maths puzzles

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Oh lord. A mathematical debate....Cool! đź‘Ť

Let's say, hypothetically the world is a cube. With North on top and South on the bottom like so.

cubemh6.jpg

So you can still move south (180 degrees to North), and then west (270 degrees to North), then back north (0 degrees to North)
northnb3.jpg
 
Okay, it makes sense. I guess. SO that's the difference between Aussies and Britons: The Aussies still think the earth is flat. Your explanation makes sense, but it's just more logical to think of the earth as a spere--because it is--since that would more readily explain the reason for your journey west to be a curved line, and not perfectly straight like your north/south movements.

Basically I'm telling you that your drawing is wrong in the fact that the west movement should be a curved, semicircle line, no matter if your earth is round or square.

EDIT: And Danoff was the first to answer the question, which asked simply the color of the bear. His answer is more realistic, in fact.
 
keef
The Aussies still think the earth is flat.
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And if we didn't put magnets on the soles of our shoes we'd all fall off the bottom.
 
keef
Okay, it makes sense. I guess. SO that's the difference between Aussies and Britons: The Aussies still think the earth is flat. Your explanation makes sense, but it's just more logical to think of the earth as a spere--because it is--since that would more readily explain the reason for your journey west to be a curved line, and not perfectly straight like your north/south movements.
Click to expand...

That was great Keef :D





Ciao!
 
You're on a spacecraft traveling at 0.5c velocity in the x direction and 0.5c velocity in the y direction, for a magnitude of ~0.7c.

You emit a laser pulse in the +y direction at time t=0 toward a body with Earth's GM, and radius, located 1 billion km in the +y direction.

What are the x and y components of the velocity of the pulse at time t=15613 seconds (on the spacecraft's clock).

Edit: Famine is allowed to answer this question.
 
:lol:

Meanie... :D
 
Famine
:lol:

Meanie... :D
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For the answer I originally wrote this question to get, I knew you'd know it too quickly. But then I realized the question was accidentally slightly trickier than that, so you should feel free to venture a guess. :)
 
Ok, seriously, somebody has to know the answer...
 
I came up with 2 possible answers, depending on something not specified in the problem.

First: pulse is at ~0,-3.684 billion km.
Second: pulse no longer exists.

I think this is one of those where most of the presented information has nothing to do with the problem.
 
wfooshee
I came up with 2 possible answers, depending on something not specified in the problem.

First: pulse is at ~0,-3.684 billion km.
Second: pulse no longer exists.

I think this is one of those where most of the presented information has nothing to do with the problem.
Click to expand...

Ok, the first answer is out because it has to be in units of velocity. The second answer is the correct one. But when I first wrote this problem I was looking for the velocity... so what do you think that would be (assuming the planet were transparent)?

(btw, you got it right so it's your turn)
 
danoff
Ok, the first answer is out because it has to be in units of velocity. The second answer is the correct one. But when I first wrote this problem I was looking for the velocity... so what do you think that would be (assuming the planet were transparent)?

(btw, you got it right so it's your turn)
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I misread the problem, and went for the pulse's location, assuming it reflected. :dunce:

The velocity is c, which is constant regardless of the observer's velocity.

Is this one of those that the teacher says, "Oops, my bad!" and it doesn't count on the exam? :sly:

It'll take me a bit to find a problem, since I'm at work, assuming I still qualify after admitting I didn't actually read the problem correctly. . . .
 
wfooshee
The velocity is c, which is constant regardless of the observer's velocity.
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Yea, that's what I was going for, c (in the y direction)... easy unless you got scared by all the extra info. Then I realized I hit the planet.
 
OK, my problem comes from being old enough to have used one of these in college. . . .

Why does a slide rule make multiplication easy?


BTW, sorry, but I can't let this go, the cube world on the bear problem doesn't work, those aren't 90-degree turns, and which way is west, anyway? You can't have a pole on a sheet. You can have a center, but on a flat map, what most people are used to, there's no way to make 2 90-degree turns and be where you started. (90-degree turns are required by going south, then west, then north.) Move to a sphere, though, and start at the pole, and it works. That's how the "curvature of the Earth" fits in.
 
Yup, Casio's answer was never correct.

BTW, I'm thinking on yours right now. My older borther used to use a slide rule back in the day. What I understood at the time was that it was mostly used by engineers and therefore decimals played a big role there...but I can't explanate why it's easier to multiply.




Ciao!
 
Hint: Abe Lincoln had a {blank} cabin

More hints: 100 times 1000 = 100,000 is the same as 10 squared * 10 cubed = 10 to the fifth, and 2 + 3 = 5
 
22 hours, and no bites? Have I killed another thread?

Maybe this is more of a real problem than an actual puzzle, so nobody wants to play. What I'm asking for is the mathmatical explanation of how multiplication using a slide rule works. See if anybody knows any high school precalculus.

Too deep?
 
^^ I'd have to look that up (aside from your generous hints). I'm not old enough to have used a slide rule.
 
Before the advent of the pocket calculator, it was the most commonly used calculation tool in science and engineering. The use of slide rules continued to grow through the 1950s and 1960s even as digital computing devices were being gradually introduced; but in the early 1970s the electronic scientific calculator made it largely obsolete and most suppliers exited the business.

I was born in 1988 not 1948 :lol:
 
wfooshee
BTW, sorry, but I can't let this go, the cube world on the bear problem doesn't work, those aren't 90-degree turns, and which way is west, anyway? You can't have a pole on a sheet. You can have a center, but on a flat map, what most people are used to, there's no way to make 2 90-degree turns and be where you started. (90-degree turns are required by going south, then west, then north.) Move to a sphere, though, and start at the pole, and it works. That's how the "curvature of the Earth" fits in.
Click to expand...

Because I was thinking about this still on the weekend.

Say the polar bear moved 1m (rather then 1km) south from the north pole, then 1m west. Then surely his next trip back to the north pole is not 90-degrees.
 
Will somebody quote the first law of logarithms, then show what kind of ruling is on a slide-rule's scales, then we can move on?
 
Hmm, not sure whether this is the place to post this, but it's the closet thing I could find. Plus, the ever-talented members at GTPlanet beat my parent's answers.

There is a statement in my Maths resource book that states '3√4 is a surd as it cannot be written as an exact value'. Well, me and the calculator beside me both agree that the square-root of four multiplied by 3 would in fact equal 6, which is an exact decimal value and can be expressed as 36/6.

Is there something I am missing that makes 3√4 a surd or is it just me?
 
When you type in 3√4 in your calculator, it actually is 3 * √4
I think (but i'm not sure) they mean this:
4^(1/3) = 1,587... => surd

(3 * √4 = 3 * 4^(1/2) = 3 * 2 = 6) => not a surd
 
dustdriver
When you type in 3√4 in your calculator, it actually is 3 * √4
I think (but i'm not sure) they mean this:
4^(1/3) = 1,587... => surd

(3 * √4 = 3 * 4^(1/2) = 3 * 2 = 6) => not a surd
Click to expand...

Hmm, thanks for that. I'll check into it. đź‘Ť
 
Yes - the CUBE root of 4.
 
Got another query.

'Irrational' numbers are numbers that cannot be represented using a[FONT=&quot] ∕ b
whereas a and b are integers and b cannot be zero.

However, [FONT=&quot]√[/FONT]10 (3.16227766) is seen to be a 'irrational number' in my resource book where [FONT=&quot]√10 = 3.16227766.
But couldn't this number be multiplied by 100,000,000 (equaling 316,227,766) and therefore be applied as [/FONT][FONT=&quot]316,227,766[/FONT][FONT=&quot] ∕[/FONT][FONT=&quot]100,000,000. The result would be the original [/FONT]3.16227766, a & b are integers (which are whole numbers; no decimals if I am correct?) and b is not 0.

Therefore 3.16227766 would be rational no? Though I might be overlooking something here, I don't know...[/FONT]
 
GT Pro
Got another query.

'Irrational' numbers are numbers that cannot be represented using a[FONT=&quot] ∕ b
whereas a and b are integers and b cannot be zero.

However, [FONT=&quot]√[/FONT]10 (3.16227766) is seen to be a 'irrational number' in my resource book where [FONT=&quot]√10 = 3.16227766.
But couldn't this number be multiplied by 100,000,000 (equaling 316,227,766) and therefore be applied as [/FONT][FONT=&quot]316,227,766[/FONT][FONT=&quot] ∕[/FONT][FONT=&quot]100,000,000. The result would be the original [/FONT]3.16227766, a & b are integers (which are whole numbers; no decimals if I am correct?) and b is not 0.

Therefore 3.16227766 would be rational no? Though I might be overlooking something here, I don't know...[/FONT]
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All square roots of non-perfect-squares are irrational. The number in the table you looked up, or the number your calculator gives you, is the number to that many decimal places. If a square root is not an integer, it has an infinite number of decimal places, the very definition of irrational.

If it were EXACTLY 3.16227766 then yes, it would be a rational number, but it's not exactly that; there's ALWAYS one more decimal place.
 
wfooshee
All square roots of non-perfect-squares are irrational. The number in the table you looked up, or the number your calculator gives you, is the number to that many decimal places. If a square root is not an integer, it has an infinite number of decimal places, the very definition of irrational.

If it were EXACTLY 3.16227766 then yes, it would be a rational number, but it's not exactly that; there's ALWAYS one more decimal place.
Click to expand...

Thanks, should've thought about that. So in otherwords, any square roots of numbers not being perfect squares and pi multiplied/divided/added/subtracted by any other numbers are 'irrational' because the answer would have infinite decimal places right?

I guess it was a simple answer, but the lack of an ℮ symbol was misleading.
 
GT Pro
Thanks, should've thought about that. So in otherwords, any square roots of numbers not being perfect squares and pi multiplied/divided/added/subtracted by any other numbers are 'irrational' because the answer would have infinite decimal places right?

I guess it was a simple answer, but the lack of an ℮ symbol was misleading.
Click to expand...

By e you mean the base of natural logarithms? Has nothing to do with square roots, although e is also an irrational number, as is pi. (Doesn't have to be multiplied/divided/added/subtracted by any other number to be irrational.)

And we should clarify, it's infinite non-repeating decimals that makes it irrational.

0.333333333333333 (3's forever) is infinite decimal places, but rational: 1/3.
 
Thanks for all that but I've got another question now. Yer I know, you must be getting annoyed but since I don't start at my new school til' Monday you are all I have to ask questions to.

The resource book asks to simplify 3√5+2√6+√5. Now, would'nt the logical step be to subtract any surds of the same number in which would = 3√5+2√6?
The actual answer seems to be 4√5+2√6 but I have no idea why the integer four is there instead of what I initially thought of 3...

Also, when more than two surds are found in an expression, (Or whatever the whole string of terms are called) such as 3√6+7√6-7√6 would simplifying still leave one root term of √6 in the expression?
 
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