/sci/ - Science & Math

How does one show that a specific function is strictly increasing. I've just computed f'(x) and it's obvious that f'(x) > for all x in R. Not sure if this is enough tho. In my calc class the prof shows its increasing by computing its inverse???

>>9644682
>How does one show that a specific function is strictly increasing.
By showing that function satisfies the definition of "strictly increasing".

>>9644692
Like so is it enough to compute the derivative and write f'(x) > 0 for all x in R

>>9644659
whats the point anymore?

>>9644682
https://en.wikipedia.org/wiki/Mean_value_theorem

If not and there exist a and b s.t. f(a)=f(b) then there exist a c in (a,b) such that f'(c) = 0 by MTV. Contradiction! QED.

>>9645018
>If not and
If not, then

In our lab we're meant to consider a relationship, say a = bx. In our lab instructions it asked us to make a 'linear plot'. The lab program we use has two distinct plots, linear (y = ax + b) and proportional (y = ax). Obviously the relationship is proportional, but am I assuming the instruction to make a linear plot wasn't considering this, and they actually want a proportional plot, or am I expected to analyze the data with an intercept?
It sounds incredibly autistic and nitpicky, but I've simplified things a lot and really we're meant to be analyzing the slope, comparing it to theoretical values, etc. which if we were to botch it allowing an intercept to be present would just be retarded.

>>9645037
a=bx is linear.

>>9645037
nigger just subtract the y intercept if that's what's worrying you

>>9645224
Yeah but 'proportional' is more accurate. I'll just put in an explanation why I'm doing a proportional fit.
>>9645301
It's not the intercept, doing an a=bx+c fit gives a different slope.

>>9645397
you have no clue what you're doing

>>9645400
retard
'subtract the y intercept' isn't the issue, the issue is fitting a line through any possible intercept instead of (0,0) gives a different slope.

>>9645408
>retard
yes, im the retard of course. maybe you should listen to your elders fuckboi

Is chemical biology a meme?

>>9645408
>fitting a line through any possible intercept instead of (0,0) gives a different slope.
No it doesn't.

Are you given data points? What data are you using to draw your linear plot?

>>9645420
Mostly. Most biologists learn biology first then shit their pants when they release how much chemistry they need to know to understand how the human body functions.

Biologists have a significantly lower IQ compared to real scientists. In my university there are multiple chemistry professors that actually bother to learn physics from the ground up before applying nuclear chemistry to their work. Biologists don't do that because they're mentally ill.

ok so im doing a lab report, experiment on e/m using magnetron and im stuck with N= number of turn per metre of solenoid.

the solenoid has 19 turns per cm and 12 no of layers. what exactly is my n? is it 19x12x100? help pls its 2:40am

>>9644659
>Hurp de durple
>Hands of purple

why do we need so many ways to express the same thing?

>>9645710
autism.

>>9644659
Okay so I was bored at work today and I thought of something(sorry brainlet here I can't do latex)

A+BC-D=X

Could you put values for A B C and D that x would yield the same result as if you "did it" from Left to right? Meaning (A+B)C-D=X

Or would that violate some fundamental rule of math, idk I kind of got obsessed with the idea of a mathematical palendrome

>>9646250
Obviously there's at least one solution, A=B=C=D=X=0. The question is what are all the solutions. Set the two equal and do some algebra, see what you get.

>>9646329
Damn it outside of 0

Thats a good point though I guess I'll just brute force with some algebra.

who was the influential scientist/physicist who had an equally intelligent wife who had to publish her works in his name because women weren't allowed to be smart back then (i think they were alive during the 18/19th centuries)

>>9646463
Probably a bullshit story. Women can't perform science.

>>9646250
[eqn]\begin{align}A+BC-D&=(A+B)C-D\,;\\ A+BC&=AC+BC\,;\\A&=AC\,;\\ A(1-C)&=0\,. \end{align}[/eqn]
So the two expressions are equal for any values A,B,C,D, when either C=1 or A is zero.

>>9646558
Thats so fucking awesome thanks!!
I kinda feel stupid for not figuring it out in my head while at work

What do chemists do? I know what they "do" but do they just stay in a lab all day?

>>9646583
Chemistry professors spend most their time in an office and instruct their graduate students what to do in lab.

>>9644659
Why isn't the substraction in natural numbers the same as the natural numbers between those 2 natural numbers including them? For example 5 - 2 = 3 however the natural numbers between [2,5] are 4

>>9646703
What in the fuck are you asking?

>>9646703
>Why isn't the substraction in natural numbers the same as the natural numbers between those 2 natural numbers including them?
Because subtraction is defined as the inverse of addition

how do i make methamphetamine?

>>9646703
>>9646769 is basically the answer: -a is the number such that a+(-a)=0. The number of numbers between two numbers m and n, say, is m-(n-1)=m-n+1. You add the one because subtracting n from m does not account for n itself, which is a consequence of how subtraction is defined.

>>9646814
Take orgo, you'll learn how to make very similar molecular structures. If you have a baseline intelligence, you'll be able to apply that information to methamphetamine. Then you have to turn your reactions to actual procedural steps.

>>9647036
Is it hard? How much time/money would i have to sink in it?

>>9647047
You can take online organic chemistry lessons for free.

As far as time, I don't know how intelligent you are. Probably not very if you're seriously considering manufacturing illegal drugs in your future.

Can someone help me understand mutivariable graph that are subject to one variable. For example how would I know how to graph something like z=y or z=y^2 and what does x mean in this situation

Can anybody help me with part F? The panel on the left is all the information I was given for this question. I feel like it should be pretty obvious but for some reason I'm just blanking out.

Hi, I just started with Velleman's "How to Prove it" and my question is about the example 1.1.1 at the beginning of Chapter 1.

In the arguments 1 and 3 the word "either" is what confuses me, my questions are: is the "or" in those statements "inclusive or" or "exclusive or"? Also, lets say we remove the word "either" from the statements, would the type of disjunction change or remain the same "or"?

>>9647072
First consider what numbers you have available. Are you working with integers or sinwaves? Then consider the slopes of each graph. The slope of each of them should correspond to the double derivative of the integral, and as such should waste no time at solving this problem

>>9647112
Integers i guess, but like more importantly what happens to the x values. Are they defined or something?

>>9647072
Just think of the yz-plane. Visually, z=y^2 should look a lot like y=x^2 in the xy plane.

>>9647133
z is not a function of x so it doesn't matter. Any change in x will not affect z.

>>9647154
>>9647157
this is what confuses me with double integrals when integrating with only one variable. I dont get the integration of dx when theres no x to find a integral of, if that makes sense

thanks for the help

>>9647166
There is an x and a y. A double integral is performed over a region R in the xy plane. If there's a function z defined on R, then z is a function of x and y. So you're integrating with respect to dA=dxdy which are just differential forms that help you keep track of what you're doing.

>>9647166
Also, if no x appears in the function you can still integrate by treating all the other variables as constant.

>>9647172
having a tuff time visualizing it. Like if the region is a x^2+y^2=5 for example and z=y^2 wouldnt that mean the region is outside the function thats being integrated meaning its undefined at the region?

>>9647184
No. It sounds like your R is bounded by the circle with radius root 5. z=y^2 is defined for all (x,y) in R. You can picture a circle lying in the plane. z is a "height" function for the points in that circle (or as a surface that floats above R). Notice that z doesn't vary with x. You can interpret that as meaning the gradient of z has no x component.

>>9647204
I'd like the add that if you integrate z over the region R, you get the "volume" of the space bounded by z on top and by R on the sides and the xy plane. Hopefully that can help you visualize what's happening.

>>9647204
Im sorta getting that, its just what im trying to say is if i were to plug in some x and y value into the circle(R) and figure out a point z. That z wouldnt be on the function z=y^2 since the circle is outside the function

>>9647222
The points in the circle represent the domain of the function z. The domain of a function doesn't need to intersect the range of a function (in this case the domain is all the points in the circle and the range is a real number output of z=y^2). In fact, the elements in the domain a completely different type of thing from the elements in the range (points vs numbers) so they will definitely never have any elements in common.

>>9647240
Things if the one dimensional analogue. For a definite integral, your region R is some open interval on the number line. The function integrated is traditionally y=f(x). y doesn't have to intersect the x axis for this to make sense.

>>9647240
>>9647244
alright i think im starting to get this. thanks a lot for the help

>>9646160
>motion has to start somewhere, unless you can somehow draw your curve in affine space.

Why? Linear constant motion can be described at any point.

Consider bullet, fired from a gun. The actual description of a movement starts few meters later when camera's objective captures it. This is point zero and we start to calculate time and distance/position from it. We KNOW it was moving before but because it is LCM we dont care where to start the measurements and we've already taken different than actual Xzero.

>>9647084
In english "either" usually means exclusive OR, in logic it can be ambiguous, it really depends on the intent of the writer.

>>9647084
>Also, lets say we remove the word "either" from the statements, would the type of disjunction change
I' say change. There is no more exclusion with "either" therefore even if it will both rain and snow tomorrow the statement is valid since at least one condition is passed

if ((1 > 0) || (2 > 0)) -> always true when any condition met

>>9647377
What are you trying to say here? Of course [math]P \oplus Q \neq P \vee Q[/math] in general, but I have no idea what you mean by
>if ((1 > 0) || (2 > 0)) -> always true when any condition met
Anyway removing either could still be exclusionary, since the two events could be mutually exclusive. It depends on the intent of the writer which is why we use logic and not english in the first place.

>>9647403
>It depends on the intent of the writer which is why we use logic and not english in the first place.
But you dont judge it by intent, you have no knowledge of intent here. All you have is laid down conditions and you judge them by hat's available.

Now, IF the writer specified region or weather conditions of the region then that would be context we could use to adjust logic. In some regions you can have both, snow and rain.

>>9647413
Correct, we have no knowledge of intent and therefore it's ambiguous. This problem would have been averted had it been formulated in logic to begin with. You do realize we're agreeing, right?

>>9644694
Yes

>>9647424
>You do realize we're agreeing, right?
n-no, we are arguing!

>>9647430
That picture makes me uncomfortable.

>>9647457

>>9647458
hmm

>>9644659
Homework question:

List all the impurities that occur during mixing of formic and sulfuric acid on 80C temperature.

I know it produces CO, but what are the others? This question is confusing.

>>9645437
>Biologists have a significantly lower IQ compared to real scientists.
you have a significantly lower IQ compared to a biologist

When should a transjugular intrahepatic portosystemic shunt procedure not be performed?

How do I bin data?
I have a lot of observed data points following a log function. I want to compress my data into several bins. How do I do this?

Do I fit this log function using the data I have for the whole range or do I fit it inside each bin interval?

I CANT COPY AND PASTE IN OCTAVE ON WINDOWS
please send help or explain how I can fix this

>>9647574
use matlab

>>9647593
I don't want to sign into the website and I want to support free software with octave ;_;

>>9647500
Look in harrisons gs or blamgarts surgery.
Mb when we have decompensation of systemic disorders, coagulation failure or can stop bleeding with less invasive methods

>>9644659
Why not permaban brainlets from /sci/?

>>9647084
"Either" means XOR, but since it is natural language, it would be assumed to be XOR anyways, the "either" just makes it clearer.

>>9644659
Letter's of recommendation.

I'm applying to PhD programmes and my main adviser told me I could write an LoR for him to sign. I'm going to ask my external examiner for another.

My third one, however, is a lecturer and secondary advisor who hasn't complete his PhD yet. Would this be acceptable to most schools or should I ask my HoD (didn't do any of my master's research with him).

>>9647595
>free software
>windows
PEBCAK

Could someone explain to me why the sqrt(2g) became sqrt(g/2)

I'm lacking in algebraic fundamentals it seems

Working the logic on paper would help a ton

>>9647645
Oh nvm, I guess the 2sqrt(h0)-2sqrt(h2) in the numerator translates to that in the denominator, just seems overly complicated to just change the denominator like that

>>9647574
use python

>>9647574
ctrl-shift-v

>>9647333
Thats irrelevant. When you start measuring the bullet is where you define your x0. Just because you don't measure where it starts doesn't mean the bullet wasnt there. In fact, that's the whole point of (classical) physics - to be able to determine either the future or the past of a system. This is similar to a discussion about potential. It doesn't matter where you define your potential to be zero, as long as you maintain the convention until the end.

>>9647060
i'm above average
Would you say it's harder than learning C# and coding a smallish game?

>>9644659
HELLO MISTER CONFUSED SCIENTIST, YOU ARE NOT ALLOWED TO TOUCH THE BINO WITH NITRIL GLOVES, GET OUT

>>9647875
yes
Unity will not explode in your face, no matter how shit your code is

>>9647905
dont worry i dont intend on making TNT

>>9647914
chemistry is nothing like programming
you're dealing with the laws of nature, not an API that someone designed to be useful
you've heard of meth lab explosions, yes? which do you think is more likely: they deliberately synthesized explosives for fun? or that they made a minor fuck-up when dealing with dangerous compounds that are a non-optional part of the process?

>>9647973
>you've heard of meth lab explosions, yes?
how often it is lethal?

This 2-vector: [math]v_{1}\land v_{2} + v_{2}\land v_{3} + v_{3}\land v_{4}[/math] is not decomposable right?

>>9647973
Chemistry isn't hard
quantum is hard

I saw this question in Liddle's introduction to cosmology:

If the cosmic microwave background is ~3K, how do microwaves heat food without violating the second law of thermodynamics?

I think the answer is that the spectrum produced by a microwave oven is not a black body spectrum, and is not in thermal equilibrium, but I'm not really sure. Anyone know?

If [math]P_n[/math] is the set of all polynomials with degree at most n, is [math]0\in P_n[/math].

I'm fairly confident it is, but i don't know how to reason it. My main problem is that if the degree of 0 is not even defined, how can i say it is less than n or make any comparison at all?
The book solution says "The zero polynomial 0 does not contain any terms at all. In particular, it does not contain any terms of degree more than n". Though i think i'm misunderstanding something because the zero polynomial does have terms doesn't it (namely 0)?.

>>9648124
https://en.wikipedia.org/wiki/Degree_of_a_polynomial#Degree_of_the_zero_polynomial

>>9648136
so in that case i can consider it to be -1 or -infty

>>9648146
>so in that case i can consider it to be -1 or -infty
Yes, it's just convention

Hey /sci/ what are some must have books if someone wants to get into biology? Starting entry level to more advanced stuff.

Isn't it ironic how "stupid questions thread" is the most sane and productive thread, where people actually ask smart questions? Every other thread on the frontpage is brainlet shit from HS dropouts.

>>9647975
Well, given that most methlabs are in enclosed spaces or even underground they can get pretty lethal. But no need to be worried as you certainly don't own one as a law-abiding citizen.

>>9648058

Can you elaborate on the connection between CMB and the the microwave?

Why would you even think that the 2nd law is being violated?

I had to take an IQ test when I was 12. How accurate are the results I got back then for my current, adult IQ?

>>9648146
Only [math]-\infty[/math] makes sense. That way, you keep these:
[eqn]\deg\left(P \,\times\, Q\right)\ =\ \deg\,P+\,\deg\,Q[/eqn]
[eqn]\deg\left(P\,+\,Q\right)\ \leqslant\ \max\left(\deg\,P,\, \deg\,Q\right)[/eqn]

To solve the lagrange equation for any coordinate system, is the particle always required to be on a surface?

>>9648306
CMB and microwave radiation are at similar wavelengths, that's all.

>Why would you even think that the 2nd law is being violated

I wouldn't, the 2nd law isn't violated. It would however be violated if an object in deep space which was only in thermal contact with the CMB was heated up to above the temperature of the CMB, since then heat would be flowing from cold to hot. Obviously that doesn't actually happen. Then, to restate the question, why can you heat your soup up in a microwave oven where the radiation is of a similar wavelength to that of the CMB, but not in deep space?

Here's the actually question in Liddle if I've not done it justice.

>>9645037
Specifically what type of data are you modeling? Does it make sense for the point (0,0) to exist, as with absorbance? If yes, stick with y=ax.

>>9645427
Yes it does. A proportional plot and a linear plot of the same data would have different slopes, assuming the y intercept was not zero.

If there are 22 days in a month and 8 hours in a day, then:
Daily salary = Annual Salary/22
Hourly = (Annual/Daily)/8
?
Is that wrong?

>>9648571
Hourly should be:
(Annual/22)/8
My bad.

>>9648571
>Daily salary = Annual Salary/22
>Is that wrong?
Yes.

>>9648571
>is that wrong?
yes

Daily salary = annual salary / (number of days in a year)

>>9648540

That's a simple question of the difference between energy and power. The intensity of radiation in open space from CMB is going to be nothing in comparison to the intensity of microwave radiation in an oven.

Also while microwaves in a microwave oven have the comparable wavelengths, I am not sure that you can also apply statistical mechanics to that situation, since you do not have something resembling a gas, as with CMB photons in free space. So you cannot just assign a temperature to the microwave radiation in the same way.

I'm building a Class 2 Type B2 biosafety fumehood, should I use a stainless steel interior or some type of coating? I don't know much about the interior specifications that define this type of hood, but I'd like to get it right.

Anyone here who has ever or using Moodle? I have been asked to simply put the course's titles, but the thing is, I get to Courses-[Section]-[Subsection]-and from this point I would have to create 5 more sections, one for each year which would require a subsection each for all the courses in that year.

But, when I reach the subsection I dont see how I can create these 5 with a dropdown menu.

>>9648571
>Daily salary = Annual Salary/22
no, it will be monthly salary total/22

however, some months may have less working days so

>>9648585
>The intensity of radiation in open space from CMB is going to be nothing in comparison to the intensity of microwave radiation in an oven.
If I have one black body maintained at say 500K, and an object at room temperature which is brought into thermal contact with the black body, then its temperature will increase until it comes into equilibrium with the black body. If I repeated the experiment, but added a second black body at the same temperature, thereby increasing the intensity of the radiation but not changing the temperature of it's black body spectrum, the only difference would be that the cooler object would heat up faster. It could never become hotter than 500K.

I don't think you can just say the CMB is lower intensity than the radition in a microwave oven, because given enough time, an object in thermal contact with the CMB would still be able to exchange any amount of energy with the CMB, it would just take longer.

>I am not sure that you can also apply statistical mechanics to that situation, since you do not have something resembling a gas, as with CMB photons in free space. So you cannot just assign a temperature to the microwave radiation in the same way.
This feels right, but I guess I am still left wondering why you can't treat the radiation as a boson gas since it is after all just electromagnetic radiation. It's not black body radiation, but radiation produced by the magnetron though some other mechanism.

Is there a more optimal way to transform this to standard polynomial without doing the multiplication?

>>9648655
>Is there a more optimal way to transform this to standard polynomial without doing the multiplication?
No.

>>9648655
its not like doing the multiplication is that hard

>>9648665
it is not about being hard just thought there is more optimal way

>>9648339
Sum of infinity and a number is not well-defined

A bottomless pit brainlet is coming into this thread. Soon to be third-year (I hope) applied math (comp. sci) major, but in spite of that fact I've managed to get this far, my skills are completely underdeveloped since I struggled with depression, and I usually:

1. acquire a good reputation with professors by bullshitting professionally, pretending to be smart, etc, so i receive a good mark, so exam becomes unnecessary.
2. cheat on exams by making cheat sheets or using tech like microheadphones
3. english is not a native language here, so if there's a coursework or essay or whatever is to be done, i just google all *.pdf using arxiv/sci-hub/libgen i can find and translate, if there's a unique task i am probably fucked or hope that profs will let me pass as is
4. trying to get into the group who would do all the work
5. we have programming tasks here and there, I just simply Google everything I can find and then re-write, code is easy to read but I will never write something like that by myself

We have pretty advanced topics right now, and I do struggle with everything, in general. Even calculating integrals is tiresome, I'd simply stare at the problem for an hour. Ready to bet one hundred bucks that my groupmates are laughing how stupid I am. So, soon enough I'll have four free months. Is there anything I can do? Simply gather analysis/linear algebra/diffeq/whatever and try to solve problems by myself? I have NO fucking clue how to study, doing this since 9th grade.

>>9648678
>Sum of infinity and a number is not well-defined
https://en.wikipedia.org/wiki/Extended_real_number_line#Arithmetic_operations

I want to improve my math.
give me some good books to start with, please.

How do I know if I'm depressed?

>>9648053
doesnt look like

>>9648419
if by surface you mean abstract manifold, then yes

>>9648419
No. The fact the particle isn't on a surface means you have potential energy (I'm assuming).

Give more information for a better answer than that.

>>9648693

>>9648696
What responsibilities are you supposed to be doing that you aren't because you've given up and don't have the care or the energy?

>>9648716
meme books

>>9648737
meme iq

>>9648261
Campbell

>>9647499

t. bio undergrad in fiery defense of his major

>>9644659
Why does the gravitational force decrease after going 1m into earth

>>9648890
The reason underlying it is quite mathematical, but the basic result is that you feel no gravitational force from the inside of a spherical shell of matter.

When you go deep into the earth, the contributions to the gravitational force you feel then are the contribution from the sphere of matter deeper than you, and the contribution from the shell of matter outside of you. So if you dig down to a depth d (see figure), then the sphere of matter you're outside of is of radius R-d if R is the radius of the earth. Since the spherical shell of matter around you of thickness d doesn't exert a force on you, then you are only feeling gravitational force due to the smaller sphere, which contains less matter than the entire sphere, and is hence less massive, so exerts a smaller force on you.

In addition, I would add that to get some intuitive understanding of why a spherical shell exerts no force on you if you're inside it, imagine you dug down to the centre of the earth. There's equal amounts of mass above you, below you, to the left, to the right, etc. So whatever gravitational force each bit of matter would exert on you is cancelled out by a force in the opposite direction from a piece of matter opposite to it.

>>9648924
>So whatever gravitational force each bit of matter would exert on you is cancelled out by a force in the opposite direction from a piece of matter opposite to it.

So as you go from the origin to the surface of the sphere, the net gravitational pull does not change because even though you're closer to the surface, there's less of that surface that can tug you in that direction. And the same principle would then follow for the Lorentz force on a sphere.

>>9648960
yes basically.
that follows from the form of the force as [math]\frac{1}{r^2}[/math] but would not be generally true for any force law. it's quite a remarkable result that also is true in electrostatics for shells of constant charge since the electrostatic force also goes as [math]\frac{1}{r^2}[/math].
If you're familiar with maths you can show this by solving the equation of the gravitational field[math]\nabla^2 \phi = 4 \pi G \rho[/math] considered for a shell of constant density where [math]\phi [/math] is the gravitational potential.

>>9648715

My idea of a surface was purely arbitrary and a sort of elementary name for a manifold, as >>9648713 points out.

>>9648713

That's insane. This really changes how I think about motion in space. fuck man, that's awesome.

>>9649051
symplectic geometry deals with this sort of stuff, may be worth checking out more math oriented books like Arnold classical mechanics

>>9649069

Awesome, I'll check it out. Thank you for the input

For pentagrid tubes, the oscillator section: can I opt to not use the Hartley oscillator with the tapped coil and instead set up that section not as an oscillator but rather as a cathode follower and I'll feed in a signal generated by a semiconductor oscillator? Will it still still amplitude modulate when configured like that?

Can I also construct this circuit without coupling and IF transformers. My application is fairly broadband and I don't need or even want selectivity. The output of the mixer is going to an envelope detector, log amplifier, and video amplifier. Not to an antenna.

Any geologists here? Did you make the right choice or do you wish you went for something else?

How exactly does this imply that every finite dimensional complex division algebra is of dimension 1?

>>9648615
Can't help, but when I used Moodle years ago I remember it being fucking shit, so you have my sympathies.

>>9648817
>fiery
you sound like a homosexual

>>9649722
I think I solved it, I dont really like this interface, wonder if this Canvas is actually better. Oh well, thanks.

Was doing this problem earlier and had a cubic polynomial (-1/2)*x^3 + (2)*x^2 + (-5/2)*x + 1

and I needed to factor it into (1-.5*x)(1-2x+x^2) to finish the problem.

so I get that I can check that it turns into the cubic when you multiply it out but I need to be able to do that factorization. What are the steps to always be able to figure out how to factor a term out of a cubic?

>>9649869
too much effort
dont bother

I did just fine on all the other problems in the chapter, but I've literally spent an hour trying and failing to get this equation down to only one [math]x[math] term. What am I missing?

I did just fine on all the other problems in the chapter, but I've literally spent an hour trying and failing to get this equation down to only one [math]x[/math] term. What am I missing?

>>9649869
Even better, this guy will teach you how to do a quartic

https://youtu.be/olRi5-AOn1A

Can someone tell me what in the actual fuck a "field" is in the context of algebra? The best I could find (that I could actually understand), is that a field is group that transforms like the real number do. But then how do you describe what the real number are without circular logic?

>>9649986
Try writing legibly holy shit

Whats the best way to study/engage with something youre only mildly interested in?

>>9648684
Bump. Is there any hope?

Should I even bother going to med school if I wouldn't graduate until I'm 29 or 30? I feel like I could move up to good paying positions with my undergrad before I would have even finished med school.

>>9650039
I did a lot of this and what helped was having a goal or something on the line. If there is nothing on the line then why are you worried? For example I had to do several nonsense subjects completely unrelated to anything to get into my major so every time I thought about slacking off I remembered how I'd feel if I had to waste another year of my life because I didn't get a high grade in fuckass subject #3.

>>9650048
If you have a desire to do it then age is not a factor. Medicine is a field that you can do at almost any age. Like law. People, not so rarely, become doctors in their 30s and 40s. Some lawyers dont start law school until 40.

Take the opportunity. Its better than a research field like math or physics. If you start late in those, youll never get post grads.

>>9650059
Sounds good. My main concerns come from money, job conditions and wasting my youth but I guess they're pretty minor. Can always fall back on my undergrad which is in a practical field.

>>9649986
FUCK I realized what it was. I got the [math]B[/math] numerator for my partial fraction wrong because I divided by 3 instead of multiplying. God dammit I'm so disappointed in myself.

>>9650018
That writing's a hell of a lot neater than the homework I turned in in college, and the professors never had a problem with it. Maybe it was readable to them because they actually understood the mathematics?

>>9650136
>fraction decomposition and odes
>understood
hmmmmmmmmmmm

On series:
How can you add a finite to an infinite series?
And when is a partial sum good enough (had converged on a value good enough) for a finite and an infinite series?

>>9650140
I have no idea what you're getting at.

>>9650087
>wasting my youth
As opposed to what? Running around sticking your dick in everything you can?

Im 28 and only recently did I discover my love for physics. I actually did waste my youth doing bullshit and now Im too old to make it in physics. Still 3 years away from my undergrad degree even tho ive been in school for 9 years. Education is not a waste, trust me. Me and so many others would give almost anything to go back and focus on education

>>9650165
>How can you add a finite to an infinite series?
What does that means?
A finite series is just a number, just add it to the first, or n-th part of you series, or shift the whole thing by one and start with that number.

>And when is a partial sum good enough (had converged on a value good enough) for a finite and an infinite series?
All finite series converge, that should be obvious.
And for an infinite series there is no "good enough", you have to *show* that the partial sums converge, there are many tricks and theorems to do that, but it is by no means always easy.

>>9644682
idk if its correct, but this is what i remember from my hs years
A,B included in R
f:A->B
f is strictly increasing if for any x,y included in A we have f(x)<f(y)

>>9650006
>Can someone tell me what in the actual fuck a "field" is in the context of algebra?
It is a set with two operations which satisfy the axioms described here:
https://en.wikipedia.org/wiki/Field_(mathematics)

It is conceptually very similar to what a group is, just that you have "two groups", who also have an interaction, the distributivity.

>>9650006
Someone pls point me in right direction :(

>>9650184
So it's like a group with two operations defined instead of one

>>9650192
More like "two groups", who work together, but yes.

>>9650192
i believe two groups is a more accurate definition because a group (at least in my abstract algebra course) is canonically defined with only one operation and a set

>>9650174
Good advice thanks.

Best book to self-study linear algebra? I have exposure to basic concepts such as matrices, determinants, linear transformations, eigenvectors/values from uni, but at taking a more advanced course next semester and want to prepare a bit beforehand.

>>9650174
Why do you think it's too late now?

still don't understand what a surface integral is

>>9650522
a surface is made of an infinite number of infinitely small little squares of dx*dy size
When you're integrating a surface you're summing all of them, which gives the size of the surface in it's entirety

>>9650594
why is it dy/dx if dy = dx since it is square?

Ssquare = a^2

>>9650612
they're the differentials of the y and the x axis
they're both equally infinitely small

>>9650522
when you do a standard integral you're adding up the contributions from lots of little segments of a curve.
when you do a surface integral you're adding up the contributions from lots of little segments of a surface.
to take a simple example, if we do the surface integral over a circle with nothing in the integrand it should be the same as the area of the circle since you are just summing the area of the circle
[eqn] \int_S d a = \int^{2\pi}_0 \int^R_0 r d\theta dr = \pi R^2 [/eqn]
as expected. If you had something else in the integrand it would weight each term in the sum, so you wouldn't get the area of the circle.
for a more interesting example, consider Gauss's law for the electric field in integral form:
[eqn]\oint_{S} \mathbf{E} \cdot \mathbf{n} d a = Q/\epsilon_0[/math]
where Q is the total charge enclosed by the surface S. The left hand side is an integral over any closed surface you could imagine in space, with the integrand the dot product of the electric field and the normal to the surface. If then you have 0 charge enclosed within your surface, the left hand side must evaluate to zero, so you must have as much electric field pointing inwards as pointing outwards. To give an analogy to hydrodynamics, if you imagine the electric field as a fluid flowing through space, this statement would be that in a region of zero charge, you would see a net flow of zero into/out of the region. In a region with a positive charge in however, you would see a net flow outwards, and vice versa for a negative charge.

>>9650723
oops
[eqn]\oint_{S} \mathbf{E} \cdot \mathbf{n} d a = Q/\epsilon_0[/eqn]

I must have brain problems because I literally don't fucking understand electricity.
If Voltage is the "push" of electrons around a circuit, and adding elements to the circuit causes a voltage drop, then what happens in the part of the circuit whose voltage is 0? The voltage is 0 so there shouldn't be no movement at all, but that of course makes no sense.

Ok so having issue wrapping my head around this:

According to specs of similar triangles, only corresponding sides are proportional in equation.

Therefore, since AOB similar to COD then corresponding sides should share the equal angles.

Therefore, CD/AB = CO/OB = AO/OD

But the proper solution for this exercise uses proportion:
BO/OD which is wrong, because these ARENT corresponding side, they share different angle with CD and AB (if you can rotate AOB 180deg you will get a "smaller" version of COD) so their ration shouldnt be equal.

Wtf?

>>9651134
fucked up pic

>>9651131
If the voltage across an entire circuit is 0 then 0 current will flow in the circuit.
>what happens in the part of the circuit whose voltage is 0?
it doesn't make any sense to say that a part of the circuit has 0 voltage. Voltage is only defined between two points in a circuit. If you have no resistance between two points in a circuit then there is no potential difference between those two points, meaning no energy is lost by electrons between those two points.

>>9651156
Okay I get it now, thanks.

Hi.
So I'm trying to understand this algorithm. Please tell me where I'm messing up. It's from Final Fantasy 6.

I'm trying to find a theoretical highest possible melee damage for a single attack. Lets suppose this game wasn't limited to just 16 bits, and the damage cap wasn't 9999. Lets pretend the overflow problem doesn't exist, so once it hits about 65,000 it doesn't loop back around to 0.

So, I'm using Terii Senshii's FF6 algorithm FAQ on GameFAQs. Going by those steps.
1.) Assume vigor to be 128. Therefore, Vigor2, the stat used for determining damage, is 255.
2.) Battlepower will be considered 255 for purposes of this exercise. Assume Lightbringer weapon.
3.) Assume wearing a Gauntlet
4.) Level 99
5.) Wearing a Hero Ring.
6.) Single Target
7.) Front row/row closest to enemy (full damage)
8.) A Morphed (+2), Berserk (+1), Critical Hit (+2). I presume this means you take the regular damage and multiply it by 6.
9.) For Random Variance, assume 255. We doin' max damage.
10.) No Safe (full physical damage.)
11.) No Defending (full damage)
12.) Target not morphed
13.) Target is in front row, as well (full damage)
14.) Target hit from behind.
15.) Assume target has NO defense stat. Full exposure to all damage. Impossible, but exercise.

The result I got was 211,371 + 1 damage. I think I messed up. Algorithms are kind of new to me.

How do I prove the Fourier series for [math]e^{x}[/math] doesn't converge to [math]e^{x}[/math] for all but finitely many values?

>>9651263
Damage maxes out at 9,999 in that game. Only way to do ore damage in a single round is to have multiple attacks, like the Genji glove or whatever it was that let u deul weld

>>9651315
>Lets suppose (...) the damage cap wasn't 9999

>>9644659
The automatic grader will accept this as an answer, but could this be simplified any further?

Why are most automata theory vids on youtube made by indians?????

>>9651327
if you take the limit as h->0 you could simply write the derivative but I guess you've not been asked to do that.
You could multiply out the fractions in the numerator and see if you get any simplifications, but I think how you've written it is much clearer.

Let's assume I drop something rigid onto the floor. Newton's third law tells me that the floor exerts a force equal and opposite to that of the rigid object.
Now what my low IQ mind doesn't understand is: why does the object (like my pen) bounce instead of dropping dead?

>>9650616
>infinitely
Infinitesimally.

>>9651351
>Infinitesimally
Infinitesimal literally means infinitely small my good friend

>>9651315
yes, I'm aware of that.

But, you can do more. It just doesn't show up.

For example, take Celes.
Raise her Magic stat as high as you possibly can by leveling her up with Zoneseek, or some other +2 Mag.
You can do so much damage that it causes buffer overflow. Damage is actually calculated over 9999, it just doesn't display it.

>>9651337
Clear your entire view history and search history.

Once you click on a video from India, everything Youtube shows you will be Indian shit.

>>9651306
it does converge to e^x.
What type of convergence? Uniform? i don't fucking know what this is meant to mean.

>>9651349
Think about what happens if you drop a spring. It'll hit the floor and compress, which imparts some potential energy to the spring (it literally gets heavier), and its remaining energy will translate into a force applied to itself across a distance. Determining how much energy a given material can reabsorb I think is fairly complicated, but I'm sure there's a formula for it.

>>9651352
So when the author of a calculus textbook inevitably writes "infinitesimally small" they're actually saying "infinitely small small"?

>>9644659
Is it theoretically possible for us to create a new strain of bacterium that can digest and therefore destroy carbon to carbon bonded plastics? If so, would it be a good idea to construct garbage plants that contain this bacteria so we could break down some of the plastic in landfill?

>>9651413
yes and yes

>>9648924
Brilliant, thanks. These threads are very useful for brainlets like me.

>>9651414
I think this is the first time I've got an affirmative answer to an idea i've posted on this board.

OK. So, I mostly understand what is the "determinant" of 3x3 matrix, which is a volume of parallelepiped, placed upon vectors [math]\vec{a}, \vec{b}, \vec{c}[/math] as basis.

But I fucking fail to comprehend how does jacobian, hessian, etc are graphically represented. Does the question even make sense?

>>9651551
I don't know about the others, but the jacobian has a geometrical interpretation as the factor by which the volume element changes under a change of variables

>>9651551
[math]H(f(x) = J(\nabla f(x))^{T}[/math]

What were Ancient World maths problems like ?

Suppose a laureate of the Fields medal travel back in time and become somehow consul or Rome. What is going to change ? What would calculus bring to the daily life or Romans ?

>>9651686
https://en.wikipedia.org/wiki/Moscow_Mathematical_Papyrus#Exercises_contained_in_the_Moscow_Papyrus
>If you are told: a truncated pyramid of 6 for the vertical height by 4 on the base by 2 on the top: You are to square the 4; result 16. You are to double 4; result 8. You are to square this 2; result 4. You are to add the 16 and the 8 and the 4; result 28. You are to take 1/3 of 6; result 2. You are to take 28 twice; result 56. See, it is of 56. You will find [it] right

>>9651551
> So, I mostly understand what is the "determinant" of 3x3 matrix, which is
It's probably more useful to think of it as the volume scale factor. Transforming any solid by the matrix will scale its volume by the determinant.

> But I fucking fail to comprehend how does jacobian, hessian, etc are graphically represented. Does the question even make sense?
If a function is smooth, then you can find a sufficiently small neighbourhood around any point where the transformation is approximately linear. The Jacobian describes that transformation.

If you imagine transforming a grid by a function, then the Jacobian describes the scale and orientation of the grid when you zoom in far enough that the lines appear to be straight.

>>9651694
Geometry and construction, so

Then what else ? Did they need advanced mathematical reasoning for adjusting taxes, optimizing production, ballistic aiming ?

Let's talk hydrogen bonds. What's preventing the hydrogen from getting closer to the proton acceptor? Why is a h-bond distance always within the range of 1.5 - 2.5 A and very rarely less?

>>9651686
>>9651694
It is worth also mentioning the Rhind Papyrus from Egypt. https://en.wikipedia.org/wiki/Rhind_Mathematical_Papyrus

Check pic related out if you're interested in more, I think the 2nd or 3rd chapter goes over both of these in more detail.

>>9651724
>What's preventing the hydrogen from getting closer to the proton acceptor?
The oxygen's negative charge is distributed too thinly across the molecule to keep a third proton fully connected. It'd kinda be like sprinting while holding 3 basketballs; both your hands are occupied, so the third ball has to sit tenuously on top of the other two - which won't be for long if you're actually sprinting.

>>9651724
>Why is a h-bond distance always within the range of 1.5 - 2.5 A and very rarely less?
Mostly due to the fixed value of electromagnetic forces, and similarity between different types of hydrogen-bonded molecules. Inherent properties in matter make it energetically unfavorable for molecules to drift too far away or pull too close up to one another; springs work the same way.

Anything i can do to boost my intelligence similar to Adderall?

>>9651776
>100 bread loaves will be distributed unequally among 10 men. 50 loaves will be divided equally among 4 men so that each of those 4 receives an equal share y , while the other 50 loaves will be divided equally among the other 6 men so that each of those 6 receives an equal share x . Find the difference of these two shares y − x and express same as an Egyptian fraction.
Perfect, I was also looking at problem they didn't even tried to solve or thought there was a solution for, like time varying problem that required integrals

>>9651814
study

>>9651814
Meth

>>9651814
>boost my intelligence similar to Adderall
That's really not how it works.

The only thing that has ever made me work quicker and more sharply than I'm normally capable of is sheer emotional stress. And it's not reliable at all. You've honestly gotta accept that your raw brain power can only be augmented indirectly and temporarily. If boosting overall intelligence was remotely possible, it would no doubt be part of a treatment plan for retards who are too dumb to button their own shirts, but it's not. Retards are born retarded and stay retarded; and genius kids grow up to be genius adults.

>>9648684
oh my

>>9648684
>>9650044
Get a TI-Nspire CX CAS or TI-89 Titanium if you haven't already. Learn to use the CAS so you at least have the option of turning off your brain a little if you're pressed for time.

Excuse the armchair psychiatry, but it sounds like you might be struggling with more than depression. Have you considered treatment for generalized anxiety or ADHD?

My Linear Algebra class is being taught more like an engineering course that a math course. She barely touches the proofs and theorems, and none of the quizzes/tests ask anything about them. It's almost all computations.
Is this normal? Do these theorems not matter much for later classes? Or am I getting shafted and will have to redo the course on my own time?

>>9650214
axler LA done right>>9652041

I'm young.
What math problem should I dedicate my life to?

I don't care about fame or anything. I just want to commit myself to something.

>>9652049
P=NP

I used the following inequality in a question:
since sin(x)<=1 for all x, then [math]x^3\left(\sin x+\frac{1}{x}\sin\left(\frac{1}{x^2}\right)\right)\leq x^3\left(1+\frac{1}{x}\right)[/math]

it is obviously wrong just by looking at the graphs, but why? i cant figure out what is wrong with my reasoning

>>9652087
[math] x^3\left(\sin x+\frac{1}{x}\sin\left(\frac{1}{x^2}\right)\right)\leq x^3\left(1+\frac{1}{x}\right) [/math] idk why mathjax doesnt seem to work for me today

>>9651349
How can something be equal and opposite?

>>9652087
>it is obviously wrong just by looking at the graphs, but why?
Why should it be right?

>>9652096
Equal in magnitude; opposite in direction.

>>9652105
it's not and shouldnt be right. my main question is why is my reasoning wrong?
not sure why i "but why?" actually

>>9649986
You don't hand shit in like that do you?

>>9651776
>https://en.wikipedia.org/wiki/Rhind_Mathematical_Papyrus
nice tinfoil you fucking spazz

Anybody have the picture where it has the quote "Run in the direction of your fears" And some dude running towards Maxwell's equations with a sheet over his head

>>9652049
Don't think like this if you haven't even started an undergrad.

>>9651790
>The oxygen's negative charge is distributed too thinly across the molecule to keep a third proton fully connected. It'd kinda be like sprinting while holding 3 basketballs; both your hands are occupied, so the third ball has to sit tenuously on top of the other two - which won't be for long if you're actually sprinting.
Thank you!
Can I ask another question if this is the case, what happens if the hydrogen atom does move closer to the proton acceptor/oxygen atom? Such as through vdw forces or heat vibration.

Is it forced away to a more reasonable distance? Or does it just stay where it is, in a lower energy state?

>>9647430
The food doesn't look good

>>9652236
>Is it forced away to a more reasonable distance?
If unperturbed, yes. When the hydrogen bond gets very short, there's a build up of potential energy - exactly like a spring - and the shorter it is, the more violently the particles will rebound as they move back into equilibrium. The "reasonable" distance is the lowest energy state, and the bond will approach that distance once the excess heat energy leaves the system and it reaches equilibrium.

>>9652161
I've got dysgraphia. Trying to write very neatly would probably take me about 5 times as long as anyone else, and trying to write semi-neatly just makes my stray marks more pronounced when I inevitably drag my pen in the wrong direction. Believe it or not, I was actively trying to make my work in that post more readable than usual. So, if you think that's bad, my notes and back-of-the-envelope calculations will fucking shock you. Maybe I'll find an especially ugly one and post a picture.

>>9652336
>dysgraphia
aka undisciplined soyboy

>>9651790
>The oxygen's negative charge is distributed too thinly across the molecule to keep a third proton fully connected.

I mean, H3O+ is a thing, I think it's more the fact that the other oxygen is more strongly bonding to it.

>>9652203
Why?
Honest question.

>>9652401
>H3O+ is a thing
It's a thing that doesn't exist on its own. Hydronium is a product of an equilibrium reaction involving two water molecules, and it's unstable enough that you can assume protons are constantly detaching and reattaching to different molecules - keeping the overall concentration the same, but also keeping the protons in a continuous state of flux.

Find the probability that at least one member of a married couple will watch this show.

Probability of Husband = 0.4
Probability of Wife = 0.5
Probability of Husband Given Wife = 0.7

I thought I could just find the probability that neither watched (0.6 * 0.5) and take the complement, but that's wrong.

I assume I'm violating some assumption of independence here. I am having a hell of a time with conditional probability right now. I get the principle with classical probability, but I am getting absolutely fucking dicked on these questions. For the love of god, somebody help me figure out what I'm missing in this topic.

>>9652600
I think the reason you can't do that is that the probability that the husband doesn't watch the show includes the possibility that the husband doesn't watch but the wife does. you'll have to find some way of subtracting out that probability, probably by using Bayes theorem.
I'm not quite sure right now, it's a while since I've done stuff like this so I'd have to have a think about it.

How do I go about these?

>>9652600
>>9652623
Figured it out. Fuck me. There was this very small aside where they stated a very useful technique where after calculating P(AnB), you could then find all other combinations of the given statement.

For instance, given P(A|B), you can find P(A|B') and P(B|A').

>>9644659
I store the amount of grams of bananas that I eat in my head for around 7 hours and then I forget them. Would that be considered short term memory or long term

>>9653068
Long term.

>>9653076
I have to rehearse it in my head every hour or so though

>>9653086
The formal definition of long term memory is anything past short-term. Short-term memory is about 30 seconds. There's obviously more to it than this definition lets on.

The fact that you can recall it after letting it drop out of your conscious focus of attention for more than a minute indicates that it's in long term memory.

I do some autistic shit like that too, but if I recall it to myself after several extended periods throughout the day, it stays committed to memory for like a week. I'm amazed that you manage to forget it.

>>9653093
I usually am able to chose if I want to forget something

>>9652168
The fuck are you on about? Kys you retarded fag

>>9649671
Because it's the variety of a 1-dimensional ideal [math]\langle d-a |a\in \mathbb{C}\rangle[/math].
>>9650522
Let [math]M[/math] be a manifold, and let [math]C^k(M,\mathbb{R})[/math] be the vector space of [math]k[/math]-forms with coefficients in [math]\mathbb{R}[/math]. The dimension of these vector spaces are given by [math]\binom{n}{k}[/math], and hence there is only one [math]n[/math]-form [math]\sigma \in C^n(M,\mathbb{R})[/math] that spans it, called the volume form. Suppose [math]p: E \rightarrow M[/math] is a projection of co-dimension 1, then we can define the pullback [math]p^*(\sigma)\in T^*E[/math] such that [eqn]\int_M \sigma = \int_E p^*(\sigma). [/eqn] [math]p^*(\sigma)[/math] is the induced volume form of [math]M[/math] on [math]E[/math], or the "surface form". I hope this clears up any misunderstanding.
>>9651306
It was proven by Fejer that the Fourier series converges for [math]f[/math] strongly iff [math]f \in L^\infty[/math] in the Lebesgue sense. [math]e^x[/math] isn't bounded.
>>9651349
Newton's third law gives you the equal and opposite force in another reference frame. Let [math]S,S'[/math] be non-inertial reference frames related by an acceleration [math]S \rightarrow S': v \mapsto v - a_0t[/math], then the Euler-Lagrange equations for the [math]same[/math] action [math]A = \int_0^td\tau L[x(\tau),v(\tau)][/math] takes different forms, namely [eqn] \frac{d}{d\tau} \left(\frac{\partial L}{\partial v_i}\right) = \frac{\partial L}{\partial x_i} \quad \text{in frame}~ S[/eqn], while
[eqn] \frac{d}{d\tau} \left(\frac{\partial L}{\partial v_i} - ma_0\tau\right) = \frac{\partial L}{\partial x_i} \quad \text{in frame}~ S'[/eqn]. The term [math]-mv_i[/math] is the fictitious force that is present in [math]S'[/math] but not in [math]S[/math] due to them not being non-intertially related, and for free particles this gives [math]F|_{S} + F|_{S'} = ma_0[/math], and for intertial frames this means [math]F|_S=-F|_{S'}[/math]

>>9653315
>>>9649671
>Because it's the variety of a 1-dimensional ideal ⟨d−a|a∈C⟩.
>>>9650522
>Let M be a manifold, and let Ck(M,R) be the vector space of k-forms with coefficients in R. The dimension of these vector spaces are given by (nk), and hence there is only one n-form σ∈Cn(M,R) that spans it, called the volume form. Suppose p:E→M is a projection of co-dimension 1, then we can define the pullback p∗(σ)∈T∗E such that
>∫Mσ=∫Ep∗(σ).
>p∗(σ) is the induced volume form of M on E, or the "surface form". I hope this clears up any misunderstanding.
>>>9651306
>It was proven by Fejer that the Fourier series converges for f strongly iff f∈L∞ in the Lebesgue sense. ex isn't bounded.
>>>9651349
>Newton's third law gives you the equal and opposite force in another reference frame. Let S,S be non-inertial reference frames related by an acceleration S→S:v↦v−a0t, then the Euler-Lagrange equations for the same action A=∫t0dτL[x(τ),v(τ)] takes different forms, namely
>ddτ(∂L∂vi)=∂L∂xiin frame S
>, while
>ddτ(∂L∂vi−ma0τ)=∂L∂xiin frame S
>. The term −mvi is the fictitious force that is present in S but not in S due to them not being non-intertially related, and for free particles this gives F|S+F|S=ma0, and for intertial frames this means F|S=−F|S
based

>>9653315
How does one achieve this level of autism?

>>9651551
The Hessian is the curvature tensor of a function in flat space. Its determinant is precisely the curvature.
>>9651563
This is the correct geometric interpretation. The determinant of a Jacobian [math]J_{ij} = \frac{\partial x_i}{\partial y^j}[/math] for a coordinate transition [math]\{x_i\}_i \in U \rightarrow V \ni \{y_i\}_i[/math] between patches of a manifold [math]M \supset U,V[/math], say, is the ratio of the volumes of each of them: [eqn]\operatorname{det}J = \frac{\operatorname{vol}U}{\operatorname{vol}V}[/eqn].
>>9652093
It's correct away from [math]x = 0[/math]. Don't trust computer-generated graphs for something as pathological as [math]\sin(1/x)[/math].

if two black holes are moving at a high speed past each other such that their singularities don't cross each others' event horizons, is it possible for their effects to cancel each other out enough for information formerly trapped by the event horizon to escape? or would it just switch black holes if anything?

>>9653331
>if two black holes
impossible, there's only one black hole

>>9652600
> I thought I could just find the probability that neither watched (0.6 * 0.5) and take the complement, but that's wrong.
You can find the probability that neither watched and takes its complement. That part is correct. The wrong part is that P(A&B)=P(A)*P(B) is only true if A and B are independent i.e. P(A|B)=P(A|B'), P(B|A)=P(B|A'). Which isn't the case here.

Conditional probabilities are defined as P(A|B)=P(A&B)/P(B), so P(A&B)=P(A|B)*P(B)=P(B|A)*P(A).

Also: P(A&B)+P(A&B')=P(A). So:

P(H|W)=0.7, P(W)=0.5, P(H)=0.4
P(H&W)=P(H|W)*P(W) = 0.7*0.5=0.35
P(H&W')=P(H)-P(H&W)=0.4-0.35=0.05
P(H'&W)=P(W)-P(H&W)=0.5-0.35=0.15
P(H'&W')=P(H')-P(H'&W)=0.6-0.15=0.45
P(H'&W')=P(W')-P(H&W')=0.5-0.05=0.45

>>9653328
>[math]\{x_i\}_i \in U \rightarrow V \ni \{y_i\}_i[/math] between patches of a manifold [math]M \supset U,V[/math]
what do I have to study in order to understand what this means?

>>9653548
topology, differential geometry

>>9653185
>>/alexjones/
>>/reddit/

>>9653331
You're saying if the two event horizons crossed, could the larger black hole pull material out of the smaller black hole's event horizon? Like in pic related?

If there are two coordinate references A and B.
B is at 45 degree clockwise to A.
If I have a vector in A then to represent same vector in B should I be rotating it with 45 degree clockwise?

>>9653331
Honestly this sounds like exactly the sort of thing that r/askscience was made for.

>>9653716
the vector remains unchanged, but its representation in B will be different

I am a self-studying faggot and I was looking for collections of (math) exams, like this one: https://wumath.wustl.edu/math-exam-archives, but with more subjects (such as abstract algebra & other advanced topics covered in the later years), and if it could have no "math for social sciences" and the like, all the better.

Why does every formulation of the inclusion-exclusion principle I find only refer to the cardinalities of the sets and not the sets themselves? I could have sworn this is how we were taught it in grade school. Also I can't think of a counterexample that would prove the necessity to limit the principle to cardinalities only.

>>9644659
Brainlet here. Is it possible to make something that can keep itself permanently cold under normal Earth conditions without need for electricity or any outside help?

I remember watching years ago about how someone once sealed frozen gas inside a reinforced canister and because the gas wasn't allowed to expand, it remained solid and therefore cold... This doesn't seem right to me, surely the gas would return to gaseous form at room temperature, but the canister would be under extreme pressure? Is that right?

>>9654199
im not a physicist but isnt temperature a function of particle movement which are a function of outside forces? ie temperature isnt an intrinsic quality

>>9644659
are postdocs supposed to be intelligent?

>>9654214
So if something like frozen nitrogen is kept in perfect insulation, it is possible for it to stay cold forever?

Not really what I was thinking of though, I was thinking along the lines of something staying cold at room temperature, meaning it's always going to have outside forces of higher temperatures against it. The more I think about it, the more it doesn't seem possible.

>>9654260
>it is possible for it to stay cold forever?
nah

>>9654260
>frozen nitrogen is kept in perfect insulation, it is possible for it to stay cold forever?
yes but youre insulating it. i thought you meant it was isolated in our eadthly environment

>>9654269
>what is heat death

>>9654282
Is insulating not isolating it from outside influences? But no, I was wanting to see if something can stay cold under practically conditions.

Perhaps if I explain why I'm asking, it might help you understand what I'm asking. I was reading an article about how air conditioning was contributing to the urban heat island effect and was wondering that instead of simply transferring the heat outside, as most air conditioners basically do, was it possible to channel a pipe through or around a material or canister that was permanently cold, cooling the air down instead of simply moving the hot air around? It got me thinking about how how "easy" it is to keep things cold when out of sunlight (e.g the poles in winter, shadows on the Moon, etc) and also how someone said about putting frozen gas under pressure kept it cold as well.

But I'm realising now that you can't just simply make heat disappear when in contact with a cold object, the heat has to go somewhere and cold materials are the absent of heat energy.

Someone help me with this
Let's say a point after the rotation is somewhere in the negative Z. That would mean a light source would just go right through the xy plane without ever projecting any shadow on to it.

>>9654335
there are ways to get rid of heat. water resorvoirs (sp) for example. so if you could use the heat as another form of energy, it would effectively cool/disappear

yeah you could have something cold take the heat and become a moderate temperature but that sounds difficult to physically implement

How does my brain separate from people I've met personally to characters I've read about?

>>9654659
The brain sorts things through context. Over time,you can forget the context.

Like think of a random fact you understand to be true then think of where you learned it. School? Online? Read in a book? Probably a lot of things you know but don't know why you know that.

It's also completely possible to mistake a person you read about as somebody you actually talked to. If you remember a story of ancedote you read in a book and remember it as 'a story a friend/ some guy told me'.

>>9654704
So overtime, when the brain decays and we get old, this will happen right?

You could literally end up believing fiction.

How do we maintain a real sense of reality/memories in our heads?

>>9654934
>How do we maintain a real sense of reality/memories in our heads?
Psychology has all but proven you can't. People are dumb - like literally all people.

>>9654495
Projection_matrix * rotation_matrix

Hint: rotation is
[math]
\begin{bmatrix}
1 & 0 & 0 & 0 \\
0 & \cos(\pi/3) & -\sin(\pi/3) & 0 \\
0 &\sin(\pi/3) & \cos(\pi/3) & 0 \\
0 & 0 & 0 & 1 \\
\end{bmatrix}
[/math]

I want f(x)=x for x ≥ 0 and f(x)=0 otherwise WITHOUT having to specify domains and shit.
This is the simplest expression I came up with [math]\frac{(\sqrt{x} \:-\: i\sqrt{-x})^2}{4}[/math]

Am I retarded and missing a simpler expression?

>>9655313
I pretty much get that but why is the question phrased in terms of a shadow when a shadow will simply not exist on the xy plane at z=0 if the thing casting the shadow is somewhere in negative z

if youre allowing functions like sgn, then [math] \dfrac{x(1+\operatorname{sgn}(x))}{2} [/math]

>>9655361
[math]\int_\mathbb{R}\frac{dp}{2\pi}\frac{e^{ipx}{p}[/math]
>>9655388
Sign is defined piecewise.

>>9655387
or am I wrong about how I'm thinking about the problem and a shadow will exist for some reason

>>9655389
Oops.
[eqn]\int_\mathbb{R}\frac{dp}{2\pi}\frac{e^{ipx}}{p}[/eqn]

>>9655387
>shadow will simply not exist
A single point exists.

>>9655396
what do you mean by this
are you saying a single point is infinitesimally small and can't cast a shadow
if I write that down I'll get a good grade for sure

>>9655397
A vector along the z axis casts a shadow given by [math](0,0)[/math] on the x-y plane. [math](0,0)[/math] exists.

>>9655389
i thought by specify domains he meant a function where i wasnt explicitly writing the cases. after all his function is essentially [math]\frac{|x|+x}{2}[/math], which i presume he is fine with

>>9655392
>[math]\mathbb{R}[/math]

>[math]\frac{|x|+x}{2}[/math]
OH FUCK! I knew I was missing something stupid simple
Thanks m8

>>9655410
|x| is defined piecewise (i.e. domain-by-domain) though.

>>9655403
>[math]\frac{|x|+x}{2}[/math]
OH FUCK! I knew I was missing something stupid simple
Thanks m8

>>9655414
Yeah, but that's fine. If it needs to be super anal about the imaginary part, I guess I could adapt my original expression

So assuming:
T : V -> V
T is NOT injective
Then V = Null(T) + U, where U is some subspace of V
Since T is not injective, Dim Null(T) >= 1, so Dim U <= n-1 where Dim(V) = n
if x_1 ... x_m is a basis of Null(T), then the only eigenvalue of Null(T) is 0
if u_1 ... u_n is a basis of U, it consists only of eigenvectors
Then x_1 ... x_m, u_1 ... u_n is some basis b that makes the matrix M(T, b) diagonal

I feel like everything is accurate up to the last line. I feel like that's not true because if the eigenvalue for x_1 ... x_m is 0, then clearly M(T, b) does not have non-zero diagonals until we reach u_1

Am I wrong in this thinking or is something earlier in this false?

>>9655447
>if u_1 ... u_n is a basis of U, it consists only of eigenvectors
No. By primary decomposition [math]T[/math] decomposes [math]U[/math] into a direct sum of eigenspaces [math]U = \bigoplus_{\lambda \neq 0}W_\lambda[/math] on which [math]Tw = \lambda w~ \forall w \in W_\lambda[/math]. In general a basis [math]\{u_i\}_i[/math] of [math]U[/math] need not decompose into a union of the bases of the eigenspaces, namely [math]Tu_i \neq \lambda u_i[/math] for some [math]\lambda[/math].
>then clearly M(T, b) does not have non-zero diagonals until we reach u_1
0 is a diagonal matrix,

>>9655467
First part: It's gunna take me a hot minute to read that, partly because my browser refuses to do latex on 4chan.
I've never seen [math]\bigoplus_{\lambda \neq 0}[/math] before. Is this shorthand or implicit of something?
Second part: I got the definition of diagonal backwards. I keep thinking it's non-zeros along the diagonal, not all-zeros outside the diagonal.

What am I doing wrong? the answer is suppose to be 4250 for max profit, I just don't know how to get there.

>>9655475
[math]\oplus[/math] is the direct sum. The upshot is that a basis element [math]u_i[/math] of [math]U[/math] can be a linear combination of vectors from different eigenspaces, i.e. [math]u_i = \frac{1}{\sqrt{2}}(w_\lambda + w_{\lambda'})[/math], for instance.

Can someone do this problem, and double check that the answer is pi? I keep getting 4pia^2 -1 as the answer.

The Pinewood Furniture Company produces chairs and tables using two resources – labor and wood. The company has 800 hours of labor and 360 pounds of wood available each day. Demand for chairs is limited to 50 per day (this implies that the production of chairs per day would be no more than 50). Each chair requires 8 hours of labor and 2 pounds of wood to produce, while a table requires 10 hours of labor and 6 pounds of wood. The profit derived from each chair is $45 and the profit from each table is $50. The company wants to determine the number of chairs and tables to produce each day in order to maximize its daily profit. Assume that every chair and table produced will be successfully sold.

What is the optimal solution to the number of chairs that should be produced?

What is the maximum profit?

What am I doing wrong in excel?

>>9655514
Well right I know what a direct sum is, I'm less sure on the subnotation on it. U = DSUM_stuff + something_else
I've never seen that, I've only seen stuff liek U = Null(U) DSUM Range(U), for instance

>>9655522
[math]\bigoplus_{\mu = 1}^m V_\mu = V_1\oplus \dots \oplus V_m [/math]

Hi guys.
AB' vector (orange) is rotated 30 degree CC to AB''.
AB' vector x and y components are shown in bold red.
AB'' vector x and y components are shown in light blue.

We know
X'' = XCos(α) -YSin(α)
Y" = XSin(α)+YCos(α)


What is the geometric meaning of these individual expression of sum shown above?
What does XCos(α) mean geometrically.
Algebraically it would mean X times Cos(α).
But how it can be perceived in the picture shown?

>>9644659
I'm building a simple floating potential probe to map out potential structure in a low-T plasma, but I need to reduce the output voltage low enough to be readable by our DAQ (+/- 10 V)

... can I use a voltage divider with a floating probe?

How much large is the space of degree 2 polynomials compared to degree 1 polynomials?

>>9655770
>>9655679
So sad that there are more people who ask question than there are people who can really reply. That diagram above is my question. I wish I knew degree of freedom.

>>9655679
Sorry man, wish I could tell you but I suck at circuits.

>>9655770
Vector spaces represented by polynomials have n+1 dimensions

>>9655568
>>9655802
It's just defining your coordinate transformation
Bx'' = Bx Cos(α) - By Sin(α)
By'' = Bx Sin(α) + By Cos(α)

Also don't fucking whine just because nobody answered your question immediately.

>>9655516
It's pi.

Area of the spherical cap is
A=2*pi*a^2*(1-cos(t)).

sin(t/2)=1/2a (pic related)
cos(t)=cos(2*(t/2))=cos^2(t/2)-sin^2(t/2)
=1-2*sin^2(t/2)
=1-2*(1/2a)^2
=1-1/2a^2
=>1-cos(t)=1/2a^2

=> A=2*pi*a^2*(1/2a^2)
= pi

>>9655828
"Geometric interpretation "
What does BxCos(α) look like in the diagram. This is what I am looking for.

>>9645408
>asks for help
>gets corrected
>calls them retarded

nice work, anon.

>>9647574
copy by cntrl c
paste with center mouse wheel (there’s also a keyboard way to do it but I forgot, though you have enough info here to find out)

>>9655679
not sure - my instinct would be no, because the divider circuit is grounded and therefore anything connected to it should be grounded... but I don't remember enough from circuits to say for sure, any EEbros in the thread who can help?

>>9648275
dunning Kruger effect or something

>>9648684
capped

>>9655848
Bx' and By' are the projections of B' onto the X and Y axes (the red lines), Bx'' and By'' are the projections of B'' onto the X and Y axes.

Bx'' = Bx' Cos(α) - By' Sin(α)
Bx'' = B Cos(α)Cos(β) - B Sin(α)Sin(β)
Bx'' = B Cos(α+β)

By'' = By' Sin(α) + By' Cos(α)
By'' = B Sin(α)Sin(β) - B Cos(α)Cos(β)
By'' = B Sin(α+β)

B = 6 so Bx'' = 3 and By'' = 5.196

>>9648275
This is because a lot of questions that are deemed "stupid" are questions where the answer should be straightforward, but turn out to be more complicated than you expect or bring up a lot of really interesting tangents. These can also often be questions where straightforward and interesting answers do exist, but they're not questions that gets asked a lot because people are concerned about looking foolish for asking a "stupid question".

Like >>9655679 seems like it should be a really obvious yes or no answer, but I have no idea which, and if the answer is no then it brings up a lot of interesting questions like how *would* you make a measurement like that

>>9650059
What’s considered late for math?

>>9654199
You may wanna look into an icee ball

>>9654229
that depends

>>9655942
>Bx' Cos(α)
I agree with what you said.
Look at the equation for Bx''
Bx'' = Bx'Cos(α) -By''Sin(α)
What does individual expression of above sum represent in diagram.

>>9655679
Yes; the source being floating isn't an issue. The main issue with using a passive divider is that it's going to draw more current than a DAQ would. If the probe is supposed to be drawing negligible current, you'll need an active buffer before the divider.

>>9655837
I got it afterwards, but thanks.

>>9655516
>>9655837
which surface areas neede to be found in that question, I didnt quite get it?

>>9656331
The portion of the surface of the large sphere (radius a) which is inside the small sphere (radius 1).

>>9656512
oh so it wasnt the dotted circle area but the convex one part?

>>9656032
Thank you for replying so quickly, that's very interesting and it's good to know there won't be any issues (on paper anyways) with using this setup to get floating source measurements.

To go into a little more detail - at the moment I have basically a hub of dividers for several different inputs, the idea being I want to be able to measure potentials on my anode, the electrodes confining the plasma, and the floating potentials at the tips of an array of probes - the floating probes should (in theory) be drawing almost no current, the plasma generating anode will, after it reaches the breakdown voltage of the gas, draw a few mA of current with a surface potential of around 300 V, and the confining electrodes all draw something on the order of a few hundred μA at around +/- 10-20 V.

I'm currently working out some issues with plasma generation in conjunction with the divider (basically the current for my HV supply is all going through the divider instead of the anode) and my plan at the moment is just to ramp up the impedance of the divider enough to basically force current to travel through the anode.


Since ramping up the resistance on all the dividers would drive down the current going through them, would that accomplish roughly the same effect as an active buffer? I'm trying to avoid active components in the circuit.

>>9656551
Increasing the resistance will reduce the current. But the resistance has to be much lower than the DAQ input (either that, or you have to know the resistance of the DAQ input and factor it into the calculations).

The DAQ input is likely "almost infinite", i.e. at least megohms and possibly much higher, so that isn't much of a constraint ... unless you were counting on the probe driving a near-infinite impedance.

>>9656694
Hmm, I hadn't considered that. The DAQ is an NI USB-6229 BNC, I think that's got an analog input impedance of like... 10 GΩ or something stupidly big like that, so I think I *should* be safe going up to MΩ resistors for the divider without it throwing things off too much. That should increase the resistance enough to force the bulk of the current into the anode. Alternatively I may need some kind of switch for the divider input from the anode so I can turn it on after it's already generating the plasma.

The main priority here is accurate measurements of the potentials. The currents on the electrodes can all be measured independently with multimeters (which are really only necessary for evaluating their power draw) and the potential probes should be drawing almost zero current since they're electrically floating in the plasma.

You've been a huge help, thank you.