How do we calculate numbers to an irrational exponent like x^pi? | AskScience Blog

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Friday, October 13, 2017

How do we calculate numbers to an irrational exponent like x^pi?

How do we calculate numbers to an irrational exponent like x^pi?


How do we calculate numbers to an irrational exponent like x^pi?

Posted: 13 Oct 2017 04:54 AM PDT

I always understood that am/n = a times a m number of times and then take the nth root

but for irrational exponents, we just have an infinite non-repeating decimal that doesn't fall into that form.
I was thinking maybe for something like pi, calculators just round off somewhere and make the number something like 314159/100000 but I wasn't sure if it would overload the calculator first or something.

submitted by /u/ilikebutteryfries
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What are the specific values volcanologists would use to conclude that a major volcancanic eruption could be imminent at Yellowstone with the next 10-20 years?

Posted: 12 Oct 2017 07:10 PM PDT

Several news articles noted that yellowstone's 40mi wide caldera rose by 10 inches within the last seven years. These articles also noted that scientists believe conditions preceding an eruption could occur over as little as a few decades instead of over centuries as was previously thought. What are the expected values of gas emissions, seismic activities, deformation rates etc.. that would lead volcanologists to conclude that a major eruption of Yellowstone would be eminent within 10 to 20 years or less?

submitted by /u/imdabes
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Can a homogeneous mixture of two miscible liquids become non-homogeneous over time?

Posted: 13 Oct 2017 04:29 AM PDT

I work in the chemistry laboratory of sanitizer/soap manufacturing facility. On occasion, we have noticed some weird results when testing samples from the top of a tank compared to a sample from the bottom of the tank.

Mainly we noticed this with a product that is primarily water and isopropanol. I know that water and IPA are miscible. Would the difference in testing of a top and bottom sample be a result of improper mixing or do the two liquids form a gradient concentration mixture throughout the tank after a certain period of time?

submitted by /u/lxBATESxl
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What exactly makes aged wine better?

Posted: 13 Oct 2017 06:53 AM PDT

Could a helium balloon with a GoPro™ attached reach a high enough altitude to record the curvature of the earth?

Posted: 12 Oct 2017 11:39 AM PDT

Understandably, maybe not a regular store bought balloon, but my real question here is; couldn't "flat-earth" be disproven on a shoestring-budget?

submitted by /u/n0tL3nny
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Why does the Second Law of Thermodynamics include both a statement on Entropy and the impossibility of a completely efficient heat engine?

Posted: 13 Oct 2017 05:50 AM PDT

I'm having a hard time understanding how the two are related and why they are both grouped under the second law.

submitted by /u/miciah1_reddit
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What's the farthest a satellite can go into space and still send a reachable signal to earth?

Posted: 12 Oct 2017 09:27 PM PDT

Edit: Learning that I meant to ask about space probes and not an orbiting satellite.

submitted by /u/fisherdude123
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Can I have an "electricity leak" similar to how I can have a water leak in my house that will drive up my electric bill?

Posted: 12 Oct 2017 02:45 PM PDT

Would a very very cold bell sound the same as a very very hot bell?

Posted: 12 Oct 2017 02:01 PM PDT

Imagine two identical bells.

One is dunked in liquid nitrogen to cool it down.

The other is heated until it's red hot. It's not melting.

Each bell is then struck with a clapper.

Would they sound the same?

submitted by /u/murgleburgle88
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How is it possible to cool helium past the lambda point?

Posted: 12 Oct 2017 07:10 PM PDT

As the temperature of helium reaches the lambda point the specific heat approaches infinity.

Since your specific heat becomes so incredibly large, how is it possible to cool helium to below 2.17 degrees?

Additionally, since the specific heat tend to infinity, shouldn't helium at the lambda point (~2.17 K) have an near infinite specific heat, and thus have a static temperature independent of its energy?

submitted by /u/Vir_Maximus
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What is the different between Chaos and Randomness ?

Posted: 13 Oct 2017 12:00 AM PDT

As far as I know, chaos can be predicted as the result is based on initial conditions, while random is impossible to know, all we can do to random is to calculate the chance of the outcomes.

Sorry for my English.

submitted by /u/SPR-MKO
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What caused the different branches of Proto-Indo European (PIE) to have different order in grammar (subject verb object etc.)?

Posted: 12 Oct 2017 07:26 AM PDT

Does the probabilistic nature of quantum mechanics extend to non-quantum phenomena?

Posted: 12 Oct 2017 12:21 PM PDT

My understanding of this topic is very basic, but from what I can gather, everything (?) at a quantum level is described in a probabilistic sense rather than a deterministic one. Not because of measurement error, but for more fundamental reasons.

My question is this: does the uncertainty we observe in quantum mechanics manifest in any way in non-quantum phenomena? Are phenomena at a non-quantum level deterministic, as far as we can tell?

submitted by /u/Chicagodivemaster
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How is the "power" of dish soap measured? How can a company claim one of its products is "3 times as powerful" as another one?

Posted: 12 Oct 2017 04:33 PM PDT

There will be a geomagnetic storm on Friday 13th?

Posted: 12 Oct 2017 12:11 PM PDT

I'm reading in Spanish sites saying that there will be a geomagnetic storm on Friday 13th according to the russian site TASS, but there are no news in English

Is this a hoax?

submitted by /u/Yilku1
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Do aerosol droplets have the same concentration as the original bulk solution, irrespective of the droplet size?

Posted: 13 Oct 2017 12:37 AM PDT

Hello,

So, I think I have some guesses here, but I'm likely missing the correct search terms to feed google scholar.

When you're working with a spray, the easy assumption to make is that each drop is just a tiny sample of the bulk. If you have Xparts/L, that will just scale down to the micro or nano liter, is the hope. I trust that for the molecular level, but I'm working with something that has largish particles around the 10-30micron scale, and some sprays with a mean drop diameter around 100microns. There's a relation called Gibb's Isotherm that accounts for the "measured excess" at an interface in multi-component systems. That says, to me, one can expect you bulk to be somewhat inhomogenous. What does that mean for the drops one produces at an interface? Even just thinking of marangoni stresses, pinch off results in a radius of curvature one could expect to shuffle particles around.

Experimentally, the easy way to do this is probably stick beads into solution, spray on a glass slide measure drop size, evaporate, count particles. Has anyone done something like that? I cannot find it.

Thanks.

submitted by /u/Fizzix42
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Is there a condition that exists that would cause someone to perfectly understand English, but only be able to speak one word, like Hodor from GoT?

Posted: 12 Oct 2017 09:30 AM PDT

Watching GoT (finally) has made me curious if this is actually something that could happen, or if it was just something made up for the story.

submitted by /u/vayperwayve
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Does There Exist A Series Smaller than the Harmonic Series that STILL Diverges?

Posted: 12 Oct 2017 12:34 PM PDT

Is there such a thing, or is the Harmonic series the smallest series we know of that still diverges? I'm not exactly sure if I'm phrasing the question properly, in the sense that it may not be exactly clear what "a series smaller than the harmonic series" even means, right?

I mean, there's an argument to be made that the harmonic series is greater than the series:

1/2 + 1/2 + 1/2 + 1/2 + 1/2...

which clearly diverges, right? Because they can be re-written as:

1/2 + 1/4 + 1/4 + 1/8 + 1/8 + 1/8 + 1/8...

1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8...

But is there some way to describe how "large" a series is? Or how quickly it diverges? And if there is, is there a series that is "smaller", or diverges slower, but still diverges?

submitted by /u/garrettj100
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When we watch videos on YouTube do they get temporarily stored on the hard-disk or phone's storage or are they just stored in the RAM for some time ?

Posted: 12 Oct 2017 11:36 AM PDT

How fast does Kinetic energy travel?

Posted: 12 Oct 2017 10:50 AM PDT

To preface this question I wanted to say that I'm not sure if kinetic energy is the correct term.

As it stands, I'm under the impression that the speed of light is the fastest anything can travel. So in a completely hypothetical situation, if we were to build a tube(cylinder) that held a single file line of marbles (all being in direct contact) that stretched to the moon. How long would it take a marble on the receiving end to be pushed out of the tube when a marble on earth was pushed into the tube?

As a follow up, if there is a delay, how does this work?

submitted by /u/Koalchemy
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