middle count
#help-0
vocal hawk
carmine thistle
oh yeah
carmine thistle
11/25
vocal hawk
it's 4/25
carmine thistle
oh
carmine thistle
alright
sturdy glen
when do I use the integral symbol with a circle in it and when don't I?
sturdy glen
from what I understand, it's a line integral along a closed curve that's positively oriented, but aren't both positively oriented?
why use the circle integral symbol for 4. but not 5. ?
lone heartBOT
@sturdy glen Has your question been resolved?
inner vector
when do I use the integral symbol with a circle in it and when don't I?
The "circled" notation is optional
So yeah, you could use it for 5.
rapid crow
Use Euclid’s algorithm to find the HCF of 4052 and 12576.
lone heartBOT
Use Euclid’s algorithm to find the HCF of 4052 and 12576.
rapid crow
is the ans 2?
inner vector
Nope
rapid crow
4 right?
inner vector
Yes
main ruin
i am confused on the u-substitution here. how does u^(3/2) come to be?
tacit arch
i am confused on the u-substitution here. how does u^(3/2) come to be?
Solve for x in terms of u
x^2 = 1-u...
main ruin
ah that makes more sense
either i missed something or i was never taught to do that because i havent seen anyone do that yet. thank you so much!!!
.close
pulsar grotto
I get what it represents (like the (x+h) thing) but since it's in the denominator i don't really understand what I'm meant to do with it, I tried plugging in h to every deltax and evaluating it but that was also wrong so im just confused
buoyant kayak
well you recognized it is in the form of the definition of a derivative
so by that, you should know what your function is
tbh you don't even need to do any math, you should know what the graph of this function looks like
pulsar grotto
i don't though
I know its in the form of a derivative but would that make it 3(x)^-1 ?
do i take the derivative of that or
buoyant kayak
weird way of writing 3/x but yes, that's the function
if you really don't know the graph of it's parent function then you should try getting a common denominator and simplifying, see how it works out for you
pulsar grotto
I graphed it and i get infinity but that's not the correct answer
buoyant kayak
yes it is
pulsar grotto
and yea i write it that way just cause it makes more sense to me
webassign doesnt like the answer 💔
buoyant kayak
well "infinity' isn't the correct answer
pulsar grotto
buoyant kayak
when we write a limit "equals" +-infinity, we're saying the limit DNE while describing it's behavior
so (if the answer does not exist, enter DNE)
pulsar grotto
dne is also not the answer though
I got dne earlier and tried it already
does not want
buoyant kayak
hm
well ain't that something
i'd argue that it's wrong
,w limit as x approaches 0 from the right of 3/x
ocean sealBOT
buoyant kayak
indeed your website is wrong
pulsar grotto
it's something about the way its written then that's making it different
we never covered this kind of problem in class and i really need this right
pulsar grotto
if you're dumb then im moreso
buoyant kayak
let me write somethin real quick
pulsar grotto
👍 ty for the help so far
buoyant kayak
oh yeah i'm mad dumb
this whole time i've been thinking "x is approaching 0 from the right hur dur" yet literally the first thing i said to you was "you noticed it was definition of derivative 👍 "
it is quite literally just taking the derivative of 3/x
pulsar grotto
OH
ok im stupid t oo
because i tried that earlier and i did the derivative of 3/x wrong...
THANK YOU that was correct
.close
lone heartBOT
lone heartBOT
Available help channel!
versed sluice
I need different ways of making numbers using operations only using 3
shell narwhal
I need different ways of making numbers using operations only using 3
What ?
proud basin
for 0 you can use 3*3 -3-3-3
shell narwhal
(3x3x3)/3-3=6
lone heartBOT
@versed sluice Has your question been resolved?
fathom mantle
What is there to help? just use please excuse my dear aunt sally
versed sluice
Sorry I just need that last one
lone heartBOT
@versed sluice Has your question been resolved?
pliant lotus
Could anyone suggest me how to approach this mathematics IA HL and comment if its suitable for an investigation
pliant lotus
So basically I want to find
Basically I want to find the fastest way down this track from the top sattele to the bottom reinswald using the bellman-ford graph
The weightings will be the time it takes to ski down a particular track so as we can see there are red trails blue trails and black etc
and they have a particular angle which will influence how steep the slope is so the velocity
and then the length of each trail i take from google earth
and at the end i use the bellman ford algorithm to find the quickest way down
Would really appreciate some feedback on it
or does it seem too "SL"
lone heartBOT
@pliant lotus Has your question been resolved?
pliant lotus
<@&286206848099549185>
lone heartBOT
@pliant lotus Has your question been resolved?
summer kite
lone heartBOT
summer kite
my uncle sent me this but im a lil confused
i suppose its saying that 20% of the pocket money = 240
thats what im understanding rn
and im a lil struggling about b)
buoyant kayak
the way it's phrased implies that she spent 20% of her pocket money on top of $240
vale wigeon
if x is the amount of pocket money, yes
vale wigeon
though this feels like insufficient info
summer kite
well my first idea is
the 20% is refering to the 240
and apparently my uncle said the answer of a) is 4k
which im 
to understand how
240+0.2x = 1.3y
vale wigeon
wait, hold on.
maybe what was meant is
that she spent $240 on books, and 20% of pocket money on stationery
summer kite
bruh no shot
imma try that theory
bc if its like that, there should be a respectively
else it gonna be scuffed as hell
oh crap you are right
dusky jacinth
lone heartBOT
velvet pelican
weren't you alr given the source tho
dusky jacinth
dusky jacinth
also we don't give out solutions here
Oh
dusky jacinth
weren't you alr given the source tho
Wasn't able to find the solution online
vale wigeon
have you made any progress on this yourself or are you stuck not knowing how to begin
vale wigeon
have you made a diagram?
dusky jacinth
Yes that's the only thing I did but I didn't knew how AD can be written as m/n like do you use trigno ratios or what specifically?
vale wigeon
can you show your diagram
vale wigeon
it should be clear to you that your real goal is to find AD; the "written as m/n with m and n coprime" is just a crutch to force the answer to be a positive integer (for whatever reason)
do you understand that much at least
y/n
dusky jacinth
do you understand that much at least
Yeah definitely that's understandable
vale wigeon
ok
vale wigeon
that stands for "yes or no"
dusky jacinth
Oh ok
vale wigeon
also your 1 looks very easy to misread as 2, just saying
dusky jacinth
Yeah I should make it like the classic I shaped
vale wigeon
anyway, ok, so your diagram seems not to include D
dusky jacinth
Thanks for the advice
dusky jacinth
anyway, ok, so your diagram seems not to include D
Yeah I didn't got the concept of ray like where is a ray
They are line segments
Ray AC but AC is a segment
Sorry idk this sounds too stupid but I didn't got that😅
@vale wigeon sir?
vale wigeon
don't call me sir.
dusky jacinth
Ok
vale wigeon
would you call a woman sir?
vale wigeon
...i don't like being called ma'am either but whatever
this is what your diagram should look like
dusky jacinth
...i don't like being called ma'am either but whatever
Ok
dusky jacinth
this is what your diagram should look like
Oh
vale wigeon
do you see how to proceed from here or should i go into more detail
dusky jacinth
So basically AD here is m/n
vale wigeon
forget about m and n
dusky jacinth
Ok
vale wigeon
it should be clear to you that your real goal is to find AD; the "written as m/n...
you read this and you said you understood it but then it went right out of your head
dusky jacinth
Like I understand this diagram very well but what next
No m/n where m and n are co prime is because it stands for a fraction instead of a non fractional integer
vale wigeon
sigh
dusky jacinth
Like that's what I understood
vale wigeon
look at the diagram again.
dusky jacinth
Sorry no?
vale wigeon
our goal is to find AD.
vale wigeon
do you see how you can say something about one of the angles here?
something trigonometric.
vale wigeon
yes
dusky jacinth
Yeah if we got CD it's pretty easy to get AD then
vale wigeon
you don't need CD!!!
dusky jacinth
I said the opposite wait
vale wigeon
getting CD will be more effort than it's worth.
dusky jacinth
Oh ok
vale wigeon
the problem has been reduced to finding the value of tan(3a) knowing that tan(a) = 1/5
which is pure trigonometric bashing and nothing else
dusky jacinth
Yes
vale wigeon
do you know the angle sum identity for tan
dusky jacinth
Angle sum identity for tan? Can you explain what do you mean?
vale wigeon
do you know how to express tan(x+y) in terms of tan(x) and tan(y)?
vale wigeon
??
vale wigeon
so you don't know $\tan(x+y) = \frac{\tan(x)+\tan(y)}{1 - \tan(x)\tan(y)}$?
dusky jacinth
But not with variables
ocean sealBOT
Ann
dusky jacinth
No I didn't knew that thanks for letting me know right now
vale wigeon
then you do not have the right tools to do this problem, i'm afraid.
dusky jacinth
Oh
Ah but can you continue further I'll just keep this tan(x+y) in my mind till then
vale wigeon
i don't want to keep going with one hand tied behind my back
that's what it'll be like to find tan(3a) in terms of tan(a) without using angle sum and/or double angle identities for tan
dusky jacinth
Oh
Ok I'll learn about them today
And probably that'll just help me solve it
Thanks for your time
.close
tiny minnow
Can someone Teach me about The Millenium Problems
P vs NP
lone heartBOT
Can someone Teach me about The Millenium Problems
P vs NP
jagged imp
you're not allowed to get help with tests here sorry.
you also posted into a channel already in use.
tiny minnow
<@&268886789983436800> Some 1 ask Test + Interrupcting my channel ;/
night geyser
tiny minnow
Yeah i Know
That why i ask
but only info that i know
maybe should i close
.close
alpine sable
not sure if its relevant to ask here but the basic primitive recursive functions are all using natural numbers in their definitions?
lone heartBOT
not sure if its relevant to ask here but the basic primitive recursive functions...
@alpine sable Has your question been resolved?
alpine sable
.close
thorn echo
how do i find the value of x y and r of special angles?
lone heartBOT
how do i find the value of x y and r of special angles?
thorn echo
<@&286206848099549185>
little drum
^^"
thorn echo
sorryy
pale kestrel
you draw a right angled triangle for each.
and/or familiarize yourself with unit circle
thorn echo
i dont really have time to familiarize myself with the unit circle 😅 our activity is due today
were supposed to look for the 6 trigonometric functions using the x y and r of special angles
but i cant find the value of x y and r
alpine sable
Do you know what are the special angles?
thorn echo
30 45 and 60
alpine sable
And 0 and 90
thorn echo
yeaa
thorn echo
wdym?
alpine sable
Nvm i thought of something else
thorn echo
ohh lol
this is our homework
but i dont know the value of x y and r that's why i cant find the trigo functions
thorn echo
do you know what tan theta is?
yes yes
alpine sable
Tell
thorn echo
y/x
thorn echo
idk t-t
ik the definition of tan, but idk the x y and r that's why i cant substitute it
i asked my classmate btw, is it this one?
alpine sable
It's fine, just draw a right angled triangle (with any lengths you like) with angle theta as 30°. Take the side (y) opposite to angle theta, and divide it by the side (x) adjacent to theta (not the hypotenuse). You'll always get the ratio 1/sqrt(3)
thorn echo
so if i try to look for the tan of 30 degrees, it's √3/3?
thorn echo
It's fine, just draw a right angled triangle (with any lengths you like) with an...
wait lemme try, i dont get it lol
thorn echo
Or 1/sqrt(3)
yeah but i have to rationalize
alpine sable
Well, alright
alpine sable
wait lemme try, i dont get it lol
For ease, take base of triangle 1 cm, angle theta as 30°. Use scale and protractor
To draw
Trigonometric functions for angle theta in case of right angled triangles are just the ratios of two sides of the triangle
thorn echo
ooooh
alpine sable
You understood right?
thorn echo
i dont rlly have a protractor, but i understand the following msg
alpine sable
👍
alpine sable
Yw
thorn echo
.close
lethal dock
What are pythagorean triples
lone heartBOT
What are pythagorean triples
vale wigeon
A Pythagorean triple consists of three positive integers a, b and c such that a^2 + b^2 = c^2.
@lethal dock does this answer your question?
lethal dock
Yes but I dont really understand how the Euclid formula works in there
lethal dock
What does it refer to when it says m and n
vale wigeon
given an arbitrary pair of integers m and n with m>n>0
lethal dock
So m and n can be anything, if I follow m>n>0
vale wigeon
m and n can be any integers, so long as they are positive and m is bigger than n.
wary jay
can I get some help doing this?
lone heartBOT
can I get some help doing this?
wary jay
I've figured out theta as -26.57 (2dp) but what do I do from there
oh wait nvm i figured it out
.close
sharp hamlet
Help! We get 5$ from our teacher if we solve this if we solve this.
sharp hamlet
I get the steps for solving for absolute equations, but im stuck at whatever is in it.
sharp hamlet
how do I get the value for k?
sharp hamlet
ty ty..
pale kestrel
As for the inside...
having a sqrt in there looks fun
idk, I would recommend graph sketch to get an idea
At least.
sharp hamlet
having a sqrt in there looks fun
so fun 😒
pale kestrel
As for algebra its 🤔 🤔 🤔 🤔 🤔 🤔
sharp hamlet
idk, I would recommend graph sketch to get an idea
I did, but still its an aberration
little drum
oiiiiii
pale kestrel
$$\abs{x+\sqrt{1-x^2}} = \sqrt2(2x^2-1)$$
ocean sealBOT
Shuri2060
little drum
take conjugate XD
sharp hamlet
The RHS is also 😵💫
little drum
Uhh
sharp hamlet
take conjugate XD
which one XD
pale kestrel
Oh wait this is a fripping equation
little drum
:p
little drum
$\frac{|(2x^2 - 1)|}{|x-\sqrt{1-x^2}|} = \sqrt{2}(2x^2 - 1)$
ocean sealBOT
Ansh
sharp hamlet
It is tricky, but I think it is really this way.
little drum
can you work from here?
sharp hamlet
still 😵💫
little drum
hmm?
little drum
da heck an identity
pale kestrel
$$\abs{x+\sqrt{1-x^2}}\abs{x-\sqrt{1-x^2}} = ???$$
ocean sealBOT
Shuri2060
pale kestrel
This was the hint 👀
alpine sable
sharp hamlet
**Shuri2060**
oooh.. then I just assume the absolutes are not there?
multiply to get a trinomial.. still inside the absolute?
pale kestrel
oooh.. then I just assume the absolutes are not there?
multiply to get a trinomi...
what no
$\abs{x}\abs{y}=\abs{xy}$
ocean sealBOT
Shuri2060
vale wigeon
@alpine sable please post your question in an available channel.
sharp hamlet
yeah that was I was thinking.
pale kestrel
sorry, didnt realise
sharp hamlet
how about the RHS?
sharp hamlet
would it give me k for free?
sharp hamlet
reffering to this
pale kestrel
ignore this
sharp hamlet
oki oki
sharp hamlet
If I multiply get the conjugate on LHS, does that mean I should also multiply it on the RHS? or is it like multiplying by 1 case?
where I put it under the denominator.
pale kestrel
you multiply both sides of the equation by the same thing?
just note multiplying by 0 could cause issues
sharp hamlet
you multiply both sides of the equation by the same thing?
yes.
sharp hamlet
just note multiplying by 0 could cause issues
so, would it be better if...
little drum
the right hand side of equality is $\sqrt{2}(2x^2 - 1)$
ocean sealBOT
Ansh
sharp hamlet
ah I forgot the x^2.. sorry
little drum
so, would it be better if...
And yes, this is fine. Simplify the left hand side denominator
sharp hamlet
this is what I got. I can't get the root out of the equation. I'm looping.
little drum
._.
sharp hamlet
And yes, this is fine. Simplify the left hand side denominator
This is the simplified LHS, I was able to cancel (2x^2 - 1).
Then I did conjugate again. then the result is above..
little drum
I don't think you're allowed to cancel (2x² - 1) without any conditions lol
sharp hamlet
I don't think you're allowed to cancel (2x² - 1) without any conditions lol
really, oof.. coz getting the simplified version of LHS got me (2x^2 -1)
so I thought they should cancel
little drum
$\abs{x+\sqrt{1-x^2}} = \sqrt2(2x^2-1)$
ocean sealBOT
Ansh
little drum
$|x-\sqrt{1-x^2}| = \frac{|(2x^2 - 1)|}{\sqrt{2}(2x^2-1)}$
ocean sealBOT
Ansh
little drum
Either ways, I think I probably know where you got this question from... And you're supposed to be practicing how to deal with absolute value functions
So
sharp hamlet
'Somehow, Palpatine returned' XD
little drum
I shouldn't walk you through any far than this
little drum
'Somehow, Palpatine returned' XD
Not really lol. no
sharp hamlet
**Ansh**
Yeah, but giving this to grade 8 is a bit demanding.
So let me just summarize the steps
sharp hamlet
copying the initial problem, and rationalizing
Still, getting identities from who knows where and with only tools of equality and a bit of absolute. We were never meant to get that 5$ XD
one last ques
sharp hamlet
**Ansh**
how did the (2x^2-1) get into the RHS's numerator
I get that's the conjugate, but something is missing for me.
little drum
$\abs{x+\sqrt{1-x^2}} = \sqrt2(2x^2-1)$ \
$\implies \abs{x+\sqrt{1-x^2}} \cdot \frac{\abs{x-\sqrt{1-x^2}}}{\abs{x-\sqrt{1-x^2}}} = \sqrt2(2x^2-1)$ \
$\implies \frac{|(2x^2 - 1)|}{\abs{x-\sqrt{1-x^2}}}= \sqrt2(2x^2-1)$
ocean sealBOT
Ansh
little drum
I think after this its repetition of the conjugate steps.
You're free to think, if you're the next Sir Isaac Newton or LeBobbe Newton or something but my instructor always advised me to solve stuff on pen n paper ^^"
sharp hamlet
what I mean was the |x-sqrt(1-x^2)| will keep reappearing.
ocean sealBOT
Ansh
pale kestrel
You're free to think, if you're the next Sir Isaac Newton or LeBobbe Newton or s...
bad.
Pencil and paper smh 😠
📝
sharp hamlet
I shouldn't walk you through any far than this
Sorry didn't read this.
little drum
hint: ||the right hands side in the last equation is free from the variable "x" as long as you know the right conditions for the absolute value function to disappear||
sharp hamlet
uhm so anyway, I won't take up much of your time.
Thanks for the steps. It propelled me closer. I guess we aren't suppose to get that 5$. It's a bonus question anyway.
sharp hamlet
hint: ||the right hands side in the last equation is free from the variable "x" ...
will do!
lone heartBOT
pale kestrel
????? no idea what you mean... but alright.......
sharp hamlet
x=1/2
lone heartBOT
Available help channel!
empty forge
Could someone help me understand how to answer this question? I know the answer is dependent but I am not sure how to prove it mathematically.
empty forge
lone heartBOT
@empty forge Has your question been resolved?
empty forge
<@&286206848099549185>
lone heartBOT
@empty forge Has your question been resolved?
noble sinew
Our null hypothesis is indepedent, so that would mean that we would assume that the prob is the same for each job position
so find prob of that observation or a more extreme observation happening
drifting hull
@noble sinew Independet is not the same as evenly distributed and a null hypothesis has nothing to do with independence
noble sinew
what?
drifting hull
Two events A and B are independent, if $P(A \cap B)=P(A)P(B)$. So you just take to events, e.g. "Person is male" and "Person belongs to the Faculty and check whether P(Person is mal and part of Faculty)=P(Person is mal)P(Person is part of faculty)
ocean sealBOT
Alexander42
noble sinew
yes job position is independent with gender?
noble sinew
Could someone help me understand how to answer this question? I know the answer ...
use whatever test you have been taught to use on contingency table
noble sinew
Two events A and B are independent, if $P(A \cap B)=P(A)P(B)$. So you just take...
No relationship between job and gender is the same as saying Job and gender are independent?
drifting hull
jes
noble sinew
so what is your problem?
drifting hull
i only know the null hypothesis from significance hypothesis testing and as far as i know, these tests aren't related to this problem.
so i thought that the term null hypothesis was unappropriate
noble sinew
Which is the same we are doing here
For example Chi square test for independence is 1 way (there are many tests for contigency tables)
This will give us a p-value, if less than 0.05 we reject they are independent
drifting hull
I assumed to randomly pick a person and then check for independence of the events to Pick a certain gender and job. with the formula i mentioned. I have never heard any lectures on statistics and i don't know Chi sqaure test or p-values, so i guess you have a different understanding of whats going on (and probably better one, as i don't see the connection to the hypothesis test i learned in school)
noble sinew
Another way to view it is we have a general model, this follows a multinomial distribution, where the parameters varies freely. Now we wish to test if we can simplify our model to a simpler model, namely prob is the same (so independent between job and gender).
We can accept our simplification of our model if prob of them being independent is p>=0.05
But we have two hypothesis, so this fits the definition of hypothesis-testing
empty forge
.close
lone heartBOT
empty forge
thanks guys
lone heartBOT
Available help channel!
pale kestrel
@dense sleet All the strings you need to subtract contain ONLY 0,1,8
One string of seven is written on each coupon of the spring lottery with the inscription spring number
digits, from 0000000 to 9999999. If the coupon is rotated by 180∘
, digits 0 and 8 are
they do not change, digits 6 and 9 pass into each other, and all other digits lose meaning.
Thus, the spring number 9980896 will rotate to 9680866. Such coupons, whose spring
numbers rotate by 180∘ change their decimal value, we consider invalid.
How many invalid coupons are there?
(Note: Coupon with spring number 8680898 or 0808080 is a valid coupon.)```AND they need to be palindromic
dense sleet
What do you mean by that
pale kestrel
And they need to contain at least one 6 or 9
dense sleet
And they need to contain at least one 6 or 9
0808080 is a valid combination
It should be all combinations - valid combinations
4⁷ - 4*4*4*2
But thats wrong
pale kestrel
INVALID:
Choose 1st 3 digits. Must be from 0 1 8 6 9. Must contain at least one 6 or 9
Choost 4th digit. Must be from 0 1 8
=========
This is what you need to count.
dense sleet
INVALID:
Choose 1st 3 digits. Must be from 0 1 8 6 9. Must contain **at least on...
It cant be 1
pale kestrel
???
pale kestrel
One string of seven is written on each coupon of the spring lottery with the inscription spring number
digits, from 0000000 to 9999999. If the coupon is rotated by 180∘
, digits 0 and 8 are
they do not change, digits 6 and 9 pass into each other, and all other digits lose meaning.
Thus, the spring number 9980896 will rotate to 9680866. Such coupons, whose spring
numbers rotate by 180∘ change their decimal value, we consider invalid.
How many invalid coupons are there?
(Note: Coupon with spring number 8680898 or 0808080 is a valid coupon.)```No.
dense sleet
All other digits lose meaning
pale kestrel
It should be 0 1 6 8 9
dense sleet
1 is in other too
dense sleet
It says 0 and 8 stays same , 6 and 9 switch and all others loose meaning
Im guessing 1 is in the other
pale kestrel
Why
0
You could say 0 is in other
????
All depends how you write it
For all intents and purposes
Usually 0, 1, 6, 8, 9
Are considered
Unless your question says otherwise
dense sleet
I mean we could try with 1 that would then be
5⁷ - 5 * 5 * 5 * 3
pale kestrel
no it isn't.
===
INVALID:
Choose 1st 3 digits. Must be from 0 1 8 6 9. Must contain at least one 6 or 9
Choost 4th digit. Must be from 0 1 8
This is how to count.
Remove 1 if you want, but this is the correct method
surely?
You need to include the fact AT LEAST one 6 or 9
is contained.
Otherwise it is valid.
dense sleet
Well 609 is valid too
pale kestrel
arghhhhhhhhhhhhhhhh nooo
In any case, what you wrote is not the correct counting method either
Need to think about it carefully
write down examples with only 3 digits
Inclusion Exclusion is probably the correct method
little drum
count valids maybe?
dense sleet
I mean a 3 digit digit is valid if first is one of 5 second is one of 3 and last must be firsz digit or opposite if 6 or 9
Invalid = all possible - valid
little drum
Yha, which 5 btw? 0, 6, 8, 9?
pale kestrel
var l = [['0', '0'], ['1', '1'], ['6', '9'], ['8', '8'], ['9', '6']]
var invalid = 0
for (var a = 0; a < l.length; a++) {
for (var b = 0; b < l.length; b++) {
for (var c = 0; c < l.length; c++) {
for (var d = 0; d < l.length; d++) {
for (var e = 0; e < l.length; e++) {
for (var f = 0; f < l.length; f++) {
for (var g = 0; g < l.length; g++) {
if (`${l[a][0]}${l[b][0]}${l[c][0]}${l[d][0]}${l[e][0]}${l[f][0]}${l[g][0]}` !== `${l[g][1]}${l[f][1]}${l[e][1]}${l[d][1]}${l[c][1]}${l[b][1]}${l[a][1]}`) invalid++
}
}
}
}
}
}
}
invalid```=====
(very primitive js program)
77750 or 16256
=====
So I agree with this counting method. 5^7 or 4^7 minus valid strings
5^7 - 5.5.5.3
4^7 - 4.4.4.2
@dense sleet Are neither correct ???
Exactly what you wrote
dense sleet
Its around 25k btw
dense sleet
Yes but idk how to get to it
dense sleet
77750 or 16256
Thats what i thought too
pale kestrel
Can you give the exact given answer
dense sleet
26256
pale kestrel
Surely must be typo
16256 makes perfect sense
Oh
unless 2 and 5
are considered opposites too???
Question is vague with how the numbers are written
Could it be 7 segment display?
dense sleet
16256 makes perfect sense
Thats what im thinking too
Im goona ask today if its a typo
glass meteor
Hello, beginner problem here
lone heartBOT
Hello, beginner problem here
glass meteor
How do i aproach this problem
x∈ (0,pi/2)
cosx=1/5
Demonstrate that tanx=2√6
pale kestrel
Draw a right angled triangle
buoyant kayak
did you label it
glass meteor
Label it with what? >-<
buoyant kayak
you're given a ratio with respect to angle x
glass meteor
I might be too dumb
But how does drawing a triangle prove that tanx=2√6
Isn't there a formula for this?
buoyant kayak
did you label it
glass meteor
That i can't find
glass meteor
did you label it
yes
buoyant kayak
do you know the ratio for tangent
glass meteor
No
buoyant kayak
never heard of SOH CAH TOA?
buoyant kayak
how'd you know the ratio for cosine
pale kestrel
@alpine sable .
lone heartBOT
<@456226577798135808> .
pale kestrel
- Make forwards statements throughout. Upon reaching the final answer, verify to make the final backwards statement, in order to do the same as above.
===
Construct me an example where this does not work please.
pale kestrel
I am serious.
alpine sable
no
pale kestrel
If I am wrong, then I need to know.
alpine sable
Do you need help?
pale kestrel
Yes, when does this method of solving equations fail
pale kestrel
What?
alpine sable
this is the method
alpine sable
wrong order
pale kestrel
what???????
pale kestrel
I'm confused as heck what you'are asking me to do here
You told me to solve x = 2 for x
alpine sable
Now solve the equation x=3
pale kestrel
I am doing as above.
alpine sable
since x<2031 x=2
pale kestrel
$$x = 2$$
$\implies$
$$x < 2031$$
glass lichen
tf
alpine sable
so now 2=3
ocean sealBOT
Shuri2060
alpine sable
okay I need to create a more complicated example
pale kestrel
👌
If it really doesn't work, then I need to know.
Not joking, not being sarcastic.
alpine sable
solve x+2=5
Solution:
Since it's cloudy outside, x = 3
Verification:
3+2=5
It works
pale kestrel
huh?
pale kestrel
Solution:
Since it's cloudy outside, x = 3
Verification:
3+2=5
how is this a valid implication
cloudy does not imply x = 3
pale kestrel
huh???
My point is you construct a solution using VALID implications
And then check the reverse by validating the answer
alpine sable
No, that is MY point
YOUR point is to make ANY implications and then as long as the verification is good, we're good
glass lichen
x+2=5
implies x+2-2=5-2
implies x=3
3+2=5, hence x=3 is a solution
pale kestrel
what?
alpine sable
read your method 2 carefull
pale kestrel
How do you interpret my point in such a way
alpine sable
carefully
glass lichen
Yeah, you're the one misinterpretting here flr
pale kestrel
make VALID forwards statements throughout, clearly.
frigid geyser
Why would anyone tell you to make invalid statements, that's implicitly implied
lone heartBOT
glass lichen
The weather is a quintessential part of doing math btw \s
alpine sable
In the question whence this dialogue came
pale kestrel
.reopen epic snipe
lone heartBOT
✅
alpine sable
You did not say to verify that both expressions should be positive
pale kestrel
You don't need to.
I don't get it.
As long as your implications are valid
Then uh... I don't see what can go wrong, really.
glass lichen
sqrt{} is defined for any real number, some you just get iR
pale kestrel
Invalid implications are just bad math. Rather than bad method.
glass lichen
the only check needed is if the thing inside is well defined, which it clearly is
glass lichen
Oh great, I needed another weather forecast
alpine sable
when you square x you have to do three operations
pale kestrel
Let $x = \sqrt{6+4\sqrt 2}+\sqrt{6-4\sqrt 2}$.\\
$\implies$
$$x^2 = 12 + 2\sqrt{6+4\sqrt 2}\sqrt{6-4\sqrt 2}$$
I can't math, 1 sec.
gray isle
hah
alpine sable
exactly ou can't XD
glass lichen
12+2sqrt() no?
alpine sable
yes
pale kestrel
probably
ocean sealBOT
Shuri2060
pale kestrel
😂
alpine sable
there ya go
little drum
Yeah
pale kestrel
yh ok, step 1 successful
alpine sable
okay
glass lichen
but yeah, regardless there's nothing wrong with that step in practice
pale kestrel
😓
alpine sable
now what do you do
pale kestrel
move 12 to the left
alpine sable
the problem is the next step
pale kestrel
and square again? idk
alpine sable
exactly : )
little drum
$x^2 = 12 + 2\sqrt{(6+4\sqrt{2})(6-4\sqrt{2}})$
ocean sealBOT
Ansh
little drum
?
pale kestrel
I mean I haven't ACTUALLY tried the questoin but imo that isnt bad
alpine sable
Thanks Ansh
little drum
da heck
gray isle
I'd just simp the radicals from diff of two squares ^
pale kestrel
Let $x = \sqrt{6+4\sqrt 2}+\sqrt{6-4\sqrt 2}$.\\
$\implies$
$$x^2 = 12 + 2\sqrt{6+4\sqrt 2}\sqrt{6-4\sqrt 2}$$
$\implies$
$$x^2 = 12 + 2\sqrt{36 - 32}$$
alpine sable
The step that Ansh took is the one I was talking about
ocean sealBOT
Shuri2060
pale kestrel
I hope I did that right?
frigid geyser
You did
pale kestrel
🤔
little drum
The step that Ansh took is the one I was talking about
You're implying that's wrong because $\sqrt{6 - 4\sqrt{2}}$ can be negative and we can't combine the two square roots together?
ocean sealBOT
Ansh
little drum
alpine sable
combine is not defined
pale kestrel
Let $x = \sqrt{6+4\sqrt 2}+\sqrt{6-4\sqrt 2}$.\\
$\implies$
$$x^2 = 12 + 2\sqrt{6+4\sqrt 2}\sqrt{6-4\sqrt 2}$$
$\implies$
$$x^2 = 12 + 2\sqrt{36 - 32}$$
$\implies$
$$x^2 = 16$$
$\implies$
$$x = 4\quad\lor\quad x = -4$$
alpine sable
you used the property sqrt(a)*sqrt(b)=sqrt(ab)
ocean sealBOT
Shuri2060
alpine sable
that is the problem
little drum
Then $\sqrt{2}\sqrt{5} \neq \sqrt{10}$?
gray isle
or implying that we made a mistake of not checking whether 6-4sqrt(2) ad 6+4sqrt(2) are positive?
ocean sealBOT
Ansh
little drum
I wonder
alpine sable
or implying that we made a mistake of not checking whether 6-4sqrt(2) ad 6+4sqrt...
correct
pale kestrel
**Shuri2060**
In actual writing I should 'justify' my implications but...
little drum
hm
pale kestrel
There is nothing wrong with them, mathematically.
alpine sable
You will straight up get a wrong answer if a and b are negative
alpine sable
and get a correct answer accidentally if one of them is negative
glass lichen
yeah it fails when they're both negative.... but that isn't relevant here
alpine sable
how so?
glass lichen
cause they're both positive
gray isle
that is strongly implied and I didn't feel the need to mention that 6 -4sqrt(2) is approximately 6-5.7 and clearly positive
alpine sable
cause they're both positive
you decided to do the genius step of verifying your step
gray isle
in the explanation
alpine sable
that is what was required
glass lichen
It's not required though
alpine sable
then get a wrong result
alpine sable
cause 6+4sqrt(2) is (clearly) positive
what you are doing here is called checking
alpine sable
what you are doing here is called checking
which is what you need to do
frigid geyser
Gosh if someone verifies that 6 \pm 4\sqrt{2} are positive in my homework
.. i might write a comment saying "please omit trivial details, i have 500 people to grade"
glass lichen
6>0 4sqrt(2)>0
their sum is positive
alpine sable
Everything is trivial until you make a mistake
alpine sable
That is your philosophy
glass lichen
No
frigid geyser
How do you not know that on top of your head?
glass lichen
You do math, you know numbers, simple as
gray isle
i was even being generous
little drum
glass lichen
Not every single step needs, nor should be, explicit imo
alpine sable
How do you not know that on top of your head?
If you have n-digit approximations of square roots in your head then ok
glass lichen
cause then your work becomes clunky
alpine sable
but the guy who asked the question does not
frigid geyser
I didnt do any square root approximation
pale kestrel
Let $x = \sqrt{6+4\sqrt 2}+\sqrt{6-4\sqrt 2}$. Then\\
$$x = \sqrt{6+4\sqrt 2}+\sqrt{6-4\sqrt 2}$$
$\iff$
$$x = \sqrt{6+4\sqrt 2}+\sqrt{6-4\sqrt 2}\quad\land\quad x \geq 0$$
$\iff$
$$x^2 = 12 + 2\sqrt{6+4\sqrt 2}\sqrt{6-4\sqrt 2}\quad\land\quad x \geq 0$$
$\iff$
$$x^2 = 12 + 2\sqrt{36 - 32}\quad\land\quad x \geq 0$$
$\iff$
$$x^2 = 16\quad\land\quad x \geq 0$$
$\iff$
$$x = 4$$
alpine sable
whatever this discussion is fruitless
ocean sealBOT
Shuri2060
alpine sable
But i know 36 > 32
Yep. this is called checking
glass lichen
It isnt
pale kestrel
**Shuri2060**
How is this for a bidirectional proof?
alpine sable
what I said needed to be done
pale kestrel
Logically sound imo
alpine sable
okay then 36 does not exist?
frigid geyser
Sure you can check it in your head i guess
alpine sable
whatver
alpine sable
close this
glass lichen
K, stop putting words in peoples mouths
gray isle
excessive rigour
alpine sable
for me I saw the expression and I saw all the steps and arrived at 4
glass lichen
yeah, and we all arrived at 4 too
glass lichen
g4u, want a cookie?
alpine sable
so then you are suggesting that the guy who asked should write "4"
and get full points,
alpine sable
I am just saying the requirements that are likely expected by the school
alpine sable
This discussion is moronic
frigid geyser
No we are saying something as trivial as sqrt(36) > sqrt(32) can be omitted
alpine sable
bye
glass lichen
You cant say shit about their expectations
frigid geyser
It really is
pale kestrel
That inequality is verified in the backwards proof anyways
If I'm not mistaken
That 3rd last line going to the 4th last line
verifies it.
little drum
Yeah
gray isle
oh no but based on your explanation you seemed to imply you "know" that
sqrt(6-4sqrt(2)) is 2 - sqrt(2)
and not sqrt(2) - 2
you didn't feel the need the check that
little drum
frigid geyser
You omitted that 4 >= 0 this is so wrong
pale kestrel
.close
undone hinge
$$ 3*(a+b) / ( 3a+b) $$
lone heartBOT
$$ 3*(a+b) / ( 3a+b) $$
ocean sealBOT
Big xdddd
ocean sealBOT
Big xdddd
undone hinge
i can write it like this: $$ 3a /(3a+b) + 3b /(3a+b) $$
ocean sealBOT
Big xdddd
undone hinge
but this wont help
so the actual problem is that i want to proof that:
$$ 3(a+b)/(3a+b) <= b $$
ocean sealBOT
Big xdddd
placid zinc
,w graph 3(x + 1) / (x + 3) and x between -5 and 5
undone hinge
i can write $$ 3a+3b/(3a+b) $$
ocean sealBOT
Big xdddd
undone hinge
and then i can estimate that too
undone hinge
$$ 3+b/(3+b) $$
placid zinc
Hmm. Looks like the sign flips a few times.
ocean sealBOT
Big xdddd
placid zinc
So the thing you are trying to prove is false.
undone hinge
nah its correct
undone hinge
this works
i dont even know what you were trying to plot
but thank you!
.close
lone heartBOT
lone heartBOT
Available help channel!
placid zinc
Yeah, that's just a brand new equation lol
lone heartBOT
Yeah, that's just a brand new equation lol
limpid garnet
2ce^-c^2 = -1/2e^4 + 1/2 solve for c
lone heartBOT
2ce^-c^2 = -1/2e^4 + 1/2 solve for c
little drum
$2ce^{-c^2} = -\frac{1}{2e^4} + \frac{1}{2}$ ?
ocean sealBOT
Ansh
lone heartBOT
@limpid garnet Has your question been resolved?
alpine sable
@limpid garnet e and c are just variables ?
alpine sable
I think i got a question above my level 😅
I thought it was just variable and try solving it
limpid garnet
alpine sable
And got something weired
limpid garnet
it sll hoof
alpine sable
it sll hoof
Huh ?
alpine sable
little drum
,w 2xe^(-x^2) = -1/(2e^4) + 0.5
ocean sealBOT
little drum
x ~ 0.5!?
alpine sable
Can i ask u the value of e if any ?
limpid garnet
?
alpine sable
2.71828 ?
limpid garnet
sorry what is this
pine tiger
what is x when (3x+2)^2=4
my work
2x+2=√4
3x+2=2
3x=0
x=0
this answer was right but my math book said it was 0 or -4/3
little drum
$2ce^{-c^2} = -\frac{1}{2e^4} + \frac{1}{2} = K$, say
$$\implies 4c^2e^{-2c^2} = K^2$$
$$\implies (-2c^2) = W(-K^2/2)$$
$$\implies c = \sqrt{-\frac{W_0(-K^2/2)}{2}}$$
ocean sealBOT
Ansh
little drum
,calc -1/(2e^4) + 1/2
ocean sealBOT
Result:
0.49084218055563
,w W(-0.49^2/2)
ocean sealBOT
limpid garnet
dont u take the ln
little drum
Well, you can't separate the variable "c" from e^{-c^2} here
limpid garnet
ok then how do we bring the -c^2 down
little drum
we can use the Lambert W function here to solve for "c"
limpid garnet
sorry how do you use lambert function never heard of it before
little drum
btw, where'd you get this equation from?
if I know some context, maybe it's just a troll question or smth?
limpid garnet
It one of my homework problem
little drum
Is it explicitly written to solve for "c", the equation: \
$2ce^{-c^2} = -\frac{1}{2e^4} + \frac{1}{2}$ ?
ocean sealBOT
Ansh
limpid garnet
no it a mean value theorem