This is my math challenge. The problems are probably too easy for you guys at the moment, but I'll make it super hard later as the week passes.
I guess, I'll rate each problems from easy to super hard. But that's just me.

#1 (Easy) Excalibur and I are assembling computers. It takes Ex and I 6 hours to assemble 50 computers. When I assemble 50 computers alone, It takes 5 more hours assembling 50 computers than it takes Ex to assemble 50 computers. How many computers can Ex assemble per hour?

#2 (Moderate) Find the volume of the x-axis revolution of f(x) defined from -1 to 1. ( f(x) ={ 0<x<=1|(1-x^2)^1/2}, f(x) ={ -1<=x<=0| x+1}, x is defined as real numbers. )
(Solution)
integral -1, 0 (x+1)^2pi = [1/3x^3 +x^2 +x]-1 to 0 = -(-1/3 + 1 - 1) = 1/3pi
integral 0, 1 ((1-x^2)^1/2)^2pi = [x-1/3x^3] 0 to 1 x pi = 2/3pi
(1/3 + 2/3)pi is pi.

#3 (Moderate) Find the general antiderivative of secx. x is defined as real numbers. Use the letter C as general constant.

*#2 Corrected

RAPIN ENUF!? Also @ #2: The Radius of Earth is approximately 6400 km. The mass of the ball is 100 grams. HAPPY PROBLEM SOLVING.

Post has been edited 9 time(s), last time on Jun 6 2010, 3:30 am by BeDazed.

Number 1 Not Solved
[encasebox](E + B)6 = 50
(B)(E + 5) = 50

(E + B) = 8.33


B + E = 50/6
B = 50/6 - E
(50/6 - E)(E + 5) = 50
41.67 + 8.33E - E² - 5E = 50
8.33E - E² - 5E = 8.33
-E² + 3.33E - 8.33 = 0

Using quadratic --> E = -1.67 or 4.99

B(4.99 + 5) = 50
B = 5

or

B(-1.67 + 5) = 50
B = 15

Neither of those solutions work, so I'm guessing I set up my original two equations incorrectly.[/encasebox]

Number 3 Solved
[encasebox]∫sec(x)dx
∫(sec(x)((sec(x) + tan(x)/sec(x) + tan(x)) dx
∫(sec²(x) + sec(x)tan(x))/(sec(x) + tan(x)) dx

u = sec(x) + tan(x)
dx/du = sec(x)tan(x) + sec²(x) dx

∫du/u
ln|u| + C
∫sec(x)dx = ln|sec(x) + tan(x)| + C[/encasebox]

I'm not even going to bother with number 2.

Post has been edited 2 time(s), last time on Jun 3 2010, 4:45 pm by CecilSunkure.

The subtitle says "PM Me your solutions" not "Post your solutions"

What? That's lame. Plus, I need help with number 1. People can just not read my post if they don't want to see the solutions?

ITT: BeDazed posts his math homework and expects us to do it for him.

How dare you! I made these problems up.

Oh and on #2, I actually made the problem wrong. It was actually meant to be an x-axis revolution. It might have confused some people.

@Cecil - I'll PM you my solution.

Here's a hint Cecil, check your second equation.

The problem is is that the question is too easy for you to solve... its basic Algebra I
You set up a system of equations and solve it from there, either by graphing or substitution.

You want it raping?! <_<

On note, since nobodies participating, I will post the solutions 10 hours from now, plus 3 more problems. C'mon guys participate <_<

Post has been edited 1 time(s), last time on Jun 5 2010, 3:01 am by BeDazed.

Yes please

6*(E + B) = 50
E*Y = 50
B*(Y+5) = 50

Where Y is the amount of time it takes Excalibur to assemble 50 computers, then Y+5 hours is the amount of time it takes BeDazed to assemble 50 computers. For Cecil

The problems aren't interesting, BeDazed. If these were Mandelbrot or AIME questions (or something along these lines), they'd be possibly worth solving and showing off. What this is is just testing your knowledge of specific aspects of mathematics - basic algebra for the first, basic integration for the second and third. They're not interesting. <_<

I agree.

If you're going to challenge us challenge us in things we don't already have experience in. These are all basic stuff we've been doing forever. A mathematics challenge is one where you are forced to play around and think analytically as well as creatively to discover the answer. Ever done the JETS competition? We need stuff like that.

Quote from Sacrieur

Ever done the JETS competition? We need stuff like that.

Can you give us some examples of this?

So basically they gave us engineering problems. We had to figure out how to solve them and read up on the literature they gave us about the methods typically used to figure out similar things. Basically we had to come up with formulas ourselves without help and evaluate them as well as understand the engineering concepts behind something. It was essentially real life applications of math (engineering).

Sample Problem

This shit was hard. It is a high school competition, but only given two hours or so for a shit ton of problems like this leads to very low scores. The winners typically get 35% - 40% of the questions right.

Thanks!

Well. I'm not really into copying sample problems already out from previous tests. They do look pretty hard.. <_< Super hard for weekly 1.5 .

Those problems aren't really good. Good problems are those that can be easily understood and that are very difficult to solve. If you want excellent problems, I heavily recommend those of the Putnam Competition available here. They're from one of the best north-american competition in mathematics. If you're talented in math and are motivated in competing, you should participate.

And if you're a hardcore mathematician, try out the clay institute's unsolved problems available here. Some of the problems require advanced knowledge of mathematics but it's nothing that can't be overcome with the help of wikipedia. Also, if you ever manage to solve one, you win One Million Dollars.

If you're really obsessed about money, you could try to crack the RSA encryption algorithm. In essence, the problem is very simple: Find an algorithm to factor the product of two huge prime numbers in computable time. If you ever solve this, you'll become rich beyond your wildest dreams. Seriously.

You know, I'm really bad when it comes to using English mathematical terms. I'm a native Korean. But, rapin' problems here it comes.
*Urgh. I'm finding some errors within my problems. Takin' some time to fixin <_<..

Post has been edited 1 time(s), last time on Jun 5 2010, 4:13 pm by BeDazed.