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Killjoy

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Posts posted by Killjoy

  1. I am surprised at how small amount of information I could find on this subject when surfing the web. My teacher a while back showed us a clever little quick way to find the sqaure root of a number, does anyone know how to do this?{if so, please list} Thanks. :)

     

    Here's another trick that can work.

     

    1) Take your original number (the one you want to find the square root of) - lets call it x1

    2) Produce a new number thus: x2 = x1-(x1^2-x1)/(2*x1)

    3) Produce a third number thus: x3 = x2-(x2^2-x1)/(2*x2) [iMPORTANT: Notice the second term in (x2^2-x1) (and only this term) is x1 - this is not a typo - it has to be the original number all the way through]

    4) Repeat. The values of 'x' get closer to the square root of the original number. You can repeat as often as you want. The more you repeat the more accurate the answer, but you'll find that 4 or 5 repeats will be accurate enough for most purposes

  2. If the average man is 175 cm tall with a variance of 6 cm and the average woman is 168 cm tall with a variance of 3cm, what is the probability that the average man will be taller than the average woman? What is the probability that the average woman will be taller than the average man? What is the probability that the average man will be shorter than the average woman?

     

    If the average woman has an IQ of 101.41 with a standard deviation of 13.55 and the average man has an IQ of 103.08 with a standard deviation of 14.54, what is the probability that the average man will have a higher IQ than the average woman? What is the probability that the average woman will have a higher IQ than the average man? What is the probability that the average man will have a lower IQ than the average woman?

     

    Express the final results as percentages.

     

    Can anyone show me how to solve these problems? Can someone show me the work and list the steps needed to solve these problems? I need to have these problems solved by tomorrow ASAP.

     

    Does anyone know of any websites that deal with finding the solutions to such problems?

     

    Thank you


    Merged post follows:

    Consecutive posts merged

    Is anybody out there? Can someone also tell me the kind of equations needed to solve this problem?

     

    If the average man is 175cm and the average woman is 168cm, the probability that the average man is taller than the average woman is 1. I think the problem is poorly phrased.

    Here are some possible alternatives:-

    What is the probability that a randomly selected woman is taller than the average man?

    What is the probability that a randomly selected woman is taller than a randomly selected man?

    Of course it could be a trick question.

  3. Hi,

     

    Suppose I have two points A, and B in some N-dimensional manifold.

     

    I would like to define distance (or metric) between A and B as follows:

     

    [math]d(A,B)=min | \int_\gamma f(s) ds | [/math] along some curve [math]\gamma[/math]

     

    In my head, it seems to be possible to evaluate a line integral without precisely defining distance. (ie. we just take tiny little points along this line, and evaluate f(s) at each tiny little point).

     

    However, all equations I've seen uses something like:

     

    [math]ds=\sqrt{{dx}^2+{dy^2}}[/math] which seems like a euclidean metric.

     

    So here are my ultimate questions, 1) is it possible to evaluate such a line integral without defining a metric, and 2) would make it sense to define such a line integral

     

    I think you would need a metric to define ds in your first definition, which would then become circular.

  4. Firstly, welcome to the forum

     

    Secondly, The guy the theorem is named after is Stokes, not Stoke, so it would be properly written Stokes'

     

    Thirdly, the link is broken (extra http://) in it

     

    Fourthly, Stokes' Theorem isn't the same as the fundamental theorem. Stokes' Theorem is how to turn surface integrals into line integrals. The Gauss-Green-Ostrogradsky divergence theorem (has many names depending on the reference you are looking at) is how to turn volume integrals into surface integrals. Divergence is how to turn 3-D volume into 2-D surface and Stokes' is the 2-D to 1-D equivalent. Neither one covers the same ground as the fundamental theorem which proves the truly fundamental property that differentiation and integration are intricately related and are inverse operations (to an arbitrary constant).

     

    WRT point 1: Thank you

     

    WRT points 2&3: Sorry - my bad

     

    WRT point 4: The name "Stokes' Theorem" sometimes refers to a specific case of a more general theorem which, rather confusingly, is also called "Stokes' Theorem". This more general theorem relates what happens in an N-dimensional hypervolume to what happens on the orientable (N-1)-dimensional hypersurface of that hypervolume, all embedded in an M dimensional manifold. Depending on the values of M and N, and what kinds of functions are being considered you get the various different theorems mentioned, and many others. If N=1 you recover the fundamental theorem of calculus.

    I'll try to find a better reference and post it.

  5. The fundamental theorem of calculus

     

    This one gets my vote by and far. Not a whole lot gets done without this being true. I guess that's why it's been named "fundamental" eh?

     

    I agree that the fundamental theorem of calculus should be included. There is also a generalisation called Stoke's Theorem which, while perhaps a little advanced to be called "fundamental", actually incorporates several concepts in physics and mathematics - including the fundamental theorem (and Green's theorem, and the divergence theorem), is used to derive equations such as the wave equation and the diffusion equation, and is of central importance in differential geometry, general relativity, and many other fields.

  6. What are people's opinions on which are the most important theorems in mathematics? By important I mean those with the most significant consequences both in pure and applied mathematics (not just obscure results that happen to be interesting to a few individuals). I would suggest the the Pythagoras Theorem should be up there. What else?

  7. Originally Posted by Killjoy

    In the absence of a diagram my question may be a bit hard to follow' date=' but I'll do my best...

     

    Imagine I have a barbell floating in empty space - ie two equal weights connected by a rigid bar (a single rigid pole would do as well, but the barbell might be clearer).

    I start it spinning on an axis that passes through the center of mass of the system (ie, middle of the bar) but is neither parallel nor perpendicular to to bar.

     

    My intuitions as to what will happen lead in contradictory directions:-

    1) Centrifugal force will cause the spinning barbell to straighten out so that the axis of spin becomes perpendicular to the bar;

    2) Conservation of kinetic energy and angular momentum will mean that the barbell will continue to spin on the same axis as it started.

     

    Which is right and why is the other one wrong?

    [/quote']

    3) wobble

     

    Is this the same as (2)?

  8. In the absence of a diagram my question may be a bit hard to follow, but I'll do my best...

     

    Imagine I have a barbell floating in empty space - ie two equal weights connected by a rigid bar (a single rigid pole would do as well, but the barbell might be clearer).

    I start it spinning on an axis that passes through the center of mass of the system (ie, middle of the bar) but is neither parallel nor perpendicular to to bar.

     

    My intuitions as to what will happen lead in contradictory directions:-

    1) Centrifugal force will cause the spinning barbell to straighten out so that the axis of spin becomes perpendicular to the bar;

    2) Conservation of kinetic energy and angular momentum will mean that the barbell will continue to spin on the same axis as it started.

     

    Which is right and why is the other one wrong?

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