/sqt/ - Stupid Questions Thread

should be a negative 90 and a positive 45

In classical mechanics, [math] \dot{x} = \frac{\partial{\mathscr{H}}}{\partial{p}} [/math] and [math] \dot{p} = -\frac{\partial{\mathscr{H}}}{\partial{x}} [/math]. Whereas in quantum mechanics, [math] \displaystyle \dot{\psi} = \frac{H }{ i }\psi [/math], with \hbar as 1.
Purely formally, define [math] H(x, p) \doteq (H_x, H_p) [/math], where the subscripts denote partial derivatives and the ordered pairs are identified with complex numbers. Then the Hamiltonian equations are [math] \dot{(x, p)} = \frac{H}{i}(x, p) [/math], which is essentially the same as the Schrodinger equation. This isn't a coincidence right? I don't have a proper education in physics so please no bully.

I have to show something similar to:
|a+b|-|a|=sign(a)|b|
How do I write it properly?

what do you mean, something similar to

thanks family

What do subspaces have to do with this at all?

When do i use laplace transforms?

DE's

What you posted is not true. Just take a = -2 and b = 5 for example.

well no shit

say i get a list of DEs
just by looking at them, how would i pick out the ones to use laplace transform on?

What exactly is your question?
Of course it's not a coincidence, both derive the time evolution from the total energy of the system

list of common LTs and their inverses

How much programming knowledge is required for computer integrated manufacturing? My school offers a class in it for my Mech program.

when you have the boundary conditions for them and you run out of other ideas on how to solve them.

Aw true that...
But pic related is my problem, isn't is false too then?
The gâteaux operator for a norm is defined as: ||.||' (u,v) = lim (||u+hv||-||u||)/h as h tends to zero

How do you write properly irregular movement's values in english? Let's say a body traveled 50m in 5s and then it traveled 30m more in 15s. Now we need to find V(avg)

So we have t1, t2. How do you properly write final t? Just t or t(avg) = t1+t2?

Find the volume of the solid that is generated when the region is revolved as described.
The region bounded by [math]f(x)=\sin{x}[/math] and the x-axis on [math][0,\pi][/math] is revolved about the y-axis.

I used the shell method so that
[math]2\pi \int_{0}^{\pi}\sin{x}\,dx[/math]
[math]=-2\pi(\cos{\pi}-\cos{0})[/math]
[math]=4\pi[/math]
But I'm told the answer was [math]2\pi^2[/math], what did I do wrong?

>what did I do wrong?
that's not the shell method, needs to be x*f(x)dx

Thanks, can't believe I didn't catch that

So if we take an abstract body moving with constant speed and over all possible observable time speed does not change i.e. there are no other bodies affecting it - the said body technically in the state of inertia? Like, for example, a sattelite? Or does gravitation of the earth affects its inertia state?

Is a professor allowed to cancel a lecture in order to attend a conference?

What is the soul? What makes me I?

If I have a number, and at least half of it was erased
How do I find the whole number (lowest possible), knowing that it was the result of 2 to the N-th power, knowing that n is a positive integer?

For example, if the given number is 1, i want 128

if you were a professor, would you?

>How do I find the whole number (lowest possible), knowing that it was the result of 2 to the N-th power, knowing that n is a positive integer?
You can't.

Typically you arrange for someone to cover for you in that situation.

Hey can someone help me with understanding blood pressure. I was confused until I recently just had a moment and I think I understand blood pressure.

So blood pressure is the pressure of circulating blood on the walls of blood vessels. If we imagine a tube that is 1m and we pinch (vasoconstriction) at 50cm in, then upstream of the constriction (before the constriction) will have an increase in blood pressure since there is more blood there (decreased blood flow as we are constricting). But after the constriction point, downstream, we will have a decrease in blood pressure since there's less blood there (so less blood is hitting the walls of the blood vessels).

The body can change BP by vasoconstrictors and vasodilators (hormones) and nerve innervation.

I also have a q: is BP mainly important because if we have a high BP, then it could potentially burst vessels open since blood builds up and we also strain the heart since more contraction is needed to push the blood through a narrower space. Low BP means that its harder for the blood to go to the organs since there's less of a push/force to move the blood though. So in both high and low BP, the heart works harder to rectify the condition.

I have a = 2.5cm, b= 1 cm, c= 0.7cm and mass is 0.32g
I need to find p (density)
My solution is 0.32g/1.74cm3 which is 0.18g/cm3 yet the answer says it should be 1.8g/cm3

where did I fuck up?

m/v = 0.32g /( 2.5cm * 1 cm * 0.7cm) = 0.18g/cm^3

Yeah, that's my solution which is wrong because answer is 1.8g/cm3
Which does make sense, since it is sugar but then the mass make no sense, it could not be 0.32g, has to be 320g or 0.32kg

I'm right or missed something important?

The answer is wrong.

If I wanted to find the average position of a function
[math]s(t)=6e^{-t} \sin{t}[/math]
on the interval [math][0,2\pi][/math]
Would I do
[math]\frac {\int_{0}^{2\pi}6e^{-t} \sin{t}\,dt}{2\pi}[/math]

Why does the existence a basis [math] B = \{ \alpha_1, \alpha_2,...,\alpha_n \} [/math] with [math] T \alpha_i \in \mathrm{Span}(\alpha_1,...,\alpha_i) [/math] guarantee that [math] T [/math] is triangulable? I'm currently reading page 203 of Hoffman & Kunze and I understand the construction of this basis, I just don't get why the matrix [math] T [/math] is necessarily triangular with respect to it. Any help would be much appreciated.

Go over the units again in your book

Have you tried writing out the matrix? It follows immediately from the condition you're given

Anyone?

Got it, I feel pretty stupid now. Thanks for the reply.

what happens on the last line? the transpose seems to be done entrywise
why is it not [math](A^T,-A^T,I)^Tz=\begin{pmatrix}A^T\\-A^T\\I\end{pmatrix}z[/math]?

This.

It's basically to reduce the order and turn a calculus problem into an algebra problem if you have a table of common Laplace transforms with you. If you do it by hand, then inverse Laplace transforms only turn the calculus problem into a complex analysis problem and you have a nasty cauchy integral to deal with. If you have conditions of the original function and you do not want to or can't use other methods of solving the differential equation, then you use Laplace transforms.

> My problem was with the image I posted under my first post - the exercise is asking to you draw a machine accepting any string not in a*b*, with the alphabet consisting of {a, b}. So the resulting machine will not accept any string including the empty string, correct?
It will reject any string consisting of zero or more "a"s followed by zero or more "b"s. IOW, it will reject:
- the empty string
- any string consisting solely of "a"s
- any string consisting solely of "b"s
- any string consisting of a run of "a"s followed by a run of "b"s.
It will accept anything else; which essentially means any string having "ba" as a substring.

I'm such a goddamn brainlet: I seriously do not fucking understanding radians and degrees. Are they fundamental and unitless like "5" or "7". Or are they units in the same sense meters and Newtons are? If the latter, does that mean e^(pi*i) + 1 = 0 is only true in the units of radians? And, if by convention we used degrees more often, we could claim e^(180*i) + 1 = 0?

What does the less than symbol mean when referring to operator spaces?

So like I've got some hilbert space A and the set of hermitian operators on this space is L(A). In this paper I'm reading there's another operator space S defined on the hilbert space B (which may or may not be equal to A) such that

S < L(A)

What does this mean?

That means they differ by a positive semi-definite self-adjoint operator that is not zero.
That is, a > b, if and only of a-b is a nonzero element of the positive cone of L(A).

Ok, forget about that, I misunderstood your question. Probably it is some embedding relation?

Just realised I misread something in the paper, the operator space S actually is defined on the hilbert space A.

With that being the case what does an inequality between operator spaces on a hilbert space mean?

I understand that for individual operators an inequality A

subspace?

How would I prove b) here? W is supposed to denote the domain of the function/program. Really have no idea how I'm supposed to use the hint

Can someone help me with indifference curves? How can you have multiple of them?

chem questions, would appreciate any portion of input you can give
1: How could you identify a sample of cyclohexene?
I have written down "weigh out known volume of liquid and compare to density of cyclohexene (0.811g/ml)". What other test could say to make this answer more complete?
2.(long) Show all the structures of the possible acid-catalysed dehydration products of the following:
i)Cyclopentanol
ii) 2-Butanol
iii) 1-Methylcyclopentanol
If more than one alkene is possible, predict which one will be in the largest amount.
3. What is the major disadvantage of using concentrated sulfuric acid instead of 85% phosphoric acid as a reagent in the dehydration of an alcohol?

Forgot my answers for 2 and 3, and writing them now they look complete
2.
a) Cyclopentene
b)Trans-2-butene (largest amount)
1-butene
Cis-2-butene
c)1-methyl-1-cyclohexene (largest amount)
Methylenecyclohexane
I think I got them all
3.
sulfuric acid is an oxidizing agent and can oxidize the alcohol to form other products (sulphur dioxide, carbon dioxide)

I'm not entirely sure what you're asking.

There are multiple indifference curves because each one maps a set of bundles that gives the same utility and a higher curve represents higher utility. So for example, any point on I3 has the same utility but any point on I3 gives a higher utility than every point on I2.

The budget constraint is used to see what affordable bundle gives you highest utility. This is usually found on a utility curve that runs tangent to the budget constraint.

>any point on I3 has the same utility but any point on I3 gives a higher utility than every point on I2.
sorry, let me reword this: all points on I3 give Kevin the same utility but any point on I3 gives Kevin a higher utility than any point on I2 would give him.

So anything above the budget constraint would be a utility not achievable?

Yeah. Basically in these questions you're just always looking for the highest curve that is still touching the budget line.

are quadratics the first mong filter

Is Econometrics really a good course for getting hired?

What's on the blackboard? It's definitely physlcs... EM?

Similarly here.

Looks like utter nonsense.

On closer inspection, this one isn't physics, but absolutely is.

I took Diff Eq the summer of my freshman year and I am now in grad school, where I find myself using it constantly. Long story short, I had a shitty professor but still did fine in the class but I didn't come away with much. I want to actually understand the more complex shit so I can understand and solve harder problems.

Any recommended books for refreshing knowledge/learning more? Please and thank you anons.

Does [math]Int(\overline{A}-A)=\emptyset[/math] always happens in the topo0logy of a metric space? Can't find counterexamples, but I can't prove it either

Angles are unitless; they're ratios of lengths. One radian is one metre of arc length per metre of radius, or one foot of arc length per foot of radius, etc.

I believe this is it, though it's been a while.
[math]e \in \texttt{Tot}\leftrightarrow W_e=\omega \leftrightarrow (x,e)\in \{(x,y)~|~W_x=W_y\}.[/math]

Looks like cylindrical or spherical capacitor or something like that.

See you in 2 days barneyfag

Since the region isn't closed, Green's theorem gives you 0. I know the answer is 20, because you have to include the distance from (0, 10) to (0, -10). You only get 20 if you go from bottom to top; if you go from top to bottom, you get -20. My question is, Does it have to be done in a certain direction? Is there a way to end up with +20, if I go from top to bottom?

FUCK
ME

>[math]x = A e^{st}[/math]
>if s may have 2 values, [math]x = A e^{s_1 t} + B e^{s_2 t}[/math]
why?

What exactly is your question?

why is that statement true? I feel like it's some basic algebra but I can't figure it out

>why is that statement true?
What is the context? "if s may have 2 values" is a meaningless notion.

...

that's just the superposition principle

anyone?

s gets 2 values from assuming a differential equation has an exponential form (how you solve every differential equation) then solving for the coefficient in the exponent

other than that i think there's a linear algebra reason for it having two exponentials in its solution. probs something to do with the eigenvalues and probs 2 derivatives

are there any infographics out there showing all human spaceflight orbits done up to today?

depends on the school but generally i'd assume yes, as long as you do a makeup class or have someone fill in for the lecture. i had professors do this occasionally in classes

can someone show me the proof of lagrange error bound? prof did a shitty job of explaining it.

Best books regarding linear algebra / diff. eq.?

How about Schaum's Outline series? Cheap and to the point with several practice problems with solutions.

If I put the neck of a whiskey bottle (assume 40%abv) up my ass and do a handstand for ten seconds, am I likely to die of alcohol poisoning?

If I put the neck of a whiskey bottle (assume 40% abv) up my ass and do a handstand for ten seconds, am I likely to die of alcohol poisoning?

To any LaTeX whiz:
Why is there no table of contents showing up?

I clearly have several sections and subsections, but for some reason they just aren't appearing after I call \tableofcontents
(Pastebin: pastebin.com/pvqkTRyh)

I want to start learning differential geometry. Can someone recommend me a good book to start with?

section* -> section

I'll check it out, thanks user

Funny you mention this. I was in a really similar boat up to a few weeks ago.

I very highly recommend Kreyzig's "Differential Geometry" text.
I'm going through it rather slowly, but at least up to describing surfaces the explains a lot of important formulas pretty well. They have a lot of interesting problems (and thankfully very detailed answers for the problems), so you'll get a lot of interaction with both theory and practice.
books.google.com/books/about/Differential_Geometry.html?id=P73DrhE9F0QC

Gotcha... I'm personally not a huge fan of having the numbers, but removing the asterisk works, so I'll have to make do.

>What is the soul?
There isn't one.

>What makes me I?
The consciousness you have is from your brain chemistry and sensory system. Living things need senses to interact with their environment and to process the information a brain system develops. That's all your conciseness is.