what is preventing you from doing the usual methods
#help-10
next wind
agile knoll
yeah my friend just sent me what he did and it makes sense now
i have to bring the n^n down to the denominator
next wind
yes, the exponent was preventing you from doing anything
next wind
exactly
agile knoll
and the roc is e via the squeeze theorem
next wind
and the limit of that is e
do you have a proof for that yet ?
next wind
and the roc is e via the squeeze theorem
yep
agile knoll
i think we learned it a while ago
i don’t remember the proof but out teacher just told us to memorize it
next wind
well if you want another proof, you can look at what i sent you at first
agile knoll
i understand it until you get to the e
how do you know to you use e in that situation
next wind
how do you know to you use e in that situation
this is a classic method that you will often use
when dealing with the variable as an exponent, we use the exp(log) method
agile knoll
is that something you learn in later math?
next wind
as we look at the limit when n -> +inf, we take the exp(log) of the function so that we can bring down the exponent
next wind
is that something you learn in later math?
didnt see you were pre uni, yes this is a very classic method you learn later on
agile knoll
yeah im still in highschool lol
next wind
ok, makes sense you havent learnt it yet then
agile knoll
my brain was getting fried from the explanations i was getting
next wind
im postgrad, sometimes i forget what i knew and didnt know in high school
you good now
?
next wind
makes sense
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
eager marsh
x^2 + y^2 = 25
what is the output here? y^2 or 25?
obtuse pebbleBOT
x^2 + y^2 = 25
what is the output here? y^2 or 25?
eager marsh
i am used to seeing the output of functions as being y
y = x*2
but here x and y are on the same side of the equation
versed stratus
express y in terms of x
eager marsh
?
dim temple
it means, isolate y
eager marsh
i am just confusd on the naming choice
is y a special variable
i thought conventionally x was input and y was output
but here they are both inputs to give output 25
left vault
no y is still technnically the output
but in this case
you have two outputs for a given input
thats why you don't see it written in terms of y explicitly
eager marsh
what is the function
left vault
$y=\pm \sqrt{25-x^2}$
warm shaleBOT
The Great D
left vault
note this not a function
eager marsh
i dont know why you would ever write both x and y on the same side
left vault
its more convient and simpler to understant that way
eager marsh
i dont understand it still. its like you take a normal input -> output form, and then grab the output and warp it into the input
now its tangled spaghetti
like shoelace knots
left vault
yes because its not as simple as an input and a corresponding output
some inputs have two outputs
some have one
and some dont have any outputs
did you try graphing it and seeing how it looks?
eager marsh
i know it is not a function
but i want to read this as x and y being inputs
and 25 being an output
doesn't make sense otherwise
"the input squared plus the output squared equsl 25" what???
how can I ever possibly come to that intuitively
left vault
id break out from the thought patter of inputs and outputs
these only work well when dealing with functions
eager marsh
if these are just random variables x y then i am fine
but you've said y means outpout
so now the output is warped like a knot in the middle of the equation
left vault
you'll get used to it dw
untold pawn
how am i supposed to know that the slope intercept form is that?
algebra
eager marsh
yes i am not finding any algebraic rules to do that
inverting the multiplications dont do anything
switching the subtraction to a plus does not either
untold pawn
,ask 2x-3y=6 in slope intercept form
warm shaleBOT
grizzled shore
x^2 + y^2 = 25
what is the output here? y^2 or 25?
This is not a function
eager marsh
i dont know how to get this
eager marsh
This is not a function
Yeah its just the notion of y being an output that is weird to me
grizzled shore
Think about more like x and y are linked
I know you may have seen always y = something
grizzled shore
But the equality is more just a relationship between x and y
No we technically want to use f() notation for that
f(x, y) can be a function
eager marsh
,ask 2x-3y=6 in slope intercept form
was this link supposed to enumerate the steps on how to get it? because i just see the end result
grizzled shore
Very common in programming to have a function with multiple inputs
untold pawn
was this link supposed to enumerate the steps on how to get it? because i just s...
it's just simple algebra?
isolate y
then rearange to intercept form
eager marsh
it's just simple algebra?
everything I know past arithmetic is self taught in adulthood
I know you can take multiplications and divide them to undo
and make subtractions additions
neither of those ioslate y
in this example
grizzled shore
From 2x - 3y = 6
You can subtract 2x from both sides
That brings you to -3y = 6 -2x
grizzled shore
Then you’re just 1 step away from isolating y
eager marsh
y = (6-2x)/-3
grizzled shore
Ah but now you know $\frac{a+b}{c} = \frac{a}{c} + \frac{b}{c}$
warm shaleBOT
Frosst
eager marsh
y = (6/-3) - (2x/-3)
warm shaleBOT
tzy
grizzled shore
y = (6/-3) - (2x/-3)
I’d suggest keeping the -‘s inside the brackets
Stick to + where you can
It makes everything easier because order doesn’t matter for +, a + b = b + a
eager marsh
how do I get +s here?
eager marsh
like 6/(-3)?
grizzled shore
I was talking more about the 2nd one
untold pawn
ur teaching him the confusing way
untold pawn
y = (6/-3) - (2x/-3)
just continue this
what would it be after
divide the 6 by -3
6 divide negative 3...?
eager marsh
y = -2 - -.066x
eager marsh
-2
untold pawn
leave the - 2x/-3
eager marsh
y = -2 - 2x/-3
eager marsh
2 + 2x/-3
eager marsh
y = 2x/3 + -2
eager marsh
y = 2x/3 - 2
untold pawn
there you go
eager marsh
why not y = 0.66x - 2
untold pawn
It sounds complicated with all these steps but trust me with practice youll nail it easily
eager marsh
are both graded the same in exams
untold pawn
but if you're in a non calculator exam then you would use 2x/3
tbh any answer is accepted dw
eager marsh
so when I see this, am I supposed to go and write out all the algebra
and try to isolate y for each?
that seems time consuming
untold pawn
is this a calculator allowed exam?
eager marsh
i think it will be yes
untold pawn
then just graph each of those functions on the calculator
and use the verticle line test
eager marsh
ahk. and if it's not allowed, is there any easier analytical method
besides attepmting to isolate
untold pawn
Tbh not really
I'm still in highschool so I don't know the technicals
But how I would determine if something is a function is by looking at the graph
And use the verticle line test
But where I'm from, every multiple choice question is in the calculator allowed exam
So that's easy for me
,ask y^2 + 2 = 7x^2 graph
thats not a function
,ask 2x-3y^2=18 graph
not a function
,ask -x^4+y^2=3x^2-5 graph
,ask x^3+2y=54 graph
warm shaleBOT
untold pawn
Answer would be D as the graph only cuts once across the verticle direction
eager marsh
Answer would be D as the graph only cuts once across the verticle direction
yeah that is what i concluded
.close
obtuse pebbleBOT
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Available help channel!
brisk arrow
Is 4 * sqrt(17) bigger than 17 or the other around?
obtuse pebbleBOT
Is 4 * sqrt(17) bigger than 17 or the other around?
teal turret
@high lily whats your answer
brisk arrow
Intelligent
last pilot
lmafooespxozops
warm shaleBOT
ren
last pilot
im so used to using geq i forgot that's not the case here 💀
brisk arrow
im so used to using geq i forgot that's not the case here 💀
“geq”. What it stands for
warm shaleBOT
! What the hell am I doing here?
brisk arrow
I see
last pilot
greater than/equal to
brisk arrow
Works on every scenario involved compare two sqrt numbers
last pilot
.close if done
brisk arrow
Works on every scenario involved compare two sqrt numbers
Is it true
last pilot
what is?
last pilot
yea
brisk arrow
I see
high lily
if the numbers aren't nice, it may not be practical to do it by hand
last pilot
^^
i mean it works
it's just common sense tho tbh
4 = sqrt 16
and sqrt 17 times sqrt 16 is obv less than 17
brisk arrow
I will name it “rauONwV” method
last pilot
:O
last pilot
oh this is the emoji i was looking for
brisk arrow
I will name it “rauONwV” method
rauONwV and ten method
last pilot
last pilot
rauONwV and ten method
"ten"
brisk arrow
*ren
last pilot
oh hell nah
pine sail
brisk arrow
.close
obtuse pebbleBOT
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Available help channel!
pale urchin
obtuse pebbleBOT
pale urchin
That just becomes 2/9 right?
trim portal
That just becomes 2/9 right?
Yes, assuming x^2 + 3x - 28 isn't equal to 0
last pilot
@pale urchin ^^
worldly lagoon
obtuse pebbleBOT
worldly lagoon
Is my process accurate here?
I use a limit comparison followed by a p-series to confirm the divergence
I mainly want to know if it's ok to just apply the limit comparison test here
obtuse pebbleBOT
@worldly lagoon Has your question been resolved?
radiant marsh
obtuse pebbleBOT
radiant marsh
Would this be a viable way to use for proving that (a^-1-b^-1) = (a-b)^2/a^2b^2?
here's a larger screenshot of the same thing
nvm I made a mistake
can someone hint on how I should start proving it?
trim portal
Would this be a viable way to use for proving that (a^-1-b^-1) = (a-b)^2/a^2b^2?
Hmm
that doesnt feel right
$\frac{1}{a}-\frac{1}{b}=\frac{\left(a-b\right)^{2}}{a^{2}b^{2}}$
warm shaleBOT
MethIsAlwaysRight
trim portal
are you proving this?
radiant marsh
that doesnt feel right
you're right I made a mistake when opening it
radiant marsh
**MethIsAlwaysRight**
no
trim portal
oh wait, the right expression should be
$\left(\frac{1}{a}-\frac{1}{b}\right)^{2}=\frac{\left(a-b\right)^{2}}{a^{2}b^{2}}$
warm shaleBOT
MethIsAlwaysRight
radiant marsh
left side should be this
radiant marsh
do you know how to subtract fractions?
yeah I know how to do stuff with fractions
radiant marsh
try writing the LHS into one fraction
what does LHS stand for?
trim portal
left hand side
radiant marsh
I'm less familiar with english terms for math as I'm studying it in hebrew
radiant marsh
left hand side
oh ok
radiant marsh
Have you made any progress?
just turned it into ((b-a)/ab)^2
gonna think what I can do next
trim portal
just turned it into ((b-a)/ab)^2
that's nice
$\left(\frac{b-a}{ab}\right)^{2}=\frac{b-a}{ab}\cdot\frac{b-a}{ab}$
here is a hint for you
radiant marsh
ok so I'm on the right path
warm shaleBOT
MethIsAlwaysRight
radiant marsh
thanks
trim portal
indeed
you are just few steps away from the result
little bit more of the hint
$\left(\frac{b-a}{ab}\right)^{2}=\frac{b-a}{ab}\cdot\frac{b-a}{ab}=\frac{\left(b-a\right)^{2}}{a^{2}b^{2}}$
warm shaleBOT
MethIsAlwaysRight
trim portal
to get b^2-ba-ab+a^2
Note that you are trying to get the left hand side equal to the right hand side
right hand side is this ^
radiant marsh
so I'm guessing I have to multiply (b-a)^2 * -1 to get (a-b)^2
trim portal
so I'm guessing I have to multiply (b-a)^2 * -1 to get (a-b)^2
not really
radiant marsh
ok
trim portal
(b-a)^2 is actually equal to (a-b)^2
to prove that, try writing (b-a)^2 as ((-1)*(a-b))^2
(-1)*(a-b) is b-a
so (b-a)^2 is ((-1)*(a-b))^2
and when you try to simplify that, you get (-1)^2 * (a-b)^2, which is same as 1*(a-b)^2 which is simply (a-b)^2
radiant marsh
how does that prove (b-a)^2 = (a-b)^2 I don't really understand
warm shaleBOT
MethIsAlwaysRight
trim portal
here it is written in latex
all the steps should be fairly simple algebra with exponents
radiant marsh
**MethIsAlwaysRight**
oh ok I get that, where did you get the -1 from though?
is it related to some math property that I forgot about
trim portal
oh ok I get that, where did you get the -1 from though?
I can rewrite it like that, because (b-a) = (-1) * (a-b)
you can verify this yourself
radiant marsh
I can rewrite it like that, because (b-a) = (-1) * (a-b)
but why -1
sorry maybe I'm missing something simple, I don't really get where that -1 comes from, what's the logic behind putting -1 there out of nowhere
trim portal
because it helps me turn (b-a) into (a-b), which is the expression that we need to achieve
radiant marsh
so I'm guessing I have to multiply (b-a)^2 * -1 to get (a-b)^2
isn't that what I did here?
trim portal
isn't that what I did here?
multiplaying (b-a)^2 times -1 doesnt get you (a-b)^2 though
what gets you (a-b)^2 is rewriting (b-a)^2 as ((-1)*(a-b))^2
if this operation is too hard for you to comprehend for now, you could instead modify the equation like this
it's slighly less elegant, as it requires expanding and also working with both sides of the identity, but it works
radiant marsh
if this operation is too hard for you to comprehend for now, you could instead m...
so here this can be explained by the math property a + b = b + a?
trim portal
so here this can be explained by the math property a + b = b + a?
indeed
radiant marsh
okay, yeah that one is easier to comprehend for me
trim portal
you'd just need to switch b^2 and a^2 at whatever side you choose, and get same expression at both sides
trim portal
I'd use = instead of <->
radiant marsh
I'd use = instead of <->
we have to use => and <=> signs in this assignment
trim portal
we have to use => and <=> signs in this assignment
those need to be used only between statements
such as equations
radiant marsh
those need to be used only between statements
using those when simplifying an equation is fine right
trim portal
so u'd have to write something like (a^-1 - b^-1)^2 = (a-b)^2 / (a^2b^2) <-> (1/a - 1/b)^2 = (a-b)^2 / (a^2b^2) <-> .....
radiant marsh
so u'd have to write something like (a^-1 - b^-1)^2 = (a-b)^2 / (a^2b^2) <-...
can you write that in latex?
warm shaleBOT
MethIsAlwaysRight
trim portal
Now you would use <=>
warm shaleBOT
MethIsAlwaysRight
trim portal
and continue with this
$\left(a^{-1}-b^{-1}\right)^{2}=\frac{\left(a-b\right)^{2}}{a^{2}b^{2}} \iff \left(\frac{1}{a}-\frac{1}{b}\right)^{2}=\frac{\left(a-b\right)^{2}}{a^{2}b^{2}}$
warm shaleBOT
MethIsAlwaysRight
trim portal
yeah, like this ^
distant seal
idk how to go about it
obtuse pebbleBOT
idk how to go about it
versed pier
Oh lhoptial
*hospital
worn yoke
distant seal
i've only learner l'hospital
obtuse pebbleBOT
@distant seal Has your question been resolved?
quiet plaza
Hello, everyeone! I need help with two things.
-
What are some good resources to learn math from zero?
-
How would you define math? What is math?
obtuse pebbleBOT
Hello, everyeone! I need help with two things.
1. What are some good resources...
bronze nova
Hello, everyeone! I need help with two things.
1. What are some good resources...
- mit courseware
on youtube
quiet plaza
1) mit courseware
Thank you!
Now, regarding my last question, how would you concretely define math?
bronze nova
there isnt a concrete definition of math
but the methods of math r concrete
we have induction and deduction
deduction is where we accept certain premises and if we assume them to be true, the conclusion must be rigorously valid
if we assume 0=0 and there exists a successor to every successor, hence there exists succ(0), succ(succ(0)) and so on
we can define the natural numbers
induction on the other hand
assumes a specific case and generalizes it
quiet plaza
deduction is where we accept certain premises and if we assume them to be true, ...
Alright, makes total sense.
And how would you define the study object of math? What does math study?
Reality? Perhaps, but in that case, what is the formal study object of it?
quiet plaza
So math isn't a science?
bronze nova
no
quiet plaza
Alright.
bronze nova
given certain axioms, math studies the behaviour and implications of those axioms
and derives theorems
which somehow managed to work well in describing the natural world
quiet plaza
which somehow managed to work well in describing the natural world
Alright, so math is more like a language then?
bronze nova
u could call anything a language
quiet plaza
u could call anything a language
Let me know what you think of my definition then:
Math is the language that, through the lens of reason, expresses the reasoning behind the axioms of this world.
The problem with this definition is that it is really broad. I mean, if this is true, the problem would be in identifying what ISN'T math.
quiet plaza
it accepts the axioms
And through the axioms it explains the structure of the world, would that be?
bronze nova
it doesnt care about the world either
quiet plaza
it doesnt care about the world either
Even if it doesn't care, it ends up doing so because all of our reality is made up of it, I guess. Am I correct?
Is it the language of the structure of this world?
bronze nova
it can be seen as that
but its cuz we made it that way
science is completely about observations
and we fit our math to the observations
its not that we fit the observations to the math
quiet plaza
its not that we fit the observations to the math
I see, I see.
"Mathematics are the means that we use to express the structure of the world, given certain axioms?"
bronze nova
just get rid of the idea that math cares about the structure of the world
there r two branches of math
pure and applied
Pure is the real math
applied is when we use mathematical methods to express observations from the natural world
bronze nova
Pure is the real math
pure math discusses the implications of math with if else statements
if A is true then B must be false
quiet plaza
Alright.
quiet plaza
there r two branches of math
But if there are two branches of math, shouldn't there be a first one from which these other two stem? I guess we'll be doing some reverse engineering to get to the definition of math.
bronze nova
yeah applied math branched from pure math
quiet plaza
yeah applied math branched from pure math
And is pure math derivated from anything else?
bronze nova
axioms
bronze nova
no
they r accepted facts
in science we have postulates
like the law of thermodynamics
we cant prove it
but it seems legit
quiet plaza
So axioms are assumed principles then. I see.
bronze nova
yes
quiet plaza
but it seems legit
They are assumed principles because they seem to be the best to express a given question.
bronze nova
They are assumed principles because they seem to be the best to express a given ...
they seem too obvious to prove and counterintuitive if it werent true
so we assume them to be true
quiet plaza
they seem too obvious to prove and counterintuitive if it werent true
Alright, alright.
"Mathematics are the deductive discipline that, through the lens of logical reasoning, studies the behaviour and effects of given laws".
obtuse pebbleBOT
@quiet plaza Has your question been resolved?
bronze nova
"Mathematics are the deductive discipline that, through the lens of logical reas...
given axioms instead of given laws then u r good ig
limber eagle
obtuse pebbleBOT
limber eagle
i was thinking between 0ml to 125ml
distant fossil
I feel like this is not a math question, but a scientific method question, no?
limber eagle
it is a math question though
i think it has some graph method or something, i'm not clear on it
distant fossil
is there any more context?
limber eagle
that's all i have
distant fossil
the way I see it if you never checked on it anything from 0-500mL
but that's not an option, not sure without more context there will be an answer, but maybe someone sees something I don't or is smarter than me
limber eagle
oh okay thanks for trying
distant fossil
what iks professors lohs method?
wait maybe I misread, I guess the beaker is more than 500mL?
limber eagle
it ended with 500ml
distant fossil
right, but the beaker did not leak/overfill?
cloud sparrow
i think it should b, not a very rigorous proof tho
inland basalt
but that's not an option, not sure without more context there will be an answer,...
i guess its about constant rate
limber eagle
i think it should b, not a very rigorous proof tho
but it is incorrect, i tried
cloud sparrow
o.O
distant fossil
don't give answers 😛
distant fossil
so if the higher rate went the whole time
it would be 500mL/60mins
so anything more than 500mL/60mins*15mins would be impossible as the highest constant rate was 500mL/min according to the problem
quiet plaza
given axioms instead of given laws then u r good ig
Thank you, mate!
limber eagle
so anything more than 500mL/60mins*15mins would be impossible as the highest co...
so i see it if the light constant rain was between 0-125, and if it was 125 it would in 60 min fill up to 500ml
so i thought 0-125
distant fossil
that logic does give you b as an answer
yeah not sure
please do DM me with the correct answer/logic
limber eagle
is there any other way to look at it?
obtuse pebbleBOT
@limber eagle Has your question been resolved?
tight sail
obtuse pebbleBOT
oak gyro
Reflexive means that xRx is always true
Symmetric means that if xRy is true, then yRx is also true
Antisymmetric means that if xRy is true, then yRx must be false
Transitive means that if xRy and yRz are true, then xRz is also true
It asking which of the properties that * and ♡ satisfy for #3 and #6
obtuse pebbleBOT
@tight sail Has your question been resolved?
tight sail
It asking which of the properties that `*` and `♡` satisfy for #3 and #6
but dont all of them need to have the property
?
oak gyro
What do you mean
tight sail
What do you mean
like it must apply to all elements
obtuse pebbleBOT
@tight sail Has your question been resolved?
obtuse pebbleBOT
@tight sail Has your question been resolved?
tired shell
like it must apply to all elements
yes every element has to follow those rules to be reflexive, sym, or tran
and since your graphs are kinda just random lines neither satisfy the rules for every element
tight sail
yes every element has to follow those rules to be reflexive, sym, or tran
what about
anti-sym
tired shell
oh that one might actually hold
it's pretty loose
it essentially says there's no ↔ in the graph between different numbers
tired shell
yes for both yea
tight sail
ok
obtuse pebbleBOT
@tight sail Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
fathom flicker
obtuse pebbleBOT
fathom flicker
Hi, can anyone look over my proof for this please?
molten grove
I think you have the right idea but wrong details
You let f(i) =iU but f is an automatism on Zn and Un is a group of matrices
fathom flicker
Sir, U_n here represents the units of Zn
not matrices
our notation might be different
fathom flicker
No problem
molten grove
Sec lemme reread
wooden cipher
Can we see problem 7 and problem 3 for context
fathom flicker
Can we see problem 7 and problem 3 for context
they're not very helpful, but sure I will show you
fathom flicker
Can we see problem 7 and problem 3 for context
I am happy to feedback on these aswell XD but I know that's a lot. I guess if you're curious and looking and spot anything wrong let me know @wooden cipher
wooden cipher
well idk what a ___morphism is, so i cant help sorry
obtuse pebbleBOT
@fathom flicker Has your question been resolved?
molten grove
for h is a homomorphism in the original problem how are you getting that phi(psi(1) 1)$ = phi(1)psi(1) ?
for your question 7, you should show that the function f is a well defined function as well
besides that everythign else looks fine
molten grove
yeah im asking you to argue the 3rd equality
fathom flicker
it is because psi(1) is in Zn
so for additive homomorphisms we have f(n*g)=nf(g)
n=psi(1) g=1
molten grove
yep
fathom flicker
for h is a homomorphism in the original problem how are you getting that phi(psi...
Do you think it is necessary to do that?
To show it is well-defined
molten grove
the well defined part?
fathom flicker
yes
molten grove
yes, in general when you have a homomorphism from G to H, and the representatives of G can be written in different ways, its important to show that homomorphism is well defined
for your example if say a^x = a^y in the cyclic subgroup
but for x not equal to y
is it necessarily the case that the homomorphism maps them to the same thing?
fathom flicker
if a^i=a^j => a^(i-j)=e => i-j = |a| mod n = |b| mod n
f(a^i)=b^i
f(b^j)=b^j
since i-j = b mod n
b^i=b^j
and it is well defined
does that work?
molten grove
did you mean the first line to be a^i = a^j
fathom flicker
no, but we could do that instead
yeah that is not true what I wrote
I should've said a^i=a^j
molten grove
you have the right idea as doing the injective part backwards, in alot of cases, you can just combine showing injective and well defined in a sequence of if and only if's
but i think for this particular example you can do it more succicntly
suppose a^i = a^j
then e = a^(i - j)
fathom flicker
fathom flicker
Does this also work? I see how yours is more succinct
molten grove
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
empty salmon
Why is the answer to this question not the summation of the general term, instead of just the general term?
obtuse pebbleBOT
Why is the answer to this question not the summation of the general term, instea...
@empty salmon Has your question been resolved?
empty salmon
<@&286206848099549185>
versed pier
<@&286206848099549185>
hi bro
versed pier
Why is the answer to this question not the summation of the general term, instea...
this is a common identity
versed pier
you can show this combinatorially
spare steeple
Can anyone recommend me a good book for calculus undergraduate
versed pier
Can anyone recommend me a good book for calculus undergraduate
spivak calculus
empty salmon
Can anyone recommend me a good book for calculus undergraduate
not the right channel mate
wind oriole
empty salmon
I will rewrite this a lil
yeah nah i did get the answer but
i feel it's the answer plus the summation sign to the left of it
isn't the general term pretty much any particular random term that you can take out of the expression
versed pier
in general we have this
you can prove this both combinatorically or algebraically
you would consider either the coef of (x+1)^n(x+1)^m and (x+1)^{n+m}
in particular this
@empty salmon
empty salmon
in particular this
ohhhh
right on
yeah I got the exact same answer as you tho
cept the answer key doesn't give the summation symbol
versed pier
cept the answer key doesn't give the summation symbol
it's the same idea
empty salmon
it's the same idea
how so
isn't that just giving us any one term
oh wait
i got it now
thanks
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quartz ferry
i have math problem
obtuse pebbleBOT
i have math problem
oblique nebula
static furnace
maybe something along the lines of similar triangles?
quartz ferry
maybe something along the lines of similar triangles?
wdym
static furnace
my initial thought is that these triangles are proportional to each other
quartz ferry
my initial thought is that these triangles are proportional to each other
1 and 2?
ah you mean adc and dbc triangle?
static furnace
They share a same side and angle
and they're both inside another triangle
which also has a right angle at C
quartz ferry
ohhhh
static furnace
maybe try to find the angles of the triangles
quartz ferry
i forgot thattt
static furnace
it should come out pretty clean
static furnace
yea np!
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static furnace
yea
quartz ferry
adc and dbc tirangles are
static furnace
right
static furnace
they're rotated and flipped
quartz ferry
yep
quartz ferry
static furnace
okay so
put their corresponding values on each triangle
and then look at their ratio of similarity
static furnace
yes
quartz ferry
oh dangg
static furnace
i think it's also similar
quartz ferry
yeaa ofc
strange bone
which and what?
strange bone
Question'
quartz ferry
adc angle and bdc angles are 90 degrees too
strange bone
D is perpenicular point from c?
quartz ferry
cd is height
strange bone
ok
tawny copper
By the look of it, u probably need to set up a system of equations
strange bone
thats true
quartz ferry
By the look of it, u probably need to set up a system of equations
um
like
how
you korean?
strange bone
Like you have to make CD common for both the 2 triangles and make some eqns to get the answer
quartz ferry
아 제가
한국인이 아니라
그냥 한국어를 좀 아는 정도
한국어로 안 배워서
외항 내항이 뭔지 모르겟ㅆ네여;;
mongolia
n
넵
그냥 한국어로 대화는 좀 해도 수학 쪽 단어들은 몰라요
tawny copper
I get AB = 6.0422
strange bone
I get AB = 6.0422
how?
quartz ferry
I get AB = 6.0422
how
tawny copper
Not sure if it's correct but its a terrible number
quartz ferry
tawny copper
there is answer 6.1
The solution is AB = 6.1?
tawny copper
Oh
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modest ingot
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modest ingot
I think it's uncorrelated, but the "clusters" make me think it could be "possibly linearly correlated"
alpine verge
i would say it’s uncorrelated, it doesn’t look like there’s any pattern here
obtuse pebbleBOT
@modest ingot Has your question been resolved?
modest ingot
i would say it’s uncorrelated, it doesn’t look like there’s any pattern here
hmm the clusters though could indicate that there's some possibility of linear correlation?
<@&286206848099549185> could someone clarify?
jaunty seal
obtuse pebbleBOT
@modest ingot Has your question been resolved?
hybrid gyro
<@&286206848099549185> could someone clarify?
I would say uncorrelated as well, the data are too spread out
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modern linden
Does multiplying both sides by variable introduce extra roots? Why?
obtuse pebbleBOT
Does multiplying both sides by variable introduce extra roots? Why?
@modern linden Has your question been resolved?
tropic sand
Does multiplying both sides by variable introduce extra roots? Why?
well yeah, because when multiplying both sides, you have to check what happens if the value if 0
obtuse pebbleBOT
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modest ingot
I would say uncorrelated as well, the data are too spread out
sure thanks
radiant marsh
can someone please explain where do I start with this equation to prove that for every natural n there's this equation?
obtuse pebbleBOT
can someone please explain where do I start with this equation to prove that for...
fringe rampart
Hi, first of all, you'll need to try simplifying the expression for more readibility, for exemple by multiplying the expression by the denominator of the left hand member of the equation
warm shaleBOT
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fringe rampart
The you can regroup the terms with n on one side of the equation
radiant marsh
and then I get 2^-n+2-24 = 16^-n-1 - 24
so I'm guessing my next move is to get rid of the 24
fringe rampart
and then I get 2^-n+2-24 = 16^-n-1 - 24
Not exactly, it is $8 * 2^{-n-1}$, not $16^{-n-1}$
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radiant marsh
ah I can't do (8*2)^-n-1
fringe rampart
but you can notice that $16 = 2^4$
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crude coral
srry to interept but im pretty sure u are not supposed to solve for n but to show that all natural numbers follow this which can be proved by induction (i think)
radiant marsh
srry to interept but im pretty sure u are not supposed to solve for n but to sho...
yes
fringe rampart
oh well
radiant marsh
I have to prove that all natural numbers follow this
fringe rampart
yeah, so a proof by induction is interesting
fringe rampart
but simplifying the expression will help you
radiant marsh
have u gotten somewhere while trying to prove with induction?
I just have no idea where to start, the -n-1 is really throwing me off
crude coral
not really sure if this is correct (i hate proofs in general tbh) but u could MAYBE do something like this
$$\frac{2^{-n+2} - 24}{2^{-n-1}-3} = \frac{2^{-n+2-3+3} - 24}{2^{-n-1}-3}=\frac{2^{-n-1+3} - 24}{2^{-n-1}-3}=\frac{2^{-n-1}\cdot2^3 - 24}{2^{-n-1}-3}$$ and maybe substitute $2^{-n-1}$
fringe rampart
you don't need induction in fact
warm shaleBOT
JustToPro
crude coral
not really sure about this , maybe the other guy can help
fringe rampart
Start by the bottom and here is your proof
warm shaleBOT
radiant marsh
not really sure if this is correct (i hate proofs in general tbh) but u could MA...
same the concept of proofs seems foreign to me
radiant marsh
Start by the bottom and here is your proof
why 2^3 and not 8?
fringe rampart
Because then you can see how we went from $2^{-n +2}$ to $2^{-n-1}$
warm shaleBOT
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fringe rampart
yea
radiant marsh
and getting rid of the -24 is by adding 24 to both sides? @fringe rampart
do I have to explain why I'm starting with 2^-n+2 = 2^-n+2?
fringe rampart
yes, but the idea of the proof is to start by something that is always true ($2^{-n+2} = 2^{-n+2}$), and then substracting 24 on both side, and then factorising by $2^3 = 8$
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radiant marsh
it's because a^n * a^n = a^n+n
cus the assignment requires me to explain every move I do like for example with this being the reason for 2^3 * 2^-n-1
fringe rampart
do I have to explain why I'm starting with 2^-n+2 = 2^-n+2?
You'll maybe learn this later in your studies, but the idea of a proof is generally to say :
i have A
- If i have A then I have B.
So I have B.
radiant marsh
**Info**
wouldn't I have to do *2^3 for both sides? isn't it wrong to add something to just one side
fringe rampart
Well, you're not adding anything
radiant marsh
Well, you're not adding anything
I'm multiplying by something, wouldn't I have to do it for both sides?
fringe rampart
you're juste rewriting $2^{-n+2}$ as $2^{3}.2^{-n-1}$
warm shaleBOT
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fringe rampart
You are not really "multiplying"
fringe rampart
Yeah, so :
as you said, $2^a * 2^b = 2^{a+b}$
You have $-n + 2$ = $-n - 1 + 3$
So $2^{-n - 1}*2^3 = 2^{-n - 1 + 3} = 2^{-n+2}$
warm shaleBOT
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fringe rampart
You can always replace expressions in your equation as long as they are equal.
If you have $a = 2b$ and $b = c$, then you have $a = 2c$
warm shaleBOT
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radiant marsh
makes sense, thank you
radiant marsh
thanks you too!
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native flare
Show that for all integers n:
If n is a multiple of 16, then n+3 and n^2+7 are coprime.
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Show that for all integers n:
If n is a multiple of 16, then n+3 and n^2+7 are c...
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native flare
how should i say that there doesnt necessarily exist an m for which the congruence is true
basically how do i say that the LHS of the congruence isnt necessarily divisible by m
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supple fog
On the seeds packet it says that seeds have 90% to grow up (The probability that a seed will germinate is 0.9). In a packet there were 5 seeds and grandmother planted them. Accidental size Y - germinated seeds number. Write down the distribution and calculate the Mathematical hope and dispersion.
obtuse pebbleBOT
On the seeds packet it says that seeds have 90% to grow up (The probability that...
supple fog
So i tried doing it this way: If Y = 0 then P = 0.1^5
If Y = 1 then P = 0.9 * 0.1^4
Y = 2 then P = 0.9^2 * 0.1^3
Same principle up to Y = 4
And on the last one
Y = 5 P = 0.9^5
But this seems to be incorrect
Because if i add all the P values from Y 0-5 I get less than 1
I have the “answers” which i cannot figure out how they were calculated and after adding up all the P values in the answers i get a little more than 1 (the answers might be wrong)
I will add the answers photo
10 B
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@supple fog Has your question been resolved?
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@supple fog Has your question been resolved?
candid yarrow
Can you send a picture of the original question?
obtuse pebbleBOT
@supple fog Has your question been resolved?
supple fog
Can you send a picture of the original question?
its in a different language but sure
B)
hybrid shoal
can someone help me here?
obtuse pebbleBOT
can someone help me here?
hybrid shoal
i've tried a lot and still no result, i left all the cos so may be easier
i sent the screen when i think i may still doing good(?
winter cargo
i've tried a lot and still no result, i left all the cos so may be easier
just convert sec to 1/cos
raw torrent
1+tan^2(x) is not sec(x)
winter cargo
can someone help me here?
hmm what if we take the cos^3 x to the other side
and try messing around with that
we would get
hybrid shoal
1+tan^2(x) is not sec(x)
?
winter cargo
$\frac{tan^2(x)cos(x)}{1+tan^2(x)} = cos(x) - cos^3(x)$
warm shaleBOT
winter cargo
$\frac{tan^2(x)cos(x)}{1+tan^2(x)} = cos(x)(1 - cos^2(x))$
warm shaleBOT
raw torrent
:<
hybrid shoal
mb :<
winter cargo
$\frac{tan^2(x)cos(x)}{1+tan^2(x)} = cos(x)sin^2(x)$
warm shaleBOT
winter cargo
$\frac{tan^2(x)cos(x)}{sec^2(x)} = cos(x)sin^2(x)$
warm shaleBOT
buoyant igloo
you wanna prove that?
hybrid shoal
yes
winter cargo
yep
winter cargo
$tan^2(x)cos^3(x) = cos(x)sin^2(x)$
warm shaleBOT
winter cargo
now its super easy
winter cargo
or am i wrong when i say sec = tan + 1?
no thats not right
high lily
sec = tan + 1
is wrong
hybrid shoal
sec = 1/cos ?
winter cargo
ok and
hybrid shoal
sec = 1/cos?
sec^2 = tan^2 + 1?
winter cargo
sec = 1/cos?
sec^2 = tan^2 + 1?
yeah
winter cargo
yeah obv
hybrid shoal
i wasnt being carefully with the ^2
winter cargo
its like 90+90 and 90*90
winter cargo
then also
tan^2 = sin^2/cos^2 = 1/cos^2 - 1?
how did the numerator convert to 1
hybrid shoal
cause sin^2 + cos^2 = 1 :1/cos^2
tan^2 + 1 = 1/cos^2
hybrid shoal
so i can get tan^2
winter cargo
ah
winter cargo
1 min
winter cargo
can someone see if that's good?
yeah looks valid 👍
winter cargo
valid? do u think could be a better way?
no this looks perfect
valid in the sense correct
winter cargo
there are like many
obtuse pebbleBOT
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ember monolith
{{x-2,Power[(40)x-1(41),2],Power[x,3]},{x-1,Power[x,2],Power[(40)x+1(41),3]},{x,Power[(40)x+1(41),2],Power[(40)x+2(41),3]}}
obtuse pebbleBOT
{{x-2,Power[\(40)x-1\(41),2],Power[x,3]},{x-1,Power[x,2],Power[\(40)x+1\(41),3]}...
ember monolith
<@&286206848099549185>
haughty coyote
,w det({{x-2,Power[(40)x-1(41),2],Power[x,3]},{x-1,Power[x,2],Power[(40)x+1(41),3]},{x,Power[(40)x+1(41),2],Power[(40)x+2(41),3]}})
warm shaleBOT
ember monolith
i didnt get it, :]
haughty coyote
,w det({{x-2, (x-1)^2,x^3},{x-1,x^2,(x+1)^3},{x, (x+1)^2, (x+2)^3}})
warm shaleBOT
haughty coyote
looks like a -2 to me
haughty coyote
painfully
ember monolith
which method i mean
haughty coyote
a few row and column operations can probably make it triangular
haughty coyote
I was thinking of how to actually make it work, and was not finding a way
Then I realized working with polynomials makes that a lot harder
So you need to temporarily go into the field of fractions to make it triangular
ember monolith
oh
can u explain me summation,?
like wht does this means
also this,
u there?
haughty coyote
oh? can u be more specific? (im sorry im just too dumb)
I'm still writing out the working of the determinant
ember monolith
I'm still writing out the working of the determinant
ohhhhh
ember monolith
I'm still writing out the working of the determinant
oh,is there any other way to slove it?like polynomials?
maybe u can first help me with summation?
i m sorry for the question ,i didnt know it would take this much time(┬┬﹏┬┬)
haughty coyote
It would be half as long if I didn't fuck up
ember monolith
It would be half as long if I didn't fuck up
oh ,is it bad (￣_,￣ )
it seems like an annoying question