💔
#help-43
kind viper
work out this angle using either the sine law or the cosine law (you have enough data for either one; no preference on execution difficulty either)
then work out angle ACD as 52 minus that
then find the area of ACD as 1/2 * AC * AD * sin(ACD)
fossil sage
ah I see
kind viper
i mean thats a good general tip for life in general
not merely for math problems
but in math it is especially strong
if you have to make an assumption, state it outright
compact pewterBOT
compact pewterBOT
Available help channel!
remote cosmos
The prompt is to solve for x.
6^2x + 10 = 88
compact pewterBOT
The prompt is to solve for x.
6^2x + 10 = 88
remote cosmos
8 already isolated 6^2x to get 6^2x = 78
I now am confused what to do after moving into logarithmic form.
toxic cipher
8 already isolated 6^2x to get 6^2x = 78
Just to be absolutely clear, you want $6^2x = 78$, as is shown in the image?
boreal girderBOT
toxic cipher
or do you want $6^{2x} = 78$
boreal girderBOT
remote cosmos
This one.
remote cosmos
Have you come up with log in the first place?
Yes.
azure vault
I now am confused what to do after moving into logarithmic form.
well what happened when you did as you said
what's the result of "moving into logarithmic form"
remote cosmos
This is what I got. I might have done it wrong.
Because I forgot how to work with logs.
azure vault
no that's correct
peak talon
Looks very decent
azure vault
so $2x = \log_6 78$
boreal girderBOT
Raphaelisius Maximus MMIII
remote cosmos
So what do I do from here? I don’t remember how to get past this.
toxic cipher
This is what I got. I might have done it wrong.
divide both sides by 2
remote cosmos
**Raphaelisius Maximus MMIII**
Yes. That is what I got.
remote cosmos
so how do you get x
But how would I simplify that?
thorny urchin
log_6(78) is just some number
solve the same way as you would something like
2p = 15
remote cosmos
? I think I wrote it wrong. Looks unfamiliar.
wispy knot
by the properties of exponentiation
$6^{2x}=(6^x)^2$.
then we take the square root of both sides and get
$|6^x|=\sqrt{78}$.
obviously 6 to no power is negative, so we can take the absolute value away: $6^x=\sqrt{78}$.
from here using logarithms we get $x=\log_6(\sqrt{78})$.
boreal girderBOT
@wispy knot
azure vault
? I think I wrote it wrong. Looks unfamiliar.
that's just the correct form
if you want to "simplify" log_6(78), just try to write 78 = 6^... * ...
peak talon
? I think I wrote it wrong. Looks unfamiliar.
That's all you need
azure vault
that's the best you'll do
toxic cipher
? I think I wrote it wrong. Looks unfamiliar.
absolutely nothing wrong with writing it like this
azure vault
But my answer choices (it’s multiple choice) are numbers.
and what are they?
wispy knot
<@711992718729019452>
\sqrt{78} unfortunately can’t be simplified any further, as it’s 2 times 3 times 13
toxic cipher
But my answer choices (it’s multiple choice) are numbers.
plug it into your calculator
azure vault
plug it into your calculator
most likely
remote cosmos
and what are they?
2.1784, 2.5286, 0.946, 1.2158
azure vault
2.1784, 2.5286, 0.946, 1.2158
yep... calculator time or approx
wispy knot
,w log_6(sqrt(78))
boreal girderBOT
remote cosmos
plug it into your calculator
How do I change the 10 to a 6? In my calculator the number next to the log is always a 10.
wispy knot
2.1784, 2.5286, 0.946, 1.2158
the last one
azure vault
don't think so
toxic cipher
How do I change the 10 to a 6? In my calculator the number next to the log is al...
use your change of base rule
wispy knot
How do I change the 10 to a 6? In my calculator the number next to the log is al...
there probably is a log_x(y) button somewhere
remote cosmos
How did you get the result part?
toxic cipher
there probably is a log_x(y) button somewhere
nah some calculators only have ln or lg/log
near jay
Sorry typos
remote cosmos
That is what I am worried about.
azure vault
look at the given answers
remote cosmos
nah some calculators only have ln or lg/log
Yes.
remote cosmos
use your change of base rule (x2)
Huh?
boreal girderBOT
@wispy knot
near jay
$\log_{6}(\sqrt{78})=\frac{\log(\sqrt{78})}{\log(6)}$
wispy knot
$$
\log_6(\sqrt{78}) = {\ln \sqrt{78} \over \ln 6}
$$
remote cosmos
How did I forget??
boreal girderBOT
@wispy knot
wispy knot
anyway it’s 1.2158
near jay
I’m abismally slow on a phone
toxic cipher
holy latex fail
wispy knot
\log not log
\sin not sin
\cot not cot
…
boreal girderBOT
BBMaths
wispy knot
`\log` not `log`
`\sin` not `sin`
`\cot` not `cot`
…
the tex math mode mantra
near jay
I know that
wispy knot
dw it’s alright
near jay
This was more of a comparison of latex on phone vs computer than a log question
remote cosmos
How does natural log work?
near jay
I have to wrestle against autocorrect and the text selection placing me not where I want to be
near jay
How does natural log work?
Natural log is log in base e=2.71828…
toxic cipher
How does natural log work?
if we have
$$\ln a = x$$
then
$$e^x = a$$
boreal girderBOT
remote cosmos
if we have
$$\ln a = x$$
then
$$e^x = a$$
And e is roughly 2.71?
wispy knot
How does natural log work?
$
\ln a = \log_e \left(a\right)
$, where $e \approx 2.71$.
toxic cipher
yup
boreal girderBOT
@wispy knot
wispy knot
<@711992718729019452>
why is the e so small
toxic cipher
why is the e so small
looks perfectly sized to me imo
cursive harbor
Cuz they used it as a subscript
toxic cipher
So in my case 2x = ln13?
how did you get this?
remote cosmos
how did you get this?
I took this number.
near jay
Ln(78)/ln(6)
remote cosmos
I used the thing someone sent above to make it look like this.
near jay
That’s as far as you can go really unless you use powers, but then it’s a bit of a mess
wispy knot
I used the thing someone sent above to make it look like this.
${\ln a \over \ln b} \ne \ln {a \over b}$
boreal girderBOT
@wispy knot
wispy knot
<@711992718729019452>
as much as we’d like it to
remote cosmos
${\ln a \over \ln b} \ne \ln {a \over b}$
I know.
But if I take the natural log of 78 and divide that by the natural log of 6, that works, no?
thorny urchin
yes
toxic cipher
I used the thing someone sent above to make it look like this.
this is correct tho
wispy knot
i assume you got $2x=\ln 13$ by $2x = \ln {78 \over 6}$, which is wrong
boreal girderBOT
@wispy knot
boreal girderBOT
@wispy knot
remote cosmos
right, that’s equal to $\log_6 78$, not $\ln 13$
Yeah. I figured.
But I took ln78 which is roughly 4.35.
And divided it by ln6 which is roughly 2.43.
Divided that by 2.
1.21
wispy knot
,w ln(78)/ln(6)
boreal girderBOT
wispy knot
,w 2.4315/2
boreal girderBOT
toxic cipher
just plug this $\frac{\ln 78}{\ln 6} \div 2$ straight into your calculator, dont bother with rounding off
boreal girderBOT
wispy knot
yeah, the answer is 1.2158
remote cosmos
just plug this $\frac{\ln 78}{\ln 6} \div 2$ straight into your calculator, dont...
I rounded off for the sake of typing. lol not in my calculator. I promise.
I just took the raw answer for calculations.
toxic cipher
I rounded off for the sake of typing. lol not in my calculator. I promise.
ah sure okay
remote cosmos
ah sure okay
See?
toxic cipher
dang bro your calculator got a screenshot function
remote cosmos
dang bro your calculator got a screenshot function
Yeah. And SD card port to download and save data.
compact pewterBOT
@remote cosmos Has your question been resolved?
forest token
compact pewterBOT
compact pewterBOT
@forest token Has your question been resolved?
forest token
<@&286206848099549185>
rotund sphinx
Pretty sure you’re just supposed to inspect these antiderivatives
paper anchor
take cosx as t for the first one
forest token
Pretty sure you’re just supposed to inspect these antiderivatives
oh numerator and denominator separately?
rotund sphinx
Yes
forest token
oh ok let me try that
how do i integrate
(xsinx-1)e^cos x dx
oh wait i see something
oh ok
yes i got it now
paper anchor
Damn I think I see the answer, it's pretty neat unless I'm messing something (doing it in my head so that's probable)
forest token
thank u
forest token
Damn I think I see the answer, it's pretty neat unless I'm messing something (do...
yeah no i got it..its just i thought we had to make the numerator in a way
such that the integral from the denominator cancels
forest token
from here the left handside part is easily integrable
the right hand side
(xsinx-1)e^cos x
xe^cos x sin x - e^cos x
paper anchor
Yes
paper anchor
Yoooo, I saw IBP for -e^cosx, that works too ig
compact pewterBOT
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Available help channel!
storm sky
Can anyone help me with calculating this limite
compact pewterBOT
Can anyone help me with calculating this limite
safe olive
,rotate
boreal girderBOT
strange ermine
Start by making a substitution, i.e. u = x - 5
storm sky
yeah?
near jay
Try it, see what you get
misty quail
you can first put the sin function outside the limit
strange ermine
It isn't mandatory, but it will clear everything out, and possibly letting you see what to do next
storm sky
so I replace the x with u + 5 right?
near jay
you can first put the sin function outside the limit
You can do this but there are reasons not to unless you’re skilled with extended reals
storm sky
You can do this but there are reasons not to unless you’re skilled with extended...
I tried now replacing x with u+5 and I'll see how it goes
I got stuck here
near jay
I was thinking we were going to do substitution at the first step
near jay
Start by making a substitution, i.e. u = x - 5
^
It’s usually better to keep sqrt out of denominator
storm sky
i study maths in french so I might have didnt understood it correctly
can I do the limite of whats inside the sin alone then if i got a real number i just calculate its sin
?
strange ermine
If x → 5, what does α approach?
Remember that α = x - 5
strange ermine
Yup
storm sky
yeah yeah it makes more sense like tht
strange ermine
And also, $x\sqrt{x - 1} \neq u+5\sqrt{u+4}$
boreal girderBOT
Alberto Z.
storm sky
its should be, $(u+5)/sqrt{u+5}$
boreal girderBOT
AymanRhz
boreal girderBOT
AymanRhz
strange ermine
Rather, $x\sqrt{x - 1} = ( u+5) \sqrt{u+4}$
boreal girderBOT
Alberto Z.
storm sky
oh yeaah, thankss
should I multiply then divide by $(((u + 5)\sqrt{u+4}) + 2\pi)$
actual
boreal girderBOT
AymanRhz
storm sky
they told me to calculate the limite not to proov it equals something
strange ermine
Because I get indeterminate
storm sky
its sin (infinity)
strange ermine
they told me to calculate the limite not to proov it equals something
Yeah sure but have you been given the result?
strange ermine
its sin (infinity)
Yeah exactly
storm sky
Yeah exactly
yeah thats where i got stuck
storm sky
Yeah sure but have you been given the result?
nope
strange ermine
Yeah exactly
But that's something weird (not per se) but because it's very rare in the school problems
strange ermine
yeah thats where i got stuck
You cannot go further, because $\nexists \lim_{t\to \infty} \sin t$
boreal girderBOT
Alberto Z.
storm sky
just to let you know what its exactly, we were studying that two functions f and g, I is the intervalle of f and J the intervalle of g
if f(I) C g and lim x -> x0 f(x) = l , then we'll have lim g(f(x)) when x approaches x0 = g(l)
I'm sorry my english isnt the best but its just the propriety we were given and this exercice should be an application for this
boreal girderBOT
AymanRhz
novel narwhal
Can someone please tell me where to start. I tried to make a system using a = sqrt(5 - x) and b = sqrt(5 + x), but i just got a fourth degree polynomial.
compact pewterBOT
Can someone please tell me where to start. I tried to make a system using a = sq...
sonic oasis
Hello, my name is Henry Whitmore
red musk
Idt u need to ask twin
sonic oasis
The expression inside the square root must be non-negative
boreal girderBOT
Henry Whitmore
novel narwhal
this is competition math, i know the basic stuff
sonic oasis
Okay.
Since the fundamentals are clear to you, let’s proceed to the actual solving step. Squaring both sides gives
boreal girderBOT
Henry Whitmore
novel narwhal
ok
sonic oasis
This simplifies to
boreal girderBOT
Henry Whitmore
sonic oasis
Yes?
sonic oasis
But couldn't the numbers be replaced directly?
Can you explain why?
compact pewterBOT
compact pewterBOT
Available help channel!
quartz yoke
How do I do this? Been on this question for 30 minutes, tops.
compact pewterBOT
How do I do this? Been on this question for 30 minutes, tops.
wheat pasture
Were you given any introduction as to how you would solve these types of questions?
verbal kiln
How do I do this? Been on this question for 30 minutes, tops.
Dude, anybody can recognize that this is an unsolved problem In mathematics. This is like trying to solve the Riemann hypothesis.
quartz yoke
Apologies, but I've turned to this discord as my last hope and planned on completeing my homework that my teacher gave.
quartz yoke
Were you given any introduction as to how you would solve these types of questio...
No, absolutely not.
verbal kiln
I understand. If you manage to solve this, please do tell!
quartz yoke
By your reaction, it seems like this is impossible, I'll have to close this question, thank you very much.
.close
compact pewterBOT
compact pewterBOT
Available help channel!
bleak garnet
in what ways could i write this to a proposition?
compact pewterBOT
in what ways could i write this to a proposition?
bleak garnet
rn im thinking of V(x) and T(y)
where V is x is a valid argument and T is y has true conclusion
but uh im not too sure what to do from now on
slate sand
What’s the difference between an argument and a conclusion
bleak garnet
What’s the difference between an argument and a conclusion
uh
idk how to answer that sry
slate sand
Then how do you know what you answer with
ripe ether
in what ways could i write this to a proposition?
this feels awfully vague whats the full question (like the general discription before the part a,b,c) and what class is this?
slate sand
You don’t even know what kind of answer you’re supposed to give
Oh actually I don’t think that’s too important
Yeah I think so, do show the first few parts and also what you might try
bleak garnet
this feels awfully vague whats the full question (like the general discription b...
its completely unrelated im just asking this to understand more of how to translate english to like logical propositions
near jay
Actually nvm
It would be better if you asked all of these questions in the same channel
That way we don’t have to get back up to where we were
bleak garnet
😭 its not the same question
near jay
But they are related to the previous
ripe ether
its completely unrelated im just asking this to understand more of how to transl...
there is this thing from first order logic that says "provable implies consistent" Ie, if a set of axioms T gives a proof of a statement phi, then T along with phi will not run into contradictions, and any universe for which T is satisfied will satisfy phi.
but this is a rather involved theorem in logic
weak cobalt
there is this thing from first order logic that says "provable implies consisten...
I don't think that's the right context here
bleak garnet
from V(x) and T(x),where V is x is a valid argument and T is y has true conclusion, for all x (V(x) --> T(x))
weak cobalt
This is just basic translation of sentences into propositions
bleak garnet
thats what i have rn
ripe ether
I don't think that's the right context here
honestly i have no idea what the context is, mb
weak cobalt
from V(x) and T(x),where V is x is a valid argument and T is y has true conclusi...
Well, that's all you need
bleak garnet
honestly i have no idea what the context is, mb<:sully:651816820122189834>
sorry 😭
just translate it to logical propositions is all i was asking
bleak garnet
Well, that's all you need
ah okay tyty
weak cobalt
Why do you think there is more to it?
bleak garnet
sorry for being unclear i need to work on my math language lol
bleak garnet
Why do you think there is more to it?
it uh
i felt like
i couldve added like
2 variables etc
weak cobalt
bleak garnet
;like a third predicate
weak cobalt
Let's rephrase the statement
weak cobalt
Any valid argument has a true conclusion
ripe ether
how is V(x) defined?
weak cobalt
This is like "any [ argument that is valid ] is an [argument that has a true conclusion ]"
You could technically bother with a "conclusion" predicate, but there is really no need at all since it's only used once
ripe ether
so in the op's context, x is "arguments" and V(x) is the verification for validity of arguments, and T(x) outputs the conclusion of argument?
weak cobalt
The "any" is just a "for all", and the "is an" is just an implication
bleak garnet
You could technically bother with a "conclusion" predicate, but there is really ...
ah okay okay
weak cobalt
so in the op's context, x is "arguments" and V(x) is the verification for valid...
More like T(x) is whether the argument has a true conclusion
(I guess you could say "whether the argument's conclusion is true", since presumably all arguments have a conclusion)
bleak garnet
yeah i think i got it
but ngl i need to learn latex this is so
yeah
hard to write LMAO
ripe ether
(I guess you could say "whether the argument's conclusion is true", since presum...
well the conclusion of ops question assumes all correct argument has a conclusion so
weak cobalt
$\forall x (V(x) \implies T(x))$
boreal girderBOT
Nel
ripe ether
highkey overthought it
ur not alone 
weak cobalt
\forall, \exists, \land, \lor, \implies, \iff basically all you need to write these things
ripe ether
\neg too?
slate sand
\neg
weak cobalt
Right yeah
rigid perch
or \lnot
weak cobalt
$\neg \lnot$
ripe ether
$\lnot$
slate sand
$\neg.\neg$
boreal girderBOT
frosst
ripe ether
$\rnot$
boreal girderBOT
qwertytrewq
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
rigid perch
,, \land \lor \lnot \ \wedge \vee \neg
boreal girderBOT
κλαοδ ☁ (cloud)
ripe ether
oh shoot i thought the l in lnot stands for left
rigid perch
there are two versions of each, one for logical contexts and one for not. unlike the other two the distinction between \lnot and \neg is more nebulous
slate sand
logic
ripe ether
there are two versions of each, one for logical contexts and one for not. unlike...
is there prove symbol in the package?
slate sand
Yeah id say \neg for negation makes total sense in logic so I’m not fussed about that
calm trout
don't forget to distribute the \land
weak cobalt
$\vdash$ ?
boreal girderBOT
Nel
ripe ether
$\vdash$ ?
i mean logic version like lnot
weak cobalt
I think that's the logic version
ripe ether
they got everything but had to not rename vdash
near jay
Fun fact: did you know you can do $\today$
boreal girderBOT
BBMaths
weak cobalt
You also have $\therefore$ and $\because$
boreal girderBOT
Nel
ripe ether
I think that's the logic version
like how they have \models for Vdash i think
weak cobalt
$\models$
boreal girderBOT
Nel
weak cobalt
I'm out of my depth here
rigid perch
this is all of the redundant symbol names included in base TeX (from the TeXbook)
ripe ether
$\models \vDash$
boreal girderBOT
qwertytrewq
rotund sphinx
near jay
$\forall \land (channels) it \owns \to me$
boreal girderBOT
BBMaths
chilly basalt
If we close this one there won't be any left!
Technically we can since $s \times \infty$ is no longer here
boreal girderBOT
🌙 ЅκψΑиdΝιɡħτ
rotund sphinx
I would like to see all help closed
near jay
I’ve been trying for the last few hours now
chilly basalt
<#903430334681608232> <:happy:908558103992225822>
You could have posted it in hlounge while you decides to be a fun police/ jk
compact pewterBOT
If you are done with this channel, please mark your problem as solved by typing .close
chilly basalt
.solved
compact pewterBOT
chilly basalt
I think our opportunity is gone now
Nah, #help-18
compact pewterBOT
Available help channel!
untold haven
Need help solving this limit
compact pewterBOT
Need help solving this limit
bronze bison
first we have to check if the limit is of any of the 7 indeterminate forms by substitution of the limit value
by substitution it yields that it does NOT correlate to any of the indeterminate forms
so we have to evaluate the limit as it is tending to 3 FROM THE LEFT and as it is tending to 3 FROM THE RIGHT
try doing that rq and send what you get
untold haven
got this, I don't know if it's right or not
bronze bison
got this, I don't know if it's right or not
sweet
now as x gets closer and closer to "3" from both ends,
approaching from the left will yield a VERY LARGE positive value
which is +inf
approaching from the right will yield a VERY LARGE negative value
which is -inf
for the limit to exist at that point, both the left hand and right hand limits must exist, and must be equal to each other
which in this case they're not
so clearly, the limit doesnt exist
bronze bison
alrighty
untold haven
.solved
compact pewterBOT
compact pewterBOT
Available help channel!
cloud warren
How do I find the value of x in x^3 - 3x^2 + 6= 0 without graphing
compact pewterBOT
How do I find the value of x in x^3 - 3x^2 + 6= 0 without graphing
cloud warren
algebraically
quartz yoke
How do I find the value of x in x^3 - 3x^2 + 6= 0 without graphing
U know anything about the log with base e which is ln
cloud warren
yh
quartz yoke
Ouch sorry not sure why I saw e (just solved em I'm sorry my brain 😭)
No no I'll tell u somehow else to solve that
We got x power 3
cloud warren
yh
quartz yoke
So the method we used that apparently fails here
Is u check for which x = 0
Since it's power 3 u got 3 solutions
And we literally just try -2 -1 0 1 -2
If = 0
The uhm let's call it f can be divided by x - (the number)
Our or my main issue here is to find that number
I'll get up and try
pastel epoch
How do I find the value of x in x^3 - 3x^2 + 6= 0 without graphing
Do you know how to use Cardano's formula? Or can you use it?
cloud warren
Do you know how to use Cardano's formula? Or can you use it?
what is that
pastel epoch
it is the formula for the solutions of cubic polynomials
molten coral
yea this root is nasty idk how else you get it
if RRT doesnt find it i dont think random guessing is gonna help
upper bane
probably overkill for this. you can try maybe depressing the cubic?
cloud warren
it is the formula for the solutions of cubic polynomials
elaborate pls
quartz yoke
Unfortunately I checked all the 3 solutions are not natural numbers that's why
I'll check up Kitsu's method
pastel epoch
elaborate pls
alr!
pastel epoch
Unfortunately I checked all the 3 solutions are not natural numbers that's why
...
pls check it
upper bane
!occupied
compact pewterBOT
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pastel epoch
Umhh.. I just used the discriminant and it tells me there are two conjugate complex roots and one real one.. I'm not sure if that's correct 
compact pewterBOT
@cloud warren Has your question been resolved?
pastel epoch
Hi again, sorry for the delay
I'm not sure if they are correct.
To be honest, I stopped working with polynomials a few months ago 
peak talon
wtf, this is intimidating
pastel epoch
That was my reaction too he
cloud warren
I'm not sure if they are correct.
wooh, how did you find it
pastel epoch
Cardano's formula (or at least what I remember about it)
compact pewterBOT
cloud warren
.reopen
shy stump
Hey how are you doing that
vocal idol
do i just send in my question here
compact pewterBOT
do i just send in my question here
hazy sky
Id say babb but i might be wrong cuz i haven’t done that in like 2 years
hazy sky
Oh greatt
compact pewterBOT
Available help channel!
molten grotto
compact pewterBOT
molten grotto
How do i do it?
brazen quiver
Do you know the probability of getting at least one spade?
molten grotto
Do you know the probability of getting at least one spade?
I guess yeah
I will minus it from 1?
For not getting any spade+ace
brazen quiver
Well, let's focus on just spade for now
compact pewterBOT
compact pewterBOT
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rose goblet
tf c go
rose goblet
oh its because its the complimentary solution so it adds nothing i think
is that it?
jagged blade
oh its because its the complimentary solution so it adds nothing i think
Let's say you included them
You'd get:
jagged blade
$- e^t (\frac{1}{2} \ln(1 + t^2) + c_{3}) + t e^t (\tan^{-1}(t) + c_{4})$
boreal girderBOT
💪 Greenie The Power Queenie 💪
jagged blade
Which if we expand it out, we get:
$- \frac{1}{2} e^t \ln(1 + t^2) - c_{3} e^t + t e^t \tan^{-1}(t) + c_{4} t e^t$
boreal girderBOT
💪 Greenie The Power Queenie 💪
rose goblet
yea ok its the complimentary solution
jagged blade
yea ok its the complimentary solution
More like it can be absorbed into it, but yeah
rose goblet
More like it can be absorbed into it, but yeah
how can it be absorbed
c3 e^t is a function not a constant
jagged blade
c3 e^t is a function not a constant
You have a complimentary function of the form c1 e^t + c2 t e^t
rose goblet
yea ok
jagged blade
c1 is just an arbitary constant
rose goblet
but how do we know it doesnt affect it
like that it would still be a solution without the complimentary one
jagged blade
Wdym?
rose goblet
why can it be removed
jagged blade
You have a complimentary function of the form c1 e^t + c2 t e^t
c1 is an arbitary constant
Which means it can take any value
c1 - c3 is also an arbitrary constant
We could give the new arbitary constant a new name, like c5
rose goblet
no no that wasnt the question
c1 there isnt from the solution
its from the complimentary solution
which there is a theorem for
my question was in Yp(t)
where the c of the integrals go
why if Yp(t) + c1y1+ c2y2 is a solution then Yp(t) is one basically is what im asking
jagged blade
Because the c1y1 + c2y2 gives 0 when you put it into the differential equation
rose goblet
it doesnt?
jagged blade
Why doesn't it?
rose goblet
complementary solution is the general solution to the homogeneous ode
rose goblet
b(t) y
jagged blade
What this means is that if we put y1 into this differential equation, we get 0
And the same for y2
rose goblet
in the homogeneous version yes
that is true
whats that gotta do with the non homogeneous
jagged blade
So let's say the non-homogeneous equation has a solution yp
rose goblet
So let's say the non-homogeneous equation has a solution yp
we call it Yp(t)
p as in particular
yes and we find that Yp(t) = f(t) + yc(t) is a particular solution
now the page here proceeds to say this means also Yp(t) = f(t) is a solution
jagged blade
If we have y1 + y2 + yp, and we put them in, we get:
d^2/dt^2(y1 + y2 + yp) + a(t) d/dt(y1 + y2 + yp) + b(t) (y1 + y2 + yp) = f(t)
d^2/dt^2(y1) + a(t) d/dt(y1) + b(t) y1 + d^2/dt^2(y2) + a(t) d/dt(y2) + b(t) y2 + d^2/dt^2(yp) + a(t) d/dt(yp) + b(t) yp = f(t)
0 + 0 + d^2/dt^2(yp) + a(t) d/dt(yp) + b(t) yp = f(t)
d^2/dt^2(yp) + a(t) d/dt(yp) + b(t) yp = f(t)
So adding on c y1 + c y2 onto our function makes no difference
rose goblet
ok ty
flint wing
not sure how to start
compact pewterBOT
not sure how to start
kind viper
inclusion-exclusion tbh.
let S_1 = {f : A -> A s.t. f(1)=1}, S_2 = {f : A -> A s.t. f(2)=2} and so on.
apply incl-excl on these 5 sets
flint wing
let S_1 = {f : A -> A s.t. f(1)=1}, S_2 = {f : A -> A s.t. f(2)=2} and so on.
but that would take a long time wouldnt it
is there an easier way?
kind viper
not that long a time
strange ermine
Isn't this problem something you've already gone over with Renato? Or at least very similar
@kind viper
kind viper
if you realize theres a lot of symmetry in the problem
winged dock
I guess we can apply derrangement
kind viper
Isn't this problem something you've already gone over with Renato? Or at least v...
tfw selfping
oh
uhhhhhh i dont remember if i went over it with renato
probably not
flint wing
I guess we can apply derrangement
thats like the !n thing right
winged dock
Yes
We can find the ones where none are at the right place
That will save some time
flint wing
We can find the ones where none are at the right place
so thats !5 ?
kind viper
5! - !5
flint wing
5! - !5
so 5! is the total number of permutations and the !5 is the number of permutations where none stay at the same place but why do we subtract?
winged dock
I havent seen this notation
kind viper
so 5! is the total number of permutations and the !5 is the number of permutatio...
you want the ones where something stays in place.
strange ermine
probably not
My bad, you're right. It was Mtt and not you.
By the way, it was this #help-48 message
compact pewterBOT
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undone topaz
$(\frac{x}{y^{2}}+\frac{y}{x^{2}}\ge \frac{1}{x}+\frac{1}{y})$
compact pewterBOT
$(\frac{x}{y^{2}}+\frac{y}{x^{2}}\ge \frac{1}{x}+\frac{1}{y})$
boreal girderBOT
prya༊*·˚
undone topaz
can anybody help me prove this >
kind crane
what's x and y
undone topaz
real positive numbers
$(\frac{\left(x+y\right)\cdot \left(x-y\right)^{2}}{y^{2}x^{2}}\ge 0)$
boreal girderBOT
prya༊*·˚
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
undone topaz
this is what i got so far
strong cloak
you already solved it
strong cloak
prya༊\*·˚
Compile Error! Click the <:errors:504266556054962196> reaction for mor...
this is trivially true
undone topaz
but how do i express it mathematically
undone topaz
x+y positive, x-y)^2 positive and (xy)^2 positive ?
pallid rune
each term that's multiplied and divided are all positive
undone topaz
and that's it ?
pallid rune
x+y positive, x-y)^2 positive and (xy)^2 positive ?
squares of real numbers are always positive, yes
undone topaz
alright
pallid rune
and that's it ?
yes
undone topaz
thank you very much
pallid rune
if you don't have any more questions abt this problem, you can .close 
compact pewterBOT
pallid rune
you too!
compact pewterBOT
Available help channel!
steady needle
i need help i dunno how to start
compact pewterBOT
i need help i dunno how to start
steady needle
or what to do
gilded kayak
what notation is this
mortal nimbus
Coords
steady needle
wym by notation
gilded kayak
notation is a system of how you write stuff
so this is a 3d space and those are x y z coords?
steady needle
u mean first x then y then z
gilded kayak
howd you check diagonals so fast without d wth
gilded kayak
visually, see the difference between A and B, and apply a negative value of that exact change onto C, it should land on a new point D
so, if B is 1left, 1up from A, D is 1right, 1down from C
formally idk
tulip spear
i need help i dunno how to start
this had a standard result too for the remaining coordinate, but the basic idea behind it was that bisection occurs at the intersection point of the diagonal
steady needle
how do i know if i needa do a+c/2 = b+d/2 or a+b/2 = c+d/2 ...
gilded kayak
when a parallelogram is named abcd, the vertices are joined from a to b to c to d
that means a is at the opposite of c
gilded kayak
sure thats one way to do it, the vectors on lhs and rhs will be the same vector that points to the center of the parallelogram
but thats not what others meant when they say diagonals bisect each other
gilded kayak
sure thats one way to do it, the vectors on lhs and rhs will be the same vector ...
actually this is indeed related to diagonals bisecting each other but it doesnt appear in an intuitive and visual way so
i would see that AB = CD, so i let vectorAB = -vectorCD
steady needle
😭
gilded kayak
what else do you need?
gilded kayak
ykw
solving this doesnt necessarily require the use of vectors
gilded kayak
do i put only c negativ or the sum of c and d
negative sign in front of a vector means that this vector that points to the opposite direction
vectorOC and vectorOD can both contain just positive numbers really
gilded kayak
vectorAB is not made from adding the coordinates of A and B
gilded kayak
is that right ? i never divided an vector idk how to do all that
i prefer you use this method if youre that confused
how much did you learn about vectors
steady needle
not much
this is the task we did the last time in schoon before the homework
its translated with chatgpt so idk if its accurate
and this
thats mostly it with vectors
oh wait now i know whats wrong
im so dumb
holy
steady needle
vectorAB is not made from adding the coordinates of A and B
now its correct right ?
gilded kayak
vectorCD points in the opposite direction of AB, your vectorCD should be (-6, -2, -6)
steady needle
vectorCD points in the opposite direction of AB, your vectorCD should be (-6, -2...
if this is wrong now ill just quit this stupid hw
gilded kayak
looks correct
steady needle
what does the 0 means in 0A or 0B
gilded kayak
origin, the point O, at (0,0)
since ur working with vectors i thought id do it the traditional way
gilded kayak
is that right ? i never divided an vector idk how to do all that
i followed up on this method
if you just do A+C, youre better off treating it as a coordinates question, with (A+C)/2 being the midpoint of AC
if you do it like me, then (vectorOA + vectorOC)/2 would be a vector pointing from O to the midpoint of AC
compact pewterBOT
steady needle
.reopen
compact pewterBOT
✅
steady needle
i followed up on this method
wait 1 last question how do i check now if its an rhombus
gilded kayak
does lineAB have the same length as lineBC?
steady needle
does lineAB have the same length as lineBC?
no, so it isnt an rhombus?
gilded kayak
right, its not a rhombus, because a rhombus needs all 4 sides equal…
gilded kayak
yeah
steady needle
oh perfect
gilded kayak
but since you are given c, just use c why not
gilded kayak
what i just did, did not involve vectors, no need to overthink stuff
steady needle
oh ye i got an question about this, where did the 1/2 go on both sides ?
like u jsut vanished them
steady needle
and u did that because if u would did /2 it just would be the half of the diagonal and not the full length
gilded kayak
more like, if i did /2, then lhs is 2,2,2, and rhs is some ugly abomination that slows me down
i need x,y,z, i dont need x/2, y/2, z/2
steady needle
but then why did u wrote a+c/2 = b+d/2 and not just a+c=b+d
gilded kayak
because thats how you wrote it, and it also shows that the thought behind it was about bisecting diagonals
vivid wedge
Why does variance even matter in statistics
compact pewterBOT
Why does variance even matter in statistics
gilded kayak
Why does variance even matter in statistics
say, someone uses statistics to investigate an aging population
city A and B have the same mean, at 40, but the var of A is low, meaning most people are around that age, few teens and kids and elderly; while the var of B is high, theres more teens.
youd know that city A is gonna face a crisis in 25 years where they cant retire
vivid wedge
say, someone uses statistics to investigate an aging population
city A and B ha...
And does the interpretation of the value of the variance depend on the mean
vivid wedge
Well yeah but I mean you would interpret something with a mean of 16 and a variance of 8 differently from something like a mean of 250 and a variance of 8
gilded kayak
uh that depends on context ofc
if its lifetime of a product, ofc id trust the ones with mean lifetime of 250 months over 16 months
if its lies spoken per person, then id trust the community with 16 avg lies than 250 lies
vivid wedge
Okay fair enough
I'm just not entirely sure how to interpret a value of variance though
vivid wedge
Is there any reason to use it over standard deviation ?
gilded kayak
high variance of product quality ratings, youd have to replace your factory belt
uh
with var, you can do some math on it and analyse ur dataset further
vivid wedge
Oh okay so SD is kinda just an application of variance then?
gilded kayak
yeah
what i told you about interpreting var, they all apply to sd, and usually sd is given
var is just convenient in formulas
you gotta convert sd to var to do that
vivid wedge
Okay I'm just doing AP Statistics so I'm not really sure how much I'll use it
vivid wedge
Oh well I'm in high school lol
vivid wedge
AP is like taking a college class in high school and you take a test at the end of the year on everything to determine whether you get credit for it or not
gilded kayak
i just didnt study stats in high school, i have courses starting from uni which doesnt have a complete syllabus for the entire subject
compact pewterBOT
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rancid quarry
Hiiii
rancid quarry
Can someone help me? with my math?😭🙏
paper kindle
what is it?
rancid quarry
Percentage
cursive harbor
Hi, you can just post your question! Someone will help you
rancid quarry
Sureeeeeeeeeeeeeeeeeeee tysm>_<
paper kindle
im so bad at that sorry i cant help
rancid quarry
oh
dw
Xavier is still here:D
In 2012 there was an election for the president of France. The two candidates were Monsieur Hollande and Monsieur Sarkozy. These are the numbers of votes cast in two regions of France. In the paragraph- Candidate | M Hollande | M Sarkozy Paris | 60459 | 447499 Corsica | 70148 | 88799 Find the percentage of the regional vote for M Hollande in: a. Paris b. Corsica.
It's gonna be ez for you
Here
rancid quarry
Oki
cursive harbor
There are 100 candies in total
You take 20 of them
What percentage of the candies did you take
rancid quarry
80%?
cursive harbor
Why do you think so
rancid quarry
U need percentage right?
cursive harbor
Yes
rancid quarry
so 20/100 x 100%?
cursive harbor
Good, and how much is that
cursive harbor
Good
karmic stirrup
Good, and how much is that
20/100 x 100**%**
cursive harbor
Now let's do the same in the problem
rancid quarry
Sure:D
rancid quarry
Yea
cursive harbor
And then do the same calculation
cursive harbor
It says just 60459
rancid quarry
OMG wrong
rancid quarry
M Hollande
Paris 560459
cursive harbor
Now what's the total in Paris
cursive harbor
M Hollande
Paris 560459
Ah gonna trust you on this
rancid quarry
SOO
Percentage for Hollande?
right?
560459/ the total
560459 + 447499
the total
it's
560459/1007858
boreal girderBOT
Result:
0.55603408078511
,calc 560459+447499
boreal girderBOT
Result:
1.007958e+6
You've added them wrong
cursive harbor
Just use a calculator are you not allowed to
rancid quarry
it is allow
cursive harbor
Just use it then
cursive harbor
Well it's the same calculation just with different numbers
cursive harbor
Ok
rancid quarry
the answer is = 44.13% right?
cursive harbor
,calc 70148/(70148+88799)
boreal girderBOT
Result:
0.44132949977036
Yeah
cursive harbor
Sure, feel free to post another question
rancid quarry
really?
cursive harbor
Yes
rancid quarry
it's 35.94% right?:D
cursive harbor
,calc 23/64
boreal girderBOT
Result:
0.359375
Yup
cursive harbor
No it's still tennis
rancid quarry
67.53%
cursive harbor
Read the table properly
cursive harbor
It's okay
rancid quarry
41/64 x 100
cursive harbor
Yes
cursive harbor
,calc 41/64
boreal girderBOT
Result:
0.640625
hehe:D
cursive harbor
Feel free to ask more questions, or to close the channel if you're done
rancid quarry
I'm already done
near jay
!done
compact pewterBOT
If you are done with this channel, please mark your problem as solved by typing .close
compact pewterBOT
near jay
I wish I had helpful
cursive harbor
You'll get there
near jay
How long did it take you until you got it like yesterday or something
chilly basalt
I wish I had helpful
You’re very helpful 🔥🔥
cursive harbor
How long did it take you until you got it like yesterday or something
I have no idea when I hit requirements lol
It had to be manually assigned to me
No clue why
compact pewterBOT
Available help channel!
turbid canopy
Lord help me
compact pewterBOT
Lord help me
turbid canopy
Question 5
Cant do this for the life of me
How tf do u simplify factorials man
shell horizon
,rotate
boreal girderBOT
shell horizon
How tf do u simplify factorials man
whatd you try and get
shell horizon
never cross product when dealing with factorials lol
turbid canopy
Oops
shell horizon
what is (r+1)!
?
shell horizon
no like what does the notation of factorial mean for (r+1)!
shell horizon
n!=n(n-1)(n-2)...
turbid canopy
Well yeah r is contained in it
shell horizon
r!
turbid canopy
I just dont know hwo to express that
shell horizon
(r+1)r!
worn loom
(Aside, do you need to express the sum in terms of f(r) or just find a general closed form?)
turbid canopy
Uhhhhhhhh
Just general i think?? But obv u gotta use f(r) bc what other way is there
I have arrived here
Idk how id get to the general term of the series with this tho
shell horizon
Idk how id get to the general term of the series with this tho
you want to make it look similar to the expression in the sum, so you may write it in the form of f(r)
firstly its negative which isnt ideal
how would you change it?
compact pewterBOT
@turbid canopy Has your question been resolved?
turbid canopy
how would you change it?
Multiply by -1 no?
turbid canopy
How do u get to that n+2 in the denom
shell horizon
f(r)-f(r+1)=...
shell horizon
How do u get to that n+2 in the denom
r=...?
turbid canopy
Dunno..
shell horizon
you want to plug in a number into r such that it resembles the expression
("a number" which contains n)
turbid canopy
r = n - 1 ?
shell horizon
r = n - 1 ?
r=n+1
shell horizon
(r+1)r!=(r+1)(r)(r-1)...
boreal girderBOT
AkitoLite
shell horizon
it very much resembles $$\frac{n+1}{(n+2)!}$$
boreal girderBOT
AkitoLite
shell horizon
i mean just from looking youll see the substitution
shell horizon
Why can you just change r tho whaat
to make it look like the summ expression
turbid canopy
I thought u could only do that by multiplying or dividing
shell horizon
its similar to having 3 eqn with 3 variables
turbid canopy
I thought u could only do that by multiplying or dividing
Like with integrals
shell horizon
i mean
turbid canopy
You cant add anything but you can multiply outside