Let's start a thread for Useful Mathematical Formulae

What’s the tonic, subdominant and the dominant?

1,4 and 5 duh!

[QUOTE=Malacandra]
And “Minus forty” is the temperature for which you don’t need to give the scale (use either formula above and substitute F=C).
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Plus, it’s almost exactly the temperature mercury freezes at.

[QUOTE=HeadNinja]
if you take someone’s hourly rate of pay and multiply it by 2000 you have a decent approximation of their annual wage. (this obviously works in the other direction as well)
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I thought that was 2080? 52 work-weeks times 40 hours.

[QUOTE=NinetyWt]
I thought that was 2080? 52 work-weeks times 40 hours.
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Some people only get paid for a 37.5 hour work week, so it evens out.

Multiplying by 5 is the same as taking half and moving the decimal place.

5 X 422 = 2110, for example.

You can approximate easily for other numbers too. Multiplying by 3 approximates to taking a third and moving the decimal, etc.

[QUOTE=Leaffan]
Some people only get paid for a 37.5 hour work week, so it evens out.
[/QUOTE]
Color me surprised. Pour quoi? Are they not getting a paid lunch?

[QUOTE=NinetyWt]
I thought that was 2080? 52 work-weeks times 40 hours.
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That’d be why he said “decent approximation”, then - 4% out ain’t bad.

[QUOTE=NinetyWt]
Color me surprised. Pour quoi? Are they not getting a paid lunch?
[/QUOTE]

May differ from country to country, but I’ve worked 37.5 (or 37) hour weeks many times.

[QUOTE=NinetyWt]
Color me surprised. Pour quoi? Are they not getting a paid lunch?
[/QUOTE]

Correct. We don’t get paid for lunch here. I am paid for 8 hours a day; I’m expected to be here for 8.5 hours.

[QUOTE=Malacandra]
That’d be why he said “decent approximation”, then - 4% out ain’t bad.
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Agreed, but my brain piped up and sez “why not use the exact number?”. Here 40 hours is standard - it’s very ingrained.

I learn more stuff on the Dope! :slight_smile:

ETA: I see, Leaffan. Thanks.

[QUOTE=NinetyWt]
Agreed, but my brain piped up and sez “why not use the exact number?”. Here 40 hours is standard - it’s very ingrained.
[/QUOTE]
Sure, but if you’re doing a quick in-your-head calculation, x2000 is just doubling the number and moving the decimal over three places. x2080 requires more thought or a calculator.

[QUOTE=Bosstone]
Sure, but if you’re doing a quick in-your-head calculation, x2000 is just doubling the number and moving the decimal over three places. x2080 requires more thought or a calculator.
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What? Your calculator is not within arm’s reach 24/7 ??? :stuck_out_tongue:

[QUOTE=Pseudocode]
Sorry, I saw what he did and misremembered summation as 7(6)/2, or n(n-1)/2, instead of n(n+1)/2.
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You had the summation formula right, you just misread the problem as having 7 people, when there are really 8.

[QUOTE=NinetyWt]
What? Your calculator is not within arm’s reach 24/7 ??? :stuck_out_tongue:
[/QUOTE]

Mine takes the weekends off.

The main reason the trick is useful is for spot math. if someone tells you they make 20$ an hour knowing they make about 40K is about as useful as knowing they make 41600. Unless you are approving a loan application.

for tip math you can multiply the dollar figure by two and slide a decimal place. 7.40 tab? 1.40. Round as you see fit.

To convert PSI to head (ft of water) multiply by 2.3 .
i.e. 14.7 PSI = 33.81 ft of water

From the fortune files:



        How many seconds are there in a year?  If I tell you there  are
3.155  x  10^7, you won't even try to remember it.  On the other hand,
who could forget that, to within half a percent, pi seconds is a
nanocentury.
                -- Tom Duff, Bell Labs


[QUOTE=HeadNinja]
The main reason the trick is useful is for spot math.
[/QUOTE]
Yes, yes I got that (finally). Sometimes I forget that most people don’t enjoy multiplying in their head and/or that estimating is faster and more useful than figuring out the ‘real’ number. Usually I can refrain from posting idiot replies but I that one snuck through the filter. :slight_smile:

[QUOTE=Inner Stickler]
And the derivative of a real number is xn^x-1. So the derivative of x^4 is 4x^3
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Actually, the derivative of a number - real, imaginary, complex, or whatever - is zero. Numbers being constants and all, and the rate of change of a constant being zero.

Now if x is a real variable, then the derivative of x[sup]n[/sup] is nx[sup]n-1[/sup].

Sorry to be a stickler :smiley: about that, but I couldn’t help myself.

I get a surprising amount of traction out of the Euler formula. It is especially nice when you need to so some trig transformations and don’t have a table handy. I may also be the only living engineer who still uses decadic logarithms for calculation, which allows me to save a few microseconds per calculation in a totally meaningless exercise in computational efficiency. The natural logarithm, on the other hand, is eminently useful, and I’ll know that I’ve found my one true love in a woman who appreciates the Laplace transform as much as I do.

Beyond that, Pythagoras’ Theorem and the Golden Ratio have served me pretty well. As for units, I just convert everything into Planck units, which doesn’t make it easier but confuses the hell out of everyone.

Stranger

12345679 x 9 x (your favorite single digit number) = a string of your favorite digit number. Ex., if your favorite digit is 6, then multiple 12345679 x 54 to get 666666666.

I’m going to make some error here, so bear with me:

I remember from one of my maths textbooks in high school something like:

If you have a cylinder, a cone and a sphere of height h and the diameter of the sphere (or circular face) is also equal to h then the ratio of their volumes will be 3:2:1.

Someone correct me… please.

[QUOTE=Hyper Aware]
I’m going to make some error here, so bear with me:

I remember from one of my maths textbooks in high school something like:

If you have a cylinder, a cone and a sphere of height h and the diameter of the sphere (or circular face) is also equal to h then the ratio of their volumes will be 3:2:1.

Someone correct me… please.
[/QUOTE]
The ratio between a cylinder:cone:sphere of height h and radius = h/2 is 3:1:2.

Stranger