The one you've seen many times in school or at work. For me it's picrel.

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# What's the formula you've seen the most in your life?

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The one you've seen many times in school or at work. For me it's picrel.

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Same but I've never worked a day in my life and I only learned high school math. I'm 24 yrs old, degreeless. Considering my job prospects (supermarket clerk/backbreaking labor) will I ever need to use this formula again?

Same. I have been denied a career, relationships (both romantic and platonic), opportunities, hobbies and interests and even family bonds.

Being acoustic and neglected at the same time is a lethal combo. I learned the hard way that in order to pursue careers and degrees you need a lot of support and not just monetary but also emotional and moral too; I didn't get either. My last wish is to one day provide at least the latter to my future kids.

Though I have used the quadratic formula myself countless times, I actually only literally saw it enough times to memorize it. That includes the time when I was a mathematics tutor as well.

I think that, overall, due to their mainstream popularity, E=mc^2 or the Pythagoras Theorem formulas might be the ones I have seen the most in my five decades of existence.

u = R*i and U = Z*I

I never use this formula, just complete the squares instead

That's the same thing with more steps

When I was young I refused to memorize OP pic and instead used

[math]displaystyle x = -frac{b}{2a} pm sqrt{left( frac{b}{2a} right)^2 - frac{c}{a}}[/math]

which is what you get from completing the square directly, without any attempt to rationalize the denominator.

>which is what you get from completing the square directly, without any attempt to rationalize the denominator

Yes, as I said it's the same thing with more steps. You do the stages separately and then potentially have to rationalise the denominator at the end. You're simply remembering a process rather than an explicit formula.

There is a difference between remember a process you understand and can justify and simply outright memorizing a formula which is how most students approach the quadratic formula. If your suggestion is to derive the formula once and then remember it, that is satisfactory, but not something most students are going to do.

As far as

>have to rationalise the denominator

this is a useful skill in certain contexts (especially when the denominator is a binomial), but is heavily overused in schools, not for the benefit of the students or their education, but in order to force answers into a standard form to make grading easier. Rebelling against such nonsense should be encouraged.

Rationalising the denominator is useful if you have to do further calculations with your answers to the quadratic equation. For example, a student may intuitively be able to calculate [math] frac{9 + sqrt{6}}{15} + frac{7 sqrt{5}}{5} [/math] using their knowledge of how to add rational numbers, whereas [math] frac{5}{9 - sqrt{6}} + frac{7}{sqrt{5}} [/math] looks much less approachable. If you're going to need to rationalise the denominator anyway to add/subtract your fractions, it's good to get into the habit of doing it as standard.

>If you're going to need to rationalise the denominator anyway to add/subtract your fractions

*2bh I didn't really mean "need" here, as you could of course just cross-multiply and accept that you'll have irrationals in both the numerator and the denominator. It's more that rationalising the denominators makes the whole calculation a lot neater.

You are confusing calculating a value with simplifying an expression, and not even choosing a good example of simplification. (Next time try [math]tan(75^circ)[/math].) Yes, rationalizing the denominator is useful sometimes. No, putting things into "standard forms" as a matter of unthinking habit is not good.

>putting things into "standard forms" as a matter of unthinking habit is not good.

I think that anon's point was that rationalizing the denominator puts surds into a consistent form which is much easier for students (and anyone else actually) to recognize; which helps with learning how to perform calculations using them. It also makes it far easier to identify equivalent irrational expressions.

How to remember them all? Like without any card formulas

same way you learn anything. You do enough problems that anytime you shut your eyes you can see the burnt impring of these formulas on your eyelids.

Understand what all the pieces mean and why they are all there.

I know but my brain enjoys doing that over punting the formula in my calculator

f=ma

cos^2(x) + sin^2(x) = 1 and pretty much any equivalent trig identity.

Pythagorean theorem easily, not only is it arguably one of the most famous math results but it also is just so incredibly useful in almost every area of math and science imaginable

rate times time

Verification not required.

>tfw this is probably not even particularly difficult but looks so intimidating to me I would never try to learn it

being beaten by getting multiplication tables wrong as a kid was not fun

It's just a normal curve function lol. 80% of statistics uses it and I don't even bother writing it out since Excel has simple functions for it

good, now integrate that from -inf to x

3blue1Black person has a cool video about how this crazy looking one got derived

E=mc^2

Normies use it as the canonical "math formula" everywhere.

for me, it's the gradient of the loglikelihood

Extremely useful, should be taught to elementary school children, but sadly very few people understand it.

Heres a nice video that briefly explains ideal gas law

good video

Mouf, now

How the frick has nobody said the area of a triangle or rectangle or circle?

How often do you need to calculate the areas of circles?

Is there any intuitive logic for solving third degree equations, beyond just following some algebra? Something akin to completing the square

With a quadratic equation you can try to find some unique shift that would make the roots symmetrical (say, as opposites, or perhaps as complex conjugates), and then the equation is turned into a linear equation. How is this to be done for a third degree?

Dont just post the formula, which is over 500 years old, not the point

0+1=1, 1+1=2, 2-1=1, and 1-1=0. All of mathematics can literally be reduced to these four equations.

2+2=4

as a chemist

n [mol] = m [g] / MM [g/mol]