rotating

1. Rotating the region y=x^2 and y=1 around y=6

Hi all, I've been having difficulty with this problem. Rotate the region of y=x^2 and y=1 around the line y=6 I have done it a couple times now and the homework website keeps saying that its wrong. I'm just looking to see if anyone sees an error in my work. So I would integrate...
2. Help calculating a point in 2d space on a rotating right angle triangle

I am trying to solve for a point on a triangle that rotates around a fixed point. For ease of calculation this point is at X: 0 Y: 0 The length and width of the triangle are always fixed, the only thing that changes is the rotation angle. How can I solve for X: ??? and Y: ??? taking into...
3. rotating strings of vectors

Let's say I have a vector, (3.8, 0), and I add a vector to it that I know will give me a resulting vector of equal magnitude (-1.11, 2.69). By doing this I have effectively rotated the original vector by a certain amount. My question is, utilizing only this first vector and the added vector...

Find the focus of the parabola created by rotating the parabola 4x=y2+4 45 through the origin. How do I do this? I'm really confused and I need some help. Thank you!!
5. Point rotating in a coordinate system

The point P rotates with angle α to point P'. the coordinates of the old P are x1 and x2 and for P': x'1 and x'2. Prove that: $$x'_1=x_1\cos\alpha+x_2\sin\alpha$$ $$x'_2=x_2\cos\alpha-x_1\cos\alpha$$ I drew on the left the problem and on the right my attempt. the line OA, which is made of...
6. Help finding the area of the surface

Find the exact area of the surface obtained by rotating the given curve about the x-axis.x = 9t − 3t3, y = 9t2, 0 ≤ t ≤ 2

8. Volume of rotating solid

I need to find the volume of a rotating solid , which is rotated around y-axis limited from above with f(x)=1/2x^2+1 and from bellow with the x-axis , above the interval [0,1]. Here`s the graph of this function...
9. Rotating shaft

A shaft 2 m long rotates at 1500 rpm between bearings. The bearings experience forces of 5 kN and 3 kN acting in the same plane. The shaft is to be balanced using two masses (m1 and m2)placed 0.5 m and 1.5 m from end A and 180° from the direction of the bearing reactions, each on radius arms...
10. rotating in diagram

Hi. I have question in rotating. please see attechment. I draw this diagram, but I have some problem. the formula are need rotating or ....? what can I do for this problem? thanks.
11. rotating acceleration and velocity.

so... I have a rotating cylinder. there is a path plotted out on the cylinder for a cam follower to move on. I "unrolled" the cylinder about its axis. It's 1 inches in diameter. So now I have a 2D plot of X axis = 1*pi inches wide and Y axis is lets say 4 inches high. I know what my...

Here's the current scenario: Our current math teacher has a student teacher this year. He's absolutely awful at teaching. He's been teaching the rotation of conic sections unit and pretty much NO ONE understands what's going on. He teaches it with the assumption that we all have learned conics...
13. Rotating Top: Euler Angles?

Hi all, I've just started studying the motion of a rigid heavy (i.e. with gravity) spinning top using Euler's angles. It mostly makes sense, but there's one point in my notes where we've derived the equations of motion using Euler-Lagrange and one of them is (theta, phi are the usual Euler...
14. Rotating a cube

Consider the cube with vertices at (+-1, +-1, +-1) how many rotations of this cube have the property that is you compose a rotation with itself, you get the inverse of the rotation? Any hints or help with this, I have no idea where to begin with this?
15. find the volume of the solid obtained by rotating the region bounded by..........

find the volume of the solid obtained by rotating the region bounded by: y=x^3, y=8, x=0 about the y-axis I drew the graph up it the attachments. Im using tube method to solve this ∫ 2*pi*r*h, so for me it will be integral from 2 to 0 ∫ 2*pi*x*8 from that i get 32pi. And the answer is...
16. Find the volume of the solid obtained by rotating the region bounded by the curves...

The region bounded by: y=1 and y=x^8 Rotated around: y=4 I used to know how to do these, but I can't remember it appears and after about an hour of trying to figure it out by trying new things I've given up. I really just need the correct integral that comes out of it I suppose, not an...
17. moving a circular object along a surface and rotating it around the end

Im trying to move a circular object along a surface and then rotate it around the corner / end point of that surface. I think it can be soloved using trigonometry, but not 100 percent sure. I can move the object along the surface using this calculation...offset = tan(A) x radius of circle. this...
18. 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...
19. Rotating point about the line y=-x

If you have the point 4,3 and you have to rotate about the line y=-x, how do you do it? I thought it would be either -4,-3 or -3, -4.
20. Rotating object

I have a space ship that I want to rotate. Here is my current code (it executes when .turning = true): a = System.Math.Sin(.destStoppingAngle + System.Math.PI) b = System.Math.Cos(.destStoppingAngle + System.Math.PI) c =...