#help-17
vocal sleetBOT
bleak rampart
i think it's b
vocal sleetBOT
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icy orchid
vocal sleetBOT
icy orchid
<@&286206848099549185>
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onyx veldt
can anyone help me with remainder theorem?
vocal sleetBOT
can anyone help me with remainder theorem?
onyx veldt
merry python
find p(3)
frozen bobcat
,w remainder theorem
twin meteorBOT
vocal sleetBOT
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hushed flint
Any advice for where to even start with this?
vocal sleetBOT
Any advice for where to even start with this?
@hushed flint Has your question been resolved?
hushed flint
Would this be considered vector geometry ?
vocal sleetBOT
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wary mantle
{\bf Theorem (Division with remainder)}: Let $n \in \mathbb Z$ and $m \in \mathbb N$. Then there exist $q, r \in \mathbb Z$ with $n = qm + r$ and $0 \leq r < m$. \ $q, r$ are clearly defined. (If $n \geq 0$, then $q \geq 0.$) \[20pt] {\bf Proof.} \begin{enumerate} \item[] $m \geq n$: Take $q = 0$ and $r = n$. \item[] $n > m$: Let $G = {k \in \mathbb N_0 \mid km < n}$. \ Let $\ell$ be the greatest element of $G$ (well-ordering theorem). \ Then, $\ell = q$ and $r = n - \ell m$. \end{enumerate}
vocal sleetBOT
{\bf Theorem (Division with remainder)}: Let $n \in \mathbb Z$ and $m \in \mathb...
vocal sleetBOT
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wary mantle
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visual island
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visual island
I don't quite get the induction part of this proof how those terms add up (at the integration by parts) to equation for n+1
is this something you can do without steps?
dull bear
For the evaluation of $x^{n+1} e^{-2x}$, you have that $\lim_{x\to\infty} x^{n+1} e^{-2x} = 0$ ("exponentials beat powers") and of course evaluating it at $x=0$ gives you zero, and for the integral you assumed that $\int_0^{\infty} x^n e^{-2x} \dd x = \frac{n!}{2^{n+1}}$ so they just replaced that
twin meteorBOT
@dull bear
dull bear
If you're asking that?
visual island
is 1/2(n+1)*n!/2^n+1 equal to (n+1)!/2^n+2 then?
would you need to show steps to assume that?
dull bear
would you need to show steps to assume that?
Assumedly you wouldn't need to, but if you did, you could do $\frac{1}{2} (n + 1) \frac{n!}{2^{n + 1}} = \frac{(n + 1) n!}{2 \cdot 2^{n+1}}$, with $(n + 1)n! = (n + 1)!$ by the definition of the factorial, and $2 \cdot 2^{n + 1} = 2^{n + 2}$ just being an application of the rules of indices
twin meteorBOT
@dull bear
clear lake
vocal sleetBOT
clear lake
so we want to find the probability that 100 customers can be served in less than 2 hours
so basically probability that the sum of the service times is less than 120
which is the same as the sample mean being less than 1.2
so using CLT, we find the probability of (sample mean - mean ) / (standard deviation/sqrt(100)
which is P(Z<-3) right
which is .0013 according to the z table
is this correct?
vocal sleetBOT
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@clear lake Has your question been resolved?
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@clear lake Has your question been resolved?
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@clear lake Has your question been resolved?
vocal sleetBOT
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Available help channel!
solemn fulcrum
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solemn fulcrum
i dont know how to rotate them please help
solemn fulcrum
i know that how do you rotate it each point
glass ginkgo
i will take one triangle
solemn fulcrum
and how does that like with the centre of rotation
solemn fulcrum
yeah
solemn fulcrum
oh
glass ginkgo
no problem !
vocal sleetBOT
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terse grotto
Hi this is a physics questions if anyone can please help.
Part C please
vocal sleetBOT
Hi this is a physics questions if anyone can please help.
Part C please
@terse grotto Has your question been resolved?
waxen portal
!show
vocal sleetBOT
Show your work, and if possible, explain where you are stuck.
vocal sleetBOT
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tacit cairn
i have no idea how to solve this:
vocal sleetBOT
i have no idea how to solve this:
paper depot
!occupied
vocal sleetBOT
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).
paper depot
i have no idea how to solve this:
do you know how to solve quadratic equations in general?
tacit cairn
do you know how to solve _quadratic equations_ in general?
yes, just only when it = 0
tacit cairn
well you can _make_ the right hand side 0.
im guessing you just take 24
tacit cairn
do you see how?
5x^2 - 11x - 21 = 0?
paper depot
yaeh
you subtract 24 from both sides and thats exactly what you get
do you see how to continue now?
tacit cairn
do you see how to continue now?
i thought so, i put it in my calculator and got it wrong though
I got 2.829 (rounded to 2.83) and -0.629 (rounded to -0.63)
i think i just put it in wrong though
tacit cairn
do you see how to continue now?
would the answer be 3.43 and -1.23?
or have I done that wrong again?
paper depot
,w 5x^2 - 11x - 21 = 0
twin meteorBOT
tacit cairn
ive got it correct un rounded then, just to check have I rounded it right? it gives you 2 chances before giving a new question
un rounded its:
-1.2259
and
3.4259
thanks
.close
stoic lodge
vocal sleetBOT
stoic lodge
can you show ur working
vocal sleetBOT
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north gull
#help Find the limit as x approaches 0 of (sin(x))/x.
vocal sleetBOT
#help Find the limit as x approaches 0 of (sin(x))/x.
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vocal sleetBOT
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eager hearth
Does the serie converge: sin(n^-3/2) converge from 0 till infinity.
eager hearth
I would say yes because if n goes to infinity, it becomes sin(0). And sin 0 = 0
How would I write this correctly? Normally I use Alembert or Cauchy. But I dont know which characteristic I can use now. Do I just write it as a limit?
vocal sleetBOT
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hybrid flicker
I would say yes because if n goes to infinity, it becomes sin(0). And sin 0 = 0
this is not a valid argument, as you might recall that $\lim_{n\to\infty}\frac{1}{n} = 0$ yet $\sum_n \frac{1}{n}$ diverges
twin meteorBOT
rafilou2003
hybrid flicker
here you might want to use the well known upper bound that $|\sin(x)|\leq ...$
twin meteorBOT
rafilou2003
eager hearth
this is not a valid argument, as you might recall that $\lim_{n\to\infty}\frac{1...
its number 21.
hybrid flicker
I don't understand how in exercise 22 you used the correct thing with tangent but you didn't do the same here with sin
eager hearth
I redid 21 in the same way as 22 I think? You only have to look above the line.
hybrid flicker
yeah it's better
eager hearth
Would that be a valid solution?
I know its written down unclear. But I just need to know if the concept is correct.
.close
dense anchor
vocal sleetBOT
vocal sleetBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
2
magic wasp
Ok, show us what you have then
dense anchor
magic wasp
Ok so you have lh=9m^3 and the surface area, ok
The question asks for cost, so can you derive a formula for that?
dense anchor
lw(10)+5(2)hl+5(2)hw?
dense anchor
40l+10hl+40h
magic wasp
Remember lh=9
magic wasp
Ok so you have lh=9m^3 and the surface area, ok
That was supposed to be lh=9m^2 btw, not 9m^3
magic wasp
Looks reasonable
dense anchor
what do i do from there?
magic wasp
Do you know derivatives?
dense anchor
yes
magic wasp
Yes
dense anchor
are the critical points -3, 3 and 0?
magic wasp
If I understand "critical points" correctly, then yes
dense anchor
so the minimum is 3
dense anchor
so is the minimum cost $1140?
dense anchor
plug it back into the volume equation?
magic wasp
As a first step, yes
dense anchor
so since it equals 36 is it correct?
magic wasp
Ok the volume is correct, but what we're more interested in is that the cost is minimal
You had this formula for the cost 40l+10hl+40h
Only h and l are variables since we know w=4
If you plug in h=3 and l=3 it gives you 330 which is great, but how do you check that it's the minimum?
I'm not looking for a precise thing here, just a practical check
@dense anchor ?
dense anchor
If you plug in h=3 and l=3 it gives you 330 which is great, but how do you check...
i used a sign chart earlier to check if 3 was the minimum
dense anchor
Something practical you can do is just plug in h=3.1 and l=9/3.1
thank you!
vocal sleetBOT
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dense anchor
vocal sleetBOT
magic wasp
!status
vocal sleetBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
1
magic wasp
Ok it asks for the average rate of change of v over an interval
What's the rate of change of v?
dense anchor
between 8 and 20?
magic wasp
No, what's a rate of change
dense anchor
-5/6?
magic wasp
Ok well that's correct, so you knew where to begin
The average rate of change of v between 8 and 20 is (v(20)-v(8))/(20-8) = -5/6
Now what's the mean value theorem
dense anchor
i’m not sure sorry
magic wasp
Well if you have an exercise about this I would assume it's in your course material somewhere
But ok I can give you the short version
dense anchor
i found the formula but i don’t remember what you plug in
magic wasp
If f is a differentiable function on the interval [a,b] then there exists a value c such that $$f'(c) = \frac{f(b)-f(a)}{b-a}$$
twin meteorBOT
Nel
magic wasp
So you have the right hand side already, right?
dense anchor
yeah
magic wasp
What are a and b?
dense anchor
8 and 20?
dense anchor
yes
magic wasp
What's v'(t) then? (for t in [8,20])
dense anchor
0?
magic wasp
On [8,16), sure, but certainly not on (16,20]
The blue and green lines represent the interval [8,20]
dense anchor
oh so itd also be -5/6?
dense anchor
5/2?
dense anchor
.close
vocal sleetBOT
dense anchor
sorry class starting
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cunning ravine
vocal sleetBOT
cunning ravine
All of the following questions is based on the circle figure above
Don’t know where to start
minor jolt
its trigonometry
you know the radius of the circle is 4 because both point A and point C have a difference of 4 with the origin and theyre both on the horizontal axis
B is just as far from O as A and C
let me draw it real quick
you can get started by calculating where B is along the x-axis using trigonometry
cunning ravine
I don’t know the rule lmao
minor jolt
do you know how to cos and sin?
cunning ravine
Yeah
minor jolt
you know the length from O to B = 4
and you know the angle
how do you get either of the other distances using cos or sin?
vocal sleetBOT
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vocal sleetBOT
@cunning ravine Has your question been resolved?
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twin quail
Hello, I am currently having an issues with Regular Expressions.
Imagine a language with L = {a,b} , give me a regular expression which makes sure that any string doesnt have the same charachter neighbouring itself ( so no aa,bb etc).
Hopefully i translated this to english well enough^^.
Also, In my research I`ve found the ?! (operator?) but we havent got this far yet in our course so its not ment to be used to solve this.
regal bane
It's just a bit of case work.
Some examples of things you can accept:
abababababa
babab
There's definitely a pattern in those you want to exploit
I don't think it can be done without an optional though
Actually maybe it can
For example that first one:
- Starts with a
- Repeats ba
twin quail
For example that first one:
- Starts with a
- Repeats ba
problem is, that for example in regex it seems like theres an order in operations for the way it matches?
It basically snatches away the "a" from "ab". As far as we were told its supposed to have () as otp of the operation, and "or" | as last step.
twin quail
For example that first one:
- Starts with a
- Repeats ba
it doesnt just repeat ba tho, it can also be just b
f.e. "ab" should be accepted aswell. which u will run into an issue if u do
a?(ba)*
regal bane
Yes this will take a few cases
twin quail
as in, ull need multiple regular expressions? Im pretty sure the problem is ment to have only one
regal bane
You can combine multiple into one
twin quail
problem is, that for example in regex it seems like theres an order in operation...
thats what this should be, but I cant get around the order of matching. It basically snatches away a or b before it can match ba or ab
regal bane
You're doing it above. Your cases are:
- a
- b
- Repeat ab, then optionally take a
etc
So you want to change the order. Since the case "a" comes first, it checks and accepts it first
twin quail
like this?
regal bane
I believe that should do better
I also don't regularly use regex so don't take my word for any of it haha
twin quail
It does, but then I run into an issue of this:
regal bane
Fair. Nothing should have been accepted here, right?
twin quail
nothing is supposed to be accepted yes
Ive tried using negation but it doesnt seem like negation works for a group of charachters, as in: [^(aa+)] (this seems intuitively correct to me, but appearently doesnt work at all)
vocal sleetBOT
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@twin quail Has your question been resolved?
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clear lake
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clear lake
i don't understand the third line where u have sum of i and sum of j and i not equal to j
so when we're taking the sum we do it from j=1 to n right
same with i
so how does i not equal to j work
vocal sleetBOT
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clear lake
<@&286206848099549185>
vocal sleetBOT
@clear lake Has your question been resolved?
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@clear lake Has your question been resolved?
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flat whale
so how does i not equal to j work
You skip the inner sum when i=j
Try it for i=1 to 3 and j=1 to 3 with i not equal to j
clear lake
You skip the inner sum when i=j
yup i see it now
vocal sleetBOT
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west harbor
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west harbor
hi I need help in these practice question for integrals
vocal sleetBOT
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vocal sleetBOT
vocal sleetBOT
✅
proven garden
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marble kettle
hi i need help with this question, it doesnt seem to make sense to me. It travels at a slower velocity but arrives ealier? or is there a mistake in the question?
vocal sleetBOT
hi i need help with this question, it doesnt seem to make sense to me. It travel...
worthy citrus
also one train travels from Kuala Lumpur to Kota Bahru and the other from Kota Bahru to Kuala Lumpur
so yeah no idea how they can be comparing the times at which they both arrive in Kuala Lumpur
vocal sleetBOT
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old niche
how do you prove this
vocal sleetBOT
how do you prove this
fast cipher
how do you prove this
Let's try a few examples before anything.
old niche
okay
fast cipher
(a, b, c) = (6, 18, 30)
gcd(a,b) = 6
gcd(gcd(a, b), c) = 6
6^^^^^^ ^^30
gcd(b,c) = 6
gcd(a, gcd(b,c)) = 6
6^^ ^^^^^30
Makes sense right? We're just taking the gcd of some numbers.
Now comes the question: the order matters?
Taking the gcd of the first two and then taking with the third is the same of taking with the last two and then with the first?
old niche
right
fast cipher
Let's think about the simplest of cases: when the gcd is 1.
If the gcd(a, b) = 1, then pretty sure the gcd(gcd(a,b), c) = 1.
fast cipher
I know. I trying to make you go from the simplest case to the general case.
old niche
this weirdly looks like transitivity
fast cipher
I would say associativity.
old niche
like if you let d = gcd(a, b) then d must divide a AND d must divide b. If you let j = gcd(b, c) then j divdes b AND j divides c.
But notice that both d and j divide b
fast cipher
I would say associativity.
Because you are doing a operation to three trings and no matter what two you do first, you get the same result.
old niche
that basically shows they HAVE to have the same gcd
because if j divides b and c, it divides BOTH b AND c, and d divides both a AND b
b = b
which means the gcd has to be the same
fast cipher
d = gcd(a, b)
j = gcd(b, c)
d divides a and d divides b
j divides b and divides c
Therefore j = d.
That's what you are saying.
old niche
yeah
old niche
yes
old niche
okay rip
fast cipher
Well, the conclusion is wrong but it's not a waste.
d = gcd(a, b)
j = gcd(b, c)
d divides a and d divides b
j divides b and divides c
old niche
i see the conntection, maybe i just dont know how to word it
fast cipher
d = gcd(a, b)
j = gcd(b, c)
d divides a and d divides b
j divides b and divides ...
We know that.
Now we have to think about gcd(gcd(a, b), c) and gcd(a, gcd(b, c)).
Let's call them m and n.
fast cipher
m = gcd(gcd(a, b), c)
n = gcd(a, gcd(b,c))
We know that m divides d and c.
We know that n divides j and a.
If j divides b and c, then n divides a, b and c.
If d divides a and b, then m divides a, b and c.
Makes sense?
Like, it's the gcd. You just are taking divisors from two numbers.
old niche
from those assumptions you can determine it is equivalent right
fast cipher
Almost.
We just need the definition of the gcd: the biggest number that divides two given numbers.
There is always only one biggest numbers.
Right?
I am monkey, sorry.
old niche
nw i got what u meant
fast cipher
d is the biggest number that divides a and b.
j is the biggest number that divides b and c.
They might no be equal.
gcd(d, c) is the biggest number that divides d and c. And d is the biggest that divides a and b.
So gcd(d, c) is the biggest that divides a, b and c.
gcd(a, j) is the biggest number that divides j and a. And d is the biggest that divides a and b.
So gcd(a, j) is the biggest that divides a, b and c.
gcd(a, j) and gcd(d, c) are both the biggest numbers that divides a, b and c.
old niche
sorry if im not responding, im just reading this and thinking about it, i am still here
fast cipher
sorry if im not responding, im just reading this and thinking about it, i am sti...
It's fine.
fast cipher
gcd(a, j) and gcd(d, c) are both the **biggest** numbers that divides a, b and c...
There can't be two different biggest numbers.
There is only one biggest number, so they are equal.
fast cipher
Just one thing.
old niche
ok
fast cipher
It feels obvious?
old niche
i do not find any of this math obvious ngl
fast cipher
But is my explanation obvious. Like: how could it be otherwise?
fast cipher
i do not find any of this math obvious ngl
I may assume that i started to explain without having solved the problem.
old niche
can i ask another question
fast cipher
Of course.
old niche
I am having difficulty with an induction problem, could we break it down together
fast cipher
Of course. Let me just finish lunch and i will ping you.
old niche
it is this question, my first question is for a) is the base case 2?
fast cipher
I will be back soon.
old niche
sounds good
fast cipher
@old niche, finished.
old niche
okay cool
fast cipher
would you do this with proof by contradiction
To prove by contradiciton we just have to do a couple things differently.
Let's assume that
gcd(gcd(a, b), c) = gcd(a, gcd(b, c))
Is false.
old niche
its okay, i just did a direct proof
fast cipher
Oh, so let's move on to your second question.
fast cipher
its okay, i just did a direct proof
Do you mind showing it? I'd love to see a different approach.
old niche
could i ask about the second question first
fast cipher
Fine.
fast cipher
it is this question, my first question is for a) is the base case 2?
Not. The first natural number that is grater or equal to 1 is 1 (1 is equal to 1).
The base case is r = 1.
old niche
so then its like p |a1
fast cipher
Yes.
old niche
but idk how you even reason about that
old niche
p is just some positive prime and a is some integer
fast cipher
It's given to you:
• a prime number, call it P.
• a list of r numbers, call its elements a1, a2, ... ar.
It's said:
IF P divides the product of all numbers in the list THEN P either divides a1 or a2 or a3 ... or ar (in other words: p divides at least one element of the list).
The base case:
a list of 1 element. Call its one element a1.
What is the product of the number of a list if there is only one number in it?
old niche
its self
fast cipher
Great.
old niche
okay i see how the base case works
since a1 is the only member of the product, then P MUST divide a1
fast cipher
IF P divides the product of the numbers (the result is a1), THEN P divides a1 (the only element in the list).
Before trying the induction step (if it works n, then it will work for n + 1). Try some small examples of r.
r = 2 and 3 for example.
Were all of your questions answered?
old niche
you assume its true for r right?
wts its also true for r + 1?
is this strong induction
fast cipher
Yes.
No.
Strong induction is when you assume it's true for r and all the cases before r.
Weak induction is when you assume it's true only for r.
old niche
can you help me clairify the inductive hypothesis
fast cipher
I see.
Would be something like:
• it's given a positive prime number p
• it's given a list of positive r numbers a1, a2, a3, ..., ar.
Statement: IF p divides the product of a1, a2, ... ar THEN it divides a1 or divides a2 or ... divides ar.
Base case: prove the statement is true for r = 1.
Inductive step:
- assume that the statement is true about all positive prime numbers and all list with r postive numbers.
- prove it's also true for all postive primes numbers and lists of with r + 1 positive numbers.
old niche
okay can i do it and then show you my proof
old niche
@fast cipher
fast cipher
It's almost perfect.
fast cipher
okay hmm what am i missing
I think it's just a small techcality.
old niche
what is that
fast cipher
Sorry for losing focus. I was just resolving a small thing.
Looking twice at the proof, i see i was wrong.
You make no mistakes.
I thought you assert one statement instead of the other, but i misread.
old niche
naw your hints were very helpful
fast cipher
Thank you.
fast cipher
Sorry.
I'm have to leave right now but i really want to help you.
Would you mind accepting my friend request so i can help you later?
vocal sleetBOT
vocal sleetBOT
Available help channel!
clear lake
vocal sleetBOT
clear lake
kinda confused on the definition of parameter space
but so far I have that model e is nested in modal a and b
is that right?
vocal sleetBOT
@clear lake Has your question been resolved?
clear lake
<@&286206848099549185>
someone with expertise in stats pls help
i've seen other answers for models nested in a
some people say model b , d and e are nested in a
are we only looking at the parameters b1, b2 ,b3 etc
or does the x have anything to do with it
cause model a has b0 , b1, b2 and so does model b so does that mean they are nested models on each other
or does it matter that on model b beta 2 has x1 and x2 as predictor variables
vocal sleetBOT
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@clear lake Has your question been resolved?
vocal sleetBOT
@clear lake Has your question been resolved?
elfin pendant
We shall find the inverse mapping of:
vocal sleetBOT
We shall find the inverse mapping of:
elfin pendant
Isnt it just y^-1: R^3 -> R^3 ((x1-x2),(x2+x3),(x3-x1)) -> (x1,x2,x3)?
I cant imagine its that easy
dusty ice
Isnt it just y^-1: R^3 -> R^3 ((x1-x2),(x2+x3),(x3-x1)) -> (x1,x2,x3)?
how do you find the x1 and x2 to map from
that's what the question is asking
e.g. if I give you the vector (0,2,0), how are you going to determine that this is in fact meant to be read as (1-1, 1+1, 1-1)
elfin pendant
AH
Okay, that makes sense
thanks, i felt lost.
i guess i now know what to do
.close
merry cosmos
i am doing my homework but im not exactly sure what i am doing or what the solution represents
question and soln:
vocal sleetBOT
i am doing my homework but im not exactly sure what i am doing or what the solut...
vocal sleetBOT
@merry cosmos Has your question been resolved?
vocal sleetBOT
@merry cosmos Has your question been resolved?
vocal sleetBOT
@merry cosmos Has your question been resolved?
trim belfry
hey
trim belfry
for a.
why is it (3,4) not (3,3)
and why can’t the interval be (-5,-2)?
and(2,4)
i didn’t answer these my teacher did
there’s no specific explanation tho
<@&286206848099549185>
wait nvm i read it wrong
how do i close this
/close
,close
,sfop
.close
slender star
vocal sleetBOT
vocal sleetBOT
@slender star Has your question been resolved?
flat whale
a matrix of contraction
It's explained in the textbook. Look for it
Use the index at the back of the book
vocal sleetBOT
@slender star Has your question been resolved?
hushed niche
vocal sleetBOT
hushed niche
im trying to negate, so minimize -c1x1 - c2x2
vocal sleetBOT
@hushed niche Has your question been resolved?
lime skiff
I'm doing some exercises that I know the result. Why is that the area under the curve of f(x)=e^5x, h(x)=e^-20 and g(x)=e^(-5x) equals the attached image?
First I found the intersections between f and h (-4), f and g (0) and g and h (4). After that I thought that the answer was integral over-4 and 0 of f(x)-h(x) + integral over 0 and 4 of g(x)-h(x), but nope... I can't really understand the logic behind this.
vocal sleetBOT
I'm doing some exercises that I know the result. Why is that the area under the ...
@lime skiff Has your question been resolved?
ancient knoll
I'm doing some exercises that I know the result. Why is that the area under the ...
note that g(x)=f(-x)
then it immediately follows that min(g(x), f(x)) is even
also im not sure what your talking about because it is equal to the integral you got at the end
vocal sleetBOT
@lime skiff Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
amber sonnet
Guys how is {{2}} subset of B?
vocal sleetBOT
Guys how is {{2}} subset of B?
edgy gulch
Guys how is {{2}} subset of B?
because {2} is an element of B
so the set {{2}} is a subset of B
amber sonnet
so the set {{2}} is a subset of B
but how the first is wrong and the second is right?
sorry i'm very confused about this topic
edgy gulch
but how the first is wrong and the second is right?
shouldnt it be both right...?
amber sonnet
shouldnt it be both right...?
yeah that what i think, but i think my instructor is drunk
anyway thank you ❤️
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
lavish tendon
vocal sleetBOT
pallid forge
,rotate
twin meteorBOT
pallid forge
C(S(30)) is asking what the value of C is (oxygen consumption) when the speed, S, is t=30. since the input of the C function is the output of the S function, then you're really just asking what the oxygen consumption is at 30 seconds
lavish tendon
C(S(30)) is asking what the value of C is (oxygen consumption) when the speed, S...
S(30)
Is the value ?
pallid forge
the value of C(S(30)), so take the value of S(30), and plug it into C(S), because S is the input of the C function
i can go through it step by step if you'd like
pallid forge
no problem!
vocal sleetBOT
@lavish tendon Has your question been resolved?
eager hearth
How do I find the value of the series: k=1 till inf of (2sin(kx)(-1)^k)/k for x=pi/2
vocal sleetBOT
How do I find the value of the series: k=1 till inf of (2sin(kx)(-1)^k)/k for x=...
@eager hearth Has your question been resolved?
Available help channel!
vast shale
vocal sleetBOT
vast shale
If i'm not wrong, it can't be b or d since their exponents are negative
Idk where to start honestly
left talon
you mean D?
tidal dock
oh lol
vast shale
you mean D?
Yeah typo sorry
tidal dock
try substituting some x values and you'll see
vast shale
I did
left talon
see what is f(5)
vast shale
I tried (0;50)
For some reason
This point?
@tidal dock @left talon is it C? Since when substituting into A the number gets too big
drifting jackal
<@474467399207223307> <@328315001427197954> is it C? Since when substituting int...
If you eliminated b and d because of the negative exponents and eliminated a because plugging in 5 resulted in a large number, then it has to be c, no need to second guess yourself if you eliminated the options it's not
vast shale
If you eliminated b and d because of the negative exponents and eliminated a bec...
Thank you!
spice garden
o
livid tapir
do u have a question
spice garden
yes
after the quiestion u can see where i am stuck
the last sentence with p(k+1) is where i am at
its about induction
<@&286206848099549185>
Can anyone help?
vocal sleetBOT
@spice garden Has your question been resolved?
vocal sleetBOT
spice garden
.reopen
vocal sleetBOT
✅
devout trellis
try to simplify it maybe?
spice garden
Now i have this question:
Can anyone help from here?
<@&286206848099549185>
devout trellis
Can anyone help from here?
maybe
vocal sleetBOT
@spice garden Has your question been resolved?
devout trellis
@spice garden
the way I did it was pretty straightforward but requires a lot of algebra xd
flat whale
Can anyone help from here?
solve the last inequality for k, then when you get to something that's true for all k in N, that will become your scratch work and your solution will be your scratch work in reverse
flat whale
it's easiler if you put all the square root on one side first
but there are a lot of ways to do this, so do whatever you're comfortable with as long as your algebra is correct
spice garden
how do i do that
twin meteorBOT
riemann
spice garden
so
over ?
could u maybe do it for me because i swear i have been on this exercise for days
and i have asked many people
?
is this correct?
@flat whale
<@&286206848099549185>
flat whale
could u maybe do it for me because i swear i have been on this exercise for days
no you should do your own work
flat whale
yea that's fine
spice garden
idk can reduce it more?
flat whale
how did 20n become 20
once you fix this, you'll be done with scratch work, then your proof will start there and go backwards
flat whale
yes that's right
twin meteorBOT
twin meteorBOT
spice garden
,w expand(1/\sqrt(3k+4))^2
twin meteorBOT
flat whale
where did this come from if you didn't get here?
spice garden
i squared wrong on both sides
thats my problem to square on both sides
from this
flat whale
still not answering me
spice garden
i just dont understand
I have this quiestion about multiplying
is this a valid move?
in induction step
spice garden
so its not valid
flat whale
i never said that
why did you do that multiplication if you think it's not a valid algebra move?
if you have the full solution, just show it
flat whale
you can do algebra in induction problems yes
spice garden
okay
flat whale
induction has nothing to do with algebra
spice garden
no but u do a lot of algebra in induction
flat whale
yes that's right
working on induction problems doesn't mean all the algebra you previously learned goes out the window
flat whale
if you have the full solution, just show it
.
flat whale
you said you got it from here, but like i asked multiple times before, how did you get it
you're being evasive and uncooperative
spice garden
flat whale
this is where i got it from
where did this come from
flat whale
you said you got it from here, but like i asked multiple times before, how did y...
which is what i replied to here
spice garden
it said if i square both sides i get that
i did all before
and then i couldn't move on
but u said i should do it on myself
even tho i didnt know..
flat whale
it's just algebra
spice garden
but it looks wrong
flat whale
...
spice garden
wait do u know how to solve it? Is it easy?
lemme try calculating on my own real fast i need to see it
flat whale
lemme try calculating on my own real fast i need to see it
why didn't you do this an hour ago
flat whale
and yet you have to do it now!
spice garden
yes
flat whale
so you just wasted like an hour of time working on steps you didn't do yourself in the first place
spice garden
ye
is it a fine move if i square both sides?
wait i seeit now
Here it is my own work
So it is valid
did i calculate it correct this way
ow i forgot to write 4k^2 instead of 4k in two spots
@flat whale i need to say thx for your time
man
sry for wasting ur time if u feel like it
hearty gust
would the x^4 in the problem cancel each other out leaving only the y variable?
vocal sleetBOT
would the x^4 in the problem cancel each other out leaving only the y variable?
@hearty gust Has your question been resolved?
vocal sleetBOT
@hearty gust Has your question been resolved?
vocal sleetBOT
@hearty gust Has your question been resolved?
vocal sleetBOT
@hearty gust Has your question been resolved?
pallid zenith
would the x^4 in the problem cancel each other out leaving only the y variable?
no
theres two terms in the bottom
only one of them has x^4 in it
hearty gust
@pallid zenith yes but does the x^4 in the numertator divide into x^4 in the denominator leaving y/36y
pallid zenith
<@331558346333224964> yes but does the x^4 in the numertator divide into x^4 in ...
I guess its not clear to me exactly what you mean. If you're asking if its possible to write the expression inside in an equivalent way without having x's in it, then the answer is no
vocal sleetBOT
@hearty gust Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
wraith nimbus
Hello, how can I find the domain of this function ?
vocal sleetBOT
Hello, how can I find the domain of this function ?
wraith nimbus
I know that x+sqrt(x^2+y^2)>0 but what should I do next ?
lean lark
if x is positive then you have no issue
if x is negative, take it to the right and square everything
wraith nimbus
I will get x^2+y^2>x^2
lean lark
aha
lean lark
I will get x^2+y^2>x^2
you just get y^2>0, that means you can use any y you want except for 0
that's it
lean lark
we just discussed that using x > 0 and then x<0, the only remaining case is x=0
you do the same for y
(y=0)
and get a condition for x
wraith nimbus
Thank you @lean lark
wraith nimbus
I have the solution already but I didn't know how they get it but now it makes sence
lean lark
you from where?
wraith nimbus
tunisia
lean lark
7attena hhh
wraith nimbus
hhhh
lean lark
el solution heki ne9sa
wraith nimbus
eyy ne9es x<0 hakeka ?
lean lark
el mafroudh R^2 {(0,0)}
ey just lezem ma yjiwech fard wa9t 0
ynajjem ay we7ed fehom ykoun 0 walla negatif el mouhem mouch el zouz mab3adhhom 0
wraith nimbus
wada7 3aychou @lean lark
lean lark
men ghir mzyya, nsakker el channel?
finite halo
help
finite halo
i wanna simplify this equation
(x+1)/2 -x^2 - x = (x+2)/3
so I thought multyplyng everything with 6
tidal umbra
just cross multiply it
tidal umbra
$\frac{(x+1)}{2} -x^2 - x =\frac{(x+2)}{3}$
twin meteorBOT
🐱!Yajat! 【Catfan1398】🐱
finite halo
yeah
tidal umbra
is this your question?
twin meteorBOT
🐱!Yajat! 【Catfan1398】🐱
finite halo
what if something is being divided?
do i just divide the multiplicator?
so (x+1)/2 = 3(x+1)?
$\frac{(x+1)}{2}=3(x+1)
:(
$\frac{(x+1)}{2} = 3(x+1)
,,(x+1)/2 = 3(x+1)
twin meteorBOT
kiril kyotaka
finite halo
this
twin meteorBOT
kiril kyotaka
vocal sleetBOT
tidal umbra
!nogpt
vocal sleetBOT
Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).
tidal umbra
no gpt, no gpt or get a timeout gpt
vocal sleetBOT
Available help channel!
alpine storm
i need help with showing K is closed
vocal sleetBOT
i need help with showing K is closed
alpine storm
i considered a sequence of sequences (x^(n)) in K, and a limit point x in ell2 such that (x^(n)) converges to x.
now i want to show that x is in K
paper depot
are you allowed to use topological shit like "intersection of any family of closed sets is closed"
alpine storm
yeah, my class covered that
paper depot
right
for each k in N let S_k be the set of all sequences whose first coord is >=0
you can show each S_k is closed
thereby show that your K, which is the intersection of them all, is also closed
alpine storm
for each k in N let S_k be the set of all sequences whose first coord is >=0
wait what does k denote here
paper depot
a natural number
oh omg fuck i typoed
i meant k'th coordinate, not first coordinate
alpine storm
ah okay, thanks
vocal sleetBOT
@alpine storm Has your question been resolved?
alpine storm
.close
tired cradle
i need help
vocal sleetBOT
i need help
loud pivot
!status
vocal sleetBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
loud pivot
Hint: ||L'Hôpital's rule||
loud pivot
You can do something in the denominator for starters
tired cradle
can you show?
vocal sleetBOT
@tired cradle Has your question been resolved?
vocal sleetBOT
@tired cradle Has your question been resolved?
tired cradle
<@&286206848099549185>
vocal sleetBOT
@tired cradle Has your question been resolved?
untold needle
Your question is this?
[\lim_{x\to 1}\frac{\sqrt{2^x+7}-\sqrt{2^{x+1}+5}}{x^3-1}]
twin meteorBOT
luke1337
lament linden
@tired cradle have you multiplied and divider by conjugate of the numerator?
lament linden
Oh alright
lament linden
Yeah nice question
vocal sleetBOT
vocal sleetBOT
Available help channel!
torn tree
Why is r(a1 + a2) in (r)?
vocal sleetBOT
Why is r(a1 + a2) in (r)?
lyric relic
torn tree
ok that makes sense
ty
when my question is solved should I type .close or do anything?
lament linden
Latex output of this for better readability: $a_1 + a_2 \in \mathbb{R}$
\ $rx \in (r) for every x \in \mathbb{R}$
lament linden
when my question is solved should I type .close or do anything?
Yeah .close
torn tree
kk
twin meteorBOT
Cyrenux
torn tree
.close
little canopy
Hi I need help on an area q
hushed pewter
trail notch
can someone please help me with number 3? I don’t know where to start
grizzled halo
then what'd you get for L?
trail notch
L=p^2*g/4pi^2
grizzled halo
and then you need the length L, when the period p=1
trail notch
huh
grizzled halo
find the length needed for the pendulum to have a period of 1s.
i.e. sub in p=1 to find L
trail notch
> find the length needed for the pendulum to have a period of 1s.
i.e. sub in p=...
isnt L just 1/4pi^2 then?
if p = 1?
grizzled halo
g/4pi^2
grizzled halo
L=p^2*g/4pi^2
L=(1)^2*g/4pi^2