/sci/ - Science & Math

>>5025455
>>5025455
>>5025455
stop fucking with the guy so much.
OP, you definition is correct as long as you consider the Riemann integral and that (x1,x2...,xn) is a subdivision of [a,b].

Measure theory is probably too complicated for you atm judging by your question in the original post.
tl;dr: stick to that for the moment, you're fine.

>>5006693
so there still could be a "dense" lattice?
Just like [tex] \mathbb{Q}[/tex] is dense in [tex] \mathbb{R}[/tex], for example?

>>5006568
>mfw my profs lessons are still funnier and more interesting than his
>>5006570
he basically says that if space was not continuous, he would know about it.
tl;dr: he doesn't give any explaination, I am disappoint

>>5006563
I'll watch it and tell you, there might be something interesting

are you talking about dry friction or fluid friction?

Fourier, because he was able to derive some pretty neat mathematical stuff in order to solve the physics problems he stumbled over.

the roots are roots of the polynomial <span class="math">P=X^n-1[/spoiler] (for n >1)
derive the motherfucker:<span class="math"> P'=nX^{n-1}[/spoiler]
the only root of P' is 0, and 0 isn't a root of P.
Therefore all the roots of P are simple. (if they weren't, at least one of them would also be a root of P')

the roots are roots of the polynomial <span class="math">P=X^n-1[/spoiler] (for n >1)
derive the motherfucker:<span class="math"> P'=nX^(n-1)[/spoiler]
the only root of P' is 0, and 0 isn't a root of P.
Therefore all the roots of P are simple. (if they weren't, at least one of them would also be a root of P')

>>5002103
Khanacademy is good if you need to see examples, it's more like a diy tutorial.
But you won't find many proofs, and the lack of rigor is not very appealing.
tldr; depends on what you're looking for.

>>5001389
yep, I think it is the right answer!

>>5001325
what?

pH=pKa + log([RO-]/[ROH])
so log([RO-]/[ROH])=pH-pKa
=> [RO-]/[ROH]= 10^(pH-pKa)
=>[RO-]=[ROH]*10^(pH-pKa)!

>>5001271
ok, as CH3COOH (let's call it ROH) is a weak acid, and you know the pH (pH=4), you can determine [RO-]/[ROH] by using the expression of pH in terms of pKa.
But you also know the initial concentration in ROH ( [ROH]=2.0 mol/L)
you can therefore deduce [RO-], right?

(do they give you the pKa? it's around 4.7 if I remember well)

whatever:
you know [RO-] and [ROH], and those are different since initially pH != pKa, but you want them to be equal.

This is why you need to adjust the concentrations.
By adding NaOH, HO- will mainly react with ROH to give RO-;
I guess you can go on your own from now on?
I'm staying for a while and I'll check later if you still have any questions.

>>5001244
usually, a buffer solution is made such as pH=pKa (so you have to use a weak acid anyway).
But you still need to have the good proportions.

You still need to figure how much NaOH you need to add...
writing CH3COOH = H+ + CH3COO- is a good idea.
You understand that the solution is too acid to be used as a buffer solution, so you want to get a higher pH, and to do that you can indeed add HO-.
Now write the reaction and all the related stuff!

>>5000000
gg

why isn't there anything about torsors, loop systems, stability, linkages.. What about exact constraint, overconstrained mechanisms?
What are the courses that cover these?

>>4997521
the y^2 comes from the fact that x is always greater than -6/5. So x can be written as -6/5 + something non-negative.
That something can therefore be expressed as y^2!

square root exists if and only if
<span class="math">x \geq -2 [/spoiler] AND <span class="math"> x \geq -\frac{6}{5}[/spoiler]
so let's write x as <span class="math">x=-\frac{6}{5}+y^2[/spoiler], with <span class="math">y \geq 0 [/spoiler].
solve for y now, it should be trivial.

>>4993622
geometrical significance: bring the invariant fields to the origin.

>>4993411
let the denominator be A(x)
A(x)=x/A(x)
so x=A²(x)
it follows that >>4993414 is right indeed

>>4992933
this isn't the definition of O(), is it?
the definition is: there exists k, and N such as
for all n>N, |f(n)|<= k.|h(n)|.

write the definition of f(n)=O(h(n))
you'll find the answer by yourself.

>>4974165
forgot pic

I don't really see why the distribution would be anything simple enough to be described...

However, if you imagine a uniform contact between two objects, you can proceed by decomposition.
Pic related:
the cube is made of infinitely many parts of width dx
Each sub-solid (like the blue one) behaves just like the whole cube does.
I think we can then show that the frictional force here is uniformly spread across the area of contact between the cube and the black object.
However, I think that this is far from being close to anything real because of the hypothesis.
One way to measure this could be by using inverse dynamics maybe?