Yes, then you found what BOC is
#help-13
plucky owl
Now you want to find the other angle plus BOC to make 90
The other angle is what the problem is asking for
drifting isle
If x plus boc =195 and the supplementary angle is 180 then isn’t the difference 15
plucky owl
I don't think you're understanding
plucky owl
Do you get that <AOB + <BOC = 180 because it says they are supplementary?
drifting isle
Yes
plucky owl
Then the next statement asks about the compliment of <BOC
drifting isle
Right
plucky owl
And complimentary angles add to 90
drifting isle
Wait
So
Is it saying
There are to complimentary angles inside the 180 degrees right
plucky owl
No
drifting isle
plucky owl
It's saying that there is an angle that is the compliment with <BOC, what is that compliemented angle
crimson sedge
<BOC is in two separate equations. It's important to keep them separate.
drifting isle
Hmmm
plucky owl
Let me summarize again, the problem says <AOB and <BOC are supplementary angles, meaning <AOB + <BOC = 180
drifting isle
Yep
plucky owl
Now it's wanting you to find the compliment of BOC, meaning BOC would also be in an equation involving complimentary angles
So <BOC + z = 90
Do you get that?
drifting isle
Boc+z =90?
plucky owl
I used z to as a placeholder variable for the other angle that is compliment with BOC
crimson sedge
Since the complementary angle is not specified, you can call it by any variable you like
drifting isle
Okay im confused about the 90 degree part because all I think is that there are two angles in 180 degrees and together they add 180 because they are inside of the 180 degree but one could be 80 and one could be 100 but I know that one is x-15 which doesn’t mean much to me and I don’t know where this 90 degree is coming from
plucky owl
Because the problem says, "what is the measure of the compliment of <BOC"
crimson sedge
they are separate criteria
plucky owl
Compliment referring to complimentary angles
drifting isle
So it’s saying there’s a complimentary angle inside the supplementary one?
plucky owl
Not necessarily
crimson sedge
supplementary angle is like equation 1 with 180 degrees and <BOC
complementary angle is only concerned with <BOC and some unknown angle, say z
<BOC appears in both equations, but what you want is z
plucky owl
It's saying that <BOC is supplement with <AOB
But <BOC is also compliment with some other angle, z
drifting isle
Can someone draw a picture
plucky owl
You don't necessarily need a diagram. Just follow what I'm trying to explain
drifting isle
Im trying im getting confused
plucky owl
Let me summarize again, the problem says <AOB and <BOC are supplementary angles, meaning <AOB + <BOC = 180
That makes sense to you so far. The next statement of the problem sayswhat is the measure of the compliment of <BOC
Compliment, as stated, in that context is complimentary angles, so <BOC is a complimentary angle with some other angle. Because you don't know said angle, you can use a variable, I used z. So that means z + <BOC = 90
drifting isle
Okay but I don’t have anything to work with if x+boc = 90 how am I suppose to work stuff out further
plucky owl
Your goal is to find z
Using my explanation
You have two equations <AOB + <BOC = 180 and z + <BOC = 90
The overall goal is to find z
Which is the compliment of BOC
Using the first equation <AOB + <BOC = 180, you can find what BOC is in terms of x
Basically what you did here
Then using z + <BOC = 90, and BOC = 195 - x, you can find what z is
drifting isle
Jesus Christ, give me a second
plucky owl
Which part is still not making sense?
crimson sedge
I'm going to guess the x is the problem
we aren't trying to find x. but it's basically got to work through the formulas
the angle you seek is going to have x in its formula. try to just move it along through the process without trying to figure out what x is
plucky owl
Not quite but almost, specifically this part. You wrote BOC + z = 90 then did 90 = 195 - x, which I'm assuming you replaced BOC with 195 - x
But where is the z
That z is the angle the expression that the problem is asking for
drifting isle
It’s so hard
plucky owl
No
You found what BOC is equal to, when you used it in the supplementary part
BOC = 195 - x
crimson sedge
take a few breaths, relax if you can. the more we push for something, sometimes the further away it gets
drifting isle
I don’t know how you guys find it so easy
crimson sedge
the calmer you can get breathing and the mind, the more in focus this'll be
it's difficult for me. you were quite into this before i figured it out
I taught univ calc for 15+ yrs for an online math program. this problem is a challenge
so please don't feel bad
breathe a bit, take the pressure off, look at it again, step by step
(by taught, think TA type position, not full prof)
drifting isle
Hmmm
plucky owl
I think the overall complication is you are trying to relate, BOC as both a supplementary and complimentary angle, for the same one diagram
drifting isle
What do you mean
plucky owl
You're basically finding that purple angle
drifting isle
Why do you have two
crimson sedge
it's can be 1 picture ... gets crowded. One key point is that the angle you're looking for, z, doesn't need to be in the figure above. It could point to the lower right. It doesn't have to be inside the 180
that lower right one will take me a minute for the software cause I have to use precise points 😦
drifting isle
So your saying the angle z is not even in that picture!
I thought it was between b and c
crimson sedge
drifting isle
Omg
drifting isle
What the hell
crimson sedge
if you can keep them separate, its' easier. one sketch for each scenario, supplementary, complementary
drifting isle
I thought I was trying to find aob and boc which are percentages of 180 degrees
Angles
crimson sedge
you need boc to find the goal
the goal is z
and z is not on the supplementary setup
plucky owl
drifting isle
So im finding 2 angles, the angle that makes up 180 degrees and the angle that compliments the angle that makes 180
plucky owl
There, I made BOC the same color so it's not confusing
plucky owl
So im finding 2 angles, the angle that makes up 180 degrees and the angle that c...
So im finding 2 angles, the angle that makes up 180 degrees and the angle that compliments the angle that makes 90
It's 90
The second 180 is suppose to be 90
drifting isle
Oh yea
plucky owl
But you use the first diagram I have, to find the expression for BOC
Then using the second diagram, and BOC, you can find z
drifting isle
Are we able to find the angles of aob and boc without the compliment of boc first
crimson sedge
i get the feeling you're trying to find numbers for all 3 angles
drifting isle
Yep
plucky owl
If you're trying to find actual values, that's not what you are doing
crimson sedge
that path heads to a wall
plucky owl
You are finding the expression
drifting isle
What do you mean expression
crimson sedge
each angle will have an x in it somewhere. we cannot find the exact angle numbers without more information
drifting isle
Okay that’s a relief because I thought you could and I didn’t know how. So I’m actually not even looking for a angle
crimson sedge
in a sense, we want one particular angle, but it cannot be a number like 20 degrees
drifting isle
So a possibility of an angle?
plucky owl
The possible equation for that angle
drifting isle
Okay that i understand
plucky owl
Do you understand what you are solving for now?
drifting isle
Possible variables that can fit the angles
plucky owl
You don't need multiple variables, use the image I provided
Can you find the expression for BOC?
In the blue image
drifting isle
plucky owl
,rotate
wraith daggerBOT
plucky owl
Now using the fact that BOC = -x + 195 and BOC + z = 90
Can you find what z is equal to?
drifting isle
1 sec
crimson sedge
you're on the path. you can do it 🙂
drifting isle
Tryingggg
plucky owl
Where are you stuck?
drifting isle
Just looking at boc=-x+195 and boc-z =90 I think if I minus boc from z maybe the leftover will be what z is equal 2 but I don’t want to make another mistake so I’m thinking
plucky owl
First it should be BOC + z = 90
And second what if I said something like h = -x + 195 and h + z = 90, if you were to use both equations, can you find z?
plucky owl
And second what if I said something like h = -x + 195 and h + z = 90, if you wer...
The only difference with this and BOC = -x + 195 and BOC + z = 90 is that I just replaced BOC with a singular variable, to simplify things a bit
If you were to use this, h = -x + 195 and h + z = 90, in the second equation, you can replace h with -x + 195, do you see that?
crimson sedge
It's down to a system of equations like algebra. We use the angle info to make the equations. Then it's algebra.
plucky owl
Look at your answer choices
Is there one that matches that expression?
You have z = -105 + x
drifting isle
Yeah I messed it up
plucky owl
No you didn't
Addition is commutative
z = -105 + x is the same as z = x + -105 which is z = x - 105
plucky owl
The z is used to represent the angle, the problem is primarily looking for the expression
The equation is z = ....
The question wanted the ... part
drifting isle
Okay, thanks so much for the help, it just seems like it’s going to be really tuff stuff from here on
crimson sedge
in the hand calculation, you need parenthesis.
drifting isle
I didn’t even realise what it was asking for
crimson sedge
sometimes, that's the hardest part of a problem
in math, in life
what is it we are trying to do?
if we can lock that down, sometimes the rest just goes into focus on its own
crimson sedge
and it's really difficult when problems jumble stuff up like a puzzle and the pieces seem to go together when they shouldn't
take your time with it, I'm sure it'll be easy when you've got the hang of it
plucky owl
And I thought geometry was going to be easy
I think the complicated part was you were trying to find set values for each angle, not expressions
drifting isle
By the way how did you know it wasn’t asking for set values so I can know in the future
plucky owl
And that BOC related to a supplement and compliment
plucky owl
By the way how did you know it wasn’t asking for set values so I can know in the...
The answer choices still had x in them
crimson sedge
same reason you had so much frustration, couldn't find an x
plucky owl
So you know it's not set values already
crimson sedge
Captain knows math, so Captain can tell by seeing x
you and I had to hit the wall first
crimson sedge
everyone's good at some aspect of it
many without realizing it
it's tough problems that can send some people packing and avoiding it
you worked through it and that takes a lot of strength to keep going with us, thank you
I look on here and there's tons of problems I've never seen or thought about before
and then I see one and I'm like, I can help with that
drifting isle
Well thanks for helping
crimson sedge
I've watched people in life give up on stuff, that builds walls and limits what they can do later
work through the challenges, keep trying, stick with it
and you'll open more doors than you may realize possible now
and in more than math
I congratulate you on this problem and getting to the end of it! 🙂
drifting isle
Thanks 🙏 I’ll keep trying
drifting isle
So you know it's not set values already
Thanks captain nova!
crimson sedge
drifting isle
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
ripe wasp
cedar kilnBOT
ripe wasp
I got the minimum area = 28/4+pi
I initially thought you sub the minimum area into the given area equation and find x and sub that in the perimeter equation to get r but I was wrong
so not really sure how to move forward from here
uhh
ello
<@&286206848099549185>
tawdry pelican
x = 5.6m ?
just differentiate the area A and find value of x for which it is minimun, comes out to be x = 5.6m
cedar kilnBOT
@ripe wasp Has your question been resolved?
ripe wasp
just differentiate the area A and find value of x for which it is minimun, comes...
💀
ur as lost as me my g
cedar kilnBOT
tawdry pelican
isn't my answer correct?
cedar kilnBOT
Available help channel!
hybrid prawn
how to prove that the limit of f(x) when x aproches 0 is the same as f(-x)
hybrid prawn
am only given its domain ]-a;a[
tropic oxide
you want to prove $\lim_{x \to 0} f(x) = \lim_{x \to 0} f(-x)$?
wraith daggerBOT
Ann
crimson sedge
this is impossible to be true for all f
opal basin
Maybe they assume the left limit exists
bold hinge
Assuming f is continuous?
opal basin
not sure if they would be equal if both don't exist
hybrid prawn
whell its told that it is continous
dull oxide
whell its told that it is continous
!xy
cedar kilnBOT
whell its told that it is continous
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.
crimson sedge
how to get this to 4^(r+2) - 4 ??
cedar kilnBOT
how to get this to 4^(r+2) - 4 ??
carmine dock
Try factor out 4
uneven iron
There you have x = 1
Oh
I thought "x" wasn't a multiplication simbol
Factor 4^(r+1)
crimson sedge
Factor out the 4 and it should be clear
didnt work
carmine dock
Uhh it’s not that complicated
uneven iron
Factor 4^(r+1)
.
carmine dock
1 (4^(r+1)) + 3(4^(r+1)) = 4(4^(r+1)) = 4^(r+2)
crimson sedge
Factor 4^(r+1)
4^r+1 ( 1- 4^r . 3 )
wraith daggerBOT
Rub05
rain olive
hi guys just a question by curiosity, i'm trying to do this simple quiz of math ( coordinates ) but i didn't understood something, how from (0,0) to (1,0) takes 1 minutes which is correct, then back to (0,0) to (1,1) takes 2 minutes ? normally its takes 3 because we back to (0,0) ! : 👉 here's the link to the quiz https://www.mathopolis.com/questions/q.html?qs=6142_11189_11193_2730_6140_6145&t=quiz
fervent jackal
which question of the quiz?
rain olive
its about cartesian coodinates
fervent jackal
why does it take 3?
fervent jackal
$n+\sum_{k=1}^{n}2k$
wraith daggerBOT
lebesgue
fervent jackal
I think this should be the formula
rain olive
yes this the patter i was looking for
fervent jackal
if k is odd then it ends up on the y axis, if its even it ends up on the x axis
rain olive
oh yes cool
fervent jackal
but idk how to do case curly brackets in latex
but does that solve your question?
rain olive
yes super
fervent jackal
can you close the forum then?
fervent jackal
can you do .solved?
fervent jackal
thank you so much
no problem
rain olive
solved
rain olive
how to?
rain olive
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
civic coral
I have a explanation about why the power of complex numbers is restricted in the realm of integer, and i need people to check on it
civic coral
so here's my explanation:
expressions like "z^(1/n) where n is integer" are ambiguous.
It is due to the fact that when the power of a complex number is a fraction (let's say z^(1/n)), it will possess more than one points on the complex plane that can be used to denote z^(1/n).
As a matter of fact, these points, which represent z^(1/n) on the plane, can all be converted into z after being raised to the n'th power.
However, if you describe "the nth root of z" by saying it is equivalent to z^(1/n), we wouldn't be able to know which of the points that you're referring to.
Therefore, to avoid such a awkward situation, we restrict the "n" which is the power of z in the realm of integer.
crystal raptor
It's not that we say n must be an integer, we certainly can talk about nth roots of complex numbers. We either conventionally take z^1/n to be the nth root of z with the smallest argument (or some other convention) or we accept the fact that nth roots are multivalued functions
civic coral
It's not that we say n must be an integer, we certainly can talk about nth roots...
it is interesting that we treat z^1/n to be the nth root of z with the smallest argument
crystal raptor
It's what we do with say 2^1/2
civic coral
I think im going to post the session about "z^n" on my textbook.
De Moivre theorem:
$z^n = r^n [cos(n\theta)+isin(n\theta)]$ where n has to be integer
crystal raptor
\theta
civic coral
god using texit to convey my thought makes me sweating so bad
So
So it is written on my textbook
However, the theorem would work as well when n is fraction
crystal raptor
Think you also mean nθ
civic coral
ohh
wraith daggerBOT
Please Correct My Grammar
civic coral
so the possible reason for the writer to say that n must be integer
civic coral
so here's my explanation:
expressions like "z^(1/n) where n is integer" are ambi...
is this
crimson delta
It's what we do with say 2^1/2
however it runs into problems for example with (-8)^(1/3)
crystal raptor
however it runs into problems for example with (-8)^(1/3)
Yeah this is true
civic coral
"pretty much" I think I will consider it as "exactly"
civic coral
is that from the wiki
crystal raptor
Ye
civic coral
I think I have already checked on them before
and it says that n has to be integer as well
ohh
crystal raptor
Yeah this is showing an example of why it fails for non integer
civic coral
there is some new shit on your picture
crystal raptor
Which is essentially what you were saying
civic coral
Which is essentially what you were saying
would you mind post the address of the page
civic coral
https://en.m.wikipedia.org/wiki/De_Moivre%27s_formula
It is written and explained perfectly
I have another question tho
How I express the nth roots of z
in which z is a complex
through math terms?
crystal raptor
Scroll down on wiki
civic coral
to say that "z^(1/n) is the nth roots of z" seems pretty intuitive in my opinion
crystal raptor
Well it depends what you mean by "express"
You can certainly write z^1/n to describe a set along as you clearly say that's what you're doing
But would be safer to just write { w | w^n = z}
civic coral
But would be safer to just write { w | w^n = z}
That's lit
what a perfect expression
I have no questions now, thank you the sum of AC
crystal raptor
Welcome!
civic coral
.close
last jungle
Q117?
vague rapids
didn't you come with the same question yesterday?
mighty shuttle
Q117?
Don't have paper with me right now so I can't guide you through all the steps but perhaps start by finding A and B
@last jungle
last jungle
Yes
mighty shuttle
After you have 3 points you should have enough information to find the 4th point and this 2a+b
last jungle
Diagram?
last jungle
Yes next?
iron scarab
its deleted this year relax
mighty shuttle
its deleted this year relax
They may be in 11th
last jungle
No I want the process
vague rapids
so like are you able to find equation of tangent?
use the formula yy1=2a(x+x1)
here a is 2, y1 is -4 and x1 is 2
dense ridge
cedar kilnBOT
olive crescent
iron scarab
Or 150 by 1000 ×100
this
iron scarab
yup
cedar kilnBOT
cedar kilnBOT
Available help channel!
edgy flint
What happens to the cos(2x) and why is sin chosen as the u substitute?
slow jewel
What happens to the cos(2x) and why is sin chosen as the u substitute?
Which step?
edgy flint
Just below now solving:
slow jewel
Ah
rocky harness
edgy flint
It just seems like cos(2x) and du are disregarded
silver oxide
wdym
slow jewel
What happens to the cos(2x) and why is sin chosen as the u substitute?
By taking u=sin(2x), wherever there was sin(2x) in the original expression it has been substituted by the variable u
now du= 2cos(2x)dx, which means cos(2x)dx = du/2
So in place of cos(2x)dx in the original one, it has been replaced by du/2
edgy flint
Oh so the cos(2x) from the du is the same one from the original expression?
slow jewel
Yes
edgy flint
And if I used u=cos(2x) the final expression would have to be multiplied by - 1/2?
slow jewel
It would be -1/2 int (u du), yes
edgy flint
Ok thanks
slow jewel
Np
slow jewel
It would be -1/2 int (u du), yes
Over here u= cos2x tho**
edgy flint
I got confused and thought that du was completely separate from the original expression
slow jewel
I see
bright sorrel
could someone help me understand this?
cedar kilnBOT
could someone help me understand this?
bright sorrel
so for the numerator I suppose 2^n+1=2^n * 2
so the two 2^n cancel out
but then how is the sinuses
how do we get to 2/3
do I have to use that
lim x->inf sin(x)/x=1?
stoic gale
yes
stoic gale
thats how the sin's 'cancel' out, leaving you with pi/3^n/ pi/3^(n+1), giving 1/3
cool
cedar kilnBOT
wraith daggerBOT
…
silver fable
you need to find ax+b first (find a and b)
crimson sedge
plug it into the inequality and solve for x 👍
Well substitute in then start moving stuff about
You’re probably going to have to form a quadratic
then solve the quadratic
crimson sedge
that function might be a quadratic 😨😨
silver fable
$x\sqrt{6-x}-\frac{7}{4}x+\frac{15}{4} > 0$
wraith daggerBOT
Adam Chebil
lone plinth
solve this using this video pleasehttps://www.youtube.com/watch?v=6rXByMcuAyI
tropic oxide
solve this using this video pleasehttps://www.youtube.com/watch?v=6rXByMcuAyI
!noans
cedar kilnBOT
solve this using this video pleasehttps://www.youtube.com/watch?v=6rXByMcuAyI
The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.
tropic oxide
we won't do your homework for you.
lone plinth
its not my homework
I just dont know how to solve this
as its not shown in the video
tropic oxide
do you want to be taken through how to solve it
or did you ONLY want someone to just hand you the solution
lone plinth
I want to know how to solve such integrals
peak minnow
partial fractions prob
lone plinth
Ye Ik that
crimson sedge
solve this using this video pleasehttps://www.youtube.com/watch?v=6rXByMcuAyI
so you won't even watch the video yourself but expect someone else to in order to solve your work?
lone plinth
holy shit
are u stupid
go read what I wrote
before typing. I said they dont bring that up in the video in exactly those kind of integrals and yet u try to be picky for no reason
tropic oxide
do you want to be taken through how to solve it
you haven't answered with an unambiguous "yes" to this
lone plinth
baiting for no reason
crimson sedge
Probably didnt get mentioned bcs u dont need partial fractions for it?
just by looking i dont think u need them
it looks like (3x-1)^-2
lone plinth
It's a exercise in the chapter about it but I tried doing it the way It was shown in the video but I dont get to the right answear
crimson sedge
which doesnt need partial fractions to solve
you can insult me if you want, but that won't take you any further to your solution
as for the video, it's redundant to send it if it has nothing to do with the problem
(because it does have nothing to do with this problem)
u can solve it with partial fractions though
you could, but it would be a waste of time
pure cloak
I need help with linear functions
crimson sedge
just waste of time bcs theres ways 10x faster
cerulean harness
I need help with linear functions
!occupied
cedar kilnBOT
I need help with linear functions
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
crimson sedge
I need help with linear functions
lone plinth
so I put the whole thing below as (u)^2 and move it to the top so it becomes (u)^-2?
silver fable
solve this using this video pleasehttps://www.youtube.com/watch?v=6rXByMcuAyI
factor denominator then use u-sub
lone plinth
so (1-3x)^2 and (u)^2 to (u)^-2
ok I see now it how you do it thanks
but If I would wnat to solve it with partial fractions how would I do it
crimson sedge
it's literally in the video
go watch it
before asking any more questions related to it
lone plinth
someone useful help me please as I get the wrong answer
crimson sedge
yes chances are, me, who has helped hundreds of people is less useful than you, who can't solve a basic integral
i digress
tropic oxide
someone useful help me please as I get the wrong answer
show us what you're doing
so we can diagnose what you are doing wrong
lone plinth
legit these guys are helpers and are just trying to bait me I dont get it
If you dont want to help dont bother texting here
lone plinth
I mean the other guy not you sorry
tropic oxide
you're like a patient who goes to the doctor and complains about a sore throat but then when the doctor asks to see your throat you refuse and say he's baiting you
that's what it looked like
lone plinth
wraith daggerBOT
tropic oxide
ah, your factorization is wrong
or rather
no your factorization is correct
but the way you set up the partial fractions afterward
that's what is wrong
(1-3x)^2 ≠ (1-3x)(1+3x)
tropic oxide
it would be A/(1-3x) + B/(1-3x)^2
but you would get A=0 anyway
and you would just be right back to square one
silver fable
so is it like A/(1-3x)^2 only
why do u want to use PFD? to integrate 1/(ax^2+bx+c) u only use PFD if the discriminant b^2-4ac>0
if it's <0 u complete the square and do u-sub, if it's =0 u do u-sub directly
tropic oxide
so to conclude and reiterate: partial fraction decomposition won't help, and even if you try it anyway, it will literally do nothing for you.
lone plinth
why do u want to use PFD? to integrate 1/(ax^2+bx+c) u only use PFD if the discr...
Most exercises in the chapter that I am at in at the moment is mostly solved that way to exercise solving integrals that way but maybe its not meant to be solved like that
tropic oxide
it is indeed not meant to be solved like that.
slim jasper
Don't speak in meme gifs in a help channel, please. If you can't attempt to correct the helpee in a respectful way, it's better not to say anything.
lone plinth
Alright thanks for the help
toxic coral
cedar kilnBOT
toxic coral
i know angles in a triangle add up to 180 degrees
annd i know b + c = the corner line
and i know c = d(the alternate angle)
so how do i do this
also b is correspoding to e
oh wait
i got the answer
bye
abstract laurel
wispy shoal
in this example i got 1/0^-, i know its not the right answer, what sould i consider doing?
violet flume
well you are inventing notation so you have to explain to me what it means
wispy shoal
when lets say x approches 1 from the left side
or it means its close to beeing 1 but never, its number like 0.999999999999........
but never is*
marble pagoda
well you are inventing notation so you have to explain to me what it means
we tried inputing it in the photomath
but we don't get this
lemme send you a screen shot
violet flume
we tried inputing it in the photomath
you are writing something thats not standard is all
im talking about what you sent initially
marble pagoda
you are writing something thats not standard is all
violet flume
sure, its divergent
so how you show that is up to you
i suggested you show its unbounded
do you get what i mean?
@marble pagoda im not sure where your confusion is if not
photomath is doing a weird intermediary step i dont think is necessary but whatever
wispy shoal
ok, thanks!!
scenic brook
1^- it's like 0,9999999999 i think
wispy shoal
its confusing to us because its something that our professor explained poorly
violet flume
oh, are you both asking the same question here?
marble pagoda
oh, are you both asking the same question here?
yes\
wispy shoal
@scenic brookyee thats what i mean
marble pagoda
we rn practicing together
violet flume
okay okay
so yea, i mean to go through it
the 1^- means that x is always less than 1
wispy shoal
ye
violet flume
it gets close to 1, but from below
you should look at a graph, if you can
,w Plot[ (1+Log[x])/(x-1) ]
wraith daggerBOT
marble pagoda
it's ln
violet flume
do you see the asymptote?
marble pagoda
ye yei k
violet flume
okay so
were approach it from the left
so visually it looks like -inf makes sense
okay
so if you agree its divergent
wispy shoal
im still young in this area of mathematics so this is what i picture it does this makes sense??
violet flume
i dont really understand what its supposed to be saying
do you both believe that this function goes to infinity in the limit?
scenic brook
im still young in this area of mathematics so this is what i picture it does thi...
just know that (1^-)-1 is approaching the zero from the left side cause it's -0,00000000...1
wispy shoal
ooohhh
i got it
im so dum xD then i get 1/-0.00000000001 it goes to the - infinity
scenic brook
you can watch 100 limits to understand limits, you know 🙂
scenic brook
you can watch 100 limits to understand limits, you know 🙂
In youtube
wispy shoal
but i stopped one step earlier cuz i taught its 1/0 jesus am I dumb
thanks for help guys!
scenic brook
im so dum xD then i get 1/-0.00000000001 it goes to the - infinity
That's true i think
wispy shoal
you can watch 100 limits to understand limits, you know 🙂
will do ty!
amber sonnet
I need help with evaluating the integral of 4 * sqrt(1+4x^2) dx, with bounds of integration being from 0 to sqrt(2). I have tried using u-sub (u = 1 + 4x^2), but then I end up with 4 * sqrt(u) * 1/(8x) du
cedar kilnBOT
Available help channel!
errant tendon
Without drawing venn diagrams and without formal proof so by pure intuition if I have two sets S=(A intersection Bc) union (C intersection Dc)
T=(A intersection Bc intersection Dc) union (C intersection Bc intersection Dc). I have proven that T is a subset of S and it's cordrect but i don't truly understand the intuitivness behind it
errant tendon
the proof isn't the issue it's the fact that to me it makes no sense that a bigger set is a subset of a smaller set
crystal raptor
wdym "bigger set"
errant tendon
well T has one more element in each parenthesis
crystal raptor
okay but the more sets you intersect the "smaller" the set becomes
errant tendon
yes but an an interseection between those three sets is a set with the elements that belong in all those three sets
crystal raptor
so they belong to any two of them
errant tendon
wdym
crystal raptor
e.g. $X \cap Y \cap Z \subseteq X \cap Y$
wraith daggerBOT
ΣΑC
crystal raptor
if you are an element of all 3 then you are an element of any two
errant tendon
oh i am neurologically disabled i see now
sometimes my neurological issues make it impossible to see such thingsd
that makes perfect sense
crimson sedge
Without drawing venn diagrams and without formal proof so by pure intuition if I...
Venn diagrams are a great way to get intuition, I don't see why you wouldn't draw one if what you're trying to achieve is an intuitive understanding
errant tendon
because i can't see them properly
crimson sedge
They let you see everything at once in a way that is easy to process mentally
crystal raptor
yeah this would have been easy to see in a venn diagram tbh
errant tendon
i have amongst other things perception issues
crimson sedge
sometimes my neurological issues make it impossible to see such thingsd
This may be too personal of a question but am I allowed to ask what neurological issues you have out of pure curiosity?
crimson sedge
Ah, problems with visuals?
errant tendon
the lines get all muddled up in my head
crimson sedge
I see
errant tendon
yea
been doing this without any visual help all through highschool and now my third year of ug
ty peeps
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grand crystal
cedar kilnBOT
grand crystal
I have the answer, it's 1/64, but I don't understand.
steel heart
What part of this you don't understand?
grand crystal
My approach was to figure out the chances of those 4 squares making a diamond inside a 2x2 grid.
The chances that the square is in the right position is 1/4, and for all of them it would be 1/4^4 = 1/256
But now I don't know what to do for the 3x3
Oh wait don't I just multiply it by 4 because the 2x2 diamond can be in any 4 positions in the 3x3 grid?
I understand now
.close
gritty escarp
How do I prove that the matrixes
1 0 1 2
2 1 and 0 1
are a subspace of M4(R)
orchid panther
@gritty escarp you mean form a subspace?
sage forge
How do I prove that the matrixes
1 0 1 2
2 1 and 0 1
are a subspace o...
Do you mean the span of those two is a subspace?
gritty escarp
yeah both of those
Im having trouble with subspaces since in my university we dont use that span thing
orchid panther
Well i assume they want by asking you that to prove that the vector space (matrix space in this case) generated by those two matrices would be a subspace of M4(R), in that case just prove that you have 0 is contained in that set, as well as that it is stable by linear combination
gritty escarp
but then wouldn't any two matrices form a subspace
orchid panther
Yea pretty much
You can prove it for any one, two, three, four whatever matrices
(Definition of the Vect() that generates vector subspaces)
gritty escarp
so here b) is a subspace and a) isn't
orchid panther
Well for a what are they asking for
A subspace of what
(I assume those to be polynomials)
(But which degree)
Also
gritty escarp
Well, the question itself is "Determine the vectorial subspaces of P(X) and Mn,m(R)"
gritty escarp
yeah I meant M2,2(R)
orchid panther
Oh alright
gritty escarp
my bad
orchid panther
a) depends on if its K[X] or K_n[X] with some n in N
(And if n is superior to 1-2 or not)
gritty escarp
can I decompose the polynomials into vectors by the way?
a) would become something like (1,0,1) + a(x,0.0) + b(0,x^2,0) + c(0,0,x^3) ?
gritty escarp
a) depends on if its K[X] or K_n[X] with some n in N
it's K[x], they would specify if it was K_n[X]
and I think they do it in the next exercise
orchid panther
Well if its K[X] its a subspace with no problems
As K[X] is itself a vector space
gritty escarp
the only other polynomial in the exercise is this one
which by my understanding is also a subspace then?
then what would be an exemple of a polynomial that is not a subspace
orchid panther
Question states to "determine" right
gritty escarp
Yes
orchid panther
So i think they want a specific form of the subspaces
If thats the case for the matrix example it would be:
a+b 2b
2a a+b
With a, b in R
gritty escarp
which contains 0 and is stable by linear combination
therefore a subspace, correct?
orchid panther
Of course by definition of the Vect() (or span i think its called), but you can verify it if you want
And youd do the same for the polynomials
cedar kilnBOT
cedar kilnBOT
Available help channel!
crimson sedge
is the PDF of a continuous random variable the equivalent to the PMF of a discrete random variable?
crimson sedge
as in like i know it's not exactly the same
but
if u had like P(X = 3) would it be equal to subbing in x = 3 into the PDF function
and the output is the number P(X = 3) ?
upper abyss
They're very similar concepts, to the point where the notation is even matched up
crimson sedge
so am i right to say that if i had P(X = a) for some a in the real numbers then it's the same as subbing in x = a into the PDF function
(for a continuous rv)
upper abyss
Not in that case, no. You'd want the area under the pdf between X = a and X = a
As continuous distributions express probabilities in terms of integrals
And discrete ones are in terms of sums
crimson sedge
Not in that case, no. You'd want the area under the pdf between X = a and X = a
wouldnt that just always be 0 tho
unless im misunderstanding
upper abyss
Yep, you understand perfectly!
upper abyss
There's no way to roll "an exact real number", the probability is 0.
cedar kilnBOT
@crimson sedge Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
vapid mauve
cedar kilnBOT
vapid mauve
<@&286206848099549185>
dire geode
<@&286206848099549185>
!15m
cedar kilnBOT
<@&286206848099549185>
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
vapid mauve
-y
slow jewel
And x² is 1.44?
vapid mauve
Yes
vapid mauve
Yes why not
slow jewel
Just sub the values of x² and y in x²(x²+y)²⁰¹ then
tropic oxide
^
slow jewel
if -y= 0.44 then y=-0.44
tropic oxide
wait you won't even need a calculator for this lol
it's trivial
just plug and chug
in fact you don't even need to know that x ≥ 0
this letter x however
looks hideous
and you should never write the letter x with this shape
slow jewel
wait you won't even need a calculator for this lol
Oh right, I forgot the - for y
And added 0.44 instead
Bruh
vapid mauve
Who can help me to find the answer
steel heart
C'mon it's easy just substitute the values
plucky merlin
1.44(1.44 - 0.44)^201
vapid mauve
.close
cedar kilnBOT
1.44(1.44 - 0.44)^201
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
@vapid mauve Has your question been resolved?
quick cipher
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Want me to close it? I'll try, but if it doesn't, pls click/press the checkmark in this message.
quick cipher
<@1179704516241801219> Has your question been resolved?
Pls click the check in this message
cedar kilnBOT
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Available help channel!
austere dune
can someone help me with this question pls
cedar kilnBOT
can someone help me with this question pls
unkempt moat
how to find side length of this square hypotenuse is 3
cedar kilnBOT
how to find side length of this square hypotenuse is 3
vernal minnow
what are the 30 and 60?
also can we make assumptions about any of the angles here? Is that a right triangle? Is it equilateral?
unkempt moat
30 and 60 degree
angle
s
Isosceles right triangle
no not that one
the one which has 30 and 60 degree angles
vernal minnow
so the smaller ones are both isosceles right triangles while the big one is not?
unkempt moat
A square is drawn in an isosceles right triangle, as two of its vertices lie on the hypotenuse, the other two vertices. Find the side of the square if the hypotenuse is known to be 3
yeah i think my drawing is wrong
it should be 45 45 degree each right?
vernal minnow
" an isosceles right triangle" since the sum of inner angles is 180° the two outer angles are 45° ones
unkempt moat
ok and how to find square side length
vernal minnow
the AAA theorem should apply
if all three angles of two triangles are equal, the triangles are "similar"
unkempt moat
so 3x=3 x=1?
vernal minnow
we can solve the shorter sides of the whole triangle pythagoras, utilizing that a=b and so a²+b²=2a²=2b²
c²=3 => 2a²=3 => a²=3/2 => a=b=sqrt(3/2)
vernal minnow
so 3x=3 x=1?
not necessarily
similar in this case means the proportions of the sides within each triangle to each other are the same
unkempt moat
but triangle has those angles 45 45 90
vernal minnow
so the side-length of the square is x
and since we get isosceles right trriangles in each corner, their other cathetus must be x as well
so 3x=3 <=> x=1
vernal minnow
happy to help!
unkempt moat
.close
normal shore
cedar kilnBOT
normal shore
is there any other way to find AB other than cosine rule?
since its 3 marks, shudnt be too long..?
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vagrant tundra
cedar kilnBOT
vagrant tundra
i dont even know how to begin, q7
next hornet
What have you tried
tropic oxide
which part(s)
next hornet
Ok i guess i should ask if you know what absolute values are
vagrant tundra
Ok i guess i should ask if you know what absolute values are
Oh well yeah
-2 will become +
but if it's x-2, i reckon we can't just take x+2 can we?
tropic oxide
you will have two cases, one for x>=-a and the other for x<-a
and in the first case the equation will resolve to that
but from x+a=2x+a you probably should not be getting 3x=(something)?
vagrant tundra
you will have two cases, one for x>=-a and the other for x<-a
I don't get it
what I did was,
x + a = 2x + a
and then I moved the a to the left side and the x to the right side
vagrant tundra
first off do you know what absolute values are at all
well I thought it was the distance to 0, so its like making negative numbers positive
I think
tropic oxide
gtg sorry
crimson sedge
<@&286206848099549185>
?
vagrant tundra
Then
-x-a=2x+a
i dont think i understand the topic itself
crimson sedge
If
vagrant tundra
WRONG ANSWERS
vagrant tundra
ignore that, i'll try to learn the topic once
crimson sedge
ignore that, i'll try to learn the topic once
OK
crimson sedge
ignore that, i'll try to learn the topic once
All the best
vagrant tundra
TYU
cedar kilnBOT
@vagrant tundra Has your question been resolved?
solar cipher
In each section, there are two triangles. Which sections are the two triangles congruent?
solar cipher
I think every section’s 2 triangles are congruent; but that seems to obvious so idk
manic escarp
I think every section’s 2 triangles are congruent; but that seems to obvious so ...
do you know what makes 2 triangles congruent
!status
cedar kilnBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
yeah all those. theorems
solar cipher
yeah I’m aware and I think I answered my question correctly, but I want to double check
manic escarp
can you show me your answers
or what you did to get them
you dont need to show me all of them just show me one or two
solar cipher
Sure
In each section, say if the triangles are indeed congruent. Explain your answer
manic escarp
ok yeah so all of them are congruent
but you need to explain why
i.e which theorem proves it
solar cipher
Top far left - SAS
Bottom far left - SAS
Middle top - SAS
Middle bottom - SAS (they share a side)
manic escarp
yeah those are right
solar cipher
Top right - ASA
Bottom right - ASA
manic escarp
you get the idea so you should be fine for similar questions
manic escarp
?
solar cipher
In other questions (not this one) it tells me to write a mathematical explanation, idk if it’s only in my country or it’s taught in other countries too
Idk how to really explain it but I have no idea how to write congruency in mathematical language
Like how to prove congruency
If that makes sense
manic escarp
generally i think it wants you to explain how that theorem matches up with the two triangles
in my country, or at least my teacher
they would make a chart
give me a sec ill show you
solar cipher
Yeahhh exactly
That’s what I’m talking about
I just haven’t really been listening so idk how to really make a chart
manic escarp
youd have a chart similar to this
on the left side you'd give a statement(i.e △ABC≅△DEF)
and on the right side the proof would be congruency proven with SAS or another theorem
solar cipher
Yeahh that’s what I’m talking about
That’s exactly what I’m talking about
But with something like this (hold on the pic is sending) how do you prove this:
manic escarp
for the first question(topleft most) ill fill the chart so you can understand better and you can do the rest
solar cipher
How do you use the chart to prove that ABD is congruent to CBE
A=C is given, AD = CE is given
How do I prove that the E and D are equal though
in that chart
sorry for my English typing skills if it’s an inconvenience
manic escarp
describe it
solar cipher
All three sides are different
manic escarp
in this case
angle D=E right
if those two angles are the same then that means its an isosceles
isosceles has two sides of the equal length or two angles that are equal
solar cipher
if those two angles are the same then that means its an isosceles
How exactly
It’s not given to us that A=D or C=E
so how would knowing that D=E prove that both triangles are isosceles
manic escarp
if you look at the two given interior angles of BDE
they both have two dashes on them meaning the angles are the same
if two angles are the same in a triangle, the triangle is an isosceles
solar cipher
Ohh yeah
Yeah I see what you mean
But how can I prove like
The outer part of D=E angles
Are the same
If that makes sense
manic escarp
what is the angle of a flat line
solar cipher
180
I get what you’re saying
How do I write that in the chart tho
Do I just explain it
Like how
manic escarp
first you'd write that △BDE is an isosceles triangle
proof= angle D=E
then as second statement
BD=BE because △BDE is isosceles
solar cipher
Ye
manic escarp
you can write 180-D=180-E because D=E
write
angle BDA=angle BEC as statement
and as proof you would write D=E so 180-E=180-D=BDA=BEC
manic escarp
np
solar cipher
mind if I send you a friend request?
manic escarp
i used to hate these questions because there was less math more explaining and english
go ahead
dms are open
solar cipher
i used to hate these questions because there was less math more explaining and e...
yeah exactly
alright bet
thanks a lot man
manic escarp
np
daring needle
im working with proofs and parallel lines
cedar kilnBOT
im working with proofs and parallel lines
@daring needle Has your question been resolved?