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Groups > sci.physics > #571204
| From | vallor <vallor@cultnix.org> |
|---|---|
| Newsgroups | alt.free.newsservers, alt.usenet.kooks, sci.physics |
| Subject | Re: Walking through a problem that uses a derivative |
| Date | 2016-04-17 18:08 +0000 |
| Message-ID | <dni1p4FhphdU1@mid.individual.net> (permalink) |
| References | (4 earlier) <dncv8iF8ojjU1@mid.individual.net> <1d9aa9e18defb410fa7c9e3c0db0005d@dizum.com> <dnf1lrFddd5U22@mid.individual.net> <2016c0381b63613e1e8c616ea2224e2a@dizum.com> <op.yf1uiaa1tm21m2@benson.localhost> |
Cross-posted to 3 groups.
On Sun, 17 Apr 2016 01:50:24 -0400, \"Fakey's\" dogwhistle holder living
at 5907 Stanton Ave., Pittsburgh, PA (aka Teh Mop Jockey), socked up as
5907 Stanton Avenue, Pittsburgh, PA 15206-2117 wrote:
> AS IF YOU DIDN'T JUST GOOGLE "DERIVATIVE" AND THEN POAST YER RESULTS.
>
>
> lolol
>
> OLOOL
>
> LOL
That's about the size of it.
His graph:
http://i.imgur.com/sO60qV6.png
The graph that he apparently didn't look at:
http://imgur.com/PMbfGPj
Apparently, he doesn't get it.
for f(3) = x^2
d/dx(x^2) = 2x
m = 2x = 2(3) = 6
So we have the slope, m.
y = mx+c
9 = 6(3) + c
c = -9
So we have the constant.
y = 6x-9
So we have the formula for the line tangent to the curve x^2 at x=3.
http://imgur.com/PMbfGPj
Checks out.
Anything else is chinese room mathematical word salad.
--
-v
>
>
> On Sun, 17 Apr 2016 01:35:06 -0400, Friendly Neighborhood Vote Wrangler
> Emeritus <FNVWe@altusenetkooks.xxx> wrote:
>
>> Time to spin the kooks up again. Melt, kooks, melt. <snicker>
>>
>> vallor, in <news:dnf1lrFddd5U22@mid.individual.net> did thusly jump
>> head first into the wood chipper again:
>>
>>> On Sat, 16 Apr 2016 07:38:38 +0200, Friendly Neighborhood Vote
>>> Wrangler Emeritus wrote:
>>
>>>>> I'm glad you caught that, I totally missed it. (Got just a couple
>>>>> of paragraphs into his post, then ennui set in.)
>>
>>>> You caught Shiny Tinfoil Spankard wondering why x^2 and 2x aren't
>>>> co-functions?
>>
>>> He never did that.
>>
>> Sure he did.
>>
>> "The derivative of x^2 is 2x. Does that make them also co-functions?"
>>
>>>> That's because he's a confused little kooktard.
>>
>>> Looks more like you are _very_ confused.
>>
>> Not really, you're just shifting the goal-posts and being ambiguous in
>> your diversionary bleating. LOL
>>
>>>>> Let's see if we can generate a koan-like moment for the budding
>>>>> mathematician:
>>>>>
>>>>> d/dx( 2x^3 + 69 ) = 6x^2
>>>> d/dx(2x^3 + 69) = (3*(2x)^2 + 0) = 6x^2 = 2*6x = 12x
>>
>> Correct. LOL
>>
>>>> Did you forget to simplify? LOL
>>
>>> That isn't "simplifying" you did, you took the second derivative.
>>>
>>> No where in my post did I try to muddy the waters with second
>>> derivatives, I was talking about the basics. Obviously.
>>
>> You didn't specify what your goal was.
>>
>>> So you get an "A" for effort, but I'm going to have to mark you down
>>> for being over-enthusiastic with the process.
>>
>> Awww, he thinks he's a teacher... and he can't even read a graph. LOL
>>
>>>>> d/dx( 4x^2 ) = 8x
>>>> d/dx(4x^2) = 2*(4x) = 8x
>>
>> Correct.
>>
>>>>> d/dx( 4x^2 + 7x + 3 ) = 8x + 7
>>>> d/dx(4x^2 + 7x +3) = (2*(4x) + 7 + 0) = 8x + 7
>>
>> Correct.
>>
>>>> You should try teaching Shiny Tinfoil Spankard. LOL
>>
>>> I'll let you in on an open secret:
>>>
>>> He knows more about this than you do.
>>
>> Really? Is that why he denied that a sinusoid is a transform of a
>> circle; denied that wave interference and superposition are the same
>> thing; denied that sin^2 is a sinusoid; claimed that "within 10% error"
>> equaled "10% error"; didn't know what LaTeX notation was or that
>> there's a formula in that plain text LaTeX notation (he thought it was
>> a script. LOL!); didn't know what the "co" in cosine means nor what
>> co-functionality was nor the difference between inverse operations and
>> cofunctionality; didn't know that finding the anti-derivative is the
>> same as finding the integral; denied that stock trading requires
>> mathematical derivatives; claimed that mathematical derivatives as used
>> in stock trading are stock options; demonstrated that he didn't know
>> what the Fundamental Theorem of Calculus is; demonstrated that he
>> didn't know that the derivative of a constant is always equal to zero;
>> claimed that no math was being done unless an equal sign was in there
>> somewhere; confused a formula and an equation;
>> and completely fucked up the definitions of the first, second and third
>> derivatives? Amongst many other of his hilarious fuckups. LOL
>>
>>>>> You can't fake knowing math.
>>
>>>> Says the guy who fucked up above. LOL
>>
>>> Actually, no, it was you who over-enthusiastically took the second
>>> derivative when all we were dealing with were first derivatives.
>>
>> Ok, so I went over your head. I'm marking you down for that. LOL
>>
>>>>> Prediction: the response to this will be "jess trollin'".
>>
>>>> Wrong. Again. LOL
>>
>>> Except, see below...
>>
>> Still wrong. Again. LOL
>>
>>>>> And I hesitate to give a sensible answer regarding 2x for a specific
>>>>> point x, because _that_ does use trigonometry, but not for the
>>>>> reasons you think. for r = sin(theta), r is the ratio, and theta is
>>>>> the angle.
>>>>> But let's take that example of x^2 for x = 5 (picked out of thin
>>>>> air) and see what we get:
>>>>> x = 5 f(x) = (5)^2 = 25 d/dx( f(x) ) = 2x; for x = 5, this is 10
>>>>>
>>>>> So we know a few things about that point on the curve:
>>>>> It is at (x,y) = (5,25).
>>>>> The slope of the point tangent to the curve at (5,25) is 10.
>>>>>
>>>>> What is the slope? It is the ratio of y/x.
>>>>> So the "angle of 2x" for x=5 would be solved by using the
>>>>> trigonometric function that solves for y/x ratios -- arctan.
>>>>> (Remember tangents? This is a song about tangents.)
>>
>>>> But we're not talking about the slope of x^2,
>>
>>> Actually, we are. In purely mathematical terms, that's what a
>>> derivative is _for_.
>>
>> And what's the derivative of x^2? Oh, it's 2x. So yet again I'm
>> correct. LOL
>>
>>> Let's take the case of when you were dropped on your head as a child.
>>
>> Fanfic. LOL
>>
>>> The formula for the distance covered is d = (1/2)At^2.
>>>
>>> In english units, acceleration of Earth's gravity is approximately 32
>>> ft/
>>> sec/sec. I'll leave off the units, and you can see how this works.
>>>
>>> d = -16t^2
>>>
>>> This is a parabola. First derivative (as you point out elsewhere)
>>> give velocity:
>>>
>>> s = -32t
>>>
>>> This is a straight line,
>>
>> The equation for free-fall distance (discounting air resistance and
>> buoyancy effects) due to gravitational acceleration is:
>> y=\frac{1}{2}(9.80665\cdot x^2)
>>
>> The instantaneous velocity of a falling object due solely to
>> gravitational acceleration (discounting air resistance and buoyancy
>> effects) that has traveled distance x is:
>> y=\sqrt{2\cdot 9.80665\cdot \left(\frac{1}{2}\left(9.80665\cdot
>> x^2\right)\right)}
>>
>> Thus (taken straight from the graph):
>> Time: Distance Fallen: Vi:
>> 1 second 4.903 m 9.807 m/sec 2 seconds 19.613 m
>> 19.613 m/sec 3 seconds 44.13 m 29.42 m/sec
>>
>> Compare that to your equation.
>> Time: Distance Fallen: Vi:
>> 1 second 16 feet (4.9768 m) 32 feet/sec (9.7535 m/sec)
>> 2 seconds 64 feet (19.5072 m) 64 feet/sec (19.5072 m/sec)
>> 3 seconds 144 feet (43.8912 m) 96 feet/sec (29.2609 m/sec)
>>
>> <http://i.imgur.com/5fT3sCp.png>
>>
>>> but its units are in a different frame of reference. You don't plot
>>> this line with the parabola and hope to see something meaningful
>>
>> Huh, I just did. You apparently can't. LOL
>>
>>> -- you use this resulting formula (the first derivative) to develop
>>> the formula that gives you a line tangent to the curve for any given
>>> x.
>>
>>>> we're talking about the slope of its derivative, for which the only
>>>> two true conditions are [0,0] and [2,4].
>>
>>> I'm afraid you're still confused.
>>
>> Says the guy who can't figure out how to read a graph. Do you not
>> understand that the graph represents the equations, and can thus be
>> used to figure out the same results as the equations? Are ya skooled
>> yet? LOL
>>
>>>>> arctan(10)
>>>>> 1.47112767430373459185287557176173085185530637718323
>>>>>
>>>>> So there's your answer in radians, Cadet Fakey.
>>>>>
>>>>> Oh, you want that in degrees?
>>>>> 84.28940686250035748730411865176563988852083893309440
>>>>>
>>>>> So the curve x^2 at that point (5,25) is about 6 degrees from
>>>>> vertical,
>>>>> leaning to the right...political pun not intended.
>>
>>>> It's just as easy to graph it.
>>>> <http://i.imgur.com/x2Z9U7s.png>
>>>> <http://i.imgur.com/emGGhNA.png>
>>>> Gee... I got the same answers you did.
>>
>>> No you didn't,
>>
>> Yeah. I did. Same angle in radians and degrees as you got. LOL
>>
>>> you graphed formulas that are only orthogonally related to each other.
>>
>> I got the correct answers. Again. LOL
>>
>>> Let me show you what it looks like closer to the origin:
>>> x = 3 f(x) = x^2 so for the point in question, you have (3,9)
>>
>> That's exactly what I got. LOL
>>
>> <http://i.imgur.com/sO60qV6.png>
>>
>>> d/dx(f(x)) = 2x so the slope of the line tangent to the curve at (3,9)
>>> is 6.
>>
>> That's exactly what I got. LOL
>>
>> <http://i.imgur.com/sO60qV6.png>
>>
>>> But that is the slope of the line _that passes through 3,9_. So the
>>> formula for _that_ line -- the line that would make sense to graph
>>> with it -- is
>>>
>>> [ insert here: you know the formula for the line of a given slope is
>>> y=mx+c, I hope, where "m" is the slope. If not, then welcome to first
>>> semester algebra.]
>>>
>>> y = 6x + c, where "c" is some constant to make the line pass through
>>> (3,9). (That is to say, the value of y when x=0).
>>>
>>> So solve for c:
>>>
>>> 9 = 6(3) +c c = -9
>>>
>>> So the line that makes sense to plot with the parabola is:
>>> y = 6x-9
>>>
>>> *NOW* you can start plotting:
>>> http://imgur.com/PMbfGPj
>>>
>>> The _line_ I plotted is tangent to the curve at (3,9). It passes
>>> through (3,9), and it's "parallel" (instantaneously) at that point.
>>>
>>> All the derivative gives you is the _slope_ of the line I plotted --
>>> but you still need to figure out the formula for the line, and that
>>> changes from point to point.
>>>
>>> _That_ is how you use a derivative. Look at the graph. Do you see
>>> now?
>>
>> And that gives 80.538 degrees, or 1.40565 radians, at that point.
>>
>> <http://i.imgur.com/a1KIqCN.png>
>>
>> Gee... I was right. Again. Why can't you read a graph? Are ya skooled
>> yet? LOL
>>
>>>> Seems I have an intuitive grasp on the mechanics and the mathematics
>>>> of it,
>>
>>> I'm afraid not, you just plotted a bunch of functions that were
>>> orthogonally related, but not the line that would have been obvious to
>>> plot, given what a derivative is _for_.
>>>
>>> Unless you can come up with some kind of utility to plotting the line
>>> indicated by the formula that gives you the slope of a line tangent to
>>> the curve at a given point, I'd have to say you're utterly at sea.
>>
>> Is that why I've gotten it right twice now, with even greater accuracy
>> than you could manage in the second instance? LOL
>>
>>> (Say...are you on a bote?)
>>
>> Paranoid fanfic.
>>
>>>> whereas Shiny Tinfoil Spankard has yet to produce even a single graph
>>>> *or* correct equation. LOL
>>
>>> But he knows how to take a derivative, and doesn't call them "co-
>>> functions" (or claim that other people are using the term when they
>>> clearly haven't).
>>
>> Shiny Tinfoil Spankard asked why x^2 and 2x aren't co-functions. Sine
>> and cosine are co-functions, thus the "co" in cosine. Yet again, I'm
>> right. LOL
>>
>>>> Now... what's all that got to do with the fact that Shiny Tinfoil
>>>> Spankard is a backpedaling bleatfarting blither-blathering liar
>>>> desperately raping Google
>>
>>> You know, you'd get a lot farther in this process if you'd learn a
>>> little charity.
>>
>> I give none to those who give none.
>>
>>> I'm x-posting this to afn so that interested parties that can't
>>> participate in this group can comment.
>>
>> You mean Paul Derbyshire's kensi sock? I SPNAK!d that tard right out of
>> AUK. He ran away and melted down after being proven to be delusional on
>> politics, astrophysics, geometry, climate change and a whole lot more.
>> LOL
>>
>>> --
>>> Won a Checky(tm) on 2016-04-15
>>> ...for schooling a kook about derivatives.
>>> (Including working through a sample problem.)
>>
>> Chimpy only hands out his 'awards from a kook' to people he wants a
>> "hawt wet 69" (Chimpy's words) with... that's why he's given one to
>> Paul Derbyshire... but Derbyshire had to perform two "hawt wet 69s"
>> (Chimpy's words) to get it... strange then, that Chimpy's been begging
>> for and demanding from Derbyshire another. LOL
>>
>> Did I mention Chimpy's into fat dudes? If you've got pink spandex,
>> boxing gloves and some lube, you're *in*, Scott.
>>
>> <snicker>
>>
--
Won a Checky(tm) on 2016-04-15
...for schooling a kook about derivatives.
(Including working through a sample problem.)
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Re: Our very own "chinese room" Friendly Neighborhood Vote Wrangler Emeritus <FNVWe@altusenetkooks.xxx> - 2016-04-13 06:58 +0200
Re: Our very own "chinese room" "\"Fakey's\" dogwhistle holder living at 5907 Stanton Ave., Pittsburgh, PA (aka Teh Mop Jockey), socked up as 5907 Stanton Avenue, Pittsburgh, PA 15206-2117" <root@127.0.0.1> - 2016-04-13 01:20 -0400
Re: Our very own "chinese room" Skeet <invalid@invalid.invalid> - 2016-04-13 13:23 -0600
Re: Walking through a problem that uses a derivative Friendly Neighborhood Vote Wrangler Emeritus <FNVWe@altusenetkooks.xxx> - 2016-04-16 07:38 +0200
Re: Walking through a problem that uses a derivative vallor <vallor@cultnix.org> - 2016-04-16 14:48 +0000
Re: Walking through a problem that uses a derivative Friendly Neighborhood Vote Wrangler Emeritus <FNVWe@altusenetkooks.xxx> - 2016-04-17 07:35 +0200
Re: Walking through a problem that uses a derivative "\"Fakey's\" dogwhistle holder living at 5907 Stanton Ave., Pittsburgh, PA (aka Teh Mop Jockey), socked up as 5907 Stanton Avenue, Pittsburgh, PA 15206-2117" <root@127.0.0.1> - 2016-04-17 01:50 -0400
Re: Walking through a problem that uses a derivative vallor <vallor@cultnix.org> - 2016-04-17 18:08 +0000
Re: Walking through a problem that uses a derivative Friendly Neighborhood Vote Wrangler Emeritus <FNVWe@altusenetkooks.xxx> - 2016-04-18 07:29 +0200
Re: Walking through a problem that uses a derivative vallor <vallor@cultnix.org> - 2016-04-18 06:24 +0000
Re: Walking through a problem that uses a derivative Rick Sabian's Allstar Canadian Assworm Zydeco Band <Lunatic.Fringe@The.Edge> - 2016-04-17 23:28 -0700
Re: Walking through a problem that uses a derivative Friendly Neighborhood Vote Wrangler Emeritus <FNVWe@altusenetkooks.xxx> - 2016-04-19 08:28 +0200
Re: Our very own "chinese room" Friendly Neighborhood Vote Wrangler Emeritus <FNVWe@altusenetkooks.xxx> - 2016-04-16 07:58 +0200
Re: Our very own "chinese room" Rick Sabian's Allstar Canadian Assworm Zydeco Band <Lunatic.Fringe@The.Edge> - 2016-04-16 00:01 -0700
Re: fakeys meltdown Skeet <invalid@invalid.invalid> - 2016-04-16 02:27 -0600
Re: Our very own "chinese room" "\"Fakey's\" dogwhistle holder living at 5907 Stanton Ave., Pittsburgh, PA (aka Teh Mop Jockey), socked up as 5907 Stanton Avenue, Pittsburgh, PA 15206-2117" <root@127.0.0.1> - 2016-04-16 11:22 -0400
Re: Our very own "chinese room" Friendly Neighborhood Vote Wrangler Emeritus <FNVWe@altusenetkooks.xxx> - 2016-04-17 06:56 +0200
Re: Our very own "chinese room" "\"Fakey's\" dogwhistle holder living at 5907 Stanton Ave., Pittsburgh, PA (aka Teh Mop Jockey), socked up as 5907 Stanton Avenue, Pittsburgh, PA 15206-2117" <root@127.0.0.1> - 2016-04-17 01:20 -0400
Re: Our very own "chinese room" Friendly Neighborhood Vote Wrangler Emeritus <FNVWe@altusenetkooks.xxx> - 2016-04-18 07:19 +0200
Re: Our very own "chinese room" Janithor <Janithor@comcast.net> - 2016-04-16 23:06 -0700
Re: Our very own "chinese room" Friendly Neighborhood Vote Wrangler Emeritus <FNVWe@altusenetkooks.xxx> - 2016-04-16 08:15 +0200
Re: Our very own "chinese room" Friendly Neighborhood Vote Wrangler Emeritus <FNVWe@altusenetkooks.xxx> - 2016-04-17 07:40 +0200
Re: Our very own "chinese room" "\"Fakey's\" dogwhistle holder living at 5907 Stanton Ave., Pittsburgh, PA (aka Teh Mop Jockey), socked up as 5907 Stanton Avenue, Pittsburgh, PA 15206-2117" <root@127.0.0.1> - 2016-04-17 01:53 -0400
Re: Our very own "chinese room" Friendly Neighborhood Vote Wrangler Emeritus <FNVWe@altusenetkooks.xxx> - 2016-04-18 07:04 +0200
Re: Our very own "chinese room" Skeet <invalid@invalid.invalid> - 2016-04-17 23:56 -0600
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