mystic oak
nvm think i figured it out just trying to formulate an actual question
#help-27
livid blade
devout snowBOT
livid blade
in b) i) how will I show that?
i don't get it
will I write numerical values X b?
i get FG = 12/5 X b
devout snowBOT
@livid blade Has your question been resolved?
livid blade
<@&286206848099549185>
devout snowBOT
@livid blade Has your question been resolved?
lavish gust
devout snowBOT
lavish gust
yesterday I got the right answer
but when I review it today
I couldn't get the same answer
rare mantle
that is correct
lavish gust
I got the same answer but just the +12 I didn't get when I rewrite it
rare mantle
show your work
zinc pewter
devout snowBOT
craggy quiver
devout snowBOT
craggy quiver
patent tartan
@craggy quiver I think by chopping off they literally mean it
that is, without rounding the third decimal digit
$\frac{0.367 - 0.367879441}{0.367879441}$
woven radishBOT
Navix
grave bobcat
Yo I'm really bad at math, how do I get the answer of 12y=x-3? (Originally what x is g(x) =0 if g(x)=12x+3 )
grave bobcat
g(0)=12x+3
grave bobcat
Yeah
inland seal
Ok
So let me explain to you
g(x) is a function
and you know it equals 12x + 3
g(0) is the value of the function when x = 0
So you just plug in x = 0 to the function
g(0) = 12(0) + 3
g(0) = 3
grave bobcat
Really that's it? My mathbook says its 1/4 or 0.25 and I have no idea how they got that, like dividing 12 to both sides or what
-1/4*
-0.25*
grave bobcat
I dont understand
Well yeah y=12x+3 then 12y+3-3=x-3
12y=x-3
Right?
The rest I dont get
wicked turtle
where is y coming from if the original question is "what x gives g(x) = 0 if g(x) = 12x+3"?
inland seal
where is y coming from if the original question is "what x gives g(x) = 0 if g(x...
You forgot the x there
grave bobcat
x=12x+3?
wicked turtle
You forgot the x there
thx, fixed
grave bobcat
12x+3-3=x-3, 12x=x-3 right?
inland seal
Where do you get this? 12x+3-3=x-3
grave bobcat
From putting what I did to the other side of the equation
grave bobcat
When X is G(x)=0 and the question is g(x)=12x+3 (maybe this is a better explanation)
grave bobcat
exactly
inland seal
that means 12x + 3 = 0
inland seal
Sorry, I'm just going through a few channels
grave bobcat
all good
inland seal
Do you have notes or anything of how to solve equations like these?
if you are already learning functions and do not know how to do this, you should probably go over that
you will find it hard to continue without knowing earlier material
grave bobcat
Yeah I have solved this in the past, lost the note but my mathbook explains things weirdly and I cant seem to understand what the question really is honestly
devout snowBOT
@grave bobcat Has your question been resolved?
restive river
I need help understanding a question
devout snowBOT
I need help understanding a question
restive river
During a heavy downpour, 90 liters per square meter fell in half an hour. How many millimeters of rain fell? (How high would the water have stood if it had not run off?
Just want help to understand how i calculate the answer
red bobcat
During a heavy downpour, 90 liters per square meter fell in half an hour. How m...
-How many millimeters of rain fell?
depends how many square meters we take into consideration
-How high would the water have stood if it had not run off?
not enough data
don't you have a box or something?
sour cloud
During a heavy downpour, 90 liters per square meter fell in half an hour. How m...
Insufficient information
sour cloud
don't you have a box or something?
He is right
grave bobcat
During a heavy downpour, 90 liters per square meter fell in half an hour. How m...
90000
Right?
sour cloud
grave bobcat
90000 millilitres
sour cloud
It doesn't state how many square meters of ground is present ola
restive river
Even before translating it didn't state jack shit
grave bobcat
ah fuck that's true
sour cloud
Even before translating it didn't state jack shit
Which language
grave bobcat
But how many fell
restive river
Swedish
sour cloud
Wouldn't that be 90k?
If it was one one square meter yes
sour cloud
Is the 3rd question related to 4th
sour cloud
Then there's no way
Sorry man
You should go and enjoy some swedish meatballs now you won't have to solve the 4th part coz it's wrong
restive river
Yo @grave bobcat Can u translate the 4th question
restive river
You should go and enjoy some swedish meatballs now you won't have to solve the 4...
Balls
Ima enjoy some kebab instead
sour cloud
Culture
grave bobcat
4th question
Basytan= 1 kubikmeter 1 kubikmeter=1000 dm^2 90mm så svaret e 90mm 1 kubikmeter =100dm^2
volymen är 90L vilket motsvarar 90dm^3
90=100dm^2*x
x=0,9dm = 90 mm .. ingen aning hahahaha
I dont get this ngl
restive river
Ja tror han vill veta höjden
På rätblockeb
Ja vet inte
Fuck han och fick hans svenska hhahah
grave bobcat
hahhaha true
restive river
Just gonna close this
grave bobcat
solving 12x + 3 = 0?
I got it now, 0-3=12x
-3 = 12x
-3/12
12/12
= 1/4 or 0.25
devout snowBOT
I got it now, 0-3=12x
-3 = 12x
-3/12
12/12
= 1/4 or 0.25
grave bobcat
Right?
elfin orchid
-1/4 better
elfin orchid
yes
thank you
shrewd pine
What do I do if I want to Check if a directional vector is parallel or identical and one of the parameters ends up 0 divide by 0
devout snowBOT
What do I do if I want to Check if a directional vector is parallel or identical...
restive river
You cant divide by 0 in math
lean matrix
You cant divide by 0 in math
Well try not to start a debate here
restive river
I think you know what i meant
restive river
What do I do if I want to Check if a directional vector is parallel or identical...
2 vectors are parallel if the xi and yj components are proportional
If they are identical then the vectors are identical
And you can also write the vectors as
vector a = k × vector b
Lemme know if helped@shrewd pine
shrewd pine
one second
it's in german but still intelligible right
Our teacher said we'd learn it later but I was just curious on what to do
eh this isnt urgent so I'll clear the room up
.clear
.close
potent needle
can someone guide me into answering this question
all I know is that I have to use logs to solve
devout snowBOT
can someone guide me into answering this question
all I know is that I have to u...
potent needle
I can plot the graph
I just need help with parts i and iii
devout snowBOT
@potent needle Has your question been resolved?
restive river
I dont understand the i question tbh, just put Ak^x on the x axis and u get a straight diagonal line @potent needle
For the iii part i guess after you've estimated A and k simply insert y=600 in the equation and solve for x
devout snowBOT
potent needle
I ended up applying logs to get
log(y) = log(A) +xlog(k)
which the the equation of the line of the form y=mx+c
.close
devout snowBOT
Available help channel!
restive river
What is the greatest power of 2 that divide 3^2008 - 1?
devout snowBOT
What is the greatest power of 2 that divide 3^2008 - 1?
restive river
The answer is 2^5, but I'm not sure on how I would solve it
elfin orchid
you could try checking some congruences : $$3\equiv 1 [2]$$
$$3\equiv -1 [4]$$
$$3^2 \equiv 1 [8]$$
et caetera
woven radishBOT
Silfer
soft shore
do you know modular arithmetic
restive river
nope
elfin orchid
what
restive river
let me show you something
elfin orchid
did a teacher ask you sucha question without modular arithmetic
restive river
I've found a explanation but I didn't quite understand it yet
well..
I saw everyone doing it this way
let me show you
soft shore
hmm, I’d like to see the explanation
elfin orchid
oh i thought about factoring by 3 - 1 not 3^8 - 1
restive river
In this factor, we have 251 odd terms, that is, not divisible by 2.
soft shore
yeah
restive river
Then, 3^8 - 1 = 2^5 times 5 times 11
Then the greatest power of 2 that divides 3^2008 - 1 is 2^5
my question is
elfin orchid
that's smart
restive river
I understood most of it
restive river
but I didn't understand 3^8250 + 3^8249
elfin orchid
tho i think pursuing with modular arithmetic could've solved it pretty neatly
elfin orchid
but I didn't understand 3^8250 + 3^8249
3^(8*250) + 3^(8*249)
restive river
but still, I'm not there yet
soft shore
3^(8*250) + 3^(8\*249)
elfin orchid
but still, I'm not there yet
the method you gave is pretty good
elfin orchid
why 3^8250 + 3^8249 + ...
3^(8*250) + 3^(8*249)
soft shore
wait so
soft shore
for a^n-1 where n is a positive & odd integer
you’d factor it like this:
(a-1)(a^(n-1)+a^(n-2)+...+a+1)
in that case, n=251
soft shore
3^(8*250) + 3^(8\*249)
and then this
patent tartan
x^n - 1, one solution is always x=1 so you can apply polynomial division and get the thing you posted
devout snowBOT
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Available help channel!
celest tide
why is the range of tan(x) - cot(x) R?
devout snowBOT
why is the range of ``tan(x) - cot(x)`` R?
wooden zodiac
the sub or add of functions that have R-range, has R-range again i think
celest tide
I was hoping for an algebraic proof
wooden zodiac
rally
placid rover
take x and -x
wooden zodiac
really
placid rover
or x and x
placid rover
I was hoping for an algebraic proof
The start to understanding why is often from a picture.
wooden zodiac
well if sub or add isnt zero xd
placid rover
And then you can start thinking about a rigorous proof
placid rover
well if sub or add isnt zero xd
???
I can think of an infinite number of examples where what you said doesn't hold.
wooden zodiac
x+(-x)=0, x-x=0
placid rover
For starters, take the question itself. tan x - cot x has range R. tan x does as well. But cot x doesn't.
wooden zodiac
cotx has range R
placid rover
did i choose a sht example kek
yes i didnt mean this then
But im sure u can easily come up with non trivial examples
celest tide
Hmm im thinking between 0 and π/2
tan increases from 0 -> inf
and cot decreases from inf -> 0
so at 0: 0 - inf = -inf??
and at π/2: inf - 0 = inf???
hm maybe this isnt as concrete
placid rover
You can try algebraically by attempting to simplify
celest tide
yeah that didnt seem to work out for me
wooden zodiac
sinx doesnt have range real numbers
placid rover
Yes exactly
celest tide
$\frac{tan^2x - 1}{tanx}$
wooden zodiac
i meant addition of functions that have range real numbers not one function that has range real number
placid rover
(sin x + x) - x is a clear counterexample to what you claimed.
woven radishBOT
kinglacto
placid rover
**kinglacto**
yes and then?
celest tide
**kinglacto**
0 ≤ tan^2 x ≤ inf
-1 ≤ tan^2 - 1 ≤ inf
-inf ≤ tanx ≤ inf
this is the range of numerator and denominator
celest tide
**kinglacto**
you mean this?
placid rover
yes ofc
when i said simplify, i did not mean combine fractions and leave it at that
Do note when simplifying you should pay attention to domain
celest tide
use an identity?
celest tide
Do note when simplifying you should pay attention to domain
yeah i seem to have added tanx ≠ 0
celest tide
Can you not try to simplify this further?
perhaps you mean express in terms of sin and cos?
placid rover
There's a lot of things I could mean
But I'm not going to explicitly say
try them out yourself
celest tide
ok
I tried expressing in terms of sinx and got $\frac{2sin^{2}x - 1}{sinx \sqrt{1 - sin^{2}x}}$
woven radishBOT
kinglacto
celest tide
@placid rover
The numerator has range [-1,1]
at x = 0 rad (and at πn ig)
numerator : -1 and denominator is 0
at x = π/2
numerator: 1 and denominator is 0
does that help?
nvm thats dumb
celest tide
**kinglacto**
the graph is completely different holy shit
devout snowBOT
@celest tide Has your question been resolved?
steel comet
is there an exact answer for a limit??
devout snowBOT
is there an exact answer for a limit??
steel comet
i dont know how to explain. hopefully u get my point
zealous rapids
most of the time yes there is a numerical answer, unless it is "DNE" or "-∞" or "∞"
steel comet
most of the time yes there is a numerical answer, unless it is "DNE" or "-∞" or ...
yeah i get it, but what if the function given with the limit is conditioinal. like if, x=1 then y=5, else y = x*2
it could be like almost any number in decimal
like mili decimals. if that makes sense
zealous rapids
the limit may not be the same as the function evaluated at that point
so you're trying to find the limit as x approaches 1?
steel comet
yep ik that too. thats my point.
steel comet
so you're trying to find the limit as x approaches 1?
its not a quetion, just getting to know the DEFINATIOn of limits
steel comet
like its easy to evaluate but sometimes, it does not make sense
zealous rapids
wdym
steel comet
wdym
just like the example bove, lets say as x approaches one we take the limiut of f(x). where f(x) is the equation above. so it could be almost any number havinbg like 100 decimals.
but not 5
so that means it does not have an EXACT answer
right?
steel comet
wait.
steel comet
f(x) = {
5, if x=1
x*2, if x not equal to 1
}```whats the limit of x approachesd one here
it could be any number having thousands of decimals
steel comet
x*2 means x²?
uh no its 2x
zealous rapids
oh, so then 2*1=2
zealous rapids
but that is irrelevant to the limit
steel comet
now if we take the limit. people count it as 6
zealous rapids
it doesn't matter what happens at x=1
steel comet
5*
zealous rapids
just what happens around x=1
zealous rapids
yes
steel comet
but like 3.999999999999999999999999999999 multiply by 2 is not equal to 4
so it could be almost any number with like millions of decimals
so its hard to prove.
thats why i am here
zealous rapids
it is equal to 4 if you have infinite decimals
oh multiplied by 2?
then it's equal to 8
steel comet
it is equal to 4 if you have infinite decimals
infinite decimals..... i see
zealous rapids
2*3.999...=8
zealous rapids
np
steel comet
.close
graceful marlin
devout snowBOT
woven radishBOT
graceful marlin
this is the answer
who's that? 😂
yeah thats an error
no its not a typo
we did such questions in class
where its dxdy, but bounds of the inner integral are functions in x
in such questions the bounds of the inner integral needs to be changed to function in y
dxdy remains as it is
wait i'll send u the questions we did in class
check this 😂
graceful marlin
in such questions the bounds of the inner integral needs to be changed to functi...
.
look
hmm
can u show me how?
here's another similar problem
right.
and afaik, thats one of the two types of double integrals...the second being this weird "dxdy but bounds in x" form
yeah it looks more meth than math to me 🤣
okayy
ping me when u do so...there are hundreds of channels here lol
thats basically the method to do these 'weird integrals'
keep dxdy (or dydx, whatever it is) as it is given
plot it
and then re-write the bounds the 'normal' way
👌
okay I'll try the problem again
hopefully wont get stuck this time
I can't find the bounds of the second intgl. @devout shore
Can u help a bit?
The inner integrals limits in my opinion should be Lx to a
And outer will be am to aL
Correct??
graceful marlin
this is the answer
The answers seems to be incorrect because the second integral isn't double xD
oh yeah right 
what about the second integral?
right right...
thanks a lot 
.close
devout snowBOT
graceful marlin
.reopen
devout snowBOT
✅
devout snowBOT
devout snowBOT
Available help channel!
restive river
For the problem For what values of x does the series ∑(from n=0 to ∞) of (2x−3)^n/n! converge?, I'm trying to use the ratio test to find the interval of convergence and after simplifying, I am comparing the absolute value of the ** lim (x -> ∞) of (n+1)/(2x-3) ** less than 1. At this point I'm stuck because after substituting ∞ for n, the result is almost always ∞ (unless x=∞), which is well greater than 1, indicating that the series always diverges. Since this is a multiple choice question, and none of the answers are "always diverges", I was wondering if I'm making a mistake in simplifying the limit or finding the limit.
devout snowBOT
For the problem **For what values of x does the series ∑(from n=0 to ∞) of (2x−3...
@restive river Has your question been resolved?
copper mango
$\lim_{n\to\infty}\frac{(2x-3)^{n+1}}{(n+1)!}\frac{n!}{(2x-3)^n}$
woven radishBOT
Mosh
restive river
$\lim_{n\to\infty}\frac{(2x-3)^{n+1}}{(n+1)!}\frac{n!}{(2x-3)^n}$
thanks, I accidentally did the reciprocal of the first and the second
.close
devout snowBOT
copper mango
yeah ratio test is a_(n+1)/a_n
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Available help channel!
frosty gyro
There is a 1% chance one machine needs to be fixed in 1 hour. Workers are paid $45 per hour. I will lose $1000 if no one fixes the machine. How many workers do I need if I have 10 machines?
devout snowBOT
There is a 1% chance one machine needs to be fixed in 1 hour. Workers are paid $...
@frosty gyro Has your question been resolved?
celest bough
There is a 1% chance one machine needs to be fixed in 1 hour. Workers are paid $...
uhm, this is a bit of a weird question
are workers supposed to fix the machine?
celest bough
ok, cause that was not clear from the way you worded it
how long does it take them to fix it? can one worker fix 1 machine?
celest bough
lol, your homework has grammar errors.
celest bough
well if you have 1 worker, there's a 0.99^10 chance it won't break. I'm guessing you need to calculate the potential costs if one does break versus what happens if you hire more workers.
for many hours
frosty gyro
yep doing that now
frosty gyro
well if you have 1 worker, there's a 0.99^10 chance it won't break. I'm guessing...
can you do an example of five workers pls
devout snowBOT
@frosty gyro Has your question been resolved?
devout snowBOT
@frosty gyro Has your question been resolved?
devout snowBOT
@frosty gyro Has your question been resolved?
ancient field
need help in this
devout snowBOT
need help in this
celest tide
what is the edge here?
ancient field
thats my doubt , i think it means the base
ancient field
yes
celest tide
whats the formula?
the most common one that uses values - some of which (or rather one of which) you already know
ancient field
1/2 * b * h
ancient field
yes
celest tide
1/2 * b * h
and you know what this entire expression evaluates to
ancient field
yes
ancient field
yes
celest tide
do you see the answer?
ancient field
do you see the answer?
i can get the formula , but figuring out this is the difficult part for me
are you here?
celest tide
yeah
celest tide
so ``1/2 * b * 25 = 480``
so you see that this expression has 1 variable?>
and its value is the answer that you are looking for?
ancient field
yes
?
are u here?
<@&286206848099549185>
i think lacto is gone , so can anyone else help me?
ancient field
is this the correct formula 480/25
celest tide
its not a formula also you're missing 2
celest tide
idk
woven radishBOT
kinglacto
celest tide
substitute and find
ancient field
substitute and find
this one
celest tide
$\frac{base * height}{2} = area$
woven radishBOT
kinglacto
celest tide
its a .png image
ancient field
ok i can see it now
can you explain this to me pls
im confused
how do i find the base?
celest tide
**kinglacto**
so you know the area and the base yeah?
ancient field
yes
celest tide
do you know how to solve linear equations in 1 variable
ancient field
uhh no , i wasnt taught that
celest tide
hmm
im not sure how your teacher intends for you to solve this problem
perhaps you should take it up with them
devout snowBOT
devout snowBOT
Available help channel!
magic crater
devout snowBOT
magic crater
Ive also posted it in the trig and geometry channel
wanton star
we want to find the marked segment on the right?
magic crater
Nah i wanna find OC
wanton star
so this?
magic crater
yes
so I reflected the circle over
and by drawing line |AC|
I made a right triangle
so
24 squared + 7 squared = |AC|
so |AC| = 25
so I did some other stuff
to get OC = 15
however my teacher said I needed to explain why the reflected line must hit point z
I just realized I never marled a point z
ok
wanton star
ah this one is tricky
magic crater
so my teacher is asking
wanton star
hint: AOCD is cyclic
magic crater
why the line cant be outside the semicircle
and what would Happen if it did
and why Its cant be inside
novel goblet
hint: AOCD is cyclic
is it?
wanton star
hint: AOCD is cyclic
use this
wanton star
wdym both ways
magic crater
like she said
"We went over reflections, and cylic shape shapes today, I want you to try both ways"
i think i may have the cyclic down
I just need to prove ofr the reflection
wanton star
i think i may have the cyclic down
what did you do for that one
hmm, reflection does work but I would rather work from drawing the extension of DC
and then prove reflection
devout snowBOT
@magic crater Has your question been resolved?
magic crater
and then prove reflection
ok
devout snowBOT
@magic crater Has your question been resolved?
wanton rapids
(3- i)(a+bi)=7+i
= 3a+3bi - ai + bi^2
= 3a + 3bi - ai - b
b(3i-1) + a(3-i)
wanton rapids
How do I proceed?
copper mango
proceed with what?
wanton rapids
The equation
copper mango
no clue
wanton rapids
I need them to be equal
copper mango
Post your actual question
"Find a and b such that they are equal"
Is what you meant to say
wanton rapids
Yeah
copper mango
But anyway,
(3- i)(a+bi)=7+i
= 3a+3bi - ai + bi^2
= 3a + 3bi - ai - b
b(3i-1) + a(3-i)
is nonsense imo
or at least very shitly written
wanton rapids
How would you do it?
copper mango
Expand the LHS and simplify
wanton rapids
= 3a+3bi - ai - bi^2
copper mango
right so $3a+3bi-ai-bi^2=7+i$ is properly written
woven radishBOT
Mosh
copper mango
now simplify the LHS
wanton rapids
3a+3bi-ai+b = 7+i
how do I separate the real and imaginary here
wanton rapids
So 3a+b = x and 3b-a = y
y*i = (3b-a)i
So (3a+b)+i(3b-a) = 7+i
wanton rapids
3a+b=7
3b-a = 1?
wanton rapids
3a+b=7
9b-3a=3
10b=10
b=1
3a+1=7
3a=6
a=2
So z2=2+i
z₂=(a+bi) where a = 2 and b = 1
winter patrol
where's z_2 coming from
wanton rapids
I just called it that because we needed to find a and b for the equation to be true
.close
devout snowBOT
winter patrol
you found that
a=2 and b=1
unless you're being asked for something else, that's where you stop
devout snowBOT
Available help channel!
restive river
Sup guys, I am trying to prove my answer in this equation -
x - 6 -x
----- = 2 * ------
x - 3 x + 3
I have these results -
x1 = 3/2 + sqrt(33) / 2
x2 = 3/2 - sqrt (33) / 2
But I have been stuck on proving them for like an hour. This is what I have so far -
devout snowBOT
@restive river Has your question been resolved?
devout snowBOT
devout snowBOT
Available help channel!
forest chasm
.help
devout snowBOT
Commands:
clopen: .close, .reopen
factoids: .tag
help: .help
Type .help <command name> for more info on a command.
upbeat coral
How would I formally show that $\lim_{(x,y)\to (0,0)} \sqrt{x^2+y^2} = 0$ ?
woven radishBOT
ducktape
upbeat coral
Like, I guess it's continuous so I can just substitute it in. But is there some epsilon-delta argument I could use with more than one-variable ?
copper mango
yeah, use e-d for multivariable limits
$\forall\varepsilon>0,\exists\delta>0$ st when $\norm{x-a}<\delta$, we have that $|f(x,y)-L|<\varepsilon$
woven radishBOT
Mosh
copper mango
where $f:\mathbb{R}^2\to\mathbb{R}$, and $\lim_{\vec{x}\to\vec{a}}f(\vec{x})=L$
woven radishBOT
Mosh
upbeat coral
Do you have a link to an example e-d proof for more than one variable ?
devout snowBOT
@upbeat coral Has your question been resolved?
tall idol
A certain factory stores its products in boxes with 12 units. To assess the quality of their products, employees must remove and evaluate 2 products per box, taken sequentially. Knowing that in a given box there are 4 defective products, we want to know the probability of both products being perfect if they are removed without replacement.
devout snowBOT
> A certain factory stores its products in boxes with 12 units. To assess the qu...
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wicked turtle
agree, the probability that the first one is perfect is 8/12
tall idol
(LOL the bot is buggy)
wicked turtle
after that one is withdrawn, how many good products are still in the box, and how many total products are still in the box?
tall idol
I have this approach (wait a second), but I'm really unsure about it:
So, the way I see it, we have two distinct possibilities for the second step:
- The product removed in the previous step was perfect. There are still 4 defective products left and the chance at the current step is
,tex \frac{11-4}{11}
OR
- The product removed in the previous step was defective. Now there are 3 defective products left and the chance at the current step is
(11-3)/11
wicked turtle
all true
but focus on what you actually need
P(both are perfect) = P(first is perfect and second is perfect) = P(first is perfect) P(second is perfect | first is perfect)
so you don't care what happens if the first one is not perfect
tall idol
I was so off track, I was doing p2 = p1 * 7/11 + (1-p1) * 8/11 🤦♂️
wicked turtle
that's valid, it just isn't answering the question that is posed
that's finding the probability that the second one is perfect, without knowing whether the first one was perfect
tall idol
You're correct once more.
Just a question, all we discussed is correct when both are taken separately, right?
wicked turtle
what do you mean by separately?
tall idol
Rather than two being taken at the same time. Not sure if it makes any difference
Probably not and I'm being silly here
wicked turtle
they're taken consecutively but they are not independent, if that's what you are thinking
i.e. the probability that the second product is perfect or not depends on whether the first one was
wicked turtle
pleasure, good luck!
tall idol
.close
wispy nova
I have a quick question about the area of a circle compared to the volume of a sphere
devout snowBOT
I have a quick question about the area of a circle compared to the volume of a s...
wispy nova
So if you take a slice of a unit sphere right through the center you'll get a unit circle
That unit circle as an area of pi, and the unit sphere has a total volume of 4/3 (pi)
wicked turtle
all true so far
wispy nova
Dividing the area of a unit circle by a volume of a unit sphere gives 75%
So that has to be illegal
Where is my logic failing me here
wicked turtle
why must it be illegal?
wispy nova
If you took a slice where the radius of a circle is 0.999, just below the original
It'd contain 74.99% of the volume of the sphere, mirrored above
already we're at like 225% from three slices
celest tide
Dividing the area of a unit circle by a volume of a unit sphere gives 75%
75 % of what?
wispy nova
of the volume contained within that area
So I assume you can't do that and my logic is flawed
wicked turtle
it's true that the ratio of the area of the circle of radius R to the volume of the sphere of radius R depends on R: $\frac{\pi R^2}{(4/3)\pi R^3} = \frac{3}{4R}$
woven radishBOT
OurBelovedBungo
celest tide
to get a volume percentage, you divide m^3 by m^3
what you are doing here is dividing m^2/m^3 = 1/m ????
youre certainly not getting a volume percentage
wispy nova
Hmm that's true
wicked turtle
that shouldn't be too surprising, because if you want to get volume from area you need to multiply by length
wispy nova
To get the volume of a cylinder you take the area of a circle and multiple by the length
so you add sequential circles of uniform size
why can you not get the volume of a sphere by adding circles of increasing than decreasing size
celest tide
ig you can and should
wispy nova
Then what am I doing wrong with my assumption here
It has to be something pretty basic, surely
celest tide
Then what am I doing wrong with my assumption here
what's your assumption?
wispy nova
Trying to add the center slice of a sphere, and then a very very slightly smaller slice above and below
The added area between them adds up to more than the volume of the sphere, though
So I guess there would be some assumed thickness?
The area of a circle is the same as a volume of length 1, so in trying to translate it is stretched that way.
Okay, I see I see. That checks out
Makes the units work and all that, comparing the area of a circle to a sphere is turning it into a cylinder of length one of that radius.
The only way to do it then would be to take infinitely small slices dz yadda yadda math works, thank you :)
.close
restive river
Currently stuck
devout snowBOT
Currently stuck
main gull
Currently stuck
What did you try?
restive river
I did (x^2-8x+41) (x-7) (x-1)
main gull
Can you post your work?
restive river
Plugged in 5 for x and set equation = to -1040
When I tried to change leading coefficient it removes my root of x=1
main gull
Sorry for the delay, trying to determine the best way to explain it
main gull
When I tried to change leading coefficient it removes my root of x=1
So the goal is to make some sort of function that looks has this kind of form, (x^2-8x+41) (x-7) (x-1), pass through (5, -1040)
That means that function is scaled by some constant, let's call it a, so then the general form is y = a(x^2-8x+41) (x-7) (x-1)
Does that make sense?
Now you can use that, plug in (5, -1040), determine that a constant and that's it
main gull
Not exactly
restive river
How would I plug in (5,-1040)
main gull
3632/-1040 = a
It's similar to what you did here
You just calculated the value wrong, when you plugged in 5 for x
The function you wrote was x^4 - 116x^3 + 112x^2 - 384x + 287, which is correct. In your calculator, you typed +384, and not -384
restive river
Yes
main gull
The other method was doing what you did, y = a(x^4 - 116x^3 + 112x^2 - 384x + 287) and plugging in the coordinate (5, -1040) and solving for a
main gull
Oops. Thanks for the help
.close If you are done
restive river
I have 1 more question
I need the leading coefficient to be 4, so I multiply 4 to the entire equation?
devout snowBOT
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Available help channel!
summer lynx
Trying to solve this for a semi-popular indie game i've built (can send you the link to the leaderboard). I usually figure out how to solve these things in Excel before coding them, but I'm stuck on this one.
devout snowBOT
Trying to solve this for a semi-popular indie game i've built (can send you the ...
summer lynx
.
There are a group of X people. Let's say 5 to make it easy.
A, B, C, D, E
They all give me some $ amount.
E.g.
A: $10,000
B: $30
C: $420
D: $150
E: $3400
Total of $14,000
I've committed to give the group as a whole, 50% more than they give to me. So $21,000 will be returned to them.
But I don't want to give them each 50% extra. I want to give them more or less than 50%, based on how they rank in a game. Let's assume they ranked in the order above. So, I want A and B to get more than 50% back. C to get exactly 50% back. D and E to get less than extra 50% back.
How can I calculate absolute numbers for A, B, C, D, E so that I stick to my $21,000 budget, and so their gain in % terms matches that order?
polar bolt
Not possible to do the payout you said. Say A entered with 1000000000 and B,C,D and E with 1. Not possible to even give A more than 50% (well you can give 50.01% or whatever)
summer lynx
Yes, I get that in certain situations it would have to be 50.0000X to make it work
but that doesn't make it impossible?
in other situations the payouts would be further from the the 50.0000x mark
polar bolt
The percentage possible to give out is gonna depend on ratio of given money
So wont be a static percentage
So just gonna be weird then
summer lynx
I'm trying to get those percentages esssentially, programatically
if the winner gave me a lot than of course the range would be tiny
since we need to give them almost the entire pool
polar bolt
There are an infinite amount of ways to give A>B>C>D>E
Where C=50%
So need to restrict it somehow to make your problem make sense
summer lynx
One restriction is that the total amount going out is an exact amount
summer lynx
I'm happy to have some kind of variance paramater/constant in there
or add any arbitrary constraint
but I don't know how to get started to solve a single case programatically
if I can understand how to calculate a single working case, that's not just cherry picking numbers, I can then code it
polar bolt
You need a ratio between payout of percentage between A and B (and presumly the same between D and E)
Then it has a single solution
summer lynx
Can I pick any ratio tho?
Feels like that ratio itself would depend on the initial numbers
how much the each gave me in the example
polar bolt
Yes you can pick any ratio
Say you want A to get 1.2 times more than B in percentage or whatever
summer lynx
ok, let's say I pick these 2 ratios. 1.2 for A:B and 1.2 for D:E
How do I then solve it?
You sure it's solvable with fixed ratios like that?
ah, maybe I'm getting it. do I go calculate and check how much value is above and below C
and then split that value twice again using the chosen ratios you mention
summer lynx
ok, i'll go back to the drawing board and try again
it there's more than 2 people on either side of the middle
what kind of constraints / ratios do I need to make it solvable you think?
polar bolt
Just ratio for all payouts needed
summer lynx
ok
so just to reiteate, you think is solvable in a closed form type of solution, I could put in excel
it doesn't need some kind of iterative algorithm
that picks values and then tries to converge to a solution, etc
This server is an amazing resource. Is there an option of paying/tipping people to do work? Like I'd love to see my problem solved on an excel sheet.
polar bolt
Isn’t it just smth like
,w 1.2100x+110x+0.530x+0.8300x+0.6*21x=(100+10+30+300+21)*0.5
woven radishBOT
polar bolt
100,10,30,300,21 are the values input
summer lynx
what is x?
polar bolt
The variable that connects the ratio
Oh whoops need a little fixing but the idea is there
If A needs payout 1.2 more than B then he needs 1.2x compared to B’s x
summer lynx
so in your example, payouts are 0.579*1.2 , 0.579 , + 3 other numbers?
polar bolt
Just 0.579 * 1.2 * 100+100
summer lynx
I can try this to see if it works. one sec
polar bolt
Oh whoops need a little fixing but the idea is there
The ratios are wrong
0.6 * x compared to 0.8 * x is not D gets 1.2 more than E
summer lynx
it doesn't need to be 1.2, right?
polar bolt
No just saying ratio between A and B not same as D and E as I wrote it
summer lynx
right
ok, so I can isolate x there and will try to solve in excel one example to see if it adds up
I feel like I'm a kid again! 😄
summer lynx
Doesn't seem to add up to the expect 50% increase
maybe I'm doing D and E wrong. could you confirm how I should get those?
this is B
A is 1.2 that amount, D is 0.8, E is 0.6
ohh I got it
the formula had 0.5 for C, when it should be a number between 1 and 0.8 (between C and E)
it works!!!
I think I can generalize this now
you're a god
devout snowBOT
@summer lynx Has your question been resolved?
grizzled lantern
if a funtion f(x) ineq 0 does that imply that f'(x) ineq 0?
devout snowBOT
if a funtion f(x) ineq 0 does that imply that f'(x) ineq 0?
narrow plank
if a funtion f(x) ineq 0 does that imply that f'(x) ineq 0?
It depends
If f(x) = 0 for all x, then f'(x) = 0
If f(x) = 0 only at some places for x, then f'(x) isn't always 0
Consider y = f(x) = 0 and y = f(x) = cos x
grizzled lantern
sorry I meant ineq
narrow plank
Consider f(x) = c for some constant c
devout snowBOT
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Available help channel!
tranquil osprey
hey
devout snowBOT
Available help channel!
obsidian violet
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obsidian violet
<@&286206848099549185>
wicked oasis
wait how do i solve the equation
You know right how to solve equations involving inequality ?
obsidian violet
You know right how to solve equations involving inequality ?
not really
i get stuck
obsidian violet
You know the properties of inequality right?
no 😭
wicked oasis
no 😭
c can be any real number
-
a>b then a+c>b+c , a-c>b-c
-
a<b then a+c<b+c , a-c<b-c
-
a>b then ac>bc (if c>0)
-
a>b then ac<bc (if c<0)
These properties
There are more tho
I just wrote a few
obsidian violet
c can be any real number
1. a>b then a+c>b+c , a-c>b-c
2. a<b then a+c<b+c , ...
alright so c can be any real number i get that a bit
wicked oasis
Yes
Just for an example
Let's assume
2<1
You agree to this right
Now you can add and subtract any real number to it
2-1<1-1 = 1<0
c=1
Just an example
The equation stay same
devout snowBOT
@obsidian violet Has your question been resolved?
whole field
.
i need help solving this
Without doing any calculations, explain why we can be sure that 3/5 x 7/11 is the same as 7/5 x 3/11 .
drifting ibex
because we multiply both factors with each other anyway
novel goblet
```The pattern below is continued for 200 numbers. What is the total in the end...
This can be understand as sum up all the odd numbers from 1-200 and subtract with all the even numbers from 1-200
whole field
wdym
drifting ibex
Okay it actually needs to be 201
should have only have gone up to 99
and then it is 100
devout snowBOT
@whole field Has your question been resolved?
stuck field
wdym
They meant think of it as
1+3+5+7...199
-(2+4+6...200)
You could obviously do it many other ways too.
stuck field
and then it is 100
It really is not.
Do not give away answers.
Especially when you're giving incorrect ones.
haughty cloak
I got this diophantine equation, and have to find integer solutions if there are, or if there aren't then prove that:
5x^3 + 4y^2 = 535
I got stuck on this one because I have never yet encountered both a and b to be set larger than 1, and I can't think of a way to solve this. Any help will be appreciated
devout snowBOT
I got this diophantine equation, and have to find integer solutions if there are...
@haughty cloak Has your question been resolved?
finite shore
Have you consider modulus arithmetic? For example considering mod 5?
haughty cloak
Have you consider modulus arithmetic? For example considering mod 5?
I tried taking modulo 5 but couldn't get any further than this
4y^2 = 535 - 5x^3
-> y = 5t
100t^2 = 535 - 5x^3
(divide by 5)
20t^2 = 107 - x^3
x^3 = 107 - 20t^2```Consider y=5n+t, where 0<=t<4
Typo. Should be 0<=t<=4
4(5n+t)^2 = 535 - 5x^3
Since the right hand side can be divided by 5, t=0
haughty cloak
Can you provide an explanation using congruences ≡ ?
finite shore
Sure $5x^3 + 4y^2 \cong 0 + 4y^2$ (mod 5)
woven radishBOT
ryker.chen
finite shore
Also $535 \equiv 0$ (mod 5)
woven radishBOT
ryker.chen
finite shore
Since $y^2$ (mod 5) can only take the value of 0, 1 or 4 (mod 5), it can only be 0 (mod 5)
woven radishBOT
ryker.chen
haughty cloak
Makes sense to me, y has to be a multiple of 5
haughty cloak
I tried taking modulo 5 but couldn't get any further than this
```
4y^2 = 535 - ...
So i substituted 5t as y but then reached a dead end
107 is a prime number
Alright I just noticed that 20t^2 = 107 - x^3, so 107 - x^3 must be divisible by 20, obviously it is the case for x=3, but how can I prove that there are not any more solutions after this?
I understand that you have been typing for a long time but dont delete anything I'd like to hear what you think (Navix)
patent tartan
by symmetry, say y >= 0. consider positive x-values first. by taking the equation mod 5 we can find that 4y^2 is a multiple of 5, so we can set 4y^2 = 5k.
substituting and simplifying, we arrive at x^3 + k = 107. because k > 0, and 5^3 = 256 > 107, we can rule out all x >= 5. y^2 also needs to contain the prime factor 5. because 4^3 = 64 and 107 - 64 = 43 = k which is neither divisible by 4 or 5.
so we can already establish the upper bound x <= 3.
hmm it remains to show that x is bounded below by 3 as well but not sure how atm
haughty cloak
how did you get that y^2 has to be divisible by 5?
patent tartan
mod 5 we've shown that
$5x^3 + 4y^2 = 535$
reduces to
$4y^2 = 0$
which is equivalent to saying $4y^2$ is a multiple of 5.
woven radishBOT
Navix
finite shore
Makes sense to me, y has to be a multiple of 5
Didn't you say it makes sense?
haughty cloak
ahh, and since 5 is prime, y^2 will have prime factors 5 and 25, alongside some others
Totally forgot about that sorry
let me just type this so I can remember it
$$4y^2 = 4(5t)^2$$
woven radishBOT
musava_ribica
haughty cloak
I understand we got a solution x=3 and , well by substituting, y = plus minus 10, but how can I be sure there aren't any other solutions?
finite shore
How did you get x=3?
Sorry. I miscalculated
You may expressions such as 5(x^3+1) = 4(135-y^2) and factorization
haughty cloak
where did 135 come from here?
finite shore
Just a random example. You should consider an example that allows you to factorize both sides. For example, $5(x^3-3^3)=-4(y^2-10^2)$
woven radishBOT
ryker.chen
