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Old 01-02-2013, 10:35 AM   #9181
sfaune92
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How do you rearrange:

v = 1 + bx + cx

to get a straight line?
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Old 01-07-2013, 06:25 PM   #9182
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When doing linear equations, how would you write the equation for a vertical line?
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Old 01-07-2013, 07:25 PM   #9183
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Quote:
Originally Posted by ThrashUnleashed
When doing linear equations, how would you write the equation for a vertical line?


x=something
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Old 01-07-2013, 07:28 PM   #9184
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Quote:
Originally Posted by ThrashUnleashed
When doing linear equations, how would you write the equation for a vertical line?



x = constant, much like y = constant is a horizontal line!
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Old 01-12-2013, 03:27 AM   #9185
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I have just started integration and I'm still a little confused... how would you integrate this?

(square root of x - 1/x)^2
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Old 01-12-2013, 03:31 AM   #9186
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Is the entire square root being squared?
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Old 01-12-2013, 06:55 AM   #9187
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Quote:
Originally Posted by MakinLattes
Is the entire square root being squared?


Ok yeah that wasn't very clear... it's [(square root of x)-(1/x)]^2
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Old 01-12-2013, 07:07 AM   #9188
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So (√(x) - 1/x)^2.

Foil and simplify:
(√(x) - 1/x)(√(x) - 1/x)
= √(x)^2 - 2(√(x)/x) + 1/x^2
= x - 2x^(-1/2) + x^-2.

So for the indefinite integral we have
∫ x - x^(-1/2) + x^-2 dx
= ∫x dx - ∫2x^(-1/2) dx + ∫x^-2dx
= (1/2)x^2 - 4x^1/2 - x^-1 + C

Last edited by MakinLattes : 01-12-2013 at 07:08 AM.
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Old 01-13-2013, 06:37 AM   #9189
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How do you find a dy/dx expression when:
sin(xy) = y + x
?
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Old 01-13-2013, 06:58 AM   #9190
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Quote:
Originally Posted by sfaune92
How do you find a dy/dx expression when:
sin(xy) = y + x
?

Implicity differentiation dy/dx=-Fx/Fy, so take the sin to the right and simply partial differentiste to x and y.
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Old 01-13-2013, 07:31 AM   #9191
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Thank you!
The answer key just said: (to a simlar question; there's no answer key for exam sets)
1.  sin(xy) = x
2.  [x(dy/dx) + y] cos(xy) = 1
3.  (dy/dx)=[(cos(xy))^-1 - y] / x

Though the method you mentioned yielded the same answer on that question.
I'm curious about what happens between step 1. and 2. here...
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Old 01-13-2013, 08:49 PM   #9192
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Quote:
Originally Posted by sfaune92
How do you find a dy/dx expression when:
sin(xy) = y + x
?


cos(xy)[xdy/dx+y]=dy/dx+1
dy/dx(xcos(xy)-1)=1-ycos(xy)
dy/dx=(1-ycos(xy))/(xcos(xy)-1)
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Old 01-14-2013, 08:50 AM   #9193
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Hey guys, doing a computing report and was wondering if there's a way to get the convergence of this series for different values of a? Is there a way to express this limit in terms of a? I'm still not great with just plucking limits out of thin air
Any help is appreciated!
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Old 01-14-2013, 09:50 AM   #9194
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Sorry, this is a really stupid question but I'm having a hard time visualising this question in my head. Can anyone explain it to me a little better?

A pendulum with a cord length, r=0.5m, swing on a vertical plane. When the pendulum is in the 2 horizontal positions of theta=90' and theta=270', its speed is 5.00ms^-1
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Old 01-14-2013, 11:20 AM   #9195
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Quote:
Originally Posted by a_7_x
Sorry, this is a really stupid question but I'm having a hard time visualising this question in my head. Can anyone explain it to me a little better?

A pendulum with a cord length, r=0.5m, swing on a vertical plane. When the pendulum is in the 2 horizontal positions of theta=90' and theta=270', its speed is 5.00ms^-1


Imagine the pendulum upside down, completely vertical, with the weight at the top - this is with θ = 0. Now rotate it clockwise 90, that's the first horizontal position, and the other is, yeah, 270. It's saying that each time θ=90, v (instantaneous speed) is 5m/s.

...what's the actual question though? :p

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I learned about Bose-Einstein Condensation today.

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Dayum that looks pretty fascinating... Are you in 3rd year or something?
I've seen some stuff about this in IOP news, I never understand anything in physics news though
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Old 01-16-2013, 06:43 AM   #9196
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I've got a simple stats question...

So I've calculated mean, variance, standard deviation, and standard error of the mean.

How do I find "the 70% confidence limit for the true value"?

EDIT: Another question...

How do you linearise this:
t = (d + 4h) / v
Given that
t: dependent variable
d: independent variable
h: constant
v: constant

(Or is it possible to have v as a function of d?)
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Old 01-16-2013, 01:15 PM   #9197
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Quote:
Originally Posted by sfaune92
I've got a simple stats question...

So I've calculated mean, variance, standard deviation, and standard error of the mean.

How do I find "the 70% confidence limit for the true value"?

EDIT: Another question...

How do you linearise this:
t = (d + 4h) / v
Given that
t: dependent variable
d: independent variable
h: constant
v: constant

(Or is it possible to have v as a function of d?)


I was taught something about a 67% confidence level, I'm assuming this is the same thing - if you have your standard deviation s then the error on your average value (at the 67% confidence level) should be s/sqrt(N) where N is the number of values used to calculate the standard deviation.

And I'm not really sure what that second question is asking is that something to do with taking the first order of the Taylor expansion?
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Old 01-16-2013, 01:30 PM   #9198
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Thank you.
Also, the second part seems to be asking of t as a function of d. I don't think series has anything to do with it as it is not included in that module. I tried using logs as well, but it didn't go over to well because of that annoying plus on top of the denominator.

Regarding your question on the previous page, is it based on a binomial series?
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Old 01-16-2013, 11:20 PM   #9199
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Well can't you just square root it? t = (d+2h)/v ?
which is essentially t = (1/v)d + (2h/v) in straight line form

and uh, my question was finding the limit/convergence of that series, in terms of a :/ still stuck on it lol, need to finish writing the report by sunday :'(
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Old 01-16-2013, 11:39 PM   #9200
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You can't square root it because those values are squared independently and then added. To linearize it you have to get both the dependent and independent variables to a power of 1, but I'm not actually sure how to do that for that problem (been through calc 3 and math methods, I'm ashamed of myself).

What class is that question for?
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