Tilted Forum Project Discussion Community  

Go Back   Tilted Forum Project Discussion Community > The Academy > Tilted Knowledge and How-To


 
 
LinkBack Thread Tools
Old 01-13-2006, 07:41 AM   #1 (permalink)
Crazy
 
linearizing equations

Hey,

Y = [ax + b/x]^1/2

Now, I made this:

Y = ax^1/2 + (b^1/2 / x^1/2)

Now, I would plot Y vs. X^1/2 for a linear plot, with a slope of a. But whats my intercept ?

Or can someone else suggest another way to linearize, or what the intercept is for the plot I just stated.

Thanks!
danny_boy is offline  
Old 01-13-2006, 10:05 AM   #2 (permalink)
Insane
 
no! bad!

you can't distribute an exponent!
square both sides to remove the square root, then work from there.
rlbond86 is offline  
Old 01-13-2006, 10:12 AM   #3 (permalink)
Insane
 
AngelicVampire's Avatar
 
Y^2 = Ax + b/x

So we have a line which does strange things at the origin (when x = 0 b/x = ??) and from then on we have a square relationship that will tend towards Y^2 = Ax (as x-> inf b/x -> 0).
AngelicVampire is offline  
Old 01-13-2006, 03:17 PM   #4 (permalink)
Crazy
 
If I square both sides, I get:

Y^2 = aX + b/X

So, I can plot Y^2 vs. X, where the slope is a, and the intercept is b/x..is that correct ?
danny_boy is offline  
Old 01-13-2006, 09:30 PM   #5 (permalink)
Insane
 
AngelicVampire's Avatar
 
No, both terms include X so there can be no intercept other than the origin for a truly linear equation, however this isn't linear.

normally you have y = mx + c, which gives the intercept as c, in this case we have two X terms, when we evaluate this as X -> 0 then we get 0a + b/+-0 (a very small number), as such at the origin the actual value is undefined, similar to a tan curve at various points.

For large values of X aX dominates the equation and we have a function which says Y^2 = aX or Y = (aX)^1/2, and again for negative X, at the origin the b/X dominates and we have the graph rapidly shooting off to +ve/-ve infinity for +0/-0.
AngelicVampire is offline  
Old 01-14-2006, 04:39 AM   #6 (permalink)
Junkie
 
filtherton's Avatar
 
Location: In the land of ice and snow.
When i first read this i thought the op was referring to the linearization where you find the equation for the tangent line at any given point on the graph:

L(x) = f(x1)+f'(x)*(x-x1)

But now i don't really have any clue what the op needs.
filtherton is offline  
Old 01-14-2006, 12:02 PM   #7 (permalink)
Insane
 
AngelicVampire's Avatar
 
I thought he was just trying to graph the equation...
AngelicVampire is offline  
Old 01-15-2006, 10:52 AM   #8 (permalink)
Crazy
 
Hey,

What I need to do with the original equation, is somehow manipulate it so that it is linear, and I need to specify the slope and y-intercept.

So, So, I can plot Y^2 vs. X, where the slope is a, and the intercept is b/x..

That plot does in fact yield a linear line....and the intercept does work out to be b/x.

Unless I've messed something up...?
danny_boy is offline  
Old 01-16-2006, 07:08 AM   #9 (permalink)
Insane
 
AngelicVampire's Avatar
 
Well b/x is +/- infinity as x tends to 0... that equation is in no way straight.

Input (8x+8/x)^.5 in this url: http://www.coolmath.com/graphit/

That will show you what the function should look like
AngelicVampire is offline  
Old 01-16-2006, 11:03 AM   #10 (permalink)
Crazy
 
I see I see,

So, I am still at a loss how to linearize my original equation...and what the intercept and slope should be..

The whole aim of the question was to linearize a given equation, and specify its slope and int...
danny_boy is offline  
Old 01-16-2006, 11:52 AM   #11 (permalink)
Junkie
 
filtherton's Avatar
 
Location: In the land of ice and snow.
What class is this for?
Can you use logarithms?
filtherton is offline  
Old 01-17-2006, 08:34 AM   #12 (permalink)
Insane
 
AngelicVampire's Avatar
 
http://www.cbu.edu/~rprice/lectures/lineariz.html

Talks about Taylor expansions and suchlike to approximate a non-linear equation with a linear one.
AngelicVampire is offline  
Old 01-17-2006, 02:18 PM   #13 (permalink)
Crazy
 
This is an engineering course...
danny_boy is offline  
Old 01-17-2006, 09:26 PM   #14 (permalink)
Mine is an evil laugh
 
spindles's Avatar
 
Location: Sydney, Australia
The Y intercept is simple, isn't it?

solve for X when Y is 0

Y^2=Ax + B/x

0 = Ax + B/x
-Ax = B/x
-Ax^2 = B
x^2 = B/-A
x = (B/-A)^1/2
__________________
who hid my keyboard's PANIC button?
spindles is offline  
Old 01-18-2006, 08:18 AM   #15 (permalink)
Insane
 
Are you trying to fit data to a model to solve for a and b?

If so, you could do this:

y^2=ax+b/x
xy^2=ax^2+b

Plot xy^2 vs. x^2. You'll get an intercept of b, and a slope of a.

OR....

y^2/x=a+b/x^2

Plot y^2/x vs 1/x^2. You'll get a intercept of a and a slope of b.
Amano is offline  
 

Tags
equations, linearizing


Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are On
Pingbacks are On
Refbacks are On



All times are GMT -8. The time now is 03:59 AM.

Tilted Forum Project

Powered by vBulletin® Version 3.8.7
Copyright ©2000 - 2024, vBulletin Solutions, Inc.
Search Engine Optimization by vBSEO 3.6.0 PL2
© 2002-2012 Tilted Forum Project

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360