Quick question - Quick answer thread.

[Spell]

If you have a short and relatively simple/easy question*, don't make a thread, post it here. Maybe someone will be able to answer it.


*Examples:

When did Caesar die?
What is the capital of Burkina Faso?
What is the fastest animal on Earth
Who invented a light bulb.

etc...


Have fun ^____^

[Mider T]

Uh 44 B.C.
Ouagadougou (I think that's how you spell it)
Chettah?
James Bowman Lindsay (That's a trick question)

[infinite]

Just in case someone wanted to know the answers :amuse

- Ceasar died: March 15, 44 BC
- Capital is Ouagadougou
- fastest animal is Peregrine Falcon
* note: fastest land animal is Cheetah
-inventor Davy, Swan and Edison

[fghj]

Does God exist?

[fghj]

I thought this is pretty cool:

How much square meters will fit in a cubic meter?

[EvilMoogle]

I thought this is pretty cool:

How much square meters will fit in a cubic meter?

Infinite, since they have no depth? If you're talking surface area the answer is 6, but just "how many would fit inside" mathematically speaking you can stack them forever and never get any height.

[myle]

Does God exist?

Do you exist?

[fghj]

Infinite, since they have no depth? If you're talking surface area the answer is 6, but just "how many would fit inside" mathematically speaking you can stack them forever and never get any height.
Nope, a meter! m^3 / m^2 = m :amuse

[myle]

Hahaha! That was clever!

[Fonz_Kakashi]

How many people were killed in World War II ? The number 60 million comes to mind, but I'm not sure, and that must be including civilians if it's correct.

[Commander Red]

How many people were killed in World War II ? The number 60 million comes to mind, but I'm not sure, and that must be including civilians if it's correct.


http://en.wikipedia.org/wiki/World_War_II_casualties

Estimated around 72 million deaths.

[Fonz_Kakashi]

http://en.wikipedia.org/wiki/World_War_II_casualties

Estimated around 72 million deaths.

Wikipedia also says the world population in 1940 is estimated at 2.3 billion.

This means about 3 % of the world's population was lost in WWII. Though there's no way to pin down a moving number like that.

[Shaidar Haran]

How much dirt is in a hole that is 5 meters deep and 6 meters in diameter? Please, in cubic meters.

[EvilMoogle]

How much dirt is in a hole that is 5 meters deep and 6 meters in diameter? Please, in cubic meters.

In a hole? None :P

Assuming you want to fill the hole, it's 9*pi*5 m^3 (about 140 cubic meters).

[Shaidar Haran]

Darn it, someone got the trick question. I've seen people spend several minutes on a harder version of this.

[Fonz_Kakashi]

Darn it, someone got the trick question. I've seen people spend several minutes on a harder version of this.

I fell for it. :notrust Those things always get me.

[Commander Red]

Darn it, someone got the trick question. I've seen people spend several minutes on a harder version of this.

Huh? I didn't fell for it, but I fell for it, where I was supposed to fell for it. I think I missed the joke here?

[Shaidar Haran]

Most people listen and pay attention to the measurements rather than the actual description of the object being measured. Essentially, I asked how much dirt is in a hole.

[infinite]

Nice trick question, I am definitly going to try that one :P

[Grrblt]

Most people listen and pay attention to the measurements rather than the actual description of the object being measured. Essentially, I asked how much dirt is in a hole.

You do realize there can be dirt in a hole?

[Shaidar Haran]

You do realize there can be dirt in a hole?A hole by definition is hollow or empty.

[Anaiya]

What color was George Washington's white horse?

Where was Noah when the lights went out?

[Grrblt]

A hole by definition is hollow or empty.

... :huh

No. A hole is a space in a solid object. That space can be occupied. A hole doesn't stop being a hole because you put something in it.

[Anaiya]

... :huh

No. A hole is a space in a solid object. That space can be occupied. A hole doesn't stop being a hole because you put something in it.

This debate is amusing. Ya'll should start a "what is a hole" thread over in the debate section. :amuse

I'll jump in. I'm with Grrblt on this one. By definition (you can verify the definition at Webster by clicking here) (http://mw1.merriam-webster.com/dictionary/hole) a hole is "an opening through something". You can't always make a hole not a hole by filling it. If you drill a hole for a screw and then put the screw in, isn't there a hole still for the screw to be in?

[Grrblt]

This debate is amusing. Ya'll should start a "what is a hole" thread over in the debate section. :amuse

I'll jump in. I'm with Grrblt on this one. By definition (you can verify the definition at Webster by clicking here) (http://mw1.merriam-webster.com/dictionary/hole) a hole is "an opening through something". You can't always make a hole not a hole by filling it. If you drill a hole for a screw and then put the screw in, isn't there a hole still for the screw to be in?

The question isn't even about filling a hole. According to Dragonus, a hole can per definiton contain no dirt at all. If I drill a hole in a tree and small amounts of dirt in it, it apparently is no longer a hole.

I wonder if air is exempt from this definition of his.

[Shaidar Haran]

Fine then, no dimensions are ever given for the amount of dirt in the hole anyways. If you filled the hole back up with dirt, there wouldn't be a hole.

[Kaki]

I have a simple one about thermodynamics.

for a reaction with constant volume, like in a bomb calorimeter, does q reaction = -q from the equation q=ms ^ T from the solution?

And for a constant pressure problem, does q rxn =q solution ?

[Sunuvmann]

This is the second part of a 2 part question. I already got the first part.
Part 1.

In a pool game, the cue ball, which has an initial speed of 4.2 m/s, makes an elastic collision with the 8-ball, which is initially at rest. After the collision, the 8-ball moves at an angle θ = 38.3° with respect to the original direction of the cue ball, as shown in the figure. At what angle (in degrees) Φ does the cue ball travel after the collision? Assume the pool table is frictionless and the masses of the cue ball and the 8-ball are equal.

Ans: 51.7
Part 2.


Continuation: What is the speed (in m/s) of the cue ball after the collision?

How does one find that without the mass?

[EvilMoogle]

This is the second part of a 2 part question. I already got the first part.
Part 1.

In a pool game, the cue ball, which has an initial speed of 4.2 m/s, makes an elastic collision with the 8-ball, which is initially at rest. After the collision, the 8-ball moves at an angle θ = 38.3° with respect to the original direction of the cue ball, as shown in the figure. At what angle (in degrees) Φ does the cue ball travel after the collision? Assume the pool table is frictionless and the masses of the cue ball and the 8-ball are equal.

Ans: 51.7
Part 2.


Continuation: What is the speed (in m/s) of the cue ball after the collision?

How does one find that without the mass?

I've got a headache at the moment so I apologize if this is incorrect

But if the masses of the balls are equal then they should cancel out when you simplify the equation. Just put "m" in for both m1 and m2 and see what happens.

[Sunuvmann]

Nah thats not it. But some guys on my floor helped me with it so no worrys. Its something like

sin m1 * v1 = sin m2 * v2
cos m1 * v1 + cos m2 * v2 = 4.2 and then you substitute to find em.

Thanks anyways *reps for effort*

Edit: Bloody 24 hour rule :D:

[Fonz_Kakashi]

Quick question:

What does "schadenfreude" mean when used in English? A literal German translation is fine, too, but I'm curious specifically about its English use.

[Anaiya]

Quick question:

What does "schadenfreude" mean when used in English? A literal German translation is fine, too, but I'm curious specifically about its English use.

In German it means to gloat or gloating. It can also mean something like getting a malicious joy out of something.

[Fonz_Kakashi]

It can also mean something like getting a malicious joy out of something.
I think it means something along those lines. "Dark humor", maybe, but it seems more specific than that.

[Anbu117]

I have ten questions

if a tree falls in a forest ans your not there to here it does I'd still make a sound?

if you pour water into a cup untill it reaches the half way point is it half empty or half full?

why is water clear , but the ocean is blue

what is the number before infinte

that's it for now, I'll be back later

[EvilMoogle]

if a tree falls in a forest ans your not there to here it does I'd still make a sound?
Yes, sound is defined by a reverberation through a medium (such as air). Clearly this will exist even if no one is present to observe it.

if you pour water into a cup untill it reaches the half way point is it half empty or half full?
Both answers are technically correct. Which answer people provide tends to reflect their observations on the source, either due to a mental predisposition towards one answer or other factors (in your example since the cup is in the process of filling more people are likely to say it is half full, however half empty still remains a factually correct statement).

why is water clear , but the ocean is blue
It appears to be blue due to the refractive properties of water as light passes through it.

what is the number before infinte
Infinity is a mathematical concept not a number, as such there is no "number before infinity"

that's it for now, I'll be back later
Next time use just one post.

[Anbu117]

why is the freezing point of something, the melting point as well

this is just a theory but, if it is true that the universe is expanding, ( and the universe is the only space that exists) what is it expanding into.

what is a blackhole made out of?

what happens to the matter sucked into a blackhole.

If there are five birds sitting on a fence and you shoot two of them, how many birds are left on the fence?

How fast can the average human run?

Bonus question-How can a Groundhog prodect the weather?

I would have put all of these questions into one post, but a need to raise my post count.

I am not trying to make it inconvenant for the viewers.

[Anaiya]

why is the freezing point of something, the melting point as well

Which you are referring to would depend on whether you are adding or removing energy. When adding energy, the melting point is the point at which the item will begin to melt which is the same point it will start to freeze if you are removing energy from it.

this is just a theory but, if it is true that the universe is expanding, ( and the universe is the only space that exists) what is it expanding into.

Space.

what is a blackhole made out of?

Space. :)

what happens to the matter sucked into a blackhole.

It spaghettifies at or near the even horizon. It is unknown what happens to it once it hits the singularity since objects can not be retrieved for study at that point.

If there are five birds sitting on a fence and you shoot two of them, how many birds are left on the fence?

None, any you didn't hit flew away.

How fast can the average human run?

The general consensus is about 21 mph (35 km/h).

Bonus question-How can a Groundhog prodect the weather?

It can't. :zaru

I would have put all of these questions into one post, but a need to raise my post count.

I am not trying to make it inconvenant for the viewers.

Your post count will come. Patience, young padawan. :amuse

[Toby]

Quick question:

What does "schadenfreude" mean when used in English? A literal German translation is fine, too, but I'm curious specifically about its English use.

Translated literally it means "joy of harm", and like Anaiya said it is a malicious form of joy. However, it is not just the evil genius kind of malicious joy. An error in lingual translation occurs here, but there are two English expressions which can explain it more accurately. A "Roman holiday" or "epicaricacy" would suffice, as schadenfreude is a very euphoric feeling of pleasure at someone else's often extreme misfortune (love-sickness for example) rather than just any kind of misfortune (tripping over a step for example).

Roman Holiday, if a nonplussing word for you, refers to the joy the Roman mob got from watching the gladiatorial games held in the Colosseum.

[Blackskull]

how do you get crossed out text

[EvilMoogle]

how do you get crossed out text

[.s] text to cross out [/s]

Without the "."

[Blackskull]

thy very much

lol

[Anaiya]

[.s] text to cross out [/s]

Without the "."

You can use the noparse command to show commands without activating them. Next time, try typing something like this:
text to cross out

:amuse

[Link]

What is lint?
Why does it accumulate in belly buttons and in other places?
Why is it blue?

[dreams lie]

http://en.wikipedia.org/wiki/Navel_lint

Wikipedia is your friend.

[pezz85]

There's an Australian scientist (i guess you'd call him that) who spends his days researching cool and weird science stuff, he's called Dr Carl Kruszelnicki.
Anyway he did some research into belly button lint, specifically into why it's blue...
This page doesnt say too much, but yeh its a start...
http://www.abc.net.au/science/k2/lint/
Australia represent! (does that make me sound cool??? I'm almost certain the answer will be no, but anyway enjoy!)

[Anaiya]

There's an Australian scientist (i guess you'd call him that) who spends his days researching cool and weird science stuff, he's called Dr Carl Kruszelnicki.
Anyway he did some research into belly button lint, specifically into why it's blue...
This page doesnt say too much, but yeh its a start...
http://www.abc.net.au/science/k2/lint/
Australia represent! (does that make me sound cool??? I'm almost certain the answer will be no, but anyway enjoy!)

That's cool. I liked the "green lint" blurb. Fascinating stuff! :laugh

[GrimaH]

Are all positions in space ultimately relative?

[Ram]

^ No.

[GrimaH]

^ No.

Why? :headscrat

[EvilMoogle]

Are all positions in space ultimately relative?

Yes, they are.

Because there is no magical "spot that does not move" in space, so all speeds and positions are relative to other objects.

[kimikouchiha]

how much wood could a woodchuck chuck if a woodchuck could chuck wood?



if two trains are comin in a criss cross and 1 train come a min earlier then the other on,whould the still crash deppending if the were very long or would they just pass each other?



why is the grass green?



why is the middle of the earth so hot if the magma or lava or wat ever they call it come out to the top of the earth?



why is their magma in the core of the earth anyways?



why is the earth round?



and why is dirt brown?

[EvilMoogle]

how much wood could a woodchuck chuck if a woodchuck could chuck wood?
A woodchuck would chuck no amount of wood because a woodchuck can't chuck wood.



if two trains are comin in a criss cross and 1 train come a min earlier then the other on,whould the still crash deppending if the were very long or would they just pass each other?
Well, I've never seen rails cross one another. Assuming they were actually crossing tracks of some kind it would depend on the length of the train and the speed they were traveling.



why is the grass green?
Chloroplast in the grass absorbs light in such a fashion that the portion of light reflected off of it is green.



why is the middle of the earth so hot if the magma or lava or wat ever they call it come out to the top of the earth?
The middle of the Earth is hot due to the immense pressure.


why is the earth round?
When the Earth was first forming it was a ball of various gasses under a gravitational force. A roughly spherical form is the most energy-efficient form in such conditions.


and why is dirt brown?
Same reason grass is green. The materials that make up dirt absorb part of white light and reflect a portion that appears brown.

[Tagatski_sojiro]

are there arabian people in israel ? how much ?

[EvilMoogle]

are there arabian people in israel ? how much ?

According to Wikipedia (http://en.wikipedia.org/wiki/Demographics_of_Israel#Ethnic_groups) there are 1,413,300 arabs in Israel representing 19.86% of the population.

[fghj]

How to solve those simultaneous equations:

4 = (4-a)^(-g)
16,75 = (8-a) ^(-g)

[lord_itachi]

why is the middle of the earth so hot if the magma or lava or wat ever they call it come out to the top of the earth?

it's not exactly in the center, but the reason it comes out is not really short. it's basically because it rises up and puts alot of pressure on the surrounding rock making it break, allowing the magma to get to the surface. when magma reaches the surface, we call it lava.

why is their magma in the core of the earth anyways?

well...we don't really know what's actually in the earths core...it's thought that it's predominantly metal, so they don't think there's any magma there.

why is the earth round?

it's not perfectly round.

[Elijah Snow]

What are some great news sites that can give me any info on Dubai. This is an assignment for my World History class and she wants us to do a recent events piece on dubai. Any credible news site with political happenings or information would be appreciated

[choco bao bao]

What are some great news sites that can give me any info on Dubai. This is an assignment for my World History class and she wants us to do a recent events piece on dubai. Any credible news site with political happenings or information would be appreciated
You can try:
Khaleej Times Online (http://www.khaleejtimes.com/Index00.asp)
The Dubai Life (http://www.thedubailife.com/index.php/main/news/C4/)
Gulf News (http://www.gulfnews.com/home/)
Dubai News Online (http://dubaionline.mconet.biz/)

[bloodchidori]

who is raiga.

[Sky is Over]

What is the strongest steel for knives?

[Susano]

How to solve those simultaneous equations:

4 = (4-a)^(-g)
16,75 = (8-a) ^(-g)

[[when i lg i mean log (logarithm) in base 10 (as in the one on the calculator]]

the answer i got is

g(lg2)=lg4-lg16.75

Don't have a calc, but you can do it from there. :zaru

Something tells me i made a big error or misjudgment or screwed up or somethingg somewhere lol.

[Gecka]

How do I shot web?

[adee]

How do I shot web?
You go to a nuclear experiment lab, free the spiders and have them bite your hand so as to increase your probability of finding that right spider and hope that your mutation doesn't cause you to shot web out of your ass instead of your hands.

[Kagutsuchi]

Do octopuses shoot out oil as opposed to ink?

[Table]

Do octopuses shoot out oil as opposed to ink?

It is "ink"... a highly concentrated form of melanin (like what makes our skin color). The octopus releases it to form a sort of smoke screen for protection.

But the ink of cuttlefish (kind of like an octopus) was used by humans long ago as ink.

[Registrator]

How do I pass my exam? :(
*besides working hard*

[choco bao bao]

How do I pass my exam? :(
*besides working hard*
Work harder.

And smarter too. :3

[shirish]

No that's not how it happens miss Chcomint :3

[Camille]

A good topic for an essay on Hamlet?

[Fig Tree]

I need to find the other product in this dehydration reaction in acid, it's not water but it is neutral. It's really easy, but I really don't have it.

http://img241.imageshack.us/my.php?image=fffffffrx3.jpg

[adee]

What's the reaction?

[choco bao bao]

I need to find the other product in this dehydration reaction in acid, it's not water but it is neutral. It's really easy, but I really don't have it.

http://img241.imageshack.us/my.php?image=fffffffrx3.jpg
http://i293.photobucket.com/albums/mm65/chocomint07/fffffffrx3.jpg
The compound will eliminate via E1. The carbocation will undergo a hydride shift to become more stable.

http://i293.photobucket.com/albums/mm65/chocomint07/dehydration.jpg

[Fig Tree]

Thanks very much for the detailed mechanism.

One last problem is giving me trouble.
http://img444.imageshack.us/my.php?image=ddyl0.jpg
http://img444.imageshack.us/img444/4348/ddyl0.th.jpg (http://img444.imageshack.us/my.php?image=ddyl0.jpg)
On the left is the solution I have currently, but it either wants me to alter it or give another product.

[Sharada]

Best way to start a hard hitting story?

[choco bao bao]

Thanks very much for the detailed mechanism.

One last problem is giving me trouble.
http://img444.imageshack.us/my.php?image=ddyl0.jpg
http://img444.imageshack.us/img444/4348/ddyl0.th.jpg (http://img444.imageshack.us/my.php?image=ddyl0.jpg)
On the left is the solution I have currently, but it either wants me to alter it or give another product.
Sn2 always occurs in competition with E2, so you would get another elimination product.

[Camille]

What exactly is a false positive?

[Smoke]

What should my question be?

[parker pyne]

Best way to start a hard hitting story?

"Jennifer stood there, quietly ovulating."

[useeher]

cos^2x-sinx=0

solve for x

[Yasha]

Use cos2 x = 1 - sin2 x

1 - sin2 x - sin x = 0

sin2 x + sin x - 1 = 0

sin x = 0.618 or -1.618 (rejected since -1<= sin x <=1)

x = 38.17o or 141.83o

[useeher]

Use cos2 x = 1 - sin2 x

1 - sin2 x - sin x = 0

sin2 x + sin x - 1 = 0

sin x = 0.618 or -1.618 (rejected since -1<= sin x <=1)

x = 38.17o or 141.83o

I was a little confused there.

Thanks a lot. I now see how you got cos^2 x = 1 - sin^2 x.

Thank you very much. I have an assignment due in a few hours and this was a part of one of the questions.

[Skatma]

how many dynasties did china have?

[bsktbll28082]

how many dynasties did china have?

here's a list- http://www.travelchinaguide.com/intro/history/. it depends how you count them. another website said 23 and another said 83 :/

[Mattaru]

Hey folks, what's it called when you start seeing faces and stuff in ordinary surroundings? E.g. Satan's face in the smoke of 9/11 TT collapse?

Para- something?
Thanks!

eg:

http://sattlers.org/mickey/site/archive/2001/09-01/images/20010916-satan-face-close-up.jpg


edit: found it, Pareidolia

[Lord Genome]

3^2x=81

I understand that it ends up 3^2x=3^4 but im not sure what to do after that :p

[EvilMoogle]

You need to use an operation that addresses exponentials.

Work with that a minute, if that's not enough of a hint I'll say more.

[Lord Genome]

wait would x=2 since b^z=c^y is only possible if z=y?

[EvilMoogle]

Yes, x=2.

Your teacher will want steps for proof though :)

Do you know what the opposite of exponential growth is?

[Lord Genome]

not off hand

maybe not at all actually :(

though its probably something i know and forgot

[EvilMoogle]

Sadly there's not a lot of hints I can give you that won't just tell you outright.

If you can solve this that's all you'll need:
3^x = 9
(The answer is 2, but the question is how?)

[Lord Genome]

3^x=9

3^x=(9) (square root)

3^x=3^2

So x=2

I think i did that right

[EvilMoogle]

Well, that's true. I'm not sure the teacher will consider that complete.

But it might be something you need to check with him/her about.

[Lord Genome]

Are there more steps to it? just by looking at it i cant see what else to add

[EvilMoogle]

Look at it this way. If you had:

3^X = C

And you were trying to solve in terms of the unknown constant "C" your method wouldn't work.

You'd need a way to figure out how many times 3 goes into C. There's an operation you can do to solve for this, but short of telling you I don't know what more to say.

You may not have gotten this far yet, I don't know. I don't want to end up confusing you more so I'd suggest asking your teacher about it.

/Edit:
((And I'm off for the night, if you still have questions tomorrow I'll try to help again then))

[Lord Genome]

Yeah i dont think im that far yet ill just ask him

thanks for the help

one i just got stuck on thats similar

(2^x+1)(2^x-2)=32

i ended up getting 17/2 but it seems very wrong

[Lord Genome]

also a logarithm problem thats giving me a little bit of a headache
Log8(1/4)=t

I understand that it goes to 8^t=1/4 but i cant figure out what to do with it from there :/

[adee]

Yeah i dont think im that far yet ill just ask him

thanks for the help

one i just got stuck on thats similar

(2^x+1)(2^x-2)=32

i ended up getting 17/2 but it seems very wrong
It is.
do the same thing you did for precious problem.
btw, d you know the rule for ->
(a^b)(a^c) = ?
also a logarithm problem thats giving me a little bit of a headache
Log8(1/4)=t

I understand that it goes to 8^t=1/4 but i cant figure out what to do with it from there :/

convert it to a base you're comfortable with. What is a number which is exponentially related to all the ones given?

[Lord Genome]

It is.
do the same thing you did for precious problem.
btw, d you know the rule for ->
(a^b)(a^c) = ?

I looked it over and got 2^2x-1=2^4

2x-1=4 using one formula i forget
2x=5
x=5/2? I think?

convert it to a base you're comfortable with. What is a number which is exponentially related to all the ones given?

8^t=1/4
2^3t=1/2^2
2^3t=2^-2
3t=-2
t=-2/3?

[KFC]

Writing question:

When I'm writing dialogue, do I end a complete sentence with a period or a comma?

As in this:

"We went to the movies." he said.

or

"We went to the movies," he said.

Comparing it to books, it seems like you'd end it with a period when the speaking has completed a sentence, but when I Googled the question, I've gotten a lot of different answers

[EvilMoogle]

Short answer, it depends.

If the quote is the start of a sentence, it should end with a comma and the framing continues afterwards:

"The dog is red," he said.

If the quote is the end of a sentence, it should end with a period.

He said, "the dog is red."

[KFC]

AH!

That helps me completely. I just needed to know a reason WHY there was a comma, I was so confused before.

[NURawlz]

How much dirt is in a hole that is 5 meters deep and 6 meters in diameter? Please, in cubic meters.

Google ?????

[Quincy James]

Hi guys :)

I thought of a situation on my way to getting an ice cream sandwich. My father couldn't answer it for me (he's qualified, he works in aerospace).
If one had a really high core temperature (i.e. recently working out, sitting in the sun, etc.) and then was stuck in a chest freezer, would the sweat on one's skin work for or against oneself, and how would one's core temperature affect that?

[EvilMoogle]

I would say it would work for you, but the difference would be negligible.

Water (and thus sweat) has a rather high specific temperature, so it would provide a very small amount of insulation.

Having a higher core temperature would help much more directly as it will take longer for you to cool to a critical temperature.

[Quincy James]

Jesus, that was confusing me. Thanks :harley

[kumabear]

013 (part 2 of 2) 10.0 points
What is your average velocity if you drive a
distance of 412 kmat a speed of 43 km/h, then
the same distance at a speed of 60 km/h?
Answer in units of km/h.

can someone explain to me how to do this...

[EvilMoogle]

Find the total time it takes you to travel the total distance.

[kumabear]

yah i did that

the problem is i submitted the answer on an online testtaking problem and it came up as wrong

weird.

[Kamioto Furin]

013 (part 2 of 2) 10.0 points
What is your average velocity if you drive a
distance of 412 kmat a speed of 43 km/h, then
the same distance at a speed of 60 km/h?
Answer in units of km/h.

can someone explain to me how to do this...

Is the answer approximately 31.66 km/hr?

[kumabear]

004 (part 1 of 2) 10.0 points
A Cessna aircraft has a lift-off speed of
133 km/h.
What minimum constant acceleration does
this require if the aircraft is to be airborne
after a take-off run of 247 m?
Answer in units of m/s2.
005 (part 2 of 2) 10.0 points
How long does it take the aircraft to become
airborne?
Answer in units of s.

T_T

[Rob`]

Firstly I needed to prove that 0.9999...=1 "By referring to the definition of the real numbers and their decimal representation" so I did it like this.

0.999...=max{0.9, 0.99, 0.999, ...} = 1-min{0.1, 0.01, 0.001, ...} = 1-lim(n->infinity)1/10n=1-0=1

Does that count as using the definition or do I think up a different proof?

Also my lecturer did show us this proof but it wouldn't be first time he's shown us something then not accepted it as a complete answer.

x1=0.9<1 but 1.0>1
x2=0.99<1 but 1.00>1
x3=0.999<1 but 1.000>1
...
It follows that 0.999... is a decimal representation of 1.

Does that sound like the proof he's asking for or no?

[Jesus]

which definition of the decimal representation did you see with that teacher?

[Rob`]

Cardinality of Real Numbers > Cardinality of Rational Numbers so each p/q (p and q are integers) is a part of the real numbers.

We can introduce relations <, > between real numbers and the coincide (I can not read my own handwriting but that's what it looks like) with usual ones for rational #'s.

We have operatives +, -, * satisfying the usual laws of algebra.

For each x is a real and =/= 0 we have x-1 such that xx-1 = 1

If S c Reals is bounded from above ==> it has a suprenum sup(S) is a real.

I think the last one is the one we're meant to use specifically.

Now that I think about it might this be what's needed.

0.999...=sup{0.9, 0.09, 0.009 ...} = sup{1-10-n}=1 ?

[Jesus]

^_^ yeah, that is probably the demonstration he is expecting



on a random note here's my favorite proof of this result:

x = 0.9999...
10x = 9.9999....

therefore 10x = x+9
9x=9
x=1 !!! :P



Another way to look at it is that you cannot pick any number that would be located strictly between 0.999... and 1.

but if you pick two distinct real numbers a<b, then a<(a+b)/2<b

therefore we must deduce that 0.999... = 1, or we would get a contradiction.

[Zil]

Another way you can prove 0.999...=1 is by using geometric series.

You can write 0.999... as

9/10 + 9/102 + 9/103+...,

which is a geometric series with common ratio 1/10. Therefore,

0.999... = (9/10)/[1-(1/10)] = 1.

[Rob`]

Thanks guys, I have another question

What is arctan(x) expressed as a logarithm?

Wikipedia seems to think it's arctanx=i/2(ln(1-ix)-ln(1+ix)) and someone in the discussion section thinks it's arctanx=ln(1+ix)-ln(1-ix) and googling is turning up nothing.

Edit: If it helps this is for integrating a real value function so you can assume x is real.

Edit2: Wolfram appears to agree with wikipedia

[Zil]

Yes, it is (i/2)ln((1-ix)/(1+ix)). You can show this by comparing series expansions.

http://img402.imageshack.us/img402/9045/seriesn.jpg

[Jesus]

^didn't know this result, pretty neat

[Rob`]

Thanks again zil.

If anyone's interested my proof that 0.9999...=1 didn't get the marks. On the plus side the people that used the lecturer's (lecturer=/=marker) didn't get the marks either. Only marks I lost on the sheet as well :(