Math Problems

Here is a hard one it is from one of my professors while I was in school:

Give a rough order-of-magnitude estimate of how acceleration might affect the rate of a clock through modification of the energy-level structure of the atom. Express your results, for example, in the acceleration (g), the size or the atom (l). How many earth gravitation acceleration must be imposed before there is a sizable change in the rate of modern atomic clocks?

Then because he was a dick he tells us this: You should be able to find relevant parameters for atomic clocks from sources like google, Wiki, ect.


Have fun! I will put up the solution later if you guys surrender.

How many earth gravitation acceleration must be imposed before there is a sizable change in the rate of modern atomic clocks?

What would be considered "sizeable"?  1 millisecond?  1 second?

Air is being pumped into a spherical balloon at a rate of 3 cm3/min.  Determine the rate at which the radius of the balloon is increasing when the diameter of the balloon is 12 cm.

(for simplicity, say the balloon is a perfect sphere)

I got 144(pi)/3, not sure if its correct...no scientific calculator

Quote from: Wakka Wakka on January 19, 2009, 07:03:31 PM

Air is being pumped into a spherical balloon at a rate of 3 cm3/min.  Determine the rate at which the radius of the balloon is increasing when the diameter of the balloon is 12 cm.

(for simplicity, say the balloon is a perfect sphere)

I got 144(pi)/3, not sure if its correct...no scientific calculator

Too high.  It looks like you differentiated volume and not radius, but I can't really tell without seeing your work.

Ooops sorry..meant 3/144(pi)..stupid numbers.

V(t)= 4/3(pi)[r(t)]^3

Take the derivative of both sides, fill in the blanks, v = volume, r = radius

V' = 4(pi)r^2(r')
3 = 4(pi)(36)r'
3 = 144(pi)r'
3/144(pi) = r'

Probably wrong but at least I tried.

about 67?

about 67?

you phail.

My bad. Infinity.

Here is a hard one it is from one of my professors while I was in school:

Give a rough order-of-magnitude estimate of how acceleration might affect the rate of a clock through modification of the energy-level structure of the atom. Express your results, for example, in the acceleration (g), the size or the atom (l). How many earth gravitation acceleration must be imposed before there is a sizable change in the rate of modern atomic clocks?

Then because he was a dick he tells us this: You should be able to find relevant parameters for atomic clocks from sources like google, Wiki, ect.


Have fun! I will put up the solution later if you guys surrender.

Magic???  If you really want me to I can put down so nice Electrical and Magnetic Physics problems down...though i barely understand the basics myself.

My bad. Infinity.

The response remains the same.

3

√(1+√(2+√(3+√(4+...)))) = ?

MAI TERN!

7 x 3 = x

Quote from: John Jackson on January 20, 2009, 06:58:27 PM

3

√(1+√(2+√(3+√(4+...)))) = ?

You are correct.

The expression you gave diverges. I found a proof.

The expression you gave diverges. I found a proof.

ORLY?

Quote

The expression you gave diverges. I found a proof.

ORLY?

Actually, I found a mistake in my reasoning, but I still can bet that it diverges.

Actually, I found a mistake in my reasoning, but I still can bet that it diverges.

Then say DNE. 



Find the value of x, and post your visual proof.

Rules:
You can only use elementary geometry. For instance, the angles of a triangle add up to 180 degrees, or use the basic congruent triangle rules (side-angle-side, et cetera.).  Trigonometry, like using the law of sines, the law of cosines, et cetera is strictly forbidden.

I figured out most of the angles. Got stuck, and decided it's bed time.

2 + 2 = 5

Prove me wrong, FES.

2 + 2 = 5

Prove me wrong, FES.

2 + 2 = 4

4 +1 = 5

4 = 5-1

2 + 2 = 5-1



so... no.

Quote from: John Jackson on January 20, 2009, 07:28:27 PM

Actually, I found a mistake in my reasoning, but I still can bet that it diverges.

Then say DNE. 



Find the value of x, and post your visual proof.

Rules:
You can only use elementary geometry. For instance, the angles of a triangle add up to 180 degrees, or use the basic congruent triangle rules (side-angle-side, et cetera.).  Trigonometry, like using the law of sines, the law of cosines, et cetera is strictly forbidden.

Yawn.

Quote from: Euclid on January 20, 2009, 07:19:53 PM

Quote

The expression you gave diverges. I found a proof.

ORLY?

Actually, I found a mistake in my reasoning, but I still can bet that it diverges.

Apparently, it does converge, but no closed-form expression is known.  http://mathworld.wolfram.com/NestedRadicalConstant.html

Quote from: Proleg on January 20, 2009, 09:08:45 PM

2 + 2 = 5

Prove me wrong, FES.

2 + 2 = 4

4 +1 = 5

4 = 5-1

2 + 2 = 5-1



so... no.

And if the Party says that it is not four but five - how many?

Quote from: Raist on January 20, 2009, 09:10:28 PM

Quote from: Proleg on January 20, 2009, 09:08:45 PM

2 + 2 = 5

Prove me wrong, FES.

2 + 2 = 4

4 +1 = 5

4 = 5-1

2 + 2 = 5-1



so... no.

And if the Party says that it is not four but five - how many?

Sad book. Stop it. You'll make me depressed.

Under the spreading chestnut tree
I sold you and you sold me...

Meh, pointless symbolism won't depress me.

Quote from: Euclid on January 20, 2009, 07:19:53 PM

Quote

The expression you gave diverges. I found a proof.

ORLY?

Actually, I found a mistake in my reasoning, but I still can bet that it diverges.

It doesn't. The solution to 20 decimal places is 1.7579327566180045327. As of now, I cannot find a closed form in terms of some fundamental mathematical constants for this expression.

The right side of the equation is a Fourier series that sums to 0.

How can it, when every value of the sine function for angles in the domain (0,π] is positive or zero? The only way I can see for that series to sum to 0 is if n=1.

Find the value of x, and post your visual proof.

Rules:
You can only use elementary geometry. For instance, the angles of a triangle add up to 180 degrees, or use the basic congruent triangle rules (side-angle-side, et cetera.).  Trigonometry, like using the law of sines, the law of cosines, et cetera is strictly forbidden.

After applying sine theorem to triangles AED and BDE on one hand and ABD and ABE on the other, and making some equalities and a considerable ammount of trigonometry, I finally got a nasty solution for x:

x = 27^o 33' 17''

Since it is a nasty result, it means I either made some mistake or you wanted to fuck with us. This problem is impossible to solve without trig.

I'm pretty sure you can logically solve it when you find enough corners. But it would be a guess and check method.

Here is a hard one it is from one of my professors while I was in school:

Give a rough order-of-magnitude estimate of how acceleration might affect the rate of a clock through modification of the energy-level structure of the atom. Express your results, for example, in the acceleration (g), the size or the atom (l). How many earth gravitation acceleration must be imposed before there is a sizable change in the rate of modern atomic clocks?

Then because he was a dick he tells us this: You should be able to find relevant parameters for atomic clocks from sources like google, Wiki, ect.


Have fun! I will put up the solution later if you guys surrender.

And the answer is.... 3mgel/h

I used hydrogen atoms when I solved