psi20

I don't know how to do powers either, except the old 3^2 - 8^2 + 7^2 + 10 = 4 But you can't do that because you didn't draw any twos. If you're going to use powers, both base and exponent must be drawn.

I made up this new card game and the first version goes like this. You get a deck of cards and remove the jacks, queens, and kings. Now you have Aces and 2 to 10. Aces are worth 1 and the numbers are worth themselves. Shuffle the cards and pick 5 cards. Now with those five cards, make an equation. You can use + - x / ( ) powers and roots. For example, if you picked up 9,5,1,2,7 you could make the equation (1*9+5)/2 = 7 If you picked up 9,5,6,3,3 you could make the equation 3*3^(6-5) = 9 The game gets harder--for me at least-- with the face cards in them. It's even harder (perhaps impossible) with some sets of 4 cards. But all the 5 card sets I've drawn can be made into equations. This set of numbers gave me a hard time. The puzzle is to make an equation with 3,4,7,8,10.

uncool, those are interesting sums, but not the sums I'm looking for. The sums I'm looking for are like the sum of consecutive powers of numbers. Like 1^3 + 2^3 + 3^3= (3^2)((3+1)^2)/4 Primarygun I couldn't find any match on interpolarization. Care to explain what you're talking about?

x,y, and z can only be positive integers, forgot to mention that

How does the logic for the method of infinite descent work? Fermat indirectly proved that x^4 + y^4 = z^4 has no solutions through this. "In order to prove that there were no solutions, Fermat assumed that there was a hypothetical solution (A,B,C). By examining the properties of (A,B,C), he could demonstrate that if this hypothetical solution did exist, then there would have to be a smaller solution (D,E,F). Then by examining this solution, there would be an even smaller solution (G,H,I), and so on. Fermat had discovered a descending staircase of solutions, which theoretically would continue forever, generating ever small numbers. However, x,y, and z must be whole numbers. So the never-ending staircase is impossible because there must be a smallest possible solution. This contradiction proves that the initial assumption must be false." Something to that effect. But I don't get how it works. Can someone explain it to me?

The person who invented a lever must've been pretty smart.

1 + 2 + 3 + ...+ n = n(n+1)/2 1 + 4 + 9 + ...+ n^2 = n(n+1)(2n+1)/6 1 + 8 + 27 + ...+n^3= (n^2)((n+1)^2)/4 Besides just looking at the numbers and figuring out through mathematical induction, how do you find these formulas. For the first one, there's a way that goes something like this. Sum = 1 + 2 + 3+...+(n-1)+ n Sum = n +(n-1)+...+ 2 + 1 2 Sum = (n)(n+1) Sum = (n)(n+1)/2 Can this method be applied to higher powers? If so, can you show a couple of examples? I also saw a method using dots. Like for n(n+1)/2, you can form a n(n+1) rectangle of dots by placing together 2 trianglular array of dots with one dot in the top row, 2 in the second, ..., n in the nth. How can you use dots to find the formula of the sum for higher powers?

Only some people will benefit from this; the rest will die off.

Try racism in the education system and language. There's also racism in politics. Why do politicians make the policies they do? What kind of policies promote racism? When a new group of people come to America, sometimes there's racism against them. Lost jobs, homes, etc. When some people come to America, sometimes they aren't accustomed to the diversity of some areas in America so they're racist.

Interesting. This problem was discussed during my math class as well, in California. Anyways, there are some teachers who grade you down because of you political views, race, gender, etc. If you're going to do something, always do it formally or politely. Stay calm, too. See if other friends or previous students feel that way. If they do, then this problem should go to the principal. If any previous students felt the same way, they can help you out. Here are the steps I would take. Talk to the teacher 1 on 1 by making an appointment. "Excuse me, may I request an appointment afterschool to discuss my grades." Basically, the teacher can't say, "No, I don't want to talk to you." If he/she does, then tell the principal. During the appointment, bring up some of your evidence. Request to see a record of your assignments. Stuff like that. If you find that your teacher's grades for you are lower than the actual grades on you assignments (assuming your teacher shows you back your assignments), then show him/her (hopefully you keep a folder of your assignments for a semester). If your teacher refuses to show you the assignments, ask your parents to request an appointment. Same thing again. If that fails, request a meeting with the principal along with your parents and the teacher. If your grades go down because of this, then report it again. It's against the teacher's code.

There is a calibration curve due to the absorption? Light is absorbed by air, scattered, converted to other wavelengths, etc. So the diameter reaches a certain maximum before decreasing again. Is that right?

Sorry, I was talking about irradiance. The farther away you go from a light source, the greater the area the light spreads over. The power intensity decreases over a unit area. It's supposed to decrease by the square of the distance from the light source. The problem was to find if it applies to lasers.

Does the inverse square law apply to a laser beam? I couldn't tell when I did it. It didn't look like it did. As I got farther from 1 meter, the diameter of the beam got bigger. After about 5 meters away, the beam didn't expand anymore. But I didn't measure the diameter accurately enough to tell what happened.

I don't know much about machines, hydraulics, or engineering, but I want to make something that can shoot badminton birdies at high velocity. I'm not sure how to make it, how the machine would work, what the machine is made of, etc. I'm limited on money so I can't make anything that costs a lot. My first idea was to use pressurized air or something. Would that even work? The birdie is light. Where would the pressurized air come from? How do I build a machine that uses this concept? How would the birdies load? Where do I get my supplies from?

My dryer makes a very loud and continuous noise when the timer's up. How do I stop it? I'm no mechanic, but I want to stop the noise somehow.

Try http://mathworld.wolfram.com/RegularPolygon.html They refer to the Greeks and pi and trig functions.

What kind of number system did they use?

Sorry, tried to make it look more mathematical.

I'm trying to prove that, hopefully this comes out right, [math]\sum_{r=0}^{n}{(-1)}^{r}{_n}C{_r}{(n+1)}^n = n![/math] Can anyone help? The pattern is from 1 4 9 3 5 2 1 8 27 64 7 19 37 12 18 6 1 2 1 etc.

Well, now all math, science, and english teachers are gone. The only teachers that seem to have immunity are P.E. teachers. Very strange.

I'm in 10th grade, it was for the entire school.

Well, it's interesting to see that so many teachers in my district have been laid off. There will be, of next year, 1 math teacher, 1 or 2 science teachers, no english teachers, ... in the school. All the teachers received pink slips, they've been laid off. So next year, ... nevermind. It's stupid. And I haven't heard of it in the news yet. Sooner or later, this story is going to be on the news. Or at least it should. I can't believe that the district just laid off like 700+ teachers, and that's just right now. They'll probably go upwards to 1000+ soon enough.

I want to learn some metallurgy and metalworking. Where can I learn this stuff with hands on experience?

I got one! Dan, 15, present

Was that a question or a statement? This works for a triangle in a rectangular coordinate-system formed by any 3 given points. If the determinant is 0, that means no triangle is formed and the 3 points are co-linear.