fresh ocean
and that makes the curve QP a 60 degree arc of circle
#help-41
amber waspBOT
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elfin kayak
I need help w this using elimination method for non linear equations
verbal siren
Value of x substitue in 4x-y=-1 eqn you will get the value of y
simple
verbal siren
You can do that way also but lengthy becasue of sloving many times x and x2 terms
In eqn 2 less terms so easy
elfin kayak
What do I do if my x looks like this tho?
verbal siren
You will get 2 values
verbal siren
Slove them simple maths i guess
verbal siren
If x vlaue is in square root then you will get y also in sqaure root terms only
But if you want excat values then use the calcultors or any standard values for the near values
elfin kayak
But if you want excat values then use the calcultors or any standard values for ...
Ok idk how to solve it π
rancid raven
Use calculator to find value of β13
Then it's just multiplication division addition subtraction
elfin kayak
even if it's decimal?
rancid raven
Or if you want to keep it in β form
rancid raven
Then simplify a bit more
elfin kayak
aight
rancid raven
even if it's decimal?
Does your question ask you to get it in decimal form?
elfin kayak
I dont get it im sorry
rancid raven
Its ok no need to say sorry π
elfin kayak
oh okay
rancid raven
Do you know fraction addition subtraction?
elfin kayak
yeah
elfin kayak
I forgot how to solve fractions πΏ
rancid raven
elfin kayak
So you will make -1 into -1/1? then solve
which I forgor how
I mostly focus on other subjects im sorry
rancid raven
Can be written as
2/3 -1/1
Multiply 3 in numerator and denominator of 1/1
2/3 - 3/3
(2-3)/3
-1/3```I remember it being multiplied by numerator then divide it by idk
rancid raven
Can be written as
a/b -1/1
Multiply b in numerator and denominator of 1/1
a/b - b/b
(a-b)/b```ty
rancid raven
No problem
rancid raven
ty
Just remember you have found out -y = ...
At the end you need to multiply left and right with -1
To get y = ....
rancid raven
Cool
elfin kayak
um now that it turned into 4+8sqroot((13)) - 3/ 3 what now do I still solve it... if so idk how
rancid raven
um now that it turned into 4+8sqroot((13)) - 3/ 3 what now do I still solve it.....
(4+8β13-3)/3
4-3=1 so
(1+8β13)/3
elfin kayak
why only 4 is subtracted
rancid raven
Because you can't subtract a perfect number from root
elfin kayak
oki thnx
rancid raven
8β13-3 ? It will only make sense once you convert β13 to decimal
rancid raven
if I somehow turn that into decimal what will happen to 8?
Multiply
rancid raven
8β13 = 8xβ13
elfin kayak
should I just turn it into decimal? since x and y is represented as points
rancid raven
should I just turn it into decimal? since x and y is represented as points
You can if you want but it all depends what is being asked in question
Sometimes it's written give answer to decimal place or something
Sometimes just find x,y
elfin kayak
well with how our teacher solved the other given there was still a square root..
Ig I should leave it as is lol
rancid raven
Yep
elfin kayak
thank you!
rancid raven
No problem
amber waspBOT
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languid whale
Can someone check my work
amber waspBOT
Can someone check my work
languid whale
inland pulsar
Hey
Is there a relation given between V, y, x, z?
If not I think you can assume them to be independent of V
And just take them outside the integral
@languid whale
languid whale
wym V?
I pressumed we can set up an integral using any of these bounds in any order
Inner = dy
Middle = dx
Outter = dz
Thats the order in which I tried to solve it
(((y^2(sin(3x+2z)))dy)dx)dz)
amber waspBOT
@languid whale Has your question been resolved?
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wet depot
The value of 6+log 3 2 sqrt 1 3 sqrt 2 sqrt 4 - 1/(3sqrt(2)) sqrt 4- 1 3 sqrt 2 sqrt 4- 1 3 sqrt 2 ... ) is
wet depot
The value of 6+log 3 2 sqrt 1 3 sqrt 2 sqrt 4 - 1/(3sqrt(2)) sqrt 4- 1 3 sqrt 2 sqrt 4- 1 3 sqrt 2 ... ) is
mint nacelle
The value of 6+log 3 2 sqrt 1 3 sqrt 2 sqrt 4 - 1/(3sqrt(2)) sqrt 4- 1 3 sqrt 2 ...
this is unreadable
amber waspBOT
@wet depot Has your question been resolved?
granite shard
The value of 6+log 3 2 sqrt 1 3 sqrt 2 sqrt 4 - 1/(3sqrt(2)) sqrt 4- 1 3 sqrt 2 ...
send a foto.
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final wyvern
Hello, I'm currently studying the Mann Whitney U Test as I'm looking for non parametric testing in our research, question: how were they able to rank this? how did decimals appear out of nowhere?
mint nacelle
Hello, I'm currently studying the Mann Whitney U Test as I'm looking for non par...
so those decimals come from when you are breaking tied ranks
say if you have 10, 20, 20, 30 and 10 is rank number 4
30 is rank number 7
so (4 + 7)/2 = 5.5
both 20s have rank number 5.5
final wyvern
both 20s have rank number 5.5
why'd they skip 5 and went ahead to 6
mint nacelle
why'd they skip 5 and went ahead to 6
originally you have 3, 4, 5, 6
with the tied ranks you have 3, 4.5, 4.5, 6
does that make sense?
and then same thing, 6, 7, 8, 9 becomes 6, 7.5, 7.5, 9
final wyvern
and then same thing, 6, 7, 8, 9 becomes 6, 7.5, 7.5, 9
i see the pattern, but why that way
final wyvern
with the tied ranks you have 3, 4.5, 4.5, 6
is it because 4.5 + 1 = 5.5 then when rounded = 6?
mint nacelle
i see the pattern, but why that way
- you don't want to change the number of entries
- you want both values to be the same
- you want the tied rank to be equidistant to 3 and 6, or 6 and 9
mint nacelle
is it because 4.5 + 1 = 5.5 then when rounded = 6?
no
final wyvern
1) you don't want to change the number of entries
2) you want both values to be ...
oh i see it especially no 3
1.5 + 1.5 = 3 units
mint nacelle
yes!!
final wyvern
another question:
when do we know that theres either a separation or
an even distributionm
and lastly, is there a non-parametric test that can utilize big samples?
mint nacelle
and lastly, is there a non-parametric test that can utilize big samples?
if you have large samples you can approximate the data using a normal distribution
mint nacelle
when do we know that theres either a separation or
just look at your data
a complete separation means that the highest value of dataset 1 is lower than the lowest value of dataset 2
or vice versa
and evenly distributed mean that you get patterns like ABABBABAB
instead of the complete separation AAAAABBBBB, if you rank them from lowest to highest, or highest to lowest works as well
mint nacelle
if you have large samples you can approximate the data using a normal distributi...
oh wait forgot to post what m and n are
final wyvern
i see
so the data set here i assume is placebo and new drug
does this mean equal distribution kasi its not complete separation
mint nacelle
does this mean equal distribution kasi its not complete separation
it still looks fairly separated
but it doesn't mean it's equally distributed or a complete separation
final wyvern
it still looks fairly separated
how so
mint nacelle
basically new drug = 6 is the only value that stands out
also we do have placebo = 4 and new drug = 4 so it's not completely separated
nevertheless most data will not be as separated as this
it's like about 80 to 90% separated I'd say
final wyvern
basically new drug = 6 is the only value that stands out
stand out in the sense that..?
im sorry im asking a lot
mint nacelle
stand out in the sense that..?
as in, if you remove the 6
then you would have [1, 2, 3, 4] and [4, 5, 6, 7, 12]
final wyvern
as in, if you remove the 6
what happens
final wyvern
so like
mint nacelle
but they are the same value
final wyvern
stand out in the sense that they appear in both datasets
mint nacelle
stand out in the sense that they appear in both datasets
stand out as in that 6 is an inconvenience, if you get what I mean
from making it be separate
final wyvern
stand out as in that 6 is an inconvenience, if you get what I mean
i still dont get it, im sorry π
is it like context based?
mint nacelle
is it like context based?
yeah it's subjective
the thing you posted just took two extreme cases of what can happen with the data
final wyvern
yeah it's subjective
so its 6 because its the most amount of episodes?
mint nacelle
I would rephrase it as, the more the data are separated, the closer U will be to 0
and the more the data are mixed together, the closer U will be to the maximum possible value
something like (n1 * n2)/2 or whatever
oh N(N + 1)/2 where N is the total number of observations
final wyvern
oh N(N + 1)/2 where N is the total number of observations
gotchu
final wyvern
then you would have [1, 2, 3, 4] and [4, 5, 6, 7, 12]
what makes placebo = 6 not stand
mint nacelle
what makes placebo = 6 not stand
cause 6 is in the middle of [4, 5, 6, 7, 12]
but 6 is an outlier in [1, 2, 3, 4, 6]
final wyvern
but 6 is an outlier in [1, 2, 3, 4, 6]
what makes nd = 1 and placebo = 12 and 4 not stand out
final wyvern
what makes nd = 1 and placebo = 12 and 4 not stand out
question still stands
mint nacelle
it's the fact that 6 is an outlier in the new drug dataset
AND the fact that it would be in the middle of the placebo dataset
so that means that 6 is a 'mixed' value
final wyvern
final wyvern
does the table show that literallyβ the 6 is separated from 1-4
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fallow oriole
What are the points (-24, 12) after the transformation of
y = 3\sqrt{f(-x + 2) + 4} - 1?
fallow oriole
<@&286206848099549185>
mint nacelle
What are the points (-24, 12) after the transformation of
y = 3\sqrt{f(-x + 2) ...
do you know what f(x) is?
also only ping helpers after 15 mins
fallow oriole
My bad
fallow oriole
do you know what f(x) is?
Same as y?
mint nacelle
no, like is the function f(x) given to you?
fallow oriole
No they just gave me the points of (-24,12) after I create a mapping rule I guess
mint nacelle
What are the points (-24, 12) after the transformation of
y = 3\sqrt{f(-x + 2) ...
I guess choose a mapping rule where you don't use sqrt()
fallow oriole
Wym?
mint nacelle
Wym?
doing something like this would be easier
the problem with the square root is that it's not a neat transformation
it will change the point differently depending on where in the coordinate plane it is
mint nacelle
whereas this transformation only moves everything in the x- and y- directions the same amount
only stretches everything in the x- and y-directions by the same amount
amber waspBOT
@fallow oriole Has your question been resolved?
keen pawn
amber waspBOT
quick spoke
what have u done so far?
amber waspBOT
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lapis acorn
Hello
lapis acorn
I need some help on trig limits
night ember
I need some help on trig limits
yes?
lapis acorn
If vc is possible that would be super super appreciated
12/13 on the first one
My trig in general is not great at all
And I really need help with trig limits because I have understand most of everything else
Just trig identities and functions I donβt have a good understanding of
Even after watching multiple videos
amber waspBOT
@lapis acorn Has your question been resolved?
past ibex
I understand that the correct answer is 4/3 > x but why would my operations not work?
amber waspBOT
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normal dove
cant find a solution online which i can understand
amber waspBOT
cant find a solution online which i can understand
normal dove
You want to simplify that sum term?
solve for Summation in terms of n
i tried simplifying an everything to the best of my abilities but it only got uglier
amber waspBOT
@normal dove Has your question been resolved?
past wyvern
i tried simplifying an everything to the best of my abilities but it only got ug...
Im in the same situation
amber waspBOT
@normal dove Has your question been resolved?
deep raven
Given $\varphi = xy + yz + zx$ and $\vec{F} = {x^2y, -y^2z, z^2x}$.
Determine at the point $(3,-1,2)$:
$\vec{F} \cdot \nabla\varphi$
grizzled pagodaBOT
rainy
tulip tapir
are you sure about that? check the gradient again.
deep raven
ah
tulip tapir
after that, simply substitute the values of x, y, and z into F and grad(phi)
then take the dot product
amber waspBOT
deep raven
.reopen
amber waspBOT
β
deep raven
$\nabla\varphi \cdot \vec{F}$
grizzled pagodaBOT
rainy
deep raven
What if its like this now
I'd assume just take the dot product too
But the answer here is 10, not 5
π§
Nevermind, i didnt see phi is now on the left for the last one.
.close
sage chasm
im like mega confused on how to attempt this, i tried with schroder bernstein therom but idk if this makes sense
amber waspBOT
im like mega confused on how to attempt this, i tried with schroder bernstein th...
@sage chasm Has your question been resolved?
sage chasm
<@&286206848099549185>
coral wigeon
are you asking about how to do 2 or feedback on what you wrote for 1?
sage chasm
are you asking about how to do 2 or feedback on what you wrote for 1?
mostly feedback for 1 since i assume 2 is done the exact same way
coral wigeon
if fβs codomain is Z+ x Z+, it should output a pair of positive integers
not a pair consisting of a positive integer and another pair
the second part of the proof looks good. g is injective
lime verge
is that discrete math?
sage chasm
not a pair consisting of a positive integer and another pair
could i do something like... (x, y(a, b))?
sage chasm
is that discrete math?
yes it is
coral wigeon
if y is a function that maps to the positive integers then yea sure
the inputs to f would be x, a, and b
sage chasm
if y is a function that maps to the positive integers then yea sure
is there a different way to do it?
coral wigeon
if this was proved in lecture, the proof could be pretty similar probably
sage chasm
hmmm
it was used as a lemma but we werent shown the full proof
i could lowkey just google it and follow it no?
coral wigeon
oh actually i have an idea that uses that fact from lecture
that facts implies there is an injective function y from Z+ x Z+ to Z+
coral wigeon
could i do something like... (x, y(a, b))?
then you could use this
take two different triples (x_1, a_1, b_1) and (x_2, a_2, b_2) and show f(x_1, a_1, b_1) and f(x_2, a_2, b_2) are not equal
using the injectivity of y
does that make sense?
sage chasm
sort of ? the logic just isnt sitting with me idk
coral wigeon
Z+ and Z+ x Z+ are both countable so there is a bijection between them
which is also an injection
call it y, mapping Z+ x Z+ to Z+
coral wigeon
then you make a function f: Z+ x Z+ x Z+ to Z+ x Z+ defined by f(x,a,b) = (x, y(a,b)) and you want to show f is an injection
coral wigeon
take two different triples (x_1, a_1, b_1) and (x_2, a_2, b_2) and show f(x_1, a...
then do this to show it
sage chasm
and my g is ok ?
coral wigeon
yep
sage chasm
perfect !!! thank u so much
coral wigeon
sage chasm
.close
amber waspBOT
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weak lagoon
amber waspBOT
weak lagoon
Can someone help for number 74
rocky vapor
i think first try write theta as a function of s?
rocky vapor
But then do I just find the derivative of that after??
yeah dtheta/dt in terms of s
idk why h is marked (tho nothing is written about it in the question)
weak lagoon
yeah dtheta/dt in terms of s
So I can just use inverse derivatives right
rocky vapor
So I can just use inverse derivatives right
inverse trig derivatives , yeah?
rocky vapor
wait there is no t so this should be considered as a cconstant
weak lagoon
wait there is no t so this should be considered as a cconstant
wait wdym π
rocky vapor
wait wdym π
if ur differentiating with respect to t , the other variables are considered as constants
lets think this again 
weak lagoon
if ur differentiating with respect to t , the other variables are considered as ...
wait im so confused but we dont know t
rocky vapor
wait im so confused but we dont know t
yeah ik
maybe we make 2 functions
1 of tan and 1 of cos , and then chain rule
weak lagoon
okay so theta = arctan(h/800)
but im still confused on how to differentiate w respect to t
rocky vapor
but im still confused on how to differentiate w respect to t
me to , gotta think
rocky vapor
wait im so confused but we dont know t
yeah ok i got
we need to find in terms of ds/dt and s , so its chain rule
something like
dtheta/dt = ds/dt * dtheta/ds
so we find dtheta/ds and i thnk we should get our answer (do u have answer key ?:))
weak lagoon
so we find dtheta/ds and i thnk we should get our answer (do u have answer key ?...
no not for this question π i need to ask my friend later
rocky vapor
no not for this question π i need to ask my friend later
yeah i think we are on the right track , i didnt read the question properly
chain rules states
dtheta/dt = ds/dt * dtheta/ds
we leave ds/dt as it is , and calculate dtheta/ds
weak lagoon
chain rules states
dtheta/dt = ds/dt * dtheta/ds
we leave ds/dt as it is , and ...
wait then how would you do it then π im a bit confused
can you do step by step (please)
rocky vapor
wait then how would you do it then π im a bit confused
same as u did
first find the function in terms of s (cos thingy)
then seperate the theta , u get arccos (s/800)
chain rule states
dtheta/dt = ds/dt * dtheta/ds
we differentiate our function with respect to s , get dtheta/ds
and the rest , we keep it as it is (and u should have a answer consisting of s and ds/dt , which is what they need)
weak lagoon
ohhh okay i kind of get it i think
but you dont know ds/dt tho
like i know you have to multiply it by what i found
but like how do you find it
rocky vapor
but like how do you find it
ds/dt is basically change in distance during some time
weak lagoon
but what is it or do i just leave it as ds/dt bc it says in terms of
rocky vapor
but what is it or do i just leave it as ds/dt bc it says in terms of
Just leave itr likew that
It's basically velocity
ur question is to find dtheta/dt "in terms of s and ds/dt" and we did it
amber waspBOT
@weak lagoon Has your question been resolved?
uncut sand
Not sure where Iβm going wrong here
amber waspBOT
Not sure where Iβm going wrong here
vale marsh
,rccw
grizzled pagodaBOT
vale marsh
vertex is wrong. do it again
f(-1) = -(-1)Β² - 2(-1) - 5
not sure if the axis of symmetry should be x = -1 and not just -1 π€
do the range again
@uncut sand
uncut sand
Wait
vale marsh
X=2/-2 no?
this is for x. substitute value of x to find y
vale marsh
ok. so you already have x= -1. that is correct. now, susbtitute that to the equation to find y
-(-1)Β² - 2(-1) - 5
(-1)Β² = 1
2(-1)= -2
try it yourself
@uncut sand
amber waspBOT
@uncut sand Has your question been resolved?
subtle wind
This one is quick theoretical question... How can I know if a function f(x) >= x?
subtle wind
Like if I have to graph the inverse of a function and the line y=x, how would I know if it's under the line y=x or above or if it touches?
Please ping me if you guys know how to do this without having to do complicated mathematical induction π₯² tyy
pallid canopy
This one is quick theoretical question... How can I know if a function f(x) >= x...
depends on the function
subtle wind
depends on the function
what would be the best way of determining if a usual function like a quadratic or exponential and reverse exponential crosses the line y=x without having to substitute x?
.close
amber waspBOT
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Available help channel!
sterile cipher
Help how do I do this
amber waspBOT
Help how do I do this
celest cove
,rccw
grizzled pagodaBOT
celest cove
are you asking how to graph them
amber waspBOT
@sterile cipher Has your question been resolved?
sterile cipher
Yes
And how I even know what to graph like how do I use these equations to be able to graph
Something
@celest cove
celest cove
first get them into y=f(x) form
then do the usual, find any roots, any asymptotes, y intercept
once you have those put it together and draw the graph
amber waspBOT
@sterile cipher Has your question been resolved?
sinful sky
Consider the propositional formula
F=((Bβ¨C)β((Aβ¨Β¬B)β§C))β¨(Aβ§Β¬C)
Give a formula G that is equivalent to F, but in which each atomic formula A, B, and C
appears at most once. Prove that F β‘ G by providing a sequence of equivalence transformations with at most 12 steps.
Expectation. Your proof should be in the form of a sequence of steps, where each step
consists of applying the definition of β (that is F β G β‘ Β¬F β¨ G), the following rules: F β§ Β¬F β‘ β₯, F β§ β₯ β‘ β₯, F β¨ β₯ β‘ F, F β¨ Β¬F β‘ β€, F β§ β€ β‘ F, and F β¨ β€ β‘ β€. For this exercise, Each step of your proof should apply a single rule once and state which rule was applied.
I am afraid if I did the step 4 wrong Β¬Bβ§Β¬B. is it correct?
amber waspBOT
Consider the propositional formula
F=((Bβ¨C)β((Aβ¨Β¬B)β§C))β¨(Aβ§Β¬C)
Give a formula G...
@sinful sky Has your question been resolved?
fluid pecan
i need help with part (i)
amber waspBOT
i need help with part (i)
pallid canopy
how many ways are there to choose 2 distinct integers from {0, 1, ..., 9} ?
similarly for b
fluid pecan
how many ways are there to choose 2 distinct integers from {0, 1, ..., 9} ?
but thats 9c2, and rectange would need 4 points?
9c2*5c2?
sick sandal
but thats 9c2, and rectange would need 4 points?
Rectangles are uniquely determined by two of its diagonal corners.
fluid pecan
the answer is 675 btw, im not getting there
sick sandal
Rectangles are uniquely determined by two of its diagonal corners.
I.e. if you have a rectangle with corners (0, 0), (0, 1), (1, 0) and (1, 1), you need only (0, 0) and (1, 1) (or alternatively (0, 1) and (1, 0)) to determine the rest of the points.
amber waspBOT
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Available help channel!
shrewd tartan
I need help with c), i got part a but donβt know how to use that to show the equation in c
amber waspBOT
I need help with c), i got part a but donβt know how to use that to show the equ...
formal yacht
For a) what did you write in the numerator?
shrewd tartan
f(a+t) + f(a)
formal yacht
Is there a reason you used a+t and not the intended at?
formal yacht
Yeah, or atleast from what i can tell the problem wants it as
Do you see how?
We can sort of compare to the other def.
shrewd tartan
yea I see now
formal yacht
Alright neat
shrewd tartan
for c do i just multiply on the right ?
formal yacht
For c) i think it might be suitable if you just do that yea
formal yacht
It's not quite clear to me where e.g. t^(2n-1) came out of?
shrewd tartan
i was trying to do tβ’t^n-1
shrewd tartan
oh it would just be t^(n-1) right ?
formal yacht
Almost, think of it like this, if we have the same base (t in this case), then we just add the exponents
exponent laws or whatever theyre called
shrewd tartan
t^(n) ?
formal yacht
yup!
shrewd tartan
kk thanks !
formal yacht
ur welcome, see if that changes your calculation
formal yacht
Is the last line an equality with the above?
shrewd tartan
the first two lines should be the same
and the last line is once I cancelled out terms
formal yacht
Notice that you also have terms like t^(n-2) over from your first line
so that should be cancelled too
and in fact every other such terms
apart from t^n and -1
shrewd tartan
should i not have t^3 ?
formal yacht
Like would you agree that e.g. $t\cdot(t^{n-1}+t^{n-2}+\cdots+t^2+t+1)=t^n+t^{n-1}+\cdots+t^3+t^2+t$?
grizzled pagodaBOT
Aslan
formal yacht
and that $-1\cdot (t^{n-1}+t^{n-2}+\cdots+t^2+t+1)=-t^{n-1}-t^{n-2}-\cdots-t^2-t-1$ ?
grizzled pagodaBOT
Aslan
shrewd tartan
yes
formal yacht
so notice that when we combine these two
shrewd tartan
i got left with the terms t^n + t^3 - t^n-2 -1
formal yacht
i got left with the terms t^n + t^3 - t^n-2 -1
-t^n how?
formal yacht
**Aslan**
Do you see how this is t^n +... + 1 but without 1?
Or let me maybe make it less ambiguous with sum notation, are you comfortable with that?
formal yacht
hm im not sure, thats not clear to me atleast
is it okay if i try and explain it via sum notation?
shrewd tartan
sure
formal yacht
So basically we have that $t\sum_{k=0}^{n-1} t^k = \sum_{k=1}^n t^k$ right?
grizzled pagodaBOT
Aslan
shrewd tartan
maybe sum notation isnβt the best idea
formal yacht
Hm okay thats fine
formal yacht
does this make sense
well if you feel convinced by this, i'd say go with it
its just not terribly clear to me is all
shrewd tartan
i donβt get how we cancel out the t^3
shrewd tartan
i donβt see where it would be
formal yacht
im only limiting myelf from writing out all the terms, the dots here is meant to capture the notion that the terms continue like so
i.e if n = 1000
then it would be pretty hard to write this all out
unless we used sum notation
so the dots here (if thats the confusing bit) is meant to capture a pattern
i.e 1 + 2 + ... + n
implicitly assumes a pattern
that say 3 is a term in this sum
or 4
etc
shrewd tartan
yes, i agree, i donβt know how to show that on paper
i canβt cross it off physically
formal yacht
**Aslan**
right, and thats okay. We can argue differently. Because would u agree that -t^3 has to be in this subtraction?
shrewd tartan
yes
shrewd tartan
yup, and -1 right ?
formal yacht
-1 is right at the bottom
shrewd tartan
yes
formal yacht
So we have a bunch of powers of t, one being a sum of them which does not contain -1
while the other the substraction does not cointain t^n
combining these they should all cancel apart from t^n and -1
so we get t^n - 1
formal yacht
Yeah, but i think the parts before are still a bit fuzzy
like starting from the first line
where is the parenthesis at the end?
shrewd tartan
?
formal yacht
No worries
the following lines also make it a bit confusing, im not sure where it ends or start even though you have an equality, or stuff seems missing
shrewd tartan
should i write the next two lines on one line?
formal yacht
Yes if possible
amber waspBOT
@shrewd tartan Has your question been resolved?
shrewd tartan
yes
heavy python
amber waspBOT
heavy python
and y+Ξy is r
how
vestal hatch
Because it's a radius
amber waspBOT
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warm eagle
if we being real i have tried this over and over and cant get it
warm eagle
pls help man i suck at networks
i find https://csacademy.com/app/graph_editor/ is a good place to make these graphs quickly but im still just getting stuck with these questions
<@&286206848099549185>
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@warm eagle Has your question been resolved?
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@warm eagle Has your question been resolved?
warm eagle
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humble panther
guys i want to check, are these equal???
humble panther
shell osprey
the solutions? no?
austere pond
guys i want to check, are these equal???
so then set one equal to the other
obtuse bolt
guys i want to check, are these equal???
Set cos theta to x
Making 6x^2+x-1=0
Factor the equation
(3x-1)(2x+1) = 0
We have 2 solution x = 1/3 and -1/2
Cos theta = 1/3
And cos theta = -1/2
humble panther
but yo can rearange one to equal the other
you can rearange the second one to equal the first one
@obtuse bolt
humble panther
you can use tanx = sinx/cosx
obtuse bolt
Yeah
obtuse bolt
Yeah that's right then
humble panther
but when i sub a number in, lets say 3 i get different answers
obtuse bolt
What do you want to find here
I mean where is the original equation
And what do you want to find
humble panther
i want to find why aren't they equal when i sub it in
obtuse bolt
Which equation and which equation
humble panther
both of em
obtuse bolt
In first equation
obtuse bolt
the two ones at the satar
Owhhh
Here
Sin^2 +cos^2 = 1
Phytagoras theorem
That mean sin^2 = 1 - cos^2
Hope that help
pallid canopy
its just when i sub in 3, they don't equal
Can you show how you're substituting in 3?
Are you using a calculator or something else
obtuse bolt
Yeah Riemann will take care
grizzled pagodaBOT
Result:
0.5
Follow this template
humble panther
,calc 6cos^2(3) + cos(3) -1
grizzled pagodaBOT
The following error occured while calculating:
Error: Unexpected type of argument in function pow (expected: number or Complex or BigNumber or bigint or Fraction or Unit or Array or Matrix or string or boolean, actual: function, index: 0)
The following error occured while calculating:
Error: Unexpected type of argument in function pow (expected: number or Complex or BigNumber or bigint or Fraction or Unit or Array or Matrix or string or boolean, actual: function, index: 0)
humble panther
,calc 6(cos(3 deg))^2+cos(3deg)-1
grizzled pagodaBOT
Result:
5.9821952208594
Result:
5.9904048625295
see they're different
but they're the same thing just rearanged
the funny thing is when i don't square
,calc 6(cos(3deg) + cos(3deg) -1
grizzled pagodaBOT
The following error occured while calculating:
Error: Parenthesis ) expected (char 27)
humble panther
,calc 6(cos(3deg) )+ cos(3deg) -1
grizzled pagodaBOT
Result:
5.990406743282
when i don't square they're the same
yall got any idea why this is
@pallid canopy
pallid canopy
,calc 6(cos(3 deg))^2+cos(3deg)-1
Here
pallid canopy
,calc 5cos(3deg) -sin(3deg)tan(3deg) +1
And here
humble panther
but they are the same
pallid canopy
According to what
pallid canopy
,w plot 5 cos(x) - sin(x)tan(x) +1 -(6cos^2(x) +cos(x)-1)
grizzled pagodaBOT
pallid canopy
Yea that's not zero
humble panther
wdym
pallid canopy
But that's because they have specific theta values it has to satisfy
humble panther
oh, so they're not the same thing
humble panther
uh ok
minor igloo
someone help, struggling with this, 8th grade
amber waspBOT
someone help, struggling with this, 8th grade
dull pike
What have you tried so far?
rancid raven
someone help, struggling with this, 8th grade
minor igloo
distributing a and d to get rid of the parentheses
idle light
π
dull pike
Ok
minor igloo
then i tried to divide but it just went down hill from there
idle light
do you have a paper with your work on it
minor igloo
yeah
dull pike
Show a picture of you specific status
idle light
^
dull pike
After distributing, isolate x related terms in on side and the others in the other side
minor igloo
but then wouldn't x cancel itself out?
dull pike
No, because they donβt have the same coefficient
They will be subtracted but not canceled
rancid raven
where do i go from here
Factor out x from dx-abx
minor igloo
Meaning?
rancid raven
Do .close
minor igloo
.close
amber waspBOT
minor igloo
.reopen
amber waspBOT
β
minor igloo
it didn't work
minor igloo
look at previous chats
minor igloo
then what
please
i am losing my mind
I have been on the same problem for 45 minutes
Hello?
spark dragon
minor igloo
minor igloo
yeah just realized that, sorry, have a good one
minor igloo
.close
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void steeple
just want to check my work. if anyone could confirm that those are right thatd be great.
a) should be $C = \frac{1}{\zeta_4} \$
b) using $E[g(x)] = \sum_{n=1}^{\infty} g(x_n)p_x(x_n)$, got $E[X^2] = \frac{\zeta_2}{\zeta_4}$
grizzled pagodaBOT
jack
amber waspBOT
@void steeple Has your question been resolved?
void steeple
<@&286206848099549185>
formal yacht
just want to check my work. if anyone could confirm that those are right thatd b...
Looks correct, anything specific youβre unsure about?
amber waspBOT
@void steeple Has your question been resolved?
rotund dawn
Hello, I have a problem with a decomposition into single element (I don't know if this is the right term in English)
here is the equation:
$S(p) = \frac{E}{p(1 + 3RCp + (RCp)^2)}$
I find a decomposition in:
$S(p)= \frac{A}{p}+ \frac{B}{p-p_1}+ \frac{D}{p-p_2}$
$p_1$ et $p_2$ root of the polynomial $(1 + 3RCp + (RCp)^2)$
I have:
$\frac{E}{p(1 + 3RCp + (RCp)^2)}=\frac{A}{p}+ \frac{B}{(p-p_1)(RC)^2}+ \frac{D}{(p-p_2)(RC)^2}=\frac{E}{p(p-p_1)(p-p_2)(RC)^2}$
My question is does i place correctly $(RC)^2$ (thedominante coeficient) in the equation ?
grizzled pagodaBOT
Silicium
rotund dawn
I'm pretty sure i'm wrong
amber waspBOT
@rotund dawn Has your question been resolved?
jaunty shale
I'm pretty sure i'm wrong
do like this $\S(p)=\frac{E}{p(1+3RCp+(RCp)^2)}=\frac{E}{p \cdot (RC)^2 \cdot (p-p_1) \cdot (p-p_2)} \ \ (RC)^2 , S(p) = \frac{E}{p , (p-p_1) , (p-p_2)} = \frac{A}{p} + \frac{B}{p-p_1} + \frac{D}{p-p_2}$
grizzled pagodaBOT
Emily
jaunty shale
so basically, the (RC)Β² doesnt show up only under B and D
it shows up under A as well
amber waspBOT
@rotund dawn Has your question been resolved?
tough mica
amber waspBOT
tough mica
Let $B = {(4, 1, 2), (0, 1, 0), (-3, -1, -1)}$ be a basis of $\mathbb{R}^3$.
Find all vectors of $\mathbb{R}^3$ such that their coordinates in the canonical basis are double their coordinates in the basis $B$.
grizzled pagodaBOT
938c2cc0dcc05f2b68c4287040cfcf71
amber waspBOT
@tough mica Has your question been resolved?
rotund dawn
it shows up under **A** as well
I feel really stupid but if I want to find the factors by multiplying by the denominator how do I do it,
For A it's give me
$\frac{E}{(RC)^2}=\frac{A}{(RC)^2}$
For B, what would that give me then, I think that:
$\frac{E}{p_1(p_1-p_2)(RC)^2}=\frac{B}{(RC)^2}$ ? I know it's incorrect but I can't understand why I've been stuck on this for too long, I can't think anymore ;
grizzled pagodaBOT
Silicium
amber waspBOT
@tough mica Has your question been resolved?
keen pawn
amber waspBOT
keen pawn
Trying to prove this via contradiction
mint nacelle
hint: show that the square of an integer can never be 2 mod 4
grizzled pagodaBOT
Veni, vidi, perii is not f(wai)
keen pawn
I start by assuming $\exists a,b \in \Z$, such that $a^2-4b-2 \neq 0$
grizzled pagodaBOT
Veni, vidi, perii is not f(wai)
rotund oak
I think youβre assuming the wrong thing
half rover
I only know $a \equiv b (mod(n))$
then show that aΒ² β‘ 2 (mod 4) is false
amber waspBOT
@keen pawn Has your question been resolved?
keen pawn
then show that aΒ² β‘ 2 (mod 4) is false
hmm why that specifically?
indigo cloud
what does a^2 = 2 mod 4 mean
keen pawn
$4 \mid (a^2-2)$
grizzled pagodaBOT
Veni, vidi, perii is not f(wai)
indigo cloud
which means?
keen pawn
$a^2-2=4b$
grizzled pagodaBOT
Veni, vidi, perii is not f(wai)
indigo cloud
see the connection now?
keen pawn
yes
We wish to proceed via a proof by contradiction, so we start off by assuming $ 4|(a^2-2)$. Case 1: We assume $a$ is even, and is thus of the form $2n$. We thus have $4n^2-2$. Which isn't a multiple of $4$. We now assume $a$ is odd, and thus of the form $2n+1$. We thus have $4 |((2n+1)^2-2$. So we have $ 4n^2+4n-1$, which isn't a multiple of 4 either. We thus conclude that $4 \nmid (a^2-2)$. QED
grizzled pagodaBOT
Veni, vidi, perii is not f(wai)
olive quiver
help @here :https://i.imgur.com/H2XMTl5.png
keen pawn
!occupied
amber waspBOT
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).
keen pawn
<@&286206848099549185>
keen pawn
.close
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solemn escarp
"Let O be the center of a semicircle which is tangent to circle A and B where RS is tangent to A,B,O and PQ is tangent to circle A,B as in the image. If A,B have radii of 25 and 49 respectively, then find the radius of O"
solemn escarp
what ive wrote is basically all ive done
im not good at geometryπ
<@&286206848099549185>
amber waspBOT
@solemn escarp Has your question been resolved?
solemn hazel
solemn escarp
"Let O be the center of a semicircle which is tangent to circle A and B where RS...
how do i do this
nvm
.close
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split sail
Help
amber waspBOT
rancid raven
Is this test/exam live ?
rancid raven
Well
in bigger cylinder the circumference will be length of rectangle
In smaller cylinder circumference will be breadth of the rectangle
split sail
Yes I got that
rancid raven
Heights will be vice versa
spiral zealot
split sail
Yh
spiral zealot
there also seems to be tangible prizes involved
rancid raven
spiral zealot
at risk of other potential participants around, probably best not to discuss it here.
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quick mesa
amber waspBOT
quick mesa
can someone hgepl me
i need to find the degree
i asked chat gpt and it did 82 - 25
not -82 - (-25)
im confused
keen topaz
i need to find the degree
The degree of h(x)?
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vital quiver
amber waspBOT
vital quiver
why is the end result 7 bits, not 8?
i understand the leftmost bit is the sign bit, but the discard is a bit confusing
i guess when using signed-magnitude arithmetic, we only add 7 bits, and keep track if any leftmost bit is a 1 to be negative
gilded pine
amber waspBOT
grizzled pagodaBOT
gilded pine
,rotate
grizzled pagodaBOT
gilded pine
i am stuck
L'hospital would be very interesting to apply and I doubt it is going to work
split sail
ik
gilded pine
Any ideas?
gilded pine
((n+1)/n)^n = (1+1/n)^n
And how will this help me?
alpine flower
standard limits
amber waspBOT
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normal dove
ap,gp,or hp
strange field
ap,gp,or hp
normal dove
a-b/b-c = a/a
isnt this for ap
alpine flower
you can say 1/x-1/y = 1/y - 1/z
normal dove
but what abt square root
the book assumes some kinda constant after making that ugly aahh form
and does some plain ugly math
alpine flower
what can you write the first term as
alpine flower
you can say 1/x-1/y = 1/y - 1/z
btw 1/x, 1/y and 1/z are in AP
strange field
$\frac{\sqrt{yz}}{\sqrt{y}+\sqrt{z}} = \frac{1}{\frac{1}{\sqrt{y}} + \frac{1}{\sqrt{z}}}$
grizzled pagodaBOT
Astar777
hollow quartz
So I did a work but I'm not sure about it.
The translation is:
We consider a and b two real numbers different from zero such as aΒ²+bΒ²=6ab
1/ Prove that a and b have the same sign
2/ Determine the value of a+b/a-b
mint nacelle
So I did a work but I'm not sure about it.
The translation is:
We consider a an...
,rccw
grizzled pagodaBOT
hollow quartz
Here's my work
mint nacelle
So I did a work but I'm not sure about it.
The translation is:
We consider a an...
yep, part 1 is correct
hollow quartz
Tnx and part 2 ?
mint nacelle
yep that also is correct! good job on the casework
I think you should write $a - b = \pm 2\sqrt{ab}$ though
grizzled pagodaBOT
higher's secret twin brother
mint nacelle
or you don't actually need that part
hollow quartz
Ok thank you so much ! I think the redaction can be a little be better that's why I was worried about the content
hollow quartz
or you don't actually need that part
Yeah I removed it
mint nacelle
yeah you can just skip straight to if a > b after you obtain (a + b)^2 / (a - b)^2 = 2
no worries!
hollow quartz
Thanks for going through it even though its not in English! Thanks a lot !
mint nacelle
no worries it helps that I can read French but not speak it
amber waspBOT
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split sail
Hi, how does one "describe Aut(C5) and Aut(C7)"?
amber waspBOT
Hi, how does one "describe Aut(C5) and Aut(C7)"?
quick spoke
Hi, how does one "describe Aut(C5) and Aut(C7)"?
find a group isomorphic to Aut(C5) and Aut(C7)
(hint: for each automorphism, think about what 1 maps onto)
amber waspBOT
@split sail Has your question been resolved?
quick spoke
does that *describe* though?
generally, a question that goes "describe a group G" means find a 'normal' group that's isomorphic to G
there's a very 'simple' group that's isomorphic to Aut(C_5) in this case
(using simple and normal in the normal english way lol)
heady moss
quick thing
amber waspBOT
quick thing
celest cove
with pythagoras
sqrt(3^2+4^2+4^2)
amber waspBOT
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surreal hedge
i know the answer, but im not sure of the equation i'd have to set up
wanton sentinel
A two-digit number is just 10a+b where 1 <= a <= 9 and 0 <= b <= 9
surreal hedge
okay
uhh
π
how would i write out the equation tho
like ik id have to subtract 54 at some point
wanton sentinel
Well, reversing its digits gives you 10b+a instead
mint patio
why not?
pallid canopy
$\int dx = x + C$
wanton sentinel
You forgot the 3?
grizzled pagodaBOT
riemann
amber waspBOT
mint patio
.reopen
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β
mint patio
second ever integral