Math Challenge for you math geeks.

42:wink:

blackbrandt said:

OK, another one. No calculators, abaci (!) or any other calculation devices except your head. (Yes, I am talking to you, sully.)
What is 111111111x111111111?

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12345678....and a big E for error on my handheld calculator..LOL Okay, so I cheated..LOL

It is: 123456787654321 <--Used pen and paper..Really..Scouts honor!:tongue:

cjl said:

5i (or 5j if you've done a lot of circuits)

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50% correct.

jderimig said:

50% correct.

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Yup, you forgot -5i. The correct answer is +/- 5i.
And Plano-Doug, the natural numbers are 1,2,3...
The whole numbers are 0,1,2,3...
The positive numbers are NOT the same as the whole numbers. The positive numbers include 1/2, pi, e, and 12563.3463. Do you get what I mean?
Irrational numbers are like sqrt 5, sqrt2, 15.3sqrt6, etc...
Numbers like 5/0 are either infinite or undefined, depending on who you talk to.

The sum of the first 10,000 natural numbers are the average of the first and last term, multiplied by the number of terms. So that is (1+10000)/2=5000.5. This is multiplied by the number of terms, which is 10,000. So the actual answer is 50005000. This was completely done in my head.

Thanks, this is Matt's math lesson for the day.

blackbrandt said:

So that is (1+10000)/2=500.5. <snip> This was completely done in my head.

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10001/2 = 5000.5. Your head dropped a decimal place - easy to do with mental division. That is why I prefer to do the formula without the average, by thinking in terms of pairs: (10000 + 1) X 5000 pairs = 50005000

LW Bercini said:

10001/2 = 5000.5. Your head dropped a decimal place - easy to do with mental division. That is why I prefer to do the formula without the average, by thinking in terms of pairs: (10000 + 1) X 5000 pairs = 50005000

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And this explains why I hate typing math on the computer.

blackbrandt said:

And Plano-Doug, the natural numbers are 1,2,3...

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Or 0, 1, 2, 3 ....

https://en.wikipedia.org/wiki/Natural_number

-- Roger

And is wikipedia always correct? Nope. Also, did you see this at the top of the page?

blackbrandt said:

And is wikipedia always correct? Nope.

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Rather than just bash someone else's source, it's best to provide your own superior one as well. If I had to decide between the authenticity of Wikipedia or "some guy on a forum" I'd lean toward Wikipedia but wouldn't feel good about either, depending on the fact in question.

As far as "natural numbers," there is a nicely referenced article over at Wolfram that states:

The term "natural number" refers either to a member of the set of positive integers 1, 2, 3, ... or to the set of nonnegative integers 0, 1, 2, 3, ... (e.g., Bourbaki 1968, Halmos 1974). Regrettably, there seems to be no general agreement about whether to include 0 in the set of natural numbers. In fact, Ribenboim states "Let P be a set of natural numbers; whenever convenient, it may be assumed that 0 is a member of P."

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So it appears that in this case, Wikipedia, and Jadebox, are indeed correct.

As Pete Townsend once wrote:
"one & one don't make two,
One & one make one.."

Sully said:

Rather than just bash someone else's source, it's best to provide your own superior one as well. If I had to decide between the authenticity of Wikipedia or "some guy on a forum" I'd lean toward Wikipedia but wouldn't feel good about either, depending on the fact in question.

As far as "natural numbers," there is a nicely referenced article over at Wolfram that states:


So it appears that in this case, Wikipedia, and Jadebox, are indeed correct.

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I was aware of the Wikipedia confusion when I said "Natural Numbers" - and thought it would be kinda fun to see where it went.

blackbrandt said:

Yup, you forgot -5i. The correct answer is +/- 5i.

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Very true...

blackbrandt said:

Numbers like 5/0 are either infinite or undefined, depending on who you talk to.

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In general, that would be undefined, as there are multiple possible answers that could be argued as valid. For example, if you take that to be equivalent to the limit of 5/x as x goes to 0, the answer could be positive or negative infinity, or it could not exist at all, depending on which side the limit is taken from.

cjl said:

In general, that would be undefined, as there are multiple possible answers that could be argued as valid. For example, if you take that to be equivalent to the limit of 5/x as x goes to 0, the answer could be positive or negative infinity, or it could not exist at all, depending on which side the limit is taken from.

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Yes, that's how I recall it as well. 5/0 is undefined. But the limit of 5/x as x approaches 0 from the left (or right) is defined.

Of course, it's only been about 33 years since I took calc 1, so I'm a bit rusty

Doug

.

Blackbrant, what math class are you taking this year?

3 salesman get a hotel room for the night and the desk clerk charges them 30.00.After paying the money the men go to their room,At this point the desk clerk realizes he had over charged the men by 5$ (25$ room) The clerk gives the bellhop the five bucks and tells him to return this to the men.So the bellhop,not being able to divide 5 three ways ,gives each man a dollar and keeps the last two for himself. Now each man has paid 9.00$ for the room ,the bellhop kept two bucks.9x3=27 plus the 2.00 $ the bellhop kept where is the other 1.00$?

pepe said:

3 salesman get a hotel room for the night and the desk clerk charges them 30.00.After paying the money the men go to their room,At this point the desk clerk realizes he had over charged the men by 5$ (25$ room) The clerk gives the bellhop the five bucks and tells him to return this to the men.So the bellhop,not being able to divide 5 three ways ,gives each man a dollar and keeps the last two for himself. Now each man has paid 9.00$ for the room ,the bellhop kept two bucks.9x3=27 plus the 2.00 $ the bellhop kept where is the other 1.00$?

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You don't add the $2 to the total the men are out of pocket ($27), you add it to the amount that the hotel kept ($25).

The hotel has $25, plus the $2 the bellhop kept, is $27. Adding the $1 that each man has makes $30.

Another way to say it is, "Now each man has paid 9.00$ for the room ,the bellhop kept two bucks.9x3=27" $27 equals the $25 for the room plus the bellhop's "tip"

reminds me of the 11 finger thing for children. Tell the kiddies you have 11 fingers. They look at you funny. On one hand, count backwards from ten: 10, 9, 8, 7, 6.. And you have 5 on the other. 6+5=11..

dr wogz said:

reminds me of the 11 finger thing for children. Tell the kiddies you have 11 fingers. They look at you funny. On one hand, count backwards from ten: 10, 9, 8, 7, 6.. And you have 5 on the other. 6+5=11..

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You can also do a thing where you say "six" between each number when counting your fingers ... 1,6, 2,6, 3,6, 4,6, 5,6, 7,6, 8,6, 9,6, 10,6, 11,6 ... 11 fingers! It'll confuse younger kids at least once or twice before they give you that look.

-- Roger

plano-doug said:

Yes, that's how I recall it as well. 5/0 is undefined. But the limit of 5/x as x approaches 0 from the left (or right) is defined.

Of course, it's only been about 33 years since I took calc 1, so I'm a bit rusty

Doug

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That's correct - the limit of 5/x as x goes to zero from the left is negative infinity, from the right it is positive infinity, and the general limit does not exist (since the left hand and right hand limits are not equal).

OOOO KAAYY, I'm sitting down to my first glass of wine and HUH -WHA ? How does my twelve toed dog fit into this.

Lets test if anyone is a mathematical genius:

e^(pi X i) + 1 = 0

What does this prove?

BLKKROW said:

Lets test if anyone is a mathematical genius:

e^(pi X i) + 1 = 0

What does this prove?

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Love is complex and irrational?

You have too much time on your hands! LOL

Just for grins, let's inject some more calculus into this thread:

Solve the following:
2x'' + 4x' +8x = 0
x(0) = 1
x'(0) = 0.5

Bonus points if you can tell me what physical system this commonly represents...

cjl said:

Bonus points if you can tell me what physical system this commonly represents...

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The sound waves emanating from my wife's vocal chords reminding me for the Nth time to take out the &#*$ trash.

Solve for N.

cjl said:

Just for grins, let's inject some more calculus into this thread:

Solve the following:
2x'' + 4x' +8x = 0
x(0) = 1
x'(0) = 0.5

Bonus points if you can tell me what physical system this commonly represents...

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If the " means ^2, then I know the answer.

blackbrandt said:

If the " means ^2, then I know the answer.

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The (') means first derivative and (") second derivative.

OK, scratch that. I have no Idea.

cjl said:

Just for grins, let's inject some more calculus into this thread:

Solve the following:
2x'' + 4x' +8x = 0
x(0) = 1
x'(0) = 0.5

Bonus points if you can tell me what physical system this commonly represents...

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Mass/spring/damper. Or the response of the pitch of a stable rocket in flight to a disturbance. Or an R-L-C circuit with low Q.
Estimated response is exp(-x)(-10cos(1.75x+theta)). Don't feel like solving for the phase response. ;-)

We have a winner!

(I'm assuming you got the response right - I don't feel like checking at the moment, but the physical system is definitely correct)