre of circle X2 + y2 + 4x – 16y + 18 = 0, show it's radius is 5√2 and find the co-ordinates where it is intersected by y = 3x - 6 Homework Equations The Attempt at a Solution X2 + y2 + 4x – 16y + 18 = 0 by completing the square using X2 + 2px = (x...

Homework Statement Find the point of intersection of two lines x = -9 + 5t y = 1 + t z = 10 - 4t and x = -2 -3t y = 5 + 2t z = 5 + 3t Homework Equations N/A The Attempt at a Solution I have read that you should set two of the equations equal to find the value of t, and...

Homework Statement |2x-1|+|x+2|\geq 4x Homework Equations The Attempt at a Solution For x<-2 , -(2x-1)-(x+2)\geq 4x x\leq -\frac{1}{7} For x\geq \frac{1}{2} 2x-1+x+2\geq 4x x\leq 1 For -2 \leq x < \frac{1}{2} , -(2x-1)+x+2\geq 4x x\leq \frac{3}{5} after...

Homework Statement Prove true: For any subspaces U,V of R^n dim(U intersect V) <= min(dim(U), dim(V)) Homework Equations Min(a,b) = the minimum value of A and B The Attempt at a Solution I know this statement is true however I can't quite figure out where to start on how to...

So for my homework I have to prove (or disprove) this statement: If U, V are two subspaces of Rn then U \cap V \neq \phi. I just want to make sure; \phi is the null set right? The set with nothing in it?

Homework Statement Find the parametric equation for a line of intersection of these two planes x+2y+3z=0 4x+5y+6z=5 Homework Equations Normal to plane 1= <1,2,3> Normal to plane 2= <4,5,6> The Attempt at a Solution I know the way to do this problem is to take cross product of...

Homework Statement Suppose L, M, and N are subspaces of a vector space. (a) Show that the equation L \cap (M+N) = (L \cap M)+(L \cap N) is not necessarily true. (b) Prove that L \cap (M+(L \cap N))=(L \cap M) + (L \cap N) Homework Equations N/A The Attempt at a Solution...

A couple of months ago I was pulled over by a police officer for running a stop sign. The officer claimed I "plowed right through" the stop sign. I honestly had no idea what he was talking about but wasn't about to argue with a cop. I realized after going back to check the intersection after...

L1: r(t) = (-5 + 2t)i + (5 + t)j L2: r(t) = (3 + 4t)i + (4 - 8t)j I know that they are perfendicular but how do I go about finding the point of intersection?

Homework Statement The starting position of a particle in R3 is (1,1,1) and it's traveling with constant velocity (2,-1,1). Where does it hit the plane {(x,y,z)|x - 2y + z = 4}. And find the angle between the path of the particle and the plane. Homework EquationsThe Attempt at a Solution

Hi everybody! I have a question, if I have A and B simply connected subspaces of a geodesic space X, what can be said about their intersection? When is it simply connected? Are there rules for this? I need to prove it in a special case, but I am not able to do it and I was wondering if...

Homework Statement Consider the intersection between the following two planes given in parametric form: P1 : x = [2, 4. 3] + s1[1, 2, 1] + s2[2, 5, 4] P2 : x = [1, 0, -5] + t1[3, 8, 7] + t2[2, 1, -5] Find the intersection of the two planes as a line in parametric form. Homework...

Homework Statement Find the point of intersection Homework Equations Equation 1 y=1/5(2)4x-7 Equation 2 y=1/10(1/2)9-3x The Attempt at a Solution Made them equal each other got rid of the 1/5 one one side and it made the 1/10 turn into 1/2 and now i don't know...

i have the following double arrays: 165 7077 165 7045 165 5175 168 7305 168 3487 169 6196 169 10213 170 7048 165 7077 165 7045 168 5175 169 7305 169 3487 170 6196 170 10213 170 7048 how do i obtain the number and percentage of common values in column 2 of array1 and array2...

Homework Statement prove that (U\bigcapW)^{\circ}=W^{\circ}+U^{\circ} First prove That (U\bigcapW)^{\circ}\supseteqW^{\circ}+U^{\circ} Take any f\in (U\bigcap W)^{\circ} Then it is easy to see that for any f\in (U\bigcap W) f(v) =0 but since v\in U and v \in W then f \in...

Hey Guys. I have some questions about vector spaces, I would really apreciate if somone could read this and let me know if I understand things or not, and if not let me know where I have it wrong. I am having a lot of trouble UNDERSTANDING how to find the intersection of two vector spaced...

Consider the intersection of the sphere (x-3)^2+(y+2)^2+(z-1)^2=13 with the plane x+y=0 a) This intersection should be a familiar curve. Describe the curve. b) Substituing x=-y or y=-x into the equation of the sphere does not give this curve. Explain the difference. I know that the...

Homework Statement y=x-x^3 y=0 Must find intersection points by way of the x-axis Homework Equations The Attempt at a Solution I know you have to set them equal to each other i just do not know what to do from there.

Homework Statement f(x) = 2x2-5x-12 is given; part a: find derivative of f(x) using first principles, part b: find the rate of change of f(x) at x=1, part c: the points at which the line through (1, -15) with slope m cuts the graph of f(x), part d: the value of m such that the points of...

Is it correct that the angle of intersection of two curves is the same in x,y coordinates as in r,theta coordinates? If so, why is this?

Homework Statement Find an equation of the plane that passes through the point (-1,2,1) and contains the line of intersection of the planes x + y - z = 2 and 2x - y + 3z = 1 Homework Equations Equation of a plane: a(x-x0) + b(y-y0) + c(z-z0) = 0 The Attempt at a Solution n1 =...

Homework Statement Note the picture... 11. Two cars approach an intersection as shown. Car 1 weighs 4500 lbs and has a speed of 55.0 mi/hr. Car 2 weighs 3750 pounds with a speed of 60.0 mi/hr. They collide in a completely inelastic collision at the intersection. a) Calculate the...

Here's a math problem that's giving me a head ache (though to some of you it might seem to be quite trivial) r,s\in N^\ast , r+1\leq s ; |A_i|=r, \forall i\in \{1,2,...,s\} the intersection of any r+1 of sets A_i is nonempty [1] prove that \bigcap_{i=1,s} A_i \neq \emptyset [C]...

the graph of y=kx+3 intersects the graph of y=x^2 +8x at two distinct points for 'k 'equals what? to be honest I do not know where to start

Homework Statement Find the tangent vector at the point (1, 1, 2) to the curve of intersection of the surfaces z = x2 + y2 and z = x + y. Homework Equations The Attempt at a Solution I haven't started the problem, because I'm not sure what the first thing to do is. Do I have to parametrize...

How do I find this?