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#help-39
pearl pondBOT
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tribal echo
pearl pondBOT
tribal echo
wheres the circled bit coming from? the main Q (with final answer) is on the right, working solution on the left
uneven smelt
if u draw a right angled triangle with one side being north, one side being east. and the hypothenuse being northeast of length 1, the two sides will have length of 1/sqrt 2 or sqrt2/2
pearl pondBOT
@tribal echo Has your question been resolved?
tribal echo
ooo
tribal echo
if u draw a right angled triangle with one side being north, one side being east...
i get it, but srry im confused with where the 2 comes from
uneven smelt
north and east would be the same length, let x denote that length
by pythagoras, x^2+x^2=1
2x^2=1
x^2=1/2
x=1/sqrt2
brittle onyx
pearl pondBOT
brittle onyx
,rccw
jolly parrotBOT
brittle onyx
need help w this
pearl pondBOT
@brittle onyx Has your question been resolved?
pearl pondBOT
@brittle onyx Has your question been resolved?
pearl pondBOT
@brittle onyx Has your question been resolved?
pine dock
what is the rule called again where angle qps is double angle qrs when inscribed in a circle
pine dock
nvm i found it, but does anyone know if i could use the theorem, which is apparently called angle at the centre theorem, in triangles that are not inscribed inside circles
i would assume u could if qr is equal to rs?
rain turret
pearl pondBOT
rain turret
11?
hybrid haven
how do u know if this is bionomial or normal
pearl pondBOT
how do u know if this is bionomial or normal
hybrid haven
like how do u know that this is binomial
pearl pondBOT
@hybrid haven Has your question been resolved?
hybrid haven
<@&286206848099549185>
pearl pondBOT
@hybrid haven Has your question been resolved?
midnight haven
like how do u know that this is binomial
cuz it’s discrete? you can’t have -1 successes, can you?
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real rose
how do i do 2c?
pearl pondBOT
how do i do 2c?
real rose
can any1 explain why this integrtes this way
pearl pondBOT
can any1 explain why this integrtes this way
real rose
as in why we leave 1/2v^2
as it is
just abit confused on how the d/dx * f(x) or at least 1/2v^2 works
real rose
yes
vital anchor
pretty sure its cuz the integral basically cancels the d/dx
vital estuary
integrating and differentiating are inverses
vital estuary
so doing one then the other is the same as doing nothing
vital anchor
its as though you multiplied by 21 and then divided by 21
real rose
why is it sometime slike dy/dx of .... and sometimes just d/dx ....
without the 2nd variable on numerator next to d
vital anchor
dy/dx is normally used if youre given a y = something x equation
its the change in y in terms of the change in x
i think
real rose
yup
vital anchor
if youre given a curve like y = x^2 and want to find the gradient youd use dy/dx
but you dont have to worry about y in the image above
pearl pondBOT
light helm
d/dx is the derivatie operator that when applied gives the derivative
dy/dx is the derivative itself
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ocean grove
how o you know if an equation is quadratic?
pearl pondBOT
how o you know if an equation is quadratic?
real rose
how o you know if an equation is quadratic?
it has x^2. i think
highest power is x^2
thick dagger
define a quadratic equation 💀
ocean grove
~~it has x^2. i think~~
highest power is x^2
for example (x-1)(x+2) = 0, is that a quadratic equation?
tulip mason
All powers of x are positive integers. The highest power is $x^2$.
jolly parrotBOT
Max
real rose
for example (x-1)(x+2) = 0, is that a quadratic equation?
since the most expanded form indeed has a x^2
spare lark
since the most expanded form indeed has a x^2
X^3 +x^2 has a x^2 but its not a quadratic
spare lark
Well a quadratic has the form ax^2 + bx + c with a non zero in general
pearl pondBOT
ocean grove
.reopen
pearl pondBOT
✅
spare lark
No
summer gorge
yesnt
spare lark
Well indeed but not in this form
summer gorge
if you let $z=\sqrt{x}$ then yes
ocean grove
Why though?
spare lark
Why though?
Do what not divergence said
jolly parrotBOT
convergence
next dove
is √𝑥 + 𝑥 = 0 a quadratic equation?
quadratic is a subset of polynomials
Polynomials are defined only for positive integer exponents of variables
light helm
*non-negative integer
next dove
oh yeah
pearl pondBOT
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visual canyon
pearl pondBOT
visual canyon
I have a few questions with this as context
im trying to figure out
I have some context but I'll explain when someone sees this because the whole block of text was overwhelming last time ig
pearl pondBOT
@visual canyon Has your question been resolved?
visual canyon
<@&286206848099549185>
visual canyon
<@&286206848099549185>
here is some more context, please let me know if my work looks iffy
<@&286206848099549185>
visual canyon
.close
pearl pondBOT
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Available help channel!
warm roost
a circle is divided into concentric rings. (circle has a radius of 3) all of this concentric rings are placed in ascending order on a x-y graph. (they are approximated as a rectangle) why would the approximated slope of a triangle like structure of these concentric rings be 2xpixr?
unborn abyss
because 2πr is the circumference of the circle
warm roost
because 2πr is the circumference of the circle
i still dont understand
unborn abyss
that's a 3blue1brown video; does the voiceover not give explanation?
unborn abyss
I would expect the slope to be 2π
um, if you had a radius of 1 then the circumference would be 2π right?
warm roost
radius is 3
unborn abyss
so the outer rectangle would have a height of 2π
tawny drift
I thought diameter was 3
warm roost
I thought diameter was 3
ah my bad
hollow gull
a circle is divided into concentric rings. (circle has a radius of 3) all of thi...
is this 3blue1brown or what
looks familiar
warm roost
yes
hollow gull
oooooh
unborn abyss
radius is 3
okay..... so the radius is 3. what's the circumference?
warm roost
2pi3
warm roost
yes
unborn abyss
when you unwrap that ring it's the height of the tallest rectangle
unborn abyss
clarifying question what do you mean when you say slope
tawny drift
gradient of line
unborn abyss
I was not actually asking you
tawny drift
mb, sorry
warm roost
clarifying question what do you mean when you say slope
oh nvm why is the lenght of that line 2pir tho
the one which looks like the hypotenuse
stray cove
a circle is divided into concentric rings. (circle has a radius of 3) all of thi...
I think there's typo since he said in the video and also written in subtitle that slope is 2pi
unborn abyss
"a nice way to think about this setup is to draw the graph of 2πr"
do you know how to graph a line?
warm roost
do you know how to graph a line?
yes
unborn abyss
if I asked you to graph the line y = 3x could you do that?
warm roost
yes
unborn abyss
ok now if I asked you to draw the line y = 2πr could you do that?
it's the same thing
warm roost
well yes
stray cove
I think there's typo since he said in the video and also written in subtitle tha...
and from the given things we can deduce the slope is infact 2pi not 2piR😅
unborn abyss
I think there's typo since he said in the video and also written in subtitle tha...
there's no typo but yes the slope is 2π
warm roost
ok now if I asked you to draw the line y = 2πr could you do that?
i plugged it to desmos and i got a different graph than the one in the vid
unborn abyss
the thing on the screen is (y =) 2πr
warm roost
is it just not drawn to scale?
unborn abyss
i plugged it to desmos and i got a different graph than the one in the vid
that's the same graph.... just with different axis scaling
look at the axes
warm roost
huh?
stray cove
there's no typo but yes the slope is 2π
I was talking about the 2piR written beside the slope which created the confusion
warm roost
look at the axes
ohh
unborn abyss
I was talking about the 2piR written beside the slope which created the confusio...
the line is (y =) 2πr
he just didn't write the y = part
warm roost
"a nice way to think about this setup is to draw the graph of 2πr"
why would he graph 2pir tho
warm roost
the thing on the screen is (y =) 2πr
do we need to add the brackets?
unborn abyss
he says it out loud.... it's the slope of the line created by those rectanglws
no, those are to indicate that he didn't write it
warm roost
he says it out loud.... it's the slope of the line created by those rectanglws
isnt it 2pi?
warm roost
no, those are to indicate that he didn't write it
what
unborn abyss
isnt it 2pi?
yes, the line which has a slope of 2π and goes through the origin is y = 2πr
stark knot
what
the brackets are to indicate that he didn't write them but Hayley wanted to show that he meant it with the y = part
warm roost
yes, the line which has a slope of 2π and goes through the origin is y = 2πr
why is it 2pir
unborn abyss
because it has a slope of 2π and goes through (0,0)
if you plug that into your y = mx + b form then that's what you'll get
warm roost
because it has a slope of 2π and goes through (0,0)
why is the slope needed to be 2pi
gtg
unborn abyss
slope is rise / run
stray cove
why is the slope needed to be 2pi
pearl pondBOT
@warm roost Has your question been resolved?
opal lagoon
someone please help me with part b
pearl pondBOT
someone please help me with part b
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
cinder bane
@opal lagoon
tulip mason
Can you explain what you did for a)
Because if you did a) I think b) is just generalizing those ideas
opal lagoon
<@912634044435558430>
hello again!
opal lagoon
Because if you did a) I think b) is just generalizing those ideas
alright so for a
i got the answer 50
should i just send you the proofing i did on paper?
cinder bane
Because if you did a) I think b) is just generalizing those ideas
I think B is easier than A though
tulip mason
Surely you can do better than 50
tulip mason
I think B is easier than A though
Yea exactly
opal lagoon
Surely you can do better than 50
no not really
opal lagoon
I think B is easier than A though
i mean i did it but im not sure my answer is correct
tulip mason
You can select 3 numbers at a time essentially
Are you sure your answer to a) is correct?
cinder bane
Surely you can do better than 50
It is really 50
We solved it before
opal lagoon
Are you sure your answer to a) is correct?
yea
slender viper
yeah looks like 50
tulip mason
You want to find the product of all 50 numbers
slender viper
looks very linear algebra over F2 tbh
opal lagoon
You want to find the product of all 50 numbers
yea
tulip mason
And can find out the product of 3 in a row
opal lagoon
yea
tulip mason
(a1 a2 a3)(a4 a5 a6)... ?
cinder bane
And can find out the product of 3 in a row
You may see the trick when you have 4 numbers
opal lagoon
(a1 a2 a3)(a4 a5 a6)... ?
let me send you the proofing i did yesterday
tulip mason
Oh but there is the end 2
cinder bane
a1*a2*a3 * a2*a3*a4
tulip mason
`a1*a2*a3 * a2*a3*a4`
You can find the product of the first 48 in 16 hint's right?
opal lagoon
You can find the product of the first 48 in 16 hint's right?
yes
cinder bane
You can find the product of the first 48 in 16 hint's right?
Yeah but then you got 2 numbers that you don't have
opal lagoon
Yeah but then you got 2 numbers that you don't have
wait lemme explain
opal lagoon
You can find the product of the first 48 in 16 hint's right?
yes you could but then two left over numbers that you have are, yes in the next hint, hint number 17
tulip mason
There is no way it takes 34 hint's to figure out the parity of the remaining 2
opal lagoon
There is no way it takes 34 hint's to figure out the parity of the remaining 2
it does because your numbers are either -1 or 1
and if(-1)^2
then you get 1
which means that number is lost in the product and you're no longer multiplying it
slender viper
There is no way it takes 34 hint's to figure out the parity of the remaining 2
my intuition says you should be able to prove you are forced to by gaussian elimination
opal lagoon
my intuition says you should be able to prove you are forced to by gaussian elim...
w h a t
is that 10th grade level math
slender viper
is that 10th grade level math
maybe, depending on which school
cinder bane
I suggest going to the main problem B @opal lagoon
What have you did for it ?
tulip mason
But you don't actually need to know the signs
slender viper
but usually you see it more in university
tulip mason
That would be to find out all of the signs
opal lagoon
maybe, depending on which school
its the like uhhhh 4th best school in my country
tulip mason
You only need the signs of 2
opal lagoon
but im in ig so
opal lagoon
I suggest going to the main problem B <@912634044435558430>
What have you did f...
used a similar method
initially i thought it was n/k
or just n
but
i dont think thats correct
because k<n
so that means
k could also just be n-1
so the minimum number of hints you'd need is like 2 or 3
cinder bane
We saw that if N is divisible by K then the answer would be N/K yeah
opal lagoon
We saw that if N is divisible by K then the answer would be N/K yeah
yes
but in the circumstance that k = n-1
then what would it be?
because they didnt define us a range
cinder bane
But other than that like in the first question the answer is N
opal lagoon
just the fact that k < n
opal lagoon
But other than that like in the first question the answer is N
huh?
oh yes
yes the answer is n
tulip mason
The minimum hints is 19
opal lagoon
The minimum hints is 19
in part a?
tulip mason
Yes
opal lagoon
but we'd lose some values
cinder bane
@tulip mason
For the problem to be easier I recommend considering a smaller similar problem
cinder bane
Like 5 numbers
tulip mason
Suppose a1 and a2 are the missing ones.
We already know the parity of a3 a4 a5 from the 16 hints
Suppose the parity is positive.
Then atleast 2 were negative or none were negative.
then hint:
a1a2a3
a1a2a4
a1a2a5
You will have either all signs are the same or 2 are different. Take the one which is the same, that is the product of a1a2
Alternatively if a3a4a5 is negative we know that either 1 is negative or 3 are negative
Consider again
a1a2a3
a1a2a4
a1a2a5
We will either all 3 are the same sign in which case the sign of a1a2 is the negative of that
Or 2 are the same sign, in which case that sign is the product of a1a2
slender viper
a1a2a4 is not consecutive
tulip mason
Hmmm
True
Still there has to be a way, can I atleast see the proof, if you didn't write it formally it's fine I'll just pretend I agree 😭😂
opal lagoon
Still there has to be a way, can I atleast see the proof, if you didn't write it...
i sent the proof
opal lagoon
right here
its really scrappy
but uh
its just a math hw problem thingy
so its not formal
tulip mason
Okay yea nice you considered the smallest number 2 mod 3
Cool, damn what a sad problem, I hate when algorithm problems are minimized by exactly the number of elements 😭😂 so unsatisfying
opal lagoon
Cool, damn what a sad problem, I hate when algorithm problems are minimized by e...
lol yea someone said a similar thing yesteryda
"50 is such a boring answer"
opal lagoon
lol yea someone said a similar thing yesteryda
yesterday*
cinder bane
A1, A2, A3, A4 ,A5
We can choose between 5 different hints
A: A1 * A2 * A3
B: A2 * A3 * A4
C: A3 * A4 * A5
D: A4 * A5 * A1
E: A5 * A1 * A2
Let us use A & C
Using both of them would eliminate A3 so to substitute for it we gonna use B, but using that would eliminate A2 & A4
So we need to use D & E with it so we use 5 hints
And doing so would make us multiply each number by itself 3 times so every 2 would go away keeping the product of all numbers
tulip mason
Yeah because it's the one where you can create an algorithm instantly
opal lagoon
`A1, A2, A3, A4 ,A5`
We can choose between 5 different hints
A: `A1 * A2 * A3`
B...
buddy i think he gets it now
cinder bane
Ok
tulip mason
If the word consecutive didn't exist this would be a good problem
tulip mason
Haha
opal lagoon
a grood problem for phds and stuff but i dont think 7th graders would want to do this
i've been stuck on these problems for like 5 days now
tulip mason
You should try a hat problem if you like this
opal lagoon
wdym by that
cinder bane
About what is said in problem B I think it may not work
cinder bane
Let n = 5 and k = 4
opal lagoon
yes
cinder bane
A1, A2, A3, A4, A5
Hints:
A: a1*a2*a3*a4
B: a2*a3*a4*a5
C: a3*a4*a5*a1
D: a4*a5*a1*a2
E: a5*a1*a2*a3
Here number of hints didn't change but the number of elements in each hint changed
opal lagoon
Here number of hints didn't change but the number of elements in each hint chang...
yea
tulip mason
wdym by that
They are probability problems, where you get really unexpected answers.
The classic is 3 prisoners stand in a circle, they are wearing a black or white hat but cannot see their own hat. The prisoners must guess what colour their hat is or pass, at least one prisoner must guess correctly to survive. They cannot communicate but can create a strategy before hand. What is the best strategy and probability of success of the prisoners surviving.
cinder bane
And the number of times each element gets repeated there has also changed to k
opal lagoon
what if you did
tulip mason
opal lagoon
They are probability problems, where you get really unexpected answers.
The cla...
you see i suck at probability
tulip mason
It's a fun problem for later
opal lagoon
It's a fun problem for later
sure
cinder bane
@opal lagoon
So in that state above you can't really say 5 hints cause by that you multiply each number by itself even number of times thus they go away
Giving you 1
opal lagoon
<@912634044435558430>
So in that state above you can't really say 5 hints cause...
yea
tulip mason
For b) you'll need to do cases
opal lagoon
cases?
opal lagoon
<@912634044435558430>
So in that state above you can't really say 5 hints cause...
you could do a,b and c
thats k-1
tulip mason
If k divides n then the answer is n/k
If k doesn't divide n and k>1
Then we are expecting it to be n again right?
Atleast we can say the maximum of the answer is n as we can just do GJ
opal lagoon
If k divides n then the answer is n/k
If k doesn't divide n and k>1
Then we are...
GJ?
is it the gaussian thingy
cinder bane
Actually I think if k is even and n is odd it is not possible to solve it
Or if n is not devisable by it
opal lagoon
Actually I think if k is even and n is odd it is not possible to solve it
Or if ...
if both are odd it slims the chances more
also yes it is possible to solve the question
opal lagoon
Actually I think if k is even and n is odd it is not possible to solve it
Or if ...
for the question you posed where n=5 and k=4, just multiply hints a b and c together
cubing every number in the hints
therefore giving you the product of all 5 numbers
so
opal lagoon
i think from that we can conclude, it depends on the amount of numbers in a hint as well
tulip mason
So yeah you're right
opal lagoon
2 and 3
a1a2
a2a3
a3a1
oh yea
tulip mason
No if k is even then it's not possible
opal lagoon
so k must be bigger than 2
opal lagoon
No if k is even then it's not possible
yes it is
tulip mason
I don't think so inductively
tulip mason
You can reduce the even equations into smaller even equations
Whereas for odd you can always reduce them to a1s
opal lagoon
Whereas for odd you can always reduce them to a1s
wdym by reduce
tulip mason
hmm actually even might work just not 2
tulip mason
Do you understand the process the other suggested?
Try to repeat it for evens, you'll see the problem it creates, whereas choosing odds doesn't work
Evens only works if k divides n
tulip mason
Evens only works if k divides n
Im not confident that is true
opal lagoon
Im not confident that is true
i think it is
if we have n+16
sorry
n=16
and k=4
then we only need 4 hints to find the product of all 16 numbers
same goes for if
tulip mason
Yeah here k divides n
opal lagoon
yea
tulip mason
I mean I'm not confident that's the only time it works
opal lagoon
oh
i think the solution is more of just, if n is divisible by k, then your answer is the quotient, otherwise ur answer is just n
tulip mason
Like take k=6 and n=8
You can create a scheme for it in 8 moves
opal lagoon
Like take k=6 and n=8
You can create a scheme for it in 8 moves
alright this might not work
because ur product would be 48 numbers
since the number of total hints = n
and if each hint has 6 numbers
then we'd be multiplying 48 numbers
which would mean we're going to lose the values in the product
so we wont get a product of eavh number
since k=6 means each number is multiplied 6 times, which is an even power, so in case of -1 it'd be (-1)^6 = 1
which means our product wont be the result of all numbers
so we could divide the values?
ok so sheriff was right, we cant have a solution if k is an even number
the only exception is if n is divisible by k
tulip mason
take a1a2a3a4a5a6 multiply that by a2a3a4a5a6a7, it leaves you with a1a7, repeat that for each permutation and you find:
- a1a7
- a2a8
- a3a1
- a4a2
- a5a3
- a6a4
- a7a5
- a8a6
Then use 1), 2), 5), 6) and you are done
opal lagoon
so now we use thesea?
to use a new set of hints
or the products of the hints
to find the number of hints
opal lagoon
take a1a2a3a4a5a6 multiply that by a2a3a4a5a6a7, it leaves you with a1a7, repeat...
yea
tulip mason
k is 3
opal lagoon
yes
pearl pondBOT
@opal lagoon Has your question been resolved?
pearl pondBOT
pearl pondBOT
Available help channel!
stoic imp
,, \int_{0}^{\infty} \left( \frac{x+1}{3x^2+1} - \frac{a}{2x+1}\right)dx
jolly parrotBOT
938c2cc0dcc05f2b68c4287040cfcf71
stoic imp
fibd a s.t. integral converge
stoic imp
no
stoic imp
but the upper bound of integral is infty
rough forge
The first term notice it is something like f'/f as the 2nd
rough forge
but the upper bound of integral is infty
We will take care of it later
stoic imp
can u do a drowing
rough forge
no i am in bed
stoic imp
The first term notice it is something like f'/f as the 2nd
elaborate
i dont get it
how so
rough forge
,,\frac{x}{3x^2+1} + \frac{1}{3x^2+1}
jolly parrotBOT
𝔸dωn𝓲²s
rough forge
3x² + 1 diff. is 6x
So if you get a factor 6 you can use ln|3x²+1| and so on
Other one will be arctan something
Same idea with a/(2x+1)
I wonder how many here are watching 👁️
rough forge
It isn't for 3x² + 1 indeed
spare lark
It doesnt hurt tho
rough forge
Just a Gewohnheit
spare lark
Just a Gewohnheit
Es keine schlechte Sache
rough forge
,, \int_{0}^{\infty} \left ( \frac{x}{3x^2+1} + \frac{1}{3x^2+1} - \frac{a}{2x+1}\right) : \dd x
jolly parrotBOT
𝔸dωn𝓲²s
stoic imp
,, \frac{d}{dx}\left(\frac{x+1}{3x^2+1}\right) = \frac{d}{dx}\left(\frac{x}{3x^2+1}\right) + \frac{d}{dx}\left(\frac{1}{3x^2+1}\right)
rough forge
d/dx ?
stoic imp
im so stupid sorry i didnt understood
rough forge
what
spare lark
Integrate
jolly parrotBOT
938c2cc0dcc05f2b68c4287040cfcf71
stoic imp
,, \int_{0}^{\infty} \left ( \frac{x}{3x^2+1} + \frac{1}{3x^2+1} - \frac{a}{2x+1}\right) : \dd x
jolly parrotBOT
938c2cc0dcc05f2b68c4287040cfcf71
rough forge
Also lemme do this
,, \lim_{t \to \infty} \int_{0}^{t} \left ( \frac{x}{3x^2+1} + \frac{1}{(\sqrt{3}x)^2+1} - \frac{a}{2x+1}\right) : \dd x
jolly parrotBOT
𝔸dωn𝓲²s
rough forge
i dont know much about inverse trigonometric substitutions
good thing we dont need them
We will use this rule
jolly parrotBOT
𝔸dωn𝓲²s
rough forge
what change of variable is this
wdym you act like it's your first help channel
stoic imp
**𝔸dωn𝓲²s**
i just have been on vacation and forgot a bit of the basics, which rule is this btw
rough forge
This is just a consequence if chain rule
When you diff. ln(f(x)) you get 1/f(x) * f'(x)
stoic imp
fair
rough forge
So you basically want to recreate the first derivative of the denominator in the numerator
stoic imp
recreate(?)
rough forge
,, \lim_{t \to \infty} \int_{0}^{t} \left ( \textcolor{cyan}{\frac{1}{6}} \cdot \frac{\textcolor{cyan}{6}x}{3x^2+1} + \frac{1}{(\sqrt{3}x)^2+1} - a \cdot \frac{1}{2x+1}\right) : \dd x
Now you can use the rule about an also integrate the first term
jolly parrotBOT
𝔸dωn𝓲²s
stoic imp
2
rough forge
So we need a factor 2
,, \lim_{t \to \infty} \int_{0}^{t} \left ( \textcolor{cyan}{\frac{1}{6}} \cdot \frac{\textcolor{cyan}{6}x}{3x^2+1} + \frac{1}{(\sqrt{3}x)^2+1} - \textcolor{cyan}{\frac{1}{2}} \cdot a \cdot \frac{\textcolor{cyan}{2} \cdot 1}{2x+1}\right) : \dd x
jolly parrotBOT
𝔸dωn𝓲²s
rough forge
Now we can intrgrate all terms
spare lark
That cyan pretty useful 📝
rough forge
,,\lim_{t\to\infty} \left [ \frac{1}{6} \ln(3x^2+1)+ \frac{1}{\sqrt{3}} \arctan (\sqrt{3}x) - \frac{a}{2}\ln (2x+1) \right ]_0^t
jolly parrotBOT
𝔸dωn𝓲²s
stoic imp
okay
rough forge
for x = 0 what happens obv
jolly parrotBOT
rough forge
bro
stoic imp
,calc tan^(-1)(0)
jolly parrotBOT
The following error occured while calculating:
Error: Unexpected type of argument in function pow (expected: number or Complex or BigNumber or bigint or Fraction or Unit or Array or Matrix or string or boolean, actual: function, index: 0)
rough forge
it's 0
arctan is odd
And ln(1)
is also 0
,,\lim_{t\to\infty} \left ( \frac{1}{6} \ln(3t^2+1)+ \frac{1}{\sqrt{3}} \arctan (\sqrt{3}t) - \frac{a}{2}\ln (2t+1) \right )
stoic imp
how do we get a so it converges
jolly parrotBOT
𝔸dωn𝓲²s
stoic imp
wtff
stoic imp
3t^2 +1 > 0
spare lark
No its always the case
stoic imp
arctan converges to π/2
wdym
rough forge
spare lark
Arctan --> +inf = pi/2
rough forge
,w arctan(inf)
jolly parrotBOT
stoic imp
i didnt know
jolly parrotBOT
𝔸dωn𝓲²s
rough forge
,w ln(x) -ln(y) = ln(x/y)
jolly parrotBOT
stoic imp
spare lark
Well its rule 2
stoic imp
**𝔸dωn𝓲²s**
this
spare lark
Ofc it is
rough forge
is still legal ?
Bro
stoic imp
🍇
spare lark
Ln is just a log base e
stoic imp
im newbie, sorry if it was obvious
spare lark
Your job mate
stoic imp
,,\lim_{t\to\infty} \left ( \frac{1}{6} \ln(3t^2+1)+ \frac{1}{\sqrt{3}} \arctan (\sqrt{3}t) - \frac{a}{2}\ln (2t+1) \right )
rough forge
i only have 2 minutes
if they pass what happens
jolly parrotBOT
938c2cc0dcc05f2b68c4287040cfcf71
rough forge
Do some grouping now
rough forge
Also $y\ln(x) = \ln(x^y)$
jolly parrotBOT
𝔸dωn𝓲²s
stoic imp
okay
rough forge
Then come back later
stoic imp
how do i find a
we dont know what it converges to
we only know arctan converges to pi half
the other ones are 0
okay
,w limit x to infinity ln(x)
jolly parrotBOT
rough forge
Ja bro
You got inf - inf
Transform your terms
,,\lim_{t\to\infty} \left ( \frac{1}{6} \ln(3t^2+1)+ \frac{1}{\sqrt{3}} \arctan (\sqrt{3}t) - \frac{a}{2}\ln (2t+1) \right )
jolly parrotBOT
𝔸dωn𝓲²s
rough forge
,,\lim_{t\to\infty} \left ( \ln((3t^2+1)^{\frac{1}{6}})+ \frac{1}{\sqrt{3}} \arctan (\sqrt{3}t) - \ln ((2t+1)^{\frac{a}{2}}) \right )
jolly parrotBOT
𝔸dωn𝓲²s
rough forge
,,\lim_{t\to\infty} \left ( \ln(\frac{(3t^2+1)^{\frac{1}{6}}}{(2t+1)^{\frac{a}{2}}}) \right ) + \lim_{t\to \infty} \left ( \frac{1}{\sqrt{3}} \arctan (\sqrt{3}t) \right )
jolly parrotBOT
𝔸dωn𝓲²s
rough forge
Right limit is easy left ist difficult
rough forge
If it's greater it would go to 0 and ln 0 is -inf
And if it was less then it would go to +inf
stoic imp
Same degree coeffi num denomi so the limit of fraction conberges
Something like that!?
jolly parrotBOT
stoic imp
no
rough forge
,w Limit[ln[ (3t^2+1)^(1/6))/((2t+1)^((2/3)/2)) ], t->inf]
stoic imp
Ok
jolly parrotBOT
stoic imp
Butbwhen u put denomi 1/3 it converged aswell
jolly parrotBOT
feral mango
Currently working on some Physics problems and i encountered some math that i can't quite work out to get the expected result.
This is the current step that i am at, and i am kind of confused as to how the f-2 is created (used wolfram alpha to help check my results and this doesn't quite line up with what i expected).
tropic saddle
did you mean to write $\frac{2}{f+2}$ ? what you wrote is $\frac2f +2$
jolly parrotBOT
Denascite
tropic saddle
if you mean the first one, write 2/(f+2)
feral mango
ah fuc that may be it
darn syntax. i am so out of training with my math skills. thank you for the help
next bloom
pearl pondBOT
cosmic raptor
you multiplied the fractions by (x-5) twice
you could just cancel out the denominators and solve using just the numerators
which would be considerably easier
next bloom
wait I kno what I did for last step it's supposed to be 64 but then what happens
do I leave it just that or
next bloom
you multiplied the fractions by (x-5) twice
where
wait huh
so it's wrong
this is what I got
i need help on the 1st question
<@&286206848099549185> Rationals and Radicals Precalc 11
tawny drift
Hmm
When it says restriction, is it essentially asking for where it is defined in the real world?
In other words, where the inside of the radical is nonnegative?
green dew
yea pretty much
next bloom
When it says restriction, is it essentially asking for where it is defined in th...
i need to solve 3 questions
first is the checking
on the very top
os this right?
next bloom
then I need help with these 2 questions
next bloom
then this one
tawny drift
Just to ask, here are you finding x, or simplifying...?
next bloom
In other words, where the inside of the radical is nonnegative?
I habe a vocab problem like I'm diagnosed w vocab problem
I can't understand stuff
tawny drift
Oh, I am sorry
tawny drift
so you need to find x, okay
next bloom
Oh, I am sorry
no its ok I js dont understand what nonnegative and stuff
like easy words
green dew
It didnt ask to solve 5
Only 6 and 7 are the ones to solve
I think 5 is js simplification
next bloom
Only 6 and 7 are the ones to solve
I meant solve as like I need help solving it
the 5th one I think it says simplify or something
yes
tawny drift
so your working is correct atm
next bloom
how do I find x when it's like x^2
sorry my wifi kinda slow so the response will prob b slow
tawny drift
tawny drift
sorry my wifi kinda slow so the response will prob b slow
all good
next bloom
yes
tawny drift
here, everything is equal to zero
next bloom
how
tawny drift
because you took away from both sides of the equation
next bloom
so like
next bloom
tawny drift
you need to get one side equal to 0
next bloom
like this
tawny drift
wait
next bloom
wait if I root then I can't do the -4
next bloom
yes
tawny drift
and to undo times, you divide
next bloom
how do u even do 0/4
green dew
0 divided by anything is 0
Huh
green dew
lmao
next bloom
r u sure
green dew
you can't root 0
whoever tutored u should be emprisoned fr
next bloom
WHAT
tawny drift
nah
next bloom
0 is like not factor number
tawny drift
you should be concerned about what I said earlier 💀
tawny drift
no problem
next bloom
pls
tawny drift
which one?
tawny drift
alright
next bloom
6 first cus I alr kidna solve 6
tawny drift
okay
tawny drift
yep
you can get rid of the bottom of the fraction
since it is the same on both sides
if you look at the bottom of the left fraction
when you multiply out the brackets
you get 2x - 14
like on the other side
and if you times by that amount on both sides
it should disappear on both sides
tawny drift
perfect
tawny drift
now remember, you took everything from the right and brought it to the left
tawny drift
so you are left with zero on the right
next bloom
no 5**
next bloom
so you are left with zero on the right
ok so I write 0
wait I'm not done
what am I supposed to do
tawny drift
yeah
so you have the two brackets equal to 0
so this means that both of them on their own could equal 0
next bloom
so this means that both of them on their own could equal 0
what do u mean
tawny drift
imagine this
next bloom
thank u
smoky umbra
tawny drift
It sent from my phone, that is why the sender is different
next bloom
that is very confusing
tawny drift
alright
let me explain
so
when you multiply things, and you get 0, that means one of the things must be 0
at this level, anyways
for example, 1 x 0 = 0
2 x 0 = 0
next bloom
oh
tawny drift
so we know
next bloom
^
tawny drift
I don't have too much time, but let me see
next bloom
thank u
tawny drift
so are we solving?
next bloom
no its simplyfiy
tawny drift
oh okay
next bloom
yes
tawny drift
first, let's see if we can make the denominator cleaner
so we have
this as the bottom of the fraction
next bloom
yes
tawny drift
I would get both numbers with the same bottom
next bloom
what
tawny drift
do you remember here
next bloom
how
tawny drift
3 times u = 3u, and 3 x -4 = -12
so 3 is a factor of both of them
so you could rewrite the top as something with a bracket
tawny drift
sure
next bloom
thank you
smoky umbra
tawny drift
so on the right, the top of the fraction is the same as on the other side
even if we write it with the same factor 3x and -12 have
tawny drift
and then
you can write the top as 3(x-4)
because if you multiply out, you will get the same
tawny drift
okay
one second
back to this example
from the last question
I told you earlier, that the bottoms are the same
next bloom
yea
tawny drift
because on the left side, if you multiply out the bottom part, you will get the same on the other bottom part
and when we multiply out 2(x-7), in this case, what that means,
is we times x by 2, and -7 by 2
to get 2x - 14
so you times what is in the inside of the brackets, by the outside
are you still with me?
tawny drift
yeah
so what we are doing is the opposite
we are putting the top of that fraction, into a form with brackets
like the 2(x-7) we saw
tawny drift
you can write the top as 3(x-4)
so we are still here
so if we do that
to the top
it is the same as saying
3(u-4)
next bloom
can i take a break
this is like
my brain is all stuffed
i cant process anymore i think my meds r wearing off or something
tawny drift
no problem
next bloom
i very very appreciate it
pearl pondBOT
@next bloom Has your question been resolved?
midnight haven
Hi, I want to find perimeter of this shape, but I don’t know how to find the missing side (yellow line).
midnight haven
I cut the shape by making a rectangle that is (6*7)
midnight haven
midnight haven
I am not sure
kind rampart
Ok
kind rampart
You can show that this is perpendicular
Because of the parallel lines
Can you see how?
midnight haven
Yes
kind rampart
Ok
midnight haven
But how do you find the sides?
restive briar
The blue is also 6m
kind rampart
But I only know one side
You said yourself you made a rectanhle 7x6
kind rampart
midnight haven
Oh right
restive briar
If you work out the bottom side of the triangle on the right, it will help you get another side length of the triangle on the left
midnight haven
Oh ok I got it
kind rampart
Yawesome
pearl pondBOT
@midnight haven Has your question been resolved?
pearl pondBOT
pearl pondBOT
Available help channel!
dusk moat
can someone please help walk me through this? ive been trying for a while and i havent been able to do it
dusk moat
i have q1 of the unit circle drawn and i see sin(x) = sqrt2/2 and so it must be pi/4 and that logic isnt working
stoic arrow
you should try to memorize the unit circle
dusk moat
i do
dusk moat
im not sure how to find the other answer though
stoic arrow
try to memorize the unit circle beyond the first quadrant
sin is always positive in quadrant one and two
dusk moat
well i know q1 so i can just graph the rest
heady finch
remembering ASTC helps for where each function is positive or negative
stoic arrow
graph the rest?
dusk moat
like draw the other quadrants and stuff
stoic arrow
well
it goes pi/6 pi/4 pi/3 2pi/3 3pi/4 5pi/6
and all values on the unit circle that are /4 are +- sqrt2/2
heady finch
can someone please help walk me through this? ive been trying for a while and i ...
To clarify your answer you know sine is positive in the second quadrant which gives you pi-pi/4 = 3pi/4
stoic arrow
and since the values i gave are quadrants one and two, and these are positive for sin, the two values that are /4 correspond to an output of sqrt2/2
stoic arrow
To clarify your answer you know sine is positive in the second quadrant which gi...
good way to think about it too
dusk moat
To clarify your answer you know sine is positive in the second quadrant which gi...
i understand this logic but i just dont get how pi-pi/4=3pi/4
can u explain that real quick
heady finch
i understand this logic but i just dont get how pi-pi/4=3pi/4
4pi/4-pi/4 = 3pi/4?
dusk moat
oh yeah gotcha
heady finch
You're starting from 2nd quadrant which is pi-theta so that's the reasoning
dusk moat
it makes sense now
thanks guys
im just trying to make sure i understand everything
im taking a summer pre calc class and theyre moving really fast and im studying a lot on my own to make sure i understand everything
they introduced this topic and so many others across one 2 hour long lecture
stoic arrow
i can relate bro, i took a similar class last summer and got a D 💀
dusk moat
i can relate bro, i took a similar class last summer and got a D 💀
yeah i didnt do too well on the first test but thankfully it was stuff i can easily solve (like basic precalc stuff)
stoic arrow
this server carried me through it ngl
dusk moat
now im getting to the more advanced parts and im doing better but i know i need to study a lot
im taking a pre calc class at a local uni meant for high school students
but the curriculum is equivalent to alg 2 at my school (the uni course lacks Conics, Matrices, Vectors, Limits, Derivatives, Antiderivatives, and a lot more), im taking this so i can pass the alg 2 exit test
heady finch
You got this :D
pearl pondBOT
pearl pondBOT
Available help channel!
dusk moat
i want to confirm i got this right: the bottom right angle is 60 because 180-120 is 60. then i can do sin(60) = d/50, sin(60)*50 = d
dusk moat
and then d should be like 43.3
yeah i checked it w pythagorean theorum and it looks right
.close
pearl pondBOT
pearl pondBOT
Available help channel!
fast lion
pearl pondBOT
fast lion
I just want to double check
because n = 1 and etc
the cords would be
(1, 2)
(2, 4)
(3, 6)
and so on?
Im studying this packet and it doesn't have examples, if anyone could see if Im correct, then thank you very much!
pearl pondBOT
@fast lion Has your question been resolved?
fast lion
<@&286206848099549185>
cinder bane
What's the question
fast lion
Oh, sorry, its graphing the sequence
cinder bane
the cords would be
Yeah correct
But the problem here could be at how you are going to put numbers on the graph
fast lion
Oh yeah, because the coordinates of the y axis is a bit off
Thank you very much though
.close
pearl pondBOT
cinder bane
Oh yeah, because the coordinates of the y axis is a bit off
On y-axis you just increase by 2
But on x you increase by 1
So the y-axis won't be 2, 3, 4
It will be 2, 4, 6
fast lion
I see, okay, I will extra careful
pearl pondBOT
Available help channel!
somber schooner
