x-intercept is the remainder when you plug in y = 0
#help-19
cinder elk
cinder elk
For the x intercept, plug in y = 0 and solve for x
Or you can can solve for x than plug in y = 0
same for the y intercept but solving for y instead
gloomy mason
im sorry i didnt understood this
gloomy mason
yeah
cinder elk
So solve for something you reverse it to solve for a variable
So $6y - 3x = 5$ if you add 5x to both sides you get $6y - 3x + 3x = 5 + 3x$ and the -3x + 3x on the left side cancel out leaving $6y = 5 + 3x$
clever fjordBOT
dragonbreath
cinder elk
Do you know how to "get rid" of transfer the 6 from the left side to the right side
gloomy mason
**dragonbreath**
okayy i got this
gloomy mason
Do you know how to "get rid" of transfer the 6 from the left side to the right s...
divide 6 from both sides ?
cinder elk
Yep!
gloomy mason
im getting y = x+5/2
cinder elk
?
cinder elk
$\frac{3x + 5}{6}$
clever fjordBOT
dragonbreath
cinder elk
$\frac{3x}{6} + \frac{5}{6}$
clever fjordBOT
dragonbreath
cinder elk
Also, sorry if I disappear, it's 3am
gloomy mason
Also, sorry if I disappear, it's 3am
thats very kind of you helping others at this time
gloomy mason
**dragonbreath**
oh
cinder elk
Those two I sent above are equal statements
gloomy mason
im so stupid that i divided 6 with 3x forgetting that they are unlike terms
cinder elk
Well
cinder elk
$\frac{3}{6}x$ is equal to $\frac{3x}{6}$
clever fjordBOT
dragonbreath
vernal yacht
i am getting 1/2 as a slope
incorrrect, the slope shouldn't be positive
odd edgeBOT
@gloomy mason Has your question been resolved?
odd edgeBOT
wild crater
odd edgeBOT
wild crater
then do u do ibp?
mystic saffron
isnt required
the rational expression is broken down into sums of two easy to expressions
that can be integrated directly
4x^2/2x+1 can be written as (2x-1)+ 1/(2x+1)
wild crater
Yeah in that soln I tried u sub
But idk where exactly I went wrong
i;m trying to figure that out first
mystic saffron
x^2 - x +1/2ln|(2x+1)|
u get this with a -3/4 added but it can just be considered a constant
wild crater
oh okay, that's good, so i just picked a tougher method but my math checks out?
mystic saffron
yeah
odd edgeBOT
odd edgeBOT
Available help channel!
sinful grove
!help
odd edgeBOT
To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.
sinful grove
i still need help with question 8
what ive done so far
is
name the centers of the circle C1 C2 C3 from biggest radii to smallest
then the lines C1 C3 and C1 C2
im not sure how to find the radii after?
sorry
typo
question 8
if anyone can help me?
@here?
odd edgeBOT
@sinful grove Has your question been resolved?
odd edgeBOT
@sinful grove Has your question been resolved?
odd edgeBOT
@sinful grove Has your question been resolved?
tacit haven
i got it
tacit haven
use pythagoreom to solve for x
substitue x in x + r2 = 4 and solve for r2
ans: ||r2 = 1||
after that, do the same with drawing C1C3
@sinful grove
tacit haven
feel like ive seen this question before when i was in 6th grade haha
odd edgeBOT
@sinful grove Has your question been resolved?
mystic saffron
this thing is related to Assembly Language Program,
i dont get the solution
i mean its kinda incomplete
can somebody check it ?
please ?
mystic saffron
the first image shows the method that how do we conclude if its even or odd
also ask me fullform of any mnemonics if you dont get it
hollow quarry
also ask me fullform of any mnemonics if you dont get it
RRC is Rotate Right Acculumator, right?
hollow quarry
Yes
You have to consider the decimal representation of a binary number
For example
1011 in base 2 is 2^3 + 2^1 + 1
mystic saffron
mhm
hollow quarry
Everything before the one is a factor of 2
mystic saffron
true
hollow quarry
I'm not familiar with 8085 but you'll just need to figure out instructions are used for comparison
hollow quarry
Branching actually
mystic saffron
cause i have doubt in the JMP code
hollow quarry
can you understand the code till RRC ?
Yeah
hollow quarry
cause i have doubt in the JMP code
I have a tab open right now. I could take a look
mystic saffron
i will deduce what i am confused with;
mystic saffron
so we JUMP to SKIP if there is no carry ( which mean the number is even)
At the SKIP step we increased the H-L counter ( moved to C001H )
and then in the next step me loaded C001H with E ( but here we defined E just two lines above, which was 00h ; which is for odd) but we just loaded E even tho the number is even
@hollow quarry is the SKIP statement limited to that line only? or we have to do all the below lines for it
hollow quarry
Remember, I'm not familiar with 8086 so you'll have explain some things
mystic saffron
sure, ask me
hollow quarry
What's the HL counter?
mystic saffron
Its a register pair
and the the stack is somewhat like this ( the address is different ) sake of illustration
hollow quarry
Could I see the full solution if that's alright?
hollow quarry
and the the stack is somewhat like this ( the address is different ) sake of ill...
Oh okay, that makes more sense. I was a little confused about what were values and addresses
mystic saffron
sadly thats the whole solution given 😦
hollow quarry
Oh I see. Does the question at least specify what addresses/registers to write the output to? Like if it's even, do you write a particular value to a specific register?
mystic saffron
yeah we have to write at C001H
even --> FFH
odd--> 00H
till this line,
on very first line we defined some E register
we have our number from C000H to H-L
then we moved the data ( M is contents of H-L) of H-L to accumulator
then we did RRC
its fine till now
hollow quarry
Ever used the JC instruction?
hollow quarry
till this line,
on very first line we defined some E register
we have our numb...
Alright, I think I understand what comes next
mystic saffron
Ever used the JC instruction?
my first time
i mean i know how it works, but cant really understand stuff goin on here
you can explain to me for more clarity, i might be missing some stuff too
hollow quarry
So JC is essentially a JMP that only makes the jump if the carry = 1
So right after the RRC,
RRC
JC odd_branch
; even stuff here
We'll only jump to the odd_branch if Cy = 1
mystic saffron
yeah i get it
hollow quarry
Within odd_branch, we can store FF H in C001H
Is all that clear? I can elaborate further
mystic saffron
uhm wait a sec lemme think
RRC
JC odd_branch ( this has to be on single line ?? , storing FF H in C001H has to be in one line ?)
; even stuff here
by one line , i mean
it has to be done in one single code ?
here, the guy defined SKIP ( the same as odd_branch you mentioned )
and later on when defining it, it has 1 more line beneath it ?
is it part of SKIP ?
hollow quarry
here, the guy defined SKIP ( the same as odd_branch you mentioned )
and later o...
Tbh, I'm not sure. The formatting is kinda weird. Doesn't matter though. The program will just execute the next instruction after skip anyway
So in a way, it is
mystic saffron
Tbh, I'm not sure. The formatting is kinda weird. Doesn't matter though. The pro...
i see, i think i will just skip this prog. for now and move on
i have about 20 more to go
so i think maybe after doing all of that i will understand it and get used to the notations
mystic saffron
So in a way, it is
mhm say ?
hollow quarry
JNC SKIP ---|
MVI E, 00H |
|
SKIP: <-----|
INC H
MOV M, E
HLT
mhm that might be the case most probably
hollow quarry
I noticed INX isn't an 8086 instruction as well. Seems like a typo
mystic saffron
also notice, we just set E as 00H
and at skip we just used the same value of E ??
mystic saffron
I noticed INX isn't an 8086 instruction as well. Seems like a typo
might be, did not checked
it just changes the value of HL from C000H to C001H ( just increment )
@hollow quarry @hollow quarry dude we just need to know one single thing and the whole question is solved
should i explain ?
JUST FORGET ALL THE CRAP TILL NOW
hollow quarry
Yeah go on
mystic saffron
this is the first line;
we defined some Reg E with value of FFH ( notice that this is answer if the number is even)
this line is just below the JNC line;
we defined it to be 00H
this is second last line;
WHAT value of E should we consider here ? ( the comment says FFH, but we already changed it to 00H just few lines above)
hollow quarry
Right, so it remains FF if Cy = 0
hollow quarry
this is second last line;
WHAT value of E should we consider here ? ( the comme...
I don't understand why we even need that MOV tho
mystic saffron
```
JNC SKIP ---|
MVI E, 00H |
|
SKIP: <-----|
INC H
MOV M,...
Is this like a IF,ELSE statement ?
is MVI E, 00H applied when the carry is there
and
INC H
MOV M, E
HLT
applied when the carry is not there ?
mystic saffron
Is this like a IF,ELSE statement ?
is MVI E, 00H applied when the carry is ther...
prioritize this thing
hollow quarry
Is this like a IF,ELSE statement ?
is MVI E, 00H applied when the carry is ther...
Yeah it's like an if else statement but the structure isn't what you proposed
It's more like
If carry is there: { MVI E 00H }
INC H
MOV M, E
HLT
The stuff in skip will execute unconditionally
But the MVI E 00H is only executed when cy = 1
hollow quarry
Another thing: "MOV M, E" looks like it's the wrong way round
mystic saffron
YOO
thanks
it was just the bad writing way
😭
oh my god
the guy writing these answer maybe just copied the text as it is
hollow quarry
Probably lol
mystic saffron
oof
mystic saffron
Yeah it's like an if else statement but the structure isn't what you proposed
I...
this thing helped
@hollow quarry you are a great guy, even after not having full knowledge of these things
you pulled it off
chad
bye have a great day
hollow quarry
Ahaha you are welcome
mystic saffron
you wanna say smth? or should i just close ?
mystic saffron
?
hollow quarry
The last line "MOV M, E", should that actually be a mov in the first place?
I thought you were meant to write to C001H
But MOV can only read from addresses(and registers) as far as I'm aware
mystic saffron
The last line "MOV M, E", should that actually be a mov in the first place?
yeah it should be mov,
what we did is, we first moved on to C001H ( INX statement )
then M is pointing at C001H only ( because M is contents of HL its the same thing)
when M is at C001H we did the mov thing
hollow quarry
Ohhhh I see
Didn't realise MOV could do that
Well, that's cleared. Thanks and Glad I could help!
mystic saffron
.close
odd edgeBOT
odd edgeBOT
Available help channel!
shrewd sapphire
How would I be able to prove $X(\omega)$ is only defined if $x(t)e^{i\omega t} \to 0$ as $R \to \infty$?
clever fjordBOT
KySquared
shrewd sapphire
I tried integration by parts but that would involve needing either the derivative or the integral of x
odd edgeBOT
@shrewd sapphire Has your question been resolved?
odd edgeBOT
odd edgeBOT
Available help channel!
fallow adder
why/how did we get n*(1/(n-1))?
odd edgeBOT
why/how did we get n*(1/(n-1))?
cold sage
A^2=nA so they replaced A^2 with that
odd edgeBOT
@fallow adder Has your question been resolved?
fallow adder
<@&286206848099549185>
spice geyser
wouldnt it be 2 * A?
thats a 2 by 2 matrix
fact: for a n by n matrix A, A^2=nA
@fallow adder can you try and prove this?
odd edgeBOT
@fallow adder Has your question been resolved?
odd edgeBOT
sand horizon
All good ronaldo
wary helm
For which one
ok
ill fix that
wait thats what i put u just cant see it well cuz of my photo
sand horizon
Oh ye indeed
odd edgeBOT
odd edgeBOT
Available help channel!
delicate kindle
where did i mess up in this question
odd edgeBOT
where did i mess up in this question
delicate kindle
thats what i did
but when i check using a online calculator it gives me
confused on the numerator on how it got that
mystic saffron
please check the first line of your calculation
delicate kindle
did i mess up on the xy inside cos?
used product rule
f(x)*g'(x) + f'(x)g(x)
x1(y') + 1(y)
xy'+y?
delicate kindle
ohh so i cant move that y like that
latent scaffold
Yeah it's just from the chain rule. You multiply cos(xy) by the derivative of xy, which is (xy' + y).
I guess the only difference is that when you move your y to the other side in line 2, you'll be moving y * cos(xy) instead.
delicate kindle
hmm still stuck on how to isolate for y' to give me that numerator
cause now i can only divide no?
factoring out the y'
latent scaffold
It's the same thing you did, but once you distribute the cos(xy) you'll get that y * cos(xy) term.
delicate kindle
ohhh im so dumb
latent scaffold
Then you can bring that to the other side and proceed as you had already done
delicate kindle
i get what your saying, thank you!
odd edgeBOT
@delicate kindle Has your question been resolved?
twin wyvern
odd edgeBOT
twin wyvern
Could someone help me understand the proof of convergence for this
was confused how they got this term using MVT
and g`(c) turns into alpha because it is bounded by 1 right?
wintry cairn
no it turns into alpha because it is bounded by some constant
twin wyvern
no it turns into alpha because it is bounded by some constant
this is the theorem for fixed point
so
wintry cairn
no it turns into alpha because it is bounded by some constant
a continous function on a closed interval has a derivative at all places right
twin wyvern
no it turns into alpha because it is bounded by some constant
how so
wintry cairn
so a derivative in a closed and bounded interval implies a set of derivative values along that interval right
then you can set the max of that to alpha
wintry cairn
no g'(c) is just the derivative of g at c
twin wyvern
yea
wintry cairn
but we know that its bounded by some value
which we can denote as alpha
and note they use a less than equal sign
twin wyvern
but we know that its bounded by some value
which is the highest derivative possible between a and b
wintry cairn
because all g'(c) <= alpha
wintry cairn
which is the highest derivative possible between a and b
yes
twin wyvern
oh that makes sense
twin wyvern
yes
but how did we get to this term
from g(x) - g(x^*)
USING
MVT
oh its f`(c) * b-a = f(b) - f(a)
wintry cairn
the g(x) isnt a big deal. it essentially just mapping a function to the sequence which is relevant since in the next step we care abt the derivative of that function
so if i have a bunch of values a_k, i can just put g(k) = a_k
and use the sequence of g(k)
twin wyvern
the g(x) isnt a big deal. it essentially just mapping a function to the sequence...
what?
wintry cairn
from g(x) - g(x^*)
like you asked how to get to this term right
so imagine x_k is a sequence (i will use a specific case here to build the intuition)
so imagine x_k is a sequence 1,2,3,4,5,6,7,8,9,10 and k=1,2,3,4,5,6,7,8,9,10
s that means x_10 = 10
x_1 = 1
imagine i just make this a function instead, g(k)
so now the sequence x_k is equivalent essentially to the function
in the question x_k is a CONTINUOUS Sequence , so we can build a CONTINUOUS function from it
twin wyvern
in the question x_k is a CONTINUOUS Sequence , so we can build a CONTINUOUS func...
for example here
fixed point convergeswhen g`(x) < 1
which is |x| < 1
so how is hte interval of converges (-1,1)?
shouldnt it be anything less than 1
wintry cairn
no the magnitude of the derivatives have to be less than 1
(a,b) means not incuding a to b
so (-1,1) includes everything in between except -1 and 1 which is good because the magnitudes of those equal 1 which isn't satisfactory
twin wyvern
what?
im lost
in this exmple
in this example
they solved for the inequality
and anything greater than -2 as the initial guess would converge
in this case since g`(x) is = x and x< 1 anything less than 1 as a initial guess should converge
how are they getting -1,1 as interval of convergence
wintry cairn
because anything above -2 makes the value of 2x+5 bigger than 1
wintry cairn
opposite
the derivative function is x
so anything between -1 and 1 (exclusive) makes it <1
thus convergent
wintry cairn
no its not anything
twin wyvern
which is (-inf, 1)
twin wyvern
so anything between -1 and 1 (exclusive) makes it <1
how are u getting this
im so lost
wintry cairn
because the derivative function g'(x) is x right
i want u to go step by step so say yes/no after every line
wintry cairn
because the derivative function g'(x) is x right
so yes/no ?
twin wyvern
yes
wintry cairn
now we get that it converges if the absolute value of the derivative function is less than 1 right
twin wyvern
yes
wintry cairn
imp distinction its not actually the derivative function, its the ABS VALUE of the derivative function
which implies the MAGNITUDE of the derivative function is less than 1
so now in what case is the absolute value of x less than 1 ?
what values can x be ?
twin wyvern
which implies the MAGNITUDE of the derivative function is less than 1
oh so the distance of the convergence cannot be greater than 1?
wintry cairn
i dont know what you mean by distance of convergence
twin wyvern
imp distinction its not actually the derivative function, its the ABS VALUE of t...
im nto sure what your trying to say here
yea the abs value of the derivative
|x|<1
wintry cairn
yea so it has to be less than 1
twin wyvern
x can be negative or positive
wintry cairn
yea
twin wyvern
and less than 1
twin wyvern
yeah so (-inf,1)
wintry cairn
no
twin wyvern
How is it bounded by -1
wintry cairn
-2 for example makes |x| >1
wintry cairn
How is it bounded by -1
we take the absolute value
wintry cairn
it all depends on the derivative function
wintry cairn
because we need abs value of this as well
well they square it anyways
wintry cairn
ohh okok
wintry cairn
i mean just do -1 / sqrt(27 - 2x) = -1 and -1 / sqrt(27 - 2x) = 1 and ull find the two cases
u can put it in desmos to just see without solving
in this case it actually doesnt matter cuz the sqrt is always positive no matter what
twin wyvern
i mean just do -1 / sqrt(27 - 2x) = -1 and -1 / sqrt(27 - 2x) = 1 and ull find ...
why -1 and 1
should we be looking at x
wintry cairn
why -1 and 1
those are the bounds of the derivative function
twin wyvern
those are the bounds of the derivative function
i see
and did u understood what 13.5 represented
like why did they do this
27-2x > 0
wintry cairn
cuz u have to make the sqrt positive
cuz if its negative ur gonna get an undefined
so they get that bound also
wintry cairn
so our initial guess can be between less than 13 then?
so in this case we have two conditions
- x < 13.5 ( This implies the sqrt function is positive)
- x < 13 (implies derivative function magnitude < 1)
this just amounts to x<13 cuz the first one becomes redundant
twin wyvern
so in this case we have two conditions
1) x < 13.5 ( This implies the sqrt func...
yea ok
thanks
👍
wintry cairn
yea nw
sinful cloud
I need help
odd edgeBOT
I need help
odd edgeBOT
@sinful cloud Has your question been resolved?
odd edgeBOT
@sinful cloud Has your question been resolved?
iron mist
What is your question?
You are going to need to write a concept to write the example it seems
0 clue as to what u r asking tbh
odd edgeBOT
@sinful cloud Has your question been resolved?
sinful cloud
I don’t know how to write the example lol
odd edgeBOT
odd edgeBOT
Available help channel!
blazing tulip
Good evening everyone, I want to ask about geometric sequence/series.
The question goes by:
Every year, the percentage of growth in a population never changes since 2000 until 2012. The total number of population in 2000 is A people and in 2012, B people.
What is the total number of population in the year 2003?
a. Sqrt(A sqrt(B))
b. A sqrt(B)
c. B sqrt(A)
d. Sqrt(AB)
e. sqrt(A sqrt(AB))
blazing tulip
I tried finding the ratio but I got root in 12 (or basically the fraction to the power of 1/12).
I tried manipulating, but to no avail
dawn tiger
let's say the growth rate is some constant r
then in 2000, there are A people, and in 2012, there are Ar^12 people, so Ar^12 = B
then r = (B/A)^(1/12)
you got up to this point?
blazing tulip
Yup
dawn tiger
How do you got Ar^12?
you multiply by r for each year
2012 is 12 years after 2000
now that you've found r in terms of A and B, you can substitute that into Ar^3 to find the population in 2003
so if you simplify A ((B/A)^(1/12))^3, you'll get your answer
blazing tulip
so if you simplify A ((B/A)^(1/12))^3, you'll get your answer
I see. Thank you
Turns out i used the sum of terms instead of to find the term
odd edgeBOT
@blazing tulip Has your question been resolved?
odd edgeBOT
pastel orbit
odd edgeBOT
Available help channel!
somber jackal
what's f(x, y) in the context of a DE? here f(x, y) = y' obviously but i dunno if that's always true or
somber jackal
also what's a unique solution? only one valid value of $c$ in, say, $f(x, y) = ce^x$ or whatever the general solution is?
clever fjordBOT
b
latent scaffold
what's f(x, y) in the context of a DE? here f(x, y) = y' obviously but i dunno i...
This is just what the Existence and Uniqueness theorem tells you.
If you have a DE of the form y' = f(x,y), then if f and df/dy are both continuous on a region, a point (x,y) in that region will yield a unique solution. So yes, your DE has to be of the form y' = f(x,y), but I don't think there are common cases where it's not possible to write it in this way.
And by unique solution, your interpretation is essentially right. When functions are nice enough, the solutions should essentially not "cross" each other. This is desirable because for instance, when modelling physical phenomena, we don't want multiple different models for a given initial value.
odd edgeBOT
odd edgeBOT
Available help channel!
slow cosmos
Help!
slow cosmos
How did dh become 0.08. I think dh is 0.04
bitter lodge
How did dh become 0.08. I think dh is 0.04
a tin can will have a sheet at the top and also the bottom
each of which is 0.04 thick
slow cosmos
a tin can will have a sheet at the top and also the bottom
I get that part, shouldnt that double the derivative of the radius instead?
Since there's two tops of which the radii are a part of them?
bitter lodge
theres no derivate going on here
slow cosmos
Yeah I know its just the dr dh, I meant should dr be 0.08
bitter lodge
dh is just another variable like h thats being used to represent the small increase in h
tacit haven
Yeah I know its just the dr dh, I meant should dr be 0.08
wouldnt that be the diameter?
bitter lodge
I get that part, shouldnt that double the derivative of the radius instead?
why should it effect the radius
slow cosmos
wouldnt that be the diameter?
Yeah but in the formulas for cylinder we don't use diameters
slow cosmos
why should it effect the radius
Because wouldn't there be two pieces that have diameter instead of one?
Because the height is the side of the walls of the tin can going up no?
Why does having two tops double the thickness of the walls?
bitter lodge
let me draw a diagram, maybe that will help
slow cosmos
okok
bitter lodge
i think youre just getting mixed up
this would be a top down view
do you see how the radius only goes through one layer of tin
and this would be a cross-section down the middle of the can
it goes through two layers of tin
bitter lodge
nws
odd edgeBOT
Available help channel!
outer abyss
my question is why (-2)^2 is 4 and (-2)^3 is -3
odd edgeBOT
my question is why `(-2)^2` is 4 and `(-2)^3` is -3
frigid canopy
$(-2)^3 \neq -3$
clever fjordBOT
🏳🌈f(why am i here )= idk
outer abyss
hmm
outer abyss
oh wait i meant -8
merry finch
well -2 * -2 is 4
outer abyss
i put 3 by mistake
merry finch
times -2 again you get -8
outer abyss
oh yeah, didnt know why i didnt get that 😅, must be tiredness, thanks for the info!
.close
odd edgeBOT
odd edgeBOT
Available help channel!
cunning dust
just started matrices, is it hard or na, any tips or things that i should look out for?
cunning dust
What all do you know?
well we literally JUST started today
and we got up to uh
multiplying them
frigid canopy
Uh, That's all I learnt at school too 
. DO you have more than that in your course?
cunning dust
Uh, That's all I learnt at school too <:opencry:586078614865444865> . DO you hav...
no idea
but looking ahead in my powerpoint
frigid canopy
Like is this a uni course?
frigid canopy
If that's the case, I can't help as I'm starting uni myself in a few days
frigid canopy
we got identity matrix, inverse matrix
Ah, I can help with that.
cunning dust
cunning dust
oh okay sweet
i wasnt looking to do much right now cause its late
and i need to sleep
but yeah
is there anything in particular that i should look out for
like any common mistakes
frigid canopy
Computing the inverse of a 3 by 3 matrix by hand is tedious
You can easily make mistakes!
Be careful!
cunning dust
mmm okok so just be extra careful with calculations
got it
ill head to sleep and prob work tomorrow
so prob expect to see me here in the coming weeks
got exams soon so yeah haha
thank you
.close
odd edgeBOT
narrow holly
can i ask u bro
how to i find the domain, sound stupid question but rly need ur help ty @cunning dust
narrow holly
try <#908078493655502919>
oke
odd edgeBOT
Available help channel!
fast edge
odd edgeBOT
ivory dock
,rotate
clever fjordBOT
fast edge
yeah so, the length of the interval is not pi/2 right?
marble cobalt
yeah so, the length of the interval is not pi/2 right?
if i am correct, from my understanding it is slight greater/lesser than pi/2
fast edge
if i am correct, from my understanding it is slight greater/lesser than pi/2
lesser if my im correct
so the answer must be D?
odd edgeBOT
marble cobalt
No problem
urban rose
No problem
the pythogras theorem should apply here, right? its closely related
marble cobalt
the pythogras theorem should apply here, right? its closely related
i dont get your thinking; might i ask why?
urban rose
i dont get your thinking; might i ask why?
I am thinking based on a cartian system here so yeah
those are cords right in the assertion yeah? so yeah
marble cobalt
how to i find the domain, sound stupid question but rly need ur help ty <@800520...
i) All real values
ii) All real values except 5/2
iii) All real values
iv) All real values except negative numbers
v) Try urself 🙂
marble cobalt
those are cords right in the assertion yeah? so yeah
gimme a second lemme think
urban rose
gimme a second lemme think
its interesting, lets talk bout it in dms, leave here
marble cobalt
how do i dm ya?
odd edgeBOT
Available help channel!
sinful salmon
I wish to prove the transformation law for the Riemann curvature tensor using the Christoffel Symbol definition of the components. I am able to expand the left hand side into a bunch of terms (I don't know if I did this correctly), but I am unable to find a way to cancel most of them. Can I have help here? (Levi-Civita Connection assumed)
rose radish
what fuckin language is this
coarse sigil
Lol
odd edgeBOT
@sinful salmon Has your question been resolved?
odd edgeBOT
@sinful salmon Has your question been resolved?
odd edgeBOT
@sinful salmon Has your question been resolved?
shy patio
silly and quick question about logarithms
odd edgeBOT
silly and quick question about logarithms
zinc glacier
6 is correct
odd edgeBOT
zinc glacier
youre welcome
odd edgeBOT
Available help channel!
hot rain
hello this is a physics question but has a math side
how do i calculate this output like this 10^7
unkempt condor
hello this is a physics question but has a math side
how do i calculate this ou...
Bro, how arw you calculating stress and not know what simplification is?
Basically this number is same as45600000 N/m2, but that would be funny and unpractical to write, so you move the decimal point for 7 places therefor 10^7
hot rain
why 7?
unkempt condor
Because thw number is that big?
hot rain
i mean i could let it be 6
45.6
unkempt condor
You could write is in 0.456 x 10^8 form
unkempt condor
i mean i could let it be 6
45.6
Yes
hot rain
oh so it odnes't matter
unkempt condor
Doesnt matter
hot rain
alright thank you
unkempt condor
You can also have MN, mega newtons which would be 10^6
So 45.6 MN / m^2
Without the 10^x
mossy ruin
odd edgeBOT
tepid pelican
this triangle is congruent by AAS
Why angle angle side?
What 2 angles are surely equal?
it might not be inherently wrong, because you could prove 2 of the angles (other than the right ones) to be equal
but there is definitely a simpler approach
note that the triangles also share 1 side, and hence that one shared side must be same for both of them
odd edgeBOT
@mossy ruin Has your question been resolved?
odd edgeBOT
odd edgeBOT
Available help channel!
still egret
I came up with a series that diverges at all rational numbers but I don't know to check it for other arguments:
$\sum_{k\ge1}e^{-\pi k^2}\cot k\pi z$
clever fjordBOT
MCAntDJC
I came up with a series that diverges at all rational numbers but I don't know to check it for other arguments:
$\sum_{k\ge1}e^{-\pi k^2}\cot k\pi z$
mystic saffron
the problem is that if z is rational, then for a large enough integer k, the term (k pi z) is a multiple of pi, which makes cot undefined
still egret
I know, but I want to find other values that make the series diverge
ember oak
I came up with a series that diverges at all rational numbers but I don't know t...
the series doesn't diverge. It's undefined.
There's a difference
still egret
Is it undefined when $z$ is imaginary?
clever fjordBOT
MCAntDJC
mystic saffron
didn't check that, but my suspicion is that when z is purely imaginary it might converge.
still egret
It should because then $\cot k\pi z$ will approach $i\operatorname{sgn} z$ as $k\to\infty$, so the Gaussian factor will overpower it
clever fjordBOT
MCAntDJC
odd edgeBOT
@still egret Has your question been resolved?
odd edgeBOT
@still egret Has your question been resolved?
still egret
Is checking for absolute convergence enough here?
odd edgeBOT
@still egret Has your question been resolved?
odd edgeBOT
@still egret Has your question been resolved?
still egret
If $z$ has an imaginary part, then the summands' denominators can never vanish, and will have about the same magnitude as $e^{-\pi k^2}\tanh 2k\pi y$; thus the series can diverge only on the real line.
clever fjordBOT
MCAntDJC
split gyro
Ok
odd edgeBOT
@still egret Has your question been resolved?
odd edgeBOT
@still egret Has your question been resolved?
odd edgeBOT
@still egret Has your question been resolved?
still egret
No
tidal jewel
.close
faint knot
if your question isnt a standard textbook question, or involves math at calculus or above, there isnt much of a chance that someone can answer the question you asked
you can cheat by using a function that can get you a major step of the way there https://en.wikipedia.org/wiki/Dirichlet_function
tidal jewel
The question's been neglected and I've no hope nor means to answer it myself
what type of math is this? Nobody can solve it lmao
still egret
what type of math is this? Nobody can solve it lmao
I'm not sure—maybe calculus/real analysis? (I'm definitely not versed in the latter)
still egret
Of all the math problems or questions I've thought to post in this server, the one here's the easiest to describe...
I've also wanted to ask about residues of a squared hyperbolic series.
tidal jewel
you should try gohar's guide
its a good math server too
in the math chat type !calculus
onyx badge
Is gohar that tik tok guy?
split gyro
What
faint knot
@still egret if youre really out of options, $\sum_{k=1}^\infty\mathbf{1}_{\mathbb{Q}}(x)$ can work as a very uninteresting series that only diverges for real rational numbers
clever fjordBOT
mtt
faint knot
along with $\sum_{k=1}^\infty\mathbf{1}_{\mathbb{Z}}(kx)$
clever fjordBOT
mtt
meager juniper
Is the point to try to find a parametric series that diverges for rational values but converges for irrational values of k, or a series that diverges for any value of k, rational or irrational?
Or to simply check if the series given in the original post converges or diverges for any specific irrational value of k?
If the latter, because k is irrational it will never hit the undefined values, but it can get arbitrarily close to them, meaning the tan argument can get arbitrarily large. Because tan can be written in terms of the exponential function, and turns out to be roughly linear in the exponential function, whereas the gaussian is negative quadratic, we have a summation that is roughly exponentially decaying but will rarely have "spikes" where there is a near miss, but these "spikes" are also suppressed by the exponential decay. So intuitively I think it would be absolutely convergent; however, actually proving it is a little tricky. Remind me to revisit this maybe Sunday or Monday when I have a little more time.
meager juniper
This Michael Penn video seems germane, and might have an application here for proving this proposition. https://youtube.com/watch?v=OFQ959ZNh_A
split gyro
This Michael Penn video seems germane, and might have an application here for pr...
How to find the sum of this converging series
cosec(n)/n!
I guess we need to plug cosec n in maclaurin series of some f(n)
clever fjordBOT
split gyro
,w maclaurian expansion of e^(cosecx)
clever fjordBOT
split gyro
,w maclaurin expansion of e^(cosecx)
clever fjordBOT
clever fjordBOT
odd edgeBOT
@still egret Has your question been resolved?
meager juniper
@still egret did my previous post help at all? Did you follow along with the proof in the video?
It should be straightforward to adapt that proof to your case
meager juniper
First, we define the irrationality measure. I'll omit it inline, but you can get it from Mathworld and I'll be using the terminology within this page.
We choose z to be an irrational number. If the irrationality measure of z is not infinite, then there is some positive integer exponent n >= mu(z) such that there are only finitely many exceptions to inequality given in the mathworld link. Thus we have that the sum is less than sum exp(-pi k^2) cos(k pi z) (k pi)^n, which is clearly convergent.
If the irrationality measure is infinite (and z is a Liouville number), then this is not conclusive.
@still egret
I don't know how to handle the case where z is a Liouville number though
odd edgeBOT
@still egret Has your question been resolved?
still egret
I don't know how to handle the case where z is a Liouville number though
Perhaps it diverges at those numbers...
I suspect there can always exist a real number whose multiples approximate $\pi$ so precisely their cotangents cannot be bounded, even by, say, $k!^{-((k^2)!)!^{k^k}}$
clever fjordBOT
MCAntDJC
meager juniper
Perhaps it diverges at those numbers...
I suspect there can always exist a real...
Undoubtedly some Liouville numbers diverge, but some converge, as they are overwhelmed by the gaussian factor. The problem is distinguishing the two
odd edgeBOT
odd edgeBOT
Available help channel!
ebon forge
How can I set up a function to calculate the probability P of receiving M items in a set of N with T trials. I think this should be some variant of the coupon collector's problem after some quick research, but I'm not good with statistics so I'm unsure exactly what the differences are between all the listed functions. I'm mainly just trying to set it up as a P = f(M,N,T) function for simple visualization purposes for a gacha game.
odd edgeBOT
How can I set up a function to calculate the probability P of receiving M items ...
@ebon forge Has your question been resolved?
odd edgeBOT
@ebon forge Has your question been resolved?
static totem
@ebon forgeyou mean it's like dice rolls, each one equally likely?
ebon forge
That's effectively the same, yes.
So in this example, the odds P of receiving at least one 1, 2, 3, 4, 5, and 6 out of T trials (with a given set of N = 6 and M = 6 in this example).
static totem
e.g. t=11
it's called stirling number of the second kind, how many ways to group 11 things in 6 non empty groups
times 6! to pick which items are those
or 6p4 if M=4
ebon forge
So which variable would be replaced with M in the format of S2(T,N) * N! / N^T in that formula?
static totem
S2(T,M) * P(N,M) / N^T
wolfram understands P() but not in this context, i can't imagine why
ebon forge
Go figure. Out of curiosity, what is the P() referring to here?
ebon forge
Gotcha. So P(N,M) is a factorial of N for M terms?
static totem
yes
ebon forge
Alright, thanks! I think that answers the question! Now I just have to figure out a program capable of graphing it since desmos doesn't seem to support S or P at a quick test...
.close
odd edgeBOT
odd edgeBOT
Available help channel!
mystic saffron
hello, can someone help me
odd edgeBOT
hello, can someone help me
lament urchin
U need to send the question
compact edge
Real
fossil hawk
hello, can someone help me
What a profound question 
odd edgeBOT
@mystic saffron Has your question been resolved?
mystic saffron
yes, i'm going to send it
compact edge
yes, i'm going to send it
mystic saffron
it is allowed to send a picture of the exercise?
compact edge
Yes
warped badger
this please
Alright, what are you stuck at?
warped badger
Let's see
First off, suppose S is the sample space set, then P(S)=1
P(S) also equals the sum of the probabilities of all the other events(assuming their intersection is null, that is to say, that they're incompatible events)
Since you're not given much more info here, we'll suppose that
warped badger
P(S) also equals the sum of the probabilities of all the other events(assuming t...
With this you should be able to tackle the first question
warped badger
In general, for the other two questions, let S={a1,a2,...an}be a composite event such that P(S)=k≤1 and such that P(ai∩ak)=0, for all i and k, then P(s)=P(a1)+P(a2)+...+P(an)=k≤1
warped badger
Np
odd edgeBOT
@mystic saffron Has your question been resolved?
odd edgeBOT
odd edgeBOT
Available help channel!
kind bane
How do I do this question I’m stuck I spent 15 minutes on it scratching my head I got that far and I’m just stuck I tried graphing both and seeing the solutions but I can’t do anything about it as I can’t reverse engineer the process and stuff
kind bane
Sure
dense moth
So we will first form the equation
Whose roots are 4 times the root of yours
Can you do that ?
dense moth
Wdym is it a polynomial w degree 8
Nah i mean
If one root is a then it will become 4a
kind bane
Isn’t that just horizontally stretching it by 4
dense moth
The term with x³ with 4 , the next term with 4² the next with 4³ like that
Wait
Multiplying by 2 works
So increase all roots twice
Bro
kind bane
Multiplying by 2 works
How
dense moth
Just wanted to ask , do you know Ferraris or Descartes method ?
kind bane
Just wanted to ask , do you know Ferraris or Descartes method ?
No
What’s Descartes method
dense moth
Ok so what we will be following is Ferraris
dense moth
What’s Descartes method
That's a method to solve biquadratics or quartics
kind bane
That's a method to solve biquadratics or quartics
Ty
dense moth
So
First generate equation with all roots multiplied by 2
Can you observe why we multiply x³ term with 2 ,x² term with 2² and so on?
kind bane
So I multiply x^3 w 2 x^2 w 4 and so one
dense moth
Can you get why?
kind bane
First generate equation with all roots multiplied by 2
If I multiply by just 2 the roots will stay the same
And I can factor out 2
dense moth
If I multiply by just 2 the roots will stay the same
nah
kind bane
Only 2 not powersbif 2
dense moth
We want the equation where all roots are two times the initial
kind bane
Powers of
dense moth
So in biquadratics
If four roots are a,b,c,d the eqn is of the form
X⁴-(a+b+c+d)x³ + (summation(ab))x² ...
dense moth
How do I do this question I’m stuck I spent 15 minutes on it scratching my head ...
Hey wait , do you want an easy way?
kind bane
X⁴-(a+b+c+d)x³ + (summation(ab))x² ...
Oh I was doing the same thing with quadratcs
dense moth
What level are you ?
kind bane
What level are you ?
11th grade IB
dense moth
Can you divide the polynomial with factor (x-1)
kind bane
?
kind bane
Can you divide the polynomial with factor (x-1)
Yea
dense moth
Can you divide the polynomial with factor (x-1)
?
kind bane
Easy
dense moth
And with (x+2)
thorn fractal
(Cant you just / x^2 ) ?
dense moth
After dividing you re left with a quadratic
kind bane
(Cant you just / x^2 ) ?
U can’t
dense moth
(Cant you just / x^2 ) ?
It's not symmetric
kind bane
Cus there is x and constant term as well
dense moth
Cus there is x and constant term as well
Constant term won't matter if it were symmetric
kind bane
Constant term won't matter if it were symmetric
Oh
dense moth
If it were symmetric
We could have considered
x+1/x or x-1/x as z
Then our equation would reduce to a quadratic
kind bane
If it were symmetric
Symmetrical to what, y axis
dense moth
Symmetrical to what, y axis
Nah x³ + 3x² +3x + 1 = 0 is a symmetric eqn
The terms from starting and ending terms will have same coefficient
kind bane
That’s (x+1)^3
kind bane
That’s (x+1)^3
Binomial theorem coming in clutch
kind bane
Is symmetric
Oh it’s just palindromic
thorn fractal
he means like if it made a nice number like this
/x^2 = x^2 +6/x^2 +x -1/x -4
Bc then u can say
(x^2 +6/x^2) +(x -1/x ) -4
and then
a = x +1/x
so a^2 + a - 4
kind bane
he means like if it made a nice number like this
/x^2 = x^2 +...
Oh Ty that clears it up
dense moth
🥲
dense moth
A symmetric eqn of odd degree will always have root either +1 or -1 or both
dense moth
This is a symmetric
dense moth
Yeah
dense moth
Fine do it you will get the answer
kind bane
Ik
kind bane
Fine do it you will get the answer
Is there a better method
dense moth
Is there a better method
"When I used the word "long" there must be short "
Both are same actually , just writing diff ways
kind bane
"When I used the word "long" there must be short "
Yea I always wondered that what is short division
kind bane
We actually only write coefficients in the short method
Doesn’t seem very short
dense moth
Doesn’t seem very short
Nah it is
kind bane
Ok then
dense moth
You from India?
dense moth
NEET or JEE ?
kind bane
NEET or JEE ?
Neither I’m doing IB
kind bane
International baccalaureate
dense moth
Oh good
kind bane
You from India?
Wbu
dense moth
I'm currently in engineering nd mathematics
dense moth
Cool 🙂
kind bane
X=-2
clever fjordBOT
dense moth
These ?
kind bane
Yea
dense moth
Any higher degree polynomial with real coefficients can be expressed, in linear and quadratic factors with real coefficients
kind bane
And remainder
kind bane
No u can add remainder as well
dense moth
No u can add remainder as well
Oh well
kind bane
Like not every polynomial can be factored into integer coefficients
Polynomials
With lower degree
dense moth
Yeah not integer coefficients, but real coefficients
Let me give you some insight on quadratic
clever fjordBOT
dense moth
So our eqn becomes x²-4 = 0
kind bane
We reduce both roots by 6
Wdym reduce
dense moth
Wdym reduce
I mean if 4 and 8 are two roots , we will do 4-6 and 8-6
kind bane
Oh ok
dense moth
Let's consider a quadratic , x²-12x +32 = 0
This is because the form is x²-(a+b)x + c = 0
There is a specific method on continuous polynomial division to do this sorcery of reducing all roots by certain value
If we could reduce the roots , and vanish the x term
The eqn becomes , x² = k
Or x = ±k
kind bane
The eqn becomes , x² = k
Then just take sqrt
kind bane
Yea
dense moth
Now you know another method of solving quadratic
If this were a cubic we could have vanished the x² term
And get another equation what we call a depressed cubic, which could be solved
kind bane
Other than factoring completing the square and formula
dense moth
Other than factoring completing the square and formula
Yeah !
dense moth
You will later learn about all this stuff !
dense moth
A depressed cubic is just a cubic without x^2
Without x²
kind bane
Ah I didn't watch
Discovery of complex numbers
kind bane
Ok bro byee !
Byee
odd edgeBOT
@kind bane Has your question been resolved?
odd edgeBOT
odd edgeBOT
Available help channel!
tacit haven
Find the sum of the squares of all the roots of x^2 - 8floor(x) + 9
tacit haven
is there a way to solve this without guessing?
put it into desmos and it looks very messy
odd edgeBOT
@tacit haven Has your question been resolved?
nocturne belfry
Find the sum of the squares of all the roots of x^2 - 8floor(x) + 9
just a thought but could you solve this like
$\frac{x^2+9}{8} = n$
clever fjordBOT
jan Niku
nocturne belfry
youll have some collection of solutions here
tacit haven
what’s n?
nocturne belfry
just some number
tacit haven
oh
nocturne belfry
floor(x) looks like the graph of n
or, whatever, you know what i mean
this will give you a lot of solutions
but you know that you can bound them between the roots of just $x^2-8x+9$
tacit haven
could you give an example?
clever fjordBOT
jan Niku
