yeah, that's how you should split is
#help-27
mellow panther
restive river
thankyou, need to work on it
there is one error, the second brackets sign isnt mathchin
split radish
hi, I'm trying to find the tangent equation to this. I understood I can replace t with the upper limit of the integral and multiply it by its derivative for finding the slope. The slope I got after evaluating -pi was 2pi, but after that I'm stuck, how can I find points for writing the equation of the tangent? ;-;
devout snowBOT
hi, I'm trying to find the tangent equation to this. I understood I can replace ...
sonic smelt
Before writing the equation for the tangent it would be nice what value does the function take at that place
In this case, f(-pi) = 0
So, let's say we'll have the equation for the tangent as y = 2pix + c for some constant c, right?
split radish
Before writing the equation for the tangent it would be nice what value does the...
yes!
split radish
I thought that was illegal
sonic smelt
If you want to evaluate the function's value at some point x = a
Then you have to plug in x = a into the function's definition
sonic smelt
And the upper bound becomes 0
And when the upper and lower bounds are equal, the entire integral becomes 0
So f(-pi) = 0
split radish
I see :0
split radish
And when the upper and lower bounds are equal, the entire integral becomes 0
I didn't know this was possible
sonic smelt
Now, we could like out tangent to take the same value as our function as x = -pi, right?
split radish
yes, I guess that could make it y=-2pi(x+pi)
sonic smelt
Yes, and that's pretty much it
y = -2pi(x + pi) has the same slope as f at x = -pi
And it also takes the same value
Meaning it does touch the graph there
split radish
right, thank you so much for helping me :'D I think I have to restudy some integration rules again, it's been a long time since I learnt them
.close
mystic musk
does this mean the summation is postive or every number in the summation is posstive
devout snowBOT
does this mean the summation is postive or every number in the summation is poss...
mystic musk
'positive terms'
I assume every number in the summation is postive so every an is postivie?
devout snowBOT
@mystic musk Has your question been resolved?
mystic musk
<@&286206848099549185>
vernal anvil
could anyone verify this proof looks right?
devout snowBOT
could anyone verify this proof looks right?
vernal anvil
knowing now that this is wrong, I am not sure how to change it
mild basin
devout snowBOT
mild basin
Just wanna be clear on one thing here
To show work
if it was 8x^3 instead of 8x^2
you would multiply top and bottom by 1/x^3, right?
azure sun
yes
restive river
Yeah
mild basin
great, thank you!
restive river
But the answer should be clear regardless
mild basin
Yes, but just in case I need to show my work for full marks
I would just divide highest power if they match on top and bottom
to find the limit, but i guess this multiplication shows it too
.close
dusty valley
This question fills me with anger and rage. It's purposefully ambiguous in my opinion. Who agrees? https://imgur.com/yIpMVNV
devout snowBOT
This question fills me with *anger* and *rage*. It's purposefully ambiguous in m...
dusty valley
Say it....SAY IT!!!
dim perch
Say it....SAY IT!!!
cos(pi/3)?
dusty valley
What is the first question to ask myself so I can learn how to approach this?
I don't want to be told answers, I wanna learn how to do it.
dim perch
no im asking you is that your issue?
restive river
This question fills me with *anger* and *rage*. It's purposefully ambiguous in m...
It seems you have just entered the length of JL
dusty valley
The whole question is my issue. They tricked me into thinking they wanted the distance of the shortest leg but the answer was the ratio of the shortest leg. But how can I know what they want?
dim perch
The whole question is my issue. They tricked me into thinking they wanted the di...
it said cos
when they have trig(angle)
dusty valley
Okay, I guess, it's easy enough but they tricked me here.
dim perch
you will always have a ratio
restive river
The whole question is my issue. They tricked me into thinking they wanted the di...
They said it pretty clearly: Enter in the value of cos(pi/3)
I don't think they really tried to trick you
dim perch
they wouldve said “find the leg length”
restive river
And it isn't actually ambiguous whatsoever
prisma cargo
yo
prisma cargo
winter brook
!status
devout snowBOT
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
dont evenknwo what to take as a limit
like
i was doing it by considering x approaching 0
winter brook
Do that, what do u get for the left and right sided limits?
prisma cargo
ig am going to consider x is aproaching c which is less then 0 for the time being
and then x approaching c which is more then 0
woven radishBOT
Jukelyn
prisma cargo
dude
winter brook
what
prisma cargo
cant you just send me what you trying to say
winter brook
**Jukelyn**
this
prisma cargo
is this your solutions?
winter brook
this is what u said u wanted to do
prisma cargo
ig there's a miscommunication
winter brook
I suppose so
prisma cargo
i asked how to take the qus further
winter brook
it was uncool dude
I mean, you know that sinx/x is continuous everywhere except x=0 but that's not in that domain anyways and then the other function is clearly continuous as well and there is no jump discontinuity either since the two sided limits are equal. so therefore it's continuous
devout snowBOT
I mean, you know that sinx/x is continuous everywhere except x=0 but that's not ...
devout snowBOT
mystic musk
I mean, you know that sinx/x is continuous everywhere except x=0 but that's not ...
when x approaches zero from right it is 1 and when x approaches zero from left its -infinity no?
mystic musk
how
prisma cargo
.reopen
winter brook
.reopen
I accdentially claimed the channel by typing soon after u closed it
the channel is closed now
prisma cargo
I mean, you know that sinx/x is continuous everywhere except x=0 but that's not ...
i cant explain like this
i have to do some maths
dude
continuity is not just theory here
winter brook
it's just the two limits that you and I wrote and then sinx/x for x=0 isn't in that piece of the function so there isn't an issue
just write those
prisma cargo
i looked somewhere else and what i got hat we have to consider a c which is approaching 0
and x is appriaching c
by placing them
i got the both continious
winter brook
yeah that's to show that they're continuous, yes
winter brook
Ah I see, I thought you were just stating the fact, but asking about the limit for 0 when you said this:
so that's when I wrote
prisma cargo
man
i cant even properly seeing this
a miscomunication and that also for an easy qus
np @winter brook
.close
devout snowBOT
Available help channel!
meager rose
Does anyone know what the question "3 choose 2" means?
devout snowBOT
Does anyone know what the question "3 choose 2" means?
wooden veldt
thats not a question
meager rose
Well what about this?
wooden veldt
still not a question that just a true statement
meager rose
so you can't solve that?
lunar harbor
You're giving a mathematical expression with no directing prompt.
meager rose
So no one's able to go in depth on how that's true?
topaz axle
if you get to choose 2 out of 3, you can choose all except 1st, or all except 2nd or all except 3rd
Yes, Yes, No
Yes, No, Yes
No, Yes, Yes
so 3 options
mild basin
devout snowBOT
mild basin
Are you allowed to distribute like this?
hybrid snow
That violates an exponent law I'm pretty sure
mild basin
I should get sqrt(9 + 1/x) for the denominator but I’m not sure how?
hybrid snow
You can only combine bases if the exponents are the same
wooden veldt
write 1/x as sqrt(1/x^2)
mild basin
I need to review exponent laws and logarithms
wooden veldt
assuming x >= 0
mild basin
write 1/x as sqrt(1/x^2)
I need to?
wooden veldt
if you want to get to sqrt(9+1/x) then yes
wooden veldt
they just skipped the step i told you to do
for $x > 0$, $\frac{1}{x} = \sqrt{\frac{1}{x^2}}$
woven radishBOT
ΣAC
mild basin
Thank you.. I don’t know why some videos skip steps
The way he wrote it doesn’t make sense
wooden veldt
well the point is if you've gotten to the topic of limits, basic algebraic manipulation is assumed
which is why they'd skip steps
mild basin
well the point is if you've gotten to the topic of limits, basic algebraic manip...
But I think the way that Organic Chemistry Tutor wrote it is wrong..
It should be 1/x^2
To get to the next step
mild basin
well the point is if you've gotten to the topic of limits, basic algebraic manip...
If he multiplies the bottom by 1/x^2, isn't he supposed to multiply the top by 1/x^2?
so that x in the numerator would become x/x^2... 1/x instead of 1?
mild basin
write 1/x as sqrt(1/x^2)
oh, I misunderstood.. lemme try this again..
mild basin
i feel like you're not actually reading this
So here I can distribute into the denominator?
wooden veldt
yes
mild basin
Since both factors are the same exponent
wooden veldt
exactly
mild basin
Ah OK
wooden veldt
that was the point of writing 1/x as sqrt(something)
so we could pass it inside the other sqrt
mild basin
And I can choose to just cancel the sqrt for the numerator, to match the exponents again
Power of 1
mild basin
Ah OK
Thanks, I need to remember that for any time I see radicals and wanna distribute into them
wooden veldt
yes you should really know exponent laws like the back of your hand
mild basin
I can see why exponents are a better choice over radical signs
I think I will try to adjust radicals to exponents from now on
^ (power / root)
.close
proper dome
help
warm fulcrum
Are you familiar with which matrices that matrix multiplication is defined between?
devout snowBOT
@proper dome Has your question been resolved?
proper dome
Are you familiar with which matrices that matrix multiplication is defined betwe...
not very much
warm fulcrum
Matrix multiplication between an m × n-matrix and an k × j-matrix is defined if and only if n = k and the result will be an m × j-matrix.
For the first part you have a matrix A with currently unkown dimensions m × n. We know that the matrix you multiply with is a k × 1-matrix which becomes a n × 1-matrix for our definition to be met. We know that our function T is defined on ℝ⁷ → ℝ⁵ which means our n × 1 matrix is a 7 × 1-matrix.
In the same way, we know that the resulting matrix from the multiplication will be a m × 1-matrix (remember our definition) which from the mapping T : ℝ⁷ → ℝ⁵ we know to be a 5 × 1-matrix.
So from knowing this about the values m and n, what would you say the dimensions of the matrix A is?
proper dome
5 x 7 ?
warm fulcrum
Yes, exactly!
And from this argumentation we can actually generalize the dimensions of the matrix A that represents a linear mapping f : ℝᵐ → ℝⁿ which will be a n × m-matrix
gray agate
devout snowBOT
gray agate
how do we know what symbol to use
when writing it in formal way
<@&286206848099549185>
vast rain
the same way you'd know what words to use when you write a sentence
just look at what they mean, and figure out which one conveys the required meaning
there's no magic to it
gray agate
the same way you'd know what words to use when you write a sentence
like the ->
how would i know when to use that
restive river
like the ->
if you have a universal quantifier you restrict the domain using a conditional
if you have an existential quantifier you restrict domain using AND
vast rain
like the ->
the -> means implies
i.e. if you know the first thing, then you know the second
gray agate
if you have a universal quantifier you restrict the domain using a conditional
ah
makes sense
vast rain
like you don't have to memorize that particular rule; it follows pretty logically
if you want to say that for every circle x, x is above f
that's equivalent to saying for every object x, if x is a circle, then x is above f
and if you want to say there exists a square x that is black
then that's equivalent to saying there exists an object x that is both square and black
gray agate
like you don't have to memorize that particular rule; it follows pretty logicall...
its just easier
vast rain
if you switch them around, it doesn't make much logical sense
gray agate
to follow the rule
vast rain
no it's not easier, because then you can't check your work effectively
gray agate
no it's not easier, because then you can't check your work effectively
how so?
vast rain
because then you're just writing symbols without understanding what they logically mean
you're writing them because someone told you to follow a rule about them
it's the difference between being fluent in another language and using a dictionary of phrases, words, and grammar to translate things
gray agate
that's equivalent to saying for every object x, if x is a circle, then x is abov...
this is how i say it
i just ixed em up
vast rain
this is how i say it
right, if it's intuitively obvious to you that you say it that way, then it really isn't hard to translate it into symbols
for every object x if x is a circle then x is above f
upside down A x, Circle(x) -> Above(x, f)
you won't mix them up because writing something like "for every object x, x is a circle and x is above f" is clearly false
devout snowBOT
@gray agate Has your question been resolved?
brave lily
$e^{x\ln(A)} \neq e^x \cdot e^{\ln(A)}$
woven radishBOT
Shell
spring goblet
alternatively, you could try a u-substitution
lean cipher
Remember (or rather, understand)
2^3 * 2^4 = 2^7
(2^3)^4 = 2^12
devout snowBOT
Available help channel!
raven lynx
#53
woven radishBOT
Result:
0.77539749661075
supple knot
,calc sin(asin(0.7))
woven radishBOT
Result:
0.7
So for this one u can just cancel @supple knot ?
when could u not cancel
like this one u cant cancel
oh wait isnt that just a coterminal angle
topaz axle
i think you can cancel if sin is outside but not if it applies first
raven lynx
topaz axle
no wait i'm not thinking straight
exotic stump
i heard u dont just cancel the sin/arc sin
you heard this because sin and arcsin have different domains and ranges
so they don't just "cancel"
exotic stump
the domain of arcsin is [-1, 1], yes
raven lynx
yep
topaz axle
it makes sense, we know the number is in the domain of arcsin, which means it's in the range of sin
raven lynx
so we can just cancel
topaz axle
when the sin is outside, it happens after and you can cancel
i must be missing something...
raven lynx
ahhh why are ppl saying diff things
the first guy said u can cancel
and now ur saying i cant
From what i understand
exotic stump
in quotes
raven lynx
If the domain matches
then u can cancel
like if the restriction fits
that what i mean by cancel
exotic stump
sure, you can "cancel" in such a case
raven lynx
Okk
exotic stump
but it's not really canceling
raven lynx
well crossing out the sin and arcsin
and just having the number is what I mean by cancelling
exotic stump
that's not exactly what's happening behind the scenes, though if you do that in certain situations you will be correct
but it doesn't always work like that
exotic stump
your method is correct -- it's just not "canceling" in the form that canceling is used in
raven lynx
Im confused
exotic stump
like with x/x, you can cancel the x's
raven lynx
R u just question my terminology
exotic stump
yes
raven lynx
because im not trying to find a better word
Ok
well
well im trying to understand the concept
topaz axle
i'm saying you can cancel sin(arcsin(x)) always, i'm just not sure
topaz axle
yes, the expression may be invalid from the start
topaz axle
you can't say 99 for sin(arcsin(99)) but you can always say it's x if the domain is fine but it may not be true for arcsin(sin(x))
exotic stump
what is sin(3pi)
exotic stump
and what is arcsin(0)
topaz axle
it can only be one
raven lynx
but u exclude pi cuz its not in domain right
topaz axle
right
raven lynx
Ahh tysm
topaz axle
do yousee what i;m talking about?
you didn't get 3pi
but if the order was reversed, sin(arcsin(something)), then you would get (something)
devout snowBOT
devout snowBOT
Available help channel!
restive river
help please
devout snowBOT
help please
red sierra
You need to differentiate k(x) and find k'(x)
restive river
I have no idea where to even start.
Do I need to plug in the f(3)=1 for the values before I can differentiate?
What is the first thing I need to do?
winged rapids
Do I need to plug in the f(3)=1 for the values before I can differentiate?
nah
if you plug in right now, on the left it still is going to be k(x)
restive river
I'm kinda dumb. Just trying to learn.
winged rapids
you want to find k'(x)
dont worry bro
you basically do derivative of both sides immediately
on the left you will just have k'(x)
which is what you want
you want to have an equation like k'(x) = blah
and you just plug in values that they give for the blah expression
restive river
I need to study more.
winged rapids
o
are you familiar with basic derivatives
like derivative of x^2
or derivative of sin(x)
winged rapids
ya exactly
restive river
yeah my bad
winged rapids
well all the 'more complicated' derivatives are still just plugging in formulas
the point of something like quotient rule is to split a harder derivative into easier chunks
restive river
Does it matter if I derive by the product or quotient rule first?
winged rapids
well you could use product rule. i know a lot of people who do that, but to do so you would have to get rid of the denominator and put it as exponent -1
you know what i mean?
restive river
nope
winged rapids
because product rule works based on multiplication of two functions
f(x) times g(x) = derivative of f(x) times g(x) + derivative of g(x) times f(x)
in this problem you have a function divided by another function
so to use product rule, you would have to make the 'divded' into a multiplication
restive river
ah okay. I was thinking I would have to use both rules.
winged rapids
you do though
if i were to do this problem i would probably use quotient rule first
and then the simpler derivative that i would then have to solve is still product rule
but if you did product rule first you would have to do it twice, so its still the same amount of work
restive river
right. okay
low holly
is this person getting flagged as a likely spammer for anyone else?
winged rapids
the reason you have to do product rule after is cuz the numerator has a multiplication between two functions and you can't get around that
winged rapids
is this person getting flagged as a likely spammer for anyone else?
yes for some reason
winged rapids
the first step to doing quotient rule, or product rule, or any of these more complicated derivative techniques is to identify which is what to plug in
bruh does this image even work
restive river
I can read it.
restive river
nice. much better.
winged rapids
ok
so what i meant is you have to identify what f(x) is and what g(x) is
then plug into this formula
its easy its just like quadratic formula you just plug in shit into a formula
except its derivatives so its more deez
woven radishBOT
negativerizz
winged rapids
@restive river its not as hard as you think you just make the entire thing on the numerator f(x) and the entire denominator g(x)
restive river
I dont even know what my f(x) and g(x) are.
winged rapids
restive river
oh snap
winged rapids
**negativerizz**
sorry its confusing that in the problem you have f(x) already but this was just the general formula you could use any way to write it like h(x) it doesn't matter
restive river
You might of just made something click in my brain. Let me work this real quick.
winged rapids
ok
restive river
Can I derive the numerator?
winged rapids
yeah but you have to use product rule
its x^2 times f(x)
again, its the same as in quotient rule. you just identify your f(x) and g(x) and plug into the formula
$\frac{d}{dx}(f(x)g(x)) = f'(x)g(x) + f(x)g'(x)$
woven radishBOT
negativerizz
winged rapids
derivative of one times the other, and vice versa
restive river
Do I need to plug in a value for the f(x)?
winged rapids
i feel like many people use product rule rather than quotient rule because its so much easier to remember
winged rapids
Do I need to plug in a value for the f(x)?
after you have the complete expression
restive river
My brain is in knots right now.
winged rapids
right now you have k'(x) = (you're trying to calculate the derivative of this)
after you finish calculating the derivative
you plug in k'(3) =
restive river
ok
restive river
Will I need to use to values for f(3) and f'(3)?
winged rapids
yes
because the expression you end up with will have f(x) and f'(x) in it
if you're trying to find k'(x) when x is 3
then you plug in x is 3
winged rapids
because the expression you end up with will have f(x) and f'(x) in it
the f(x) and f'(x), you replace the x in them as 3 so f(3) and f'(3)
restive river
How do I get f'(x) for the quotient rule without inserting values?
the derivative of x^2(f(x))
winged rapids
ya basically you can't get it in one step so you do it next step
because its product rule
you just write [x^2 * f(x)]'
and then next step you would find what [x^2 * f(x)]' is by using product rule
do you want to discord call it would be faster
restive river
sure
winter brook
lol what
winged rapids
is this person getting flagged as a likely spammer for anyone else?
idk bro someone else said that too
winter brook
discord got something against u bro
lament sequoia
yeah
devout snowBOT
Available help channel!
tiny rain
devout snowBOT
untold lance
This has a binomial distribution
tiny rain
oh it is?
untold lance
Yes
tiny rain
o
untold lance
Success in i tosses
tiny rain
hm
untold lance
Actually wait
What does this actually ask
We want to keep tossing until we get what we need right?
tiny rain
yeah
untold lance
So, let's say you get the head after you tossed like 5 times
tiny rain
yeah
untold lance
So, if head appears with p probability then it doesn't appear with (1-p) probability
Each toss is independent
Hence getting the success after tossing i times has Probability of (1 - p)^(i - 1) times p
tiny rain
hmm
untold lance
p = 1/2 so it's (1/2)^i
You set the random variable to be like this
X = i if ith toss gives success
untold lance
It's supposed to be sum of pixi
untold lance
I meant $\sum p_i x_i$
woven radishBOT
rikusp2002
untold lance
P is probability
X is the value of random variable
Where X is mapped from Omega to R, the random variable
tiny rain
untold lance
Let's go it does
Ratio test says
(i+1)/(i) * 1/2 this goes to 1/2 when i goes to infinity
Hence < 1, must converge
Somewhere
tiny rain
man im confused
tiny rain
ok wait so we start of by saying that this is a binomial distribution
and p = q = 1/2 right
so the random variable X_i means that the ith iteration is a head
untold lance
The value of expectation is
$\sum_{i = 0}^{\infty} \frac{i}{2^i}$
woven radishBOT
rikusp2002
tiny rain
untold lance
ok wait so we start of by saying that this is a binomial distribution
My bad, it's a geometric distribution, I was wrong in that part - that's why I asked to "actually wait " and then did everything step by step
untold lance
So, let's say you get the head after you tossed like 5 times
Read from here
untold lance
It's nothing but same thing keeps getting multiplied to each term
tiny rain
oh i see
untold lance
Probability of success of ith toss is p * (1-p)^(i - 1)
(1-p) gets multiplied each faliure
tiny rain
ok hold on kinda lost cuz of the amt of texts, lemme write it out
untold lance
oh i'm sorry 👍
untold lance
Noo
untold lance
The (n 2) thing won't be there
tiny rain
oh why tho
untold lance
The experiment doesn't talk about how many heads we get
It talks about tossing and then stop when you get first head occurence
That's why it's not binomial but geometric
untold lance
yes
untold lance
Yes, that is the weighted average of random variable
Basically multiply each probability each corresponding value and add
untold lance
Niceee
tiny rain
yay
tiny rain
right yes
untold lance
Now find the sum
tiny rain
this is sus
tiny rain
o.o
untold lance
You know the sum of this series i'm typing wait
tiny rain
okie
untold lance
$\sum_{i = 0}^{\infty} x^i$
woven radishBOT
rikusp2002
woven radishBOT
rikusp2002
tiny rain
hm
untold lance
$\sum_{i = 1}^{\infty} ix^{i - 1} = \frac{d}{dx} \frac{1}{1-x}$
woven radishBOT
rikusp2002
untold lance
This is only possible because 1/2 < 1
untold lance
Right?
tiny rain
ok i kinda gtg lol needa go somewhere
untold lance
okk bye
tiny rain
but thanks so much for the help
untold lance
Glad to help
tiny rain
untold lance
You're welcome
tiny rain
.close
devout snowBOT
devout snowBOT
Available help channel!
solar warren
devout snowBOT
fickle ember
k
devout snowBOT
@solar warren Has your question been resolved?
solar warren
<@&286206848099549185>
winter patrol
what seems to be your issue here?
twilit blade
<@&286206848099549185>
we are here to help, so please tell us where you are stuck by explaining how far you have (not) gotten and what you tried so far
solar warren
we are here to help, so please tell us where you are stuck by explaining how far...
dont know where to start
twilit blade
dont know where to start
do you generally know how to find the cosine ratio?
if so, this task becomes very easy, because you don't even have to use an angle and you can just test both cases
solar warren
do you generally know how to find the cosine ratio?
if so, this task becomes ver...
i forgot how to
twilit blade
i forgot how to
$\cos{\alpha}=\frac{adjacent}{hypotenuse}$
woven radishBOT
Zabbx
twilit blade
where alpha is your angle, and the sides are clear
solar warren
48/50?
twilit blade
yes
twilit blade
so which angle is that
twilit blade
48/50?
those are the sides, but the tasks ask you for the angle right
so you have to find out where 48 is the adjacent side, and 50 is the hyp
solar warren
those are the sides, but the tasks ask you for the angle right
ye
solar warren
so you have to find out where 48 is the adjacent side, and 50 is the hyp
ye
sooo what do i do to find angle
twilit blade
I mean I just told you
you just have to decide between beta and theta
which of those has 48 as adjacent and 50 as hypotenuse
solar warren
which of those has 48 as adjacent and 50 as hypotenuse
theta
devout snowBOT
@solar warren Has your question been resolved?
gleaming socket
When to use equivalence and implication symbol? Like why did @pastel pasture write $a = \log_c b \implies c^a = b$ ?
devout snowBOT
When to use equivalence and implication symbol? Like why did <@71846158723671658...
woven radishBOT
Diesel
stone stump
ask them lul
pastel pasture
Technically I suppose I was meant to use a double arrow
but I didn't know the LaTeX so
stone stump
its never wrong to write an implication instead of an equivalence
pastel pasture
gleaming socket
Are they both correct?
stone stump
its just a weaker statement but still correct
pastel pasture
I don't pay attention to this stuff generally
So uh if the notation is ever incorrect or inconsistent I'm sorry
stone stump
if you can write <=> then you can write => or <=
pastel pasture
iff
gleaming socket
I never payed attention in school but the logic class really made me reconsider
pastel pasture
Also you look senile if you do that
gleaming socket
Since primary school I have been using =>
Some people use nothing at all moving to the next line
pastel pasture
I believe abuse of notation should be accepted as long as you get what is meant to be said
$\dv{x}[x^2 + y^2 = 1]$
woven radishBOT
NEONPerseus
gleaming socket
.close
proud nimbus
how to solve this kind of problem ?
devout snowBOT
how to solve this kind of problem ?
random vine
Why is the number of faces here 1 and not 3
pastel pasture
Is it a hollow cylinder
proud nimbus
.close
gentle nymph
devout snowBOT
gentle nymph
not sure whats next
pastel pasture
Instead just write secant in terms of tangent
And just like the log question you did earlier you have a quadratic
gentle nymph
Instead just write secant in terms of tangent
how?
pastel pasture
$\sec^2 x - \tan^2 x = 1$
woven radishBOT
NEONPerseus
pastel pasture
It's 2tan^2 + 2
pastel pasture
You wrote 2tan^2 + 1
devout snowBOT
@gentle nymph Has your question been resolved?
devout snowBOT
@gentle nymph Has your question been resolved?
muted gull
devout snowBOT
muted gull
umm...can anyone help me?
<@&286206848099549185>
guys please help me?'
ok ill just go
.close
earnest palm
A cylinder vessel of radius 18 cm and height 70 cm is half filled with water. Rohan put a spherical ball in the vessel. By doing this, the height of water raised 24 cm. Based on this, find answer to the following questions: Find the diameter of the sphere.
(a) 18cm (b)9cm (c)24cm (d)36cm[8:54 PM]hello how do i fidn the diameter here[8:54 PM]find[8:55 PM]can someone please help me with this oneIdunnohello how do i fidn the diameter here
devout snowBOT
A cylinder vessel of radius 18 cm and height 70 cm is half filled with water. Ro...
earnest palm
hello here how do i find the diameter of sphere
only the radius of cylinder is given can i just take the radius of cylinder as the radius of the spehere?
polar chasm
Can you find out volume of the sphere?
earnest palm
yes
4/3pir^3
but here r isnt given
radius of only cylinder is given
nor is the volume of sphere given
knotty bolt
yes it is
that was the point, you have to find the volume and then the radius using it
polar chasm
Yep, can you find the volume of sphere given the fact that water raised by 24 cm?
earnest palm
hmm where?
water rasied by 24 cm means the volume?
yes 4/3piR^3
4/3piR^3=24?
why not surface area
why is the water rasied only by volume?
earnest palm
Um?
polar chasm
Thats because the sphere pushed out that volume of water
polar chasm
Okay, so first compute the violet/purple volume
earnest palm
4/3pir^3=24
polar chasm
4/3pir^3=24
You did just the height
But it's 3 dimensional
it pushed out some VOLUME of water
earnest palm
Hmm
polar chasm
Cylinder is radius 18, and the height is 24
earnest palm
isnt 24 the volume and by what i just did we can equate
and the water rasied is also 24 cm
36! Ans
polar chasm
and the water rasied is also 24 cm
It pushed out whole the blue volume
You need to find the blue volume first
devout snowBOT
@earnest palm Has your question been resolved?
shadow elk
help with part c pls
devout snowBOT
help with part c pls
supple knot
show your work for a and b
shadow elk
alrr, but im not too sure abt part b, ill show u
supple knot
part c depends on b, so it's important to get b right
shadow elk
part c depends on b, so it's important to get b right
Idk what it means by k8near factors tbh
The ms shows something weird
I'm pretty sure what I did is right, I just need to take an extra step, but idk what step to take
supple knot
if you have the solution just show that
shadow elk
Alrr
shadow elk
if you have the solution just show that
supple knot
Idk what it means by k8near factors tbh
linear factors is products of terms like:
$z - a, z - b, z - c, ...$
woven radishBOT
riemann
supple knot
so that when you multiply them, you get the starting polynomial
$(z^5 - 1) = (z-1)(z-a)(z-b)(z-c)(z-d)$
woven radishBOT
riemann
supple knot
yes
supple knot
shadow elk
ah, good to know
then part c?
how am i gonna do that
i tried using $z+\frac{1}{z} = 2\cos(n\theta)$
woven radishBOT
Candor.
supple knot
you didn't do b correctly, so start there
shadow elk
oh right let me finish it
supple knot
you're close with your cosine observation, but you're not actually adding the roots right away. use this fact
supple knot
**riemann**
so going back to this, $a, b, c, d$ have to relate to each other in that two of them are complex conjugates of each other. e.g. $\overline{a} = b$ and $\overline{c} = d$, where the line above means complex conjugate
woven radishBOT
riemann
supple knot
**riemann**
confusingly, i chose a,b,c,d but they're completely unrelated to the a+bi and a-bi in the image.
shadow elk
so going back to this, $a, b, c, d$ have to relate to each other in that two of ...
ohhhh
ok i think i have an idea now
@supple knot im lost again, should i start by expanding brackets?
shadow elk
**Candor.**
im thinking this but we dont know theta
wait nvmm
i gotta multiply by z^2
supple knot
these are the $a,b,c,d$ in your linear factors
woven radishBOT
riemann
supple knot
did u try the w substitution
shadow elk
did u try the w substitution
nah, i dont get what it does
supple knot
use the sub and plug it into c
shadow elk
alr
devout snowBOT
@shadow elk Has your question been resolved?
shadow elk
ive expanded it and everything, but i cant see anything useful
wait
nah nvm
oh ive got something
but im left with cos theta
how do we know theta is 2pi/5?
not got 4pi/5?
@supple knot ?
devout snowBOT
Available help channel!
zinc pecan
Q5. show that if -1<x<0 then 0<p(x)<12
P.S : this question have a realation whit the last 4 Q.
zinc pecan
the polynomials
devout snowBOT
@zinc pecan Has your question been resolved?
zinc pecan
Like i only need how i can solve this
devout snowBOT
@zinc pecan Has your question been resolved?
devout snowBOT
@zinc pecan Has your question been resolved?
spring goblet
@zinc pecan tu pourrais factoriser le polynome
et puis voir où c'est positif ou negatif
la 4eme question doit t'aider
real grail
et calculer the dérivation de P(x) pour trouver le max et le min de P(x)
dans l'intervalle ]-1,0[
spring goblet
et calculer the dérivation de P(x) pour trouver le max et le min de P(x)
jpense que c'est pas une necessité pour q5
il suffit de calculer le signe
real grail
mais il faut monter que P(x) est enter 0 et 12
spring goblet
ah ouais bien sur j'ai pas voir l'inequalité complete mdr
spring goblet
et calculer the dérivation de P(x) pour trouver le max et le min de P(x)
donc +1
woven radishBOT
Mehdi_Moulati
jaunty dagger
devout snowBOT
jaunty dagger
How would i solve this problem
I get that its
the integral of pi fx^2 - gx^2 but what would the bounds be in this case
problem 79 by the way
devout snowBOT
@jaunty dagger Has your question been resolved?
jaunty dagger
.close
jaunty dagger
devout snowBOT
jaunty dagger
how do i figure out where sinx=cosx
magic pine
do you remember the unit circle?
magic pine
that is not true
magic pine
in general it's at pi/4 + npi, n any integer
but im guessing you just want the first time they're equal
jaunty dagger
this question is a bit off
idk weather to intigrate to the first intersection point
so in this case from 0 to pi/4
or where else
magic pine
they mean 0 to pi/4
jaunty dagger
ok perfect lets try that
is it possible to solve this without trig identities btw because he wants us to use u sub but idk how that would apply here
mellow bone
For $\mu$ i got 3.4 and for $\sigma^2$ I got 6.24, however, I don't really understand what the rest of the question is asking...
devout snowBOT
For $\mu$ i got 3.4 and for $\sigma^2$ I got 6.24, however, I don't really under...
woven radishBOT
heheitsop
undone mango
ㄴ[
mellow bone
do i literally just find all possible combos of sample size 2?
undone mango
몰라요ㅕ
mellow bone
그럼 왜 대답 하나요?? ㅠㅠ ㅋㅋ
gentle nymph
devout snowBOT
gentle nymph
where does that value from upper right corner come from?
main gull
nova idol
is there a way to manually find it
yes
you can derive it
at pi/4, width and height of triangle are equal
so c^2 = a^2 + a^2
solve for a
where c is 1
mellow bone
yes
gentle nymph
so c^2 = a^2 + a^2
is it c^2 = a^2 + b^2
nova idol
a = b
devout snowBOT
@gentle nymph Has your question been resolved?
sour needle
devout snowBOT
sour needle
how do you find the points of tangency
I know how to find the derivative at a certain point but im not sure what poitns to uuse
grim agate
sour needle
yeah ttheres two lines that go thru that point
but idk where the two lines touch the graph of y
hushed wraith
Consider the point where it touches the graph to be (x,y) or something and find a system of equations ig
sour needle
Consider the point where it touches the graph to be (x,y) or something and find ...
im not sure what equations to use, can you lmk what to do?
hushed wraith
Okay what is the derivative u found
sour needle
y'=2x+2
hushed wraith
Yes so 2x+2 gives the slope of a line drawn tangent to the graph at x coordinate x
sour needle
ye
hushed wraith
At x coordinate x, you also know the y coordinate of the graph
Interms of x
What is that
sour needle
y=x^2+2x+4
hushed wraith
Right, now what is the slope of the line joining the origin and this point
The point (x, x²+2x+4)
And the origin
sour needle
2x+2
sour needle
(x^2+2x+4 - 0)/(x-0)
hushed wraith
Yes
sour needle
=(x^2+2x+4)/x
hushed wraith
So now u have an equation that you can solve for x
hushed wraith
=(x^2+2x+4)/x
This should also be equal to 2x+2
The solutions to that equation would give you the points on the graph that you are looking for
sour needle
x= +-2?
hushed wraith
Yes
sour needle
bet, thanks 🙏🙏
hushed wraith
👍
sour needle
.close
signal crag
hello
signal crag
i was wondering if you could prove the am-gm inequality using backwards reasoning
,rotate
woven radishBOT
signal crag
in order to remove the square signs, i need to square root both sides
however, that would give a positive and negative case
messing up the proof
btw, we can also assume the fact that both a and b are greater than or equal to 0
devout snowBOT
@signal crag Has your question been resolved?
signal crag
<@&286206848099549185>
lilac portal
Wait, <@788719345676189736> from this
cause ur saying backward reasoning, I assume u want to proof it from this to the picture u sent
signal crag
uh
i wanted to prove the amgm inequality using backwards reasoning
which is what you said
i think
lilac portal
Wait, <@788719345676189736> from this
Ah my bad this is wrong
Its not supposed to be equals
signal crag
yeah its lesser than or equal to
lilac portal
I think I just automatically pressed it, habit
signal crag
nw
signal crag
square?
signal crag
wouldn't that give you plus or minus cases
signal crag
Ah my god, i'm still groggy just got out from my sleep
all good