MATH questions - It has begun once again!

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4RM3D

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SaikyoKid said:
Then what about the original link that I've posted to explain things?
(http://en.wikipedia.org/wiki/Boy_or_Girl_paradox [http://en.wikipedia.org/wiki/Boy_or_Girl_paradox])

Vegosiux said:
I did make a disclaimer about that:

4RM3D said:
A women gives birth to twins. One of them is a boy. What is the chance the other one is a boy also? (Excluding biological factors and statistics)
 

Llil

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This isn't maths. Something like proving that irrational numbers exist is maths.
And now that I got that out of the way, here's a cool puzzle I heard a while ago:

Alice and Bob are playing a guessing game.
Alice: "I have three kids. Multiplying their ages together equals 36 and the sum of their ages equals the number of my neighbours house. Can you guess their ages?"
Bob goes and checks the house number, then comes back.
Bob: "I'll need more info."
Alice: "Alright. My oldest child plays piano."
Bob: "Okay, I got it now..."

...How old are the kids?

4RM3D said:
And finally, onward to the last question.
A women gives birth to twins. One of them is a boy. What is the chance the other one is a boy also? (Excluding biological factors and statistics)
I think a better wording might help with some of the confusion. Like "I have two kids. One of them is a boy. What is the chance the other is a boy?" That way it's more clear that the second child's sex isn't independent in this situation. At least I think so.
 

4RM3D

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isometry said:
I see, but there is still the boy or girl paradox [http://en.wikipedia.org/wiki/Boy_or_Girl_paradox]. What it comes down to is that I've asked the wrong question. My intend was to point out the aforementioned paradox.
 

Melon Hunter

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Palademon said:
SckizoBoy said:
... yeah... next time, give us something proper by way of questions, like game theory or differential equations, or even geometry, ffs!
I started differential equations today.

I would've been all like "COME AT ME BRO!"
x''(t) + 4x'(t) + 4x = 0

Off you go!
 

SckizoBoy

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Palademon said:
I started differential equations today.

I would've been all like "COME AT ME BRO!"
Heh... how're you finding it?! I can't remember them at all, tbh (haven't done them in... eight years, and even then it was only 'for fun'!) ¬_¬

...

Bah! OK, I've got one for everyone:

Calculus: differentiate sin(x) from first principles!
 

Woodsey

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Boo! Ask us interesting questions. By which I mean non-mathematical ones, obviously.
 

Knusper

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Yay maths! Got that last one wrong because I thought you specifically meant identical twins.
 

BiscuitTrouser

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SckizoBoy said:
Palademon said:
I started differential equations today.

I would've been all like "COME AT ME BRO!"
Heh... how're you finding it?! I can't remember them at all, tbh (haven't done them in... eight years, and even then it was only 'for fun'!) ¬_¬

...

Bah! OK, I've got one for everyone:

Calculus: differentiate sin(x) from first principles!
cosx. I know that as a rule.

A man drops a ball off of a building. It takes 10 seconds to hit the ground. The ball weighs basically nothing and there is no wind, the ball generates negligable air resistance. How tall is the building.
 

isometry

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4RM3D said:
isometry said:
I see, but there is still the boy or girl paradox [http://en.wikipedia.org/wiki/Boy_or_Girl_paradox]. What it comes down to is that I've asked the wrong question. My intend was to point out the aforementioned paradox.
Yes. Also, I wouldn't read too much into that wikipedia article. Partly because it's tagged with "original research claims", but also because it is basically mathematical amateurs making much ado about nothing. Better to spend the time learning these basics and moving on to more interesting questions.

Melon Hunter said:
Palademon said:
SckizoBoy said:
... yeah... next time, give us something proper by way of questions, like game theory or differential equations, or even geometry, ffs!
I started differential equations today.

I would've been all like "COME AT ME BRO!"
x''(t) + 4x'(t) + 4x = ?

Off you go!
That's not a differential equation, you have to put something on the RHS. You are supposed to figure out the unknown function x(t), not guess what the RHS is. :p

SckizoBoy said:
Palademon said:
Bah! OK, I've got one for everyone:

Calculus: differentiate sin(x) from first principles!
Depends what you consider first principles. You probably have in mind the geometrical version using the angle sum formula:

sin(A + B) = sin(A)cos(B) + cos(A)sin(B)

So, putting this into the numerator of the difference quotient:

sin(x+h)-sin(x) = sin(x)cos(h)+cos(x)sin(h) - sin(x)

At this point the student has previously found

lim_{h->0} (1-cos(h))/h = 1

and

lim_{h->0} sin(h)/h = 1

so (sin(x))' = cos(x). That's the way a geometer would do it, an analyst might define sin(z) in terms of its power series, or in terms of complex exponentials, so that makes it easier.

A more challenging problem that students usually don't see is to differentiate the natural log function.
 

Redingold

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SckizoBoy said:
Palademon said:
I started differential equations today.

I would've been all like "COME AT ME BRO!"
Heh... how're you finding it?! I can't remember them at all, tbh (haven't done them in... eight years, and even then it was only 'for fun'!) ¬_¬

...

Bah! OK, I've got one for everyone:

Calculus: differentiate sin(x) from first principles!
Okey dokey.

Let y = sin(x)

Now, the gradient of this is (y[sub]2[/sub]-y[sub]1[/sub])/(x[sub]2[/sub]-x[sub]1[/sub])

Let x[sub]1[/sub] = x+h and x[sub]2[/sub] = x

Now dy/dx = (sin(x+h)-sin(x))/h = (sin(x)cos(h)+cos(x)sin(h)-sin(x))/h

Now let h tend to 0

As h tends to 0, cos(h) tends to 1, and sin(h) tends to h. Therefore sin(x)cos(h) tends to sin(x), and dy/dx tends to (sin(x)+cos(x)h-sin(x))/h, which is cos(x)
 

Thaliur

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4RM3D said:
You have 2 separate events (triggers) that can happen simultaneously. Each event has a 50% chance of happening. What is the chance that event 1 or event 2 or both happens?

75% | It is not 50% + 50% = 100% For starters you can't add the two possibility, unless they are mutually exclusive.
There is a 50% * 50% = 25% chance that both events occur at the same time (and there is a 25% chance none of them occur at the same time).
But what about either one? For that you have to remove the possible overlap, which is 25%. Thus (50% + 50%) - (50% * 50%) = 75% For completion sake the mathematical formula: P(A or B) = P(A) + P(B) - P(A and B)
I don't want to nitpick, and might have missed some part of the question, but wouldn't there still be a 25% chance that both event do NOT happen? Like in a Pacman diagram? You get one quarter 0 (no event occurs) one only A, one only B, and one A+B.

[edit]Sorry, I saw my answer as different when it was actually the same as yours.
 

SckizoBoy

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BiscuitTrouser said:
cosx. I know that as a rule.
True... but me wanted loads of calculus scribbles! -_-

A man drops a ball off of a building. It takes 10 seconds to hit the ground. The ball weighs basically nothing and there is no wind, the ball generates negligable air resistance. How tall is the building.
490m?
 

Melon Hunter

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isometry said:
Melon Hunter said:
Palademon said:
SckizoBoy said:
... yeah... next time, give us something proper by way of questions, like game theory or differential equations, or even geometry, ffs!
I started differential equations today.

I would've been all like "COME AT ME BRO!"
x''(t) + 4x'(t) + 4x = ?

Off you go!
That's not a differential equation, you have to put something on the RHS. You are supposed to figure out the unknown function x(t), not guess what the RHS is. :p
Sorry, I dun goofed. That question mark should be a zero.
 

4RM3D

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Llil said:
Alice and Bob are playing a guessing game.
Alice: "I have three kids. Multiplying their ages together equals 36 and the sum of their ages equals the number of my neighbours house. Can you guess their ages?"
Bob goes and checks the house number, then comes back.
Bob: "I'll need more info."
Alice: "Alright. My oldest child plays piano."
Bob: "Okay, I got it now..."

...How old are the kids?
Hmmm, I am not sure what the point is of mentioning: "...and the sum of their ages equals the number of my neighbours house."

Also, the only thing I can distill from: "Alright. My oldest child plays piano." is that the oldest two children are not the same age.

Anyhow, what it boils down to is: A * B * C = 36

Which gives the following possibilities:
1 * 2 * 18 = 36
1 * 3 * 12 = 36
1 * 4 * 9 = 36
1 * 6 * 6 = 36
2 * 2 * 9 = 36
2 * 3 * 6 = 36
3 * 3 * 4 = 36

I could at least remove 2 answers:
1 * 6 * 6 = 36
3 * 3 * 4 = 36

But I don't see how to narrow it down more.
 

SckizoBoy

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isometry said:
A more challenging problem that students usually don't see is to differentiate the natural log function.
From first principles? Yeah... that'd be a toughie... though reversal of the variables and re-expression with the Taylor series makes it semi-palatable as a problem and it's not overly unwieldy... but I don't think I want to write it out... -_-
 

Redingold

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Melon Hunter said:
isometry said:
Melon Hunter said:
Palademon said:
SckizoBoy said:
... yeah... next time, give us something proper by way of questions, like game theory or differential equations, or even geometry, ffs!
I started differential equations today.

I would've been all like "COME AT ME BRO!"
x''(t) + 4x'(t) + 4x = ?

Off you go!
That's not a differential equation, you have to put something on the RHS. You are supposed to figure out the unknown function x(t), not guess what the RHS is. :p
Sorry, I dun goofed. That question mark should be a zero.
Then as a general solution, x = (A+Bt)e[sup]-2t[/sup]
 

BiscuitTrouser

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SckizoBoy said:
BiscuitTrouser said:
cosx. I know that as a rule.
True... but me wanted loads of calculus scribbles! -_-

A man drops a ball off of a building. It takes 10 seconds to hit the ground. The ball weighs basically nothing and there is no wind, the ball generates negligable air resistance. How tall is the building.
490m?
Sorry :p I did it once or twice as proof but we know that as a given rule in my sylibus. Anyway you answered my question correctly, i assumed you applied SUVAT? Im doing more advanced versions of these in my second year of mechanics, and jesus its hard. I liked the old questions though, very real world style.
 

isometry

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SckizoBoy said:
isometry said:
A more challenging problem that students usually don't see is to differentiate the natural log function.
From first principles? Yeah... that'd be a toughie... though reversal of the variables and re-expression with the Taylor series makes it semi-palatable as a problem and it's not overly unwieldy... but I don't think I want to write it out... -_-
Here is a quickie from abusing Liebniz notation, although it can be rigorously justified.

Since y(x) = ln(x), x(y) = e^y, so dx/dy = e^y, so treating this as a fraction dy/dx = 1/e^y = 1/x.

The fraction abuse is the statement that the derivative of the inverse function is the reciprocal of the derivative of the function, which is true in general (when the denominator is not zero) and can be derived by applying the chain rule to f^{-1}(f(x)) = x.
 

4RM3D

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BiscuitTrouser said:
A man drops a ball off of a building. It takes 10 seconds to hit the ground. The ball weighs basically nothing and there is no wind, the ball generates negligable air resistance. How tall is the building.
Equation for a falling object near the earth's surface: g = 9.8 m/s²

So, 10 * 9.8 = 98 meters??
 

Llil

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4RM3D said:
Hmmm, I am not sure what the point is of mentioning: "...and the sum of their ages equals the number of my neighbours house."

Also, the only thing I can distill from: "Alright. My oldest child plays piano." is that the oldest two children are not the same age.

Anyhow, what it boils down to is: A * B * C = 36

Which gives the following possibilities:
1 * 2 * 18 = 36
1 * 3 * 12 = 36
1 * 4 * 9 = 36
1 * 6 * 6 = 36
2 * 2 * 9 = 36
2 * 3 * 6 = 36
3 * 3 * 4 = 36

I could at least remove 2 answers:
1 * 6 * 6 = 36
3 * 3 * 4 = 36

But I don't see how to narrow it down more.
All the info you'll need is there and there's nothing unnecessary (except the framing).
The sum part is important.