whats AP?
#help-28
twilit heart
half lava
arithmetic progression
half lava
did u get my doubt ?
half lava
umm
twilit heart
youll get the help
half lava
ohh
twilit heart
if you go to #discussion or a channel like that myabe you can ask them to help you in your help channel
half lava
but its urgent for me i have a test in 2 hrs
twilit heart
bro lock in
half lava
if you go to <#268882317391429632> or a channel like that myabe you can ask them...
ok i will ask
zenith kernel
Clearly Σa_i i in I =Σa_i i in J when |I|=|J| and sum of elements of I equals sum of elements of J, (by expression of arithmetic progression)
half lava
?
native glade
All need be distinct?
half lava
yeah all are distinct
zenith kernel
You asked for |I|=|J|=3, I say it’s true in general. And they don’t need to be distinct
half lava
You asked for |I|=|J|=3, I say it’s true in general. And they don’t need to be d...
im not able to understand what you are saying never seen those symbols
zenith kernel
I put it in Tex then
half lava
?
native glade
I put it in Tex then
Bro he is kid
zenith kernel
$\sum_{i \in I}a_{i}=\sum_{i \in J}a_{i}$ when $|I|=|J|$ and $\sum_{i \in I}i =\sum_{i \in J}i$
glossy valveBOT
Cogwheels of the mind
half lava
no they represent the terms of ap like first term+5th term+8th term= same
zenith kernel
I,J can have identical elements, not necessarily sets
half lava
umm
zenith kernel
Bro he is kid
I will use example
half lava
my teacher didnt teach me this
zenith kernel
my teacher didnt teach me this
Give me four positive integers, can be duplicated
native glade
my teacher didnt teach me this
Put up the proper question
half lava
ok wait
In an Arithmetic Progression (AP), the sum of any two numbers equidistant from the beginning and the end is constant and always equals the sum of the first and the last term
right?
native glade
In an Arithmetic Progression (AP), the sum of any two numbers equidistant from t...
Yup
zenith kernel
Anyway, 1+7+7+8+5=4+6+2+13+3, okay, this is an example, then a1+a7+a7+a8+a5=a4+a6+a2+a13+a3
zenith kernel
So not just 3, 5 works, any n works. And not necessarily distinct
This is obvious once you plug in expression of AP
half lava
Yup
for this i am asking like here it is applicable to sum of pairs na like terms are pairs so like if i take triplets is it applicable there also?? over here 1st and last term term sum 1 pair equal to 2nd and 2nd last term another pair and so on so in my class teacher told us that there is no such property of an AP for triplets but like when i discretely like took some examples of AP and checked i found out like they are saying see i took (a1+a7+a8=a9+a4+a2) my teach told it like a trick ;like on both sides try to take the base sum same see 1+7+8=9+5=2=16 same so i am checking any such property exists
native glade
for this i am asking like here it is applicable to sum of pairs na like terms ar...
I understand now
Wait I'm working
half lava
you got it? like my doubt
half lava
but
my teacher said there is no such thing for triplets or quadruple numbers which you took
this is random na
native glade
Such property exists and it’s not a big deal
Bro treat him like 10th class kid not college student
half lava
And I answered: Yes
which you took in example
zenith kernel
That’s why i gave him an example
half lava
Bro treat him like 10th class kid not college student
i am in 11th
zenith kernel
Your teacher is wrong
native glade
i am in 11th
Don't worry
half lava
Your teacher is wrong
pls can you explain again
zenith kernel
I didn’t give you explanation, I gave you a statement without proof. I can prove it if you want
tame cradle
ok i am here
native glade
In case of triplet that will not be true
zenith kernel
**Cogwheels of the mind**
a(n)=rn+s, so first equation is simply second equation multiplied by r and add |I| s
half lava
I didn’t give you explanation, I gave you a statement without proof. I can prove...
yes pls
half lava
In case of triplet that will not be true
yahh where is that like the limitation case
can u explain
that is the part i need
zenith kernel
I better slow down, okay for a AP a(n), there exists r and s such that a(n) has an expression a(n)=rn+s, right
half lava
what is r and s
zenith kernel
numbers
half lava
yes
native glade
Counter example. Let 1,2,3,4 be ap
Is 1+2+3 = 4+3+2?
half lava
an=a+(n-1)d
half lava
Counter example. Let 1,2,3,4 be ap
Is 1+2+3 = 4+3+2?
pls go ahead
zenith kernel
Like 1,3,5,7,9… a(n)=2n-1, r=2, s=-1
native glade
pls go ahead
Counter example completed
half lava
Counter example. Let 1,2,3,4 be ap
Is 1+2+3 = 4+3+2?
no like the sum should be same
over here it is not same
zenith kernel
Like 1,3,5,7,9… a(n)=2n-1, r=2, s=-1
Got it? Any AP, there exists r and s such that a(n)=rn+s
half lava
if the sum is not same if we expand ofcourse it will not be true
native glade
Okay.
half lava
Like 1,3,5,7,9… a(n)=2n-1, r=2, s=-1
yes
zenith kernel
5+5+5+17=4+4+15+20 for example
half lava
Got it? Any AP, there exists r and s such that a(n)=rn+s
i leant with different variables sorry i was confused
zenith kernel
Multiplied by r on both sides, then add n=4 many s
half lava
5+5+5+17=4+4+15+20 for example
ok
zenith kernel
r(5+5+5+17)+4s=r(4+4+15+20)+4s
half lava
ok
zenith kernel
This is exactly a(5)+a(5)+a(5)+a(17)=a(4)+a(4)+a(15)+a(20)
Because for example a(5)=5r+s
zenith kernel
Sure
(I do the whole explanation, using examples. Give a general expression in the beginning is my habit as a mathematics lover, for the sake of accuracy)
native glade
You want to prove if in ap
ax+ay+az=au+av+at then x+y+z=u+v+t?
native glade
I don't know why that feels obvious
zenith kernel
Which holds for any n terms not just 3
half lava
but this an = rn+s
zenith kernel
It is, that’s why i said it’s not a big deal
half lava
its confusing for me as i leant an=a+(n-1)d
native glade
its confusing for me as i leant an=a+(n-1)d
2 mins
half lava
a-first term , d-common difference
zenith kernel
then a(n)=dn+(a-d), so my r, s are your d, a-d
Oh don’t be confused, only n is variable, r and s are just numbers
native glade
You want to prove if in ap
ax+ay+az=au+av+at then x+y+z=u+v+t?
Try to simplify in terms of a and d you will get the proof.
half lava
Try to simplify in terms of a and d you will get the proof.
i tried but
failed
@zenith kernel
you mentioned s=1 so a-d=1 but d=2 so a=3 but ap a=1
zenith kernel
r(5+5+5+17)+4s=r(4+4+15+20)+4s
Similar. What is your example again? 1+7+8=9+5+2?
This gives your r(1+7+8)+3s=r(9+5+2)+3s, thus a1+a7+a8=a9+a5+a2
zenith kernel
a(n)=1+2(n-1)=2n-1
half lava
yes
zenith kernel
2,-1
half lava
then a(n)=dn+(a-d), so my r, s are your d, a-d
but you said a-d=s and d=r
native glade
One mistake that (y-1)d
zenith kernel
but you said a-d=s and d=r
Yeah, r=d=2, s=a-d=1-2=-1
zenith kernel
Sure
zenith kernel
Yeah
half lava
or only triplets
zenith kernel
I just showed you 4
half lava
how did you think of this method
half lava
yeah like multiply by r and add 4s
zenith kernel
Yeah n, terms then add n many s
half lava
I think it’s not a big deal
well ig its cleared now thnx
zenith kernel
Np
zenith kernel
Any time, ping, DM, whatever you like
native glade
Any time, ping, DM, whatever you like
What are you studying and at what level?
zenith kernel
Whatever i feel interested, representation theory for now. Obtaining PhD
half lava
What are you studying and at what level?
a hit bro are u from india
native glade
Whatever i feel interested, representation theory for now. Obtaining PhD
Phd in maths?
half lava
oof
zenith kernel
Yeah
native glade
What is your research topic?
half lava
how did you think of this method
i guess that answers this question
native glade
a hit bro are u from india
Yup
zenith kernel
Not a serious one though, just found a very very small branch, quandle theory, in order to write a thesis. And graduate, no ability to do research, so math as a hobby
half lava
.close
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native glade
Not a serious one though, just found a very very small branch, quandle theory, i...
What were your subject at post graduation?
zenith kernel
Same, Quandle theory
autumn token
how do u do htis
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how do u do htis
sudden chasm
how do u do htis
you've been given the rate of flow
dV/dt
for part a) if water is flowing @ 20L/min for 10 min, then can you tell me the volume that increased in the tank?
for part b) you've to solve the differential equation dV/dt = 10 for t=0 to t=10
the constant c is the volume that gets filled up in the initial 10 mins
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@autumn token Has your question been resolved?
autumn token
for part a) if water is flowing @ 20L/min for 10 min, then can you tell me the v...
200
ok i got a = 10
b = 15
c = 200
d = 53
?
autumn token
ok so its 1000 liters
minus 200
because of the first 10 minutes
and then u have 800
so then 800 / 15?
sudden chasm
yeah
sudden chasm
is c meant to be 200
yeah
sudden chasm
how do i sketch this
well we're working only in the 1st quadrant here. from x=0 to x=10, the graph will be a straight line passing through origin
sudden chasm
is c meant to be 200
oh wait no. lemme recheck
sudden chasm
ok i got a = 10
a=20
sudden chasm
c=50
because dV=15dt
the limits of the integral go from 200 to V, 10 to t
d=63.33
b=15
strange mason
for this
strange mason
wldnt this method
jst disregard
the small area
between
curve and y axis
u see the small triangle
foggy vapor
I mean thats just a graphical representation. a and b are arbitrary. You could totally have a graph that wouldnt include that bit
strange mason
I mean thats just a graphical representation. a and b are arbitrary. You could ...
well
no i dont think so
no no
u cant
cos when x is 0
(0,ab)
a and b is greater than 0
its impossible
we both arrived at the same answer
foggy vapor
,w plot x^2 - 2
strange mason
but i dont see how his method is correc
glossy valveBOT
foggy vapor
No region here
strange mason
but
u jst changed
the entire graph
no combination of a and b
cld result that
foggy vapor
the entire graph
Their equation is for any arbitrary quadratic
strange mason
Their equation is for any arbitrary quadratic
not any though
cos it has a and b to be in a range
of values
for ur quadratic to work
and and b would have to be the same and opposite
as in
like
-2,2
for e.g
foggy vapor
and and b would have to be the same and opposite
Where in there does it say that
next cedar
not a calculus guy but they just said 0 < a < b
so there's no way a and b could be opposites if they're both positive
rough plaza
u see the small triangle
note that this small triangle is counted only if y-axis is also a condition for region bound.
sonic stratus
althought im not completely sure the fact that they both have to be positive is really needed for the formula to work
strange mason
so there's no way a and b could be opposites if they're both positive
thats my point
he showed a graph of
x^-2
theres no x term
hence
theyd need be opposite and equal for that to occour such as (x-2)(X+2)
so his example was wrong
sonic stratus
theyd need be opposite and equal for that to occour such as (x-2)(X+2)
again, i dont think the formula stops working when both roots are opposites
strange mason
note that this small triangle is counted only if y-axis is also a condition for ...
wdym
next cedar
tbh it still wouldn't justify including that tiny bit
if you include the red bit, you'll also have to include the orange bit because you are not bounding by the y-axis
and then you run into the issue of that orange bit being infinite
rough plaza
wdym
oh. um, well the question didn't state about "find region among curve,x-axis and y-axis", but just between "find region between curve and x-axis"
so, what the question really wants is just this region
strange mason
bro
rough plaza
without using the y-axis
sonic stratus
sonic stratus
In fact the formula also works for negative and positive values too
next cedar
perhaps show your method?
sonic stratus
i included this small red triangle
Including the triangle is wrong tho
rough plaza
i included this small red triangle
is it possible for you to show your work?
sonic stratus
Youre prob getting a close answer because its small
strange mason
i cant im on PC, but i basically did integral from a to 0 and the equation - integral of b to a and the equation
expaneded it out correctly
and got the answer
strange mason
Youre prob getting a close answer because its small
possibly
next cedar
uh if I'm interpreting it correctly
sonic stratus
i already showed my own way of doing it, but just to leave it as latex
$\int_a^b (x-a)(x-b) dx = \int_0^{b-a}u(u+a-b)du = \int_0^{b-a}u^2+(a-b)u du$
glossy valveBOT
next cedar
it sounds like you did this?
sonic stratus
its a breeze to get the formula this way
strange mason
it sounds like you did this?
it was the first line but limits switched arnd and signs the same
like
the a is at the top
and the b is at the top
next cedar
then it's 0 to a, not a to 0
strange mason
sorry
next cedar
but hm
I probably will have to concede to zzz's judgment of the triangle part being small enough
strange mason
once u integraet thjat
like the small triangle part
u get -a^3/3 +(a^2b)/2
so
seems small
but it did matter
as it cancelled stuff from the other integra;
one other question
how come
if u do
ok
so take this
so blue is = to k
so how wld u know the pink
equals to k asw?
sonic stratus
K is "some number", and given that doing f(-x) is just a reflection about the y axis.
If you integrate with symetric bounds, the answer has to be the same
remembering that integrals are just an accumulation over a region:
thorny bluff
so u cant get negative area right?
you can if its signed area and the function is below x axis
sonic stratus
area scalar
If we are still talking about the problem revolving around the parabola, you technically can.
But if the result is negative, just like, take off the negative sign.
since we consider area to be strictly positive.
for the formula $\frac 16 (b-a)^3$
glossy valveBOT
sonic stratus
if you get a negative value is basically because you messed up the order for a and b
which isnt really a big deal.
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@strange mason Has your question been resolved?
strange mason
you can if its signed area and the function is below x axis
thanks
strange mason
But if the result is negative, just like, take off the negative sign.
ok
yh yh
.close
unborn glade
det a,b,c,d = 8
det a,3,c,-1=8
det a,3,c,0=10
det a,3+b,c,-1+d=?
unborn glade
how do i start
sacred yarrow
What’s det?
unborn glade
determinant i think
worn matrix
determinant
sonic stratus
det a,b,c,d = 8
det a,3,c,-1=8
det a,3,c,0=10
det a,3+b,c,-1+d=?
You know the formula for a 2x2 determinant?
unborn glade
no
foggy vapor
The notation certainly is strange. Are those 2x2 matrices?
unborn glade
yes
sonic stratus
This is essentially a system of equations. But it requires you to know the formula for the determinant first.
unborn glade
is it ad-bc?
sonic stratus
Try to translate the problem into equations to solve.
unborn glade
ad-bc=8
-1a-3c=8
0a-3c=10
sonic stratus
Try to clear these a little bit then
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slate hill
yo chat
slate hill
how to find length and breadth when area given
delicate torrent
of a rectangle?
like a rectangle with area 20
how to find length and breadth?
@slate hill
devout meadow
delicate torrent
how to find length and breadth when area given
!original
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how to find length and breadth when area given
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.
lofty egret
how to find length and breadth?
Area alone isn’t enough 😭
L × B = area has infinite answers — you need one more detail
delicate torrent
Area alone isn’t enough 😭
L × B = area has infinite answers — you need one more...
again, im not the OP
slate hill
hiiii
next cedar
don't hi, provide the question lol
warped frost
hiiii
so do you have a more specific question, as asked by like three or four helpers here?
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mental pewter
how can i find SK/SD, know that AB//CD, AB=3CD, M, N are the midpoints of SB, SC relatively, K = SD ∩ (AMN)
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spice raven
need work power energy questions
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need work power energy questions
spice raven
any suggestions
/
chrome canyon
any suggestions
/
u a jee guy?
austere cove
need work power energy questions
Khan Academy?
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chrome canyon
@spice raven ?
gritty rose
need work power energy questions
calm perch
Are there any easy ways to solve this without plugging in the value for the roots?
calm perch
Context: The original question was "if x = 3 - root 5, y = root 5 - root 7, and z = root 7 - 3, then find the value of x cube + y cube + z cube". I managed to apply the identity x+y+z=0 to get to 3xyz.
But I can not go further than that, everytime I solve it; There is a new answer.
grave elm
one way would be just brute force multiplying it out
and its not that bad either
its gonna have 8 terms, some of which will cancel out
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proven pulsar
Hello helper, this is my query related to double integration Evaluate ∬(xy−y
2
)
1/2
dydx, where R is a triangle with vertices (0,0),(10,1),(1,1)
next cedar
might wanna show the picture of the original question, cuz your question is kinda wack in formatting from the copypasting
zenith kernel
$\iint \sqrt{xy-y^{2}}dydx$?
glossy valveBOT
Cogwheels of the mind
zenith kernel
(When calculate it, do it by dxdy, x first will make things easier, but I don’t know what your question is)
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@proven pulsar Has your question been resolved?
proven pulsar
There
proven pulsar
what I want to know is why there's a 1/y there, where did it come from?
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flint ore
Q16
slate violet
which one is q15
glossy valveBOT
1 divided by 0 equals Infinity
next cedar
hint: $2025 = 45^2$
that's q17.
delicate torrent
idk
next cedar
did you not see what OP said in his message
that's why we are all asking which one q15 is
delicate torrent
OP ticked 16
keen vector
so what
next cedar
that's why we asked!
delicate torrent
so i assumed 17
keen vector
people just be opening help channels then going afk
delicate torrent
ping mods?
keen vector
for what
delicate torrent
wasting help channels?
next cedar
I mean, it's not a troll question
keen vector
wasting help channels?
there are enough
next cedar
and it's not like they're done with the question but refused to close
keen vector
so it doesn't matter
slate glacier
Shouldn't the ticked one be q16
next cedar
Shouldn't the ticked one be q16<:KEK:586240877358350341>
that's why we're asking lol
keen vector
Shouldn't the ticked one be q16<:KEK:586240877358350341>
yes most likely
delicate torrent
i even thought q16 is done
flint ore
Q16
keen vector
but the tick is hiding the number
flint ore
Q16
next cedar
so once again: what have you tried?
keen vector
lmao
next cedar
let's not repeat like a broken record, shall we
but do you not get the whole thing, or what
next cedar
do you wanna answer my question first?
keen vector
Can anyone help Q16 the tick mark
yes
sacred yarrow
👀
slate glacier
You gotta cooperate with the helper to get help mate
next cedar
can't help you if we don't know where you're stuck at
flint ore
Volume portion
next cedar
so you don't know the formula for the volume of a cuboid?
flint ore
Lbh
next cedar
or is there something else about the volume that bothers you?
flint ore
After percentage
next cedar
you are told that the tank starts out 70% full
so what is the volume of the tank? how much is 70% of that volume?
first: what is the volume of the tank?
flint ore
I got it now thank you
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delicate torrent
hold up
delicate torrent
I got it now thank you
is there any more questions left that you don't understand/don't know how to do it?
sacred yarrow
I got it now thank you
.solved 
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fluid prawn
how do u use squeeze theorem for this
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how do u use squeeze theorem for this
onyx glen
well you want to find a pair of squeezing functions obviously
but i would go polar before that anyway
fluid prawn
well you want to find a pair of squeezing functions obviously
yeah how i know which ones to use
like for sin its between 1 and -1
onyx glen
are you permitted to re-express this function in polar coords yes or no
wary badge
how do u use squeeze theorem for this
Its wont work
fluid prawn
are you permitted to re-express this function in polar coords yes or no
ye but i wanna use squeeze for practice
wary badge
Y^2 first line
fluid prawn
Its wont work
they did this but i dont understand how they chose those values
wary badge
they did this but i dont understand how they chose those values
Which value
wary badge
the 0 and x^2+y^2
0 bc the lim say so
fluid prawn
So u can bound the function
ok so it could be anything
like it coulda been x instead of y^2?
and how did this 0 become -|x|(x^2+y^2)
if all they added was a x
fluid prawn
what i was saying replace y^2 with x but keep the x^2+y^2 and 0
wary badge
what i was saying replace y^2 with x but keep the x^2+y^2 and 0
But the function contain y^2
Not x^2
fluid prawn
But the function contain y^2
Not x^2
i thought the middle number can be anything
wary badge
i thought the middle number can be anything
But ^2
fluid prawn
as long as its true for left and right bound
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@fluid prawn Has your question been resolved?
late blade
i thought the middle number can be anything
y^2 is easier and more meaningful
you cant know if x is greater or smaller than xy^2 cuz y < 0 is possible
you cant know if x is smaller than x^2 + y^2 cuz x < 0 is also possible
starting with x gets you nowhere basically
fluid prawn
y^2 is easier and more meaningful
do they choose y^2 cus its in the numerator?
late blade
they choose y^2 cuz its a good starting point
i think starting with the denominator works too for some questions it just depends on which thing is more useful
fluid prawn
they choose y^2 cuz its a good starting point
but is it cus its in the numerator and denominator
like how else i know if its a good starting point
late blade
no its cuz ^2 guarantees that its >0, we know 1 thing
and y^2 gotta be smaller than y^2 plus a positive number, we know 2 things, we can squeeze
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late blade
pluh
fluid prawn
no its cuz ^2 guarantees that its >0, we know 1 thing
and y^2 gotta be smaller t...
so the y^2 isnt even from the fraction?
i dont get it
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late blade
its in the fraction this time, but it doesnt need to. it just gotta be useful and related
the usefulness this time doesnt come from the fact that its in a fraction
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its in the fraction this time, but it doesnt need to. it just gotta be useful an...
late blade
bro
fluid prawn
its in the fraction this time, but it doesnt need to. it just gotta be useful an...
so i can basically write x^4 in the middle if i wanted
late blade
if you can link it back to the problem sure
fluid prawn
ok how come in this the 0 become -|x|(x^2+y^2)
shoudlnt it stay 0 forever
cus they r multiplying by 0
fluid prawn
what
for squeeze its multiplying all sides by x in the second step
so it should be 0 on the left still?
late blade
so it should be 0 on the left still?
you dont know if x is -ve or +ve, so you cant determine the inequality sign if its still 0
the accurate limit now is that behemoth
fluid prawn
you dont know if x is -ve or +ve, so you cant determine the inequality sign if i...
whats ve
late blade
(negati)ve and (positi)ve
astral sinew
Ve
late blade
my shorthands
late blade
for the left it doesnt, but for middle and right it does. so the left would ruin everything
the principle isnt to strictly "do the same thing to all 3 parts", its to "do sth to the middle and see what the new bounds are"
fluid prawn
it gives 0<=xy^2/x^2+y^2<=x so ig its still works
late blade
it gives 0<=xy^2/x^2+y^2<=x so ig its still works
wrong cuz when x = -1 ur thing fails
fluid prawn
wrong cuz when x = -1 ur thing fails
dont i make it x goes to 0 tho
late blade
thats the goal
but u still gotta make ur rpoof make sense
also x can approach 0 from the negative side
so ur line is false for half the x'es
safe nova
Here i don’t understand how the teacher showed us this in certain parts:
i don’t get the structure story here besides the end i do know its binomal
next cedar
,rccw
glossy valveBOT
safe nova
Thanks🫶
woeful moth
Here i don’t understand how the teacher showed us this in certain parts:
i don’...
Could you rephrase your question please?
german is fine as well 😄
safe nova
ahh perfekt hahaha
also am freitag hat uns der mathelehrer diese seite mit uns gemacht: multiplikation/division/potenzieren/wurzelziehen bei gleicher basis.
Auf dem bild bei j) hat der lehrer das so zu uns gezeigt während der mathestunde.
Ich komme einfach nicht draus von derer struktur um es zu verstehen
do u understand now?
safe nova
Could you rephrase your question please?
.
woeful moth
also am freitag hat uns der mathelehrer diese seite mit uns gemacht: multiplikat...
Ah also ist das sein Rechenweg da?
safe nova
Ja genau
woeful moth
Verstehst du, wie er zur ersten Zeile kommt?
woeful moth
Er nutzt die 2. binomische Formel aus dem Kasten unten links, habt ihr die besprochen?
safe nova
Ja das hatten wir schon mal am anfang
Ich erkenne es aber erst am schluss in die lösung
woeful moth
Okay. Wenn du dir die Klammer in j) anguckst und mit dem Kasten vergleichst, was wäre a und was wäre b?
safe nova
Okay. Wenn du dir die Klammer in j) anguckst und mit dem Kasten vergleichst, was...
hmm gute frage😭
Kann das sein dass a sei die 3 und dieser wurzel das b?
woeful moth
hmm gute frage😭
Kann das sein dass a sei die 3 und dieser wurzel das b?
Ja genau, das a ist die 3 und das b ist die dritte Wurzel aus a
jetzt hast du $a^2 - 2ab + b^2$. Kommst du darauf, wie man von da aus auf die erste Zeile der Musterlösung schliessen kann?
glossy valveBOT
Ladan
safe nova
Nein, komme ich nd darauf. Ich weiss nicht wieso diese struktur
Dieses 3^2 - 2 mal 3* diese wurzelzahlen
Ist das eig ne regel die sich hier hereinschleicht?
woeful moth
Hmm okay.
Also die binomische Formel ist $(a-b)^2 = a^2 - 2 \cdot a \cdot b + b^2$.
In deinem Fall ist $a = 3$ und $b = \sqrt[3]{a}$.
Jetzt setzt du die beiden in die rechte Seite der binomischen Formel von oben ein, also:
$3^2 - 2 \cdot 3 \cdot \sqrt[3]{a} + (\sqrt[3]{a})^2$.
Ist das verständlich? Die Struktur die du beschreibst ist die selbe wie in der binomischen Formel mit a und b als Zeichen, nur dass a hier 3 ist und b die dritte Wurzel aus a.
glossy valveBOT
Ladan
safe nova
Hmm okay.
Also die binomische Formel ist $(a-b)^2 = a^2 - 2 \cdot a \cdot b + b^...
Ohh demfall ist das eig repetitionssache. Ich müsste demfall nochmals diese regeln sonst gucken weil ich hatte ein bisschen mühe gehabt mit dem 2^3 diesdas
woeful moth
Ohh demfall ist das eig repetitionssache. Ich müsste demfall nochmals diese rege...
Genau, du machst eigentlich genau dasselbe wie immer. Der einzige Unterschied ist dass die Wurzel etwas komplex aussieht
safe nova
Genau, du machst eigentlich genau dasselbe wie immer. Der einzige Unterschied is...
Okay demfall schaue ich mir in der zukunft derer thema wieder an. Danke dir!
take care and peace
woeful moth
Okay demfall schaue ich mir in der zukunft derer thema wieder an. Danke dir!
Gerne, frag wieder wenn was unklar ist
woeful moth
take care and peace
you too
safe nova
Gerne, frag wieder wenn was unklar ist
Mach ich gerne und danke! also ich kann dir dann pingen?
woeful moth
Mach ich gerne und danke! also ich kann dir dann pingen?
kannst du machen 👍
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storm jasper
okay so i need help with functions and relations one sec ill send a pic
leaden ermine
With what would you like to start with first of all?
storm jasper
i think the first page looks more complicated
leaden ermine
You mean page 22?
leaden ermine
Ok, you need to first know what a domain, range is and how to test if a graph is a function
storm jasper
function if it has a repeated number correct
leaden ermine
domain is x range is y right?
almost
domain refers to the allowed values of x, and range of all y values that the function/graph attains possibly
leaden ermine
function if it has a repeated number correct
uhm not quiet
you can just do the vertical line test
storm jasper
ahh yea i remember that i think
leaden ermine
you have a function if each element of the domain is assigned exactly one element of the codomain
storm jasper
you have a function if each element of the domain is assigned exactly one elemen...
uhh can u dumb this down a bit
english isnt my first language
storm jasper
why not
leaden ermine
because it fails the vertical line test, which means an x value is being mapped to two y values
storm jasper
ahh yea
leaden ermine
but we just said it must only be mapped to one y value
ancient zinc
in easy language: all x values can only have 1 y-value
glossy valveBOT
neon basin
in easy language: all x values can only have 1 y-value
at most 1
leaden ermine
x=0 can be mapped to y=-1 or y=1
storm jasper
in easy language: all x values can only have 1 y-value
yes thats what i mean by it cant have repeated numbers
how do i do the verticsl line test?
ancient zinc
*at most 1*
yes this is important too
the vertical line test is a fancy way of saying: can you find a value of x where there is more than 1 y value
ancient zinc
so when you look at the circle, if you move along the x axis, can you find a point where there are two y-points?
leaden ermine
how do i do the verticsl line test?
you draw a vertical line simple as that
storm jasper
and how does that help me know if its a function or not
leaden ermine
rather, visualize a vertical line, like take your pen
and scan through the graph
if you realize it would hit two y-values then it cannot be a function
neon basin
and how does that help me know if its a function or not
A function must output at most one value for a given input. Say we have $f(x) = 5x$
glossy valveBOT
USS-Enterprise
storm jasper
so for the first example
neon basin
Any x you pick, you will always end up with one value
leaden ermine
here for example, you instantly realize that your pen would beep twice since it'd hit two y-values
storm jasper
it would not be a function ?
neon basin
However, if we look at this circle
If you pick x = 0, you get y = 1 and y = -1
But as we just said, a function can only output at most one value for a given input
leaden ermine
blud repeating me
storm jasper
ok i get this one can someone help me understand this
neon basin
Here we get 2 outputs
storm jasper
bc i didnt take it whatsoever
neon basin
And that is a vertical test
You just draw an imaginary vertical line somewhere
Here it was x = 0
storm jasper
yes i remember it now my teacher told me ab it
neon basin
And you see it intersects with the graph of whatever we are looking at twice
at y = 1 and y = -1
storm jasper
ok i get this one can someone help me understand this
what is this tho
neon basin
Therefore it is not a function
Well this is not about determining whether they are functions or not
storm jasper
wait nvm this is honors math im not honors math i dont have to do it i just needed the first one
i get it now
thank u guyssss appreciate yall
.close
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neon basin
thank u guyssss appreciate yall
beautiful profile picture
storm jasper
🫰🏻🙌🏻🙌🏻🙌🏻
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fathom dagger
Can someone help me figure out where I messed up, the answer is supposed to be 1/8
fathom dagger
robust slate
,w tangent to 3x^2-3xy-3y^2=-33 at (-2,-3)
glossy valveBOT
robust slate
Can someone help me figure out where I messed up, the answer is supposed to be ...
I’m the future, please use the ,rotate command
,rotate
glossy valveBOT
fathom dagger
sorry, will do
robust slate
Sign error
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robust slate
thank you sm
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solid mesa
question the same formula for standard deviation and variance of grouped data can be used for ungrouped ?
solid mesa
Sorry
onyx glen
if you want, you can treat an ungrouped data set as a grouped one where every single group has frequency 1.
also opening a channel happens by sending any message into it -- ideally the one containing your question
but starting a message with a . suppresses this effect
solid mesa
Alright
solid mesa
if you want, you can treat an ungrouped data set as a grouped one where every si...
The thing is some numbers repeat
onyx glen
yeah that kinda isnt an obstacle
if you really want to saddle yourself with like 17 years of extra work then you can make a freq table for each one
and then have most of the freqs be 1 but some be 2 or whatever
like tbh the whole thing with grouped vs ungrouped data. the formulas arent really that different.
solid mesa
Soo I could resuse it ?
onyx glen
"resuse"?
solid mesa
Yeah
Like the specific formula for standard deviate of grouped data
And variance
Can I sued it for ungrouped data
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thick hedge
I don't really get how this metric space is defined
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I don't really get how this metric space is defined
minor crater
as we saw in ¶15
have you seen the proof of that
it's basically an extension of that but for sequences
thick hedge
it's basically an extension of that but for sequences
I get that bit
What I don't get is A_n
fast peak
any sequence you want
for which the series converges
eg a_n=1/n^2
or 1/2^n
or whatever
thick hedge
okay, so it's $\sum_{n=1}^{\infty} \left( A_n \frac{\abs{x_n-y_n}}{1+ \abs{x_n-y_n}} \right)$
glossy valveBOT
wai
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neon basin
nimble crane
mellow oriole
😂
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cinder terrace
A is a given point and P is any point on a given straight line. If AQ = AP and AQ makes a constant angle with AP, find the locus of Q.
maiden vapor
A is a given point and P is any point on a given straight line. If AQ = AP and A...
What have you tried?
cinder terrace
What have you tried?
i found the locus of q is straight line
maiden vapor
Yes
cinder terrace
now how do i give an eq for that line
let the angle be theta base =ap then y= ap sin theta
?
correct me if i am worng
.close
fallen ivy
I have
h(x) = x-2/x+3
full forumBOT
I have
h(x) = x-2/x+3
sonic stratus
LMAO
fallen ivy
So I’m doing -2,9
sonic stratus
3 seconds
sonic stratus
Show the problem again, and no, i will not indulge in the same discussion again.
Google Translate Exists, I can read it.
torn sand
I have
h(x) = x-2/x+3
!xy'
fallen ivy
Jeez… demanding
full forumBOT
I have
h(x) = x-2/x+3
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.
torn sand
Jeez… demanding
thanks
fallen ivy
sonic stratus
!xy'
tbh id advice not too clutter this chat cause we will have problem (again) if so.
maiden vapor
,rccw
glossy valveBOT
fallen ivy
onyx glen
h(-2.9) seems to be -49, not -45. can you show how -45 is happening?
sonic stratus
Jeez… demanding
Is "Formengi" a way to say domain? So, the values that are accepted by the function as a valid input?
fallen ivy
,w -2,9-2
maiden vapor
I think's it means "Find the range of the function."
glossy valveBOT
fallen ivy
,w -2,9+3
glossy valveBOT
fallen ivy
Bruh is this bot acustic
onyx glen
"acustic"?
gritty rose
Ironic
grave elm
use . not ,
maiden vapor
What did you expect with that input?
grave elm
and for simple calculations you can use ,calc or your brain, ideally
sonic stratus
I think's it means "Find the range of the function."
literal translation is "preposition", idk, wild guess from me anyways.
here we go again btw
onyx glen
she expects the bot to do the calculations -2.9 - 2 and -2.9 + 3, with the caveat that Wolfram Alpha doesn't understand , as a decimal separator
you need to use a point
fallen ivy
Domain is x€r except x /€/ -3
onyx glen
,w (-2.9 - 2)/(-2.9 + 3)
glossy valveBOT
onyx glen
Bruh is this bot acustic
what did you mean with "acustic" here
fallen ivy
You know what it means
fallen ivy
No. Look it up.
onyx glen
"acoustic" is something to do with sound
fallen ivy
I HAVE TO LOOK THINGS UP CAUSE YOU CANT HELP ME PROPERLY.
gritty rose
I HAVE TO LOOK THINGS UP CAUSE YOU CANT HELP ME PROPERLY.
!vol
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I HAVE TO LOOK THINGS UP CAUSE YOU CANT HELP ME PROPERLY.
Helpers are just people volunteering their time to help you. Be polite and patient.
onyx glen
no, i'm trying to get you to admit that you used the word "autistic" in a rather not-OK way. and then, worse, you even tried to censor it.
sonic stratus
what did you mean with "acustic" here
most incriminating question ever
knotty grail
"acoustic" is something to do with sound
internet humor
do not engage
onyx glen
nah fuck that noise.
"internet humor" is not an excuse for being ableist.
i'm gonna take this to #discussion so as not to clog up this channel
leaden ermine
,tex .exp rules
glossy valveBOT
onyx glen
.close op gone
digital saffron
Does f”(x)>0 mean positive slope or above x value
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Does f”(x)>0 mean positive slope or above x value
digital saffron
=0 is x int?
gritty flax
Does f”(x)>0 mean positive slope or above x value
Slope is below the function
umbral dome
on the function plot f(x) it looks like this
digital saffron
Slope is below the function
hmm so when I say f”(x) >0
does that mean the slope is >0
or that f”(x) is above the x value
Would the red show f”(x)>0
like the red highlighted area since it’s above the x axis?
sweet onyx
no
digital saffron
is it where the slope is increasing?
digital saffron
so f''(x) < 0
how??
Wouldn’t this be decreasing
Where the blue circle is since the slope is decreasing
sweet onyx
sweet onyx
Wouldn’t this be decreasing
the slope is always decreasing on your curve
imagine if f(x) is the position of a person
*depending on x
then f'(x) would be its speed
and f''(x) would be its acceleration
so
you can decelerate
and being still on a positive speed
digital saffron
Tbh I don’t think I’m following
I understand speed velocity and acceleration and what not, but I don’t think I can conceptually understand it yet
take a look at this
the table finds that f”(x) is positive in x<-1
digital saffron
the table finds that f”(x) is positive in x<-1
does it have nothing to do with it being positive/negative or above the x axis?
and instead it refers to strictly the concavity of f(x)?
gritty rose
Someone help this guy in <#903481106819612714>
!noadvert
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Please do not advertise your help channel or thread in other parts of the server. There are many people who need help, so advertising can quickly turn into spam.
@digital saffron Has your question been resolved?
north moth
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gritty flax
Well which ones sum up to -b = 7sqrt(3)
gritty flax
how do you square the 7 square root 3y
No need
north moth
so you leave it like 7 squareroot 3y ^2
gritty flax
No you don't need to square anything to answer the question
onyx glen
so you leave it like 7 squareroot 3y ^2
bad bracketing and spacing
(7sqrt(3)*y)^2 can be simplified if you so wish
but you don't rly need to complete the square here at all
gritty flax
Yes
onyx glen
missing \] but yes
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maiden vapor
so the answer is [y = 3\sqrt{3} \quad \text{and} \quad y = 4\sqrt{3}]
gritty flax
Yes
maiden vapor
Bruh
gritty flax
Yes
maiden vapor
gritty flax
Yes
maiden vapor
Agreed
gritty flax
Yes
maiden vapor
Yes
restive geyser
gritty flax
Yes
north moth
yeah i guess
maiden vapor
,texitshape \replicate9{\replicate9{Yes! }\par}
glossy valveBOT
クーリー
gritty flax
Yes
maiden vapor
Who does this blud think he is
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loud elbow
https://tenor.com/view/a-carai-smile-blink-gif-14907522
WE HAVE THE SAME DECORATION
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WE HAVE THE SAME DECORATION
grave elm
WE HAVE THE SAME DECORATION
Looks like you accidentally opened the channel
if it was an accident, could u close it with .close
loud elbow
Looks like you accidentally opened the channel
Probably
grave elm
if not, you can ask your quesiton
loud elbow
Well im doing my math hw rn and its lowk hard since we still hadn't studied this lesson yet but I tried my best
grave elm
I see, well, if you need help with it, you can try sending it here and someone might help
zinc ginkgo
Can I show u the exercise?
Feel free to post it
loud elbow
Feel free to post it
THANKS
loud elbow
Yes
glossy valveBOT
Tree man
glossy valveBOT
MathIsAlwaysRight
loud elbow
Do you know how to write tan in terms of sin and cos?
No
zinc ginkgo
Alright, so $\tan(x) = \frac{\sin(x)}{\cos(x)}$
glossy valveBOT
Tree man
loud elbow
AHH IK THIS
zinc ginkgo
Try to manipulate the things you need to solve you you have sin/cos
zinc ginkgo
How would you solve question 1 now?
zinc ginkgo
Try dividing both terms by $\cos^2(x)$
loud elbow
How?
glossy valveBOT
Tree man
zinc ginkgo
So the question asks for the value of 6sin^2(x)+5cos^2(x), right?
loud elbow
Yes
zinc ginkgo
Try to reshape the equation using algebra to get sin(x)/cos(x)
Because that is tan(x) and you know the value of that
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@loud elbow Has your question been resolved?
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north moth
i need help with triangles hypnotuse
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i need help with triangles hypnotuse
north moth
.close
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sour shore
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muted flare
I feel like this is better done with vectors 
foggy vapor
What do you need help with?
sour shore
I feel like this is better done with vectors <:thonkzoom:533366356536721418>
Idk much abt vectors
foggy vapor
,rccw
glossy valveBOT
foggy vapor
i made these 2 eqn and now im stuck
divide them
by symmetry you can assume c = 3d after you do that
foggy vapor
also are we working with integers
sour shore
I got c=3d or 3c=d
sour shore
also are we working with integers
Wdym?
foggy vapor
are a, b, c, and d integers
sour shore
Oh oh yes a,b,c,d are all positive integers
sour shore
you can just assume c = 3d because the whole thing is symmetrical
Wait how
foggy vapor
do you know what to do
sour shore
do you know what to do
No this is where im stuck i had divided already :3
foggy vapor
Wait how
the equations treat c and d identically
so it doesnt matter if you pick c = 3d or d = 3c
sour shore
Oh ryt bcz there was a mod?
sour shore
Ok...
foggy vapor
ok but also
before you start minimising
you should find the relationship between |a-b| and d
foggy vapor
sub in c = 3d here into equation 1
sour shore
And do i keep the mod?
foggy vapor
what mod are you talking about
,tex also you can just write that as
\e{gather*}{
\4{(c-d)^2}{\abs{a-b}} = 18 \
\4{(c+d)^2}{\abs{a-b}} = 72
}
glossy valveBOT
sour shore
Yes thts wht i was asking