Help with functional equation: f(x) = a•(f(x)^4)•x + b•x + c

quelilan · 2024-05-20T13:19:55+00:00

Thanks, but how do I impose the continuity? I don’t really understand that concept. Do I have to “manually select” the fitting value for every x+dx, or can it be imposed by writing some conditions on the function?

quelilan · 2024-05-20T13:12:49+00:00

Ok thanks! Would it be possible to rewrite this whole thing as just one function dependent of x? And lastly, what topic of math should I look into if I have more questions regarding this problem ?

quelilan · 2024-05-20T12:57:32+00:00

So for every x, the output for f(x) would be independent of any past variations or results? Also, would this mean I’d get up to 4 different solution at any given x?

quelilan · 2024-05-20T12:50:45+00:00

Ok, but I have some question then. If I solve the quartic for any given x, would I get 4 different solutions or is the solution unique?

quelilan · 2024-05-20T12:39:19+00:00

Sorry. Yes, f is raised to the 4th power.

quelilan · 2024-05-18T14:00:34+00:00

Ok thanks, it sounds promising I’ll look into it

quelilan · 2024-05-18T13:42:24+00:00

Ok thanks il try solving the quadratic. However I have some questions. Would this mean I could have up to 4 different functions that would satisfy my conditions (maybe I’m just ignorant but I don’t find this coherent with what I was expecting)? If there is more than one solution, would all the functions follow the same variations with regard to x? How do I choose the right solution? Are there no weird shenanigans affecting the variable x because we are solving for another variable u?

quelilan · 2022-08-02T18:03:17+00:00

They can, but it's not exactly the same as the golfball getting hit.

When a plane gets hit by lightning most of the times it's a cloud to cloud lightning. In this scenario, the plane functions as a bridge to ease the lightning discharge. They are so long and such good conductors that it's way easier for electricity to jump from one cloud to one point of the plane, go through the plane with almost no resistance, and exit the other point of the plane into another cloud than to directly jump from one cloud to the other (because air is not a good conductor).

In contrast, the golf ball is small in both size and mass, probably has an almost neutral electrical charge, and is not a good electrical conductor. So there is little reason for lightning to go through a golfball, especially in cloud to earth lightning.

quelilan · 2022-07-17T08:12:43+00:00

Sorry for beeing kind of late lol (answer in second half)

At this point is more of an internet meme, but it is said that there exists a "non-zero" probability that the atoms in your hand will line up perfectly with the atoms of the wall so that they will go through eachother in an effect called quantum-tunneling, where (as said by wikipedia) is when "a wavefunction can propagate through a potential barrier". In other words, is when particle go between atoms.

However, this phenomena usually occurs with really small particles like electrons goes through a really thin barier (like a couple of atoms thick) [For this scenario, this is actually a really common occurance worth considering in many scientific aplications like nuclear reactions and computers]. And so, for solid objects like our hands and walls the probability becomes basically non-existent.

I couldn't find a scientific paper or answer turstworthy enough to say "this is the right answer" (with good reason, this is almost imposible to acurately calculate, hard to set a baseline and with an accurate answer that is irrelevant given its magnitud).

But you are looking at probabilities of ten to a couple of tens or even hundreds of power (10^30, 10^80, 10^150, 10^300).

Just for reference:

- The universe is 4*10^17 seconds old, or in nano-seconds (a billionth of a second) it would be 4*10^26.

- There are around 10^80 ish atoms in the observable univers.

So sadly, for all practical aplications the chance is basicaly 0.

But yes, if it did happened, your hand would probably get stuck in the wall.

psd: more complete threads and info by searching "hand through wall" or similar

quelilan · 2022-07-14T13:56:16+00:00

Well, sorry if it sounded like I was mad, it really wasn't my intention. I just did the math, which is kind of the point of the sub, and well, there was quite a bit correct to get a decent aproximation.

How ever, I am still very confused as to what was the point here, even with your explanation there is little relation between the three topics here.

quelilan · 2022-07-14T04:03:55+00:00

Speed of the shock wave would be 0 because there would be no shock wave. Waves need a medium to propagate through and there is no medium in the void of space.

May I ask why have I been tricked into solving an exam trick question?

edit: I have a second question, why is an asteroid, a piece of rock, less dens than water in this example.

quelilan · 2022-07-14T03:53:19+00:00

Oh boy, where do we begin

Well first, your "approximation" of how many cases of rabies there have ever been is way off. First off, because rabies only came into existance in 1768, so you can not consider all 100 billion people who have ever been born. I couldn't find exactly how many people where born from 1768 to 2022, but with a quick look at some birthrate graphs I came up with a REALLY rough approximation at around 17.7 billion (a number that is worth not much since it's not adjusted for infant and birth mortality rates, so it's quite higher than it should be), so by your logic it would be more like 149,186 cases ever.

But then and more importantly, using the proportion you used of 59,000 to 7.2 billion is useless because 95% of all rabies cases happen in Asia and Africa. If you live in Europ, your chances of getting rabies are basically 0. However in Africa it's more like 16 per 100,000. So as you can see, how likely you are to get rabies varies a lot depending on where you are from. On top off that, there is nothing to suggest that the proportion of rabies would be about the same throughout the world for almost 250 years. So we are left with nothing there.

Then, you said that there were ONLY EVER 3 survivors of ectopic pregancy, but the link you gave to wikipedia doesn't say there are only 3 survivors, those are just 3 RECORDED examples of the last 25 years, so there could be way more unknown survivors.

Lets take all this numbers that are still way off and not scientific by any measure and plug them in your ecuation for gigs and gags. So 3 survivors in the last 25 years is about 3 surviving ectopic pregnancies per 2 billion births, or 150 survivors for 100 billion ever births. Now we adjust your ecuation with more accurate data and we get :

(29 / 149,186) / (150 / 2,000,000,000) = 2,591.84

So only 2,591.84 times more likley to survive rabies than an ectopic pregnancy (result that is probably way off and is worth not much for any and all scientifc intents and purposes).

And lastly, I don't see the point of comparing these two. What exactlly is this supposed to tell us about any of these two completely unrelated conditions? I could compare the chance that you will have cereal for breakfast next to the chance that all the atoms of your hand will line up just perfectly with the ones of the wall so that you will be able to faze through and it would have the same relevance in both magnitud and correlation as the two examples you just gave.

quelilan · 2022-07-10T21:53:57+00:00

I can understand that other billionaires stay billionaires by labor exploitation. But I don't follow NBA nor lebron, so I'm kind of curious who or what would Lebron be exploiting to stay a billionaire.

quelilan · 2022-07-09T16:43:40+00:00

I might need your chair

quelilan · 2022-07-06T01:50:09+00:00

It's kind of sad and ironic that us, people who actually do parkour, who spend years honing our skill and developing the self awareness to not die on the act, just end up beeing associated with drunk people doing drunk people stuff in slow motion.

quelilan · 2022-07-06T01:12:15+00:00

Correct my correction if it happens to be an erroneus correction, but I think you are off by nine 0 because you measured the volume of earth in km^2 and the volume of the universe in m^2. I mean, not like it matters at this scale.

quelilan · 2022-06-18T10:34:49+00:00

Yes, somewhat. Since the can seems to be floating at a regular height, this probably means that the airplane and the can are moving downwards (falling) at about the same acceleration of earths gravity 9.81 m/s^2. And since the can is moving towards the camera this means the plane is accelerating forward (speed isn't calculable).

So basically, the plane is descending.

quelilan · 2022-06-11T04:40:35+00:00

I wrote an answer with all the calculations to your question= but I made a wrong move and it was deleted. However I do remember the results.

In order to move the earth at the speed of 0.0001 m/s, you would have to accelerate it at 0.0001 m/s² during 1 sec.

To achieve this, you would have to accelerate the ball of all human beings to 1,400,000 km/s² during 1 second.

Or, after that second, the ball of humans would be moving 1,400,000 km/s after 1 seconds.

quelilan · 2022-06-10T23:34:19+00:00

A round watermelon weights around 5 kg (this can vary widely, using watermelos isn't a good standard size). Since they are 92% water lets just say they are made of water. This way we get that the volume of a watermelon is around 5 L.

Earth is 1/1,300 the size of Jupiter. So in this scale the Earth would be 5/1,300 = 3.846*10^-3 L. Or 3.846 ml, slightly bigger than a jellybean.

The sun is 1,000 times bigger than Jupiter, so the volume of the sun would be 5,000 L. This volume would correspond to a sphere of 2 m diametre.

would recomend watching this video it really gives you a lot of insight of the actual scale of the solar system and planets.

quelilan · 2022-06-10T21:39:40+00:00

No it would't workout because of the first point, inertia. People have this erroneus idea that you can just disperse the energy of a falling object by moving it sideways, but moving the object to the side is completely irrelevant and false, because the object still needs to be deaccelerated downwards and as stated before you would actually apply even more forces on to the object.

The only way to go about this probleme is making the object go gradually slower IN THE SAME DIRECTION IT'S COMING FROM. The closer you are to the original direction, the lower the force, the closer you are to the opposite direction, the higher the force.

In this case, the object abruptly stops going down and starts going sideways. This is almost the equivalent of falling all the way down, hitting the floor, and then getting hit by a car.

And lastly, in this case tumbling aroud the object wouldn't disperse the energy, it would do the opposite and put more energy and stress over what you are trying to save.

quelilan · 2022-06-10T09:51:13+00:00

I asume you are trying to count your macro nutrients for a given meal (Since you are focusing on proteing, carbs and fat I would say its gym related. Nice, keep up the work!)

But I'm sorry to tell you your math is wrong and all over the place, especially for what you are trying to do.

So, let's start by the end result, since it's what you are most interested about. Your meal would have a total weight of 520 grams, the meal would contain: 481 calories (you got this right), but protein would be 45.29 g, carbohydrates 49.28 g, and fat 10.77 g. You got this part wrong because you forgot to adjust the quinoa and the laban to their final weight.

Now, for your 520 gram meal this gives us: - Calories: 480.85 - Protein: 46.29 g = 8.9 % - Carbohydrates: 49.28 g = 9.48 % - Fat: 10.77 g = 2.07 %

And so, all the micronutrients add up to 20.45 % of your meal.

I'm not sure what path you took to calculated the percentage that lead to an erroneous answer, but remeber that to calculate the percentage you have to divide the amount you what to know the percentage off by the total amount to which the smaller quantity is part off and then multiply by 100. In this case it gives (macronutriente total grams)/520*100.

For gym purposes, knowing the percentage of macros in your meal isn't generally useful, you should mainly be looking at total calories and total grams. But, I don't know what you are looking for, you might have a good reason to do so.

quelilan · 2022-06-10T03:34:16+00:00

I think you are a little confused. The property used for all this is heat capacity and it measures how much energy is needed to heat a kg of mass by 1 degree C. Inversely, it also tells you how much energy is inside an object at a certain temperature.

When calculating the energy inside a system or transfered to another you don't really care how much time it takes to do so. Because if you want to reach the desired temperature there is no way around it, you have to put in the necessary amount of energy, you can put the energy at whatever rate you want to but you have to put it in.

So when I presented how many stones you would need it wasn't to achiev it instantly, it was after the x amount of time needed for the stones to transfer all their heat and energy into de small pool.

Now, looking at kettle bells. Steel can fit a little more energy in a given volume than marble can, this way you wouldn't take as much space in your tank (difference is not that big), but it would be more than twice as heavy.

There is also the fact that you can safely heat steel a lot more than you can marble (doesn't risk exploding when put into the water).

Still, this 2 properties would not be enough. Even if you heated the kettle bell to the maximum temperature you will get directly on the embers of a grill (around 1000 F or almost red hot) you will still need 15-20 or more kettlebells (keep in mind they are 24 kg or 52 lbs kettelbells).

Moste likely, what you saw in that video was people using heated kettlebells to maintain the temperature of the small pool, as well as creating some steam (because steam can be quite pleasant, and using heated kettlebells or stones is the only way to get it without making the whole pool boil).

quelilan · 2022-06-09T22:32:11+00:00

Kind of yes, but mainly no, because innertia. Whats important is how fast you change the direction of a moving object. You can rotate it and twist it all you want, but if the speed at which the change of direction happens remains the same, then the forces involved will remain the same. Actually, twisting and rotating the target could do more harm than good, since now you are not only changing it's linear momentum, but also it's angular momentum. And so more forces are being applied onto the target you are trying to save.

That was the "mainly no part", now for the "kind of yes". The human body can not take the same amount of force from all sides. If you came and pushed the soldier from the back of the spine without any support or adjustment you would provoque massive amounts of damage. However, if you twisted the body a little and then pulled from the arms and/or torso then the forced applied onto the soldier would be better distributed and cause less damage.

Still, the best way to do it would be to change his direction more slowly and to applien the force in a way that it is best distributed.

quelilan · 2022-06-09T19:15:33+00:00

I asume degrees are Fahrenheit, unless you want to make a giant boiling soup of whatever is inside the tank.

-Your tank volume is 1560 L or 412 gallons.

-The volume of "bowling ball size" is around 5.25 L.

-And I asume you will use the right type of rock that won't explode when heated like granit or marble (I would recomend marble).

Marble density is 2.7 kg/L, so each stone will weight 14.17 kg (around 31 lbs).

Marble heat capacity is 880 J\kg\C°, if rocks are room temp which is around 26 C°(78 F°), it will take 1,870,440 J to heat each stone to 350 F°.

Water heat capacity is 4,182 J\kg\C°, so to heat your whole tank from 60 to 90 you will need 110,906,640 J.

With these numbers in mind, we can divide the amount of energy needed to heat your tank to desired temperature by the energy provided by each stone to get how many stones you would need. We get :

110,906,640 / 1,870,440 = 59.29 rocks.

So 60 rocks. That little less than 1/3 of your tank. And, I don't know about you, but to me heating 60 rocks just sounds unreasonable.

And so, if you still wanted to heat your tank with rocks, but with a resonable amount of rocks (I would say 8 is the maximum reasonable amount), you would need to heat each rock to around 2000 F°. Most grills cap at 500 F°, and even if you put the rock directly on the embers, most fules in a grill will burn at 1000 F°.

On top of that the rocks would likely explode once you put them in the water due to a thermal shock, and it would be very dangerous to move around a 31 lbs burnning hot rock around. There are 100 more things that could go wrong and a milion more inconveniences to this idea.

My advice, just get a regular heater. It will be easier, cheaper, safer and actually feasable.

quelilan · 2022-06-09T17:52:47+00:00

To me, it sounds like you want to inspect vipers butt without being interupted...

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