next crescent
oops
#help-10
zenith raft
yep
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
uneven perch
I don't understand what this problem is asking me
obtuse pebbleBOT
I don't understand what this problem is asking me
tired shell
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quiet rapids
not entireyl sure how to find the upper reimann summ given this parition, do i need to leave my answer a a number or could i just type it out using the n's?
obtuse pebbleBOT
not entireyl sure how to find the upper reimann summ given this parition, do i n...
quiet rapids
because i believe its just going to be for the upper sum b-a * b + ...
second term mius first * second term
obtuse pebbleBOT
@quiet rapids Has your question been resolved?
obtuse pebbleBOT
@quiet rapids Has your question been resolved?
whole geode
1
timid silo
can you show the original question
timid silo
could anyone please explain what k means?
a_ij is notation of describing an element of a matrix, i represents the i-th row and j represents the j-th column
the ^3 superscript is to signify this is for the A^3 matrix i suppose
grizzled shore
I’ve not seen that notation before
viral blade
The subscript is normal but the superscript is bad notation lol
but yeah Qylo is right I'm sure
timid silo
Its third column..?
you have [
a^k_{ij}
]
$i$: the $i$-th row of the matrix
$j$: the $j$-th column of the matrix
$k$: the $k$-th order of the matrix (this is not common notation)
\vs{5 mm}
For example, $a^5_{63}$ describes the element of a matrix of order 5, where that element lies on the 6th row and the 3rd column of the matrix
warm shaleBOT
obtuse pebbleBOT
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grim zenith
I would kindly like to ask how should I approach this qn, we only have done cross products for vectors in 3d, not 4d😦
obtuse pebbleBOT
I would kindly like to ask how should I approach this qn, we only have done cros...
grim zenith
My initial idea was the find the cross products for both planes and compare if they are of multiples of each other to determine if they are parallel, but I’m not so sure
obtuse pebbleBOT
@grim zenith Has your question been resolved?
obtuse pebbleBOT
@grim zenith Has your question been resolved?
obtuse pebbleBOT
@grim zenith Has your question been resolved?
nova shard
"1. Given an n x n grid, calculate the number of paths that start from the top left corner and end i the bottom left corner, visiting all the cells in the grid.
2. For the previous exercise, what if there are m walls in the grid?"
I honestly have to idea where to start, if this was a programming exercise I'd do it with backtracking, but it's not 💀
I'm also given a hint that for 7x7 grid without walls there are 111712 paths
obtuse pebbleBOT
"1. Given an n x n grid, calculate the number of paths that start from the top l...
fathom flicker
"1. Given an n x n grid, calculate the number of paths that start from the top l...
Non backtracking paths?
nova shard
Non backtracking paths?
Idk what this means in math context I said I'd create a program with backtracking algorithm to solve it if it was a programming exercise
fathom flicker
Can the path go from one vertex to another, and then backwards, and repeat
Or not
nova shard
Nope
fathom flicker
There is something called the non back tracking matrix which might help you count these paths, but maybe there is a simpler combinatorial argument
nova shard
Maybe something like variations would work but not with the standard formula already tried that and a few other things, lemme check that matrix ig
fathom flicker
I think the matrix is not the way to go
nova shard
We solved something like this in class using combinatorics (which my smart ass decided not to write down because the professor was talking too fast) but it was limited only to moving down or right, so it was pretty intuitive
nvm his was just all possible paths not all possible paths that visit all cells
and was limited by movement directions as well
nova shard
We solved something like this in class using combinatorics (which my smart ass d...
which would be [2(n-1)]! / (n!*n!)
Okay that's a little progress 💀
plush minnow
I may be wrong, but this sounds a lot like the hamiltonian path problem
But in a grid, so you can move only to adjacent cells
obtuse pebbleBOT
@nova shard Has your question been resolved?
cursive mirage
R = { (a,a), (a,b), (b,c), (c,b), (c,c) }, S = { (b,a), (c,a), (a,c), (b,b) } find R ∘ S
obtuse pebbleBOT
R = { (a,a), (a,b), (b,c), (c,b), (c,c) }, S = { (b,a), (c,a), (a,c), (b,b) } fi...
cursive mirage
My solution was { (a,c),(a,b),(b,a),(c,b),(c,a) }
river falcon
what does R ∘ S mean
cursive mirage
My solution was { (a,c),(a,b),(b,a),(c,b),(c,a) }
I saw a solution that included (b,b) and (b,c) but I don't know how
Oh it's R to S not S to R
Yeah that what was wrong
.close
obtuse pebbleBOT
obtuse pebbleBOT
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kindred basin
obtuse pebbleBOT
kindred basin
for part 2, how do we know which equation to use?
since it says first second so t = 1, but both of them have t =1?
the first one feels like the right one just cause its intervapl is 0-1 and its asking for first second
but thats not a mathematical reason i dont think; thats just my gut feeling and my thoughts after looking at the markscheme (they used the first one)
static furnace
in the first second, aka from 0 to 1 seconds?
the acceleration is constant for the first second. i think it's asking you what that acceleration is
obtuse pebbleBOT
@kindred basin Has your question been resolved?
echo gazelle
How did they set the bounds?
obtuse pebbleBOT
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vague elk
what does x=/= 0 mean? can i proceed to get thr particular solution as usual?
timid silo
,rotate
warm shaleBOT
river falcon
what does x=/= 0 mean? can i proceed to get thr particular solution as usual?
that just means x cant be 0 because its in denominator
vague elk
that just means x cant be 0 because its in denominator
so i can get the particular as usual?
river falcon
so i can get the particular as usual?
im not sure sorry
radiant marsh
can someone please explain how do I draw a graph for something like this?
bright pumice
can someone please explain how do I draw a graph for something like this?
You draw the graph for the x²-x equation between 0≤x≤2
radiant marsh
You draw the graph for the x²-x equation between 0≤x≤2
and how do I go about that
I understand that I have to draw a seperate line for each and that the x^2 - 1 graph is not linear therefore it'd be something curved, but that's where my understanding ends
I don't know what points I have to connect or anything to draw it
sage dagger
Find the roots of the quadratic
bright pumice
I find the vertex of the quadratic (curved one), the x intercepts and the y intercepts and I use that to graph the curve
bright pumice
can someone please explain how do I draw a graph for something like this?
And make sure to put a complete point at the end of your quadratic and an empty point at the beginning of your linear
radiant marsh
Find the roots of the quadratic
so I have to use the quadratic formula for x^2 - x and find x1,x2?
sage dagger
its x^2 - x
radiant marsh
And make sure to put a complete point at the end of your quadratic and an empty ...
empty point is for ( and the full one is for ]? as in for (x,y] it would be an empty point at the start and a full one at the end, did I understand that right?
sage dagger
you dont need the quadratic formula
just set x^2 - x = 0 and factor out the x
and solve individually
bright pumice
empty point is for ( and the full one is for ]? as in for (x,y] it would be an e...
Yes
radiant marsh
just set x^2 - x = 0 and factor out the x
why do I set x^2 - x = 0?
sage dagger
because you are finding the roots of the quadratic
radiant marsh
because you are finding the roots of the quadratic
I'm a bit confused here, if x is equal to 2 then 2^2 - 2 wouldn't be 0, then why is that fine to do here?
sage dagger
I'm a bit confused here, if x is equal to 2 then 2^2 - 2 wouldn't be 0, then why...
im sorry? I dont understand what you mean by if x = 2, we arent setting x = 2 we are setting the quadratic x^2 - x = 0
radiant marsh
im sorry? I dont understand what you mean by if x = 2, we arent setting x = 2 we...
my logic is that there's also the information that 0 =< x =< 2, so doesn't that mean that x is any number between 0 and 2 including 0 and 2, therefore if x were to be 2 then this equation wouldn't right? What sense does it make to say that it equals 0
tired sierra
we use 0 because we just want to graph it
we can graph the whole thing then we can constrict them to the domain of 0 to 2
sage dagger
hello rice
sage dagger
are u doing a major or minor in math perchance
radiant marsh
perchance
sage dagger
oh your a helper now
nah
radiant marsh
we use 0 because we just want to graph it
so for anything that I want to graph I do = 0?
radiant marsh
graphing is completely new to me
tired sierra
oh boy
radiant marsh
do you know how to find x and y intercepts in general
I think so? I'm studying the topic in a different language so I don't know what exactly you mean
sage dagger
I think so? I'm studying the topic in a different language so I don't know what ...
an x intercept is a point on the graph that crosses the x axis
same thing for y
radiant marsh
of stuff like y = x + 2
this is related to y = ax + b right?
radiant marsh
an x intercept is a point on the graph that crosses the x axis
I used to know how to do it and I can't remember now
oh I have to set x = 0 and solve for y
radiant marsh
of stuff like y = x + 2
so in this case it'd be (0,2) and (-2,0)?
obtuse pebbleBOT
@radiant marsh Has your question been resolved?
obtuse pebbleBOT
@radiant marsh Has your question been resolved?
radiant marsh
.close
obtuse pebbleBOT
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river roost
Sorry if not being clear, but I don't even know where to start to solve 10a
river roost
Like, I have the answer right in front of me but I wouldn't be able to solve it
ocean ingot
Okay, are you having trouble with both lines? y = f(x) and y = 1/f(x) ?
river roost
The first one is fine, the second (y = 1/f(x)) is difficult for me
ocean ingot
Fair enough!
Can you expand 1/f(x) into its full equation?
As in, f(x) = x + 2, 1/f(x) = ?
river roost
1/f(x) = 1/(x+2)?
ocean ingot
Yup! Though it's good practice to use brackets like 1/(x+2) to prevent ambiguity
So, do you know how to graph 1/x ?
river roost
So, do you know how to graph `1/x` ?
Nah not really🫠
river roost
Sure
ocean ingot
Just graph 1/x on it
river roost
This is what happens
ocean ingot
You'll see as x approaches 0 from the positive side it'll climb up to positive infinity, and go to negative infinity from the negative side
And as x gos to positive or negative infinity, 1/x goes to 0
Funny enough, this graph is actually reflected along the line y = x, though that's not super important
I'd suggest taking some time to try to get a grasp of why that graph looks the way it does, why it's most curved around x = 1 and x = -1
But aside from that, moving back to 10.a
Do you know methods of moving a graph? Like, f(x+a) + b
river roost
Yeah
ocean ingot
So if you can figure out why 1/x looks the way it does, you can understand why 1/(x+2) is the same but 2 to the left?
river roost
Wait let me think this thru
ocean ingot
Okay! Feel free to bounce ideas off me 🙂
river roost
Because the x and y values in the graphs have a direct relation to each other, by adding 2 to x
Hmm
Well the graph is most curved at x = 1 and x = -1 because that's when the x and y values are closest to each other, and after that
ocean ingot
Rather than x and y having a relation to one another, it might be more accurate to say that y is dependent on x
river roost
True
ocean ingot
So when you add 2 to x, the value of y is treated as though x was 2 larger
river roost
If 2 was added to x in that situation, shouldn't the graph move to the right instead of the left?
ocean ingot
Yeah that's the obvious intuition right?
You could think of it instead of the curve being moved to the left, the grid itself was moved to the right
x+2 = 0 when x = -2
river roost
Ohhhhhh
ocean ingot
That's one of those things that will probably take some time to really sink in, so don't worry if you continue getting caught up on it for a while
river roost
I see
Thank you so much for the help, Desmond seems like a really cool tool
Desmos*
river roost
I'm kinda confused on the next 2 ones as well, I noticed that the 3x one has its own point at (-1, -0.33) and (1, 0.33), Idk what that means but I just wanted to bring it up
ocean ingot
Gimme a minute, need to take care of a thing
river roost
I assume for 10c, we have to factor it into (x-3) (x+3)?
ocean ingot
For 10b, the value of y =3x will be 3 times the value of y=x
So at x = 1/3, y = 1
And 0.33 is close to 1/3 so sometimes that gets used instead
For 10c you could do that, but you could also acknowledge that x^2 - 9 will be 9 lower than x^2
river roost
For 10c you could do that, but you could also acknowledge that `x^2 - 9` will be...
True
OK that makes a lot of sense now, thank you so much, you're saving my ass
obtuse pebbleBOT
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wind pecan
Hi , I’ve been trying to work out the arc length of this equation. And I have found the derivative of both x and y . I have also plugged them in the arc length equation but when I integrate it. I can’t seem to find any pattern to make my integration “simple” if x had been e^t-t it would have made things simpler but since it’s. -1 I’m struggling. Please help 🙂
obtuse pebbleBOT
Hi , I’ve been trying to work out the arc length of this equation. And I have fo...
shut lagoon
The constant term doesn't change the derivative of x though
Are you sure you've computed the derivatives correctly? The integral should be fairly simple
shut lagoon
Yeah ok it's more intricate than I initially thought but if you let $u=e^t$ you and complete the square in the result you can get a manageable integral with trig sub.
warm shaleBOT
Azyrashacorki
obtuse pebbleBOT
@wind pecan Has your question been resolved?
wind pecan
Okay so I completed the square and got
Im pretty sure I did something wrong there
I know the square root and the square will cancel out
As for the negative 4
Won't that give me like an imaginary number or something
obtuse pebbleBOT
@wind pecan Has your question been resolved?
elfin bone
What do i do when i have two sigma notations?
obtuse pebbleBOT
What do i do when i have two sigma notations?
green epoch
Sum of (k*Tn) is k * sum of (Tn)
Tn being the nth term
So you can simply plug in the sums in that expression
-19(-2) -24(18)
elfin bone
oh then i just multiply the answer of -19(-2) -24(18) to 100?
warm shaleBOT
elfin bone
yea then i do -394 * 100 no?
green epoch
Nah
It's just -394
We're dealing in sums already
The number of terms don't matter
obtuse pebbleBOT
obtuse pebbleBOT
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flat hinge
i need help on question B pls
obtuse pebbleBOT
i need help on question B pls
daring ravine
flat hinge
well basically understanding it
im trying to follow bidmas but THAT DONT WORK when the things above all else to follow are both in the calculation
viral blade
!show
obtuse pebbleBOT
Show your work, and if possible, explain where you are stuck.
flat hinge
so so far all the ways i have tried have failed giving me huge decimals which for a question like this shouldnt happen for example i do x sqaured so 144 then x2 so 288 then x-5 so 7 then idk if i add or subtract so i do both then divide by 10 but always comes up with a decimal
tawny copper
so so far all the ways i have tried have failed giving me huge decimals which fo...
Yeah, the result is a fraction
Not interger
flat hinge
Yeah, the result is a fraction
is it a recuring fraction?
viral blade
what's a recuring fraction?
flat hinge
what's a recuring fraction?
a decimal going on forever with a remainder
viral blade
ah probably not
tawny copper
no
viral blade
it should be a terminating decimal
tawny copper
If its a fraction, then its decimal could never going on forever
flat hinge
If its a fraction, then its decimal could never going on forever
well thats what i was taught idk
flat hinge
honestly no clue also just noticed i read his question wrong abt the recuring fraction
.close
obtuse pebbleBOT
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glass mauve
How am I supposed to find interquartile range here?
obtuse pebbleBOT
How am I supposed to find interquartile range here?
sinful plover
can u define interquartile range to me once
glass mauve
It's the smaller range that is typically in the middle. I only know it in terms of the box and whisker plot
Not this kind of graph
sinful plover
it is actually the difference between 75th and 25th percentile values
glass mauve
Do you mean on the y-axis?
sinful plover
so if you sort 100 numbers in an order the difference between 25th and 75th number is the interquartile range
glass mauve
How am I supposed to find interquartile range here?
But what about the case of this graph? How to find that range here?
sinful plover
for this you need to corresponding x-values for 1/4 of 120 and 3/4 of 120 and subtract them
https://www.youtube.com/watch?v=pDjlQ--9-74&ab_channel=MathsKitchen
this video will be helpful for you
glass mauve
thanks
obtuse pebbleBOT
@glass mauve Has your question been resolved?
distant summit
Find the sine of Points(-4,-6)
obtuse pebbleBOT
Find the sine of Points(-4,-6)
distant summit
My teacher said the answer is wrong but I can’t seem to figure out why
I guess my question is more how would I simplify -4/2√ 13
<@&286206848099549185>
.close
obtuse pebbleBOT
obtuse pebbleBOT
✅
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tiny rune
obtuse pebbleBOT
tiny rune
it might be because hours of math has fried my brain
but i dont understand this first step
can someone explain how they substituted
like in a more clear steps
pseudo swift
[2 1] = T [1 2]
so T [2 1] = T( T[1 2] )
that's just applying T on both sides of the equation
but T (T [1 2]) is just T^2 [1 2]
which is the other piece of info you're given in the question
@tiny rune
zenith raft
tiny rune
which is the other piece of info you're given in the question
tysm thats exactly what i needed
.close
obtuse pebbleBOT
teal turret
<:hmmcat:831508801646755850>
fake laila moment
tiny rune
o.o
restive gorge
o.o
pseudo swift
o.o
zenith raft
chain breaker
teal turret
i thought ur name was layla thats why i said
zenith raft
wait no i'm not
that's why i said that
:pensibthis:
zenith raft
i said that's why i said that because i thought you repeating i thought ur name was layla meant you thought my name wasn't layla
molten grove
is one piece a good anime
yes
zenith raft
m8of48...
molten grove
slayla is just laila at home
molten grove
zenith raft
i can do whatever i want
restive gorge
i can do whatever i want
your pfp says otherwise 💀
tiny rune
is one piece a good anime
yuh
zenith raft
i can't do this
teal turret
i said that's why i said that because i thought you repeating i thought ur name ...
I knew my message would provoke your message before I typed it.
molten grove
i need this final yuh thanks
was my affirmation not enough
zenith raft
was my affirmation not enough
evidently
restive gorge
was my affirmation not enough
you were like the 99th of 100
i needed a 100th candidate
pseudo swift
when is this damn channel gonna close
tiny rune
fr lmaooooo
zenith raft
:deadassFaint:
restive gorge
😂
molten grove
yamato>>>
restive gorge
i need to make surehow to wisely waste my time
zenith raft
i want nitro again
molten grove
well you have 1100 episodes to wisely waste your time with
restive gorge
one episode a day
zenith raft
i hate having only commoner emojis
molten grove
better start 
restive gorge
seems like the goal
restive gorge
the main character is called one piece right
restive gorge
and his girlfriend is luffy
obtuse pebbleBOT
Available help channel!
vocal obsidian
little confused on this integral
obtuse pebbleBOT
little confused on this integral
vocal obsidian
integrate 2/3 sec^2(x/3)
ik the answer is 2tan(x/3)
but how
this is in a problem set that isnt supposed to use u substitution
isnt this u substitution
even then it doesnt give the right answer
flat anvil
I think the point of this question is to just sub in x/3 = u
Then recall that d/dx tan(x) = sec^2(x)
so yeah u sub like you said
cold gust
why do you have both a u and a dx in your integral
flat anvil
^
vocal obsidian
bc idk i just didnt write x/3
ik its improper but im not turning this in
.close
obtuse pebbleBOT
flat anvil
This is not 🔠 ...
vocal obsidian
this picture doesn’t load
worn yoke
probably for the best
vocal obsidian
thats fine with me i dont like rude people anyways
obtuse pebbleBOT
Available help channel!
obtuse pebbleBOT
lofty hare
Unsure how do i paramterise the cube
do i do 6 separate integrals of a surface
or hmm
how does one do this?
how do we paramterised a cube
obtuse pebbleBOT
@lofty hare Has your question been resolved?
obtuse pebbleBOT
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vague isle
if i have the DE
mx"+kx = 1
why the solution is x=1/k and not x=m/k ?
obtuse pebbleBOT
if i have the DE
mx"+kx = 1
why the solution is x=1/k and not x=m/k ?
severe plover
limit as x goes to 0 of x/(x+sinx)
obtuse pebbleBOT
limit as x goes to 0 of x/(x+sinx)
lapis charm
Lhopital
severe plover
i tried using squeeze theorem but i get that the limit approaches 0
pliant tide
cuz what u tryna squeeze
severe plover
sinx
pastel wren
how did you squeeze it?
severe plover
wait ill send a picture
then if you take the limit as x approaches 0 its squeezed between 0 and 0
0/(0-1)=0
and 0/(0+1)=0
i solved by using the taylor series for sinx and i got 1/2
which i know is the right awnser
sudden sage
when dividing by x, how do you know if its positive or negative
pastel wren
not completely sure bit i think dividing by x might be the problem, cuz you dont know how signs changes since you dont know if its postive or negative
as youd plot all 3 function they dont squeeze around 0
pastel wren
as i checked on internet its squeezed between cosx and 1
tho i didnt prove this limit myself im not completely sure
severe plover
as i checked on internet its squeezed between cosx and 1
which limit are you talking about?
pastel wren
sinx/x
severe plover
yes but in the process you divide by sinx which you dont know if it is positive or negative
pastel wren
look up the proof by yourself, but i dont think there is any dividing as far for inequalities themselves
cosx<=sinx/x<=1 there is no actual dividing by x
in inequalities
severe plover
but wouldent dividing by sinx be the same thing as it is a variable in itself?
and varies between -1 and 1
pastel wren
you mean dividing by x?
severe plover
and therefor could also be either positive of negitive
no if you look at the proof using the circle with a radius of 1 you can see you divide by sinx
to get to the awnser
severe plover
ok i get it he specificaly says he is looking at the limit as x approaches 0+
pastel wren
oh ok
severe plover
but why wouldent that work for the limit im trying to solve
looking at 0+ and 0- individually i would get the same awnser using squeeze theorem
obtuse pebbleBOT
@severe plover Has your question been resolved?
narrow shoal
anyone?
narrow shoal
learn alevel as math ing
at topic parallel to
i can't understand why when it parallel to j, have to let p+lamda q is 0
narrow shoal
yes?
narrow shoal
OK! i try on geogerbra now
when parallel to j, i have
to be come 0
i become to 0, get parallel to j
dame,why can i got it for first time,it's seen so easy to understant on graphs
pastel wren
looking at things graphically is really helpful to understand
narrow shoal
ture
pastel wren
most topic in math or even other science
obtuse pebbleBOT
@narrow shoal Has your question been resolved?
runic arrow
obtuse pebbleBOT
timid silo
draw a rough graph
dark stirrup
The function could look like anything
dark stirrup
!original
obtuse pebbleBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
runic arrow
Consider a strictly increasing function ƒ : [1, 2] → [3, 4] with the interval [3, 4] as the range.
dark stirrup
All this describes is a function with domain [1, 2] and codomain [3, 4]
runic arrow
whats a codomain
dark stirrup
Consider a strictly increasing function ƒ : [1, 2] → [3, 4] with the interval [3...
There are a number of ways that could look. The easiest would be a straight line
dark stirrup
whats a codomain
Another word for range
runic arrow
ah
dark stirrup
range, codomain, and image all mean roughly the same thing
dark stirrup
looks good
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
tight zealot
does the extreme value theorem say a function which is continuous on the interval [a, b] is bounded above and below and attains a maximum and minimum ?
obtuse pebbleBOT
does the extreme value theorem say a function which is continuous on the interva...
scenic wind
Yes
tight zealot
aight thx
scenic wind
The local max and min are
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
timber flame
obtuse pebbleBOT
timber flame
Anybody knows the solution for this
raw torrent
U see that 60 degree
white knot
Anybody knows the solution for this
use sin (DBA) then cos(CDA)
raw torrent
What do u mean
white knot
What do u mean
or u can get the CAB
white knot
Then you can use sin
yeah yeah
raw torrent
Then we use special triangle
alpine verge
we’re given that the two events are disjoint, or mutually exclusive, so is the intersection of event A and B possible?
obtuse pebbleBOT
i'd say j
The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.
obtuse pebbleBOT
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timber flame
<@&286206848099549185>
balmy wind
prime wind
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digital fiber
Hello guys. Can anybody help me?
obtuse pebbleBOT
Hello guys. Can anybody help me?
@digital fiber Has your question been resolved?
obtuse pebbleBOT
@digital fiber Has your question been resolved?
digital fiber
No
daring rock
Have you tried anything?
@digital fiber
Seems like we should be able to find the critical points of (gof) and go from there
digital fiber
I'm trying to find the domain from f(x) that cause 5<f(x) <14
daring rock
Really, we only need to find where f(x) = 5, because that's where g'(f(x)) may change signs
If f(x) => 14 or f(x) <= -2, g'(f(x)) is undefined anyway
digital fiber
If f(x) => 14 or f(x) <= -2, g'(f(x)) is undefined anyway
Okayy, thankssss so much
obtuse pebbleBOT
Okayy, thankssss so much
daring rock
Okayy, thankssss so much
np 👍 Did you figure the rest out from there?
digital fiber
Yep, I got the rest. Thanks mate
daring rock
Awesome 👍 sure thing
river falcon
you're shifting the phae by +pi/4
which shifts the graph to left by pi/4
though the period of both is still same
worn yoke
we have that f(x) = cos(8x) so then f(x + pi/4) = cos(8(x + pi/4))
timid silo
Jus had a question any tips to become better at math ?
obtuse pebbleBOT
Jus had a question any tips to become better at math ?
high lily
practice
wooden cipher
rugged barn
Learn every definition by heart
Understand every property and theorem
In that order
timid silo
Like I got my report card back
rugged barn
And practice as always
timid silo
And my grade was very low even tho I study
Like crazy
They told me I complete home work but struggle to perform well on test
high lily
review what you got wrong, try to read and get better understanding of the related concepts
timid silo
review what you got wrong, try to read and get better understanding of the relat...
Okay I’ll take these in to mind
And do them
eternal ore
you got this man
timid silo
I have a quiz on Tuesday
timid silo
you got this man
I appreciate u bro
high lily
would you be able to complete those of you weren't in a test environment
timid silo
would you be able to complete those of you weren't in a test environment
Most of them yes but I think I jus need to u understand the material
high lily
this also would've been better suited for a #discussion channel (there are a few)
these are intended for assistance on math questions/problems.
obtuse pebbleBOT
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fathom flicker
@flat anvil
obtuse pebbleBOT
<@328662734008745984>
fathom flicker
yah okay
ur right
I've proven all but injectivity
suppose f(a,b)=f(c,d) then ab=cd
and I need to use this to prove a=c and b=d
hm
flat anvil
Hint to my sir: use all the assumptiions
fathom flicker
hmm okay so
ab=cd=ba
abd^(-1)=c
if bd^(-1) = e
then a=c
and so
if bd^(-1) in A cap B
then a=c
b, d^(-1) in B certainly
but I can't show they're in A also
flat anvil
Ah i see where you are stuck
There is a critical step that you have gotten very close to
basically, you want to show that bd^{-1} is = to something in A
does that make sense
flat anvil
Should I use ab=cd <@328662734008745984>
Indeed siur
fathom flicker
flat anvil
You have concluded that bd^{-1} is in A
So you get they are in the intersection which indeed shows injectiity
nice job sir
fathom flicker
thank you
obtuse pebbleBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
obtuse pebbleBOT
zenith raft
sakatayaksha
obtuse pebbleBOT
Available help channel!
distant seal
obtuse pebbleBOT
distant seal
how do i get -1 to 1?
shut lagoon
Looks like a trapezoid to me, no?
mellow wraith
what i suggest is break them into normal shapes
ike -1 to 0 theres unit sqaure and half a square
like*
distant seal
i got 23/2
shut lagoon
Yeah well you can break it down however it makes sense to you, keeping in mind that area BELOW the x-axis is counted negatively
distant seal
those triangles cancel out right?
shut lagoon
Yeah 10
obtuse pebbleBOT
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fathom flicker
obtuse pebbleBOT
fathom flicker
flat anvil
Theorem. A cyclic group G has a unique subgroup of every order dividing |G|
Try proving this
The converse is also true but the proof is much harder
(I have written this up)
fathom flicker
Why does that help
flat anvil
What is the size of gHg^-1?
fathom flicker
the size of H right?
fathom flicker
uh
N cyclic normal of G
H subgroup of N
H is cyclic because its a subgroup of a cyclic group
According to ur theorem, H has a unique subgroup of order |H| yes since |H|*1=|H|
and this must be H itself
fathom flicker
What is the size of gHg^-1?
I don't actually rememember why this is true though
flat anvil
Would my sir like to prove that phi(x) = gxg^-1 is an (inner) automotohism of G?
flat anvil
and this must be H itself
Yep
fathom flicker
Would my sir like to prove that phi(x) = gxg^-1 is an (inner) automotohism of G?
ah I've done that before on HW or something
flat anvil
Have you seen that G/Z(G) cyclic => G abelian?
fathom flicker
No quotient stuff yet
flat anvil
Ah gotcha
Anyways it turns out that G/Z(G) is iso to Inn(G) = {phi(x) = gxg^-1 : g in G} which is p cool
fathom flicker
Hmm
fathom flicker
Have you seen that G/Z(G) cyclic => G abelian?
Yes we actually have this in lecture notes from Monday I'm seeing now
if it's useful
obtuse pebbleBOT
molten grove
ABCD
zenith raft
m8of48...
molten grove
slaaayla
zenith raft
present
obtuse pebbleBOT
Available help channel!
zinc stump
Given the following subring of $\mathbb C$:\
$\mathbb Z \sqrt{-3} = {a+b\sqrt{-3}|a,b\in \mathbb Z}$ (it's an integral domain and principal ideal domain)\
I need to prove the following:
let $c \in \mathbb Z$ \
a. if there exists $a,b\in \mathbb Z$ such that $a^2+3b^2=c$ then $c\equiv 0,1,3,4,9~(mod~9)$ pretty sure I managed to do that ok \
b. prove that if $p\equiv 2,5,6,8 ~(mod 9)$ odd prime integer so p is also prime in that subring we defined.
c. let p prime that satisfies section b. prove that in the ring $\mathbb Z[\sqrt -3]/ \langle p\rangle$ there is a solution to x^2 = -1
obtuse pebbleBOT
Given the following subring of $\mathbb C$:\\
$\mathbb Z \sqrt{-3} = \{a+b\sqrt{...
warm shaleBOT
mtr123
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
obtuse pebbleBOT
@zinc stump Has your question been resolved?
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obtuse pebbleBOT
@zinc stump Has your question been resolved?
obtuse pebbleBOT
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Available help channel!
night plume
obtuse pebbleBOT
novel knoll
You are given total should sum to 100. Use that
obtuse pebbleBOT
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pulsar jewel
Hello, it should be fairly obvious for me but for some reason the solution doesn’t stick out
obtuse pebbleBOT
Hello, it should be fairly obvious for me but for some reason the solution doesn...
pulsar jewel
I’ve tried using a tree diagram but didn’t really work
The Line in the middle means given that
alpine verge
so lets just use the formula for conditional probability to figure out what P(A) is first
then we can just use that to find P(A')
pulsar jewel
so lets just use the formula for conditional probability to figure out what P(A)...
I thought P(a) would just be 0.6
But maybe there is more than just A and B
So I can’t assume that
alpine verge
yeah we cant assume that
pulsar jewel
That’s the first mistake I made then
warm shaleBOT
y0shi
alpine verge
we can rearrange that to find what P(A and B) is
pulsar jewel
So essentially AIB is the probability of people who do A and B out of the total of B
If that makes sense
pulsar jewel
and the n is or
pulsar jewel
warm shaleBOT
y0shi
pulsar jewel
It’s the wrong side whoops
pulsar jewel
Oh right
alpine verge
so we now know what P(A and B) is
pulsar jewel
0.124
alpine verge
yep thats it
pulsar jewel
So 0.504
alpine verge
yeah
pulsar jewel
Thanks so much, the mark scheme matches that
alpine verge
yw!
pulsar jewel
Have a great day 🙂
alpine verge
you too
pulsar jewel
.close
obtuse pebbleBOT
obtuse pebbleBOT
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stoic laurel
\lim_{x \rightarrow -2^{+} } \frac{3-x^{2}}{ \sqrt{x+2} }
obtuse pebbleBOT
\lim_{x \rightarrow -2^{+} } \frac{3-x^{2}}{ \sqrt{x+2} }
warm shaleBOT
ƒ(Why am. I here)=misery
versed stratus
this?
stoic laurel
how can i show my work for this, I found the answer to be -inf, but the teacher took off points just bc of I didn't show proper work
yes
marsh geyser
Is anything wrong with just sub or am i missing something?
normal cairn
Is anything wrong with just sub or am i missing something?
right?
verbal goblet
Is anything wrong with just sub or am i missing something?
dividing by 0
normal cairn
but its not 0/0 so its not an indeterminate form
so we can see where the result goes
-infinity
marsh geyser
Just take care of the sign
verbal goblet
yep
normal cairn
best guess ive got is the prof wanted u to calculate the sqrt limit seperately and see it goes to 0+ so you can then calculate the limit as a whole
if you even did that then im not sure whats wrong
stoic laurel
I appreciate the feedback
I should probably had clearly shown which side the number is being approached
marsh geyser
You should only show
The sign of the denominator
Showing that x is a little bigger than 2
So you get a very close number to 0 but possitive
Then when u divide -1/positive u get negagice
normal cairn
yeah if it approached from the left then the limit wouldnt exist, thats why i think thats what the professor wanted
marsh geyser
Did u show that?
marsh geyser
yeah if it approached from the left then the limit wouldnt exist, thats why i th...
?
If it goes from left the limit would be +infinity
normal cairn
this same limit approaching -2 from the left doesnt exist
stoic laurel
bc sqrt can't have neg
normal cairn
theres no function of the sqrt from the left
marsh geyser
this same limit approaching -2 from the left doesnt exist
Correct
stoic laurel
alright
normal cairn
If it goes from left the limit would be +infinity
if we assume its in the imaginary plane yes, but i just assume this isnt that
marsh geyser
Apologizes i overread
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
wicked pebble
does my teacher made a mistake while taking a square or am i missing a point?
minor furnace
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next magnet
hello
next magnet
i am trying to figure out how
(3 / x^2 - 1) + 1
becomes
x^2 + 2 / x^2 - 1
obtuse pebbleBOT
@next magnet Has your question been resolved?
teal turret
make common denominators
next magnet
make common denominators
ive had chat gpt break it down for me like 10 times and my brain cant wrap around it. Ik i have to make common denominators but like i just dont understand. i need a visual example lol
teal turret
$\frac 3{x^2 -1} + \frac {x^2 -1}{x^2 -1}$
warm shaleBOT
Stephen
teal turret
Then add the fractions
teal turret
Did u not read what I wrote
next magnet
Did u not read what I wrote
i did but like how the fck do you go from
(3 / x^2 - 1) + 1
to
$\frac 3{x^2 -1} + \frac {x^2 -1}{x^2 -1}$
warm shaleBOT
akuzie
teal turret
What do u get when dividing the second fraction
next magnet
okay but why do you have a second fraction
we started with 1 fraction
what is the step to make it 2 fractions
how does the 1 turn into x^2 - 1 / x^2 - 1
teal turret
It’s not
teal turret
The reason you think that is because your basic math foundations are probably shaky
next magnet
yeah they are
teal turret
How would u add this: (3/4) + 8
teal turret
i never focused in school
How can u complain about it being bs if it’s on u that u didn’t focus
teal turret
3/4 + 8/4 = 11/4
No
teal turret
Just start focusing
next magnet
How can u complain about it being bs if it’s on u that u didn’t focus
u right im not tryna complain but yeah i do regret not focusing. just didnt care abt school till junior year high
teal turret
$\frac 34 + 8$
next magnet
wait
warm shaleBOT
Stephen
next magnet
ok hold on let me try
teal turret
u right im not tryna complain but yeah i do regret not focusing. just didnt care...
At least you admit this, many don’t
next magnet
8 = 32 / 4?
teal turret
Yes
next magnet
At least you admit this, many don’t
i mean ppl dont wanna take accountability. at the end of the day excuses are just that brother. gotta just do what u can to improve yourself
next magnet
What values are excluded?
i just checked w the answer sheet ngl forgot i had it for this problem but im right
but x = +/- 1 are exluded
bc
(1)^2 - 1 = 0
(-1)^2 - 1 = 0
domain cant = 0
im sure yk wayyy better than i do lol
but good practice to explain
teal turret
Good explanation
next magnet
Good explanation
Ty sir, i need an A on this exam. and my econ. i hate college man
are u in college?
teal turret
Yea
next magnet
yeah i wanna transfer
hopefully
BC level school would be nice
somewhere in boston or nyc
but like uva or umich are also possibilities
teal turret
Aren’t those places super expensive tho
teal turret
Ah nice
next magnet
but ya thats y i need high scores on my finals
next magnet
bc i had some unforeseen shit happen during the semester so like i did not focus bc yk mentally wasnt there type shit
but we good now
teal turret
Ah dang
teal turret
Yea ikwym
teal turret
Lol bruh