@remote gust Has your question been resolved?
#help-27
devout snowBOT
Available help channel!
waxen drum
Hey
quiet sail
How can you split the bottom expression?
coral crescent
How can you split the bottom expression?
what do 9x^2 and 12x have in common
warped relic
quiet sail
what do 9x^2 and 12x have in common
That was a question to help jacks :)
quiet sail
No worries, happens
waxen drum
How can you split the bottom expression?
3x(3x-4)
?
Ah I got it
Thank you
.close
worldly dust
Hi there, I'm trying to understand this proof of the law of itterated expectations (part of my statistics class). But I don't understand what is being done in the following step?
Could someone tell me what the first integral of the pdf and joint pdf gives? and then how the second integral gives the E(Y)?
Thank you!
devout snowBOT
Hi there, I'm trying to understand this **proof of the law of itterated expectat...
supple knot
Use fubini and Integrate dx first
worldly dust
Oh I think I get it. So I do a bit of rearranging to get the inner integral with respect to x and take the y outside.
Then the first integral will give me the pdf of y because we integrated out the x.
Then we are left with the integral of y and f(y) which is just the definition of the E(Y)
worldly dust
Use fubini and Integrate dx first
Is this right?
supple knot
sounds right
stone axle
devout snowBOT
stone axle
not sure how to start
restive river
Hi! You can use Euler's formula for cos then Binomial Theorem then Euler formula again
supple knot
is this precalc/trig class?
restive river
Hi! You can use Euler's formula for cos then Binomial Theorem then Euler formula...
😵💫 inb4 this is 10th grade
stone axle
im 17
idk what you get from that
but zamarus, i dont think thats the way
this is the full q
supple knot
Start with
$\cos(3\theta) = \cos(2\theta + \theta) = \cos(2\theta)\cos(\theta) - \sin(2\theta)\sin(\theta)$
copper flower
weird flex
woven radishBOT
riemann
supple knot
then repeat for double angle formula for each cos and sine
supple knot
idk what you get from that
it tells us what class it's for. there are more advanced techniques that can also prove your statement, but you haven't learned them yet.
wispy mango
how to calculate a unit vector that forms a 30º angle with vector a (1, sqrt 3)
wispy mango
i have no idea how to do this
tender marsh
Hold on
wispy mango
i literally dont undesrtand what to even do or where to start
tender marsh
I dont know what you mean by vector in this
tender marsh
SO what are you calculating?
tender marsh
What are you tryin to find?
wispy mango
i literally dont know how to find it thats the thing
scarlet peak
do you know the formula for angle between 2 vectors?
wispy mango
What are you tryin to find?
a unit vector that forms a 30º angle with said vector
scarlet peak
it starts with cos(theta)=...
wispy mango
its an equation system that i need but i dont know what to put in it you know?
i know the formula, i just don't know what to do
wispy mango
said a = (1, sqrt 3) then b = (b1, b2) and forms an angle of 30 degrees
???
what do you mean
i have no values of vector b
you're not helping
wispy mango
???
tender marsh
wispy mango
issue is i need the procedure to obtain (b1,b2)... that's why i said calculate...
scarlet peak
yes, i know that. compute (1,sqrt3) . (b1,b2), algebraically
wispy mango
through a system of equations yes i already know that that's the first thing i said
where one equation is cos(theta) = b1 · sqrt3·b2 / 2
the other is what?
where do you get that other equation from
scarlet peak
thats not how the dot product works
(x1,y1).(x2,y2) = x1x2+y1y2
the equation now youve edited is correct
what do you know about the magnitude of (b1,b2)
wispy mango
still got 2 unknown values, i need another equation to fill out the equation system
literally nothing
wispy mango
its a unit vector which means sqrt (b1^2, b2^2) = 1
scarlet peak
yes
wispy mango
if i said it's a unit vector it's because i know what it means
i'm looking for the method to solve it
not for the basics
i literally dont know where to start, i have 2 unknown values which i require a system of equations for
scarlet peak
you have your 2 equations now...
wispy mango
???
scarlet peak
your two equations:
wispy mango
how am i going to find the value of either through that
devout snowBOT
devout snowBOT
Available help channel!
tepid shadow
I am struggling with some logarithmic differentiation over here. I need to find the derivative of y = cos(x^x). I have already taken the log of both sides of my equation, and got ln(cos(x^x)) on the right side.
Is there a way to expand this anymore, or no? (If not I am hella stuck)
devout snowBOT
I am struggling with some logarithmic differentiation over here. I need to find ...
upper schooner
My guess is that the intention is you use logarithmic differentiation to differentiate the x^x, then once you know that, chain rule?
tepid shadow
can I do that separately first, then take the result and plop it back in (in place of x^x), then use the chain rule?
upper schooner
Yea that's perfectly fine to do, e.g. let y=cos(u), u = x^x then work with that
The latter is the one you'd use logarithmic differentiation on
tepid shadow
okay sounds good. Thank you so much, I really appreciate your help!
I'll try that here and see where it takes me
upper schooner
No worries, at least that's the way it would make sense to me 
tepid shadow
okay, this feels promising.....but my brain has also turned to putty here recently lol
looks kinda, almost, sorta not trash?
upper schooner
looks kinda, almost, sorta not trash?
agreed, buutttt, why this?
My personal advice is to have used u here rather than y...
tepid shadow
Gotta write it in terms of x, just looking at my previous examples I have done, looks like we substitute y back in to write it as a function of x
upper schooner
As we already have another y somewhere else, and, if you write it as du/dx...
...all you have to do is put that here!
tepid shadow
This is why I am thinking what I have is correct:
this is one of the solutions to past questions:
heres another one with the strange substitution:
so I am thinking this form is what they would be looking for
upper schooner
You're close, but at any point did you think of differentiating the cos?
tepid shadow
oh balls
I think you are right
I am def missing something
I did differentiate it, but did nothing with it lol
upper schooner
I did differentiate it, but did nothing with it lol
Yep, think of the chain rule for that one
tepid shadow
okay, there we go, finished off the chain rule there and then substituted y back in
(also apologies for my absolute trash hand writing here lol, its been a day)
upper schooner
Don't think there should be a cos here...
Let me give you a hint: what is the derivative of x^x?
tepid shadow
but for all the solutions, they are just plugging that starting equation y = (someStuff) back in, which is where that cos came from. That matches the idea for the other solutions too, no?
upper schooner
but for all the solutions, they are just plugging that starting equation y = (so...
Yes, but, you should be doing that when it comes to differentiating x^x
upper schooner
Yea that's perfectly fine to do, e.g. let y=cos(u), u = x^x then work with that
That's why I said to use u here
tepid shadow
Let me give you a hint: what is the derivative of x^x?
according to what I have: y(ln x+1). But not a lot of confidence in that lol
tepid shadow
Yes, but, you should be doing that when it comes to differentiating x^x
okay, I think I am picking up what you are putting down
upper schooner
My personal advice is to have used u here rather than y...
(+ here )
upper schooner
according to what I have: y(ln x+1). But not a lot of confidence in that lol
Yea, that y is not the same as the original y 😉
tepid shadow
oh ffs, I was not picking up what you were putting down. I am an idiot haha
upper schooner
oh ffs, I was not picking up what you were putting down. I am an idiot haha
Hahah I think this is a deliberate question to try and trip people up, to catch as many people out as possible(!)
tepid shadow
upper schooner
Some will fail at the first hurdle, and others will make mistakes in chain rule/differentiating x^x
tepid shadow
yeah I def agree. This one is very different from the examples that we were given
tepid shadow
this has gotta be less trash than the last one, right?
upper schooner
There we go, that's the derivative of x^x here!
tepid shadow
also again, thank you so much @upper schooner. I could kiss you right now haha
tepid shadow
There we go, that's the derivative of x^x here!
yeah my dumbass was totally looking at the wrong y
upper schooner
Awww, you're making me blush
upper schooner
yeah my dumbass was totally looking at the wrong y
Yea, listen to my bars next time 😂
tepid shadow
Here, take a cat pic as a token of my appreciation:
tepid shadow
Yea, listen to my bars next time 😂
Yeah I gotta do a better job of reading lol
upper schooner
Awww I'm feeling sooo special right now 
Now, let's put it all together...
This should be the easy part!
tepid shadow
Whattya mean? I thought that was put together. The circled part at the top should be the result of the chain rule, which used the logarithmic differentiation to get the derivative of x^x, no?
that is all put together isn't it?
upper schooner
that is all put together isn't it?
For the derivative of x^x, but remember, that's not it...
upper schooner
I am struggling with some logarithmic differentiation over here. I need to find ...
Check your original q
upper schooner
...all you have to do is put that here!
And the mention of chain rule
upper schooner
Oh I've seen your answer nvm! Maybe I need to read 😂
tepid shadow
oh ok, thank F. I was so confused for a sec there haha
upper schooner
Should teach me to read everything 🤦♀️
tepid shadow
My emotions went all the way up, came all the way down, and then went all the way back up hahaha
upper schooner
My emotions went all the way up, came all the way down, and then went all the wa...
Hahah that's my bad there, sorry about that! 
Could you find it in your heart to forgive me 💜
tepid shadow
All good! Thanks again for all your help, you the real MVP!
Already forgiven and forgotten
upper schooner
All good! Thanks again for all your help, you the real MVP!
Hahah no worries, it's all good 💜
My pleasure to be of assistance!
tepid shadow
I'll let you go though, and open this channel back up for the next poor soul fighting math
.close
silver sand
(Calculus Question) If you are given a graph of a function, but no formula, how can you find the second derivative at a specified point?
devout snowBOT
(Calculus Question) If you are given a graph of a function, but no formula, how ...
silver sand
For example, on this graph, my value at f(n) is 0, and the slope at f(n) appears to be 1. f(n) is not a local max or minimum, no concavity changes at f(n), but the function does cross the x axis at n
silver sand
I dont believe we've studied this method so i dont think its the intended answer
supple knot
can you show the original question
devout snowBOT
@silver sand Has your question been resolved?
restive river
Can Someone Help with This?
devout snowBOT
Can Someone Help with This?
granite owl
Finding x?
restive river
Yes, But you also have to find the Derivative of the Question (y’ on the Table), and then Use that to make a Variation Table and find the Relative Extreme Values, Then You have to Graph It
Hello? @granite owl
granite owl
Hello? <@326509168280469507>
Uh i didnt get derivative yet so srry
restive river
Oh, Okay, It’s Fine
<@&286206848099549185> Can You Help me With the Problem?
Come On, Someone, Please Help Me, <@&286206848099549185>
supple knot
Yes, But you also have to find the Derivative of the Question (y’ on the Table),...
show your work so far
restive river
Well, I Have to Find the Derivative First, But I Can’t, Because I Would use the Power Rule, But everything is multiplied by 1/4, Which Makes it more Complicated
supple knot
$\frac{d}{dx} [af(x)] = a\frac{d}{dx} f(x)$
woven radishBOT
riemann
supple knot
**riemann**
here, a is a constant. like 2, 3.5, 99, 0.25
supple knot
<@261933205387477002> Can I Get some Help?
do you have a table like this in your book?
supple knot
what examples have you done then?
restive river
All of Them, It’s Just That They Teach by Repetition and Expect you to Remember Everything, They don’t Teach it like a Regular Math Teacher Do
@supple knot And the Thing is, I am only in 8th Grade
So, It’s a Little Hard
supple knot
Yes, But you also have to find the Derivative of the Question (y’ on the Table),...
i mean specifically what derivatives have you done before?
supple knot
do you have a table like this in your book?
these are the most common derivative rules that's widely taught
supple knot
supple knot
do you have a table like this in your book?
i don't know what you want then. 2 and 3 here are the minimum you need to do your problem
if you haven't done them, read that link or just accept it as fact
restive river
Yeah, I Know
So, I have Done Derivatives with Algebraic, Trig, and Exponential Functions
@supple knot Is that Impressive for an 8th Grader?
supple knot
i'm not here to judge impressive or not.
restive river
Wdyt?
supple knot
So, I have Done Derivatives with Algebraic, Trig, and Exponential Functions
then what's so hard about power rule?
restive river
It’s Not Hard, It’s Very Easy, Just That, What am I Supposed to do with the 1/4?
supple knot
do you have a table like this in your book?
use 2. here
supple knot
Can Someone Help with This?
f(x) = stuff in parentheses
restive river
Oh, I See, Thanks a Lot Man
Okay, So Then how do I Create a Variation Table?
I actually Think, I Get It
Okay, Then
.close
devout snowBOT
devout snowBOT
Available help channel!
sage socket
e^{2x}-\left(e\right)^x-72=0
devout snowBOT
e^{2x}-\left(e\right)^x-72=0
sage socket
didn't work
dense jay
$e^{2x}-\left(e\right)^x-72=0$
woven radishBOT
Azo
sage socket
oh
ty
So I have a question about this problem. I got as far as substituting e^x for u and getting 9 and -8
dense jay
yup, then you have u=e^x so x=ln(u)
sage socket
Before I substitute anything back, is -8 a problem? If so, why?
dense jay
cannot take logs of negative number
sage socket
yup, then you have u=e^x so x=ln(u)
That's the natural log right?
dense jay
yeah
sage socket
cannot take logs of negative number
That's right! I knew I was forgetting something
ty
that make sense
sage socket
yup, then you have u=e^x so x=ln(u)
I will have to look up natural logs again, but you're saying I can rewrite u=e^x as the natural log, where x=ln(u)
sage socket
ln(u)=ln(e^x)=xln(e)=x
so, would the solution be x = ln(9) ?
dense jay
yeah thats the only solution
sage socket
yeah thats the only solution
How do we know that 9 is a solution again?
dense jay
wdym?
sage socket
I understand the relationship with u = e^x and x = ln(u)
oh
umm
I think I'm missing why we take the natural log
IIRC, for problems like this I would just sub what I got for u back into the original problem and go from there.
dense jay
i mean, you could take the log of any number, could take log base 20 if you wanted and the answers would be numerically identical, its just when working with e, log base e (ln) gives the cleanest answers
sage socket
ok
okay
So here's my thought. Why can't I just return the 9 back into the original equation and go from there?
I remember doing that in the past
sage socket
Yes
dense jay
so you mean to let x=9?
bleak sun
The solution isnt x=9
sage socket
wouldn't 9 replace e^x ?
bleak sun
so, would the solution be x = ln(9) ?
.
dense jay
yes
dense jay
sorry, you can do that to check but it doesnt give the solutions for x
you have to reverse your substitution to get your x
dense jay
ln(u)=ln(e^x)=xln(e)=x
like here
sage socket
sorry, you can do that to check but it doesnt give the solutions for x
Maybe that's what I'm misremembering
dense jay
yeah, that only lets you check that you have solutions for e^x that satisfy the equation
dense jay
yeah but you have to be mindful of when you get a solution like e^x=-8, as e^x>=0 for all x
sage socket
gotcha
I wrote that down
I remember that now
In blue ink, this is where I left off.
dense jay
yeah thats fine
just state that e^x>0 so people know why you excluded a solution, when you do a test they generally expect some kind of justification
sage socket
yeah
I always try to explain my steps
but here I didn't really
There's usually more written words lol
anyway
what is step 8 here then?
dense jay
there is none
dense jay
just leave it like that
sage socket
yeah yeah
My professor isn't gonna let us have a calc on the exam. So I hope that answer is fine.
dense jay
yeah, it would be weird if they wanted a non-exact answer in this case
sage socket
an exact answer is just one that hasn't been rounded right?
dense jay
yeah
dense jay
go for it
sage socket
yeah 9 also works
sage socket
then take a log of base 9 of each side
so for the lhs,(1/81)^x, if I were to take the log of base 9 for this, how does that work again?>
dense jay
Wrong picture ha
sage socket
ooof
woven radishBOT
dense jay
there we go
sage socket
ok ok
so the first step was to take the log of base 9 of everything on the lhs and the rhs
dense jay
yeah
sage socket
next, you use some property of exponents to bring x to the front (I think this is also a property of logs?)
dense jay
after seperating the LHS log yeah, its log(x^a)=alog(x)
dense jay
which line?
dense jay
ah, the -x becomes -2x because i treated the 81 as 9^2. the -log(243) i used a calculator, and on the RHS i just took out the power -(-3x-1)
the additional (-) flips the fraction inside the log
then its just using that log_a(a)=1
sage socket
ah, the -x becomes -2x because i treated the 81 as 9^2. the -log(243) i used a c...
is there a way to get to line 4 without a calculator ?>
dense jay
hm, i mean yes, everything except the exact value of the log243 is easy. log243=log9+log27 = log9+log3+log9 = 2log9+0.5log9 = 2+0.5 = 2.5
not too tricky
just requires a bit of seperating
sage socket
ok ok
oh wait
I meant line 3
err
no no it was 4
yeah
cool
for line 3, did you use the power rule?
dense jay
yeah
dense jay
(1/81)^x=((81)^-1)^x=81^-x
sage socket
5/2?
dense jay
logs are only negative if the x in log(x) is less than 1
dense jay
hm, i mean yes, everything except the exact value of the log243 is easy. log243=...
this
sage socket
ooo
dense jay
,w graph ln(x)
woven radishBOT
sage socket
I guess I was confused cause you wrote - 5/2
dense jay
ah thats just because its not log243 its -log243
( it was originally log(1/243)), i just skipped that step
sage socket
(1/81)^x=((81)^-1)^x=81^-x
but isn't 1/243 also 1/243 ^1?
wouldn't the same thing happen?
dense jay
yeah? thats what did happen
dense jay
1/243 = 243^-1
sage socket
I'm brain farting
dense jay
so +log(1/243)=-log(243)
sage socket
oh! I figured it out. So it's technically -log(1/243) from the original problem
dense jay
huh
dense jay
on the LHS im pretty much using that log(a/b)= loga-logb which is from log(a/b)=loga+log(1/b)=loga-logb
a=(1/81)^x , b=243
sage socket
why is b not 1 / 243?
sage socket
ah, the -x becomes -2x because i treated the 81 as 9^2. the -log(243) i used a c...
Is treating 81 as 9^2 necessary?
dense jay
if you didnt youd just get that log81=2 anyway
treating it as 9^2 just makes it simpler while youre keeping things as logs
since log9=1
doesnt particularly matter overall
sage socket
I see I see
dense jay
no worries
sage socket
are you a math major?
dense jay
maths and physics yeah
dense jay
cya👋
sage socket
.close
devout snowBOT
devout snowBOT
Available help channel!
normal oyster
Prove if x is rational and x-y is irrational then y is irrational
how do i go about making the proof for this?
low holly
contradiction
normal oyster
so if x is rational and x-y is irrational than y is irrational can be proven by contradiction
so the contrapositive would be if x is irrational and x-y is rational then y is rational
and if thats the case we could assume
z is an element of Q
x is an element of R
and y is an element of Q
low holly
that is not the contrapositive
the contrapositive is: if y is rational, then x is irrational or x-y is rational
low holly
i recommend just doing a proof by contradiction
normal oyster
so is what i said a contradiction? and should i solve it that way
low holly
Prove if x is rational and x-y is irrational then y is irrational
how do i go a...
assume, from here, that y is rational
why can’t the premises hold?
normal oyster
i never learned it that way
low holly
if you want to prove p implies q by contradiction, you assume p and the negation of q and derive a contradiction
normal oyster
that makes sense
what about if i were to do the problem if x eQ and x-y eR then y eR?
could i do
if x is irrational and xy is rational then y is irrational?
or is that a bad contrapositive again?
low holly
that is not a contrapositive
let’s call the original statement p implies q
the contrapositive would be: not q implies not p
you are trying to prove: not p implies not q
by the way, your antecedent is incorrect
you have not negated p correctly because the and would become an or
normal oyster
ok
i go figure got this right doing it this way, maybe i just got a pass cause the rest of my solution was pretty good
im glad i asked about this before jumping into it
ok so lets return to the main topic at hand
normal oyster
if you want to prove p implies q by contradiction, you assume p and the negation...
here
low holly
so what are your assumptions according to this?
normal oyster
by contradiction if x is rational and x-y is irrational then y is rational
low holly
there’s no implication
you have as true the statements p and not q
so you assume: x is rational, x-y is irrational, and y is rational
now use these to derive a contradiction
normal oyster
there’s no implication
what does this mean?
low holly
you should assume p and not q rather than p implies not q
normal oyster
im confused its the same thing?
also the way my brain works we kind of have p f and q
where p is x is rational
f is x-y is irrational
and q is y is rational
assume x is rational, x-y is irrational and y is rational
and if thats the case we could assume
z is an element of Q
x is an element of R
and y is an element of Q
x-y=z
y=x-z
im getting stuck here
low holly
what is z?
low holly
so you assume: x is rational, x-y is irrational, and y is rational
put simply, this set of statements contains a self-contradiction because x and y being rational means that x-y must be rational too
normal oyster
yah i was re reading and seeing that
ohhh if x and y are both rational in assumptions
i could substitute x for y or y for x and show that rational =rational
so rational -rational cant be irrational
is that a good approach?
assume x is rational and y is rational than we can say because R = R that there exists solutions for x and y if they are both rational that x=y
so x-y=irrational
x-x is irrational
and 0 is not irrational
or y-y is irrational
and 0 is not irrational
is this right?
low holly
sorry dude don't have the energy to help you right now
normal oyster
tomorrow?
low holly
Prove if x is rational and x-y is irrational then y is irrational
how do i go a...
basically the argument is that y cannot be rational because if it were, then x-y would be too
low holly
just write x or y as a/b and c/d respectively
normal oyster
that makes sense
low holly
nothing more complicated than that?
not at all
low holly
i was under the impression that you already knew how to show that the difference of two rational numbers was rational
devout snowBOT
devout snowBOT
Available help channel!
coral tulip
devout snowBOT
https://media.discordapp.net/attachments/269573202018041856/1052971561654702110/...
coral tulip
In this question r ≠ ±1
My question is that why only value of x for which D = 0 are the values for which r=±1
Can't it be like For D>0 there exists some values of x for which r=±1 then we have to exclude that
devout snowBOT
@coral tulip Has your question been resolved?
coral tulip
<@&286206848099549185>
coral tulip
<@&286206848099549185>
tender marsh
Prove if x is rational and x-y is irrational then y is irrational
how do i go a...
You have a number than can be written as an integer/integer - a number that can't be written as an integer/integer
So x can be written as a/b where a and b are integers
(a/b) - irrational number
I'm thinking
normal oyster
Well I made the assumption that x and y were rational and showed that rational -rational = irrational is a contradiction
But that question I closed 🙂
I think anagh needs help
devout snowBOT
@coral tulip Has your question been resolved?
devout snowBOT
@coral tulip Has your question been resolved?
devout snowBOT
devout snowBOT
Available help channel!
wicked perch
Hey, would a function that has a terrace point be considered a strictly increasing function
devout snowBOT
Hey, would a function that has a terrace point be considered a strictly increasi...
restive river
potentially, yes
devout snowBOT
@wicked perch Has your question been resolved?
wicked perch
@restive river why potentially? if we assume that there are no other places where f'(x)=0
restive river
if its only a single inflection point, then yes
viral rapids
Consider the function f(x)=(9x-b)^2/(x^2+25) where b is some constant
(a) Solve, in terms of b, for x when f(x)=0
(b) What is the sign of the numerator? What is the sign of the denominator? Explain your reasoning.
(c) Solve for the solution set of f(x)<0
devout snowBOT
Consider the function f(x)=(9x-b)^2/(x^2+25) where b is some constant
(a) Solve,...
viral rapids
guys
for part b
i said the numerator is positive when x≠b/9 and 0 when x=b/9 and the denominator is always positive is this right
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tame palm
i said the numerator is positive when x≠b/9 and 0 when x=b/9 and the denominator...
Looks good.
narrow thunder
say we take the Wronskian and we get out something like sinx, would the solution set be linearly independent or dependent
or would you specify by intervals
devout snowBOT
say we take the Wronskian and we get out something like sinx, would the solution...
narrow thunder
this question is for the subject of differential equations
lusty sapphire
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proven parcel
Can someone help me solve this
devout snowBOT
Can someone help me solve this
gleaming socket
Factor
proven parcel
How
gleaming socket
See what you can take common
royal tiger
whats the common factor between 5 and -30
gleaming socket
What did you get?
proven parcel
Wdym what did I get
main gull
What is the equation you have after you factored?
proven parcel
I have no idea how to set it up
main gull
What is that factored expression?
proven parcel
Idk
main gull
In my example, 5x + 10, you stated that you can factor out a 5, what does it mean to factor out 5?
proven parcel
You can take 5 from both numbers?
main gull
So if you do that, what would the expression be?
proven parcel
X+2?
proven parcel
How do I write it
main gull
Here's my suggestion
https://www.youtube.com/watch?v=gRfr-5xGtzc&ab_channel=BrianMcLogan
This concept is the same for your problem
forest geode
!help
knotty bolt
What is this
can you be more specific?
could be 7 vertices
forest geode
I didnt add the question
The question was
What is the mathematical name given to angle ABCDEFG
uncut crow
angle ABCDEFG?
forest geode
ye
radiant drift
devout snowBOT
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devout snowBOT
@forest geode Has your question been resolved?
keen sigil
I have a quick question I'm right now doing geometry and it says that since we are splitting the segment into a ratio of 2:3 is becomes 5 but then when you turn it into a fraction is becomes 2/5 I'm confused because where did the 2 come from in 2/5
devout snowBOT
I have a quick question I'm right now doing geometry and it says that since we a...
ember palm
2 part out of the whole part
grizzled yew
If I have 2 dogs and 3 cats, the ratio of dogs to cats is 2:3. But the ratio of dogs to animals is 2:5.
ember palm
Imagine you and your friend are sharing pizza
ember palm
If I have 2 dogs and 3 cats, the ratio of dogs to cats is 2:3. But the ratio of ...
Yeahh
ember palm
Imagine you and your friend are sharing pizza
You said you will take 3 slices and he said he will take 2
So the ratio is 3:2
Total slices are 5
But how much are you taking individually?
3 slices out of 5 ryt?
3/5
keen sigil
Oh so I'm guessing that 3:5 would also be 3/8
ember palm
No worries you will get 1 slice only tho
ember palm
Oh so I'm guessing that 3:5 would also be 3/8
Yep
fossil moth
how can I solve this?
devout snowBOT
how can I solve this?
wooden veldt
Consider |w|²
devout snowBOT
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fossil moth
<@&286206848099549185>
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plush osprey
to be closed does a set need all boundary points
devout snowBOT
to be closed does a set need all boundary points
devout snowBOT
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karmic umbra
to be closed does a set need all boundary points
i think so
charred grove
I have been looking at the solution for 10 minutes and still don't understand how they got the inverse matrix
devout snowBOT
I have been looking at the solution for 10 minutes and still don't understand ho...
charred grove
torn vessel
a - b = [a b c] * [1 -1 0]^T
right?
mighty crane
Can someone help me with this q?
devout snowBOT
Can someone help me with this q?
mighty crane
This is what I’ve done so far but I don’t understand the qs and how to get the answer in a qs like this
<@&286206848099549185>
devout snowBOT
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mighty crane
<@&286206848099549185>
devout snowBOT
@mighty crane Has your question been resolved?
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@mighty crane Has your question been resolved?
spice island
Hello, i'm supposed to solve this problem using similarity but I can't find any
outer root
Hello, i'm supposed to solve this problem using similarity but I can't find any
well ADC and ACB are similar for example
spice island
well ADC and ACB are similar for example
how can you know that?
outer root
they both have a 90° angle and they both have the same angle at A
so basically the angles are identical
spice island
yeah
outer root
you know how to proceed now?
spice island
you know how to proceed now?
no I managed to figure out the base length but not anything else
outer root
what did you get for the base length
outer root
how did you get that
spice island
well I took the larger side / smaller side on the similar triangles
and then I got to Y = 6
outer root
AD / AC = AC / AB
thats how you get AB
yeah that works too but she/he is supposed to use similarity
spice island
I don't understand how I can solve this
hushed wraith
When like something is a scaled up or down version of something else
The ratios of the lengths of corresponding sides are equal
outer root
I don't understand how I can solve this
Well you know that ACD and ABC are similar
spice island
but I should be able to take AB/AC
hushed wraith
Well u will need to find CD using Pythagoras theorem I
spice island
Well u will need to find CD using Pythagoras theorem I
I am supposed so solve this by using simularity only
hushed wraith
Once u have CD, use similarity of ACD and ABC
Mm
Okay then still u can use similarity of the same triangles
Ig
spice island
am I able to use the bisector theorem here?
hushed wraith
U can find AB right?
spice island
yes
hushed wraith
Okay then use similarity of ACD and BCD
spice island
Okay then use similarity of ACD and BCD
what? how can I do that
this is what I have so far
outer root
yeah 5 is right
outer root
just pythagoras theorem
spice island
I can't use that I need to solve this using similarity
I just got the ratio by dividing the large side over small side
I don't have the measurement for cb or the corresponding measure for cd
so can't use that
spice island
Ur gonna need to solve some simultaneous eqns
how
spice island
And try to write some eqns
I have no idea how to do that could you explain how
hushed wraith
Okay so using similarity of ACd and ABC, what can u write
spice island
Okay so using similarity of ACd and ABC, what can u write
ab/ac = ac/ad
but that just gets me the length of the base
hushed wraith
Put in the values u already know
spice island
I already got the length
hushed wraith
Yeah that's not all u can writr
spice island
ok what more can I do]
spice island
yes but I don't know either the big side or the small side
spice island
yeah I can do AB/AC = CB/CD
hushed wraith
Gimme a min imma login with my computer
spice island
okay
hushed wraith
now use similarity of ABC and BCD
what can u write using that
spice island
oh I didn't know they were similar aswell
hushed wraith
do u see why they are
hushed wraith
what can u write using that
?
spice island
okay I got the length of cd aswell now but answer was still wrong
hushed wraith
what did u get
hushed wraith
I took 5/CB = CB/3.2
one of these must be CD ?
spice island
okay I realized I made a misscalculation
hushed wraith
or
spice island
one of these must be CD ?
why
hushed wraith
uhm no maybe not
spice island
okay mb it was because of my misscalculation I took 2cb instaed of CB^2
I got the answer now
hushed wraith
ah
devout snowBOT
devout snowBOT
Available help channel!
pulsar ermine
devout snowBOT
pulsar ermine
Could someone annotate to give me an idea of how it’s forming the volume about the y-axis?
mortal moth
devout snowBOT
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jaunty seal
can someone explain the answer of this, i got 14.7cm but my answer in class is 14.14 which is correct apparently, i divided the radius so 5/2 and got 2.5, from there i just did the pythagoras theorem
devout snowBOT
can someone explain the answer of this, i got 14.7cm but my answer in class is 1...
winter patrol
,rotate
woven radishBOT
winter patrol
why are you dividing radius by 2
jaunty seal
because the line points at all of the line
idk if it makes sense
but i thought the entire radius is 5
how do i know if it’s 5 for the entire radius or just that part is 5
winter patrol
do you know the definition of radius
jaunty seal
no tbh
winter patrol
have you ever done anything with circles before
jaunty seal
idk
winter patrol
do you know what a circle is
jaunty seal
do you know what a circle is
is this a joke
winter patrol
no
jaunty seal
⭕️
winter patrol
if you don't understand a term, in this case radius
the first thing you should do is look it up instead of trying to go into the problem blind and make poor assumptions about it
jaunty seal
are you going to explain what a radius is or just scold me for not knowing it
winter patrol
i'm scolding you for not looking it up
jaunty seal
A radius is a straight line from the centre to the circumference of a circular or sphere.
i’ll write that down
winter patrol
yes, it can also refer to the distance of such a line
jaunty seal
so a radius is from like the side of a circle to the center
winter patrol
line and/or its distance from the circumference of a circle to the centre
winter patrol
yes
devout snowBOT
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Available help channel!
stuck cipher
Hi, I'm dumb and need help. I can't even think of where to start. The solutions available to me, but if anybody could just point me in a direction, that'd be great.
devout snowBOT
Hi, I'm dumb and need help. I can't even think of where to start. The solutions ...
stuck cipher
P 37
twin needle
Looks like discrete fourier transform
pulsar ermine
How does this apply to y=x in any interval?
devout snowBOT
How does this apply to y=x in any interval?
devout snowBOT
devout snowBOT
Available help channel!
fringe olive
do you calculate area by adding all the sides or multiplying the sides
thorny lintel
do you calculate area by adding all the sides or multiplying the sides
for area you multiply the length and width.
A = L x W
Adding all the sides would be perimeter
P = 2(l) + 2(w)
Or
P = l + l + W + W
of course it somewhat depends on the shape you have
if it circle related then it's different
devout snowBOT
thorny lintel
np :>
devout snowBOT
Available help channel!
agile fiber
Hey
quaint citrus
A and B are angles ?
quaint citrus
Recognize that points on the same horizontal line segment will have the same y value and points on the same vertical line segment will have the same x value
agile fiber
yes but they are not horizontal to OX
trail garnet
you don't have enough information to solve for the coordinates of A and B here
agile fiber
are you sure?
clear phoenix
if u have the length of the sides i think u can use the distance formula
trail garnet
you can calculate the middle of the segment made by C and D, and place a circle centered at the middle passing by C and D
(C and D are the points you know the coordinates of)
and then place A anywhere else on the circle, B will then be on the diametrically opposite point, and ABCD will always form a rectangle
agile fiber
yes but its rectangle you cant create a circle where A, B, C and D are on the circle
if i get your idea
trail garnet
well to be honest at first I wasn't sure if it the coordinates of 2 points was enough to determine the rectangle but it didn't feel like it was enough
so I tried to draw it out a bit
agile fiber
AC, DC - radius; we can find them easily, we know AD and then?
so i know all sides of the triangle ACD
and the coordinates A and C
trail garnet
how did I obtain this you mean?
Since the diagonals of a rectangle intersect in their middle, I first found the middle, then I knew that for any line passing by that middle, if I constructed two points on that line that are both a distance AC from the middle, I'll get a rectangle
agile fiber
i didnt get how to get D if we know every side of the Triangle ACD and we know the coordinates of A and C
trail garnet
what do you mean we know every side of the triangle ACD?
agile fiber
look we can find the length of AB and divide it by 2 so we get AC
Coordinates of C is just the center of AB
trail garnet
yes
trail garnet
in length, yes
agile fiber
- i know both sides of the reactangle
agile fiber
if i know the side lengths of the rectangle
.
trail garnet
ohh
agile fiber
so i know what AD is
ancient marlin
Hi, what does my teacher mean with R x R
devout snowBOT
Hi, what does my teacher mean with R x R
tall knoll
Hi, what does my teacher mean with R x R
It means both x and y are real numbers
ancient marlin
Cant he just put a single R for that
stone stump
R is the set of real numbers
RxR is the cartesian product of R with itself and contains of all tuples (x,y) with x,y real numbers
the set your teacher wrote down is a subset of RxR
ancient marlin
the set your teacher wrote down is a subset of RxR
because a singular R would not have 2 real numbers in the brackets and just 1?
So that (x,y) would be be a possibility in one of the tuples that RxR creates?
.close
fresh cloak
I just need to know x and y
devout snowBOT
I just need to know x and y
stone stump
what happens if you subtract 2 times the first equation from the second
fresh cloak
uh
devout snowBOT
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fresh cloak
<@&286206848099549185>
mellow panther
Just follow what the previous comment said and you'll get the answer
devout snowBOT
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sharp dagger
Limit -x+ln(2 ℯ^(x)+1)
x--> +inf
devout snowBOT
Limit -x+ln(2 ℯ^(x)+1)
x--> +inf
sharp dagger
prove it = ln(2)
restive river
[
\lim_{x \to \infty} -x + \ln(2e^{x}+1)
]?
woven radishBOT
♡LexQa♡
sharp dagger
\[
\lim_{x \to \infty} -x + \ln(2e^{x}+1)
\]?
Yea
neon folio
+inf
hybrid snow
Well it's to positive infinity
So you can literally just use properties of infinite limits
And erase low order terms
Lemme type this out
sharp dagger
K
hybrid snow
$$\begin{align*}
\lim_{x\to\infty} (-x + \ln(2e^x+1)) &\equiv \lim_{x\to\infty} (-x + \ln(2e^x)) \
&= \lim_{x\to\infty} (-x + x + \ln(2)) \
&= \ln(2)
\end{align*}$$
woven radishBOT
Umbraleviathan
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
sharp dagger
$$\begin{align*}
\lim_{x\to\infty} (-x + \ln(2e^x+1)) &\equiv \lim_{x\to\infty} ...
Where did the +1 go?
- How could we add x
restive river
I believe you can rewrite it as follows
sharp dagger
I believe you can rewrite it as follows
How?
arctic field
patiently waiting for lex's latex
sharp dagger
patiently waiting for lex's latex
?
restive river
Actually nvm I tried to do something but it didn't work out 
arctic field
sharp dagger
Actually nvm I tried to do something but it didn't work out <:cryingLaughing:583...
Lol
arctic field
guess i'll type it up
restive river
I tried to say t = 2e^x +1
sharp dagger
Ok
restive river
It does seem close tho
sharp dagger
I tried to say t = 2e^x +1
LOL, I swear I've done the same thing but it didn't work
arctic field
unfortunately its a different trick for this one
restive river
lex trying to copy my tricks
Of course
restive river
unfortunately its a different trick for this one
Always down for more introspection from snow 
sharp dagger
unfortunately its a different trick for this one
But why did not work🤔
restive river
Also I give up trying to copy your tricks, I will just rationalise them until doing them makes sense
sharp dagger
Let's see
arctic field
too may brackets
restive river
Oh actually that's not too snow-level crazy, phew
woven radishBOT
restive river
But yeah use that it is the proper way all in all
I just turned ooga booga mode and tried to think of something crazy
sharp dagger
arctic field
i think t = 2e^x + 1 might work but like all it does is transfer the log to the other term
sharp dagger
It looks very simple now 
restive river
i think t = 2e^x + 1 might work but like all it does is transfer the log to the ...
Yeah
Also it still goes to infinity yeah?
arctic field
oh hm theres another way
restive river
Yes I figured
woven radishBOT
restive river
OMG I JUST THOUGHT OF THAT TOO
LET'S GOO 😵💫
Okay I'm done feeling a bit happy about high school limits
woven radishBOT
xeus
sharp dagger
When t =2e^x +1?
arctic field
well it doesnt help
its not an incorrect substitution per se it just doesnt help you make progress
sharp dagger
Oh ok
restive river
Yeah probably a good idea is to recognize when it is necessary to substitute to begin with