SQT

>>8401083
I know absolutely nothing about probability but i'm gonna guess it's 75

>Stupid Question Thread as the last one reached comment limit.

no it didnt

>>8401083
65 at a guess

it should be 65 mg
Just conduct a pdf at 65, 75, 85, 95 and 105 mg for both hair loss and effectiveness of drug.
The ideal dosage is that the probability of hair loss is minimal, and the probability of effectiveness is maximised.
Assumption: hair loss from drug and effectiveness of drug are independent of each other

>>8401317
You legend! How do you work out the corresponding probability?

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I got 1.66 grams of Carbon for the answer. Is this right?

My working for the questiom:

>Find moles of Mg
moles Mg = 0.0011/24
= 0.0000458

>Then find moles of C
moles C = 55 * moles Mg
= 0.002519

>Find C in grams
g = 0.002519 * 660
= 1.66 g

Let's see how dump /sci/ is
Let f(x) be 1 for x where cos(e**x)=1. 0 otherwise.
What is integral of f(x) from 0 to infinity?

You should be able to solve this.

>>8401632
It should be 0 because e^x (which I assume you mean by e**x) will never be 0, therefore the cos will never be one. Or am I missing something?

>>8401670
Oh yes, it's c because of >constant.

>>8401632
For large x, distance between two points where f(x)=1 tends to zero. Therefore for large x, f(x) ~ 1. And integral of 1 to infinity diverges. Therefore integral f(x) to infinity also diverges.

>>8401632
The set of points where f is 0 almost everywhere except at a countable number of 1s.
Therefore the integral is 0.

>>8401632
For the integral of a function to exist, the function must be integrable over the selected interval.

For a function to be integrable, it must be continuous over the selected interval.

f(x) is discontinuous in the interval from 0 to infinity.

Proof: Consider the point x=ln360. The limit from both sides as x approaches ln360 is 0 but f(ln360) = 1 and this contradicts the definition of continuity.

Therefore it contradicts the definition of integrability.

Therefore such a function is not integrable under the interval 0 to infinity.

So the answer is NaN, not a number.

That said. We could partition the real numbers into intervals of the form 0 to ln360, ln360 to 360, ln360 to (next point where f(x) = 1)

There we would have infinitely many integrals but of simple form. Consider the integral from 0 to ln360. Here the area is 0.

Then consider the integral from ln360 to ln360, it is also 0.

Such integrals repeat infinitely, giving us 0+0+0+0... = 0

So a more practical answer is 0, as in this function covers no area at all.

>>8401682
You asked for the integral, not the antiderivative. An integral is an area. There is no 'C' in an integral. A C is the free variable in the family of functions that contains the anti derivatives of another function.

Learn 2 calculus.

>>8401705
This, it is NaN, because lim f(x) to infinty doesn't exist

I have one:

lim (x,y)->(0,0) (xy^2)*cos(1/xy^2)

WolframAlpha says it does not exist (not time out, litteraly does not extist)

I say:
substitute t = xy^2, consider lim t->0 t*cos(1/t)
cos(1/t) is bounded to <-1;1>
lim t->0 t*bounded = 0*bounded = 0

Why am I wrong?

What's some cool shit I can expect by 2030 like full immersion VR? Will we have anti-ageing shit up?

Why do you need to use the chain rule to differentiate y when using implicit differentiation?

>>8402697
because by convention y is a function of x

>>8402657
>Why am I wrong?
likely it matters which direction you approach the origin from which value you get as a limit

>>8402657
>cos(1/t) is bounded to <-1;1>
then there is not a delta for every epsilon such that yadda yadda

>>8401494
No, the answer is 0.02988914g, or 0.0299g (3sf).
Divide g of mg by molar mass of mg, then times by 55, then times by molar mass of c.

"A function with an unbounded domain D ⊆ R has no limiting value at infinity"

What do they mean by "a function with an unbounded domain"? Do they mean the function is unbounded on its domain? The example they go on to use next is f(x) = sin(x) with x in D = R^+, so i don't think my interpretation is correct, since sin(x) is clearly bounded above by 1.

>>8402739
>Do they mean the function is unbounded on its domain?
they mean there is no maximum element in the domain

>>8402739
And surely they don't mean the actual domain being unbounded, since there are plenty examples of unbounded above domains where the limit exists at positive infinity. Please help, this textbook is driving me insane.

>>8402745
post a pic of the book

>>8402742
but how can this be? the example before is a function f(x) = x / (x+2) defined on D = R\Q that converges to 1. Isn't this domain also unbounded above?

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>>8402749
It's called A Friendly Introduction to Analysis by Kosmala. I'm not sure I've had a shittier math text.

>>8402761
That's why I wanted the pic, I knew they'd clarify the remark and not leave it like that. It's a shitty "remark" since as you note, it is not generally true; but, they way they clarity it in the next phrase (that is...) makes it clear.

>>8402761
Holy fuck I feel bad for anyone who has to read this

>>8401698
This is the correct answer.

>>8401705
integrable does not imply continuous

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>>8402761
>"unbounded above domain"
>"plus infinity"

>>8402767
Its still not entirely clear to me. Isn't that second part the definition of a function that doesn't have a limiting value as x approaches infinity? I still don't see how that follows from the first part of the Remark

>>8402801
The Remark is worded and punctuated very retardedly: the first semicolon should be a comma, so it's just an iff statement that defines what it means to have a limit at infinity. Plus, holy quantifiers Batman.

>>8402801
>I still don't see how that follows from the first part of the Remark
It doesn't follow at all, hence your confusion.

>>8402801
The Remark is a single sentence. There is no "first part".

>>8402814
>how do I semicolon

>>8402807
>>8402809
Gotcha. Believe or not this is a routine occurrence with this book.

Are introductory analysis books all typically structured the same in terms of content? I have a couple other books I bought myself. They're old, but fuck they have to be better than this.

>>8402821
A semicolon doesn't end a sentence. That's also why you use a lower case letter after a semicolon.

>>8402814
Right. I should have been more specific. I was referring to first of the two interdependent statements.

>>8402830
>A semicolon doesn't end a sentence.
Yes, and?

Is there a business degree that can pay me 50+K a year? I couldn't cut it in the intro to EE course. I'm planning to change majors to business, but I'm not sure what's a good business degree. I want to work in the tech field area at least.

>>8402832
>A iff B
Is a single statement. Just like
>A; that is C, iff B
which is the same thing just with an extra explanation of what A means.

Are there a pair of infinite fields so that the additive group of one is the multiplicative group of the other? what do they look like?

>>8402871
well [math]x^a \cdot x^b = x^{a+b}[/math]

>>8402838

Accounting or Finance.

>>8402880
i had a play around with that, negative numbers make everything a huge mess

>>8402807
> The Remark is worded and punctuated very retardedly:
The book is out of date. It needs to be updated to account for the fact that the average millenial's attention span is roughly ten words.

I'm changing my major from Engineering to Business. Should I drop Physics and take the W or just continue to take it?

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>>8403092
>>8402838

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>>8403100

Not as much as I am in myself.

>>8403092

Depends if it's hard or easy for you. If it's hard, don't bother unless you want to save your financial aid. If you just transferred, I think you have to have at least one class active or they kick you out, so if that's your only class then continue to take it.

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how come one can do stuff like
dy/dx = k
dy = kdx

its like doin ln 5 and diving by the l,
is there any other notation that actually makes sense and doesn't allow this fuckery?

why is the dx in the integral notation?

what does it mean

in an integral, how come you can do u-subs
I understand the steps in the process and the outcome,
but not the process itself

are there any texts out there I can read that try to explain this?

please I WANT TO UNDERSTAND, I DON'T WANT TO MEMORIZE FORMULAS AND STEPS

>>8403184

just Google your questions, you brainlet

there are already full answers to everyone of those that come right up on stack exchange

>>8403184
You can't do that. But you can just skip the step of multiplying both sides by dx and go directly to integrating both sides with respect to x
so
dy/dx=k ->
int dy/dx dx=int k dx
the dx is to tell you what variable you're integrating with respect to.

u-subs are the chain rule in reverse

you got some fucky integral like
int e^(x^3-4x)*(3x^2-4) dx
notice that if you set u=x^3-4x then du/dx=3x^2-4 and if you treat derivatives as fractions you can get du=3x^2-4 dx
plug that into your integral you get
int e^u du=e^u+C=e^(x^3-4x)+C

rigorous method

int e^(x^3-4x)*(3x^2-4) dx
f(x)=x^3-4x
g(x)=e^x
so g(f(x))=e^(x^3-4x)
note that e^(x^3-4x)*(3x^2-4)=dg(f(x))/dx
so int e^(x^3-4x)*(3x^2-4) dx=int dg(f(x))/dx dx
=g(f(x))+C

If a speck of dust traveling at near light speed collided with the Earth, would it destroy the Earth?

>>8403303
no

>>8402871
Hey, I remember you. Other anon showed that if [math]E^+ \cong F^*[/math], then E doesn't have characteristic two. I'll see if I can make any more progress.

>>8402761
Almost every sentence on that page is written so fucking poorly. I would strongly recommend using a different textbook. Most analysis books cover pretty much the same stuff, but some of them are actually written well.

>I do not know the phrase in English for this situation, so permit me to write in Japanese: tutusinde Yoneda sensei no gomeihuku wo oinori mousiagemasu.

What does this mean? Google Translate didn't work.

Do just automorphisms have a non 0 determinant? I saw a proof which shows that somethings isn't an automorphism and from there concludes that the determinant is 0. Am I missing something?

>>8403542
If A is invertible then [math]\det(A)\det(A^{-1}) = \det(AA^{-1}) = \det(I) = 1[/math] so [math]\det(A)[/math] is invertible, hence nonzero. The converse is true as well.

>>8401705
Retard, continuous implies integrable not the other way round. There are plenty if discontinuous integrable functions

>>8401739
Sum of integers diverges but it's still -1/12, retardo

>>8403563
>continuous implies integrable
No, continuous implies locally integrable (integrable over every compact set).

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>>8403594
>not allowing [math]\infty[/math] as a value of integration

>>8403544
Ah yes,makes perfect sense now, general linear group, sutomorphism etc. How does one keep all of these definitions and theorems in ones head when doing a proof?

>If a set has exactly three points, what are the possible metrics on that set?

Am I retarded? Isn't this just all metrics (since the triangle inequality will be sure to hold as long as you have 3 different elements)?

>>8403606
Just practice

>>8403610
>>8403610
>the triangle inequality will be sure to hold as long as you have 3 different elements?

No, you need to ensure that any individual distance is less than the other two added together.

>>8403617
And doesn't that follow from the definition of a metric doe?

>>8403622
...They want you to say what functions are metrics, not what metrics are metrics. Yes, every metric is a metric.

>>8403623
aite thanks hammie

>>8403536
>>>/int/

I`ll end

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I want to prove that lim_(x -> -1) (1 / sqrt(x^2 + 1)) = 1 / sqrt(2).

I'm having quite a bit of trouble with this one, but here is what i have so far. I'm not sure where to go from here, but was thinking since we are concerned with x approaching -1, we could put a bound on x, maybe an interval of +/- 1, to guarantee the absolute value of the denominator is less than 2. any help would be monumentously appreciated

>>8404127
You can just substitute x=-1.

If a function is continuous and defined at some finite argument k, then lim[x->k]f(x) is just f(k).

Limits are only complicated when you want the limit at infinity or at a point where the expression is undefined (e.g. a quotient where numerator and denominator are both zero), or at a discontinuity.

>>8404214
Unfortunately I don't think I can do that for this problem as the book said to use the definition for the proof, and we don't encounter continuity until next section.

>>8401632
>not a continuous function

If we take the limit of a Riemann sum we get 0, though.

>>8404127
x+δ goes inside

now you have a relationship between delta and epsilon

solve this relationship

Then you have shown how for any epsilon > 0 there exists a delta > 0 such that etc etc

"In a large state university wages paid to graduate students are normally distributed with a mean of $20 and a standard deviation of $3.50. What is the probability of choosing two individuals at random from this university who earn an hourly wage of $24 or more?"

So far I have the probability for one individual at P=0.1271. What do I do for two individuals? Do I multiply P by itself or do I already have the correct answer?

>I'm definitely a tard.

Is the z in the Nernst equation charge in coulombs or in electron charge?

E = RT/zF ln(C1/C2)

>>8404291
moles of electrons

>>8404295
used equivalently for ions? I presume so, but still.. wiki says
"... potential of an ion of charge z across a membrane ..."

which leaves me confused

>>8404301
Yeah it is.

>>8404283
i think so, since they are independent events

so it would be Q((24-20)/3.5)

For my algorithms class I'm supposed to give the tilde approximations for some shits, which I've got fine. But I'm also supposed to describe what is special about #2 and #3. The only thing I can think of is that they approach 1, but so does #5.
Asked my teacher about it and he just hints about what happens as N gets larger, in other words, they approach 1.

N +1 ~N
1 + 1/N ~1
(1 + 1/N)(1 + 2/N) ~1
2N^3 - 15N^2 + N ~N^3
lg(2N)/lg(N) ~lg(2) or 1
lg(N^2 + 1)/lg(N) ~lg(N^2)

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>>8401705
>For a function to be integrable, it must be continuous over the selected interval.

I am disappointed.

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Hope you don't mind me crossposting this here. How do shortest route problems work in cases like the next one? Let's say there are 30 villagers trying to go from Start to 5, where the numbers are the traveling times of the routes they can take. Lets say that I'm asked what's the minimum time they all take to go from Start to 5, I can think of two different ways it could work and I don't know which one is the correct:

1. It could mean that the shortest time is when every individual villager takes the shortest time, thus 100*30. This one looks like most of these problems, where time is just a number that you add.

2. It could mean that time is a global resource that keeps running, then when 5 villagers have moved from Start to 1, one villager has moved from Start to 2. This means that some villagers reach 5 through the shortest route, but some other villagers reach 5 through longer routes; since this is in parallel then the total time is not the sum of the individual times, but less. This one would be more like reality.

Which one is the right way to approach these problems?

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by chance I got this one right but I don't understand how the molecule to the far right isn't an enantiomer of the far left; when you twist it upwards (shifting every atom CC) don't you get the mirror image thats non-superimposable?

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>>8402731
I knew 1 gram sounded too big. Cheers mate

>>8404988
Hey fellow 1st yr chembro
Think of it like a steering wheel.
The OH is the shaft of the steering wheel (those hash lines going away from you), and the other 3 are spokes. Spin them around to try and make them match, and you'll see the middle 2 are the same, which is how I remember to identify enantiomers. The far left one doesn't match no matter how much you spin the wheel.

If you have any Blutak or whatever the equivalent product is in your country, if you start playing with a 3D constructed molecule in your very own hands it makes it easier to make sense rather than buying a molecule model kit that you'll probably never use again unless you become a chemistry teacher.

https://www.cpp.edu/~cba/computer-information-systems/curriculum/index.shtml

Can I get into cyber security or become a programmer with this degree? I'm planning on getting this degree and getting certificates in network to supplement the degree.

Consider the m by n grid graph: n vertices in each of m rows, and m vertices in each of n columns arranged as a grid, and edges between neighboring vertices on rows and columns (excluding the wrap-around edges in the toric mesh). There are m n vertices in total.
a. What is the diameter of this graph?
b. From the top left vertex to the bottom right vertex, how many shortest paths are there? Please explain.

>>8404975
>Which one is the right way to approach these problems?
They are different problems, and both of them are meaningful. Your first problem is what's usually called the "shortest path" problem, and it's the problem that tools such as navigation devices solve. Your second problem is known as the maximal flow problem: imagine pipes of a certain diameter, and you want to get the maximum amount of water from point S to point 5. It is used in analyzing the capacity of infrastructure networks, and things like that; but it's not usually applied to planning individual routes.

can someone explain what inertia is in everyday terms, along with an inertial frame of reference?

>>8405082
The concept of inertia has been replaced with conservation of momentum. If you throw a ball against a moving truck, its velocity isn't going to change much because its momentum is much larger than the baseball.
An inertial frame of reference is a coordinate system that isn't accelerating. Rotating frames of reference are commonly mistaken for inertial ones but they aren't since they are changing direction.

>>8405053
For b: Any shortest path will be some combination of m-1 movements down and n-1 movements to the right. Then there are [math]\frac{(n + m - 2)!}{(n-1)!(m-1)!}[/math] paths.

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Can somebody help me to graph this? i don´t know why i can graph this in wolfram alpha

>>8405122
So uh, this is an expression not an equality?

How do I prove that if the directional derivative [math] D_{\vec{u}}f(\vec{x_{0}}) [/math] exists then [math] D_{\vec{-u}}f(\vec{x_{0}}) [/math] Also exists and [math] D_{\vec{-u}}f(\vec{x_{0}}) = -D_{\vec{u}}f(\vec{x_{0}}) [/math]

>>8405151

it goes something like this: if [math]D_{\textbf{u}}f(\textbf{a})[/math] exists and we know [math]D_{\textbf{u}}f(\textbf{a})=\textbf{u}\cdot\nabla f(\textbf{a})[/math] (I assume we can use this fact, if not the problem is a touch harder)
then [math]D_{\textbf{-u}}f(\textbf{a})=-\textbf{u}\cdot\nabla f(\textbf{a})=-D_{\textbf{u}}f(\textbf{a})[/math] and clearly it exists as it is a scalar multiple of a scalar.

>>8405122
it is an ellipsoid that needs to be set to some radius squared

>>8405180
*set equal to

Does there exist a sequence of real numbers such that the set of subsequential limits is R?

>>8405208
yes

>>8405208
actually, nvm, I think I solved it, ty anyway holmes

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Can someone help me get part A?

What do no need to know from topology before I can start learning analysis?

And what's the difference between analysing and numerical analysis?

>>8405220
>What do no need to know from topology before I can start learning analysis?
nothing, you'll learn what open and closed sets and sequences are in any analysis book anyway

>And what's the difference between analysing and numerical analysis?
numerical analysis is about approximating things, whether it be the sum of an infinite series, a differential equation, etc., not really related to analysis in any way except in name

>>8405220
>What do no need to know from topology before I can start learning analysis?

Point-set topology, but that should be taught in your first real analysis course.

>And what's the difference between analysing and numerical analysis?

What do you mean with analysing? Do you mean doing work in mathematical analysis (real, complex etc)? If so, then numerical analysis is just muh algorithms and muh approximations and not supposed to be precise like "real" analysis.

If I flip 5 coins, my chances of coming up with at least 5 heads is 3.125%, right?

[eqn]0.03125 = (^5_5)(\frac{1}{2})^5(\frac{1}{2})^0[/eqn]

I hope I did this shit right.

>>8405237
Yes

>>8405226
>>8405227
Awesome thanks. Whoops i mean "analysis" instead of "analysing" in that second question but the first anon caught my mistake. Thanks again

>>8405246
Okay. Now if I only needed at least 4 heads, my chances increase to 18.75%, right?

[eqn]0.1875=(^5_4)(\frac{1}{2})^4(\frac{1}{2})^1+(^5_5)(\frac{1}{2})^5(\frac{1}{2})^0[/eqn]

>>8405213
Use your capacitor rules. Equivalent capacitance in parallel is the sum of the capacitors, in series it's the inverse sum (1/Ceq = 1/C1 +1/C2 + ...).

>>8405259
Yes. Its essentially the binomial distribution

>>8405273
Not gonna lie, I really don't understand what you mean by that....

>>8404700
As N approaches infinity, we can see that 1/N approaches 0 at a faster rate that 2/N

>>8405278
Alright, thanks man. You've really helped me out here. Wasn't sure if I was calculating these chances right or not.

>>8405104
thanks, that makes more sense

>>8405283
Do you know how to add capacitors in series and parallel?

>>8405182
Thanks man

>>8405327
Sadly no

Why the fuck is it referred to as "raising the boiling point" instead of "lowering the boiling point". It makes it sound as if more energy (heat) is required to get to the boiling point, when in reality it's the other way around.

>>8405290
Actually, 2/n tends to 0 at twice the velocity of 1/n

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How do babies recognize themselves if they've never seen themselves before?

>>8405381
No, raising the boiling point means you need to add more heat to reach the boiling point.
The terminology is correct. You are wrong.

>>8405381

how did you manage to screw up something so simple?

if you raise the boiling point, you increase the temperature at which it starts boiling, meaning you need to add more heat

if you decrease the boiling point, it starts boiling at lower temperature, and so you need less heat

This is probably a stupid question but, are differential equations actually functions?

>>8405454
no, equations are not functions, in the same way you wouldn't call y^2=x a function

but the solutions to the differential equations are functions

functions are sets of ordered pairs (x,y) where (x,y)=(x,z) implies y=z

>>8405454

Well you're certainly in the right thread

no, they're differential equations

the solution to a differential equation is a function

>>8405383
Are you sure about that?

I have three coordinates

(0,0,0)
(1,2,1)
(3,0,1)

These form a plane in 3d space

I need the Y point on that plane at (.5,.5)[X,Z]

I KNOW there is a way to solve this mathematically but my brain is just gone to mush

Not classwork or anything it's actually programming-related
Anyone know?

>>8405383
This is stupid questions thread, not stupid answers thread.

>>8405458
I realize the solutions are functions. I ask because often DEs are denoted, using a third order ODE as example, d^3y/dx^3 = f(x, y, y', y''). So why use this notation if they aren't functions? Further, some of the existence theorems require you to take the partial derivative of the equation

>>8405457
Whoops, missed your response. But yes I'm familiar with functions being defined as sets of ordered pairs. See >>8405472

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>>8403184
look at it this way

u: is the species you must integrate
du: is the APPROPRIATE infinitesimally small representation of 'change' with respect to you, in layman's terms, the "derivative"

du becomes sacrificed to the math gods as a blessing to perform the integration

also, you're gonna have to remember the forms for quick integration, you're never going to be able to work backwards (by deriving) in order to find the correct integral.

tl;dr
Do your fucking homework and get off 4chan you degenerate brainlet

>>8405469

Given Ax=b, let b=(0.5, Y, 0.5), then make an augmented matrix with that vector as your answer vector and find all the values of Y that make that solution consistent.

>>8405476
with respect to *u*

my apologies

>>8405470
yes it is, so Lrn2velocity then STFU

>>8405485
Are you mentally handicapped?

>>8405479
I don't know what you mean mate, I never got to linear algebra (just calc 2)

could you help me out a bit more in detail?

Or even just help me figure out a augmented matrix calculator

>>8405490
ah nevermind I found something for it, after that just need to plug in the desired variables

http://www.math.cornell.edu/~froh/231f08e1a.pdf

>>8405507
>>8405490
>>8405469
aand here's the calculator! that was suprisingly easy

int[] f = {0,0,0}; //beginning coordinates
int[] g = {1,2,1};
int[] h = {3,0,1};

int[] a = new int[3];
int[] b = new int[3];
int[] c = new int[3];

a[0] = f[0] - g[0];
a[1] = f[1] - g[1];
a[2] = f[2] - g[2];

b[0] = h[0] - g[0];
b[1] = h[1] - g[1];
b[2] = h[2] - g[2];

c[0]=a[1] * b[2] - a[2] * b[1];

c[1] = a[2] * b[0] - a[0] * b[2];

c[2] = a[0] * b[1] - a[1] * b[0];

int d = c[0] * a[0] + c[1] * a[1] + c[2] * a[2];

Console.WriteLine(c[0]); //a
Console.WriteLine(c[1]); //b
Console.WriteLine(c[2]); //c
Console.WriteLine(d); //d

float answer = (float)((d - c[2] * .5 - c[0] * .5) / c[1]); //at (.5,.5) [X,Z]
Console.WriteLine(answer);

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The answer is 1, right?

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>>8405547
why do you brainlets always post what you think is the answer but not your reasoning? it makes it like 50x easier to see if youre on the right track or not

>>8405552
because this is a simple computational problem

like wtf nigga u want me to tell you that R is an ordered field and what that implies before I add my numbers together?

help a brainlet or get lost mane

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>>8405554
>because this is a simple computational problem
yet you're not sure if you're correct?

you can even check this on wolfram, piss off brainlet

>>8405556
I've been up for 36 hours and honest to Allah I am not sure if I am correct

and that's true, I can do that, thanks m8

What is the expectation value of the position of the ground state in a one-dimensional harmonic oscillator?

<0|x|0> = ?

what is the meaning of transposing a matrix? and how can we interpret them as linear functions? thank

>>8405547
It never converges because division by 0.

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What's the best path to choose for embedded systems?
EE, CE or CS? Why?

>>8405639
race identity is 100% a social construct

>>8405625
you reflect the entries along the top left-bottom right diagonal

(i,j) entry goes to (j,i) entry

its a linear map from m x n matrices to n x m matrices

>>8405547
[eqn] f(z) = \sum_{n=1}^\infty \frac{z^n}{n^2} [/eqn]
Differentiate:
[eqn] f'(z) = \sum_{n=1}^\infty \frac{z^{n-1}}{n} [/eqn]
Multiply by z:
[eqn] z \cdot f'(z) = \sum_{n=1}^\infty \frac{z^n}{n} [/eqn]
Differentiate:
[eqn] z \cdot f''(z) + f'(z) = \sum_{n=1}^\infty z^{n-1} = \frac{1}{1 - z} [/eqn]
Integrate:
[eqn] z \cdot f'(z) = - \log(1 - z) [/eqn]
Divide by z:
[eqn] f'(z) = - \frac{\log(1-z)}{z} [/eqn]
Integrate:
[eqn] f(z) = Li_2(z) [/eqn]

A = 80
B = 40
C = 20
D = 10
E = 8
F = 4
G = 2
H = 1

Number X can be made up of any of the above numbers, but each one at most can only be used once.

How can you test number X for the existence of the above numbers, without employing trial and error?

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How does sex work?
In the education books and videos one can see how the sperm swim to the egg but in my mongolian cartoons the girls are all empty inside and has no liquid for the sperm to swim in.
Or is the sperm supposed to be "swimming" in sperm liquid itself, splattered across the inside of the girl?

>>8405721
Test whether X > 165.

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>>8405485

>>8405734
X may never be greater since all the elements may only be used once at most, that also wouldn't answer which of the specific numbers were used to create number X.

The issue here is that number X may be anything from 0 ~ 165

is a set of disconnected vertices considered a valid digraph? does a digraph require at least one pair of connected vertices?

>>8405721
1 was used iff X is odd.
If so, subtract 1 to get X1, else let X1 = X.
2 was used iff X1 is 2 mod 4. Again subtract it off to get X2.
4 was used iff the last digit is now 2 or 4. Subtract it to get X3.
8 was used iff the last digit is now 8. Subtract it off.
10 was used iff the second-to-last digit is odd.
20 was used iff the number / 10 is 2 mod 4.

Now you're essentially done.

Exercise: determine what multisets of numbers you can recover the original counts for.

>>8405773
1. yes. 2. no.

>>8405466
Am I on to something? Is there truth to my hunch?

>>8405470
btfo

Not sure how to do part c and as to how the ∇ interacts with the logarithms.
I got the answer to be 0 as r(bar) x ∇ =0 but i don't know if my vector algebra is solid.

>>8405907
Hello newfriend. Give us some more context as to your problem.

Why are some cancer cells immortal?

What is the solution to this equation?

[eqn] \int^{\infty}_{-\infty} \mathrm{d} x' \, \left(\mathrm{u_1}(x - x') - \delta(x - x')\right) f(x') = 0 [/eqn]

>>8405954
Cancer cells aren't immortal, but when a regular cell replicates, the copy is "slightly older" than the original. After a real lot of replications, the cell is too old to replicate anymore, so when it dies (because, spoiler, it dies), it isn't replaced. Some cancer cells don't have this caveat and replicate into perfectly identical cell, with no "aging".

And I used these quotation marks around "age" and "aging" because obviously, the new cells are in fact younger than the cells they originate from. They just have slightly less material to replicate themselves.

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Can someone explain the parts in the blue boxes to me? I vaguely remember how to do the second one but can't remember all the rules since I only had is hard-memorized as opposed to really understood. The first box is what I'm more lost about.

So you're taking the right side of the equation, you set each term as L[Y], then you "guess" the form of the Y based off of the form of L[Y] (At+B when Y=5t, presumably since 5t is linear, I guess?) and use that to somehow get another L[Y] and set up an equation. getting the other part of that equation is what I don't get, where did -2A+5(At+B) come from?

>>8405990
Oh fuck, I just got it, you're taking Y and getting the first and second derivatives, then plugging them into the left side of the original equation. Still though, I have no idea why I'm doing that, nor a clue what the relation between Y and L[Y] is.

Can someone explain to me how to multiply two matrices together?

>>8405974
Is that also why cancer cells use up the majority of the body's energy?

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>>8405990
>>8405994
Wait, where'd the 5A=5 come from? I feel stupid, I thought it was just a system of equations from that point onward.

>>8406002
this might help you

>>8406003
I have no idea. I don't think it's related but I haven't heard about that before so I'm only guessing.

>>8406002
Matrix multiplication is function composition.

Suppose that you have:
y1=a.x1+b.x2
y2=c.x1+d.x2
and:
z1=e.y1+f.y2
z2=g.y1+h.y2

Substituting the first set of equations into the second gives:
z1=e.(a.x1+b.x2)+f.(c.x1+d.x2)
z2=g.(a.x1+b.x2)+h.(c.x1+d.x2)
=>
z1=(a.e+c.f).x1+(b.e+d.f).x2
z2=(a.g+c.h).x1+(b.g+d.h).x2

In matrix form, this is:
[e f][a b] = [(a.e+f.c) (b.e+d.f)]
[g h][c d] = [(a.g+c.h) (b.g+d.h)]

I am still trying to wrap my head around the validity of Rieman Sum, I asked you guys in the last thread and I came up with some sort of proof now.

Given any interval in a real number ,it is agreed (i am not gonna prove this) that there must be a value in the set that is the upper bound and lower bound of the set. let call this set V_(c) where c is the difference between upper and lower bound.

So in a Rieman Sum we have the interval (b - a)/n and as n -> inf for the 'width' of a partition, P_k. We get the expression approaching 0. What this implies is that for any P_k in the Rieman Sum we have that the set of P_k will only have 1 number, let call this element a_n where n -> inf.

Note or corollary is what they call it: This is exactly the definition of a real number, a limit of a rational number. We also have that each partition is distinct because originally no partition would have the same upper bound.

This is all I got, I still am not sure how to connect this idea and the fact that the integral of a graph f(x), which is using real number is equal to the sum of partitions which are represented using natural number.

But then again isn't it impossible for the set of N to be bijective to R? So the Rieman Sum is at best just an approximation of the area and somehow becomes equal when we take the limit. I am still unconvinced.

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Is it just the intersection of each pair added together and then the intersection of all three subtracted? i.e. 4/5?
idk if I should use conditional probability or not

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What is a kilotap and how do I convert it to more commonly used units?

>>8406134
>But then again isn't it impossible for the set of N to be bijective to R? So the Rieman Sum is at best just an approximation of the area and somehow becomes equal when we take the limit. I am still unconvinced.

Nowhere do you need that N is in bijection with R. It's a limit, just like the derivative.

>What this implies is that for any P_k in the Rieman Sum we have that the set of P_k will only have 1 number, let call this element a_n where n -> inf.

No, that's not what it means. When you use narrower and narrower rectangles your approximation is going to close in on a limit, which is the area. You just have to show that this limit exists. Nowhere do you need that each element of the partition only has one number in it. Each block in a partition will be refined by many different blocks of a finer partition, but none of the partitions have exactly one point in a block.

It's just like when you say lim 0.9, 0.99, 0.999... = 1. None of the digits of 1 are 9, yet every member of the sequence has all nonzero digits equal to 9.

>>8406170

so given any stochastic function where the area equals 1, the integral of any such function over the sample space is 0.9999999... because it's a limit? Like at no finite value of n will the integral ever equals 1 but as we take it to infinity the integral equals 0.99999999... hence 1.

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Finite element experts please help me out.

I would like to add mesh elements (preferably cubes) during simulation to a model. Say i have an initial mesh to start with, i run the simulation for some given time, then i add a cube element to it, continoue running it again then add a new cube element, and i repeat this a couple of hundred-thousand times. Is this even possible?

I feel the solver needs to have some scripting interface to allow this low level interaction with the mesh.

I know ABAQUS has a python interface but have not found anything related to this. I have ANSYS too, but i dont know where to start.

Are there any guides on how to do this with a specific program? Is this even possible with the available commercial solvers?

>>8405436
I'm talking about the cases where salt is added and then it's referred to as raising the boiling point.

>>8406154
Kilotap is when you tap it but you are not proud of it because she is many kilos heavier than you. No one is proud of fucking a fatty.

Example sentences:
Guy 1: Fuck man, did you really tap that?
Guy 2: Yeah, I kilotapped it.

Another one:
Guy 1: Fuck, I am going to tap that!
Guy 2: (laughing) Nigga you don't lie to yourself, you ain't tapping that, you are going to kilotap that.

>>8406276
Dissolved salt enhances intermolecular cohesion of the solution, so - where is your problem? The boiling point is higher as you need more heat.

considering doung a double bsc in molecular biology and chemistry, yea or nay?

>>8406193
Not exactly, because you might have approximations that go over 1. 0.999... stands for the sum 0.9 + 0.09 + ..., you should not think of it as the actual sequence of partial sums.

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I can't do this one /sci/ what the fuck is wrong with what I do:

(8/10)(7/9)(6/8)....(4/6)(2/5)

it's the probability of not choosing the wrong one 5 times times the chance that the 6th time will be the wrong one.

Why the FUCK is the answer 2/10 REEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE

you told me i can do it but I can't do it /sci/

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>>8406509

contd.

here is the question [spoiler]fuck[/spoiler]

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>>8406509
>>8406511

samefagging here with another fallacy in statistics:


IF A AND B ARE INDEPENDANT THEN HOW THE FUCK IS THE PROBABILITY OF A AND B NON ZERO IF THE INTERSECTION IS EMPTY SET

>>8406531
independent does not mean mutually exclusive
it means that the outcome of one does not affact the outcome of the other

>>8406141
It's
[eqn] P((A \cap B \cap C^c) \cup (A \cap B^c \cap C) \cup (A^c \cap B \cap C)) = \frac{6}{10} [/eqn]

What are Taylor Polynomials?
I can find lots of overcomplicated explanations of them (fortunately my university actually wrote a decent one), but none of those explanations say when and how they're applied.

>>8406899
stop a taylor series at finite number of terms.

Why doesn't South America get hurricanes?

>>8406531

they're not independant they're independent

>>8405990
>>8406009
>Wait, where'd the 5A=5 come from?
AAAAAAAAAH
WHY CANT I FIGURE IT OUT

can I, realistically, get good enough for an exam this friday on circuit analysis from finding current and voltage all the way up to thevenin and nortons theorems?

I cant for the life of me figure this shit out. I'm currently practicing Transformations and superposition, but the practice problems I'm doing I keep getting the wrong answers.

shit is pissing me off reeeeeeeee, any tips?

>>8407152
Oh, figured it out. 5At+5B-2A=5t+0, so the coeff in front of the T term needs to be 1 to get 5t and the rest needs to be 0 to not get anything more. Seems obvious in hindsight.

>>8407118

what in the world are you talking about mr 8407118

Okay we're doing exam corrections and my prof's comment on this problem was "I don't think this works." The proof is rushed, I know, but bear with me.

Let [math]a, b, c \in \mathbb{Z}.[/math] Prove that if the greatest common divisor of [math]a[/math] and [math]b[/math] equals one and [math]a|bc[/math] then [math]a|c[/math]

Proof: Because [math]a|bc[/math], [math]bc=ka[/math] for some integer [math]k[/math]. Dividing out [math]a[/math] gives [math]\frac{bc}{a} = k[/math]. Now, [math]k[/math] is an integer so [math]\frac{bc}{a}[/math] is an integer. For [math]\frac{bc}{a}[/math] to be an integer, [math]a[/math] must divide at least one of either [math]b[/math] or [math]c[/math].

For [math]a[/math] to divide [math]b[/math], the equation [math]b=qa[/math] must be true for some integer [math]q[/math]. However, [math]a[/math] and [math]b[/math] have no common factors besides 1, so [math]a[/math] cannot divide [math]b[/math] unless [math]a=1[/math], in which case [math]a|c[/math]. If [math]a \neq 1[/math], then [math]a[/math] does not divide [math]b[/math] and thus must divide [math]c[/math].

>>8407308

I was giving
>>8406531
shit because they spelled independent wrong

>>8407316

Your ending sentence is a bit weird namely:

>...in which case a|c . If a≠1, then a does not divide b and thus must divide c.

Well for pa = c, it still holds if a = 1 right?

What you want to show is instead since b = qa is not true for all integer q, therefore a|c must be true for bc/a = k for some integer k to hold.

>>8407328

I'm not sure what your point is. I believe I showed that a has to divide at least one of b or c and that if it divides b it must divide c because a would have to be one.

>>8407316
>For bc/a to be an integer, a must divide at least one of either b or c.
false, it just has to divide bc. consider a=4 and b=c=2.

>However, a and b have no common factors besides 1, so a cannot divide b unless a=1
no, a could also be -1

what you want to do is (assuming you know this basis property about gcd):

gcd(a,b)=1, so you can write ax+by=1 for some x,y in Z. multiply by c to get acx+bcy=c. by assumption a divides bc, and so we have acx+akx=c for some k in Z. factoring gives a(cx+kx)=c so a divides c.

>>8407416

In that case of a, b, and c you gave, gcd(a,b) != 1 and also if a=-1 then a still divides c.

However, the whole ax+by=1 thing was pretty big in our course so the proof you described was likely what he was looking for.

I really love chemistry and chemical engineering but I already have a degree in something else and a bunch of debt.

How can I learn about ChemE without learning to hate it? Just read an intro book?

>>8407436
>In that case of a, b, and c you gave, gcd(a,b) != 1
yes, but what you wrote was wrong without further reasoning (note you haven't even mentioned the gcd at this point in the proof). the claim 'a divides at least one of b or c' does not follow from a and b having gcd 1 (it would follow if b and c have gcd 1 but thats not the case).

>if a=-1 then a still divides c.
yes but this would need to be written down.

>>8407465
I can accept that.

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Do you know a good book to help me?

send help, pls ;_;

>>8407509
What does "x" mean? In R^3 it'd be the cross product but I can't see that that is the case.

>>8407529
Well, assuming we're in R^3 you can assume that v and d are not perpendicular because if they were then d would be equal to its cross product with v, which would mean that it was 0, contradiction.

Now take the inner product of the equation with v, then you get that |v|^2=1.

Take inner product with d and you get that (v*d)^2=d^2
d^2v^2cos^2t=d^2
cos^2t=1
t=0 or pi
so v=+-d/|d|

>>8406899
> What are Taylor Polynomials?
Polynomials of finite degree which locally approximate some continuous function at a point. A Taylor polynomial is obtained by truncating a Taylor series to a finite number of terms.

>>8407509
Do you not have a linear algebra book? Pick any.

For #1, assume that v is in both U and U perp. What do you get?

>>8407436

>gcd(a,b)=1, so you can write ax+by=1

whaat? The only thing that I notice from gcd(a,b) = 1 is that they are relatively prime.

>>8407790
Yes. They are relatively prime.

>>8407802

But thst does not explain the equality senpai. Teach this brainlet why

>>8407804
https://en.wikipedia.org/wiki/B%C3%A9zout%27s_identity

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>Riemann hypothesis
Show me mathematical proof that the german was right. Or something that just makes it look good. Just give me something to belive in it.
>…it is very probable that all roots are real. Of course one would wish for a rigorous proof here; I have for the time being, after some fleeting vain attempts, provisionally put aside the search for this, as it appears dispensable for the immediate objective of my investigation.
- Riemann

So the Riemann hypothesis is just fuck my shit up ??

>>8401083
How does crispr cas9 avoids cutting its own host dna sequences

>>8407509
>using capital theta for the zero vector

how can one interpret matrices as linear mappings? thank

>>8405657
thank

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How does this work?

If I use their formula for the game in their table, for the row player, the value is minimised when the column player chooses L (-100,2). Then If I want to maximize the value, I would choose M, no? So I get (M, L) for the row player and (following the same thought process) (T, L) for the column player.

How do they get (T, L) for both?

>>8407905
[eqn] \underset{a_{-1}}{\min} \; v_1(a_1, a_{-1}) = \begin{cases}
2 & \text{ if } a_1= T \\
-10 & \text{ if } a_1= M \\
-100 & \text{ if } a_1= B
\end{cases} [/eqn]

[eqn] \underline{v_1} = \underset{a_1}{\max} \underset{a_{-1}}{\min} \; v_1(a_1, a_{-1}) = 2 [/eqn]

[eqn] \underset{a_{-2}}{\min} \; v_2(a_2, a_{-2}) = \begin{cases}
0 & \text{ if } a_2= L \\
-20 & \text{ if } a_2= R
\end{cases} [/eqn]

[eqn] \underline{v_2} = \underset{a_2}{\max} \underset{a_{-2}}{\min} \; v_2(a_2, a_{-2}) = 0 [/eqn]

>>8408070
It's a geometric series.

>>8407820
> So the Riemann hypothesis is just fuck my shit up ??
It's a hypothesis, i.e. it might be true (and if it isn't then it's very interesting that it's true for so many cases), but no-one has yet proven it.

>>8407873

Let [math] \mathbb{F} [/math] be a field and [math]m,n \in \mathbb{N} \setminus \{0\} [/math].

If you have a matrix [math] A \in \mathbb{F}^{m \times n} [/math] then you can always consider the linear map [math] T: \mathbb{F}^n \to \mathbb{F}^m [/math] defined by
[math]T(x) = Ax [/math].

I do not consider myself a smart man.
I also do not consider myself an organized person.
This all could be a result of being grown up from a non-supportive environment and the depression I am tackling, which has stunted my last 3-4 years until I have acknowledged it and started working against it.
Maybe it is ALL my fault and I am lying on my bed I have worked on the last 25 years.
Nonetheless, I have become genuinely curious.
I always hear about good math students who spend 40 hours a week learning math.
I would be very astonished being able to spend 20 hours total a week in my studies.
How do they do this?
Where does this planning come from?
And how can I become able to spend the same time for my degree?

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>>8408157

>I always hear about good math students who spend 40 hours a week learning math.
I would be very astonished being able to spend 20 hours total a week in my studies.

Depends on your intelligence desu. If you can't understand something, read and study more until you understand it. It doesn't matter how much time you spent on something. If you can do a revision in 20 minutes or 20 days who the fuck cares. In the end it all comes down to you if you want to spent a life doing this shit.

In my experience studying doesn't really help, I don't understand all of the stuff when I read the book but as I walk down to buy poutine my brain begin to actually grinds.

Does anyone has a link for the solution of the mice problem https://en.wikipedia.org/wiki/Mice_problem. using pursuit curves? Or could you show me how?

I have a slope and a distance, how do I calculate the x and y of that point? Assuming the line starts at (0, 0).

>>8408253
change to cartesian

>>8408253
slope of a line is y/x

squared distance by pathagorean is the sum of the squares of x and y

apply algebra

>>8408253
x = distance * cos(arctan(slope))
y = distance * sin(arctan(slope))

Anybody help me with >>8408169?

I didn't see this thread or I wouldn't have started my own.

>>8408266
>transcendental functions
absolutely disgusting

>>8408271
https://www.youtube.com/playlist?list=PLIljB45xT85AMigTyprOuf__daeklnLse

>>8408266
> cos(arctan(slope))
> sin(arctan(slope))
No need for trig:
x = distance / sqrt(slope^2+1)
y = distance * slope / sqrt(slope^2+1)

Or, if you have the slope in the form dy/dx:
x = distance * dx / sqrt(dx^2+dy^2)
y = distance * dy / sqrt(dx^2+dy^2)

Which works even if dx=0 (i.e. the line is vertical).

why is the mathematical community so based when it comes to sharing knowledge? nearly every math book ever is easily found online as a pdf/djvu file, but whenever my friends in other fields look for books they can never find them

>>8407905
That's amazing thank you. But the Wiki page says that their maxmin strategy is (T,L). Didn't you get (T,R) for player 1 and (M,L) for player 2?

>>8408316
Meant to quote >>8408088

"I flipped a fair coin: if it came up two heads I used 10 triangles, if it came up heads I used 5 triangles; otherwise I used 15"

What is this sentence? Was the coin flipped 2 times? Does he mean that he flipped the coin twice and if both came up heads then x, if it came up heads only once then y, etc....? Where are the words? It doesn't mention how many times it was flipped, and the whole formulation is odd. Can someone explain me what it means?

My friend has been starting to get into spiritualism. He thinks it's weird that people see reptiles while being high, he thinks the pineal gland to be supernatural, that sort of stuff. Can someone give advice how to get him out of it or arguments against the stated beliefs?

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>>8408330

I think there are 3 possible and in fact only 3 possible cases:

2 heads - > 10 triangles
1 heads - > 5 triangles
0 heads - > 15 triangles

>>8408371

That explanation was extremely autistic, what I meant was that there are only 3 possible states when you flip 2 coins.

You either get 2 heads, 1 head or no head at all

>>8408316
The maxmin strategy for the first player is T since it guarentees a payoff of at least 2.
The maxmin strategy for the second player is L since it guarentees a payoff of at least 0.


If both player use their individual maxmin strategies than the payoffs are 3 and 1.

>>8408368
When he starts about that shit just tell him it's BS in a few words and don't talk about it with him. My m8 started going on about that shit (egyptians chakra the whole zim zam) and I still feel kinda bad for just nodding along while he went off the deep end.

>>8408227
Anyone?

>>8408380
Yeah but he doesn't mention hwo many times the coin was flipped wtf

Also there are 4 states i think: HH, HT, TH, TT (i.e. one head is more probable than than the others)

>>8408402
Ohhhh ok I see now thank you!!

Why do they use tensors in general relativity and not differential forms?

>>8408422

yes there are 4 states but we are talking about the states of "head". I do agree the sentence is retarded.

>>8408406
Thanks, the only problem there is that he see me as narrow minded for refuting his ideas

>>8408429
Differential forms are special cases of tensors (well tensor fields)

>>8408502
Don't waste your time refuting that shit.

I have a basic grasp of geometry and want to learn up to calculus, specifically I want to be able to understand proofs for the madhava - Leibniz series for pi. All I've been able to figure out so far is that the if you have a 45 degree right angle, you can subtract the length of the adjacent side from the length of the hypotenuse and divide that by the length of the opposite to get the tangent of 22.5 degree angle, and that you can continue doing this with each triangle to get the tangent for half of its angle.

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The difference is allowed to be zero as well. I've tried pairing the numbers in pairs and just cancelling out the differences of one's (doesn't work since you have 25 pairs).

I've tried tripling all the numbers I can (eliminating 1-15, 21, 24, 27, 30, 39, 42)

Seems like it is not possible. Why?

>>8408604
No, and you made the right observation: there are 25 odd numbers. Multiplying any number by 3 doesn't change its parity, hence the number you get at the end will be odd (the easiest way to see this is to look at the situation mod 2: there, 3=1 and -1=1, hence the number you get at the end has the same parity as the sum of all numbers from 1 to 50, ie. it's odd)

>>8408558
Ah, thank you, now I see. I should've consider them as linear functionals from the beginning.

Problem 4. At each vertex of a cube we write either 1 or −1. Then in the middle
of each face we write the product of the numbers at the vertices. Can the sum of the
obtained 14 numbers be zero? Hint: Find the product of these 14 numbers.

Well the sum has to be 1. Seven 1s, 7 negative ones. Ive noticed when you change the sign of a vertice it changes the sign of three faces. Is this possible?

>>8408604
Why not? Pick 1, and then 1 again, and their difference is 0.

>>8408760
You cant pick the same number twice

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Does uni rankings mather?
Would you go to a top 150 uni insted of a top 50 just because it's more comfy?

>>8408756
You have all the important beginning bits for the solution, which are this
>Seven 1s, 7 negative ones
and this
>Ive noticed when you change the sign of a vertice it changes the sign of three faces.

Consider a vertex. Of the 3 faces next to it, either 0, 1, 2, or 3 are the opposite sign.

How many of the opposite sign can you add by flipping the vertex in each case?
If you do the casework (I'm not going to include it in the post because it's long) you'll see you can either add 4, add 2, add 0, or lose 2.

Notice these are all even numbers.

What about the case when every vertex is 1? There are 14 ones in this case.

That's enough to prove it, because there's no way to transform 14 ones to 7 ones just by adding/subtracting even numbers.

>>8408411
>https://en.wikipedia.org/wiki/Mice_problem

http://math.stackexchange.com/questions/479836/solving-the-continuous-mice-problem

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>>8407572
>>8407612
thanks guys, you saved me

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>>8408979

Are most lectures a waste of time?

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Theorem 3.2.3 is the arithmetic operations with sequences.
lim(X)=x, lim(Y)=y
lim(XY)=xy
lim(X=Y)=x+y
etc.

Why won't lim(XY)=xy work for pic related?

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i feel like an idiot
how do i prove that the union of finite sets is finite?

also, i -think- that the cardinality of the union of finite sets is equal to the sum of their cardinalities minus the cardinality of their intersection, but again, i don't know how to prove it

i would also appreciate a book with practice problems and solutions for stuff like topology and set theory if you happen to know of any

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>>8409038
>how do i prove that the union of finite sets is finite?
You don't. Take the set of reals. It is an uncountable union of finite sets, namely the singletons, but not finite itself. On the other hand, if you had a finite union of finite sets, then it would be proven easily like this:

Let [math]n[/math] be a positive integer, and for each [math]1 \le i \le n[/math], let [math]A_i[/math] be a finite set. If now [math]m_i[/math] is the cardinality of [math]A_i[/math] and [math]m[/math] the cardinality of their union, then [math]m \le m_1 + m_2 + \cdots + m_n < \infty[/math] as a finite sum of integers.

>>8409068
I supose he means the fintie union of finite sets

>>8408912
That makes sense. I've done tons of examples and noticed that the number of changes in 1's to -1's has often been 4, 2, or zero.

I think I have what I need to prove it now. Much appreciated.

>>8409068
>>8409071
yes, i meant finite union of finite sets, i should have clarified

If the normal unit vector of a planar curve is constant, does it mean its a parabola?

>>8409038
Just do a proof by contradiction.

>>8409038
>also, i -think- that the cardinality of the union of finite sets is equal to the sum of their cardinalities minus the cardinality of their intersection, but again, i don't know how to prove it
Not quite. This will still result in overcounting if one number is in at least 3 sets (because subtracting the intersection only removes 1, but you overcounted by 2).

You need to subtract many intersections, and then add some back, and then subtract some more...
It's a pretty formula but it's not short.

What you're trying to prove is essentially inclusion-exclusion principle and there are too many good proofs of that on google to bother writing one out

>>8409094
exactly what i was looking for, thanks

>>8409080
More generally, the question states to find a curve that has the reflective property of the parabola (That it deflects rays of light from a single source in the same direction). What I did is consider that the angle made between the tangent and the normal vector of this curve make must be the same as the angle formed by the tangent and the reflected ray. So I just equated the dot product of the normal and tangent vectors to the vecotr (0,1) , asuming this was the direction of the ray.

>>8408783
University rankings are based on fresh graduate pay
So yes, if i want to lead a comfy life when i graduate, i would choose a top 50 school

I'm a physics undergrad applying to applied math grad schools. How difficult is the jump from physics to applied math? I did pretty well on the math gre - 85th percentile, I'm interested mainly in computaitonal math - CFD/Electromagnetics

I have a couple of lab questions related to Fourier Transformations (context is physics)

>Describe what happens if you apply a lowpass filter to an image.
>Describe what happens if you apply a highpass filter to an image.
For these first two, am I correct in saying that the lowpass one allows parts of the image with a low frequency to appear, and hides parts of the image with a given limit? And for a highpass the opposite would apply.

>What image features correspond to the high spatial frequencies?
The light parts of the image?
>What is the Fourier transform of a periodic feature in an image. How can you distinguish this feature from a similar feature with a longer period?
I'm not sure how to answer this one.

>>8409175
it sounds like they're referring to a spatial transformation, not brightness

>what image features correspond to the high SPATIAL frequencies
Not "light" parts. Rapidly changing parts.

>>8409223
Thank you, I think I got the rest.

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>>8401083
I don't fucking get vectors at all. I got the same answer by double-integrating, but this answer is completely confusing me. It makes sense to me if ihat dot khat is zero and khat dot khat is one and the book is in error, and we have found errors in the solutions manual.
halp?

>>8409296
What kind of barbarian uses khat for y instead of z?
Either way, yes, there's a mistake.

To measure flux you need to take into consideration the vector components colinear to the normal vector of the area being studied. In this case, the area being studied has a normal vector khat, meaning that only vector components in the direction of khat matter in measuring flux.

This is why you do the dot product: it extracts the colinear components. khat cancels ihat, which is why when you integrate it completely dismisses the ihat component.
khat dot product with khat equals 1, so all of the contribution of khat is being taken into account.

The math seems fine. The error is in the last line. It should read:
"Where the ihat term was eliminated since ihat dotproduct khat = 0"

>>8406154
Anyone?

>>8409333
Thanks, I completely understand now.
Well, no, but I understood what you said and that's almost as good.

If I want to write a KK-long word with just LL letters if K>LK>L and you can use a letter up to MM times is there a way to determine a function f(K,L,M)f(K,L,M) to calculate the number of words?

>>8404127
Rationalize, factor (x^2-1), use crude bounds on (x+1) and 1/(x^2+1) and you'll get some constant times delta.

You may want to say something like let 0<eps<1 to bound |x-1|

>>8409014
Why should the limit of a bounded sequence exist in the first place?

Think of b_n=(-1)^n

I'm practicing chain rule problems and checking with wolfram.

>(2x-1)^5
I get 10(2x-1)^4, they get 10(1-2x)^4

Likewise for:
>1/(3t^2-2)
I get -6t/(3t^2-2)^2, and they get the same except 2-3t^2 in the ()

Why are the numbers reversed?

Can I get a recommendation of a book and/or online page about basic Algebra that teaches good polynomial factorization + (simplification of) rational expressions?

I've been getting destroyed by these lately because it's been ages I don't practice my little math skills.

>>8409175
Low-pass filter = "blur", high-pass filter = "sharpen".

A feature which is periodic in one dimension will manifest as a sequence of regularly-spaced peaks in the frequency domain, with the offset between peaks equal to the repetition frequency.

Similarly, a feature which is periodic in two dimensions (i.e. a regular tiling) will manifest as a regular grid

>>8409489
> I get 10(2x-1)^4, they get 10(1-2x)^4
> I get -6t/(3t^2-2)^2, and they get the same except 2-3t^2 in the ()
In both cases, the expressions are equivalent. If n is even, (-x)^n=x^n.

>>8409131
But the 150 one acutally has higher gratuate pay. The highest in the country for CS. Bout 10% higher then the top 50 school.

>>8409517
http://www.cimat.mx/ciencia_para_jovenes/bachillerato/libros/algebra_gelfand.pdf

Find the 12 prime numbers that are constructed of the four digits 1,5,7,9

>>8401083
why the FUCK does gcd(a,b)=gcd(b,r).
pls halp!

>>8409626
so here's what i have so far,
let d=gcd(a,b)
>d|a and d|b
and we know, a=qb+r so,r=a-qb
so d|a-qb(cuz common factors) so d|r
but now how do we know its the greatest common factor of b and r;_;

>>8409631
because a=qb+r, and so if there was a greater common divisor of b and r then it would also divide a

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>>8405470
BTFO!

I have a couple of question on NMR
a)how do I calculate T1, T2 and NOE from the spectral density function? I know it's possible, I found an equation, but it doesn't explain what everything is.
b)From T1, T2 and NOE, how do I calculate S^2?

>>8409667
Ok, I found the answer to a with https://deepblue.lib.umich.edu/bitstream/handle/2027.42/30338/0000740.pdf?sequence=1

But b I still don't get it

If someone develops hives a day after taking penicillin orally would that be a type 1 hypersensitive reaction?

>>8401083
I know jack shit about rocketry as will soon be apparent:

Say I have a rocket system that can hover for maximum 10 seconds - any added fuel mass is below some pre-determined threshold of returns.
If I take it to a planet with 1/3 of the gravity, I just get 30 seconds of flight time if I keep the same predetermined cut off right? Because the "tyranny of the rocket eqn" is based on mass fraction?

>>8409756
Yes, assuming that you can generate 1/3 of the thrust with 1/3 of the rate of propellant consumption (i.e. exhaust speed is unaffected).

When does math gets hard for you /sci/ that you just dont see any intuition in it.

Inb4 calculus 2

a, b reals

a =< x =< b

how demonstrate than 0 < x^2 < b^2 ?

>>8409923
0 =< x^2 =< b^2

of course

>>8409925

Any number squared is either positive or zero. Look at arithmetic axiom

>>8409925
First you'd need also to state that 0<a<b, otherwise the statement isn't actually true.

>>8409933

What? Its squared bros so it will always be zero or positive.

>>8409935
consider a= -10, x=-2 and b=0

then x^2 > b^2

>>8409923

Minus all by a, so you have 0=< x-a =< y-a , square this, then apply that square will always be non zero so the ineuqality holds.

Whats the forumula to calculate something like this

What's the probability of picking up 3 white balls when picking up 5 balls (with replacement) given that there are 5 white balls in the bag and 10 balls in total?

>>8409998
Or another way to put it

What's the probability that there are 5 white balls in a bag if I draw 6 balls with replacement and I get 2 white balls, and I know that there are 10 balls in the ba?

>>8409873
Depends on the subject and how it is taught. A good teacher will help you get intuition or at least teach the definitions in a motivated way.

>>8409998
> What's the probability of picking up 3 white balls when picking up 5 balls (with replacement) given that there are 5 white balls in the bag and 10 balls in total?
There are 2^5=32 possibilities for picking 5 balls with replacement, all equally likely. 3C5=10 of those will have 3 white balls. So 10/32=0.3125.

In the more general case where the probability of picking a white ball is p, the probability of getting a specific combination with n white balls is p^n*(1-p)^(5-n).

>>8410010
That's a different (and harder) problem. Also, you need to know the probability of picking a white ball when filling the bag.

Assuming that black and white balls are equally likely when filling the bag, then:

Let p[i] = (i/10)^2 * (1-i/10)^4 * C(6,2)/(2^6) * C(10,i)

The probability of there being 5 white balls in the bag when you get 2 white balls out of 6 is
p[5]/sum[i=0:10](p[i]) ~= 0.278

It's feasible to check this empirically by enumerating all (2^10)*(10^6) possible cases.

Very important question here guys:

do we need to restart science?

>>8409873
It never has.

>>8405958
What is u_1 ? I assume delta is the Dirac delta distribution.

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>>8401083
How did they get the first term of the gradient ([math]Qx[/math])?

-1 < x =< 3
1 =< y =< 7

it gives 0 < x + y =< 10
and not 0 =< x + y =< 10

right ?

>>8411699
correct

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suppose C,D are two nxn matrices with integer entries satisfying (C^T)D = (D^T)C where C and D (^T means transpose)

why is det(iC+D) not 0?