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During AMC testing, the AoPS Wiki is in read-only mode. No edits can be made.

# Difference between revisions of "2013 AMC 12A Problems/Problem 13"

## Problem

Let points $A = (0,0) , \ B = (1,2), \ C = (3,3),$ and $D = (4,0)$. Quadrilateral $ABCD$ is cut into equal area pieces by a line passing through $A$. This line intersects $\overline{CD}$ at point $\left (\frac{p}{q}, \frac{r}{s} \right )$, where these fractions are in lowest terms. What is $p + q + r + s$?

$\textbf{(A)} \ 54 \qquad \textbf{(B)} \ 58 \qquad \textbf{(C)} \ 62 \qquad \textbf{(D)} \ 70 \qquad \textbf{(E)} \ 75$

## Solution

If you have graph paper, use Pick's Theorem to quickly and efficiently find the area of the quadrilateral. If not, just find the area by other methods.

Pick's Theorem states that

$A$ = $I$ $+$ $\frac{B}{2}$ - $1$, where $I$ is the number of lattice points in the interior of the polygon, and $B$ is the number of lattice points on the boundary of the polygon.

In this case,

$A$ = $5$ $+$ $\frac{7}{2}$ - $1$ = $7.5$

so

$\frac{A}{2}$ = $3.75$

The bottom half of the quadrilateral makes a triangle with base $4$ and half the total area, so we can deduce that the height of the triangle must be $\frac{15}{8}$ in order for its area to be $3.75$. This height is the y coordinate of our desired intersection point.

Note that segment CD lies on the line $y = -3x + 12$. Substituting in $\frac{15}{8}$ for y, we can find that the x coordinate of our intersection point is $\frac{27}{8}$.

Therefore the point of intersection is ($\frac{27}{8}$, $\frac{15}{8}$), and our desired result is $27+8+15+8=58$, which is $B$.

## Solution 2 (Shoelace)

Let the point of intersection be $E$, with coordinates $(x, y)$. Then, $ABCD$ is cut into $ABCE$ and $AED$.

Since the areas are equal, we can use Shoelace Theorem to find the area. This gives $3 + 3x - 3y = 4y$.

The line going through $CD$ is $y = -3x + 12$. Since $E$ is on $CD$, we can substitute this in, giving $3 + 3x = -21x + 84$. Solving for $x$ gives $\frac{27}{8}$. Plugging this back into the line equation gives $y = \frac{15}{8}$, for a final answer of $\boxed{58}$.

~sugar_rush

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## Thursday, October 09, 2014 ... /////

### Fusion: dynomak, a new compact rival of tokamak

Fusion is the energy of the future, and it always will be. Despite this proverb, many teams are working hard to confine the hot plasma for a sufficient time and allow the fusion to be sufficiently long-lived and economically feasible.

I do follow the fusion research in some moderate detail because I do think that it's the most likely future advance that could make a "qualitative abrupt change" in the methods that we exploit to obtain energy. If you look at the fusion category of TRF blog posts, you will find some texts debunking Andrea Rossi's cold fusion but many more "real experiments" such as NIF with its lasers, the Z-machine, and – obviously – ITER, a French-international version of the tokamak concept.

Yesterday, University of Washington released a press release on their dynomak paradigm.

The picture above shows that it is a nicely compact prototype. I haven't been able to see what the successes have been but they say that it could be cheaper to be built than coal power plants etc.

The design originated from term paper in the classrooms of University of Washington which is pretty cool. In April, Elsevier's journal Fusion Engineering and Design published their
The dynomak: An advanced spheromak reactor concept with imposed-dynamo current drive and next-generation nuclear power technologies
by 10 UW authors including Derek Sutherland and Thomas Jarboe.

The design is known as "spheromak" – it's a word used at least since the late 1970s – or "dynomak" – which is their new name for this particular University of Washington incarnation of the idea. The word "spheromak" has mostly meant that the magnetic field needed to confine the plasma is generated... by currents running through the plasma itself. The abstract of that paper tells you quite a lot what molten salt they propose for first-wall cooling and tons of other technical issues as well as some economic and efficiency estimates.

I wish them a lot of good luck. If electric energy were produced mostly by similar gadgets in the future, I think that it would get cheaper and people would finally start to switch to electric cars and other things that are economically inferior these days.

#### snail feedback (88) :

If the corrosion problem with molten salt (of some sort) thorium reactors can be overcome it could be a nice solution until this still further into the future prospect (it seems to me) might be realized.

Meanwhile, back in the real world, the unmentionable fusion seems to be doing well. Another test, another report, but still the fraudulent method that must be there is elusive:

It's doing well, especially the "Gentlemen" who perpetrate this fraud. It just hasn't generated a single joule of energy.

Yet more fusion fraud. At least Fleischmann and Pons were merely confused. These criminals should be in prison.

Huh, do you mean the dynomak? I can't believe you have these ideas. Why do you think that the Sun is shining? Is it due to lots of blue LED diodes on the surface?

The dynomak research should be given a boost of a billion of dollars and copied at several other places.

OK, fusion is *much* cooler - I shouldn't use this adjective, I guess LOL - and it can't be quite excluded that it will run before the modest thorium-based fission reactors.

Given that energy density is the central concept for assessing the technologies of energy production, there can be no doubt that fusion is the [future advance that could make a "qualitative abrupt change" in the methods that we exploit to obtain energy].

But I’m betting one of physics' more embarrassing lacuna, a thorough characterization of turbulence, will stifle the magnetic confinement approaches. Given the intrinsic non-linearities of gas dynamics, plasma’s at those temperatures are riddled by turbulent instabilities giving rise to most daunting of engineering challenges.

I’ll bet on laser inertial confinement winning the race.

Thanks for this first remotely on-topic and not staggeringly insane comment, Tom. ;-)

I think that the masks are automatically deployed whenever there is a sudden depressurization, as would surely happen if the aircraft's fuselage was ruptured at high altitude.

Excellent you said it this explicitly. How quickly do you think the folks would die after the hit by a BUK missile?

Could the oxygen mask end on his neck by coincidence?

Just an opinion for sure, but I did do a fair amount of CFD back in the day.

You are in for a big surprise and a lot of self-doubt.

Cool, you should have said.

What seems sort of strange is that you make it sound that the MHD instability is a "new threat" of a sort that makes this spheromak harder.

It makes fusion harder but spheromaks are already an *answer* to the pre-existing MHD instability problem - that's why the MHD instability appears in the title of the first famous spheromak article.

Thanks, Lubos, I’ll read these links later in the day. No doubt, MHD instability was the issue from day one in fusion research so my writing is (not-unusually) flawed to have conveyed a “new threat” tone.

My intuition is simply that the engineering responses to refine the confinement as instabilities arise will never be fast enough to keep up with the turbulence. I’m guessing we’re talking nanosecond time scales in a domain where only statistical fits are available. Now, if somebody gives the energy density in a turbulent flow in some kind of closed form, then maybe the engineers can come up with the necessary super-fast control circuits.

Maybe if he was scared and fast enough

Lots of things could happen in such a chaotic situation. I have no idea what the probabilities might be, and I suspect no one else does, either.

There is a reasonably informed discussion of this incident here: http://www.pprune.org/rumours-news/543733-mh17-down-near-donetsk.html
The fragmentation warhead of a BUK missile would create multiple high speed chunks peppering the fuselage. The airplane would be torn apart by aerodynamic stresses, but the pieces would still be plenty large enough to hold passengers and very 'lucky' individuals might survive decompression long enough to grab an oxygen mask. It is very unlikely that a mask would slip around a passengers neck from air turbulence.

You are too pessimistic, Lubos. Reason eventually wins out over ignorance. You can safely ignore the stupidity. And should, I think.

The masks deploy automatically when the pressure drops, or can be triggered from the flight deck:

I think it is more likely that the plane broke up (SAMs generally detonate NEAR the target and blast shrapnel through it, not exploding inside the plane like a movie) and one of the passengers remained conscious long enough to try to get the mask on. That it was only partially on shows how quickly he blacked out from the altitude.

I am sure you are right about this happy end, Gene - but I won't be around to see it.

Thanks, and concerning the last point, I think that what I wrote was nonsense because the mask was "attached" around the neck which requires one to "click" the pieces into each other - impossible to happen randomly.

Could please the people who believe that fusion is a non-existent process and those who believe that fusion may be "cold" stop posting their idiotic "contributions" to this website?

After several hours I had to cool down after those comments that made me so upset, I am still very upset so I decided to ban everyone who is this stupid and posts something like that again, whether or not he has been posting here for years.

Maybe world governments can get together and make a deal that if physicists focus on building a usable fusion reactor then the governments will pay for a great big particle accelerator.

Great. The fields are correlated although true particle physics is done for completely different motivations than fusion physics. Fusion research is applied, particle physics is pure science. Also, fusion research is a relatively low-energy (I mean QCD scale, not cold-like low haha) physics while the cutting edge is at much higher energies.

But even if one ignores the differences, I don't think that the correlation is any helpful because, as the structure of the comments before I started to impose the ban shows, the hostility against (hot!) fusion research is exactly as intense as the hostility towards pure particle physics. Most people, at least most of the loud active trolls on the Internet, are complete science---illiterate imbeciles!

I want my Mr. Fusion

wow! I think the abstract caused set my pc on fire, and I have no insurance on it. Are they even using real words?

BUK missile or fighter jet, I doubt that people would immediately become unconscious after a plane's hull is breached. Rapid decompression obviously leads to the breathable air being sucked out of the aircraft, but even if the people couldn't breath anymore, they still would have had enough oxygen in their bloodstreams to remain conscious for a minute or so. Of course, there's also the sudden extreme temperature difference after rapid decompression, but is that enough to knock someone out? Hypothetically speaking, if I leave my warm room and walk into a meat freezer, I remain conscious too, so I doubt it.

Sadly, I think only the people that were directly hit by a bullet or fragment were killed. All the others lived much longer.

In fact there are even scientists amateurs who get to do authentic fusion at home. Through a design called fusor. (Without reaching energetic gain, obviously)

http://en.wikipedia.org/wiki/Fusor
http://www.fusor.net/

A fission reactor's energy is mostly recoil of nascent fission fragments - thermal output - plus a couple or three average 0.8 MeV neutrons to chain react. D + T belches He ( 3.5 MeV ) + neutron (14.1 MeV ) 80% of fusion reactor energy is in the neutron. Go ahead, recover the energy. You then have an ocean of thermal neutrons activating everything, and decaying into beta-rays outside the reactor.

A thick blanket of molten lithium used for breeding fuel and heat exchange is cute. Look up pumping liquid lithium.

Hasn't generated a single joule? Did you read the report? In the summary it clearly says the Rossi device generated 1.5MWh over 32 days. I'll let you convert that to joules.

Which part of the report do you suspect is bad? Dishonest reviewers? Hidden wires? Bad calorimetry?

The Russians have done a test shooting at a plane, and then they show the impact. Quite amazing the comparisons (from around 7:30, at 8:24 you see the comparison with the MH17 in one picture). They also mention the wing:

Also the straight patterns at 7:55 are similar to the ones you also see at MH17:

https://pbs.twimg.com/media/BxBNE99IAAEYZAa.jpg:large

Also interesting is this interview where 2 people mention a 2nd airplane:

See how Paris Match tried to hide this fact by twisting the translation of the text, and cutting short fragments about the other airplane (see also comments below). The BBC had also such a report, but that one disappeared for some unknown reason from their website:

Sorry guys, I forgot to include the Russian video:

When comes the time - when you will need to eat those words ... What will you do (just saying if) ? ... You are taking a monumentally strong position and are very well may be significantly deceiving your poor readers .. so I think when proven wrong, you should do something monumental ... I have a suggestion ... I would like you to carefully place your head... safely .. but firmly ... where it belongs ... If you need any help don't hesitate to call :)

OMG, that's hilarious, are they really trying to say that a few gun rounds (with nice round entry points) are at all similar to a massive shrapnel type cloud observed on the wreckage?

When it comes to nuclear power, either fission of fusion, I do not understand why the left is against both. Inexpensive energy would lift all boats, spending money on fusion or fission power make a whole lot more sense than studying climate change, Oh I forgot the educated idiots need to do something, and nuclear physics is way beyond them on any level. To bad the are hogging most of the money! Yet that not surprising the only thing dumber than a AGW climate scientist is the media and the politician whom are financing them.

Is it some shaving or why is it male? ;-)

The right figure is clearly 0.0MWh over any number of days, I didn't like that it's wrong from the first page to the last one and, most seriously, that this whole industry is complete fraud that continued without any punishment of the culprits for many years. I allowed you to post this one but banned you immediately afterwards.

Gene. I wonder why you are at even older age than I still optimistic to think that reason will win? There seems to me overwhelming stupidity and monumental ignorance at every turn. I am somewhat less sure I am joking each time I say that Idiocracy is a documentary.

Could not agree more!

Fer, I would just add that fusors still make the normal, hot fusion - the temperature has to reach those 45 million kelvins which is achieved by acceleration with 4 kilovolts. Nothing "cold" about fusors.

Savage, I banned you. This is *not* a place for savages to legitimize their utter delusions and fraud.

I do harbor a hope (not sure how well justified) that the type of fission technology that would utilize thorium also would be able to make use of and use up much of the radioactive waste that the currently entrenched fission technology keeps causing a cumbersome accumulation and storage requirement of.

Exactly. Even if one "needed" to switch to other sources, one would have to achieve a breakthrough by studying particular things that the conservatives often fund and leftwingers criticize - such as nuclear technologies. Or some other high-energy physics etc.

(Just to be sure, in Czechia, there is a pro-nuclear consensus across the political spectrum, so the left-wing opposition is a matter of local group think. After all, our first nuclear power plants were built during communism.)

I found this Russian video much more interesting than the other ones.

The first detail that struck me was the near-intersection of the MH17 flight with a very similar plane that had Putin on the board. That's pretty amazing if true.

I am no expert but the first thing I would say when I see these holes *is* that they are round gun rounds.

The idea that the plane was shot down by cannon fire from the Su-27 does not seem to make a great deal of sense to me. If the Ukes wanted to perpetrate a false flag event why would they use a method involving a plane that did not really have the height capability unless pushed to the limit and furthermore have the possibility of leaving evidence on the ground in the form of regular cannon shot holes in the plane that could be conclusively identified if required.

So it makes sense that you would just use a BUK missile since that can easily be blamed on the warmongering separatist incompetents and their Russian patrons. Looking at the available pictures it certainly appears that the plane was hit by a cloud of shrapnel from the alleged BUK although there are oddities such as the appearance of holes going both ways and the hit on the wingtip which appears to come from another direction.

In my opinion the Su-27 was more likely using the Malaysian plane as radar cover for a bombing run which was known to be occurring. Possibly MH17 was diverted over the warzone for this purpose. Or Mh17 was shot down by a BUK fired by the Ukes and the Su-27 was there for observation purposes. Or the presence of the Su-27 is illusory at present.

Those particular Germans are loonies. The variety of sizes of holes, their two-dimensional spread, and their sheer number, are all inconsistent with fighters' guns.

but how do you really feel,lubos?

Lubos, I followed your link and read a few abstracts and I am somewhat surprised on the ubiquity of the MHD model. The conditions for ideal MHD to hold, principally, I guess, overall charge neutrality and infinite conductivity, I would think break down in fully turbulent regions of flows at such temperatures. So I expected to see full-up electro-magneto gas dynamics equations, which introduces a wave family much more complex than Alfven waves alone. But, then, CFD was at the beginning of my career, so I’m guessing I am now a fossil.

(OT but what a nice arrow-of-time post you put up today, I doubt it can be put any simpler.)

Hi, my understanding is that turbulence is ultimately lethal for the spheromak and other gadgets but the very point of this construction is that it reduces or delay turbulence (isn't it what the "MHD stability" helps to achieve?) so that equations neglecting it may be used for a very long time.

yes, could be true. For me it is all interesting information (not only the Russian video), because combined it all points towards another airplane, and not to a BUK missile.
There is of course much more, such as the flight data and black box that has not been released, the secrecy of the investigation committee in which Kiev takes part (very weird), etc, etc... All together makes it for me 95% sure it was Kiev.

Dear Luboš,

I'm not much good at physics but I feel we share a lot in common. I'd say was down to your general attitude.

I do so feel at home here. :)

Well, just look at the images, and you can see that 'the few gun rounds' of the Russians show more holes than those on the MH17. But you also forgot another very interesting detail. Away from the cockpit there is no snaprel on the MH17 at all.
http://cdn4.independent.ie/incoming/article30460508.ece/39d99/ALTERNATES/h342/ISIS-AIRPLANE_322.jpg

LOL, you probably are, but I am often among those who are stunned by some of your comments.

Loves and kisses to you too. XXX

:)

How do you explain that you see the same inconsistencies in the Russian 30mm gun shot results? (8:24 Russian video you see the comparison with the MH17 in one picture). You claim here that that is impossible...

The planes move so everytime the angle of impact differs, making different holes. So they are not at all inconsistent. The patterns showing holes in a row together with the wing and the absence of snaprel in other parts of the plane make a BUK scenario almost impossible.

Maybe you have put your finger on the main problem - all these gadgets assume they can reach the fusion point without turbulence occurring, but it seems to have a nasty habit of always cropping up. The inertial confinement case is interesting in this light because even with the 192 lasers that Livermore uses to generate a field on the pinhead-sized target’s surface it still deviates enough from spherical symmetry to induce turbulence.

Yes, the intelligent support does extend across left/right lines. There is a documentary called Pandora's Promise on Netflix featuring Stewart Brand (The Whole Earth Catalog) and
others who would be characterized as left wing. They have been convinced that nuclear is the better and safer option for power.
BTW has Ron Maimon ever explained to you why he believes in cold fusion? Schwinger did also, and I don't accept that he was senile in any way, but I also am not arguing with you that cold fusion is correct...just wondering why two people who are obviously intelligent seem fooled. They must have some rationale to explain.

lol--- the sun obviously doesn't work using leds---it uses plasma screen technology :)

Ron has always miraculously run out of time when there was an indication that he may want to explain his belief in cold fusion. ;-)

Of course, fusor is hot fusion. (I wrote 'authentic hot fusion at home'). Although you were talking mostly about cold fusion scams in previous comment, I was thinking rather the other crank-group: fusion-impossible. So I remembered the fusor: if someone had doubts about the reality of fusion in stars,etc. always would be possible to test it for themselves at home, following the steps in the second link (With enough time and brain)

--------------------------------
OffTopic/OnTopic always:

In chrome, the right column of this blog, from "trf global facebook like button", is vibrating wildly when zoom is 110, 150, 175, 250 or 500 %.
(but not in 100,125,200, 300, 400%)
Maybe a bug in a components in that column. Perhaps depends of pixels of each monitor, I haven't checked in other computer.

I used to read with 110% and it was uncomfortable when I reached this depth. I even thought it might be a dirty trick to force click that like-button :) (because vibrato start at that point) Then I realized that it was due to zoom.

I find it funny how someone that believes in hidden dimensions and believes that a cat can be dead and alive at the same time would have such a visceral reaction to the possibility that there might possibly be something going on in this world that cannot be explained!

Hi, before I blacklisted you, I approved your comment to sort of show to others more representatively how many stunning aggressive imbeciles are being attracted to my blog.

There is nothing going on in nuclear physics - or any phenomena up to 100 GeV, with a possible exception of some hypothetical very weakly interacting particles to be found - that hasn't been understood. And there is nothing at all in the Universe at all that can't be understood at all.

The fact that cats and all other objects in the world are generally found in a complex superposition of states has been known for 89 years and no one except for hopeless mental cripples has any doubt about it. And the evidence backing the existence of extra dimensions is less waterproof but still very strong.

Hi Lubos,

I think it is because he discovered there was something wrong with his theory.

He takes some "results" from the "research" as reliable and thought his theory could explain the results, but apparently he is no longer sure.

You can read his statement here http://en.wikiversity.org/wiki/Talk:Cold_fusion/Theory/Ron_Maimon_Theory#Conclusions

, at the bottom of the page if you are interested (maybe you aren't ;-).

I am only posting this, as it shows he is honest and does admit mistake.

Hope you are well, and this little post did not annoy you.

Yes. Fusion is very problematic.

Fission energy product fragments are heavy and slow. Not fusion. Fast neutrons.

Uncle Al, how many mega-curries of tritium will there be in a fusion reactor? How easy is it to contain hydrogen?

Looking at a single reaction fission produces more energy but if you instead look at energy by unit of mass fusion produces more.

There is a method for dealing with thermal neutrons: control rods. These are used every day in existing fission reactors to absorb excess neutrons in order to avoid a meltdown. Of course, for a fusion reactor you might need to change the shape and form of those rods and instead use some kind of shell but the technique would still work. As a fusion reactor is not dependent on free moving neutrons to produce energy there is no need to regulate as you do in fission reactions - you can just capture all of them instead.

This is why a fission reactor typically uses electromagnets to control the rods. Should the power go out the rods will drop into place and capture enough neutrons to stop the chain reaction. This kind of safety is not neccessary in a fusion reactor as it would stop working as soon as the power goes out.

A fusion reactor is like a fire you have to feed in order to keep it going. A fission reactor is like a bomb you constantly need to control for it not to "blow" up.

physics junkie,

Mr Fusion won't ever be.

But Philo Farnsworth came *only* several orders-of-magnitude short of that... 1 exp minus 10,000 energy multiplication. You can built a desk-top fusion device. http://en.wikipedia.org/wiki/Fusor

Lubos,

Mr Fusion was a stupid movie, time travel. No logical arrow of time.

It's an extremely long conversation and I am not able to locate a paragraph you want me to read. So sorry.

Otherwise good to hear if it's true. Still interested in his text why he believed what he did and what was wrong.

Hi, should have been more specific then, I apologize and will give you quotes instead.

(He still does not question the experimenters though,)

From the bottom of http://en.wikiversity.org/wiki/Talk:Cold_fusion/Theory/Ron_Maimon_Theory#Conclusions

"Hagelstein is completely right. I removed the claims that this theory matches the experimental data."

From the bottom of http://en.wikiversity.org/wiki/Cold_fusion/Theory/Ron_Maimon_Theory (where his theory also is described in a little detail, not much math though)

"This theory has no ad-hoc theoretical assumptions, and it is consistent with some of the data, but it predicts too many incoherent neutrons from the fast charged particles, and is excluded by Hagelstein's analysis of the limits on energy of the He nuclei produced."

And the lower picture you posted also disproves the claim. The caption to Figure 12 is totally the wrong way around - the heater wires have to be the bright bands in the central 'reactor', whether there is a central reaction or not (because they would be heated by the central reaction and they add heat of there own). As the glow in the 'reactor' is so similar to the glow of the outer rods, and the region between the heater wires is so dark, there is nothing going on here. This would have been seen if they did the calibration run under the same conditions as the live run, but (yet again!) they didn't.

Another fusion advance: the Z-machine at Sandia, see

http://news.sciencemag.org/physics/2014/10/z-machine-makes-progress-toward-nuclear-fusion

claims new progress. They produce 100 times more reactions than before, still 10,000 times less than needed to achieve a positive energy budget, and they saw the first neutrons, a sign of the "secondary" deuterium-tritium reaction, indicating that the fuel was really confined for quite some time.

I see---but I do have a copy of Ron's proof:
https://www.flickr.com/photos/jpallan/4633000725/

LOL, sometimes I would like to know whether those guys were just fooled by some cheap tricks or whether they're bought. If it is the former, it is pretty embarrassing for them.

Lubos
Cold fusion guys also watch Ancient Aliens as though it is a documentary. Also believe we never landed on the moon too.....LOL

Just a thought wouldn't it be better to use a larger containment vessel with the same amount of fuel they use now. The larger containment would allow the turbulence more room and may start a convection zones similar to what we see in stars. Stars use gravity to contain the reaction but we don't have that luxury here on Earth. My thought is that maybe setting up convection may contain the turbulence. My two cents.

They may be on the opposite, "Yes we can", side, Jim! The CIA has artificially produced the moon and planted it on the orbit in order for the people to confuse it with the Sun.

Good questions but it's too complicated for me. A lower density could perhaps reduce the problems with turbulence but it also reduces the pressure and a high pressure is needed for the reaction to burn well etc.

In the Sun, the temperature and the pressure are a bit lower than in the usual fusion devices, real or proposed ones, and the reaction is much slower (per cubic meter). But the Sun's gravity can actually hold the gas for billions of years - while tokamaks and dynomaks are unlikely to ever be this patient. So one needs to rely on a faster reaction and for that, it is better to have a higher temperature than in the Sun.

I was thinking keeping the density the same with a stronger magnetic container thus would allow the magnetic container more volume to create convection and contain the turbulence. Yes, speeding up the reaction is needed. Not making a comparision to the stars just stating how they contain but the physics remains true for both high temps and or pressure.

Lubos,

Something for nothing fusion is not real, as you say.

But cold, desk top fusion is real. EGG nuke bomb 'triggers' (neutron sources) throw tritium at deuterium, cause fusion, and throw off big bad 14mev neutrons. Cold.

Energy multiplication is many exponents to the wrong side of unity for 'free lunches', but it *is* cold, desktop, fusion.

There can be no cold fusion. The obstacle is Coulomb - electrostatic - repulsion between the nuclei, any nuclei, and deuterium and tritium are no different. Neutrons are electrically neutral so they don't affect the electrostatic repulsion at all. They can't help.

To overcome (most of) the Coulomb barrier to make the probabilities of the nuclei fusion significantly nonzero, one needs a huge kinetic energy of them which is equivalent to millions (or tens or hundreds of millions) of degrees in temperature. If the bulk of the fuel isn't at this temperature, it can't fuse.

My apologies Lubos. Had I read your critique first I would not have taken the report seriously.

I have decided to seek professional psychiatric help tomorrow in the hope of obtaining a lobotomy for my sins or perhaps some more strong hormone therapy on top of the drugs I am already taking.

However your comment on the apparent coincidental complete conversion of the isotopes as shown in the fraudulent document, if I may suggest, depends on the theory for example that the alleged heat production must be associated with the said isotope conversion.

Given the impossible nature of the alleged nuclear reaction perhaps the isotopes converted quickly at the beginning in order to facilitate the heat production. After no radiation is given off so there is no need to assume any form of conventional reaction.

We will have to wait until the next fraudulent report to see if this issue is resolved further, or perhaps one or more of the wretched experimenters will finally confess to the hoax.

It does seem fairly plausible that containment volume could help, especially if it where on the scale of power plant size.

Pondering on this stuff for the last few days, especially with the news from Sandia, I guess my thinking comes back to control methods. Turbulence is so ubiquitous that it is always going to arise as temperatures reach the fusion point no matter what the geometry is. So my guess is some manner of very fast control techniques will be needed. Reactive controls for the optical path through a turbulent flow are fairly well developed, so maybe something similar could be used for inertial confinement. The Sandia approach, a mix of inertial and magnetic confinement, might be best for this as control circuits linked to the magnet fields might be able to modulate the turbulence from the inertial crunch.

One thing for sure, fusion energy is the toughest engineering problem mankind has yet seriously faced. It’s pretty likely that a good number of decades will pass before it comes on line.

What are your Thoughts on the Focus Fusion Project at
the Lawrenceville Plasma Physics in Middlesex New Jersey? Does it have potential
to work in the near future, if at all?

Actually, they have a very neat solution to this by proposing a (molten) lithium fluoride salt(FLiBe) for the task, which is much nicer than liquid lithium. It has been proposed for use in "regular" Gen-IV nuclear reactors as a combined moderator/coolant as well, since it has a similar heat capacity to water and is an excellent moderator.

It's a very good competitor to water for transporting(and/or storing) heat even in a regular nuclear, coal or solar thermal power plant. The fact that it can double as the lithium blanket in a fusion reactor is a very nice surprise.

Dear Jim,

Making things bigger is exactly what ITER is doing. By making things larger, the time scales involved in the fluid equation become larger, so containment times become larger and things become easier.

The thing is, big means expensive. Expensive means useless when fusion has to compete with other power sources. ITER and future evolutions of it are already kind of too big and expensive, and ideally you would want to have a design which is smaller, not bigger, if it were possible.

Lubos,

Use electric field to accelerate tritium ions, aim them at deuterium, (14mev neutrons occur), and you have the neutron source 'trigger' of a fission device. Very special gadgets. They 'insert reactivity' at the most advantageous time in the assembly.

They are "cold" in my use of the word; the initiation kinetic energy is electrical not thermal. The device sits on a desktop, it is room temperature, it causes some small amount of fusion, and it is still room temperature on the desk top.

I know that my use of "cold" is incorrect by your correct definition of temperature.

But on the other hand: Tritium, in the center of a fission mass or "pit", boosts the yield of a fission device. That's a fact. The (average) temperature and pressure of the tritium at the center of the assembled critical mass is never high enough to overcome the Coulomb barrier. Yet the fusion (some) occurs. How does that happen?


text:
# POSIX Shell: Basic Examples and Common Operations

Last updated:

WIP Alert This is a work in progress. Current information is correct but more content will probably be added in the future.

There are some times when you cannot use Perl, Python or even Bash because you need to run scripts on legacy systems or systems you can't know for sure what shell they are using.

The POSIX shell (usually invokable via /bin/sh) is a basic shell and a set of standards that you can use to make sure your scripts run no matter what shell you have.

POSIX-compliant scripts are supported by all major shell versions such as bash, tcsh, zsh, csh, etc. So if it works in sh it will also work in other shells.

If you need to make sure your scripts will run no matter what shell you have, POSIX-shell is the way to go. Avoid bashisms, i.e. code that works in bash but not on POSIX shells

## Detecting that you are running sh

Run the following command:

ps -p

If you are indeed running sh, you'll see an output like the following:

PID TTY          TIME CMD
10552 ?        00:00:00 sh

The sh under CMD means you're running POSIX shell (likely /bin/sh)

## Simple if then else

if [ -f myfile.txt ]; then
cat myfile.txt
elif [ -f otherfile.txt ]; then
cat otherfile.txt
elif [ "foo" = "bar" ]; then
echo "this will never be run!"
else
fi

## Testing a string matches a regexp

A popular way is to use echo and grep together:

SOME_VAR="foo-bar-3"

if echo "$SOME_VAR" | grep -P '\d$';then
echo "it ends in a digit!"
else
echo "it doesn't end in a digit!"
fi

or, as a one-liner:

if [ 'a' != 'b' ]; then echo 'great success'; fi

### Finding the return code of the last command run

# the following command will fail as it doesn't exist
foo

if [ "\$?" != 0 ];then
echo 'failed!'
else
echo 'all ok!'
fi


text:
Math Help - a box of paper

1. a box of paper

A box contains 25 slips of paper numbered 1 to 25. What is the probability that one will randomly select a number that is divisible by 3 or 7?
help me anybody.....
I'll be very appresiate you!

2. Originally Posted by busyboy
A box contains 25 slips of paper numbered 1 to 25. What is the probability that one will randomly select a number that is divisible by 3 or 7?
help me anybody.....
I'll be very appresiate you!
Write out all the numbers between 1 and 25 that are divisible by either 3 or 7. Count how many there are. Divide that number by 25. Viola!

3. Originally Posted by mr fantastic
Viola!

Jhevon made the same mistake !
It's voilà
Viol...means rape ! but don't worry, I would give my consent xD

4. Originally Posted by busyboy
A box contains 25 slips of paper numbered 1 to 25. What is the probability that one will randomly select a number that is divisible by 3 or 7?
help me anybody.....
I'll be very appresiate you!
A number divisible by 3 is = 3, 6, 9, 12, 15, 18, 21, 24
= total 8 numbers.

A number divisible by 7 is = 7, 14, 21
= total 3 numbers.

Probability that a number divisible by 3 or 7 is $= \frac {8+3}{25}$

$= \frac {11}{25}$

5. Originally Posted by Shyam
A number divisible by 3 is = 3, 6, 9, 12, 15, 18, 21, 24
= total 8 numbers.

A number divisible by 7 is = 7, 14, 21
= total 3 numbers.
Shyam, if you are going to simply handout complete solutions at least do them correctly.
Probability that a number divisible by 3 or 7 is $= \frac {8+3{\color{red}-1}}{25} = \frac {10}{25}$
You counted 21 twice.

6. Originally Posted by Moo

Jhevon made the same mistake !
It's voilà
Viol...means rape ! but don't worry, I would give my consent xD
The viola is my favourite instrument. I like to hear it sometimes when I post. Hence my deliberate transposition of letters. As for Jhevon, I think he's just lousy at French


text:
# Aerodynamics Questions and Answers – Compressible Flow through Diffusers

«
»

This set of Aerodynamics Multiple Choice Questions & Answers (MCQs) focuses on “Compressible Flow through Diffusers”.

1. What is the role of the diffuser?
a) Increase the flow velocity after test section
b) Decrease the flow velocity after test section
c) Increase the flow velocity inside test section
d) Decrease the flow velocity inside the test section

Explanation: Diffuser is a duct used mostly in the subsonic wind tunnel in order to slow down the high flow velocity post test section to a lower velocity at the diffuser’s exit.

2. Diffuser is only applicable for incoming subsonic flow.
a) True
b) False

Explanation: Diffusers work for both subsonic and supersonic incoming flows. Although the design and shape of diffuser in both the cases vary. In both the cases, the work of the diffuser is to lower the speeds by least total pressure reduction.

3. Which of these properties remain constant in the ideal isentropic supersonic diffuser?
a) Total pressure
b) Velocity
c) Mach number
d) Mass flow

Explanation: Isentropic supersonic diffusers have a constant entropy throughout the diffuser duct. Since the entropy is constant, the total pressure along is the duct is also constant.

4. Why is ideal supersonic diffuser not feasible?
a) Presence of shock waves
b) Varying cross – sectional area
c) Varying throat area
d) Choked flow

Explanation: Due to the presence of oblique shock waves on the convergent portion, the ideal supersonic diffuser is far from achievable. This contributes to the breaking of the isentropic flow characteristics according to which the entropy in the diffuser is constant. In fact, the flow in reality is viscous and there is an increase in entropy near the boundary layer.

5. Which of these processes is involved in slowing down the air inside the subsonic diffuser?
c) Isentropic expansion
d) Isothermal compression

Explanation: The process of slowing down the incoming flow inside the diffuser is done using adiabatic expansion. The pressure is constant throughout, if this was not the case then reduced total pressure in front of the compressor would yield less flow velocity.

6. Which of these results in decrease of the flow inside the actual supersonic diffuser?
a) Test section
b) Convergent nature
c) Divergent nature
d) Shock waves

Explanation: In case of actual supersonic diffuser, there’s a series of oblique shock formations. It’s present in the convergent and the test section of the wind tunnel. The interaction between the viscous flow and the shock waves resulting in slowing down the flow velocity.

7. What is the relation between the entry and exit entropy of an actual supersonic diffuser?
a) s1 = s2
b) s1 > s2
c) s1 < s2
d) s1 s2 = 1

Explanation: When the flow interacts with the oblique shock waves inside the supersonic diffuser, the flow diffuses to a slower velocity. This results in a normal shock wave at the end of the diffuser. Thus the exit entropy is higher than the entropy at the inlet section.

8. Normal shock diffuser is more efficient than the oblique shock diffuser.
a) True
b) False

Explanation: The goal of the diffuser is to reduce the flow velocity with small total pressure loss. If we reduce the incoming supersonic flow through a series of oblique shock followed by a weak normal shock wave, leads to lower total pressure loss compared to reducing the incoming supersonic flow to subsonic using one strong normal shock.

9. How is the flow compressed in an ideal supersonic wind tunnel inside a diffuser?
a) Isentropic
c) Isochoric
d) Isobaric

Explanation: In an ideal supersonic diffuser, the air is slowed to subsonic speed and then expended to the atmosphere. This is done by isentropic compression as ideally there should be no loss in total pressure.

10. Which of these factors contribute to additional total pressure losses inside the oblique shock diffuser?
a) Abrupt change of convergent – divergent sections
b) Shock wave interaction with walls
c) Isentropic flow
d) Presence of normal shock

Explanation: In real life, oblique shock diffusers have viscous flow. The presence of shock waves inside the diffuser leads to interaction with the viscous boundary layer of the diffuser walls which leads to additional pressure losses. There’s also friction involved which makes oblique shock diffusers far from the ideal diffusers which have no total pressure losses.

11. What is the formula to compute the efficiency of diffusers?
a) ηD = $$\frac {(\frac {p_{d_0}}{p_0})_{actual }}{(\frac {p_{0_2}}{p_{01}})_{normal \, shock \, at \, M_e}}$$
b) ηD = $$\frac {(\frac {p_{d_0}}{p_0})_{actual }}{(\frac {p_{0_2}}{p_{01}})_{oblique \, shock \, at \, M_e}}$$
c) ηD = $$\frac {(\frac {p_{0_2}}{p_{01}})_{normal \, shock \, at \, M_e}}{(\frac {p_{d_0}}{p_0})_{actual }}$$
d) ηD = $$\frac {(\frac {p_{0_2}}{p_{01}})_{oblique \, shock \, at \, M_e}}{(\frac {p_{d_0}}{p_0})_{actual }}$$

Explanation: The efficiency of diffuser is measured by the ratio of actual total pressure ratio $$\frac {p_{d_0}}{p_0}$$ to the total pressure ratio across hypothetical normal shock wave at test section Mach number $$\frac {p_{0_2}}{p_{01}}$$.

12. What is the diffuser efficiency of a normal shock diffuser?
a) 1
b) 0
c) Inifinty
d) $$\frac {1}{2}$$

Explanation: The diffuser efficiency is given by the formula:
ηD = $$\frac {(\frac {p_{d_0}}{p_0})_{actual }}{(\frac {p_{0_2}}{p_{01}})_{normal \, shock \, at \, M_e}}$$
In case of normal shock diffuser, the numerator will be equal to the denominator, hence the efficiency is one.

13. What is the diffuser efficiency for hypersonic conditions?
a) ηD = 1
b) ηD > 1
c) ηD < 1
d) ηD = 1/2

Explanation: Usually for low supersonic test section Mach numbers, diffusers perform better than the normal shock diffuser, hence the numerator is greater than the denominator in the efficiency formula. This leads to ηD being greater than 1. But for hypersonic conditions, this is not the case and ηD < 1 as the normal shock recovery is not that great.

14. How is diffuser throat area At2 related to the nozzle throat area At1?
a) At2 = At1
b) At2 > At1
c) At2 < At1
d) At2 At1 = 1


text:
# Is an atom most stable when it has eight electrons in its outermost energy level?

Apr 29, 2017

Yes if the outer most energy level is the combination of ${s}^{2} {p}^{6}$

#### Explanation:

If the the outmost energy level is ${s}^{2} {d}^{6}$ it is not the most stable.

In the case of Iron $F {e}_{26}$ The $3 {d}^{6}$ electrons could be considered to not be part of the outermost energy level because Iron is in the fourth energy level and the $3 d$ electrons are part of the lower third energy level.

Practical however the $3 d$ electrons are part of the valance electron structure of the transition metals and therefore are part of the outermost electron shell.

So it is important to specify that the stable octet is only for the
${s}^{2} {p}^{6}$ configuration.


text:
# L'hospital's Rule

• October 21st 2009, 03:16 PM
mlckb1
L'hospital's Rule
I'm supposed to be finding the limit of a function using L'hospital's Rule but with this limit:

limit (as x goes to infinity) of (e^x)/(x^3)

I just can't see how L'hospital's Rule applies since the numerator is going to infinity while the denominator is going to zero(Wondering) But the answer in the back of the book is infinity, so i think I'm looking at it wrong. Can someone explain to me how L'hospital's Rule applies?
• October 21st 2009, 03:19 PM
skeeter
Quote:

Originally Posted by mlckb1
I'm supposed to be finding the limit of a function using L'hospital's Rule but with this limit:

limit (as x goes to infinity) of (e^x)/(x^3)

I just can't see how L'hospital's Rule applies since the numerator is going to infinity while the denominator is going to zero(Wondering) But the answer in the back of the book is infinity, so i think I'm looking at it wrong. Can someone explain to me how L'hospital's Rule applies?

try again ... as $x \to \infty$ , $x^3 \to \, ?$
• October 21st 2009, 03:56 PM
mlckb1
Quote:

Originally Posted by skeeter
try again ... as $x \to \infty$ , $x^3 \to \, ?$

Oh i see it now (Sun) thank you!


text:
+0

# HELLPPPPP

0
91
1

From point $A$, Leigh walked 40 yards south, 60 yards west, 10 yards north, and 20 yards east to point $B$. What is the length, in yards, of $\overline{AB}$?

Oct 9, 2020

#1
0

40 south, 60 west 10 north, 20 east totals to

30 south, 40 west

$$\sqrt{30^2 + 40^2}$$ = 50


text:
# 澳门新葡8455最新网站,www.8455.com,新葡京最新官网

Fuglede's conjecture in Q_p

I will report on our recent progress in studying Fuglede's conjecture in the filed Q_p of p-adic numbers.  We proved that Fuglede's conjecture concerning spectral sets and tilings holds in the field of p-adic numbers, i.e. a Borel set of positive and finite Haar measure is a spectral set if and only if it tiles the space by translation, although the conjecture remains open in the field of real numbers. Our study is based on the investigation of a convolution equation of the form f * \mu =1, where \mu is a measure supported by a discrete set and f is a non-negative integrable function. I. J. Schoenberg's result concerning the p^n-th roots of unity plays a crucial role. These are joint works with Ai-Hua FAN, Lingmin Liao and Ruxi Shi.


text:
# Differing variance equations

I see both of these equations on Wikipedia and Cross Validated being referred to as "variance":

$$\mathrm{Var}(x) = \mathrm{E}\left[ \left( x - \mathrm{E}[x] \right)^2 \right]$$

$$\frac{1}{n} \sum_i \left(x_i - \bar{x} \right)^2 \quad \text{ where } \quad \bar{x} = \frac{1}{n} \sum x_i$$

Does the $$\mathrm{E}$$ simply imply that the equation in brackets needs to be averaged over all iterations, hence why we place the $$\frac{1}{n}$$ at the front of the equation?

I just need to be walked through how the top equation allows us to arrive at the bottom equation and both of these are referred to as variance.

Also, is there a term you could use to refer specifically to $$\sum_{i=1}^n(x_i-\bar{x})^2$$ when not multiplied by $$\frac{1}{n}$$? Just sum of squares?

• To understand the distinction, you should understand the difference between the population and a sample. – Matthew Gunn Oct 6 '18 at 5:15
• I think understand the difference but am still confused. Lets assume the total population was 100 and I measured some variable $x$ in every member of that population. In order to determine the variance of $x$, I would still have to multiply $\sum_{i=1}^n (x_i - \bar{x})^2$ by $\frac{1}{n}$. The top equation does not have a $\frac{1}{n}$. I'm asking is that what the $\mathrm{E}$ implies? – Dylan Russell Oct 6 '18 at 5:20
• Try to find the difference between "parameter" and "the estimate of parameter". In your case, the first one is parameter and the second one is the estimate (guess) of the first one. More specifically, the first one is variance of $x$ and the second one is the estimate of the variance of $x$. – user158565 Oct 6 '18 at 5:59

The second equation is an estimation procedure, so it is an estimation of the variance, i.e. $$\hat{var(X)}$$. And, in practice, it is usually not equal the theoretical value calculated from the first equation. Moreover, another estimation of variance uses $$\frac{1}{n-1}$$ instead of $$\frac{1}{n}$$ because it is unbiased. Please check calculation of $$E[S^2]$$ in the link.
Finally, yes, the $$E$$ sign implies taking mean of the inner expression; but they're not equal. For example, approximating $$E[g(X)]$$ via $$\frac{1}{n}\sum{g(x_i)}$$ from data is not a rare situation in statistics.


text:
# Proof of Prime Number Theorem using Abel summation

I am trying to show that the prime number theorem is equivalent to the statement that $$\sum_{p\le x} \log(p) \sim x \implies \pi(x) \sim x/\log(x)$$. It was suggested that I use Abel summation with $$a_n = \begin{cases}\log(n), \ \text{n prime}, \\ 0, \ \text{otherwise.} \end{cases}$$ and $$b_n = 1/\log(x)$$. It was also recommended I begin by showing $$\int_2^x \frac{1}{\log^2(t)} \sim O\left(\frac{x}{\log^2(x)}\right)$$ and splitting up this latter integral to $$\int_2^x = \int_2^\sqrt{x} + \int_\sqrt{x}^x$$. I've done the latter, and I end up with $$\int_2^x \frac{dt}{\log^2(t)}dt = \frac{2}{\log(2)} + \int_2^x \frac{1}{\log(t)}dt - \frac{x}{\log(x)}.$$ Using Abel summation, I can say that $$\sum_{1 \le k \le x} \frac{a_k}{\log(k)} = \left(\sum_{1 \le k \le x} a_k\right) \frac{1}{\log(x)} + \int_1^x \left(\sum_{1 \le k \le x}a_k \right)\frac{1}{t\log^2(t)} dt.$$ Beyond this, I'm a tad stuck...

• I side the last integral the bounds for $k$ should be $1\leq k\leq x$ – Julian Mejia May 3 at 4:09

You are almost there. Note that $$\sum_{1\leq k\leq x} \frac{a_k}{\log k}= \pi(x)$$
Now, if $$\sum_{1\leq k\leq x} a_k=\sum_{p\leq x}\log p\sim x$$ Then $$(\sum_{1\leq k\leq x} a_k)\frac{1}{\log x}\sim x/\log x$$ And $$\int_1^x(\sum_{1\leq k\leq t} a_k)\frac{1}{t\log^2t}=O(\int_1^x t\frac{1}{t\log^2t})=O(x/\log^2x)=o(x/\log x)$$


text:
# Write an equation for a like that is parallel to the given point. Explain how you found the equation.

1 answer
###### Question:

Write an equation for a like that is parallel to the given point. Explain how you found the equation.

## Answers

3 answers

### What are the three basic storage of computer

what are the three basic storage of computer...
1 answer

1 answer

### An electron has a charge of positive one negative one positive two negative two

An electron has a charge of positive one negative one positive two negative two...
1 answer

### Why is it difficult to distinguish between asteroids and meteoroid

Why is it difficult to distinguish between asteroids and meteoroid...
2 answers

### What is the greatest integer that is less than √6+√7? It would make me happy if someone answered this question :)

What is the greatest integer that is less than √6+√7? It would make me happy if someone answered this question :)...
1 answer

### Need Help ASAP. Match each graph with the correct slope.

Need Help ASAP. Match each graph with the correct slope....
1 answer

### Traits are controlled by DNA through the order of its A hydrogen bonds B nitrogen bases c. deoxyribose sugars D phosphate backbone

Traits are controlled by DNA through the order of its A hydrogen bonds B nitrogen bases c. deoxyribose sugars D phosphate backbone...
1 answer

### De acuerdo al numero de terminos que contiene la expresion 2a+b reciba el nombre de:

de acuerdo al numero de terminos que contiene la expresion 2a+b reciba el nombre de:...
1 answer

### Explain what an apprentice is and how he becomes a journeyman

explain what an apprentice is and how he becomes a journeyman...
2 answers

### What is another way to write this number: 300+70+5/10+8/100

What is another way to write this number: 300+70+5/10+8/100...
2 answers

### On which day did Kay bike a whole number of miles?

On which day did Kay bike a whole number of miles?...
1 answer

### Read the excerpt from we beat the street how do the friends change after they attend Seton Hall Presentation?

Read the excerpt from we beat the street how do the friends change after they attend Seton Hall Presentation?...
2 answers

### How many prime numbers are between 0 and 20? [1 marks] 7 8 9 10

How many prime numbers are between 0 and 20? [1 marks] 7 8 9 10...
1 answer

### If an atom has 17 protons, 18 neutrons, and 17 electrons, what is the mass of this atom?

If an atom has 17 protons, 18 neutrons, and 17 electrons, what is the mass of this atom? ...
1 answer

### PLEASE HELP MEEEEEEE:((((

PLEASE HELP MEEEEEEE:((((...
2 answers

1 answer

### ARGUMENT You are a magazine writer assigned to find out how people feel about the Populist Party. Write your article describing the support for and opposition to the party. (4-6 sentences).

ARGUMENT You are a magazine writer assigned to find out how people feel about the Populist Party. Write your article describing the support for and opposition to the party. (4-6 sentences)....
1 answer

### Hydraulic press is a force multiplier . show mathematically

Hydraulic press is a force multiplier . show mathematically...
1 answer

### What were paints made from during the Renaissance Period? (Answer with at least 1-2 complete sentences)

What were paints made from during the Renaissance Period? (Answer with at least 1-2 complete sentences)...
1 answer

### Alicia has $20 in her savings account. Option one will add$50 to her account each week. Option two will double the amount in the account at the end of each week. For which week will the amount in her account with option to first exceed the amount in her account with option one?

Alicia has $20 in her savings account. Option one will add$50 to her account each week. Option two will double the amount in the account at the end of each week. For which week will the amount in her account with option to first exceed the amount in her account with option one?...

-- 0.046750--


text:
# Plotting to Get a Straight Line

## Homework Statement

State what you would plot to get a straight line if experimental (x,y) data are to be
correlated by the following relations, and what the slopes and intercepts would be in
terms of the relation parameters. If you could equally well use two different kinds of plots
(e.g. rectangular or semilog), state what you could plot in each case [the solution to part
(a) is given as an example]

a) y^2=a*e^(-b/x)
solution: construct a semilog plot of y^2 vs 1/x or a plot of ln(y^2) vs 1/x on rectangular coordinates, slope = -b, intercept =lna.

c) 1/ln(y −3) = (1+ a*sqrt( x))/b

e) y = exp(a sqrt(x) +b)

g) y=(ax+b/x)^(-1)

## The Attempt at a Solution

I'm really confused about this. I tried looking in the book, but I couldn't find anything. I feel like the answer should be pretty easy, but I'm just not getting it. If you could help me with one of the questions it should definitely help me solve the other ones. Thanks in advance!

## The Attempt at a Solution

NascentOxygen
Staff Emeritus
Do you understand how to arrive at that answer you have for (a)?

The answer for a was given. I was looking at it so that I could get an idea as to how to complete the problem, but I don't see how they got it.

NascentOxygen
Staff Emeritus
y^2=a*e^(-b/x)

Taking the natural log of both sides gives:

log (y^2) = log ( a*e^(-b/x) )

The RHS can be simplified using rules associated with logs, viz., log (x*y) = log(x) + log(y)

= log (a) + .......

Can you fill in the blank?

log(e^(-b/x))

NascentOxygen
Staff Emeritus
log(e^(-b/x))
This can be simplified. Remember the log we are using is loge

So it would be just log(-b/x)

NascentOxygen
Staff Emeritus
When you reach an impasse in algebra, it can be enlightening if you substitute numbers and play with the expression. When you think you have found the simplified form, test with numbers to see whether it equals the expression you started out with.

Perhaps first try to simplify log10(10^7)

jtbell
Mentor
So it would be just log(-b/x)

You can go further than that.

CWatters
Homework Helper
Gold Member
So it would be just log(-b/x)

$$2\ln{y}=\ln{a}-\frac{b}{x}$$


text:
Ideal Gas Model. The ideal gas is defined as a gas which obeys the following equation of state: Pv = RT. The internal energy of an ideal gas is a function of

Ideal Der Ernst des Lebens [LP, 1981]Låt: Erschießen Savoy Anotimpuri [LP, She No Home Alfred E. Neuman — It's A Gas Eurythmics — You Take Some

In real life, there is no such thing as a truly  There is no such thing as an ideal gas, of course, but many gases behave approximately as if they were ideal at ordinary working temperatures and pressures. Jul 3, 2019 An ideal or perfect gas is one whose pressure, volume, and temperature are related by the ideal gas law. Dec 1, 1999 The gas laws. Although we're now familiar with the ideal gas law, which relates the pressure, volume, and temperature of an ideal gas in one  A gas is said to be ideal when there is no net force of attraction between the molecules of the gas .However, This is also one of the postulates of Kinetic theory of  Feb 2, 2015 real gases have volume.

Nu har jag ett litet klurigt problem inom termodynamiken igen! En enatomig ideal gas genomgår en kretsprocess. Processen  En ideal gas är en modellering där man antar att gasen består av ourskiljbara partiklar och där den enda växelverkan partiklar emellan, eller  Thermodynamics part 2: Ideal gas law Thermodynamics Physics Khan Academy - video with english and De ideal gaslag relaterar trycket, volymen, kvantiteten och temperaturen för en ideal gas. Vid vanliga temperaturer kan du använda den ideala gaslagen för att  Om idealgasekvation är formulerad med idealgas-koncept, varför används samma ekvation för riktiga gaser, de är inte de ideala gaserna. Consequently,[1] an irreducible ideal of a Noetherian ring is primary. The original ideal gas law uses the formula PV = nRT, the density version of the ideal gas  William and mary bar essays essay on consumer protection act 1986, ideal gas law research paper francis bacon essays quiz, research paper on ethnographic. Redan luften uppfyller tillnärmelsevis i detta fall fordran på en idealgas , och noggrannhet utförts försök med olika gastermometrar , hvarvid man funnit en  Video games and child development essay essay for my class room, organization of the essay contoh soal essay conditional sentence type 1 beserta  Ekvationstillståndet för en ideal gas.

Se hela listan på powderprocess.net A Diatomic Ideal Gas. A Diatomic Ideal Gas Equation: $$\Delta{U} = \frac{5}{2}nR\Delta{T}$$ In a diatomic gas, it has a total of three translational kinetic energy modes and two rotational energy modes (hence, the 5/2). 2017-09-18 · What is an Ideal Gas. An ideal gas is a hypothetical gas that does not really exist in the environment.

för att återskapa resultatet för ideal gas i klassisk gräns. 11.5.1 Uttryck för µ. Orbitalerna är nu en lösning till schrödingerekvationen för partikel i

The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is amenable to analysis under statistical mechanics. An ideal gas in a sealed container has an initial volume of 2.55 L. At constant pressure, it is cooled to 20.00 degrees Celsius where its final volume is 1.75 L. An ideal gas that is said to be a theoretical gas that does not exist in reality but is assumed to exist for the purpose of simplifying calculations.

Vi har tidigare sett att tryckberoendet hos den kemiska potentialen för en ideal gas har utseendet: Misslyckades med att tolka (MathML med

2019-04-03 2018-10-03 2015-08-04 2020-06-09 2017-09-18 2013-10-02 An ideal gas is a hypothetical gas whose molecules exhibit no intermolecular attractive forces and undergo elastic collision with each other and with the walls of the container. An ideal gas conforms to a particular idealized relation between pressure, volume and temperature referred to as ideal gas law. Ideal gas molecules do not attract or repel each other. Ideal gas molecules themselves take up no volume. In detail, they have negligible intermolecular forces of attraction between molecules.

Inga betyg satta.
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No known gas is an ideal gas, but actual gases approximate this behavior at relatively low pressure and high temperature. American Heritage® Dictionary of the English Language, Fifth Edition. 2018-10-03 · Kinetic Theory assumptions about ideal gases There is no such thing as an ideal gas, of course, but many gases behave approximately as if they were ideal at ordinary working temperatures and pressures. Real gases are dealt with in more detail on another page. Se hela listan på powderprocess.net A Diatomic Ideal Gas. A Diatomic Ideal Gas Equation: $$\Delta{U} = \frac{5}{2}nR\Delta{T}$$ In a diatomic gas, it has a total of three translational kinetic energy modes and two rotational energy modes (hence, the 5/2).

An ideal gas contains molecules of a negligible size that have an average molar kinetic energy that depends only on temperature. Intermolecular forces and molecular size are not considered by the Ideal Gas Law. The Ideal Gas Law applies best to monoatomic gases at low pressure and high temperature. An ideal gas is a hypothetical gas dreamed by chemists and students because it would be much easier if things like intermolecular forces do not exist to complicate the simple Ideal Gas Law. Ideal gases are essentially point masses moving in constant, random, straight-line motion.
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A thorough treatment of ideal gas thermodynamic processes is presented in the book. In a process two quantities are given as functions of time and other

An ideal gas conforms to a particular idealized relation between pressure, volume and temperature referred to as ideal gas law. Ideal gas molecules do not attract or repel each other.

This means that no attractive or repulsive forces are involved during collisions. An ideal gas is defined as a gas composed of randomly moving particles as all gases do, the only difference being that for an ideal gas when its particles collide with each other, these collisions are assumed to be perfectly elastic which means no energy of either of these particles is wasted.


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# What is a nuclear waste? What are the hazards of nuclear waste to living things?

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The byproducts obtained in a nuclear reaction are called nuclear wastes. These, are radioactive wastes and emit radiations ($\alpha$, $\beta$ and $\gamma$) which may cause skin cancer and severe genetic disorders.