.close
#help-41
mint patio
amber waspBOT
amber waspBOT
Available help channel!
rich comet
How do I make this into the form in the question (ii)
amber waspBOT
How do I make this into the form in the question (ii)
rich comet
prev working but not rlly needed ig
rich comet
ohh u mean like rationalize ?
inland pulsar
Yeh
rich comet
ā3 x 1/ā2 ?
inland pulsar
Yes
rich comet
so then take out 1/2 ln(3/2)
inland pulsar
Do you see where this is going?
rich comet
ohh
amber waspBOT
amber waspBOT
Available help channel!
hazy whale
(4sqrtx + 5)^2
amber waspBOT
(4sqrtx + 5)^2
hazy whale
so i got 16x + 20x^1/2 + 20x^1/2 + 25
= 16x + 40x^1/2 + 25 right
but then we have to derive that so i got 16 + (40 * 1/2)x^-1/2
so 16 + 20x^-1/2
but someone else got 16 + 20/x
pallid canopy
,w expand (4 * sqrt(x) + 5)^2
grizzled pagodaBOT
pallid canopy
= 16x + 40x^1/2 + 25 right
this is right
inland pulsar
but someone else got 16 + 20/x
He is wrong
hazy whale
,w derive 16x + 40sqrtx
inland pulsar
Teamwork op
grizzled pagodaBOT
amber waspBOT
amber waspBOT
Available help channel!
rich comet
For (a) (i) why is it 40/800 instead of 40/(223+177+40)
amber waspBOT
For (a) (i) why is it 40/800 instead of 40/(223+177+40)
@rich comet Has your question been resolved?
weak zinc
For (a) (i) why is it 40/800 instead of 40/(223+177+40)
If the question were "a randomly chosen household in Shan has a poor broadband service", you'd be fine, but they're asking that out of everyone, you're both in Shan and also have poor broadband
wooden zenith
prev working but not rlly needed ig
ŁŁŲ§ ŁŁŲ“Ų
weak zinc
So out of everything here, rather than just the Shan households exclusively
amber waspBOT
amber waspBOT
Available help channel!
vapid schooner
how do i draw it? i dont get it
amber waspBOT
how do i draw it? i dont get it
vapid schooner
is this how
amber waspBOT
@vapid schooner Has your question been resolved?
shadow stump
remember that gauss' law says that the flux through a surface is equal to [ \frac{\sum Q}{\epsilon_0} ] where $\sum Q$ is the sum of all the charges contained inside the surface
grizzled pagodaBOT
cloud
fierce edge
if f(x) = 1/(x-1) then how does one tell whether f is a function or a relation?
fierce edge
Like is there notation for distinguishing between the two?
rancid raven
if f(x) = 1/(x-1) then how does one tell whether f is a function or a relation?
f(x) itself means function of x , f stand for function
rough trail
if f(x) = 1/(x-1) then how does one tell whether f is a function or a relation?
vertical line test or the presence of a Ā± when in y =... form
fierce edge
f(x) itself means function of x , f stand for function
I mean yeah but i appended that
they only said 1/(x-1)
shell osprey
i mean, something written in the form of an expression is most likely going to be a function unless it has something funky going on
y = 1/(x-1)
1/(x-1) is gonna be unique cuz that's numbers work and thus it's a function
shell osprey
vertical line test or the presence of a Ā± when in y =... form
this is like the only practical way you can make it not a function
fierce edge
y = 1/(x-1)
1/(x-1) is gonna be unique cuz that's numbers work and thus it's a f...
so you just guess?
iām thinking of not mapping x = 1 anywhere but keeping it in the domain
so itās now a relation, no?
rough trail
x = 1 is just an asymptote
shell osprey
nvm i guess you can
shell osprey
iām thinking of not mapping x = 1 anywhere but keeping it in the domain
Well, y isn't even in the expression so you can easily argue y would not be unique and thus it's a relation
fierce edge
Well, y isn't even in the expression so you can easily argue y would not be uniq...
okay what about y = 1/(x-1), but it can still be a relation over the extended reals right?
Okay i think if it was over R then itās surely a function right?
Because infinity isnāt an element of R
but since none of this was specified lol
Isnāt this just ambiguous
shell osprey
okay what about y = 1/(x-1), but it can still be a relation over the extended re...
I'm not familiar with extended reals 
fierce edge
wait itād be a function on the extended reals
fierce edge
I'm not familiar with extended reals <:thinkies:827642567775748163>
hmm, my question is like
canāt i just keep stuffs on my domain
without mapping it anywhere
no domain restriction is given so why should i conform to only applying whatever works?
rough trail
sorry but are you aware what a function is?
rough trail
no
fierce edge
?
rough trail
It can still be a function if it has an asymptote
fierce edge
every element of the domain is mapped to an output
^
itās a function if it excludes x = 1
fierce edge
itās not a function if a domain is not specified
fierce edge
mmmmmmmmmmmmmmmmmmmmmmmmm is right
Lol mmmmmmmm
rough trail
continuity is not a prerequisite for a relation to be a function.
rough trail
'every element of the domain is mapped to an output'
the output does not exist for x = 1
fierce edge
f(x) = 1/(x-1) is not a function on R
but it is a function on R excluding 1 because i canāt write \ for some reason
shell osprey
\{ cancels because { is symbol
fierce edge
shell osprey
use \\ to cancel the cancelling
fierce edge
okay thanks
rough trail
$f: R \rightarrow R, f(x) = 1/(x - 1)$ does not exist as a relation or a function, can't divide by 0
grizzled pagodaBOT
eththorn
rough trail
could've used frac and mathbb but excuse me
fierce edge
'every element of the domain is mapped to an output'
that answers your question
also exactly the same definition i wrote
rough trail
but 1/(x - 1) is always a function over its maximal domain
fierce edge
not that itās unique but yeah
rough trail
no, you literally cannot define 1/x for x = 0, it's not a relation or a function. It is always a function over its maximal domain
fierce edge
šbut you can though over the extended reals
but also i donāt see how this is related to my question
1/x is not a function on R because x = 0 is never mapped to anything
rough trail
your question is 'how do we know if it's a function and not a regular relation', yes? The answer is the vlt.
shell osprey
šbut you can though over the extended reals
i don't think you can over extended reals
divide by 0 is still divide by 0
rough trail
extended reals you still can't because it's still an indeterminate form
left and right limits aren't equal.
the thing is, it says 'every element of the domain must map to exactly one output' which is correct. This is because x-asymptotes can never be part of the domain, else the function is undefined. You can't have an x yielding no output, that's undefined. So no need to overthink, vertical line test works perfectly
fierce edge
the thing is, it says 'every element of the domain must map to exactly one outpu...
but you just said it was wrong
rough trail
it's wrong over the graph not the function
fierce edge
also yep i know vertical line test works um im just saying isnāt it ambiguous because i can call that whatever i want
i donāt have to construct it to be a function
over the extended complex
rough trail
elaborate
fierce edge
division by 0 is defined because of the riemann sphere thing
rough trail
maybe over the extended complex, I'm not familiar with those. Over the extended reals, no due to limit being indeterminate
fierce edge
anyway i think we agree on one more
1/x is not a function on R and the functionās maximal domain excludes x = 0
but i was asking why i canāt put x = 0 into the domain set
not map it anywhere
iām aware it canāt be mapped
but putting x = 0 into the set of the domain is not illegal by any chance
is it?
i can put anything into my set
rough trail
not strictly, unless it yields indeterminate form or undefined
fierce edge
nobody is stopping me because no restriction on the domain was defined
fierce edge
not strictly, unless it yields indeterminate form or undefined
wdym?
iām not mapping it anywhere though
why does it matter at all
if itās undefined or undetermined only matters if iām mapping it to an output
which iām not
rough trail
in that case you can yes
fierce edge
yeah so thatās what i meant above
fierce edge
iām thinking of not mapping x = 1 anywhere but keeping it in the domain
^^
all the way here
rough trail
You can also use a piecewise
fierce edge
so y = 1/(x-1) can be interpreted as a relation or a function
right?
itās ambiguous without
mentioning the domain
for the reason we just mentioned
rough trail
if you can find the notation then I guess technically yes
fierce edge
if it said for x not in \{1}
then yeah it is necessarily a function
also well all functions are relations
fierce edge
if you can find the notation then I guess technically yes
wdym?
fierce edge
also well all functions are relations
so if something doesnāt work u can always fall back on the general thing: a relation
but yeah this was given on a test
made by phdās so um
maybe im wrong
hence i asked
itās also i think a state exam
rough trail
well you can't just go f:R ā R, f(x) = 1/(x - 1) because that's inherently undefined, doesn't exist as a function OR a relation. You need something more clear, or you can make an assumption at the top.
just need to communicate the idea that you're mapping it to nothing for x = 1 instead of undefined
that is what I mean
fierce edge
that is what I mean
iām not constructing it
i wanted to argue that the question is ambiguous š
cuz i think it eas
since it never specified anything
rough trail
do you have the exact question?
fierce edge
nope, but the question isnāt the issue
rough trail
if it didn't specify a domain, you can definitely say it's ambiguous and explain your thinking
fierce edge
they just went y = 1/(x -1) and yeah something else
the something else is irrelevant ig
fierce edge
if it didn't specify a domain, you can definitely say it's ambiguous and explain...
hmm sure thanks
rough trail
I mean to some extent it's conventional to assume the maximal domain when nothing else is mentioned, but you can still argue.
fierce edge
hmmm fair enough
amber waspBOT
@fierce edge Has your question been resolved?
dusty field
I need help with finding the limit
amber waspBOT
I need help with finding the limit
idle light
can you post the question
dusty field
vestal gale
danggg these limit questions!
well i think it might not be as bad as it looks, recall that the limit as x -> infinity of 1/x^2 would be 0
so i think in problems like these a good first step is to try factoring out an x^2 from those polynomials, does it make sense when i say that?
dusty field
I use the formula b-q/2āa
vestal gale
im not sure about that, i think you want to factor out an x^2 from both radicals
so for example, 4x^2 - 3x - 1 = 1/x^2 (4 - 3/x - x^2)
tropic wadi
Is the solution -1/2
you've messed up the signs a little
dusty field
1/2
vestal gale
ah yes that's it, i messed up
vestal gale
this looks like one of those magical problems designed to bug students š if i said to multiply by the conjugate of the numerator on the top and bottom, would that make sense?
dusty field
Yeah
vestal gale
i think if you do that and simplify a bit you'll be able to solve it
dusty field
Is it 1/14
vestal gale
i think youre close, did you forget about the (2+sqrt(x-3)) on the bottom?
vestal gale
yeah that's what i got too!
vestal gale
sorry lemme see here!
so this is a lhopitals chapter, right? im assuming from the first one
so if you simplify the t's a little bit, i think you can get this into the indeterminate form of 0/0
also consider that sin(0) is 0, and as such tan(0) is also 0!
dusty field
I didn't get zero
mint nacelle
I didn't get zero
the other person said you have a 0/0 form
probably sub $t = \frac{1}{u}$ so that you have $\lim_{u \to 0} \frac{3u/4 \cdot \sin^2 (-2u^2)}{3u^4 \tan(u/3)}$
grizzled pagodaBOT
higher's secret twin brother
mint nacelle
$\to \frac{3/4 \cdot (-2)^2}{3 \cdot 1/3}$
grizzled pagodaBOT
higher's secret twin brother
vestal gale
ah sorry i got distracted!! glad it worked out!
mint nacelle
no worries!
amber waspBOT
Available help channel!
sage horizon
amber waspBOT
jovial field
Do u know log?
vestal gale
you're gonna need to use the properties of logs to rearrange this for x
amber waspBOT
@sage horizon Has your question been resolved?
distant quartz
@sage horizon bro look through the messages
amber waspBOT
amber waspBOT
Available help channel!
austere bloom
can someone help?
amber waspBOT
can someone help?
neat wind
austere bloom
hi, if all the numbers are filled I know the answer but this time only 40 out of 42 are filled
how to take that into consideration?
austere bloom
7c3?
coral wigeon
sure
now suppose you picked 3 rows
how many ways can you pick 3 entries that don't share a column
coral wigeon
coral wigeon
hi, if all the numbers are filled I know the answer but this time only 40 out of...
oh sorry missed this
what does that even mean though
neat wind
can someone help?
is this the original wording of the problem
austere bloom
is this the original wording of the problem
yea
It was in my own language but I put it through google translate
neat wind
can we see what the untranslated version says
coral wigeon
so... no it was not the original
neat wind
neat wind
maybe this is missing a "dua" near the start
coral wigeon
mqnic i think the question is:
how many ways are there to choose 3 cells in a 7 x 6 grid such that none of them share a row or a column
coral wigeon
as for the 40/42 question though i'm still not sure exactly what that means
lost star
as for the 40/42 question though i'm still not sure exactly what that means
2 cells are empty
neat wind
mqnic i think the question is:
how many ways are there to choose 3 cells in a 7 ...
this seems legit ye
this is also the same conclusion i came to
"empat puluh dua" would modify the problem to say 42 instead of 40
austere bloom
mqnic i think the question is:
how many ways are there to choose 3 cells in a 7 ...
yeah but it's a competition no way the organizers would make a wrong question
neat wind
since this other version kind of does not make sense
i c someone posted this same exact problem online but used 42 instead of 40 so
lost star
since this other version kind of does not make sense
such a question in a competition can make sense
neat wind
such a question in a competition can make sense
not rly
this is very computationally intensive for competition problem
dull pike
Guys
coral wigeon
this is very computationally intensive for competition problem
which version of the problem?
neat wind
which version of the problem?
the 40 filled in boxes
dull pike
This is not about what do you think the problem says. This is about this exact problem
neat wind
i get that however i think this problem presentation is very suspicious
dull pike
He already said he knows how to do with 42
neat wind
:/
neat wind
I think you need to make cases (a lot of cases)
well then
coral wigeon
the 40 filled in boxes
what even is the statement of the 40/42 question
neat wind
what even is the statement of the 40/42 question
i guess sum over all possibilities of 42C40
again makes no sense but ig (this is definitely not how the problem would be phrased in indonesian nor english if this were truly the case)
coral wigeon
This is not about what do you think the problem says. This is about this exact p...
that would make sense if the exact problem had been stated already
dull pike
Isnt this the exact problem?
austere bloom
yea
coral wigeon
i don't see a 40 there
austere bloom
empat puluh is 40
coral wigeon
ok i don't see a 40 in the translated version either
coral wigeon
ok i missed that
dull pike
I am sorry
coral wigeon
but the question is still unclear
dull pike
I agree, that doesnāt mean it is wrong
lost star
can someone help?
you can try this question at MODS
dull pike
When a question is wrong, we should be able to say exactly why is it impossible to solve
And I canāt do here
austere bloom
you can try this question at MODS
what is MODS?
lost star
what is MODS?
Mathematical Olympiads server
austere bloom
Mathematical Olympiads server
where is that
neat wind
i have found like 7 different sources online that have used this exact problem but with 42 not 40
lost star
austere bloom
thanks
dull pike
the 40 version makes no sense
Although I agree it should say 42, i donāt see why it doesnāt make sense 40
neat wind
you will be wasting people time if you post this problem in that server
lost star
i have found like 7 different sources online that have used this exact problem b...
if MODS can't answer that, then the question is wrong
dull pike
Thats why i used both
coral wigeon
i have found like 7 different sources online that have used this exact problem b...
i mean look at this journalist work
brazen birch
$\left( \binom{7}{3} \binom{6}{3} 3! \right) - 2 \left( \frac{\binom{7}{3} \binom{6}{3} 3!}{42} \right)$
grizzled pagodaBOT
Mary
brazen birch
i guess this is what the problem is saying
brazen birch
i might be wrong but, if 2 are empty then u just calculate the number of times each cell participated in a 42 full grid, then u subtract two of them
but i really dont ser any mistake in my calculation
maybe @coral wigeon @neat wind wanna check
coral wigeon
it's still not even clear what the 40 version of the problem is supposed to be
brazen birch
i see as the 42 but 2 cells are empty, you can put these 2 empty cells in random spots (because they dont matter where) and calculate, without touching those cells
coral wigeon
the amount is the same no matter which two cells are empty... yes i've convinvced myself of that i think
brazen birch
so then my solution is correct?
neat wind
no
brazen birch
what is the mistake?
coral wigeon
not sure about the thing you substracted off
brazen birch
it is the amount two cells participate in the whole combinations
brazen birch
is it the same?
coral wigeon
well nvm i'll need another minute
neat wind
coral wigeon
hm i got something else
neat wind
is your number a perfect square
brazen birch
what he got
coral wigeon
let me think about it again
amber waspBOT
@austere bloom Has your question been resolved?
coral wigeon
x x 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
say the two empty cells are the top left ones. for "non-attacking rook" 3-combinations from the 6 x 7 grid that use the top left corner, the ways to assign two non-attacking rooks with the top row and left column taken out of consideration (because the top left corner uses those) correspond to a choice of 2 of the 5 rows along with columns to use, and there 6*5 ways to choose (well order matters so that's kinda a bad word but whatever) columns. so (5 choose 2)*6*5 3-combinations use the top left corner. similar for the one right next to it. so there are 2*(5 choose 2)*6*5 combinations that use either of the blank cells
neat wind
coral wigeon
the amount is the same no matter which two cells are empty... yes i've convinvce...
i'm also maybe not convinced of this anymore
neat wind
that's good
coral wigeon
x x 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0...
because this will be different if the empty ones don't share a row or column
neat wind
coral wigeon
oops my grid is 6 x 7 not 7 x 6 but that doesn't really matter
k that's fine now we'll just use a 6 x 7 grid instead
neat wind
coral wigeon
because this will be different if the empty ones don't share a row or column
and i'm also back in the this problem makes no sense boat because of this
neat wind
i guess sum over all possibilities of 42C40
could do this still
not particularly exciting but well
amber waspBOT
coral wigeon
could do this still
neat wind
idk you were looking for a way to make the problem make sense and that's the only reasonable way i can come up with
well when first reading the problem that's what i assumed before thinking to myself "this interpretation actually makes no sense"
amber waspBOT
Available help channel!
coral wigeon
.who says i was looking
neat wind
.might have assumed given you were considering how a solution might look
coral wigeon
.when you assume you make an ass out of u and me
.i'm just messing with ya
.there was a time i was looking for a sensible interpretation of the problem
keen pawn
amber waspBOT
keen pawn
so the negation, and thus what I assume to prove this by contradiction successfully would be $a$ is irrational and $ab$ is rational and $b$ is irrational
grizzled pagodaBOT
Veni, vidi, perii is not f(wai)
coral wigeon
severe scroll
helo
coral wigeon
hi mommy
keen pawn
Am I right?
cloud scarab
yes, this can be proven by contradiction
keen pawn
Yeah, but is my negation right?
vast spade
cloud scarab
Nope, proving A => B by contradiction typically means showing that not(B) => not(A)
severe scroll
Nope, proving A => B by contradiction typically means showing that not(B) => not...
what no
cloud scarab
Proper negation would be "suppose b is rational. Then ab must be rational (because a is rational), hence we arrive at a contradiction"
coral wigeon
"reverses the conclusion of the implication" or something
severe scroll
the negation of A implies B is A and not B
keen pawn
I know
oops
sorry
so the negation, and thus what I assume to prove this by contradiction successfully would be $a$ is irrational and $ab$ is rational and $b$ is rational
grizzled pagodaBOT
Veni, vidi, perii is not f(wai)
coral wigeon
no
severe scroll
okay, try writing your original statement formally.
keen pawn
a is rational and ab is irrational and b is rational
coral wigeon
Nope, proving A => B by contradiction typically means showing that not(B) => not...
kinda silly to call that contradiction
keen pawn
Nope, proving A => B by contradiction typically means showing that not(B) => not...
That's contrapositive
cloud scarab
Proper negation would be "suppose b is rational. Then ab must be rational (becau...
I tried describing this statement
severe scroll
a is rational and ab is irrational and b is rational
this is the negation (modulo you putting in the right quantifier)
cloud scarab
Sorry, language barrier
cloud scarab
kinda silly to call that contradiction
Well, we assume that not(B) holds for A
But then we show that not(B) => not(A) and arrive at a contradiction
severe scroll
in the āsupposeā bit
keen pawn
$\exists a,b \in \R$?
grizzled pagodaBOT
Veni, vidi, perii is not f(wai)
severe scroll
idk what youāre asking me
keen pawn
in the āsupposeā bit
Is this the hidden qunatifier in the suppose bit?
severe scroll
Is this the hidden qunatifier in the suppose bit?
other one :P
cloud scarab
We're working in the setting that a is rational
keen pawn
$\forall a,b \in \R$?
grizzled pagodaBOT
Veni, vidi, perii is not f(wai)
severe scroll
We're working in the setting that a is rational
can you stop please š we have an if-then statement so it works for all a and b in R
severe scroll
**Veni, vidi, perii is not f(wai)**
yeah
cloud scarab
can you stop please š we have an if-then statement so it works for all a and b ...
sorry, I didn't want to ruin anything
keen pawn
so I have $\forall a,b \in \R; a \in \Q \land ab \in R \setminus Q \implies b \in R \setminus Q$ and now I negate this and assume that to be true
cloud scarab
but I'm genuinely confused about what I said wrong
grizzled pagodaBOT
Veni, vidi, perii is not f(wai)
severe scroll
but I'm genuinely confused about what I said wrong
iām sorry itās just kind of hard to do this and also help the person iām supposed to be helping. i can talk to you about it in a sec in #math-discussion
coral wigeon
but I'm genuinely confused about what I said wrong
you aren't "wrong" it's just weird to frame a contrapositive proof as a contradiction proof
severe scroll
so I have $\forall a,b \in \R; a \in \Q \land ab \in R \setminus Q \implies b \...
this is right.
keen pawn
So to start , let's assume $\exists a, b \in \R;a \in R \setminus Q \land ab \in \Q \land b\in \Q$. We now digress for a bit to prove that the product of an irrational and non-zero rational number is irrational. Let $a \in \Q$ and $b$ be irrational. so we have $ab=c$, which means that $b= \frac{a}{c}$, which isn't possible by definition of irrationality. Thus $\exists a, b \in \R;a \in R \setminus Q \land ab \in \Q \land b\in \Q$, isn't true. We have arrived at a contradiction, which means our original assumption was wrong. Which completes our proof.
grizzled pagodaBOT
Veni, vidi, perii is not f(wai)
severe scroll
wait thatās not the right negation though. you had (a in Q, ab in R\Q) implies (b in R\Q) as your original
so the negation of that part is (keep this part) and not (thing after arrow)
pseudo crescent
Btw, unless you are required to do it by contradiction as a whole, this approach might be easier for you:
Suppose a, b in R, with a rational and ab irrational.
Now, for sake of contradiction, assume b is rational...
This way, you dont need to take negations of such monstronous statements
keen pawn
I know
keen pawn
so the negation of that part is (keep this part) and not (thing after arrow)
Oops. Is it fine other than that
quick spoke
also i would like to point out that this proof is a 'fake contradiction'
bcus really it's just the contrapositive
coral wigeon
@robust isle would be disgusted
robust isle
<@118663865264242688> would be disgusted
correct
pseudo crescent
Assume that the statement in question is false.
[Insert a sane proof of the statement in question]
Which contradicts the assumption, and so the statement in question is true.
split sail
what is Df/Dx where f,x are both vectors?
amber waspBOT
what is Df/Dx where f,x are both vectors?
@split sail Has your question been resolved?
chilly jackal
Found this monster on MSE
amber waspBOT
Found this monster on MSE
chilly jackal
My intuition to simplify the bounds led me to substitute $\frac{(2x-1)^2}{4} = k$
grizzled pagodaBOT
rakĀ³en
chilly jackal
but then the integral is simply the integral of something from a to a, which is 0
So the answer's 0?
neat wind
mfw
elfin vale
My intuition to simplify the bounds led me to substitute $\frac{(2x-1)^2}{4} = k...
This is not a valid substitution because it is not injective
elfin vale
You would have to split the integral into the negative and the positive part first
chilly jackal
Ah okay okay
wait still
I would split it as $\int_{\frac{1}{2} \left(-\sqrt{1+u} + 1 \right)}^{0} + \int_{0}^{\frac{1}{2} \left(\sqrt{1+u} + 1 \right)}$
grizzled pagodaBOT
rakĀ³en
chilly jackal
no?
elfin vale
Yes
grizzled pagodaBOT
rakĀ³en
chilly jackal
which is again, 0
chilly jackal
Yes
Splitting doesnt help, because I still get 0. I assume the problem is with the substitution itself?
elfin vale
I would split it as $\int_{\frac{1}{2} \left(-\sqrt{1+u} + 1 \right)}^{0} + \int...
You should split as $\int_{\frac{1}{2} \left(-\sqrt{1+u} + 1 \right)}^{\frac{1}{2}} + \int_{\frac{1}{2}}^{\frac{1}{2} \left(\sqrt{1+u} + 1 \right)}$
grizzled pagodaBOT
d
elfin vale
You still get the same problem however
chilly jackal
Hmm
I see
thanks
i giving up because
wolfram spat out the worse possible mess of polylogs
elfin vale
Oh
chilly jackal
and that too just for the dx one
god knows how u would do the whole integral
.close
amber waspBOT
amber waspBOT
Available help channel!
hard raptor
In this question f(x) is defined at x=0 lim from the right exists and is Ā½ but lim from the left DNE what type of discontinuity is this ?
amber waspBOT
In this question f(x) is defined at x=0 lim from the right exists and is Ā½ but l...
chilly jackal
its called a jump discontinuity
amber waspBOT
amber waspBOT
Available help channel!
chilly jackal
solve y*ln(y) - y= x for y
amber waspBOT
solve y*ln(y) - y= x for y
chilly jackal
I know the answer is in terms of the lambet W function, but I can't get it into that form
good idea actually
amber waspBOT
fresh hatch
I don't seem to see what y=e^ln(y) would do there though
inland pulsar
It will become ln(y^y/e^y) = x
fresh hatch
Ok but how is this supposed to be solved
inland pulsar
e^x = y^y / e^y
x * e^x = (y/e)^y *y * ln(y/e)
fresh hatch
This way you are solving for x
inland pulsar
You are right idk
amber waspBOT
Available help channel!
fresh hatch
You are right idk
Oh found it lol
It is easier than I thought
amber waspBOT
Oh found it lol
It is easier than I thought
fresh hatch
.close
amber waspBOT
inland pulsar
Oh found it lol
It is easier than I thought
This is not easy for me lmao
fresh hatch
This is not easy for me lmao
You know the lamperet W function?
If not then it is like the inverse of
y = x * e^x
Which is
W(y) = x
As long as you have a function multiplied by e to the power of the same function you can use it
inland pulsar
Yes I know it but not from school because of yt ppl like rpbp
fresh hatch
Yeah
Math is cool by the way out of school
inland pulsar
Hmm
amber waspBOT
Available help channel!
marsh mason
hi guys
marsh mason
I have this domain that I parameterized with 4 vector functions
with these normal vectors
and I had to solve this closed curve line integral:
which should sum up to 0
but I dont get 0 
I tested with this so it really should be 0, but I have to solve it with the line integral
oh sorry this is the vectorfield forgot to send that
nvm I figured it out
,close
.close
amber waspBOT
amber waspBOT
Available help channel!
chilly jackal
tried solving this guy, got thrashed for doing integration the wrong way
chilly jackal
anyhow
I remember using the D-method to solve DEs
could I use that here?
Here's my working
write the equation as $(4(1-x^2)D^2 + 1)y= 0$
grizzled pagodaBOT
rakĀ³en
amber waspBOT
amber waspBOT
Available help channel!
undone hamlet
- The position function of a particle is given by (t+3)(5t-5)in meters,
a. Find the position of the particle after 3s?
b. Find the velocity of particle after 5s?
c. Find the acceleration/deceleration after 3s?
Hello is my answer correct?
a. x(t) = (t + 3)(5t - 5)
x(3) = (3 + 3)(5 * 3 - 5)
x(3) = 6 * 10
x(3) = 60 meters
b. x'(t) = d/dt [(t + 3)(5t - 5)] = 5(2t + 1)
x'(5) = 5(2 * 5 + 1)
x'(5) = 5(11)
x'(5) = 55 meters/second (velocity)
c. x''(t) = d^2/dt^2 [(t+3)(5t-5)] = 20
x''(3) = 20m/s^2 (acceleration)
(I have no idea how to do this last part.)
undone hamlet
i think my a and b are okay
Maybe not-, please guide me, but C i am completely lost
Frick, okay
MAYBE MY B was wrong
inland pulsar
b is wrong
undone hamlet
Is it 60ms?
inland pulsar
Lol
undone hamlet
Yeah okay sorry uh
inland pulsar
The differentiation is wrong imo
undone hamlet
Hrn okay so
undone hamlet
x(t) = (t+3)(5t-5) = 5t^2 + 10t - 15
inland pulsar
Rookie mistake š¤
undone hamlet
Did I do better?
undone hamlet
Rookie mistake š¤
WUAHAUHA god i am so cooked
inland pulsar
inland pulsar
Is it 60ms?
This is correct tho the units are wrong
undone hamlet
This is correct tho the units are wrong
Wait wdym
undone hamlet
AH alright thanks, wouldn't want another 60 what applesor bananas thing
inland pulsar
10t+5 or 10t+10
Neither gives 20
undone hamlet
10t+5 or 10t+10
Neither gives 20
YEAH MB
okay lemme redo it
SO
BECAUSE OF THE ANSWER WE GOT FROM B
undone hamlet
d/dt(10t+10) =10
inland pulsar
Yes
undone hamlet
AJQIHAAHA
thank you so Much wunUPUS MANANNB
OKAY SO
I have a couple questions but have answers to them already
Lemme just close and reopen..
inland pulsar
The royal cat has given you the presidential pardon to not follow !1q this one time
Feel honoured
undone hamlet
The royal cat has given you the presidential pardon to not follow !1q this one t...
gah thanks
Okay so heres the other ones
.close
amber waspBOT
undone hamlet
-
A man falls from a bridge that is 30 m above the water. He falls directly into the boat that is moving with constant velocity that was 7 m from the point of impact when the man falls. What is the speed of the boat?
-
Sandor Clegane jumps from the ground with an initial speed of 20.6 m/s; at the same instant, Gregor Clegane falls from the top of a building 18 m high. After how long will Sandor and Clegane be at the same height above the ground?
-
How long(in s) does it take a plane to take off if it needs to reach a speed on the ground of 200 kph over a distance of 600m. (assume the plane starts from rest)? What is the acceleration(in m/s^2) of the plane after 600m?
amber waspBOT
Please stick to your channel.
undone hamlet
amber waspBOT
To ask for mathematics help on this server, please open your own help channel or help thread. See #āhow-to-get-help for instructions.
amber waspBOT
ā
undone hamlet
But yeah above are
Fhe questions and in order my answers
Could you please give em a quick glance and tell me if
inland pulsar
! status
undone hamlet
I goofrd
amber waspBOT
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
4?
undone hamlet
Yes!
undone hamlet
OKAY THANK YOU
undone hamlet
YEAAAAAHH
ALEIFHT THANKS YOU SO MUCH WUMPUS
I got twenty minutes imma pass itin
Tysm
.close
amber waspBOT
inland pulsar
Btw is calc allowed
.?
inland pulsar
(calc is slang for calculator lmao)
.
undone hamlet
Yes
inland pulsar
@undone hamlet
undone hamlet
It's online class
inland pulsar
Oh
amber waspBOT
Available help channel!
split sail
prove that x+y+z = a and x^2 + y^2 + z^2 = b^2
amber waspBOT
prove that x+y+z = a and x^2 + y^2 + z^2 = b^2
split sail
,, {x+y+z = a}, and, {x^2 + y^2 + z^2 = b^2}
grizzled pagodaBOT
anjali
inland pulsar
Is there a relation between a and b
inland pulsar
The question doesn't make sense atm
inland pulsar
! original
amber waspBOT
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.
split sail
if these are the relations, then the solution only exist in real x,y,z if and only if abs(a) < root3 * abs(b)
split sail
if these are the relations, then the solution only exist in real x,y,z if and on...
s is to be proved
this
i just want to know one thing
for the 'if' part
inland pulsar
are x, y, z +ve?
split sail
not given
inland pulsar
Or else you could have used AM GM
split sail
for the 'if' part
do we only have to show that there are real x,y,z if abs(a) < abs(b) * root3? for the if part
inland pulsar
I guess
amber waspBOT
split sail
okay!
amber waspBOT
Available help channel!
amber waspBOT
split sail
(1+cos(x))^2 =/= 1+(cos(x))^2
when u multiply the 2 fractions u did that
idk i just tell u where u were wrong
so when u simplify the fraction it was also wrong
mint nacelle
try letting x = 2u so that you want the RHS to simplify to tan u
then there are some nice double angle identities you can use
can you simplify $\frac{\sin 2u}{1 + \cos 2u}$ then?
grizzled pagodaBOT
higher's secret twin brother
rancid raven
x=2u so u = ?
mint nacelle
yep! amazing
rancid raven
Done
rancid raven
With practice you can
mint nacelle
whenever you have x/2 and x, then it's natural to let u = x/2 so that you can use the double angle identities like you just did
it just follows by substitution
you can let u be anything!
oh well, time for you to prove that
that is indeed equal to |tan(x/2)|
try $\frac{1 - \cos}{1 + \cos} \frac{1 - \cos}{1 - \cos}$
grizzled pagodaBOT
higher's secret twin brother
mint nacelle
basically once you get to the absolute value of sin(x) / (1 + cos x), you've shown it
great, now take the square root
you get the absolute value of (1 - cos x)/(sin x)
either way can you make (1 - cos x)/(sin x) become sin(x) / (1 + cos x)?
multiply top and bottom by something
your exercise
oh wait, 1 - cos^2 x = sin^2 x
yeah
yeah
$\cos^2 x = (\cos x)^2$
grizzled pagodaBOT
higher's secret twin brother
grizzled pagodaBOT
higher's secret twin brother
amber waspBOT
@split sail Has your question been resolved?
shell barn
i know that the nested radicals can be simplified, but i'm not sure how
split sail
i would just note the first sqrt as A and second as B
but im not sure that gives me anything
what lesson are you on?
shell barn
its not really a lesson,, i got it from a competition and it's the only problem i just couldnt solve
shell barn
what grade are you
12
shell barn
this looks most likely as an irational equation
the square roots are but they cancel each other out
split sail
ok yeah irational equation
amber waspBOT
@shell barn Has your question been resolved?
raven knot
I mean, you're literally given that a is natural. Could just approximate the cube root of 4 as 1.6-ish, right expression is inbetween 0 and 1, left is about 20x1.6^2-16=35.2, to be a bit more precise 20x1.59^2-16=34.562, so the answer is about 5
shell barn
the answer is 5, yeah, but i found that you can simplify the nested root expression, so thats like the problem here - i dont know how write it
shell barn
<@&286206848099549185> if y'all dont mind
ancient snow
<@&286206848099549185> if y'all dont mind
Sorry what's the exact question?
shell barn
Sorry what's the exact question?
#help-41 message ,, the problem is that i want to express how to unnest it
ancient snow
Since a is natural I would try to square both sides
Maybe that can give you a form that's simplifyable
But that 31 gives me doubt about it
shell barn
i tried that, makes it worse lowkey
ancient snow
Yeah if it was a 32 maybe it could work
ancient snow
the answer is 5, yeah, but i found that you can simplify the nested root express...
I think you're just supposed to find which squre it is for the second root like this
I don't see a better way to go about it
shell barn
I think you're just supposed to find which squre it is for the second root like ...
i found both of them using wolfram alpha lol,, i just want to know if theres a neat way to show the solution
ancient snow
i found both of them using wolfram alpha lol,, i just want to know if theres a n...
I mean this one is -1 + 2cbrt(4) and the other one is 4+2cbrt(4) and the cube roots will cancel out
shell barn
I mean this one is -1 + 2cbrt(4) and the other one is 4+2cbrt(4) and the cube ro...
it does, yeah, but i want to know how i'd get here
like how could i simplify to get it to that form
ancient snow
like how could i simplify to get it to that form
So lets take the 20cbrt(4) - 31 for example you can get $20cbrt(4) - 31 = 202^{\frac{2}{3}}-31 = 1 - 32 +42^{\frac{2}{3}} + 16*2^{\frac{2}{3}}$ and now I'll say that some $b = 2^{\frac{2}{3}}$ to get $1 - 32 + 4b + 16b$ and futher more since $b^3 = 4$ we can get $1 + 4b - 8b^3 + 4b^4$ which is somewhat simplified
grizzled pagodaBOT
Goran
ancient snow
Hopefully didn't mess up some step there
shell barn
Hopefully didn't mess up some step there
like this?
ancient snow
like this?
Yeah
shell barn
so id assume i could also do this for the first expression too?
ancient snow
Yeah you should be able to
amber waspBOT
amber waspBOT
Available help channel!
low forge
I'm not exactly sure what to ask, here. I'm trying to figure out how to plot an intercept with the equation -5=2x+y. I'm familiar with y=mx+b, but I'm pretty confused on how I'm supposed to plot this? Slope is 2, what is the -5? I'm afraid I don't understand, but I'd like to.
grizzled pagodaBOT
riemann
low forge
subtract 2x from both sides
Subtract 2x from both sides? I'm not sure what this means
This is apparently the solution, but I don't get why that is
gentle dome
He's asking you to rearrange the equation into the form y=mx + b
pallid canopy
Subtract 2x from both sides? I'm not sure what this means
Watch the video
pallid canopy
https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:forms-of-linear-equat...
.
low forge
Oh okay
gentle dome
When you do that you'll see why the slope isn't 2
low forge
Well, guess I'll hop off here. Since all I need is the video
you can use the .close or whatever it was
Thanks.
pallid canopy
.close
amber waspBOT
amber waspBOT
Available help channel!
cyan tiger
For 11a, I don't get the (f/g)(x) graph
It looks weird
amber waspBOT
For 11a, I don't get the (f/g)(x) graph
It looks weird
fervent oasis
do you have f(x) and g(x)?
cyan tiger
Yep, i divided the values, and got the values for (f/g) (x)
However, when I plot it, it's making this weird shape
fervent oasis
you are looking composite functions?
cyan tiger
I have no clue what that is. Nor did we learn about it
We have only done graphs that involve parabolas, lines, and sometimes cubic and radical functions
But that's pretty much it
fervent oasis
f(x) = x+3, g(x) = -x-4
so: (f * g)(x) its just multiplying f(x) with g(x)
try multiplying (x+3)(-x-4)
cyan tiger
It's giving me a lot of decimals as the y values
And when I plot them, it's forming a weird thing, that I don't know how to connect
fervent oasis
have you tried graphing the function? https://www.desmos.com/calculator?lang=es
fervent oasis
yeah, some functions make some weird curves
cyan tiger
Ohhh so it's supposed to be this way?
fervent oasis
Ohhh so it's supposed to be this way?
yep
do you see that if x=-4, then the function would be -4+3/0
you can't divide by 0, thats why that weid figure is formed
cyan tiger
Ahh I get it now
Thank you so much!!!
You explain really well
I really appreciate it!
Have a good one! :))
.close
amber waspBOT
amber waspBOT
Available help channel!
calm pewter
for the last bit would it be A?
amber waspBOT
for the last bit would it be A?
wheat grotto
for the last bit would it be A?
how long is that homework 
wheat grotto
i have 40 slides more
heavy on the
wheat grotto
b) B
wheat grotto
becasue as speed decreases time increases
yeah thats what we call inversely proportional ratios
its when 1 value increases the other one decreases
wheat grotto
S = d/t
That's a directly proportional ratio
The speed increases as much as the distance travaled increases in the unit of time
wheat grotto
kinda yeah
wheat grotto
gn
calm pewter
.close
amber waspBOT
fathom cradle
you need help?
amber waspBOT
Available help channel!
arctic zealot
floor(log10(n)) + 1 is the number of decimal digits left of the decimal point
how would I compute the number of digits needed to the right of the decimal point to express the precision of a number?
for example:
- 6 -> 0
- 0.5 -> 1
- 0.99 -> 2
- 0.003 -> 3
mossy geode
floor(log10(n)) + 1 is the number of decimal digits left of the decimal point
ho...
okay so like
You want to take the floor of the negative of the log base 10 of one over the number
i think let me check
arctic zealot
nope
I tried that already
I realize now that I'm not sure how such a function would act given a number whose decimal expansion is infinite
grizzled pagodaBOT
Lilly (NasaExploration)
mossy geode
,, x =a_{1} a_{2} \dots a_{n} \times 10^{n}
grizzled pagodaBOT
Lilly (NasaExploration)
mossy geode
,, log_{10} (x) = n + log_{10} (a_{1} a_{2} \dots a_{n})
grizzled pagodaBOT
Lilly (NasaExploration)
mossy geode
And we have a formula for the $log_{10} (a_{1} a_{2} \dots a_{n})$
grizzled pagodaBOT
Lilly (NasaExploration)
mossy geode
Hummmmm how to formalize that properly
I want to say that $log_{10} (a_{1} a_{2} \dots a_{n}) = n -1$
grizzled pagodaBOT
Lilly (NasaExploration)
mossy geode
So :
Waiiiitttt no
,, \floor{log_{10} (x)} = \floor{n + log_{10} (a_{1} a_{2} \dots a_{n})}
grizzled pagodaBOT
Lilly (NasaExploration)
grizzled pagodaBOT
Lilly (NasaExploration)
grizzled pagodaBOT
Lilly (NasaExploration)
grizzled pagodaBOT
Lilly (NasaExploration)
mossy geode
,, x =a_{1} a_{2} \dots a_{n} \times 10^{n}
Here it's nto that
It's
,, x =a_{1} a_{2} \dots a_{n} \times 10^{-n}
grizzled pagodaBOT
Lilly (NasaExploration)
grizzled pagodaBOT
Lilly (NasaExploration)
mossy geode
,, \floor{log_{10} (x)} = \floor{log_{10} (a_{1} a_{2} \dots a_{n}) - n}
grizzled pagodaBOT
Lilly (NasaExploration)
arctic zealot
this is for a program I'm writing
I might just end up converting the number to a string and counting the characters
mossy geode
this is for a program I'm writing
I might just end up converting the number to a...
Oh as a programmer myself I would understand not wanting to do that cu
amber waspBOT
@arctic zealot Has your question been resolved?
grim forge
We have this function
Basically when a number like 1247.056 is passed in, it returns 0.056
We keep multiplying the number by 10 and checking if the result the function returns is 0
When it returns 0 the number of times we multiplied by 10 is the precision
@arctic zealot
mossy geode
We have this function
It's fancy but no analitical
grim forge
š¦
arctic zealot
I just went ahead with the method of counting the digits after the decimal point in the string representation of the number
mossy geode
I just went ahead with the method of counting the digits after the decimal point...
Oki doki
It's still on the back of my head cuz I still don't undertsand why the method I made doesn't work
grim forge
We have this function
Anyway float precision would probably kill this method anyway
mossy geode
It's quite triggering if I must say
mossy geode
Anyway float precision would probably kill this method anyway
Yeah
arctic zealot
Anyway float precision would probably kill this method anyway
yeah
float precision is the reason I even have this problem in the first place
I have 0.05 as a starting number and 0.05 * 3 ends up being 0.15000000ā¦2
mossy geode
I have 0.05 as a starting number and 0.05 * 3 ends up being 0.15000000ā¦2
Taht's my actual nightmare
arctic zealot
I have 0.05 as a starting number and 0.05 * 3 ends up being 0.15000000ā¦2
and I needed to be able to dynamically tell how much precision was needed for the original number of 0.05 to know how much to round the output
grim forge
Why do you need that much precision though
arctic zealot
wdym
grim forge
Like I mean 0.15000000000...2 isn't that far off from 0.15
arctic zealot
I'm making a data plotting program
(before)
mossy geode
@arctic zealot I literally did the proof again and endded up on -floor(log10(n)) - 1
Which doesn't works
I genuinely don't see where my logic is wrong
arctic zealot
floor(log10(n)) clearly isn't going to give you enough information
mossy geode
floor(log10(n)) clearly isn't going to give you enough information
Yeah likely
mossy geode
(before)
Oh hey someone made a lookup
For the left digit
But you could do that for the right I think
grizzled pagodaBOT
Lilly (NasaExploration)
mossy geode
Where n is the number of digit
Which is exactly what Denzio321 gave earlier hahahahahaha
mossy geode
**Lilly (NasaExploration)**
Fun fact, this is actually always true
Well I am sorry it was a lots of fun to look into but I can't seems to find something
I am terribly sorry I need to sleep
split sail
amber waspBOT
split sail
I'm supposed to find the equation of this plane
So what I've gathered so far is that the plane has the same line of intersection and must pass through the point (-1,2,1)
vestal hatch
Have you found the line of intersection
split sail
yes I found the vector parallel which means i could just write the parametric equation of the line
the vector is <2,-5,-3>
which i found using the cross product of <1,1,-1> and <2,-1,3> (both are normal vectors to the two planes, so their cross product goes through the line of intersection)
but i'm honestly unsure how to find the vector normal to the plane i'm trying to find
amber waspBOT
@split sail Has your question been resolved?
vestal hatch
but i'm honestly unsure how to find the vector normal to the plane i'm trying to...
A point and a direction vector aren't enough on their own
You actually need to find points on that line of intersection
At least 1 anyways
spark dragon
have u learnt about family of planes? like the general form of any plane which passes through line of intersection of two planes
split sail
i haven't unfortunately
i only know how to construct the equation of a plane given a point on the plane and the normal vector
which would be a(x-x0)+b(y-y0)+c(z-z0)=0, where <a,b,c> is a vector normal to the plane and (x0,y0,z0) is a point on the plane
this equation is derived from the fact that the cross product of two orthogonal vectors is 0
i'm currently working through finding the normal vector and i think i'm getting it but i have to verify it
spark dragon
i haven't unfortunately
do you mind if i show it to you? trust me it will save u alot of time
split sail
do you mind if i show it to you? trust me it will save u alot of time
yes please