(Also, please do ping me)
#help-17
white whale
languid spruce
i mean theres no sheet
im not sure its wrong
actually it might be right
but i still want to make sure
white whale
Well, it's possible that your teacher interpreted the question differently, like treating c, (a, b), d as the different grouping, as the grouping labels are not interchangeable.
But in this situation, there is no way to find out.
languid spruce
the teacher didnt solve it
languid spruce
Well, it's possible that your teacher interpreted the question differently, like...
and its explicitly stated that they are
but whats not clear is whether all the groups can be empty or not
but i asked 2 classmates and they both came up with (n choose 2) + 1
so that seems to be right
white whale
If you think the question is solved, please close it with .close
vocal sleetBOT
vocal sleetBOT
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robust tide
vocal sleetBOT
robust tide
Can someone help me with this qn
brisk moss
first think about all the ways you can arrange the vowels into the 8 letter positions
robust tide
I mean how to ensure that U comes before the other vowels?
brisk moss
you have to put the 3 vowels somewhere
once you choose 3 places for them, there is only one order they can be in
robust tide
Hmmm so we need to consider each possibility separately?
Isn't there like a gen sol?
brisk moss
you have to put the 3 vowels somewhere
we don't need to "consider each possibility separately" for this
just need to know how many of them are
robust tide
But they need to be in a certain order right
brisk moss
yes, but that's no trouble
brisk moss
right
robust tide
Wait so (56 times 5 factorial/2)-1 ?
Lol ok that was pretty simple
So dumb of me
.close
vocal sleetBOT
robust tide
Thanks for ur help @brisk moss
robust tide
Who
brisk moss
how tf is she still here
vast shale
u didnt sleep? ๐ญ
brisk moss
nope
vocal sleetBOT
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carmine root
vocal sleetBOT
vocal sleetBOT
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lapis sentinel
vocal sleetBOT
deft vapor
well in MVT it just states that there exist a point 1 < x < 5 such that f'(x) = f(5) - f(1) / 4
in this question it asks specifically for f'(3)
so MVT doesn't apply
deft vapor
have you tried plotting it on a graph?
lapis sentinel
have you tried plotting it on a graph?
lapis sentinel
And i just realized, the 2nd derivative > 0 means always concave up right
lapis sentinel
what's closest to 0.75
0.7
deft vapor
And i just realized, the 2nd derivative > 0 means always concave up right
convex you mean
deft vapor
0.7
that must be it then
it asks you to approximate after all
if you really wanna know the exact answer, you can try to fit a polynomial through it using polynomial regression
but I think that's beyond your course
lapis sentinel
ya, anyway, thanks!
deft vapor
you are welcome !!
lapis sentinel
.close
vocal sleetBOT
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sly summit
vocal sleetBOT
sly summit
where does the *2^x at the end come from?
civic otter
They multiplied the whole equation by 2^x
sly summit
why
ember ledge
gritty isle
I'm having a hard time trying to understand how subtracting the 2 functions would result in a function that then can be integrated to find the area? why subtract it?
vocal sleetBOT
I'm having a hard time trying to understand how subtracting the 2 functions woul...
signal pendant
Think of it as subtracting areas
gritty isle
Think of it as subtracting areas
but how would subtracting g(x) from f(x) give me the function that I need?
signal pendant
$\int_{a}^{b}f(x)-g(x)dx = \int_{a}^{b}f(x)dx - \int_{a}^{b} g(x)dx \newline$= Area under f in [a,b] - Area under g in [a,b]
$\newline$
=Area between f and g in [a,b]
twin meteorBOT
quickdoom
signal pendant
@gritty isle does this make sense?
gritty isle
<@535155458143420476> does this make sense?
@signal pendant thank you for explaining it. I think I'll watch this video.
lethal heart
$\int \frac{x}{x^2+3x+5}$
vocal sleetBOT
$\int \frac{x}{x^2+3x+5}$
twin meteorBOT
Norman Price
twin parrot
**Norman Price**
!status
vocal sleetBOT
**Norman Price**
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
I'm trying to do 2x+3=x to find the solutions but I know that's not the case
lethal heart
```
What step are you on?
1. I don't know where to begin.
2. I have begun but go...
2
lethal heart
Is substitution used?
I have to have the derivative above so I have the logarithm
It appears that this is how it is done
twin parrot
Yes.Heres a hint:
$\newline \frac{x}{x^2+3x+5}=\frac{1}{2}\frac{2x+3-3}{x^2+3x+5}=\frac{1}{2}\left(\frac{2x+3}{x^2+3x+5} -3 \frac{1}{x^2+3x+5} \right)$
twin meteorBOT
bathroom mug
twin parrot
Read the image
grand linden
I'm trying to do 2x+3=x to find the solutions but I know that's not the case
Why are you doing this?
lethal heart
Why are you doing this?
To do the derivative
grand linden
**bathroom mug**
But what are you doing?
lethal heart
I need an instant method
grand linden
Bro you're just making him get into trouble, I understand what he wants to do
grand linden
I need an instant method
Listen to me
lethal heart
Ok
grand linden
You have to take the derivative up
lethal heart
Yes
lethal heart
2x+3
twin parrot
Bro you're just making him get into trouble, I understand what he wants to do
Im not, lol.$\int \frac{x}{x^2+3x+5} = \int \frac{1}{2}\left(\frac{2x+3}{x^2+3x+5} -3 \frac{1}{x^2+3x+5} \right)=\newline ln(2x+3)-3\int \frac{1}{x^2+3x+5}$. Its the fastest way
grand linden
Wtf
twin meteorBOT
bathroom mug
lethal heart
!nosols
vocal sleetBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
grand linden
Now you have to find a number that when Is multiplied by the derivative gives you x
lethal heart
Yes
grand linden
(only for the first x)
lethal heart
1/2
mellow oyster
**bathroom mug**
the ln(2x+3) is wrong here lmao from this it should be 1/2 ln(x^2 + 3x + 5)
grand linden
the ln(2x+3) is wrong here lmao from this it should be 1/2 ln(x^2 + 3x + 5)
I hate it when people don't understand help, and do their own thing
This guy was using another method, and here he was, he did something completely different
Of course one doesn't understand anything
mellow oyster
what are you trying to have him do? partial fractions?
grand linden
But now you also have to multiply this number by 3
@lethal heart
lethal heart
Yes
grand linden
So?
lethal heart
I have to subtract 3/2
grand linden
Why
lethal heart
So I didn't alter the integral
grand linden
Can you write in latex what you mean?
grand linden
Can you write in latex what you mean?
?
lethal heart
$(2x+3)*1/2-3/2$
twin meteorBOT
Norman Price
lethal heart
All this in numerator
grand linden
The derivative part only goes on the number that has x
lethal heart
Yes
lethal heart
Now I have to separate the fraction
grand linden
Yes
lethal heart
So on one side the logarithm comes out
grand linden
Mm wait
lethal heart
On the other hand I have to see the โ of the denominator
grand linden
Wait
lethal heart
๐คฆ
grand linden
Let me see
grand linden
I said wait
lethal heart
Ok
lethal heart
Because the numerator is the derivative of the denominator
lethal heart
The logarithm(derivate)/2 comes out
This
lethal heart
What
lethal heart
$\frac{\ln|x^2+3x+5|}{2}$
grand linden
You have to put the denominator part in the absolute value
lethal heart
?
lethal heart
๐คฆ
grand linden
Edit the message
twin meteorBOT
Norman Price
lethal heart
On the other hand I have to see the โ of the denominator
This
grand linden
Ok
lethal heart
If the โ is negative the arctangent comes out
grand linden
Ok
lethal heart
In this case it is negative
grand linden
๐
lethal heart
So this is used
grand linden
Are you done ?
lethal heart
Yes
grand linden
Okay , bye!
lethal heart
Thank you
grand linden
vocal sleetBOT
vocal sleetBOT
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vital loom
I forgot
vocal sleetBOT
vocal sleetBOT
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thorny rain
How do i do this
vocal sleetBOT
How do i do this
lone linden
How do i do this
Consider taking the reciprocal of both sides
vocal sleetBOT
vocal sleetBOT
Available help channel!
vocal falcon
Anyone know how to do this?
vocal sleetBOT
Anyone know how to do this?
vocal falcon
specifically 35)
mighty stone
help?
hot heath
vocal sleetBOT
hot heath
Confused on what I need to do here
vocal sleetBOT
@hot heath Has your question been resolved?
desert glen
can someone help me figure out how to algebraically solve this limit
desert glen
the main thing thats messing with me is that x is an exponent
crude arrow
can someone help me figure out how to algebraically solve this limit
what does this limit remind you of
desert glen
im honestly not sure
desert glen
oh
crude arrow
what is x in this case
desert glen
the n
crude arrow
2 lol
desert glen
ive never seen this before
vocal sleetBOT
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naive heron
The square root of 416-210i can be expressed as a+bi, where a and b are integers. Find a and b, without a calculator or computer.
vocal sleetBOT
The square root of 416-210i can be expressed as a+bi, where a and b are integers...
tawny nacelle
The square root of 416-210i can be expressed as a+bi, where a and b are integers...
what have you tried?
naive heron
what have you tried?
nothing. no idea how to do this problem
i'm currently solving this https://artofproblemsolving.com/wiki/index.php/2012_AIME_II_Problems/Problem_8
and im confused on that specific step
tawny nacelle
okay, note that we should have (a+bi)^2 = 416 - 210i
that's the first thing we should observe
tawny nacelle
okay, note that we should have (a+bi)^2 = 416 - 210i
does this make sense to you?
if not, I can elaborate
naive heron
yeah, but doing that seems like a lot of work is there a better solution
as a mathematician im lazy
tawny nacelle
I can't think of a better way...
there might be one, but this method is what I would do personally
naive heron
the fact that the solution didn't even explain this means there is a really easy solution im ignoring
sharp frost
the fact that the solution didn't even explain this means there is a really easy...
This one is easy
a^-b^2= 416
2ab=-210
That's it
tawny nacelle
tbf, it's not that complicated
you can just substitute and solve
oh, wait
you don't have a calculator
ahhh
naive heron
not even 4 func
tawny nacelle
my apologies; I don't know of any other method to solve this 
maybe somebody else will come by and help you out
sharp frost
that causes a billion complicated square roots
Lol, not that much
naive heron
Lol, not that much
no calculator
sharp frost
?
naive heron
calculator is not allowed
sharp frost
calculator is not allowed
How do you even use a calculator for this
naive heron
How do you even use a calculator for this
we have to take square root of 217156
i have a 12 min time limit to do this problem
if i were to do this problem on a test
so that does not work
sharp frost
I see
Square root of 217156 will take at least a min to find
Hmm, but idk if there is a easier method
vocal sleetBOT
@naive heron Has your question been resolved?
naive heron
<@&286206848099549185>
question is find square root of 416-210i WITHOUT A CALCULATOR, given result is in the form of a+bi where a and b are integers
vast shale
<@&286206848099549185>
Ok wait
naive heron
don't just give me the answer pls explain because im self studying this isnt homework lol
hybrid flicker
you have 2ab = -210
so ab = -105
find divisors of 105
since a,b are integers
they're divisors of 105
hybrid flicker
it's a good candidate
naive heron
a=21 b=-5 or a=-21 and b=5
hybrid flicker
though it's not the only one, you can start with those
vast shale
where a^2-b^2=416
Hmm like u can directly apply formula tho
vocal sleetBOT
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crisp zenith
I am a bit confused on this question
vocal sleetBOT
I am a bit confused on this question
crisp zenith
What I did was use the fact that the unit vector is <cos(2pi/3), sin(2pi/3)>
then multiplied that by 14
so I'd have got 14(-(1/2)i + (sqrt(3)/2)j )
which would give me the components -7, 14sqrt(3)/2
I also tried it with pi/3
which would just make the 7 positive
but it was still wrong
any thoughts?
sweet flower
I also tried it with pi/3
It looks like the angle is pi/2+pi/3=5pi/6?
So just flip your i j components around?
vocal sleetBOT
@crisp zenith Has your question been resolved?
crisp zenith
It looks like the angle is pi/2+pi/3=5pi/6?
hmm that wasnt correct
was given a similar one after exhausting my attempts ill let you know if I get it
crisp zenith
I am a bit confused on this question
though I am still curious on why this one is wrong
crisp zenith
Got this one right
crisp zenith
I am a bit confused on this question
if someone could let me know why this was wrong that would be great
vocal sleetBOT
@crisp zenith Has your question been resolved?
vocal sleetBOT
@crisp zenith Has your question been resolved?
vocal sleetBOT
@crisp zenith Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
vast shale
I need help deriving this: (I have always find it difficult deriving things with a square root of or similar things like that)
vocal sleetBOT
I need help deriving this: (I have always find it difficult deriving things with...
vast shale
I first got it to 0,5 (2x-1)^-0,5
But that is of course wrong
on my answersheet is says:
brisk tinsel
,,\frac{d}{dx}\sqrt{x}=\frac{1}{2\sqrt{x}}
twin meteorBOT
Renz
brisk tinsel
and chain rule from there
vast shale
I need to check what you mean, because I am not familiar with the english terms of stuff. Hold up
vast shale
I guess I don't really know?? Because I am quite new to drivative
small quarry
ye just show the formula
he will know how to do
Note that F(x) = f(g(x))
ok I let you to help him then
vast shale
I am hella confused right now. There is so many helping rn ๐ฅฒ
river kettle
๐ฎโ๐จ
vast shale
Apparantly not
small quarry
lol
vast shale
I cannot prosses anthing hahhaa, why is there new people coming here
Where did you get g(x)
you mean this?:
then no I do not get it
Oh okay, then I am mixing stuff uf
up
Yeah okay
vast shale
I am trying to process the information
okay I got
Yeah I figured it out rn
4x would be the derivative for it?
righhtt??
And how is that done
twin meteorBOT
..,,
vast shale
But how do you seperate them?
twin meteorBOT
..,,
atomic pine
h'(g(x)) is simply defined as h' exaluated at g(x), i think u meant to set f(x)=h(g(x)) and use f'(x) rather than h'(g(x))
vast shale
Ngl this made me kinda more confused. Is there any server where someone can help you with vc, because I do not understand this though text. It looks so weird.
really?
yeah sure, let me just get my mic
vast shale
i dont understand why mod 16 is used here
vocal sleetBOT
i dont understand why mod 16 is used here
vast shale
im under the impression binary is mod 2
brisk moss
for the last digit, sure
but think about how in base 10, the last 2 digits are given by the number mod 100
and the last 3, mod 1000
it's similar here just with powers of 2 instead of powers of 10
sudden compass
does there exist a function which has the property $f(0) \to \infty$ and $f(1) \to - \infty$ or vice versa?
sudden compass
I dont really care about its values in between 0 and 1, or beyond 0 and 1, or continuity in general
kind wadi
can a function ever equal infinity
fervent wasp
No there isnโt
brisk moss
how can that be a real valued function
real valued function means the codomain is a subset of R
sudden compass
can a function ever equal infinity
equal as in limit ๐
sudden compass
real valued function means the codomain is a subset of R
nvm should remove that
fervent wasp
The definition of a function is whenever you plug in a certain value, it gives you an another in feedback
twin meteorBOT
rakยณen
vast shale
yeah why not ?
hard atlas
sure, f:{0,1}->{infty, -infty} given by your two points. thats a function
lavish river
waw
sudden compass
sure, f:{0,1}->{infty, -infty} given by your two points. thats a function
...i mean a closed form thought that was obvious?
brisk moss
are you asking for a function $f:\bR\setminus{0,1}\to\bR$ such that $\lim_{x\to 0}f(x) = \infty$ and $\lim_{x\to 1} f(x)= -\infty$
twin meteorBOT
slayla
sudden compass
the $R \setminus{0,1}$ isn't necessary
twin meteorBOT
rakยณen
kind wadi
,w interpolate infinity, -infinity
hard atlas
...i mean a closed form thought that was obvious?
you meant it maybe, sure. but thats not what you wrote. closed form isnt even a precisely defined thing
twin meteorBOT
brisk moss
it seems like it is...
hard atlas
function and "formula" arent the same things either
kind wadi
was wondering what it would say
sudden compass
function and "formula" arent the same things either
its stupid to ask something if a function like that exists thats easy to assure, my question is what the function's definition would look like
brisk moss
it seems like it is...
nvm
vast shale
something like tanx
maybe ?
hard atlas
look, its not my fault that you wrote a question but you actually meant a different question. this is an exercise about being precise about what you want
brisk moss
so you want a function $f:\bR\to\bR$ such that $\lim_{x\to 0}f(x) = \infty$ and $\lim_{x\to 1} f(x)= -\infty$
twin meteorBOT
slayla
sudden compass
Yeah
hard atlas
you can easily have 1/|x| for the x->0 and -1/|x-1| for the other one
sudden compass
look, its not my fault that you wrote a question but you actually meant a differ...
alright, sorry
hard atlas
and then build something piecewise between those
but presumably thats not closed form enough?
sudden compass
I see..any other ideas?
sudden compass
but presumably thats not closed form enough?
I mean, sure its fine ig
it just doesn''t look good to me ๐
brisk moss
some rational function probably works
and you can define f(0) = f(1) = 0 or whatever
if you want the domain to be R
hard atlas
$\frac{1}{x^2}-\frac{1}{(x-1)^2}$
twin meteorBOT
Denascite
sudden compass
o that looks nice
hard atlas
of course if your closed form is supposed to include f(0) and f(1) then you are a bit fucked
cause most things we can write down are continuous
sudden compass
some rational function probably works
yes
sudden compass
of course if your closed form is supposed to include f(0) and f(1) then you are ...
no its not necessary
sudden compass
some rational function probably works
might be interesting to look into the conditions such that P(x)/Q(x) satisfies the given limits
well thank you for all the ideas everyone
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
bitter sequoia
vocal sleetBOT
bitter sequoia
hi! could someone please explain how to solve this question?
without a calculator
pale perch
1/2 ab sin(c)=7.5
hidden bloom
let's set cosA=-0.8
bitter sequoia
yup
bitter sequoia
wait why?
hidden bloom
cosA<0,agree?
bitter sequoia
yes
hidden bloom
so b=c
bitter sequoia
how is sinA 0.6
hidden bloom
how is sinA 0.6
sinA=โ๏ผ1-cosA^2๏ผ
bitter sequoia
yess i got it
vocal sleetBOT
@bitter sequoia Has your question been resolved?
graceful spoke
J is the midpoint of line segment HL. I and K are on HL such as that HI = IJ and JK = KL. what percent of HI is HK
vocal sleetBOT
J is the midpoint of line segment HL. I and K are on HL such as that HI = IJ and...
left sparrow
Draw it out
vocal sleetBOT
@graceful spoke Has your question been resolved?
vocal sleetBOT
@graceful spoke Has your question been resolved?
gentle kayak
Hi, I have an exercise like this:
The sides of the triangle are 15 cm, 18 cm, and 21 cm. The triangle is cut by a line parallel to the shortest side, forming a trapezoid whose shorter base is 10 cm. Calculate the perimeter of the trapezoid.
I made a drawing of it and got the shorter base of 10 and the longer base of 15, but how am I supposed to find the other 2 sides? :)
vocal sleetBOT
Hi, I have an exercise like this:
The sides of the triangle are 15 cm, 18 cm, an...
tranquil trellis
since the line you drew to make the triangle is parallel to one of the sides, it'll create a smaller similar triangle
gentle kayak
like that
tranquil trellis
don't draw a separate diagram for the trapezoid
tranquil trellis
this triangle is similar to the original one
so you might want to draw it a bit bigger
tranquil trellis
my brain doesn't take it
you're not buying that they're similar?
gentle kayak
yeeah I do
tranquil trellis
or you're just not sure how to continue given that they are similar
gentle kayak
yeah im not sure how to continue
tranquil trellis
So you're given the smaller base of the trapezoid is 10
tranquil trellis
okay so what are the two other sides of the trapezoid then
tranquil trellis
vocal sleetBOT
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opal flare
Set $I := [0, 1]$, denote the set of continuous real valued functions on I by $C(I)$, let d1 be the L1 metric on C(I), and let d2 be the supremum metric on C(I). Are d1 and d2 equivalent? prove your answer.
I know that they are equivalent iff for every $x \in X$ and ${xn}{n=1}^\infty \subset X$ we have $x_n \overset{n} \to x$ in(X,d1) if and only if $x_n \overset{n}\to x$ in(X,d2).
I feel like it should be false, and there should be some example, but not sure how. Any help?
vocal sleetBOT
Set $I := [0, 1]$, denote the set of continuous real valued functions on I by $C...
twin meteorBOT
mtr123
round plover
I think if you take the constant zero function, then define f_n to be a piecewise linear "spike" of height 1 and width 1/n (and is zero outside of the spike), then the supremum distance between them will always be 1, but you can make the L1 distance arbitrarily small
in the supremum metric, (f_n,0) -> 0, so there is no constant C such that C d_2(f_n,0) <= d_1(f_n,0) so they're not equivalent metrics
basically, any pair of functions that bound vanishing area between them but remain at least a fixed distance apart at some point should work as a counterexample
vocal sleetBOT
@opal flare Has your question been resolved?
opal flare
in the supremum metric, (f_n,0) -> 0, so there is no constant C such that C d\_2...
actually the defintion they gave us for equivalent is whether an open set with respect to d1 is open with respect to d2
and not that C constant you used here
opal flare
I saw that defintion too online
but that's not what I got to work with sadly haha, it looks easier
round plover
lipchitz is stronger than topological though ๐ญ
opal flare
lipchitz is stronger than topological though ๐ญ
I was thinking about spike function too, cuz the integral should converge to 0 if I recall correctly as n goes to infinity, and the supermum gonna still to 1 so fn gonna converge in L1 but not in the supermum thingy
round plover
can you just say that the metrics are topologically equivalent iff the same sequences converge?
opal flare
well I'm suppose to prove that in another question ๐
round plover
since you can define convergence purely in terms of open sets, if they're topologically equivalent, they'll have the same set of convergent sequences
๐ญ
opal flare
round plover
oh, well
that's before this question
so if you prove that first you can use it ๐
opal flare
just need to figure out how to construct those spikes ๐
opal flare
that was quick lol
round plover
I knew I had it lying around somewhere
I think the argument might be clearer if you have the spike centred on 1/2 constantly though
but the modification should be similar
opal flare
I think it gonna be easier for me to just use this one honestly
thanks ๐
Just need to prove that other question now haha
.close
round plover
I think it gonna be easier for me to just use this one honestly
I made one that's centred for on 1/2 just in case ๐ญ
vocal sleetBOT
I made one that's centred for on 1/2 just in case ๐ญ
opal flare
I made one that's centred for on 1/2 just in case ๐ญ
oh wow, much appreciated!!! I might use it, just need to focus on the other question now because im relying on it!
round plover
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opal flare
thank you @round plover
round plover
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austere arrow
austere arrow
can i get some help please
im sorry
i cant think about it
can i get some help by you , please?
@ebon silo
oh yeah ik that
just that , in bulgaria its explained diffrently
(x-1) (x-1)-1
down its (2-x)(2+x) am i right
oh thanks
(x-1)(x-1)-1
(2-x)(2-x)
(x-1)^2
same thing
x^2 - 1^2
?
delicate oracle
she means make it a trinomial
austere arrow
I dont understand what trinomal means thats the thing
Not my first launglage
sorry abt that
delicate oracle
I dont understand what trinomal means thats the thing
a expression/equation with 3 terms
austere arrow
okay
tha thing is
i know the stuff
just cant understand the way to do it
thanks for the help
yes but in a different way
wait
idk about the convertion right at the top tho
oh wait dw about it
i missundestood
so it becomes x(x-1)
x^2 - 1
no wait
x^2 - x
got it
let me solve the entire thing
(2-x)^2 is 4-x^2
right
delicate oracle
sorry am back got banned for some reason
delicate oracle
(2-x)^2 is 4-x^2
no
austere arrow
wait really?
delicate oracle
4-2x+x^2
squared of the first term
multiply everything inside the bracket and then ny the exponent which is 2 the square the second term
delicate oracle
alr
austere arrow
i know the formula
delicate oracle
good luck
delicate oracle
okay
delicate oracle
second term?
austere arrow
the thing i just send
austere arrow
the entire thing
i gotta go tho
tommorow
im going to tell what i got on my exam
delicate oracle
lemme solve and give u
random musk
x=2
delicate oracle
he gone
vocal sleetBOT
@austere arrow Has your question been resolved?
austere arrow
im here
austere arrow
<@555797609021833217> Has your question been resolved?
no
austere arrow
lemme solve and give u
can you add me on here?
on discord
i have to ask u something
@delicate oracle check dms
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low trail
Hey, I completely don't know how to do this. Someone is able to explain more or less exactly how to do it?
vocal sleetBOT
Hey, I completely don't know how to do this. Someone is able to explain more or ...
@low trail Has your question been resolved?
worn bobcat
low trail
I didn't count
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undone aurora
I just want to make sure that im on the right path so this is what I got for one of the cases:
Case 1: 3, 4, 5, 6, 7 (3 to 7 diamond) (discard 5) need 1 of each
vocal sleetBOT
I just want to make sure that im on the right path so this is what I got for one...
undone aurora
Honestly u dont even have to read the question
the second, third, fourth image is enough
oh also in the 4th image I meant to divide all of that by (26C5)
but basically this is what I was thinking
Ik we need 1 of each for case 1 because we dont have any of those cards in the hand
so to get atleast 1 3 diamond the prob would be
(3C1)(3C1) (3 cards to choose 3 from)(3 suits to choose diamond 3 from)
oh wait is it suppose to be all of them multiplied instead of adding each
because we need 1 of each not 1 of 3 or 1 of 4 and so on
jolly flame
dude balatro isnt that hard
undone aurora
jolly flame
(i dont know math sorry) < i just always build 2 pair
undone aurora
i dont even play poker I just discovered abt this recently
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undone aurora
<@&286206848099549185>
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elfin pendant
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@elfin pendant Has your question been resolved?
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@elfin pendant Has your question been resolved?
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@elfin pendant Has your question been resolved?
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leaden crane
How would I do this problem?
leaden crane
<@&286206848099549185>
twin meteorBOT
Alberto Z.
civic otter
**Alberto Z.**
This one
civic otter
Yes
civic otter
Yep exactly
leaden crane
Easy enough, what would happen if there's two points though and no slope? @civic otter
brisk moss
Easy enough, what would happen if there's two points though and no slope? <@6413...
a robust way to do problems like these is to write the line as y = mx + b and then use the information given to determine m and b. so here for example, we have 17 = m(-2) + b
and you can get another equation from the other point and determine m and b
if you are given slope, you can just put that right in for m and then determine b with a point on the line
you don't have to remember different "forms" for writing lines if you do it like this
brisk moss
either works but probably easier to solve for b because no fractions
brisk moss
(15,6) is also on the line so we have 6 = m*15 + b as well
brisk moss
sorry i messed that up
brisk moss
yep
leaden crane
what shall i do next?
the only thing i can think of is setting both b's to each other lol
brisk moss
yea you can do that
if you mean put -15m+6 = 2m+17
fuck
sorry messed that up again lol
leaden crane
yeah, that's what i meant
brisk moss
you can solve for m from there
leaden crane
m=-11/17
leaden crane
would i need to do it to both?
brisk moss
you can use either equation but don't need to use both
they should give the same thing
leaden crane
then i just plug in 3+t for x
hmm, any ideas? @brisk moss
I've tried that +
$\frac{1308}{119}-\frac{11}{7}t$
twin meteorBOT
Someone
brisk moss
yea it appears we made an algebra error somewhere
i take that back, we did not make an algebra error
brisk moss
hmm, any ideas? <@984319941417250907>
11/17, not 11/7
brisk moss
sooo you have y = -(11/17)x + 267/17
i typo'd here again
for like the 3rd time
sorry lol
brisk moss
sorry i was never any good at algebra
brisk moss
np :3
leaden crane
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vast shale
Can anyone help me with antiderivates that consist of trignometry?
lavish river
just ask the question
heavy yoke
u-substitution?
vast shale
u-substitution?
I dont know how to do it
heavy yoke
as in you haven't learned substitution or you don't know what to substitute?
heavy yoke
a good place to start is usually something in the denominator
heavy yoke
you can try that (or something similar) and see if it works
vast shale
In my cb it is like that ok
What abiut du
The numerator is 1/2 sin2x
How did he solve that
<@&286206848099549185>
Where did he get the 4 from
1/4
Helppp
twin meteorBOT
jandro
grand linden
?
twin meteorBOT
jandro
grand linden
I think your doubt Is this
twin meteorBOT
jandro
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
jandro
jandro
twin meteorBOT
jandro
grand linden
Substituting backwards
grand linden
So the result is
twin meteorBOT
jandro
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urban snow
I suppose it's because sqrt(-6) is an imaginary number, so you can't really compare it to a real number in the real plane
I'm not exactly sure what you mean by the square root should be as well
Yea, good analysis, if f(x) is never negative then the square root of f(x) is also defined for the domain of f(x)
By solving it algebraically are you referring to quadratics only or other functions too?
Well you can't always solve for the variable in every radical equation, i mean technically you can but it might not always be real. Functions like radical quadratics and quintics for example don't always go below the x axis so all x values work
Just know that if you ever get an imaginary value that means either it's domain is all x values or no x values
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jagged cargo
Given $f(x)$ differentiable and positive on $(0,+\infty)$ such that [
f(x)\ln f(x)=x(2f(x)-f'(x)),\forall x \in(0,+\infty)
]
Given $f(1)=f(3)$, calculate $f(2)$
vocal sleetBOT
Given $f(x)$ differentiable and positive on $(0,+\infty)$ such that \[
f(x)\ln f...
twin meteorBOT
jagged cargo
not sure how to approach this
vocal sleetBOT
@jagged cargo Has your question been resolved?
cobalt crypt
Given $f(x)$ differentiable and positive on $(0,+\infty)$ such that \[
f(x)\ln f...
use the fact that $f$ is positive to make a substitution
[ f(x) = e^{x + g(x)} ]
twin meteorBOT
jagged cargo
hm, thats smart
alright let me try, ill notify when i encounter another problem
thanks!
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arctic patio
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arctic patio
Why is the angle 90 - alpha?
heady ibex
because the total angle at X is 180
wait actually
they don't show anything about reflection
if the incoming and outgoing rays are parallel that would make sense
heady ibex
if they aren't then it cannot be correct
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daring marsh
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lone linden
$2^{\log_2 x}=x$ for $x>0$ if thatโs what youโre asking
twin meteorBOT
Civil Service Pigeon
daring marsh
what does that mean exactly
lone linden
?
daring marsh
for x>0
so I cancels out so long as I add the it to other side?
idk what the formula means
daring marsh
Okay I see
lone linden
Meaning thatโs only true for positive x
Because if x is zero or negative, the logarithm in the exponent is undefined (over the reals)
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frank pier
hiii i need help , it's to do with basic logs but im kinda confused lol
frank pier
no
tidal dock
$x^3 = 3x$
twin meteorBOT
artemetra
tidal dock
no idea how to do this?
frank pier
do u do 3logx=3x?
tidal dock
let's use t as the variable to not confuse the names
yes, i let t = log(x)
so what you get is t^3 = 3t
now, solve for t
hint: move 3t to the other side and factor
lethal heart
$x^3 = 3x$
but here you can't multiply on both sides with 1/x?
frank pier
uh. t^2=3?
tidal dock
but here you can't multiply on both sides with 1/x?
careful: ||what if x=0 ?||
lethal heart
0=0
tidal dock
uh. t^2=3?
correct, but by doing this you are missing one of the possible solutions, namely t=0
so if t is NOT 0, t^2 = 3 applies
frank pier
would u square root 3 at the end?
tidal dock
yes, $\pm$
twin meteorBOT
artemetra
lethal heart
correct, but by doing this you are missing one of the possible solutions, namely...
I agree
crude arrow
yes, $\pm$
no -\sqrt(3) is useless here
lethal heart
I saw
tight orchid
**artemetra**
you cannot do that, since multiplying logs is not the same as multiplying the results of logs
crude arrow
you cannot do that, since multiplying logs is not the same as multiplying the re...
lmao they are saying let x = log(whatever)
pprob shouldn't have used x
but it's wtv
lethal heart
Ok I found a way to do it
tight orchid
I suggest to start by bringing the right side to the left, and then take one common log as a factor
tidal dock
that's what i did broski
tidal dock
you shouldn't have used x
yeah woops
tidal dock
i thought OP was confused by the use of t
lethal heart
Bringing the 3x to the left and factoring?
twin meteorBOT
artemetra
frank pier
yes
tidal dock
awesome
frank pier
but wait why there 0 as well?
tight orchid
ah, sorry guys, didn't understand that you substituted originally, thought you just wanted to cancel out the logs
lethal heart
$x\cdot(x^2 -3)=0$
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Gordon Ramsey
lethal heart
Is this right?
tidal dock
can i just help on my own guys
