Oh thank god, thanks.
#help-13
fluid rivet
hollow minnow
After writing down all that you can work backward
fluid rivet
Oh dw I've done this before but for some reason I had a brainfart moment where I forgot how to calculate the remainder for the first part of the euclidean theorim and I couldn't remember for the life me. Thanks for the save!
hollow minnow
cedar kilnBOT
cedar kilnBOT
Available help channel!
ionic finch
cedar kilnBOT
ionic finch
How did they arrive from one equality to other?
I understood 0<=a+b<=2n-2
as the maximum we have is n-1, thus n-1+n-1= 2n-2
but 2n-2 is also equivalent to n-2 mod n, not n-1
Essentially my question is, does first inequality imply other?
<@&286206848099549185>
mental trail
but 2n-2 is also equivalent to n-2 mod n, not n-1
n-2 <= n-1
either a+b <= n-1 and we're done
or a+b > n-1, which means a+b-n <= n-2 <= n-1
ionic finch
Oh, makes sense,
n-1 already belong to Zn, now we see how big can a+b get
a+b<=n-2, and clearly it’s less than n-1 in modulo
like that?
mental trail
a+b<=n-2, and clearly it’s less than n-1 in modulo
$a+b$ is not $\leq n-2$, it's $a+_n b\leq n-2$ as soon as $a+b \geq n$
wraith daggerBOT
rafilou2003
ionic finch
I mean if I do usual addition i get something less than 2n-2, taking modulo of it is less than n-2<n-1
@mental trail
potent saffron
are u guys good at pre algebra
cedar kilnBOT
are u guys good at pre algebra
glass horizon
hes not good at pre algebra i think
glass horizon
im not good either
drifting marlin
are u guys good at pre algebra
!da2a
cedar kilnBOT
are u guys good at pre algebra
No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/
sly pier
wtf is that
u have the chess tag?
umbral dew
are u guys good at pre algebra
either just ask ur question or close the channel dude
sly pier
are u guys good at pre algebra
what's ur question
potent saffron
hollow minnow
You know y=mx + c
umbral dew
!status
cedar kilnBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
ok
spare plaza
can you guys tell me wht u guys are discussing
hollow minnow
this is a help channel. Read #❓how-to-get-help
spare plaza
no like is this where i get or help smn (cuz i would like to help someone)
hollow minnow
You can help someone yes
spare plaza
oh cool
cedar kilnBOT
cedar kilnBOT
Available help channel!
gusty grove
cedar kilnBOT
gusty grove
i need help
digital cliff
definitely not right
im not sure how you did that
but i can say youre overcomplicating it
gusty grove
yea ik, i was trying like everything
digital cliff
are you aware that $\left(\frac{p}{q}\right)^{-1}=\frac{q}{p}$
wraith daggerBOT
AℤØ
gusty grove
i tried to make the base equal
digital cliff
you just need to do that to one of them and youll have the same base
gusty grove
thats wat i was tryna do inna way
gusty grove
nvm, im high
lol no worries
digital cliff
the exponent isnt across everything, at least i think its not, so that wont work
gusty grove
i moved the right hand side to left, so i can get base q, then i tried to make the powers equal
digital cliff
i can see how one could get $p^{2m+3}=q^{10-m}$
wraith daggerBOT
AℤØ
digital cliff
how did you get this first bit
digital cliff
so you subtracted?
gusty grove
i tried to make the base equal
digital cliff
you mean a common denominator?
gusty grove
yes
digital cliff
youd have to multiply the right fraction by q^{m-8} or multiply the left fraction by q^{8-m}
you wouldnt get what you did
gusty grove
i dont get it >_<
digital cliff
$\frac{p^{2m+2}\cdot q^{m-8} - p}{q}=0$
wraith daggerBOT
AℤØ
digital cliff
were you given any information beyond whats there
digital cliff
honestly im suspicious
gusty grove
my first time doing a sum like this
digital cliff
im not entirely certain you can get the answer unless the exponent is across the entire fraction
gimme a min
gusty grove
am i missing a formula or something for this ?
gusty grove
im not entirely certain you can get the answer unless the exponent is across the...
yea
digital cliff
yeah, if its not, then the value of m would have to be in terms of p and q
so its either none of the above, if its intentional
or its one of the others if not
gusty grove
oh okay
i might try this in primal mode too lol
ill try putting numbers to variables and see if i can go anywhere
Thanks alot tho for ur time
digital cliff
np
if you do it as being over the whole fraction, you do get one of the numbers there btw
cedar kilnBOT
@crimson sedge Has your question been resolved?
cedar kilnBOT
@crimson sedge Has your question been resolved?
cedar kilnBOT
@crimson sedge Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
crimson sedge
X^2-ax-bx-abx how to simplify
cedar kilnBOT
X^2-ax-bx-abx how to simplify
versed fulcrum
What are the common factors?
cedar kilnBOT
@crimson sedge Has your question been resolved?
crimson sedge
x*2-ax-bx+abx
cedar kilnBOT
x*2-ax-bx+abx
versed fulcrum
!status
cedar kilnBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
livid hound
also did you mean x^2?
cedar kilnBOT
@crimson sedge Has your question been resolved?
crimson sedge
What is the question
Yeah
Sorry I didn’t give enough info but yeah I need factoring
crimson sedge
also did you mean x^2?
Yeah
livid hound
first thing to do would be to identify if all terms have a common factor
long belfry
cedar kilnBOT
long belfry
A bag contains 3 red, 4 blue and some black balls. If probability of drawing
blue ball is - , then number of black balls in the bag is
tidal zodiac
try drawing a graph, or using a tool like desmos.com/calculator to aid with finding the solution.
long belfry
oki
cedar kilnBOT
@long belfry Has your question been resolved?
long belfry
<@837000127239028776> Has your question been resolved?
which one
only one has been resolved blud
crimson sedge
first thing to do would be to identify if all terms have a common factor
The question is factoring as is the question does not have anymore info
livid hound
yes, and what i said is the first step in approaching the task
cedar kilnBOT
@crimson sedge Has your question been resolved?
crimson sedge
yes, and what i said is the first step in approaching the task
They have x as a common factor but after that I don’t see any progress
crimson sedge
It becomes x(x-a-b-ab)
opal basin
x^2 - ax - bx + ab, right?
opal basin
It becomes x(x-a-b-ab)
If so, then this is wrong
because ab doesn't have a factor of x
cedar kilnBOT
@crimson sedge Has your question been resolved?
livid hound
original had an x unless that was a typo
quaint skiff
Hi. I need help with this limit please. I tried to do it by factorising with x and x^2, but it doesn’t seem to work. Thank you
tired mirage
Do you know L'Hôpital's?
quaint skiff
Do you know L'Hôpital's?
Yes but we’re not allowed to use it in this exercice
tired mirage
tried dividing by x^2?
quaint skiff
tried dividing by x^2?
No, how can I do it?
tired mirage
you divide both the numerator and denominator with x^2, equivalently this can be stated as multiply the numerator and denominator with 1/x^2
quaint skiff
you divide both the numerator and denominator with x^2, equivalently this can be...
Ok thx, I’ll try it rn
cedar kilnBOT
@quaint skiff Has your question been resolved?
quaint skiff
you divide both the numerator and denominator with x^2, equivalently this can be...
Is that allowed? lol
I tried to do it by substitution. X=1/x
quaint skiff
<@&286206848099549185>
tired mirage
can you send the picture rotated? 😇
quaint skiff
Is that allowed? lol
quaint skiff
can you send the picture rotated? 😇
Here it is
tired mirage
you didnt substitute it completely, since still have x-> 0-, it should now be x-> -inf
and what happened here?
quaint skiff
you didnt substitute it completely, since still have x-> 0-, it should now be x-...
Oh yeah I see
quaint skiff
and what happened here?
I wanted to proof that lim (-X^2)*e^X=0
tired mirage
ah
quaint skiff
I wanted to proof that lim (-X^2)*e^X=0
Which then allows us to conclude that lim X-X^2*e^X=-inf
tired mirage
yes since (-inf)^2 vs e^-inf we have e^-inf wins making that 0 and we then have -inf-0
quaint skiff
you didnt substitute it completely, since still have x-> 0-, it should now be x-...
The thing is I took it into consideration, but failed to write it
quaint skiff
yes since (-inf)^2 vs e^-inf we have e^-inf wins making that 0 and we then have ...
Exactly
tired mirage
well, then you are gotten to the goal!
quaint skiff
well, then you are gotten to the goal!
Thanks a lot
tired mirage
Have good day!
quaint skiff
You are very kind and helpful
quaint skiff
Have good day!
Thx, to u too
tired mirage
remember .close
quaint skiff
.close
teal geyser
$y = e^{-\sqrt{\abs{ln(\abs{ln(\abs{x})})}}}$ has minima and maxima along the asymptotes of $y'$ instead of roots (there aren't any). Why?
wraith daggerBOT
7aman
cedar kilnBOT
@teal geyser Has your question been resolved?
white latch
Uhhhhhhhh there are no roots in the function
as eulers number itself can never equal 0
I think you meant critical points.
There are no critical points in our case.
specifically for when the derivative is 0 there are no critical points on our function
but for the sections where the derivative does not exist (the vertical asymptotes)
peak relic
$y = e^{-\sqrt{\abs{ln(\abs{ln(\abs{x})})}}}$ has minima and maxima along the as...
Maxima and minima usually happen at points where the derivative is 0, but they can also happen at points where the derivative jumps PAST 0, whether with a jump discontinuity or a vertical asymptote.
For example, |x| (in red) has a minimum at 0, and in the derivative (in blue) we see that it has a jump discontinuity which jumps over 0.
this makes sense because the function goes from decreasing to increasing, so it should have a minimum at that point.
here's another example. in red, i plotted x^(2/3). this function has a cusp at 0, which gives it a minimum. in the derivative 2/3 * x^(-1/3), we see that there's a vertical asymptote at 0. that happens because the slope at the cusp goes to -infinity from the left, and +infinity from the right. but even so, the slope jumps from negative to positive (past 0) and so the original function has a local minimum there.
the takeaway is: critical points of y are the points where either y' = 0 or where y' doesn't exist. you'll have to check whether any of these points gives you a local min or a local max.
teal geyser
Maxima and minima usually happen at points where the derivative is 0, but they c...
Ah okay
True
Perfect, thank you
-close
.close
feral nacelle
Graph looks something like this
cedar kilnBOT
Graph looks something like this
swift siren
why are you starting with 1/280
feral nacelle
1/280 is smaller than 1/80
feral nacelle
But I don’t get why the graph is backwards
swift siren
well it doesnt look like you associated the right pressures with the volumes
feral nacelle
How come, I marked it accordingly
feral nacelle
Let me try
swift siren
feral nacelle
Nope
feral nacelle
It has to go through origin as a straight line tho
How do I know what intervals I need to go up in
swift siren
well for all intents and purposes of this question that's asking you to explain why these measurements verify boyle's law, it can be assumed that the slight discrepancy is due to measurement errors
swift siren
the big part of boyle's law isn't necessarily that it goes through the origin, but that pressure is inversely proportional to volume
swift siren
well then just make your line go through the origin ;)
even if it technically isnt the line of best fit
hardy zephyr
help
feral nacelle
I want to actually get the question right tho
swift siren
I want to actually get the question right tho
you would still get it right if you drew a close enough line
since i assume you're being asked to plot this by hand?
feral nacelle
since i assume you're being asked to plot this by hand?
Ye
hardy zephyr
its multiple choice
swift siren
swift siren
its multiple choice
this channel is occupied regardless
with someone else's question
this line works even though it isn't the best fit technically
feral nacelle
How would ik by which intervals to go up by on the left tho
Would I go up by 40 or what
swift siren
well it seems you can go up by 50 and get a nice graph
really just something that doesnt make it too compressed
swift siren
probably because your x axis is janked up
your increments seem to be just the points from the table
and you spaced them equally
feral nacelle
feral nacelle
How would I properly increment them
swift siren
it seems like you could get away with having it in increments of 0.0010
since the max value is 0.0125 and the min is 0.0036
feral nacelle
I’m going to try brb
It worked 😭😭🙏🙏
It was the increments not being spaced properly that was the issue
Thank you so much for your patience
cedar kilnBOT
@feral nacelle Has your question been resolved?
hollow minnow
Have you tried drawing a graph
cedar kilnBOT
@jovial mist Has your question been resolved?
hollow minnow
Maybe you could argue x_(i-1) <= sqrt(x_i • x_(i-1)) <= x_i
It should still be fine no? each deltaxi will be the same for Ln or Rn or any sum
Right for different intervals but if we just look at one interval we can use the same detla xi for Ln, Rn
Yeah
cedar kilnBOT
@jovial mist Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
crimson sedge
pls help
crimson sedge
@astral gazelle
crimson sedge
this
austere hull
can you expand it
astral gazelle
Oh, right, tricky stuff indeed! The trick is to do it in smaller sections
fickle trellis
uh well.
astral gazelle
Not quite, no - to be honest, I'm not sure if your working is on the right track
Could you step ne through what you tried?
cedar kilnBOT
Show your work, and if possible, explain where you are stuck.
umbral dew
,w expand 5(3x+10)^3
astral gazelle
Bruh
umbral dew
okay waait
astral gazelle
That teaches nothing ;-;
umbral dew
that could be just
fickle trellis
okay waait
crimson sedge
i expanded it so it was 5(3x+10)(etc)(etc)
astral gazelle
i expanded it so it was 5(3x+10)(etc)(etc)
That's a great start
fickle trellis
aight no thats a bit offensive
astral gazelle
A good way to proceed then would be to join together two of the 3x + 10 terms to get:
5(...)(3x + 10)
crimson sedge
then i multiplied the first to brackets for 5(9x^2+60x+100)(3x+10)
crimson sedge
then i tried multiplying those two to get 5(27x^3+270x^2+900x+1000)
@astral gazelle
astral gazelle
Yeah just checking
crimson sedge
ok thanks
astral gazelle
Ah, I'm seeing an issue with your x^2 and x terms
I'm not sure how you arrived at 270 and 900
astral gazelle
Oh yeah my bad ;-;
crimson sedge
and then 9x^2 x 10
crimson sedge
and for the x, i did 100 x 3x for 300x and then 60x x 10 for 600x
astral gazelle
Yup
crimson sedge
so 900x
crimson sedge
yeah my mistake every 2 times i get it wrong it changes answer
im in middle of this question as we speak
crimson sedge
then i tried multiplying those two to get 5(27x^3+270x^2+900x+1000)
so this checks out?
crimson sedge
ok and then i times all by 5
astral gazelle
Yup!
crimson sedge
yea
astral gazelle
Sorry again for the false alarm
astral gazelle
Ayyyyyy
Happy to help - but to be honest you did it all yourself, I was just encouragement :0
crimson sedge
thanks for the encouragement then bro
cedar kilnBOT
@crimson sedge Has your question been resolved?
spice monolith
Heya , i need help with understanding the wording of a maths question
glass sky
perform dimentional analysis
glass sky
just try to find the dimentions of density with given info
not unit
dimentions
in form of M^a L^b T^c
spice monolith
its just kg/m^3?
spice monolith
i never got to do dimensional analasys
glass sky
dimentions
in form of M^a L^b T^c
explain in this form
spice monolith
so im a little behind on how it works
the question itself dosent have any numbers in it so my brain is confused
glass sky
i would suggest redo the question of dimentional analysis from ncert / ask your teacher to explain the topic?
1 sec i can try to explain
spice monolith
yes please that would be appreciated
spice monolith
no
glass sky
M - mass unit
L - lenght unit
T - time unit
these are the fundamental units
all units can be formed with the product of these units
spice monolith
kg^m?
spice monolith
kilograms
glass sky
so the dimention will be M L^0 T^0
spice monolith
yee
glass sky
what is it for volume
spice monolith
L M^0 T^0?
spice monolith
L^3?
glass sky
mass/volume???
glass sky
yeah so what you left with?
glass sky
yeahhh
spice monolith
the rest cancells out
spice monolith
okay now am confused LOL one second lemme decipher this
glass sky
its like at which dimention a thing depends on
mass / lenght / time
anything to the poiwer 0 is 1 right
spice monolith
ohh okay
glass sky
i just wrote it as like convection
spice monolith
it makes sense now
glass sky
yeahhh
also instead of denominator use exponential law and write it in negative power thing
like M L^-3
spice monolith
my brain is too small for this LOL
spice monolith
okay quick mini question too
glass sky
sup
spice monolith
when it says
show that the expression is homogenious?
does that just mean , re arrange the expression to = 1?
glass sky
wait
are you talking about homogenious in certain degrees?
like a equation is homogenised with degree 2 means that every term has the degree 2
spice monolith
glass sky
not sure what it means here
spice monolith
i was told it just means show that the expression can = 1
glass sky
like a equation is homogenised with degree 2 means that every term has the degre...
(this what the math implication from pair of straight line chapter)
not sure if this helps
but yeah this works
makese sense
glass sky
cool np
spice monolith
I will come back to the homogenious bit in a different ticket at a later time
glass sky
(do lmk when you get the answer)
im kinda curious
just dm when you get if if you can
kind ridge
cedar kilnBOT
kind ridge
I have a question
I'm working on a project for algebra, and they want us to make a word problem based on two parabolas and their intersections. I made the parabolas and found good intersections, but I didn't know what to do for the real-life situation. They said I cannot use vertical motion, which cancels out all projectile motion. Does anyone have any ideas?
Ping me if you can help.
cedar kilnBOT
@kind ridge Has your question been resolved?
torpid urchin
could someone explain to me how to set this question up? i know im setting my expectation=100 but im not sure where the deductable fits in
cedar kilnBOT
could someone explain to me how to set this question up? i know im setting my ex...
@torpid urchin Has your question been resolved?
hardy swift
Whats the point of the x?
cedar kilnBOT
Whats the point of the x?
south tundra
To emphasize that the composition $f \circ g$ is being applied to some variable $x$
wraith daggerBOT
A Lonely Bean
south tundra
Just writing $f \circ g$ would mean you are referring to the composition itself
wraith daggerBOT
A Lonely Bean
hardy swift
Does it mean f(g(x))? Cuz sometimes the question just gives you something to put in it other than x
south tundra
Yes
hardy swift
Can you write anything istead of x
south tundra
As long as it's in the domain of g
hardy swift
But it has to be a variable if you want to replace it with something?
south tundra
What do you mean?
tepid sail
Can you write anything istead of x
well I'm assuming $f o g$ is from R to R
wraith daggerBOT
nosqldb
hardy swift
In one of my questions it tells me to put f inside g and it tells me what both those functions are
tepid sail
so yes, you can input any $x \in$ R into the function f o g
wraith daggerBOT
nosqldb
hardy swift
Or is the "(something)" the variable used and it doesnt have to be "directly" put into the inner function?
south tundra
In one of my questions it tells me to put f inside g and it tells me what both t...
That sounds more like $g \circ f$ though
wraith daggerBOT
A Lonely Bean
south tundra
Or is the "(something)" the variable used and it doesnt have to be "directly" pu...
When applying a composition, the inner function is applied first to "(whatever)" and then the outer function
Not sure if I still understood your question though
What would putting the variable not "directly" into the inner function look like?
crimson sedge
this graph is not a one-to-one function, right?
cedar kilnBOT
this graph is not a one-to-one function, right?
crimson sedge
the x value 0 has multiple y values?
sharp lotus
i mean its probably just going through 0, 0 and the rest of the values are close, but a screen has only so many pixels to cram different tiny decimals in, you can't really say unless you have an equation you can see what's going on analytically, looks one to one to me
crimson sedge
One to one means there is no value of y that has 2 x’s mapping to it
But no this is a function probably so there by definition cannot be 2 values for the same x
oh okay
thanks guys
.close
agile grail
cedar kilnBOT
agile grail
How do i do this
hollow minnow
Which part?
agile grail
I know what the answer is, I just don't know why
sharp lotus
so if 4b = 9a, obviously 4 is a factor of the left side, correct?
agile grail
why?
sharp lotus
because 4b = 4 * b
agile grail
oh yeah
sharp lotus
thats kinda the definition of a factor
sharp lotus
so that means 4 must also be a factor of 9a right? (9a sorry)
agile grail
why 9b
hollow minnow
9a
agile grail
yeah
sharp lotus
ok so it's either a factor of 9 or a factor of a right? well obviously not of 9
agile grail
ohhhhhhh
that makes so much sense
and the same applies for 3 being a prime factor of b
sharp lotus
yeah
jolly knoll
Does someone know of a online course on yt or someother website that does calculus? I have to study it by myslef and i have a textbook but was wondering if there is some course that could help me
jolly knoll
for reference
The set of real numbers and related properties. Complex numbers: algebraic, trigonometric and exponential forms. Limits of numerical sequences. Numerical series and convergence tests. Functions of one real variable and limits of real functions. Continuous functions and related properties. Study of the graph of a real function. Some optimizations problems. De L'Hospital's Theorems and Taylor's Formula. Integral calculus for real functions. The definite integral and its properties. Indefinite Integrals and integration methods. Improper integral and convergence tests. Power and Taylor series. Introduction to Fourier series. Ordinary differential equations, existence and uniqueness results. Linear ordinary differential equations and methods of solution of some ordinary nonlinear differential equations.
syllabus
that i want to do
books that i have are biocalculus by james stewart
and
Calculus A complete course 9th ed Pearson by Robert A. Adams ......
dire geode
Does someone know of a online course on yt or someother website that does calcul...
And Khan academy
jolly knoll
thank you i missed that
cedar kilnBOT
Available help channel!
meager finch
cedar kilnBOT
arctic condor
nah what its not even that hard ur trolling
arctic condor
anyway um its at the 2nd step, youre multiplying everything by 4, but 4*(1/4)x is not 4x
meager finch
anyway um its at the 2nd step, youre multiplying everything by 4, but 4*(1/4)x i...
oh my god
thank you
.close
cedar kilnBOT
torpid urchin
could someone help me out with this question
cedar kilnBOT
velvet mortar
Create a new channel with question
cedar kilnBOT
Available help channel!
hard flame
Hello!
hard flame
I don't know how to do this other than drawing the carteaian plane and checking exactly: A line that passes through the points (3,-7) and (14,k) has a slope of 5/6. Determine the exact value of k
patent hearth
do you know the definition of slope?
hard flame
k-(-7)/ 14 - 3 = 5/6
rare sail
cedar kilnBOT
cedar kilnBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
@rare sail Has your question been resolved?
rare sail
what have you tried
I tried doing dx dy, but we get x variables into the y integral and we dont get a value, idk.
rare sail
turn this into dxdy and change bounds
Yeah, I'm not sure how I'd channge the bounds if I do that
usually, I could graph it and look at the graph but this idk
spark cosmos
usually, I could graph it and look at the graph but this idk
well you can do like y=4-x^2 and get x from there
rare sail
oh right, just remembered that
spark cosmos
graph it and and should look ok
rare sail
Alright Im gonna giv etht a try
spark cosmos
tell me what you come up to. cuz i have a 1 integral that i have difficulty solving
rare sail
tell me what you come up to. cuz i have a 1 integral that i have difficulty solv...
Don’t u have to change the integrand when u change the boundaries
But its with respect to two variables
idk how to change that
spark cosmos
Don’t u have to change the integrand when u change the boundaries
I don't see a reason why you should change the integrand. You are integrating a function on the area and you just change the way you cover the area.
rare sail
I don't see a reason why you should change the integrand. You are integrating a ...
Thats what I was thinking too, my friend made me think otherwise
raw gulch
btw: i have calculated this integral, changing order of integration and then it works really nice
so it loosk that iwas intentioally designed for this method
faint yacht
Anyone got a clue what happened in the second line of working out for this question https://media.discordapp.net/attachments/988786913114722309/1175605987563020368/20231119_091724.jpg?ex=656bd765&is=65596265&hm=04ba7950b8a65bcb130ce7b761257b7c5ca4c8bc84424f673f61c9c72ded1f32&=&width=2052&height=420
hollow cloak
They're just factoring terms without i and with i
faint yacht
its not adding up tho
cause the terms that like cos^4 theta dissapeared
unless im missing something critical here
hollow cloak
No they didn't
hollow cloak
They're just pulling terms with i out
faint yacht
wait lmaoooooooooooo
hollow cloak
And btw i^2 is -1
faint yacht
i read
the bottom bit
as a completely different line
LMAO
i was literally clueless
ok lol what a silly
mistake
alr thanks for poining it out
.close
sand jay
cedar kilnBOT
sand jay
onyx dove
you need to perform long division before the partial fractions
if you look at the first line, you'll see that one side has u^3 but the other only goes up to u^2
fallen oxide
So for this question, I am stuck on c). I am just not quite sure how to get this as a percentage, and nothing I have tried is working.
cedar kilnBOT
So for this question, I am stuck on c). I am just not quite sure how to get this...
@fallen oxide Has your question been resolved?
fallen oxide
<@&286206848099549185>
cedar kilnBOT
@fallen oxide Has your question been resolved?
fallen oxide
<@&286206848099549185>
bold vine
this is more of an engineering or physics problem than a math problem
Ik there's a physics server linked somewhere in this server
cedar kilnBOT
@fallen oxide Has your question been resolved?
fallen oxide
Ik there's a physics server linked somewhere in this server
It's a math word problem with a physics application
cedar kilnBOT
@fallen oxide Has your question been resolved?
cedar kilnBOT
@fallen oxide Has your question been resolved?
raven walrus
tell the values of x,y,z amaong the following 50, 18,34
cedar kilnBOT
tell the values of x,y,z amaong the following 50, 18,34
hollow minnow
Whats the issue
crimson sedge
SA=2lw+2lh+2hw
raven walrus
From picture y<x<z
okey, now tell which one is the height, lenth and breadth
plucky owl
okey, now tell which one is the height, lenth and breadth
You can tell that z is the largest and y is the smallest
You gave the values of 50, 18, 34
raven walrus
You can tell that z is the largest and y is the smallest
yup right now tell,
okey, now tell which one is the height, lenth and breadth
plucky owl
What's the largest and the smallest, then x is defaulted to the last value
hollow minnow
yup right now tell,
okey, now tell which one is the height, lenth and breadth
z is the largest and y is the smallest
raven walrus
(i knew z is biggest so it is 50, x is a bit small so its 34 and y is the smallest so its 18)
what i want you to do is, tell what is the breadth, length and height
plucky owl
Well height is normally the vertical distance
Length is the horizontal
And breadth is the width
But it also depends on the perspective
raven walrus
so height would be 50, length would be 34, and width which is breadth is 18 right?
raven walrus
But it also depends on the perspective
yeah, this
plucky owl
so height would be 50, length would be 34, and width which is breadth is 18 righ...
Yes, that's if you look at it straight, from the front side
raven walrus
supoose i am the seller and i am selling this,
what should be the profectional answer?
plucky owl
If you were selling it, perspective is from the front
Like if you were looking at it from the x side
raven walrus
If you were selling it, perspective is from the front
tell me what should i put it
height =
length =
breadth =
plucky owl
Sure
raven walrus
this is what bard says
plucky owl
As mentioned, based on perspective
raven walrus
As mentioned, based on perspective
see it as a customer which is good in maths, what will you pick?
plucky owl
this is what bard says
And as mentioned, height is normally the vertical distance. So this was in the perspective of it laying down
plucky owl
see it as a customer which is good in maths, what will you pick?
If you were selling it, perspective is from the front
Like if you were looking at it from the x side
I told you what perspective is more ideal
But it's option based, it's up to you on how you want to view it
raven walrus
okey,
but generally we can concider height as vertical distance right?
plucky owl
That's what I stated multiple times
raven walrus
That's what I stated multiple times
perfect then
how in this would you would consider lenth as 24 cm, height as as 15cm and widgh to be 6 cm right
@plucky owl
sand cradle
Regarding the proof from earlier
cedar kilnBOT
Regarding the proof from earlier
sand cradle
That we did with @crimson delta
How would we generalize this?
To A_1 x ... x A_n
sand cradle
How would we generalize this?
Complete induction?
sand cradle
induction would work, yes
Would you say that would be the fastest way?
restive hedge
Complete induction?
You don't even need complete induction
sand cradle
Oh
crimson delta
its pretty fast so yeah sure why not
sand cradle
You don't even need complete induction
What do we need then?
restive hedge
(A_1 x ... x A\_(n-1) ) x A_n
just what Denascite wrote here
sand cradle
just what Denascite wrote here
That is complete induction
sand cradle
its pretty fast so yeah sure why not
Base case n = 2, right?
And paste in our proof above
crimson delta
yes
restive hedge
That is complete induction
Complete induction requires you to assume it is true for P(1),...,P(n-1), no? You only need to assume for P(n-1)
sand cradle
Complete induction requires you to assume it is true for P(1),...,P(n-1), no? Yo...
strong induction
crimson delta
you also need that if |A|=|B|, then |AxC| = |BxC|
which you might have proven before, dunno
sand cradle
Complete induction requires you to assume it is true for P(1),...,P(n-1), no? Yo...
I should just say induction, sry, I'm used to complete induction because that's how we say it in German
But it's just induction in English
restive hedge
ah sure. it's a pedantic point anyway
sand cradle
which you might have proven before, dunno
We haven't
This'll be a long proof, lol
Just the base case is half a page
crimson delta
the base case is the hard part here
sand cradle
you also need that if |A|=|B|, then |AxC| = |BxC|
Where do we need that?
crimson delta
(A_1 x ... x A\_(n-1) ) x A_n
to use this
replacing A_1 x ... x A_(n-1) by eg N
well ok actually no you dont need it
nvm
cedar kilnBOT
@sand cradle Has your question been resolved?
sand cradle
well ok actually no you dont need it
Wdym? What can we do then?
crimson delta
by IH the set (A_1 x ... x A_(n-1) ) is countably, so its again countable x countable
sand cradle
by IH the set (A_1 x ... x A\_(n-1) ) is countably, so its again countable x cou...
So just like the proof above?
Another page long section, lol?
crimson delta
why would you need to prove it again
sand cradle
why would you need to prove it again
Well, we are given $\mathbb N \rightarrow A_1 \times \dots \times A_{n - 1}$ is bijective and we need to show $\mathbb N \rightarrow A_1 \times \dots \times A_{n} = \big(A_1 \times \dots \times A_{n - 1}\big) \times A_n$ is bijective too.
sand cradle
crimson delta
also that wording makes no sense
sand cradle
"there exists a map N->A1x...xAn-1 which is bijective"
Yeah
crimson delta
lets not skip wording like that cause its crucial
sand cradle
just talk about stuff being countable
Well how do we show A_1 x ... x A_n is countable?
crimson delta
that said, you dont have to say anything about any bijective maps here
sand cradle
Given A_1 x ... A_{n - 1} is countable
sand cradle
Yes
crimson delta
so its again countable set x countable set
sand cradle
Yes
sand cradle
which you have proven in your base case is countable
We've only proven it for two specific sets?
We've basically proven the general case of countable x countable in our base case, right?
crimson delta
yes
we have used nothing specific for A_1 and A_2
they are two general countable sets
cedar kilnBOT
umbral dew
@sand cradle ive pinged them already just in case ur gonna do so
<@&268886789983436800> pinging again to let u guys know they arent banned yet
slate lintel
<@&268886789983436800> pinging again to let u guys know they arent banned yet
they have both been timed out, should be banned soon. are they dming you?
cedar kilnBOT
umbral dew
they have both been timed out, should be banned soon. are they dming you?
no, the msg was still not deleted that's why...
slate lintel
no, the msg was still not deleted that's why...
messages don't always get deleted on ban
crimson delta
only timed out?
slate lintel
only timed out?
i cant ban people myself
crimson delta
I thought thats what the little janitor role was for
slate lintel
I thought thats what the little janitor role was for
no, i can time people out and delete messages but not ban
cedar kilnBOT
Available help channel!
sand cradle
cedar kilnBOT
sand cradle
For injectivity, just pick l', m', n' and see if f(l, m, n) = f(l', m', n') => l = l', m = m', n = n'
What about its surjectivity though?
lethal jackal
well, are there any numbers l, m, n such that f(l, m, n) = 7?
surjective in this case means that f produces all of the natural numbers for suitable inputs
idle tusk
the function doesn't account for any number whose prime factorization includes primes greater than 7
cedar kilnBOT
@sand cradle Has your question been resolved?
sand cradle
the function doesn't account for any number whose prime factorization includes p...
Oh, thanks
sand cradle
well, are there any numbers l, m, n such that f(l, m, n) = 7?
No
cedar kilnBOT
Available help channel!
sharp hill
if i have a linear transformation f that I PROVED that dim(Ker)=0, function goes from R2->C, (C is here defined over R, therefore 2 dimensions), since R2 has 2 dimensions, C has 2 dimensions, and according to the equation dim(R2)=dim(Ker)+dim(Img), image of the function, R2 and C all have dimension 2. Now that means that the image, R2 and C are isomorphic. In my un slides though, theres a similar example, and he just deducts that the function is also surjective, therefore, an isomorphism. But the idea now is, we just found out that Image and C are ISOMORPHIC, but not the same vector space. How do you just say that the function is surjective from that?
sharp hill
because two vector spaces being isomorphic doesnt just mean that the Img=codomain
right?
dawn junco
because two vector spaces being isomorphic doesnt just mean that the Img=codomai...
but the image is a subspace of the codomain always
there's not a lot of subspaces of C isomorphic to C
sharp hill
ah fuck that makes so much sense
would never think of visualizing it that way
thank you!!
.close
ivory finch
cedar kilnBOT
rain drift
yep pretty much, the difference here is what the domain/co-domain is
hollow minnow
If A=R
ivory finch
i suck at algebra so i just use graphs
rain drift
oh I guess it's not asking you for proof, lol just a justification
nvm
ok so let's think about this logically
ivory finch
injective pass horizontal line test
surject covers all CODOMAIN i think?
codomain or range, not sure actually
so for example y=x^2 is not either cuz injective has 2 value same with diff x
rain drift
correct on the surjective! Injective it also is true on a real number line but we aren't necessarily working with a real number line or graph here
rain drift
so for example y=x^2 is not either cuz injective has 2 value same with diff x
very good!
ivory finch
surjective doesnt cover entire codomain if r to r
codomain/range?
anyway cuz negative numbers dont reach
rain drift
surjective just means that all points of the codomain (to clarify the range here is a subset of the co-domain) have a function mapping
ivory finch
and its ot a funct if R-> R+? cuz 0 no more?
rain drift
the question isn't asking for R -> R. It's asking for a generic set from A to A
like it could be Z -> Z (the integers)
rain drift
or it could just be A = {1, 2, 3} so {1, 2, 3} -> {1, 2, 3}
ivory finch
very generic, so hard to intuitive
rain drift
yeah no problem
ok so let's take a step back
start off from scratch
Injective basically means that every element of the domain has a unique mapping to the co-domain (note that not all of the co-domain has to have a mapping with this definition)
ivory finch
surjective then means every codomain thingy needs to have smthn in it rite
but it can also be more than 1 domain element in each codomain
then bijective means domain-> codomain, ONLY 1, and no missing rite
rain drift
yep! The rule for surjective is that all of the domain has to have a mapping to something codomain, and all elements of the codomain have to have a mapping
I'll show you a simple more abstract example
Let f : X -> Y, where X = {1, 2, 3} and Y = {0, 1}.
We define our function to have the following mapping f(1) = 0, f(2) = 1, f(3) = 1.
Notice here all of our elements in the codomain are "touched" and have a mapping, as well as all of the domain's elements map to something.
But since we have f(2) = f(3) = 1, then f is not injective in this case
let me know if that makes sense or if I need to clarify anything
Let me see if I can draw you up a quick visual
ivory finch
like this?
rain drift
yep exactly!
sorry I don't have quick drawing tools at my disposal lol
a small thing to make it more readable is maybe fill in teh dots, it looks like 00 and 01 🙂
but yes you got the right idea
rain drift
yep exactly!
the logic for injectivity is that since I_A(x) = x, then all elements of A gets mapped to itself in the codomain, so each mapping is unique.
the logic for surjectivity is that since I_A(x) = x, then all elements of the co-domain have a mapping from the domain and all of the elements of the domain have some mapping to the co-domain.
so it's bijective!
with formal proofs there's some strategies using the formal definitions for injective or surjective. But it's just asking you to justify the answer with logic, not write a formal proof, so I think this would be acceptable 🙂
ivory finch
does this matter what the domain and codomain are?
rain drift
well in this case they're the same!
ivory finch
wat if R->R+
how do u know that
they are same domain and codomain?
Oh cuz A->A?
same thing?
rain drift
ivory finch
So replace A with R, Z, N, etc?
rain drift
what we're showing here basically is that if we have a set A and we map a function from A to itself, with the function f(x) = x for x in the domain, then it's bijective
rain drift
oh like its generalization? like when you have generics in java?
ah you're a CS major haha, I was too
yep pretty much!
in generics you inject the object type. Here the object type are just various sets
but they have to have a mapping to themselves
like say if A was the set of prime numbers and f: A -> A was defined as f(x) = x. Then all of the prime numbers just get maped back to themselves
ivory finch
all the prime numebrs to the prime numbers
rain drift
f(2) = 2, f(3) = 3, f(5) = 7, f(7) = 7 and so on and so forth
ivory finch
so there is never any conflict? like when its diff R->R+
rain drift
yeah let's take that example
so we have a function from R to R+. Consider the function f(x) = x^2 + 1.
this would be a surjective function, but not injective
rain drift
yep!
rain drift
ok wait let me take a step back
ivory finch
R+ means x > 0 rite
ivory finch
so then neeither?
rain drift
yeah sorry neither because technically we'd have an open hold where x = 0
in reality it'd look like this
ivory finch
rain drift
we have a hole at x = 0 since it's not in the codomain
wait
soryr
i"m getting mixed up here lol
yeah you're right it's neither
nvm
ivory finch
is my graph good
rain drift
yeah that's sound logic.
rain drift
yep!
rain drift
you were totally right
rain drift
Here's a good chart to help cover the possibilities
and if it's none of those cases, it's neither
Ok so let's define a function $f : \mathbb{R}^- \mapsto \mathbb{R}^+$ and define $f(x) = -x^3$. Would our function be injective, surjective, bijective, or neither?
wraith daggerBOT
MellowDramaLlama
ivory finch
bi?
rain drift
very good!
can you give me like a 1 or 2 sentence explanation (without graphs)?
without graphs lol
ivory finch
😭