#help-39
shrewd basin
opal moss
anyways
if you remember n choose k formulas you should be able to determine the ways to choose 5 colours from n colours
if vertices are distinct then yes
oh wait i might actually be wrong that’s funny
i forgot you divide by 2 in nc2 :p
pearl pondBOT
@grizzled lodge Has your question been resolved?
mossy canopy
hey
mossy canopy
i am given this sequence
with b_0 being arbitrary and in R
the sequence obviously diverges to +infinity
any idea on how to show this?
i was told that there exists a proof that is like 2 rows
that this diverges is obvious, because
(b_0)^2>=0
therefore b_1 >= 1
and so on
in general we get:
b_n >= n
but i have not proven this
just "observed"
toxic lichen
if your sequence approaches a finite limit L then L = sqrt(1+L^2)
shy totem
Can someone help me with my physics hw questions
pearl pondBOT
Can someone help me with my physics hw questions
fast zealot
shy totem
Need help with answering these questions
pearl pondBOT
@shy totem Has your question been resolved?
hollow spade
How do I find the range of y = 5 + ln(1/(x-4))? (without a calculator). my part b is wrong
pearl pondBOT
How do I find the range of y = 5 + ln(1/(x-4))? (without a calculator). my part ...
@hollow spade Has your question been resolved?
merry carbon
Hint: can you find a value of $x$ that would give $(f\circ g)(x)=0$? How about a solution to $(f\circ g)(x)=-5$, say?
jolly parrotBOT
chartbit
pearl pondBOT
@hollow spade Has your question been resolved?
merry carbon
Looking good, matter of fact that should rule out three of the choices there, no?
merry carbon
Well one thing I'd say is that ln(u) would output all possible values for u>0
hollow spade
right but what about the inside function
merry carbon
As here we can rewrite $\ln\left( \frac{1}{x-4} \right) = -\ln(x-4)$
jolly parrotBOT
chartbit
merry carbon
so you put it in the front right?
Yep basically, or rewrite $\ln(a/b) = \ln(a) - \ln(b)$
jolly parrotBOT
chartbit
hollow spade
oh i see
merry carbon
In this form it should be clear that (x-4) > 0 for our domain?
Alternatively, you could also find the range of $\frac{1}{x-4}$ and then argue from there
jolly parrotBOT
chartbit
merry carbon
Either way, it should be clear?
hollow spade
ooh
does it make it difference that it's negative ln
nvm it just reflects over the y axis
thank you soo much!! @merry carbon
merry carbon
No problem, hope that helped 
pearl pondBOT
Available help channel!
zinc grove
Hi
i need to show if w is an nth root of unity, then 1/w is an nth root too. is my solution correct?
$w^{-n} \implies (w^n)^{-1} \implies 1^{-1} \implies 1$
That is the same as
$(\frac{1}{w})^n = 1 \qed$
jolly parrotBOT
AJ_l0l
zinc grove
<@&286206848099549185>
pearl pondBOT
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grim siren
How do u get domain and range?
pearl pondBOT
How do u get domain and range?
grim siren
The domain for the function is the range for the inverse function
How do I find the range tho?
wild charm
i know it but i forget how to find it
buoyant panther
(3x+a)/(x-1) = 3 * (x+a/3)/(x-1) = 3 * (x-1+1+a/3)/(x-1) = 3 * (1 + (1+a/3)/(x-1))
it helps if it comes to the range
to find domain check when denominator is zero
grim siren
it helps if it comes to the range
Wdym?
grim siren
to find domain check when denominator is zero
Oh I see
buoyant panther
or you can find f^(-1) firstly then do that with inverse
grim siren
f^-1(x) = a+x/x-3
buoyant panther
so (x+a)/(x-3) = (x - 3 + 3 + a)/(x-3) = 1 + (a+3)/(x-3)
it gives you range immediately
grim siren
I am confused
How is it the range?
buoyant panther
you know concept of homographic functions or calculus (limits)?
grim siren
I know basic limits but just learned it
buoyant panther
I know basic limits but just learned it
you can also get this doing limit when x tends to +/- inf
you just remove HA from the real set and this becomes your range
grim siren
So as x approach infinity the value will give vertical asymtop
buoyant panther
So as x approach infinity the value will give vertical asymtop
horizontal*
grim siren
That will give the range for function right?
buoyant panther
asymptote is the line (value of y here) which function goes to but never reaches, e.g. if y = 1 was an asymptote then range would be R \ {1}
for the function like this obviously
grim siren
0
Whould I write it as
For inverse function
Domain: {x€R ,x=/=0}
Range: {f(x)=R f(x)=/= 1}
buoyant panther
why x neq 0
f^(-1)(x) = (a+x)/(x-3)
then f^(-1)(0) = (a+0)(0-3) = -a/3
(exists)
grim siren
Oh
grim siren
then f^(-1)(0) = (a+0)(0-3) = -a/3
Is it 3?
buoyant panther
ye, x can't equal 3
grim siren
3 don't exsist i think
Oh so
Whould I write it as
For inverse function
Domain: {x€R ,x=/=3}
Range: {f(x)=R f(x)=/= 1}
pearl pondBOT
@grim siren Has your question been resolved?
quiet wren
Whats the square root of -5900
pearl pondBOT
Whats the square root of -5900
quiet wren
What does complex mean
quiet wren
Huhh
quiet wren
That doesnt help
wild charm
so sqrt of -5900 is
honest bough
√(-5900) = √(-1 * 5900) = √(-1) * √(5900)
wild charm
10*sqrt(59i)
quiet wren
√(-5900) = √(-1 * 5900) = √(-1) * √(5900)
Huh 🦍
wild charm
10*sqrt(59i)
see this
quiet wren
Yes
honest bough
The i should not be in the square root
quiet wren
stop with the confusing number thingd
honest bough
?
quiet wren
Huh
distant trench
Help man this is so hard for me
honest bough
Help man this is so hard for me
quiet wren
Help man this is so hard for me
Its 1
quiet wren
https://youtu.be/BV6VT20up0c
I dont have time for that
distant trench
The first one?
honest bough
The first one?
This is not your channel
honest bough
I dont have time for that
Why not?
honest bough
The square root of a negative number is i * the square root of the positive number
quiet wren
The first one?
No the first one is 71
quiet wren
Huhh
honest bough
√(-5900) = i √(5900)
I'm not sure where you're getting confused
This shouldn't be weird if you learned square roots of negative numbers
quiet wren
I dont know where im getting confused either
quiet wren
This shouldn't be weird if you learned square roots of negative numbers
I swear i learnt square roots of negative numbers
Just didnt pay attention in maths
honest bough
What's √(-4)?
honest bough
No
quiet wren
2.sonehtubf
quiet wren
I CANT DO THE WEIRD SYMBOL
honest bough
Then just say sqrt(x)
You can do the symbol on paper
It's just the square root sign
quiet wren
Kk
pearl pondBOT
@quiet wren Has your question been resolved?
pearl pondBOT
pearl pondBOT
Available help channel!
pearl pondBOT
vivid coyote
mystic spade
any help pls
pearl pondBOT
any help pls
mystic spade
i need ideas 😭
pearl pondBOT
@mystic spade Has your question been resolved?
pearl pondBOT
@mystic spade Has your question been resolved?
queen drift
pearl pondBOT
queen drift
Need some help
pearl pondBOT
@queen drift Has your question been resolved?
midnight haven
If you have an event A which has a higher probability than another, event B, given infinite time, is it guaranteed that event A will occur more than event B?
broken ivy
If you have an event A which has a higher probability than another, event B, giv...
so the event repeats with time right?
It is not clearly guaranteed for any set of time
rough axle
If you have an event A which has a higher probability than another, event B, giv...
No. Considering they can be independant, those two events can be happen at different frequencies
broken ivy
No. Considering they can be independant, those two events can be happen at diffe...
I think they just formulated/translated wrong, its never said that events happen based on time, they might just not happen at all
midnight haven
Okay thanks, I guess I was just thinking that if you did it infinitely many times it might be somehow guaranteed that it would happen a certain percentage of the time
broken ivy
I think its meant there are 2 chances, if both happen equally often and thats infinity, is A more likely
rough axle
I think they just formulated/translated wrong, its never said that events happen...
Yeah could be. Probability can be expressed of a function of time yes
broken ivy
Okay thanks, I guess I was just thinking that if you did it infinitely many time...
the chance just becomes infinitely small (aka, something like $\frac{1}{inf}$
jolly parrotBOT
Jigglyproff
rough axle
Okay thanks, I guess I was just thinking that if you did it infinitely many time...
Yeah thats just theoretical axiomatic probability. The variations in the outcomes for tossing a coin reduce and the probability gets closer and closer to 0.5 for each event as it approaches infinity
midnight haven
So at infinity is it technically 0.5 or not necessarily?
rough axle
Its exact 0.5 at infinity
midnight haven
Okay cool, I just wanted to make sure because I felt so stupid for a second there, thanks a lot!
broken ivy
So at infinity is it technically 0.5 or not necessarily?
its expected 0.5 AT ALL time
Like, lets say you do infinite coin tosses
the first time its heads
afterwards its always heads and tails in cycle
after infinite throws, you have 1 more heads than tails
just because it happened once more
rough axle
its expected 0.5 AT ALL time
Like, lets say you do infinite coin tosses
the fir...
No not necessarily in experimental probability
broken ivy
for that example it is since the chances didn't change and there was no mean asked
rough axle
If you toss it 10 times and you get 7 heads your experimental probability is 0.7
It just starts getting closer to 0.5 if you toss it more and more
Thats how you arrive at the standard axiomatic approach to probability
You look at favourable events and possible events, instead of positive experiments and negative experiments
And the experiment count for those is at infinity
broken ivy
If you toss it 10 times and you get 7 heads your experimental probability is 0.7...
experimental probability is *probable * to approach the expected mean with more tries, but in no way guaranteed
or so to say, the chance for experimental probability to not be the expected probability gets reduced with tries
rough axle
experimental probability is *probable * to approach the expected mean with more ...
Exactly. It starts approaching the actual event probability at infinity
broken ivy
aka
in 10 tosses I get 7 heads
in the next 90, i get 90 heads
my probability now derives more from the expected probability than before
rough axle
Think of it as instantaneous velocity in physics. Velocity cant be zero, it approaches it
rough axle
aka
in 10 tosses I get 7 heads
in the next 90, i get 90 heads
my probability now...
You cant theoretically get more heads than tails at infinitety
broken ivy
yes, but equallty, I am just not able to do an infinite amount of tries
since the second I reach that point i break the definition of infinity
rough axle
yes, but equallty, I am just not able to do an infinite amount of tries
No one is
Infinity is always an abstract concept
rough axle
since the second I reach that point i break the definition of infinity
Thats why you approach it, like a limit in calculus
Id drop an academic source here if i remembered the name of it
Some italian dude from the 20s
Either way @midnight haven you can close the thread if you are done
sour badger
pearl pondBOT
pearl pondBOT
sour badger
.reopen
pearl pondBOT
✅
sour badger
<@&286206848099549185>
muted fossil
if x_n converges to L then L = 1/2(L + 5/L)
L = 1/2 (L + 5/L)
2L = L + 5 / L
2L - L = 5/L
L = 5/L
L² = 5
L = | sqrt(5) |
and since x_n >= 0 then L = sqrt(5)
so x_n converges to sqrt(5)
i'm not sure 100%
rare pecan
i thjink you neeedd to introduce a sigma for this method
rare pecan
and an n and say for all n >= N works
but also i think it wants you to sue earlier parts of the question
sour badger
.close
midnight haven
pearl pondBOT
muted fossil
is this correct so far
nope
midnight haven
What to do
muted fossil
first of all do you know the domain of log(x) ?
midnight haven
Domain of log of x is 0 to infinity
muted fossil
Domain of log of x is 0 to infinity
do you know why ?
midnight haven
Idk the vertical asymptote is 0 and the graph goes forever to the right
muted fossil
because inside the log must be positive
muted fossil
log(x) is correct when x > 0
since log(-1) doesn't exist (undefined)
so 16x - x² > 0
muted fossil
so 16x - x² > 0
try to find the domain from here
muted fossil
16x - x² > 0
x(16 - x) > 0
midnight haven
oh ok
muted fossil
16x- x² is positive when x and 16-x have the same sign
which means :
x > 0 and 16 - x > 0
or
x < 0 and 16 - x < 0
muted fossil
x > 0 and 16 > x means 16 > x > 0 (x between 0 and 16)
muted fossil
$x \in ]0, 16[$
jolly parrotBOT
Mehdi_Moulati
muted fossil
since 0 and 16 are not in the interval
midnight haven
why cant i (0,16)
muted fossil
log(0) doesn't exist
midnight haven
oh ok
muted fossil
remember :
in log(x) x must be positive means : x > 0
midnight haven
oh ok thank you
midnight haven
y
muted fossil
you need to study this x < 0 and 16 - x < 0
muted fossil
u learned math in french?
yeah
muted fossil
since there is two possible ways where x(16 - x) > 0 :
1) x > 0 and 16 - x > 0
or
2) x < 0 and 16 - x < 0
you studied the first
muted fossil
do the same thing but when :
x < 0 and 16 - x < 0
midnight haven
i dont get it osrry\
muted fossil
okay your function is :
f(x) = log(16x - x²)
= log(x (16 - x) )
inside the log (i mean 16x - x² ) must be positive
so x(16 - x) > 0
is this clear , right ?
midnight haven
yea but how u switch > < if its already there
u said something like x > 0 or x < 0
muted fossil
if we want x (16 - x) to be positive x and 16-x must be with the same sign
both positive or both negative
for example :
-1 * -1 = 1 > 0 (both negative)
1 * 1 = 1 > 0 (both positive)
midnight haven
Does this give me domain
muted fossil
supposed that x and 16 - x are negative , right
muted fossil
my teacher said the argument within a log cannot be negative
it's true , but there is 2 cases for 16 x - x² to be positive
the first case is when : 16-x <0 and x < 0
the second case is when : 16-x > 0 and x > 0
midnight haven
the first one makes x negative
muted fossil
the first one makes x negative
yeah x and 16 - x
because negative multiply by negative gives positive
muted fossil
this becomes (- inf , 0 ) U ( 16 , inf ) ??
don't forget :
16< x and x < 0 (both must come true)
midnight haven
i have no idea im sorry i cant understand
it doesnt make sense
i am only taking a lower math course what u r saying seems something past what i understand
the homeowrk just to find domain
midnight haven
its > 0
muted fossil
replace x by -2 in x² - 1
midnight haven
wym
muted fossil
(-2)² - 1
muted fossil
$\sqrt{x²} = |x|$
jolly parrotBOT
Mehdi_Moulati
muted fossil
$|x| > 1$
jolly parrotBOT
Mehdi_Moulati
midnight haven
oh ok
muted fossil
$
|x| > 1 when
\begin{cases}
x > 1 or -x > 1
\end{cases}
$
$|x| > 1 when x > 1 or \ x < - 1$
jolly parrotBOT
Mehdi_Moulati
midnight haven
oh ok ty
jolly parrotBOT
Mehdi_Moulati
muted fossil
it's this same for 16x - x²
midnight haven
oh ok
muted fossil
16x - x² = - (x - 8)² + 64
muted fossil
16x - x² = - (x - 8)² + 64
this will make it easy for you
muted fossil
16 x - x² > 0
- (x - 8)² + 64 > 0
-(x-8)² > -64
(x-8)² < 64
|x-8| < 8
so x - 8 < 8 or - (x-8) < 8
pearl pondBOT
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Available help channel!
plucky swift
plucky swift
how do you do number 1
cobalt mango
Is this answer for probability correct?
pearl pondBOT
Is this answer for probability correct?
@cobalt mango Has your question been resolved?
cobalt mango
<@&286206848099549185>
pearl pondBOT
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cobalt mango
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twin oar
can someone explain to me which quadrants these two restrictions allow?, and if you can give me more expamples of it. For some reason its hard for me to visualize it
twin oar
I'll give my guess that pi/2<theta<pi is only q2 and 3pi/2 <theta <2pi is just q4
midnight haven
holy what the
twin oar
I cant really find good images online last time i checked
midnight haven
thats extremely impossible
faint prism
What specifically is confusing you?
Is it radians?
twin oar
idk just for some reason its hard for me to visualize it as quick as i want to
especually when its negative
like 2pi<theta<-2pi is that just 1 full rotation?
midnight haven
can someone help me please
sleek swift
like 2pi<theta<-2pi is that just 1 full rotation?
thats 2 rotations
twin oar
can someone help me please
12th but in america i think its an 11th grade course
faint prism
like 2pi<theta<-2pi is that just 1 full rotation?
You can't have that, you have a smaller value on the left than the one on the right
Basically with that you are implicitly saying that 2pi < -2pi
If you mean -2pi < theta < 2pi, that's two rotations
(< means less than, so what's smaller goes on the left)
twin oar
yeah alright i guess i just need to practice it then
midnight haven
can someone help me please, I do not understand how to turn an fraction into a decimal and the opposite too
faint prism
can someone help me please, I do not understand how to turn an fraction into a d...
Don't write in other channels if you don't want to help, be patient
twin oar
ask help in these channels
faint prism
You should get used to this, think where you are starting and where you are ending
If there's a negative sign, it means to go clockwise instead of counterclockwise
twin oar
oh thats helpful actually thank you
and what do you do if your answer doesn't lie in there?
faint prism
Can you give an example?
twin oar
i think i have one in my notes hold on
faint prism
faint prism
both are fine
But in this case, you are ok with every value of x (remember that x is an angle) as long as it's between 0 and 2π
Isn't that every possible angle you can have?
twin oar
but its negative wouldn't that be outside?
faint prism
but its negative wouldn't that be outside?
Try to put that on a circumference
Or maybe, non that, because it's very hard to put -0.9273 on a circumference
But maybe, try putting an angle of -π/2 on the circumference
You'll notice that it's the same as a 3/2π angle
twin oar
oh that makes sense
faint prism
And you can add 2π to that value and you'll keep getting to the same spot on the circumference, because it's like doing a full rotation which brings you where you started
twin oar
alright thats all i really needed thank you
faint prism
faint prism
Another small thing, in this exercise for some reason they didn't find a solution? (just making sure you noticed)
when you do sin⁻¹ of something, that gives two "values", the one you actually get and another one
The other one is the one missing, you get that by doing π - (the first value you get)
This happens because sin(x) = sin(π - x), but an angle x and an angle π - x aren't the same angle
the first solution is x₁ = -0.9273, and the other one is x₂ = π - (-0.9273)
twin oar
do you always subtract pi? i think thats where i'm mostly confused with it
faint prism
because sin(x) = sin(π - x), but an angle x and an angle π - x aren't the same angle
let me draw something that may help
As you can see, these two points have the same sin value (same y value)
But those don't share the exact same angle
twin oar
right
faint prism
If you know the angle of a, then to find the angle of b you can do π - (angle of a)
and the angle of a is what pops up when you do sin⁻¹ of something
so you need to find the angle of b too
because both are good solutions
faint prism
No, it's different
twin oar
whats the difference?
faint prism
Yup! that's good
usually you see -theta
But it's the same
with tan⁻¹ it doesn't matter, whatever you get is good as it is
twin oar
oh thank you
well i have a test in an hour, i had a rough idea on everything but i just didnt want to waste time thinking about it, this cleared up a lot 👍
faint prism
Good luck
languid swan
Maria is driving on the highway. She begins the trip with 14 gallons of gas in her car. The car uses up one gallone of gas every 35 miles.
Let G represent the number of gallons of gas she has left in her tank, and let D represent the total distance (in miles) she has traveled.
midnight haven
$G=14-\dfrac{D}{35}$
jolly parrotBOT
Zamarus
midnight haven
How to find it? When D=0 there is 14 gallons of gas in her car so G=14 when D=0
Then every 35 miles she uses one gallon so she loses 1/35 gallon per mile
opaque hearth
How would you go about solving this?
pearl pondBOT
How would you go about solving this?
opaque hearth
The work formula given is to find work for a single constant force
pearl pondBOT
@opaque hearth Has your question been resolved?
opaque hearth
<@&286206848099549185>
fleet lotus
Idk why you are talking about work when the questions don't
To get the resultant forces you need to draw them as vectors and add the vectors
opaque hearth
.close
midnight haven
When having something like
[
\log_{2}2^5
]
Is the answer 1 or 5?
midnight haven
Kind of curious but is there some law that makes the power rule take precedence first?
jolly parrotBOT
♡LexQa♡
midnight haven
Fixed I think 
midnight haven
no, this expression is ambiguous
How so
jolly parrotBOT
riemann
plush bramble
for some assumptions on b, probably > 0
midnight haven
Okay so it makes sense I guess
[(\log_{2}2)^5 = 1, \log_{2}(2^5) = 5]
jolly parrotBOT
♡LexQa♡
pearl pondBOT
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verbal vine
I solved this problem but just realized that my justification assumes that the pentagon is on a flat (euclidean) plane
verbal vine
do I need to re-do it? Is it still considered a pentagon if it's not on a flat surface?
old geyser
I'd think you'd assume it's on a flat XY plane
verbal vine
okay so I don't need to redo it then?
old geyser
I mean it depends how far in math you are
verbal vine
it's part of a problem set for a high school math competition
(this isn't dishonesty since they let you get help from others, it's just a preliminary problem set before the exam, if you cheat on the preliminary you won't pass the exam)
old geyser
Id say assume Euclidean then
hazy horizon
did I do this corerct
pearl pondBOT
did I do this corerct
old geyser
Where's the 7.5 coming from
hazy horizon
alri
old geyser
Uhhh
hazy horizon
ty
old geyser
Yeah id just leave it as such lol
pearl pondBOT
@hazy horizon Has your question been resolved?
midnight haven
pearl pondBOT
pearl pondBOT
stiff girder
.close
faint onyx
In order to reduce traffics, the government has passed a new law - cars are not allowed
to go in circles. If you drive around in a circle, you will be charged a fine. Your job is to deploy a
set of cameras to monitor the roads and catch drivers that are violating the new law.
For this problem, you are given a road map of a city as a connected, undirected graph G =
(V, E). For each road (i.e., edge) e, you are given the cost w(e) of building a camera station that
can detect when the same car passes twice. Your job is to find a minimal set of roads (i.e., edges)
such that you can detect any car that makes a circle.
faint onyx
i have like, no idea how to do this
my only idea is to place a camera at cycles (?) but that doesnt seem like it can do anythign
@rustic gate 
slender viper
In order to reduce traffics, the government has passed a new law - cars are not ...
consider the edges without a camera
what sort of structure do they form
slender viper
so the black edges, what did you notice about them
slender viper
yes, edges without a camera
faint onyx
they dont form a cycle and they are equal to the nodes - 1
wait..
they form a tree?
faint onyx
yes, edges without a camera
so if i remove all the elements that is stopping the graph from being a tree
ill get all the edges
that i should put a camera on
slender viper
but there's a cost of building a camera
faint onyx
so if i remove all the elements that is stopping the graph from being a tree
maybe ill get rid of all the larger edges
that disrupts the graph from being a tree
.close
faint onyx
pearl pondBOT
faint onyx
hi can someone tell me whats the basis now?
is it 0,0?
if yes, how do i conitnue with a basis like that
pearl pondBOT
@faint onyx Has your question been resolved?
faint onyx
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toxic lichen
,w det {{0-t, 1},{1, 2-t}}
jolly parrotBOT
toxic lichen
you fucked up calculating the eigenvalues and so your A - λI (which you incorrectly conflated with the eigenspace itself, which should instead be its kernel) turned out not to be singular
faint onyx
sry but i dont see where i went wrong calculating the eigenvalues
humble beacon
x^2 - 2x - 1 =/= x^2 -2x + 1
sterile lichen
Why we can omit the "Re" for this term? Is it true that the norm in general would not be complex?
pearl pondBOT
Why we can omit the "Re" for this term? Is it true that the norm in general woul...
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dense iron
pearl pondBOT
jolly parrotBOT
dense iron
but yes i wanted to ask where i went wrong here?
old geyser
The very last step.
9 - (1/3 - 2)
Should be 9 + 5/3 because you're gonna subtract a negative
9 - (-5/3)
= 9 + 5/3
= 32/3
old geyser
,w Integrate[1, {x, -1, 3}, {y, 5-x^2, 2-2x}]
jolly parrotBOT
peak thorn
pearl pondBOT
coarse dawn
You can apply the concept of $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$ and simplify
jolly parrotBOT
dldh06
peak thorn
.reopen
pearl pondBOT
✅
peak thorn
<@&286206848099549185>
old geyser
I'd just try to simplify them
peak thorn
how do you simplify it?
brisk sigil
By using a calculator
In the first case 8 and 79 are not perfect squares so go for the calc
Seems like its the same case all other questions too
midnight haven
what does "find" mean here exactly. Find exact value or find simplest form?
peak thorn
yeah
brisk sigil
So all u got to do is put the values in the calculator and you would get the answer
midnight haven
i have a feeling it is meant to be simplified, just not written well enough
brisk sigil
That might be the case
peak thorn
the numbers are all irrational
midnight haven
yes, u can only approximate if you are finding "Exact" values
well anyways
i am just going to assume u meant simplify
brisk sigil
The last one can be simplified to √13/2
midnight haven
Write the numerator and denominator of this as products of primes, if they are not a prime number themselves
[\sqrt{\frac{8}{79}}]
jolly parrotBOT
♡LexQa♡
peak thorn
alright ty
brisk sigil
The first one would be √2(4)/√79= 2√2/√79
peak thorn
ohh
midnight haven
4*3
midnight haven
I have no idea where to start
pearl pondBOT
I have no idea where to start
tired violet
ok so the most important thing about this problem is understanding the cross product
what do you know about it?
do you recall the right hand rule for instance?
midnight haven
do you recall the right hand rule for instance?
right hand screw rule
?
not much ngl
midnight haven
the cross product of two vectors is a vector
yes
tired violet
so do you know how to determine which direction that vector faces?
it's perpendicular to both E and B
ill share this diagram for you
this is called the right hand rule
midnight haven
oh ok
tired violet
so in your case which direction is S facing
tired violet
just use the rule above to figure out which direction S is in
literally use your hand
line your index and middle finger up with the E and B vectors on the page
and which direction your thumb points
thats the direction S is
tired violet
E is in the x direction
so thats where your index is
your middle finger is then facing in the y direction
tired violet
yessir
midnight haven
i got you sry i was being so slow
midnight haven
ty
jolly parrotBOT
llspacebarll
old geyser
Was gonna say
midnight haven
vector product
old geyser
I'm like "hey wait a minute that's a scalar"
tired violet
well yeah you have |E| and you have |B|=|E|/c
so plug those in and dont forget to divide by \mu_0
midnight haven
So how am i using the vector product if ive been give the formula for the magnitude of S
tired violet
you're trying to find the magnitude of S
so use the magnitude of a vector product formula i gave you
dont forget to multiply by 1/mu
midnight haven
so in this case it would sin 90 in the vector proudct formula
36 * 1.2*10^8 * sin
1.2*10^8
tired violet
seems so
midnight haven
i assume so since i dont think its sin (-90)
what would the units for my answer ?
nvm watts per sqaure meter
How does this look
pearl pondBOT
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@midnight haven Has your question been resolved?
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@midnight haven Has your question been resolved?
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hot finch
Good afternoon I need explanation to find all x
pearl pondBOT
Good afternoon I need explanation to find all x
hot finch
X=12 and i need to figure the degree for all angles
Please and thank you
Nvm I got it
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dense iron
pearl pondBOT
dense iron
,rotate
wild charm
lol
dense iron
why doesnt this rotate lol
pearl pondBOT
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edgy kiln
In the diagram:
I have a transform in 3D represented by the black X. I will call this transform the parent transform.
I have a child transform relative to the parent represented by the black triangle.
I have a vector somewhere in space.
I want to know the rotation (no translation) to apply to the parent transform to get the child transform either on the vector or as close as possible to the vector, in my diagram it is the red X
pearl pondBOT
In the diagram:
I have a transform in 3D represented by the black X. I will cal...
@edgy kiln Has your question been resolved?
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fair frost
pearl pondBOT
night pagoda
are those imaginary numbers? the i"s
night pagoda
isnt it -3x^2-i
cerulean ridge
a²b
(-x)²(-3-i)
x²(-3-i)
If you want to expand further it becomes
-3x²-x²i
@fair frost
fair frost
If you want to expand further it becomes
-3x²-x²i
Tysm
cerulean ridge
np, just simple algebra rules from 7th grade
fair frost
pearl pondBOT
fair frost
Can somebody explain to me how he got -4-7i
pearl pondBOT
@fair frost Has your question been resolved?
fair frost
i - 8i = -7i
Oh
hasty breach
So it says multiply relative to the y-axis by a factor of ½ but idk how it went for 2-x to 2-2x
cerulean ridge
The x got replaced with 2x
hasty breach
Where did that 2x come from
cerulean ridge
From multiply relative to the y-axis by a factor of ½
hasty breach
<@&286206848099549185>
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plush bramble
<@&286206848099549185>
show the whole problem
hasty breach
show the whole problem
Its in dutch so...
plush bramble
then translate the whole thing
hasty breach
K
Given are the functions f ( x ) = 6* ( 1/3 )^2-x and g ( x ) = 2*9^x The graphs of the functions f and g intersect at point A. Calculate exactly the coordinates of point A. ( 5 pt )
B. The following transformations are applied to the graph of function f. First a multiplication relative to the y-axis by a factor of 1/2. Then a shift by 1 to the left. And finally a multiplication with respect to the x - axis by a factor of 1/3 . You then get the graph of function h . Determine the function rule of h and show by reduction that it is equal to the function rule of g . ( 5 pt )
@plush bramble
plush bramble
$f(x) = 6 \left(\frac{1}{3}\right)^{2-x}, g(x) = 2\cdot 9^x$
jolly parrotBOT
riemann
plush bramble
is that correct for f and g?
plush bramble
Given are the functions f ( x ) = 6* ( 1/3 )^2-x and g ( x ) = 2*9^x The graphs ...
have you seen these transformations before
https://www.onlinemathlearning.com/image-files/transformation-rules-graphs.png
hasty breach
In my book there is only x but not y
plush bramble
y = f(x) in the image above
hasty breach
Everything except f(-x), f(bx)
plush bramble
Everything except f(-x), f(bx)
Then a shift by 1 to the left.
use the table to find out how that affects f(x) and plug that new x into f
plush bramble
plush bramble
It went from 6(1/3)^2-x to 6(1/3)^2-2x
this comes from shifting x
plush bramble
> Then a shift by 1 to the left.
use the table to find out how that affects f(...
look at the table for shifting left and right
hasty breach
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olive stream
I need help on a question, its not an equation or anything. Though it asks me how do you get a linear model for a scatterplot
plush bramble
plush bramble
olive stream
I don’t understand
plush bramble
go through all those lessons and you'll be a pro
plush bramble
you're saying you don't understand
i'm assuming you're saying you don't understand linear regression
so khan's a great start
hallow remnant
What is even going on
old geyser
go through all those lessons and you'll be a pro
My literal worst subject, never clicks with me
olive stream
Ik linear regressions
old geyser
I'm real fucking good with calculus but when it becomes to@probability and stats and z tests and bell curves, shit hits the fan 😭
plush bramble
My literal worst subject, never clicks with me
this is all you need
olive stream
But like
plush bramble
Ik linear regressions
okay, can you ask a more explicitly detailed question
rustic gate
OLS is just linalg 
hallow remnant
Ok like there is one way where you just eyeball it
plush bramble
can you screenshot / take a picture of the problem you're solving
plush bramble
I have to provide a how to but its not like
this isn't very detailed
plush bramble
can you screenshot / take a picture of the problem you're solving
so do this please
hallow remnant
The other way is the Wikipedia hell which he posted
olive stream
its not a problem
😭 i said this..
Its a question im asking for help on how to do it
plush bramble
I need help on a question, its not an equation or anything. Though it asks me ho...
Though it asks me how do you get a linear model for a scatterplot
what is "it"
plush bramble
yeah its just a question thats all
show the question. screenshot/take a picture
hallow remnant
Okay here is how you do it
Do you know point slope form?
So one point is the mean of the Xs and the mean of the Ys
olive stream
hallow remnant
And the slope is the ratio of the std devs
olive stream
?..
hallow remnant
Okay you really should just read the textbook if you haven’t
olive stream
Its just abt linear regression
plush bramble
Its just abt linear regression
that's the answer to your question
"how do you get a linear model"
olive stream
For a scatterplot?
plush bramble
For a scatterplot?
does your scatterplot fit the assumptions of simple linear regression?
olive stream
Wdym
plush bramble
"contains only two variables"
olive stream
Ig
plush bramble
yea then that's all you need to do simple linear regression
olive stream
So basically thats a how to?
plush bramble
the variables for alpha hat and beta hat is your "linear model"
olive stream
Do linear regression?
plush bramble
you have to describe it using more words than just that
plush bramble
https://en.wikipedia.org/wiki/Ordinary_least_squares#:~:text=In%20all%20cases%20...
read this and put it in your own words
just the first few paragraphs should be enough
plush bramble
Okay you really should just read the textbook if you haven’t
or even better, read your book like minion mentioned
olive stream
the variables for alpha hat and beta hat is your "linear model"
Where is this
plush bramble
.
olive stream
So basically using simple linear regression
plush bramble
https://en.wikipedia.org/wiki/Linear_regression
Yup. Been saying that for a while.
olive stream
So if i say the strps
Steps
To a simple linear regression
That answers my question?.
plush bramble
That's up to you to decide. You probably want to be more descriptive.
plush bramble
read this and put it in your own words
.
plush bramble
or even better, read your book like minion mentioned
.
pearl pondBOT
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hollow pike
Can anyone tell me what I did wrong? I feel like i am missing a step here
I did the same process for other problems that were similar and they are wrong too
modern fjord
can you ask what the actualy answer is
if its close to 12.05% it could just be choosing more precise values
hollow pike
i could but if someone could verify for me then that would be helpful
hollow pike
yes please
pearl pondBOT
@hollow pike Has your question been resolved?
hollow pike
@modern fjord were you able to find out if its correct?
hollow pike
thank you
pearl pondBOT
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delicate beacon
I just started learning complex speech plane. How to solve equation x^2+4z+5=0 and x^2+4z+1=0
glacial rock
To solve the equation x^2+4z+5=0, we can use the quadratic formula, which states that the solutions to a quadratic equation of the form ax^2+bx+c=0 are given by the following formula:
x = (-b +/- sqrt(b^2-4ac)) / 2a
In this case, a=1, b=4, and c=5, so we can plug these values into the formula to find the solutions:
x = (-4 +/- sqrt(4^2-415)) / 2*1
This simplifies to:
x = (-4 +/- sqrt(16-20)) / 2
And finally,
x = (-4 +/- sqrt(-4)) / 2
Since the square root of a negative number is not a real number, this equation has no real solutions.
To solve the equation x^2+4z+1=0, we can use the same process. This time, a=1, b=4, and c=1, so the solutions are given by:
x = (-4 +/- sqrt(4^2-411)) / 2*1
This simplifies to:
x = (-4 +/- sqrt(16-4)) / 2
And finally,
x = (-4 +/- sqrt(12)) / 2
Since the square root of a positive number is a real number, this equation has two real solutions:
x = (-4 + sqrt(12)) / 2 = 1
x = (-4 - sqrt(12)) / 2 = -3
Therefore, the solutions to the equation x^2+4z+5=0 are not real, while the solutions to the equation x^2+4z+1=0 are x=1 and x=-3.x = (-b +/- sqrt(b^2-4ac)) / 2a
In this case, a=1, b=4, and c=5, so we can plug these values into the formula to find the solutions:
x = (-4 +/- sqrt(4^2-415)) / 2*1
This simplifies to:
x = (-4 +/- sqrt(16-20)) / 2
And finally,
x = (-4 +/- sqrt(-4)) / 2
Since the square root of a negative number is not a real number, this equation has no real solutions.
To solve the equation x^2+4z+1=0, we can use the same process. This time, a=1, b=4, and c=1, so the solutions are given by:
x = (-4 +/- sqrt(4^2-411)) / 2*1
This simplifies to:
x = (-4 +/- sqrt(16-4)) / 2
And finally,
x = (-4 +/- sqrt(12)) / 2
Since the square root of a positive number is a real number, this equation has two real solutions:
x = (-4 + sqrt(12)) / 2 = 1
x = (-4 - sqrt(12)) / 2 = -3
Therefore, the solutions to the equation x^2+4z+5=0 are not real, while the solutions to the equation x^2+4z+1=0 are x=1 and x=-3.
honest bough
To solve the equation x^2+4z+5=0, we can use the quadratic formula, which states...
This is wrong
It's x² + 4z + 1, not x² + 4x + 1
Moreover, don't just give answers
Moreover, stop using chatGPT istg
delicate beacon
Yeah this is wrong
delicate beacon
It's x² + 4z + 1, not x² + 4x + 1
So i figured out my rots for both equations