| Author |
 Topic  |
|
|
Kevitzinn
Average Member
USA
14 Posts |
 Posted - 10/06/2007 : 20:43:16
|
OK, the question is:
For the circle x + y = r show that
|y''/[1+((y')]^(3/2)| = 1/r.
What I'm confused about right now is what do with the r. Should I say that the, y' = (-2x/2y) or is it, y' = (2r-2x)/2y or may be something else? Any help anyone can give me would be very much appreciated. Thank you for your time.
-KG |
 |
|
|
skeeter
Advanced Member
USA
5634 Posts |
Posted - 10/06/2007 : 21:14:16
|
you sure its not ...
|y''/[1+((y')]^(3/2)| = y/r
? |
|
|
|
Kevitzinn
Average Member
USA
14 Posts |
Posted - 10/06/2007 : 21:45:23
|
Nope, the text book says 1/r, and just to clarify to the max, it's
|(y'')/([1+(y')[square]]^(3/2))| = 1/r.
Why do you believe it would be equal to y/r? |
|
|
|
galactus
Advanced Member
USA
1464 Posts |
Posted - 10/07/2007 : 09:34:55
|
| An image can be inserted by using ImageShack. |
|
|
|
skeeter
Advanced Member
USA
5634 Posts |
Posted - 10/07/2007 : 12:22:35
|
o.k. ... missed a factor of "y" in my initial attempt, found my error.
y' = -x/y
1 + (y') = 1 + x/y = r/y
y" = -r/y
-----------------------------------------
y"/[1 + (y')]3/2 =
(-r/y)/(r/y)3/2 =
[(-1/y)*r/y]/(r/y)3/2 =
(-1/y)/(r/y)]1/2 = -1/r
since r > 0 ... |-1/r| = 1/r
|
|
|
|
Kevitzinn
Average Member
USA
14 Posts |
Posted - 10/07/2007 : 13:22:51
|
| Wow, thank you so much, I really appreciate it. You guys are the coolest of the cool! |
|
|
|
sahsjing
Advanced Member
USA
2399 Posts |
Posted - 10/09/2007 : 17:41:04
|
quote:
Originally posted by Kevitzinn
OK, the question is:
For the circle x + y = r show that
|y''/[1+((y')]^(3/2)| = 1/r.
What I'm confused about right now is what do with the r. Should I say that the, y' = (-2x/2y) or is it, y' = (2r-2x)/2y or may be something else? Any help anyone can give me would be very much appreciated. Thank you for your time.
-KG
The left side |y''/[1+((y')]^(3/2)| is called the curvature, which is always equal to 1/R, where R is called the radius of the curvature. |
|
|
| |
Topic |
|
Interactive Math Goodies Software
Topic Locked
