studiot

OK step 1 WWE are told the the 'population' is 20,000 and that 50% of them drink coffee in the morning. This means that if we asked every one of them 10,000 would say yes and 10,000 would say no. We don't, however want to expend the effort of asking every one so we only ask some of them. We call the the group that we ask the sample. Unfortunately it is entirely possible that all the ones we ask could be coffee drinkers (perhaps we make the mistake of asking in the coffee lounge), or non drinkers (perhaps we only asked those under 6 years of age). Clearly this is not a good way to go about things. We want a systematic method. In particular we want our results to reflect the actual split between drinkers and non drinkers in some rational manner. So we find a way of selecting members of our 20,000 population to ask at random. This means that every member has the same probability (1 in 20,000) of being selected. This is our definition of random. Now another way of saying "This means that if we asked every one of them 10,000 would say yes and 10,000 would say no." is to say that the probability of a yes answer is exactly 0.5 for a random population member. I expect you understand these intuitively, but what I ahve said so far provides a formal basis (puts things on a firm footing) towards step 2. How are we doing so far?

With the greatest respect you introduced it. Further you did not address my post#12, contrary to the rules of this forum. The energy is supplied by the other agent that must act in order for work do be done. Gravity, (or any other force) cannot do work by itself.

The same way I know that seven eights are fifty six or thirteen thirteens are one hundred and sixty nine, although I've neve calculated them, or that Lagos is the capital of Nigeria, although I've never been there. My teacher told me. And I believed her. It is very difficult to progress unless you have enough confidence in your teacher to believe her.

Let us break it down into easy steps. Did you understand this statement, ignoring how the numbers themselves were calculated?

So far as I can make out in your two posts this is your only reference to analysis and calculus (the forum you have posted in) and your only question which you answered yourself. Unfortunately, your basic premise that a tangent is defined as only 'touching another curve at one point' is flawed. So what is this thread about please?

What a nonsensical definition. Hydroelectricity is the generation of electricity by the movement of water. If I pumped water uphill, through a turbine, would that not be hydroelectricity? But nothing requires the movment of water to be gravitationally induced. I was actually thinking of compressed air (like any good diver would). Of course using the compressed air to move the water through the turbine is less efficient than using the air directly, but the question required the water. It did not require gravity.

Turbines operate on momentum, not weight. All you need is a stored energy source you can take into space with you (plus the water of course), to make it operate in space.

This is a disappointing question since you have not properly stated the conditions at the outset. In particular you did not specify a tidal hydrogenerator in post#1, but delayed introducing this new fact in post#10 Now I am trying to reassure a young student in another thread here that he or she has every right to expect academic questions to contain sufficient information to uniquely determine the answer. How does this play with that? I hold that I could build a hydro electric generator that does not depend upon gravity for its function and that weight play no part in the machine. So my hydroelectric generator could operate either in the presence or absence of gravity. So where would I get the energy?

Do you prefer this semi verbal, semi pictorial question? Edit I also like harshgoel's idea of separating into cases. Unfortunately that would not be acceptable in an exam, even if you had time. Further the effects in each case would have to be independent to be thus separable.

The frequency of the sounds you hear are a multiple of the number of blades of the fan. Sound is, of course, generated by moving air, which is what a fan does.

Yes innovation can be important, but there is a time and a place for everything. There is a time to innovate and a time to be straightforward, boring and conventional. I give you the words of the song "Turn Turn Turn" http://en.wikipedia.org/wiki/Turn!_Turn!_Turn!

Well yes it is true that you have to start somewhere to develop a theory or whatever. This is exactly what you will do when you leave college and work in the outside world. There you often have to decide for yourself what level of accuracy, what parameters want to calculate, what level of sophistication your calculation (remembering that in general the more sophisticated the more it costs) ans finally if your answer or result is sufficient. But in school or college you are looking to achieve a predetermined result, set by the curriculum, so you don't have the luxury of trying an approximation and refining it. The nearest I can think of in a college setting would be to check if a formula you think is correct by substituting some simple easy to calculate numbers to see if it yields a known result. Which all still comes back to Don't add things they haven't asked for.

Not always. Just look at some traffic lights. The colour you see is the colour radiated by the source.

You would also need basic Physics to first degree level to pursue what swansont and ajb mean by 'mechanics', So my advice still holds good in this case.

If you are up to the job there are good career prospects if you take Physics as your first degree, specialising in options that will allow you to follow this with postgrad in Mechanical Engineering. Taking things is the other order is not recommended. If you eventually don't like Mech Eng you are a bit stuck with other fields to move on to. But it is relatively easy to move on from Physics to many other technical disciplines. I know medical doctors, surveyors and undertakers with first degress in Physics. Work from the general to the particular. If all else fails you can go with your first option and you will always be able to predict the future.

Yes of course you are. But you don't need to make that assumption, any more than you dont need to make other assumptions like The balloon is not rising through the air and cooling and so shrinking. The expansion of the balloon is not sufficient to burst it. and so on. Each of these possibilities can be calculated by more complicated physics, leading to more complicated maths, but we ignore them. We ignore them because the original question has not mentioned them so we don't either. We concentrate on what the question does mention. If you look, all these assumptions contain the word 'not', they are about what the question is not. Try to avoid negative assumptions about what questions are not. They don't help solve the real question itself.

I am going to look at this question of yours from some different perspectives. What is the context of the question? What does the question want you to find? What is an assumption? Why are any assumptions needed and under what circumstances do you need to make them? Are there any other sources of information? What sort of questions are out there and what is their purpose? How do you become good at extracting information and supplying what’s missing? OK so last two perspectives first (the easy ones together). You become good by lots of practice. It also helps if you can enjoy it. There are several ways to get this practice. Many people enjoy doing puzzles, brainteasers and the like. You can find these in magazines, books of puzzles, online and quiz programs. Older maths books aimed at the 12-15 age range often had many word based questions for pupils to practice with along with advice on how to do them. For example: 54 pots of jam were tested and it was found that some were 1oz overweight and the remainder 1/2oz underweight. The total weight was correct however. How many jars were underweight? A tank X contains 1000 gallons of water and water flows out at a rate of 5 gallons per minute. Another tank Y is empty and water is flowing in at 10 gallons per minute. (1) How much water is in each tank after the water has been running for t minutes? (2) How much more water is there now in tank X than in tank Y? (answer in terms of t) (3) Find this amount when t= 10; t=60; t=100. What does the last answer mean? The second question shows an important point that often part (1) of such a question calculates something you will need in the second or later parts. For the rest of the perspectives I will use your example. So context Had this been from a physics book then physics considerations might have been important. Such as temperature, pressure, Boyles or Charles law, the elasticity of the balloon. But this was from a mathematics book in the mathematics section so mathematics is important and such physics considerations are unimportant and can be discarded. But what mathematical considerations? Well first we extract the information given. This information is only the information given. Nothing else. No assumptions, guesses, inspirations or whatever. The balloon is a sphere. Then we supply relevant (mathematical) information that we know. This information is not an assumption. It is a hard fact or formula that we have learned/been taught. In this case the volume of a sphere is [math]V = \frac{{4\pi {r^3}}}{3}[/math] Do we need to assume that the balloon does not change shape? Not really since the volume of any boxy or blocky object is still proportional to the cube of it’s ‘radius’. What is the context? Well calculus and the books want us to differentiate an equation connecting volume with radius. So do we need any assumptions about holes in the balloon? Well no because holes are not included in the standard formula connecting volume and radius. So long as we extract the facts given and add facts that the book expects us to know as part of our course, we should not need to make any assumptions.

Lizzie L put a lot of effort into this thread. http://www.scienceforums.net/topic/82666-can-a-white-piece-of-paper-reflect-light/

At this time of year, we occasionally see the green ones in the Wiki picture. There were a couple of these orange ones. Thanks acme, I will see if any better information comes along.

Can anyone identify this moth or insect please. About half inch long, bright orange, dart shaped two prominent round black spots, Found on a lavender bush.

You need to develop a hypothesis to test. For instance that the measured effect is independent of concentration, normally distributed over some range of concentration or whatever. That is what John's analysis of variance will do for you. Better advice will come if you can state your hypothesis or hypotheses. Better still, next time, formulate your hypotheses before carrying out the measurements.

Well this is a continuous distribution of the probability density function p(x) for x>0 (it is zero for x<0) [math]p(x) = \lambda {e^{ - \lambda x}}[/math] :x > 0:lambda > 0 It has one parameter, lambda which is positive. The mean is given by [math]Mean = \frac{1}{\lambda }[/math] and the variance by [math]Variance = \frac{1}{{{\lambda ^2}}}[/math] As you can see, the probability falls with increasing x so you might use this distribution to model say your chances of living x years beyond 100 years of age.

University of Hawaii? Magnum PI will never look the same again.

This is homework then? Binding energy is the energy that holds the nucleus together, hence the question is about atoms. It is the release of binding energy that allows lighter atoms to undergo nuclear fusion and heavier ones to undergo nuclear fission. There is a maximum around nickel - iron the the periodic table, which divides prospective fission or fusion. Read this and come back if you still cannot complete your homework. http://en.wikipedia.org/wiki/Nuclear_binding_energy

In the past I have helped preserve research confidentiality by use of the private messaging system. However I am not a cosmologist, and ajb knows a great deal more about tensor gravity models than I do so I am not the right person to help further here, since the last time I did that with tensors was in fracture mechanics.