Need Math Help?

[Death]

Oh. Don't I look stupid. :embarrass

 

[Death]

Okay then. How about this.

For z = 1+i, find z^2, z^4, z^2(with a bar on the z) and z^4 (with a bar on the z)

Repeat z = -1 +i.

Solve z^4 + 4 = 0.

WHAT IS Z!? And how do I even do this?

 

[marthanoob]

Okay then. How about this.

For z = 1+i, find z^2, z^4, z^2(with a bar on the z) and z^4 (with a bar on the z)

Repeat z = -1 +i.

Solve z^4 + 4 = 0.

WHAT IS Z!? And how do I even do this?

It's stated in the problem that z = 1+ i.
So for z^2, do (1+i)^2. That comes out to 1+2i-1 = 2i
And from that z^4 would be (2i)^2 so -4.
Idk what the bar over z you are talking about is.

I'm guessing the last question is a lesson to show that z=(+ or -)1+i.

 

[Death]

Z bar means the conjugate. So if z = 1 + i, Z bar = 1- i.

 

[marthanoob]

Z bar means the conjugate. So if z = 1 + i, Z bar = 1- i.

Ok, cool. I assume you're good now?

 

[Death]

Okay, I don't understand how to get the answer.

A rectangular field is to be enclosed and divided into two sections by a fence parallel to one of the sides using a total of 600 m of fencing. What is the maximum area that can be enclosed and what dimensions??

 

[AltF4]

Death:

The most efficient use of area will always be a square. (Except if you're allowed to make curved fences. In which case it'd be a circle.)

So you know what the final layout will look like. You just have to figure out the values. It's the same problem as before, except now you've got 5 sides instead of 4.

area = w ^ 2
fenceUsed = w * 5

You know that you use 400m of fence, so the length of each side must be 80m. Thus the area is 80^2, or 6400 m^2.

 

[Death]

The teacher wants us to use maximum minimum values to find out the values.

Like to get x: x = -b/2a and y = 4ac - b^2 / 4a

????

 

[AltF4]

Yes, I suppose your teacher DOES want you to use calculus, huh? How about this, then:

area = length * width

and we also know that the total fence length is 600m. which means:

length * 2 + width * 2 = 600
length +width = 300

Now, let's rewrite our equations with an arbitrary variable 'x' thrown in for reasons you will see...

length = 150 + x

which means that

width = 300 - length = 300 - (150 - x) = 150 - x

plug those values into the area function and we get...

area = (150 - x)(150 + x)

Now you need to find a value of x that maximizes area. Simple calculus from here out, right?

area = 22,500 - x^2

area' = -2x

so we know the maximum occurs at x=0

Thus, the optimum length and width are with x=0!

length = 150 + x = 150 + 0 = 150
width = 150 - x = 150 - 0 = 150

Square!

 

[Agi]

Jean is shorter than Brutus, but taller than Imhotep.
Imhotep is taller than Jean, but shorter than Lord Scotland.
Lord Scotland is twice the height of Jean and Brutus combined, but only 1/10 the height of Millsy.
Millsy is at a constant height of {x-y}.
If Jean stands exactly one nautical mile away from Lord Scotland, how tall is Imhotep?

Ok, but seriously. I'm having difficulty understanding derivatives, (1st year calculus), particularly roots and negative exponents. Are there any rules that I should know to help out with this? Thanks.

 

[choomer]

i need help with the quadratic formula (i think i spelled that right), i always seem to mess it up;
is there some type of trick or something to make it easier to understand?

 

[AltF4]

Ok, but seriously. I'm having difficulty understanding derivatives, (1st year calculus), particularly roots and negative exponents. Are there any rules that I should know to help out with this? Thanks.

Just remember that roots are fractional exponents. For example, the square root of X is the same as X^(1/2)

And when you take the derivative of something, you subtract the exponent by one then bring it down. So X^(1/2) -> (1/2) X^(-1/2)

Negative exponents aren't any harder. Just that you have to remember you're subtracting by one, so the exponent will get increasingly negative as you derive it further.

i need help with the quadratic formula (i think i spelled that right), i always seem to mess it up;
is there some type of trick or something to make it easier to understand?

Like, help memorizing what the formula is? Or how to use it?

 

[choomer]

Like, help memorizing what the formula is? Or how to use it?

how to use it;

 

[marthanoob]

how to use it;

Quadratic equations are always in the form
0=ax^2+bx+c
If they are not, then manipulate the equation so that they are.

Then plug that into the quadratic formula.

(-b plus or minus sqrt[b^2-4ac])/2a

 

[_Phloat_]

Alright, say you were playing a game in a casino that gave you a 53% chance of winning.

You can be 1 dollar, 2 dollars, 4 dollars, etc etc.. You have 300 dollars.

While I realize that all betting strategies are extension of gambler's fallacy, which would you use? You cannot leave till you have 1,000 dollars.

Fun is not a factor, which is mathmatically best.

IIRC there is a strategy "2P-1" or something.

 

[AltF4]

I don't think I understand the question, Phloat. If you have a positive chance of winning (over 50%) then you can just keep betting and you will statistically tend to gain money. The amount of money you bet per game is irrelevant. Though, I suppose you would make money faster by betting larger.

 

[_Phloat_]

Makes sense. I was just wondering what you would do.. Statistically would it not be safer to bet lower.. but at time is always a concern..

Also, if you bet too much a few losses could take you to 0, and you would have nothing to bet.

What about this:

I bet a dollar. If I lose I bet two dollars. If I lose that, I go back to a dollar.

Now, to a person that fails at statistics like me, when you look at that you lose 3 Dollars 25% of the time, but win a dollar 66% of the time.. which should eventually put you at the top? (Assuming chance was 50% this time).

Just wondering, I find it interesting that people have all their betting strategies, none of them are mathematically correct... so I was wondering what a mathematician would do =D

 

[AltF4]

Well, think of it like this:

Imagine having the situation where you win 53% of the time. So over time, you will tend to gain money. Suppose that you only bet 1 penny each bet. Even though you'll be gaining money statistically, it will take you a very long time to do so by getting only one penny at a time!

By contrast, if you were betting 1 Million dollars each bet, you will gain a lot of money a lot faster.

But in either case, you will be getting a 53% return on your "investment". You're only changing the quantities involved.



As for your second situation, the one where you said:

I bet a dollar. If I lose I bet two dollars. If I lose that, I go back to a dollar.

Now, to a person that fails at statistics like me, when you look at that you lose 3 Dollars 25% of the time, but win a dollar 66% of the time.. which should eventually put you at the top? (Assuming chance was 50% this time).

You are falling for the same misconception in this situation, too! You see, you have a 50% chance of winning each bet. So you will statistically tend to not gain nor lose money. The quantity that you bet does not affect whether or not you lose money. The percentage is what determines whether or not you'll be gaining or losing money over time. The amount you bet determines only how fast you'll be gaining/losing it.

 

[_Phloat_]

Thanks for the helpful responses =].

Let me re-phrase. In the situation above, you couldn't do anything over 300. And, betting it all at once is a huge risk, losing all of your bankroll in one round of this game. But, betting too low is a huuuuge waste of time, you can leave once you have 1000 so you don't wanna do that pennies at a time...

So, my revised question: Personally, in the previously posted situation, how would you balance time with risk; if you are using flat betting how much would you bet at a time.

Thanks for the help =].

 

[NickTheGreat]

You guys make me feel stupid.

 

[_Phloat_]

Nick, you will be surprised at how fast your knowledge will grow (assuming you attend school). First time I saw this thread I just about exploded, now a large part of it makes sense, and I feel like I can use it for my benefit =]

 

[1048576]

Thanks for the helpful responses =].

Let me re-phrase. In the situation above, you couldn't do anything over 300. And, betting it all at once is a huge risk, losing all of your bankroll in one round of this game. But, betting too low is a huuuuge waste of time, you can leave once you have 1000 so you don't wanna do that pennies at a time...

So, my revised question: Personally, in the previously posted situation, how would you balance time with risk; if you are using flat betting how much would you bet at a time.

Thanks for the help =].

It's always going to be a function of number of bets vs. probablity of winning. You will never win 100% of the time and it will never take less than two or three bets. Pick an arbitrary point on the curve based on how important those variables are to you, I guess.

Are you looking for a formula to determine your odds of walking away with $1000 with a given betting function? We can help with that, I suppose. (Well, I probably can't )

 

[_Phloat_]

I was just wondering about what mathematically-gifted people would do personally...

But a formula would be nice =D

 

[marthanoob]

Thanks for the helpful responses =].

Let me re-phrase. In the situation above, you couldn't do anything over 300. And, betting it all at once is a huge risk, losing all of your bankroll in one round of this game. But, betting too low is a huuuuge waste of time, you can leave once you have 1000 so you don't wanna do that pennies at a time...

So, my revised question: Personally, in the previously posted situation, how would you balance time with risk; if you are using flat betting how much would you bet at a time.

Thanks for the help =].

Intuitively, it makes sense to me that the more times you bet less money, the more chance of getting closer to your given probability of winning.
So if you bet a penny every time, you will have very close to 53% gain over time.
On the other hand, if you bet more money at a time over time, there will be more fluctuation.

I don't think there are any arbitrary formulas on efficiency of gambling.
It all depends on the speed of the games and length of time you consider reasonable. The pursuit of such formula sounds somewhat nonsensical to me.

 

[_Phloat_]

I know there isn't a "best" option by any means. I was just wondering what the better mathematicians would do in this situation. This isn't a get-Phloat-rich-quick scheme.

 

[marthanoob]

I know there isn't a "best" option by any means. I was just wondering what the better mathematicians would do in this situation. This isn't a get-Phloat-rich-quick scheme.

I know it's not a scheme, I'm just saying that it all depends on your frame of mind and how much fluctuation from 53% you are willing to gamble.
I guess one could find a formula with an unnaturally quantity of variables. There really needs to be more constraints on the problem if you are introducing time. A minimum game time and a maximum play time for example.

 

[AltF4]

I was just wondering about what mathematically-gifted people would do personally...

But a formula would be nice =D

Mathematically inclined people don't gamble. Because no real casino game has positive odds.

 

[1048576]

Lol, I was making a formula using Java's random number generator to calculate whether you won or lost the particualar bet, but Java ran through my loop faster than the random number generator could acquire new seeds (it uses the clock) so I'm stuck.

 

[_Phloat_]

Mathematically inclined people don't gamble. Because no real casino game has positive odds.

I know plenty of mathematically inclined people that gamble.

They see it as paying for entertainment, rather than a job to gain money with.

 

[AltF4]

Lol, I was making a formula using Java's random number generator to calculate whether you won or lost the particualar bet, but Java ran through my loop faster than the random number generator could acquire new seeds (it uses the clock) so I'm stuck.

Yea, you have to pass a seed into the PRNG. Usually, you can get away with using the time (in milliseconds) as a seed, since it changes rapidly. But not always. If you're getting multiple hits for the same seed in your PRNG, try doing a wait for 1 millisecond before every call to rand(). That way you ensure the seed will increment.

I know plenty of mathematically inclined people that gamble.

They see it as paying for entertainment, rather than a job to gain money with.

Well, sure. That's different. I've gambled before. It's fun to in Vegas. But never with a lot of money, and never with the goal of gaining money in mind.

 

[Narukari]

Mathematically inclined people don't gamble. Because no real casino game has positive odds.

Nah, they will gamble too. There are lots of ways to have a ton of fun without wasting much money. The Cannery has a weekly Texas-Hold-Em tournament with a $20 buy in, and you get to start out with $1,000 in chips. Over a hundred people will enter the tournament and if your good you can be playing for easily 5 hours. If you make it to the semi finals you're guaranteed to double your money too, and if you have any knowledge of statistics you have a higher chance of making it to the top than half the people there already.

But if your talking craps/roulette, then yes I don't see how anybody that knows basic statistics could enjoy that. Its like throwing money away. (Some people do find it fun though ^_^)

 

[AltF4]

Right, right. I meant "not taking into account the entertainment value of gambling" - mathematically inclined people don't gamble. When you start talking about stuff like doing poker tournaments, it's essentially paying entrance into playing a game. Which is very different than "gambling" in the sense that I meant it.

I pay to enter smash tournaments (on the occasions I do play), and have a chance to win money. But don't consider it "gambling".

 

[arrowhead]

students who conceive of 0.999… as a finite, indeterminate string with an infinitely small distance from 1 have "not yet constructed a complete process conception of the infinite decimal".

but the limit as x approaches infinity of 1/x also has an infinite amount of decimals that are zero. so what's the difference between 1/x=0 and .999~=1?

also, i don't see how the method of digit manipulation is valid as a proof that .999~=1. when the .999~ is multiplied by 10, it loses one decimal point. so when you subtract the original .999~ from it, it is one decimal longer than the .999~ in 9.999~.

edit: oh wait, the limit of x as it approaches infinity of 1/x IS 0, GAH

 

[AltF4]

That wikipedia article is just trying to say: "Don't think of .999~ as a finite string". It is a number. This number has a value. The way that the number is represented and shown to you is ultimately not important.

As for your second paragraph, .999 has an infinite number of 9's in it. So when you multiply it by 10, it STILL has an infinite number of 9's in it. It doesn't "lose one".

 

[arrowhead]

the way i see it is .x9 vs .x where x is 999~ written in. is this wrong? because it doesn't contradict the fact because an infinitely small number is zero.

so back to a 2D asymptotic graph, the function, y, would reach its asymptote as x approaches infinity, but it just never does because x can never actually reach infinity, right?

 

[SuperBowser]

Something from the debate hall (out of my own curiosity)

Okay, some quick math fixes:

1) You cannot "plug infinity into an equation". Infinity is not a number. It is a concept. You cannot plug infinity into an equation any more than you can plug Santa in.

2) .999~ does in fact equal 1

3) .000~1 is not a number. Think about it. The "~" means "repeating infinitely". So you can't plop a one at the end of an infinite series because there's no end!

While I agree with 2) and 3), I don't understand 1). Isn't the concept enough? That is to say, if you are arguing that the universe has always existed, it is only logical to say that time has lasted an infinite amount too?

 

[arrowhead]

but hawkings isn't saying the universe always existed. it extends asymptotically into the finite past, so that you never actually reach the moment of the big bang.

 

[AltF4]

No, the "concept isn't enough". You can only plug numbers into equations. You can't plug colors into equations, you can't plug people into equations, and you can't plug concepts into equations. Infinity is not a number.

But it is more correct to say that time extends finitely into the past, but with an infinite duration. Time is not just a simple line that can be counted. It can be bent, warped, and even broken. It's a geometrical object with a shape. You can't just sum it up in one word by saying it is "infinite".

 

[Death]

As much as I enjoyed the past two weeks, I have to get back to school on Monday .

I need some help setting up the equation for this problem and actually solving it.

A strip of sheet metal 30 cm wide is to be made into a trough by turning strips up vertically along two sides. How many cm should be turned up at each side to obtain the greatest carrying capacity?

 

[1048576]

Let S be one of the sides turned up
Let P be the wire on the bottom

2S + P = 30
P = 30 - 2S
(30 - 2S)S = Carrying Capacity

30S -2S^2 = C

derive both sides

30-4S = 0

S = 15/2

When S is smaller, eq is positive, when S is larger, eq is negative, so S = 15/2 is a relative maximum

15/2 cm should be turned up at each side.