thanks man
#help-36
final saddleBOT
@tranquil pine Has your question been resolved?
tranquil pine
Everything is there
bro whats this mean π
quiet garden
final saddleBOT
quiet garden
how u do this
final saddleBOT
@quiet garden Has your question been resolved?
vernal fiber
This looks like a green's theorem problem
Because otherwise you would have to do a line integral for each segment
cursive bough
pretty ugly for a green's theorem problem, I think it would suck either way lol
but green's is easier i agree
vernal fiber
Yeah but that's just the bounds at that point that are tedious
final saddleBOT
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wind flame
.reopen
i need help, i have a revision sheet but there is no answer key. i am wanting to know if my answers are correct.
final saddleBOT
i need help, i have a revision sheet but there is no answer key. i am wanting to...
wind flame
hasty mist
i need help, i have a revision sheet but there is no answer key. i am wanting to...
Why the $cong$?
soft zealotBOT
γ―γΌγͺγΌ
wind flame
wdym? in which question and which statement?
hasty mist
This here
wind flame
opposite angles of a parallelogram are congruent
hasty mist
Should be fine
wind flame
im sorry if i annoy you, im gradually doing the worksheet so im gonna be sending stuff every few minute.
hasty mist
Okay
wind flame
final saddleBOT
@wind flame Has your question been resolved?
naive wyvern
I need help: (2π₯+1)(3π₯β6)=π(ππ+π)(πβπ) shouldn't the 3 go next to (x-2) instead of at the start? dosen't that change the value of the equation?
final saddleBOT
I need help: (2π₯+1)(3π₯β6)=π(ππ+π)(πβπ) shouldn't the 3 go next to (x-2)...
tired walrus
multiplication is commutative
so $(2x+1) \cdot 3 \cdot (x-2)$ and $3 \cdot (2x+1) \cdot (x-2)$ are one and the same anyway
the 3 has no special emotional attachment to specifically the (x-2) bracket!
naive wyvern
ohhh
soft zealotBOT
Ann
tired walrus
there we go
worldly spruce
there we go
sorry 
naive wyvern
okay so this makes sense but i do still need some help with something
so the next exercise after is
solve E=0
e was the equation that was above
so
π(ππ+π)(πβπ)
but
on the correction it says
(2π₯ +1)(π₯ β2) = 0
so im a little confused lol
maybe it was on the test like that
and i didn't see it
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worthy radish
Why does this person put -1 in brackets?
final saddleBOT
Why does this person put -1 in brackets?
worthy radish
What would it mean without brackets?
severe canyon
Again??????
rich mesa
Did you just ask the same question in a different channel?
severe canyon
Did you just ask the same question in a different channel?
YES, #help-42 message
rich mesa
Why does this person put -1 in brackets?
Anyway, the person puts -1 in brackets because you dont put two operators right after another to make it more readable
worthy radish
Anyway, the person puts -1 in brackets because you dont put two operators right ...
You mean for example
5+(-5)
Instead of 5+-5?
rich mesa
yes
worthy radish
,w 5+(-5)
soft zealotBOT
worthy radish
,w 5+-5
soft zealotBOT
lethal drum
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trail mango
i can help
chilly pollen
Try simplifying B a little @lethal drum using row operations
trail mango
good idea
chilly pollen
Taking the determinant directly would be painful 
lethal drum
Try simplifying B a little <@449711874141847567> using row operations
there has to be a simpler way right? i dont think our prof would want us to fill 2 whole pahes of just step by step row operations
if so then after changing the columns am stuck there, do we take every single number outside as cofactor since theyre similar in all the rows or what do even do
chilly pollen
there has to be a simpler way right? i dont think our prof would want us to fill...
I suggested you to simplify because of the pattern you notice with coefficients in each column
So really it won't be too much and you possibly get a neat relation
lethal drum
I suggested you to simplify because of the pattern you notice with coefficients ...
yea thats what i thought of at first glance, but then it gets too complicated
chilly pollen
Element as in the entry in a row and column
Like b 1,1 and so on
Like a cell in a table
Term as in a letter
lethal drum
so 1 letter and 1 number?
chilly pollen
Like each cellular block with one letter
shadow pewter
Please i need help about this topic. Logarithm
chilly pollen
!occupied @shadow pewter
final saddleBOT
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #βhow-to-get-help for instructions).
lethal drum
Like each cellular block with one letter
well yea in first glance it seems like thats what we sshould do
but then it gets too complicated
chilly pollen
Try going systematically
Eliminate one variable at a time
Also it suffices to do it for only one column @lethal drum
Because of symmetricity
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meager hamlet
should i memorize this
final saddleBOT
should i memorize this
meager hamlet
or am i better off conceputalizing this somehow
storm haven
or am i better off conceputalizing this somehow
Conceptualizing is the way
worthy radish
UwU
meager hamlet
Conceptualizing is the way
how do i go about that
cuz rn i see some paterns but dont understand how it all corelates
meager hamlet
yes
storm haven
We know that when the derivative of a function is 0, that function is at an extrema right?
loud sundial
So F''(x) = 0
F'(x) has a rel min or max
hi 
storm haven
hi <:happy:908558103992225822>
Hiiiiii
meager hamlet
So F''(x) = 0
F'(x) has a rel min or max
following that patern yes
storm haven
And by definition, when f'' = 0, that's an inflection point 
That's for the first row
meager hamlet
So F''(x) = 0
F'(x) has a rel min or max
or would it be potential rel min/max
and potential inflection point
storm haven
or would it be potential rel min/max
It's actually a certain min /max iirc, but in the first row they actually say "or undefined" for f''x, that's why it's "potential"
But if they said f'' = 0, NOT undefined, then it would be certain
meager hamlet
It's actually a certain min /max iirc, but in the first row they actually say "o...
oh so when f(x) = undef there's potentaly a inflection point or relative extra
storm haven
oh so when f(x) = undef there's potentaly a inflection point or relative extra
Yup, like the absolute value function
meager hamlet
and when f''(x) = 0 theres defo inflection/rel min/max
storm haven
Yup, like the absolute value function
At its vertex, the derivative is undefined. But it's at an extrema
meager hamlet
At its vertex, the derivative is undefined. But it's at an extrema
ohhhh that makes sense
crystal schooner
To add onto that, for an abs function, it is not differentiable at zero due to a "cusp" (Sharp point)
meager hamlet
To add onto that, for an abs function, it is not differentiable at zero due to a...
ahh ok i see
wait and then i think the bottom 2 clicked for me
when f''(x) crosses the x axis, it measn theres a point of inflection, and then building off of previous knowlegde that when f'(x) changes from pos to neg f(x) has rel max so same thing is applied for f''(x) and f'(x)
explanation might be not so good 
storm haven
explanation might be not so good <:kekw:752021756650455061>
That's a perfect intuition alr
meager hamlet
That's a perfect intuition alr <:catthumbsup:614540188747563008>
greatttt
storm haven
For the F'' > or < 0, by definition F is concave up or concave down
meager hamlet
so just memorize that?
storm haven
I don't think you could put any intuition on that, cause that's literally the definition of concaveness!
storm haven
so just memorize that?
Yep
meager hamlet
okay thats pretty easy to memorize thankfully
storm haven
But, for F' u can use intuition
meager hamlet
f''(x)>0 --> f'(x) is increasing
storm haven
f''(x)>0 --> f'(x) is increasing
F' is increasing
When a functions derivative is positive, then that functiin is increasing
And F'' is the derivative of F'
And that's it for your whole table
Simple wasn't it??
final saddleBOT
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β Original question: #help-36 message
meager hamlet
when putting this table all together now
im assuming i can have a wide range of questions? concavity, where f'(x) has point of inflection, does it have potential point of inflection, if f'(x) is inc or dec
all of those are fair game now?
if its asking about something different i can change the f into like f' and determine different stuff right?
pliant shore
im assuming i can have a wide range of questions? concavity, where f'(x) has poi...
check with your teacher, but all of those are fair game
though if f'(x) has a point of inflection, that would be setting the 3rd derivative to zero, so the function better be easy to differentiate
crystal schooner
i'd say that's fair game also
This question is also nicer too. It already gave you the 1st derivative. So you need to take the derivative of that to determine concavity and/or inflection points of g(x)
meager hamlet
check with your teacher, but all of those are fair game
and the intervals used on tbale on the last photo was just found using the crirical values of g''(x)
meager hamlet
This question is also nicer too. It already gave you the 1st derivative. So you ...
my teacher said thats becasue she didn't want to spend instructional time doing simple differentiation
shouldnt expect nice questions on exam sadly
crystal schooner
This may be different for you, but my exam for calculus (Assuming its hs math) was really straightforward. All the questions on the exam were questions that I have seen. Exams questions tend to be easier than tests.
pliant shore
I think your teacher wants to test how well you know properties of graphs
they're not going to have any crazy differentiations beyond the product rule, quotient rule, chain rule as you've seen before
meager hamlet
when putting this table all together now
over here where you find where the denominator of g''(x) = 0
u do (x^2+3)^3 = 0
x^2 + 3 = 0
x^2 = -3
pliant shore
yep, and that's impossible for all real numbers
meager hamlet
and then since that would give imaginary numbers there is no value?
ok i see
if it were to give real numbers
then id use those in the table?
crystal schooner
over here where you find where the denominator of g''(x) = 0
That wouldn't be possible
x^2 + 3 = 0
x^2 = -3
x = sqrt(-3)
You can't take a sqrt of a negative
pliant shore
cause if you changed (x^2 + 3)^2 to (x^2 - 4)^2 for example
the sign of that doesn't change: it's always 0 or positive
but if you had (x^2 - 4)^3 instead, the sign of that changes
pliant shore
cause if you changed (x^2 + 3)^2 to (x^2 - 4)^2 for example
so whenever you have something squared, or to the power of 4 or 6
the sign of that doesn't change, so you don't need to make a column for it in your sign diagram table
meager hamlet
oh bc its always positive?
pliant shore
cause if you changed (x^2 + 3)^2 to (x^2 - 4)^2 for example
you'd just use your table and then write $x \ne -2, 2$
soft zealotBOT
south
pliant shore
oh bc its always positive?
zero or positive, yes
pliant shore
no worries!
pliant shore
good luck!
meager hamlet
.close
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meager hamlet
this is just using second deriv rule
final saddleBOT
this is just using second deriv rule
meager hamlet
do i need to know my unit circle to find 7Ο/6
and 11Ο/6
or is there a way to find that by hand
i normaly use the table method when it comes to trig
but idk if i can use that here
vital crag
,tex .reflect trig
soft zealotBOT
riemann
soft zealotBOT
riemann
barren hound
using a unit circle (even a small sketch of one) will far and away be the fastest way to find sin 7Ο/6
warm python
this is just using second deriv rule
what's the question
meager hamlet
Oh terminal or coterminal angles
ok so honestly its probs easier to memorize the unit circle? lol
barren hound
yes
well at least memorising Ο/6, Ο/3, and Ο/4
and then you can kinda work with it from there
meager hamlet
what's the question
use 2nd derivative therom to find rel extrema
yea okay ill memorize it ig
while im here... i have a question abt 2nd deriv test
barren hound
for 7Ο/6 for instance i'd scribble something like this
crystal schooner
ok so honestly its probs easier to memorize the unit circle? lol
It's best to know 2pi, pi, pi/2, pi/3, pi/4, pi/6, and 0. You can figure the rest out using CAST
meager hamlet
while im here... i have a question abt 2nd deriv test
from my understanding its as followed:
if x=a is a critical value of f(x) then f'(x) = 0 or undef and is therefore a potential rel min/max
does that mean i should then take the 2nd derivative of f(x) and test all critical values to see if f"(x) > 0 f"(x)<0 or if f"(x)=/0
meager hamlet
It's best to know 2pi, pi, pi/2, pi/3, pi/4, pi/6, and 0. You can figure the res...
okay ill look into it
meager hamlet
for 7Ο/6 for instance i'd scribble something like this
righttt i forgot out the special right triangles
the midterm isnt till another month so i have time to learn that ig
barren hound
from my understanding its as followed:
if x=a is a critical value of f(x) then ...
yup
vital crag
ok so honestly its probs easier to memorize the unit circle? lol
,tex .unit circle
soft zealotBOT
riemann
crystal schooner
okay ill look into it
I will show you an example in a sec
meager hamlet
yup
okay i was confused cuz i didn't realize im meant to test all critical values
so basically i can use 2nd deriv test any time?
barren hound
the second derivative test says that if f ' (a) = 0, then:
- if f '' (a) > 0 -> f has a relative minimum at a
- if f '' (a) < 0 -> f has a relative maximum at a
- if f '' (a) = 0 -> f has neither a relative minimum nor maximum at a (for example, x^3 at 0)
meager hamlet
the second derivative test says that if f ' (a) = 0, then:
- if f '' (a) > 0 -> ...
and i can just set f'(x) = 0 by having everything everything on one side right?
dumb question but my brain is totaly fried today
barren hound
ummmm i'm not sure what your question is. you can set f ' (x) = 0 by.... setting f ' (x) = 0
like if f(x) = sinx + x^2
then f ' (x) = cosx + 2x
crystal schooner
okay ill look into it
meager hamlet
like if f(x) = sinx + x^2
okay yea that clarifies
meager hamlet
ahh i remember this a bit
ill need to do some practic e
thanks for the help guys
ive been studying since 9am and now its almost 2am i think im gonna call it a day today π
crystal schooner
the second derivative test says that if f ' (a) = 0, then:
- if f '' (a) > 0 -> ...
literally the 2nd derivative is used to determine the concavity at the critical point.
So if c is a critical point, then if f''(c) > 0, it is a concave up, therefore min. If f''(c) < 0, it is a concave down, therefore max.
barren hound
oh actually i slightly misspoke --- if f ' ' (x) = 0 then it's inconclusive (e.g. x^4 at 0)
final saddleBOT
@meager hamlet Has your question been resolved?
meager hamlet
one tiny thing more
when it says f"(x) is >0 it means above x axis right?
and when f"(x)<0 it's bellow x axis
or am i meant to look at the slopes
final saddleBOT
@meager hamlet Has your question been resolved?
formal trail
means above x axis
means what is above the x axis? f(x), f'(x) or f''(x)?
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slate narwhal
?
scarlet lantern
I think i may have done something wrong I'm not so sure
so I'm checking over it again
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wooden marsh
In the figure, the curve y = 7 - x^2 A rectangle is drawn under the curve in the first quadrant according to the figure. Determine the largest value that the area of ββthe rectangle can take.
final saddleBOT
In the figure, the curve y = 7 - x^2 A rectangle is drawn under the curve in the...
wooden marsh
I got quite far but ended up doing something wrong idk what
leaden moon
In the figure, the curve y = 7 - x^2 A rectangle is drawn under the curve in the...
Where's the figure
leaden moon
I got quite far but ended up doing something wrong idk what
- show your work
wooden marsh
Where's the figure <:opencry:586078614865444865>
Question 20
wooden marsh
+ show your work
Ya one sec
viral jungle
,rccw
soft zealotBOT
leaden moon
inequality time
leaden moon
,rccw
soft zealotBOT
wooden marsh
Thanks
wooden marsh
Oh alright
leaden moon
Hilariously, i can do it without touching calc at all
final saddleBOT
@wooden marsh Has your question been resolved?
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worthy radish
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worthy radish
Really is the vertex (3,-11)?
severe canyon
!1c
final saddleBOT
Please stick to your channel.
severe canyon
Why do you always open another channel immediately after closing the previous????
worthy radish
Stop it
worthy radish
β¦
severe canyon
If it is "because I have a question on another topic" you could have just said this and everything would be fine
Instead, you chose to say "stop it" to a helper...
Why?
final tangle
Different question, no multiple channel flag by the bot so it's fine unless I'm missing something
tired walrus
the original question seems to be missing
severe canyon
Different question, no multiple channel flag by the bot so it's fine unless I'm ...
Yeah I rushed too much, my bad
tired walrus
but judging by the a=1, b=-6, c=-2: did it ask to graph y = x^2 - 6x - 2?
@worthy radish
severe canyon
Instead, you chose to say "stop it" to a helper...
Why?
But still this is not a good behaviour in my opinion
tired walrus
in this case yes, (3, -11) really is the vertex.
worthy radish
Itβs so weird that it is -11
worthy radish
in this case yes, (3, -11) really is the vertex.
See I calculated it correctly
Iβm not idiotic.
.close
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severe canyon
Iβm not idiotic.
No one said that π€
severe canyon
Itβs so weird that it is -11
Why?
worthy radish
Ann always thinks so.
tired walrus
nice mind-read
if only it wasn't 100% wrong...
just to be absolutely clear here: no, nenni, i do not consider you "idiotic" or anything similar.
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rustic light
Let V be an euclidean space with inner product <.,.> and T:V->V a linear operator
Show that if T is self-adjoint, then every eigenvalue Ξ» of T is real.
This question was given to us as an exercise by the professor, but I believe it to be misplaced and I need some conceptual clearing.
So far we have only been working with real inner product spaces, I'm aware of other definitions for complex spaces but that has not been mentioned yet.
Then the proof would be trivial because V is an euclidean space and from the definition of eigenvalue, Ξ» is in R. Am I missing something?
final saddleBOT
Let V be an euclidean space with inner product <.,.> and T:V->V a linear operato...
rustic light
The fact that T is self-adjoint does not even seem to matter here
vital crag
You use definition of self adjoint and axioms/properties of vector spaces
Do you have a list of axioms for euclidean space
rustic light
a vector space with an inner product (in this case the real inner product that we have been working with)
that is the definition he gave
of what an euclidean space is
vital crag
Do you have properties of the inner product
rustic light
The axioms?
vital crag
Sure
rustic light
<,>:V X V -> R
i) <v, v> >=0, and =0 iff v=0
ii)<u, v>=<v, u>
iii)<u,v+w>=<u,v>+<u,w>
iv)<ku,v>=k<u,v> with k being a scalar in R
gritty drift
You might be missing an important property (definition?) of hermitian operators:
If T hermitian, then <a, T(b)> = <T(b), a>
rustic light
<,>:V X V -> R
i) <v, v> >=0, and =0 iff v=0
ii)<u, v>=<v, u>
iii)<u,v+w>=<u,v>+...
the axioms for real inner products that we were given
if it meets those properties then it's a real inner product
desert mantle
just treat the exercise as if you had a complex inner product
rustic light
That hasn't been introduced yet, that's the problem
vital crag
Yea idk how to do this without<u, v> = <v, u>*
gritty drift
You need to know inner product space properties for complex IPs to disprove that it is complex... If you haven't covered complex IPs yet, how can you prove an eigenvalue is "real"?
Like if we don't know what an complex number is, what other than "a real number" can a constant value be
rustic light
Yes that's exactly what I said, I was just asking for guidance. I wasn't sure if I was missing something or not. But I guess the question was actually just misplaced
gritty drift
Its a standard question if you can use properties like <cu, v> = c* <u, v> but you can't really disprove c being complex if you can't define a complex number
hasty mist
Sloppy
rustic light
So is it correct to say that the proof is trivial? That is basically what I want to know
Following those definitions
vital crag
Depends what you consider trivial
gritty drift
I mean you can't wave your hand and say it's trivial lmao but it's not a super hard proof with the requisite tools
vital crag
That's a subjective word
rustic light
I have an uneasy feeling that I am missing something
since V is a vector space over the reals, then any eigenvalue of T:V->V must belong to the reals
But I was thinking about something like the 90ΒΊ rotation transformation from R^2 to R^2, doesn't that have complex eigenvalues?
gritty drift
I have an uneasy feeling that I am missing something
since V is a vector space o...
Well is the 90 degree rotation even hermitian?
You only guarentee real e-vals for a hermitian operator, otherwise its free game
Here's the setup for the evals of a Hermitian are real proof (I gave this in a tutorial recently so I have it typed up nicely). Notice how we assume lambda is a complex number
vital crag
just treat the exercise as if you had a complex inner product
Should just do this
rustic light
You only guarentee real e-vals for a hermitian operator, otherwise its free game
Alright, so I tried writing this down:
<Tv, v>=<Ξ»v, v>=Ξ»<v,v>
then Ξ»=<Tv, v>/<v,v>
Since we're working with real inner product spaces then the numerator and denominator are both real, and <v,v> isn't 0 because v is not zero
This seems to imply that any transformation with a real inner product only has real eigenvalues, but that can't be true. So what is incorrect about this?
The fact that T is self adjoint should come into play somehow but I don't know how
gritty drift
Okay...
There's nothing stopping lambda from being a complex number, that's why the general case fails
Now if T is hermitian you can do the switcharoo <Tv, v> = <v, Tv>
gritty drift
Alright, so I tried writing this down:
<Tv, v>=<Ξ»v, v>=Ξ»<v,v>
then Ξ»=<Tv, v>/<v...
If you apply the same process you just mentioned to <v, Tv>, you will get Ξ»*=<Tv, v>/<v,v> (recall you can pull out a constant from the IP, but it gets conjugated if you do it from the left side)
This will imply Ξ» = Ξ»*...
rustic light
There's nothing stopping lambda from being a complex number, that's why the gene...
Right, but why would lambda be complex? If V is a vector space over a field F then Ξ»βF. Since euclidean vector spaces are spaces over the reals then how can Ξ» be complex
isn't that the definition of an eigenvalue? Ξ»βF is an eigenvalue of T if there exists v in V, vβ 0, such that T(v)=Ξ»v
gritty drift
Who says V is a real VS?
rustic light
Are euclidean vector spaces not spaces over the reals?
gritty drift
Oh alright... that makes your question poorly phrased. Your prof (or you during transcription) probably misspoke/miswrote
Let V be an euclidean space with inner product <.,.> and T:V->V a linear operator
Show that if T is self-adjoint, then every eigenvalue Ξ» of T is real.
.... Assuming euclidean means "real VS" is an idempotent statement, it's like saying "If we get the real roots of any polynomial, they'll all be real"
rustic light
Yea thats why I asked if I could just say the proof is trivial lol
Sorry I might have not been explaining myself very clearly because I am a little confused about this
gritty drift
I mean in the way you state it sure, but I'm like 95% sure your prof meant:
Let V be ANY vector space with inner product <.,.> and T:V->V a linear operator
Show that if T is self-adjoint, then every eigenvalue Ξ» of T is real.
rustic light
Yes I see. Now I wanna go back to the other question that I had about the 90Β° transformation from R^2 to R^2
"A Euclidean vector space is a finite-dimensional inner product space over the real numbers." This is basically the definition of euclidean vector space that we are using
So R^2 is an euclidean vector space right?
rustic light
"A Euclidean vector space is a finite-dimensional inner product space over the r...
With the axioms of inner product that I sent before
gritty drift
R^2 is a euclidean VS if you go by the word-for-word definition, but we usually work in C^2 under the hood
rustic light
I see. So if I'm working extrictly in R^n then that transformation does not have eigenvalues or eigenvectors yes?
gritty drift
Like your rotations and stuff all happen in C^2, we just typically chose matrices that happen to be R^2, so we don't notice
Exactly
You can't define them cause they're complex
But we usually want to define them, so we work in C^2 even if our matrices are all real
rustic light
Basically the trivial "question" could be rephrased to something like: if T has an eigenvalue then it is real.
So it does not fail because in this case it doesn't have an eigenvalue since we are in R2
gritty drift
Exactly
We don't even need T to be hermitian in that construction, it's like saying "all real numbers are real"
rustic light
Yes I see. Thank you.
Unfortunately this isn't the first mistake that I have encountered in this course, it isn't uncommon for this professor. Really makes the learning process way more confusing. Makes me a little sad
Thanks for the help
.close
worthy radish
Here
worthy radish
Do I have to do 1/3*3/2 etc?
tired walrus
if you are simplifying this by first turning it into $(a^{1/3})^{3/2} \cdot (b^{1/2})^{3/2}$ then yes, the exponents multiply together.
soft zealotBOT
Ann
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soft pewter
Two devices, located at points A and B, pull with forces of 720 N and 810 N respectively in order to lift a load vertically to a height of 3.5 m.
If the work W (in J) is defined as the dot product of the force \vec{f} (in N) acting on an object and the displacement \vec{d} (in m) of that object, that is,
W = \vec{f} \cdot \vec{d},
what is the work done by the resultant force acting on the load?
final saddleBOT
Two devices, located at points A and B, pull with forces of 720 N and 810 N resp...
soft pewter
cos 63 = a/810 = 367,63
sin 63 = b/810 = 721,71
(367,63;721,71)
cos 27 = a/720 = 641,52
sin 27 = b/720 = 326,87
(641,52;326,87)
do i multiply these components or do i add them
i dont understand why i have to add them when in my book it says when u want to do scalar product of composants u multiply them
<@&286206848099549185>
.close
final saddleBOT
noble stone
sine of both to get the upwards components, since the side opposite (as opposed to adjacent with cosine) the angle is vertical
add them to get the total upwards force
work is force times displacement
i'm not french but it seems to be lifted by 3.5 meters?
so multiply the displacement by the sum of forces
i haven't done physics problems in a while but that's what i'd do
final saddleBOT
Available help channel!
distant scarab
if we have a prime number "q" that is 1024 bit and another large number "a" (1020-1024 bit) number that we want to check if its Quadratic residue , using Legendre symbole
we need to compute a ^ (p-1)/2 which is kinda impossbile , is there another way to find if our number is Quadratic residue
final saddleBOT
if we have a prime number "q" that is 1024 bit and another large number "a" (102...
distant scarab
i.e q = 25081841204695904475894082974192007718642931811040324543182130088804239047149283334700530600468528298920930150221871666297194395061462592781551275161695411167049544771049769000895119729307495913024360169904315078028798025169985966732789207320203861858234048872508633514498384390497048416012928086480326832803
and
a = 45471765180330439060504647480621449634904192839383897212809808339619841633826534856109999027962620381874878086991125854247108359699799913776917227058286090426484548349388138935504299609200377899052716663351188664096302672712078508601311725863678223874157861163196340391008634419348573975841578359355931590555
trail mango
not claiming there isnβt a better way, but doesnβt seem impossible to compute that mod q
distant scarab
not claiming there isnβt a better way, but doesnβt seem impossible to compute th...
a ^ (q-1)/2 (mod q)
how would u compute it
trail mango
let me get on my computer for this one
hasty mist
Bruh
trail mango
do you have a way to check it?
i got 12198191382510180130171785779099635405775646886012417221562882673911806474606622930917413991202999512582284613332305654295896813876410078041259926827289489544738064234567425318685278617664636888180070131538546281599196217240157921967978943264140230808292994118880960193709071196232722730098178814120258104487
hasty mist
Hm one sec
trail mango
when you think it's impossible i think you are just underestimating how fast exponentiation can be
distant scarab
i got 12198191382510180130171785779099635405775646886012417221562882673911806474...
is this the end result of the entire operation ?
i mean it should be {0,1,-1}
trail mango
the value of a^(q-1)/2 (mod q)
distant scarab
hasty mist
I got 1
bleak jay
a = 45471765180330439060504647480621449634904192839383897212809808339619841633826534856109999027962620381874878086991125854247108359699799913776917227058286090426484548349388138935504299609200377899052716663351188664096302672712078508601311725863678223874157861163196340391008634419348573975841578359355931590555
q = 25081841204695904475894082974192007718642931811040324543182130088804239047149283334700530600468528298920930150221871666297194395061462592781551275161695411167049544771049769000895119729307495913024360169904315078028798025169985966732789207320203861858234048872508633514498384390497048416012928086480326832803
Calculate (q-1)/2
exp = (q - 1) // 2
Compute a^(exp) mod q using python's built-in modular expo.
result = pow(a, exp, q)
Output the result
print(result)
i ran this code on python
and it crashed
gg
trail mango
that's quite the code
distant scarab
somebody run this
pow cant even hold 3 values
hasty mist
trail mango
bleak jay
yeah im gonna gts
hasty mist
bleak jay
goodnight 
hasty mist
bleak jay
distant scarab
yeah id sleep too
hasty mist
bleak jay
yeah id sleep too
dab me up
candid hull
that q ain't even fking prime
trail mango
is q prime
hasty mist
Bruh
trail mango
sagemath says it is not
hasty mist
Itβs not
trail mango
i got 12198191382510180130171785779099635405775646886012417221562882673911806474...
plus if it was prime i wouldn't have gotten this answer
trail mango
undeniable fact
hasty mist
Can we please get me helpful already
trail mango
same
trail mango
anyway you can compute these pretty simply in sage.
a = 3
q = 7
R = Integers(q)
x = R(a)^((q-1)/2)```it works fine with big boi numbers
exponentiation is FAST
there's even a built in legendre symbol function too
but just wanted to show exponentiation is fast
hasty mist
oily_flapjacks
candid hull
too much oil for oiler
hasty mist
final saddleBOT
@distant scarab Has your question been resolved?
tranquil lake
even odd decomposition is pretty cool. but I want to understand how the equations get derived
I get the algebra basics of even vs odd, but I want to understand this follow up
final saddleBOT
even odd decomposition is pretty cool. but I want to understand how the equation...
bleak granite
even odd decomposition is pretty cool. but I want to understand how the equation...
A function (f(x)) is called even" if and only if \(f(-x)=f(x)\iff f(x)-f(-x)=0\). Also a function \(f(x)\) is called odd" if and only if (f(-x)=-f(x)\iff f(x)+f(-x)=0).
In general if we have some function, take (f(x)) again, then we can construct another function (O(x)=\frac{f(x)-f(-x)}{2}) which will always be odd. This comes right from the idea that (f(x)-f(-x)) encodes oddness. Simiarly, define (E(x)=\frac{f(x)+f(-x)}{2}) which will always be even. If you add them then you get back the original function (f(x)=E(x)+O(x)).
As a side note, if (f(x)=e^x) we can actually get the functions (\sinh(x)) and (\cosh(x)) in this way, but that is by definition of those latter functions.
soft zealotBOT
Ξ Ξ±Ο³Ξ±ΞΌΞ±ΞΞ±ΞΌΞ±Ξλαμα
tranquil lake
so sinh(x) is the odd signal from e^x
bleak granite
oh whoops I flipped the order 
but the idea still stands
formal trail
similarly you also get cos(x) and i sin(x) by applying to e^(ix)
tranquil lake
woah
Is there a calculus-y way for finding that E(x) = f(x) + f(-x) / 2
Like how did they get it in the first place
formal trail
you can think of it via the taylor series
taking f(-x) keeps all the even terms the same and flips the signs of all the odd terms
so taking the taylor series of f(x) + f(-x) , all the even terms add up (so now they are doubled) and all the odd terms cancel
tranquil lake
A function \(f(x)\) is called ``even" if and only if \(f(-x)=f(x)\iff f(x)-f(-x)...
also thank you very much! this is very well written even clearer than the textbook I'm looking at
(signals and systems on libre text)
bleak granite
higher's taylor explanation is another good justification
formal trail
you can think of it via the taylor series
and the even-odd decomposition is literally just taking the even and odd powers from the taylor series respectively
bleak granite
perhaps less ad hoc than mine
tranquil lake
I saw that
1/2 ( f(x) + f(-x)+ 1/2 (f(x) - f(-x)) easily simplifies to f(x)
since 1/2 f(-x) - 1/2 f(-x) = 0
and 1/2 (f(x) + 1/2 (f(x) = f(x)
tranquil lake
so taking the taylor series of f(x) + f(-x) , all the even terms add up (so now ...
I don't have a strong enough understanding of Taylor series to really understand what you are saying π
opaque ember
I don't have a strong enough understanding of Taylor series to really understand...
write out the taylor series of f(x) and f(-x) then add them
formal trail
,, e^x = \frac{x^0}{0!} + \frac{x^1}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + \frac{x^4}{4!} + \frac{x^5}{5!} + \cdots \
e^{-x} = \frac{x^0}{0!} - \frac{x^1}{1!} + \frac{x^2}{2!} - \frac{x^3}{3!} + \frac{x^4}{4!} - \frac{x^5}{5!} + \cdots \
\cosh x = \frac{x^0}{0!} + \frac{x^2}{2!} + \frac{x^4}{4!} + \cdots \
\sinh x = \frac{x^1}{1!} + \frac{x^3}{3!} + \frac{x^5}{5!} + \cdots \
\begin{multlined}
e^x + e^{-x} = \ab(\frac{x^0}{0!} + \frac{x^1}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + \frac{x^4}{4!} + \frac{x^5}{5!} + \cdots) \ + \ab (\frac{x^0}{0!} - \frac{x^1}{1!} + \frac{x^2}{2!} - \frac{x^3}{3!} + \frac{x^4}{4!} - \frac{x^5}{5!} + \cdots) \ = 2\frac{x^0}{0!} + 2\frac{x^2}{2!} + 2\frac{x^4}{4!} + \cdots = 2\cosh x
\end{multlined} \
\begin{multlined}
e^x - e^{-x} = \ab(\frac{x^0}{0!} + \frac{x^1}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + \frac{x^4}{4!} + \frac{x^5}{5!} + \cdots) \- \ab(\frac{x^0}{0!} - \frac{x^1}{1!} + \frac{x^2}{2!} - \frac{x^3}{3!} + \frac{x^4}{4!} - \frac{x^5}{5!} + \cdots) \= 2\frac{x^1}{1!} + 2\frac{x^3}{3!} + 2\frac{x^5}{5!} + \cdots = 2\sinh x
\end{multlined}
soft zealotBOT
cloud β
opaque ember
big tex whiplash
formal trail
i just wrote out the algebra for e^x but the same arithmetic would apply to any taylor series
hasty mist
Anytime
tranquil lake
(In the mean time I was watching 3b1b to remind myself of Taylor series since my calc class only briefly brought them up and I haven't used one in a few months)
.close thank you all!!
final saddleBOT
final saddleBOT
Available help channel!
late spoke
final saddleBOT
late spoke
CAN SOMEONE HELP ME WITH THIS MATH QUESTION PLZ?
proper dagger
,rccw
soft zealotBOT
late spoke
Huh....?
rugged merlin
CAN SOMEONE HELP ME WITH THIS MATH QUESTION PLZ?
Why the urgency lol
proper dagger
CAN SOMEONE HELP ME WITH THIS MATH QUESTION PLZ?
SURE THING. WHAT HAVE YOU TRIED?
(try unsticking your caps lock!)
proper dagger
what is the topic being tested here
late spoke
Algebra
proper dagger
and what are the other questions like?
well yea it's algebra alright, but what topic in algebra? reasoning? modelling?
also, again, what are the other questions like?
late spoke
(don't mind the other stuff) but this is the rest of the paper
soft zealotBOT
proper dagger
so from my understanding you're being asked to say if it is a valid statement to make
late spoke
well yea it's algebra alright, but what topic in algebra? reasoning? modelling?
I think moddeling
But like i don't get the equation
And I don't know what x is
rugged merlin
And I don't know what x is
Well, you can definitely notice that the equality won't hold for all values of x, right? As seen simply by x = 0 with 4 = 0
proper dagger
can you use algebra to find one value of x? are there any others?
late spoke
My teacher just started teaching us of algebra a week ago
but
I'll try the equation again
rugged merlin
My teacher just started teaching us of algebra a week ago
Do you know how to isolate a variable on one side of the equation?
An example might do you well here.
late spoke
No T w T
proper dagger
have you learnt about equation balancing then?
late spoke
X would be two then
proper dagger
good, but how did you get to that conclusion?
late spoke
Cuz 7 - 5 is 2
proper dagger
and what gave you the right to subtract 5?
the steps are more important than the answer here
rugged merlin
Take the equation [
3x - 5 = 10
]
Our first step is to isolate the $3x$ on one side of the equation. To do so, you can add 5 to both sides:
[
3x-5\0b{{}+5} =10 \0b{{}+5} \Implies 3x = 15
]
proper dagger
you missed a 10 somewhere
soft zealotBOT
rugged merlin
Yeah fixed
proper dagger
OP, pay attention to this very step
note that in algebra, if you do something to one side, you must do it to both
this is the step I was testing you about
late spoke
the steps are more important than the answer here
Well, I know that when I use addition when I add 2 to five that makes seven so when I look at x + 5 = 7 then I think that's just phrasing the equation differently and using a different operation
proper dagger
you are correct in this simple case
but suppose you have x + 5 = 6x instead
now you cannot simply eyeball a solution
this is where equation balancing (aka the "do to one side = do to both" principle) comes into play
late spoke
My teacher told me a method of finding an answer is guess and check
proper dagger
oh nonononono.
late spoke
I'm scared-
proper dagger
you don't have the luxury of taking 10 years per question
and come on. there IS a better method - algebra!
you learn algebra precisely so that you don't have to do it by trial and error
ok so the basic idea in all of algebra is equation balancing
late spoke
Okay
proper dagger
which I've been drilling over and over here
now, why is this so important, you might ask
proper dagger
take this example
maybe you can eyeball a solution directly. maybe you can't. but we don't care because we don't need to guess.
we can simply isolate x (that is, turn the equation into x = something)
the first step is already shown here (adding 5 to both sides)
but you now have 3x on the left instead of x
late spoke
But how do I turn x into something if that something is not what x is supposed to be-
proper dagger
But how do I turn x into something if that something is not what x is supposed t...
see, by isolating x, you are in fact finding the one value that could apply to x!
in fact, not could, but must
late spoke
Ohh
WAIT
SO IF I JUST TAKE AWAY X
AND DO THE REST OF THE EQUATION
THEN I COULD POTENTIALLY FIND OUT EHAT X IS
proper dagger
hold up, what are you thinking
late spoke
X*
proper dagger
show an example please
late spoke
So the question I'm stuck on
proper dagger
mhm
proper dagger
7x*
late spoke
Okay
proper dagger
now, you give me $4
late spoke
Okay
proper dagger
with your money, I have an amount of money equivalent to seven packets of money
so x here represents the amount in one such packet of money
now, to solve this one, you'll have to bring the two x's to the same side of the equation
this is most easily done by subtracting 3x from both sides of the equation.
can you see why that works?
if this is confusing we can go back to Lex's example
proper dagger
as I've mentioned, the steps are more important than the answer
proper dagger
and no, I will not accept guess and check as a method
late spoke
3x +4 = 7x
SO
YK THE +4
JUST DO THAT
BUT LIKE YOU MENTIONED
MOVE TO THE OTHER SIDE
AND THIS MADE ME THINK BACK
proper dagger
you can chill off the caps lock lolz
proper dagger
nw
late spoke
And she said
proper dagger
continue
late spoke
You have to turn the operation into its opposite when you are placing it on the other side
late spoke
Cuz your doing the equation backwards right
proper dagger
not... exactly
proper dagger
You have to turn the operation into its opposite when you are placing it on the ...
ok focus on just this one sentence and nothing else
late spoke
Okay
proper dagger
why is it that you use the inverse operation when you move an operator and its operand to the other side?
late spoke
It's cuz your like
Doing the equation backwards, like you would in like for your example earlier x + 5 = 7
Me doing
proper dagger
doing the equation backwards may explain why we need to move stuff to the other side
but it does not explain why we use inverse operations
for example
late spoke
HOW DO I EXPLAIINNNN
proper dagger
x + 5 = 7, right?
why can't we say x = 7 + 5? why must it be x = 7 - 5?
if you can answer this one question, you are set for most of algebra
proper dagger
how so
proper dagger
not too bad of an explanation but unfortunately I was looking for something more specific
late spoke
The answer is to the equation is SUPPOSED to be 7
proper dagger
in fact, the answer I'm looking for is exactly what you're doing when you "move" terms from one side to the other
right, I think enough beating around the bush
late spoke
Since the answer to the equation is supposed to be seven you can't ADD to seven
Then that wouldn't be the answer
proper dagger
that still doesn't cut to the heart of the problem
late spoke
I'm sorry
proper dagger
but it's ok, that's why we're here
late spoke
I would type in caps but you told me to cut back on that
proper dagger
the answer as to why you flip the operations / use the inverse operations when moving from one side to the other is because you are doing the same thing to both sides
suppose you want to know the answer to x + 5 = 7
you don't know that x = 2 beforehand and you dw to guess and check
but you know that if you manipulate the equation to say x = something, then you have the value of x for which the original equation works
now, that +5 is getting in the way of that at the moment
we would really want to remove the +5 so that the x stands alone
and what do we do to remove the +5? we subtract 5.
late spoke
Ohhh
proper dagger
but wait! equations are like a pair of balancing scales. if you do one thing to one side, it will now become unbalanced
late spoke
Ooooohhh
proper dagger
therefore, you balance it by subtracting 5 from the other side as well
but let's see what happens after that
proper dagger
and this is precisely why we "flip" the operations when moving it over to the other side
we are not actually flipping the operations per se
we are just doing the inverse of those operations so that the original and inverse operations on our chosen side cancel to leave x alone
but by doing so we also need to rebalance the equation by doing the same to the other side
proper dagger
late spoke
I owe you my first born if that's how it works
proper dagger
no thank you LMAO
proper dagger
Also I'm writing down your explanation in my notes
you could have asked
here, my personal notes
late spoke
I'm crying your so nice
proper dagger
nps
late spoke
You have to be like a college professor
Also
what do you mean it holds up will uni
Till*
does it change in uni?
final saddleBOT
If you are done with this channel, please mark your problem as solved by typing .close
late spoke
.close
final saddleBOT
final saddleBOT
Available help channel!
untold wagon
final saddleBOT
untold wagon
I know the E[X] = 1/p
with the PMF defined as P(X=k) = p^(k-1) * p
what's an approach to calculate the variance tho?
Maybe there's a formula? But not sure how to derive it
rugged merlin
Maybe there's a formula? But not sure how to derive it
Yea
Yk
,, \Var[X] = \vb E[X^2] -\vb E^2[X]
untold wagon
Yes I know this property
soft zealotBOT
atomic moon
But we need E[X^2]
You can do it with the transfert formula
sonic crystal
yakuuuuuuuuuuu
rugged merlin
You can then recover it by [
\vb E[X^2] = \vb E[X(X-1)] + \vb E[X]
]
soft zealotBOT
final saddleBOT
final saddleBOT
Available help channel!
marble vale
So, expanding a number is easy
4Β² = 4*4 = 16
But what if I need to go back from 16 to 4 and I don't know that 4Β² = 16? Is there a formula for that?
final saddleBOT
So, expanding a number is easy
4Β² = 4*4 = 16
But what if I need to go back from...
rugged merlin
So, expanding a number is easy
4Β² = 4*4 = 16
But what if I need to go back from...
Yes
Its called the square root function
It is the "inverse" of the squaring operation
,align
4^2 &= 16 \
\3{16} &= 4
soft zealotBOT
rugged merlin
As you dee the first line starts from 4 and gives you 16, the second line starts from 16 and gives you 4
marble vale
Sure
But what if I don't know that 16 = 4Β²? Putting a sign wouldn't help me
rugged merlin
Sure
But what if I don't know that 16 = 4Β²? Putting a sign wouldn't help me
What does "putting a sign" mean
But I mean, that's why the square root function exists
You dont have to know (although you should)
For example 29929 = 173^2
You probably did not know that but you dont need to
,w sqrt(29929)
soft zealotBOT
rugged merlin
The square root function just tells you
marble vale
What does "putting a sign" mean
The symbol before 16
rugged merlin
Like you are asking how to compute a square root then, I guess?
marble vale
The square root function just tells you
I won't have access to internet on an exam though
rugged merlin
It comes from knowing your squares, yes
marble vale
Like you are asking how to compute a square root then, I guess?
Probably
rugged merlin
Like yeah I wouldnt know that sqrt(29929) = 173 either
marble vale
x Γ x = 16
x = ?
marble vale
It comes from knowing your squares, yes
Which squares should I memorize then?
rugged merlin
I won't have access to internet on an exam though
Id recommend you memorise 1^2 to 20^2. Anything else (besides multiples of 5) would take you work to figure out
marble vale
Id recommend you memorise 1^2 to 20^2. Anything else (besides multiples of 5) wo...
And what about Β³, β΄, etc? Should I do those too?
marble vale
x Γ x = 16
x = ?
What are you guys laughing at? π
rugged merlin
Id recommend you memorise 1^2 to 20^2. Anything else (besides multiples of 5) wo...
I mean i have 1^3 to 10^3 memorised but not anything after that
Oops wrong reply
lilac moat
What are you guys laughing at? π
Because having three x's in a row looks funny
Generally, we would write xΒ² = 16 instead of x Γ x = 16
marble vale
I mean i have 1^3 to 10^3 memorised but not anything after that
And what about β΄, β΅, etc?
rugged merlin
Well $x^4$ is in reality $(x^2)^2$ so I can work it out from that
^5 I wouldn't know at a glance
Unless its a power of 10
soft zealotBOT
marble vale
I picked a number from 1 to 20 and put it in (xΒ²)Β²
rugged merlin
No sane teacher would expect you to either
marble vale
So, I should
Β² - from 1 to 20
Β³ - from 1 to 10
And then just say that's enough?
ornate knot
28,561
u could factorize the number and then find groups of 2 numbers
to find the sqrt of 28561
marble vale
u could factorize the number and then find groups of 2 numbers
How?
ornate knot
rugged merlin
So, I should
Β² - from 1 to 20
Β³ - from 1 to 10
And then just say that's enough...
I mean all the discussion above has been relating to answering what the square/cube root of a number is at a glance
To do that you should probably memorise those yes
Otherwise youd need to do work by noting down the prime factors of the number
boreal smelt
What should I do in this question?
final saddleBOT
What should I do in this question?
desert mantle
probably split (t^2+5)^(n+1) as (t^2+5)^n * (t^2+5) and use ibp
boreal smelt
I was trying to solve for n=1
but how do I integrate $I_2 = \int_{0}^{x} \frac{1}{(t^2 + 5)^2}$
soft zealotBOT
Prathmesh
left echo
Integration by parts works fine
Differentiate 1/(t^2 + 5)^n and integrate 1
You'll end up with $I_n = \frac{x}{(x^2 + 5)^n} + 2n \int_0^x \frac{t^2}{(t^2 + 5)^{n+1}}\dd{t}$
soft zealotBOT
jewels!
left echo
Inside the integral do a + 5 - 5 and after a bit of moving things around you'll have what you need
tiny kraken
final saddleBOT
tiny kraken
Okay so, the question here is not exactly what I want to ask
But a slightly different version of it, what if we're allowed move diagonally to the left
Then how would I do the problem
left echo
How did you do it originally?
glossy zephyr
oh no right mb you end up with 3 options per
woven ledge
maybe fill in each letter with the number of ways to get to it
Hmm
woven ledge
Oh no recussive
recursion isnt allowed?
bold turtle
diagonally to the left is not mentioned here
tiny kraken
recursion isnt allowed?
Not really, just that the topic is addition and multiplication
bold turtle
And also, you should recognise what pattern you end up with if you do what CherryMan is suggesting
woven ledge
maybe fill in each letter with the number of ways to get to it
i mean id do it this way
tiny kraken
_diagonally to the left_ is not mentioned here
yeah, I asked a slightly different version of it
desert mantle
Not really, just that the topic is addition and multiplication
and if you change the question then you cant always expect to still be able to solve it with the same method
bold turtle
You're not really doing anything more complicated than adding three numbers together at a time, in order to generate the structure
tiny kraken
and if you change the question then you cant always expect to still be able to s...
Hmm, yeah you're right
okay thanks y'll
.close
final saddleBOT
pliant shore
maybe fill in each letter with the number of ways to get to it
goated method
woven ledge
And also, you should recognise what pattern you end up with if you do what Cherr...
trinomial triangle π―
tiny kraken
I would love a method that can get me answer in a single calculation
That was what I looking for lol
bold turtle
That requires overgeneralisation, to an extent that it's like the "Bill Gates with a massive ping pong paddle" meme
desert mantle
well there is a solution to the recursion
final saddleBOT
β Original question: #help-36 message
desert mantle
but thats just overcomplicated
desert mantle
all linear recursions are solvable
tiny kraken
all linear recursions are solvable
Yeah you're right
Wait, so just solve the recursions ?
tiny kraken
Wait, so just solve the recursions ?
Okay i'll try, I'll be back if I'm stuck thanks
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tiny kraken
It would be great if someone can check my working of this problem
final saddleBOT
It would be great if someone can check my working of this problem
tiny kraken
So took the base case when all the diagonals are drawn from a vertex to others
Then I generated other cases by rotating one diagonal at the time
After n-3 rotations, all the diagonals should be drawn from the next vertex to others
Repeat this process n times
chilly pollen
Notice that we always have to choose two consecutive sides, for two of the triangles
@tiny kraken The remaining triangles always contain only one side of the polygon for an n-gon
desert mantle
one problem with your approach is that
- its not clear that you indeed get every option
- its not clear that you get every option exactly once
pliant shore
that's two problems, mr can't count /j
desert mantle
I'm a mathematician, of course I cant count
tiny kraken
one problem with your approach is that
- its not clear that you indeed get every...
Hm, so is it wrong? or do I need to reason for that
desert mantle
dunno about wrong. but those things are certainly problematic and without addressing those its definitely not right
tiny kraken
Notice that we always have to choose two consecutive sides, for two of the tria...
sorry the chapter is addition and multiplication so don't really want to use combinations
chilly pollen
mb. Looked combinatorial
tiny kraken
dunno about wrong. but those things are certainly problematic and without addres...
okay I'll fix it, gimme min
if it's possible
you're right it is wrong 
I'll deal with this problem tomorrow then, it's late here
Thank you all
icy tulip
sorry the chapter is addition and multiplication so don't really want to use com...
so principle of counting?
tiny kraken
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icy tulip
its ez
tiny kraken
I don't want to rely too much on the technique
I meant rely on combinations if that makes sense lol
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steady vale
hello! i was wondering if this is legal math
final saddleBOT
hello! i was wondering if this is legal math
steady vale
i just wanna confirm that the way i did it is okay to do
loud sundial
hello! i was wondering if this is legal math
You're taking the natural log of both sides, not multiplying both sides by ln
looks fine other than that
continuity
steady vale
You're taking the natural log of both sides, not multiplying both sides by ln
ohhh thanks for the clarification, iβll make sure to fix that!
thanks so much!!
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crisp spade
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crisp spade
In the computation of the curvature of this curve, why is the absolute value of the denominator taken?
Stupid question
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quiet garden
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gleaming spear
Looks good so far
quiet garden
Looks good so far
itβs right answer then?
gleaming spear
Well you're not really done yet, still 1 step to do
quiet garden
What step
gleaming spear
The answer should be a number, but you have x and y
quiet garden
The answer should be a number, but you have x and y
I donβt see where they give me it
gleaming spear
||The first line of the question||
quiet garden
I change it to sin(u+v)?
gleaming spear
Yeah, given it's =x
quiet garden
Yeah, given it's =x
Ok I got 2e is that right
gleaming spear
Seems good to me
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@quiet garden Has your question been resolved?
next wraith
alright i need help
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alright i need help
glossy zephyr
!da2a
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No need to ask βCan I askβ¦?β or βDoes anyone know aboutβ¦?ββitβs faster for everyone if you just ask your question!
next wraith
im typing the instructions
theres a quadrilateral that can have a circle inside it, AD=a, AB=2a. then theres a line that divides ADC in half, and it intersects AC at point E: AE/CE=2/3. the perimeter is 84 and cosADC=1/16
plucky rover
Well the first step would be to draw a diagram
next wraith
and i need to find the radius of 2 circles, triangle ACD is inside circle 1 and triangle ABC is inside circle 2
its like that ig
so uh now idk, any clue would be helpful, im awful at geometry
plucky breach
i thinnk you could use incenter theorm for this
next wraith
incenter?
plucky breach
its the meeting point of 3 medians
its the same distance from all sides
so you could find incenter
then plug both incenter andd the point perpendicular to it on a line to find the radius
next wraith
can you walk me through it? im not familiar with it