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Offline KennyRTopic starter

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Simplish maths question
« on: November 25, 2004, 10:27:36 PM »
My indice algebra is rusty, but I can't find my old maths books. And google isn't helping.

Basically, I want to solve C=(1-D)^T for T. (^T means to the power of T). I just can't remember what law to use to get that T down from there. Anyone?
 

Offline KennyRTopic starter

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Re: Simplish maths question
« Reply #1 on: November 25, 2004, 10:46:48 PM »
Aha, thanks Karlos! :-D I remember now.

It just went totally out of my head there, and nothing I could do would remind me...it's amazing how quickly you forget the things. :-(
 

Offline KennyRTopic starter

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Re: Simplish maths question
« Reply #2 on: November 25, 2004, 10:54:09 PM »
Quote
Karlos wrote:
What things?


Well, I really meant bizarre abstract rules and laws governing algebra, but since it's obviously the flavour of the month here in Amiga.org, my answer is: socks.
 

Offline KennyRTopic starter

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Re: Simplish maths question
« Reply #3 on: November 25, 2004, 11:23:31 PM »
Oh, something incredibly trivial. I was trying to work what battery manufacturers call "shelf life". They say that the shelf life of batteries is how long they take to get to 85% of original charge, just sitting there and not being used.

T=time, in years
D=discharge (per year)
C=charge level (1 being full, 0 being empty)

I worked out that C=(1-D)^T, but got stuck trying to get it for T. But with your help:

T = ln(C)/ln(1-D)

Cheap alkaline or zinc chloride batteries, for instance, have a self-discharge rate of 4% per year, therefore:

T = ln(0.85)/ln(1-0.04)

= 3.98

So it works out as a shelf life of 4 years. Which is exactly what they are advertised as having.

I needed to get this for other kinds of battery. It may be pointless, but it beats chewing a sock, even if I do need the fibre. :)
 

Offline KennyRTopic starter

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Re: Simplish maths question
« Reply #4 on: November 25, 2004, 11:42:41 PM »
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Karlos wrote:
I think you'd get more semi decomposed protein and sugar and amines than you would fibre from chewing "The Sock" ;-)


Especially bloodline's socks ;)
 

Offline KennyRTopic starter

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Re: Simplish maths question
« Reply #5 on: November 26, 2004, 12:11:33 AM »
None must resign themselves to the dubious pleasures of forbidden laundry now we've armed ourselves with the knowledge of batteries. What woman could resist pick-up lines like "Wow, do you know that NiMH batteries, once fully charged, will self-discharge while unused to 85% of capacity in only SEVEN DAYS!?!"
 

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Re: Simplish maths question
« Reply #6 on: November 26, 2004, 06:29:35 PM »
That's the formula for cumulative percentages, blob. It's (1+D) for additive, such as when working our interest on an account, (1-D) for subtractive. D is the percentage you lose or gain every iteration.
 

Offline KennyRTopic starter

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Re: Simplish maths question
« Reply #7 on: November 27, 2004, 07:53:35 PM »
Quote
Karlos wrote:
The manufacturers could have chosen the half life of the cell to make it more obvious, but I doubt that a cell at 50% charge is not much use so they picked the 85% threshold instead.


Right. It's a matter of internal resistance. Most cell chemistries gain internal resistance as they lose capacity, decreasing the output voltage of the cell. At 50% capacity, your average alkaline battery would have an output of only 1.1-1.2 volts rather than the advertised 1.5, which is actually just not enough for some stuff. Their performance gets worse as they drain.

Incidentally, NiCd and NiMH don't have this effect (low internal resistance), which is why I like them. Pity they only have 1.2V even when fully charged, and they lose charge like fiends. And even worse, shops only sell padded crap like 2300 mAh NiMH D batteries (the theoretical capacity of an alkaline D battery is around 18,000 mAh, which should mean NimH D should be around 9000 mAh. These do exist, but they can only be bought specially and cost about £12 each!!).

Someone should do the world a favour and invent rechargeable batteries with 1.5V, low self-discharge and low internal resistance, but which aren't full of explosive ether like Li-Ion are. They'd be a rich man/woman! ;)

Until consumer fuel cells came out that is... :-P
 

Offline KennyRTopic starter

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Re: Simplish maths question
« Reply #8 on: November 27, 2004, 08:27:50 PM »
Electrochemistry is my forte. ;) I didn't want it to be, that's just how it ended up. I'd rather have specialised in nerve agents or explosives, but unbelievably they wouldn't let me at uni, and gave an oscilloscope and some electrodes instead. Now I'm cursed with being specialised in perhaps the most horribly boring of all the sectors of chemistry.

Still, given today's choice between researching mind-numbingly mundane battery facts and anthropod/sock interaction, I made my choice and I'm sticking to it. It's better than getting drawn into the bickering on the front page, for sure.
 

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Re: Subverted to socks in just five posts!
« Reply #9 on: November 29, 2004, 03:26:42 AM »
Conincidentally, I was just thinking about using one of the platinum group in an oxygen related reaction.

I was actually wondering if we could trap platinum ions in a heme and make biomechanical blood cells. Synthetic pink blood that gives human beings superhuman capabilities! Yay!