i dont get it
#help-26
prisma torrent
1/cos +1/sin
so u get (sin +cos)/cossin
wouldnt i get cosec*sec from this
not add
charred moat
so u get (sin +cos)/cossin
think again. you split it as sin/cossin +cos/ sincos = sec+cosec
prisma torrent
think again. you split it as sin/cossin +cos/ sincos = sec+cosec
no but
i got
this
from the left handside
charred moat
this is correct
prisma torrent
so u get (sin +cos)/cossin
this is from right hand side
prisma torrent
this is correct
isnt it 1/cos sin tho
charred moat
this is from right hand side
simplify lhs fully
charred moat
isnt it 1/cos sin tho
simplify the left hand side fully first
prisma torrent
sin/cos + cos/sin
prisma torrent
so (sin^2 + cos^2)/sincos
charred moat
yes
prisma torrent
yh
prisma torrent
what identity
charred moat
so (sin^2 + cos^2)/sincos
so this becomes 1/sincos
charred moat
but you still have sin+cos left to multiply
charred moat
isnt that cosec * sec?
true, but you you have more on the lhs
charred moat
yes
prisma torrent
thanks very much
charred moat
np
topaz sinewBOT
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peak onyx
Hello.
trim ermine
Please ask your question
topaz sinewBOT
No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/
peak onyx
Please ask your question
ok thanks can I take a pic?
topaz sinewBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
neon iron
Show the problem
neon iron
Interesting problem yeah
peak onyx
u realize no one likes a snitch
What do you mean?
trim ermine
For x, as given that EF || CDE, so EFC = FCD = 30°( Using alternate angles) . So DCA = 120°
fair thorn
u realize no one likes a snitch
first off, i think you mean pinging mods; he was pinging helpers
secondly, there's absolutely nothing wrong with that if they're doing something wrong
thirdly, please remain on topic
peak onyx
For x, as given that EF || CDE, so EFC = FCD = 30°( Using alternate angles) . So...
Wow thank you its right.
fair thorn
god i love house
peak onyx
first off, i think you mean pinging mods; he was pinging helpers
secondly, there...
Thank you to.
fair thorn
nw
trim ermine
For x, as given that EF || CDE, so EFC = FCD = 30°( Using alternate angles) . So...
And the sum of co-interior angles DCA and CAB is then 180 which is hence proving that AB || CD
peak onyx
And the sum of co-interior angles DCA and CAB is then 180 which is hence proving...
Right now I understand.
trim ermine
peak onyx
how to close it?
topaz sinewBOT
peak onyx
do I use close to?
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neon iron
OR .solved
topaz sinewBOT
**OR** .solved
trim ermine
topaz sinewBOT
peak onyx
Thank you so much bye.
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stuck pawn
topaz sinewBOT
stuck pawn
Is this RREF , REF or neither
loud oasis
get the list of requirements for REF and RREF and check off the ones that are met
stuck pawn
Yeah i think it's REF
stuck pawn
get the list of requirements for REF and RREF and check off the ones that are me...
But i asked someone he says it's neither
loud oasis
Yeah i think it's REF
can you post the list of requirements for REF?
stuck pawn
can you post the list of requirements for REF?
Any rows consisting entirely of zeros are at the bottom
In each nonzero row , the leading is in a column to the left of any leading entries below it
So i think it's REF
Or it's wrong
loud oasis
some textbooks impose the additional requirement that the leading entries (pivots) be 1. you should check if that's true for your class
stuck pawn
some textbooks impose the additional requirement that the leading entries (pivot...
You mean the leading equals 1 ?
loud oasis
yes
loud oasis
some textbooks require it for REF and some require it only for RREF. that's why you will get conflicting answers
stuck pawn
Alright that's a bit strange
I think math should be The same everywhere
But alright i think it's a satisfying answer
Thanks
.close
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proven vapor
\int _{0+}^{1-}\frac{ln\left(x\right)}{1-x}: converges or diverges?
proven vapor
I already know that in 0+ it converges since I have analyzed it, comparing it with ln(x) and it converges
However, I still don't know what happens in 1-
sweet shard
,w int 0 to 1 log(x) / (1-x)
thorny flameBOT
sweet shard
there's a lot of ways to show it converges. what did you learn so far
sweet shard
,w plot log(x) / (1-x)
thorny flameBOT
proven vapor
,w plot log(x) / (1-x)
Even if it is 0+ and 1-, does it still converge?
sweet shard
yes that's exactly how the integral is defined as, the 0+ is the same as 0 and 1- is the same as 1
proven vapor
yes that's exactly how the integral is defined as, the 0+ is the same as 0 and 1...
I understand, what I have been doing for cases like this, is comparing the function with another one, which has a similar behavior, that way, I can integrate it and get what I am looking for.
proven vapor
do you know geometric series?
No, I haven't given anything about series, if it helps, I'm currently in a Mathematical Analysis 2 course, I know that all the courses have different information, but maybe it helps you to guide yourself.
loud oasis
the limit as x goes to 1 of ln(x)/(1-x) is finite
proven vapor
the limit as x goes to 1 of ln(x)/(1-x) is finite
Is there a function I can compare ln(x)/(1-x) with to check that?
<@&286206848099549185>
loud oasis
Is there a function I can compare ln(x)/(1-x) with to check that?
you can calculate the limit directly with L'hopital's rule
proven vapor
you can calculate the limit directly with L'hopital's rule
So, by proving that the limit as x tends to 1- of the function, without having integrated it, is finite, is it already proven that that part of the function converges?
sweet shard
So, by proving that the limit as x tends to 1- of the function, without having i...
i don't think so
proven vapor
i don't think so
I was thinking the same thing, I feel like something needs to be done in this case, can you think of a way to do it with the tools I currently have?
sweet shard
oh i was wrong, geometric series does work
turbid zodiac
what country are you from?
proven vapor
oh i was wrong, geometric series does work
The thing is that I still don't know anything about geometric series, I'm sorry.
turbid zodiac
what country are you from?
sweet shard
what country are you from?
can you leave
proven vapor
what country are you from?
Sorry, this is a channel to ask for help with math, on the server there are channels to talk to other people about other topics, I hope you can understand it :)
sweet shard
The thing is that I still don't know anything about geometric series, I'm sorry.
it's something you're suppose to learn before calculus
proven vapor
it's something you're suppose to learn before calculus
Oh, in that case, maybe I'm confusing myself with some more complex issue, would you like to explain to me what your idea was and we can see if it's something I know?
sweet shard
1/(1-x) = 1 + x + x^2 + x^3 + ...
since x is in (0, 1), so is (1-x). so all terms on the right are positive
you can just drop all terms except for the first to get 1/(1-x) <= 1
then multiply both sides by log
turbid zodiac
alguem pode me explica como que calcula trigonometria com triangulo retangulo?
sweet shard
alguem pode me explica como que calcula trigonometria com triangulo retangulo?
actually you don't even need geometric series
just 1/(1-x) <= 1 for any x in (0, 1)
proven vapor
actually you don't even need geometric series
I just talked about it with my friends, and we see all about series later in our courses, so if there is a way that they are not used, that would be better for me.
proven vapor
just 1/(1-x) <= 1 for any x in (0, 1)
I understand, and where would 1/(1-x) come from?
thorny flameBOT
riemann
proven vapor
$\frac{a}{b} = \frac{1}{b} \cdot a$
Oh, I mean, we first separate ln(x) from 1/(1-x) to see that that's less than 1, right?
proven vapor
$\frac{a}{b} = \frac{1}{b} \cdot a$
I've been talking to some friends, and we don't teach geometric series until the next course, so I can't understand how to get to something more
sweet shard
just 1/(1-x) <= 1 for any x in (0, 1)
read
but like i said before, you're supposed to learn geometric series before calculus: e.g.
https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-factor/x2ec2f6f830c9fb89:geo-series/v/geo-series-intro
proven vapor
read
Ohhhh, so there I have the integral of ln(x)/1 and there I manage to conclude that for 1-, it is convergent, right?
proven vapor
do you realize that log(1) = 0?
I understand, so once we reach the integral of ln(x), it would be enough to prove that it converges, right?
sweet shard
then multiply both sides by log
.
proven vapor
is that unclear?
Not at all, I wanted to check that I had understood it correctly.
Thank you
.close
topaz sinewBOT
cyan pier
Did you graph them?
topaz sinewBOT
@cloud locust Has your question been resolved?
serene solstice
I can't get it
topaz sinewBOT
I can't get it
serene solstice
that makes sense
long stirrup
the distance is the area on the graph
3 up, 2 up, 4 up, so 9 makes sense
oh but that's at 8s
long stirrup
yeah −2.5
serene solstice
so 5.5 cm is the total distance?
long stirrup
no that's height
serene solstice
oh
long stirrup
the total is proly 10.5
serene solstice
5.5 for height up the wire and 10.5 for distance are both incorrect, the 8 seconds was correct though
long stirrup
intresting
serene solstice
yeah im confused
long stirrup
oh 6.5
serene solstice
for height?
serene solstice
hmm ok
Now i need distance from 0 to 13
I failed the question it was 11.5
Can you help me with this one?
.close
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thorny flameBOT
w
topaz sinewBOT
@solid solstice Has your question been resolved?
stoic dagger
How do I do this problem? I entered this but it's not correct.
topaz sinewBOT
How do I do this problem? I entered this but it's not correct.
thorny remnant
How do I do this problem? I entered this but it's not correct.
Do you know the power rule ?
stoic dagger
x^n=nx^n-1
thorny remnant
Yes also you can write$\frac{5}{\sqrt[3]{x}}=5x^{\frac{-1}{3}}$ i think you can apply the power rule now
stoic dagger
isn't it x^-(1/3)?
thorny flameBOT
convergence
hollow drum
,w derivative of 2e^x +5/x^(1/3)
thorny flameBOT
hollow drum
Your answer looks correct, probably the formatting
hollow drum
How do I do this problem? I entered this but it's not correct.
Oh why did you put y =?
In the answer
stoic dagger
I got the answer wrong and it spit out this
hollow drum
Why are you typing "y =" into the box?
hollow drum
What does the screen look like before you submit the answer?
stoic dagger
I can
I can't submit anymore I got the question incorrect. I'm just trying to figure out if I did the math wrong
hollow drum
How do I do this problem? I entered this but it's not correct.
This was correct
There's a y = for some reason
topaz sinewBOT
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ancient valve
When completing the square if you fscored something out of everything do you just leave the thing in front of it the entire time?
topaz sinewBOT
When completing the square if you fscored something out of everything do you jus...
ancient valve
Idk how to word it well
sweet shard
It really doesn't matter. Do whatever is easiest for you
ancient valve
Example 6: What are the roots of - 2x ^ 2 - 3x + 7 = 0 ?
Like for example for this
Yo factor out -2
ancient valve
It really doesn't matter. Do whatever is easiest for you
x ^ 2 - 3x/-2 + 7/-2 = 0 ?
Can I just do that and forget about the -2 forever?
topaz sinewBOT
ancient valve
.reopen
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fossil drift
Could I get help solving this question
topaz sinewBOT
Could I get help solving this question
agile harness
fossil drift
I was thinking somewhere along the lines of having an x in the denominator but I’m not too sure after
Ie tried square root functions as well but I think I’m something vital
agile harness
are there any restrictions really
i mean you could easily make a piece wise function
also consider a hole at x = 0
they never said f(0) had to be defined
fossil drift
Ill try some things with ur advice and get back to u thank u
Can this be possible sorry there’s no answers provided
craggy haven
,w plot ln(x-1)
thorny flameBOT
craggy haven
$\lim_{x\to0} y$ looks a lot like $-\y$ to me
thorny flameBOT
hayley is not layla
fossil drift
How about instead of ln I use 1+x^2
agile harness
well 1+x^2 isn’t greater than 1 for all x oh but you mean in a piece wise?
fossil drift
Yes
agile harness
yea that works
agile harness
Can this be possible sorry there’s no answers provided
but not 1 if x=0
it needs to be anything greater than 1
fossil drift
But it would work in a piecewise no?
topaz sinewBOT
@fossil drift Has your question been resolved?
fossil drift
Yes
serene escarp
topaz sinewBOT
chilly walrus
!status
topaz sinewBOT
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
I'm done with the majority of the questions,I just need to find d.
I can't get any suitable value from any of the equation
topaz sinewBOT
@serene escarp Has your question been resolved?
heady horizon
I don't think this is enough information to find d. For instance, d=0 is valid with x^3 - 9x^2 + 18x, but so is d=-24 with x^3 - 9x^2 + 26x - 24. Both have the three roots consecutive in an arithmetic sequence, and b=-9.
serene escarp
Hmm thanks for the help mr.
topaz sinewBOT
@serene escarp Has your question been resolved?
jolly vale
Is the point of these questions to let us know that knowing that where are taking the limit of 0/0 not enough to conclude whether or the limit exists?
topaz sinewBOT
Is the point of these questions to let us know that knowing that where are takin...
mellow arrow
yes
topaz sinewBOT
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formal oriole
i am confused on what to do. what does it mean by 1/2 of PET and label it KID?
mellow arrow
measure ange PET
topaz sinewBOT
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neon iron
Solve for distance traveled and final speed.
topaz sinewBOT
Solve for distance traveled and final speed.
merry hill
Solve for distance traveled and final speed.
do you know what area under velocity-time graph is
neon iron
do you know what area under velocity-time graph is
no im not aware
sorry im new to this
merry hill
no im not aware
its displacement
merry hill
Solve for distance traveled and final speed.
here distance and displacement is same
so for distance travelled find the area of that triangle
topaz sinewBOT
@neon iron Has your question been resolved?
topaz sinewBOT
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hard mesa
Hello
hard mesa
oh
fair thorn
and don't forget the negative versions
hard mesa
i see now
thorny flameBOT
ren
hard mesa
since only 1 is divisble with p, +- 3 is cancelled out yes?
fair thorn
??
hard mesa
am i wrong?
i am wrong.
What are the possible rational roots then?
+- 1, 2, 4, 8, 16
What do i do with 3
.close
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hard mesa
.reopen
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sweet trout
hi i was wondering that how do i use function notations for this
neon iron
15 minutes
mortal steeple
The reflection of (a, b) about y= x is (b, a)
@sweet trout
There is a formula for general lines but I don't remember it
sweet trout
y=mx+c?
mortal steeple
No
Like reflection about any general line
Similarly we can use this to say that x, y will also get swapped
So x = ym + c
This is cursed lol 
Or y = x-c / m
mortal steeple
Yeah
You can calculate m and c using the points given
Wait I think I have a better method
Calculate A, B, C reflection and then use 2 point form to get the line easy
!done?
topaz sinewBOT
If you are done with this channel, please mark your problem as solved by typing .close
mortal steeple
I just wanted to try that lol
sweet trout
💀
sweet trout
I just wanted to try that lol
actually u can close thanks a lot
mortal steeple
Only for OP
sweet trout
i c
mortal steeple
Oh lol
topaz sinewBOT
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topaz sinewBOT
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neon iron
hi
hallow depot
hi there
hallow depot
google it
neon iron
Is this definition of the rectangular function incorrect (incomplete)?
neon iron
It just doesn't mention what happens at the two discontinuities
online, i find that at the boundary it is assumed that rect(t) = 1/2
but here it just doesnt so idk
strange whale
wdym it doesn't tell you what happens at the boundary
"otherwise" is pretty explicit
neon iron
well yes but it is contradictory to what im finding regarding the regular definition of rect
that filled dot would be on the t axis according to what they are saying anyways
strange whale
it's not like it should matter a lot
even wikipedia mentions alternate definitions, so they're common
neon iron
alright no worries
ill keep this channel open a tad bit longer as i have a question that continues on this
strange whale
sure
topaz sinewBOT
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dreamy radish
hey just need to confirm something
topaz sinewBOT
hey just need to confirm something
burnt badger
If possible please post the original question
dreamy radish
If possible please post the original question
this is the original question
i think the textbook solution is wrong
i just want to confirm
should the implication
not be the other way
burnt badger
In this case
"To receive a master's degree" then all the following must be true
This structure of the argument
Is telling you
Master's Degree => all the following
dreamy radish
Is telling you
Master's Degree => all the following
but if the requirements are fulfilled
then the student will receive
the masters degree
burnt badger
From a "regular" logic perspective you can do all that course work without getting masters degree
If you got the degree
Then you definitely did all that
If you did all that
You may not have gotten the degree
dreamy radish
You may not have gotten the degree
hmm how can we derive that from the question itself
how do i know that the question is saying
logically fulfilling the requirements
is necessary
for a degree
aka degree -> fulfilling requirements
what im asking
how is the wording different
from other typical implication questions
where its more clear
burnt badger
Well i don't have a huge amount of experience with formal logic so I'll try to explain
When they say
You need to do X to achieve Y
It's like I'm saying
dreamy radish
what is the part before implication
dreamy radish
makes sense
but then for example
how is this question
different
from example
for example*
from this
in this question its quite clear
that if the man and woman meet the times
then they qualify
but why cant we use the logical converse
or say that if the man qualifies
then his previous time is less than 3 hours
burnt badger
Because here they said it more clearly
If X then Y
If he beats the time then he qualified
dreamy radish
It's a bit less obvious
do you have any advice
for tackling these kinds of questions
in the future
like should i look out for
the to do x
burnt badger
Like I mentioned I have a low formal.logic experience I just know some basics
dreamy radish
one must do y
burnt badger
Can't give great advice unfortunately
dreamy radish
Like I mentioned I have a low formal.logic experience I just know some basics
alright, thanks for the help
lean sinew
I got this problem. I thought about rewritten the set A to intervals (0,2]x(-4,4), but I am not sure if that would be a good start.
topaz sinewBOT
I got this problem. I thought about rewritten the set A to intervals (0,2]x(-4,4...
lean sinew
the part about the openess or the other one?
The part about openess, sorry my fault for not clarifying. I think I know how to show it is Borel but I am not so sure
hallow depot
you can prove that is not open just by taking a sequence non in A that converges to a point in A
for example : (2+1/n,0)
it converges to (2,0) that is in A
lean sinew
Oh that is smart. So the argument is that because we have some sequence non in A that converges to a point in A, A is indeed not open?
lean sinew
it converges to (2,0) that is in A
is (2,0) a boundary point in A?
lean sinew
and open set doesn t contain their boundary points
ahh okay that is true, I see now. Thank you, you gave a great help. Just a quick question if you would be interested in helping with showing A is Borel. Would it be right to look at A as the intersection of {(x,y):0<x<=2} and {(x,y):-x^2<y<x^2}? or would it be easier to look at A as the intervals (0,2]x(-4,4)?
lean sinew
I have this problem. To show sigma(G) is equal to P(X) I need to show that sigma(G) is a subset of P(X) and that P(X) is a subset of sigma(G) correct? I think the one way showing sigma(G) is a subset of P(X) is trivial, but I am not sure how to show the other way
topaz sinewBOT
I have this problem. To show sigma(*G*) is equal to *P*(X) I need to show that s...
hearty turret
wait i'm dumb nvm
lean sinew
It is okay, I thought the same when I first looked at the problem
hearty turret
I have this problem. To show sigma(*G*) is equal to *P*(X) I need to show that s...
could we try a contradiction?
so clearly if we show sigma(G) contains all singleton sets, we'd be done
lean sinew
yeah we just need to show sigma(G) contains all singleton sets {x}
hearty turret
clearly there exists a set containing x so take S to be the minimum set containing x
(minimum when partially ordered by inclusion)
hearty turret
clearly there exists a set containing x so take S to be the minimum set containi...
if S = {x} then we're done
otherwise S = {x,y, stuff}
and then could we attempt to remove the y (but not the x)?
lean sinew
yes that makes sense
or what if we have something like for each y in X where y is not equal to x, and then show there is A in sigma(G) with x in A and y not in A. Then show we have all singletons {x} in sigma(G) if that makes any sense
hearty turret
or what if we have something like for each y in X where y is not equal to x, and...
yh that would work
so sps all subsets of sigma(G) that contain x contain y
hearty turret
yh
hearty turret
then we show with contradiction?
(cus then G does not separate x and y)
(cus either we have x and y in our subset)
(or no x and no y in our subset)
lean sinew
hmmm
lean sinew
so sps all subsets of sigma(G) that contain x contain y
so with the assumption we conclude that G does not separate points but that is the contradiction right? then how do we get from this to show {x} is in G? Is it because we know there is a set A in G that does not contain y for each y in X given the contradiction we shown.
hearty turret
so with the assumption we conclude that G does not separate points but that is t...
so with the assumption we conclude that G does not separate points but that is the contradiction right?
yep
hearty turret
clearly there exists a set containing x so take S to be the minimum set containi...
oh wait no this doesn't quite work
wait no it's fine
hearty turret
otherwise S = {x,y, stuff}
so then intersect S with {x, no y, stuff} to remove y
then intersect with {x, no smth else, etc} to keep removing stuff from it
(which is allowed cus countable)
lean sinew
okay yes and then we end up with {x} is in sigma(G). would S be a subset of X or sigma(G)? or G?
lean sinew
okay so we have our contradiction. This shows that there is this S in G with {x, no y, some stuff}, then we can take intersection since G separates points until we have {x} which shows {x} is in sigma(G)
I am not sure if I understand correctly
hearty turret
okay so we have our contradiction. This shows that there is this S in G with {x,...
yeah
lean sinew
okay thank you for the help!
clear crescent
An approach could simply be to fix $x$ and observe a $y_{n} \in X$ (with $y_{n} \neq x$), for each $G_{n}$ that makes $\mathcal{G}$ separate points. You have that either $x$ is an element of $G_{n}$ and $y_{n}$ is not an element of $G_{n}$ or vice versa.\
Notice that if $x$ is not in $G_{n}$ and $y_{n}$ is in $G_{n}$, then it simply follows that for the complement $G_{n}^{c}$ (which is in $\sigma(\mathcal{G})$!) that $x$ is an element of $G_{n}^{c}$ and $y_{n}$ is not an element of $G_{n}^{c}$.\
No matter what, you now have a way to pick sets $G_{n}^{}$ for each $n$ (i.e. $G_{n}^{} = G_{n}$ in the former case and $G_{n}^{*} = G_{n}^{c}$ in the latter), such that $x$ is in each set but $y_{n}$ is not. Now simply take the intersection over each to generate the singleton ${x}$.
thorny flameBOT
lean sinew
An approach could simply be to fix $x$ and observe a $y_{n} \in X$ (with $y_{n} ...
oh yeah that is smart. I see. Thank you
proven narwhal
topaz sinewBOT
proven narwhal
topaz sinewBOT
@proven narwhal Has your question been resolved?
proven narwhal
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topaz sinewBOT
@proven narwhal Has your question been resolved?
proven narwhal
<@&286206848099549185>
thorny flameBOT
riemann
stoic moon
Lm
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@proven narwhal Has your question been resolved?
soft salmon
Anyone know how to solve these? I searched online and they were saying something about cosine and sine, but I am in geometry and we haven't learned that yet, so is there another way?
topaz sinewBOT
Anyone know how to solve these? I searched online and they were saying something...
whole ermine
do you know your special right triangles?
soft salmon
maybe???
Never hear anything called that
whole ermine
like 30 60 90 triangle or 45 45 90 triangle?
soft salmon
yes
whole ermine
you should be able to apply that with pythagorean theorem to solve these
soft salmon
but like for 1, i only have the measure of 60, so how would I get the other side?
whole ermine
well since in a 45 45 90 triangle, the legs equal eachother, so the bottom leg will also bo 60
whole ermine
is there a specific question?
soft salmon
no, but this one might apply. I have no clue if it is 60 and 90 or not though
raven field
I think it’s a mistake
Cuz all the triangle are right-angled
soft salmon
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golden blade
how would i do 30-60-90?
do you know trigonometrry
golden blade
damn
raven field
how would i do 30-60-90?
ok I’ll try to send a proof is it ok with you ?
soft salmon
ok I’ll try to send a proof is it ok with you ?
sure
this isnt a graded assignment or anything, just some practice problems for a test I have later
pallid hare
a question stated:
"A 7x5 augmented matrix has a pivot in every column, what can you say about the solutons to the corresponding system of equations? Justify your answer."
icy sky
icy sky
yes
icy sky
think about the row with the pivot in the last column
pallid hare
so it would be
no sol
cause all zeros in coefficient?
and nonzero for the augmented matrix row
lsat row
last*
icy sky
yup
topaz sinewBOT
proven narwhal
how did $tw' + 5w = 0$ become $(t^5 w)' = 0$?
Multiplied both sides by the integrating factor
The right side is 0
proven narwhal
torpid nimbus
Hey guys, I'm new here
proven narwhal
<@&286206848099549185>
topaz sinewBOT
@proven narwhal Has your question been resolved?
proven narwhal
<@&286206848099549185>
vestal sigil
im not sure, but i think the y(t) is not like that
do the same thing, but with
$y(t) = (c_1 + c_2 , t^{-4}) , e^{-t}$
thorny flameBOT
Emily
vestal sigil
i think this is the actual formula of y(t)
vestal sigil
you didnt multiply t^{-4} by e^{-t}
topaz sinewBOT
@proven narwhal Has your question been resolved?
proven narwhal
you didnt multiply t^{-4} by e^{-t}
why is it multiplied by e^-t?
I dont think u have to multiply it by e^-t unless im missing something?
here's the example that I tried following along with
vestal sigil
**Emily**
i did it my own way, and this is the expression i got
its like when you have a homogeneous solution y = c y1
when youre looking for a particular solution, you let c=c(t)
yp = c(t) y1
anything is multiplied by y1
$y(t) = \left( \frac{13}{2} - \frac{5}{2} , t^{-4} \right) , e^{-t}$
thorny flameBOT
Emily
vestal sigil
yeah, tedious :d
vestal sigil
haha
proven narwhal
so u did everything the same as me except for the last page?
thorny flameBOT
Emily
vestal sigil
i substituted it in the diff eq
i ended up with a differential equation in c(t)
when i solved that differential equation, i got
$c(t) = c_1 + c_2 , t^{-4}$
thorny flameBOT
Emily
proven narwhal
so u didnt do the reduction of orders thing where you set y2 = ve^-t
vestal sigil
i dont know what that is :d
proven narwhal
actually wait yeah nvm
vestal sigil
ill read about that some other time
seems interesting
proven narwhal
thats the same thing I did I think
nah I think its the same
u set y2 = ve^-t and then u find y2' and y2'' and sub it back into the original equation?
vestal sigil
and then you must get a differential equation in v
proven narwhal
yeah thats what I got
solved that and got t^-4
this is where I went wrong tho
I just wrote it as c1e^-t + c2*t^-4
vestal sigil
solved that and got t^-4
you didnt account for constants
proven narwhal
why's the second term multiplied by e^-t?
vestal sigil
how can a differential equation's solution have no constants
proven narwhal
oh wait
I think I see it now
I divided the whole thing by e^-t
im guessing u cant do that?
vestal sigil
$v(t) = c_1 + c_2 , t^{-4}$
thorny flameBOT
Emily
vestal sigil
or is the * e^-t just when u sub it back
yeah, just when i subbed back into y2
proven narwhal
yeah so we both got the same thing
vestal sigil
i suggest you check the integration
proven narwhal
is that not 0?
vestal sigil
you cant find it at all
proven narwhal
so do u not just set that equal to 0 then?
thorny flameBOT
Emily
proven narwhal
yeah
vestal sigil
and when you integrate, the c1 appears
how is it 0 ?
its just c1
$v(t) = \int w(t) , dt = - \frac{c_2}{4 , t^4}+c1$
thorny flameBOT
Emily
vestal sigil
yep, dunno what they mean
proven narwhal
lmao
vestal sigil
but you leave the constants
leave them c1 and c2
then, when you sub back into y2, use the 2 given initial conditions to determine them
like why rush to determine them
😛
proven narwhal
idk I was just trying to follow that example
they didnt even teach us this in class
vestal sigil
yeah yeah, i absolutely understand
proven narwhal
but they decided to assign it to us for fun or something ig
vestal sigil
mhm, its really interesting
vestal sigil
then this
vestal sigil
so u didnt do the reduction of orders thing where you set y2 = ve^-t
this
sub v(t) here
this is the particular solution
and call y2 as y
vestal sigil
-constant/4 is just another constant
i kept the name c2
when you grab a constant, multiply it by - and then divide it by 4, its still just a constant right?
i kept the name c2
i think youre familiar with this stuff
ig ive seen you before having
$ln(y) = ln(x) + c$
thorny flameBOT
Emily
vestal sigil
when you exponentiate both sides, it becomes
$y = e^{ln(x)+c} = e^{ln(x)} \cdot e^{c}$
thorny flameBOT
Emily
vestal sigil
$y= e^c \cdot x = c_1 \cdot x$
thorny flameBOT
Emily
vestal sigil
exponential of a constant is still another constant right?
proven narwhal
yeah
vestal sigil
same thing here
its just that i didnt change its name
i still called the constant c2
proven narwhal
yeah that makes sense
wait one thing
you know how the form of the solution is usually like c1y1 + c2y2
proven narwhal
and this is asking for a particular solution?
vestal sigil
no, this is the general solution
e^{-t} is really just a case
when c1 = 1 and c2 = 0
what we did is that we found the actual expression of the general solution
proven narwhal
so if e^-t is a solution why isn't it c1e^-t + c2 * (c1 + c2t^-4) ?
vestal sigil
c1 + c2 t^{-4} is not even a solution, what are you talking about 😛
the rule says, if y1 is a solution and y2 is a solution
then c1 y1 + c2 y2 are all solutions
vestal sigil
so if e^-t is a solution why isn't it c1e^-t + c2 * (c1 + c2t^-4) ?
but here
c1 y1 + c2 y2
y1 is a solution (given), y2 is NOT
this example is a little different than the usual, dont compare too much
proven narwhal
so the second solution is given by v(t) * y1?
vestal sigil
thats not a second solution
thats the general solution
this example is different than the usual, dont compare too much with what you studied before, i suggest
to conclude, in this type of problems, when youre given that y1 is a solution
set y = v(t) y1
work out the expression of v(t)
substitute it back into y = v(t) y1
then find the constant(s)
proven narwhal
so what they give u, y1 is a particular solution
and what ure looking for is the general solution
which is given by y2
vestal sigil
i think the name y2 is what got you confused
you studied that y2 is the second homogeneous solution
but they meant the general solution by y2
i prefer naming it y(t)
y(t) = v(t) y1(t)
vestal sigil
and what ure looking for is the general solution
yes, thats it
one trick to differentiate between a particular and a general solution is that
a particular solution has no constants in its expression
proven narwhal
i think the name y2 is what got you confused
yeah I was under the impression that y2 was the second solution thats where I got confused
vestal sigil
a general solution has always constant(s) in its expression
vestal sigil
youre welcome!
proven narwhal
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sweet shard
Just show the problem and your attempt
strange kindle
Try induction
Ohh
The second box is just straight up wrong
1-1 != (1+1)/2
In induction
..
..
..
We first prove the base case
n=2 here
Then we assume that the statement holds for some arbitrary integer
Then show that it holds for the integer k+1
Which would imply that it holds for 3 then 4 and so on
strange kindle
Then show that it holds for the integer k+1
This step is just algebra
topaz sinewBOT
@neon iron Has your question been resolved?
topaz sinewBOT
@neon iron Has your question been resolved?
hasty cobalt
|-2x+8|=20
can somebody help
topaz sinewBOT
|-2x+8|=20
can somebody help
hasty cobalt
how do i solve the absolute value
basically it just wants me to solve for x
the x = 1 or x = -1 type stuff
idk what to do at all
vivid stone
|-2x+8|=20
can somebody help
As |-a|=a and |a|=a
You can separate it to -2x+8=-20 and -2x+8=20
hasty cobalt
what is domain?
vivid stone
Domain is the set of x that make equation be true
In my understanding
Polynomial domain always be R (real number)
hasty cobalt
ah, okay
big words, ill probably learn them sooner or later
i have another problem
2|x + 8| = 20
would i do 2x + 16 = 20
2x = 4
4/2 = 2
x = 2?
or
hasty cobalt
okay
vivid stone
would i do 2x + 16 = 20
2x = 4
4/2 = 2
x = 2?
Yeah that's right
hasty cobalt
idk were not learning functions yet
and for the other value id just reverse the sign on 20
right?
2x + 16 = -20
or something
hasty cobalt
okay
now what about these
2 <= |x| - 8
Solve each absolute value inequality. Graph the solution.
vivid stone
Absolute is actually the size of vector inside it
You can visualise that |x|≥10 that the size of x from - and + is greater than 10
vivid stone
You forgot to transposition+5?
vivid stone
Correct
hasty cobalt
tysm
frosty iron
Max writes every natural number that is >9 but doesn't have more than 6 digits where every number must consist only of 1's and 0's, find how many times max writes the digit 1
topaz sinewBOT
Max writes every natural number that is >9 but doesn't have more than 6 digits w...
topaz sinewBOT
@frosty iron Has your question been resolved?
frosty iron
<@&286206848099549185>
prisma spade
What
frosty iron
more 1s i think
prisma spade
Yea aye
frosty iron
oh
odd pagoda
if he also wrote those then he would write equal numbers of zeros and ones, yes
how many digits does he write in total
frosty iron
idk ):
odd pagoda
he always writes 6 digits
all of them either 0 or 1
how many options are there to do that
frosty iron
64?
odd pagoda
yes. why
frosty iron
cause each digit has 2 states 0 or 1
and theres 6 digits
so 2 x 2 ... 6 times = 2^6
odd pagoda
good
so he writes all of those except 000000 and 000001
so how many digits does he write
how many of those are ones
frosty iron
2^5 -1 are ones
odd pagoda
check again
odd pagoda
how many numbers does he write and how many digits does each number have
little lantern
if he also wrote those then he would write equal numbers of zeros and ones, yes
whoa
this is smart
little lantern
why 3
odd pagoda
again, its better for a moment to imagine he also wrote 0 and 1
little lantern
oh you said ones
little lantern
he writes 3(2^6 - 2)? 1's
closee
frosty iron
why 3
well he would write a total of 6(2^6 - 2) digits, half of those are 1's another are 0's
little lantern
well
odd pagoda
its only half if he also writes 000000 and 000001
little lantern
half of the 6(2^6) total digits are one/zero
little lantern
its only half if he also writes 000000 and 000001
but yeah, he got rid of these which aren't half and half
so just mind if we subtract before or after
odd pagoda
yes
frosty iron
wait is that the answer?
frosty iron
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