i think my solution is a bit of cheating because i got something that looks simillar but im not sure how to make sure i correctly made a greater series i.e b_n
#help-0
proven tendon
tacit arch
you're right that that $1/(n^2+1) < 1/n^2$
ocean sealBOT
riemann
tacit arch
but is $2n + 3 < 2$ ?
proven tendon
no
ocean sealBOT
riemann
tacit arch
so your comparison is incorrect
proven tendon
so the numerator should be greater or then same
tacit arch
well yes if you're gonna use the < symbol, you want the right side of that symbol to be greater than the left side
proven tendon
so if i had something like 2n+3/n^2
what could i do to that to show it converges or diverges
i was thinking of making it a geometric series
but i dont think thats possible
can i just do a simple divergence test
tacit arch
you just care about the highest terms
proven tendon
and say 3 is insignificant and 2n < n^2
tacit arch
yes
proven tendon
gotcha
tacit arch
so 2n / n^2 should be compared with what?
proven tendon
1/n?
since its almost basic fact that 1/n -> 0
we can say that the factor of is insifnificant
so n/n^2 = 1/n
i think pulling out the 2 and showing 1/n is 0 is a bit more logical
tacit arch
when you say b_n converges, what do you think that means
proven tendon
oh right
since its 0 that means it needs more testing
so maybe divergence test wasnt the best method
proven tendon
since its 0 that means it needs more testing
i.e its inconclusive
tacit arch
comparison test with 1/n or 2/n is what you want
proven tendon
comparison test with 1/n or 2/n is what you want
ok i have that
3 is insignificant
and i boiled down b_n to
2/n
but isnt 1/n a diverging series?
tacit arch
it is yes
proven tendon
but shouldnt i be looking for something converging
becuase naturally i look at a_n
and see that its bottom heavy
so showing b_n diverges dosent give me any info on a_n
fervent timber
and see that its bottom heavy
does being “bottom heavy” guarantee that it converges?
proven tendon
no not really
fervent timber
why’s that?
proven tendon
i dont know, when i think about it, being bottom heavy it should converge
since the numerator is gitting divide smaller as n approaches inf
but doing this question im arriving to the fact that bn is diverging when it should be converging
atleast i think it should be
does a p series have to be in the form 1/n?
can 2n/n^2 work to?
fervent timber
but isnt 1/n a diverging series?
1/n looks bottom heavy to me
and yes, it diverges
it’s counterintuitive
same for your sequence b_n btw
proven tendon
1/n looks bottom heavy to me
yeah but it diverges by p series
fervent timber
it doesn’t, yeah
proven tendon
so my b_n is pointless no?
since b_n diverging tells me nothing about a_n
so should i find a b_n < a_n and show that diverges
fervent timber
I mean you compared it to 1/n and showed that 1/n diverges
but that feels a bit handwavy to me
you need to show that b_n > a_n, right?
proven tendon
yeah and we are taught that showing a series greater then a_n diverges tells us nothing
fervent timber
and if a_n diverges, so does b_n
proven tendon
yeah
so then id have to show a_n diverges
which at that point i can just skip the comparison test
cause b_n serves no purpose lol
fervent timber
I thought b_n was your original series
proven tendon
no a_n is
:0
here is the question
im doing the one on the left
it asks explicitly to use comparison test
proven tendon
so i should find something smaller than a_n right?
proven tendon
ok let me write up a solution
fervent timber
so i should find something smaller than a_n right?
yeah, something smaller that diverges
proven tendon
proven tendon
yeah, something smaller that diverges
hows this?
fervent timber
are you allowed to take the limit like that?
feels kind of handwavy
like, you could just take the limit of the original function and get the same thing
@tacit arch do you know if there’s any way to do this more “rigorously”, or is the above solution fine?
proven tendon
I saw it in a organic chemistry tutor video
Usually I've seen is people just drop the constants
In my sol I showed that I multiplied them by 1/n^2 and that those will individually approach 0
lone heartBOT
@proven tendon Has your question been resolved?
proven tendon
are you allowed to take the limit like that?
do u have any tips for the other one?
.close
mellow frigate
for this question
lone heartBOT
for this question
mellow frigate
my left derivative is coming equal to -1
while my right derivative is coming equal to 0
but the answer is -1 and limit does not exist
mellow frigate
help spmeoen
please delete your messages, the channel is taken
vale wigeon
help spmeoen
!occupied
lone heartBOT
help spmeoen
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
tacit arch
while my right derivative is coming equal to 0
Show how you get 0
ocean sealBOT
tacit arch
You got f(0) wrong
bitter leaf
mellow frigate
You got f(0) wrong
so the lim becomes 2/h?
lone heartBOT
@mellow frigate Has your question been resolved?
molten pivot
compact kestrel
lone heartBOT
compact kestrel
is the correct answer for 11 b?
if it is, why is it still considered correct when x^2 isn’t the first variable
gray isle
commutative property of addition,
the same value is still represented
compact kestrel
So the correct answer is b then?
gray isle
yes
compact kestrel
Ok thank you so much!!
lone heartBOT
@compact kestrel Has your question been resolved?
silver cave
lone heartBOT
scarlet dune
hi
silver cave
hello
scarlet dune
i got x=100/7 is that what you got?
silver cave
yes
scarlet dune
when x=20, y=10 thus k=(20)(10)=200
so when y=14, the equation becomes 14x=200
x=200/14=100/7
scarlet dune
all g
i was here tryna get my problem solved and then i saw urs so i decided to help lol
anyways cya have fun
silver cave
lool tahnkss
can anyone help check my answers
and i was told by a tutor that the second to last is inverse variation but idk why
.close
gentle berry
I actually just want this help channel to do some things on my own. Will be working in here for maybe 20 or so minutes 😄
gentle berry
Equivalence Relations and Quotients
So relation definition is just
$R \subseteq S \times S$ for a set $S$
ocean sealBOT
JayRoc (The Hurricane Panda)
gentle berry
So the elements in R are ordered pairs (a,b)
Let's let $S={1,2,3}$. Then we could say $R={(1,1),(2,2),(3,3)}$
ocean sealBOT
JayRoc (The Hurricane Panda)
fickle sandal
gentle berry
ah ok thanks!
I'm not worried tho
just thinking out loud really
haha
If $(a,b)\in R$ then $aRb$ or $a$ is related by $R$ to $b$. OK.
ocean sealBOT
JayRoc (The Hurricane Panda)
gentle berry
3 properties of equivalence relations
We say ~ is an equivalence relation if: it's reflexive, symmetric and transitive
Reflexivity: $\forall a \in S, a \sim a$
echo socket
Btw it's \sim for ~ in mathmode
gentle berry
ah thanks!
echo socket
Reflexivity: $\forall a \in S, a \sim a$
Remove the space in a $ so that it renders
gentle berry
OK. I was wondering why it didn't output
ocean sealBOT
JayRoc (The Hurricane Panda)
gentle berry
🔥
thanks!
Symmetry: $(\forall a \in S) (\forall b \in S) a \sim b \Rightarrow b \sim a$
ocean sealBOT
JayRoc (The Hurricane Panda)
gentle berry
Transitivity: $(\forall a \in S) (\forall b \in S) (\forall c \in S), (a \sim b \text{ and } b \sim c) \Rightarrow a \sim c$
ocean sealBOT
JayRoc (The Hurricane Panda)
gentle berry
Partition is introduced in Aluffi before equivalence classes.
Partition is just a family of disjoint non-empty subsets of $S$ where the union is $S$. Almost sounds like a cover in topology.
ocean sealBOT
JayRoc (The Hurricane Panda)
gentle berry
So, I could take the set $S={1,2,3,4,5}$.
ocean sealBOT
JayRoc (The Hurricane Panda)
gentle berry
Break this into pieces: $A={1,2,3}, B={4}, C={5}$. Call the partition $T= {A,B,C}$.
ocean sealBOT
JayRoc (The Hurricane Panda)
gentle berry
So partitions aren't necessarily isolated to equivalence relations but we can always use an equivalence relation to get partitions.
Definition of Equivalence Classes:
$[a]_\sim := {b \in S | b \sim a}$
ocean sealBOT
JayRoc (The Hurricane Panda)
gentle berry
$[a]_\sim \subseteq S$
ocean sealBOT
JayRoc (The Hurricane Panda)
ocean sealBOT
JayRoc (The Hurricane Panda)
gentle berry
Let's do mod 5. Try $a \sim b$ if $a \text{ mod }5 = b \text{ mod }5$
ocean sealBOT
JayRoc (The Hurricane Panda)
gentle berry
OK, so $2 \sim 7$. $3 \sim 8$. $4 \sim 9$ so forth.
ocean sealBOT
JayRoc (The Hurricane Panda)
gentle berry
$0 \sim 5$
ocean sealBOT
JayRoc (The Hurricane Panda)
gentle berry
Also $5 \sim 10$
ocean sealBOT
JayRoc (The Hurricane Panda)
gentle berry
So, an equivalence class then would be, we should call it 0 probably:
$[0]_\sim = {0, 5, 10, 15, 20, ...}$
ocean sealBOT
JayRoc (The Hurricane Panda)
ocean sealBOT
JayRoc (The Hurricane Panda)
ocean sealBOT
JayRoc (The Hurricane Panda)
gentle berry
We wouldn't need to go further since $[5]=[0]$.
ocean sealBOT
JayRoc (The Hurricane Panda)
gentle berry
Union of those bad boys gives us the natural numbers.
this would extend to integers too
Oh, there's equivalence!
Oh so the quotient then is just
$S / \sim := T_\sim$
ocean sealBOT
JayRoc (The Hurricane Panda)
gentle berry
It's just the set of equivalence classes of $T$. idk why I made that so hard...
ocean sealBOT
JayRoc (The Hurricane Panda)
gentle berry
and I just literally did this LOL
SMH
well at least it's a good example.
Statement: Two elements of the quotient $S/\sim$ are equal if and only if the corresponding elements in $S$ are related by $\sim$
ocean sealBOT
JayRoc (The Hurricane Panda)
gentle berry
If $S= \mathbb{Z}$ then elements of $\mathbb{Z} / 2 \mathbb{Z}$ are just $[0],[1]$
ocean sealBOT
JayRoc (The Hurricane Panda)
gentle berry
mm... those aren't quite the same.
echo socket
Equivalence classes don't really have "corresponding elements", if you were to define a mapping [a] -> a, then it wouldn't be well-defined (unless all equivalence classes are just singletons of course)
Would be better to say that two elements of the quotient S/~ are equal if and only if a pair of their representatives are equivalent
echo socket
Ah wait I suppose they meant all elements from each equivalence class
Rather than taking just one from each
gentle berry
yeah that's the only way I could wrap my head around how they were stating that
just felt weird
time for Jay to go back to sleep now, rambling over 😄
.close
twilit gull
lone heartBOT
twilit gull
hows this 4m? I am getting zero
vale wigeon
show how you're getting 0
vale wigeon
,rccw
ocean sealBOT
twilit gull
skipped some steps
twilit gull
its 4 right?
vale wigeon
indeed
twilit gull
wait I think I got it
vale wigeon
so you do not just have a sum of zeros as you must have assumed
lone heartBOT
lone heartBOT
Available help channel!
ionic vine
lone heartBOT
fading citrus
ionic vine
Thanks
lone heartBOT
@ionic vine Has your question been resolved?
night scarab
.reopen
alpine sable
lone heartBOT
alpine sable
How'd we find the angle?
i tried sin alpha = a/d, so we get d as sin^-1 alpha .a but i don't see how is that even going to help
lone heartBOT
@alpine sable Has your question been resolved?
distant wadi
can someone help me solving derivative and integral problems?
distant wadi
yes and the rest is integral
distant wadi
can u solve it for me? i badly need the complete solution :((
tepid drum
i wont be able to stay alot i have some mins and then i should go
sorry we arent here to give complete solutions
we just guide to the solution
distant wadi
what to do first
tepid drum
!status
lone heartBOT
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
1
tepid drum
ok
do you know differentiation rules ?
like quotient rule,product rule,chain rule etc...?
distant wadi
yes some of it
tepid drum
what do you know
distant wadi
like quotient rule,product rule,chain rule etc...?
this
distant wadi
quotient rule in number 1?
tepid drum
nice start with this
distant wadi
what should i do next
tepid drum
what did you get
distant wadi
wait
alpine sable
I don't think there is any trigonometry involved, just geometry
could you elaborate
oh mb
I'll open a new one
lone heartBOT
@distant wadi Has your question been resolved?
lone heartBOT
@distant wadi Has your question been resolved?
soft pilot
I have a confusion about the local minimun and maximum of a function, The definition says that "a function f(x) has a local maximum at x=c if f(c) \ge f(x) for all x-values in an open interval around c". I do understand the notation and that c has to be bigger than f(x), however I dont understand the interval in which this rule applies, like we said that an open interval, that means that whenever we are looking for the local maximum or minimum of a function we have to define the interval in which we examine the points? Because otherwise it is irrelevant.
mortal trellis
"local" maximum means as the word suggest it only needs to be bigger than some values close to it. the interval takes care of that
soft pilot
"local" maximum means as the word suggest it only needs to be bigger than some v...
Yeah but see you said "some", it is not specific. Like whenever we would have to define the local maximum of a function we must define an interval in which we are looking to see the points, because otherwise the local maximum is irrelevant.
and being close to a point is subjective so again not specific
golden canyon
I think it means that c is a local maximum if there exists an interval for which the above holds
mortal trellis
wdym with irrelevant
soft pilot
wdym with irrelevant
Like you cannot determine the function's local maximum unless you define the interval in which you looking for the local maximum. Otherwise the function's local maximum would be the absolute maximum
golden canyon
I think it means that c is a local maximum if there exists an interval for which...
just any interval
digital jay
hi everyone im trying to solve a long polynomial division and something intrigues me how X-32X are equal to 2X²-6X ?? THANK YOU
mortal trellis
a point is a local max if there exists any such interval
not a specific fixed one
soft pilot
hi everyone im trying to solve a long polynomial division and something intrigue...
This is an open help conversation, write into either of the help channels
mortal trellis
it might be that the interval is very tiny
digital jay
sorry
soft pilot
a point is a local max if there exists any such interval
hmm, I dont quite get this. You mean that if a function starts increasing at any point then a local maximum can be determined?
soft pilot
hmm, I dont quite get this. You mean that if a function starts increasing at any...
Like here?
mortal trellis
for B there exists such an interval, for example the interval (A,C)
for any point between A and B there does not exist such an interval, because no matter how close you are on the right, you are always bigger
soft pilot
hmm, so I interpreted the definition wrong. So we first looking to define a local maximum within intervals, Not having to define the interval and then look for the local maximum.
It makes sense now
So we go thru every point of the function and if there is an interval in which the point can be considered a local maximum then that's a local maximum. Right?
mortal trellis
yes
soft pilot
Ohh okay, thanks for your help I appreciate it. I got it now 🙂
lone heartBOT
Available help channel!
fair musk
Are these subspaces of R^3 or C^3?
lone heartBOT
Are these subspaces of R^3 or C^3?
fair musk
I do not have answer key so I don't know how I will learn from this unless I get feedback. I said: No yes yes yes .
Requirements for a subspace: 0 vector, closed under addition and scalar multiplication.
mortal trellis
if you say no then give a counterexample. if you say yes then give a proof
two of these are wrong
fair musk
How come?
mortal trellis
for example x=z*e^(2pi/3)
fair musk
Can you explain more? I don't understand
I tried i values and that's it, I don't know why e^(2pi/3) is complex ?
fair musk
why do we multiply z by e^(2pi/3)
dont we have to replace z
and x
for counter example
this is confusing
what would be an actual counter example
mortal trellis
1 and e^(2ipi/3)
mortal trellis
which is 1
fair musk
Because cubing the e term is like multiplying the exponent by 3
How is that 1 lol
That's the most random number I've seen
Also it's still complex so it wouldn't even simplify to 1
mortal trellis
because 1 isnt a complex number?
fair musk
Should I just memorize that? I've never knew that e^(2ipi)=1
mortal trellis
then you should look a bit into complex numbers
fair musk
Are there any other formulas that are interesting like this?
mortal trellis
polar form, exponential form
fair musk
I did do that but my teacher never mentioned this
mortal trellis
you do know about the polar form but not this?
fair musk
Nope
mortal trellis
maybe your teacher assumes some basic knowledge about C
fair musk
I did calculus I and II and the 3d calculus and linear algebra and no one mentioned it yet LOL
fair musk
is it better to think of it as the smallest case?
is e^(ipi) equal to -1?
and i can just memorize that?
issue is that i'm not even sure if that's true or not
mortal trellis
e^(ix) = cos(x)+ i sin(x) if x is real
.
fair musk
its not returning anything on my clculators
oh so it's right
Nice
I wish they had it on the calculator tho
lone heartBOT
@fair musk Has your question been resolved?
mortal trellis
well depends on the calculator. most just dont have support for C
fair musk
I can't find a counterexample
fair musk
1 and e^(2ipi/3)
i tried it for every possibility
mortal trellis
wdym every possibility
fair musk
hyperbole
basically if the complex number = 1 or -1 or whatever it just resembles a real number then i dont know how to make them different when adding or multiplying by a constrant
mortal trellis
one vector could be (1,1,1). the other could be (1,1,e^(2ipi/3))
fair musk
$$2^3=\left(1+e^{\frac{2i\pi }{3}}\right)^3$$
ocean sealBOT
spetnaz
fair musk
mortal trellis
well thats wrong
fair musk
mortal trellis
I have no clue what that calc does but given that it writes it as (-1)^1/3 thats already not very promising
mortal trellis
,w 2^3 = (1+exp(2ipi/3))^3
ocean sealBOT
fair musk
should i use wolfram for everything then?
mortal trellis
basically, yeah
fair musk
So, for this one, how would I begin?
mortal trellis
try some examples until you think you know which it is, then either prove it or give the counterexample you found
lone heartBOT
@fair musk Has your question been resolved?
mortal trellis
yes
mortal trellis
have you done a few examples?
fair musk
this feels obvious
its just a matter of notation i think
0 is in P obviously rite?
so thats the 0 requirement done
then if i have 2 polynomials that equal 0 and add them
0 + 0 = 0
obviously
then if i have a random number to multiply by 0 then it's obviously 0
is that good?
mortal trellis
well thats the idea but hopefully not how you write it down
lone heartBOT
@fair musk Has your question been resolved?
dull wraith
Given a D sided dice, I want to calculate the probability of X amount of it's numbers appearing at least once in the result pool after N rolls.
Example:
If I have a 6 sided dice and I roll it 20 times, what is the chance that I get at least the numbers 1, 2 and 3 in the result pool? (Order or amount of each doesn't matter)
(D=6, K=3, N=20)
lone heartBOT
Given a D sided dice, I want to calculate the probability of X amount of it's nu...
@dull wraith Has your question been resolved?
alpine nacelle
A = the event we get 1 at least once
B = the event we get 2 at least once
C = ... 3 ...
you're looking for P(A and B and C)
so you can look for 1-P(A and B and C) first, which is easier to compute
it's the probability to get none, one of them, or two of them, but not the 3
so P(none of them)+P(A but nor B nor C)+...+P(A and B but not C)+...
and that's at least one way to do it
however, you may want to look for a quicker way to calculate these proba
dull wraith
A = the event we get 1 at least once
B = the event we get 2 at least once
C = .....
but to get 1-P(A and B and C) I need to calculate P(A and B and C), which is my objective
dull wraith
Which I don't know how to get to anyway
This is confusing
oh nvm
got it
well how would I go about doing P(A not B nor C), for example?
alpine nacelle
P(A not B nor C) = P(A | not B nor C) * P(not B nor C)
and once you know this one, by symmetry you know P(B not A nor C)
and P(C not B nor A)
the 3 are the same
high cargo
Given a D sided dice, I want to calculate the probability of X amount of it's nu...
Does $1-(\frac{D!}{D^D})^{N choose D}$ work for D=X? Asking since I believe you said at one point you have a program to test it
ocean sealBOT
FirstNameLastName
dull wraith
Does $1-(\frac{D!}{D^D})^{N choose D}$ work for D=X? Asking since I believe you ...
https://paste.pythondiscord.com/JW7A Its here. That does not work. Using N=4, D=3, K=3, we get 44.4% +- 0.1%
That formula retrieves 99.7% https://www.wolframalpha.com/input?i2d=true&i=1-Power[\(40)Divide[3!%2CPower[3%2C3]]\(41)%2CC\(40)4\(44)+3\(41)]
Also K = X, not sure why I used X in the question and K in the example
alpine nacelle
do you want exact value or good approx ? I gave a way to find exact value but it's obv quicker to run a monte carlo
dull wraith
do you want exact value or good approx ? I gave a way to find exact value but it...
I want to know how to form a formula that gets the exact value for any value N, D, K
alpine nacelle
P(A and B) = P(A)+P(B)-P(A or B), so from my formula, by "splitting events" you'll always get a formula, and you can write as a sum over K, the fact that D changes doesn't affect the lenght of this calculation
however, this method is a bit weak to a big increasing of K
since it requires to split a lot of events
and Idk if you can generalise it another way
tbh, I don't really think so because it revolves around partitioning, and it's a pain in general
dull wraith
I have been provided a working formula by frownyfrog (https://www.wolframalpha.com/input?i=(sum+i+%3D+2+to+3%2C+S2(4%2C+i)+*+C(3-2%2Ci-2)+*+i!)%2F3%5E4 N=4 D=3 K=2) but I'm too stupid to understand what it does. Calling it off for today
lone heartBOT
@dull wraith Has your question been resolved?
worn rapids
help
worn rapids
any clue with this question? im getting 32/63 but im not sure if that is correct
I said that all being open has probability (1/2)^6 = 1/64
so all being closed (conducting current) is 1 - 1/64 = 63/64
32 of which come from S1
so I concluded that if current flowing and S1 is closed its 32/63
is that the correct way of thinking about it?
it roughly comes out to 0.508
hot bluff
they don't all need to be closed for current right? circuit has a path for each switch independently. that is if current is flowing from the left to the right or vice versa.
worn rapids
yeah
they dont all
I was calculating all closed since s1 later is gonna be the one closed so im trying to compare the all closed to S1 alone
hot bluff
so all being closed (conducting current) is 1 - 1/64 = 63/64
i think this is the probability there will be current flowing at all.
worn rapids
yea
hot bluff
how did you determine 32 of the 63 combinations that allow current to flow include S1?
wouldn't it be something like P(S1 closed)*P(current is flowing)?
(1/2)(63/64)?
~49% chance that way
lone heartBOT
@worn rapids Has your question been resolved?
hot bluff
since it's a dependent event, we have to multiply the probability of S1 closed given that current is flowing.
worn rapids
yeah the events aren't mutually exclusive
but its also asking in order
the wording is very specific
probabily S1 closed if there is current
so wouldn't (1/2)(63/64) not be possible as an answer since thats considering the two things are mutually exclusive?
alpine nacelle
P(S1 closed | current) = P(S1 closed and current)/P(current)
= P(S1 closed)/P(current) = 1/2 * 64/63 = 32/63
Another way to do it is to see immediately that any S closed means current
So there is 2^6 combinations of S1 open/closed S2 open/closed ... and one of them (all open) means no current
So there is current means there are 2^6-1 = 63 such possibilities, all with same probabilities
And 2^5 = 32 of them have S1 closed
and the probability is then 32/63
lone heartBOT
@worn rapids Has your question been resolved?
serene garden
**If P(A) = 0.27, P(B) = 0.25, and P(A or B) = 0.37, then P(A|B) = ? Please round to two decimal places.
How do i solve a problem like this one?**
serene garden
I do not even know where to begin
Ik the formula for P(A|B) is P(A AND B)/P(B)
P(B) is 0.25
but how do I determine the probability of A and B?
The Formula for P(A and B) is P(A)*P(B|A)
P(A) is 0.27
Determining P(B|A) has me stuck and confused
alpine nacelle
P(A and B) = P(A)+P(B)-P(A or B)
serene garden
P(A and B) = P(A)+P(B)-P(A or B)
I thought it was P(A and B) = P(A) * P(B|A)
serene garden
these are two different true formula
Is there also something like this for P(A or B)?
So I can write it down for future references
alpine nacelle
well, the reverse of what I wrote works
since P(A and B) = P(A)+P(B)-P(A or B)
then P(A or B) = P(A)+P(B)-P(A and B)
when you have P(A) and P(B), you need P(A or B) to know P(A and B)
and you need P(A and B) to know P(A or B)
here you need P(A and B) but they give you P(A or B)
so you use this formula to get P(A and B)
then you figure out your answer
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cobalt verge
Have I done solved this IVP properly, and if so for question b) do I just take the derivative's of y(x) and replace x with l
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Have I done solved this IVP properly, and if so for question b) do I just take t...
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cobalt verge
.close
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worldly eagle
hey
worldly eagle
I need help with an explaintion on calculas 3 material
but its basically basic algebra
wait
you might be able to
becuase its not actually calc 3
its like an algebra concept
can someone explain why the begining part not the hidden part r+s=6
i can kind of undertand where they are deriving it from
but not really exactly why you get r+s=6
and r-s=-2
tacit arch
can someone explain why the begining part not the hidden part r+s=6
Just screenshot and upload the image here
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distant nymph
Hi
distant nymph
I’m confused with this. I know the answer is 2 square root 5… But, how we know that it’s 2 square root 5 and not 5 square root 2?
coral flower
that is wrong
distant nymph
I wanna simplify square root 10
wheat maple
Yo
wheat maple
What do step function brackets mean
serene junco
It's like rounding, but you always go down
[[3.2]] = 3
[[9.9]] = 9
[[-7.1]] = -8
etc
@wheat maple
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tribal monolith
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tribal monolith
help pls
old relic
Given φ = c0x^4 + x^5 and φ* = c0*(x*)^4 + (x*)^5 where x >=1. Compute the relative error in evalutating the function assuming that: all error originated from represending c0 and x, and arithmic operations include no error. Once computed derive an upper bound, (consider defining Emax)
bruh i tossed in urs
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lusty basin
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cedar juniper
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cedar juniper
Can someone explain how multiplying by 1/a+b results in that
I get that (a-b)(a+b) = a2 - b2
Is there a identity for the rest of the terms too?
thick grail
somber crown
$(a-b) = (a-b)\frac{a+b}{a+b} = \frac{a^2-b^2}{a+b}$
ocean sealBOT
musava_ribica
cedar juniper
**musava\_ribica**
Yea I understand that
What about the rest of the terms
How did we get a4 - b4 and so on
somber crown
each of these terms yield a^n plus or minus b^n when multiplied by a+b
tepid prism
9th first part ,I tried but I dont no how to find the partial diff of that r part (RHS)
tepid prism
do tag me if you are able to do it or explain anything
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inland ocean
My friend tried to integrate the quadratic formula idfk if he is correc or not cuz he is ig advanced at math at grade 9 💀 😭
opal jolt
on the second picture, bottom left corner, da is not correctly computed
da = 2udu/4c = udu/2c
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summer quarry
Kind of a dumb question but
If we start from 1st Feb 2018 and count to 30 April 2018 then it would be 89 days right?
unkempt robin
Kind of a dumb question but
If we start from 1st Feb 2018 and count to 30 April...
Is the end date included?
summer quarry
Yea it is included
unkempt robin
Yea it is included
Then it's 89 days, yes.
tepid prism
9th first part ,I tried but I dont no how to find the partial diff of that r par...
<@&286206848099549185>
lone heartBOT
<@&286206848099549185>
vale wigeon
.reopen
you can't reopen a channel that already got closed and had someone else in it
also putting a . at the beginning of your message prevents a channel being opened with it
tepid prism
you can't reopen a channel that already got closed and had someone else in it
ohh okay
latent jolt
9th first part ,I tried but I dont no how to find the partial diff of that r par...
r = constant ?
tepid prism
r = constant ?
that might be true but then how will i get the desired result
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alpine sable
9th first part ,I tried but I dont no how to find the partial diff of that r par...
for dr/dx, find x²+y², you'll get r², then just differentiate the eq. x²+y²=r² with respect to x
formal pier
can someone help me with this
heady cloud
A \Delta B
Saiyan
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
cerulean surge
can someone help me with this
Uhh
Can u explain ur working?
cerulean surge
Check again
formal pier
Check again
is that wrong?
formal pier
This math shi aint for me ngl
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subtle gate
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alpine sable
write 3.04 as 3+x/2
subtle gate
why?
coral flower
cuz u already expanded that in a
coral flower
write 3.04 as 3+x/2
shouldnt they write 3.04 as 3 + 0.08/2
alpine sable
sure so x is 0.08
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Available help channel!
river aspen
hello I need help for this question
lone heartBOT
hello I need help for this question
charred heron
well look at each time the velocity is douvled
lets start with 6 ft/s, the frst value given
(ft/s = feet per second)
when its 6ft/s, the height is 4ft
whats the height when its 12ft/s? (aka when the velocity is doubled)
and also
river aspen
8?
river aspen
its 16
charred heron
yes
and when u have 24 ft/s (which is just 12 ft/s doubled) whats the height then?
river aspen
64?
river aspen
but why does it do that? it quadruples
charred heron
it does quadruple
charred heron
but why does it do that? it quadruples
as for why
i dont know, they havent given any information about how they calculated it
they just gave the values
i mean from these values an equation u could make is
velocity of wave = 2(height of wave)
but u cant really say why that happens
charred heron
yea probably
static drum
could anyone explain how to do this
lone heartBOT
could anyone explain how to do this
static drum
whenever modelling comes into anything i just become stuck
static drum
what is the x
4
static drum
i dont know the total of the members
alpine sable
but you know 4/7 of the total members is 84
static drum
63 would be 3/7 then which would be the number of girls
but
thats just using logic
i want to understand the whole proccess
so i can do it in the future
alpine sable
Im telling you the logic
you know 4/7 is amount of boys in the population
which is 84
so you can use that information to obtain the amount of 1/7 out of the total population
then you can multiply by 3
to get the amount of girls
static drum
so you can use that information to obtain the amount of 1/7 out of the total pop...
yeah, how. if i mutiply 1/7 of 84 that would just be 1/7 of 4/7 of the total population
alpine sable
84 boys is 4/7 of the entire population
alpine sable
(4/7)T = 84
can you not solve for t here
alpine sable
yes
alpine sable
no
static drum
63*
alpine sable
yes
static drum
ah got it thanks
alpine sable
np
untold magnet
How do I go about solving the following: arctan(ax) +arctan(bx) = c
untold magnet
Wait, how is that true
untold magnet
Huh, that's awsome, lemme see whether I can solve it rn
alpine sable
sure
untold magnet
Okay so what next @alpine sable
alpine sable
arctan((ax + bx) / (1 - (ax)(bx))) = c
can be actually simplified to
(ax + bx) / (1 - (ax)(bx)) = tan(c)
i thiknk that will be easier
untold magnet
Oh wait, I read your identity wrong
mb
Lemme see
There is one slight issue tho, in the original question, I have c= pi/2 and tan(c) is undefined
@alpine sable
alpine sable
what is the origianl question
untold magnet
So it is from physics
lemme send it to you
@alpine sable
Wolfram alpha gives me t=0.35
So there is a solution
And indeed does satisify the answer key to the original physics problem
But how
<@&286206848099549185> Anyone?
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tacit arch
,rotate
ocean sealBOT
untold magnet
Can't read the handwriting
I don't think it will help but here it is:arctan((gt)/v01)) +arctan((gt)/(v02)) = pi/2
bad naming, ik
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@untold magnet Has your question been resolved?
alpine sable
Can someone help me with this Simpson’s rule problem?
lone heartBOT
Can someone help me with this Simpson’s rule problem?
@alpine sable Has your question been resolved?
alpine sable
<@&286206848099549185>
signal trellis
<@&286206848099549185>
Where are you stuck? Do you know the formula for Simpson's Rule?
alpine sable
I’m getting stuck on writing it out.
signal trellis
Ok, what'd you get for delta x?
alpine sable
I got 4
signal trellis
It should be 2, because we do (8-0)/4, the 4 comes from having 4 subintervals with S(4) I believe
signal trellis
Yes, that's what we need
Oh wait sorry, it's delta x/3, not n. The n is included in delta x
alpine sable
Oh, okay
signal trellis
But since our delta x is 2, we start from 0 (the lower bound of the integral) and take points at every second x, so at x=0, x=2, x=4...
alpine sable
Alright
signal trellis
Do you know how to plug it in to the formula from there or do you want to see that?
alpine sable
Yes, I just plugged it all in and got the answer right. Thank you!
signal trellis
Glad to hear it!
alpine sable
.close
ocean sealBOT
Bourbaki
alpine nacelle
you're done yeah
if you write all steps like you did, you have both a simplified and an unsimplified version anyway
like you can't do much more
mortal oracle
Hey can anyone spot what I’m doing wrong
lone heartBOT
Hey can anyone spot what I’m doing wrong
mortal oracle
I’m getting -6x^2 at the end
im pretty sure its only supposed to be -3h-6x+4
for finding derivative of 4x-3x^2 using the limit definition idk
how i get -6x^2 at the end
violet bear
you forgot to distribute the negative on line 2
gray jetty
is this very straight forward or am i underestimating it
lone heartBOT
is this very straight forward or am i underestimating it
gray jetty
yeah you just put in 0for n
vapid shuttle
okay sure then yeah plug in n=0 and demonstrate that it is true
0+0=0 and 0+0=0 and 0=0
gray jetty
yes
vapid shuttle
what is your inductive step then?
vapid shuttle
state it using words
suppose for some m a natural number, it is true that 0+m=m+0. We will show that this implies for m+1 a natural number that 0+(m+1)=(m+1)+0.
That is your inductive step
you must show it
using your inductive hypothesis
which was the first sentence, "suppose for some m a natural number..."
gray jetty
our assumption was n + 1
vapid shuttle
no
you are assuming it is true for a natural number
if you call this is natural number, m, or n, it doesn't matter
then you want to show that it being true for that number, implies that it is true for 1 larger
gray jetty
yeah sure thats just n + 1
vapid shuttle
can you state the inductive step using words please?
gray jetty
the inductive step is literally that we want to show this is also the case for 0 + n + 1 = n + 1 + 0
vapid shuttle
what is also the case?
this is why I used a different variable than the one used in the question statement.
you are getting confused by using "n" for everything
state the inductive step in terms of a natural number m
vapid shuttle
you still haven't ever completely stated the inductive step
gray jetty
its literally that it holds for m + 1
vapid shuttle
that what holds
gray jetty
0 + m + 1 = m + 1 + 0
vapid shuttle
no
still no
you have to state what you are assuming about m
suppose that for some m a natural number, 0+m=m+0. Then, we will show that "it still holds" for m+1 a natural number, that 0+(m+1)=(m+1)+0.
that is how you should be stating it
vapid shuttle
sure
gray jetty
then you just deduce that n + 1 and n + 1 are equivalent
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waxen turtle
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waxen turtle
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round zealot
The scale factor is what you multiply the height AND width by
waxen turtle
Uhh
round zealot
Since the area was 1/9 the original, Aimee must’ve multiplied the dimensions by 1/3
waxen turtle
Uhh
round zealot
Okay
Take a square with side length 1
And a square with side length 3
How many of the small squares do you need to make the big square
It’s not 3, it’s 9
round zealot
Yeah I think so
waxen turtle
Woo it was right
round zealot
Do you understand
waxen turtle
Yes 1/3 was one of the things I thought of in my head
Like
A square w side length 6
And like
Ii firgir
But I got to side length of 2 fr
And that is like area of 4
Something like that
Ok bye
.close
round zealot
Yeah that’s good
opal sphinx
why is this incorrect??
isn't the formula the thirteenth food processor cost - the 12th??
that gives us the thirteenth's cost
lone heartBOT
why is this incorrect??
isn't the formula the thirteenth food processor cost - t...
opal sphinx
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opal sphinx
no sir
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rapid gate
