# axis

1. ### Radical Axis of 3 circles...

Can someone help me with this. Suppose you have 3 circles and you find the radical axis of each of these. Apparently the 3 radical axes intersect at a unique point. Q1: why? and Q2: Apparently there is a unique circle ( centre point intersection of radical axes) which is orthogonal to each...
2. ### Potential V and E field of 2 rings of charge on x axis

there are 2 rings of charge, radius R on the x axis separated by a distance R, find the potential and E field. so don't you have to calculate the field to the left of the 2 rings, in between the 2 rings and to the right? I get these answers for the E field which by symmetry points only on the x...
3. ### Surface area of a curve about the y axis

the equation is . I found that x=sqrt(1-y) and that x'=-1/(2*sqrt(y-1)). I've been using integral(2*pi*x*sqrt(1+x'^2)) but i keep just getting mixed up with my calculations. help would be appreciated.
4. ### Angle of rotation and axis of rotation of a 3x3 matrix

Hi, I've been given a matrix X which is a 3x3 rotation matrix entries 2/3 -2/3 -1/3 1/3 2/3 -2/3 2/3 1/3 2/3 And I've...
5. ### translating world rotation values to local rotation axis

Hi all, I'm in a bit of a pickle. I am not a mathematician so be gentle with me. I have a problem with world and local rotation values in 3D software - I think the maths behind it uses quaternions. What I am trying to achieve is to find out whether a foot is twisted inward (onto the instep) or...
6. ### length of large and small axis of the ellipse

I need to calculate this elipse: $c^2=4x_1^2+3x_2^2-2\sqrt2{x_1x_2}$ 1. c2=1 2. c2=4 I need to calculate direction and the length of large and small axis of the ellipse. (hint: own vector and Eigenvalues) Thanks for your help. :)
7. ### Choosing axis when setting up Linear Inequality

Hi, I have a word problem that asks to set up an inequality and find possible solutions. I am able to get the right answer but have a questions about the axis. I am setting the inequality as S <= 30-6D. When I place S on the y axis, I get the same answer as the book. However, when I flip it and...
8. ### an Inquiry about principal angel and euler axis of eigen value nd eigen vector

I have the eigenvalues and eigenvectors of a transformation 3*3 matrix and on of the eigenvalues is zero I need to get the Euler axis and principal rotation angel, phi, may anyone help me in finding them and also what would be the corresponding Euler angles and elementary rotation matrices...
9. ### At least two circles tangent to y axis with nonempty intersection

Hi. Here is a problem I've been trying to solve for some time now. Maybe you could help me. We have two sets \mathcal {Q} is a set of those circles in the plane such that for any x \in \mathbb{R} there exists a circle O \in \mathcal {Q} which intersects x axis in (x,0). \mathcal {T} is a set...
10. ### need help "stretching" a line and ending on a specific angle against axis

Here's a problem I assumed would be easy, but it has melted my brain for a long time and I am not really sure anymore. So I am using cos and sin to draw round curves in a program (it's okay that it's slow). You specify an x length, y length, and angle1 and angle2 with the axises you want the...
11. ### values of x below the x axis

May i know what this problem all about... i just can imagine how it looks like but l as the values of x, how it is being done? how to write as set for the values of x? can anybody help? For what values of x is the graph of 2x – 3y – 4 = 0 below the x – axis? ​thanks a lot
12. ### Calculating rotation axis

View image: Empty I asked a similar quesion previously, but it had assumptions which may not have been true. The blue platforms are .2 high, and angled at 45 degrees away from each other. The bottom right of the grey cube is point 0,0,0. I want to rotate the grey cube 135 degrees so that it...
13. ### Acute angle between a plane and y axis

Hey guys. The question goes like this : Coordinates of A(-1,2,5) and B(2,-2,11). Plane p passes through B and is perpendicular to AB. It is required to find (a) Equation of plane p (b) Acute angle between plane p and y axis. An equation for p is 3x - 4y + 6z = 80 What is the next step to...
14. ### Where does the plane intersect the axis?

Find the points at which the plane 3x-4y+z=12 intersects the coordinate axis and find the equations of the lines where the plane intersects the coordinate planes.
15. ### Axis rotation with fractional angles

Part of the algebra I'm doing with this is producing bad results, please tell me why. Graph: 11x^2+7xy-13y^2=621 arccos 24/7 is a fraction so: sin\theta=\sqrt{\frac{1-\frac{24}{7}}{2}x=x'\frac{31}{14}-y'\frac{-17}{14} cos\theta=\sqrt{\frac{1+\frac{24}{7}}{2}y=x'\frac{-17}{14}+y;\frac{31}{14}...
16. ### Axis rotation graphing

Graph x^2-2\sqrt{3}xy+3y^2-12\sqrt{3}x-12y I seem to be getting lost in the tedious amount of algebra involved, please find my mistakes: \text{Angle=}cot2\theta=\frac{1}{\sqrt{3}}=\frac{60^\circ}{2}=30^\circ x=x'cos30^\circ-y'sin30^\circ=\frac{x'\sqrt3-y'}{2}...
17. ### Axis rotation formulas, finding them with systems

\text{Use}\:\begin{Bmatrix}x'\:=\:xcos\theta+ysin \theta &  \\ y' \:=\:ycos\theta-xsin\theta &  \end{Bmatrix} \text{To make}\:\begin{Bmatrix}x\:=\:x'cos\theta-y'sin \theta &  \\ y \:=\:y'cos\theta+x'sin\theta &  \end{Bmatrix} My book is asking me to find this before the chapter is...
18. ### Formulas for transformation of axis?

plz someone give me the formulas for rotational transformation and translational transformation of axis... and plz define the new co ordinate whether it is x or xprime.....i got the formulas, but i got confused on the old and new co ordinates, so plz suggest it again with precise notation...like...
19. ### rotation based on velocity on the x axis?

Hi this maybe more of a programming question, but I can't write any code before I get my head around how its going to work so maybe you guys can help me out. A sprite in my game can move along the x axis, to do this I'm giving it a velocity value. Now I need this sprite to rotate depending on...
20. ### Volume of body obtained by rotating around the x axis and y axis.

Hi, If y= 4x^3+3x^2-4x-3, calculate the volume of the body obtained by rotating y around 1) the x axis 2) the y axis. I'm at a bit of a loss here. I know the formula for rotating about the x axis is the integral of pi.y^2 and integral of pi.x^2 for rotation about the y axis. For the x axis...