/SQT/ - ask your math/science questions

How do you show a=1 given x^a = x using logs? I forgot how to do this and reduced a math proof to this algebra step.

Other urls found in this thread:

arstechnica.com/security/2017/03/hack-that-escapes-vm-by-exploiting-edge-browser-fetches-105000-at-pwn2own/
oeis.org/
en.wikipedia.org/wiki/Pascal's_triangle
twitter.com/SFWRedditImages

x=x^1 so if x^1=x^a then log(x^1)=log(x^a) or equivalently 1logx=alogx or equivalently 1=a

Thanks: I totally forgot you could rewrite log_{x}(x^1) as 1 log_{x}(x). That totally makes sense. Thank you!

I'd rather show this using patterns:

x^4 = x*x*x*x
x^3 = x*x*x
x^2 = x*x
x^1 = x

You need x^1 = x in order to keep the pattern consistent.

Then, define a as the exponent to get the general case:

x^a = x*x*x*...*x [where the number of x's is a]

This way, you don't need to introduce the concept of "log" to see it -- so the result is immediately understandable and more intuitive.

that only works if a is a natural number though...

A resistor reduces the amount of Q that flows every second, it reduces the current. So it wouldn't lower the voltage right? Because the amount of energy every Q has, will maintain.

Why does the voltage get lower after flowing through the resistor in pic related?

Ass Crack Man Did /Nothing/ Wrong.

I'm reading up Strang's Linear Algebra and appiication to learn about linear algebar as a step to stop being a brainlet
How long (approximately) should I take to finish the topic? and is there anything I should take be aware of while learning Linear Algebra?

visualise things in three dimensions in your head

jesus fuck delete your post and your life

Because a current flowing through resistive material requires a voltage drop. If there is no voltage drop, then no current is flowing because both points would have the same potential.

how would i go about solving this problem?

>the result is immediately understandable and more intuitive
and entirely useless unless [math] a \in \mathbb{N} [/math]

Once you open the switch no current flows between the left and right loop. Then what you're solving is LdI/dt+IR=0 in the right loop with the initial condition for I that you found

>entirely useless unless a∈N

That reminds me: complicated numbers like 3, 42, and 696969696969 can be made much simpler by defining them as a sequence of marks:

4 = ||||
3 = |||
2 = ||
1 = |

This way you don't need to introduce redundant alien symbols like "9", so equations like
|||||||| * (||||| - ||) = ||||||||||||||||||||||||
become immediately understandable and more intuitive.

If I'm driving a car at a constant speed does the amount of force the engine is applying depend in any way on the mass of the car or is it just the air resistance?

If I'm cruising in a vacuum at constant speed then I don't need to use the engine at all, right?

everyone learns the addition / subtraction / multiplication / division algorithms for base 10 very early on, so that's pointless

does anybody have the Veeky Forums-approved guide to computer science textbooks?

mechanical resistance likely depends on the mass of the car

did you miss the sticky brainlet?

shut the fuck up you retarded newfag, the sticky is shit

if the Veeky Forums-approved guide in the sticky is shit why did you ask for it brainlet?
also i've been here longer than you

>mechanical resistance
As in the friction of the tires angainst the road and whatnot? Yeah, I guess that might be a different story.

if you had been here longer than 5 minutes then you would know that the guide in the sticky is NOT Veeky Forums approved you tremendous liar faggot

a group of people made a new guide several months ago, and it has several bad things but it's still decent. on the other hand the one up there right now is COMPLETE SHIT and it has always been complete shit.

fucking baboon

>fell for the CS meme
jokes aside, I have a question that's really making me mad as fuck
apparently the following answers about Virtual Machines are wrong, anyone know why?

a. Virtual machines can be easily transferred from one computer to another TRUE
b. Processes running on a virtual machine run more slowly TRUE
c. Virtual machines allow one operating system to be ran on top of another TRUE
d. Servers running on different VMs cannot communicate with each other TRUE
e. It is safe to run untrusted executables inside a virtual machine FALSE
f. Virtual machines can be used to restrict processes' memory usage. TRUE
---------------------------------------------------------------------------------------------------------------
The following is a UTF8-encoded Unicode string. Each group of 8 binary digits represents one byte of the string. 01000001 11110001 10110000 10110110 10001010 00110110 01110010
Answer: 4 characters. three ASCII, 1-byte chars + one 4-byte character = 4

i've been here since the first day this board opened

the sticky is the only Veeky Forums approved list

whatever other 'guide' you're referring to is probably made by someone as brainlet as you

they should be correct.


VMs can be easily transferred, no need to explain this simple fact

Processes running on the VM run more slowly, obviously, even with VT-X there's a MEASURABLE delay, it's mathematically true for fuck's sake

VM allow one OS to be ran on top of another, true, because the host OS runs on top of the VM

Servers running on different VMs cannot communicate with eachother, FALSE (sorry, I made a mistake in the previous post, it's not true), communciation is possible since internet connection is possible through a VM

safe to run untrusted executables, TRUE, because that's what the lecturer said, but if I were to be fully correct here I'd say it was false because exploits have been found for VMs too that allow you to go outside of it

VM can be used to restrict processes memory usage, TRUE, one of the most basic shit you can do in a VM is set a RAM, storage and core limit to the OS, any babby knows this

you're either a liar or SO FUCKING RETARDED that you don't realize how ABYSMAL that fucking piece of shit up there in the sticky is. every Veeky Forums regular knows it's absolute shit

>d. Servers running on different VMs cannot communicate with each other TRUE
Well, I knot for a fact that's not true because I've personally done that. I don't really know how that works though, it's just an option you set in VirtualBox.
>e. It is safe to run untrusted executables inside a virtual machine FALSE
Not safe to the VM, but otherwise what could happen?

what's wrong with it? you already admitted whatever this other ""guide"" you're talking about has 'several bad things' on it

sorry about that, i said in the next post that I switched them around by mistake

so D is actually false, I agree with you
and E is true, so I agree with you on that as well

is anything else wrong, besides that? apparently I lost some points on it but I don't see where

also, breaking free from a VM is possible: arstechnica.com/security/2017/03/hack-that-escapes-vm-by-exploiting-edge-browser-fetches-105000-at-pwn2own/

yeah I told them they were idiots for several small things I personally hated but god, their guide was really good in general

so I have already posted about this several times, let me be short and on point.

specific to math:
the famous guide posted by "an user" is clearly shit for anyone who knows any math. good calculus book, good book for intro to proofs, then suddenly a TERRIBLE book for independent study of real analysis (rudin is good for lecturing but SHIT for studying alone) and all of a sudden it jumps to graduate analysis. what the fuck? no mention of literally all other math. there's a second good calculus book for some reason.
the "guide more like notes" thing is a very short comment that can be very easy to misinterpret. the calculus - linear algebra - diff eq is the standard engineering "math" sequence and you don't need me to comment on this

both math and computer science:
then there's a huge assortment of tons of shit that hasn't even been sorted by someone who knows what they're doing. some of the resources are SHIT, some of the resources are good, some of them are for highschool, some of them are graduate level, some of them are meant for lecturing, some of them are encyclopedic references, some of them are study textbooks, it's just a clusterfuck.

in math there are some charts done by a 5 year old who doesn't know what math is and a list of random math topics around too, why?

I haven't checked the other fields very closely (I have seen these two so many times it hurts) but I assume they're shit too

how do i change the cursor in mathematica from horizontal to vertical

how do i keep it from changing from vertical to horizontal

I'm stuck on a question

>Your friend wants to test your understanding of waves. She weaves together one end of two different ropes (one with greater mass density than the other, but each with the same radius and length) to make a single rope. You are blindfolded and asked to hold the other end of the stretched rope. Your friend expects you to determine not only which end you are holding (the heavier or lighter rope), but also whether your friend used a fixed or free method of attachment to the pole. You think for a minute, then laugh and declare that you can even estimate the ratio of the lenear mass densities! While she is speechless, you create a single wave pulse with your hand.

I've concluded that I can find whether a fixed or free method is being used by checking to see if the reflected pulse is inverted or not respectively, though I am having trouble finding out which end I would be holding and what the ratio of linear mass densities would be. Any advice?

>You think for a minute, then laugh and declare that you can even estimate the ratio of the lenear mass densities!
I love it when science questions really get into the roleplay.

if x and y are integers, how do i prove that x=+-1 and y=+-1 are the only solutions to xy=1

fundamental theorem of arithmetic

divide both sides by either x or y

Trick question, no one answering this has any female friends.

Is there a term for when a mathematical advancement is made because somebody shoved a number where it didn't belong?

serendipity?

Oh, I was given this as an exercise last year when we were constructing the naturals and then again when doing the integers.

A simple way of seeing it:
You are working in the integers, a ring with multiplication. So

xy=1 if and only if x is the inverse of y and vice versa.

But 1 and -1 are the only invertible integers, therefore the only pair of solutions is 1 and the inverse of 1 (which happens to be 1) and -1 and the inverse of -1 (which happens to be -1).

But here you are using algebra and you are assuming that you already know that only 1 and -1 are invertible. So I give you a more elementary approach using only the properties of the order of the integers:

Suppose there exists another pair of solutions ab for the equation ab=1

By the way multiplication works, we have that either both a and b are positive, or both are negative. Lets assume first that both are positive.

Note that a cannot be equal to 1 becuase if it is then we have b*1 = 1, so b=1 which yields the solution pair (1,1) and we are assuming that (a,b) is a distinct pair.
By the same reason, b can't be 1.

Then, by the order of the integers we have that

1 < a and 1 < b
and a < ab and b < ab
but then we have
but ab = 1 so we have
1 < a < 1
Which is a clear contradiction. No such number can exist, therefore no such pair (a,b) can exist.

Now that you got the idea, I'll let you figure out the case when both a and b are negative.

please this is driving me nuts

the last time i could find it on google but now it's ungoogleable

Lmfao you should probably end it all by now

I have a question about brown sugar. Why don't they sell the raw syrup that still contains the molases, instead of adding molases to already refined sugar? Wouldn't it be cheaper and more nutritious?

If I've already taken two semesters of Calculus, should I go back over a textbook like Apostol or just keep rolling?

No, don't waste your time learning calculus over and over again.

I went to a gifted highschool program, and straight up failed out and been a depressed mess sitting at home since.
I'm now considering doing an iq test to figure out if i'm actually a dumbass or if I just wasn't applying myself, and if I'm not a dumbass I'm going to give the sciences another shot, and if I am a dumbass I'll figure out what to do with my life from there.
Is this a good idea or no?
I've never done an iq test, are these things reliable?

"learning calculus right all over again" is what analysis is about

IQ tests are shit and will be useless for your purpose

were you fucking applying yourself or not? be honest to yourself and there's your answer, no need to jump around the issue. go study and stop feeling sorry for yourself if you want to be someone

you can literally do anything you want if you get off your ass and work hard

you're obviously not applying yourself. you're a dumbass not because of a lack of genetic potential but for your failure to grow up and become a responsible adult

i wasn't applying myself, that's the issue
what I don't know is what would have happened had I applied myself
>you can literally do anything you want if you get off your ass and work hard
that's not true mate. it's very possible that I could push myself to my highest capabilities and still not be a successful physicist/mathematician/etc. It's also possible that I push myself and can be one of those things, but I'm just wondering what's the best way to figure out if I'm cut out for it or not for fear of pursuing something I'm not quite qualified for and only realizing that fact years later.
and just as a sidenote I'm no longer depressed. Just trying to figure out what's a viable career to pursue.

this desu

How should I take notes and study a book like Lang's Algebra that has 1000 pages and still remember everything I studied?

> it's very possible that I could push myself to my highest capabilities and still not be a successful physicist/mathematician/etc.
No. Seriously. Dumb people who work hard can go the long way in math. Intuition is something you train if it doesnt come naturally. I dont know if youll believe me, lets just say I'm qualified to give this advice

i mean
i don't really believe u
lol
what's your qualifications

i didn't even realize intuition was a math thing bro

Is there anything significant about the set of numbers that can be produced by raising a prime number to the power of another prime number?
4, 8, 9, 25, 27, 32, 49, 121, 125, 128, 243, 343, 1331, 2048, 2187, 3125,...

Log base x isn't a thing, dummy.

x^a can be rewritten as e^{aln(x)}, so you get aln(x)=ln(x).

This only works for nonzero x btw.

not really.

here's a pretty nifty site for questions like this:
oeis.org/

I knew about that site, but for some reason didn't think it would have a search function that worked like that. brb, drinking bleach.

no worries user. now you know!

>Is this a good idea or no?
Judging your own self worth based on a number is a horrible idea.

Whatever the result will be it will be negative for you.

If it is high you are a failure because despite your intelligence you achieved nothing.
If it is low you are a natural failure and destined to fail at everything.

No result of an IQ test is ever good.


What you should do is find a goal and work towards it.
If you really want to make it in the sciences nothing is stopping you.
Working hard is a lot more important then being intelligent.

Does this function have a closed form?
f(a,b)=f(a-1,b)+f(a,b-1)
f(a,0)=f(0,b)=1
It's something really simple so I would be astounded if it didn't have a closed form.

en.wikipedia.org/wiki/Pascal's_triangle

i.e. f(a,b)=(a+b choose a)=(a+b)!/[a!b!]

I'm pretty sure it's f(a,b) = (a choose b)

it's not a choose b, its first sign that's wrong is that the definition of f is symmetry in a and b while (a choose b) is not equal to (b choose a)

also (2 choose 1)=2

and f(2,1)=f(1,1)+f(2,0)=f(1,0)+f(0,1)+f(2,0)=1+1+1=3

Why the fuck do I need LaPlace transform when it's just as long as variation of parameter?

Brainlet here, how do you go about solving basic calc problems like Optimization and related rates? To be more specific, how do you see/know what equations you must make and which ones u need to use? For example, i was doing an optimization problem and i needed to have used some geometry concepts that i had no idea about untill i looked at the solution key. How do u "see"/"realize" this?

>missed a single lecture on differential equations
>turns out it was an introduction to the Laplace transformation
>can't understand shit now

Any tips?

Try solving the differential equation with variation of parameters and you tell then why we need the Laplace transform

Read this guy's example. He laid it out pretty well.

...read a textbook.

I'm trying to derive Jeimenkos equations, I'm told to use the retarded Greens' function of the form: [eqn] G = \frac { \delta \left ( t - | x | / c \right ) } { 4 \pi c |x| } [/eqn]However when I use that I end up with an erroneous factor of c in the denominator. So I checked his solutions and he uses a Greens' function that looks like [eqn] G = \frac { \delta \left ( t - | x | / c \right ) } { 4 \pi |x| } [/eqn]Notice the absence of c here. This works, but when I check the lecture notes he consistently uses the first function. Have I missed something here?

Nevermind, figured it out.

So it seems that pascal's triangle describes the number of short paths that follow a grid between two points on that grid.

what is the use of pascal's triangle? what is pixar using it for?

Which was that page to bypass journals paywalls?

Anyone know if there's a function built into MATLAB to round down a number to an integer? So e.g. it would round any number on [0,1) to 0. Will I have to write that myself? All I can find is a function that rounds to the nearest integer.

does MATLAB not have a floor function...?

Thanks, I'm retarded.

You gain intuition with practice.

scihub

Step 1: Understand the problem

Draw a picture, label what the problem tells you, then label what the problem doesn't tell you with appropriate notation (V for volume, h for height, etc.). Usually these problems boil down to "Given dv/dt is some constant, and given dh/dt is some other constant find dx/dt when x is some constant"

Step 2: Find the relationship

Find a relationship between your variables (usually similar triangles, pythagorus, sometimes a little more unfamiliar like sine or cos law)

Step 3: Differentiate the relationship

Take the relationship you found in step 2 and differentiate it

Step 4: Plug in and solve

Plug in the knowns and solve the equation algebraically, you're done now.

Read one of the numerous DE textbooks available in your library/the internet?

>If it is high you are a failure because despite your intelligence you achieved nothing.
>If it is low you are destined to fail.

Dude one implies I'm a failure for life, the other implies I've failed to achieve to my full capabilities. That's a pretty important distinction (that I don't fully agree with, but that's more or less irrelevant for the purpose of this conversation), and if an iq test can really tell me that info then sign me up right now. The only thing I'm concerned with is if an iq test can even give me that info in the first place.

I also disagree with the hardwork thing. Pls no debate. I started to write out why I disagree but then I realized that would just lead to a lengthy debate.

Same retard again, how do I plot a function of multiple variables on just one variable with constants plugged in for the others?

is the mapping from lnx to x regular?im trying to imagine it in my head and the plane has to transform continously in a non regular way for it to make any sense.

you could just compute the constant*variable on paper and do it that way.

It's not that kind of function. Specifically I'm trying to do Euler's method and I can get it to approximate a function at a certain point but I can't figure out how to get it to plot the approximation given a certain step size, initial value, and function of that initial value.

...

post the code

Suppose your RHS is a Dirac delta function

x^a=x
a=log(x)x
a=logx/logx
a=1

Wildberger please go

I just realized this won't work when q is negative, but that shouldn't be hard to fix. Also I realized that the inputs in line 1 spell "hoax." Anyway here. I want to plot f(x) for a certain initial value and etc.

raise your power level

>a board of supposed intellectuals need to use the log function to prove something as elementary as x^a = 1

Lol at you faggots. Consider suicide.

>x^a = 1
Nobody wanted to prove that though

It's not obvious, and it's not even true for complex numbers.