Uhh is the question wrong or smth?
#help-27
mortal sky
Coz this will give an irrational answer
What don't you get?
You factorised it wrong
mortal sky
It was correct till here
cloud marlin
y=-5-sqrt233/2
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fierce dawn
Can sm1 help me find b xD
devout snowBOT
Can sm1 help me find b xD
astral forum
@fierce dawn
vernal monolith
Need to show this converges by leibniz test
devout snowBOT
Need to show this converges by leibniz test
vernal monolith
I have no idea how i can even show limit of this is 0
restive river
,rccw
woven radishBOT
grizzled shoal
vernal monolith
I saw that you can write this as (-1)^n.C(2n,n)/(4^n)
I managed to show that this is lesser than 1, any leads on how i can show that lim is 0?
,rotate
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@vernal monolith Has your question been resolved?
rare pelican
devout snowBOT
@vernal monolith Has your question been resolved?
gilded nova
a grocer packed 2/3 of his oranges in box 1 and the remaining in box 2 and 3 in the ratio 1:2. if box 1 holds 56 more oranges than box 3, ho wmany oranges are there in total
devout snowBOT
a grocer packed 2/3 of his oranges in box 1 and the remaining in box 2 and 3 in ...
gilded nova
box 1 = x
bo2 = y
box 3 = z
x+y+z= the total amount of oranges = a
x = 2/3
x-56=z
y+z=1/3=1:2
could anyone help me please?
long pasture
it's a very good start writing out all the information, setting up variables and forming equations
but there are so mistakes here and there
box1,2,3 as x,y,z, nice
x+y+z=a, no necessity, but ok
x = 2/3 times a
x - 56 = y
y+z = 1/3 times a
y:z = 1:2 or y/z =1/2
now that we have the right equations, we can go on
@gilded nova
all good till here?
gilded nova
because its box 3
OH
i see where i went wrong
i wrote box 2
its suppose to be box 3
gilded nova
sorry about that
long pasture
box1,2,3 as x,y,z, nice
x+y+z=a, no necessity, but ok
x = 2/3 times a
x - 56 = y...
let's start with the very bottom line
y/z = 1/2
rearrange the terms so that it looks nicer
gilded nova
ohh
long pasture
$\frac{y}{z}=\frac12$
woven radishBOT
OldBiscuit
gilded nova
reciprocal?
long pasture
we can multiply both sides by something
gilded nova
like z or 2?
long pasture
why not both
long pasture
nope
gilded nova
2y=1z?
long pasture
box1,2,3 as x,y,z, nice
x+y+z=a, no necessity, but ok
x = 2/3 times a
x - 56 = y...
let's move up one line
y+z=⅓ times a
gilded nova
okk
long pasture
can you do that?
gilded nova
not sure
gilded nova
like but the variables in that equation?
long pasture
2y=z
y+z=⅓a
since 2y=z, we can replace the z in the second line by 2y
long pasture
yea, please continue
gilded nova
?
long pasture
and we want something like
y = something something a
this
gilded nova
oh
long pasture
or
if you like it this way, it's also ok
there are many methods to do anyways
you don't really have to follow my path
gilded nova
yea
long pasture
next
x+y+z=a
we plug all we known into it
we know
a=9y
z=2y
now try to find x
long pasture
no
gilded nova
hm
long pasture
we know
a=9y
and this
gilded nova
oh ok
gilded nova
didnt we use them all
long pasture
yep
gilded nova
56=4y
long pasture
and
gilded nova
ohh
long pasture
x=6y
y
z=2y
and for the remaining ones
long pasture
nah
these type of questions seems to be real hard for you, and it takes time to understand
and I'm not staying for long
amber quarry
logarthmic question
devout snowBOT
logarthmic question
amber quarry
im stuck
i was going to put the 3 as a power o n the second part
and then since - logs are divided by each other
log10 (25-x/ 64-48x+12x^2-x^3)
woven radishBOT
Peachy
amber quarry
this is what i have right now
im not sure if i did somethign wrong
did i open
incorrectly
woven radishBOT
Peachy
amber quarry
uhm
eternal marsh
so you have $25 - x^{3} = (4-x)^{3}$
woven radishBOT
phoestaclies
eternal marsh
i made the 3 in parenthèse to cancel each other
$log(25 - x^{3}) = log((4-x)^{3})$
eternal marsh
apply the quadratic formula
eternal marsh
yes
amber quarry
and do like t = xsquared ?
eternal marsh
like $39 + 12x² -48x = 0$
amber quarry
and then i use the formula with abc
woven radishBOT
phoestaclies
eternal marsh
just solve with $\Delta = b² - 4ac$
woven radishBOT
phoestaclies
amber quarry
uhm i use a different one i think
eternal marsh
and you'll get the result 🙂
eternal marsh
yes it's the same i just mention the delta before
eternal marsh
in the equation $a = 12$ $b = -48$ and $c=39$
woven radishBOT
phoestaclies
scenic frost
devout snowBOT
distant sorrel
Think what is the opposite happening here
scenic frost
biggest number will be 4
eternal marsh
no it will be 3 in a dice because if it's 4 we can't do 5 with 3 dices
distant sorrel
My bad, I would also say (2/6)^3
scenic frost
we can't get the number 4 in a dice?
scenic frost
My bad, I would also say (2/6)^3
it's not correct
the answer is something ridiculous
eternal marsh
maybe i'm wrong but if we have 4 in a dice and 1 is the smallest number on a dice 4+1+1 = 6 that is greater than 5
distant sorrel
It the 5 in the question sum of the dices or smallest number in some dice
bright burrow
If smallest number in a dice then
bright burrow
I did (2/6)^3
This should work imo
scenic frost
yeah that's what I was thinking
bright burrow
if sum of dices then take cases ig?
eternal marsh
is something like 5/216
eternal marsh
ok so i don't know if it's very correct but just take the possible resulte that we can do with 3 dice like 666 = 216 and search the combinations that makes 5
and 5 has 7 combination and forgot 2 before
scenic frost
7? But we're only tossing 3 times
eternal marsh
like 1+1+2, 1+2+2 that repeat 2 times if i count the 2 separate to others, 1+3+1, 2+1+2, 2+2+1, 3+1+1
sorry not 666 but $666 = 216$ possibilities
woven radishBOT
phoestaclies
scenic frost
hmm, why the 3 though
eternal marsh
?
scenic frost
like 1+1+2, 1+2+2 that repeat 2 times if i count the 2 separate to others, 1+3+1...
where did 1+3+1 come from etc
eternal marsh
like 1+3+1 = number dice 1 + number dice 2 + number dice 3
and the sum must be equal to 5
scenic frost
ahh i get you, but look, this is no sum
this is literraly just saying
what is the probability that when yoiu toss a dice three times, the smallest number I'm gonna get is 5
so that means
5 or 6 are my only possible numbers
eternal marsh
so the question say you want the probabilities that the sum of dices makes 5 with three dices or i don't understand, sorry i'm not very good in english
scenic frost
it's okay
no not sum
just 5 or a bigger number
so let's say i roll a dice once
the probability of me getting the number 5 or more is 2/6
or 1/3
but
all i thought i had to do was cube the number
for three rolls
and now it's telling me the answer is 7/216
eternal marsh
ok i see now
ok make the same reasonning
and u found 7/216
so the possibilities are $666 = 216$ right
woven radishBOT
phoestaclies
scenic frost
indeed
eternal marsh
and let's say that (a,b,c) = (dice 1, dice2, dice 3)
we have just 7 combinations possible
and it's (5,5,5), (5,6,5), (5,5,6), (6,5,5), (6,6,5), (6,5,6), (6,6,6)
because we can't have a number less than 5
scenic frost
what about (5,6,6)?
bright burrow
Oh wait i think i get it
eternal marsh
oh yes you're right
bright burrow
Its 7 cuz its c(2,1)c(2,1)c(2,1)-1
You minus the (6,6,6) obs
Because theres no 5 in it
scenic frost
OMG
bright burrow
Thats how its 7/216
scenic frost
You got it!!!
eternal marsh
yes thanks
eternal marsh
yes i forgot that we cna't have (6,6,6)
scenic frost
Thats how its 7/216
can't thank you enough
eternal marsh
my english so bad 😂
bright burrow
can't thank you enough
Np
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faint valve
how do i set up #2? this is language my teacher has never used
devout snowBOT
how do i set up #2? this is language my teacher has never used
hybrid snow
Graphing window
faint valve
and how would i do that
fathom pewter
Hi, could someone explain to me why this is accepted ?
It says underneath the limit that x and y can't be equal to each other, which makes sense I guess given the denominator, but then they proceed to give 2 values that are equal to each others ?
devout snowBOT
Hi, could someone explain to me why this is accepted ?
It says underneath the li...
fathom pewter
Unless I misunderstood completely what x != y is supposed to mean
pseudo basin
does this limit not admit basic algebruh
this looks like it's equal to sqrt(x)+sqrt(y)+2
no need to bother with pathwise limits is there?
fathom pewter
no need to bother with pathwise limits is there?
Sorry, I'm confused, what do you mean by pathwise limits ? I take the course in french so some technical words in english might fly over my head
pseudo basin
that wasn't an 'official' term i said
maybe i misunderstood your question
can you show the solution you're looking at?
fathom pewter
I mean, I'm trying to solve it by simplifying it to get rid of the denominator, I still haven't figured out how to do so yet, but that's not really what's bothering me
What's bothering me is that (x,y) -> (0,0)
x and y are equal to each others, since 0 = 0, so it's ignoring its own "rule"
novel dome
I mean, I'm trying to solve it by simplifying it to get rid of the denominator, ...
how do you simplify a²-b²?
fathom pewter
how do you simplify a²-b²?
Oooh I gotcha, so x - y is really (sqrt(x) - (sqrt(y)) * (sqrt(x) + (sqrt(y))
Makes sense
novel dome
that's it you're on the right path
fathom pewter
But what about the other thing ? Am I just misunderstanding what they mean by x != y ?
Or does it simply stop mattering since we're getting rid of the denominator anyway
novel dome
Or does it simply stop mattering since we're getting rid of the denominator anyw...
i think x != y only doesn't apply for the limit itself since in a normal function f(x,y) if x and y are equal, the function will not exist. but a limit is a limit, that means that x!=0 and y!=0 but x and y approaches 0
fathom pewter
i think x != y only doesn't apply for the limit itself since in a normal functio...
Hmm, alright. It's weird they wrote it like that under the limit though. Thank you for helping ^^
This whole 2 variable functions thing is annoying, since they are so hard to visualize. There doesn't happen to be a software that can help visualize those that I don't know of, is there ? Cause Desmos isn't helping here
novel dome
it normally works for desmos right?
fathom pewter
Desmos doesn't work for me for functions higher than one dimension
fathom pewter
yeah, it only works when you make it an equality
but then that's not really the function
Anyways, that's alright, I'll free up the channel for now ^^ Thank you
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primal phoenix
I'm having trouble understanding Big Oh, Big Theta and Big Omega notation in relation to code runtimes.
Since it's about upper and lower bounds, can I just select any function when selecting a big O function? Like if I have f(x)=3x^2+3x I can say f(x) is O(g(x) if g(x)=x????
devout snowBOT
I'm having trouble understanding Big Oh, Big Theta and Big Omega notation in rel...
primal phoenix
I've tried for hours to make this stuff make sense
devout snowBOT
@primal phoenix Has your question been resolved?
leaden coral
as you said, Big Oh is used to describe the upper bounds, big Omega is for lower bounds
when saying a function f has O(x^2)
it means that there exist some starting point n, and a Constant C, such that a that f doesn't go above Cx^2 for x >=n
in simpler words, our function f, after some point, will be upper bounded by x^2
is everything clear here?
primal phoenix
So when finding big O and big Omega, we can select any function that falls below or above f(x)?
Yes
leaden coral
what do you mean below or above f(x) ?
for example if f(x)=3x^2+3x, f is O(x^2), saying f is O(x) is wrong
primal phoenix
How come? Both x^2 and x fall below 3x^2+3x
leaden coral
define fall below
primal phoenix
after a certain point on the x axis, the y values are less than the y values of f(x)
that's what this is about, right? Finding functions that go above or below f(x) indefinitely after a certain point
leaden coral
yes
leaden coral
after a certain point on the x axis, the y values are less than the y values of ...
this is Big Omega
primal phoenix
Ahh, this information just now makes a bit of sense to me, so I confuse the terms a bit
leaden coral
yeah so Omega is about the lowest bound
O is about the upper bound
sometimes one is useless and the other is useful
primal phoenix
What I now am left wondering is how finding low and upper bounds that are absurdly far from f(x) is helpful in any way
Ahhhh
leaden coral
its only helpful to categorize algorithms according to their growth rates
primal phoenix
Man, my math course is really unnuanced about this and this whole terminology confused me because it never mentions that big O and Omega aren't always useful and can be multiple functions
I had the impression that big O and big Omega were something you calculate like you have f(x) and then you find the ONE answer for big O and big Omega
What about big Theta?
That seems to be a bit more rigorous
like it has to be realistic
leaden coral
as you said
big O and big Omega can be different
and one gives the upper bound and the other gives the lower bound
big theta combines the two
for example if some algorithm is O(x)
and Omega(x)
the upper bound is x, the lower bound is also x
it means that this is the best algorithm to solve such a problem
and we say it has Theta(x)
adding two numbers is an example of this
if you have x digits, you do x opertaions
both the upper bound and the lower bound are x
primal phoenix
That makes sense to me. But what about when best-case and worst case scenarios aren't the same?
leaden coral
what do you mean?
primal phoenix
Like linear search through an array. If you search for 5 and 5 is the first number in the array, the runtime is just 1 but if it's not in the array, the function will search through the whole array and runtime will be n (n=size of array)
leaden coral
yes
primal phoenix
how do I find Theta of that
leaden coral
this should tell you that worst case and upper bound are not the same
leaden coral
its only helpful to categorize algorithms according to their growth rates
as I said Big O notation and such only study how the work of the algorithm grows according to its size
best-case and worst-case are not directly related to this
primal phoenix
this should tell you that worst case and upper bound are not the same
As a sidenote just to be sure; I shouldn't select any upper bound, like n^n if the function can't actually have an n^n runtime?
leaden coral
As a sidenote just to be sure; I shouldn't select any upper bound, like n^n if t...
well
if you have a function f(x) = 3x^2 + 2x
you can say that it has O(x^2)
or O(x^3)
or O(x^4)
etc
but most of the time you are only interested in the least case
and all of these satisfy the definition in the sense that, they are are upper bounds for f
primal phoenix
you can say that it has O(x^2)
But how does that make sense if 3x^2 will always be above x^2 on a graph?
leaden coral
and the questions expects the least upper bound because its actually the useful one
leaden coral
it means that there exist some starting point n, and a Constant C, such that a t...
read the definition again
primal phoenix
ahhh, so the C is always there, implicitly?
leaden coral
yes
3x^2 is O(x^2) because there exist a starting point n, and a constant C, such that cx^2 > 3x^2 for x>=n
an example is
C = 4 and n = 1
there are infinite examples of C and n here
but only one is enough to satisfy the definition
primal phoenix
You have been a great great help already. Thank you so much, this conversation has been a great relief for me and I've gotten to understand these terms a lot better now. But I'm still unsure about Theta
primal phoenix
C = 4 and n = 1
The witness thing finally makes sense now
leaden coral
You have been a great great help already. Thank you so much, this conversation h...
this might be a good answer that explain big theta
primal phoenix
I will read this thoroughly, thank you!
leaden coral
it also says big O has nothing to do with worst case, big theta has nothing to do with average case, and big omega has nothing to do with best case
because they measure different things
primal phoenix
Oh so big Theta only exists if big O and big Omega are the same?
primal phoenix
Oh shit, I just realized
That big O and big Omega can be the same without being the same function
because of the witness thing
and C
I reached the Aha moment hahaha
Thank you so much @leaden coral , Seriously this conversation has been a godsend. I am extremely grateful for your help, time and for you being so patient. I'm retaking this course because this stuff didn't make sense to me last year either. So thank you
Have an amazing night!
leaden coral
Thank you so much <@180305129952509953> , Seriously this conversation has been a...
Thank you for your kind words! I wish you luck in your studies!
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umbral roost
How do they factor out values for L^2-6L+13? For me, I can’t find values for L, because I can’t eye the factors, nor can I use the quadratic formula. Thanks!
devout snowBOT
How do they factor out values for L^2-6L+13? For me, I can’t find values for L, ...
umbral roost
Like when we have a square root of a negative, do multiply it by 1i?
upper schooner
Basically if it's a square root of a negative, take the square root of the positive version and then multiply that by i
umbral roost
Yeah I got it. Clear thx
devout snowBOT
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main gull
Because math
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Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
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main gull
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crimson kestrel
How is 2 + 2 4
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cursive hazel
how do i write the kernel of a matrix
i have the vector but idk how to write the solution
Ker(L) = ?
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how do i write the kernel of a matrix
i have the vector but idk how to write the...
@cursive hazel Has your question been resolved?
open pendant
trigonometry
devout snowBOT
trigonometry
open pendant
i know how to do the formulas
but sometimes it asks me to deduct my total from 180
if its obtuse
am i supposed to VISUALLY confirm that its obtuse in order to know when to do this
or is there something im missing
royal tiger
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@open pendant Has your question been resolved?
open pendant
i lost it. let me find another
like a triangle
with 2 marked sides
and 1 marked angle
wait no, that doesnt make sense, thats just
sin theta/number
sin known/number
ill find one again, hangon
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thick quail
Express 5 cosQ - 3 sinQ in the form R cos (Q + a) where R is positive and 0° < a < 90°
devout snowBOT
Express 5 cosQ - 3 sinQ in the form R cos (Q + a) where R is positive and 0° < a...
thick quail
anyone has any idea, im stuck because both sides have different signs
5 cosQ - 3 sinQ = R cos (Q + a)
long pasture
Mr. Gamer is typing... and I wish to know what he is typing.
proud perch
5cos(Q) - 3sin(Q) = Rcos(Q+a)
-5sin(Q) - 3cos(Q) = -Rsin(Q+a)
Let Q = 0:
5 = Rcos(a)
-3 = -Rsin(a)
long pasture
I have one idea only 😦
proud perch
Now you have a system of two eqns in two vars
thick quail
hmm
long pasture
hmm
mossy gale
Is it okay to let Q=0?
long pasture
HillBill is typing too!
proud perch
Yes because this is an algebraic identity
long pasture
oh!
proud perch
Rather than a conditional equation
proud perch
So we are asserting that this statement must be true for all values of Q
long pasture
interesting!
mossy gale
An equation without any conditions?
Or an equation that doesn't change irrespective of conditions?
proud perch
This is an algebraic identity:
(x+1)² = x² + 2x + 1
This is true for all values of x
This is a conditional equation:
5x+2 = 2x+3
This is only true if x = 1/3
thick quail
5 cosQ - 3 sinQ = R cos (Q + a)
would it be possible to find a and R by comparing both sides of this?
when RHS is expanded
the only problem is the signs are not the same
proud perch
Yeah but using calculus is easier and more fun
long pasture
maybe! what is identity? i just know it is has a 3 line equal sign
long pasture
Yeah but using calculus is easier and more fun
yea, calculus is more fun!
thick quail
would it be possible to find a and R by comparing both sides of this?
well I have to do it in this way
long pasture
the only problem is the signs are not the same
what sides?
thick quail
signs*
long pasture
well I have to do it in this way
oh!
thick quail
well I have to do it in this way
so how do I change it so that the signs are the same? or so that I can compare
long pasture
can we let R=√34 and a=30.96° and try to put it in to the equation?
thick quail
how did you get those numbers?
long pasture
oh, just using calculator
proud perch
5cos(Q) - 3sin(Q) = Rcos(Q+a)
-5sin(Q) - 3cos(Q) = -Rsin(Q+a)
Let Q = 0:
5 = Rco...
Just solve this system
long pasture
I have one idea only 😦
Mr. Gamer Inspired me to get this idea!😆
if like i can put any number, why not put the right ones
proud perch
That is also a good method
We don't even have to differentiate
Since we know that it must be true for all values of Q
long pasture
I have one idea only 😦
@thick quail do you want to know my original idea?
thick quail
sure
thick quail
oh
proud perch
Which gives you the same system
near belfry
@thick quail you still need help?
thick quail
<@677886980570349580> you still need help?
if it can be done by the method I need, that is
near belfry
Yes
long pasture
yes
near belfry
Send the question again so I can easily reference if needed
long pasture
if it can be done by the method I need, that is
what is it to be needed help with? 😯
thick quail
Express 5 cosQ - 3 sinQ in the form R cos (Q + a) where R is positive and 0° < a < 90°
long pasture
let's see el pepega's response
near belfry
You have to make 5cosq-3sinq=CosaCosq-SinaSinq
long pasture
interesting!
near belfry
You can then split this equation into two
And to find r would be 5^2+3^2
Then root the answer of that
You can get sina cos a
long pasture
that's a good approach too
long pasture
do tell 🙂
thick quail
You have to make 5cosq-3sinq=Cosa*Cosq-Sina*Sinq
how do I start with this?
long pasture
And to find r would be 5^2+3^2
and our friend here says, you can find R by this
and root it
near belfry
You expand using the addition formula
You can find it either way but finding r first would just make it more systematic
thick quail
oh
near belfry
Cos(a+b)= (cosacosb)-(sinasinb)
thick quail
I don’t understand how to do that..
near belfry
You don’t need to
I don’t think
There are formula booklet with the formulas on
It’s basically saying that there’s two angle to one
There are 3 formulas for addition that I know of
Cos(a+b) sin(a+b) and tan(a+b)
Probably many more
thick quail
yeah but how do I apply it now?
thick quail
5 cosQ - 3 sinQ = ?
long pasture
very clever question!
thick quail
yeah
near belfry
It’s more of proof
thick quail
oh
thick quail
R cos (Q + a) = R (cosQ sina + cosa sinQ)
long pasture
nice!
near belfry
So everything in brackets multiplied by r
long pasture
R cos (Q + a) = R (cosQ sina + cosa sinQ)
except its a little bit wrong
near belfry
We know that Rcos(q+a) is equal to
long pasture
nice first step
long pasture
R cos (Q + a) = R (cosQ sina + cosa sinQ)
next, sina becomes cosa
near belfry
And then prove it to find what r cos q+a equals
long pasture
R cos (Q + a) = R (cosQ sina + cosa sinQ)
and + become negative
long pasture
R cos (Q + a) = R (cosQ sina + cosa sinQ)
and finally cosa become sina
thick quail
how does it become?
long pasture
R cos (Q + a) = R (cosQ sina + cosa sinQ)
then we will have
R cos(Q+a)=R(cosQcosa-sinQsina)
long pasture
how does it become?
because it was wrong 😦 sadly
hummm lemme find something on google to help you understand
brb
back
would this help? @thick quail
long pasture
very good!
long pasture
makes sense now
so, all done?
clarified and you can tackle the rest?😆
thick quail
okay I think I got it from here
long pasture
yey!
thick quail
thank you all so much
long pasture
have a nice day!
thick quail
.close
zinc sapphire
Hey, so im doing this exercise where i need to find the lateral derivatives of a point in a function and tell if the function is differentiable.
I went to check the resolution and they went to check if the function was continuous(doing the - and + limits). I was wondering if that is really necessary since to check if a function is differentiable the easier way is to check if has a finite derivative. Or do i need to verify as well if the function is continuous even if it has a finite derivative?
devout snowBOT
Hey, so im doing this exercise where i need to find the lateral derivatives of a...
sick fulcrum
post question please
if your function has a derivative, it's already continuous
(at that point)
zinc sapphire
Translating: Look at this branch function, calculate the lateral derivatives in point 0 and check if the function is differentiable in x = 0
Do i really need to check if the function is continuous?
supple knot
Do i really need to check if the function is continuous?
It takes like 10 seconds to check continuity at 0
zinc sapphire
sure, but is it needed?
supple knot
sure, but is it needed?
If it takes such little time, why not
You're spending more time debating with yourself if you need to do it or not than just doing it
zinc sapphire
i already did it, thats not the my point. cause in my exam with limited time i need to know if a question comes like these and the limit become more complex, i would like to know if i need to check the continuity of a function to check if its differentiable or not
supple knot
That's a question for your teacher, not random strangers who aren't in your class
zinc sapphire
im asking a theoric question
supple knot
That's a teaching question, not a math question
zinc sapphire
you're telling me that checking if a function is differentiable or not depends on the teacher
supple knot
That's not your question
wicked rover
no, the exam complexities depend on the teacher
supple knot
Your question is specific to your teacher's grading
zinc sapphire
ill try to simplify my question,
Is it strictly necessary to check the continuity of a function in order to check if its differentiable?
zinc sapphire
in order to check if its differentiable
supple knot
Then no, not always in all cases, for all teachers
stuck bridge
It's just basics I think what do I do if a linear function's minimum value came out as a fraction?
devout snowBOT
It's just basics I think what do I do if a linear function's minimum value came ...
supple knot
It's just basics I think what do I do if a linear function's minimum value came ...
Do about what
Can you show a problem you're working on
stuck bridge
f:[-5;7[->R f(x)=3/4x-2
wicked rover
why would it being a fraction make it special
stuck bridge
I need representation and characterization
stuck bridge
why would it being a fraction make it special
I don't know how to calculate it
supple knot
I need representation and characterization
Show the exact instructions. Screenshot or picture is best
supple knot
Yea nothing about this looks special to fractions
stuck bridge
Right upp it's just Classroom work
supple knot
You just leave your answer in whatever form your teacher uses. Decimal or fractions are fine
supple knot
If you can use the graph, then it's the lowest y value of the graph
stuck bridge
The lowest where there's an x or the value at the left line?
supple knot
You can see the graph is increasing, so the minimum value of f(x) is the left most x value in the domain
supple knot
The lowest where there's an x or the value at the left line?
When there's an x in [-5,7[
stuck bridge
ooohhh thanks that's what I wanted! 🙂
!close
okay now how do I close the channel?
sick fulcrum
.close
stuck bridge
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short nebula
devout snowBOT
short nebula
need help not sure where to really start
sonic smelt
q5 or q7?
short nebula
5
sonic smelt
First it'd be nice to move everything on one side
Preferably on the side with highest power of x
In this case, to the left
So we have 3x^4 + 11x^3 - 4x^2 = 0, right?
sonic smelt
We can factor x^2 out of the left hand side
Yes
And we get x^2 * (3x^2 + 11x - 4) = 0
short nebula
yes
sonic smelt
A product is 0 whenever one of the terms of that product is 0
Meaning we have to consider two cases
Case 1: x^2 = 0 (and thus x = 0)
Case 2: 3x^2 + 11x - 4 = 0
short nebula
ok
sonic smelt
Are you good with quadratics or do I continue?
short nebula
still slighly lost. once their both set to 0 do i just solve
and get the two answers
short nebula
not sure how to solve second one
sonic smelt
You can either complete the square or use the shortcut aka the quadratic formula
sonic smelt
Yup
short nebula
ok then 7
sonic smelt
Again, start by moving everything on one side
Here you'd get x^4 - 29x^2 + 100 = 0
Before we had a quadratic in x
short nebula
yep
sonic smelt
If you look carefully, now we have a quadratic in x^2
This is the same as (x^2)^2 - 29(x^2) + 100 = 0
Meaning you can solve for x^2 using the quadratic formula
sonic smelt
If you look carefully, now we have a quadratic in x^2
If you don't see this, consider doing a substitution u = x^2
You'd have u^2 - 29u + 100 = 0 then
short nebula
ok 2, -2, -5, 5
sonic smelt
Yup
short nebula
1 sec
i was doing 6 but i went wrong somewhere and got stuck
what did i do wrong
after this i got (2x-32)(x-6)
keen spruce
6 is def one of the answers
to start you can move the entire equation to the left side so the right =0
2x^3-12x^2+192-32x=0
short nebula
ok
keen spruce
then factor to 2(x-6)(x+4)(x-4)
and since we need it to equal 0 now you find the restrictions (which would turn that entire side to zero too)
keen spruce
what answers did you get
short nebula
4,3
keen spruce
ok then you are forgetting about the one outside of the bracket
short nebula
exactly
keen spruce
if x was 0 then 4x^5=0
short nebula
ok so 5/4
keen spruce
?
near belfry
h
near belfry
.close
radiant drift
devout snowBOT
radiant drift
thx
radiant drift
https://brilliant.org/wiki/dirichlet-convolution/
ill look and then post further uestions
.cose
.close
forest pawn
devout snowBOT
devout snowBOT
@forest pawn Has your question been resolved?
devout snowBOT
@forest pawn Has your question been resolved?
devout snowBOT
@forest pawn Has your question been resolved?
devout snowBOT
@forest pawn Has your question been resolved?
keen spruce
what ya tryna figure out
vast rain
no sketches? hmm that's kinda dumb
I assume you're allowed to sketch but also hvae to give the reasoning
well let's see if you got the right answer
,w intersection of -3x + 4y = 0 and 4x+3y = 9
woven radishBOT
devout snowBOT
@forest pawn Has your question been resolved?
devout snowBOT
devout snowBOT
Available help channel!
tired haven
- A school is holding a table tennis tournament. In the beginning, 3/11 of the students in the school signed up to compete. Later, another 136 students signed up. At that time, the total number od students who signed up is 7/4 times the number of students who did not sign up. How many students are in the school? someone help huhu
devout snowBOT
2) A school is holding a table tennis tournament. In the beginning, 3/11 of the ...
safe tulip
devout snowBOT
safe tulip
i) is false and I dont see why
by IVT, for all choices of y in (0,2), there exists an x in (0,1) s.t. f(x) = y
oh 5/2 is 2.5
i thought it was 1.5 for some reason lol
.close
nocturne cape
In the Euro Millions game, you are asked to give 5 "numbers" between 1 and 50 (and not twice the same) and 2 "stars" between 1 and 11 (and not twice the same either). The draw then consists of 5 numbers and 2 stars drawn at random. A win is obtained as soon as you have 2 correct numbers or when you have 1 correct number and the 2 correct stars. In all other cases, nothing is won. What is the probability, in percent, of winning nothing after playing a grid?
Let see my answer (this wrong):
The probability of not winning anything after playing a Euro Millions grid is very high.
There are 50 options for each number and 11 options for each star, so :
50 x 50 x 50 x 50 = 2,118,760 options for the numbers and
11 x 11 = 121 options for the stars.
Assuming that the numbers and stars are drawn randomly and independently, the probability of not having two numbers or one number and two stars correct is :
( (49/50)^5 x (10/11)^2 ) = 98,98%.
So the probability of not winning will be 98.98%.
devout snowBOT
In the Euro Millions game, you are asked to give 5 "numbers" between 1 and 50 (a...
@nocturne cape Has your question been resolved?
bright burrow
In the Euro Millions game, you are asked to give 5 "numbers" between 1 and 50 (a...
When you pick 5 numbers between 1 and 50 are those the "correct numbers"?
nocturne cape
Yes they are well included in it
nocturne cape
😔whythis so complicate
nocturne cape
But could be wrong
This wrong
bright burrow
Whats the right answer
nocturne cape
92.663
bright burrow
That is what i have
nocturne cape
Okay no problem.
But for the proof ?
bright burrow
Okay no problem.
But for the proof ?
As in the explanation?
bright burrow
0.92663=92.663 percent
bright burrow
What is the answer💀
nocturne cape
😂😂I don't know
bright burrow
What is wrong
nocturne cape
I can't explain u
bright burrow
I can't explain u
So 92.663 is wrong?
nocturne cape
Yes
bright burrow
Does the question have an answer key?
nocturne cape
This also wrong 😶
nocturne cape
Which one ?
devout snowBOT
@nocturne cape Has your question been resolved?
topaz axle
bright burrow
Why c(20,5)?
bright burrow
Can you explain the numerator
topaz axle
all numbers wrong + 4 numbers wrong and (2 stars wrong + 1 star wrong)
(45c4 × 5c1)(9c2 + 9c1 × 2c1)
point is there are many cases where you win, so it's hard to do 1 − ...
but only 3 cases where you lose
devout snowBOT
topaz axle
even though it has all the probability
devout snowBOT
Available help channel!
drowsy atlas
devout snowBOT
devout snowBOT
real grail
anything multiplied by z take it to the LHS
and the rest to the RHS
factorize the LHS by z
an try to divide by something to make z lonely in the LHS
isn't @upper schooner 
hybrid snow
Pablo
upper schooner
But yep that's it!
devout snowBOT
Available help channel!
near belfry
devout snowBOT
long pasture
double angle formula for cosine
vernal quartz
devout snowBOT
vernal quartz
I need help with #37, #39-#41
robust acorn
,rcw
woven radishBOT
vernal quartz
For some reason i’m not understanding the negatives lol
main python
show work
vernal quartz
wym
main python
show what you tried
vernal quartz
it’s using the unit circle
you just look at it and find the answer
but i don’t understand like how
for the negatives
shadow fern
For some reason i’m not understanding the negatives lol
U just need a good teacher to tell u that
main python
for the negatives
You go on the opposite direction
vernal quartz
i would ask her but tmrws the midterm lol
vernal quartz
You go on the opposite direction
so like for tan -210°, you just go 210 in the opposite direction(clockwise)?
main python
yes
shadow fern
Cos and sec sign doesn't change when we put negative angle
And else 4 ratios left become -ve when we put -ve angle
vernal quartz
so radical 3?
shadow fern
Cos and sec sign doesn't change when we put negative angle
And else 4 ratios le...
Just remember this
woven radishBOT
vernal quartz
could someone check the circled ones?
main python
,w sec 7pi/4
woven radishBOT
main python
,w sin(-pi/3)
woven radishBOT
main python
,w csc(-2pi/3)
woven radishBOT
main python
everything correct
vernal quartz
#39 could you check
main python
,w cot(-210*pi/180)
woven radishBOT
main python
39 is wrohng
sick marsh
I assume it means X_3 equals the subspace spanned by w_31?
devout snowBOT
I assume it means X_3 equals the subspace spanned by w_31?
sick marsh
the brackets I am not sure about. Teacher usually uses L for span
sick marsh
I will post the question surrounding it hold up
From the context I assume the span
But I like to be certain haha
stone stump
would make sense
devout snowBOT
devout snowBOT
Available help channel!
maiden ginkgo
Just wanted to know, did I do this right?
devout snowBOT
Just wanted to know, did I do this right?
lusty sapphire
Why'd you do 7.5x25 and 45x25?
maiden ginkgo
because thats the number of students attending
lusty sapphire
what about the teacher and parent?
Will they not eat?
Will they not need entry to the park?
maiden ginkgo
it says that the teacehr and parent will not any money to attend this field trip
"all their costs must be covered by the student fees"
lusty sapphire
So when it says "calculate the cost each student will owe the school," I believe that these are the "student fees"
So the teacher and parent's lunch and ticket fees must be included in the student fees
So you should do 27x, not 25x
That's just my interpretation of the wording
If that interpretation is incorrect, then you set the problem up right.
maiden ginkgo
alr
lusty sapphire
This problem is also poorly worded because it says "each family" instead of "total from all families"
"each" means that if, say, there were 10 families, then all ten of them would individually be paying ~$1400. Which is absurd
I doubt this is the wording they intended though, as you have no way of knowing how many families there are, so you cannot say what each individual family must pay.
devout snowBOT
lusty sapphire
yeah np
devout snowBOT
Available help channel!
deep geyser
so i got between 0 and positive infinity but the answers say after I checked that it it 1.5 to positive infinity
devout snowBOT
so i got between 0 and positive infinity but the answers say after I checked tha...
deep geyser
why so?
devout snowBOT
@deep geyser Has your question been resolved?