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/sci/ - Science & Math

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12093089 No.12093089 [Reply] [Original] [archived.moe]

The thread for questions that don't deserve their own thread
For book recommendations, check the sticky and/or the /sci/ wiki. To download free books, check http://gen.lib.rus.ec/
For learning how to use the inboard latex, check the sticky. You can also test your latex before you post by clicking the "TEX" button in your reply box.

If you ask any question, remember that there is almost no universal notation in many fields.

>What is a BAD question?
Help me with this problem.
Do this problem for me.
What does T mean in this equation: [math] \mu \chi = \frac{33 T}{\aleph} [/math]
>What is a GOOD question?
Here's the problem I'm having trouble with. I've tried ____, but it didn't work. I don't know how to get past _____.
If m is rest mass and c is the speed of light, then what is E in the equation E=mc^2?

previous thread >>12077754

>> No.12093129

Why can't the universe exist without an observer?

>> No.12093131

Where did the touhou poster go? I know that this is a bit off topic but he really did help contribute to the /sqt/.

>> No.12093133

Says who? It literally does

>> No.12093136
File: 308 KB, 1200x1196, ligo.jpg [View same] [iqdb] [saucenao] [google] [report]

Did they build this knowing it was a waste of money?

>> No.12093141

what scientific research facilities aren't a waste of money by your standards? at least it found evidence for gravitational waves.

>> No.12093144

Really dumb question but, I find myself using the solution's manual a lot for the level 2+ physics questions (the textbook that we're using has 3 levels of problems, the 1st is really simple, the 2nd example is like a little bit more complex as it might take 10-15 minutes, while the 3rd level would be like the last question on a midterm), is this 'normal' for students who are not really that good in physics? I feel like whenever I resort to the manual after some attempts, I feel like I'm 'cheating' myself but at the same time, I know that it's better to have an idea of what to do than not have it at all.

>> No.12093148

What are gravity waves made of? What is 'waving'?

>> No.12093149

you're probably relying too much on the solution manual.
the level 3 problems aren't meant to be immediately obvious. you're supposed to sit there for a bit, think, try some things before getting an answer. same with level 2, to an extent.
if you know the solution guide exists what's most likely is you're looking at the problem, thinking about whether you know how to do it, and then just going straight to the guide if nothing pops in your head immediately.

I say this because I was the same way and getting rid of my solution guide helped a lot in my understanding.

>> No.12093154

what are light waves made of? what is "waving"?

gravity waves are composed of space distortions. like how black holes bend the space around them, except if you imagine a binary black hole system spinning around each other it would look like an oscillating dipole.

>> No.12093156

>if you know the solution guide exists what's most likely is you're looking at the problem, thinking about whether you know how to do it, and then just going straight to the guide if nothing pops in your head immediately.
True. Thank you anon, I'll just delete the manual and take it out of the trash if I've spent like 40+ minutes on it.

>> No.12093165

That thing takes us one step closer to understanding gravity. What are you even talking about? That station is going to be used for the next 100 yeas, at least.

>> No.12093184

Im struggling to understand divergence and curl. Not what they represent, I think I understand that fairly well, but how they are defined and how they are computed. I understand that [math]\nabla[/math] is an operator, and I understand how you can have something like [math]\nabla A[/math] I think (?) but where I am really having an issue is something like [math]\nabla \cdot A[/math] or [math]\nabla \times A[/math]

My issue is that if [math]\nabla [/math] is itself an operator, then what you have in the two above looks something like "operator operator operand" instead of the expected "operand operator operand". In other words, I dont see the distanction between the above and something like [math]y = +*x[/math] . Can someone tell me what I am missing? I have tried looking at a few videos and my textbook, but they all seem to focus on how to conceptualize and/or understand what the curl and divergence actually mean, not how they are computed. Like, if I have [math] A = B \times ( \nabla \times C) [/math] how would I do that? If I am trying to do "something cross C" and that something is del, what am I crossing C with, since del is an operator?

>> No.12093195
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Why is the moon a perfect circle?

>> No.12093197

when you think about del being used in front of an operator, it's helpful to think of it like: [eqn]
\nabla = \frac{ \partial }{ \partial x} \hat{x} + \frac{ \partial}{ \partial y} \hat{y} + \frac{ \partial }{ \partial z} \hat{z} [/eqn]
in the 3d case at least, obviously generalized to whatever coordinate system you're using.

>> No.12093200

most celestial objects are circular because gravity is a central force. meaning when these objects form, the lowest-energy configuration is spherical.

>> No.12093205

c isnt speed of light there dumbass. its just a magnitude equal to speed of light. theres no meters/sec anywhere in that equation.

>> No.12093206

How does one get the ratio of x1/x2 = y1/y2 from the equation x1y2=x2y1?
I don't understand the process of rearranging them.

>> No.12093209

divide both sides by x2y2
the y2 cancels on the left and the x2 cancels on the right

>> No.12093213

How fuck that worked, how did you think of that?

>> No.12093217

It's actually not a perfect circle, but it is close enough that it appears as one to us. If you were to measure it really precisely, you would find all sorts of irregularities like mountain ranges and the like. In fact, the back side of the moon is actually considerably thicker than the side that faces the earth (by several kilometers, I think, but dont quote me on that) This is the case with all rocky bodies.

If you are asking why it is a circle (as opposed to a geometrically perfect circle) see>>12093200 Basically the idea is that the center of gravity of a planet or moon is at its exact center (hence the term center of gravity) and all parts of the body are pulled towards this point with approximately the same force, so mass tends to evenly distribute itself around over time. The lowest energy state (and thus the configuration that will be reached over time) is where all mass is as close to evenly spread out as possible.

>> No.12093218

it's a very common process. think of what equation you have and what equation you want to get. think of what sort of operations you can do to both sides (since you're free to do anything as long as you do it to both sides) to get from what you have to what you want.

the more you do manipulations like this the more comfortable you'll be

>> No.12093220

I thought gravity wasn't a force, but a pseudo force. Isn't it too weak to have any affect on such massive physical objects? Or is it because these celestial objects start out as like liquid lava and then cool & harden

>> No.12093225

gravity is a force. it is one of the four fundamental forces
gravity is a weak force, but when you have extremely massive objects (i.e. planets) then the collective strength of the gravitational field they produce is large.
even everyday objects are affected by each other's gravity. there's a gravitational attraction between you and your computer screen. the difference is you're both experiencing a much larger attraction to the massive planet below you, so you don't notice anything. but if you were in space with just your computer monitor, over a long period of time you would be pulled closer together.

it's like one electron doesn't produce that much of an electric field, but if you were to put 10^20 electrons together (ignoring the impossibility) then the collective electric field would be massive.

>> No.12093230

I get that, but [math]\nabla = \frac{ \partial }{ \partial x} \hat{x} + \frac{ \partial}{ \partial y} \hat{y} + \frac{ \partial }{ \partial z} \hat{z}[/math] of what? If it was [math]A = ( \nabla B \times C )[/math] instead of [math]A = ( \nabla \times C )[/math] then I would understand. then you would be saying [math]\nabla = \frac{ \partial A }{ \partial x} \hat{x} + \frac{ \partial B}{ \partial y} \hat{y} + \frac{ \partial C }{ \partial z} \hat{z}[/math] Otherwise, what am I taking the partial derivative with respect to x *of*?

>> No.12093243

nothing, until you act on something. think of it as a vector where the entries are partial derivatives. when these derivatives hit something on the right side, they act on it.

similarly, think of a constant vector (1,2,3). when you dot this vector with another one, you multiply the components by 1,2, and 3 respectively. but when you don't act it on anything then what is it doing? it's just there.

to help your understanding, I recommend you do: [eqn] C=f \hat{x} + g \hat{y} + h \hat{z} \\
f \equiv f(x,y,z) \text{ same with g, h} \\
A= \nabla \times C [/eqn]
treat the del as you would any vector, and what would you end up with for A? (f, g, h are arbitrary)

>> No.12093253

adding to this because I always end up thinking of more helpful things, you say you understand [math] A= \nabla B [/math] . but what are you doing here? think about this in terms of the definition of del that I gave earlier.

you're taking the partial of B with respect to x and then that's the x hat component, and then repeating with y and z. is that not just the same thing as multiplying the vector representation of del by a scalar function B?
with this line of thinking, del is a vector function. vectors can be dotted with other vectors (divergence) or crossed with other vectors (curl) or multiplied by scalar functions (gradient).

>> No.12093275
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>> No.12093276

What exists outside the universe?

>> No.12093283
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How do I do this problem?
I can't relate linear density formula (u = m/L) to the density formula (p=m/V), I know that I'm supposed to get u=p*A (pi*r^2) but how though?

>> No.12093289

V = A*L

>> No.12093290

you have density that relates to the entire volume of the object
the linear density is the density per unit length. when you remove the "length" aspect of a wire, what are you left with? just a cross-sectional area. so your volumetric density times your cross sectional area is your linear density.

>> No.12093291

Define 'the universe'.

>> No.12093305

Thank you both!

>> No.12093312

Cheers, lad.

>> No.12093338

>>but when you don't act it on anything then what is it doing? it's just there
Thats my point, without anything to act on, it has no value, and if it has no value, no real meaning, how can you take the cross product between it and a vector?

>> treat the del as you would any vector, and what would you end up with for A?
How do you treat it as a vector? It isnt a vector, its an instruction. I am seeing this as being the same thing as y = +*x. It's an invalid operation, a syntax error. "+" is an instruction saying "add", "*" is an instruction saying to multiply, and "x" is some number. So I would read this as "y is equal to addition multiplied by x" or more generally, "y is equal to <instruction> <instruction> <value>". You cant multiply x by addition. addition/multiplication instructions needs to values to operate on, ie <value> <instruction> <value>. The same goes for the cross and dot product. when I see [math]A = \nabla \times C [/math] I see this as "A is equal to <instruction> <instruction> <value>"

>> is that not just the same thing as multiplying the vector representation of del by a scalar function B?
Yes, but in the case of [math]\nabla B[/math] you are taking the partial derivative of B with respect to x, y, and z respectively. But the vector representation of del still isnt a vector really, its still an instruction. If you take the B away, it has no meaning.

Thank you for helping with this by the way, I really appreciate it.

>> No.12093345


What units do you think energy is measured in anon?

>> No.12093348

Did you have a question?

That depends. if the "universe" is defined as "all there is" then nothing can exist outside of it, as by definition, if it exists, then it is contained within the universe.

Are you asking what exists in a physical location beyond the edge? If so, that also depends. First of all, there may or may not even be an "edge" in the first place. We can see about 14.5 billion light years in all directions, and we call this region of space the "observable universe" because it is what we can see. It might be that this is all there is, and there is either a boundary or something else (more on that in a bit) when you reach that point. But it could also be that there is just more stuff beyond, that the point in space 14.5 billion light years from us actually isnt any different from any other location, and there is more stuff on all sides of that point, ie there is no "boundary", it just keeps going. This is because if, hypothetically, we assume that there *is* more universe beyond the observable universe, we would be unable to see it from our current location, because light from that region of space has not had enough time to reach us. The universe is 14.5 billion years old, so anything further than the distance light travels in 14.5 billion years will be fundamentally un-observable to us.

For the sake of exploring the idea, lets say we suddenly are able to instantly teleport to any location in the universe, and so we teleport to a point in space 14.5 billion light years away. I mentioned two possibilities, that there is some sort of "boundary" or that there is not. Assuming there is a boundary, we dont know quite what it would look like. One idea is that it would be like trying to sail off the edge of the earth: you just end up on the other side, and eventually going in a circle, back where you started. It is also possible that there is a boundary, but it is further away, or it could just go on forever.

>> No.12093349
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Just posting this again!!

How do i draw this??
I'm doing organic chem first year at uni but i just have no clue how this is happening? I have only just touched on organic chemical reactions so I have no clue how they occur?
I've written this out from what I know.. I just don't know how to draw it out like the arrows and what loses what and where it comes from - and exaplain the whole pathway in detail!??
If it would be easier to explain over discord I can post my ID
Thanks frens

>> No.12093354

I hear your question, your call into the void for help, but I posses not the answers you seek.

>> No.12093359

That's okay I appreciate that.

>> No.12093366

>without anything to act on, it has no value
This is true. on its own, it doesn't mean anything.

I think a lot of your problem in understanding right now is your understanding of vectors. What is a vector? If you think it's a "magnitude and a direction," I would challenge you to try and think of them more abstractly.
Anything that you can put into a vector form is a vector. You can have a vector of functions [math] \overrightarrow{F}=A(x,y) \hat{x} + B(x,y) \hat{y} [/math] . Are you comfortable with this? On its own, what would you say the "meaning" of this vector would be? It doesn't necessarily have one, it's just a collection of functions that are to be used for a certain purpose.

>How do you treat it as a vector? It isnt a vector, its an instruction.
But it is a vector. We'll get to this.
I understand your point where you say y=+*x doesn't make sense. That's because + and * are operations that take two inputs. What kind of operation is [math] \frac{ \partial }{\partial x} [/math] ? It is an operation, correct, but it only takes one input. [math] \frac{ \partial }{\partial x} f(x,y) [/math] has a meaning, while +f(x,y) doesn't.
So, we see that we can "multiply" a partial derivative operator by an expression and it is a valid thing to do (it just returns the derivative of the expression), while the same isn't quite true for addition and multiplication.

Now, how do we treat a vector of partial derivatives? Just the same as we would treat any other vector. Instead of the entries being numbers, or functions, or expressions, they are partial derivatives.

>But the vector representation of del still isnt a vector really, its still an instruction.
Still, try to break away from thinking of this as an "instruction," rather than a vector of partial derivatives.
When you compute [math] \nabla B [/math] what are you doing? First, you differentiate this wrt x and then put this in the x component of a final vector. (cont.)

>> No.12093374

If we wanted to write this step mathematically, we would write [math] \frac{ \partial }{\partial x} B \hat{x} [/math]
What happens when we act with the vector representation of [math] \nabla \text{ on } B \text{ ? } (\frac{ \partial }{ \partial x} \hat{x} + ...)B= \frac{ \partial B}{ \partial x} \hat{x} + \text{ same for y, z} [/math] . We get the same result.

What this is all leading to is that there is an explicit vector representation of del (provided that you know how many dimensions you're working with), that is equivalent to the gradient operation. When we use this vector representation in different ways, we recover the divergence and curl.

>If you take the B away, it has no meaning.
On its own, del is a vector differential operator. The vector itself has the meaning that it is ready to act on something to the right. It "operates" on expressions. You can't graph an operator, so maybe that's what you mean by it "has no meaning"?

>> No.12093395

I think this finally has gotten through my thick skull... so if B is a vector with 3 components, you could write [math]A = \nabla \times C [/math] as [math](\frac{ \partial Ax }{\partial x} + \frac{ \partial Ay }{\partial y} + \frac{ \partial Az }{\partial z}) \times (Ax + Ay + Az)[/math] right?

>> No.12093400

wait no, I wrote that wrong, should be

[math] A = \nabla \times B [/math]


[math](\frac{ \partial Bx }{\partial x} + \frac{ \partial By }{\partial y} + \frac{ \partial Bz }{\partial z}) \times (Bx + By + Bz)[/math]

>> No.12093407

posting >>12090334 again in case someone knows some commutative algebra
in general i was just looking for a field extension of [math] \mathbb{Q} [/math] of degree 3 that wasn't pure cubic (so not of the form [math] \mathbb{Q} (\sqrt[3]{k}) [/math] for some rational k). the wikipedia article on cubic fields shows that specific polynomial as an example of a non-pure cubic field so i figured it would be easier to show, but apparently not
but if anyone has any other example of such an extension that is easier to check that would be great too, i can only think in terms of degree 3 polynomials with 1 real and 2 complex roots

>> No.12093423

Almost correct, but getting quite close.
First of all, are you writing [math] (Bx + By + Bz) \text{ when you mean } (Bx \; By \; Bz) [/math] like as a vector?

Explicitly, you would write [math] A = \nabla \times B [/math] as:
A= \begin{bmatrix}
\frac{ \partial }{ \partial x} \\
\frac{ \partial }{ \partial y} \\
\frac{ \partial }{ \partial z}
B_x \\
B_y \\
= \text{det}
\hat{x} & \hat{y} & \hat{z} \\
\frac{ \partial }{ \partial x} & \frac{ \partial }{ \partial y} & \frac{ \partial }{ \partial z} \\
B_x & B_y & B_z

let me know if this clears things up or makes it more confusing

>> No.12093447

>> First of all, are you writing (Bx+By+Bz) when you mean (BxByBz) like as a vector?

yes, thanks

This answers everything I think, but to confirm, when you do "partial derivative with respect to x times By" for example, (in the matrix multiplication) do you just then take the partial derivative of By with respect to x?

>> No.12093449

By is just the y component of the vector B. It can depend on the variables x,y,and z though. This is one of the more confusing nuances because when it's abstracted like this you don't necessarily realize that.

[math] \frac{ \partial }{ \partial x} * B_y = \frac{ \partial B_y}{ \partial x} [/math]

>> No.12093470

You have successfully freed me of a mental trap I have been stuck in for the past 72 hours, and thus have earned my undying gratitude.

When you put it like that, it seems so obvious lol. I guess everything does in retrospect. Whenever I end up getting stuck on an idea, it seems to always be that one thing that NOBODY else has an issue with, or at least nobody asks the question the way I would.

Again, thank you so much for taking the time to help me with this, I am sure most people would have just given up after round one, or not taken the effort to adapt what they were saying based on how I was interpreting what you had said before.

>> No.12093472

>Whenever I end up getting stuck on an idea, it seems to always be that one thing that NOBODY else has an issue with, or at least nobody asks the question the way I would.
yep, these are always hard to clear up because the online resources aren't geared towards these types of problems. that's why stuff like this and in-person instruction is best, because you can ask specific questions.


>> No.12093626

Should I even bother joining the research lab of a chinese professor with mostly foreign chinese students? seems like they would just converse amongst themselves in chinese and leave me out of most things, but does anyone have experience in the situation?

>> No.12093634

only if the lab is extremely well-known and you'd be doing high quality work.
otherwise if there's a lab of even remotely similar quality, join that one instead,

>> No.12093637

If I am given the task "Prove A B"
and I prove you can always get from A to B
Have I completed the task?

>> No.12093642

this falls under "horribly-worded question because we have no idea about the details"

>> No.12093646

I was doing a calculus III exercise that asked for me to show two vectors are linearly dependent if and only if they are parallel. I showed algebraically two linearly dependent lines are always parallel. Did I answer the question?

>> No.12093649

since it's "if and only if" and you proved that linear dependent -> parallel, you have to also show parallel -> linearly independent, unless your proof is symmetric (in which case you state that you could do the steps backwards and prove the converse)

>> No.12093658

Thanks anon for clearing up the logic. It does seem to indeed be symmetric.

>> No.12093659

ok thanks, i will probably just look elsewhere

>> No.12093906
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Dumb thought experiment:
I have an accelerating mass on a circular track, with a laser shining through a portion of the track. No losses due to friction, ideal scenario, etc, etc. Several questions:
>Does the laser blueshift?
>If it does, then the laser gains energy. I presume energy is transferred from the mass to the laser?
>If it does, then does the mass attempt to decelerate in the absence of a driving force?
>Finally, what happens when the mass clears the laser and it is allowed to shine back to the other end of the track? Where does the blueshifted energy go?

>> No.12093939

>Does the laser blueshift?
yes, you're moving towards the emitter
>If it does, then the laser gains energy. I presume energy is transferred from the mass to the laser?
your understanding of redshift and blueshift is incorrect. the light is blueshifted because the relative motion between the source and the observer.
energy is not conserved across different reference frames, so there is no absolute gain in energy that comes from anything.
>If it does, then does the mass attempt to decelerate in the absence of a driving force?
this makes no sense, see above
>Finally, what happens when the mass clears the laser and it is allowed to shine back to the other end of the track? Where does the blueshifted energy go?
it doesn't go anywhere because there's no extra energy in the system

>> No.12093953

>your understanding of redshift and blueshift is incorrect
How does energy not transfer from the mass to the laser?
c = (lambda) * (frequency)
E = h * (frequency)
If the laser does indeed blueshift, then the energy of the laser should increase, yea?

>> No.12093999

The energy of the laser is higher in the car's frame when it's moving towards the laser. This doesn't break any laws, it's purely due to the relative motion
>transfer from the mass to the laser
what does this mean? there's no "transfer" happening. the car sees the light as higher energy, that's it.

when dealing with different reference frames, only invariant quantities are unchanged. the relevant invariant quantity would be [math]E^2-(pc)^2 [/math] this is the same in all reference frames. the momentum p for light is given by [math] p= \hbar k= \frac{h}{ \lambda } [/math]. This quantity is the same to the laser and to the car.

>> No.12094008

also, just to reiterate. how would there be energy transfer from the mass to the laser? there's no force between them, no interaction. in order to transfer energy there has to be some kind of interaction.

>> No.12094021

I'm still reading >>12093999 but my line of thinking is as follows:
Blueshifted light gains energy. I am assuming energy is conserved (until I understand 12093999). If it is conserved, then how did the light gain energy? Naive guess is it's being transferred from the kinetic energy of the mass to the light.
I'm not really used to multiple frames of references, so I'll work out how the invariant would be used in my model.

>> No.12094282
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Is this correct?

>> No.12094427

>My issue is that if ∇ is itself an operator, then what you have in the two above looks something like "operator operator operand"
∇ is an operator, ∇· is an operator, ∇× is an operator. The naming is mnemonic, you're not *literally* taking the dot or cross product of ∇ with a vector.

Given f : R^n->R, ∇f : R^n->R^n = <∂f/∂x, ∂f/∂y, ∂f/∂z, ...>
Given f : R^n->R^n, ∇·f : R^n->R = ∂f_x/∂x+∂f_y/∂y+∂f_z/∂z+...
Given f : R^3->R^3, ∇×f : R^n->R^n = <∂f_z/∂y-∂f_y/∂z, ∂f_x/∂z-∂f_z/∂x, ∂f_y/∂x-∂f_x/∂y>
where f_x is the x component of f etc.

Now, if you don't worry too much about what it "means" to have a vector of partial differentiation operators, you just need to remember that ∇=<∂/∂x, ∂/∂y, ∂/∂z, ...>, and then you can easily remember how the actual operators are defined. Just substitute the components of that vector and the components of f into the expressions for dot and cross product with juxtaposition indicating application rather than multiplication.

>> No.12094472
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when seeing a circle, we're just seeing a 2d section of a sphere; when seeing a sphere, we're just seeing a 3d section of an hypersphere and so on, right? so this means that we're always just always seeing a section of an n-dimensional object, right? is there a name for the pure "sphere" that isn't a section of anything and has ""infinite"" dimensions?

>> No.12094477

If I wanted to make my own 2d game engine to learn programming, how much math do I actually need? Surely not as much as it would take to make a 3d game, right? So I don't have to study all of calculus 3 and linear algebra as well as physics?

>> No.12094495

infinite dimensional spheres do exist but your logic is weird. a circle is a circle, it's independent of any higher dimensional objects. it's true that a cross section of a sphere is a circle, but that doesn't mean this is what circles *really are* in some fundamental way.

>> No.12094508

It depends. "2D" usually means axis-aligned rectangles and orthographic projection whereas "3D" means arbitrary triangles with rotations and a perspective projection. Which makes 2D much simpler.

Note that even 3D only requires the "basics of the basics" for linear algebra (no eigenvectors, decompositions, etc), and doesn't necessarily require any calculus (calculus is used mostly for determining surface normals for curved surfaces, and for physics).

>> No.12094620


The nabla symbol is an operator because it's a differential operator. You can think of it as a vector filled with differential operators. Therefore, all vector arithmatic still aplies so you can take the dot product and the cross product between it and a vector.

vector arithmatic:
vector times scalar
[math]\vec v \alpha = \begin{pmatrix}\alpha v_1\\ \alpha v_2 \\ \alpha v_3 \end{pmatrix}[/math]
vector dot product:
[math]\vec v \cdot \vec u = v_1 u_1 + v_2 u_2 + v_3 u_3[/math]
vector cross product:
[math]\vec v \times \vec u = \begin{pmatrix}v_2 u_3 - v_3 u_2 \\ v_3 u_1 - v_1 u_3 \\ v_1 u_2 - v_2 u_1 \end{pmatrix}[/math]

given some scalar function [math]f(x,y,z)[/math] and some vector function [math]\vec v(x,y,z)=\begin{pmatrix}v_x(x,y,z)\\ v_y(x,y,z)\\v_z(x,y,z)\\\end{pmatrix}[/math] and using the notation [math]\partial_x = \frac{\partial}{\partial x}[/math] while also using vector components x,y,z instead of 1,2,3 we get:

gradient (nabla times some scalar function of x,y,z)
[math] \nabla f(x, y, z) = \begin{pmatrix}\partial_x f(x,y,z)\\ \partial_y f(x,y,z) \\ \partial_z f(x,y,z) \end{pmatrix} [/math]
divergence (dot product of nabla with some vector function of x,y,z)
[math]\nabla \cdot \vec v(x,y,z) = \partial_x v_x(x,y,z) + \partial_y v_y(x,y,z) + \partial_z v_z(x,y,z)[/math]
curl (cross product of nabla with some vector function of x,y,z)
[math]\begin{pmatrix}\partial_y v_z - \partial_z v_y \\ \partial_z v_x - \partial_x v_z \\ \partial_x v_y - \partial_y v_x \end{pmatrix}[/math]

>> No.12094632

Note, since it is an operator, not ALL arithmetic operations apply (BAC-CAB rule won't work for instance), but for these basic operations it does work.

>> No.12094670

i want to calculate the increasing in a stock between the value i bought and the current value, will dividing the values do the trick?

>> No.12094680

Is there any actual validity to CBD for anxiety? Used to have quick bad anxiety related to my schizophrenia, was on antipsychotics and benzos for a while but now my anxiety seems much milder and more of an annoyance than a medical issue and I've heard CBD is good for mild anxiety and stress

>> No.12094683

Divide the difference between the current value and the old value by the old value, then multiply by 100.

>> No.12094773

thanks this will do i was curious if my way of calculating was on the right path

>> No.12095000
File: 223 KB, 840x525, 1560462932178.jpg [View same] [iqdb] [saucenao] [google] [report]

Let d20 denote a die with 20 faces numbered from 1 to 20. Assume that, when thrown, a d20 has the same probability of landing in any face.
If someone throws 2d20 and pick the highest value, what is the new probability disdistribution.
How do I approach this problem?

>> No.12095098

would cos(t) * -sin(t) not be -sin(2t)/2 ?
then when you integrate that you would get cos(2t)/4 right???

>> No.12095101
File: 3 KB, 285x74, uhhh.png [View same] [iqdb] [saucenao] [google] [report]

forgot pic

>> No.12095106

also I realize they used u-sub but shouldnt the use of trig identities give the same result?

>> No.12095136

How do I select the most important things in A textbook? Like brah, how the chapter is 30 pages long, each filled with Boldface and Illustrations that have like 15 parts But the Sumary is only 1.5 pages long, makes no sence.
I'm studying campbell Bio btw

>> No.12095143
File: 602 KB, 640x624, clownworld.png [View same] [iqdb] [saucenao] [google] [report]

I'm retarded

>> No.12095174

>would cos(t) * -sin(t) not be -sin(2t)/2 ?
They're the same thing.

>> No.12095180

>you would get cos(2t)/4 right???

They're the same thing bud. You can check using the trig identities

>> No.12095186

Calculate the probability for each possible outcome.

>> No.12095209

Why the fuck do I need to learn about titrations and shit when I'm just going to be developing stock exchange algorithms for the next 30 years?

>> No.12095309
File: 27 KB, 700x467, smiling British Pepe.png [View same] [iqdb] [saucenao] [google] [report]

You need to figure out how many rolls yield a given value [math]k[/math] and divide this by the total number of possible rolls ([math]400[/math] in this case, which I hope is obvious).

When trying to calculate the number of rolls which output a given value, start small. Clearly, [math](1,1)[/math] is the only roll which will yield [math]1[/math]. Then [math](1,2)[/math], [math](2,1)[/math] and [math](2,2)[/math] will output [math]2[/math]. If you imagine the problem visually (as a [math]20 × 20[/math] grid), a pattern is already forming. [math]k=1[/math] gave a [math]1 × 1[/math] square, then [math]k=2[/math] extended this to a [math]2 × 2[/math] square. As we increase [math]k[/math] we just keep adding L-shapes to extend this square. For any value of [math]k[/math], this L-shape consists of [math]2k - 1[/math] outcomes (I'll let you verify this yourself). This gives us a probability distribution defined by [eqn]P(Y = k) = \frac{2k - 1}{400}[/eqn]

>> No.12095381

Based statspepeposter.

>> No.12095395

energy is conserved in every reference frame
between two different reference frames, it is not. if you had an electron traveling at .999c, all light would appear like it was super blueshifted and there would be a huge apparent increase of energy in the universe (if what you're saying is the case). this would not be explained by the motion of the electron.

think of it this way too: if you have one laser, and you're running towards it, it is blueshifted so there is an apparent increase in energy. if you add a second laser and run towards it, they're both blueshifted the same amount, so there is DOUBLE the apparent increase of energy. so by your logic the mass would be transferring extra energy to the lasers, but the mass didn't move any faster/have any extra energy?
but you're not adding any extra energy into the system, you're just adding a second laser. you could repeat this process for 500 lasers and the apparent increase in energy in the moving frame would be even higher without there being any added energy.

now you can (hopefully) start to see that energy is frame-dependent. that's why I mentioned the invariant [math] E^2-(pc)^2 [/math], because this quantity IS conserved between frames.

>> No.12095405

Why would the far side of the moon be thicker? Wouldn't earth's gravity, which locks the orbit so the same face is always facing earth, pull the near side more?

>> No.12095423

I just spent some time reading this
basically we don't know for sure. but one promising theory seems to be that when the moon was formed from the earth, and they were both very hot and a lot closer together, the heat from the 2500C earth led to the denser moon material migrating to the opposite, cooler side. and then when it cooled it locked these materials into place.

>> No.12095448

The radius of the observable universe is 46.5 billion ly.

>> No.12095496
File: 4 KB, 118x53, syjbcujv.jpg [View same] [iqdb] [saucenao] [google] [report]

first time using einstein notation and the problem is just to convert from einstein to vector notation. im confident i got the other problems correct but pic related im not sure of.
i think it would be just dot product of the three vectors

>> No.12095504

look for repeated indices.
V and B share an index, so it's like a dot product, which produces a scalar. this number just multiplies any following terms.
A and the unit vectors share an index, so it's like A is a vector

[math] (V \cdot B) \overrightarrow{A} [/math]

>> No.12095675
File: 37 KB, 597x433, 1594099316870.png [View same] [iqdb] [saucenao] [google] [report]

Where the fuck did (7) come from?

>> No.12095703

square 5, 6, plug them into P(Y), P(Z), and then set P(Z)=P(Y)
what you're probably looking for is this relation:
[math] \mathfrac{R} [e^{i \phi}] = \text{cos} \phi [/math]

>> No.12095708

should read
[math] \mathfrak{R} [e^{i \phi}] = \text{cos} \phi [/math]

>> No.12095739

How do I get the fancy R? I only know how to do [math]\mathcal{R}[/math].

>> No.12095755

Ah okay that makes more sense. thanks for the help

>> No.12095772


>> No.12095778

but why is it [1 + cos phi]? If we're after the real part of A multiplied by its complex conjugate, isn't it just cos phi?

>> No.12095825

the 1 comes from the P(Y)+P(Z)=2P(Y)

>> No.12095862

>the 1 comes from the P(Y)+P(Z)=2P(Y)
Christ I'm retarded. Thanks for spelling it out for me.

>> No.12095900
File: 21 KB, 480x360, monk.jpg [View same] [iqdb] [saucenao] [google] [report]

What happens if i set an alarm every hour,for 24 hours(this would include sleep hours)daily for a year?
BONUS question:i do this while remaining upright and not lying down.

>> No.12095947

you would eventually reach a point where you sleep through it because you need sleep

>> No.12095982

thanks my man

>> No.12095995

i REJECT your reply

>> No.12096042
File: 53 KB, 1366x704, file.png [View same] [iqdb] [saucenao] [google] [report]

Regular right angle prisms are coated on one side, light comes and does a 90 left on pic related.

Is there a specific name for pic on the right? Where 2 sides are coated so the image is split in half. This is different from a beam splitter.

>> No.12096095
File: 17 KB, 527x198, closed integral.png [View same] [iqdb] [saucenao] [google] [report]

can someone explain how I'm supposed to start this problem

>> No.12096104

my sister is a retarded whiney faggot, I want to bash her skull in with a hammer

>> No.12096108

need to split the path up into 2, the line integral and the curve
figure out how to parameterize the curve, might be easier to go to polar coords

>> No.12096114

You know how to apply Green's theorem, right? You need to make a parametrization for the path. In this instance, you'll need to break it up into two paths.

>> No.12096143

If I disconnect the grounding rod from my house panel or from the meters on an apartment building, is the voltage now floating or would ground to line voltage remain the same? I believe the transformer is grounded at the center tap as well, but if that’s the case why do we even need ground rods? Why can’t the transformer provide the ground?

>> No.12096144
File: 3.69 MB, 3746x3472, IMG_20200907_185551.jpg [View same] [iqdb] [saucenao] [google] [report]

I have no idea what greens theorem is
here's what Ive done so far
I dont know how to advance from here and Im pretty sure what Ive done so far for C2 is wrong anyway

>> No.12096149

actually nevermind it is right, I just forgot how to evaluate the integral properly because it's been almost 2 years since my last math course

>> No.12096186

Your body WILL just eventually take the rest it needs in the form of micro sleep. You can’t just will yourself through it. What can be done is to minimize how long these last in some way. I remember an experiment with rats, for example, where they were forced to balance on a plate and would fall in water if they lost consciousness. Don’t remember what the point of the experiment was, possibly to test the limits of their university’s ethics committee. Either way, they all died in like 2 weeks. Only being woken every hour would allow more than enough sleep, but it is fatal if you force constant wakefulness.

>> No.12096189

did you forget to simplify sin^2+cos^2=1?

>> No.12096196

Can I prove that a group is Abelian if [math]a^{-1}b^{-1}=b^{-1}a^{-1}[/math]?

>> No.12096198

no I just turned that into 4 right away and multiplied the 4 with with the -2sin(t)dt, hence the -8sin(t)dt in the first term

>> No.12096291


>> No.12096347

when integrating a given linear acceleration function from 0->t, is the added constant term v initial?
a = 2t
v = 2t^2/2 + v0

>> No.12096351

It must verify [math]v(t=0) = v_0[/math] so yeah.

>> No.12096428

What is the functional difference between resistance and reactance?

>> No.12096463

Could someone help me with this math question?
Find the equation of the tangent plane at the point P_0(4,3,0) on the surface -5cos(pi*x)+(x^2)*y+4e^(xz)+5yz=47?
My answer is 24x+21y+16z=159 but the system doesn't accept my answer for some reason.
Using the tangent plane equation, the partial derivatives of each component is:
F_x = 5pi*sin(pi*x) + 2xy + 4ze^(xz)
F_y = x^2 + 5
F_z = 4xe^(xz)
After plugging in x,y, and z values they become:
F_x = 24
F_y = 21
F_z = 16
Then putting them into the equation, it becomes:
Which should become
24x + 21y + 16z - 96 - 63 = 0
Right? I don't know where I did an error.

>> No.12096464
File: 2.31 MB, 3300x4394, IMG_20200907_211353_1.jpg [View same] [iqdb] [saucenao] [google] [report]

I have to find the work done by the force acting counterclockwise once around a triangle with vertices (1,1), (3,1) and (3,2)
the force is F = (x + 2y)i + (6y - 2x)j
the answer is apparently -4 but I really don't see what I did wrong, pic related is my attempt

>> No.12096470
File: 67 KB, 778x553, file.png [View same] [iqdb] [saucenao] [google] [report]

How toxic exactly can a non-food grade substance be? It's potassium chloride, which is a pretty safe chemical as far as I know. I made a mistake and bought non-food grade KCl even though I intended on consuming a little bit of it.

>> No.12096480
File: 229 KB, 332x492, file.png [View same] [iqdb] [saucenao] [google] [report]

This is the stuff by the way. I realized I fucked up when there was no nutrient label, but everyone says it "should be" safe.

>> No.12096586

OK it took me a bit to figure out but I actually miscopied my question onto paper and missed an z which is why I kept on getting it wrong.

>> No.12097460

Help me with this problem.
Do this problem for me.

I don't understand resonant frequencies. I was reading some shit on resonant frequencies on a spring-mass system and some engineer says frequencies either below (I think, maybe higher) the resonant frequency can't cause vibration at resonant frequencies,with some engineering handwave sounding explanation. When I google, I see two examples, the swing example and the string instrument example.

In the swing example you push at the resonant frequency, or some unit fraction of the frequency (1Hz, 1/2Hz, 1/3Hz) and that corresponds to 1 push every swing, 1 push every 2 swings and so on. On the other hand, 2Hz will fuck the swing up because you'll be stopping it when it comes back.

In the string example, there are harmonics of the fundamental resonant frequency which are multiples, and the fundamental resonant frequency is supposed to be the lowest possible resonant frequency.

So what causes things to vibrate at resonant frequency besides the frequency itself? Multiples of the resonant frequency or unit fractions of the resonant frequency? Not actually homework, it's just been many years since I've done physics and I've always been bad with waves and my googling doesn't seem to be up to par.

>> No.12097480

Are there any alternatives to ozon layer? Can we deploy any other gases on high altitudes which can block UV radiation, if yes what gases have such properties.

>> No.12097513

>So what causes things to vibrate at resonant frequency besides the frequency itself?
Resonance only makes sense when you have a driven oscillation. If that driving frequency is equal to the resonance frequency the amplitude increases dramatically.
The resonance frequency depends on the geometry of the object.
Is that what you were asking?

>> No.12097551


>> No.12097560

The parametrization looks weird
r1(t) = (4t-1,2t-1) for t in [0,1]
r1(0) = (-1,-1) ?

>> No.12097563

I mean what other frequencies besides resonant frequencies cause oscillation associated with resonant frequencies. So driving frequencies not equal to "the" resonant frequency.
With a swing or a trampoline or something I know that a unit fraction of the frequency will cause oscillation if damping doesn't kill it before the next push.
I don't really understand what harmonics (multiples of unit frequency) have to do with unit frequency but I guess they do because they're mentioned in texts alongside resonant frequencies.

>> No.12097588
File: 172 KB, 1920x1280, Mplwp_resonance_zeta_envelope.svg.png [View same] [iqdb] [saucenao] [google] [report]

Are you confusing resonance of an oscillator with standing waves/resonance in cavities?
The former is the spring driven by a certain frequency. It's resonance curve looks like pic related.
The latter happens when you have waves trapped in a cavity and the waves reflected at the boundaries interfere constructively.

>> No.12097704


huh einstein notation involves upper indices for summations

>> No.12097774

So suppose you have to determine weather if a series of one of zeros are determined by a coin toss or picked by a human:
A sequence like 101010101010101010101010101010101010101010101010 would very obviously have been produced by a human, but how would you prove so mathematically?
What tools other than the mean can you use to determine that the patterns like these are not random?

>> No.12097800

One approach is to look at the Kolmogorov complexity of the series -- the size of the smallest program that would deterministically generate the series. That's a pain to compute in general, but easy in this case. The smaller the program required, the more likely it is that the series was generated deterministically.
Judging whether a sequence was produced by a true randomizer or by a human trying to emulate one without any tools is a separate question, and I think it involves questions of psychology.

>> No.12097807

I will add that, in the case of coin tosses, all sequences are equally likely under the hypothesis of iid Bernoulli randomness. The real question is which sequences are more likely under the hypothesis of human generation.

>> No.12097824

Do photons have mass? If they do how they reach such speed and don't destroy everything on their path?

>> No.12097836

Can you make a particle decay faster somehow?

I just read that the average time for neutron decay when it's alone is like 14 minutes. Is there something you can do to lone neutrons that could speed that up?

>> No.12097848

They travel at the speed of light because they have zero mass. This also means they don't experience time at all.

>> No.12097856

In this case you can just look at the autocorrelation function and see that it's +-1 at every lag when for a random sequence you expect them to approach zero.

Kolmogorov complexity holy yikes.

>> No.12097860

how does a timeless thing move?

>> No.12097865

But how can something have zero mass?

>> No.12098319

if you wanted to speed it up you'd need to put it in some sort of energetically-unfavorable position. it's much much easier to put them in a position where they decay slower than normal (or not at all, as seen when neutrons are bound to atoms).

here's a discussion where it was done (for atoms) and notice how difficult it is: https://www.nature.com/articles/news040913-24
my intuition is telling me that in order to speed up free-neutron decay, you would want to have them extremely close to something that really really wants to capture the emitted electrons. I have no idea how this would be done.

>> No.12098349

"photons experiencing no time" is more of a consequence of the equations of special relativity.
since they have zero mass, they cannot be at rest. to a photon, everything is moving around them at the speed of light, meaning that lengths would be length contracted to 0 and time would be time dilated to infinity (meaning they "experience" getting from point A to point B instantaneously).

>But how can something have zero mass?
photons are the mediators of the electromagnetic force. this means that in order for things to interact electromagnetically, there must be an exchange of photons between the two objects.
now, since we know the electromagnetic force has infinite range (the strength drops off as 1/r^2), the photon must be massless because: if it was massive, the strength of the force would go to 0 much quicker, and the EM force would be extremely short range.

>> No.12098351

How do I find the area under an entire function?
It's the integral from negative infinity to infinity right?
I don't remember how to do this from calc 1 and my calc 2 professor didn't explain it at all, yet it's on HW

>> No.12098353

Can you post the question?

>> No.12098358
File: 175 KB, 848x402, sld_orig.jpg [View same] [iqdb] [saucenao] [google] [report]

No I mean like pic related, frequencies other than the singular natural frequency that cause resonance.

>> No.12098360

in general, the area under an entire function would be the integral over its entire domain. but >>12098353 is right as well it might be different.

>> No.12098366

harmonics are geometry-dependent, so there
so no general answer without knowing your system. for a fundamental frequency f and integer n, in general they will be things like n*f, or (n/2)*f, or (n+1/2)*f, or 2n*f

>> No.12098382

Wait, so is it related to the natural frequency and resonance or is that just the person writing articles not knowing what they're talking about. I've seen similar stuff come up for articles about suspension too, but obviously I have a hard time understanding what they're saying if they're not even using terminology right.

>> No.12098388

Find the area between the x axis and the graph x^2+8x +7
I know how to get the antiderivative but I don't know what to do with it

>> No.12098406

You're not asked to find the area under the whole function, that would be impossible considering it is infinite. What the question implictly means is that you need to find the area that's completely enclosed by the curve and the x axis. So you need to find the zeros of the polynomial (so the points where it intersects the x axis), and find the area that's between that parabola and the x axis in that particular region. That's just a regular definite integral over a bounded interval.

>> No.12098413

Find the roots of [math]f(x)[/math] and then integrate the function over [math]r_1, r_2[/math].

>> No.12098416
File: 5 KB, 294x83, 2020-09-08-19:31:45.png [View same] [iqdb] [saucenao] [google] [report]

I get how you can the Variance of a Binomial distribution if you add the Variance of each part together, but why can you not just get it from the whole thing?
I.e. E(X^2)-E(X)^2=np-(np)^2 != npq

>> No.12098424

so I haven't been following along with what you posted but just read your initial question.
your two systems are different in that you're conflating two different things: driving frequency and oscillation frequency.
for the swing, your driving frequency is fractions of your fundamental frequency. this works because you're delivering a "step" impulse to the swing. if you were to instead drive it with a sinusoidal frequency, anything except the frequency of the swing would cause its motion to get fucked up. think about it as if you're pushing the swing along its motion, forward when it's going forward and backwards when it's going back. even if you do half the frequency here, you're pushing forward when the swing has started going back, so it gets fucked up.
basically, in the driving frequency case what matters is the type of drive you're providing. for a step-impulse, you can do fractional multiples of the resonant. for a sinusoidal impulse, it has to match the resonance frequency.

for the string, your frequencies are the allowed modes of oscillation of the system. your fundamental is the lowest mode, corresponding to one-half wavelength across the whole string (think of holding a slinky fixed in both hands and plucking the middle. unless you pluck it really fast and far it'll just have one big peak of oscillation). you also have a 1 wavelength mode, which corresponds to two oscillation peaks. clearly in this system there's no way to have a lower frequency than the fundamental frequency, because that would correspond to "less than one oscillation peak."

>> No.12098427

you can? unless I'm misunderstanding your question
>add the variance of each part together
each part of what?

>> No.12098449

I guess what I really want to know about is a basic beam or spring (like a spring-mass system) subjected to arbitrary or random vibrations. Like what causes resonance in an dampened spring suspension under certain road conditions, or what causes a machine to vibrate more at certain frequencies, and the relation to the natural frequency if any. I'm not even sure what to try reading so explanations of harmonic(?) phenomenon don't completely go over my head.

>> No.12098459

thanks lads, I am dumb

>> No.12098460
File: 52 KB, 767x316, knyYEiXqvYMK_2020-09-08-20%3A20%3A27.png [View same] [iqdb] [saucenao] [google] [report]

>you can?
But wouldn't it result in np(1-np) as posted above? There's got to be an error in my thinking there, but I cannot find it

>each part of what?
Like in the picture, splitting the X in each of its n attempts and then adding their variance together

>> No.12098490

you should be able to calculate the variance of a binomial distribution from the binomial pdf. I've done it before in a stats class, so my best guess is you're calculating the expectation value of x^2 incorrectly

>> No.12098505

>error in my thinking
Or wait, I think I got it?:
Only for the singular X case the function would be E=1*p. The one with all of them combined must use a different one, which makes E(X^2) have a different value
I think that's it, thanks! No clue how to get it though, will have to think this one through more

>> No.12098521

okay, you seem to first be asking about step-driven systems, like the swing. in that case, your systems are exactly analogous, where the cars can be treated as swing pushes.
for machine vibrations, I don't know as much, but here's my guess: your machine has a "fundamental frequency" at which it can vibrate. so it is more like the string, and certain frequencies of operation correspond with higher harmonics of vibration in the machine.

it's hard because the cause of the things you're asking depends on the system and is different even in the two examples you gave. for an analogy for the machine example, I would look up "pipe harmonics" but instead of reading into it as air waves in a pipe, think about them as vibration waves inside the machine.
for the step-driven case, I think the swing example is sufficient. different systems will have different periods of oscillation (much like the oscillation of a swing depending on its length), but the mechanism is the same - if you hit the oscillator at the same point in its motion with an instantaneous kick, you will add to its oscillation.

>> No.12098533

do you know the binomial probability distribution function B(n,p)?
the expectation value of x^2 is: [math] \sum_{n=0}^\infty \sum_{x=0}^n x^2 B(n,p,x) [/math]
my assumption is, for your level, it's probably easier to calculate the variance of a singular X and just add them (hint: it's probably p(1-p) for one X)

>> No.12098592

Warning I'm talking a bit out of my ass here, but this is what I imagine is going on. I didn't do the calculations and may have misunderstood some things myself.
>I guess what I really want to know about is a basic beam or spring (like a spring-mass system) subjected to arbitrary or random vibrations
Use fourier series expansion for the driving force. If you really want to have a quantitative answer.
> Like what causes resonance in an dampened spring suspension under certain road conditions, or what causes a machine to vibrate more at certain frequencies
The geometry of your car/machine determines the frequency. The wave travels through it and is reflected on the other side. The reflected wave then interferes with the incoming wave. If the frequency is just right, it will interfere constructively.
If you have a random incoming wave composed of different frequencies you can imagine a wave for every frequency that gets reflected and interferes with itself. Afterwards you add the different waves together.
For example if you have a wave with two frequencies, the resonance frequency and 1.2 times resonance frequency. The first wave interferes constructively, the other doesn't (The reflected wave has a different phase depending on the material, so it's a bit complicated).
>and the relation to the natural frequency if any
Waves with the natural frequency are the ones that interfere constructively. So do waves with multiples of the frequency.

>> No.12098644

I finally got it, thank you very much!
It's [math] \sum_{k=1}^{n} k{\binom {n}{k}}p^{k}(1-p)^{n-k} [/math] for E(X) and [math] \sum_{k=1}^{n} k^2{\binom {n}{k}}p^{k}(1-p)^{n-k} [/math] for E(X^2)
Though painful to calculate it out if p isn't 0.5, so I guess best to stick with doing them one by one

>> No.12098676

How can a narcissistic person sleep? seriosly how can he allow the awesomeness of his coniuosness no go away? I suffer from that condition and I can't sleep, what to do if u were me?

>> No.12098682


>> No.12098869


>> No.12098992

Quick question about notation correctness.

Suppose you have a function [math]f[/math] defined over whatever metric space [math]X[/math] of your choosing.

Suppose also you have a transform [math]T[/math] that takes your function [math]f[/math] and produces a function [math]F = T\{ f \}[/math] that's defined over another metric space [math]Y[/math] (correct me if I'm wrong , this is how I understand transforms to work)

Then, what's the correct notation to use for how the function [math]F[/math] is defined? Is it:
[eqn]F(y) = T \{ f(x) \} (y)[/eqn]
Where [math]x \in X[/math] and [math]y \in Y[/math] ? Or:
[eqn]F(y) = T \{ f \} (y)[/eqn] ?
I ask because I feel like [math]T \{ f \}[/math] should produce the set [math]F[/math] not the element [math]F(y)[/math], but I usually see it written like [math]F(y) = T \{ f \}[/math] and that just seems incongruent.

>> No.12099399

I was using (t-1) rather than (1-t) for my parametrization. I cant believe I was just using the wrong equation this whole time lol.
Thank you.

>> No.12099543
File: 248 KB, 1424x555, 1575056236999.png [View same] [iqdb] [saucenao] [google] [report]

Where does the 1 in 1+e denominator come from?

>> No.12099553

[math] V_{ \text{voids} } = e V_{ \text{grains} } \rightarrow V_{ \text{total} }=V_{ \text{grains} }(1+e) \rightarrow V_{ \text{grains} }= \frac{V_{ \text{total}}}{1+e} [/math]

>> No.12099558

Thank you I'm a dummy

>> No.12099856

I understand why diodes don't work with AC current, but wouldn't they work when the current is in its positive phase? Or, I guess an easier way to put it would be when the current is in the direction of the forward-biased diode?

>> No.12099859
File: 39 KB, 1135x363, circuit.png [View same] [iqdb] [saucenao] [google] [report]

Is what I wrote on the screen correct? As in I_3 is equal to 0.4*I_1? My professor completely skipped this so everything is up to me to read off the textbook which is pretty confusing admittedly.

>> No.12099861

during half of a cycle, the diode would conduct and during the other half it would insulate, depending on the direction of current

>> No.12099899 [DELETED] 

[math]I_1 + I_3 = I_2[/math]

>> No.12099906

[math]I_1 + I_3 = I_2[/math] so yes you are correct.

>> No.12099911

I am writing some code to run a couple simulations. I was doing version control manually (writing what was added/removed of my program on a log) and keeping a copy of every single version of my program.

Then I learned that I can use git/github to do the version control for me. Can I just put my project on github and not worry about backups? Is there any advise to someone starting to do computational physics?

>> No.12099913

>tfw housefly won't fuck off and I have no Raid
How do I get rid of them?

>> No.12099917

pour some beer into a bunch of cups, cover the cup with plastic/metal with holes punched in it for them to fit through

>> No.12099943

OOOoooh I didn't know that, so if two of these currents are both going in the same direction into another current (I2), they 'merge'?

>> No.12099983

I feel like I'm going crazy here. wasn't the origin of the "Powerhouse of the Cell" meme a joke from a biology test that blatantly gives away the answer to it's question with very specific wording?
I can't find a trace of it anywhere, and everyone just seems to think the meme sprung up out of nowhere.

>> No.12099985

yes, you should look up the kirchoff rules

>> No.12099994
File: 22 KB, 584x306, Annotation 2020-09-08 215341.png [View same] [iqdb] [saucenao] [google] [report]

The homework is asking me for the power absorbed at the current source (the left side one) but how do I figure that out? There's no voltage description on it. Prior to this question, we had to calculate for I which was -7A.

>> No.12099997

I will, thank you. This professor didn't go over anything and just told us to read the textbook, and the textbook didn't go over this either (at least right now) which is very frustrating.

>> No.12100028

>wasn't the origin of the "Powerhouse of the Cell" meme a joke from a biology test that blatantly gives away the answer to it's question with very specific wording?

>> No.12100154

MATLAB brainlet here.
How do I compute the product of two elements from a column vector?

>> No.12100162

I dont know matlab but wouldnt it ve something like a(n1)*b(n2) where n1 and n2 are the positions of the desired elements in the vector?

>> No.12100172

your question is too vague

>> No.12100176

I have a column vector, [math]v_2[/math], with 100 elements and I want to assign a new variable to the product of the 45th and 87th elements from [math]v_2[/math]. So, basically I want [math]x=v_{45,1} * v_{87,1}[/math].

>> No.12100177

does x=v2(45)*v2(87) not work?

>> No.12100179

Wow, I didn't think it was that simple. I feel like an idiot now. Thanks.

>> No.12100184
File: 57 KB, 800x450, sci.jpg [View same] [iqdb] [saucenao] [google] [report]

How is this not /sci/'s sticky yet?

>> No.12100186

Someone pls

>> No.12100189
File: 231 KB, 432x598, 1590370744494.png [View same] [iqdb] [saucenao] [google] [report]

The potential over the current source is 15 V, just like with the stuff in parallel
if A is a column or row vector, A(i) is the ith component. A(i)*B(j) for example. To multiply equal sized vectors componentwise, it's A.*B
We probably can, but it sounds a lot easier to just to keep O3 as it is.
Resistance is the real part of impedance and reactance is the imaginary portion. Practically, resistance is something that disperses energy as heat and reactance measures energy lost to changing EM fields. Electric fields changing in a circuit contribute to negative reactance and changing magnetic contribute to positive.

>> No.12100347

How does ambient temperature affect rate of cooling on a constant heat source?
Obviously colder wind will cool the heat source better, but why, and what are the equations for it?

>> No.12100395

ODE heat equation

>> No.12100414

>a little bit of it
can mean literally anything. A tsp? tablespoon? a cup? one time, or every day for breakfast?
>How toxic
supertoxins are rare, but whatever they're using may cause things like indigestion, nausea, or be potentially carcinogenic

>> No.12100470
File: 2.17 MB, 1600x2560, Screenshot_20200908-222522_Canvas Student.jpg [View same] [iqdb] [saucenao] [google] [report]

What was wrong with my approach?

>> No.12100483

literally we have no idea what the question is

>> No.12100487

Find final velocity and angle below positive x of a ball launched at 100m/sec at 30 degrees. final position is 10m below starting

>> No.12100501
File: 20 KB, 400x450, 1406050312003.png [View same] [iqdb] [saucenao] [google] [report]

I'm taking a course on EM based on jackson and never took a class/read about about differential equations (lmao, don't ask, I learned what I had to as I went along). I'm good at pure math at a graduate level. Tell me a good resource to learn all the different cookie cutter techniques for solving differential equations. No 800 page shitty monstrosities with thousands of pointless problems for brainlets. I don't have time for any of that nonsense, desu.

>> No.12100511

It's Dover, so it's exceedingly cheap too.

>> No.12100512

>never took a class/read about about differential equations (lmao, don't ask, I learned what I had to as I went along)
by this I mean the standard undergrad cookie cutter class, I have some familiarity with the material from a need-to-know basis in some physics courses

>I don't have time for any of that nonsense, desu.
I also don't want to learn the richer theory, even though I've taken a grad class in topology.

>> No.12100524

does sfw furry count as furry in the report box, or does that get absorbing into mlp

>> No.12100525

I have a copy sitting on my shelf. That book is a monstrosity. I need to get up to speed on the material extremely quickly.

>> No.12100533

first of all it's incredibly hard to follow your work. you should organize your steps better
I'll look at it

>> No.12100535

It is, but as far as applied/computational ODEs are concerned, it's definitely the best.

>> No.12100551

What about Coddington intro to ODE?

>> No.12100555

I solved a quadratic for t at y= -10
dy = v0t + at^2
-10 = v0sint + 1/2 gt

And then used vf = v0 + at for the final y
And then solved the Pythag for the resultant

>> No.12100597

Coddington is theory based. It's an excellent text (and what I would recommend if someone wants to get into the underlying analysis of ODEs), but not comparable to Tenenbaum/Pollard

>> No.12100607

isnt this year 11 physics?

>> No.12100631

It would seem so.

>> No.12100632

Thats not the point
the point is I got it right and was given 3/10

>> No.12100653 [DELETED] 


Why do you use a quadratic to find the final time? Just solve [math]50 - 9.8t = -10[/math]

>> No.12100681

okay I'm back (nobody else since my last reply was me)
think about it for a second: how could you have the same incident angle and the same vertical velocity when you're 10m below the horizon? your vertical velocity can't be the same as when you started since it should equal your starting velocity at y=0
assuming you calculated the time correctly (which seems correct) your final vertical velocity would be -51.92, not -50

not sure about "wrong approach" maybe it's possible they just couldn't fucking follow your work

>> No.12100777


>> No.12100863

If im not wrong
final v = 69.31m/s
final theta = -30.94

>> No.12100970

Why can all complex numbers be written as [math]e^i\theta[/math]?

If you have a complex number like [math]5 + 14i[/math] how would you translate?

>> No.12100987

>What was wrong with my approach?
You calculate t then don't use it. By "final angle", are you referring to the position relative to the start point or the direction of the final velocity?

When the ball is 10m below the starting height, the position is [900.69,-10] (distance = 900.75 m, angle = -0.64°) and the velocity is [86.60,-51.92] (magnitude = 100.975 m/s, angle = -30.95°).

Clearly the final velocity isn't just the starting velocity reflected in the x axis, as that occurs when the height is zero.

>> No.12101003

>velocity is [86.60,-51.92] (magnitude = 100.975 m/s
i think you got this wrong

>> No.12101006

>Why can all complex numbers be written as e^iθ?
They can't; only complex numbers with unit magnitude can be written that way. But all complex numbers can be written as r*e^iθ where r is a non-negative real. That's just polar coordinates.
r*e^iθ = r*cosθ+i*r*sinθ = a+bi where a=r*cosθ, b=r*sinθ
=> a^2+b^2=r^2 => r=√(a^2+b^2)
=> b/a = tanθ => θ=atan2(b,a) (atan2(b,a)=atan(b/a), except it gets the quadrant correct for a<0).

>> No.12101011

He used it to calculate v_y
And sqrt(50^2+86^2) is approx. 100

>> No.12101012

Why? y=0 occurs at t=10.2, y=-10 at t=10.4, so the state at y=-10 is going to be very close to the initial state (v=[86.6,50], |v|=100) except with the vertical component of the velocity negated. Note that I'm using g=9.8 m/s^2 which is what's in the original photo.

>> No.12101018

> He used it to calculate v_y
Where? Are we looking at the same photo? I see t=10.4 calculated then that value used nowhere.

The thing is, the difference between y=0 => t=10.2 and y=-10 => t=10.4 is small enough that one decimal place isn't really going to cut it. The calculations on the paper look very much like the symmetrical case (y=0) is being assumed.

>> No.12101023

isnt the final velocity given by sqrt 86.6^2 + -51.92^2?

>> No.12101029

Well, I just assumed he used it in
But I may be too lenient when it comes to rounding errors.
I mean who gives a shit about accuracy in homework.
gotta square the -

>> No.12101043

lmao i hate my calculator, but yeah i should have checked my own answer
-2^2 = -4 apparently

>> No.12101408

this is a good idea for a general.
>prove me wrong

>> No.12101415

I still don't understand how fourth dimension works, how would things look like on four dimensions? And speaking of fourth dimension, how is Kleine Bottle supposed to works/looks in 4D since they said the 3D representation isn't exactly right because of the intersection.

>> No.12101424

In dire need of help here...

Let M =
\cos \theta & \sin \theta \\
\sin \theta & - \cos \theta

|L\rangle =
\cos x \\
\sin x

M |L\rangle =
\cos \theta \cos x + \sin \theta \sin x \\
\sin \theta \cos x - \cos \theta \sin x

If [math]|L\rangle[/math] is an Eigenvector of M, then

[math]\cos \theta \cos x + \sin \theta \sin x = L \cos x[/math]

[math]\sin \theta \cos x - \cos \theta \sin x = L \sin x[/math]

Solve for x in terms of [math]\theta[/math].

Any hints?

>> No.12101438

it looks like the tessaract. looking at 3d is a two dimensional shape which changes profile as you rotate it. 4d is then a change in 3d shape as you "rotate" it. imagine it as being able to jump over a hurdle in 3d where as in 2d that would not be possible. the 4th dimension is another direction to move over that hurdle.

>> No.12101451

>imagine it as being able to jump over a hurdle in 3d where as in 2d that would not be possible
Why is it impossible in 2d? I think i misunderstood something here because i imagined it like some 2d game where you move forward and jump over the hurdle

>> No.12101459

even if the game is in 2d the fact the guy can jump the hurdle implies there is a 3rd dimension.

4 dimensions would be like a guy being able to escape from a seeming 3d solid container by "rotating" it until there was an opening for him to escape.

>> No.12101554

\sin \theta \sin x = (L -\cos \theta) \cos x\\
\sin \theta \cos x = (L +\cos \theta) \sin x\\

>> No.12101558

if you divide i) by cos(x) and ii) by sin(x) you get L = L and then you rearrange it to get all the x on one side and all the theta on the other, which gives you cot(x) - tan(x) = 2 tan(theta).
plugging that into wolfram gave me x = arc-cot(tan(theta) - sqrt(tan^2(theta) + 1)). thats the best i can do but it makes sense to me. simple solution by equation.

>> No.12101593

whats the best branch of stem/applied math for getting rich quick?

>> No.12101703

Bro you're a genius.

Thanks but there's a simpler method. The answer is [math]x = \frac{\theta}{2}[/math]

>> No.12101706

your T looks like a functor or natural transformation in category theory. you really should look up this.

f: X->X

you can write T_f if you want to, but T(f)(y) is fine

>> No.12101726

ok thats interesting. i wonder if i went wrong somewhere but i did check the answer on wolfram again and it was right. care to go step by step? im guessing its something relating to half angle identities?

>> No.12101857

seriously can you show me how you got that? i got way too invested in your question.

>> No.12101859

Subtract both equations in >>12101554
to get rid of the L, then
\sin\theta\sin^2 x -sin\theta\cos^2x = (L-\cos\theta)\cos x \sin x- (L+\cos\theta)\cos x \sin x\\
-\cos(2x)\sin \theta = -\cos\theta \cos x \sin x - \cos\theta\cos x\sin x = -2 \cos\theta\cos x\sin x \\
\tan \theta = 2\cos x\sin x/cos(2x)=\sin(2x)/\cos(2x)= \tan(2x)\\
Seems a bit ugly, there's probably a better way

>> No.12101896

yeah thats great work. nice one anon. i need to work on re learing my identities. too long out the field.

>> No.12101897

but you forgot to mention to multiply i) by sin(x) and ii) by cos(x) in order to properly be able to eliminate L. once i did that the double angle formulas came out and nice. again, good work.

>> No.12101899

That's what the wiki article is for anon
Nobody really remembers that shit

>> No.12101928

yeah true. the fact i didnt open it up immediately shows how rusty i am.

>> No.12101982

I'm wondering how you would go about this question.

A function [math]f(x)[/math] defined for [math]x > a[/math] where [math]a[/math] is a constant, and a quartic function [math]g(x)[/math] whose leading coefficient is [math]-1[/math] satisfies the following three properties:

1. [math]\forall x \in \mathbb{R}[/math] such that [math]x > a, \ (a-x)f(x) = g(x)[/math]

2. For [math]\alpha, \beta \in \mathbb{R}[/math] with [math]\alpha \neq \beta, f(x)[/math] obtains the same local maximum value [math]M[/math] at [math]x = \alpha[/math] and [math]x = \beta. (M > 0)[/math]

3. [math]f(x)[/math] has more local extrema than [math]g(x)[/math] does.

[math]\beta - \alpha = 6 \sqrt{3}[/math]. Find the minimum of [math]M[/math].

>> No.12101993

Who the fuck invents these kind of questions?

>> No.12102002

are we assuming alpha and beta are more than a?

>> No.12102008
File: 22 KB, 789x136, Untitled.png [View same] [iqdb] [saucenao] [google] [report]

Can /sci/ identify the font used in these equations? It's not your run-of-the-mill Latin Modern. It looks so smooth :3

>> No.12102023

It's from the Korean CSAT.

It doesn't specify one way or the other.

>> No.12102030
File: 91 KB, 629x367, TRN0707.png [View same] [iqdb] [saucenao] [google] [report]

*kisses u*

>> No.12102036

Not math or science related.

>> No.12102141

are you cute?

>> No.12102229

the issue was I multiplied the t value, 10.4, by g, 10, but i performed 10x10 = 100 instead of 10.4x10 = 104
I suppose he docked me hard for lacking insight as to the impossibility of it vf=v0 but I was under time pressure
And So he gouges a gives me an F For an arithmetic error on the 2nd to last step
I’m pretty fuckin pissed, this guy needs to retire

>> No.12102244

For fucked up notation, missing units and making me work to understand what you did I'd have given you 5/10 as well.

>> No.12102261

Well he gave me a 3, and what your autistic ass wants me to carry units through the algebra? Are you retarded?

>> No.12102280

God I wish I had a cute boy to pin down and dominate so god damn much.


At what percentage do alcoholic beverages dehydrate you more than they hydrate?
Asking so I can optimize my sauna bathing.

>> No.12102293

t. undergrad

>> No.12102307

>Are you retarded?
I'm not the one who failed his homework
And yes, carry the fucking units through the algebra.
You will notice faster when you fuck something up and you won't waste your and your tutor's time with useless calculations because you don't want to write the units again.
Keeps everything short, clean and you just insert the numbers when necessary.

>> No.12102356
File: 40 KB, 647x659, 87f.jpg [View same] [iqdb] [saucenao] [google] [report]

>Are you retarded?

>> No.12102362

Is there a material that dirt and bacteria cannot cling to? I have an idea for a fork for outdoor use that never needs to be cleaned and is always sanitary to eat with.

>> No.12102366

Yes ofc
7 questions 1 hour no time to check or rewrite anything
No real instruction
Just me and my arithmetic errors getting Fs and being laughed at for making gougable errors by a sadistic professor and his army of autismal midwits

>> No.12102367

I'm the one who initially showed where you were wrong
>carrying the units
not important for this, unless your prof is autistic and wants it done
>organizing better
absolutely. your work looks like a stream-of-consciousness. at least try to make lines flow from one to another instead of having me guess where you're going with everything.
even if you box things and draw arrows from place to place that would be more helpful. or just write "get final y velocity" above your calculation for the final y velocity so I know what you're thinking of doing.

you can get easy partial credit by doing stuff like this, even when you get the answer wrong. because you're showing that you know what steps to be doing, which is really all they care about anyways.

>> No.12102404

>We can see about 14.5 billion light years in all directions

>> No.12102432

it is. Its only there for me to keep track of things. If I had more time I could rewrite but I don't. Ive failed both quizzes now due to the time factor alone, and i work quickly. These weekly quizzes are 43% of the grade and they're organized st u need to have mastered the material to get an A. Theyre some of the hardest questions you could ask on the material, and he has fucking gotchas and tries to trick you, which wow is really easy to do under time pressure. I'm likely to drop and take this from someone who is a bit younger, a bit more professional, and doesn't care about anything but students doing the work and getting it, not being precisely like the professor himself. I'm curious what justifications people can cook up for this teaching style, because it's only idiots who would do similarly if in a tenured position
He fooled me and made me think this weeks quiz was on free body diagrams and friction not 2d motion. This situation is severely depressing, nobody can justify that 3 as reflective of performance, but that 3 isn't illegal, and nobody exists to hold him accountable anyway
I mean look at the feedback I got, "this is wrong". Say what u will about my writing, but he didn't say anything about my work. He just said its wrong. Wtf kind of person am I dealing with here? Someone whose career summitted at teaching highschool burnouts high-school algebra in a weedout course and he's gonna be a demon. Its 2020 i can take this remotely from anyone else in the state
I don't expect anyome to read this I m just venting its a very frustrating position to be in

>> No.12102443

I agree that the prof is a twat, courses organized like this generally aren't worth the headache.

>> No.12102455

If you have an unknown substance how do you find out what it is?

>> No.12102459

taste it

>> No.12102467

tastes like nothing

>> No.12102469

have you considered it might be nothing then?

>> No.12102497

it is gray stuff though

>> No.12102512

Is it flammable?

>> No.12102524

not with a lighter

>> No.12102530

how do you do it in generel?
like in a lab

>> No.12102541

With a flame

>> No.12102552

there are like a hundred elements and putting a flame to it tells you what it is?

>> No.12102582

if you're not trolling, there's no general process to determine what something is. you have to use a baseline level of inference, but you start with stuff like weighing it, getting the density, doing spectroscopy. stuff that doesn't destroy the sample or cause a potentially dangerous reaction.

>> No.12102597

So I need to do a shitton of tests and narrow this down?
This sucks.

>> No.12102600

what are you expecting? unknown compound #598234 can be entirely determined from just looking at it? come on dude

>> No.12102602

If it doesn't explode and it's not poisonous it's probably boring anyway

>> No.12102613

I just hoped there was a run of the mill method to get some results in medium amount of time.


>> No.12102621

I forgot question I wanted to ask. Can someone travel back in time and remind me what question I wanted to ask? It was really important or I wouldn't have thought about it!

>> No.12102625

You wanted to know if there was any scientific knowledge about memory improvement.

>> No.12102666

How do i tell how much sugar is in a liquid by volume?

>> No.12102679

You take the sugar per volume and multiply it by volume

>> No.12102690

idk how much sugar is in it period
what im asking is if there is some kind of test i can do to see what % of a liquid is sugar

>> No.12102693

dry out a part of the liquid and weigh the sugar

>> No.12102695

there wont be non sugar solids left over?

>> No.12102703

dude if you have a generic mixture there's no fucking way to tell what's in it specifically without running a bunch of tests

>> No.12102705

Depends on the liquid obviously

>> No.12102720

Does ammonium destroy DNA samples?

>> No.12102728
File: 46 KB, 1480x720, nosbdvjjab.jpg [View same] [iqdb] [saucenao] [google] [report]

given a refracting surface I have to show that to produce a perfect image that the surface must satisfy the general equation of a bivariate quadratic. I can understand the reasoning behind it as the light rays further from the middle must be compensated for their vertical dimension to have the same optical path length of the middle rays, but Im not exactly sure how I would take this and get to an equation exactly.

would i just set the optical path lengths equal to each other and it will get to that equation?

>> No.12102747
File: 29 KB, 624x602, file.png [View same] [iqdb] [saucenao] [google] [report]

Is this notation for the slope acceptable?

Another question, clearly the slope is negative, but should I put the negative sign on either A or B or is it understood?

>> No.12102766

Even as a layman I think the stuff coming out of this place is super super amazing

>> No.12102768

I'd call it [math]\Delta x,\Delta y[/math] or dx,dy or something, but it should be alright
You can write A/B<0 if you want, but unless the picture is meant for children your audience should understand it.

>> No.12103247

how to stop being so horny all the time?

>> No.12103256

cut off porn stop masturbating
stick to this for 2 months

>> No.12103274

Anyone familiar with writing exercises in an interview?
I have an interview for an engineering assistant position and they said there will be a writing exercise after the interview. What should I expect?

>> No.12103292

Ive actually had several spells where I stopped masturbating and watching porn for 5-7 months and if was awful for my productivity.
it actually only made things worse because I got very pent up and had crazy boners while trying to work.
at least when Im jacking off with consistency I can save my horniness for when Im done with my tasks

>> No.12103300

idk go on antidepressants, those killed my urge to coom for a year

>> No.12103314

eh, I'd rather not take any mind-altering drugs. I'll stick with being horny. I was only concerned because I'd spend 40 minutes a day jacking off when I could be doing more productive things but Id take that over the takepills-pill

>> No.12103321

That’s not good. You’re a fucking human, you’re supposed to be horny

>> No.12103337

yeah well I'd take not being horny over my ability to be able to actually get up and go do things any day

>> No.12103352

That’s a you problem. Poor self control and addicted to porn. Don’t blame human nature to your own problems.

>> No.12103355

I'm not the person who initially asked. I said this in the context of taking antidepressants being preferable to depression if all I have to give up is jerking off each day

>> No.12103370

>If you start with two sinusoidal waves of the same amplitude traveling in phase on a string and then somehow phaseshift one of them by 5.4 wavelengths, what type of interference will occur on the string?
The answer was "Intermediate (closer to fully destructive)," Could someone explain to me what does "intermediate" mean? And how come it was fully destructive? I thought if they were both travelling in phase with each other, they would add up and become constructive wouldn't it?

>> No.12103392

translating one wavelength (or any multiple of) will yield constructive interference, since they overlap
translating one half-wavelength (or any n+1/2) will yield destructive interference.
5.4 is close to 5.5 which would be fully destructive, meaning the waves perfectly cancel out at every point.
>I thought if they were both travelling in phase with each other, they would add up and become constructive wouldn't it?
this is true, but then you shift the peak of one by 5.4 wavelengths, so they're no longer in phase.

>> No.12103408

Aaaaaaah, that makes so much more sense. Thank you so much anon, I'll write this down on paper and then review it again tomorrow!

>> No.12103459

new bread: >>12103457

>> No.12104291

You're OK, especially if you already smoke, then it won't matter cancerwise either

>> No.12104628
File: 77 KB, 1534x433, screenshot.2020-09-10 (1).png [View same] [iqdb] [saucenao] [google] [report]

Am I a brainlet here? Surely 20% more reach than 42% is 62% right?

If the question was 20% bigger/larger then I do 42%*20%, but the question says 20% more.

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