so there's an element g in N_H(H). then gHg'=H
(gHg')'= g'H(g')' = g'Hg and since H = gHg'
=> g'(gHg')g = (g'g)H(g'g) = eHe = H
#help-0
jovial mesa
then it's closed under inverses
Question: I just showed that N_G(H) is a subgroup of G. How do i know it's a subgroup for any subgroup H of G?
is it cuz H is in this?
of the definition of the "normalizer"
placid zinc
You let H be a subgroup, then proved N_G(H) is a subgroup only using that knowledge
So yes, you've proven that for any subgroup H, its normalizer is also a subgroup
lone heartBOT
@jovial mesa Has your question been resolved?
blissful ether
lone heartBOT
blissful ether
Stuck on how to find R(x)
Obviously it's # of units sold*price
so is it just (280-0.4x)*x?
if so, this is an issue when trying to find P(x)
nvm I'm stupid
p(x) = (280x-0.4x^2)-(5000+0.6x^2)
company must sell 140 refrigerators (c)
can anyone confirm?
mild mulch
Stuck on how to find R(x)
For revenue you want to multiply the price by how many units ||R(x)=xp|| then for profit you need to deduct the cost of manufacture from the revenue ||P(x)=R(x)-C(x)||, maximum profit is solving ||P'(x)=0|| ||140|| with total profit of ||P(140)|| ||14600|| and a per unit cost of ||280-0.4140|| ||224||
blissful ether
For revenue you want to multiply the price by how many units ||R(x)=x*p|| then f...
How the $140 represents the max profit/unit right?
oh***
not how
then plug in 140 to the price formula to figure out the price that needs to be charged
mild mulch
140 is amount of units, not price
blissful ether
Eh I confuse myself with all these variables lol any tips on how to remember?
Like what it represents after I find the maximum
oh wait nvm I'm stupid lmao
I thought c was saying there is a different number in terms of how much they need to produce vs sell
in reality they just need to produce AND sell 140 to hit maximum profit
mild mulch
With questions like this, when you see x you can assume that the x will be the same for all functions. So C(x) and R(x) will be comparable even if P(x) didn't exist
blissful ether
oh I think I just read that part of the problem wrong lol
like I thought it read as "How many refrigerators must the company produce and how many refrigerators do they have to sell to maximize profit"
I was like tf how are there 2 different numbers lol
mild mulch
Ah, yeah
blissful ether
basically my brain turned off
mild mulch
I do think it was a poorly worded question, I got mislead trying to find the optimal price per fridge and then going from there rather than doing it all together. It also never defined the terms and I know that people will go into that question not understanding the difference between R(x) and P(x)
blissful ether
Ok good so it wasn't just me lol
I'm having issues setting up this other question
C(x) = 22x * y is as far as I got lol
where x = # of rooms and y = # of days
nvm I found it on chegg
chegg is a life saver for understanding problems lol
.close
dry echo
lone heartBOT
dry echo
So this is my work so far
I'm trying to use integration by parts
To evaluate this
I got stuck because I realized it was just gonna keep repeating forever?
Unless I'm mistaken
Someone guide me through this pls 
buoyant kayak
can you show your work?
buoyant kayak
i'm confused on line 3
buoyant kayak
sorry, not line 3 not including the expression
dry echo
then I chose to differentiate (arcsinx) * x
so I did a product rule on that
inside the integral
buoyant kayak
you did product rule?
dry echo
did I mess it up
buoyant kayak
you're integrating
buoyant kayak
what are you choosing for u and v?
dry echo
when I do the integration by parts for the first time, I choose u = (arcsinx)^2
but on the second time I do it, I choose u = arcsinx * x
is that a bad idea
dry echo
what should I do differently
buoyant kayak
you should choose a different u and v
you actually set it up quite nicely right there ^
look at that $\frac{x}{\sqrt{1-x^2}}$
ocean sealBOT
a disappointing son
buoyant kayak
yep
sonic glade
Let 𝑥 ∈ R≥−1.
Prove by induction that 𝟏 + 𝒏𝒙 ≤ (𝟏 + 𝒙)𝒏 for all 𝑛 ∈ Z+
timid quest
how can i solve this?
i miss the lesson where my teatcher explain how to solve this things
sonic glade
how can i solve this?
repost on a different channel
sonic glade
<@&286206848099549185>
trim plinth
naive valley
@sonic glade do you have any thoughts on how to get started? to prove by induction you first prove the base case, right?
lone heartBOT
@sonic glade Has your question been resolved?
alpine sable
help
blissful ether
bruh
blissful ether
it is impossible
low tinsel
fervent cloak
lone heartBOT
merry depot
what is an NPV?
fervent cloak
what is an NPV?
Non permissible value
merry depot
so what would plugging in 7 do?
merry depot
Non permissible value
more specifically, what would break if you plugged 7 in? if anything
fervent cloak
more specifically, what would break if you plugged 7 in? if anything
wdym
merry depot
NPV aren't allowed because they break something about the fraction. For example, plugging in -4 would make you divide by 0 in the first term
5 makes the second term 0, and we are dividing by that term, so again we have division by 0
frigid quest
How do i know that series on the left is smaller
lone heartBOT
How do i know that series on the left is smaller
frigid quest
Is it because sqrt(n^6) is bigger than the denom on the right becuase its of a higher degree?
lone heartBOT
@frigid quest Has your question been resolved?
lethal stump
i think a sin or cos sub should do the trick
keeping in mind the trig identity sin^2(x) + cos^2(x) = 1
elder glacier
lone heartBOT
@stuck temple Has your question been resolved?
lone heartBOT
@stuck temple Has your question been resolved?
pale kestrel
desmos
alpine sable
Wait as Shuri said, did desmos not work?
pale kestrel
You intended your question to be so we aren't completely sure what you're asking?
If so, then don't expect answers ig.
stuck temple
.close
lone heartBOT
lone heartBOT
Available help channel!
tender dagger
pls help
tender dagger
honest mural
Hint: Divide both the numerator and denominator by the highest power in x and then plug in infinity and see what happens.
honest mural
Yep.
tender dagger
swet
honest mural
For the second one note that -1<cosx<1. So -1/x<cosx/x<1/x. Then apply Squeeze thm.
That will give you the result.
tender dagger
im sorry?
alpine sable
By the definition of the cosine function, -1<=cos x<=1, right?
tender dagger
yes
alpine sable
Then suppose x is a positive number
And then divide -1, cosx, 1 with x
You'll get -1/x<=(cos x)/x<=1/x
This also holds true when x>0, correct?
Now, send x to infinity
You'll get 0<=lim(x->infinity) (cos x)/x <=0
alpine sable
You'll get 0<=lim(x->infinity) (cos x)/x <=0
There's only one value of lim(x->infinity) (cos x)/x that satisfies this following inequaliy, what is it
... are there any part that you don't understand here, by chance?
alpine sable
You'll get 0<=lim(x->infinity) (cos x)/x <=0
Yep, in Korea we call this the sandwich theorem
Idk how it's called in english but
alpine sable
You used ( ) instead of [ ]
tender dagger
oh.......
alpine sable
You'd already know that the answer for this inequality is -9/4<=x<=3/4
tender dagger
yea you right haha
alpine sable
This means x can be -9/4 and 3/4
However, by stating (-9/4,3/4), you stated that x cannot be -9/4 or 3/4
Which is an incorrect answer
tender dagger
ahh
alpine sable
Be careful next time, I've once did that kind of mistake on a test and got -5/100 points on a test once
tender dagger
oof...
lone heartBOT
sudden hinge
"do not use decimals"
tender dagger
ah.'
lone heartBOT
@tender dagger Has your question been resolved?
crimson carbon
ran(f) is incorrect
crimson carbon
Extreme value theorem apply that
If the interval is not bounded ignore that
must be a closed interval
crimson carbon
What don't you understand?
tender dagger
why this is true
ocean sealBOT
crimson carbon
The EVT (Extreme Value Theorem) is only applicable to functions with closed and bounded domains
tender dagger
ohh
crimson carbon
So exclude any of those that don't follow the EVT
If the function has a closed and bounded domain within the specified interval
and it has at least one max and min then it follows the EVT
else false
i.e. doesn't apply to that function
lone heartBOT
@tender dagger Has your question been resolved?
alpine sable
How do i justify this mathematically? i dont see a way around it..
earnest mortar
You want to know if the driver takes more than 15m to stop his vehicle
So try to find the time when he stops going forward (s'(t) = 0) and plug the value you find for t into the function s to see if it took more than 15m
alpine sable
so t= 2sqrt3
alpine sable
So try to find the time when he stops going forward (s'(t) = 0) and plug the val...
so s(t)=12(2sqrt3)-2sqrt3^3?
ruby hinge
nah I think u might have made a teeny mistake
think u forgot to bring the 3 down while differentiating t^3 term
alpine sable
think u forgot to bring the 3 down while differentiating t^3 term
how do i do that? ;-;
ruby hinge
you need to know when the velocity becomes zero so yes u have to use derivative of the displacement function s(t)
alpine sable
you need to know when the velocity becomes zero so yes u have to use derivative ...
so s(t)= 12(2sqrt3)-3(2sqrt3)^2?
lone heartBOT
@alpine sable Has your question been resolved?
lone heartBOT
alpine sable
.reopen
lone heartBOT
✅
alpine sable
did u differentiate s(t)
yes, so s(t)= 12-3t^2?
alpine sable
are u familiar with differentiation
not really :( can you help?
ruby hinge
yes, so s(t)= 12-3t^2?
how did u get this
alpine sable
derivate
ruby hinge
yea derivative
is what i meant by differentiation
but what u get on the lhs is not s(t) since u took the derivative of that u would get v(t) which is the velocity function
alpine sable
i was confused when you said differentiate again 😅
ruby hinge
yea my bad
alpine sable
but what u get on the lhs is not s(t) since u took the derivative of that u woul...
oh, and how does that help me?
ruby hinge
so when u differentiate what you'd get is v(t)= 12-3t^2?
alpine sable
yeah
ruby hinge
because u need to know the time when velocity is 0
since in the qn it is mentioned that the guy applied brakes
so you equate it to 0
12-3t^2=0
tell me what u get
alpine sable
tell me what u get
t=2
ruby hinge
okay what do u think we should do with that now
alpine sable
okay what do u think we should do with that now
replace the t values
ruby hinge
in which equation
alpine sable
tell me what u get
do i leave the right hand side 12- 3t^2?
ruby hinge
no that's not the equation
that's the velocity equation
u need to know what this guy's position is
alpine sable
oh okay so the original one
alpine sable
12t- t^3?
alpine sable
n what do u get then
8
alpine sable
s(2)= 12(2)-2^3
alpine sable
s(2)=16
ruby hinge
yes
ruby hinge
huh
alpine sable
I'm stupid
alpine sable
yeah so thats it right? s(2)=16
ruby hinge
it's okay
alpine sable
so it crashed
alpine sable
thanks you sm 😭
sage kernel
lone heartBOT
@alpine sable Has your question been resolved?
arctic tartan
heyyy
ruby hinge
post the question
lone heartBOT
@arctic tartan Has your question been resolved?
lone heartBOT
@arctic tartan Has your question been resolved?
tacit arch
.close
exotic island
What am I doing wrong here
lone heartBOT
What am I doing wrong here
buoyant kayak
-9/(-1)^4
buoyant kayak
happens to the best of us
feral wind
Is this first part of the proof correct?
lone heartBOT
Is this first part of the proof correct?
feral wind
a-) ($\implies$) assume R is reflexive, let (x,y) be arbitrary and $(x,y) \in i_A$, $i_A$ is the identity relation of A so x=y and $x \in A$, our goal is to prove $(x,y) \in R$, because R is reflexive on A then for all $x \in A$, $(x,x) \in R$, finally, because $(x,y) \in i_A$ then $(x,x) \in i_A$ and $x \in A$ so $(x,x) \in R$, because (x,y) was arbitrary then $i_A \subseteq R$
ocean sealBOT
beginner
ocean sealBOT
beginner
lone heartBOT
@feral wind Has your question been resolved?
lone heartBOT
@feral wind Has your question been resolved?
feral wind
.close
blazing thunder
blazing thunder
for d i was thinking P(32 < X < a) = P(X < a) - P(X < 32)
i ended up getting P(X < a) = 0.37 (2dp) => a = 28.34 (2dp)
answer sheet says its 35.30
<@&286206848099549185> I asked in another help channel 50 mins ago but the channel was closed due to inactivity
tacit arch
<@&286206848099549185> I asked in another help channel 50 mins ago but the chann...
then reopen. don't ping
blazing thunder
I can .reopen when it’s in use?
tacit arch
oh
random wagon
Your calculations seem to be correct. Maybe you had an error with your inputs?
As in: The approach is correct
blazing thunder
Well I was thinking I might have calculated P(X < 32) incorrectly
I used a calculator for this tho
And did it a few times
random wagon
Yeah. You have only given the value for P(X < a) in this threat
tacit arch
what does this mean
P(X < a) = 0.37 (2dp) => a = 28.34 (2dp)
blazing thunder
Oh I subtracted P(X < 32) from the line above
I got 0.37
Then I can use inverse normal to get a = 28.34
tacit arch
Do a sanity check. P(32 < X < 28.34) = 0
blazing thunder
I drew a diagram too
tacit arch
for d i was thinking P(32 < X < a) = P(X < a) - P(X < 32)
i ended up getting P(...
what'd you get for P(X < 32)
blazing thunder
0.07 I think but I’ll check again
Nvm I got .65
I was trying to remember form an hour ago
tacit arch
how'd you get this then?
P(X < a) = 0.37
blazing thunder
Maybe I was doing a probability distribution instead of cumulative
Cumulative is for less than right
tacit arch
P(X = a) is zero for all continuous random variables
Gaussian distribution is a continuous random variable
blazing thunder
P(X = a) is zero for all continuous random variables
Do you mean it is exactly 0 or 1/inf?
tacit arch
Do you mean it is exactly 0 or 1/inf?
1/inf is not a well-defined concept
blazing thunder
Because I am imagining a normal distribution being perfectly continuous rn so you wouldn’t get a perfect value of P(X=x)
Is that what you mean
tacit arch
Because I am imagining a normal distribution being perfectly continuous rn so yo...
"perfect value" is nonsense
blazing thunder
Oh
Hm
To rephrase then - the value would be infinitely small to the point it’s negligible
?
tacit arch
To rephrase then - the value would be infinitely small to the point it’s negligi...
this is also nonsense
use the definition
steel turret
hello
steel turret
how can i work out distance with the 2 triangles
since theres 2 do i divide 328 by 2?
so i have a base
sudden hinge
First notice that OPQ and OAB are similar triangles
Using ratios we get $$\frac{328/2}{x-20} = \frac{4/2}{20}$$
ocean sealBOT
Navix
sudden hinge
We divide by 2 because we want to split the two triangles along the base line BQ
steel turret
yup i get that
sudden hinge
so whats the problem?
lone heartBOT
Available help channel!
high plaza
Thirteen cards are dealt from a well-shuffled standard deck. What is the probability of getting 7 spades 3 hears, and 3 clubs? Don't know where to start, any help is apreciated
olive oar
What if we first try first getting 7spades then 3hearts then 3clubs
whats the probability of that
lone heartBOT
@high plaza Has your question been resolved?
olive oar
What if we first try first getting 7spades then 3hearts then 3clubs
high plaza
What if we first try first getting 7spades then 3hearts then 3clubs
this wouldn't work because it eliminates the idea of hearts or a club being drawn first, lowering the probability
high plaza
wait i'm confused
olive oar
each of the events has a chance p of happening (and theyre all the same chance p)
and theres C of them
so you multiply the two
high plaza
I'm really sorry, I'm just a little lost (/gen). Could you show me this worked out?
olive oar
ok so if we let the chance of what i put above as p
since we dont care about the difference between. SSSHHSSSSHCCC and something else
and each of those events is equally likely
high plaza
?
olive oar
you can multiply the chance p by the amount of ways you can get 7 spades 3 hearts and 3 spades
olive oar
and each of those events is equally likely
getting SSSHHSSSSHCCC or CSSSHHSSSSHCC
is equally likely
since youre only partitioning the numerators
lets look at a smaller example maybe
2 kings and a 4 out of three lets say
if I want KK4, theres a:
4/52 * 3/51 * 4/50
chance to get that
high plaza
wait where did you get 4/50 from
olive oar
there are 4 fours in a deck of crads
high plaza
oh i misread myb
olive oar
but if I have K4K:
4/52 * 4/51 * 3/50 = 4/52 * 3/51 * 4/50
and the same for each way to do it
high plaza
you know i forgot communitive property exists and im kinda upset at myself for it
high plaza
hold on imma try writing this out and seeing if it aligns with the answer key
it does not
shit
wait like it would be something like 13 x 12 x 11 x 10 x 9 x 8 x 7 x 13 x 12 x 11 x 13 x 12 x 11 and then all that shit divided by 52 x 51 all the way to 40?
high plaza
what combinations
olive oar
remember in the king one there were 3 combinations:
KK4
K4K
4KK
so id multiply to probability of one of them by 3
high plaza
wait so i take what i had at multiply it by 13?
olive oar
here you need to figure how many ways you can arrange
SSSSSSSHHHCCC
olive oar
well we can think of it as follows
olive oar
how many ways would it be if all were unique?
olive oar
oh i know how to do it i just don't want to lmao
ah
high plaza
wait it still doesn't work
olive oar
hmm can i see the answer and your work
high plaza
the answer is 0.00021
221
and my work is (13!/(7! x 3! x 3!))*((13 x 12 x 11 x 10 x 9 x 8 x 7 x 13 x 12 x 11 x 13 x 12 x 11)/(51!/39!))
you could kill a programmer with that line
olive oar
i put that into wolfram alpha
at that thing up there is the same as 2.21 * 10^-4 = 0.000221
so i think you put smthg into your calculator weird
high plaza
you know
that assumes that I'm bad at typing, and I must say that is a REALLY good assumption
tysm for the help!
olive oar
lmao np
high plaza
.close
lone heartBOT
lone heartBOT
Available help channel!
sharp rune
lone heartBOT
alpine sable
@sharp rune
sharp rune
yes
lone heartBOT
@sharp rune Has your question been resolved?
brazen grotto
i'm having trouble figuring out whether this statement is true or not
lethal stump
i'm having trouble figuring out whether this statement is true or not
would it be easier if you proved the contrapositive?
if 8 doesn't divide n^2-1 then n mod 4 = 2 or 0
brazen grotto
lemme try that
lethal stump
also this is basically just proving if n is odd then 8 divides n^2 -1
wait i've done this proof before
you can just do two cases where n = 4k + 1 and n = 4k +3
and sub them into n^2-1
brazen grotto
also this is basically just proving if n is odd then 8 divides n^2 -1
oh that's a really good way to think about it
lethal stump
you'll get something that can be reduced to 8 * (something)
brazen grotto
yea i had n = 4k + 1 and n = 4k +3 written down earlier but i didn't know how to connect it all together
lethal stump
ah nws then
yea you just take cases in this case
yea in each case i got 8 * (something)
brazen grotto
how do i prove that n mod = 1 and n mod 4 = 3 mean that n is odd, i know that n is odd but idk how to prove it
lethal stump
you don't need to really
but you could start from n = 4k + 1 and reduce that to n = 2(2k) + 1
which is an odd number by definition
similarly n = 4k + 3 = 2(k+1) + 1
lethal stump
np
maiden valley
bro
maiden valley
nah
spice wasp
what
buoyant kayak
learn to read
spice wasp
bruh
alpine sable
alpine sable
bro
alpine sable
fine
spice wasp
bruh I still have classes to attend to
lone heartBOT
Available help channel!
worldly oracle
hello
worldly oracle
im stuck on
(x-6)(2x+1)(4-x)
i have to expand it
but idk if i should deal with the first 2 brackets first or not
hidden knoll
try splitting it up
worldly oracle
so do i deal with the first two brackets, then do the last one?
hidden knoll
x*y*z = (x*y)*z
so for example im gonna make up a random example
(2x+2)(x-5)(x+3)
this is equal to (2x+2)(x-5) multiplied by (x+3)
we can solve (2x+2)(x+5) first
try that
worldly oracle
ight
hidden knoll
are you there?
lone heartBOT
lone heartBOT
Available help channel!
cursive crescent
lone heartBOT
cursive crescent
I have been completely stumped at how to derive D'(e), D'(a), and D'(b)
And for some greater context^
I feel like since it's breezed over it has to be something simple, and I know that omega^2 * omega = 1
Slamming it into symbolab gives this nonsense, which honestly is not much help. I'd try and reduce down the forms on the right side but I'm not even sure what addition means in context of the group, unless when making a representation of groups allows you to start using addition? That doesn't really click with me either, so I'm not sure how to get the inverse.
I tried to do it by hand but got kinda stuck, once again on the addition step
lone heartBOT
@cursive crescent Has your question been resolved?
cursive crescent
<@&286206848099549185>
tacit arch
<@&286206848099549185>
It simplifies when you plug in the third roots of unity
cursive crescent
It simplifies when you plug in the third roots of unity
So this process is correct?, then?
tacit arch
So this process is correct?, then?
Looks fine so far. Just keep going
lone heartBOT
@cursive crescent Has your question been resolved?
cursive crescent
Looks fine so far. Just keep going
Okay, so it's pretty clear to me that all except the diagonals should go to zero, but I'm struggling with the algebra of the center term and bottom right term, moreof with the logic of how to resolve the twos
cursive crescent
Oh, got it. Didn't expect that to be a one hour problem, but wasn't familiar with roots of unity. Makes sense though, and got the algebra to check
.close
lone heartBOT
cursive crescent
Looks fine so far. Just keep going
tyvm
lone heartBOT
Available help channel!
hidden pier
Hellooo
hidden pier
.close
lone heartBOT
silver adder
hi
lone heartBOT
Available help channel!
alpine sable
Hello
alpine sable
Guys I am not understanding how to solve this problem
I have tried but couldn't come up with anything
hidden pier
Average speed = Total Distance / Total Time
hidden pier
set a random distance
@alpine sable
set an arbitrary distance and use the formula
you want 60 = Total distance / (time it took to complete journey + x) where x is the time it takes to get back
Then when you know the time it takes to get back along with the distance you can just calculate the speed
alpine sable
<@&286206848099549185>
hidden pier
bro
what about what i said doesn't make sense
@alpine sable mate are you just sleeping and waking up every 15 minutes to ping because ive literally given you all the help you need unless you want me to feed the answer into your mouth
alpine sable
I actually do not understand still, you can call me dumb but I need to understand the whole thing
therefore I pinged helpers
hidden pier
bruh
Alright @alpine sable do you agree that
Average speed = Total Distance / Total Time
alpine sable
yes I know
hidden pier
Ok, and let's just choose a random number for the distance; say 400 kilometers both ways
alpine sable
ok
hidden pier
Our equation becomes
$60 = \frac{400+400}{\text{time taken for trip 1} + \text{time for trip 2}}$
ocean sealBOT
🙛𝕍ѳrtєx🙙
hidden pier
right?
alpine sable
yes I get this
hidden pier
Alright, if you went 40 km/h for 400 km in trip 1, what was the time taken in that specific trip?
alpine sable
time = 10
hidden pier
$60 = \frac{800}{10 + x}$
alpine sable
h
ocean sealBOT
🙛𝕍ѳrtєx🙙
alpine sable
thank you so much I understand now
hidden pier
The value of x is the time it takes to travel the return trip. On top of that, you know the distance traveled is 400, so you just solve for the speed
weary remnant
I'm making a game and I don't know how to find the speed value
weary remnant
I'm making a game and I don't know how to find the speed value
there's no time or distance I can calculate
to find the speed value
distance will change continously
and time is infinite
tight locust
So you want r to remain constant?
weary remnant
So you want r to remain constant?
R is always constantly moving
x is always following it
but it must keep a distance
and I don't know how to make it keep a distance from R
tight locust
But what distance
weary remnant
But what distance
distance between x and r
tight locust
No more or less
about 100
Pick one
tight locust
Alright. Theres a number of ways to do this
I'm assuming you want a visually smooth solution though?
weary remnant
yep
tight locust
So it must occur over some time interval
weary remnant
yep
tight locust
It would be simpler to keep the player's speed always constant
If the distance must be exact
And let r have a constant speed as well
weary remnant
ok
silver adder
the simplest way i know to do it is mix(p,x,m*dt)
if you want the speed value its common to just do (currentframe-lastframe)/dt
if youre integrating velocity then hookes law would work nicely
dark falcon
can someone help me im having trouble answering my homework:<
hidden pier
sure!
hidden pier
alright
Try connecting HK
actually, connecting JG would be helpful as well; either works
dark falcon
u mean the 132 and 60?
hidden pier
no, I mean you should just create a line segment HK that bisects those angles
if you want, you can draw line JG as well (no need to draw both though)
dark falcon
wait how ToT
dark falcon
ohh okay so I should just draw a line?
hidden pier
yeah!
dark falcon
it says i should find measure of G:<
lime schooner
yep, that would mean that the angles 60 and 132 would be divided into half too
hidden pier
it says i should find measure of G:<
yeah, but don't worry; by drawing lines, you can often help find more angles and more relationships!
dark falcon
ohh okay
hidden pier
@dark falcon do you happen to know that all interior angles of a triangle add to 180?
hidden pier
So if you divide the kite in half, you get a triangle HKG
dark falcon
ohh okay I got it!!
dark falcon
thank u so much!
hidden pier
no problem!
By the way, drawing these extra lines frequently helps in geometry problems
They're called "auxiliary lines," specifically
ocean sealBOT
HRN
terse iron
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terse iron
isnt just the high number + the low then divide by 2 or no
olive oar
isnt just the high number + the low then divide by 2 or no
yes
olive oar
yes
olive oar
np
terse iron
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terse iron
is these correct
timid hazel
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grave hamlet
hey
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@grave hamlet Has your question been resolved?
grave hamlet
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grave hamlet
is it because fxy is non negative function ?
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noble sinew
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@grave hamlet Has your question been resolved?
autumn lantern
hi! how do we arrive at the right hand side? can't seem to fill in the calculations made
autumn lantern
X with a bar on top stands for the mean btw, this is mathematical statistics
specifically, this is a step made in estimating parameters using method of moments
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near lagoon
$$\frac{1}{n} \sum_{i=1}^{n} (X_i-\bar{X})^2 = \frac{1}{n} \sum_{i=1}^{n} X_i^2+ \bar{X}^2 \frac{1}{n} \sum_{i=1}^{n} 1 - 2 \bar{X}
\frac{1}{n} \sum_{i=1}^{n} X_i$$
$$=\frac{1}{n} \sum_{i=1}^{n} X_i^2 + \bar{X}^2 - 2\bar{X}^2 = \frac{1}{n} \sum_{i=1}^{n} X_i^2 - \bar{X}^2 $$
ocean sealBOT
Mat
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adam03
sudden hinge
factoring would help yes
plucky lynx
No f(3) does not exist.
frail grove
Since f(x) can be written as:
ocean sealBOT
adam03
plucky lynx
Now f(3) is defined. The thing is in you first one the domain is the set of all x which numerator makes is defined and denominator is defined. So 3 is not in the domain.
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frail grove
So i should stick with the given expression and not simplify when finding the domain of the function?
near lagoon
f(x) = x/x equals 1 for all x!=0 but is undefined at 0
severe sluice
Since f(x) can be written as:
no, you cant do this
you're dividing both the numerator and the denominator by x-3
which you cant do when x=3
lament forge
$f(x)=\frac{2x-6}{x^2-2x-3}$
$f(3)=\frac{2(3)-6}{3^2-2(3)-3}=\frac{6-6}{9-6-3}=\frac{0}{0}$
ocean sealBOT
bee
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severe sluice
oh ok got it thanks
*although yes, you can remove the discontinuity by defining f(3) to be 1/2.
frail grove
*although yes, you can remove the discontinuity by defining f(3) to be 1/2.
Yeah I am aware of that, the domain confused me a little bit
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clear frost
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clear frost
Given (\frac{x^4}{a})+(\frac{y^4}{b}) = (\frac{1}{a+b}) and x^2 + y^2 = 1
. Prove (\frac{x^{20}}{a^{10}}) + (\frac{y^{20}}{b^{10}}) = (\frac{2}{(a+b)^{10}})
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clear frost
help :'))
lone heartBOT
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clear frost
<@&286206848099549185>
oak perch
Given \(\frac{x^4}{a}\)+\(\frac{y^4}{b}\) = \(\frac{1}{a+b}\) and x^2 + y^2 = 1
...
You let x=cos(t) and y=sin(t)
Then the condition gives you
$\frac{(sin(t))^{4}a+(cos(t))^{4}b}{ab}=\frac{1}{a+b}$
ocean sealBOT
Cogwheels of the mind
oak perch
So $(sin(t)^{2}a-cos(t)^{2}b)^{2}=sin(t)^{4}a^{2}+cos(t)^{4}b^{2}-2sin(t)^{2}cos(t)^{2}ab= sin(t)^{4}a^{2}+cos(t)^{4}b^{2}-2sin(t)^{2}+(cos(t)^{4}+sin(t)^{4}-1)ab=0$
ocean sealBOT
Cogwheels of the mind
oak perch
Therefore $sin(t)^{2}a=cos(t)^{2}b$
ocean sealBOT
Cogwheels of the mind
oak perch
b=tan^2(t)a or a=cot^2(t)b depends on whether cos or sin equal 0. This will prove your final result
clear frost
You let x=cos(t) and y=sin(t)
i haven't learnt about sin cos tan :'))
clear frost
wut does it mean?
oak perch
Then why do you ask that…
Okay then,read about Trigonometric functions…
clear frost
Then why do you ask that…
Okay then,read about Trigonometric functions…
cuz my homework is this ;-;
and i have to solve it without using wut u did
clear frost
Then why do you ask that…
Okay then,read about Trigonometric functions…
ok ty
i'll try to understand it anyway
also any way to solve my math :'))
@oak perch can u give me some hint to solve it withouth using trigonometric funtions?
clear frost
idc if is long or short
oak perch
(cos(t))^4+(sin(t))^4+2(sin(t)^2(cos(t)^2)=(cos(t)^2+(sin(t))^2)=1
Okay then we might not need it:
$\frac{y^{4}a+x^{4}b}{ab}=\frac{1}{a+b}$
ocean sealBOT
Cogwheels of the mind
oak perch
Let me finish
clear frost
**Cogwheels of the mind**
seem like i understand this
oak perch
So $y^{4}a^{2}+x^{4}b^{2}+(x^{4}+y^{4}-1)ab=0$
ocean sealBOT
Cogwheels of the mind
oak perch
Now $x^{4}+y^{4}-1=-2x^{2}y^{2}$ because $1=(x^{2}+y^{2})^{2}=x^{4}+y^{4}+2x^{2}y^{2}$
ocean sealBOT
Cogwheels of the mind
oak perch
So $y^{4}a^{2}+x^{4}b^{2}+(x^{4}+y^{4}-1)ab=y^{4}a^{2}+x^{4}b^{2}-2x^{2}y^{2}ab=0=(y^{2}a-x^{2}b)^{2}$
ocean sealBOT
Cogwheels of the mind
clear frost
**Cogwheels of the mind**
ok i dont understand this step
oak perch
Therefore $y^{2}a=x^{2}b$ then use this you can get the final result
ocean sealBOT
Cogwheels of the mind
oak perch
$\frac{y^{4}a+x^{4}b}{ab}=\frac{1}{a+b}$
From this step
clear frost
why the previous step is y^4a + x^4b but this step is y^4a^2 + x^4b^2
oak perch
why the previous step is y^4a + x^4b but this step is y^4a^2 + x^4b^2
M/N=P/Q then MQ=NP
oak perch
Then you either replace b with (y^2/x^2)a or replace a with (x^2/y^2)b to get your answer cause x and y can’t both be zero
For example if x doesn’t equal 0, then you replace b with (y^2/x^2)a then
oak perch
Okay great
clear frost
can i add u ? :>
oak perch
Sure
oak perch
Any time, ask me anything directly without greeting. I will respond when I check my DM
clear frost
ok thank you so much again
oak perch
Np
clear frost
i sent friend req
oak perch
👍
clear frost
uhhh
so i try to replace a = (x^2/y^2)b
and i got 2y^20/b^10
@oak perch
did i do any wrong?
oak perch
but the problem is prove it equal 2/(a+b)^10
Yeah, replace that a also
oak perch
2/(((x^2/y^2)+1)b)^10
clear frost
dang it
oak perch
Damn it
clear frost
imagine forgot wut u need to do
oak perch
Lol
clear frost
how stupid i am lol
oak perch
Don’t worry, that was a long question
clear frost
holly dank
u are impressive
i got the answer
tysm
now i can rest now
it's 11:26 pm in my country :'))
.clóe
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oak perch
Good night
clear frost
u too ehh
naive valley
the vectors of any basis, expressed in terms of that basis, will have entries with one 1 and the rest 0. But this is not generally true if you express them in terms of some other basis
cinder cove
this
tawny condor
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ruby cradle
Hi, I have been out sick for a few days and didn't get to see all of the examples in class. I have this problem that I have to do, and I'm not sure what to do after what is already shown in the picture. Could someone tell me what next steps would be?
lone heartBOT
Hi, I have been out sick for a few days and didn't get to see all of the example...
@ruby cradle Has your question been resolved?
ruby cradle
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vapid python
Hi, I have been out sick for a few days and didn't get to see all of the example...
It's a isosceles triangle and a triangle total angle is 180⁰. Therefore, x= 180⁰-45⁰-45⁰ from there you will be able to find y
ruby cradle
It's a isosceles triangle and a triangle total angle is 180⁰. Therefore, x= 180⁰...
Thank you!
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vapid python
Thank you!
You're welcome
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alpine sable
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alpine sable
if a series is said to converge via ratio test, is the radius of convergence always assumed to be infinite?
raven rover
sudden hinge
@alpine sable No. Sometimes the limit of the ratio test can be dependent on x. Then you have to find bounds for x such that the limit is still between 0 inclusive and 1 exclusive