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DJBruce

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Posts posted by DJBruce

  1. I have read through the article you attached, and the first thing I noticed was that your definition of derivative is virtually identical to the standard definition of derivative. With the exception that your notation, at least in my opinion, is much more cluttered and confusing. So I really did not see anything innovative or new there. As for your take on integration I really don't like it as it has an incredibly limited scope since in order for your method to work the function must be continuous.

     

    For example using your method can you integrate the function:

     

    [math] F: \Re \rightarrow \Re [/math]

    [math] F(x) = \lbrace 1 [/math] if [math] x=5, 0 [/math] otherwise

     

    Another thing I want to point out, as far as I am able to tell you have yet to formally prove, or even define, anything. Instead you have simply given a few examples.

  2. Hi, I have a question about normal distribution. A large population of animals were found to possess a mean

    length of 18cm with a standard deviation of 2cm.

     

    What percentage of animals are longer than 20cm?

     

    so i know you use the formula to standardize the Z. But then from the cumulative table, how do we know which column to look for? :(

     

    To use a Z score table you generally go down the left hand side until your Z-score matches the one shown, and then you go across that row until the heading of the column matches the third digit of your Z-score. For example lets say I have Z=1.34, and I want to find P(x<Z). So looking at the table I linked to you go down on the left hand side to the row that says 1.3. Then I go across that row until the the heading of the column is .04. This entry, P(x<Z)=0.4099, is the number you are looking for.

     

    and then the next question is, What percentage of animals should be between 15cm and 20.5 cm in length? in the formula, how do you put both figures 15 and 20.5 ? and then the last question is What length should enclose the shortest 60% of the animals ?

    please help :(

     

    Calculate the Z-scores for these two lengths. You should then be able to find P(x<Z') and P(x<Z"). Knowing this how would you find the area between these two Z-scores. (Hint: Draw a picture of what P(x<Z') and P(x<Z") represent.)

     

    For the last question you need to use an inverse Z-table to find the what Z-score corresponds to P(x<Z)=.6. Once you have this you should be able to slove for the length. Remember:

    [math] Z=\frac{x-\mu}{\sigma} [/math]

     

    Also does anyone know a good website for statistics ?

     

    I am not sure of any great statistics websites, but I do like this website. It is a website for a high school AP program, and it has a lot of really nice handouts and links.

     

     

    Also you can avoid tables if you have a graphing calculator as most have built in functions that can calculate these for you.

  3. -2000: Alaska: Indirect Initiative Result: Failed

    -2002: Nevada Initiative Result: Failed

    -2002: Arizona Initiative Result: Failed

    -2004: Alaska: Indirect Initiative Result: Failed

    -2006: Colorado: Initiative Result: Failed

    -2006: Nevada: Initiative Result: Failed

    -2008: Massachusetts Initiative Result: Passed

    -2008: New Hampshire: Legislature Result: Rejected

    -2010: Arizona Voters Approve Proposition 203 50.13% to 49.87%

    -2010: California: Initiative Result: Failed

     

    Sorry after more research I found the Arizona's 2010 Proposition 203 was specific to medicinal marijuana. The 2002 law was the one that had more general language on Cannabis.

     

    Looking at the results of the 9 changes I have above 8 were voted on by the people, and of those 7 were rejected by the people, and one was passed into law. The other statue was voted on by the legislature, and was rejected by the state legislature.

  4. Would you mind writing your definitions out symbolically. I really don't understand what you mean when you say things like,

     

    differentiation process begins with a function increment

     

    or

     

    But actually result of integral not function but its increment.

     

    Also just to be clear when you talking about integrals you are meaning the riemann integral of a continuous function correct?

  5. Looking at recent history it appears that a few states have begun to reevaluate the criminality of Cannabis. Since 2000 the issue of complete or limited decriminalization of Cannabis on the state level has been voted on roughly 9 times. Here are the results:

     

    -2000: Alaska Voters Reject Measure 5 60%-40%

    -2002: Nevada Voters Reject Question 9 61%-39%

    -2004: Alaska Voters Reject Measure 2 56%-44%

    -2006: Colorado Voters Reject Amendment 44 60%-40%

    -2006: Nevada Voters Reject Question 7 56%-44%

    -2008: Massachusetts Voters Approve Question 2 65%-35%

    -2008: New Hampshire Senate Rejects Bill Reducing Marijuana Penalties

    -2010: Arizona Voters Approve Proposition 203 50.13% to 49.87%

    -2010: California Voters Reject Proposition 19 54%-46%

     

    So a although the initial logical used to support the criminalization of Cannabis may have been flawed it appears that currently our society might not believe that legalization is not justified yet either.

     

    "Decriminalization of Marijuana"

  6. Here are the two questions I am stuck on:

     

    "A real valued function has the property that the absolute value of the function is differentiable at o. Show by example that the function need not be differentiable at 0. Prove that if we require the function to be continuous at 0 then the function must be differentiable at 0."

     

    For the first part I was thinking of:

     

    [math] f = x^2+2x [/math] for [math]x \leq 0 [/math] and [math] -x^2-2x [/math] for [math] x > 0 [/math]

     

    Looking at the derivative of f at 0 we see that the LHD=2, while the RHD=-2, so the function is not differentiable at 0. However, looking at the absolute value of the f we see we have the derivative is 2 for both sides so it is differentiable. However, checking to see if this function is continuous I find that it is, but this would contradict the second statement on of the problem. What is my mistake?

     

    "Let g be a real valued function defined as 0 when x=0, and exp([math]-x^{-2}[/math]) when [math] x \neq 0 [/math]. Prove that g is cinfinity at 0, and that the kth derivative at 0 is 0. "

     

    I am not sure where to start with this proof, I was considering induction, bit I am not sure about that. So could anyone give me any ideas.

     


    Merged post follows:

    Consecutive Posts Merged

     

    So I just realized by idiotic error in the first question. :doh: Sorry for that.

     

    I am, however, still unsure on the second question.

  7. If you want to learn Calculus from the ground up, proving virtually everything along the way I would suggest Calculus by Spivak. Although I will say it is not a book I would recommend if you want a refresher for applied calculus.

  8. So for my mechanics class we have these two problems on our online homework:

     

    "An object in the shape of a thin ring has radius A and mass M . A uniform sphere with mass m and very small radius is placed with its center at a distance x to the right of the center of the ring, along a line through the center of the ring, and perpendicular to its plane. What is the magnitude of the gravitational force that the ring-shaped object exerts on the sphere?"

     

    and

     

    "A thin, uniform rod has length L and mass M. Calculate the magnitude of the gravitational force the rod exerts on a particle with mass m that is at a point x along the axis of the rod a distance from the closest end of the rod."

     

     

    For both of these I found the center of mass of each object, and then calculated the gravitational force from that.

     

    1) Since the ring is uniform, we know that its center of mass is located at the center of the circle. Since the point object is located a distance x from the center of the circle I found the gravitational force it feels is:

     

    [math]F= \frac{GMm}{x^2}[/math]

     

    2) Since the rod is uniform we know the center of mass of the rod is located in its center, which is a distance L/2 away from its ends. Knowing the ball is a distance x from the end of the rod I found the gravitational force to be:

     

     

    [math]F= \frac{GMm}{(x+\frac{L}{2})^{2}}[/math]

     

    I feel like these answers are correct, but the automated grading system says they are not. Can anyone explain what I am doing wrong?

  9. So here is a question I am struggling with:

     

    "There is only one unique coordinate system in which vector components can be added. True or False?"

     

    I believe this is false, as I think you could create numerous different coordinate systems, and all you would have to do is make sure you watch what signs you assign to each vector. However, I am really not very comfortable with this.

  10. I am going suggest you look at your thread about how to pass out of High School Biology as at least my advice will remain the same, and I would wager that of many others will be similar as well.

     

    As an addition to my linked post I would not recommended you try and cram for these tests and pass out of them simply to get ahead in the short term. If you don't take the time to learn the basics and fundamentals well you will suffer in the long run, and end up behind those who took the time in the beginning to create a good foundation.

  11. I would recommend you get a copy of the classes syllabus, and a copy of the textbook, and use those to study. The syllabus should be able to direct you to what is going to be covered, and what readings will be done. So you should then be able to cover the same material as the course.

     

    In addition I would not recommended you try and cram for these tests and pass out of them simply to get ahead in the short term. If you don't take the time to learn the basics and fundamentals well you will suffer in the long run, and end up behind those who took the time in the beginning to create a good foundation.

  12. It was this passage in particular:

     

    The message here is to not provoke the Islamists, even though in theory Muslims and Christians pray to the same God. Imagine a priest instructing American Jews to stop using the word "God" because some backwards Christians get upset... he wouldn't seem much like a bridge builder would he?

     

    Imam Rauf recognizes the fact that Christianity has the right to use the word Allah. In my opinion all he is telling the Chirsitan community is that although they can use the word it might not be responsible for them to do so and that it will not advance their cause. I find nothing wrong with this message. He is not saying don't do this he is saying if you do use the word Allah realize that some might find it offensive, and is offending people really the goal of a religion.

     

    Rather than taking the opportunity to admonish the very real discrimination in Malaysia against the Christians he takes the side of the Muslims in principle but argues that burning down churches isn't the best response. This will accomplish nothing. He is taking the middle road on something that has no real middle road. "Ladies, you should stop dressing so provocatively, and to the gentlemen I say that raping isn't the way you should be relieving your frustration."

     

    As for this I cannot comment on the state of religion in Malaysia. However, taking what you say as truth I find that the Imam's speech is telling people to respect one anothers religion, and that any violent actions are wrong. He does not claim Christians. He simple tells them that the should recognize that their actions might be upsetting to some.

  13. No. The problem have actual solution. When I say similar to prove 2x2=5, I mean "disguised with simplicity".

     

    Without you accurately describing the problem there are numerous correct solutions through out this thread. Therefore, could you please restate the problem so that we figure out which of the right answers you want?

     

    The error in that proof is not that disguised it is fairly obvious and easy to spot.

  14. jryan, what in the article made you think that Imam Rauf "just doesn't get it"?

     

    I read the article and found it very uplifting, and thought it was an excellent example of his attempts at bridge building and his renouncing of violent and radical acts. I mean looking at passages like:

     

    Islam and Christianity are at their roots religions of peace and tolerance. A certain amount of competition will always exist among religions. Good competition is to compete in good works. Bad competition is trying to undermine the other faith

    ...

    Fire bombing churches? From the beginning of Islam, the Prophet said our faith requires us as Muslims to protect houses of worship of all other faith traditions. Islam was able to spread throughout the world, not only because of its own ideas, but also because it protected people’s rights to practise religion freely.

    ...

    Our goal must be living together harmoniously. Our goal is freedom of conscience.

    ...

    And like him, we should all practise our religions in a way that does not provoke others.

     

    I seems to me that Imam Rauf is doing an excellent job of being respectful to all religions, and asking everyone to simply respect each other.

  15. Sorry to disappoint you John Cuthber, the details provided are sufficient to solve this problem. Only it is a hard nut to crack.

     

    This is similar to "prove 2x2=5"

     

    I know there are lot of math wizards on the SFN, who can easily solve this problem, hence I am holding back the solution, which is quite simple to crack this hard nut.

     

    Wait you are saying that this problem is completely fallacious and does not have an actual solution just like the proof of 2x2=5?

  16. DJBruce,

    His classical scattering theory was widely used (like 450 citings) and I haven't seen nonpositive comments about it (?)

    His atomic models are natural consequence - just succeeding scatterings from nearby .. and the only nonpositive comment I've found is this enigmatic 'unsatisfactory'.

    One of goal for this thread was to understand this situation - why these understandable, noncontroversial finally working modern successors of well known Bohr model are just unknown and not developed further?

    Doesn't this 'discussion' itself suggest that it's rather a sociological problem? - please give me one concrete argument why they cannot be just equivalent?

     

     

    The Gryzinkski free-fall model can be considered equivalent to quantum mechanics, and Thagard's criteria allow for a psuedoscientific field to drop that title. However, in its present state it cannot be considered equivalent, and cannot drop that title. I am not sure why you deny the argument that quantum mechanics has been more thoroughly research and has provided many more verified predictions as why they are not equivalent. However, in my opinion that is a perfect argument for why they aren't equal right now.

  17. What is it the makes a species able to breed with another?

     

    There are 5 prezygotic barriers, and 3 postzygotic barriers which make it impossible for pieces to breed. They prezygotic barriers are:

     

    - Temporal Isolation: The two pieces are reproductively active at different times.

    - Habitat Isolation: The two species live in different areas, and therefore do not meet to mate.

    - Behavioral Isolation: The two species have different mating rituals/

    - Mechanical Isolation: The two species reproduction parts just don't fit together properly.

    - Gametic Isolation: The two species gametes are incompatible making fertilization impossible.

     

    The three postzygotic barriers are:

     

    - Hybrid Inviablity: The hybrid does not mature properly into a function offspring.

    - Hybrid Sterility: The hybrid is sterile normally because of gametic abnormalities.

    - Hybrid Breakdown: Over generations the hybrids breakdown and become incapable of reproducing.

  18. If a projectile is fired straight up at a speed of 30 m/s, the total time to return to its starting point is about___.

     

    Supposedly the answer is 6 seconds, but I don't see how. Wouldn't I divide 30 m/s by the acceleration of gravity to get about 3 seconds?

     

    You will want to use the equation:

     

    [math]d=\frac{1}{2}gt^{2}+v_{0}[/math]

     

    What would the displacement be when the projectile returns to the starting location? Once you answer this use that as d, and then simply solve the equation for t.

     

     

    The vertical height attained by a basketball player who achieves a hang time of a full one second is about___.

     

    and the answer is supposedly 1.2 meters. I tried to substitute the values into the equation [math] d= \frac {1}{2}gt^{2}[/math], where g is approx. [math]10 m/s^{2}[/math] and [math]t[/math], the hang time, is 1 second, and got the value 5. Am I doing something wrong, or is this right?

     

    One second is how long the object is in the air total, however, for half of that time it is on the decesent so therefore you should use .5 s instead.

     

    And one more.

    If a projectile is fired beneath the water, straight up, and breaks through the surace at a speed of 13 m/s, to what height above the water will it ascend?

    Do I even have enough information to solve this one? Would I not need to know how deep the object is under water before it's fired?

     

    Yes you can solve this. You have [math]v_0[/math], [math]a[/math]. So which equation would give you displacement given those two variables?

  19. In evaluating free speech one compares the benefit of of this particular speech or expression with respect to limiting government control against the damage it may cause society as a whole.

     

    Free speech does not extend to shouting fire in a crowded theater because there is very little or no benefit in terms of limiting government powers while there is huge potential for damage to society. The same logic is used to limit holocaust denial speech. Allowing denial speeches provides only a small benefit in terms of limiting governmental powers, but in certain societies, there is reasonable benefit for the public as a whole to pronounce holocaust denial speech morally wrong and therefore prohibited.

     

    I have to strongly disagree with you interpretation that the evaluation of speech should incorporate the idea of how it would affect the limits of a government. No matter what type of speech it is restricting it will automatically expand the sphere of influence of the government. Therefore the criteria for deeming speech restrictable should be as Justice Oliver Wendell Holmes stated:

     

    "The question in every case is whether the words used are used in such circumstances and are of such a nature as to create a clear and present danger that they will bring about the substantive evils that the United States Congress has a right to prevent. It is a question of proximity and degree."

     

    I can see no way the denial of the holocaust presents a clear and present danger, which would require a blanket restriction. Not to mention that the restrictablity of speech should not hinge on its morality since immoral behavior does not equate to a clear danger.

     

    Perhaps one day it won't be the lightning rod it is today and prohibition will not be demanded by the majority of that society.

     

    I highly doubt that the genocide of millions of people will ever stop being an emotional lightning rob as long as there are those who continue to preach their denial of the event.

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