ok
#help-10
sharp ether
246.33 is the answer.
omg I got it!!! thank you so much!!! sorry about joining the same channel thing. I am new here...
How do I get out?
obtuse pebbleBOT
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sharp ether
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unique kraken
How do I solve these?
lavish swift
What is that?
merry yarrow
could you type that out I cannot read that
unique kraken
X^2-4x+5=0
What multiplies to 5 and adds to -4?
Imaginary numbers
I forgot how it works
obtuse pebbleBOT
How do I solve these?
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unique kraken
could you type that out I cannot read that
?
lavish swift
i is the square root of -1
unique kraken
So it’s -5i and 1?
merry yarrow
could you not just use the quadratic formula or are you not allowed to
unique kraken
Not allowed to
merry yarrow
ah
obtuse pebbleBOT
Available help channel!
prisma cobalt
This is more propositional logic if anyone knows that but we're supposed to figure out if these proofs have errors in it. I can't tell if this is valid or not or why.
obtuse pebbleBOT
This is more propositional logic if anyone knows that but we're supposed to figu...
prisma cobalt
It could be correct but im fairly certain that 9 (specifically 9, not 5) or 10 is fully wrong
I've been told that formatting is correct
lavish swift
What is appl.?
prisma cobalt
It's the name of a rule, not sure exactly what it is though
prisma cobalt
I think the proof is (J->L)->L
And we're just trying to say weather the steps are valid or not
and if not, which one and why
lavish swift
But is JVK and if KthenL given or are we assuming that?
prisma cobalt
thats given
lavish swift
O
prisma cobalt
or well, i think assumed? I don't think theres a difference i think they just write the proofs stupidly
It always uses the syntax of assume X, never given X
lavish swift
Correct me im still learning this but JtoL and L does not necessarily mean (JtoL)toL right?
I’ve never seen that done
prisma cobalt
well if J->L and L is given, then J->L could be true if J is false too
lavish swift
But L isn’t given?
prisma cobalt
so actually, (J->L)->L if L is given, (J->L) would be true even if not J, so then L?
lavish swift
Oh nevermind
lavish swift
Hmm
daring sorrel
It could be correct but im fairly certain that 9 (specifically 9, not 5) or 10 i...
What is ur reasoning
prisma cobalt
Something about it just strikes me as super wrong
daring sorrel
Well 9 is a result of lines 1 (partially),6,7,and 8 so if you think 9 is wrong then one those other lines is flawed
prisma cobalt
I don't understand case 2
J->L is assumed which doesn't include K, and we're proving (J->L)->L so technically what K is or isn't and K->L doesn't matter at all
if we assume J->L in both cases, then the entirety of K doesn't matter whatsoever
the syntax is stupid but this would be correct right?
daring sorrel
J->L being assumed doesnt prove L unless J is true, which in that section of the proof is never shown (so that line is useless).
We are given K->L, so if K is true, then L is true. And we assumed K is true in line 6
So K does matter in case 2 cuz its needed to show L
lavish swift
So would a better case be notJ?
prisma cobalt
Line 1 already gives us that K->L though
I guess if not K then the whole expr would be true though anyway i guess
daring sorrel
I guess if not K then the whole expr would be true though anyway i guess
Yeah but we don’t know whether K is true or false.
At least until case 2 where we assume its true
prisma cobalt
Im gonna assume this thing is wrong
daring sorrel
Let me just say line 7 is useless and should be ignored. It may be causing confusion.
It is true we can assume it but it has no benefit towards the proof
Overall the claim is correct but the statement in 9 can be considered wrong, because K->L and K is what proves L, not the J->L
prisma cobalt
So technically (J->L)->L is true when J is false, or when K happens to be true (since that would prove that L is also true)
but that doesn't necessarily mean that (J->L)->L is true since (J->L) being false would still make L true
basically it would be proveable if (J or K)->L but the statements are never connected in a way that you can 100% determine that the statement is true right?
daring sorrel
but that doesn't necessarily mean that (J->L)->L is true since (J->L) being fals...
I might have said something confusing. (J->L)->L IS true, its just assuming J->L does not help prove L, which is why I think saying “lead to L” in 9 is false.
In summary J->L did not lead to L, but it does imply L
If I could rewrite line 9 I would say “The assumption K along with K->L lead to L, and so (J->L)->L”
prisma cobalt
Would this one be wrong under the same conclusion (different formating)
this could be seen as wrong because it says L is proved with J->L but that assumption is made but never proven
It's proven by K->L in the case when K is true
daring sorrel
We can assume J->L without needing to prove it
When we prove implications, we assume the hypothesis true, and show that the conclusion is also true.
Btw this proof seems basically the same as the last one
The only difference I see is that instead of assuming J->L in each case, they assume it before starting the cases argument
But it does not matter when you write it down
So unless im missing something the overall argument of the proof is the same
prisma cobalt
so the problem is in the wording
for both?
This is stated btw above in the assignment "Finally, note that there are no mistakes in format, phrasing, citations, or other aspects
of presentation, so don’t worry about that sort of thing. Just pay attention to what
formulas and/or subproofs are being used, what rule is being used, what formula is
being concluded, and whether that rule can be used on those formulas/subproofs to
deduce that formula."
so if the mistake is wording then these are both true
daring sorrel
so if the mistake is wording then these are both true
I see
Then yes both are true
Only issue with the first one is the explanation in line 9 made no sense but the result was true.
It would be equivalent to saying something like:
Trees are green leads to the ocean being blue
The first part is true, the conclusion is true, but obviously saying this makes no sense
But at the same time
Trees are greens -> The ocean is blue
prisma cobalt
Hmm, i dont get it but thanks. (hoping this semester ends soon lol)
daring sorrel
Implications are confusing because they don’t really work the same way you would use them in an actual argument. Might be helpful to think of A -> B as being equivalent to not A or B
In general though if you can’t identify a single line thats wrong I think you should say its correct
obtuse pebbleBOT
@prisma cobalt Has your question been resolved?
obtuse pebbleBOT
@prisma cobalt Has your question been resolved?
sturdy ledge
obtuse pebbleBOT
sturdy ledge
I don’t think I did this right and need help to make sure if I did or didn’t
static furnace
you forgot an end parenthese before the multiplication of 20 in your calculation of volume
sturdy ledge
Can you fact check me did I still get the answer wrong
static furnace
putting that aside, i don't believe the length ratio and volume ratio are the same. for example, you can have a 1x1x1 cube with volume 1, and a 2x2x2 cube with a volume of 8
even tho sides are 1:2 ratio
sturdy ledge
Wait hold up 😭
I got a completely whole different thing
I got 1800 now
Ok can someone fact check me
obtuse pebbleBOT
@sturdy ledge Has your question been resolved?
sturdy ledge
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
unkempt quartz
how do i find the IQR?
obtuse pebbleBOT
how do i find the IQR?
untold badge
how do i find the Q3 bit
the same way you find q1
unkempt quartz
the same way you find q1
which is?
untold badge
right so once you have the median, you have 2 groups of numbers: one on the right side and one on the left
what do you think you need to do with those 2 groups of numbers
worn yoke
that's what the coefficient of determination R^2 says
graceful marten
obtuse pebbleBOT
graceful marten
So I prove its a rational number
I did root 2 = a/b
2 = a^2 / b^2 and then got stuck from there
Thats the best I could come up with
fathom flicker
What do you mean you prove it is a rational number?
It is not a rational number
that is the whole point
fathom flicker
That doesn't mean you actually prove the opposite statement
it means you prove the opposite statement is false
graceful marten
it means you prove the opposite statement *is false*
yes I get that
But how can you say its false
from 2 = a^2/ b^2
fathom flicker
The idea is to first suppose it is rational, as you have
then since it is rational (we claim), it can be written as a simplified fraction
where the numerator, and denominator, share no like terms
for example
19/3
we would not write it as 48/24
because this can be reduced to 2/1
graceful marten
yes
fathom flicker
Anyways, we don't know what these numbers should actually be, we just say, let it be of the form a/b, in reduced form
the contradiction comes from showing that a and b are both even
because if they are both even, they have a common factor of 2
which goes against the fraction being in reduced form
graceful marten
Right...
2= a^2 / b^2
You can prove a^2 is even as 2b^2 = a^2
and then 2b/b = 1 which is odd
but even(2) / (1) odd is = 2
so even..
I dont know
fathom flicker
2b/b = 1 ?
fathom flicker
Okay so you're going about this in the wrong way
graceful marten
Is that a way of solving it?
graceful marten
Yes please
graceful marten
yes
fathom flicker
To prove a is even, as you said earlier, we can write
2b^2=a^2
and it requires a little work, because it is a^2 on the right side, and not a, but we can prove this means a is even
So ignoring that for now
We know that a is even.
Well what does it mean to be even?
graceful marten
factor of 2
fathom flicker
It means that a=2n, for some integer n, right?
fathom flicker
Yes
Okay
2b^2=a^2
we know a=2n
2b^2=(2n)^2
Now do some algebra with this
and write b^2=2(....)
and b is thus also even!
graceful marten
2n^2 = b^2
fathom flicker
So, it remains to be proven that
a^2 being even implies that a is even.
that's all that's left for you
(and replace a with b, it's the same statement)
graceful marten
(and replace a with b, it's the same statement)
I dont understand
fathom flicker
Okay earlier we said
2b^2=a^2
and we concluded that a must be even
really we only know from that line, that a^2 is even
fathom flicker
2n^2 = b^2
and the same thing in this line
really we have only proven that b^2 is even
so you must prove that b^2 being even, implies that b is even
fathom flicker
so you must prove that b^2 being even, implies that b is even
I was pointing out that this proof, is the same as
fathom flicker
so you must prove that a^2 being even, implies that a is even
this proof
just swap a and b and it is saying the same thing
graceful marten
ok you might go into a rage but
If you prove if n is even n^2 is even
So
2 = a^2 /b^2
2 = (4k^2) / (4k^2)
2 = 1
Im guessing this isnt proof
fathom flicker
Not the proof, also you aren't even trying to prove the same thing I was talking about
Let me be more clear
Earlier, we showed that 2b^2=a^2
this means that a^2 is even
it does not mean that a is even
graceful marten
wait what
fathom flicker
we still have to prove that
graceful marten
Oh ok
fathom flicker
We have to prove:
IF a^2 is even, THEN a is even
Which I can give you a great hint for
Do you want it?
fathom flicker
If you're proving something of the form
"P" implies "Q"
It is the same to prove that
"Not Q" implies "Not P"
We want to prove, if the sun is out, it is daytime
we can prove instead, if it is not daytime, the sun is not out
and we've proven what we wanted to from the beginning
This is called a proof by contrapositive
Different than by contradiction
It makes the proof very simple for what we want to prove.
fathom flicker
We have to prove:
**IF** a^2 is even, **THEN** a is even
So can you restate this, in the contrapositive form?
graceful marten
If a^2 is odd then a is odd
graceful marten
and contradiction would be
for some values of a, a^2 is even but here a is odd
graceful marten
Okok Istop
fathom flicker
If a^2 is odd then a is odd
this is not correctly stated
you wrote Not P implies not Q
Which is not the contrapositive form
fathom flicker
I think you need to slow down
I'll give an example and then you can try again okay?
graceful marten
yes please
fathom flicker
We want to prove,
if |x|>5 then x^2>25
we could instead prove
if x^2 is not >25, then |x| is not > 5
fathom flicker
We have to prove:
**IF** a^2 is even, **THEN** a is even
So what is the contrapositive statement for this?
graceful marten
if a isnt even, then a^2 is not even
fathom flicker
Good
and not even just means odd
so we write
If a is odd, then a^2 is odd.
That's much easier to prove
If a is odd then a=....
graceful marten
yeah
that does make it easier
So you can use that IN contradiction is what you are telling me?
If you need to prove something within the contradicting statement
idk if that makes sense
.
fathom flicker
Yes, in our proof by contradiction, we used the fact that a^2 is even implies a is even. This fact that we used, can be proven using contrapositive.
graceful marten
ok right
fathom flicker
You can think of it as a little sidetrack from our proof
we need it to keep going, but the proof of it is unrelated to our overall proof
graceful marten
Would you have to then prove both
a = even a^2 even
a = odd and a^2 = odd then
fathom flicker
No, in our proof, the only thing that we used is a^2 even => a even
that's all we need to prove
and we proved it by showing that a odd => a^2 odd
since they are equivalent
graceful marten
yes
fathom flicker
(the contrapositive is equivalent to the original)
graceful marten
(the contrapositive is equivalent to the original)
makes sense now when you say it
fathom flicker
Are you familiar with the "=>" symbols
graceful marten
equaland or smaller/greater than
fathom flicker
No
They're logical symbols
the way that I am using them
when I write
"=>"
I mean
this implies that
fathom flicker
and if I write, <=>, I mean "if and only if"
fathom flicker
(P => Q) <=> (Not Q => Not P)
this is the idea of the contrapositive proof
Can I ask, what class you are doing this for?
fathom flicker
What's that?
graceful marten
Year 13-> grade 12 in american system
And I do A levels (UK)
Americans usually do IB
graceful marten
uhhhh simple for now?
fathom flicker
Before calculus?
graceful marten
Not sure what calculus exactly includes
fathom flicker
Okay well anyways, my point was going to be that if you ever do any proof-based math courses, (which are typically after calculus, and only if you do a bit more math courses than the usual person), that these symbols will be used very frequently
They're just like abbreviations for not writing lots of words
graceful marten
Oh ok, I will be doing math in uni
But on the side
Yeah i use the therfore symbols and arrows in my exams woooo
saves a lot of words
lol
best i got
graceful marten
Yes
fathom flicker
Great
fathom flicker
Have fun with your math
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
graceful marten
Just here to say
I think I’ll be memorising this.
Unless someone can explain why they decided to suddenly multiply all the prime numbers
And then add +1 onto it
obtuse pebbleBOT
Just here to say
I think I’ll be memorising this.
Unless someone can explain why...
graceful marten
I would understand if they did Pn+1
But they did it (p1,p2,p3)+1
cedar chasm
Because then it cannot be factorised by anything on the lidt
list
And it is a theorem that any non prime number has prime factors
wispy silo
Just here to say
I think I’ll be memorising this.
Unless someone can explain why...
It's because they want to create a number that doesn't have any of the numbers p_1, p_2, ..., p_n as a factor.
graceful marten
It's because they want to create a number that doesn't have any of the numbers p...
What’s the point of doing that
Is this like a golden rule for any infinite questions
cedar chasm
No
graceful marten
Infinite number of even number odd numbers ect
cedar chasm
What is it that we're trying to prove?
wispy silo
The point is that they want to prove (by contradiction) that there are infinitely many primes. So they assume there are only finitely many p1, p2, ..., pn.
Then they do this trick of looking at the number P = p1*p2*...*pn + 1.
graceful marten
And it is a theorem that any non prime number has prime factors
Oh ok I understand this
cedar chasm
It's an arbitrary choice to construct P like that
But algebraically we know P will have certain properties
graceful marten
Nvm
cedar chasm
Well it's not arbitrary, but it could have been constructed otherwise
wispy silo
And the number P they are looking at turns out it cannot have any of the p1, ..., pn as prime factors. Since it must have some prime factor, which cannot be any of p1, ..., pn, then there exists at least one more prime.
cedar chasm
Imagine that we want to prove that there are more than the 3 first prime numbers.
So we have our list of prime numbers, 2, 3 and 5.
Their product is 30. Now clearly 30 is divided by both 2 and 3 and 5, making it not a prime. But what about 31?
cedar chasm
No
graceful marten
Ok I guess that’s not proof
cedar chasm
What about 31? Does either 2, 3 and 5 divide it?
graceful marten
Not anymore
graceful marten
So what we did is
A b c
Abc +1
/abc is not divisible
cedar chasm
Yes
graceful marten
And the 1 shows its some number of a prime
Because it has the qualities of a prime
?
But then again I don’t think 1 is a prime
polar fossil
steps in math often seem to come "out of nowhere" which is usually the result of like days to months to decades of trying things to see what works
1 is not a prime
polar fossil
basically it's way the heck simpler to just call it its own special case (a "unit")
graceful marten
Math is suddenly getting unfun
How would you prove something prove by contradiction there infinitely number of even numbers
So finite even numbers so
2k x 2k something I guess I can do that
wispy silo
Eh
cedar chasm
You wouldn't prove that by contradiction, you show just you can go from any n to 2n, and from 2n to n again.
Uniquely
graceful marten
Ah ok
wispy silo
Suppose there are only finitely many even numbers. Let x be the largest of them. Then x = 2n for some integer n.
Let y = x + 2 = 2n + 2 = 2(n+1), which is then an even number larger than x. That's a contradiction.
graceful marten
Oh ok
cedar chasm
The definition of infinite is that something can be put in one-to-one correspondence with the natural numbers
graceful marten
Does it have to be +2 or can it be +1
Oh but then you’d get an odd number
And you are not trying to prove it’s a finite odd number
But a finite even number
Correct?
Rightt
wispy silo
Correct
graceful marten
Ok I understand the rest
I’ll do the memorisation part on this one
I need to get through other studd
Haha
Thank you all
.close
obtuse pebbleBOT
graceful marten
Suppose there are only finitely many even numbers. Let x be the largest of them....
Quick question
there are finite numbers of oddd
.reopen
obtuse pebbleBOT
✅
warm shaleBOT
graceful marten
Can that be considered odd
2n+3
Or would I have to prove that too
(Proof by contradiction)
So finitely numbers of odd
obtuse pebbleBOT
@graceful marten Has your question been resolved?
daring bramble
Well adding 2 to anything doesn't change the modulus base 2 of the number
Like if you don't have to be rigorous you could literally just say even + odd = odd
Also odd numbers are a subset of the set of integers, which has infinite domain
Therefore odd numbers also have an infinite domain
obtuse pebbleBOT
@graceful marten Has your question been resolved?
normal oracle
ol so i have to find the area between thise two functions but idk how to find one of the solutions
obtuse pebbleBOT
ol so i have to find the area between thise two functions but idk how to find on...
golden night
ol so i have to find the area between thise two functions but idk how to find on...
did you find the points of intersections
normal oracle
only one
normal oracle
i dont know how to get it
obtuse pebbleBOT
@normal oracle Has your question been resolved?
hoary knoll
There are 8 people in the classrom. In how many ways can you distribute them in a groups of 2 people
obtuse pebbleBOT
There are 8 people in the classrom. In how many ways can you distribute them in ...
hoary knoll
I tried to solve it and got
$\frac{8!}{2^{4}\cdot4!}
however the answer i got is 105, but the answer in book is 420
$\frac{8!}{2^{4}\cdot4!}$
warm shaleBOT
aq
timid silo
i think 105 is the answer as well
hoary knoll
i really dont know how the answer should be 420
but if you got 105 as well
I think the book is incorrect
brisk grove
Does the order in the group matter?
And does the order OF the groups matter?
If the answer to both is no, then the answer is 105 yes
obtuse pebbleBOT
@hoary knoll Has your question been resolved?
fossil turtle
obtuse pebbleBOT
analog tinsel
in order for z to be a power of 2, notice that x^3 needs to be equal to y^4
fossil turtle
in order for z to be a power of 2, notice that x^3 needs to be equal to y^4
Why?
brisk grove
Because for z to be a power of 2, z^5 needs to be a power of 2
therefore x^3 + y^4 needs to be one aswell
And when you add two powers of two, and you get a power of two, then they must be equal
2^n + 2^k is a power of 2 only when n = k
hoary knoll
yep
analog tinsel
2^n + 2^k is a power of 2 only when n = k
to supplement, suppose n =/= k (assume n > k wlog)
then 2^n + 2^k = 2^k * (2^(n-k) + 1)
where 2^(n-k) + 1 is odd
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
primal thunder
can somebody help me here
obtuse pebbleBOT
can somebody help me here
primal thunder
it says 1 is incorrect, and i assume that's because both of the 3x's aren't supposed to cancel out, but idk how to prevent that
obtuse pebbleBOT
@primal thunder Has your question been resolved?
primal thunder
<@&286206848099549185>
clear pollen
By direct substitution you get 0/0, do you know how to use L'Hopital's Rule?
clear pollen
<@&286206848099549185>
If we define 1/(8x-3) - 1/11 as a function and 1/(6-3x) -1/9 as another, the question can be the limit of f(x)/g(x) as x approaches -1
primal thunder
it's homework, we didn't learn l'hopitals yet
it's just algebraic manipulation atp
but idk how to do it properly ig
clear pollen
K lemme see what I can do
primal thunder
You combined the fractions and KCF right
kcf?
obtuse pebbleBOT
Available help channel!
keen badger
If f(x) is a function that is differentiable on the real line y=a is a horizontal asymptote of f(x), then can we say taht y = 0 is a horizontal asymptote of f'(x)? in other words,
if lim f(x) = k , where k is a real number
x-> +oo
then limf'(x) = 0
x->+00
if the limit of its derivative exists
obtuse pebbleBOT
If f(x) is a function that is differentiable on the real line y=a is a horizonta...
polar fossil
If f(x) is a function that is differentiable on the real line y=a is a horizonta...
that last "if" is pretty big
polar fossil
i guess what you could do
is since you're assuming the limit of f' exists
call that L
and show that L has to be 0
obtuse pebbleBOT
@keen badger Has your question been resolved?
crude hearth
If you find yourself getting stuck on a proof, another option that can often help is to try and come up with a counterexample
thin stream
using shell method
obtuse pebbleBOT
using shell method
thin stream
not sure what the shell height is
x - (-x)?
but its in terms of y
so i could also just do y - (-y)?
polar fossil
using shell to revolve around a horizontal axis? 
thin stream
using shell to revolve around a horizontal axis? <:WC_Stare:944712601785466920>
?
does it not matter as long as your normal element (idk if that's the right name) is parallel to the axis of rotation
polar fossil
yeah this would just be easier with washer but whatever
thin stream
then what's the shell radius
polar fossil
so i could also just do y - (-y)?
or I guess this
thin stream
gotcha
polar fossil
then what's the shell radius
the distance from your green line to the axis
thin stream
x - (-x)?
ik i was asking cus you said that it would be this
idk what the radius would be in terms of x
but in terms of y its just y
but thanks for the help
i got it now
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
tight bison
obtuse pebbleBOT
fickle turret
why is the 1/n^2 there?
What's the definition of the Variation?
carmine salmon
Hi everyone! It's reletively simple math I am just bad at it
obtuse pebbleBOT
Hi everyone! It's reletively simple math I am just bad at it
carmine salmon
I only got 2 out of three datas
Is it a problem with the paper itself? Because I remember only salving ones with three datas
.close
verbal niche
why is this undefined?
obtuse pebbleBOT
why is this undefined?
verbal niche
i integrated cot(x) like this
i converted it back to cos(x)/sin(x)
let u=sin(x)
then you just integrate 1/u which is ln(abs(u))=ln(abs(sin(x)))
and that shouldnt be undefined
worn yoke
notice that sin(x) = 0 on that interval, so the integral is improper
worn yoke
note that the integral still can exist with discontinuities like that, but in this case it doesn't converge
verbal niche
so it works for removable discontinuities?
worn yoke
it can work for vertical asymptotes as well, but only sometimes (the area underneath has to be finite, which it sometimes is and sometimes isn't)
verbal niche
luckily i dont think i'm there yet lol
worn yoke
you'll probably cover it at some point in your class
obtuse pebbleBOT
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final matrix
Can someone please verify my proof? One second I will type it out:
obtuse pebbleBOT
Can someone please verify my proof? One second I will type it out:
obtuse pebbleBOT
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final matrix
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junior hull
clearly my answer is not correct, but i figured to find the volume, we find whats above and below then subtract from the total volume of 1 since its 1 by 1
its a little badly written
obtuse pebbleBOT
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junior hull
<@&286206848099549185>
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fathom flicker
obtuse pebbleBOT
fathom flicker
Any hints for this? I've tried directly and contrapositive but can't really get any closer
polar fossil
can you just trace the proof of thm 6.1c but with * instead of +?
fathom flicker
It is alluded to by the hint there but I haven't looked at that yet
Looking now, I'm confused about the proof for 6.1c
so maybe that should be my question
a_n=s_n-s_(n-1)
that's where it loses me
like if {s_k} represents the kth partial sum
nvm
I understand it now
let {s_k} denote the partial product
then a_n = (s_k)/(s_(k-1))
if the product converges to something nonzero
then lim a_n = lim (s_k)/(s_(k-1))
P = P/P = 1
bazinga
thanks hayley
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obtuse pebbleBOT
polar fossil
that was great i got to help while eating taco bell
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atomic umbra
slightly complicated u-sub
obtuse pebbleBOT
slightly complicated u-sub
atomic umbra
,tex $\int \left(1 - \cos(\frac{t}{2}) \right)^2 \sin(\frac{t}{2}) dt, u = 1 - \cos(\frac{t}{2})$
warm shaleBOT
@atomic umbra
atomic umbra
so i see that i can substitute in u^2
brave bramble
u = 1 - cos(t/2)
So
du = ?...
atomic umbra
du = sin(t/2) /2
brave bramble
Close. Don't forget about the dt.
du = sin(t/2)/2 dt
atomic umbra
ok
,tex $\int u^2 \times du \times \frac{2}{dt} dt$
im confused on what we're integrating with respect to
warm shaleBOT
@atomic umbra
atomic umbra
and do i use this to cancel out dt
atomic umbra
,tex $\int 2u^2 du$
warm shaleBOT
@atomic umbra
atomic umbra
,tex $2 \left( 1 - \cos(\frac{t}{2}) \right)^2 + C$
warm shaleBOT
@atomic umbra
atomic umbra
is this right
obtuse pebbleBOT
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unborn zinc
How do i find the value of I here
obtuse pebbleBOT
How do i find the value of I here
unborn zinc
the left hand side of the equation can have an imaginary part but it can be ignored (i believe)
obtuse pebbleBOT
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minor pike
obtuse pebbleBOT
minor pike
help pls
graceful marten
Therefore odd numbers also have an infinite domain
That makes a whole bunch of sense
Thank you very much for the explanation :3
obtuse pebbleBOT
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tender tusk
help pls
it states that the 2 triangles are congruent therefore all the sidelengths and angles will be the same in both triangles
although that diagram is terrible
we know 2 angles in one of the triangles and since triangles add up to 180 degrees we can find the 3rd angle, once we have all 3 angles that means we know all 3 angles in the other triangle aswell since they are congruent
obtuse pebbleBOT
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brisk arrow
obtuse pebbleBOT
brisk arrow
I would like to discuss this one
I should compare the modified graph to its original
It is basically y^2 =9(x-2)
Then you sqrt both side
Which results in y = + or - of sqrt[3(x-2)]
short ore
It is basically y^2 =9(x-2)
9
chrome crypt
Welll note the order of reflections.
Vertical/Horizontal Reflection
Vertical/Horizontal Exp/Comp
Translation Vert & Hoz
brisk arrow
And obvious the modification takes the negative sign
short ore
Which results in y = + or - of sqrt[3(x-2)]
the radical symbol means the + sqrt
brisk arrow
And obvious the modification takes the negative sign
And then the negative sign is distributed to the sqrt(x-2)
short ore
It is basically y^2 =9(x-2)
this isnt the same equation
brisk arrow
The opening of the parabola y^2=9(x-2) becomes narrower
short ore
y^2 = 9|2-x|
timid silo
ask me if u dont understand
brisk arrow
I will save it for now, since I have to prepare for the incoming course about other subject
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stuck coral
Shouldn’t it be 2x the answer for the x component since its two vectors?
obtuse pebbleBOT
Shouldn’t it be 2x the answer for the x component since its two vectors?
@stuck coral Has your question been resolved?
obtuse pebbleBOT
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warm tide
warm tide
How would i do #36?
worn yoke
try substituting u = the denominator
warm tide
warm tide
try substituting u = the denominator
I tried
But having a hard time finding my du and dt
worn yoke
when taking the derivative of an exponential function you can rewrite
$$2^t = e^{\ln(2^t)}$$
and differentiate from there
warm shaleBOT
cloud
warm tide
when taking the derivative of an exponential function you can rewrite
$$2^t = e^...
Wut
Is there a rule for that
Thanks
I’ll try it out
worn yoke
it's just true in general that for any number x, $$e^{\ln x} = x$$
warm shaleBOT
cloud
worn yoke
which is a property of logarithms. you could also do it with other bases, for example $$10^{\log x} =x$$ but that's less useful
warm tide
warm shaleBOT
cloud
warm tide
Is this correct?
worn yoke
the t should be in the exponent of 2
you should also make sure you take the derivative with the chain rule
warm tide
you should also make sure you take the derivative with the chain rule
Gotcga
worn yoke
after you take the derivative you should also bring it back in terms of $2^t$
warm shaleBOT
cloud
warm tide
after you take the derivative you should also bring it back in terms of $2^t$
How would i do that?
obtuse pebbleBOT
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obtuse pebbleBOT
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earnest pecan
I don't understand, what is rewriting and how did it get from 1/8 to 2^-3?
obtuse pebbleBOT
@earnest pecan Has your question been resolved?
earnest pecan
first off dont use gpt for maths
Hey man i need all the help i can get alright, yeah im here
spring trail
even now?
earnest pecan
Yep
earnest pecan
bruh what
spring trail
2 raised to the power 3
earnest pecan
Its 8
earnest pecan
Some
spring trail
the negative exponent one?
earnest pecan
Nope
obtuse pebbleBOT
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dusk widget
i feel like this should be easier..
obtuse pebbleBOT
i feel like this should be easier..
obtuse pebbleBOT
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weary carbon
I nees help with a seno
obtuse pebbleBOT
I nees help with a seno
weary carbon
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obtuse pebbleBOT
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hybrid swallow
Can someone explain.. 😭
obtuse pebbleBOT
Can someone explain.. 😭
pine sail
hybrid swallow
Can you pls tell how to..
surreal forge
you need TS first
hybrid swallow
you need TS first
8cm
hybrid swallow
Common angle A and right angles T=B..
surreal forge
that’s also correct
hybrid swallow
Similarity?
surreal forge
because 2 of the angles are the same, you can conclude the 3rd angle is the same as well
surreal forge
Similarity?
thus the triangles are similar yes
hybrid swallow
Okay that concludes angle S and C are same
surreal forge
now do you know how to set up the similarity ratios to find AC?
hybrid swallow
Not sure.. I am a little confused in that..
ST/BC?
= AS/AC
=AT/AB
??
I am confused can you pls help me out with the calculation..
surreal forge
sure. (I’ll also note that everything you said is correct)
hybrid swallow
: D
surreal forge
I am confused can you pls help me out with the calculation..
because you have AAA similarity, i suppose you could like draw out the angles and make note of which are the same
then you can look at which edges correspond to each other
surreal forge
you can do that yeah
hybrid swallow
After that??..
Hello..
Thanks for your precious time
My friend sent me the solution..
Thnks a lott.. :))
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urban drum
how can i see that the singularity at 1/pi is a pole of order 2021?
obtuse pebbleBOT
how can i see that the singularity at 1/pi is a pole of order 2021?
@urban drum Has your question been resolved?
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twilit bridge
hello my school uses grasple for math testing i have a question about these logarithms the way they are written to be more precise is the 4 log10 the same as 10log(4)?
obtuse pebbleBOT
hello my school uses grasple for math testing i have a question about these loga...
willow crater
hello my school uses grasple for math testing i have a question about these loga...
no
twilit bridge
so whats the idea behind the 4 then? i guess the 10 is the basenumber of the log
wispy silo
so whats the idea behind the 4 then? i guess the 10 is the basenumber of the log
The 4 is just a factor that you multiply onto the log.
obtuse pebbleBOT
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boreal talon
Find the roots of:
(y-2)(y-3)(y-4)(y-5) - 360 = 0
rich plume
!status
obtuse pebbleBOT
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
rich plume
okay you fucked up
boreal talon
well
rich plume
open a new channel
boreal talon
yeah
proven zephyr
obtuse pebbleBOT
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timid silo
please help.............
timid silo
ok
timid silo
i dont know
i am in standard 10th
please just provide a hint how to start
rest i will do by mysel
timid silo
ok thanks
obtuse pebbleBOT
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timid silo
Tony wants to appreciate how high the tower is, He stretches out his arm, holds up his thumb and closes one eye. The thumb clicks in front of the tower when Tony is standing 150 m away. He knows that his thumb is 6 cm and that the distance between the thumb and the eye is 65 cm. How high is the tower?
obtuse pebbleBOT
Tony wants to appreciate how high the tower is, He stretches out his arm, holds ...
timid silo
Uhhh this is something ab vertex triangle theorem
I dont know how to picture this
Like the thumb is 6 cm
So both heights on the triangles must be 6?? But then the scales is wrong
sweet gulch
No, both heights are not 6cm
Picture a big triangle with a little triangle in the corner
obtuse pebbleBOT
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timid silo
f(x) is a linear function
(f o f)(x) = 9x-4
find f(x)
A) 3x-5 B) 3x-1 C) 3x + 1 D) 3x + 3 E) 3x + 5 (yes i am dumb and cant solve this question)
timid silo
idk how to relate it with the linear function
torpid cave
[(f \circ f)(x) = a(ax + b) + b = a^2x + ab + b]
warm shaleBOT
casework
torpid cave
$a^2 = 9$
But $a=3$ was only option anyways
warm shaleBOT
casework
torpid cave
Check for which b is 4b = -4
timid silo
wow this is really confusing lol
torpid cave
Which part?
torpid cave
Well you have a system of equations
\begin{align*}
a^2 &= 9 \
ab + b &= -4
\end{align*}
warm shaleBOT
casework
timid silo
ohhhh
so a is 3 and b is 1
-1
thank you so much man i will try to solve it now i hope my brain will not explode
maths is really hard
and looking at the other peoples questions just gives me a headache lol this is probably the easiest question here
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obtuse pebbleBOT
opal willow
i’m really not sure of my answers tho
so can someone also check if my answers are correct
obtuse pebbleBOT
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pliant yacht
obtuse pebbleBOT
pliant yacht
<@&286206848099549185>
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ivory mesa
how to solve this?
obtuse pebbleBOT
how to solve this?
ivory mesa
all initial conditions are 0
obtuse pebbleBOT
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glossy citrus
since there's no z nor y, can we substitute the derivatives by z and y, maybe? I'm not good with differential equations but that woudl be my first idea
obtuse pebbleBOT
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spark saffron
I think the proper negation is A and B but im unsure.
obtuse pebbleBOT
I think the proper negation is A and B but im unsure.
@spark saffron Has your question been resolved?
spark saffron
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cloud willow
im only chatting here because no one has answered yet, so take my insights with a grain of salt
"some odd integers are prime" is equivalent to "there exists odd integers which are prime"
consider that when you say "all odd integers are prime" (clearly false) it implies "there does not exist an odd integer that is not prime", so the negation is that "there exists an odd integer that is not prime"
it's much easier to understand in logic as $\lnot \forall x (P) \equiv \exists x (\lnot P)$
i probably botched that notation but it's good enough
warm shaleBOT
hskthca
cloud willow
so you could flip this logic to conclude with $\exists x (P) \equiv \lnot(\forall x (\lnot P))$
warm shaleBOT
hskthca
cloud willow
and so $\lnot \exists x (P) \equiv \forall x (\lnot P)$
warm shaleBOT
hskthca
cloud willow
(the negation of "there exists an odd number that is prime" would be "all odd numbers are not prime")
so i'd say the two possible negations are "there does not exist an odd integer that is prime" and "all odd numbers are not prime"
i'll leave the choices to you :)
obtuse pebbleBOT
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burnt thunder
obtuse pebbleBOT
burnt thunder
how do i do 20
obtuse pebbleBOT
how do i do 20
burnt thunder
what do i do with the radius
crude comet
take derivative with respect to r
burnt thunder
take derivative with respect to r
we r suppsoed to use limits
obtuse pebbleBOT
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stoic elm
Help!!
stoic elm
i dont understand any of this
what is a parabola really?
what are k values??
a values????
spark saffron
.reopen
obtuse pebbleBOT
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stoic elm
<@&286206848099549185>
<@&286206848099549185>
oops sorry
double ping was an accident
stoic elm
mhm
stoic elm
can you explain what a parabola actually is
austere yew
Understand????
stoic elm
wdym
stoic elm
mhm
austere yew
