its 2:14 am

Tatterhood

post algebra

Tatterhood

did I already make a thread identical to this, I forget

Tre

FUCK/19415.968 = 32

solve for FUCK

Bee

Ah, good memories of late-night statics and dynamics homework.  That shit was all super long-form problems.

glennmagusharvey

1. A journalist throws a shoe at a head of state.  The shoe leaves the journalist's hand at height h_j and with velocity v_0 with nonzero horizontal and vertical components.  If the shoe hits the face of the head of state at height h_hos when coming down, write an expression for the distance between the journalist and the head of state.

2. If the head of state dodges the shoe by ducking, and has face that is approximately circular with radius r_f, which the shoe would hit squarely on the nose if the head of state did not duck, and can duck at a solely-downward velocity of v_d, calculate the time at which the head of state would need to begin ducking for the shoe to just barely graze his hair.

Calica

let G be a group with a special(determinant 1) representation over a two-dimensional space V

now consider tensoring a representation with V.  the dimension will be twice as big, but it'll be a sum of other representations.  you can make a graph where U is connected to W if U tensor V contains a copy of W, because U is the same as U dual and the character math will always work out very nicely

in the weirdest case, 2A_5, the graph is: you take a node in the center, attach one node to the center, attach a chain of two nodes to the center, and attach a chain of five nodes to the center.  the one way furthest out is the trivial rep, and the one right next to it is V.

in principle you can get the whole character table from this, but i'm only going to do dimensions.  2 is twice as big as 1, 2*2 is 1+3, 3*2 is 2+4, so on until you reach 6 at the center.  the one poking out has to be 3, and then you subtract 3 and 5 from 2*6 to get 4.  then the last one has to be 2.  cool.

Tatterhood

I'm too asleep to understand that right now but cool

Calica

https://en.wikipedia.org/wiki/McKay_graph

that might be actually understandable to someone who is willing to put in the time to understand rep theory

glennmagusharvey

Kodaka: "Why are you guys so early?  We've still got 10 minutes before 1."
Yozora: "I wasn't first.  I got here 5 minutes after Rika did."
Yukimura: "Well, I only arrived 20 minutes before you did because I'm your sidekick."
Rika: "Rika managed to beat Sena to our meeting place by 15 minutes."
Sena: "But I was still here 15 minutes before Yukimura."
Kodaka: "Why are you guys talking like you're in the middle of some math word problem?"
Kodaka: "Okay, try to figure out who got here, what time, based on what they all just said."
Kobato: "Huh?"
Kodaka: "Come on, it'll be fun for you!  Now we arrived at exactly 12:50.  You have until we get to the karaoke place to answer."
Kobato: "Uh...what?!"
Kobato: "Um......ku ku ku!  You forget all I need to do is access the Akashic Records and solving a problem like this one shall be a breeze!  Watch and learn, mortal.  I'll have the answers for you in no time, probably."
Kodaka: "Why do you have to use the powers of darkness on everything?"

glennmagusharvey

it is three hours later now.  what time is it now?

Fossilmaiden

14:57

Alduin

but is the fear gone?

Bee

Your baby sister is about to drool into your brand new $1000 motherboard.  Her mouth is six inches above the surface.  The drool is highly viscous and accelerates downward at 0.3g.  You are standing at rest in the doorway, 15 feet away.  Assuming your hand is infinitely thin, how much time do you have to catch the drool, and how quickly must you accelerate to do so?

*actual question on my AP physics exam*

Klinotaxis

inches? feet? what is this shit

Obā-san

assuming your hand is infinitely thin

Fossilmaiden

Inverse yaoi hands.

Salix Babylonika

Bee said:

Your baby sister is about to drool into your brand new $1000 motherboard.  Her mouth is six inches above the surface.  The drool is highly viscous and accelerates downward at 0.3g.  You are standing at rest in the doorway, 15 feet away.  Assuming your hand is infinitely thin, how much time do you have to catch the drool, and how quickly must you accelerate to do so?

*actual question on my AP physics exam*

this question was beamed in from another dimension

Fossilmaiden

who spends that much on their mobo anyway

Yarrun XIX

Alternate dimensioneers

Bee

Jane said:

Bee said:

Your baby sister is about to drool into your brand new $1000 motherboard.  Her mouth is six inches above the surface.  The drool is highly viscous and accelerates downward at 0.3g.  You are standing at rest in the doorway, 15 feet away.  Assuming your hand is infinitely thin, how much time do you have to catch the drool, and how quickly must you accelerate to do so?

*actual question on my AP physics exam*

this question was beamed in from another dimension

If you want to talk about beamed in from another dimension, here's another from one of our homework assignments.

The Star Trek away team beams down onto a planet, and accidentally finds themselves on an alien superhighway!  Zonx, a three-eyed alien wearing glasses (his friends call him Six-Eyes), is driving at one km per second.  He sees the away team on the road from 2 km away and stomps on the brakes, decelerating at a rate of 100 m/s^2.

The ranking officers all jump out of the way of course, but does Zonx stop in time for the redshirts?  Calculate either the distance he stops from them, or the speed at which he hits them.

(spoilers, they die)

Yarrun XIX

Somewhere between 700-1000 m/s

Imipolex G

redshirts die? that question is a gimme.

Bee

Of course, but you also had to give the exact speed for maximum lulz.

Yarrun XIX

-50x^2 + 1000x - 2000 = 0. Solve for x. That seems about right.

glennmagusharvey

Yarrun XIX said:

-50x^2 + 1000x - 2000 = 0. Solve for x. That seems about right.

x^2 - 20x + 40 = 0

b^2 - 4ac = 400 - 4*1*40 = 400 - 160 = 240 > 0; real solutions available, rational solutions not available

rest of problem to be outsourced to a high school student

Calica

x^2-20x+40=0, (x-10)^2-60=0, x=10-sqrt(60), sqrt(60) is about 7.7 probably, so x is about 2.3, 1000-330=770 plus or minus some meters per second

edit: i somehow thought sqrt(60) was between 6 and 7 even though i did an in-my-head interpolation calc between 49 and 64.  derp.

Bee

v^2 = v0^2 + 2ad is actually the equation you're looking for.  It's typically more useful than a straight quadratic when you expect intermediate speeds to be relevant.

First you assume v = 0 for a full stop, then find the distance to do it is greater than the given distance.  Then you plug in the given distance instead and solve for v.

v^2 = (1000 m/s)^2 + 2 * (-100 m/s^2) * (2000 m)

 = (1000000 - 400000) m^2/s^2

v = sqt(600000) = about 775 m/s

Yarrun XIX

See,

None of us apparently took physics

So we didn't think of that

Because we have integrals

Calica

i hadn't used that particular equation since high school physics

Tatterhood

I took first year physics in undergrad but honestly I fell asleep before I finished reading that question

word problems can eat a dick imo

glennmagusharvey

I remember there are four handy two-dimensional projectile motion equations in physics except I've forgotten what they are, aside from the fact that one of them is basically the derivative of another one.

Imipolex G

as a writer, I know nothing of math

glennmagusharvey

Imipolex G said:

as a writer, I know nothing of math

what is the volume of milk that can be contained a two spheres both with radius r?

Imipolex G

look, the last time I did the math, I ended up with an Atari Jaguar.

I learned my lesson

Alduin

moves everyone's beacons under moon and star

vtk

Find the volume of the golden earring with inner diameter 66mm and outer diameter 70mm

glennmagusharvey

vtk said:

Find the volume of the golden earring with inner diameter 66mm and outer diameter 70mm

wait i know you can do this with calculus but can you do with just algebra?

Bee

Calica said:

i hadn't used that particular equation since high school physics

This was high school physics (albeit AP), so :P

Of course with my brief foray into game design hammering really hard on kinematics was pretty important.

vtk

glennmagusharvey said:

vtk said:

Find the volume of the golden earring with inner diameter 66mm and outer diameter 70mm

wait i know you can do this with calculus but can you do with just algebra?

You can if someone gives you the torus volume formula or if you derive said formula by taking an intuitive leap that probably requires calculus to prove, but the same is true for many other simple geometric figures with simple volume formulas.

glennmagusharvey

let x>=0 and y>=0

if x+y>=0 then go to other thread

Bee

vtk said:

glennmagusharvey said:

vtk said:

Find the volume of the golden earring with inner diameter 66mm and outer diameter 70mm

wait i know you can do this with calculus but can you do with just algebra?

You can if someone gives you the torus volume formula or if you derive said formula by taking an intuitive leap that probably requires calculus to prove, but the same is true for many other simple geometric figures with simple volume formulas.

Alternatively drop the earring in water and measure the displaced volume.  /engineeranswer

Alduin

When Archimedes' circles were disturbed, he knew damn well he had been cheated

vtk

So yeah I'm pretty sure the volume of a torus is V = 2π²r_ar_b² so in my problem r_a = 68mm and r_b = 2mm so V ~= 5369.06mm³ = 5.36906mL. I intuited that, and am pretty sure the calculus would check out.

Now to check Wikipedia for the correct volume formula… yeah, just slightly different parameter names.