DJBruce

As the OP indicated by saying, "=24y or 24/y?" the he was asking how we would interoperate the expression given. As for where has 48÷2y been equal to: [math](\frac{48}{2})y[/math], according the standard oder of operations taught in children operations should be evaluated in the following order Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction (PEMDAS), and when operations of equivalent order are next to each other they are evaluated from left to right. Meaning that since division and multiplication of are same order we would evaluate 48÷2y as being (48÷2)y --since division furthest to the left. To read about the standard order of operations see: http://www.purplemath.com/modules/orderops.htm http://www.mathsisfun.com/operation-order-pemdas.html http://www.math.com/school/subject2/lessons/S2U1L2GL.html

Umm, you assumed that the OP's ambiguous statement means [math]\frac{48}{2y}[/math], and surely there is no argument that if this is the case then it does equal [math]\frac{24}{y}[/math], however, the point is that this statement is ambiguous since we are not sure whether it means [math]\frac{48}{2y}[/math] or [math](\frac{48}{2})y[/math], and that you cannot prove the convention of how we interoperate the OP's expression.

Working in different bases does at times help show some interesting patterns. A few examples that come to mind are: -Defining the Cantor Set as all numbers in the interval [0,1] such that there base-3 representations do not consist of only 0's and 2's. -When working with the Collatz Conjecture you can notice certain classes of numbers that will iterate to 1 by looking at binary.

So I have been having some fun messing around with the 3x+1 problem, also called the Collatz Conjecture. What I have been able to do is create a program in Python that given an integer will print each step of function until it becomes 1. The code I wrote for this was: from __future__ import division from visual import * from visual.graph import * n= while n!=1: if n%2==0: n=n/2 if n%2!=0 and n!=1: n=3*n+1 print n What I would like to do is to modify this so that I can have the program run for a large number of numbers, and return the number of steps it took to get to 1 for each number. Sadly I really have no idea how to approach doing this as my programing is minimal. Could anyone give me some suggestions and/or pointers for how to go about doing this?

Why do you insist on inventing new definitions for the derivative and integrals, that are not mathematically correct? Can you point out a flaw in the current definitions? Also just to be clear can you give the accepted definition of the integral?

You have scientific proof of mind reading? Can you prove your claim about "the 1%"? So you are saying people suffer from mental illness because the leaders of our society are criminals? Proof please. Can you cite some studies for this? I am confused. If I am interpreting this right you think "the most sensitive of people" are those who are going to suffer from Schizophrenia, and you describe them as being ill, and needing preventive medicine to protect them. However, earlier it appears that you are arguing that Schizophrenia is not an illness, and those suffering from it are instead people to be revered. This seems like a contradiction. How do you suggest we identify those who are at risk for schizophrenia? Also do you not believe that psychiatrists who pledge to, "prevent disease whenever I can, for prevention is preferable to cure" are not currently trying to do the best by their patients? Are you sure that this is how schizophrenics were treated in the past? The medical definition of Schizophrenia is fairly recent, and so looking into the past is difficult. However, it is well documented that in the stone age those exhibiting abnormal feelings similar to those exhibited by those suffering mental illness were often treated by having holes drilled into their sculls to let the "bad spirits" out. Throughout the middle ages those possessing signs of mental illness were often considered to be possessed by demonic spirits, and so were subject exorcisms to, which included being forced to drink a mixture "made from sheep's dung and wine.", and were often ostracized social. The second part seems like a red herring to me. Yes, doctors do not completely understand how everything works, but neither does anyone. However, in the last 50 years psychiatry has made fairly large advances into the science of mental illness, and the function of the brain. I would also argue that for the most part they have done their best to apply this knowledge to successfully treated their patients. Can you prove there has been widespread harm done by psychiatrists onto their patients in present time? Also I you claim that psychiatrists are uninformed, however, you urge us to turn to two things; God and this mysterious 1% having the capacity to "read minds". Both of which are are not rooted firmly in science, and so in actuality move us further into ignorance. Wait are you arguging that Tony Blair and George Bush are: Part of this 1%. Capable of speaking to God The "ways of nature" bit here is a naturalist fallacy, and what does the Tony Blair/George Bush thing have to do with your point about Schizophrenia? Again not sure how this relates to a scientific argument about mental healthcare.

What is frustrating about it? Do you have a specific question about it we could help you understand?

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.

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. 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] 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.

-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.

So I ran across this documentary, "WikiRebels" that gives an excellent overview of not only Wikileaks' most current release, but also its foundlings and rise to prominence. Overall I thought it was an excellent documentary, and think it sheds a very interesting light on this debate.

Would you mind writing your definitions out symbolically. I really don't understand what you mean when you say things like, or Also just to be clear when you talking about integrals you are meaning the riemann integral of a continuous function correct?

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"

Yes that is correct. For a sample of size n with sample standard deviation S, the standard error of the mean is [math] SE = \frac{S}{\sqrt{n}}[/math]

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. Sorry for that. I am, however, still unsure on the second question.

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.

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?

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.

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.

As this thread is over 8 years old, and as the OP states, "ok there[sic] no prize" I am going to have to say with almost 100% certainty that there is no prize, nor is the OP even active on the site.

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.