studiot

There are enormous spin-off and long term benefits to be gained for all humanity in changing our way of life for the better in response to the climate change issue. For example as a youth I can remember walking round our towns and cities in the 1950s. Most of the buildings and particularly the railway bridges were black, due to a soot coating. Since the Clean Air Acts, I have watched the brickwork emerging from behind its coating and take great comfort that I am not breathing the shit that my ancestors did for the last couple of hundred years. This is a small example that affects over 80% of folk in the UK. The list of such improvements could go on and on. We must not stop now and say, the job is done. It is not. We still have a long way to go.

Yeay you are getting there. You get three equations connecting a, b and z . But because they refer to the same parabola they are the same a , b and z in each equation. We say the equations are simultaneous. So you can solve these three equations to find a, b and z, as you did back in post 5 In order to help a little bit I will tell you that a = 3 is a good guess, or you can just go ahead and find all three. What do you make a, b and z? So when you have found a,b and z you can write down the equation of your particular parabola, that passes through the given points. So you can find any point on it if you know x or y, you can calculate the other. The point you want to find is the minimum. Now I asked you back in post4 what you know about the parabola as you have two ways to do this. You can either use the calculus to differentiate the equation and se this equal to zero to find the minimum if you know how to do this. Or you can use the geometric properties of the parabola (in this case the symmetries) to find the axis and thus the vertex, which is the geometrical name for the minimum. So we await your next input.

But modern politics has made an amazing leap forward when it was realised that individual citizens no longer have to work hard wasting resources. Their government can do this much more efficiently for them, whilst the citizens take their ease, if they can still afford it.

OK so let's provide some motivation. Pavel has offered the equation of a parabola ax2 + bx + z = y Where a, b and z are constants. This is also known as a quadratic equation. But you are not asked to solve the quadratic, you are given the values of x and y at three points on the curve. x = -2 , y = 0 and x = 4, y = 0 and x = 3, y = -15 So can you write down what happens if you substitute these values into the quadratic equation of the parabola? What do you get?

Let's just keep going with the simultaneous equations in post9 Then we can use our information in pavels equation from post 10 to get the correct answer.

Actually you also need some calculus in theory. As pavel said, there are three constants to find, not one.

So if I wrote ax + by = 7 cx + dy = -1 Would you understand it and what would you need to solve these two equations? If you don't understand I will explain in more detail. This will lead to the more complicated example of your parabola.

So what is the equation for a parabola? Alternatively, what do you know about parabolas? Note we do not do your homework for you, just help you find the way. I do not know what maths you should know, but if you are studying quadratic equations (parabolas) then you should have met simultaneous equations. Can you not solve for instance 3x + 2y = 7 3x - 2y = -1 These are simultaneous equations. Incidentally I agree that the minimum is at x=1, y=-27.

White spirit is probably your best bet. However you would need to test for insolubility of your powder.

I usually ask those who maintain that all reality is amenable to description by mathematical formulae the following question. You are going to build an earth embankment, starting (of course) with the bottom layer and ending up with the road/rail/canal formation surface at a prescribed location, elevation and width. The original ground you are starting from is uneven and sloping. Where do you start?

Have you heard of simultaneous equations? What is the general equation between x and y for the parabola? How many constants does it have? and at how many points do you know both x and y?

Don't stand there thinking too long or the tide will ave ee.

Does that make a difference to a theoretical system or the laws themselves? Where do any of the laws of thermodynamics declare zero friction impossible? Even if we have never observed it can we not treat zero friction by the time honoured method of asymptotic approach? I don't follow how your next two lines are compatible. Don't they contradict each other as underlined? The same laws of thermodynamics are supposed to apply to all systems. I merely said one can propose a system where entropy does not increase. In the case of the universe we have a few dilemmas to resolve. We do not know if the uiverse is finite or infinite. If it is infinite, does it not possess infinite entropy? If so how can entropy increase? If it is finite then what is beyond the finite? Could not some agent there move the piston? After all, what started the Big Bang if there was one? So you see there are quite a few (apparently) conflicting principles to reconcile. As a matter of interest, what is your prognosis for the future history of my piston-in-cylinder system, once activated?

Since the question was so pleasantly asked for I will tell you. Consider a sealed cylinder of ideal gas containing a frictionless adiabatic piston, dividing it into two chambers, A and B. If the piston is mechanically displaced and then released. the entropy change is zero as (say) chamber A is compressed and chamber B expanded.

I don't think John's cartoon suggests this at all, although it does examine the case as hypothetical.

When I was a pushy youngster I had a (friendly) argument with my brother about the cost of the space race. I was all for the glamour of the rocketry, despite the cost. My brother supported spending the money on something more directly useful instead. His example was improving agriculture to feed the burgeoning world population. "But," I said, "the space race yields spin-off, for example the thermal blanket." (GPS was not even a twinkle in swansont's eye in those days). Yes, said my brother, "But all R&D will have spin off. Agriculture research spin off would be different, but it would be there and we would also have improved agriculture." You never know what will come up.

Did you mean silicon? Did you also mean silicon trioxide? Chemistry is all about answering questions like these, as well as your own in the quotes. But it is much more complicated that asking how much does 1 litre of oil weigh, which can be obtained from a simple arithmetical formula. First you need to know some chemistry. The law of definite proportions. Pure substances (including elements) always combine in the same or definite proportions. So as a first approximation we can say X amount of sulphur will combine with Y amount of oxygen to form sulphur dioxide; the ratio X/Y, is always the same. But will silicon or sulphur form trioxide or dioxide? Well secondly you need to know some chemistry, specifically elementary valency. https://www.google.co.uk/search?hl=en-GB&source=hp&biw=&bih=&q=valency&gbv=2&oq=valency&gs_l=heirloom-hp.3..0i131j0l9.1656.4172.0.6047.7.7.0.0.0.0.234.1000.0j5j1.6.0....0...1ac.1.34.heirloom-hp..1.6.1000.KgauRuffOzE (Did you look up my last reference?) This will help you form proposed chemical reactions, according to the rules of valency. Having got your stoichiometery (proportions) correct you can ask Is the reaction possible? To address this question you need to know some more chemistry, chemical thermodynamics or chemical energetics. The reaction could proceed if it releases energy in doing so. But some proposed reaction, correct on valency rules, cannot proceed without energy being added. So you have to heat up the reagents. Even if the reaction is energetically favourable, it may proceed rapidly or slowly or even so slowly as to be be negligable. To understand this you need to know some more chemistry. Rates of reaction are covered in chemical kinetics, but this mathematics may be offset by passivation or other interfering layers. So hopefully you can begin to see why chemistry is a very large and rich subject.

Your waves sound like a lot of energy, Mike. But consider these figures. Burning 1kg of petrol releases 4.6 x 107 Joules of energy.(yes 46 megaJoules) source: National Physical Laboratory tables. Raising 1kg of petrol up 100 metres takes about 103 Joules. Yes one thousand Joules. So the hydro potential energy available due to 1kg of water falling 100 metres is 103 Joules. So the enenergy density for combustion is several thousandfold greater than for gravitational potential. Collection and concentration is the key issue in alternative energy.

What about spin-off?

What if they don't react? Are they still reactants? Chemistry is not a branch of Mathematics (nor Mathematics a branch of chemistry), but both are useful to the other. You need chemical knowledge as well as the mathematical kind. In the case of sulphur and oxygen you should look up Activation Energy. https://www.google.co.uk/search?hl=en-GB&source=hp&biw=&bih=&q=activation+energy&gbv=2&oq=Activation+Energy&gs_l=heirloom-hp.1.0.0i131j0l9.1031.4672.0.6938.17.13.0.3.3.0.203.1423.0j8j1.9.0....0...1ac.1.34.heirloom-hp..5.12.1549.fcOjfyfhZs4

Hi ydoaPs, did you mean this?

It is important to realise that the second law does not say entropy always increases. It says entropy never decreases, which is not the same. It is possible to offer theoretical systems where entropy does not change, but other thermodynamic variables do.

Thank you Acme, but it doesn't always work. That is the problem. There are some issues out of control of this (or any) website due to scripting in adverts (which arise offsite). Sometimes I can't scroll properly without turning all scripting off. Then I loose some site functionality, but at least I can read the posts.

I have had this problem sometimes. It seems to depend upon which browser and operating system you are using and what the settings are, particularly older ones. So please tell us what system and browser you are using.

Can you give some examples? I would say that perhaps you mean the difference is that sometimes the equation gives the conditions of the reactants and products, for example in solution, where the solvent does not participate in the reaction but needs to be present for the reaction to proceed. for example [math]N{a_2}C{O_3}(aq) + CaC{l_2}(s) \to CaC{O_3} \downarrow + 2NaCl(aq)[/math] But what happens if you just mix solid sodium carbonate and solid calcium chloride together? Both are white powders. Note 'balancing' a chemical equation only makes sense if there is a chemical reaction and there are some products different from the reactants. In the above you could say that the chemical reaction consists of dissolving calcium chloride in a solution of calcium carbonate and that calcium carbonate is precipitated from the solution, without quantities as I have done. Or you could just say the chemical reaction in words eg a more general one Acid + Base = Salt plus Water