simple factor theorem also works
#help-13
crimson sedge
kindred ruin
(idk french so i dont ave any idea whatever u are talking before)
crimson sedge
(idk french so i dont ave any idea whatever u are talking before)
we were finding if the expression on the left is divisble by the expression on the right
@twilit escarp Could we say that if we have a function
$$f(x)$$
and
$$f(c) = 0$$
then $(x - c)$ divides that function
wraith daggerBOT
Edmund Cloudsley
agile onyx
oh that's true...
crimson sedge
Si un polynome p(x) a un facteur (x-c) alors p(c) = 0
twilit escarp
x != c at least ?
crimson sedge
what?
- Vérifions que ( p(1) = 0 ) :
[
p(1) = n(1)^{n+1} - (n+1)(1)^n + 1 = n - (n+1) + 1 = 0
]
Donc, ( (x - 1) ) est un facteur. est donc bien sur [(x-1)^2] est un facteur
wraith daggerBOT
Edmund Cloudsley
crimson sedge
c'est vrai ou non?
agile onyx
does it immediately just mean that (x-1)² is a factor?
do i not have to prove that l'ordre de multiplicité est >=2?
agile onyx
could i use horner's algorithm for this?
cedar kilnBOT
@agile onyx Has your question been resolved?
vapid basalt
help
vapid basalt
hey, what do you need help with?
this one
can i get it's oln
solution
please help me out
it would be 22
idk how to solve it
i'm not able to find upper and lower bound
for this
cedar kilnBOT
@vapid basalt Has your question been resolved?
cedar kilnBOT
@vapid basalt Has your question been resolved?
rare solstice
In 2008, the annual income was ISK 6,000,000. and they are increased by 5% from the previous year. What was Anna's total income in 2007?
rare solstice
Do these formulas work?
Sv = Kv(1+p/100) and Úv = Sv(1-p/100) - Kv is cost price, Sv is sales price (price with surcharge) and Úv is sale price (price with discount)
queen stirrup
I mean its two different concepts, so you would not apply that formula. However in this case, the actualy formula you would use to solve the question is the same as the first formula u gave.
rare solstice
if a an item costs 3.400 which includes VAT 24,5%, whats the price without VAT? @queen stirrup
queen stirrup
Let the marked price be x
thus VAT = 24.5% of x
thus x + 24.5% of x = 3400
=> x = 3400 * 100/124.5 = approx 2730.92
rare solstice
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
hot crag
you can either close this one or the other one
fresh mauve
cedar kilnBOT
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.
@fresh mauve Has your question been resolved?
hot crag
@fresh mauve close this one or the other one please
cedar kilnBOT
cedar kilnBOT
Available help channel!
rain spoke
Yo
rain spoke
If someone helps me with this question ill dm them discord nitro
<@&286206848099549185>
crimson sedge
If someone helps me with this question ill dm them discord nitro
What is your problem?
regal vale
If someone helps me with this question ill dm them discord nitro
u dont have nitro urself
surreal mauve
lmao
regal vale
uve had discord since 2019
rain spoke
can u js give me the answer pls
regal vale
and match the cumulative frequncey for each
vivid wadi
you need to calculate how many dogs were added from the point at 10kg to 34kg
mystic thistle
can u js give me the answer pls
You're not supposed to ask for answers
regal vale
then do f=d/w
rain spoke
You're not supposed to ask for answers
is there a rule that says i cant
regal vale
so like 10/2 and 34/19.5
regal vale
and then add the answers and round it up
rain spoke
what would that be
regal vale
so that would be 7
rain spoke
thx bro
regal vale
np
rain spoke
its wrong
regal vale
then 6
rain spoke
still wrong
regal vale
okay lemme see
regal vale
watch the video
rain spoke
ight
terse oasis
try 23
regal vale
so that would be 7
honestly the first answer i gave shouldve been correct
terse oasis
or maybe 17
terse oasis
yeah i think the lower bound is 4 and the upper is 21
cedar kilnBOT
@rain spoke Has your question been resolved?
lean frigate
Just a quick question, if i is used to represent √-1 which isn't defined in R is there something to represent devising by 0?
rare vault
Just a quick question, if i is used to represent √-1 which isn't defined in R is...
no(t really), it turns out to not be a useful operation
hollow trail
people have tried to do similar things with dividing by 0, but unlike the complex numbers, it hasn't turned out anything particularly useful or interesting
lean frigate
Hmm
But if we want to we technically can?
Wait ic now why
It's not gonna be useful at all
Thx guys
I'll close
.close
dim hearth
hi
dim hearth
can anyone help explain to me how to go about this type of questions
i can send the whole exercise and translate it but i think jst knowing the general thought process here will help me
thanks alot!!!
cedar kilnBOT
@dim hearth Has your question been resolved?
tired lantern
cedar kilnBOT
tired lantern
For this should I find dy/dx then set it equal to 0?
wraith daggerBOT
tired lantern
<@&286206848099549185>
cedar kilnBOT
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.
slate lintel
yep
tired lantern
Ok, so I got x-2x^3-2xy^2-2x^2y/2y^3+y
And I set the numerator to 0
How do I find xy pairs that make this equal 0?
tired lantern
Thank you
cedar kilnBOT
@tired lantern Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
void sand
.remindme 0s test
cedar kilnBOT
Created reminder test (#help-13 message) for <t:1731194896:f>
cedar kilnBOT
.remindme 0s test
@void sand asked to be reminded <t:1731194896:R>, test
heavy bramble
hii so it’s a very general help thing not with a specific question but i have a statistics exam tomorrow and i was hoping someone could help me with some lessons (conditional probability, sample events, baye’s theorem, etc…) thanks! :))
fresh patio
cedar kilnBOT
@heavy bramble Has your question been resolved?
cedar kilnBOT
@heavy bramble Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
fringe oasis
how does this happen? i understand why it becomes -6sqrt2, but why the extra number?
fringe oasis
i know the roots must multiply but i dont understand why it doesnt become 1 number
fresh patio
,, \frac{3\sqrt{2}}{-2+\sqrt{7}} \cdot \frac{-2-\sqrt{7}}{-2-\sqrt{7}} = \frac{-6\sqrt{2}-3\sqrt{14}}{4-7}
wraith daggerBOT
Bair
fresh patio
is this the equation? sort of hard to read
opaque root
Is a 7 or a 2?
fresh patio
it's a 14 on the right hand side, so should be a 7
opaque root
My eyes, but i think yes 
fringe oasis
is this the equation? sort of hard to read
@opaque root sorry, this was the original equation
fresh patio
i think that matches
fresh patio
so what is the confusion
fringe oasis
im not sure why it equals this on the right hand side
fresh patio
well we just multiply the numerators and denominators
fresh patio
,, 3\sqrt{2}(-2-\sqrt{7})=-3\sqrt{2}\cdot 2 - 3\sqrt{2}\cdot \sqrt{7}=-6\sqrt{2}-3\sqrt{2\cdot 7}=-6\sqrt{2}-3\sqrt{14}
wraith daggerBOT
Bair
cedar kilnBOT
cedar kilnBOT
Available help channel!
tawdry pendant
So, Abstract Algebra question here, from what I understand, we know that a cyclic subgroup generated from some element "a" in G has order k when a^k = e (the identity element in the group G). So when it says that g has order 15 then ik it has 15 elements and 16 for h.
Here's what I'm struggling with, a cyclic subgroup generated by an element is a set. Take U(16) which is the group of units mod 16 where the elements are relatively prime to 16, thus U(16) = {1,3,5,7,9,11,13,15}. The group operation is multiplication mod n.
Now the cyclic subgroup generated by 3 for example is of order 4 and <3> = {1,3,9,11}. The cyclic subgroup generated by 5 is also order 4 and the cyclic subgroup is <5> = {1,5,9,13}. Their intersection has 2 elements in common, mainly 1 and 9.
However, suppose we take the subgroups generated by 3 and 11, then <3> = {1,3,9,11} but <11> is also {1,3,9,11}. Thus they have the same order and their intersection is of order 4 (because they have the same number of elements), not 2 like in the third paragraph.
Since the intersection of two cyclic subgroups came out to have two different orders, how can we find the order of an intersection where g and h are cyclic subgroups of G?
cedar kilnBOT
So, Abstract Algebra question here, from what I understand, we know that a cycli...
@tawdry pendant Has your question been resolved?
dire thorn
So, Abstract Algebra question here, from what I understand, we know that a cycli...
There is something special about g and h being order 15 and 16 that gives this question a single possible answer.
Keep in mind the order of any element in a cyclic group has to divide the order of the group.
cedar kilnBOT
cedar kilnBOT
Available help channel!
umbral frost
would this be correct or no?
river estuary
To make nine cups of lemonade you mix 4.5 cups of water with three cups of lemon juice and
add 1.5 table spoons of sugar. If there are ten cups in of water and 6.5 cups of lemon juice and 3
table spoons of sugar, how many gallons of lemonade can you make? (There are 16 cups in a
gallon.)
river estuary
i need help solving this question
i think this is something with linear equations but
it doesn't make sense to me
limber sedge
i mean you only have 3 table spoons of sugar and once you are out of sugar you cant make more lemonade. since each batch of 9 cups is 1.5 tablespoons of sugar you can make a maximum of two batches
river estuary
but
is there a way to solve this without
using common sense?
and the answer is 9/8 gallon
if i check back in my
answer key
river estuary
how
limber sedge
yeah it is
river estuary
how do u get 18/16 cups?
river estuary
i think 18/16 is right
river estuary
and the answer is 9/8 gallon
?
limber sedge
18/16 gallons
river estuary
oh yea
limber sedge
18 cups = 18/16 gallons
so it works
i think you might be able to use proportions to solve it
river estuary
like
ok i get the basics
i dont know how i would do this in another question like this tho
limber sedge
for a question like this you can divide and take the lowest number as the maximum batches: 10/4.5= ~2.22, 6.5/3=~2.16, 3/1.5 = 2, so you can have at most 2 batches
cedar kilnBOT
cedar kilnBOT
Available help channel!
leaden phoenix
help please 😭
cedar kilnBOT
help please 😭
cerulean star
Is this an assessment?
cedar kilnBOT
@leaden phoenix Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
@eager hemlock Has your question been resolved?
Available help channel!
alpine lark
Looking for some help with an optimization problem, that states this, I got as far as creating the dualand I understand that I have to show that c'x* = p*'c and that if x*=p* that p* is feasible for the dual but I'm having an issue where every explanation I look up uses the same step that I don't really understand in saying that p*'A can be rewritten as A'p* and then doing the same thing for turning c'x* into the dual version
alpine lark
I thought that matrix multiplication was non-communicative, but everywhere I see talking about this problem without any explanation just states that
these are true
and I do not understand how that is true
alpine lark
yes for both
flint plinth
then yea they are equal, it's just the dot product between the two vectors
and you can take the dot product in either order
alpine lark
but A in particular is a matrix
flint plinth
oh i was looking at the second one, lemme check the first
i think that should be false
what you can say is:
$$p' A = (A' p)'$$
wraith daggerBOT
Bungo
flint plinth
(i'm not writing the * because it makes it harder to read)
alpine lark
okok, and then I can say p = x and A' = A so this is just c'
flint plinth
what is just c'?
alpine lark
oh, well, the LP is this, so the dual of it is
p'c
subject to p'A <= c' so if I can change p'A into (A'p)' then I can prove the condition because A'p is the same thing as Ax which is c and c' <= c' is true
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
versed gale
Given that the distance from point M(m+1,3m−5) to the y-axis is half the distance from point M to the x-axis, find the value of m.
cedar kilnBOT
cedar kilnBOT
Available help channel!
delicate patio
cedar kilnBOT
delicate patio
this is incorrect right?
how did it simplify to a/sqrt(a^2 + b^2)
shouldn't it be a/(a^2 + b^2)
hollow trail
chat gpt is not very good at algebra unfortunately
cedar kilnBOT
cedar kilnBOT
Available help channel!
azure swift
Denote the expression of the integral for something, say S(x)
Then check if S(-x) = S(x)
Wym in general?
You have something concrete now to prove
Try and actually cary out some calculations and you’ll see what happens
A hint for example is to make use of a variable substitution
azure swift
A hint for example is to make use of a variable substitution
Actually even that is not needed
cedar kilnBOT
@eager hemlock Has your question been resolved?
heavy bramble
is there some more context?
no that’s just the question but i have the answer if u want maybe it could clarify more i don’t understand much tho
heavy bramble
heavy bramble
yeah i guess😭? I rly hope its a part of the question since literally the question has no numbers to work with?
heavy bramble
mhm okay i might ask my friend thank you sm
past wave
!done
cedar kilnBOT
If you are done with this channel, please mark your problem as solved by typing .close
heavy bramble
.close
cedar kilnBOT
slender ginkgo
chain rule?
cedar kilnBOT
@eager hemlock Has your question been resolved?
past wave
@eager hemlock still a doubt?
cedar kilnBOT
@eager hemlock Has your question been resolved?
serene heath
cedar kilnBOT
pastel vault
no
livid hound
do you know the relation between
leading coefficient and concavity
and
discriminant and number of roots?
serene heath
do you know the relation between
leading coefficient and concavity
and
discrimin...
No
livid hound
have you been given any notes?
i'd recommend first looking up stuff like
leading coefficient of quadratics
and discriminant of quadratics
cedar kilnBOT
cedar kilnBOT
Available help channel!
hybrid hornet
Hello ladies and gentlemen
cedar kilnBOT
Hello ladies and gentlemen
hybrid hornet
I am currently working on a function in C++ (Arduino)
I have to power 36 LEDs (with a color each) so 36 colors
I want to transfer the data (36 colours) so I thought of making 2 functions
(f(n) for the colour of the n-th LED)
The first function F just returns a number, based on the colours f0 to f35
How do I make the inverse?
calculating f0 to f35 from the value of F
Do I have to make 35 functions as an argument of F?
If yes I would have no other question I can do that
crimson sedge
idk a lot about c++ but why wouldnt u make just an array ?
hybrid hornet
I swear I just thought about that
There was an issue before with that since I am working on a high speed application
Ok yeah no point I will try that again and come back in case it doesnt work, I might try pointers as well
.close
cedar kilnBOT
hybrid hornet
.reopen
cedar kilnBOT
✅
hybrid hornet
Ok sorry it's embarrassing
But the issue is that the inputs f0 to f35 aren't from my device
I am just getting a number and I have to demodulate it
The value F is transferred through bluetooth or WiFi (still undetermined)
And we can't access the same array across 2 micro controllers
That's why I thought of making 2 functions like here (1 function on transmitter the other 1 on the receiver)
cedar kilnBOT
@hybrid hornet Has your question been resolved?
restive shard
I am just getting a number and I have to demodulate it
i would say have the input of the original function be an array
or actually no
why don’t you just send the number over and demodulate it on the receiving end
hybrid hornet
i would say have the input of the original function be an array
I would be sending 35 values over
It's preferred to be 1
hybrid hornet
why don’t you just send the number over and demodulate it on the receiving end
Ik that's what I'm thinking about
It's the inverse of the first function
How do I even begin there
Either this or I make 35 functions of F to demodulate
restive shard
you won’t need a first function if you just send the raw data over to the receiver
hybrid hornet
As I said I have 35 values if I send it over it'd be easy but I'm currently working on a high speed application
I'm wondering if I can send over 1 value
hybrid hornet
Exactly and then send the number over to the receiver
restive shard
yea you could just make a binary string
hybrid hornet
you said each value is a 0 or 1?
Nope the inputs are very big, from 0 to FF FF FF (32 bit)
Thats why the controllers should make functions instead and send over 1 number
hybrid hornet
you could still conjoin the hexadecimal numbers
Yes into 1 number but
How would I demodulate that number
If I have to make 35 functions for each output it's pain
restive shard
let’s say you have the values 7 30 and 41
you convert those to hexadecimal
which is
000007
00001D
000029
respectively
(i think)
hybrid hornet
Prolly
restive shard
then you would just conjoin them
hybrid hornet
Many ways
restive shard
|000007|00001D|000029|
00000700001D000029
you would know that each number takes up only 6 spaces
and so you can iterate through every 6 values and change them into the original number
restive shard
you could also use base 64 if the string is too long
hybrid hornet
210 digits long
cyan moss
Can anyone help me at a calculus question please? but its hard
hybrid hornet
you could also use base 64 if the string is too long
If my arduinos can handle that I'll consider it
Smart solution btw thanks
hybrid hornet
I don't know how I haven't thought about this
hybrid hornet
Actually an ESP32 but programming with Arduino software
restive shard
oh yeah if it’s an esp32 you should be fine
hybrid hornet
Nice
restive shard
more than powerful enough
hybrid hornet
It's a machine
restive shard
unfortunately i’m a broke highschooler
hybrid hornet
A smart high schooler
restive shard
thanks lmao
hybrid hornet
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
marble solstice
if I know that Vsin(x) = 64, Vcos(x) = 20 and tan(x) = 9/5 how can i find V?
marble solstice
its part of a bigger question however this is pretty much all the info i have
south tundra
Think about whether you can use the Pythagorean identity here
south tundra
The identity tells you that sin^2(x) + cos^2(x) = 1, right?
marble solstice
yes exactly
south tundra
Can you express sin(x) and cos(x) using V via the given equations?
marble solstice
Can you express sin(x) and cos(x) using V via the given equations?
wait hold on but then i'm going to return straight to my equation with tan(x) am i not?
south tundra
No, why?
marble solstice
for example if i put V = 64/sin(x)
south tundra
You get sin(x) = 64/V and cos(x) = 20/V
marble solstice
oh then i don't understand where this is going then 🤔
what can i do with those two?
south tundra
Rewrite the Pythagorean identity with them
south tundra
You get sin(x) = 64/V and cos(x) = 20/V
Plug these into sin^2(x) + cos^2(x) = 1
crimson sedge
if I know that `Vsin(x) = 64`, `Vcos(x) = 20` and `tan(x) = 9/5` how can i find ...
just square and add
marble solstice
Plug these into sin^2(x) + cos^2(x) = 1
ok i see
so i'll end up with sqrt(4496) by the end of it
crimson sedge
,calc 64^2 + 20^2
wraith daggerBOT
Result:
4496
yes
harsh swallow
!done
cedar kilnBOT
If you are done with this channel, please mark your problem as solved by typing .close
@marble solstice Has your question been resolved?
Available help channel!
worldly pagoda
How do i find the SA of a pyramid when the B is 12, L is 12 and, H is 12...
spare kettle
its a square pyramid?
worldly pagoda
ye
spare kettle
you can apply geometry and then pythagorean theorem to find the height of the triangle
worldly pagoda
whats the formular th i forgot
spare kettle
the pythagorean theorem ??
worldly pagoda
yes
spare kettle
base^2 + perpendicular^2 = hypoten..^2
worldly pagoda
o a2+b2=c2
spare kettle
yess yess
use geometry and find the height of triangles
then you can find its area
worldly pagoda
so 12^2 + 12^2 = 288 then i square root it and its 16.970 which the the salnt height wut i do now
worldly pagoda
pñlpnibouivyctxr
spare kettle
yes area of base is 144
worldly pagoda
then i find the slant
worldly pagoda
so half of base^2 + height^2 which is 180 then i square root that for 13.42 which is the slant height?
worldly pagoda
then i do 12 for base x slant heigh divided by 2 x 4 for the area of 4 triangle + the base area = the SA?
spare kettle
yep absolutely correct
worldly pagoda
so volume is 576 cm3
cedar kilnBOT
cedar kilnBOT
Available help channel!
tough snow
what is it meant by f(y^2)?
cedar kilnBOT
what is it meant by f(y^2)?
dire geode
Wherever you see an x in f(x), replace it with y^2
topaz tinsel
tough snow
ok thanks
royal parrot
it was not closed
dire geode
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
fossil berry
cedar kilnBOT
fossil berry
Ich weiss nicht was ich zuerst tun sollte.
dreamy void
Ich weiss nicht was ich zuerst tun sollte.
hi
fossil berry
Hi
dreamy void
Du kannst die Matrixdarstellung erahnen
fossil berry
Aber es ist nicht Standardbasiss
queen ice
Oha Umbenennung
dreamy void
mein alter name ^^
fossil berry
wie sehen die Bilder aus von b1 und b2
Was sind b1 und b2
Sind sie basis Vektoren von B?
dreamy void
ja
fossil berry
Ok. Was soll ich damit tun?
dreamy void
Ich muss erst überlegen, wollen die B nach B oder Standardbasis nach B
fossil berry
Okay
dreamy void
Ich denke es ist B nach B deswegen brauchen wir f(b1) und f(b2)
dann müssen wir die bzgl B darstellne
fossil berry
Was ist B nach B. Ich verstehe nichts.
dreamy void
Die Vektoren die wir einsetzen sind bzgl. der Basis B und das was raus kommt ist auch bzgl der Basis B
dreamy void
Ich glaube ich habe es doch verstanden wir müssen einfach die Matrixdarstellung bestimmen
wraith daggerBOT
𝔸dωn𝓲²s
dreamy void
Man kann dann ablesen was die Matrix ist und dann die Bilder bzgl. B darstellen
wraith daggerBOT
𝔸dωn𝓲²s
dreamy void
Die Bilder sind (3,1) und (1,-2) und die jetzt bzgl. B darstellen
dreamy void
Ja ich suche eine Matrix mit 4 unbekannten Einträgen
dreamy void
**𝔸dωn𝓲²s**
Wenn ich Matrixmultiplikation rückwärts machen würde komme ich auf die entsprechenden werte
wraith daggerBOT
𝔸dωn𝓲²s
fossil berry
Ach so.
fossil berry
**𝔸dωn𝓲²s**
Diese alpha betta .. sind abcd hier oder?
dreamy void
ne
fossil berry
Ok was machst du jetzt?
dreamy void
,w rref {{1,1,3},{1,-1,1}}
wraith daggerBOT
wraith daggerBOT
dreamy void
[(3,1)]_B = (2, 1)
[(1,-2)]_B = (-1/2, 3/2)
fossil berry
Lambda -0.5andere ist 1.5
dreamy void
,, f(x_1,x_2) = \begin{pmatrix} 3 & 1 \ 1 & -2 \end{pmatrix} \cdot \begin{pmatrix} x_1 \ x_2 \end{pmatrix}
= \begin{pmatrix} 2 & -0.5 \ 1 & 1.5 \end{pmatrix}_B \cdot \begin{pmatrix} x_1 \ x_2 \end{pmatrix}
fossil berry
Ok was sind diese Zählen
wraith daggerBOT
𝔸dωn𝓲²s
dreamy void
Ok was sind diese Zählen
was meinst du
fossil berry
Achso
dreamy void
lass uns mal austesten mit (1,1)
dann kriegt man (4, -1)
und bzgl. B (1.5, 2.5)
,w rref {{1,1,4},{1,-1,-1}}
wraith daggerBOT
dreamy void
1.5 und 2.5 kommt raus
fossil berry
Einen moment warum haben wir eine 2x3 matrix?
fossil berry
Ach so
Lass uns es ein bisschen später machen.
kannst du dir meine Lösungen ansehen
dreamy void
ja
fossil berry
Sie sind weitere 4 Problemen
Manche habe ich nur Hälfte gemacht.
Ich wasche mir kurz Zähne und gesicht.
dreamy void
ach du kacke
dreamy void
sieht für mich in ordnung aus
dreamy void
Sind alles falsch?
haha
fossil berry
Ich verstehe nur es nicht.
dreamy void
was verstehst du nicht
dreamy void
Du muss mir feedback geben
Wie gesagt für mich sehen die Sachen in ordnung aus
fossil berry
Beim 6ten von 5ten Problem
Gibt es eine Multiplikation die nicht möglich ist? Was bedeutet diese Frage
dreamy void
Gibt es eine Multiplikation die nicht möglich ist? Was bedeutet diese Frage
In dem Fall haben ja v_1 * C^T und C^T * v_1 geklappt aber ich denke man könnte sich fragen, ob C mit v_1^T klappen könnte
ist meine Vermutung
fossil berry
dreamy void
Ok das ist easy
Die Menge is x+2y-z=0
Kannst z.B. nach z auflösen
z = x+2y
und dann kann man schon feststellen die Dimension is 2
und basis ist einfach (x,y,z) = (x,y,x+2y)
Ich glaube so hattest du es auch
fossil berry
Dann es ist richtig?
fossil berry
**𝔸dωn𝓲²s**
Ich habe hier 1 Frage.
Warum teilen wir die Matrix als zwei Spalten hier?
dreamy void
Warum teilen wir die Matrix als zwei Spalten hier?
Die Spaltenvektoren sind die Bilder der Abbildung
dreamy void
Dann es ist richtig?
Ja
fossil berry
Die Spaltenvektoren sind die Bilder der Abbildung
Ich verstehe den Satz gar nicht
Was sind die Bilder hier?
dreamy void
die Spaltenvektoren
fossil berry
Was sind die Spaltenvektoren
dreamy void
was
dreamy void
**𝔸dωn𝓲²s**
Einfach die Spalten der Abbildungsmatrix
fossil berry
Aber warum machst du so. Hat es keine Konsequenzen?
dreamy void
was meinst du
fossil berry
Ich weiss nicht
Ich verstehe nicht, warum die Matrx plötzlich 2 Spalten geworden ist
fossil berry
**𝔸dωn𝓲²s**
Ich verstehe es gar nicht.
dreamy void
Wir wollen die Matrixdarstellung von f in der Basis B bestimmen
Wir bestimmen zuerst die Matrixdarstellung bzgl. der Standardbasis.
dreamy void
**𝔸dωn𝓲²s**
.
Jetzt wollen wir die Spaltenvektoren bzgl. B darstellen
damit wir eine neue Matrixdarstellung erhalten, in der Basis B
dreamy void
**𝔸dωn𝓲²s**
Das heißt man schreibt sie als Linearkombi auf und sucht diese Skalare
Unsere neuen Bilder (Spaltenvektoren) bzgl B. sind die Koordinatenvektoren
dreamy void
[(3,1)]_B = (2, 1)
[(1,-2)]_B = (-1/2, 3/2)
.
wraith daggerBOT
𝔸dωn𝓲²s
dreamy void
das wars
so von meinem Verständnis
Die Spaltenvektoren werden deswegen als "Bilder" bezeichnet oder das Bild, weil sie ja den Bildraum aufspannen
fossil berry
Und es ist jetzt fertig?
dreamy void
Ja
cedar kilnBOT
cedar kilnBOT
Available help channel!
vapid otter
$$-\frac1{(s-2)^2}=0$$
cedar kilnBOT
$$-\frac1{(s-2)^2}=0$$
wraith daggerBOT
Devil Wears Prada
cerulean sail
(there are no solutions)
vapid otter
why
cerulean sail
is it like cross multiplication
Well, unless you want to say that 1 = 0, of course...
vapid otter
i want to find when s = 0
opaque root
When s=0 sub that and find out
vapid otter
wait no
opaque root
But wont be 0
vapid otter
thats not what i want
im looking for critical numbers
so when the derivative equals 0
yeah
cerulean sail
Derivative is zero or undefined, or just zero?
vapid otter
0
cerulean sail
Well, unless you want to say that 1 = 0, of course...
Well then, there aren't any, if you define critical points that way
vapid otter
Well then, there aren't any, if you define critical points that way
critical points are when the derivative equals 0 or when the derivative is undefined
the function i displayed is my derivative
so im finding when my derivative equals 0
to find the critical point
cerulean sail
so im finding when my derivative equals 0
..."or when the derivative is undefined"
cerulean sail
**Devil Wears Prada**
(as before, the derivative is never zero, if what you posted here is the derivative)
vapid otter
(as before, the derivative is never zero, if what you posted here is the derivat...
derivative is undefined at s = 2
im now looking for when the derivative equals 0
cerulean sail
And is it ever zero anywhere?
vapid otter
thats what im trying to find out
i forgot out to do this
lets say the derivative factored out to 3x(x+1)(x-1)
then i could say there are critical numbers at x = 0, -1, 1
but now i have a fraction
how do i do it
i forgot basic algebra skills
cerulean sail
Well, unless you want to say that 1 = 0, of course...
Well, do you think 1 and 0 are equal, as per before?
cerulean sail
Well, unless you want to say that 1 = 0, of course...
Look at what this was a reply to: if you e.g. multiplied by the denominator (and -1), you'd end up with the statement 1 = 0
cerulean sail
Well, do you like dividing by zero?
(there are no solutions exactly because you can't validly isolate s)
cedar kilnBOT
cedar kilnBOT
Available help channel!
severe elm
how do i find the sum
cedar kilnBOT
how do i find the sum
severe elm
is it a sum of squares thing
dull oxide
is it a sum of squares thing
The 9 factors out. Then you have a geometric series.
tiny otter
So I need help understanding the answer to this problem...
cedar kilnBOT
So I need help understanding the answer to this problem...
tiny otter
I understand the general sense of how to get almost to the answer. I end up with |x+2/2|
and then i am trying to find the actual endpoints for the convergence
gritty viper
Is your problem with solving |x+2/2| = 1 or with checking if the endpoints are included
tiny otter
checking the endpoints sorry
and if im correct, if it is < 1 then it converges, > 1, it diverges, and = 1 it is inconclusive. so wouldnt the endpoints be -1 < x < 1
i dont understand why they do that answer
gritty viper
no, |x+2/2| is not 1 for those values
hollow trail
we are solving for when
|(x+2)/2| < 1
gritty viper
the endpoints are where |x+2/2|=1
tiny otter
yes and x would have to equal 0 for it to be equal to 1
hollow trail
that is one endpoint, yes
tiny otter
i thought the endpoints of convergence has to have x in between somewhere where it diverges and converges?
maybe i misunderstood the khan academy lesson
gritty viper
They are
tiny otter
but if it equals 1 then it is inconclusive so why would an inconclusive point be included?
hollow trail
we are looking at an interval of convergence which you get from solving the inequality
|(x+2)/2| < 1
then the endpoints are the endpoints of that interval, i.e. when |(x+2)/2| = 1
hollow trail
but if it equals 1 then it is inconclusive so why would an inconclusive point be...
if |(x+2)/2| < 1 then it converges. if |(x+2)/2| > 1 then it diverges. if |(x+2)/2| = 1 then the ratio test doesn't tell us whether it converges or diverges, so we have to figure it out some other way
tiny otter
i understand that yes
hollow trail
so let's start by solving the inequality
|(x+2)/2| < 1
and put it into the form ? < x < ?
hollow trail
so we are guaranteed to converge on
-4 < x < 0
and guaranteed to diverge for x < -4, and x > 0
so then we need to find out whether it converges at x = -4 and x = 0
cedar kilnBOT
cedar kilnBOT
Available help channel!
crimson sedge
How do I prove that if A is an uncountable set and A is a subset of B then B is also an uncountable set
crimson sedge
I tried proving by contradicting but I just got confused halfway 😭
grave blade
start with
suppose for a contradiction that B is a countable set
then try to find something that contradicts the fact that A is uncountable
cedar kilnBOT
@crimson sedge Has your question been resolved?
wary copper
i dont know how to do this
cedar kilnBOT
i dont know how to do this
mental trail
do you know taylor expansion of ln(1-x)
wary copper
yes
wary copper
idk how to do that
wary copper
i dont get it
wary copper
i only know like multiplication is ading and division is subtracting
wary copper
lna + lnb ?
mental trail
yes
so we want to turn 7 - 8x^2
into constant*(1 - t)
for some t
to then apply the logarithm property
wary copper
why
mental trail
ln(constant*(1-t)) = ln(constant) + ln(1-t)
wary copper
but what about the 9
mental trail
but what about the 9
9ln(constant*(1-t)) = 9ln(constant) + 9ln(1-t)
wary copper
how do u do it on the first one if its just a constant
mental trail
how do u do it on the first one if its just a constant
constant = constant + 0x + 0x^2 + ...
Isn't that pretty obvious?
wary copper
mental trail
Do you want to try the rest?
wary copper
what do u do about the 9
wary copper
u js multiply it by everythign
mental trail
yes
wary copper
wait do u plug tje 8/7x^2 in for each x or do u multiply it by the x
wary copper
does the 2nd term become x^4?
mental trail
yes it's in the t^2
wary copper
so isnt the top 64 * 9?
mental trail
idk how to do this
do you know about 1/(1-x) series
try to differentiate it until you get something close to f(x)
wary copper
idk what u mean
wary copper
why are we doing that
mental trail
why are we doing that
we always have to start from power series we know of
here, 1/(6-x)^3 should make you think about 1/(1-x)
wary copper
dont u just plug it into that then
mental trail
how would you do that
we don't have something like 1/(1-x^5)
where you could take 1/(1-t) series
and plug t = x^5
wary copper
wary copper
? they just plugged it in
mental trail
idk how to do this
this
mental trail
idk how to do this
can you do the same for this?
wary copper
idk
mental trail
sorry but I don't think this technique applies well to our f
wary copper
well why
mental trail
if you really wanna know
we would have to expand (6-x)^3
so 216 - 108x + 18x - x^3
wary copper
ok just how am i suppose to solve it
mental trail
which would then have to be rewritten as constant(1 - t)
and the problem is that t is too complicated
to replace it by its expression in terms of x later
mental trail
ok just how am i suppose to solve it
ok so
mental trail
1/(1-x) series expansion
.
1/(1-x) series expansion
then what happens when you take the derivative
wary copper
idk how to do that
wary copper
?
mental trail
series expansion of 1/(1-x)
mental trail
1/(1-x)
and of the series
if f(x) = a + bx + cx^2 + dx^3 + ...
then f'(x) = 0 + b + 2cx + 3dx^2 + ...
mental trail
the series expansion of 1/(1-x) is indeed the sum of x^n
so what's the derivative of the series
and the derivative of 1/(1-x)
mental trail
the derivative is -1/(1-x)^2
so aren't we getting closer to 1/(1-x)^3?
and at the same time
since 1/(1-x) = 1 + x + x^2 + ...
the derivative of the right hand side is just
0 + 1 + 2x + ...
so we found the series expansion of -1/(1-x)^2
differentiating the series expansion of f gives you the series expansion of f'
cedar kilnBOT
@wary copper Has your question been resolved?
vapid otter
cedar kilnBOT
vapid otter
first derivative test
im stuck midway
i got the derivative but now i dont know how to find critical numbers
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
woeful isle
D(secx)/dx = secx*tanx
Tanx is undefined at (2n+1)pi/2
And sec is undefined at (2n+1)pi/2 aswell
vapid otter
what is 2n+1
woeful isle
I Mean you could write it like that
But It wouldn't be undefined
For all value of k
Only some
vapid otter
but what is n
vapid otter
im not sure
vapid otter
ohh
woeful isle
And so sec gets undefined
vapid otter
so pi/2
vapid otter
oh
woeful isle
Whenever cos goes to 0
vapid otter
ok
woeful isle
Tan gets undefined too
vapid otter
so pi/2
woeful isle
So Tan and sec get undefined at same values
vapid otter
pi/2 + k
woeful isle
Not all k
vapid otter
k/2
woeful isle
Nope
vapid otter
what does k stand for
woeful isle
Sec and tan are not undefined for anything
woeful isle
I think if you wrote
Pi/2 + kpi
vapid otter
pi/2 + pik
woeful isle
That will work
woeful isle
Any number of that format
vapid otter
i forgot precalc almost