DJBruce

If the person was convicted by a jury of their peers wouldn't that make it hard for the government to silent people. Maybe I am naive, but I doubt the government could convince/persuade twelve people to convict someone with out it being leaked to the press. Azure would you suggest hiring permanent expert juries who's entire job is to sit and hear case, or would you suggest that the pool of potential jurors be reduced to those dubbed as "experts"? If it is the former I would feel like it would led to many potential problems with jury tampering and bias.

I am guessing that DH's southern remark was possibly made with your statement in mind. As for your ad hominem on DH's credibility, I would say that DH, like all of the experts on this forum, is a really credible person on many topics. Also as an aside you can never attack your way to proving you are right. What does all of the astronaut, NASA, and biographical information have anything to do with your position on geophysics? As far as I can tell it simply tells me that you had this idea. Not what evidence you are actually using to support your claims. Also what did your department and colleagues think when you rewrote the entire geophysics curriculum to match your believes?

So the question is simple, "Is the death penalty ethical?'. To be more specific is it ethical for someone convicted in a fair trail of their peers to be sentenced to death for the crimes he or she committed? Is it ethical or certain crimes and situations and not others? In my opinion there are many circumstances in which the death penalty would be ethical. If a person has shown a blatant disrespect for human life and decency numerous times it would appear to me that they have lost their right to live. What are your opinions?

I should have probably been more specific. When I stated revolution I meant a full revolutionary war. There were well might be a revolution coming. If there is a major change in our political system I would certainly hope that it does occur at the voters box. You are right Thomas Jefferson actually suggested frequent changes to the constitution. Stating in his June 12, 1816 Letter to Samuel Kercheval: Do you think that such frequent changes to the Constitution would prove useful, or do you believe that such frequent change would cause to much instability for the government to endure successfully.

Sorry I misunderstood your question. In the case to prove that: [math]\frac{d}{dx}a^x=ln(a)a^x[/math] You can do it using implicit differentiation: Let: [math] y=a^x[/math] [math] y=a^x\Rightarrow ln(y)=ln(a^x)=x(ln(a))[/math] Now lets take the derivative: [math]\frac{y'}{y}= ln(a)(x') [/math] Then multiply each side by y: [math] y'=(y)ln(a)x' [/math] Now we have that the derivative of [math]a^x[/math] is [math](y)ln(a)[/math], however, we can simplify this even more. Remember in the beginning we let Let: [math] y=a^x[/math]. Therefore: [math]\frac{dy}{dx}=(a^x)(ln(a)[/math] As for arriving at this conclusion by evaluating the difference quotient. I do not know how to show the limit without using L'Hopital, which, would not make a valid proof.

Start by evaluating the limit normally, [math] \lim_{n\rightarrow 0}\frac{a^n-1}{n}=\frac{a^0-1}{0}=\frac{1-1}{0}=\frac{0}{0}[/math] The form [math] \frac{0}{0} [/math] is an indeterminate form, so we can apply L'Hopital. L'Hopital states that if [math] \lim_{n\rightarrow c} \frac{f(n)}{g(n)}=\frac{0}{0} [/math] then [math] \lim_{n\rightarrow c} \frac{f(n)}{g(n)}= \lim_{n\rightarrow c} \frac{f'(n)}{g'(n)} [/math] So in your case we say: [math]f(n)=a^n-1 \Rightarrow f'(n)= a^n(ln(a))[/math] [math]g(n)=n \Rightarrow g'(n)=1[/math] [math] \lim_{n\rightarrow 0}\frac{a^n-1}{n}=\lim_{n\rightarrow 0}\frac{f'(n)}{g'(n)} = \lim_{n\rightarrow 0}\frac{(a^n)(ln(a))}{1}=a^0(ln(a))=(1)(ln(a))=ln(a) [/math]

In this book, Transportation Energy Data Book 22 Ed., it shows the results of three different studies done on the most fuel efficient driving speed. The three studies were conducted in 1973, 1984, and 1997. The 1973 study suggest that the optimal fuel efficiency is achieved around a speed between 30 and 40 mph. The 1984 study seems to confirm the 1973 studies findings showing the optimal speed to be 35-40 mph. The 1997 study, however, suggests optimal fuel efficiency is achieved at 50-55 mph. The study does not discuss this change, however, I would be it was due to improved car technology and design. The 1997 study also analyzes the fuel efficiency of many different mid 1990's cars. This data seems to show that optimal speed varies from model to model. Also here is a graph that shows the fuel efficiency of various cars at different speeds. I found this on Wikipedia, and could not find a supporting study, however, so take it for what its worth.

Is the same true for someone wishing to pursue physics into grad school. It has been recommended by many people that double majoring in mathematics and physics would be highly beneficial if not for getting into grad school or at least for the actual material in it. Is this true, or does it not really matter in physics as well?

I highly doubt that there is any medical experiment where some degree of pain and suffering cannot be eliminated. If for example you are testing something that inhibits pain, could you not measure without doing the most painful thing to the volunteer imaginable? Probably. If a person volunteers willfully then it is not unethical. However, the volunteer must be in a stable mindset, and be well informed of everything that might/will happen to them in the study. Even after this it would be up to the researcher to limit any unnecessary pain and discomfort for the volunteer from the experiment.

Are: Alabama Arizona Arkansas California Colorado Connecticut Delaware Florida Georgia Idaho Indiana Illinois Kansas Kentucky Louisiana Maryland Mississippi Missouri Montana Nebraska Nevada New Hampshire North Carolina Ohio Oklahoma Oregon Pennsylvania South Carolina South Dakota Tennessee Texas Utah Virginia Washington Wyoming all uncivilized societies then? As for experimenting on human beings I feel like it is only acceptable if first no other option exists. If another option doesn't then the experiment should be designed in such a way that it limits the potential harm and suffering to the volunteer. Notice I said volunteer regardless if whether or not a person is a convicted criminal they should not be forced to participate in any study.

Paranoia, just a quick question. The Deceleration of Independence says: With this in mind do you honestly think you have suffered "a long train of abuses and usurpations", and if so would you care to enumerate upon them. I will say that I agree that at times revolution might be the best tool to protect the liberty and freedom of the majority, but I do not feel we have reached the point were that is necessary.

I realize that the nomination process for the user awards is already closed, but next year I would suggest adding a couple of fun categories: -Favorite/Most Interesting Signature -Favorite/Coolest Avatar -Favorite Username

I am off to study at the University of Michigan AA this fall.

Isn't [math]\frac{1}{\infty}[/math] undefined as well; since infinity isn't actually a number? Ask Dr. Math

I am not sure if saying something is 1 in infinity is even proper. Generally saying the probability of event M something is a in b means: [math] P(M)=\frac{a}{b} [/math] Generally, [math]\frac{1}{\infty}[/math] is undefined as infinity is not actually a number and therefore the expression is undefined. As such I would guess that your statement in not actually a true statement. Merged post follows: Consecutive posts mergedIf you said x in infinity you would simply be saying, [math]P(M)=\frac{x}{\infty}[/math] which would still be undefined if [math]x\in\aleph[/math]. As far as I know the only way to make your statement undefined would be say, "The probability of event M occurring is 1 in X as x tends towards infinity" since that would be, [math]P(M)=Lim_{x \rightarrow\infty} \frac{1}{x}=0[/math] And I am really not sure if this would be possible, and if so why the probability of it happening would not be reported simply as 0.

Congratulations, Insane Alien! I graduated from high school summa cum laude about a month.

I think this really shows that there is a very importance difference between conservative and Republican, and liberal and Democrat. Historically the ideology of each major political party has shifted dramatically, (I actually tried to do a research project on this topic). I think it also shows that it is important to realize that most politicians are not as polarized as the media might portray them. Yes, they tend to lean one way, but the all makes decisions that go against their supposed ideology.

I can't think of any currently, but if you have more fire away at will, and I along with many other member will try and answer them for you.

Guess who this quote comes from: This quote comes from no one other than James Madison, in the Federalist Papers. By his eventual creation of the Bill of Rights it is obvious that Madison changed his mind. I do think that it points out however that it shows that the Framers, were not in perfect agreement on anything, including the Bill of Rights.

I listened to it, and found it very patriotic and apropos to the Fourth of July. However, I still like TJ's recommendation, which is to read the Deceleration of Independence on the day.

The sun's surface is actually white. It just appears yellowish to use because the atmosphere scatters the light before it reaches our eyes.

Not quite a junior is generally 16-17 years only. They are two years from finishing high school, and entering college. Some one who is 13-14 would more than likely be a 7th or an 8th grader. Here is a brief rundown of the education system in the US. Of course there are differences in a lot of places how the grades are divided, (Middle School may be 7th and 8th), but the ages and progression remains about the same everywhere. College High School -Senior (12th grade 17-18 years old) -Junior (11th grade 16-17 years old) -Sophomore (10th grade 15-16 years old) -Freshman (9th grade 14-15 years old_ Middle School -8th Grade (13-14) -7th Grade (12-13) -6th Grade(11-12) Elementary School -5th Grade (10-11) -4th Grade (9-10) -3rd Grade (8-9) -2nd Grade (7-8) -1st Grade (6-7) Kindergarten (5-6)

Happy Fourth of July to all of you who celebrate it.

I will agree with everyone and say that your best bet is to let your son pursue the field, which he finds most enjoyable. As for finding this out, at most engineering schools you do not declare your concentration until your second year or later. This means your son could take some time and investigate, the different fields while in college before declaring his concentration. Just as another aside, just because an aptitude test suggests that engineering might be a good path for your son I would be careful to box him in to that field. Those tests are by no means perfect, and often do not give something the person is actually interested.