psi20

The area of a triangle with vertices (a,b), (c,d), and (e,f) is

(sorry, I don't know how to put it into vertical bars for determinants)

+/- .5 determinant of A

where A is

a b 1

c d 1

e f 1

and the symbol +/- indicates that the appropiate sign should be chosen to yield a positive area.

How can one prove this? I think I have a method for proving it, but it seems too tedious and long to do.

Are there any glasses right now that can ignore the effects of mirages? Meaning if you wear these glasses, you won't see the mirage.

Do you just use logic to figure it out? Why do you know x=1 from 3x + lnx=3?

"I'm sure the Europeans killed less advanced civilizations because of the fact that they were the most advanced. No matter how advanced the aliens may be, I'm sure they would still be hostile to life that is far less advanced than them. Humans do this today with other forms of life. Most people would step on a bug without thinking twice."

European advances during the late 15th century onward were not even a match for the Chinese fleet in the earlier 15th century. You gotta stop thinking of Europeans as the most advanced or superior people. My advice to you is to start researching other cultures and their expansion process. Look at how the Aztecs and Mongols expanded. Compare and contrast the two. Look at West African vs. Muslim expansion. Look at the Vikings and the later Russians.

That might give you a broader definition of humans, not just Europeans.

Aliens could be hostile, they could not be. Do they want something? If they want something, they might be hostile. If they are just checking out this part of the galaxy, they might not be.

I agree with you on our own aggressiveness, but you might want to check on the history part.

But how do you solve it? It ends up being e^3 = x e^(3x)

What do you mean e base the whole thing?

I got to 3 - 3x = ln x

Do you mean e^(3-3x) = x

y - ln x = 8

3x + y = 11

How do you solve it algebraically?

I saw a commercial about a Wild Planet episode or whatever some time soon about a lion taking care of an antelope. Now I just read an article about a tortoise taking care of a hippo. Interesting. Any comments or ideas on that? I'm really interested on why the lion takes care of the antelope, since I thought lions ate antelopes.

If you were stuck deep in the snow due to an avalanche or just slipping through and pointed a laser up, would it show on the snow's surface?

Hmm, a mobile home was moved out recently and replaced with a new one. That might explain the 6 A.M. ones and why they've stopped.

The one at school was during a test so nobody went outside. The one at home I didn't go outside either.

Interesting, I saw a mythbusters episode with where they tried to see whether subsonic frequencies of 5-9 Hz could make someone lose their bowels. The jacked the sound level up to 150 db wearing some protective ear muffs. At that sound level, they felt a lot of pressure in their chest and their breathing was changed, as if the sound itself was breathing with them. People who were farther out like 20 ft from the speakers became dizzy and sick.

The Taos hum might explain the 6 A.M. ones, but the one during class shook the class, people looked up and said, "Whoa," so it wasn't just me. I think even the windows shook.

The nearest airport is 10 miles from my house, I'm not sure if there's a fighter base though.

The 6 A.M. ones sometimes sound like motors. The first time I heard it, I thought it was the heater starting. Then, I thought perhaps it was the neighbors' heater starting, too. But I checked and it wasn't.

Haha, my bad. I meant a fork in a microwave. Like putting a fork into a microwave for a minute or two. My parents tell me it's going to explode or something.

Would putting a microwave in a fork blow it up?

Shoot, over the past few weeks I've noticed an increase in the amount of sonic booms in San Jose. Recently, due to tests and an increase in homework, I decided to wake up at around 6 A.M. to study and finish up homework and projects. Some mornings around that time, I hear this low hum that was really loud. It woke my sister up. It continued for like 10 minutes or so, unlike any kind of plane I've heard. Last Friday, when my class was taking a test, this really loud shockwave hit. It was like a jet plane was blasting off or a 9.0 earthquake hit. The windows shook and everything. Pretty crazy.

How about something that can track over 1-mile diameter?

How far can they track?

I read about a school doing that. How does it work? How can I make my own tracking device? Is it related to the GPS system in cars?

I think its a virus because the message sounded weird. It was like: I want you to be part of my group of friends. I've added you to my list. Can you confirm that you are one of my friends? Click this site. [site] If you don't want to be a part of the group, then click the site to unsubscribe.

Thanks for the info. If viruses can send themselves, then that's the most probable case.

Ok, here's the scenario. I get this email that has a virus on it. I don't open it up, though, but now I'm trying to figure out whether my friend did it or not. Here are some of the key points.

1) The sender has her name on it, and so does the email address.

2) I never received any emails from her until 3 weeks ago, one day after I sent her something. In other words, she didn't know my email prior to my sending something to her.

3) The first virus email had a list of all her friends' emails, although the next two didn't.

The first point makes it really suspicious. I can't imagine somebody without access to her email doing it.

Like 2^i , what's that? I know about DeMoivre's Theorem and conjugates.

What's the exp in exp{ylogx} mean? What's it do?

How do those work? Like 2 to the 2i power and stuff like that. And why does it work that way?

If I planted popcorn kernels in the ground, would they grow? I live in California and my history teacher said that when he was a kid, he planted those popcorn kernels and grew some form of maize.

I know how to do the problems. These were for the reader to solve for fun.