/sci/ - Science & Math

>>14713547
> However, I don't see why V_DS = 5+1.5156 = 6.5156 volts.
V_G=0, V_GS=1.5156 => V_S=0-1.5156=-1.5156
V_D=5, V_S=-1.5156 => V_DS=5-(-1.5156)=5+1.5156=6.5156

>>14714495
bump for gondola

>>14714466
Big props @SatokoFag.

considering that a purple liquid reflects purple light and absorbs colours complementary of purple, would the light wavelength used in spectrophotometry of a purple solution be that of a complementary color of purple?

Is [math] \sum_{d\leq x}[x/d] [/math] equal to [eqn] x\sum_{d\leq x}(1/d)+O(1) [/eqn] or [eqn] x\sum_{d\leq x}(1/d)+O(x) [/eqn] [math]
[x/d] [/math] is the integer part of x/d btw. I dont care about simplifying it further at the moment.

How can I be good at math?

>>14716596
What's the problem?

Is this correct math?


How many different group chats you can be in with your mom and the rest of your family.
m = Number of family members - 2
[math] \sum_{n}^{m} \mathrm{C}_{n}^{m} [/math]

It seems correct, but my sister has 65 chats with mom, which seems high even if you include cousins and stuff. A family of 7 means that each other member can have 31 different group chats with mom, and 65 is double that.
I also know add + 1 to get the initial chat with mom.

>>14717217
>How many different group chats you can be in with your mom and the rest of your family.
your question is a little ambiguous, but if a group chat consists of you, your mom, and a subset of [math]n[/math] remaining family members, then the number of unique group chats is [math]2^n[/math], including the group chat containing only you and your mom. https://en.wikipedia.org/wiki/Power_set
>>14714806
wasnt me, i only give people wrong information

>>14717615
Well I only help people with useless stuff, so it must have been someone I'm forgetting about.

>>14717615
Thanks, I was also wondering if there was a simpler way to write it. 2^n is a lot simpler.

>>14716568
purple isn't a wavelength. a purple liquid would reflect red/blue colors
inb4
>hurr violet is a wavelength
you don't have a liquid that reflects near UV only

>>14714495
>how do I post math symbols (Latex)?

>>14717988
https://sites.google.com/site/scienceandmathguide/

>>14717996
no, why is latex partially but incompletely capitalized

A few Qs

What are the main areas of math at an above high school level?

Calc
Stats
Algebra etc

And what are some books to take me from, say, a very basic understanding (very) of these subjects to just a moderately good one where I can understand what formula are trying to do, notation (I don't have to be able to solve them).

I just want a good overview. Sort've like But How do it Think for PC was. Should I try dummy books or are they too simple

Just out of curiousity:
can you fit enthalpy of laptops, perse, to a machine learning model? Can you do active topologies/neural networks with this?
Sorry if this is too stupid/non-sense for /sqt/, just curious.

>>14718004
Because that's how I wrote it.
>>14718112
>Should I try dummy books or are they too simple
For dummies books read like they're written to piss me off.
But they're not too simple, they usually have reasonable (even if not ideal) coverage.

>>14718185
thanks. Unless I get a better recommendation I will try one or two

>>14718185
cute mawisa <3

How can photons mediate the electromagnetic force when they don't carry any charge?

>>14718004
Why didn’t you write it in the correct way, either?

Hey /sci/bros, Im going to enter 11th grade in 3 weeks. is it realistic to achieve all of these within the aforementioned time period?

>>14718475
Also, I am 18 years old so suck my cock, janny.

Two days ago I travelled into a black hole whilst astral travelling. This was the first time I had experienced something like this even though I often travel the space in my astral body. It was one of the most amazing experience of my astral travels. I felt I had found a resting place for my soul. I went back to the original form of the Source. Although I was there for couple of minutes, I feel like I traveled an eternity. After resting in my Source form, I watched myself turn into a light being as I exited the black hole. Last 24 hrs I feel am in a time capsule and sleepwalking...still trying to consolidate this energy into my Consciousness. I hope that these dark black holes are resting place for stars and planets as they get primed for rebirth?

>>14718478
Nice attempt at a save, but it's not gonna work. Get banned zoomie.

>>14716655
My university doesn't include calculus as a required module for CS because single variable calculus is taught in HS and multivariable calc in HS honors class. I went to a private school that didn't cover calculus. Our first math module is linear algebra and it's starting next (second) semester. I audited some LA classes and I got super demoralized.
I'm going to have to grok LA with a precalc math education.

If you turn on a flashlight in space will it start to fly?

Thank goodness for this thread.

Question:
>If other universes exist (eg: string theory turns out to be true) is it physically possible to enter one?

Question:
>is "anti gravity" a thing in physics. I'm not asking about devices humans have made, I mean is the concept legitimate.

I can't find anywhere that can give a straight answer that is not rambling useless bullshit from fuckwits who can't preface everything with a wall of text and then not answer the question anyway (eg: Quora) Something that is so obtuse even postgrads would find it painful to read. Or skitso bullshit.

thought experiment reading up on how filthy the saudis are and their problems regarding missing sewage system in Dubai for example would it make sense to dumb all the shit in the desert and turn the sand there into fertile soil? Obviously the shit would have to first be cleansed of human diseases etc. but that would seem to be a sensible option.

>>14718475
https://pastebin.com/vDHH8t17

the response no one asked for, good luck with your studying btw...

Let [math]T[/math] be an automorphism of a measure space [math](X, \mu)[/math] such that [math]T_\ast \mu \sim \mu[/math], i.e. the measures give rise to the same collection of null sets ([math]T_\ast \mu = \mu \circ T^{-1}[/math] is the pushforward measure).

Let [math]\omega_n = \frac{d T_{\ast}^{n} \mu}{d \mu}[/math], where [math]T^n[/math] denotes the n-fold composition [math]T \circ ... \circ T[/math]. I'm trying to prove the identity [math]\omega_{n+m} = \omega_n \cdot (\omega_m \circ T^n)[/math]. By the chain rule, we have [math]\omega_{n+m} = \frac{dT_{\ast}^{n+m} \mu}{d T_{\ast}^{n} \mu} \cdot \omega_n[/math]. How to simplify this expression? (Alternatively, if someone has a simpler approach, I'd love to hear it)

>>14719183
The answer to both is no.

i'm forced to elongate related work/history in my CS master thesis to 20 pages
is this normal?

>>14714495
just want something cleared up

Mag fields are created because of moving charges while Electric field are caused by static charges?

>>14718369
why do they need to be charged? if they were charged then they'd interact with electrons and there would have to be something that mediates this interaction, requiring another neutral particle in the end anyways

>>14719845
> if they were charged then they'd interact with electrons
I think that's the point. The weak and strong force carriers are charged (hypercharge and colour). So how can a neutral particle carry information about electric charge between two locations.

When using a mosfet and applying voltage to the gate that is less than the saturation voltage, is the current limited by a fixed value or a percentage of the load current?

For example, if I have a 100 ohm load with 10 volts, and I apply 50% of the saturation voltage to the gate, will I always get 50mA through the drain-source, or is it based on some fixed maximum amperage, so any gate voltage will give me the same result as long as it's a load drawing low enough current?

Why is [math]f(A\setminus B)=f(A)\setminus f(B)[/math] with [math]f:X\rightarrow Y[/math] and [math]B\subset A\subset X[/math] only true, if [math]f[/math] is injective?

>>14719076
Yes but it would be so incredibly slow that you wouldn't notice.

>>14719183
Your first question is like asking a caveman how a clutch works. For your second question; If you mean "is there a force opposite to that of gravity?" then the answer is "No" or "we haven't discovered it" (which are pretty much the same answer from a practical standpoint).

>>14719771
A magnetic field is created when atoms have their magnetic dipoles aligned. An electric field is created between two areas of opposite electric charge. What do you mean by moving and static charges?

>>14720025
The internal resistance of the material means that you could only bump the current up so much before you melt it. Using the same voltage on different mosfets would produce different currents but the discrepancy would probably be negligibly small.

>>14720159
from my physics book, specifically #1

im just trying to understand the difference between an electric field and magnetic field

>>14720075
If [math]f[/math] isn't injective then you can find distinct [math]x_1,x_2 \in X[/math] and a [math]y \in Y[/math] with [math]f(x_1) = f(x_2) = y[/math].
Let [math]A = \{x_1,x_2\}[/math] and [math] B = \{x_1\}[/math] then
[eqn]f(A \setminus B) = \{y\} \\
f(A) \setminus f(B) = \{y\} \setminus \{y\} = \emptyset
[/eqn]

>>14720174
The first thing to understand is that electricity and magnetism are both part of the fundamental force known as electromagnetism.

Electrons generate a magnetic field (because they just do, shut up) but in a normal object all these fields are unaligned so they cancel each other out. In a magnetic object, all these fields are aligned.

An electric field is created due to an imbalance of charges. To use electricity as an example, the electric field is between the negative terminal ( has too many electrons) and the positive terminal (has too few). The field is the gradient generated. It's also known as the potential difference and voltage.

AFAIK An electric current generates a magnetic field because the electrons are all moving in the same direction (from negative to positive), they're more likely have their fields aligned.

>>14720219
you're explanations makes a lot of sense. I dont know why physics books are so damn esoteric

>>14720232
The books are probably more right than I am but if you look at all the popsci media nowadays or high school science, sometimes it's worth being a little wrong if it makes it easier to grasp as a concept.

>>14714495
any for adding
activecalculus.org
to the template of /sqt/ for whom ask for first year calc material?

This question will be super retarded. Get ready.

Are season reversed on other sides of the world?
Like if I have a summer here, does it mean country on the other side having winter? In a weather terms, not time and date. Does it mean some countries winters are warm and summers cold? How does it work?

>>14720328
> Like if I have a summer here, does it mean country on the other side having winter?
Yes. It means exactly that. That's why the Australian Xmas is in the middle of summer.

>>14719771
>>14720174
electric fields are created by charges (static or moving), but magnetic fields are only created by moving charges (and/or moving observers).
the only thing either of these fields do is exert force, but they do it in slightly different ways.
>>14720025
if youre applying a low gate voltage ([math]V_{GS} < V_{DS} - V_T[/math]), then the current is obviously limited by the gate voltage.
>if I have a 100 ohm load with 10 volts, and I apply 50% of the saturation voltage to the gate, will I always get 50mA through the drain-source, or is it based on some fixed maximum amperage, so any gate voltage will give me the same result as long as it's a load drawing low enough current?
SPICE says its closer to 25mA. this is a question that unfortunately requires math to answer.
[math] \displaystyle
I_D = \frac{W}{L} \mu_n C_{ox} \left( V_{GS} - \frac{V_{DS}}{2} - V_T \right)V_{DS} \\
I_D = I_R = \frac{V_S}{100} \; \; \; \to \; \; \; V_S = 100I_R \\
V_{GS} = V_G - V_S = V_G - 100I_R \\
V_{DS} = V_D - V_S = V_D - 100I_R \\
I_R = \frac{W}{L} \mu_n C_{ox} \left( (V_G - 100I_R) - \frac{V_D - 100I_R}{2} - V_T \right) (V_D - 100I_R)
[/math]
im not going any further, but you can go ahead and make a guess of how fucked [math]\frac{\partial I_R}{\partial V_G}[/math] and [math]\frac{\partial I_R}{\partial V_D}[/math] must be
>>14720219
never, EVER, bring up electrons when the question was about electromagnetics. Maxwell died without ever knowing what an electron was.
>>14720328
the seasons are more or less reversed for the northern and southern hemispheres of the earth. this is because the seasons are caused by the earth tilting towards or away from the sun during different parts of its orbit. when the north pole is pointing towards the sun, the northern hemisphere is exposed to more sunlight so its gets hotter than the southern hemisphere which is pointed away and gets less sunlight. then the south pole points towards the sun and the situation is reversed.

>>14720328
>Like if I have a summer here, does it mean country on the other side having winter? In a weather terms, not time and date.
yes
>Does it mean some countries winters are warm and summers cold?
no, the two hemispheres have opposite seasons, so e.g. if your current season is summer, it's currently winter on the other side
winter is colder, summer is hotter etc, but dates of these seasons change by the hemisphere

>>14720340
>Maxwell died without ever knowing what an electron was
A force carrier was hypothesised before he died and Thomson's cathode ray tube experiment was something like a decade after his death. Get with it.

Two years ago I took a (noncalc) general physics class that covered:

>kinematics
>dynamics: force and newton's laws
>friction, drag, elasticity
>uniform circular motion
>work, energy
>linear momentum and collisions
>statics and torque
>rotational motion and angular momentum
>fluid statics
>fluid dynamics
>temperature, kinetic theory, gas laws
>heat and heat transfer
>thermodynamics

Now I'm taking the second class in the sequence which covers the following. What should I review from the previous course?

>oscillitory motion and waves
>physics of hearing
>electric charge and electric field
>electric potential and electric field
>electric current, resistance, and ohm's law
>circuits and DC instruments
>magnetism
>electromagnetic induction, AC circuits, electrical technologies
>electromagnetic waves
>geometric optics
>vision and optical instruments
>wave optics

>>14720408
dont waste time looking at past topics, instead use summer vacation to get a headstart on the topics that you're going to cover. If you have access to the syllabus of the class, then take notes/do problems on whatever topics the very first exam covers. You will be well ahead of your peers if you do this

>>14720503
thanks, will do

>>14720405
my point was that electrodynamics is one of the only things in physics that is considered "finished", and it was finished before electrons were discovered. electrons are quantum particles, and QM/QFT is definitely not finished. so if someone is asking you about electrodynamics and you start talking about electrons, you are probably either not explaining electrodynamics correctly or not explaining electrons correctly. and just to illustrate that point:
>>14720219
>AFAIK An electric current generates a magnetic field because the electrons are all moving in the same direction (from negative to positive), they're more likely have their fields aligned.
in reality, magnetic fields from moving charges are caused by relativistic effects. https://www.wtamu.edu/~cbaird/sq/2016/02/18/how-is-a-magnetic-field-just-an-electric-field-with-relativity-applied/

How to not feel retarded when doing math

I know it's not possible to restore the color information from a black and white photograph, but in principle, would it be (mathematically/physically, not chemically) possible that this color information could be encoded in greyscale? Or is it not possible because every dot can only map to a certain amount of information, where color exceeds that limit? Would it be possible if several greyscale dots are collapsed into one color dot, or is that fully self-defeating as it detracts other information?
Let's assume the hypothetical camera does not "intentionally" just blow up the picture and add the color information in a plausible encoding around one real world dot (or pixel, if it's digital), because the it essentially becomes an arbitrary (e.g. binary) encoding anyway, which of course can reproduce anything.

For color, I don't know how many are actually used for human purposes (not even the magnitude), but for a naturalistic photo let's say 10 000 are enough. Or is actually 1 million? I don't know.

>>14721117
the color spectrum is one-dimensional, my dude

>>14721006
Do more math until the feeling vanishes.

I'm getting 13k in grants for next semester due to my disabilities

what should i spend it on?

>>14721340
tuition, books and your disabilities

If a nonempty set doesnt have a largest element, is it always uncountable? Why/why not?

>>14721732
Set of Natural numbers doesn't have a largest element, yet it's countable.

Trying to learn about test charges & point charges. From what I understand, point charges are charges of varying magnitudes that occupy a fixed point in space (rather than an area etc.) whereas a test charge is a charge of adjustable position & magnitude. In this photo of an electric field generated between two point charges, I could place a test charge with a magnitude of x at any point in order to determine the effect that the electric field would have on the test charge. Am I correct in my assumptions?

if you had a bright enough light source, could you shine light through a brick wall?

>>14721820
No but you could melt a hole through it.

>In contrast to the uniqueness of the inverse mapping, there may exist many one-sided inverse mappings
What is meant by that?

>>14722746
Consider
f:{0,1} -> {0,1,2}
f(0) = 0
f(1) = 1
The functions
g:{0,1,2} -> {0,1}
g(0)=0
g(1)=1
g(2)=0
and
h:{0,1,2} -> {0,1}
h(0) = 0
h(1) = 1
h(2) = 1
are both left-inverses you can easily check that
g(f(0)) = h(f(0)) = 0
g(f(1)) = h(f(1)) = 1

Actually inverses on the hand are always unique. If f is a function and g and h are both inverses then
g(x) = h(f(g(x))) = h(x) for all x.

So is showing that a function is both surjective and injective the only way to prove bijectivity or is there another nice way?

>>14722972
i dont understand your question. "surjective and injective" and "bijective" are the exact same thing.

>>14722981
to prove bijectivity, I usually prove both of these properties individually. Is there something I could do that would prove both things at once?

>>14722985
no. the definition of bijectivity is being both injective and surjective, so your proof either has that or its skipping some steps (for example, there may be a theorem that states that a function is bijective if it meets certain criteria, and you just defer to that).

Is there any proven value to early math education? Would it make more sense to optimize a child's early years for literacy and forego mathematics education entirely until maybe 12-13? Would this pedagogical strategy have any meaningful effect when compared to something like IQ long term?

How?
[eqn] \prod_{3\nmid n}(1-q^{3n})=\prod_{n=1}^{\infty}\frac{(1-q^{3n})}{(1-q^{9n})} [/eqn]

if one could remove the effects of time on an object so it became indestructible would you then even be able to move it around?

>>14723111
[eqn]\prod_{3 | n} a_n = \prod_{n=1}^\infty a_{3n}[/eqn]

[eqn]\prod_{3 \nmid n} a_n = \frac{\prod_{n=1}^\infty a_n}{\prod_{3 | n} a_n} = \frac{\prod_{n=1}^\infty a_n}{\prod_{n=1}^\infty a_{3n}} = \prod_{n=1}^\infty \frac{a_n}{a_{3n}}[/eqn]
Now let [math]a_n = 1 - q^{3n} [/math]. That's of course only for sequences for which all the infinite products converge. For instance it's easy to see that you need [math]|q| < 1[/math].

>>14723170
If it doesn't experience time it can't have a velocity so no, you would not be able to move it.

>>14723111
if [math]3|n[/math] then [math]9|3n[/math]. putting [math](1-q^{9n})[/math] in the denominator cancels out all the products that are skipped on the LHS.
cute taiga <3

>>14723183
> [math]\prod_{3 \nmid n} a_n = \frac{\prod_{n=1}^\infty a_n}{\prod_{3 | n} a_n}[/math]
Say what now? How does that work?

>>14723188
so if you removed the effect the object would fly away in reference the universe's rotation?

>>14723196
Either 3 divides n or 3 doesn't divide n.

>>14723111
why is there a giant Pi?

>>14723210
only from your relative perspective. Even then, you probably wouldn't be able to see or interact with it since most if not all interactions occur over time. No smashing through planets at light speed. It's like trying to imagine a 3d drawing without a z-axis.

https://www.youtube.com/watch?v=sTQqw2zfL88

https://www.youtube.com/watch?v=83ctKV-k-WI

i dont know why they think its okay for people to take physics without taking calc 3. But please help me understand what is happening with the i hat and j hat in this expression. Why do they magically disappear in the final expression?

>>14723216
Still don't follow. Are the n indices on the top and bottom independent?

>>14723183
>>14723190
Thank you! No idea how i missed that.

>>14723349
the cross product of two vectors gives a vector that is orthogonal to both.
The vector that is orthogonal to i and j is k

>>14723381
I was the one who asked the question, but I get i now so maybe i can answer.

The original infinite product is one only evaluated where 3 does not divide n. So take the product evaluated at all n, and divide by the product evaluated only when 3 divides n; whats left is the product evaluated only when 3 does not divide n.

>>14723399
so fi they are at right angles then they magically disappear?

>>14723477
They don't have to be at a right angle, but yes

>>14723403
> whats left is the product evaluated only when 3 does not divide n.
which is exactly my confusion because that is *not* the LHS term - all values of a when 3 divides n

>>14723520
zoom in

>>14723520
its hard to see but theres a little dash through the |

>>14723567
>>14723569
thanks 4k pixels

Venusians on Earth | Gigi Young

https://youtu.be/X-WWadeumtk

I always hear people say that when you're shocked by static electricity, it's safe because the current is low. But this seems wrong. The current is still high, but it's only high for a fraction of a second, so the total charge delivered is not high enough to do any damage.

Are they wrong, or would you still call this low current?

>>14723477
They aren't disappearing. -i×j=k. It's a simplification.

If they're parallel they disappear. The cross product of two parallel vectors is zero.

Would appreciate answers for these two. I'm working on it right now.

>>14724401
is this the answer? it's just the BFS alogorithm

>>14724407
>>14724401
samefag, I see the BFS algorithm returns the the entire path, not just the length. So I assume part a would be just the length of the queue, and part b would be the BFS algorithm I posted?

>>14724407
>>14724401
>>14724438
opened a thread here for this question:
>>>/wsr/1242654

>>14716579
idk if you're still looking to answer this but unfortunately it's probably the second one.
if you split the sum like this, you can get a good equivalent:

from x/2 to x
from x/3 to x/2
from x/4 to x/3 etc

>>14714495
I'm trying to take a graduate class (Complex Analysis) as an undergrad and the teacher seems hesitantly willing to take me on but he's been ghosting me the last five days and the deadline is this friday. What do? Should I drive to campus and make an appearance in his office? His phone is disconnected as well.

Can someone help me understand the following passage I found in an old German math book? I'll try my best translating it:

Let [math](p_1, ..., p_n)[/math] be an ordered [math]n[/math]-tuple of propositional variables. Then every proposition of the form [math]\bigwedge\limits_{i=1}^k H_i[/math] (resp. [math]\bigvee\limits_{i=1}^k H_i[/math]) is called a fundamental conjunction (resp. fundamental disjunction), if and only if for every index [math]i\in \{ 1,...,k \}[/math] there exists exactly one index [math]j\in \{ 1,...,n \}[/math], such that either [math]H_i \equiv p_j[/math] or [math]H_i \equiv \overline{p_j}[/math].
Moreover, a fundamental conjunction (fundamental disjunction) is ordered, if, for [math]i_1, i_2 \in \{1, ..., k \}[/math], [math]i_1 < i_2 [/math] implies [math]j_1< j_2[/math] ([math]j_1, j_2\in \{ 1, ..., n \}[/math]).

If each variable of the [math]n[/math]-tuple appears in a fundamental conjunction (fundamental disjunction) of variables [math]p_1, ..., p_n[/math], then it is called the elementary conjunction (elementary disjunction) of these variables. Every such proposition can be reversibly assigned a natural number [math]m[/math] as an index. [math]m[/math] is the decimal equivalent of every such n-digit dual number, that one obtains, if in the proposition every negated Variable is set to [math]0[/math], and every non-negated Variable to [math]L[/math], and remaining numbers are deleted.

>>14724957
So what exactly do you not understand?

>>14724834
>Should I drive to campus and make an appearance in his office?
Sure, why not?
Problems have a tendency of melting away when you talk to people face to face.

Do all diseases fall under the umbrella term pathology? I'm trying to reorganize my old biomed notes.

https://www.youtube.com/watch?v=HxpQ1jsn3lI

>>14725257
https://www.youtube.com/watch?v=NgK9jD_q2Ps

https://www.youtube.com/watch?v=AwvStKFMXfc

https://www.youtube.com/watch?v=FJRIg-HCy7g

https://www.youtube.com/watch?v=DWjnbptH5vI

>>14724443
bamp

can someone who understands VAE/CVAE well tell me what the fuck is going on with this prior/recognition network in this paper? i grasp the concept of encoder/decoder in normal VAE but i don't and can't understand what's going on here
basically only 3.3 point matters, no need to read the whole thing
https://arxiv.org/abs/1711.07632

When I take a shit I often leave a speck or smear of shit on the side of the toilet bowl. Now this will usually prove fucking immovable. Although its constantly wet, although it is subjected to a deluge of flushing up to dozen times a day, although I make a point of always pissing on it, it will just not fucking budge. It will remain there indefinitely.

The crazy thing is I can lay entire log down the toilet and it will not leave a trace. Despite hitting the side and bumping around. As it gets flushed its hitting the sides of the bowl, but then it goes, leaving no trace. But occasionally I will get that one speck which gets stuck and, like I said, its almost impossible to get rid of by straight liquid actions.
Now what gives with these indestructible persistent specks of poo? And why dont they build aircraft out of them?

No question just venting, I hate myself for this
The winter semester will start in about two months, my plan was to write my engineering related thesis in a company. But since I am a lazy fuck I procrastinated the whole last semester and I still have no place to write my thesis.
Problem is, that I immediately wanted to start my master next summer semester, so I HAVE to write my thesis this winter semester or else I’ll have to wait another semester.
Why am I like this

>>14725664
START RIGHT NOW MAGGOT

The only thing im confused about in the image is why they are using pi r^2 instead of area of a cylinder

>>14725688
Yes, yes. I applied to a bunch of companies today, but I’ll have to go through the whole hiring steps and bureaucracy before I can actually start doing anything beside sitting on my ass

>>14725699
>area of a cylinder
lol wut???

>>14725783
the wire in the picture is a cylinder. But in the equation, for area they use pi r^2

>>14725794
can you explain what you mean by the area of a cylinder? cylinders are 3D and have volume, not area.

>>14725800
they have surface area, but i see your point.

>>14725804
faradays law states that the voltage around a closed path is equal to the change in magnetic flux through the area that path encloses. imagine in the example that youre standing at the north pole and looking rightwards at the cylinder as it spins. when you can look directly down the cylinder, thats maximum flux because the circles of the coil appear the biggest to you. when the cylinder is sideways thats zero flux because you cant look through the circles anymore.
you might think that when the cylinder is sideways and since it has some height to it, flux is nonzero because theres a magnetic field going through it. however, the field isnt going through any closed area so its not contributing to any voltage. this is easy to see if you imagine pulling apart a slinky (which is like a coil) and looking at it from the side. the profile view of the stretched slinky doesnt have any loops or closed areas, it just looks like a zig-zag. so when it comes to induced EMF in coils, the area of the base is all that contributes, hence why they used the area of a circle for A there.

>>14725846
thank you for your explanation. When im more knowledgeable, i will help future anons just like you.

>>14725896
np fren <3

>>14720283
K.

>what is /sqt/ for?
Questions regarding math and science. Also homework.
>where do I go for advice?
>>>/sci/scg or >>>/adv/
>where do I go for other questions and requests?
>>>/wsr/ >>>/g/sqt >>>/diy/sqt etc.
>how do I post math symbols (lAtEx)?
rentry.org/sci-latex-v1
>a plain google search didn't return anything, is there anything else I should try before asking the question here?
scholar.google.com
>where can I look up if the question has already been asked here?
warosu.org/sci
eientei.xyz/
>how do I optimize an image losslessly?
trimage.org
pnggauntlet.com

>where can I get:
>books?
libgen.rs
z-lib.org
stitz-zeager.com
openstax.org
activecalculus.org
>articles?
sci-hub.st
>book recs?
sites.google.com/site/scienceandmathguide
4chan-science.fandom.com/wiki//sci/_Wiki
math.ucr.edu/home/baez/physics/Administrivia/booklist.html
>charts?
imgur.com/a/pHfMGwE
imgur.com/a/ZZDVNk1
>tables, properties and material selection?
www.engineeringtoolbox.com
www.matweb.com

Tips for asking questions here:
>attach an image (animal images are ideal. Grab them from >>>/an/)
>avoid replying to yourself
>ask anonymously
>recheck the lAtEx before posting
>ignore shitpost replies
>avoid getting into arguments
>do not tell us where is it you came from
>do not mention how [other place] didn't answer your question so you're reposting it here
>if you need to ask for clarification fifteen times in a row, try to make the sequence easy to read through
>I'm not reading your handwriting
>I'm not flipping that sideways picture
>I'm not google translating your spanish
>don't ask to ask
>don't ask for a hint if you want a solution
>xyproblem.info

>>14720283
love active calculus

this is how math should be taught. Not forcing kids to memorize how to solve problems by doing it over and over again

So inductors act like a short circuit in steady state, that is constant current correct?
Since v=ldi/dt
Only when the current is constant the voltage drop is zero and the inductor is short
But when does that ever happen?
Say you connect an inductor in parallel to a dc source, wouldn't the inductor have the same voltage (since parallel) which is constant, therefore the current must be linear and the inductor is charging up
So in this case the inductor isn't a short even though it's connected to a dc source
Qnd in something like a buck converter, when the switch is off and the inductor is releasing the energy, its current is linear too, meaning it has a voltage drop across it
So we can't treat inductors like a short circuit in power electronics/drive circuits, no?
And my professor is retarded, right?
Also in what cases does the current remain constant? If there's a resistive element? But won't the inductor keep building up energy thereby changing the current?
.

>>14726238
>But when does that ever happen?
when magnetic field surrounding the coil stabilizes and stops changing.

>Say you connect an inductor in parallel to a dc source, wouldn't the inductor have the same voltage (since parallel) which is constant, therefore the current must be linear and the inductor is charging up
>So in this case the inductor isn't a short even though it's connected to a dc source
Inductance would behave as an open circuit at first, and gradually letting current flow through it until it 'charges' and finally behaves as a shortcircuit.

>So we can't treat inductors like a short circuit in power electronics/drive circuits, no?
no as long there's any change in circuit variables as changing voltage/current.

>And my professor is retarded, right?
Who knows.

>Also in what cases does the current remain constant?
When voltage is not fluctuating in any way.
>If there's a resistive element?
Not necessarily

>But won't the inductor keep building up energy thereby changing the current?
No. An inductor can only store energy in the form of magnetic field and the ammount it can store is directly related to its own inductance value which is related to its physical configuration, dimensions, materials in the core, etc.

For more insight in this topic check any circuit analysis book in transient response chapters usually named as 'circuits with energy storing elements'

>>14718112
Calculus isn't really a study of mathematics outside of early University, but if you want to count that then sure.

Statistics
Algebra
Analysis (you can call this calculus if you want)
Differential Equations
Geometry

just got the job as an undergrad physics TA for this next fall semester. any tips before classes start?

any tips on narrowing down for my masters project, like I want to do computational and since my undergrad project was pharma, kinda want to stick to that and am interested in cheminformatics which is computational in a way
so any tips and/or suggestions?

how do you feel when you consider that everything that exists is part of a set,given number of atoms/cells/molecules, and that the rest are waves such as mangetism...and everything else:time and space,are hard as stone,set forever and everywhere .
basically wether the earth is flat and domed,or wether the universe is as depicted by respected scientists, when compared to eternity and infinity ,its just as billion-wise small.
>Im an existentialist optimist,not a nihilist

>>14726499
ironically, learning about it made me a believer
maybe i'm just too stupid to grasp the concept enough to understand it scientifically, but just the fact alone that everything is made of the same thing, that some atoms are part of you, some other atoms are a rock, others form a tree etc., that in all of that you come to have consciousness seems to be a miracle in itself

https://www.youtube.com/watch?v=azT9jPHsSUI

https://www.youtube.com/watch?v=pO4N2kj4DEU

https://www.youtube.com/watch?v=13OSDg7Ta14

https://www.youtube.com/watch?v=ANZtl4Pi0A4

What the fuck is the point of this thread when the really important questions go unanswered
>>14725531

How do i prove directly: "if 3x^2 + 2x + 1 is even, then x is odd" using direct proof?

>>14718896
just practice calc. single variable calc isn't much more difficult than pre calc imo. Im a brainlet too

Scientifically speaking, why does this board hate chemistry so much?

>>14727031
3 and 1 are always odd and 2x is always even. Knowing that odd*x^2+even+odd=odd what can you deduce about x^2?

Or just use arithmetic mod 2 if you've seen it...

>>14727081
ETA: odd*x^2+even+odd=even

>>14727068
when you make a general, you have to be very specific about what you want people to post. /sqt/ is for homework questions. /scg/ is for life advice. /mg/ is for homework questions. what are people supposed to post in the chemistry general? chemistry stuff? people scroll past that in like 2 seconds. but if you made a thread like "post the worst chemistry experience you ever had" then people would be drawn in to post in it because your thread reminded them of that time they dipped their balls in hot piranha to impress the cute lab tech.
what do you want the chemistry general to be? you have to be specific.

>>14727101
look at the image again but look at the red text at the top this time

>>14727114
i figured the thread died and was pruned. why did your thread get deleted?

>>14727117
it was at page 6 or 7 at lowest when it got deleted
>why did your thread get deleted?
I don't know
also not my thread

Is there a way to increase brain performance? Not iq but just more clarity and such.

>>14727081
ty can you show me what arithmetic mod 2 would be?

>>14721763
"test charge" and "point charge" are just names for charges used in different circumstances.
point charges are just charges present in your system that don't take up space. they are contrasted with charge distributions, in which you assume charge is smeared over some region
"test charges" are just point charges that don't actually exist in your system, you just think about what would happen if they did exist. this is helpful for calculating electric fields. "what if there was a charge right here, what would the force on this charge be?" is a common question that you use to calculate the electric field or force at a certain point, by pretending that there was a point charge with one unit of charge at that location.

>>14718896
dont worry linear algebra doesnt need calculus

also calculus is not important for CS

just work on discrete math

>>14727101
>/mg/ is for homework questions
Stop baiting me for (You)s, you can just ask for them.

>>14727253
i cant seem too desperate for remi (You)s, i got a repuatation to keep.
but in all honesty i have no clue what they do in /mg/. but the only time i ever went in there they didnt seem all that smart so i figured it was like this place.

>>14714495
bros, is ethyl or isopropyl alcohol better for killing bugs (specifically mosquitoes if it matters)? I assume isopropyl considering we drink ethanol.

>>14724834
>>14725076
I ended up not taking your advice and he said no. However, I emailed him again and got him to change his mind (no easy feat, I assure you). I think he was reluctant to say yes because I almost failed one of his classes and made disparaging remarks about his teaching with my microphone accidentally on.

>>14727403
and you wonder why he doesn't want you in his class ...

>>14727403
holy based

[Abstract] I'm retarded.

How do you calculate the odds of something happening like if you get a 1/6 16% chance of getting a 2 on a dice roll what are the chances of getting a 2 atleast once if you roll the dice 6 times?

>>14727173
>>14727050
Thank you for the advice, anons. That's a relief. I'll do my best!

>>14727435
It's the binomial distribution.
[eqn]
P(\text{At least one 2 in 6 rolls}) = \sum_{k=1}^6 P(\text{Exactly k 2's in 6 rolls}) = \sum_{k=1}^6 {6 \choose k} \frac{1}{6^k} \left(\frac{5}{6} \right)^{n-k} = \frac{31031}{46646} \approx 66.5 \%
[/eqn]
Alternatively you could just calculate the probability for the inverse event.
[eqn]
P(\text{At least one 2 in 6 rolls}) =1 - P(\text{No 2 in 6 rolls}) = 1 - \left(\frac{5}{6} \right)^6 = \frac{31031}{46646} \approx 66.5 \%
[/eqn]

Now you might ask where those formulas come from. Let [math]X_1, X_2 , \ldots, X_6[/math] be independant random variable that are equal to 1 if the i-th roll is a 2 and 0 otherwise. The sum of those random variables will tell you the number of times you rolled a 2 during those 6 rolls and the distribution of the sum of random variables is just the convolution of the individual distributions.

>>14727468
great, how do i input this properly

>>14727472
16.67, 83.33
83.33*0.833
100-69.4444444444
69.44*0.833
100-57.8472222222
...

>>14714495
Absurdly retarded and pointless question, but could a 3 kilogram iron blade accelerated to around mach 8.5 liquify from the heat generated while remaining intact due to pressure, and cut lengthwise through the entire Eurasian continent from the top of Russia to the bottom of India in about an hour?

If I roll a 6 sided die 100 times, what's the probability of getting the same number 50 times, and why?

Bought some feminist toilet paper made of bamboo and sugar cane. Will it give me rectal diabetes?

>>14727522
[eqn] {100 \choose 50} \frac{1}{6^{50}} \left(\frac{5}{6} \right)^{50} = \frac{13828628851836428200628361384616482609999366104602813720703125}{1008207752314924237803534362898237377372135355668140233862765380199841267712}
[/eqn]
Because Binomial Distribution.

>>14727545
Actually 6 times this but either way the probability is less than 1 out of 10 trillion.

>>14726279
So when an inductor is connected in series with resistance and a sink and the inductor is discharging, we can't approximate it as a short, right?
Since it's providing electromotive force for the circuit it must have a voltage?

>>14727556
Oops, didn't see the answer above. I was also wondering how you manufacture the peak of a binomial distribution, in other words;

If I want to construct a number of pigeonholes, N, such that when I release 10,000 pigeons who randomly fly into pigeonholes with equal probability, each hole will be filled on average, 100 times

>>14725531
Still unanswered. Absolutely pathetic. Is /sci/ really this dumb?

>>14725531
>>14727706
>And why dont they build aircraft out of them?
Are you dumb? If it sticks to the side of the toilet it can't fly.
Also, if by miracle it actually could fly, what do you think would happen if india got its sticky hands on such technology?

>>14727788
Superpooper by 2030

Trying to learn math by myself, downloaded 'Basic Mathematics' by Serge Lang as someone recommended me and failed at the very beginning already.
What the fuck is this? I read through the chapter several times, but there's no explanation to anything, honestly. What does he mean by 'justify'? How? I googled and it always some shit like 'well you just draw a here and b here and done' without any explanation as well. How do I justify? How do I proof? What can I do? What can I not? What's the rules? There's literally zero explanation how does any of this works in the book.
I got things like commutative law or associativity, but like, so what? How does it help me?

>>14727989
(a+b) + (c+d) = (a+b) + (d+c) because of commutativity
That equals (a+b+d) + c because of associativity
You can then swap the b+d because of commutativity and then put the brackets back where you want them because if associativity.
That's all it's asking for.
>What's the rules?
You've got the rules - associativity and commutativity. All you're trying to do is move from one expression to the other solely by applying those rules. I think you're confusing yourself by overthinking it - these properties are so familiar and ingrained that it feels odd to apply them step by step.

>>14728017
I don't understand what the end goal. I just change them however I can using those laws and that's it?

>>14728085
Yes. Why? Because mathematics is rigorous and also because if you keep progressing in math you may encounter subjects where those rules no longer apply.

>>14728085
The end goal is to prove that the equalities are true.
At this point, you've defined addition and subtraction as having some basic properties. And you're then looking at what you can prove using only those properties.
All the things you're asked to prove are obvious, because this is the first exercise in the first chapter of a book called Basic Mathematics. It's just getting you into the habit of demonstrating things explicitly.

Any ideas?

[eqn] \prod_{n=1}^{\infty}(1-xq^n)^{-1}=\sum_{n=0}^{\infty}\frac{x^n}{(1-q)(1-q^2)\cdot\cdot\cdot(1-q^n)} [/eqn]

>>14727262
>but in all honesty i have no clue what they do in /mg/
It used to have interesting shitposting but now it has mostly uninteresting shitposting.
>they didnt seem all that smart
Obviously you can't hold them up against me, anyone would disappoint.
>>14728468
Have you tried using the geometric series formula?

>>14727588
Bump >:

>>14728622
you dont need probability for that. the average number of pigeons in each hole is the number of pigeons in all holes divided by the number of holes. so [math]\frac{10000}{n}=100[/math].

>>14727583
>we can't approximate it as a short, right?
that's right. values of R and L of those elements determine the so called time constant [math]\tau=\frac{L}{R}[/math] (in time units) which states how fast a coil will charge or discharge up to about 37% of its steady state value.
The reason to this value is explained in the books of circuits analysis, and as a prereq to understand this specific case is the very basics of differential equations. I'll link you a slides thing I just found and will let you do the other book reading on your own. Sadiku book on circuits is a good starting point.

slidetodoc.com/transient-excitation-of-firstorder-circuits-1-2-3/

>>14728529
>Have you tried using the geometric series formula?
why would you think that applies here

>>14728662
[math]\dfrac{1}{1 - xq^n} = \sum_{k = 0}^{\infty} x^k q^{kn}[/math]

>>14728468
You can rewrite the right side with the Iverson bracket and then exchange sum and product.
[eqn]\sum_{n=0}^\infty \prod_{m=1}^\infty \frac{x^n}{1 - q^m} [1 \leq m \leq n] \\
= \sum_{n=0}^\infty \prod_{m=1}^\infty \sum_{k=0}^\infty x^n q^{km} [1 \leq m \leq n]\\
= \prod_{m=1}^\infty \sum_{k=0}^\infty \sum_{n=0}^\infty x^n q^{km} [1 \leq m \leq n]\\
= \prod_{m=1}^\infty \sum_{k=0}^\infty \sum_{n=0}^\infty \frac{x^{k-1}}{1 - x} q^{km} \\
= \frac{1}{x-x^2} \prod_{m=1}^\infty \sum_{k=0}^\infty x^k q^{km} \\
= \frac{1}{x-x^2} \prod_{m=1}^\infty \frac{1}{1 - x q^m}
[/eqn]

Well looks like I made a mistake somewhere but I will leave it to you to find it. This method should work.

https://www.youtube.com/watch?v=A_2uic9w-ZQ

https://www.youtube.com/watch?v=9aF6UmULqig

If I were to climb a set of stairs that would leave be breathing heavily for around 30 seconds (like 5-6 floors) when I reach the top, if I were to start breathing deeply before and during the stair climb, will I still be out of breath after?

Assuming I dont start breathing heavily until pretty much already at the top of the climb

>>14728894
I noticed I felt a slight desire to breathe more deeply right around the top, then breathed slightly deeper for 30 seconds or so, then had to breathe really deeply and was out of breath for 30 seconds after that, then breathing normally.

The stair climb was around a minute to get to the top, so why did it take a minute to start breathing deeper then a 30 second delay where I was then out of breath but had already finished climbing 30 seconds ago

Shouldn't I have been out of breath immediately at the top and then recovered?

But there was a large delay after the stress and then all at once I was out of breath

Am I dying?

Does anyone have any idea how Gauss' Multiplication theorem is used to go from this

[math]\displaystyle
x = w^{-1} - \frac{t}{n-1}\sum_{\alpha=0}^\infty \frac{\left( t w \right) ^\alpha}{\Gamma(\alpha + 2)} \frac{\Gamma\left(\frac{n\alpha}{n-1} + 1 \right)}{\Gamma\left(\frac{\alpha}{n-1} + 1 \right)}
[/math]
to this
[math]\displaystyle
x = w^{-1} + \frac{t}{(n-1)^2}\sqrt{\frac{n}{2\pi(n-1)}} \sum_{q = 0}^{n-2} \left(\frac{tw}{n-1}\right)^q n^{nq/(n-1)} \frac{\prod_{k=0}^{n-1} \Gamma\left(\frac{ \frac{nq + 1 + k}{n-1}}{n}\right)}{\Gamma\left( \frac{q}{n-1} +1\right) \prod_{k = 0}^{n-2} \Gamma\left( \frac{q+k+2}{n-1} \right) }\;{}_{n+1}F_n\left(\left\{ \frac{\frac{qn}{n-1} + 1}{n},...,\frac{\frac{qn}{n-1} + k}{n},1\right\}; \left\{
\frac{q+2}{n-1},...,\frac{q+n}{n-1}, \frac{q}{n-1} + 1 \right\}; \left( \frac{tw}{n-1} \right)^{n-1} n^n \right)
[/math]

I've never used it really.

>>14728712
Thanks but I figured it out a different way.

>>14727583
correct, but just to clarify - approximate as a short is when things are steady state. A DC circuit where there still energy stored in inductors violates this assumption

>>14725531
Still no answer to this perplexing problem. I am beginning to think you are all frauds.

>>14725531
need more cum in your diet

>>14729916
I am sure you would oblige me, as you have doubtless obliged many men, but I am an entirely heterosexual. You will eventually get over your disappointment.

>>14729329
I tried looking at the simpler case for n = 2

[math]\displaystyle
w^{-1} - t \sum_{\alpha = 0}^\infty \frac{(tw)^\alpha}{\Gamma(\alpha+2)} \frac{\Gamma(2\alpha + 1)}{\Gamma(\alpha +1)}
[/math]

So, rewritting
[math]
\Gamma(2\alpha + 1) = \Gamma\left(2 \left(\alpha + \frac{1}{2} \right) \right)
[/math]
And then by the multiplication theorem
[math]\displaystyle
(2)^{-\frac{1}{2} - 2\alpha} (2\pi)^{\frac{1}{2}}\Gamma\left(2 \left(\alpha + \frac{1}{2} \right) \right) = \Gamma\left(\alpha + \frac{1}{2}\right)\Gamma\left(\alpha + 1\right)
[/math]

Since [math]\Gamma(1/2) = \sqrt{\pi}[/math] and [math]1 = \Gamma(1)[/math]

So
[math]\displaystyle \Gamma(2\alpha + 1) = 4^\alpha \frac{\Gamma\left(\alpha + \frac{1}{2}\right)\Gamma\left(\alpha + 1\right)}{\Gamma(1/2)\Gamma(1)} = 4^\alpha (1/2)^{(\alpha)}(1)^{(\alpha)}[/math]

And since
[math]\Gamma(2) = 1[/math], rewrite [math]\displaystyle \Gamma(\alpha + 2) = \frac{\Gamma(\alpha + 2)}{\Gamma(2)} = (2)^(\alpha)[/math]

And [math]\Gamma(\alpha + 1) = \alpha![/math]

Which gives
[math]\displaystyle
w^{-1} - t \sum_{\alpha = 0}^\infty \frac{(tw)^\alpha}{(2)^{(\alpha)}} \frac{ 4^\alpha (1/2)^{(\alpha)}(1)^{(\alpha)}}{\alpha!} = w^{-1} - t\; {}_2F_1\left( \frac{1}{2},1; 2; 4tw\right)
[/math]

I wonder if it's this straightforward for the general case.

>>14729329
what the fuck

How do I sell out to the military-industrial complex and get a cushy job in the Middle East earning shitloads of money?

i remember hearing somewhere that some parts of the universe are out of our reach forever, because expansion of the universe makes them get away from us (relatively) at speed faster than speed of light
can someone explain this or link an article to this (if it's not bullshit)? i'm not looking for some elaborate proofs or in-detail explanations, because i'm too retarded at physics to understand that, just some in words description of how that makes sense

I imagine I'm not the only one here who reads PDF textbooks on an iPad. However, there's a particular issue I run into.
Let's say there are 400 pages of content and 40 pages of exercise solutions. I want to attempt every exercise and check my answer against the solutions immediately after trying it.

With a physical textbook, the process for doing this is obvious, trivial, and automatic. Keep a bookmark in the relevant part of the solutions, move it when needed, and just keep my place in the main book with a finger or something while I check the answer.

I haven't found a PDF reader that handles this well. The process for turning to the solutions is more like
>bookmark the current content page
>bring up the list of bookmarks
>press the solutions bookmark to switch to that page
>realise I've finished that page of solutions
>delete the current solutions bookmark
>move to the next solutions page
>bookmark that page
>check solution
>bring up bookmarks list
>press the content bookmark I made earlier to return to that page
>delete that bookmark to avoid later confusion
Alternatively there's usually a "back" button, but it's behaviour is very inconsistent (especially if I have to change the solutions page) and I never trust it not to lose my place. I've currently resorted to opening the same PDF on a different device just for the solutions.

Instead of normal bookmarks, I basically want to have two separate "current page" pointers which I can switch between at any time. Would love any suggestions for apps that can do this, or other solutions to this.

>>14728661
>>14729544
Thanks very much
I love the sadiku book, I'll surely check the slides

>>14730280
> because expansion of the universe makes them get away from us (relatively) at speed faster than speed of light
that's literally all it comes down to. edges of the universe are moving away from us at some sub-light speed but then add in the effect of the expanding universe and you get a combined relative speed which is faster than light.

as for proof just use google or YT and search for something like "observable universe expansion", hundreds if not thousands of links.

>>14731102
ah okey thanks, i get it now
i kept thinking that e.g. galaxies or groups of them "stand in place" and only expansion of the universe makes them move away from us

I'm not a big medfag, my area is more radiology and labs, not immunology nor pharma.
But in theory (or even nowadays), is it possible to target specific antibodies with medication/treatment?
I know for dsDna there's Abetimus and something else that starts with a B I can't remember, but what about other ones?

bonus extra stupid question
>could certain immune diseases be compared to chemotherapy in the sense that both work in a way that target and destroy both "bad" cells and your own "good" cells

i legit cannot solve any physics problems without looking it up

>>14731691
you kinda just need to have a toolbox of methods like
>conservation of energy/momentum
>some PDEs
>etc
and use the correct one for the right problem.

>>14731778
i dont know how to do anything with PDE or vectors since i havent taken calc 3 or diff eq. kinda dumb physics requires you to know math that you havent taken.

I looked up how to make two DNA strands compatible with each other for Gibson Assembly and they just basically said "just pcr it" which is super not helpful. How exactly do I go about doing that?

>>14731846
i think you probably know all the math you need. are you >>14723349?

>>14731859
i am yes. I dont know how to do anything with vectors. I dont understand how im supposed to magically know all their properties.

>>14731271
This I assume is in reference to AIDS, which means that it's not possible yet because news sites would be creaming their pants the second it was discovered.
Scientifically, you'd probably need to create a cell with that antibody's specific antigen, which would require hardcore molecular witchcraft that I have no chance of understanding. Then that would have to somehow disable antibodies without getting attacked by the immune system, which I don't think is even possible.
tl;dr: no

>>14731868
can you show me a problem where you think your lack of vector knowledge is an issue?
to help with that original question: a cross product is a particular way of multiplying vectors. a vector dot product yields a scalar (a regular number, like 4.2) and a cross product yields a third vector as the result. imagine two vectors A and B pointing off into 3D space. those two vectors will always lie in some plane together, no matter their orientation. let C = A x B. the magnitude of C is the area of the parallelogram that A and B form. the direction of C is directly out of the plane that A and B lie in. for your E&M experience, the direction part is the most important bit to know so really try to visualize that. now, theres technically two different vectors that are both out of the plane (a plane has two sides), so to figure out which side of the plane C is on you use the right hand rule: point your right hand in the direction of A, and curl your fingers in the direction of B. your thumb is pointing in the direction of C.
to recap: the cross product of two vectors is perpendicular (at right angles) to both of the original vectors. so you can see now why [math](-\hat{i}) \times \hat{j} = \hat{k}[/math]. maybe you cant visualize those directions in your head, but the equation makes sense now, right?

>geometry is an obsolete subject to study
>group theory/set theory fundamentals should be taught at the same time as +-x/
>children be required to pass a test in order to be taught in public school
Are these acceptable thread topics for this bored?

>>14731910
was working on this one yesterday. Had no idea what to do with the i hat and j hat.

its easy enough using the equations provided but any time vector notation comes up my brain goes into retard mode.

Your explanation is helping me understand things a bit better tho. had no idea a cross product creates another vector.

>>14731926
>had no idea a cross product creates another vector.
yeah thats pretty important.
how far did you get in pic rel? we can walk through it together.

>>14731933
I looked up the solution because i felt pretty frustrated after 30 min. Pic is solution. I dont fully understand how to properly multiply the j and i so we can start with that

>>14723349
That has nothing to do with calc 3, that's just the vector cross product that you should either have seen in linear algebra/geometry or somewhere in high school

ie
[math]|\vec{v} \times \vec{w}| = |\vec{v}||\vec{w}|\sin(\theta)[/math]

and
[math]\displaystyle \vec{v} \times \vec{w} =
\det \begin{pmatrix}
i & j & k\\
v_x & v_y & v_z\\
w_x & w_y & w_z
\end{pmatrix}
[/math]

[math]-i = (-1,0,0)[/math]
[math]j = (0,1,0)[/math]

[math]\displaystyle (-i) \times j =
\det \begin{pmatrix}
i & j & k\\
-1 & 0 & 0\\
0 & 1 & 0
\end{pmatrix} = -k
[/math]

>>14731960
My highschool was poor, we never did any matrices and they did not offer linear algebra. it was just from basic algebra 1 to ap calc. We did do some geometry but it was more proof based and nothing with vectors. So i have no idea what's going in the matrices you have kindly typed up.

>>14731945
heres what you need to know:
1. the cross product of a vector with itself is zero
2. the cross product of two unit vectors is plus/minus the third unit vector
how do you figure out whether its plus or minus? you could visualize the directions in your head and use the RHR if you want, but theres a slightly easier trick. if you arrange them in alphabetical order, the unit vectors are i, j, and k. when you have a cross product equation, read it right to left like "a cross b equals c" or "x cross y equals z". if, when reading out the equation, youre reading i, j, and k in their alphabetical order, like "i cross j equals k", then the result is positive. but if youre reading it backwards from their alphabetical order, like "k cross j equals i", then the result is negative. you also have to imagine looping back to the beginning, like "k cross i equals j" requires you to go back to the beginning of the order, but youre still going from left to right so its positive. see why j x i = -k now?
>>14731967
i dont think i ever did a cross product until calc 3 or lin al

>>14731980
>read it right to left
ffs, i meant left to right

>>14731980
>>14731994
This is starting to make more sense to me. Ill try to find easier examples until I'm ready to tackle on more challenging problems. thank you!

>>14731967
The cross product of 2 3-dimensional vectors is just the determinant of the matrix that I defined there.

To calculate the determinant of a 3x3 matrix you do it like this

Start with the definition
[math]\vec{v} \times \vec{w} =
\begin{pmatrix}
i & j & k\\
v_x & v_y & v_z\\
w_x & w_y & w_z\\
\end{pmatrix}
[/math]

Copy the first 2 columns and put them to the right of the matrix
[math]
\begin{pmatrix}
i & j & k & i & j\\
v_x & v_y & v_z & v_x & v_y \\
w_x & w_y & w_z & w_x & w_y\\
\end{pmatrix}
[/math]
Trace a diagonal from each element on the top to the bottom as a product
ie, the 1st diagonal is [math] i v_y w_z [/math]
the 2nd is [math]j v_z w_x [/math]
the 3rd is [math] k v_x w_y[/math]

Add them together
[math]iv_y w_z + jv_z w_x + kv_xw_y[/math]

Now trace diagonals going the opposite way but with a minus
[math]-jv_xw_z[/math]
[math]-i v_z w_y[/math]
[math]-kv_y w_x[/math]
Then add them all together
[math]-jv_xw_z -iv_zw_y -kv_yw_x[/math]

And join both of them
[math]iv_y w_z + jv_z w_x + kv_xw_y -jv_xw_z -iv_zw_y -kv_yw_x[/math]

Join like terms
[math](v_y w_z - v_zw_y)i + (v_z w_x - v_xw_z)j + (v_xw_y - v_yw_x)k[/math]
And that's the cross product of a generic 3d vector. Obviously nobody remembers this formula, as it's a pain in the ass, just the process of how to calculate the determinant.

The definition for the unit vectors is [math]i = (1,0,0), j = (0,1,0)[/math], you can calculate the cross product of [math](-i) \times j[/math] as I showed above.
[math]
\begin{pmatrix}
i & j & k & i & j\\
-1 & 0 & 0 & -1 & 0\\
0 & 1 & 0 & 0 & 1
\end{pmatrix}
[/math]

[math]
i \cdot 0 \cdot 0 + j \cdot 0 \cdot 0 + k (-1) 1 - j(-1)0 - i \cdot 0 \cdot 1 - k \cdot 0 \cdot 0 = -k
[/math]

I'm learning online about vectors as part of a series on classical mechanics. So that I can add them to my notes properly, what branch of science do they fall under? Is it algebra?

Suppose [math]\Omega[/math] is a bounded, uncountable subset of [math]\mathbb{R}[/math].
Do there necessarily exist distinct points [math]x,y,z,w \in \Omega[/math] such that
[math]|x-y|=|z-w|[/math]?

>>14732041
were you able to do the other parts of that problem besides the j x i thing?

>>14732115
Algebra and geometry.

>>14732115
yea, algebra. but thats math not sceince fyi

>>14730076
An application of lagrange's reversion theorem used to construct a series solution to an implicitly defined function and a simplification to write it in terms of a finite number of hypergeometric functions.

>>14732227
How do I calculate square root of a number without calculator?

>>14733429
https://www.basic-mathematics.com/square-root-algorithm.html

[math]
\begin{matrix}
&&1.414\\
&&\sqrt{2} \\
&1^2 & 1\\
&&1\\
&& 100\\
1 \cdot 2 = 2&24 \cdot 4 = 96 & 96\\
&&4\\
&&400\\
14 \cdot 2 = 28 & 281 \cdot 1 = 281 & 281\\
&&119\\
&&11900\\
141\cdot 2 = 282 & 2825 \cdot 4 = 11296 & 11296\\
&&604\\
&&60400\\
&&...
\end{matrix}
[/math]

What is the geometric sum formula for any initial sum (going to infinity preferably)?

>>14734369
Sorry. That should be for any initial *index*.

>>14734247

Why do masses add up when two bodies come into contact? e.g. many topics explaining momentum use two moving balls as examples are used and when they touch somehow their mass adds up. Why?

>>14734628
well if theyre touching then they presumably have the same velocity so the total momentum of the system can be simplified as [math] \displaystyle
p = m_1 v_1 + m_2 v_2 = v(m_1 + m_2)
[/math]

>>14734369
[eqn]\sum_{k=a}^b q^k \\
= \frac{1}{1-q} \sum_{k=a}^b q^k (1 - q) \\
= \frac{1}{1-q} \left(\sum_{k=a}^b q^k - \sum_{k=a+1}^{b+1} q^k \right) \\
= \frac{q^a - q^{b+1}}{1 - q}
[/eqn]

>>14732175
yes i was able to. Sorry for the late reply.

Still i wish someone would explain why no physics teacher actually teaches anything. I dont even know why i bother to go to class when all the teacher does is just do a hard problem that maybe only 1 or 2 people in the class can follow. All that time wasted could give us a basic framework on how to approach these problems or even teach us vectors. Makes me think these guys are so closed minded that they think there is only one everyone learns.

>>14734803
ive had some great physics teachers. most of the professors at my school specialized in physics education, which a lot of people like to make fun of, but it puts out results. you shouldnt resent your teachers too much, its pretty hard to teach physics. and maybe dont be such a pussy and actually ask questions in class if you dont understand something.

>>14734369
If your sum is specifically a series (i.e., an infinite sum) then, the phrase you want to look up is 'shifting the index' of the series.
For example:
Say you have the series, [eqn]\sum_{n=5}^{\infty} 2(\frac{8}{13})^n[/eqn] and you wanted the initial index to be 0 instead of 5.
What you want is a slightly different series to account for the change in the index and the way you get that is you change the original series' index of summation to some different index like [math]m[/math] which is defined in terms of [math]n[/math] so that when [math]n[/math] is equal to the initial index of the original series, 5, [math]m[/math] is equal to the initial index you want, 0.
Obviously, for this problem we're going to want to define [math]m[/math] as [math]m=n-5[/math] so that when [math]n=5[/math], [math]m=n-5=5-5=0[/math].
Note: as [math]n\to\infty[/math] so does [math]m[/math], since, as [math]n[/math] approaches [math]\infty[/math], [math]m=n-5=\infty-5=\infty[/math] so both the lower and upper bounds are unchanged.

Finally, we must define [math]n[/math] in terms of [math]m[/math]: [math]n=m+5[/math]
So that you can replace all the [math]n[/math]s with their equivalent quantities [math]m+5[/math] in the original function so you can finally change the index.
[eqn]\sum_{n=5}^{\infty} 2(\frac{8}{13})^n=\sum_{m=0}^{\infty} 2(\frac{8}{13})^{m+5}=(\frac{8}{13})^{5}\sum_{m=0}^{\infty} 2(\frac{8}{13})^{m}=(\frac{8}{13})^{5}\frac{2}{1-\frac{8}{13}}=\frac{65536}{142805}[/eqn]
You can check with Wolfram Alpha if you don't trust me but just know that I already checked myself!

>>14734815
teacher doesnt answer any questions.

>>14734831
you have a bit of a defeatist attitude and youre not gonna learn anything like that. if you ask a question and the explanation didnt land, tell him to explain it again. if it still fails, ask the room if anyone else got it. best case scenario is that another student understands it and can explain it to you. worst case is that no one gets it and the prof realizes the severity of the situation.

To prove if x is real then ceiling(-x) = -floor(x).

But you can define x as:
x= floor(x) + e, where e is fractional part of x and 0<=e<1, and floor(x) = n.

or

x = ceil(x) - e', where e' is 1 - e, and ceil(x) = n.

but if i do:
ceil(-x) = ceil(-(floor(x)+e)) = ceil(-(n+e)) = ceil(-n-e) = -n+0

ceil(-x) = ceil(-(ceil(x) - e')) = ceil(-(n+(1-e)) = ceil(-n-1-e)) = -n-1

i thought they were supposed to be equivalent, what am i doing wrong?

>>14734910
> what am i doing wrong?
Well to start with x= floor(x) + e is not true when x < 0.

The same would be true for ceil() if x > 0

>>14734898
i said teacher doesnt answer any questions. No explanations are given in any detail. all we get it "figure it out yourselves".

>>14727435
k=1,2,3,4,5,6
n=6
p=1/6

66.51%

>>14734945
well i dont know what to tell you. read the book. and of course you can always come here if you need help.

>>14733429
https://youtu.be/csInNn6pfT4?t=6m30s
https://youtu.be/-J_xL4IGhJA?t=4m30s

>>14733595
2824*4=11296*

https://youtu.be/fEBSx075AKs

>>14714495
How the fuck I solve this, please helpme

>>14735195
[eqn]
a^{b+c}=a^b a^c \\
a^{b-c}=a^b a^{-c} = \frac{a^b}{a^c} \\
a^{bc}=({a^b})^c=({a^c})^b \\
2^2 = 4
[/eqn]

>>14735195
Solve what? It's an expression. What are you trying to do?

>>14735217
>What are you trying to do?
Solve it

Calc throws a 5 and I don't know why.

>>14735227
>Solve it
i think youre trying to say "simplify it"

>>14735195
Equal to 5, too lazy to work it out here, just trust me

>>14735238
I don't care about the answer my nigga, I need to know how to reach it.

>>14735244
use the identities i spoonfed you here >>14735211 to factor out [math]2^{2n}[/math] from the top and bottom.

>>14735195
[math]
\begin{align}
\dfrac{10 \times 4^n + 5 \times 2^{2n+1}}{7 \times 2^{2n} - 6 \times 2^{2n-1}} &= \dfrac{10 \times 2^{2n} + 5 \times 2^{2n+1}}{7 \times 2^{2n} - 6 \times 2^{2n-1}} \\
&= 2^{2n} \dfrac{10 + 5 \times 2^{1}}{7 - 6 \times 2^{-1}} \\
&= 2^{2n} \dfrac{10 + 10}{7 - 3} \\
&= 2^{2n} \dfrac{20}{4} \\
&= 2^{2n} \times 5
\end{align}
[/math]

>>14735244
Refer to >>14735211 and work out from there factoring out the 2^(2n-1)

>>14735227
>Calc throws a 5 and I don't know why.
What are you jabbering on about? n is a variable.

>>14735251
lol
>>14735253
it cancels out

>>14735253
>>14735251
they cancel out and you get 5

>>14735257
>>14735258
shush. you weren't supposed to tell him.

How do i do this sum?

Sum from i =1 to n: (-1)^(i-1) * (n-i)

this is terrifying

>>14735268
somone asked this exact question like a month ago

Does quantum randomness prove free will?

>>14735275
if you want it to

>>14735275
No because all the structures in the brain such as neurons are still macroscopic in scale and so unaffected by quantum uncertainty.

>>14735275
no, randomness, its random, not a choice

>>14735277
Ok
>>14735278
What is the consensus among neuroscientists?

>>14735285
That is the consensus.

>>14735254
>>14735258
>>14735211
>>14735249
thank you

>>14735275
I have another. Is it truly random or is it that we do not understand enough to predict so we label it as random?

>>14735369
>we do not understand enough to predict so we label it as random?
https://en.wikipedia.org/wiki/Bell_test
many worlds interpretation gets around the idea of randomness.

>>14735387
Interesting. Thanks.

How do I teach myself the entirety of precalculus in 3 days

>>14735654
This plus unit circle

Can anything non physical leave black holes?

>>14735767
You mean like without mass? If so, yes, look up Kugelblitz.

>>14725531
Call this a science board? Fuck me. A bunch of monkeys would probably have answered this vexing problem by now. You are all a pack of useless cretins.

>>14735273
i think it was me, i'm studying for a test

IT GOT ME AGAIN

>>14734910
> x = ceil(x) - e', where e' is 1 - e, and ceil(x) = n
This is incorrect. For a start, if x is an integer, ceil(x)=floor(x), otherwise ceil(x)=floor(x)+1 (i.e. ceil(x)=n+1 where n=floor(x)). Also, if e∈[0,1) then 1-e∈(0,1], but ceil(x)-x∈[0,1).

>>14734942
>Well to start with x= floor(x) + e is not true when x < 0.
It's true for all real x. floor(x) is the greatest integer less than or equal to x, i.e. x rounded toward negative infinity. x-floor(x)∈[0,1) for all x.

How do we know atomic clocks are so accurate? Where is the even more accurate clock that we compare atomic clocks to

>>14725531
requires a sponge to clean it

>>14736958
> How do we know atomic clocks are so accurate?
Because the second isn't measured as such, it's *defined* as a constant by a physical process. Typically transition between two specific atomic states. So the accuracy comes down to the apparatus used to count the number of periods in that transition. Then to confirm the timing more than one atomic clock is compared against each other to make an estimate on the error bars.

>graduate uni
>keep working part time wageslave job
>stop studying obviously
>start doing nothing but watch tv/films and browse the internet
>6 months of doing this later and suddenly I have problems thinking
>brain fog and confusion, start feeling really dumb and have problems remembering things
>decide to start learning language
>feel good about learning stuff again
>start continuing my uni studies as a hobby
>brain fog and confusion goes away, mind feels normal again
Wtf happened

>>14736966
No no no no!
I have made it quite clear that I am not looking for a solution. Its understanding that I seek. The understanding of the dynamic relationship between the specks of feces and the surface of the toilet bowl. I suspect that at the heart of the matter is some fanatically complex relationship between the gravitational constant, the isomorphic manifold properties of ceramics and van der Waals forces.

>>14714495
Is the following statement true?

If [math] f: X \to \mathbb R[/math], is continuous in [math] X \subseteq \mathbb R[/math], then there exists a segment [math] [a,b] \subseteq X [/math], such that [math] a < b[/math], and:
[eqn] \forall x \in [a,b] \quad f(a) \leq f(x) \leq f(b) \: \lor \: f(b) \leq f(x) \leq f(a) [/eqn]

>>14737156
No.

>>14737171
It intuitively makes sense though. Counterexample?

>>14737184
The Weierstrass function is not monotonous anywhere.

Does IVT hold for rational points in a continuous function? Basically, for any two rational points, can I find another rational point that satisfies the IVT inequality, given the function is real valued and continuous?

>>14737190
Thanks.

>>14737205
Consider
f(x) = x^2 - 2

f(0) = -2 < 0
f(2) = 2 > 0
But there is no rational x with f(x) = 0.

What is a live virus?
What is a provirus?
Are virus-specific antibodies an innate response?
Do the new variants have an completely different s protein?

>>14737214
Instead of for all numbers in between, we can have at least on number right, for which a rational inverse exists, right?

>>14737231
[eqn]f(x) = \sqrt{2} (x - x^2) + x[/eqn]
is rational at f(0)=0 and f(1) = 1 but it's irrational for all other rational values of x.

>>14737237
The output can be real, not my concern. My objective is to find out a rational number between any segment, such that its output is in between. The output can be real.

Can anyone explain what plasma actually is
And how does it emit light
I don't understand

>>14737156
No, e.g. if X is a collection of discrete points. And more generally, I think we have a counterexample with any bounded set with empty interior, since such a set wont contain any intervals [a, b].
Hence, for such a set and for any fixed epsilon, by vacuous quantification we can find a delta, such that |f(x)-f(y)|=0 < epsilon provided that |x - y| < delta. In particular just select a delta small enough to ensure that y in B(x, delta) iff y=x.

I think your claim should work for any continuously differentiable real-valued function on a set with non-empty interior.

How does one even tackle a problem like:
[eqn]\sum_{n=1}^{\infty}\frac{e^{\sin n}}{n}[/eqn]
It looks like you want to integrate it but the sine fucks up determining whether it increases or decreases. The integral doesn't look good either.
No other tests look right to me. And wolfram alpha says it diverges but doesn't explain why.

>>14737342
Seriously. It just says diverges but every single test it tried came up inconclusive. lmao.

>>14736569
>It's true for all real x
Depends on the definition of the fractional part {x}.

If {x} is defined as
{x} = x - floor(x), x >= 0
{x} = x - ceil(x),.x < 0

Hence, {-3.14} = -3.14 - ceil(-3.14) = -3.14 + 3 = -0.14
Thus -3.14 =/= floor(-3.14) + {-3.14} = -4 - 0.14 = -4.14

>>14737342
sin(n) >= -1
e^(sin(n)) >= e^(-1)
So the series is bigger than e^(-1) times the harmonic series that divergers to infinity.

>>14737257
i think thats true since there exists infinitely many rational numbers on any interval, but i think youd need measure theory or something to prove it.

>>14737397
Fuck, how do I prove this then. I am only supposed to know Calculus.

>>14737404
i dont know analysis (im not that other guy from an hour ago) but i imagine the proof would be something like "pick two rationals a and b, b > a, such that f(a) != f(b). pick positive rational c less than b - a and positive rational epsilon such that f(a + c) = f(a) and f(a + c + epsilon) = f(b). since the rationals are continuous (or some shit like that), epsilon can be made arbitrarily small for appropriate choice of c. so the difference between f(a + c) and f(a + c + epsilon) is at least 1, but the difference between a + c and a + c + epsilon is arbitrarily small, and the somehow proves discontinuity. QED"

>>14737356
Still no. floor() and ceil() are well defined. floor(x) is the greatest y s.t. y<=x, ceil(x) is the least y s.t. y>=x.

The original question used the term "fractional part":
>>14734910
> But you can define x as:
x= floor(x) + e, where e is fractional part of x and
It doesn't define it explicitly, but it's implicitly defined as x-floor(x), so the "fractional part" of -3.14 is 0.86.

So to get back to:
>>14734942
> Well to start with x= floor(x) + e is not true when x < 0.
Any real x, positive or negative, can be written as floor(x)+e for some e∈[0,1).

If x is negative, then e isn't what most people would consider the "fractional part" of x (that would be 1-e, unless e=0). But that's unrelated to his problems.

>>14737426
Sure, if you assume that's {x} is in [0,1), instead of (-1,1), then that follows. I'm not the one who answered originally, but I imagine he could have thought he might have made a mistake in the definition, as for {x} in (-1,1), we have
x = floor(x) + {x}, x >= 0
x = ceil(x) + {x}, x < 0

>>14737404
Let [math]x \in \mathbb{R}[/math]. Since the rational are dense in the real numbers you can find a sequence of rational numbers [math](a_n)[/math] with [math] \lim_{n \to \infty} a_n = x [/math]. Also since [math]f [/math] is continuous we have
[eqn]\lim_{n \to \infty} f(a_n) = f(\lim_{n \to \infty} a_n) = f(x)[/eqn]
So [math](f(a_n))[/math] is a convergent sequence of natural numbers. The natural numbers are a closed set so the limit of the sequence must be a natural number too.

Since this is true for every [math]x[/math] we get that [math]f(\mathbb{R}) \subset \mathbb{N}[/math].
By the IVT a continuous function maps connected sets to connected sets but the only connected subsets of [math]\mathbb{N}[/math] are sets that contain only a single element so the function must be constant.

>>14737359
Wow. Thanks a lot. That makes sense.

can you use basic calculus lin. alg. intro analysis (only as helpful optional foundation), and c++ knowledge of pointers/refs as allegory to this analytical entity, along with assemble fluency to analyze an A.I's 'neurohardware' or 'hardware psychology'?
or is there more to the topology of computers of c++ then pointers/refs? i.e. including other languages as well

>>14737789
cont. sorry for short scramble post.
i mean:
if it were talking to you in particular. or would 'neurohardware' i.e. bits and stuff in there orders and domains or w/e jsut still be gibberish concealed from the user?

>>14737404
Nevermind, I think figured it out:
Consider some [math] a \in \mathbb Q[/math]. Due to continuity of [math] f[/math] in [math] \mathbb R[/math]:
[eqn] \exists \delta > 0 \: \forall x \in \mathbb R \quad |a-x| < \delta \implies |f(a) - f(x)| < 1[/eqn]
Due to density of the rationals in the reals: [math] \forall \delta > 0 \: \exists x \in \mathbb Q \quad |a - x| < \delta [/math].
Therefore:
[eqn] \exists x \in \mathbb R \quad |f(a) - f(x)| < 1[/eqn]
Since [math] f(a), f(x) \in \mathbb N[/math], it follows that [math] f(x) = f(a)[/math]. Since we did not pick any specific [math] a[/math], it follows that: [math] =_{a \in \mathbb Q} f(a)[/math].

>>14737498
I don't really know enough Analysis to understand yours. Is my proof correct? I am unsure about the last step.

>>14737803
It should be [math] \exists x \in \mathbb Q \quad |f(a) - f(x)| < 1 [/math]

What is the formula for completing the square?

What's the difference between connexity and trichotomy in math?

>>14737929
[eqn]
(x+a)^2 = x^2 + 2ax + a^2 \\
x^2 + ax + b + k \; \; \; \; \text{(you're trying to find k here)} \\
x^2 + 2 \left( \frac{a}{2} \right) x + b + k \\
b + k = \left( \frac{a}{2} \right) ^2 \\
k = \frac{a^2}{4} - b
[/eqn]

if every single chemical bond that made up a person was broken and they were reduced to atoms within a single moment, would would it look like to an outside observer?
would they just seem to vanish? would there be some release of energy and visible smoke or dust or something?

>>14738309
there would be a very large explosion

>>14732163
Choose [math]\Omega[/math] to be a base of [math]\mathbb{R}[/math] as a vector space over [math]\mathbb{Q}[/math]. By construction there are no such distinct points.

i believe a set of numerical strings of length k is based on permutations of substrings of the digits of a constant plus some noise
given two random base-10 strings of length k, what is the expected number of matching digits after one is permuted into the other?

Prove by induction: [math]\sum_{i=1}^{n}5 \cdot 6^i=6(6^n-1)[/math]
[math]S_k = 6(6^k-1)[/math]
[math]S_{k+1} = 6(6^{k+1}-1)[/math]
If [math]5 \cdot 6^{k+1}+6(6^k-1) = 6(6^{k+1}-1)[/math]then the statement should be true as far as I understand but I don't know how I'm supposed to simplify the expression. Maybe I'm doing something else wrong.

>>14738510
5 + 1 = 6

Whatever happened to diamond nanothreads? They were supposed to be a revolutionary new material but then they disappeared and I've never heard about them since.

>>14738557
I don't understand.

>>14738592
[math]
5 \cdot 6^{k+1} + 6(6^k - 1) = 5 \cdot 6^{k+1} + 6^{k+1} - 6\\
=6^{k+1}(5 + 1 - 6/6^{k+1}) = 6^{k+1}(6 - 6/6^{k+1})\\
=6^{k+2} - 6 = 6(6^{k+1} - 1)
[/math]

>>14738601
Much appreciated anon.

>>14737098
Brave Anon, battling on against the overwhelming tide of ignorance and dogma.If only more people thought like you do we would have a base on Triton by now.

>>14737498
>>14737803
Nvm, I got it. Thanks.