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Dont know if this is correct but I'll try
I got this
the net accel = gravity - resistance
And after you solve the general form of z
you have to put when z=h, dz/dt=U, to get the specific form
connect the vertexes to the center of the circle, 3x+3x+3x+5x+5x+5x= 24x , means divided 360 degress into 24 , then the corresponding angle to each side would be 3x360/24, 3x360/24, 3x360/24 , 5x360/24 , 5x360/24, then use trionometry to solve it.
Hmm, maybe you need a general prove for the algorithm? does this apply to other sequence?
I think 0.9999999... is best represented by
I dont like to consider 0.9999... as a number , rather an expression. Since the concept of infinity is not shown by putting it 0.9999...
George , I dont think there's static infinity. Of course, if you were referring that to upper/ lower bound, then there is
Oh yea, the 1 isnt canceled. Wow, mathsyperson, your method is complicated, I couldnt figure out the difference thing. how did you even come up with that , awesome
I wonder if this is correct???
Or
(x+2)(x-a)(x-b)=0
2-b-a=1/4
2ab=7
ab-2b-2a=0
wow, only one solution
awwwwwwwwww, just found out using Osculating circle to solve it.. nevermind
I dont know how to do this
It has a graph, cant put it on, so I describe it instead.
Here my work
I think he means the area between x=0 and x= 3 , area enclosed by the three?
Wow, its not define lol
Thanks dragonshade, I didn't know you could split forces into fractions of the total length
hmm, the edge is the fulcrum(pivot), when its unbalance the block will fall off, it would spin around the fulcrum, then I just simple treat it as two object connect with a pipe with the edge as pivot lol
Wait, I was wrong, Sorry about that
It should be done like this
As the picture
this kind of question is really not my thing, I guess the father would be 20+5k, k=2,4,6,8....
Father=F , x<y<z (3 children)
F x y z
30 7 11 12
40 9 15 16
50 11 19 20
I am not sure, but man, thats one heck of a father XD
In my opinion , the only force is mg so Torque = Mgx =0 , therefore x=0 , so the length would be L/2
You are trying to find gradient vector?
(a) Choosing 12 from 31 , 31!/(12!x(31-12)!) =141120525
(b) 31^12
(c) If each one could be ordered 12 times, then 31^12, If could only be ordered 11 times, then there are 31 situations, which each flavor is ordered 12 times, so its will be 31^12 -31
hope I get it right XD
First, the normal vectors for the two planes are <3,-1,4> , <1,6,10>
cross product of the two normals gives a vector perpendicular to the two normals
<3,-1,4>x<1,6,10>= <-34, -26,19>
Then you just need to find a point which lies on the line
x+6y+10z+8=0
3x-y+4z-2=0
make z=0
x=4/19 , y=-26/19
r= <4/19 ,-26/19 ,0> + t<-34, -26,19>
I've looked into that before (linear combinations of equations of planes), but I soon forgot
now I just stick to using normal vector to get the equation for plane
I think linear algebra is concerned , I havent studied it yet
Since two sides of the triangle equals to each other, it's a isocele triangle(spelling,..cough...cough), the property of that kind of triangle is that QPR=PRQ=a
2a+42=180
a=69
I believe this is called rectilinear system, I am not sure
You might use it, I am not familiar with it tho, I heard that it's used to solve for question like this
And there's another system called elliptical system, used to solve for intersection of ellipse
The normal vector of x-y+2z+5=0 is <1,-1,2>
The normal vector of 2x+3y-z-1=0 is <2,3,-1>
The cross product of <1,-1,2> and <2,3,-1> would be the directional vector of the line
So the direction vector of the line would be <-5,5,5>
Then we shall find a point which lies on the line
solving the group of equations of two planes
2x+3y-z-1=0
x-y+2z+5=0
make x=0, y=-3/5 , z=-14/5
The line would be r= <0,-3/5,-14/5>+t<-5,5,5>
The plane which include the line would be
n*r=0
n must be perpendicular to the plane's(x+2y-2z=0) normal vector <1,2,-2>
n must be perpendicular to the line's directional vector <-5,5,5>
<x,y,z>*<1,2,-2>=0
<x,y,z>*<-5,5,5>=0
make y =1, get
n=<4,1,3>
<4,1,3>*<x,y+3/5,z+14/5>= 4x+y+3/5+3z+42/5=0
So the plane would be 4x+y+3z+9=0
Too much calculation... hope I didnt get it wrong
btw, I am bad at calculating
Theres actually a formula to figuring out the sum of the angles of a polygon:
180(n-2) where n is the sides of the polygon.
Which I see he/she used by doing 180(5-2) = 540.
yea, but he wanted to know why