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Extreme Math Challenge... Squared!
humorman at 2:16AM, March 14, 2008
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TODAY'S PI DAY!!!

In honor of today, I will post math problems! If someone dares to answer a problem and answers correctly, I will post an even more difficult problem.

Your rewards through this process:
- new mathematical knowledge
- a newfound appreciation of math
- miscellaneous unknown things

FUN! FUN! FUN! GO!



Q1:
Solve.

1+1

Billy vs. Tree – The epic struggle of boy versus tree.
Sonic Colores – It looks like it's going to be a good game because I love how the way it makes me grow.
last edited on July 14, 2011 12:51PM
Renga Studio at 12:16PM, March 14, 2008
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An extreme math challenge, eh? How edumacational! Okay, I'll solve this one:

1+1=2

Ha! That was too easy (and I really suck at math)!
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Renga: I has a weather machine.
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last edited on July 14, 2011 3:04PM
AQua_ng at 1:12PM, March 14, 2008
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Hard mode guys.

4x - 1 = 7

WHAT IS X?

K.A.L.A-dan! Brigade Captain :D
K.A.L.A.-dan forums!
last edited on July 14, 2011 10:59AM
Orange at 2:24PM, March 14, 2008
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4x - 1 = 7
4x = 8 by the Subtraction Property of Equality
x = 2 by the Division Property of Equality

Therefore x = 2

:D!
last edited on July 14, 2011 2:22PM
humorman at 3:52PM, March 14, 2008
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Increase difficulty!

Solve for x:

|2x-4| = 12

Billy vs. Tree – The epic struggle of boy versus tree.
Sonic Colores – It looks like it's going to be a good game because I love how the way it makes me grow.
last edited on July 14, 2011 12:51PM
Orange at 6:53PM, March 14, 2008
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2x-4 = 12
2x = 16
x = 8

2x-4 = -12
2x = -8
x = -4

sooo…
x equals -4 or 8.

:D!
last edited on July 14, 2011 2:22PM
humorman at 12:19PM, March 15, 2008
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Increase difficulty!

Solve for x:

x^2 + 24 = 10x

Billy vs. Tree – The epic struggle of boy versus tree.
Sonic Colores – It looks like it's going to be a good game because I love how the way it makes me grow.
last edited on July 14, 2011 12:51PM
AQua_ng at 2:44PM, March 15, 2008
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x^2 + 24 = 10x

x^2 -10x + 24 = 0

(x-6)(x-4) = 0

x = 6 or 4


Increase difficulty!

In a right angle triangle, the two shorter sides are 3 and 4 inches. What is the length of the longest side?

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last edited on July 14, 2011 10:59AM
Orange at 4:19PM, March 15, 2008
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Since it's a Pythagorean triple, 5!

:3
last edited on July 14, 2011 2:22PM
humorman at 6:02PM, March 15, 2008
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Increase difficulty!

What is the sum of the coefficients in this expre20ssion:

20x^3 + 3x^2 - 7x + 13

Billy vs. Tree – The epic struggle of boy versus tree.
Sonic Colores – It looks like it's going to be a good game because I love how the way it makes me grow.
last edited on July 14, 2011 12:51PM
Baconators at 3:15PM, March 16, 2008
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The coefficients of
20x^3 + 3x^2 - 7x + 13
are 20, 3, -7 and 13.

Therefore the sum is 20 + 3 + (-7) + 13 = 29.


Increase difficulty!

Evaluate d/dx(x^2 + 2x + 4)
last edited on July 14, 2011 11:15AM
cool guy at 10:10AM, March 17, 2008
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Decrease Dificulty

3x4+56-1223+10000=
This life we live shall soon be past,only what's done for Christ shall last! ! ! ! ! ! ! ! !
last edited on July 14, 2011 11:44AM
humorman at 8:29PM, March 17, 2008
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Baconator's answer:
2x + 2

cool guy's answer:
8845


Increase difficulty!


Solve y(t) in terms of t:

y'(t) - y(t) = 0

Billy vs. Tree – The epic struggle of boy versus tree.
Sonic Colores – It looks like it's going to be a good game because I love how the way it makes me grow.
last edited on July 14, 2011 12:51PM
Baconators at 10:56PM, March 18, 2008
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I'm not quite sure about that one, but the way I see it…

y'(t) - y(t) = 0
y'(t) = y(t)

And for the derivative of a function y to be exactly equal to that function y, the only thing I could think is that..

y(t) = e^t
since d/dt(e^t) = e^t

But I'm not sure that I can exactly assume that…nor am I sure if that's the kind of thing you're looking for.

—————————–

Decrease difficulty!

If vectors u = (2x, 3(y^2), 1/z) and v = (1/x, -(y^-2), z), then what is the dot product of u and v?
last edited on July 14, 2011 11:15AM
Insanity at 8:07PM, March 21, 2008
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WTF?



Shoop Da Hoop?

AwesomeUnicorn
I feel a little bit like Hitler right now, too.
last edited on July 14, 2011 1:01PM
fazz33 at 3:21PM, March 23, 2008
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Hah I get where this is going.

ok Guys listen up!

1 + 1 =


1 = ln (e)
1 also = Sin^2(theta) + Cos^2(theta)

Where Cos^2 (theta) = (Cos2*(theta)+1)/2
Where Sin^2(theta) = (-Cos2*(theta)+1)/2


Thus giving you

ln(e) + ((Cos2*(theta)+1)/2 ) + ((-Cos2*(theta)+1)/2 ) = 1 + 1

Simple as Pi

Did I make a mistake?

Q2 was easy, like the guy up top said, e^y will do it :) since F' = F
last edited on July 14, 2011 12:25PM
humorman at 11:50PM, March 23, 2008
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To Baconator's last question:

Dot product equals 0.


*heh heh*
WARNING: EXTREME DIFFICULTY INCREASE!!!


Find the general solution of

y"(t) + y(t) = 2y'(t)

Billy vs. Tree – The epic struggle of boy versus tree.
Sonic Colores – It looks like it's going to be a good game because I love how the way it makes me grow.
last edited on July 14, 2011 12:51PM
fazz33 at 8:48PM, March 24, 2008
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oh bugger, you said general… oh well, its a general ODE anyways, no forcing function. I don't wanna write it out…
last edited on July 14, 2011 12:25PM
humorman at 10:20PM, March 27, 2008
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The answer is y(t) = c1te^t + c2e^t in which c1 and c2 are distinct constants. Simple, is it not?

Reset difficulty.

Simplify: 2+2


Billy vs. Tree – The epic struggle of boy versus tree.
Sonic Colores – It looks like it's going to be a good game because I love how the way it makes me grow.
last edited on July 14, 2011 12:51PM
Orange at 10:13PM, March 28, 2008
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4
last edited on July 14, 2011 2:22PM
spiritmonkey at 10:53AM, March 29, 2008
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INCREASE DIFFICULTY!

Solve:
6x9
Timmy And the Bleach

There are many things in this world that are uncertain
I'd say I'm one of them
But I'm not sure
last edited on July 14, 2011 3:54PM
Baconators at 1:43PM, March 29, 2008
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6x9 = 54




INCREASE DIFFICULTY!

What is the slope of the line described by the following equation:

y^2 = 16(x^2)
last edited on July 14, 2011 11:15AM
spiritmonkey at 11:52AM, March 30, 2008
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Do you mean the gradient?
Timmy And the Bleach

There are many things in this world that are uncertain
I'd say I'm one of them
But I'm not sure
last edited on July 14, 2011 3:54PM
Baconators at 6:35PM, March 31, 2008
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Nope.

Hint: the equation I gave is a line defined in 2-space…so compare it to the general equation of a line (y=mx + b)

It's a really simple question actually =P
last edited on July 14, 2011 11:15AM
humorman at 7:31PM, March 31, 2008
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Actually, it looks like a trick question since y^2 = 16(x^2) consists of two lines with slopes of 4 and -4 intersecting at the origin.

Billy vs. Tree – The epic struggle of boy versus tree.
Sonic Colores – It looks like it's going to be a good game because I love how the way it makes me grow.
last edited on July 14, 2011 12:51PM
Baconators at 10:16PM, April 1, 2008
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=) Good call

*when Bacon realizes he did something smart by accident and plays it off as if it were intentional*

XD
last edited on July 14, 2011 11:15AM
humorman at 11:40PM, April 1, 2008
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Okay, time for a word problem:

You are in a room with three doors and a guard. The guard tells you that behind one door is an exit and behind the other two are rabid tigers. He also, says that he knows which door the exit is behind. You choose a random door, but before you open it, the guard opens a different door which contains a tiger and then immediately closes it. He, then, gives you the option of choosing the other unopened door.

The question: Which door would you choose?


Let me clarify:

- You chose door #1, a tiger is behind door #2, you have the option of choosing door #3

- This ISN'T a lateral thinking puzzle in the sense that you can't stay in the room until the tigers die or make the tigers attack the guards while you escape or do some abstract stunt that “magically” gets you out.

- This question DOES involve math (mainly probability), so to get full credit, SHOW YOUR WORK (AKA Don't guess, think)!!!

Billy vs. Tree – The epic struggle of boy versus tree.
Sonic Colores – It looks like it's going to be a good game because I love how the way it makes me grow.
last edited on July 14, 2011 12:51PM
spiritmonkey at 2:35AM, April 6, 2008
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so the chances of a door not having a tiger are 1/3
but he eliminates one of the doors which does have a tiger so the chances are 1/2

but the chances of a door having a tiger are 2/3
with the revealed tiger that makes it… 1/3?

so the chances of your chosen door having a tiger are 1/3 still… i think…

I'd stay with my chosen door
Timmy And the Bleach

There are many things in this world that are uncertain
I'd say I'm one of them
But I'm not sure
last edited on July 14, 2011 3:54PM
BloodTh at 9:46PM, April 14, 2008
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I hate showing work… but I'd have to say door number three.

The Psycho… Guard I mean… shows the middle door, so, the two tigers would be in adjacent rooms. By doing this, I'd feel MUCH safer with the next door… on the chance that he showed me the SECOND tiger.

X*X=Y
Y+X=Z
Z/X=B
B-X=1

This is a little problem I figured out by accident in math once: All of the above problems leads to the next. Solve for X.
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last edited on July 14, 2011 11:27AM
Baconators at 10:45PM, April 15, 2008
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humorman
Okay, time for a word problem:

You are in a room with three doors and a guard. The guard tells you that behind one door is an exit and behind the other two are rabid tigers. He also, says that he knows which door the exit is behind. You choose a random door, but before you open it, the guard opens a different door which contains a tiger and then immediately closes it. He, then, gives you the option of choosing the other unopened door.

The question: Which door would you choose?
Well, if you initially pick the door with the exit, and the guard shows you a door with a tiger, then you have the choice between your exit and a tiger door, that's 1/2 chance each.

But, if you choose a door with a tiger initially, then, since the guard reveals the other door with a tiger, by switching, you'd end up at the exit.

Since there are two doors with tigers, this switching to the exit can occur twice, while switching to a tiger can only occur once. Thus, the probability of switching doors to the exit is 2/3, and switching to a door is 1/3.

And since there are 2 doors with a tiger, and one with the exit, by keeping the door you originally chose, that's 2/3 chance of failure, and 1/3 chance of success.

Thus it is best to switch doors.

BloodTh
X*X=Y
Y+X=Z
Z/X=B
B-X=1

This is a little problem I figured out by accident in math once: All of the above problems leads to the next. Solve for X.

B-X=1
B=1+X

Z/X=B
Z/X=1+X
Z=X+X^2

Y+X=Z
Y+X=X+X^2
Y=X^2

X*X=y
X*X=X^2
X^2=X^2

Err, yeah there is no real “solving” for x here.

———–

Here's a cute and simple one:

How do you make 1000 by the addition of numbers whose digits are only 8's and where the sum of the number of digits of all numbers used is 8?

(incase you don't understand that second part of the question, I mean say you add 34 and 233, then the sum of the number of their digits is 5)
last edited on July 14, 2011 11:15AM

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