the example you are showing is different...there the variable is in the denominator (The x), in the problem we just did the variable is only in the numerators
#help-13
sharp lotus
you do want to have the variable in the numerator to know what you need to subtract 1 from, otherwise itll get confusing
x -> variable of integration
3, 9, 17 in the problem we just did -> constants
vagrant current
the example you are showing is different...there the variable is in the denomina...
Yeah which is why this is very diffucult , since were weren't taught about the index calculus equation you showed me earlier but instead got taught something completely different
sharp lotus
by the way, that is a special case, the power rule works for every exponent of x EXCEPT FOR -1
integral of 1/x however will be log(x), you might not have learned that yet : )
if you think about it, if you try to apply power rule and you end up with x^0, that would become a constant expression which would be weird...
vagrant current
integral of 1/x however will be log(x), you might not have learned that yet : )
well were actually going to be taught logarithms and exponentials right after integration so that would be very interesting
sharp lotus
anyway good luck and just check out the michelle krummel lectures for clarifications
vagrant current
thanks a lot honestly a legend 😁
vagrant current
anyway good luck and just check out the michelle krummel lectures for clarificat...
i'll give her integration and differentiation videos a watch and see how they go
well i'll head out now also , once again thank you for your help and time it was great talking with you
have a great day 💙
sharp lotus
thanks, you as well
vagrant current
.close
olive heart
cedar kilnBOT
olive heart
im not confused its just idk how to explain it
cerulean sail
im not confused its just idk how to explain it
Give it a try 
olive heart
idk if my explanation makes sense
gritty viper
well neither do we
cerulean sail
We can be the judge of that, and explain how to improve your explanation 
sharp lotus
yes, trying to explain something to someone is best way to learn when you have an idea in mind already : )
olive heart
7^2+10^2<8^2+11^2
cerulean sail
Okay, and the purpose of that would be?
cerulean sail
is there a property you're using there?
olive heart
nope
olive heart
yea
sharp lotus
so what's the connection between the sums of the squares you did and what type of angle it is?
sharp lotus
i don't, that's why i'm asking
sharp lotus
i sincerely don't know if you are onto something i don't understand or if what you're saying makes no sense 😄
sharp lotus
i'd think about this differently, first off notice the two triangles share the side BC
olive heart
yea
sharp lotus
you can kind of just imagine folding down the vertical triangle into the flat plane, would the projection of point A fall inside BD or somewhere further out?
olive heart
furtherout
sharp lotus
really?
olive heart
yea
sharp lotus
well AB = 10 and BD = 11, so somehow the projection of the side that's length 10 would be longer than the side 11 segment?
sharp lotus
so 11 = 10?
olive heart
no
sharp lotus
well, so you don't see it this way?
doesn't seem like this method is making much sense to you
sharp lotus
ok here's a simpler way to think of it just mathematically: the sides of the right-triangle ABC are just double a 3-4-5 pythagorean triple: 6-8-10 (6^2+8^2 = 10^2) right?
sharp lotus
so the two legs of BCD Are 6 and 7, you can calculate that the length of what a hypotenuse of a right triangle would be: sqrt(36+49) ~ 9.2
olive heart
u would use pythagorean theorem
to find the middle piece
then see which one is smaller?
right?
sharp lotus
since the side 11 opposite the C angle is longer than what would be the hypotenuse of a right triangle, it follows the angle must be larger than 90
sharp lotus
is my method correct?
I guess to bring it back to the thing with the squares from the start
in a right triangle, the squares of the two shorter sides (legs) = square of the longest side (hypotenuse)
in an obtuse triangle, the square of the longest side is MORE Than the sum of the squares of the other 2 sides
olive heart
yea
sharp lotus
and if all angles are acute, including longest one then the squares of the two sides is less than the square of the 3rd
dunno if maybe thats what you were trying to come up with
so you just have to compare 6^2 + 7^2 with 11^2 and see what is the case here, this is best explanation i can think of where you can directly test it
cedar kilnBOT
cedar kilnBOT
Available help channel!
mortal stag
hello! unfortunately, i don't have my phone so i can't photograph my work. i'll try to describe it in text:
- add 26 to both sides
- divide both sides by 3
- put now- x^6/7 into radical form
i now have x 6√x = 531441 (x times 6th root of x equals 531441) and i don't know where to go from here. i'll appreciate any help i can get! thank you <3
cerulean sail
- add 26 to both sides
- divide both sides by 3
- put now- x^6/7 into radical form
all seems fine to me, but
i now have x 6√x = 531441 (x times 6th root of x equals 531441)
how did you get that?
cedar kilnBOT
@mortal stag Has your question been resolved?
mortal stag
> 1. add 26 to both sides
> 2. divide both sides by 3
> 3. put now- x^6/7 into r...
i forgot to mention that after i put it into radical form (6th root x to the 7th power) i took out 6 of the x's
cerulean sail
i forgot to mention that after i put it into radical form (6th root x to the 7th...
it's 7th root x to the 6th power
cedar kilnBOT
@mortal stag Has your question been resolved?
mortal stag
it's 7th root x to the 6th power
yeah thats what i meant 💀 i typed wrong
sorry abt that
hybrid tiger
need help!
cerulean sail
yeah thats what i meant 💀 i typed wrong
In which case, you would have
[
(\sqrt[7]{x})^{6} = 531441
]
from where you could e.g. take 6th root then raise to the power 7
wraith daggerBOT
@cerulean sail
mortal stag
In which case, you would have
\[
(\sqrt[7]{x})^{6} = 531441
\]
from where you co...
what does that mean?
cedar kilnBOT
@mortal stag Has your question been resolved?
slow thicket
what does that mean?
what does what mean
cedar kilnBOT
@mortal stag Has your question been resolved?
mortal stag
what does what mean
"you could e.g. take 6th root then raise to the power 7"
slow thicket
"you could e.g. take 6th root then raise to the power 7"
To undo the powers of x
Taking the 6th root undoes something^6
Since the bth root of a^b is a
cedar kilnBOT
@mortal stag Has your question been resolved?
mortal widget
Solve the derivative of y = arc csc x^1/2
cedar kilnBOT
cedar kilnBOT
Available help channel!
uneven lily
cedar kilnBOT
uneven lily
Hi! I need help for this question
How do I continue for oblique asymptotes? And is the way I proved the other 2, correct?
cedar kilnBOT
@uneven lily Has your question been resolved?
crimson sedge
hello! unfortunately, i don't have my phone so i can't photograph my work. i'll ...
80822.61645911532
lol
idk what u asked
but
here is the calc magic
visual zealot
cedar kilnBOT
buoyant latch
more like the product rule
visual zealot
oh ok
buoyant latch
that's a product of 2 functions of x
visual zealot
how does that work again
buoyant latch
d/dx f(x)g(x) = f'(x)g(x) + f(x)g'(x)
visual zealot
oh
ocean merlin
d(uv) = udv + vdu
visual zealot
so sec(x)tan(x)cosec(x) -cosec(x)cot(x)sec(x)
visual zealot
pff
wraith daggerBOT
buoyant latch
maybe simplify your expression
visual zealot
ah yeah thats what i got when i simplified
buoyant latch
is that hte answer they gave
visual zealot
yeah
buoyant latch
literally the same thing
visual zealot
oh
buoyant latch
so sec(x)tan(x)cosec(x) -cosec(x)cot(x)sec(x)
factor secx and cscx
visual zealot
so they just havent fully simplified then?
visual zealot
fr
buoyant latch
i mean
it doesn't really matter
they are equivalent
you justn eeded to find d/dx of it
visual zealot
ah right
visual zealot
go this textbook is so weird, some answers are fully simplified and some are not
anyway ty
.close
thin minnow
i have no idea what to do here
cedar kilnBOT
i have no idea what to do here
crimson sedge
i have no idea what to do here
For a, just multiply all your y values in the graph by $\frac{1}{2}$ while keeping your x values the same, then graph it $\newline$ For b, multiply all your x values by $\frac{1}{2}$ while keeping all your y values the same, then graph it
thin minnow
ok
wraith daggerBOT
pulse
thin minnow
so for a it would be 1 times 1/2?
crimson sedge
Yes
thin minnow
then what
crimson sedge
you have the point (2,1), so multiplying the y value by $\frac{1}{2}$ gets you the new point (2,$\frac{1}{2}$)
wraith daggerBOT
pulse
crimson sedge
do this for all points in your graph, and you will have your transformed graph
does this make sense?
marsh pond
cedar kilnBOT
marsh pond
How would I find the range of f(g(x))?
Is it just both domains of f(x) and g(x) combined?
So (-Inf, 3)?
cinder snow
How would I find the range of f(g(x))?
what class is this for?
cinder snow
that doesn't mean anything to me, is this algebra, calculus, what?
marsh pond
Calc 1
But I think it’s different in each country
So don’t know if that means anything
cinder snow
ight then u can derive g(x), set equal to zero that is your min y value for g(x)
marsh pond
Why 0 tho? It’s in the middle of domain
cinder snow
what we are doing, since we derived it, we are finding when the function turns around, so the minum
marsh pond
I’m looking for range of f(g(x)) it’s not just both domains of original functions combined?
cinder snow
ooh i didn't read that
marsh pond
what we are doing, since we derived it, we are finding when the function turns a...
What are you trying to solve for here?
cinder snow
nevermind that
marsh pond
OK
cinder snow
I read your question wrong
mortal snow
Can I get some help on my homework
candid minnow
Can I get some help on my homework
just write your question in an unused help channel
marsh pond
.close
keen owl
can someone help with 1 how do i decide if its repeating? its 0.777777777778 but it ends in an 8
keen owl
so i cant tell if its repeating or not?
lyric narwhal
vague rapids
can someone help with 1 how do i decide if its repeating? its 0.777777777778 but...
it shows an 8 at end cuz its rounded off
keen owl
ohh
vague rapids
there's a limit of decimals that calculators can show
keen owl
ah
unborn pike
if the denominator is of the form 2^a5^b, it is terminating
vague rapids
if the denominator is of the form 2^a5^b, it is terminating
ye
unborn pike
otherwise, its repeating non terminating if its rational
an irrational no. is non terminating non repeating
keen owl
so would i input it as 0.777777... ?
unborn pike
if the denominator is of the form 2^a5^b, it is terminating
a and b are whole numbers
keen owl
as it just continues with 7s?
unborn pike
that's tricky, some places accept 0.77, some accept 0.78 or 0.778
the safest wd b 0.7, and draw a dash above the 7
unborn pike
np
unique basin
The value of a for which equality is satisfied:
$\sqrt[6]{a^30}=a^5;$
wraith daggerBOT
DanielCsocsik
unique basin
ye
candid minnow
You can rewrite the sqrt as an Exponent
radiant topaz
What is 30/6?
unique basin
$a^\frac{30}{6}=a^5$
wraith daggerBOT
DanielCsocsik
violet cobalt
$\sqrt[6]{a^{30}} = \abs{a^\frac{30}{6}} = \abs{a^5}$
rustic siren
no
violet cobalt
it's true for non-negative values of a
wraith daggerBOT
rept1d
rustic siren
yes, the sqrt eliminates the negatives, cuz it can only give 0<= values
wraith daggerBOT
DanielCsocsik
unique basin
correct?
south tundra
Yes
rustic siren
try them with this new knowlegde first
violet cobalt
or, you can try solving it yourself, now that you understand the basic principle
unique basin
looking at this
it should be only 0 or nothing
cuz sqrt eliminates the negatives, and -a^5 will be a negative
we cannot use any positive number cuz it will change to negative so |a^5| != -a^5
only if a is zero
correct?
$a = 0$
violet cobalt
cuz sqrt eliminates the negatives, and -a^5 will be a negative
it's not sqrt that eliminates the negatives though, but rather raising to an even power
unique basin
then just a = 0?
rustic siren
omm, -1 is a solution, right?
unique basin
is it?
rustic siren
substitute in
violet cobalt
oh wait, it's actually all the negatives
since -a^5 is positive for negative a
so a <= 0
unique basin
so yall say (-infty ; 0]
rustic siren
always try some small values to check in cases like this
unique basin
always try some small values to check in cases like this
noted king
next one
2 remaining
$\sqrt[4]{a^4} = (\sqrt[4]{a})^4$
wraith daggerBOT
DanielCsocsik
unique basin
the first half can have negative numbers
the second half aint
so its a >= 0, correct?
and $\sqrt[4]{a^4} = (\sqrt[4]{-a})^4$ is $a \leq 0$
thats a long ass minus ngl
wraith daggerBOT
DanielCsocsik
rustic siren
both correct imo
umbral fractal
i really got stuck on this
cedar kilnBOT
i really got stuck on this
umbral fractal
i dont know how i would for a repeating number?
okay thanks i can try that
ok so i have 312 now.. but subtract what?
oh?
im not sure how i would multiply a repeating decimal
and is it 10? or 100? i thought its 10
hallow goblet
and is it 10? or 100? i thought its 10
it depends on the number
umbral fractal
oh thats kidn of confusing
so it adds the repeating part to it?
so 312.2222 - 3.12... ?
which gives us 309.1022
i thought we would do 10 and it gives us 31.22? and then subtract 3.12...
but only cuz u said 100 it confused me
since 3.12... x 10 would keep the repeating part as decimal still
urban panther
3 is 3, 0.1 is 1/10 and 0,222 is 4/18 so u can write: 3+4/18-1/10
4/18-1/10 can be set to the same nominator
(calculator)
which is 3+ 11/90
umbral fractal
i used calculator soup to check it does 10
wait so how would we usually?
like do this
like whats the general formula for converting repeating decimals
i mean it seems like you got the right answer according to the calc i use to check
the formula just isnt clear so i dont know how to do the converting
i just kinda need a walk througj
bc i dont know the
formula
umbral fractal
3 is 3, 0.1 is 1/10 and 0,222 is 4/18 so u can write: 3+4/18-1/10
so just separate em all?
vague rapids
do you need another explanation from the start?
urban panther
yes the first step is to break it up in parts and use the formula
vague rapids
like whats the general formula for converting repeating decimals
depends on where the bar is
umbral fractal
do you need another explanation from the start?
yes im sorry im kinda confused from both the diff ways
yeah i tjink i learned that before
it stays the same for repeating?
vague rapids
yes im sorry im kinda confused from both the diff ways
let the number be x
So 100x is just 312.22222222 and so on
Now similarly 10x is just 31.22222222222 and so on
If you subtract 10x from 100x you get 90x which is 312.2222222222222-31.2222222222222222222 which is 281
umbral fractal
so then would we do 90x and 281? like 281/90?
umbral fractal
OKAY that makes a lot more sense tysm bc then it comes down to 3 11/90
vague rapids
OKAY that makes a lot more sense tysm bc then it comes down to 3 11/90
yea just converted to a proper fraction
Just notice which part is recurring
There is no general formula because the answer depends on placement of bar
these are some examples
The placement of bar will decide what we use 100x, 100000x or as required
cedar kilnBOT
cedar kilnBOT
Available help channel!
hasty fulcrum
Let $\phi : G \to \overline G$. Prove that the equation $x^k = b$ for some fixed integer $k$ and fixed group element $b$ has the same number of solutions as does $x^k = \phi(b)$ in $\overline G$. \
Let $X = {x \in G : x^k = b}$ for some fixed $k \in \mathbb Z$ and fixed $b \in G$ and $Y = {y \in \overline G : y^k = \phi(b) \in \overline G}$, also for some fixed $k \in \mathbb Z$ and fixed $\phi(b) \in \overline G$. Then $\forall x \in X$, we have that $(\phi(x))^k = \phi(x^k) = \phi(b) \implies \phi(x) \in Y \implies \phi(X) \subseteq Y$. Similarly, $\forall y \in Y$, we have that $y = \phi(\phi^{-1}(y)) \implies \phi(b) = \phi(\phi^{-1}(y)^k) \implies b = (\phi^{-1}(y))^k \implies y \in \phi(X)$. Then $\phi(X) = Y$. Because $\phi$ is an isomorphism, then $|X| = |\phi(X)|$.
wraith daggerBOT
blanket
hasty fulcrum
i do believe my proof to be right but i was wondering if i can just say X is finite or is there reasoning to go along with that
cedar kilnBOT
@hasty fulcrum Has your question been resolved?
hasty fulcrum
X doesnt have to be finite
G is just a group so it can be either infinite or finite
would i have to split up the proof? or is it applicable
cedar kilnBOT
crimson delta
still works out
hasty fulcrum
.reopen
cedar kilnBOT
✅
hasty fulcrum
still works out
ah okay gotcha
do i have to be explicit in saying "in the case that G is finite, the preceding proof still follows?"
and "X need not be finite"
crimson delta
no
ebon cipher
cedar kilnBOT
ebon cipher
Would someone be able to check my working here and see if anything is wrong / if my result is correct
🙏
wraith daggerBOT
Stephen
wraith daggerBOT
Stephen
runic garnet
@ebon cipher
ebon cipher
What’s wrong about what I did here then?
So I multiplied by 1/1 ( 1^-1)
I’m not sure what mistake I’ve made here sorry 😦
ebon cipher
So what should I have done instead ? I’ve been pretty stuck on this question 😅
runic garnet
try once again, separate one side to be in terms of x, and the other in terms of v
but now that u know that ur algebraic manipulation was incorrect the last time, do it correctly this time
cedar kilnBOT
@ebon cipher Has your question been resolved?
cedar kilnBOT
@ebon cipher Has your question been resolved?
inner flax
cedar kilnBOT
boreal epoch
@inner flax you know the definition of orthogonality ?
inner flax
yeah, its perpendicular/ cross product = 0
inner flax
dot product*
buoyant latch
Not 0
If you take the cross product of 2 3d vectors you get a new vector orthogonal to the first 2
If you take the dot product of this new vector with any of the first 2 you should get 0
boreal epoch
If you take the cross product of 2 3d vectors you get a new vector orthogonal to...
yes this is the principle, but keep in mind u x v is not the same as v x u
if you cross product these vectors the output would be another vector orthogonal with the vectors u crossed
minor sigil
cedar kilnBOT
minor sigil
Ok thanks
mild arrow
re-arrange for r
mild arrow
youre intial balance (2500) and then n for you is just 1 i thing
mild arrow
mhm
thorny sun
cedar kilnBOT
thorny sun
hello need help w complex analysis qn!
cedar kilnBOT
@thorny sun Has your question been resolved?
cerulean sail
I think you posted that you managed to do the first part by Cauchy's integral formula right?
thorny sun
yep!
but for the otherwise part im not sure how to go about it other than breaking them up into cases where n is a positive/negative integer
cerulean sail
Erm, would you need to?
cerulean sail
for n != -1 I would think it would be "easy"?
cerulean sail
i thought maybe for negative integers i could use partial fractions
Why would you need to?
thorny sun
bcos as mentioned, idk how to continue on for the otherwise part for n
so i was just trying it out
but couldnt proceed from there either
cerulean sail
Okay cool cool
Erm, if instead I gave you a "normal" integration question
Hmmm it's pretty hard to explain without giving the answer away 
thorny sun
my working for the ow part so far... 😦
cerulean sail
Aha!
Not sure if that's what you meant to write(!) but there, it looks like you found an antiderivative of (z- z0)^x right?
cerulean sail
absolute clown moment sry
it honestly happens, don't worry, I have many more of those moments than I would like to admit 
But there you go
fiery ermine
um how do I get the equation from this?
cedar kilnBOT
um how do I get the equation from this?
@fiery ermine Has your question been resolved?
fiery ermine
<@&286206848099549185>
<@&286206848099549185>
<@&268886789983436800> I posted this twice and pinged helpers and I haven't gotten a response for atleast 30 mins
back to waiting
cedar kilnBOT
<@&268886789983436800> I posted this twice and pinged helpers and I haven't gott...
Helpers are just people volunteering their time to help you. Be polite.
fiery ermine
.close
native current
hello, quick question and simple but i wasnt sure how to word it on google to get a straight answer, when factoring a polynomial, such as x^2 - 5x - 14, i need to find two numbers that multiply to -14 and add to -5, or the other way around? i always get the order confused
cosmic steppe
You're right because the leading coefficient is 1
If it was anything but 1, you'd have to do a bit more work
native current
ok, thank you
cedar cypress
hello, quick question and simple but i wasnt sure how to word it on google to ge...
To get rid of this confusion see that in form (x+a)(x+b) you add ax and bx to form (a+b)x
cosmic steppe
ok, thank you
If you're done, close the channel
cedar cypress
and multiply ab to form ab
So the thing with x is what the sum of the two numbers should be
obtuse coral
Hi, did I go wrong here?
So I was given the measures of those 3 sides, and I have to solve the triangle
I also have to round to the nearest whole number
So how come my values add up to 181?
runic garnet
Cuz u had to round to the nearest whole number
obtuse coral
Isn’t that what I did?
But like how does that make sense
How can the values be greater than 180
runic garnet
They’re not, u just had to round
Try adding the original values
The ones u had before rounding
obtuse coral
Try adding the original values
Yh, I got 180
But then how come I remember my teacher’s saying that they have to add up to 180
Could u plz attempt the problem?
Bc
This is somehow what my teacher got
,rotate
wraith daggerBOT
obtuse coral
Which is rlly confusing me
31, 65, and 84
Oh wait actually
She got 115, 31, and 34
But how come she didn’t round it to 35?
runic garnet
What was the value before rounding
obtuse coral
What was the value before rounding
Here
I just added the original values of angles A and B up
Then subtracted that from 180
So where’d I go wrong?
It rounds to 35
Not 34
runic garnet
Then ur teacher did that so the angles would add to 180 and not 181
obtuse coral
Then ur teacher did that so the angles would add to 180 and not 181
Ok, so I should do it too, right?
runic garnet
I guess so
obtuse coral
And does it matter with which angle I do it?
@runic garnet
Like I don’t necessarily have to do it w angle C, right?
runic garnet
I don’t know, depends on what ur teacher said in class
runic garnet
Yea I guess so
cedar kilnBOT
@obtuse coral Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
steady remnant
need help
steady remnant
slow thicket
listen to the bot
cosmic steppe
LMAO
dire geode
dont be so cringe
what is wrong with you
cosmic steppe
Is this a bingo moment
urban ermine
so do you know how to take the derrivative?
cedar kilnBOT
@steady remnant Has your question been resolved?
ashen narwhal
cedar kilnBOT
dire geode
#old-network for CS server
slow thicket
its just sqrt(n) no?
ashen narwhal
no
flint plinth
look at the numbers that are passed to sqrt... Ignoring floor for the moment, they are n, n^(1/2), n^(1/4) ... and in general they are n^(1/2^k) for k=0 up until the value of k for which n^(1/2^k) <= 2
To simplify the condition
n^(1/2^k) <= 2
try taking logs of both sides
cedar kilnBOT
@ashen narwhal Has your question been resolved?
signal vault
for ax^3+sqrtb x^2 + x=0 how do i determine the amount of x intercepts when b-4a is bigger or smaller or equal to 0
cerulean star
for ax^3+sqrtb x^2 + x=0 how do i determine the amount of x intercepts when b-4a...
that sounds like a test question
signal vault
it is
cerulean star
b-4a is called the Discriminant
signal vault
yeah i know
cerulean star
and there is a table of values for this
signal vault
but this is not exactly a quadratic
cerulean star
👉 👉
vapid sand
cedar kilnBOT
wraith daggerBOT
vapid sand
theres a plus at the bottom which makes it inconvenient
cedar kilnBOT
@vapid sand Has your question been resolved?
vapid sand
<@&286206848099549185>
vapid sand
.close
dire tundra
What is being used to find c?
dire tundra
radiant topaz
one channel was enough roberto
dire tundra
Sorry I couldnt find channel 0 for some reason
so i decided to open another one
must of glitched
dire tundra
yeah
radiant topaz
4+4(3) = 16 = c^2 so c=+- 4
dire tundra
4+4(3) = 16 = c^2 so c=+- 4
where are you getting the 4+4(3) from?
tropic oxide
@worthy notch this channel is occupied. please open your own channel. read #❓how-to-get-help
cedar kilnBOT
@dire tundra Has your question been resolved?
sharp vale
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true matrix
Hey just looking to have my working out checked
cedar kilnBOT
Hey just looking to have my working out checked
true matrix
cedar kilnBOT
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true matrix
.close
cedar kilnBOT
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reef sedge
cedar kilnBOT
reef sedge
can someone explain
loud granite
reef sedge
how he went from the step of (2,6) to 8/sqrt(5)
lol
this is the full question
i already figured A
earnest fiber
You can easily think of it with trigonometry. Just multiply the vector whose projection has to be found by the cos of the angle between them
The angle is already found by you so it'll be easy
earnest fiber
the anglue is different isnt it
??
reef sedge
hm?
earnest fiber
What do you mean by angle is different?
cedar kilnBOT
@reef sedge Has your question been resolved?
reef sedge
You can easily think of it with trigonometry. Just multiply the vector whose pro...
the dor product from a.bcos have the same angle? as this one
earnest fiber
the dor product from a.bcos have the same angle? as this one
The question asks you the smallest angle. The smallest angle is just the smaller one between the two right?
And did you use this formula to find it
reef sedge
i want the one for b tho
earnest fiber
i want the one for b tho
Want what??
reef sedge
angle
earnest fiber
I am not sure what you're trying to say honestly
earnest fiber
This is just a derivation to find it directly without finding the angle first
This is where they get it from
cedar kilnBOT
@reef sedge Has your question been resolved?
reef sedge
u dont spot an error here? @earnest fiber
cedar kilnBOT
@reef sedge Has your question been resolved?
pseudo merlin
hi!!
pseudo merlin
can i hav some help
sage forge
What have you tried?
hidden osprey
can i hav some help
consider the two parts to be x and y
you can frame two equations with x and y and then solve for each variable
pseudo merlin
What have you tried?
idk what to do so i just skipped it and moved onto next q
sage forge
Ok, then try as Blighter suggested
pseudo merlin
consider the two parts to be x and y
you can frame two equations with x and y an...
can you show me this way it sounds easier
pseudo merlin
x+y is 36
cedar kilnBOT
@pseudo merlin Has your question been resolved?
pseudo merlin
From your notes it is unclear what you did here but x = 15, y = 21 is right
pardon
random crag
AOPS 6-3 When factoring the quadratic x^2 + bx +c, where b and c are integers, WHY do we not consider the case where u and v in the factored form (x + u) ( x + v) are fractions?
crimson delta
rational root theorem
random crag
I'm trying to argue by contradiction... trying fractional roots, I will find some contradiction somewhere... But, where?
I resoned the following, but it's not taking me nowhere....
Supposing u = a/b and v = c/d, not( b | a) and not( d | c). Then we must have bd | (ad + bc) and bd | ac (integral roots).
Also not(b|a), not(d|c) and bd|ac => b|c and d|a.
crimson delta
not a good idea to use b and c twice
lets say u=p/q is a root of x^2+bx+c. so (p/q)^2+b(p/q)+c=0. multiply out the denominator
random crag
not a good idea to use b and c twice
Thank you, you are right... I'm on a sketching phase right now... just trying to think about this thing.
random crag
not a good idea to use b and c twice
Oh, thanks! I know what you mean now by rational root theorem
Or do I... I will close and think about this. Thank you again!
.close
ionic crypt
I need some help with understanding Unit Vectors. Mostly the equation -
ionic crypt
lets say r is a vector
to get a unit vector you need to divide r by its magnitude
so we have r / | r |
and that gets the unit vector, correct?
ionic crypt
if r is [1,3,-2] then it would be
[1,3,-2] / magnitude of [1,3,-2]
crimson delta
yes
ionic crypt
(r should be nonzero)
dividing by 0 intensifies
Alright I'll go ahead and do magnitude, wish me luck
gritty viper
good luck
stoic quarry
i proved the series but how do i do the integral
cedar kilnBOT
i proved the series but how do i do the integral
stoic quarry
i got very confused
crimson sedge
firstly $t \neq 2nπ$ where n is an integer
wraith daggerBOT
bs292929
crimson sedge
And the above numerator can be written as
$2sin(\frac{t}{2})sin(nt)$
wraith daggerBOT
bs292929
crimson sedge
But you are also dividing
stoic quarry
i already done the summutation part
im confused on the definite integral by deefinition part
cedar kilnBOT
<#903430334681608232>
old lantern
Did ChatGPT fail again?
PS: I know these kinda questions aren't welcome in most places, but it's uttering absolute garbage isn't it? in a linear differential equation the degree can't be greater than 1 but the order can be
old lantern
thank you! that's enough for me to end this 🥲
crimson delta
it just says words that it has seen in similar contexts
crimson delta
speaking of powers of derivatives for meaning which derivative you take is pretty bullshit
the degree has to be 1 for linear, yes
old lantern
hey... I go to chat Gpt when there aren't good sources which can't make me understand these concepts in common words. I looked at the wiki page for Linear Differential Equations and it was dense. I could not understand it. Is there a better alternative to look up when you are trying to look up something about basic math. I had two textbooks and none of them explained what LDE is properly in detail
also, thank you for the replies
crimson delta
the wikipedia page is not that bad
I mean, math is complicated. that's pretty normal that you dont get everything immediately
old lantern
the wikipedia page is not that bad
a lil dense for a non-native english speaker.
*english
crimson delta
I mean just from a quick google search there are dozens of resources. hard to say which ones of those you would understand and which ones you wouldnt
cedar kilnBOT
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Available help channel!
hushed drift
why am i getting a negative lambda value here?
cedar kilnBOT
why am i getting a negative lambda value here?
hushed drift
integrate from 0 to inf
has to be 1
so lambda is -1/100
is that normal?
the solution says its positive
wraith burrow
did you write down your solution of this integral? can you show it?
cedar kilnBOT
@hushed drift Has your question been resolved?
hushed drift
did you write down your solution of this integral? can you show it?
sure
give me a second
cedar kilnBOT
@hushed drift Has your question been resolved?
hushed drift
.close
crimson sedge
im not sure if i know how to prove the following, but i can tell you what ive done so far
crimson sedge
Let f: A -> B and g: B -> C
a left inverse will be injective, and it is when f circ g
a right inverse will be surjective, and it is when g circ f
the definition of injectivity is, for all a, b in A, f(a) = f(b) -> a = b
surjectivity is defined, for all b in B, there exists a in A s.t. f(a) = b
for a) I said, let f : A -> B and g : B -> C wts a left inverse is injective
so we have f circ g ==> (f circ g)(B)
==> f circ (g(B))
yeah no i think im doing something wrong
cerulean sail
Remember the aim is that you’re assuming that you have a left inverse, and then you want to carry out steps that show you that your original function is injective (and similar for the other one)
Also as a tiny sidenote, how are you feeling @crimson sedge? 
crimson sedge
uh pretty terrible
i am expecting to fail this course
which lowkey sets me back a bit
lol 😝
cerulean sail
Awwww 
well of course we shall hope that you don’t
Some of these courses can be something else, and especially trying to keep up and all
crimson sedge
im just trying my best unfortunately
cerulean sail
the definition of injectivity is, for all a, b in A, f(a) = f(b) -> a = b
You’ve gotten down the injectivity definition here 
Maybe state explicitly the definition of a left inverse?
cerulean sail
it also, ensures injectivity
Injectivity of?
cerulean sail
left inverse is when g circ f is composed
When that composition is what?
crimson sedge
Injectivity of?
of the result
cerulean sail
of the result
The composition, you mean, yea? The gf you get?
crimson sedge
The composition, you mean, yea? The gf you get?
yup
crimson sedge
by definition of injectivity, wouldnt you have to conpose g circ with 2 different functions
because we want to show that different inputs give different outputs right
cerulean sail
So we have that $f$ has a left inverse, that means there is a $g$ such that when you do $g\circ f$, you get the identity
wraith daggerBOT
@cerulean sail
cerulean sail
And as you said that gf would have to be injective
crimson sedge
oh now we have to use the identity fucntion
cerulean sail
So now we want to check whether f is injective, so we may as well from the definition assume we have f(a) = f(b)
crimson sedge
would we define f with 2 different outputs
sorry
inputs
im just confused how we can show f(a) = f(b)
cerulean sail
im just confused how we can show f(a) = f(b)
We assume that we have two inputs with the same output
And for injectivity we want to show that they’re the same, so showing that actually a=b
cerulean sail
the definition of injectivity is, for all a, b in A, f(a) = f(b) -> a = b
Remember the definition here 
crimson sedge
two inputs that are different, should have different outputs
-q -> - p
if f isnt an injective then g circ f is not a left inverse
so should we do proof by contrapositive
like we could let x, y in A right (not proof by contrapositive)
f(x) = f(y)
which is x = y
thus we have an injective
a left inverse is defined by g circ f
any function conposed by an injective function, will also be injective
cerulean sail
so should we do proof by contrapositive
(You could, but there’s not much need to!)
cerulean sail
thus we have an injective
Hmmm how did you get this? Was the initial assumption that you’d assume that f isn’t injective and try and show the composition would not be either?
cerulean sail
(You could, but there’s not much need to!)
(Actually, I retract that, that might be an easier way to show it!)
crimson sedge
idk if f is not injective CLEARLY. a left inverse doesnt exist
by definition of inverses
cerulean sail
idk if f is not injective CLEARLY. a left inverse doesnt exist
Well you would need to justify that clearly 
which is what the whole question is asking of you!
crimson sedge
why would the identiy function be useful here
i mean identity function basically likes
like proves its injective
since it literally outputs its input
we can use the identity function to show that it is injective
cerulean sail
Well the identity function comes from the definition of (left/right) inverses
,w left inverse function
wraith daggerBOT
cerulean sail
The fact that you said that the composition must clearly be injective is easy to see from this definition, as identity functions are injective
crimson sedge
ah that makes sm sense
cerulean sail
in fact I think there was a similar exercise we did that we could cheat and use here(!)
identity function is clearly injective and surjective
And remember some time ago we had something where it was like "if $g\circ f$ is a bijection, then show that $f$ is injective and $g$ is surjective"?
wraith daggerBOT
@cerulean sail
crimson sedge
which you just use the identiy function
but youd have to define f and g as having the same sort of inputs and out puts
like the definition above
f : s -> t and g : s -> t
cerulean sail
I would guess that they're implicitly expecting you to have added those details in haha
crimson sedge
this isnt even a long proof
just define f : s -> t and g : s -> t, since this is the identity function g circ f ==> g(f(s)) which is just g(s) which is ids
injective
surjective is for all y in T there exists x in s st f(x) = y
cerulean sail
mhm
cedar kilnBOT
@crimson sedge Has your question been resolved?
sacred grail
And remember some time ago we had something where it was like "if $g\circ f$ is ...
this is a bit overkill 
cerulean sail
this is a bit overkill <:hmmCat:831508801646755850>
It is but it's the same idea to show it
crimson sedge
is this as bad as it looks
cerulean sail
It's pretty much the steps that we would have done that time haha
crimson sedge
huh
sacred grail
talking about the in/surjections one
crimson sedge
oh right so just define the identity function for both g and f
sacred grail
is this as bad as it looks
this isn't bad
just list out what you need to prove and unravel the definitions
crimson sedge
yeah transititivyt, reflexivity, symmetry
when they define h, they are talking about in [n]
cedar kilnBOT
@crimson sedge Has your question been resolved?
cedar kilnBOT
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lime wagon
How to simplify this further?
cedar kilnBOT
How to simplify this further?
lime wagon
Like so 19)
violet night
your second to third line is incorrect
you can raise each term to a common denominator of 9 , then since 3 = sqrt(9), after multiplying that through it cancels with your denominator inside of 9
then its just factorization
lime wagon
But how is it wrong?
violet night
because you multiplied 2/3 onto the left fraction, yet completely disregarded the 3
if you still have a * 1/3 on the right of that fraction it would still be correct
lime wagon
Okay makes sense, but I don’t understand how to solve it with a common denominator of 9
I mean I obviously know what that means
violet night
a + b/d = (ad+b) / d
lime wagon
But that doesn’t get rid of the fraction?
Oh I read your message from before
Let me try
How does it work with three parts
violet night
what
lime wagon
a+b+c/d = (ad+bd+c)/d?
violet night
sure but why are you doing that here
lime wagon
Because I have 4x^2-4x+1 all divided by 9
violet night
right
so lets call all that garbage b
now we have b/9
and we have 1
lets call that a
now we have a/1 + b/9
violet night
violet night
well its a good way to learn how to add fractions :P
violet night
what
crystal raptor
lethal jackal
reflections have to be done across planes
if you have a line for a mirror, do you see a reflection?
cedar kilnBOT
@long walrus Has your question been resolved?
cedar kilnBOT
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modest dove
cedar kilnBOT
modest dove
trying to understand the working out for ii)
I was able to successfully determine that the substituion was equal to 6
amber ridge
try expanding (x + 1/x)^2
granite ether
^
modest dove
$(\frac{x+1}{x})^2=(\frac{x^2+1}{x^2})$
wraith daggerBOT
Jshy <3
amber ridge
x + 1/x not (x + 1)/x
modest dove
Im a bit confused about what you are to say here
if its to the power of 2, don't you just square everything internally?
or would it be (x+1)^2/x^2
@amber ridge
modest dove
it’s basically the same thing
$\frac{x^2+2x+1}{x^2}$
wraith daggerBOT
Jshy <3
amber ridge
no it’s literally (x+1/x)^2