/sci/ - Science & Math

is it possible to integrate

((2x-1)^3) - 8

without substitution?

i know you do

u = 2x-1 , du/2 =dx

u^3 - du/2

u^n+1/ 2 x n+1 - 8x

=(2x-1)^4 / 8 - 8x

but is there another way?

>>10158554
Break up with her bro

Let's say a point on a one variable real function is 'kino' when it is an inflexion or stationary point.

Is it true that a point x on a differentiable function is 'kino' if and only if f'(x) = 0?

>>10158728
I guess you could do [math]\int(2x-1)(2x-1)^2dx - \int 8 dx[/math] and then integration by parts

What do you mean by "another way?"

>>10158737
its just in my head whenever i see it i jump the gun and forget about the implied dx so i go

=(2x-1)^4 / 4 - 8x

because i only do the power rule, obviously the inside function stays the same though but yeah.

Is Blackfriday/Cybermonday a scam?
Whenever I see a "deal" on a website, I google that item and then some other site has it for the same price. Maybe it's different when you go to the store in person rather than the site?

>>10158771
Just look at what the MSRP is for anything.
What they do is bottom prices out on a few limited items to bring in the marks, then you razzle dazzle them with the "sales' on everything else that's a tiny markdown on retail and still way over cost.
They're also banking on people being lazy and not doing their research.

>>10158728
>is it possible to integrate
>((2x-1)^3) - 8
>without substitution?
Sure, expand first.

Do I really need a PHD in population genetics if I have nearly 2 years of research in it with my bachelors and plan on getting another 2 years of research in my masters program? I don't want to go another 2-3 years.

>>10158904
What do you want to do? Do you want to be an academic? Then yes, you do. Post-doc is basically required, too.

No one cares about your undergrad research unless you are a supergenius, and if you are a supergenius, you don't ask questions like this, so we can rule that out.

If you just want to go to industry, the Masters is probably fine, but you'll take a hit on level/paycheck if PhDs are the norm.

>>10158904
If you want to do any meaningful research ever, yeah you have to get that Doctorate

How do I get my browser to recognize the [math] brackets? I can't read any latex on /sci/

>>10158936
use a good browser? i'm on firefox

>>10158864
fair enough, substitution it is

>>10158936
>>10158965
4chanx fucks with it

Is color science legit?

ive got my calculus exam tomorrow. any tips?

>>10159108
Colors do not exist

>>10159065
Try without adblocker

>>10159149
And yet your mom's boyfriend is black. Explain that.

>>10159154
i mean it works but im using adblock to block other things

>>10158728
> is it possible to integrate
> ((2x-1)^3) - 8
> without substitution?
Of course. Just expand it out to
8x^3-12x^2+6x-9
and integrate the individual terms.

Maple or Mathematica?

a)f(x)=ln(x+1)*sen(x)

3
∫ f(n)dx=?
0
b)
d/dx |

This was suppose to be a question in interpolation polynomial

I don't knbow how to study to this.

help

>>10159939
When doing a defined integral, and in doubt of how to integrate, approximate it.

>>10158045
I made a mistake.
What I have is a set of data points for an object's distance from the Sun as a function of the angle around the Sun. I numerically differentiated the distances to get the velocity and acceleration, but now I realize that those values are wrong, since the position values are not a function of time. Is there any way to figure out the position as a function of time, from the information that I have?

Hi there.

What would happen if something about the mass of the Everest landed on earth? (Let's asume It doesn't impact, just lands softly)

I have a idea for a story and, even if I could ignore any changes to earth gravity / rotation, I got curious

>infamous heretics

>>10160172
Yeah. An elliptical orbit implies an acceleration at each point, so the speed can only have one value. Once you have that, it's just integrating backwards.

>>10160438
not much
Everest is about 9km tall, Earth's radius is about 6371km.
If you are very generous and assume they both have the same density (in reality this is a huge overestimation since the majority of earth is extremely dense) and that the everest-sized object is actually a ball and not a pyramid, then your object is .000005% the mass of the earth. In reality this number is probably like an order of magnitude too large.

>>10160450
Well, and here I though something like that could destroy the earth or something.

Thanks for the answer anon

>>10159659
Depends on what you're doing. Maple is useful for algebraic calculations while Mathematica is better with stuff like limits and special functions.

>graduated with a bullshit degree few months ago
>hate it
>want to go back for EE which I started in
>was lazy retard and fucked around then changed majors

Should I become an electrician bros? I can't afford to go back to school like I want and I can leverage my degree down the road. I originally wanted to focus on technology with EE but my dumbass wanted to do dumb shit like party and have fun.
But, how can I make my way back into uni as an electrician apprentice ( since that's where I'll have to start) or become something more than just your run of mill electrician working for a contractor

I have the following sequence: Un+1 = sqrt(1 + Un)
How do I prove that there exists a real number x > Un for any natural number n?

Woot woot just finished my calculus exam. Was easier than expected, hopefully i get 80%+

>>10160944
what does an electrician apprentice do because my friend works for an electrician but didn't even go to college

HELP ASAP ANONS. I need some online source to learn relations, equivalence relations, reflexivity, simmetry, transitivity, etc. I couldnt find anything on Khan.

I got flashed at an intersection for speeding.
I live in Arizona, how likely is it for anything to come of it? I assume I'm basically fucked.

>>10161222
don't speed
speed limit laws are one of the laws which actually make sense

>>10161228
They were made when we had drum brakes, ply bias tyres, and shit suspension

>>10158936
disable adblock

>>10161228
You're right, though that doesn't really answer the question.

>>10161205
please :'(

>>10161205
>>10161264
Just use Wikipedia

>>10161205
Literally just use wikipedia. It sounds surreal to say this, but it's a really simple subject.

>>10161002
The sequence converges to the golden ratio, (1+sqrt(5))/2 = 1.618... So any value larger than that will be greater than Un for any n.

At the limit, the value is unchanged by iteration, i.e. Un+1=Un:
=> U = sqrt(1 + U)
=> U^2=1+U
=> U^2-U-1=0
=> U=(1±sqrt(5))/2 = -0.618... or 1.618...
The first value is what you'd get if you took the negative square root rather than the positive (both versions satisfy U^2=1+U).

>>10161395
Thanks. I’m supposed to find it without calculating the limit first but I get it.

>>10161156
Installation and maintenance of electrical systems. Think about things like hotels/houses/buildings.....

I don't get what this question is asking. Am I supposed to divide the second row by the first row and see where the function goes as t -> inf?

If I need to guess answers in a multiple choice test, would it be best to pick random numbers for each question or pick one number and mark it for all questions?
I'm going to take an exam roughly equivalent to the American SATs soon, and I couldn't for the life of me get through all the questions in the maths portion, So I would necessarily have to mark some questions I didn't get a chance to even see.

Should I take Bayesian statistics for physics

Guys I've got a stupid question.

You know how one second is defined as "the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom" (at a temperature of 0 K), right?

And then other SI units like the metre are defined using this definition of a second.

But then what about Einstein's theory of relativity? (Bear in mind I'm not a scientist, so I may have understood this completely wrong.) Didn't Einstein say that gravity slows down time? So that if you're near a black hole, time literally moves slower for you. And of course we know that for satellites orbiting Earth, their clocks go faster (because with less gravity, time moves slightly faster) and they have to adjust for this.

So then surely a second is longer or slower depending on where you are, and how much gravity there is? And then a metre will also be shorter or longer, depending on where you are.

So if you are on Mars, a second will be slightly quicker, because Mars has less gravity than Earth. And thus the metre will be slightly shorter - presuming that light travels at a constant speed, that is. And a lot of sources say that it does.

Although some sources I'm reading say the speed of light CAN change due to gravity - for example, it reaches zero once it crosses the event horizon of a black hole. So I guess if the speed of light does change with gravity, at the same rate of change that time itself changes, then a metre stick made on Mars and a metre stick made on Earth will end up being the same length. But if the speed of light DOESN'T change with gravity, then surely a metre stick made on Mars will be slightly shorter than a metre stick made on Earth, because the length of a second is shorter, and therefore the distance that light travels in 1/299,792,458 of a second will be shorter.

Does this make sense or am I retarded?

>>10161535
For a standardized test like the SAT, if you really don't have time to even read the questions it is marginally better for you to pick one number and stick with it.
The position of the "correct" answer is chosen by a computer on those tests, so there is no possible pattern to exploit. Any method of choosing answers will on average give you the same results.

However, it will probably save you 30-45 seconds to write down 15 As instead of trying to arrange 15 different random numbers.

>>10158554
is there any objection to use color instead of symbol as long as it improves readability?

so example: writing
[math] \color{green}{x}[/math]
instead of
[math][x][/math]
To denote the equivalence class of [math]x[/math]

>>10161673
*colour
Next time, learn to spell properly.

>>10161675
no

Number theory or Differential geometry for minor?

>>10161878
number theory is cancer
differential geometry is a cool subject with cancerous notation

pick DG

>>10161604
I like how you think about stuff. I suggest you look up length contraction which is an aspect of special relativity

>>10161883
lel okay

Is there any rules of thumb to decide when I should use Laplace transforms or power series methods to solve second order ODEs? I'm practicing both methods but I can't even figure out when to use each one.

Hello, this question may be retarded, so I apologise in advance.

After researches are done training a ML model how is the product saved? IE: how are the trained neurons/nodes represented in a way that can be saved and loaded on another machine?

>>10158771
very often it is but for example deathadder elite is $40 on amazon and that's a great price compared to historical prices and best buy has the same price but i think it's because they have a price matching policy

>>10163017
or for example a lamp shop might have 20% off but the lamps are still fucking expensive and they're still making a good profit on them so in that case if you wanted a specific lamp from that store then sure it could be a legitimate 20% off deal but then a different store could have a similar lamp for a fraction of price

>>10158554
does anyone know how to calculate the flow of (x'(t), y'(t)) = ((y(t))3, 3x(t)(y(t))2)?
I tried calculating the flow of (x'(t), y'(t))=(y, 3x), since these give the same 'flowlines' it's just that the derivative isn't what it's supposed to be, so if I call the flow of (x'(t), y'(t))=(y, 3x) f(t), I'm looking for a function g(t), such that D_t(f(g(t))) = (y(t))2*(D_t(f(t))). So I'm looking for a g(t), such that D_t(g(t)) = (y(t))2, but I can't seem to be able to construct such a g(t).

Is there a better method for finding the flow of (x'(t), y'(t)) = (y3, 3xy2)? or am I just being a dumbass for not finding the correct g(t).

>>10158554
does anyone know how to calculate the flow of (x'(t), y'(t)) = ((y(t))^3, 3x(t)(y(t))^2)?
I tried calculating the flow of (x'(t), y'(t))=(y, 3x), since these give the same 'flowlines' it's just that the derivative isn't what it's supposed to be, so if I call the flow of (x'(t), y'(t))=(y, 3x) f(t), I'm looking for a function g(t), such that D_t(f(g(t))) = (y(t))^2*(D_t(f(t))). So I'm looking for a g(t), such that D_t(g(t)) = (y(t))^2, but I can't seem to be able to construct such a g(t).

Is there a better method for finding the flow of (x'(t), y'(t)) = (y^3, 3xy^2)? or am I just being a dumbass for not finding the correct g(t).

>>10158554
does anyone know how to calculate the flow of (x'(t), y'(t)) = ((y(t))^3, 3x(t)(y(t))^2)?
I tried calculating the flow of (x'(t), y'(t))=(y, 3x), since these give the same 'flowlines' it's just that the derivative isn't what it's supposed to be, so if I call the flow of (x'(t), y'(t))=(y, 3x) f(t), I'm looking for a function g(t), such that D_t(f(g(t))) = (y(t))^2*(D_t(f(t))). So I'm looking for a g(t), such that D_t(g(t)) = (y(t))^2, but I can't seem to be able to construct such a g(t).

Is there a better method for finding the flow of (x'(t), y'(t)) = (y^3, 3xy^2)? or am I just being a dumbass for not finding the correct g(t).

>>10161673
how is the first any more readable than the second?

>>10163290
>readable
*legible retard

>>10158554

redpill me on the Axiom of Choice™.

How do i understand that? When is it necessary?

>>10163471
axiom of choice says that the cartesian product of infinitely many non-empty sets is always non-empty, that is, it is always possible to CHOOSE an element from every set at random.
As an undergrad I mostly use it in the form of Zorn's lemma, which is equivalent to the axiom of choice and says: in a partially ordered set, if every chain has an upper bound, then the set has at least one maximal element. This is used to proof various theroms in algebra, like Krull's theorem, which says: In a non-zero ring, for every proper ideal there is a maximal proper ideal containing this ideal.
I know that it's also used in measure theory, but I don't really recall in which proof(s). It's also used to proof that not every subset of R is measurable, search for the Vitali set if you want to see the construction of this set, it's the easiest example I know.
If you assume the negation of the axiom of choice then every set is measurable, but then there's essential stuff that you can't proof, so this isn't commonly used.
There's probably also a lot of interesting deeper logic stuff about the axiom of choice, but some other anon has to help out there.

>>10161673
I propose we use drawings instead of symbols for anything in differential geometry.

How do you blind someone temporarily, say for 5 minutes or so.

>>10163519
there's no anon to do that
you should do it

>>10163562
pepper spray

>>10163567

I didn't think about that. That could work, but it also hurts a lot.

>>10163571
blinding someone could cause a lot of butthurt either way if it's not consensual. if it's consensual, how about having them put on a blindfold?

>>10163519
The thing about the axiom of choice is that it says you can go 'eenie meenie mo' and pick a random number on the real line. The problem with this is that you can eenie meenie mo your way into picking random points of a ball until you fill out two balls. It opens up a path for giving "constructive" proofs that have no tangibility to them. It's a good axiom for some things, but it's ultimately a general proof of existence of things that can't be constructively grasped or shown to have to exist by a contradiction.

>>10163566
no, you

>>10163578
>tfw ywn find an irl dupe glitch

In a bit of a dilemma looking forward towards grad school. So at the moment I have absolutely no research experience (graduating fall 2019) but recently interested in going to grad school. I plan to get some next semester and my last semester, but not sure what to pick. I am majoring in EE at a 3.8 gpa, R1 uni, and have mainly focused on lasers, optics, and photonics, but recently got interested in computer vision and image processing (CS). Should I just keep taking classes in both and apply for both types of programs, or should I decide on one and follow through with it? If I decide to try for both should I only do the undergrad research in one or both? Really split on what I want to pursue.
Also is there any chance I get into a PhD with such little research experience? Dont expect to for CS due to have much less classes for that, but maybe for EE?

Background, not actually important to the question: I'm confused by a derivation of magnetostriction for a polycrystalline film of randomly oriented cubic crystals.

It looks like a situation where a simple surface integral across a sphere would be used, but instead of 0 to pi, one of the limits is 0 to pi/2, and the integral is divided by 2*pi. So the integral is what's shown in the picture.

Anyone got any ideas why? I don't see a physics reason for this change so I'm wondering if it's a common mathematical thing.

My dumb monkey brain insists that a) is because virtual particles are fluctuations within the lower bound of the classical minimum energy of a system (ie 0) and the upper bound of the quantum minimum energy (ie something like thats also bounded by Et >= hbar/2), and because of this difference in energy, the two plates are attracted to each other, like in an electrostatics problem. My gut says this is wrong, especially since he seems interested in the virtual particles themselves.

For b) I'm wondering, if I use kinematics (ie imagine a particle going from plate 1 to plate 2 at some speed v, arriving at plate 2 at some time t) and then apply the uncertainty relation, will I get what I'm looking for? "The longest time" seems like a weird thing to look for since the uncertainty relations lend themselves to checking "minimums" of things

>>10161418
Remember to ask your questions correctly. That sequence is not completely determined since it lacks the definition of the first term. It represents a family of sequences that vary on that choice, and so there's not a real number x that suffices your question for each one of those sequences (Archimedes property). But I'll just take [math]u_1 = k \geq -1[/math].

>>10161395 answer is incomplete since to apply limit rules, you need to be sure that these sequences converge, and I'm not sure if you can do without proving that they're bounded (maybe proving it's Cauchy?), which is exactly what you want to prove. So we'll prove it directly without needing any facts about its convergence (I used to do this a lot on my intro to calculus course, I loved it)

If we wanted to do this by induction, x being our candidate, from the induction hypothesis we'd eventually get
[math]x > u_n[/math]
[math]x + 1 > u_n + 1[/math]
[math]\sqrt{x+1} > \sqrt{u_n + 1}[/math]
[math]\sqrt{x+1} > u_{n+1}[/math]
Therefore, any number x that suffices [math]x \geq \sqrt{x+1}[/math] and [math] x \geq u_1 = k[\math] would be enough for us to complete the proof. Take [math]x = k+3[/math] for example, and you should be able to prove the whole thing through induction.

Can someone solve this linear diffeq for me?
x' = x + e^{-x}

>>10164187
1/2(x^2) - e^(-x)?
I just took the integral of both sides to get that ansewr, but I'm not sure if it works like that

>>10164187
It's not linear

>>10164187
That's not linear. If your function is x, then it can't contain e^{-x} and be linear.

>>10164197
>>10164199
Does x' = dx/dt change anything?

Man... Calculus is haunting me hard. That thing isn't separable either, right? How am I supposed to draw the trajectory for this then?

Can I skip proof and go straight into Set theory?

>>10164204
It literally says it can't be solved analytically. Try a numerical solution or just draw the vector field and sketch out the curve with that initial condition.

>>10164197
What does it mean not linear?

>>10164214
Oh, so like RK4 or Euler or something. I think that makes sense. Thanks.

>>10164187
Look into Laplace transforms. Not 100% sure but it looks like one that can be solved that way.

how to show that euclidean norm on R^2 is a closed map?

>>10158732
Do you mean an inflection point where the curve's concavity changes? That is f''(x) = 0. Points on f(x) where f'(x) = 0 correspond to where the slope of f(x) changes sign, or a local minimum/maximum.

Might as well take the chance to bump >>10162815
In general, I know Laplace transforms can be used when the function has jumps. Also power series solutions work when the point is not singular, or is at least a regular singularity. But if I had for example y''-ty'+y=1, with y(0)=1 and y'(0)=2, it can evidently be solved by both methods, yet the Laplace transform gives me a pretty ugly integral to solve (unless I'm fucking it up). Is there any way to figure which method I should without wasting time just trying it out until I can't move on any further?

>>10158732
stationary point is by definition a point where f'(x) = 0. so yeah, f'(x) = 0 implies that x is a stationary point.

>>10163541
This. Diff Geo notation is absolute cancer.

>>10164261
Shit, messed this up. Meant to say square of euclidean norm, so like x^2 + y^2.

>>10158554
Is it possible to completely cover my body in clothing and get all my vitamin D from supplements? Would this be unhealthy and have other side effects?

I'm getting fucking tripped over stupid set theoretic containments here. Suppose [math]f:A\to B[/math], and [math]D\subseteq C\subseteq B[/math]. Can I conclude that [math]f^{-1}(D)\subseteq f^{-1}(C)[/math], or are there some restrictions I need to place on [math]f[/math] for this to be true?

>>10164626
you can conclude that with no additional restrictions
write out the formal definition of a preimage if you feel confused, it will make it clearer why this is basically obvious

>>10164631
Thanks, I felt that it had to be, but my set theory foundation is really fucking shaky.

I'm an amateur cryptographer. I'm mathematically illiterate and don't have a pc to run the code to look for patterns in keystream output. In spite of that all I wish to make a playing card cipher based on a self shrinking linear feedback shift register or "Shrinking lfsr". I have several ideas on the algorithm and wants y'all's help.

Register sizes. I'm thinking of 52 cards printed 52 cards. If I do a set of registers in 11, 15, and 26/27... I don't see relative primes in my basic mathematical understanding. Does anyone have a better idea for the longest run length?

Secondly, how do I get output? I'm thinking of a bastardized xor function to cover thiz with " if or" rules. If 11 and 15 registers have differing colors (red and black) then negate output and run the shuffle. If the 11 andb15 match color check the color of the 26/27 register card. If colors match for the first 2 register face cards but don't match the color of the 26 card, dont add 13 to the value of the cards. If they do, add 13. I'm seeing a 50/50 of a 50/50 for match to not match leaning equally likely of a value of 1-13 or 13-26.

How do I shuffle the deck to match speed plussplus security? This is my major trade off. Solitaire is like one minute per character. I'd like something faster with a decent margin of security. This is where I need the most help.

If anyone can help or has ideas/questions... Lemme know.

>>10158554

Im going mad trying to figure this out on my own,
and dont copy pasta this solution either:

https://math.stackexchange.com/questions/650966/evaluate-sum-infty-n-1-frac1n4-using-parsevals-theorem-fourier-ser

unless you can tell me where tf that 8 comes from

>>10164187
First, note that dx/dt is always positive. When x ~= 0, you have dx/dt~=e^-x=1 => x=t.
As x increases, the e^-x term becomes less significant and it tends to dx/dt=x => x=k*e^t=e^(t-t0).

IOW, it starts off linear and ends up exponential. Numerical simulation suggests an offset of ~-0.767, i.e. asymptotic behaviour is x=e^(t-0.767).

>>10164870
>unless you can tell me where tf that 8 comes from
Note that it says [math]a_n^2 = \frac{4}{n^4} \quad \mathrm{for}\ \ n \in \mathbb{Z}[/math], the summation is from n=1 to infinity. The summation that has the factor 8 in front of it only sums over the positive integers. That’s why it doubles. Hth.

>>10163231
please?

>>10164993
Does it help you to know that that is a gradient field?

Anyone here use scimax for emacs? Is there any point in a math sophomore using it (or anyone in general)? Or should I just wait for certain needs to arise and install what I need then?

If 60% of a population has trait A and 40% of a population has trait B, what would be the expected distribution of trait pairings if members of the population paired randomly? In other words, what percentage of pairings would be AA, AB and BB?

>>10165114
not really, the question was to give the flow of the gradient field and hamiltonian vector field of f(x,y) = xy3

Maybe I'm overlooking something obvious, idk, when I put the equation in wolframalpha it gave some wicked ass solution with complex coefficients, maybe I'm not supposed to find a specific form of g(t), and it's enough to say that g(t) = integral of (y(t))2. Kind of unsatisfactory to write that down, but I guess it'll do

>>10165378
I guess P(AA)=P(A)^2, P(BB)=P(B)^2 and P(AB)=2P(A)P(B)
the amount of A's in your pairing follows a Binomial distribution B(2,0.6)

>>10165378
>>10165401
for info on why this is the case, check the wikipedia page on the Bernouilli distribution under the subcategory Related distibutions.

Is it possible for a blog to be a credible RRL source?

>>10164019
This is basically just computing the expectation of the Casimir element [math]a^\dagger_i a_i[/math] of the Heisenberg algebra in the [math]L^2(X,\mathbb{C})[/math] representation, where [math]X[/math] is the spacetime inside/outside the plates.The discrepancies between the particle numbers for the spacetimes between and outside of the plates should tell you that there's a pressure force being exerted.
>>10164261
Use Heine-Borel. Closed and bounded subsets [math]A,B \subset\mathbb{R}^2[/math] are compact, and since [math]d:\mathbb{R}^2 \times\mathbb{R}^2\rightarrow \mathbb{R}[/math] is continuous [math]d(A,B)[/math] is compact and so it's also closed and bounded.
>>10164870
Use [eqn]\int_\mathbb{C}dz f(z)\csc \pi z = \sum_n f(n)[/eqn]. No need for Parseval or Fourier.

So in fluid dynamics, Mass flux is velocity × density.
And then through Taylor series expansion, I am supposed to get pic related.
But how?
As in the right part of the picture is probably integration of the left part but what is the left part?

>>10164945
Hey thanks m8

>>10164261
>how do I show that the metric maps closed sets under the metric to closed sets
I'm done, someone kill me.

>>10158554
I know that a k times differentiable function will produce a constant after taking k derivatives, but I don't know how to sufficiently show this regarding fourier

>>10165981
>a k times differentiable function will produce a constant after taking k derivatives
Th-that's what k-times differentiable means? I always thought it meant that [math]f^{(k)}[/math] wasn't differentiable.
The more you know.

>>10165981
>I know that a k times differentiable function will produce a constant after taking k derivatives
Lol no.
Prove [math]\mathcal{F}f' = (\mathcal{F}f)'[/math]
>>10165995
Correct. [math]f^{(k)}[/math] must also be continuous

>>10166000
Shouldn't 108 follow immediately from L^1(R) being a Banach Space?

How long did it take you to graduate from university?
I'm in my 5th year right now. I'm currently failing combinatorics and differential equations. If I fail them, I won't be able to retake them until next fall. If I somehow pass, I graduate in spring, if not 6 full years of wasted school.

>>10166013
No.

>>10163979
The limit that represents 0 to pi/2 is related to the zenit (polar) angle, this is common to the spherical coordinates integration. Theta is the azymutal angle, so the limits go from 0 to 2pi. The 1/2pi before the integral can be the result of a previous integration using the radious, since spherical coordinates consists of three variables (r,theta,psi)

>>10163979
Jesus fucking christ anon that formula.

Just realised the atomic mass number is just the molar mass of an element.
Learned this after googling the molar mass of 210Po
Brainlet feels.

>>10163979
There is likely to be some kind of inversion symmetry [math]z \mapsto z[/math] in the integrand so that the integration over [math]\theta[/math] can be halved. Also the factor [math]\frac{1}{2\pi}[/math] comes from a Fourier transform.
>>10166125
Incorrect. The polar angle [math]\theta[/math] runs from [math]0[/math] to [math]\pi[/math].

>>10166190
>[math]z\mapsto z[/math]
Jesus I meant [math]z\mapsto -z[/math]

I'm stumped by a question relating to a very simple experiment:
I have a transmitter and a receiver. I send an impulse into the former and plot what comes out of the latter, and repeat the experiment with more distance between the two. I need to determine the distance using cross-correlation with the two signals.

Which method leads to a more accurate result: sending one impulse or multiple impulses? I can't intuitively think of the benefits that multiple impulses would provide. Pic related (but ignore the actual time values for the cross-correlation)

Hello retard here,
Why are c atoms of an acid group never asymmetric?
Pls respond

I need help figuring out how to solve nested fractions. The khan video is dogshit and he skips steps that seem obvious to. I made sure it wasn't just me having this problem and you can see people struggling with it in the comments. so anyway

If I have 1/a - 1/b over C divided by 1/d, what are the correct steps to solve this?

I understand that for 1/a - 1/b that I find the common denominator, so it goes 1*b/ab - 1*a/ab for a-b/ab. But now I'm lost. Am I multiplying by C? i.e ac-ab/abc? or or by the reciprocal i.e C/1 so a-b/abc? pls

>>10166260
whoops, meant to say ac-bc/abc

>>10166264
>>10166260
nevermind figured it out

>>10166244
Draw the Lewis model for C

going through gelfand's algebra.
I don't get what the big mistake is, assuming a, b, c are all different, and he doesn't expand on the "theory" and just says it's not THAT big of an issue

>>10165809
Heine-Borel requires boundedness also. You still have to consider any general closed set in [math]\mathbb{R}^2[/math] .

>>10166310
Let as an exercise.

>>10166125
>when you're a physishit and this diagram for spherical coordinates doesn't make sense to you anymore since EM uses another convention

>>10166022
>5th year
>failing differential equations
You should have taken the hint and switched to another degree program.

>>10166244
To have an aymmetric (chiral) carbon you need it to have 4 different ligands on that carbon, and if you mean as acid group a carboxyl, the carboxylic carbon will be bonded to a carbonyl and other 2 different ligands, since is bonded to the carbonyl twice (double bond) is impossible for this carbon atom to be assymetric since it has 3 ligands

Did I do this right? I'm suppose to evaluate the series using Riemann sums and fund thm of calc

>>10163816
please help i have a month to decide

>>10158554
To show a matrix M is positive semidefinite, it's enough to show xMx is nonnegative for (say) unit vectors only, right?

what number tool do you guys use?

>>10166677
Yes.

If x isn't a unit vector, you can write it as kx' where k is a scalar and x' is a unit vector. So xT.M.x= kx'T.M.kx' = k^2*x'T.M.x' which is positive iff x'T.M.x' is positive.

>>10166929
Thank you <3

>>10163979
>the integral is divided by 2*pi
i don't know any of the physics shit but this is probably because the area of a hemisphere (or sphere divided by 2 - maybe that has to do with the limit to pi/2?) with a radius of 1 is 2pi but you want it like a percentage

>>10166198
If you send a sine wave, you could perhaps compute the distance more accurately (using the phase shift), like in laser distance measurements.

But first tell me this, is that LabView? I was tortured with that „programming environment“ once.

>>10166543
Where did you get that factor of 2 in front of x from? if [math]x=\frac{k}{n}[/math], the summation runs from x=0 to x=2, and the function you should want to integrate is
[math] \frac{x}{1+x^2} [/math].

>>10166278
When he says "consider the LHS as a polynomial with one variable x", what he means is this: Suppose a, b, c are any three distinct numbers (like 0, 1, 2), then if you substitute those values of a, b, c in the LHS you get a polynomial in x. Then he proceeds to show that the polynomial you got by substituting the values of a, b, c is 0. That's fine. But can you conclude from this that if you algebraically expand the terms in the LHS - just using algebraic manipulation, without substituting any numbers for a, b, c - you will get 0?

For example, consider the polynomial f(x) = x(x^2 - 1). If you're working with the integers modulo 6 then f(n) = 0 for all elements of this set. But if you expand f(x), you get x^3 - x instead of 0. The reason this happens is because the set (ring, actually) of integers modulo 6 is not a field (certain multiplicative inverses do not exist).

The theory required to justify it is not really complicated but it might require some background in abstract algebra. Instead of substituting values for a, b, c and and using the resulting polynomial, you could instead form the field of rational polynomials in the indeterminates a, b, c and consider the LHS of that equation as a polynomial in x over that field. Now you can use the fact that a, b, c are 3 distinct roots and that the polynomial is of degree 2 to conclude that it must be 0.

>>10167066
Yup we have a few hours of easy lab work in order to learn to use LabView, mostly for the purpose of remote control of instruments. I'm aware of the phase shift method but we're forced to do it the way I described.

>>10167269
Alright. Well, you'd always do well to send multiple impulses, say 10 or so, in order to reduce the uncertainty of your measurement.
What is the type of wave you're sending, sound or an EM pulse? Asking just out of interest.

>>10167290
Sound, and yeah I guess I will

[math]a_1 = 1, a_(n+1) = \frac{a_n (a_n + 1)}{3} , n >= 1 [/math] is monotone and decreasing, so an >= an+1. So the base is [math] \frac{3}{4} >= 1 [/math]

For the induction step, can I do pic related?

>>10167328
Ok I don't know typesetting, I meant so say at the start that I'm trying to prove that the sequence is monotone and decreasing. Idk if I can do pic related

>>10167328
Let [math]a_1=1[/math], and for any other natural n [math]a_n=\frac{a_{n-1}(a_{n-1}+1)}{3}[/math]. [math]a_n[/math] is decreasing.
Is this what you want to show? I can't read your post.

Help me /sci/, I'm gonna kill myself.

I have a time signal, want to approximate it with its first harmonic.
>take FFT
>find peak
then what? I have the complex value which should give me the amplitude and the peak position gives me the frequency, is that it? How do I use them, do I write a sinusoid with those parameters?

I have to do all this in Fortran btw.

I've started self-studying differential equations and I'm kind of struggling to understand the fundamentals.

For example, how do I solve:
3f' - 2f = 4
First I have to solve the homogeneous diffeq 3f' - 2f = 0, right? Which gives me f(x) = exp(2/3 * x)?
Then what?

>>10167449
>do I write a sinusoid with those parameters?
Well, what else? Give some more contex — what do you need the approximation for? Do you have to go back to the time domain?

>>10167470
The homogeneous solution is Kexp(2/3x), K a real number.

Ordinarily the way to find the particular solution is to treat K as a function, K(x), and differentiate again to get f‘ = K‘ exp(2/3x) + 2/3 K exp(2/3x), then find K from there.

I recommend a different method called multiplying by an „integrating factor“ .. look it up.

>>10167484
Sorry for being obtuse, but I don't understand why I need to include K at all. Is it because since I'm searching for a primitive, there should be a constant of integration? In which case, why am I multiplying by K instead of adding K?

>>10167466
>g(x)=f(x)+2
>3g'-2g=4
>3f'-2f+4=4
>3f'-2f=0

>>10167361
yep

In regards to radioactivity:

[eqn] R = R_0 \times e^{-t/T} \\R_0=rN_0\\ T = 1/r [/eqn]

Where [math]R[/math] is the rate of decay (units in Bq which is just decays per second), [math]R_0[/math] is initial rate of decay, [math]T[/math] is the Time constant (defined as one over "rate", which is [math]r[/math]; not to confused with [math]R[/math]), and finally [math]t[/math] is the time that has past. "rate" ([math]r[/math]) is defined as

[eqn]P = r\Delta t [/eqn]

where [math]P[/math] is the probability of an atom decaying, and [math]\delta t[/math] is obviously change in time.

My stupid question is that what purpose does Bq ([math]R[/math]) have? 1 Bq means "1 decay per second" but what purpose does that serve if Bq is decreasing exponentially?
Thought of this when I was doing some work, and ended up with a result of [math]1.4\times 10^-9 \ Bq[/math] which, if my brainlet maths are correct, is 1 decay per 22 years. This obviously isn't useful though because the rate of decay is going to change drastically in that time, doesn't it?

>>10167590
got the second delta wrong but whatever. Also grammar error on last sentence.
I'd like to add that I may be wrong with some of these definitions. I'm not exactly well-versed in this.

>>10167493
> why include K at all
because f' = 2/3 f does not have a single solution if you don't specify some additional condition. K was a constant of integration, but it became a factor in the process of isolating f(x). Let me show you:

[math] f' = \frac{\mathrm{d}f}{\mathrm{d}x} = \frac{2}{3}f [/math] so [math] \int \frac{ \mathrm{d}f } { f } = \int \frac{2}{3} \mathrm{d} x [/math]
now integration gives
[math] \ln f = \frac{2}{3}x + C, \ C\in \mathbb{R}[/math].

>>10167493
>>10167601
> why include K at all
Now you apply the exponential to isolate f:
[math] f = e^{C + \frac{2}{3}x} = e^{C} e^{\frac{2}{3}x} [/math]. But that now describes only positive solutions. The ODE is valid for negative values also, so instead of e^{C} we write a different constant, for example K, that can assume all real values (including 0 in this case, because f==0 is a homogeneous solution).

Now, with the method of integrating factor, you don't need a separate step to find the particular solution. Instead, you find a factor function [math]\mu(x)[/math] that will transform the inhomogeneous ODE into a simpler one, specifically so that [math]\mu f' + \mu' f = (\mu f)'[/math]. Tell me if you want more, or can get the rest from a search engine.

Is it at all possible to synthesize Pentobarbital with home equipment?
For personal use of course

>>10167601
>>10167605
Thanks, I understand better now. Sorry for the late answer

>>10167590
If radioactive material decays, there's less of it over time, but the remaining material is just as radioactive. The amount of decays per kg of material, say, is constant. I just looked up that potassium has a radioactivity of around 30 Bq/g.

Your result of some nanobecquerel is a little confusing, what material (and amount) were you looking at? Did you calculate the decay rate for a single atom? I suspect you were missing some huge factor in there, like the Avogadro constant.

>>10167903

>>10168103
ty lad!

>>10167470
Yes, basically I need a very basic continuous approximation of the signal. It's been a while since I studied signal theory and I feel like I'm missing something..

>>10158554
Recommend me some good maths books? I'm starting to feel interested on them.

someone help with labview please

>>10168201
Ok but what kind of signal is it? You said "find peak" and "first harmonic", do you mean the first local maximum (lowest frequency)? How far away is the noise floor / how do you want to distinguish between signal and noise?
Maybe those questions help pinning down what exactly your problems will be..

>>10167969
Oh, that number is irrelevant. It's literally for 50k 210Po atoms which is why it's super low.
Your explanation makes sense; activity is constant on a per-gram basis, which is why it may not be that useful when mass changes over time (unless you're doing some integration voodoo). And turns out there are better methods to calculate decayed atoms in a given time like [math]N = N_0 \times (\frac12)^{\frac{t}{t_{1/2}}[/math] where [math]t_{1/2}[/math] is half-life (I don't know why I'm not using lamda instead but it's what I've been taught) and [math]N_0 - N[/math] will result in the number of atoms decayed (since the former is the initial number of atoms and the latter is the number of atoms after some have decayed)
In any way, thanks for the insight.

>>10168351
That's a pretty specific question, champ.
Here's some equally specific advice. LabView has a "formula node". Put C code in there, skip the silly graphical programming. Good luck.

>>10168379
I have to do the project (sr design) in labview unfortunately. Need to convert a jpg of a waveform into a waveform graph on the front panel and have no idea what im doing as ive barely used it in the first place

>>10168417
show example jpg.

>>10166198
>>>> LAB VIEW

What a fucking load a fucking crap
Like holy shit
Jeez
I hated it soooooooooooo much

It’s useful yes but the programming is so annoying plus you can’t zoom in or out

As for your question, I would assume sending many impulses and seeing how far apart they are would help tell you something about their speed and or time hence telling you about the distance

And you could also see how much the signal decayed

>>10168245
Could you narrow your question a bit? There are many fields of math and many good books for them.

>>10168423
Just any plot like pic related, some only have x-axis, some may have both x axis and y axis. What I am doing right now is just removing the axes from the pictures and then scaling it to the axis values then graphing them, but I feel like there might be a simpler way to go about this

>>10168455
>any plot like pic related
If that is truly the extent of your knowledge about what kind of pictures you need to extract function values from, I don't see an easier way.
Were they only sinusoids, for example, you could sample the picture - using the "Vision module" (or whatever they call that stuff now - along vertical lines and reproduce the waveform that way.

>>10167097
Really nice answer, thanks man.

>>10168489
okay thanks, i will just keep doing my monkey method

Does the exponential ansatz work when solving ode's because they are orthonormal and you could use chebychev or some other orthonormal polynomials instead, or does it just work because you know the solution will some kind of wave?

>>10168245
>>10168447
Yes, I was too dumb to really get on them when I was young.
Now I feel the urge to know more about math and climathology (I know thats not related, but appreciated if books for that too).
Thanks.

1. How do we solve the multivariable limits? Speaking about [lim (x, y) -> (0, 0)] and [lim x -> 0] [lim y -> 0] and vice versa. While I do somewhat understand the technique, what makes me infuriated is being unable to derive a substitution.
2. How can we determine that function in R^2 [like z = (x^2 * y^2) / (x^3 + y^3), whatever] is differentiable and/or continuous on the point? Given O(x_0; y_0), I calculate then a [lim (x, y) -> (x_0, y_0)], if limit exists, then it's enough. What did I miss?

>>10168685
http://tutorial.math.lamar.edu/Classes/CalcIII/Limits.aspx

I'm filling out grad school apps right now.
Most of my application is solid, and my GPA is not bad (about 91%), but the first two years of my undergrad were absolutely fucked. Multiple dropped semesters, failed courses, grades in the 50s-60s, etc.

Should I mention this in applications or should I just ignore it? I'm pretty sure I can frame it in a positive light rather than whining about circumstances, because I got my shit together and my grades since then have been consistently mid-high 90s, but I'm not sure if I should just let committees draw their own inferences.

>>10168910
no one will care that you fucked up early if you made up for it in your later years.

Trying to show for which permissible reals [math]f(x)=x^{a}[/math] is contained in [math]L^{2}[0,1][/math]. Is it sufficient to note that [math]\displaystyle||f(x)||_{2} = \frac{1}{\sqrt{2a+1}}[/math], which is defined only for [math]a > \frac{1}{2}[/math] ?

>>10168995
>defined only for a>1/2
You mean defined only for [math]-1/2 \lt a[/math]?

>>10168995
Yes, was a typo.

>>10169005
>>10169006
Or would I just have to show [math]|f|^{p}[/math] is integrable?

>>10169012
[math]|f|^{2}[/math]*

if you have a pumping system, and start closing off a valve in one of the pipes, cavitation begins to occur. Inlet pressure of the pump increases, while outlet pressure decreases, but what does this have to do with Net Positive Suction Head (NPSH)?

Or do the air bubbles occur at the outlet of the centrifugal pump and collapse at the valve 90% closed?

i guess that second part is correct, can someone just tell me how this relates to NPSH for a centrifugal pump?

Why is the top right part of the matrix 2^100 - 2*5^100, and not 2^101 -2*5^100?

>>10163816
>mainly focused on lasers, optics, and photonics, but recently got interested in computer vision and image processing (CS)
I don't think there's any issues in having coursework in two different areas, but when it comes to research you want to focused enough that you can actually make some tangible progress before you apply. By tangible I don't necessarily mean a paper, but at least proof of effort in the form of some preliminary results and the sweet letter the guy you work under will write. You can definitely get into a PhD program without research experience. I will say this, depending on who you work with you could possibly do both. At least in the context of medical imaging both developing non-intrusive probes and taking that data to analyze it in a way to gain sharp results are of equal importance, so I think trying to understand both sides and working in them is justified to some degree.

If [math]f(x)=g(x)[/math] a.e. on [math][a,b][/math] will [math]\sup\{|f(x)|: a\leq x\leq b \} = \sup\{|g(x)|: a\leq x\leq b \}[/math]? I'm on the fence about this. I first considered looking at [math]f(x)=x[/math] and [math]g(x) = \begin{cases}x &, -1\leq x \leq 0 \\ 2 &, x=0 \\ x &, 0 < x \leq 1 \end{cases}[/math], but this felt scummy since the supremum's didn't equal to begin with. I guess I'm wondering if there is a strong counter-example, i.e. two functions equal a.e. with equal supremum who's respective absolute values differ in supremum.

>>10169237
No.

please help me with physics, i am too much of a brainlet...
A 15 kg crate is moved along a horizontal floor by a warehouse who’s pulling on it with a rope that makes a 30 degree angle with the horizontal. The tension in the rope is 201 N and the crate slides a distance of 10.0 m. The coefficient of kinetic friction between the crate and the floor is 0.4. Calculate the change in kinetic energy of the crate.

>>10169244
Think I found one
[math]f(x) = x-1 [/math]
[math]g(x) = \begin{cases}x-1 &, 0\leq x < \frac{1}{2} \\ -\frac{2}{3} &, x=\frac{1}{2} \\ x-1 &, \frac{1}{2} < x \leq 1 \end{cases}[/math]
so [math]\sup f = \sup g[/math] but [math] \sup |f| = 1 [/math] and [math]\sup |g| = \frac{2}{3} [/math] , right?

any takers?
>>10169385

>>10169275
I don't think you need anything so complicated. Just take something like
>f(1) = -1, f(x) = 0 otherwise
>g = 0

Why do you get 2 different wavelengths of xray when you generate some of that shit?

>>10169271
Just find the work done on the box. You have the answer almost spelled out for you at that point.

>>10169578
Nevermind I got it. One is when n=2 electron fills n=1, and the other is when n=3 fills n=1. The latter has higher frequency (higher energy) but lower amplitude (happens less often). And the former is the "characteristic" one.

I have an obsession with drinking enough water to make my urine clear and I make sure to monitor it every time I piss. Is this a psychological evolutionary advantage or just autism?

>>10169403
What don't you understand about the answers you got there?

Wtf do I major in bros? I was dead set on Aerospace Engineering since 14, i’m a senior applying to unis now and my research suggests that engineers make jack shit. The dudes at /eng/ only further probe this. In fact so many majors besides medicine make jackshit unless you have daddy working at x firm waiting to give you a job.

>>10169091
It's an error. The top-right entry should be 2.2^100-2.5^100.

>>10169753
>or just autism?
yup

Suppose there is a river and I build a dam on it. Less water will flow through the turbines than the pre-dammed river. That means a reservoir will form. But wouldn't that reservoir just keep building up until it overflowed everything? I know they add spillways, but is the combined water flow of the turbine chute and the spillways equal to the flow if in the pre-dammed river?

Also, why don't they build dams where the entire volume of water is directed towards the turbines?

Let V, W be vectorspaces and f: V -> W a linear function. Let U be a subspace of Ker(f). Now define g: V/U -> W with g(v+U) = f(v) for all v in V.

How do I show that Ker(g) = Ker(f)/U?
I know that for all v in Ker(g) that v is in Ker(f), but I need it to be Ker(f)/U and the other way around of course.

Is it possible to simplify the value exp(ab)/exp(ac), where 'a' is a variable?

And by simplify I mean eliminate 'a' from the ratio.

>>10170384
that‘ll be [math](e^(b-c))^a[/math]

>>10170384
>>10170392
Jesus christ I hate virtual keyboards.
[math]\frac{e^{ab}}{e^{ac}} = \left(\frac{e^{b}}{e^{c}}\right)^a = (e^{b-c})^a[/math]

>>10170384
[math]e^{ab} = (e^{b})^{a}[/math] and e^a/e^b = e^a-b

>>10170295
I hate quotient groups so much.
h: V->V/U.
Show that h(ker(f))=ker(goh)
Just do some drawings and call it a day.

>>10170396
>>10170392
>>10170399
Yeah I realize I was supposed to make a substitution for a value which cancelled the variable(s), but I'm still left with a constant which doesn't cancel out, but I guess you can't cancel that stuff out when it's an exponential.

>>10170404
Would love to call it a day with these quotient groups, they are damn confusing for me cuz the elements of it are so weird...

>>10158554
Hey anons. I'm looking for some resources to improve critical reading, quantitative reasoning, written communication and other generic test subjects. Any books/links will be greatly appreciated.

What's the "asymptote" between exp(x) and ln(x)?
I know that's badly worded but you know what I mean. The exponential and natural logarithm functions are symmetric but what's the equation of that particular axis

>>10170500
It's the line that never crosses either graph. Basically, draw both functions and try to slip a line between them.

>>10170553
Oh, right, you want the equation.
Assume exp(x)=x had a solution. Then there's no asymptote, because exp(x) and ln(x) cross.
Thus, y=x.

>>10170447
learn logic and mathematical proof. read Euclid's elements

>>10170500
the symmetry axis is y = x since log(exp(x))=x

I feel like the answer is easy but I'm really not so sure anymore, how can I simplify this?
Do I just multiply each element of the left bracket with f and then multiply those terms with the right bracket?

>>10170295
[math]\ker(g)= \{v+u_1 \in V/U : g(v+u_1)=0_W\} =\{v+u_1 \in V/U:f(v)=0_W\} =\{v+u_1 \in V/U: v \in \ker(f), u_1 \in U \} = \{v+U:v \in \ker(f)\}= \ker(f)/U [/math]
Am brainlet too but doesn't this simply work?

How can I show that the logarithmic derivative of a function is unique up to a multiplicative constant?

That is, if [math]\frac{f'(x)}{f(x)} = \frac{g'(x)}{g(x)}[/math], then [math]f(x) = \lambda g(x)[/math] for some lambda constant. This really sounds like Cauchy's mean value theorem to me, but I don't know what to do with it.

Having a bit of trouble showing [math]L^{\infty}[a,b] \subset L^{p}[a,b][/math].
If [math]f\in L^{\infty}[a,b][/math] then [math]f[/math] is measurable and [math]\text{ess}\sup{|f|} = \inf\{M:f\leq M \hspace{0.1cm} \text{a.e.} \} <\infty[/math] . So [math]f\leq M^{*}=\text{ess}\sup{|f|}[/math] a.e. I know that if [math]f[/math] is measurable and bounded, then [math]|f|^{p}[/math] will be measurable and bounded, hence integrable. How can I make the jump from bounded a.e. to bounded or is there some other results I can invoke?

>>10170693
Sure does, but you goofed the notation a couple times.

>>10170766
perhaps I could use a convergence theorem and show it is at least bounded above by an integrable function? not sure how to set it up at the moment, but it's my only thought

I'm looking for a paper on a home experiment, specifically with results.
In order to test the rate of photosynthesis you are to place some sort of pondweed into a beaker and shine a light on it, you are then to count the number of bubbles that it produces.
I can't procure pond weed so I need to steal some other results.
Thanks.

This may be retard tier, but can someone explain to me what a non-selective ion channel is?

A car with a mass of 5000 kilos is driving on a curved road whose radius is 200 meters, at a speed of 100km/h. What should the angle of the curve be, in order for the car not to skid?

Where the fuck do you even begin, I wasn't even given the friction coefficient?

>>10170792
Yeah it was, I found it after looking in Wikipedia

>>10170762
>f'(x)g(x)-g'(x)f(x)=0
>let, without loss of generality, f(a)-g(a)>0 for some a
>then f'(a)-g'(a)>0, or f'(a)=g'(a)=0
>if there is b>a such that g(b)-f(b)>0, then there's c such that [f(c)-g(c)]'=f'(c)-g'(c)<0, or g'(c)-f'(c)>0 by the mean value theorem
>but then g(c)>f(c), which leads to the necessity of a point d between c and a, and thus in any interval x>a there's some point where g(x)>f(x), and thus some point where both are zero, which contradicts continuity
Dedekind's axiom finishes the job.

>>10170794
If we know the radius, we know the curve. Not sure what you want.

Job outlook on computer vision? Thinking of specializing in it for grad school (MS or PhD?) from physics major/CS minor as it seems pretty interesting based on the class ive had over it

>>10170794
>>10170847
The question is asking about the banking angle, and a hint is that you can do without the friction coefficient if you make the banking angle so that the car, at the given speed, experiences a gravity perpendicular to the road.

>>10170773
>>10170693
Yeah you're right, elements of [math]V\U[/math] should be cosets of [math]U[/math] containing some [math]v \in V [/math] so replacing [math]u_1[/math] with [math]U[/math] (and omitting the [math]u_1 \in U [/math] part in 3rd equality) seems to do the trick.

Hello channel!
Im trying to prove something regarding the euler function (call it p) (for m,n on natural numbers barring 0 and 1)
THE CLAIM: p(mn) is greater than or equal to p(m)p(n)
I wrote them as in their product formula and it seemed evident considering nxm(chunk of product formula for 1-1/p and1- 1/q (m and n respectively)) will be greater than n(1-1/p)m(1-1/q) since theyre both greater than 1. Am i missing something here or did I go about it the wrong way? It seems a bit to simple and I'm not confident with this.

>>10170693
many thanks

>>10170649
Distribute it out all the way, and work from right to left. Operator algebra is tricky the first time you work with it. Some of the intuition from regular arithmetic doesn't carry over.

>>10170879
Yep and I've no idea how to do that...

Say you jump as high as you can on Earth, and you end up travelling at 30 ft/s at your maximum speed. If you tried that same jump on the Moon, would your maximum speed still be 30 ft/s?

>>10170766
Here, this paper is what you're looking for.
https://www.jstor.org/stable/2322503?seq=1#metadata_info_tab_contents

>>10171024
The centripetal force is [math] F_c = \frac{mv^2}{r} [/math].. so the cosine of the angle between the vectors is [math] \tan \alpha = \frac{F_c}{F_g} = \frac{mv^2/r}{mg} = \frac{v^2}{rg}[/math]

>>10170766
>if f belongs to [math]L^{\infty}[/math], we set [math]g=||f||_{\infty}[/math]
You can finish, can't you?

>>10171128
[math]g=||f||_{\infty}[/math] bounds [math]f[/math] a.e., so [math]f[/math] will be integrable. So at least [math]|f|[/math] is integrable, but what of [math]|f|^{p}[/math]?

>>10171142
g^p bounds it a.e.

>>10171147
I see. Thanks.

im prepairing for uni claculus and im a mathlet, do i have to consume all of the themes in algebra including factorization or can i focus on solving equations and graphing functions?

>>10171191
can you simplify this?

>>10171201
Yeah, but you shouldn't post here until you're eighteen.

>>10171232
Idiot. The extent of algebra you need for calculus is no more than simplifying things, trig id's, and basic properties of graphs.Calculus-I is the easiest course on planet Earth period.

>>10171201
maybe if i find the case, but i dont want to memorize all that stuff, im wondering if i can avoid doing it

>>10171191
You need to be good at factoring to get through calculus. Solving integrals (the most prevalent "problem" in calculus) requires you to be able to rearrange algebraic expressions more quickly and thoroughly than you have in any prerequisite class. In fact, there are algebraic techniques more difficult than factoring (e.g. partial fraction decomposition) that you'll be expected to master in the span of a few days. One of the trickiest parts of calculus is not just factoring correctly, but factoring appropriately; if you have trouble with any of the algebra in and of itself, chances are it will be useless to you when you need it.

just had first internship this summer and wondering how to add it to resume. Should I add the name of the product I worked on or be generic and just say "product" instead?

>>10171201
I can with my calculator. Is that good enough?

>>10171258
Absolutely not. Algebra is the 'busy' work of calculus. You should be able to simplify things like that and more complicated things (involving radicals, logarithms, rational functions, etc) in a short amount of time without CAS'.

>>10170925
Pls halp.

>>10171261
I didn't notice how many repeating terms there were in there. That won't keep me busy for long.

What about expressions several times longer than the one in the pic that need to be expanded before they can be simplified?

>>10171261
>t. Only knows calculus
Calculus is the busy work of linear algebra

>>10171287
Have taken calculus 1-3, two courses in linear algebra, and 3 courses in analysis. There's hardly any linear algebra in calculus 1 unless you force it in there.

Is it normal for a tech. calculus 2 class to get an average of ~40 on an exam?

And why does retaking a class not give credits :(

How in the H**K do I isolate y?

x = 3y^2 + 6y

So far, I've gotten up to:

x/3 = y(y+2)

and now I'm stuck.

>>10171354
you can't

>>10171358
Maybe I'm doing the first part of the question wrong then because it's asking me to find the inverse of

f(x) = 3x^2 + 6x

Why is it that if [math]f\in L^{2}[a,b][/math] then [math]f\in L^{1}[a,b][/math]? It should boil down to showing that [math]\int_{a}^{b} |f|^{2}[/math] exists [math]\implies [/math] [/math]\int_{a}^{b} |f| [/math] exists, but am not sure how to show that.

>>10171368
x = 3y^2 + 6y+3-3
x=3(y+1)^2 -1
(x+1)/3=(y+1)^2
y+1=plus/minus sqrt((x+1)/3)
y=plus/minus sqrt((x+1)/3) -1

>>10171391
God damnit I made a school-tier mistake there
x=3(y+1)^2 -3
(x+3)/3=(y+1)^2
y+1=plus/minus sqrt((x+3)/3)
y=plus/minus sqrt((x+3)/3) -1
There

>>10158554
Pic 1/2
Question incoming

>>10171398
Whoops
Pic 1/2

>>10171372
Use holder inequality

>>10171403
So [math]||f\cdot 1|| \leq ||1||_{2}||f||_{2}[/math] which bounds the integral of [math]f[/math] above, hence exists?

>>10171402
So the second para talks about taking the derivative and proving force and velocity are in phase for resonance frequency. My question is that,looking at equations, doesnt this apply to all forced frequencies? Nothing in the derivative says force and velocity are in phase only for resonance frequency?

>>10171394
>>10171391
Thank you.

How do I find the average rate of change between the roots/zeroes of a function?

If it's

0 - 0/whatever, isn't it just going to be 0?

>>10171321
Depends on the school - or more specifically the professor

Because life ain’t fair

>>10171414
do you mean frequency of roots along an interval?

>>10171368
I know it’s not as elegant as completing the square, but would the quadratic formula work here?

>>10171417
I... don't know. I'm a complete brainlet.

The exact question is this:

"Given the function f(x) = x^2 + 5x + 4, determine the average rate of change between the roots or zeroes of the function."

>>10171414
Integrate the function’s derivative and then divide by the length of the segment?

I have no idea what I’m talking about.

>>10171429
Just find the roots of your polynomial and have at it.

>>10171429
>>10171443
Because it's the roots, just guarantee that there are two roots by discriminant, and the rate of change will be 0 between the roots.

>>10171443
But the root is always 0 right? So the average rate of change is always going to be 0 between two roots? I'm just wondering if this is a trick question or if it's just as simple as that.

Also, would anybody be willing to check my answer to this question:

Determine the value of "a" so that the average rate of change of the function f(x) = x^2 + 4x + 2 on the interval -4<=x<=a is 2

I did:

2 = (f(a) - f(-4))/(a+4)

And then plugged in values and did algebra and shit until I got

a = -4 and a = 2

>>10171449
How is the root always zero?
f(root) = 0
But root need not be zero

>>10171469
Sorry, what I meant was, the two Y values are zero, so the average rate of change between those two values will always be zero, right?

>>10171429
Roots are -4 and -1 (use mid term split)

>>10171471
Oh didn't see your main ques.
Yup always zero

is any research useful research for undergraduate experience? I am majoring in electrical engineering and want to specialize in lasers, but the few labs on campus are full or dont accept undergraduate students. Would something unrelated but still in a STEM field be useful experience for grad school applications or no?

Suppose [math]f[/math] and [math]g[/math] are defined on [math][a,b]\to\mathbb{R}[/math] and are equal almost everywhere. Should it be that their essential supremums: [math]\text{ess}\sup{f} = \inf \{ M : f\leq M \hspace{0.1cm} a.e. \}[/math] and [math]\text{ess}\sup{g} = \inf \{ K : g\leq K \hspace{0.1cm} a.e. \}[/math] be equal? That is [math] \inf \{ M : f\leq M \hspace{0.1cm} a.e. \} = \inf \{ K : g\leq K \hspace{0.1cm} a.e. \}[/math]. It seems to be an easy question but I can't formalize my thoughts

>>10171581
is it as simple as [math]f=g[/math] a.e. [math]\implies f-g = 0 \hspace{0.1cm} a.e. \geq \text{ess}\sup{f} - \text{ess}\sup{g} \implies \text{ess}\sup{g}\geq \text{ess}\sup{f}[/math] and similarly [math]f=g[/math] a.e. [math]\implies g-f=0 \hspace{0.1cm} a.e. \implies \text{ess}\sup{f}\geq \text{ess}\sup{g}[/math] ?

For #2 part b, do I just apply the comparison theorem and then I'm done? Surely that isn't correct?

I have an 80% in my class which counts for 85% of my grade.
The final is 15% meaning if I get 100% on it, I will have a 95% in my class.
How can I calculate what % I need to escape with 90%?

>>10171975
>>10171975
New new

>>10171971
multiply the score by the weight to see how it contributes to your overall grade, for example an 80% in a section weighted at 85% of total means that your total grade right now is .8 * .85 = 68% (not including final) so the highest score you can get is an 83% assuming that you ace the final

if you want to know how well you need to do to get say a 75% in the class, subtract the known grade from 75% and divide by the rest of the weight possible, (.75 - .68) / .15 = 47%

>>10171910
I'm guessing you need to use that if f(c)>0 then f is >0 on an interval around c. I would probably just use an e-d argument. For e>0 there exists a d>0 s.t. for |x-c|<d, |f(x)-f(c)|<e. Then the integral is larger than 2d*(f(c)-e).

>>10171910
By continuity, there's |x-c|<ε that implies |f(x)-f(c)|<f(c)/2.
We do a partition a, c-ε, c+ε, b, and the lower sum on it is strictly larger than zero. Done.

>>10171971
0,8*0,85+x*0,15=0,9
0,15x=0,22
x=0,22/0,15~1,47=147%
If x=1, you get 0,68+0,15=0,83=83%

IM RETARDED HOW THE FUCK DO I DO THIS SHIT AAAA

>>10172170
http://www.sosmath.com/trig/Trig5/trig5/trig5.html
sum difference formula

How do I get into math again and start counting like champ again? I literally suck at math and can't force myself to do serious countings (despite that I study engineering), because I skipped it in school for 4 years, due to laziness and shitty habits, and wish to get back into it.

>>10172229
>counting
Whachu mean?
Also, *despite studying

>>10172032
>>10172046

I think that's the wrong part, I want the part that talks about g(c) > f(c)

>>10172260
You know 1, 2, 3... I keep forgetting what comes after 3.